Question #4
Find the measure of the indicated angle.
20°
161°
61°
73°
H
G
F
73° E
195°
Answers
The measure of the outside angle F indicated in the figure is 61 degrees,
What is the measure of angle GFE?The external angle theorem states that "the measure of an angle formed by two secant lines, two tangent lines, or a secant line and a tangent line from a point outside the circle is half the difference of the measures of the intercepted arcs.
Expressed as:
Outside angle = 1/2 × ( major arc - minor arc )
From the figure:
Major arc = 195 degrees
Minor arc = 73 degrees
Outside angle F = ?
Plug the value of the minor and major arc into the above formula and solve for the outside angle F:
Outside angle = 1/2 × ( major arc - minor arc )
Outside angle = 1/2 × ( 195 - 73 )
Outside angle = 1/2 × ( 122 )
Outside angle = 122/2
Outside angle = 61°
Therefore, the outside angle measures 61 degrees.
Option C) 61° is the correct answer.
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Related Questions
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction.
The number b varies directly with the number a. For example b = 22 when a = -22. Which equation represents this
direct variation between a and b?
b=-a
0-b=-a
O b-a=0
Ob(-a)=0
Answers
b = -a
This equation states that b is equal to the opposite of a, which aligns with the given information that b is located the same distance from 0 as a but in the opposite direction.
Which is the best deal over 5 years? Investing at 7.87% compounded semi annually, 7.8% compounded quarterly, or 7.72% compounded every minute?
Answers
The best deal over 5 years would be investing at 7.8% compounded quarterly.
Although the interest rates of 7.87% compounded semi-annually and 7.72% compounded every minute may appear slightly higher, the frequency of compounding plays a significant role in determining the overall return.
Compounding more frequently leads to a higher effective annual rate. In this case, compounding quarterly provides a greater compounding frequency than semi-annual or minute-by-minute compounding, resulting in higher returns over time.
When interest is compounded quarterly, the compounding occurs four times a year, whereas semi-annual compounding only occurs twice a year. Compounding every minute may seem more frequent, but the actual effect on the return is minimal since there are a large number of minutes in a year.
Therefore, the 7.8% compounded quarterly is the best deal over 5 years as it offers a higher effective annual rate compared to the other options.
In summary, investing at 7.8% compounded quarterly is the most advantageous choice over a 5-year period. The frequency of compounding plays a crucial role in determining the overall return, and compounding quarterly provides a greater compounding frequency compared to semi-annual or minute-by-minute compounding.
It is essential to consider both the interest rate and the compounding frequency when evaluating investment options to make an informed decision.
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A high school robotics club sold cupcakes at a fundraising event.
They charged $2.00 for a single cupcake, and $4.00 for a package of 3 cupcakes.
They sold a total of 350 cupcakes, and the total sales amount was $625.
The system of equations below can be solved for , the number of single cupcakes sold, and , the number of packages of 3 cupcakes sold.
Multiply the first equation by 2. Then subtract the second equation. What is the resulting equation?
x + 3y = 350
2x + 4= 625
Type your response in the box below.
$$
Answers
The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:
-5y = -375
1. Given equations:
- x + 3y = 350 (Equation 1)
- 2x + 4y = 625 (Equation 2)
2. Multiply Equation 1 by 2:
- 2(x + 3y) = 2(350)
- 2x + 6y = 700 (Equation 3)
3. Subtract Equation 2 from Equation 3:
- (2x + 6y) - (2x + 4y) = 700 - 625
- 2x - 2x + 6y - 4y = 75
- 2y = 75
4. Simplify Equation 4:
-2y = 75
5. To isolate the variable y, divide both sides of Equation 5 by -2:
y = 75 / -2
y = -37.5
6. Therefore, the resulting equation is:
-5y = -375
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Donna joined a club that costs $80 per month with a $60.50 yearly
membership fee. Is the cost over time a proportional or non-proportional
relationship?
Answers
The cost of Donna's club membership exhibits a non-proportional relationship over time.
The cost of Donna's club membership can be analyzed to determine whether it exhibits a proportional or non-proportional relationship over time.
In this scenario, Donna pays a monthly fee of $80, along with a yearly membership fee of $60.50. To assess the proportionality, we can examine how the cost changes relative to time.
In a proportional relationship, the cost would increase or decrease at a constant rate. For example, if the monthly fee remained constant, the total cost would be directly proportional to the number of months of membership.
However, in this case, the presence of a yearly membership fee indicates a non-proportional relationship.
The yearly membership fee of $60.50 is a fixed cost that Donna incurs only once per year, regardless of the number of months she remains a member.
As a result, the cost is not directly proportional to time. Instead, it has a fixed component (the yearly fee) and a variable component (the monthly fee).
In summary, the cost of Donna's club membership exhibits a non-proportional relationship over time. While the monthly fee is a constant amount, the yearly membership fee introduces a fixed cost that is independent of the duration of her membership.
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What is the value of the expression (-2)(3)º(4)-2 ?
A. -3/2
B. -1/2
C. -3/4
D. 0
Answers
The value of the expression (-2)(3)º(4) - 2 is -164.
Based on the answer choices provided, none of the options matc.
To solve the expression (-2)(3)º(4)-2, we need to follow the order of operations, which is parentheses, exponents, multiplication, and subtraction.
Let's break down the expression :
(-2)(3)º(4) -2
First, we calculate the exponent:
(-2)(81) - 2
Next, we perform the multiplication:
-162 - 2
Finally, we subtract:
-164
Therefore, the value of the expression (-2)(3)º(4) - 2 is -164.
Based on the answer choices provided, none of the options match the value of -164.
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Let X and Y have joint pdf .
a. Compute P(X < 1/2 Ç Y > 1/4).
b. Derive the marginal pdfs of X and Y.
c. Are X and Y independent? Show some calculations in support of your answer.
d. Derive f(x|y) = {the conditional pdf of X given Y=y}
Answers
Answer:
To answer the questions, I'll assume that you're referring to continuous random variables X and Y. Let's go through each part:a. To compute P(X < 1/2 ∩ Y > 1/4), we integrate the joint probability density function (pdf) over the given region:P(X < 1/2 ∩ Y > 1/4) = ∫∫ f(x, y) dx dyb. To derive the marginal pdfs of X and Y, we integrate the joint pdf over the other variable. The marginal pdf of X can be obtained by integrating the joint pdf over Y:fX(x) = ∫ f(x, y) dySimilarly, the marginal pdf of Y can be obtained by integrating the joint pdf over X:fY(y) = ∫ f(x, y) dxc. To determine if X and Y are independent, we need to check if the joint pdf can be expressed as the product of the marginal pdfs:f(x, y) = fX(x) * fY(y)If this condition holds, X and Y are independent.d. The conditional pdf of X given Y = y can be derived using the joint pdf and the marginal pdf of Y:f(x|y) = f(x, y) / fY(y)By substituting the values from the given joint pdf, we can obtain the conditional pdf of X given Y = y.Please provide the specific joint pdf for X and Y, and I'll be able to assist you further with the calculations.Hope this help youThe marginal pdf of X is fX(x) = x + 1/2
How do you compute P(X < 1/2, Y > 1/4)?We need to integrate the joint pdf over the given region. This can be done as follows:
P(X < 1/2, Y > 1/4) = ∫∫[x + y] dx dy over the region 0 ≤ x ≤ 1/2 and 1/4 ≤ y ≤ 1
= ∫[x + y] dy from y = 1/4 to 1 ∫ dx from x = 0 to 1/2
= ∫[x + y] dy from y = 1/4 to 1 (1/2 - 0)
= ∫[x + y] dy from y = 1/4 to 1/2 + ∫[x + y] dy from y = 1/2 to 1 (1/2 - 0)
= ∫[x + y] dy from y = 1/4 to 1/2 + ∫[x + y] dy from y = 1/2 to 1/2
= ∫[x + y] dy from y = 1/4 to 1/2
= [(x + y)y] evaluated at y = 1/4 and y = 1/2
= [(x + 1/2)(1/2) - (x + 1/4)(1/4)]
= (1/2 - 1/4)(1/2) - (1/4 - 1/8)(1/4)
= (1/4)(1/2) - (1/8)(1/4)
= 1/8 - 1/32
= 3/32
Therefore, P(X < 1/2, Y > 1/4) = 3/32.
The marginal pdfs of X and Y can be done as follows:
For the marginal pdf of X:
fX(x) = ∫[x + y] dy over the range 0 ≤ y ≤ 1
= [xy + (1/2)y^2] evaluated at y = 0 and y = 1
= (x)(1) + (1/2)(1)^2 - (x)(0) - (1/2)(0)^2
= x + 1/2
Therefore, the marginal pdf of X is fX(x) = x + 1/2.
For the marginal pdf of Y:
fY(y) = ∫[x + y] dx over the range 0 ≤ x ≤ 1
= [xy + (1/2)x^2] evaluated at x = 0 and x = 1
= (y)(1) + (1/2)(1)^2 - (y)(0) - (1/2)(0)^2
= y + 1/2
Therefore, the marginal pdf of Y is fY(y) = y + 1/2.
To determine if X and Y are independent, we need to check if the joint pdf factors into the product of the marginal pdfs.
fX(x) * fY(y) = (x + 1/2)(y + 1/2)
However, this is not equal to the joint pdf f(x, y) = x + y. Therefore, X and Y are not independent.
To derive the conditional pdf of X given Y = y, we can use the formula:
f(xy) = f(x, y) / fY(y)
Here, we have f(x, y) = x + y from the joint pdf, and fY(y) = y + 1/2 from the marginal pdf of Y.
Therefore, the conditional pdf of X given Y = y is:
f(xy) = (x + y) / (y + 1/2)
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Let theta be an angle in quadrant two such that cos theta=-3/4. find the exact values of csc theta and cot theta
Answers
The exact values of csc(theta) and cot(theta) are: csc(theta) = 4√7/7
cot(theta) = -3√7/7.
To find the exact values of csc(theta) and cot(theta), given that cos(theta) = -3/4 and theta is an angle in quadrant two, we can use the trigonometric identities and the Pythagorean identity.
We know that cos(theta) = adjacent/hypotenuse, and in quadrant two, the adjacent side is negative. Let's assume the adjacent side is -3 and the hypotenuse is 4. Using the Pythagorean identity, we can find the opposite side:
[tex]opposite^2 = hypotenuse^2 - adjacent^2opposite^2 = 4^2 - (-3)^2opposite^2 = 16 - 9opposite^2 = 7[/tex]
opposite = √7
Now we have the values for the adjacent side, opposite side, and hypotenuse. We can use these values to find the values of the other trigonometric functions:
csc(theta) = hypotenuse/opposite
csc(theta) = 4/√7
To rationalize the denominator, we multiply the numerator and denominator by √7:
csc(theta) = (4/√7) * (√7/√7)
csc(theta) = 4√7/7
cot(theta) = adjacent/opposite
cot(theta) = -3/√7
To rationalize the denominator, we multiply the numerator and denominator by √7:
cot(theta) = (-3/√7) * (√7/√7)
cot(theta) = -3√7/7
Therefore, the exact values of csc(theta) and cot(theta) are:
csc(theta) = 4√7/7
cot(theta) = -3√7/7
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If x = 2, solve for y. y = 6.3x y=[?]
Answers
Answer: y = 12.6
Step-by-step explanation:
Since x = 2 and y = 6.3 * x, y = 6.3 * 2.
6.3 * 2 is equal to 12.6, so y is 12.6.
Answer:
y = 12.6
Step-by-step explanation:
y = 6.3x x = 2
Solve for y.
y = 6.3(2)
y = 12.6
So, the answer is 12.6
29.4.3 Quiz: Parabolas with Vertices at the Origin
Question 5 of 10
The equation below describes a parabola. If a is negative, which way does the
parabola open?
y=ax²2²
O A. Right
B. Down
OC. Up
OD. Left
SUBMIT
Answers
The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.
The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.
When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.
To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.
For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.
In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.
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In square $ABCD,$ $P$ is on $\overline{BC}$ such that $BP = 4$ and $PC = 1,$ and $Q$ is on $\overline{CD}$ such that $DQ = 4$ and $QC = 1.$ Find $\sin \angle PAQ.$
Answers
We can use the Pythagorean Theorem to find the lengths of $AQ$ and $AP.$ Since $DQ = 4$ and $QC = 1,$ we have $AQ = DQ + QC = 4 + 1 = 5.$ Similarly, since $BP = 4$ and $PC = 1,$ we have $AP = BP + PC = 4 + 1 = 5.$
In a right triangle, the sine of a right angle is always $1.$ Therefore, $\sin \angle PAQ = \boxed{1}.$
Hope you understood and good luck
In triangle PAD, using the Pythagorean theorem, we find AD = 5√2. Given that ∠PAQ's opposite side is PQ, which equals 3, we have sin∠PAQ = PQ/AQ = √2/10.
Explanation:In square ABCD, we are given that points P and Q are on lines BC and CD respectively such that BP=4 and PC=1, DQ=4 and QC=1. Considering triangle PAD, it is a right triangle in the given square, and, using the Pythagorean theorem, we can find the hypotenuse AD as AD = √(5² + 5²) = 5√2. The same reasoning, AD = AQ.
Because ∠PAQ is the angle we are interested in finding the sine of, we know that sin∠PAQ = opposite/hypotenuse. In this case, the opposite side is PQ which we determine is 3 using the given distances (PC+QC). So, sin∠PAQ = PQ/AQ = 3/(5√2) = √2/10. Thus, the sine of angle PAQ is √2/10.
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Find a function of the form or whose graph matches this one:
Answers
The function that matches the graph is of the form:
4cos((pi x)/7) + 1
Graphs of trigonometric functionsGraphs of trigonometric functions are graphs used in representing trigonometric functions.
From these graphs, some basic properties such as Amplitude, phase difference, period and vertical shift can be deduced.
From the given graph in the question, it can be seen that the graph crosses the y-axis at it's amplitude (highest point), so its easier to use the cosine relation.
To calculate the midline M:
Use the formula,
M = (maximum + minimum)/2
= (5 + -3)/2 = 2/2 = 1
Vertical shift: It can be seen from the graph that there is a vertical upward shift of 1 unit. C = 1
Amplitude: Maximum value - vertical shift is:
A = 5 - 1 = 4
Period = spacing between repeating patterns. There are 14 units between each peak (peak when x = -14, next peak when x = 0).
k = 2pi/Period;
So: k = 2pi/14 = pi/7
Therefore y = 4cos(pix/7) + 1 is the function that matches the given graph.
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!! Will give brainlist !!
Determine the surface area and volume Note: The base is a square.
Answers
The surface area and volume of the square pyramid is 96 squared centimeter and 48 cubic centimeters respectively.
What is the surface area and volume of the square pyramid?The surface area of a square pyramid is expressed as:
SA = [tex]a^2 + 2a \sqrt{\frac{a^2}{4}+h^2 }[/tex]
The volume of a square pyramid is expressed as:
Volume = [tex]a^2*\frac{h}{3}[/tex]
Where a is the base edge and h is the height.
From the figure a = 6cm
First, we determine the h, using pythagorean theorem:
h² = 5² - (6/2)²
h² = 5² - 3²
h² = 25 - 9
h² = 16
h = √16
h = 4 cm
Solving for surface area:
SA = [tex]a^2 + 2a \sqrt{\frac{a^2}{4}+h^2 }[/tex]
[tex]= a^2 + 2a \sqrt{\frac{a^2}{4}+h^2 }\\\\= 6^2 + 2*6 \sqrt{\frac{6^2}{4}+4^2 }\\\\= 36 + 12 \sqrt{\frac{36}{4}+16 }\\\\= 36 + 12 (5)\\\\= 36 + 60\\\\= 96 cm^2[/tex]
Solving for the volume:
Volume = [tex]a^2*\frac{h}{3}[/tex]
[tex]= a^2*\frac{h}{3}\\\\= 6^2*\frac{4}{3}\\\\= 36*\frac{4}{3}\\\\=\frac{144}{3}\\\\= 48 cm^3[/tex]
Therefore, the volume is 48 cubic centimeters.
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If the mean of a negatively skewed distribution is 122, which of these values could be the median of the distribution
Answers
118 be the median of a positively skewed distribution with a mean of 122. Option D.
To determine which of the given values could be the median of a positively skewed distribution with a mean of 122, we need to consider the relationship between the mean, median, and skewness of a distribution.
In a positively skewed distribution, the tail of the distribution is stretched towards higher values, meaning that there are more extreme values on the right side. Consequently, the median, which represents the value that divides the distribution into two equal halves, will typically be less than the mean in a positively skewed distribution.
Let's examine the given values in relation to the mean:
A. 122: This value could be the median if the distribution is perfectly symmetrical, but since the distribution is positively skewed, the median is expected to be less than the mean. Thus, 122 is less likely to be the median.
B. 126: This value is higher than the mean, and since the distribution is positively skewed, it is unlikely to be the median. The median is expected to be lower than the mean.
C. 130: Similar to option B, this value is higher than the mean and is unlikely to be the median. The median is expected to be lower than the mean.
D. 118: This value is lower than the mean, which is consistent with a positively skewed distribution. In such a distribution, the median is expected to be less than the mean, so 118 is a plausible value for the median.
In summary, among the given options, (118) is the most likely value to be the median of a positively skewed distribution with a mean of 122. So Option D is correct.
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Note the complete question is
If the mean of a positively skewed distribution is 122, which of these values could be the median of the distribution?
A. 122
B. 126
C. 130
D. 118
If two of the angles in a scalene triangle are 54° and 87°, what is the other angle?
Answers
Answer:
39°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
let the other angle be x , then
x + 54° + 87° = 180°
x + 141° = 180° ( subtract 141° from both sides )
x = 39°
that is the other angle is 39°
In a triangle, the sum of all angles is always 180°. To find the third angle in a scalene triangle where two angles are known, subtract the known angles from 180°. In this case, subtracting 54° and 87° from 180° gives a third angle of 39°.
Explanation:The question refers to finding the third angle in a scalene triangle, where we know two of the angles. A scalene triangle is a triangle where all three sides are of a different length, and therefore all three angles are also different. The sum of the angles in any triangle is always 180°.
To find the third angle in the triangle, you can use the equation: Angle C = 180° - Angle A - Angle B.
So, we subtract the known angles from 180°: Angle C = 180° - 54° - 87° = 39°.
Therefore, the third angle in this scalene triangle is 39°.
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Solve for x leave your answer in simplest radical form
Answers
Answer:
X=11 trust me on my mom
I need help with 36 please I don’t understand
Answers
The equation of the function is y = 1/(x + 3) - 1
How to determine the equation of the transformationFrom the question, we have the following parameters that can be used in our computation:
The reciprocal function shifted down one unit and left three units
The equation of the reciprocal function is represented as
y = 1/x
When shifted down one unit, we have
y = (1/x) - 1
When shifted left three units, we have
y = 1/(x + 3) - 1
Hence, the equation of the function is y = 1/(x + 3) - 1
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Compute $2^{-3}\cdot 3^{-2}$.
Answers
The value of the algebric expression [tex]2^{-3} \cdot 3^{-2}$ is $\frac{1}{72}[/tex].
To compute the expression [tex]2^{-3} \cdot 3^{-2}[/tex], we can simplify each term separately and then multiply the results.
First, let's simplify [tex]2^{-3}[/tex]. The exponent -3 indicates that we need to take the reciprocal of the base raised to the positive exponent 3. Therefore, [tex]2^{-3} = \frac{1}{2^3} = \frac{1}{8}[/tex].
Next, let's simplify 3^{-2}. Similar to before, the exponent -2 means we need to take the reciprocal of the base raised to the positive exponent 2. So, [tex]3^{-2} = \frac{1}{3^2} = \frac{1}{9}[/tex].
Now that we have simplified both terms, we can multiply them together: [tex]\frac{1}{8} \cdot \frac{1}{9}[/tex]. When multiplying fractions, we multiply the numerators together and the denominators together. So, [tex]\frac{1}{8} \cdot \frac{1}{9} = \frac{1 \cdot 1}{8 \cdot 9} = \frac{1}{72}[/tex].
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If
Answers
Answer:
I pass my classes.
Step-by-step explanation:
I had to add this sentence or else it wouldnt allow me to send it.
Answer:
In math, the word "if" can be used for piecewise functions. In piecewise functions, you can see equations where f(x) = x+3 IF x>0 and f(x) = -x IF x<0.
Which is equivalent to 4/9 1/2x*?
92x
9 1/8x
Answers
Answer:
B. [tex] 9^{\frac{1}{8}x} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{9}^{\frac{1}{2}x} = [/tex]
[tex] = ({9}^{\frac{1}{4}})^{\frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{4} \times \frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{8}x} [/tex]
need answer asappppppppp
Answers
The correct statement regarding the translation in this problem is given as follows:
A. The graph of g(x) is the graph of f(x) shifted up 3 units.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.In this problem, we have an addition by 3, hence there is a translation up 3 units.
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The functions f(x) and g(x) are described using the following equation and table:
f(x) = −3(1.02)x
x g(x)
−1 −5
0 −3
1 −1
2 1
Which statement best compares the y-intercepts of f(x) and g(x)?
The y-intercept of f(x) is equal to the y-intercept of g(x).
The y-intercept of f(x) is equal to 2 times the y-intercept of g(x).
The y-intercept of g(x) is equal to 2 times the y-intercept of f(x).
The y-intercept of g(x) is equal to 2 plus the y-intercept of f(x).
Answers
Answer:
The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept of f(x), we can substitute x=0 into the equation for f(x):
f(0) = -3(1.02)^0 = -3
Therefore, the y-intercept of f(x) is -3. To find the y-intercept of g(x), we can look at the table and see that when x=0, g(x)=-3. Therefore, the y-intercept of g(x) is also -3.
Comparing the y-intercepts of the two functions, we see that they are equal. Therefore, the correct answer is:
The y-intercept of f(x) is equal to the y-intercept of g(x).
Step-by-step explanation:
Answer:
The correct answer is A, the y-intercept of f(x) is equal to the y-intercept of g(x).
Step-by-step explanation:
First, note that the y intercept is what y is equal to when x is equal to 0.
The given function, f(x), is an exponential function. Exponential functions are written in the formula [tex]f(x) = a(1 + r)^x[/tex], where a = y-intercept!
a in the function f(x) is -3, so this means that the y intercept is -3.
In the given table, g(x), the y value is -3 when the x value is 0.
This means that in the g(x) table, the y-intercept is also -3.
Thus, A is correct and the y-intercept of f(x) is equal to the y-intercept of g(x).
Find the solution to the equation below.
2x2+3x-20=0
Answers
Answer:
[tex]x = 5.3 \: or \: 5 \frac{1}{3} [/tex]
Step-by-step explanation:
[tex]2 \times 2 + 3x - 20 = 0 \: \: \: \: \: \: 4 + 3x - 20 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:3x = 20 - 4 = 16 \: \: \: \: \: \: \: \: 3x = 16 \: \: divide \: both \: side \: by \: 3 = \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = 5.3[/tex]
7
What fraction of the shape is shaded?
18 mm
10 mm
12 mm
Answers
The shaded fraction of the shape is 2/3.
To determine the fraction of the shape that is shaded, we need to compare the shaded area to the total area of the shape.
1. Identify the shaded region in the shape. In this case, we have a shape with some part shaded.
2. Calculate the area of the shaded region. Given the dimensions provided, the area of the shaded region is determined by multiplying the length and width of the shaded part. In this case, the dimensions are 18 mm and 10 mm, so the area of the shaded region is (18 mm) × (10 mm) = 180 mm².
3. Calculate the total area of the shape. The total area of the shape is determined by multiplying the length and width of the entire shape. In this case, the dimensions are 18 mm and 12 mm, so the total area of the shape is (18 mm) × (12 mm) = 216 mm².
4. Determine the fraction. To find the fraction, divide the area of the shaded region by the total area of the shape: 180 mm² ÷ 216 mm². Simplifying this fraction gives us 5/6.
5. Convert the fraction to its simplest form. By dividing both the numerator and denominator by their greatest common divisor, we get the simplified fraction: 2/3.
Therefore, the fraction of the shape that is shaded is 2/3.
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what is the number of births in year 5?
Answers
Answer:
Step-by-step explanation:
And that is actually the case, as
816/2=408
408/2=204
204/2=102
Now, we are looking for 102/2=?
Solution: 51
The principal P is borrowed at a simple interest rate r for a period of time t. Find the loans future value A, or the total amount due at time t. P equals $9,000, r eeuals 10%, t equals 6 months. The loans future value is
Answers
The future value of the loan, or the total amount due at the end of 6 months, is $9,450.
We can use the following formula to calculate the future value of a loan:
[tex]A = P + P * r * t[/tex]
Given: $9,000 principal (P).
10% interest rate (r) = 0.10
6 months is the time period (t).
When we enter these values into the formula, we get:
A=9,000+9,000*0.10*6/12
First, compute the interest portion:
Interest is calculated as = 9,000*0.10*6/12=450
We may now calculate the future value:
A=9,000+450=9,450
As a result, the loan's future value, or the total amount payable in 6 months, is $9,450.
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SOLVE ALGEBRAICALLY!!!
The population trend for Berthoud, CO, can be represented by the function P(t) = 106.67t + 4763.67, and the population trend for Wellington, CO, can be represented by the function P(t) = 308.8t + 2844.18 where t is the time in years since 2000. When will the towns have the same population?
Answers
106.67t + 4763.67 = 308.8t + 2844.18
First, let's rearrange the equation by moving all the terms involving t to one side:
106.67t - 308.8t = 2844.18 - 4763.67
Simplifying the equation gives:
-202.13t = -1921.49
Now, we can isolate t by dividing both sides of the equation by -202.13:
t = (-1921.49) / (-202.13)
Solving this equation yields:
t ≈ 9.51
Therefore, the towns of Berthoud and Wellington will have the same population approximately 9.51 years after 2000.
Answer:
9.5 years
Step-by-step explanation:
P(t) = P(t)
106.67t+4763.67=308.8t+2844.18
Minus 106.67t on both sides
4763.67=202.13t+2844.18
Minus 2844.18 on both sides
1919.49=202.18t
Solve for t
t=9.4963...
t=9.5 years
Solve |5x - 1| < 1
please help
Answers
Answer:
|5x - 1| < 1
-1 < 5x - 1 < 1
0 < 5x < 2
0 < x < 2/5
Pls help
Consider functions fand g below.
g(x)=-x^2+2x+4
A.As x approaches infinity, the value of f(x) increases and the value of g(x) decreases.
B.As x approaches infinity, the values of f(x) and g(x) both decrease.
C.As x approaches infinity, the values of f(x) and g(x) both increase.
D.As x approaches infinity, the value of f(x) decreases and the value of g(x) increases.
Answers
Consider functions fand g below g(x)=-x^2+2x+4 is option D.As x approaches infinity, the value of f(x) decreases and the value of g(x) increases.
The limit of a function, as x approaches infinity, is defined as a certain value if the function approaches the same value as x approaches infinity from both sides. The behavior of a function, as x approaches infinity, is determined by the function's rate of increase or decrease and the value of the function at x = 0.
The value of f(x) and g(x) will both increase as x approaches infinity in situation C. This implies that the functions are continuously increasing without bound, i.e., the function's value at any given point will always be greater than the previous point. Consider the example of f(x) = x² and g(x) = 2x. As x approaches infinity, f(x) and g(x) will both continue to increase indefinitely.
This is because x² and 2x are both monotonically increasing functions.As x approaches infinity, the value of f(x) decreases and the value of g(x) increases in situation D. As the value of f(x) approaches infinity, it will eventually reach a point where its rate of increase slows and the function will start to decrease.
On the other hand, g(x) will continue to increase because its rate of increase is faster than f(x) and does not slow down as x approaches infinity. Consider the example of f(x) = 1/x and g(x) = x². As x approaches infinity, f(x) decreases towards zero while g(x) continues to increase without bound.The correct answer is d.
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Question 1 of 35
Colleen is buying a $279,000 home with a 30-year mortgage at 4.5%. Because
she is not making a down payment, PMI in the amount of $134.25 per month
is required for the first 2 years of the loan. Based on this information, what is
the total cost of this loan?
OA. $475,415
OB. $512,136
OC. $508,914
OD.
$493,776
SUBMIT
Answers
Answer:
Step-by-step explanation:
add it then subtract the value
10 points for this question
Answers
OThe presence of identical fossil plants in both Antarctica and Australia, within the same rock formations, supports the hypothesis of a supercontinent and the process of plate tectonics by providing evidence of past land connections and the subsequent separation of continents due to tectonic activity.
How to explain the informationThe presence of identical fossil plant species in rock formations of both Antarctica and Australia suggests that these two regions were once connected geographically. The similarity in the fossil record indicates that the plants existed in a shared ecosystem or environment at some point in the past.
The geological formations in which the fossil plants are found can provide further evidence. If the rock layers containing the fossils can be matched across Antarctica and Australia, it suggests that these regions were once part of the same landmass. This correlation supports the idea of a supercontinent.
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