The equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b): Of(x) = (4x + 1)(4x - 1).
The correct answer to the given question is option a or b.
The given function is f(x) = 4x² - 1. We need to choose the equivalent function that best shows the x-intercepts on the graph.The x-intercepts are the points where the graph of a function intersects the x-axis. At the x-intercepts, the value of y is zero.
Therefore, to find the x-intercepts, we need to solve the equation f(x) = 0 for x. The function f(x) = 4x² - 1 can be factored as:(2x + 1)(2x - 1)
To find the x-intercepts, we set f(x) = 0:4x² - 1 = 0(2x + 1)(2x - 1) = 0So, either 2x + 1 = 0 or 2x - 1 = 0. Solving these equations, we get:
x = -1/2 or x = 1/2
These are the x-intercepts of the graph of f(x) = 4x² - 1.Now, let's look at the given options and determine which one shows the x-intercepts on the graph:
Option (a):
Of(x) = (4x + 1)(4x - 1)
This is the factored form of f(x) = 4x² - 1. It correctly shows the x-intercepts.
Option (b):
Of(x) = (2x + 1)(2x - 1)
This is the same as option (a) and correctly shows the x-intercepts.
Option (c): f(x) = 4(x² + 1)
This function does not have any x-intercepts. It has a minimum value of 4 at x = 0.
Option (d): f(x) = 2(x² - 1)
This function has x-intercepts at x = -1 and x = 1. It does not show the x-intercepts of the given function.
Therefore, the equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b):
Of(x) = (4x + 1)(4x - 1).
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Which of the following functions is graphed me below ?
Answer:
[tex]y = |x - 2| + 3[/tex]
The correct answer is C.
3. Pi is defined as the ratio of the circumference of a circle to the diameter of that circle. Which of the following correctly explains why the formula for the circumference of a circle is 2 mr 7 (1 point)
Two times equals the distance from one side of the circle to the other. When you multiply that by r, you get the distance around the circle, or the circumference.
Pi times requals the diameter of the circle. The diameter is half the circle, so when you multiply it by 2, you get the distance around the entire circle, or the circumference.
Two times requals the diameter of the circle. Pi is needed for all circle formulas, so you multiply by since you are finding the circumference.
Two times requals the diameter of the circle. Pi equals the circumference divided by the diameter. When you multiply, the diameter is in both the numerator and the denominator, which cancels out, leaving the circumference.
Answer:
The correct answer is "Two times r equals the diameter of the circle. When you multiply that by pi, you get the distance around the circle, or the circumference." This is because the circumference of a circle is equal to the distance around it, which is the same as the length of its perimeter. The diameter of a circle is the straight line that passes through the center of the circle and touches both sides. Therefore, if you multiply the diameter by pi, which is the ratio of the circumference to the diameter of a circle, you get the circumference. Alternatively, you can also use the formula C = 2πr, where C is the circumference and r is the radius of the circle. Since the radius is half the diameter, the formula can also be stated as C = πd, where d is the diameter of the circle.
Step-by-step explanation:
what does a fraction that is horizontally compressed versus vertically compressed look like?
Answer:
Fractions are like pancakes: you can flatten them horizontally or vertically. Horizontal flattening means you shrink the x-value by multiplying it by a huge number before doing anything else. Vertical flattening means you squish the y-value by multiplying the whole function by a tiny number. For example, if f (x) = x^2, then f (2x) is horizontally flattened by 2 and f (0.5x^2) is vertically flattened by 0.5. Don't worry, it's not rocket science, it's just math.
Can anyone help me solving this question I forgot how to solve it it’s important
The statement that is correct about the dot plots is that:
A) The distribution for Class M is approximately symmetric
How to identify symmetric distribution?A symmetric distribution in dot plots is defined as a distribution with a vertical line of symmetry in the center of the graphical representation, so that the mean is equal to the median.
A symmetric distribution is one that occurs when the values of a variable occur at regular frequencies, and often the mean, median, and mode all occur at the same point. If we draw a line through the middle of the chart, we can see that the two planes mirror each other.
Now, from the given two dot plots of class M and Class N, it is very clear that class M is very close to being symmetric about the data value 3.
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A requested task is subject to be reported when:
Answer:
A requested task is subject to be reported when it has been completed according to the instructions provided.
To demonstrate this with chain of thought reasoning:
1. The task requested will have details outlining what needs to be done.
2. To fulfill the request of the task, the instructions outlined must be followed.
3. Once all instructions are met, the task is complete.
4. Completion of the task means it is subject to be reported.
Step-by-step explanation:
What is the graph of f(x) = 0.5(4)x (x is an exponent)
It should be a positive graph .
Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
The dependent variable is t.
When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155."
The dependent variable is f(t).
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t.
The independent variable
The correct statements are
The dependent variable is t.
When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced."
When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced."
The independent variable is t. Option A,D,E,F.
Let's analyze each statement to understand why it is true:
A) The dependent variable is t: In the given function, f(t), the value of f depends on the value of t. Therefore, t is the independent variable, and f is the dependent variable.
D) When f(2) = 1,323, the 2 represents "the year 2002," and the 1,323 represents "1,323 tons of garbage produced": Here, the value of t is 2, representing the year 2002, and the value of f(t) is 1,323, representing the amount of garbage produced in tons.
E) When f(4) = 1,458.6, the 4 represents "the year 2004," and the 1,458.6 represents "1,458.6 tons of garbage produced": Similar to statement D, the value of t is 4, representing the year 2004, and the value of f(t) is 1,458.6, representing the amount of garbage produced in tons.
F) The independent variable is t: As mentioned in statement A, t is the independent variable in the given function. It is the variable that we can change or manipulate, and the value of f depends on the value of t.
Statements B, C, and G are incorrect:
B) When f(12) = 2,155, the 12 represents "12 tons of garbage produced," and the 2,155 represents "the year 2155": This statement is incorrect because in the given function, t represents the time in years after 2000, not the amount of garbage produced.
C) The dependent variable is f(t): This statement is incorrect because, as mentioned earlier, t is the independent variable, and f is the dependent variable.
G) The independent variable f(t): This statement is incorrect because f(t) represents the amount of garbage produced, which is the dependent variable in the given function.
So Option A,D.E.F. Are correct.
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Note the complete question is
Let f(t) be the amount of garbage, in tons, produced by a city, and let t be the time in years after 2000.
Which statements are true for the given function?
A.) The dependent variable is t.
B.) When f(12) = 2,155, 12 represents "12 tons of garbage produced," and 2,155 represents "the year 2155."
C.) The dependent variable is f(t).
D.) When f(2) = 1,323, 2 represents "the year 2002," and 1,323 represents "1,323 tons of garbage produced."
E.) When f(4) = 1,458.6, 4 represents "the year 2004," and 1,458.6 represents "1,458.6 tons of garbage produced."
F.) The independent variable is t.
G.) The independent variable f(t)
What is the next value?
2 3 E 4 5 I 6 8
options: O 8 M N
Answer:
The correct answer is a.
Step-by-step explanation:
The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.
answer the question submitted
The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.
To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:
Step 1: Divide the coefficient of x by 2 and square the result.
(Coefficient of x) / 2 = -28/2 = -14
(-14)² = 196
Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.
g(x) = 4x² - 28x + 49
= 4x² - 28x + 196 - 196 + 49
Step 3: Rearrange the terms and factor the perfect square trinomial.
g(x) = (4x² - 28x + 196) - 196 + 49
= 4(x² - 7x + 49) - 147
= 4(x² - 7x + 49) - 147
Step 4: Write the perfect square trinomial as the square of a binomial.
g(x) = 4(x - 7/2)² - 147
Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.
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The probable question may be:
Rewrite the function by completing the square.
g(x)=4x²-28x +49
g(x)= ____ (x+___ )²+____.
please help will give brainliest...........
A
no, because they are both right triangles and
the one on the left is 88° at the right anglr
Mohammed Corporation's comparative balance sheet for current assets and liabilities was as follows:
Dec. 31, 20Y2 Dec. 31, 20Y1
Accounts receivable $20,900 $20,000
Inventory 61,800 62,500
Accounts payable 19,700 18,600
Dividends payable 24,000 22,000
Adjust net income of $98,500 for changes in operating assets and liabilities to arrive at net cash flow from operating activities.
The net cash flow from operating activities would be $100,800.
What is the net cash flow from operating activities?Change in accounts receivable:
= $20,900 - $20,000
= $900
Change in inventory:
= $61,800 - $62,500
= -$700
Change in accounts payable:
= $19,700 - $18,600
= $1,100
Change in dividends payable:
= $24,000 - $22,000
= $2,000
Change in operating assets and liabilities:
= Change in accounts receivable + Change in inventory - Change in accounts payable - Change in dividends payable
= $900 + (-$700) + $1,100 + $2,000
= $2,300
Net cash flow from operating activities:
= Net income + Change in operating assets and liabilities
= $98,500 + $2,300
= $100,800.
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A grocery store owner polled ten customers to determine how many times they went to the grocery store in April. The results of his poll are shown below.
12,9,4,8,25,6,8,5,18,13
Determine the appropriate shape of the distribution.
A. The data does not show a latter
B. Left skewed
C. Symmetrical
D. Right skewed
Answer:
D. Right skewed
Step-by-step explanation:
To determine the shape of the distribution, we can examine the given data:
12, 9, 4, 8, 25, 6, 8, 5, 18, 13
One way to determine the shape of the distribution is by visualizing it using a histogram or a box plot. However, without the exact frequency of each value, we cannot create an accurate visual representation.
Alternatively, we can examine the skewness of the distribution. Skewness is a measure of the asymmetry of a distribution. If the data is skewed to the left, it is left-skewed or negatively skewed. If it is skewed to the right, it is right-skewed or positively skewed. If the data is symmetric and evenly distributed, it is considered a symmetrical distribution.
Let's calculate the skewness of the given data to determine the shape:
Skewness = (3 * (mean - median)) / standard deviation
First, let's calculate the mean, median, and standard deviation of the data:
Mean = (12 + 9 + 4 + 8 + 25 + 6 + 8 + 5 + 18 + 13) / 10 = 10.8
Median = the middle value when the data is arranged in ascending order:
4, 5, 6, 8, 8, 9, 12, 13, 18, 25
Median = (8 + 9) / 2 = 8.5
Next, let's calculate the standard deviation:
Step 1: Calculate the squared differences from the mean for each value:
(12 - 10.8)^2, (9 - 10.8)^2, (4 - 10.8)^2, (8 - 10.8)^2, (25 - 10.8)^2, (6 - 10.8)^2, (8 - 10.8)^2, (5 - 10.8)^2, (18 - 10.8)^2, (13 - 10.8)^2
Step 2: Calculate the sum of squared differences:
(1.44 + 2.88 + 45.76 + 8.64 + 228.01 + 22.09 + 8.64 + 32.49 + 47.04 + 4.84) = 411.73
Step 3: Calculate the variance:
Variance = sum of squared differences / (n - 1) = 411.73 / (10 - 1) = 45.75
Step 4: Calculate the standard deviation:
Standard deviation = square root of variance = √45.75 = 6.76 (approximately)
Now we can calculate the skewness:
Skewness = (3 * (mean - median)) / standard deviation
Skewness = (3 * (10.8 - 8.5)) / 6.76
Skewness = 6.4 / 6.76
Skewness ≈ 0.95
Since the skewness is positive (0.95), the data is right-skewed or positively skewed. Therefore, the appropriate shape of the distribution is:
D. Right skewed
(03.01 MC)
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
three to the fourth power all over nine equals three squared
By simplifying 9 to 32 to make both powers base three and adding the exponents
By simplifying 9 to 32 to make both powers base three and subtracting the exponents
By finding the quotient of the bases to be one third and simplifying the expression
By finding the quotient of the bases to be one third and cancelling common factors
The correct answer is By finding the quotient of the bases to be one third and canceling common factors. Option D.
The Quotient of Powers Property states that when dividing two powers with the same base, you can subtract the exponents. In the given expression, we have three to the fourth power divided by nine.
To simplify this expression using the Quotient of Powers Property, we first need to recognize that nine can be written as three squared, since 3 multiplied by itself gives 9.
So, we have (3^4) / (3^2). According to the Quotient of Powers Property, we subtract the exponents: 4 - 2.
This gives us 3^(4-2), which simplifies to 3^2. Therefore, the expression three to the fourth power all over nine equals three squared.
It states that we find the quotient of the bases to be one third and cancel common factors. In this case, the bases are 3 and 3, and their quotient is indeed one third. Additionally, there are no common factors that can be canceled, as the expression does not contain any variables or additional terms.
Therefore, By finding the quotient of the bases to be one third and canceling common factors. accurately describes the steps involved in simplifying the expression using the Quotient of Powers Property.
We find the quotient of the bases (one third) and cancel common factors (which is not applicable in this case). Option D is correct.
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Note the complete question is
Explain how the Quotient of Powers Property was used to simplify this expression. (1 point)
Three to the fourth power all over nine equals three squared
A.) By simplifying 9 to 32 to make both powers base three and adding the exponents
B.) By simplifying 9 to 32 to make both powers base three and subtracting the exponents
C.) By finding the quotient of the bases to be one third and simplifying the expression
D.) By finding the quotient of the bases to be one third and cancelling common factors
Use the equation 20x+12y= 24 as an equation in three different linear systems. Write a second equation so that each system has a different number of solutions. Explain what you did for each system.
We have created three different linear systems using the equation 20x + 12y = 24.
System 1 has infinitely many solutions, System 2 has no solution, and System 3 has a unique solution.
Let's create three different linear systems using the equation 20x + 12y = 24 and ensure that each system has a different number of solutions.
System 1:
Equation 1: 20x + 12y = 24 (given)
Equation 2: 40x + 24y = 48
Explanation: In this system, we multiplied both sides of the given equation by 2 to create Equation 2.
By doing so, we have essentially created two equations that are multiples of each other.
Since the equations are equivalent, they represent the same line, and the system has infinitely many solutions.
Any values of x and y that satisfy the first equation will automatically satisfy the second equation as well.
System 2:
Equation 1: 20x + 12y = 24 (given)
Equation 2: 20x + 12y = 48
Explanation: In this system, we changed the constant term in Equation 2 to 48.
By doing so, we have created two parallel lines with the same slope. Since the lines are parallel, they will never intersect, and the system has no solution.
There are no values of x and y that satisfy both equations simultaneously.
System 3:
Equation 1: 20x + 12y = 24 (given)
Equation 2: 40x + 24y = 48
Explanation: In this system, we multiplied both sides of Equation 2 by 2 to create Equation 2.
By doing so, we have created two equations that have the same slope but different y-intercepts.
Since the lines are not parallel and have different y-intercepts, they will intersect at a single point, and the system has a unique solution.
There will be one specific pair of values for x and y that satisfy both equations simultaneously.
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Find the sum of the measures of the angles of a five sided polygon
Answer:540 degrees
The sum of the measures of the angles of a five-sided polygon (pentagon) is 540 degrees123. This can be calculated using the angle sum formula, S = (n − 2) × 180°, where n is the number of sides in the polygon12. Since a pentagon has five sides, the sum of the interior angles is (5 − 2) × 180° = 540°123.
Step-by-step explanation:
Answer:
540°
Step-by-step explanation:
Since a pentagon has n=5 sides, then we have:
[tex]180(n-2)=180(5-2)=180(3)=540^\circ[/tex]
I dont understand these can someone help?
The corresponding sides and angles of the similar and congruent triangles indicates that we get the following approximate and exact values;
Page 1;
5. [tex]\overleftrightarrow{AC}[/tex] = 4.3. 6. [tex]\overline{BP}[/tex] ≈ 7.5 7. [tex]\overline{YV}[/tex] ≈ 8
Page 2
5. [tex]\overline{DF}[/tex] = [tex]11\frac{1}{4}[/tex], 6. [tex]\overline{ED}[/tex] = 5, 7. [tex]\overline{BC}[/tex] = 22, 8. [tex]\overline{EF}[/tex] = 8
Page 3;
8. m∠ABC = 30°, 9. m∠XYP = 44°, 10. [tex]\overline{AC}[/tex] = 14
What are congruent triangles?Congruent triangles are triangles that have all three corresponding sides of the same length and all three angles of the same measure.
First Page
5. The distance from the vertex B to the line segment [tex]\overleftrightarrow{AC}[/tex] in the triangle ΔABC is the altitude of the triangle, which is 4.3
6. The distance from the vertex B to [tex]\overleftrightarrow{AC}[/tex] = [tex]\overline{BP}[/tex]
Pythagorean theorem indicates that the length of the segment [tex]\overline{BP}[/tex] can be found as follows;
[tex]\overline{BP}[/tex] = √(13.5² - 11.2²) ≈ 7.5
7. The distance from Y to [tex]\overleftrightarrow{XZ}[/tex] is the altitude of the triangle ΔXYZ, which indicates;
The distance from Y to [tex]\overleftrightarrow{XZ}[/tex] = [tex]\overline{YV}[/tex]
The Pythagorean theorem indicates that we get;
[tex]\overline{YV}[/tex] = √(13.34² - 10.67²) ≈ 8
Second page;
5. The scale factor from ΔABC to ΔDEF = 3/4
Therefore, the length of [tex]\overline{DF}[/tex] = (3/4) × 15 = 45/4 = [tex]11\frac{1}{4}[/tex]
6. The scale factor of (1/3) indicates that we get;
[tex]\overline{ED}[/tex] = (1/2) × 10 = 5
7. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 18/9 = 10/5 = 2
The corresponding side to [tex]\overline{BC}[/tex] is [tex]\overline{EF}[/tex]
[tex]\overline{EF}[/tex] = 11, therefore, the length of [tex]\overline{BC}[/tex] = 2 × 11 = 22
8. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 4/6 = 10/15 = 2/3
The corresponding side to [tex]\overline{EF}[/tex] is [tex]\overline{BC}[/tex]
[tex]\overline{BC}[/tex] = 12, therefore [tex]\overline{EF}[/tex] = (2/3) × 12 = 8
Third page;
8. The triangles ΔABV and ΔCVB are congruent triangles by the Leg Hypotenuse congruence theorem.
The angles ∠ABV and ∠CBV are corresponding triangles, therefore;
∠ABV ≅ ∠CBV
m∠CVB = m∠ABV = 15° (Definition of congruent triangles and symmetric and substitution property)
∠ABC = ∠ABV + ∠CBV
Therefore; m∠ABC = 15° + 15° = 30°
9. The angles ∠YXP and ∠YZP are right triangles, therefore;
m∠YXP = m∠YZP = 90°
The right triangles ΔYXP and ΔYZP are congruent by the LH congruence theorem
∠XYP ≅ ∠ZYP (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)
m∠XYP = m∠ZYP (Definition of congruent triangles)
m∠XYZ = m∠XYP + m∠ZYP (Angle addition property)
m∠XYZ = 2 × m∠XYP
2 × m∠XYP = m∠XYZ = 88°
m∠XYP = 88°/2 = 44°
10. The angles ∠ACP and ∠ABP are right angles, according to the indicated markings, therefore;
∠ACP ≅ ∠ABP (All right angles are congruent)
ΔACP ≅ ΔABP by SAA congruence theorem
[tex]\overline{AC}[/tex] ≅ [tex]\overline{AB}[/tex] (CPCTC)
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] (Definition of congruent segments)
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] = 14
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Which shows 2 products that both result in negative values
These are two instances where the product of two numbers yields a negative result.
To demonstrate two products that both result in negative values, we can choose two numbers with opposite signs and multiply them together. Here are two examples:
Example 1:
Let's consider the numbers -3 and 4. When we multiply these numbers, we get:
(-3) * (4) = -12
The product -12 is a negative value.
Example 2:
Let's consider the numbers 5 and -2. When we multiply these numbers, we get:
(5) * (-2) = -10
Once again, the product -10 is a negative value.
In both examples, we have chosen two numbers with opposite signs, and the multiplication of these numbers results in a negative value. Therefore, these are two instances where the product of two numbers yields a negative result.
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please help me asap with this it's getting late
The system B is gotten from system A by operation (d)
How to derive the system B from system AFrom the question, we have the following parameters that can be used in our computation:
x + y = 8
4x - 6y = 2
Also, we have the solution to be (5, 3)
Recall that
x + y = 8
4x - 6y = 2
Multiply the first equation by 6
So, we have
6x + 6y = 48
4x - 6y = 2
Add the equations
10x = 50
This means that the system B from system A is (d)
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There are 40 black marbles, 20 blue marbles, and 4 red marbles in a jar.
а. What is the probability of selecting one red marble?
b. What is the probability of selecting one black marble?
c. What is the probability of selecting one blue marble?
d. Which has the highest probability of being selected?
e. Which has the lowest probability of being selected?
Step-by-step explanation:
a. 4/64= 1/16 for red marble
b. 40/64= 5/8 black marbles
c. 20/64= 5/16 blue marble
d. highest: black marble
e. lowest: red marble
y = 1/3x -1
x-intercept (3,0)
How did they get this answer? Somebody please help
Answer:
Step-by-step explanation:
x-intercept is where the line cuts the x-axis. That is, when y=0.
Substitute y=0 and we get:
[tex]0=\frac{1}{3} x-1[/tex]
[tex]1=\frac{1}{3} x[/tex]
[tex]x=3[/tex]
So x-intercept is the point (3,0).
A building contractor is building a backyard playground and wishes to put down rubber mulch to provide safety from falls. The contractor wishes to put the mulch in a pit in the shape of a rectangular solid 24 feet long, 13 feet wide, and 6 inches deep.
a) Determine the volume, in cubic feet, of mulch the contractor will need.
b) If mulch costs 9$ per cubic foot, what will the cost of mulch be?
Answer:
A= 220.5ft
B= $2425.5
Step-by-step explanation:
A= 220.5ft
B= $2425.5
d 1 1 logx tanx
dx x
+ + +
The expression you provided appears to be an integral with multiple terms involving logarithmic and trigonometric functions. To solve it, we need to break it down and evaluate each term separately.
Let's examine each term in the given expression:The integral of 1 with respect to x is simply x.The integral of 1/x is ln|x|.
The integral of tan(x) can be evaluated using a substitution or integration by parts technique, depending on the specific limits of integration or any additional context provided.
Without specific limits or further instructions, it's challenging to provide a precise solution or simplify the expression further. However, if you provide more information or clarify the problem statement, I can help you with a more detailed solution.
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Pamela is buying a $242,000 home with a 30-year mortgage. She will make
an 8% down payment. Use the table below to find her monthly PMI payment.
Base-To-Loan %
95.01% to 97%
90.01% to 95%
85.01% to 90%
85% and Under
OA. $96.48
OB. $144.72
OC. $157.30
OD. $151.01
Fixed-Rate Loan
30 yrs. 15 yrs.
0.90% 0.79%
0.78% 0.26%
0.52% 0.23%
0.32% 0.19%
ARM 2% +1 Year Cap
30 yrs.
15 yrs.
n/a
0.92% 0.81%
0.65%
n/a
0.37%
0.54%
0.26%
In rectangle ABCD, AB = x, BC =x + 2, and AC = x +4. Find the value of x.
Answer:
x = 6
Step-by-step explanation:
the diagonal AC divides the rectangle into 2 right triangles.
Consider the right triangle ABC with legs AB , BC and hypotenuse AC
using Pythagoras' identity in right triangle ABC
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
AB² + BC² = AC² ( substitute values )
x² + (x + 2)² = (x + 4)² ← expand factors using FOIL
x² + x² + 4x + 4 = x² + 8x + 16
2x² + 4x + 4 = x² + 8x + 16 ( subtract x² + 8x + 16 from both sides )
x² - 4x - 12 = 0 ← in standard form
(x - 6)(x + 2) = 0 ← in factored form
equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
however , x > 0 , then x = 6
A box contains 240 lumps of sugar. Five lumps are fitted across the box and there were three layers. How many lumps are fitted along the box?
Prove the following?
The given statement proposition is a that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.
The given statement is a logical proposition involving the concept of induction. Let's break it down and analyze its components.
"If x is inductive..."
This implies that x is a concept or object that possesses the property of being inductive. In mathematics, the term "inductive" typically refers to the property of being a natural number or belonging to the set of natural numbers.
"...then so is (x ∈ X : x = Ф or x = y ∪ {y} for some y)"
Here, we have a set X that consists of elements satisfying a certain condition. The condition states that an element x in X can either be equal to the empty set (Ф) or the union of a set y with itself ({y}). This construction represents a recursive definition, where each element in X is defined in terms of a base case (Ф) and a recursive step ({y}).
"...hence each n ≠ 0 is m + 1 for some m."
This conclusion states that for every natural number n that is not equal to 0, there exists another natural number m such that n can be expressed as m + 1. In other words, any non-zero natural number is the successor of some other natural number.
Overall, the given statement is a proposition that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.
for such more question on proposition
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Answer:
Below, rises, more, 2, 5
Step-by-step explanation:
Its an positive exponential growth function which means it increases sharply to the right it also is above the x-axis.
The graph is 2 times the graph of 5^x so its steeper or rises more
Plug in 0 to get 1*2=2
Plug in 1 to get 5*1=5
17 students are present in a class. in how many ways ,they can be made to stand in 2 circles of 8 and 9 students
Answer:
24310
Step-by-step explanation:
17 choose 8= 17 choose 9
17 choose 8= 17*16*15*14*13*12*11*10/8!= 24310
write 718000 in standard form
Answer:
718000
Step-by-step explanation:
718000 is already in standard form
8. Given AABC~AEDC
What is the value of x?
C. 30
D. 20
A. 15
B. 12
E
60
X
C
D
10
40
B
The calculated value of x in the triangle is 15
How to calculate the value of xFrom the question, we have the following parameters that can be used in our computation:
The triangles ABC and EDC
Since the triangles are similar, then we have
(3x - 5)/(5x - 5) = 32/56
This gives
32(5x - 5) = 56(3x - 5)
When solved for x, we have
x = 15
Hence, the value of x is 15
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