Using trigonometry we know that option (B) "cosθ < 0" is correct.
What is Trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.For a right-angle triangle, the sum of the square of the legs is equal to the hypotenuse side(longest side).
Therefore, for a right triangle
a² + b² = c²For the triangle that has a² + b² > c², it shows it is not a right triangle.
Let θ be the measure of the angle opposite the side of length c.We have to find the statements which are must be true.Cosine law:
c² = a² + b² - 2abcosθSubstitute the value then we get:
c² < c² - 2abcosθSubtracting c² on both sides of the inequality:
c² - c² < c²- c² - 2abcosθ0 < -2abcosθAdding 2abcosθ on both sides then we get:
2abcosθ < -2abcosθ + 2abcosθ = 02abcosθ < 0cosθ < 0cosθ is negative in the second quadrant and third quadrants.
Therefore, using trigonometry we know that option (B) "cosθ < 0" is correct.
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Please Help With This.
The angle m∠FCD is 56°
Here the line CF is an angle bisector of ∠GCD.
By this we have,
∠GCF = ∠FCD
It is given that
∠GCF = ∠GCB - 12°
Let ∠GCB be x.
∠GCF = x - 12° = ∠FCD
BCD is a straight line which form 180°.
∠BCG + ∠GCF + ∠FCD = 180°
x + x - 12° + x - 12° = 180°
3x = 204°
x = 68°
∠FCD = x - 12°
= 68° - 12°
= 56°
Therefore m ∠FCD = 56°.
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Change the function, y=3(0.5)^x,to a function with base e
Answer:
y = 3(e)^(-0.69x)
Explanation:
Taking into account the following property
[tex]a=e^{\ln a}[/tex]We can replace (0.5)^x by
[tex]\begin{gathered} 0.5^x=e^{\ln \text{ (0.5\textasciicircum{}x)}} \\ 0.5^x=e^{x\ln (0.5)} \end{gathered}[/tex]So, now we can rewrite the function as
[tex]\begin{gathered} y=3e^{x\ln (0.5)} \\ y=3e^{x(-0.69)} \\ y=3e^{-0.69x} \end{gathered}[/tex]Therefore, the answer is
y = 3(e)^(-0.69x)
Answer:
y=3e^(ln0.5)x
Step-by-step explanation:
A population of a certain city increases exponentially at a rate of 6.5%. Initially, it is 1.50 million. After how many years will the population reach 2.31 million?6.5466.643 6.1236.142
Given that
The population of a certain city is 1.50 million initially and it gets increased by 6.5% exponentially. And we have to find the number of years in which the population becomes 2.31 million.
Explanation -
The formula for the exponential growth is given as
[tex]\begin{gathered} f(x)=a(1+r)^x \\ where\text{ f\lparen x\rparen is the final amount, a = initial amount, r = rate and x = time period} \end{gathered}[/tex]Here we have f(x) = 2.31 million, a = 1.50 million , r = 6.5% and x = ?
So let the time be t.
Then, on substituting the values we have
Can someone help me make a floor plan using the shapes on the scale factor sheet?
Answer:
k = 4
Explanation:
1) The triangles in example 1 are similar triangles but differs in size
We are to calculate the scale factor k
Using the formula
Scale factor k = size of the larger triangle/size of the smaller trinagle
Since they are similar triangles;
k = DF/AB
Given
DF = 48
AB = 12
Substitute the given values into the expression for k above to have;
k = 48/12
k = 4
Hence the scale factor from triangle ABC to DEF is 4
The perimeter of a triangle is 38 feet. One side of the triangle is one foot longer than the second side. The third side is four feet longer than the second side. Find the lengths of all three sides (in feet). (Enter your answers as a comma-separated list.)
The length of the three sides of the triangle are 11 feet, 12 feet and 15 feet.
How to find the length of a triangle?A triangle is a polygon with three sides.
The perimeter of a triangle is 38 feet.
The perimeter of the triangle is the sum of the whole three sides.
One side of the triangle is one foot longer than the second side.
let
the second side = x
longer side = x + 1
The third side is four feet longer than the second side.
Hence,
Third side = 4 + x
Therefore,
38 = x + x + 1 + x + 4
38 = 3x + 5
3x = 38 - 5
3x = 33
x = 33 / 3
x = 11
Therefore, the sides of the triangle are 11 ft, 12 feet and 15 ft.
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3) Store A sells 36 pack box of chocolates for $54. Store B sells 6-pack boxes of the same size chocolates for $12. Which store offers a better deal? (Organize your information in the tables given below) Store A Store B # of Chocolates Price $ Price $ # of Chocolates.
3) Store A sells 36 pack box of chocolates for $54. Store B sells 6-pack boxes of the same size chocolates for $12. Which store offers a better deal? (Organize your information in the tables given below) Store A Store B # of Chocolates Price $ Price $ # of Chocolates.
________________________________
# of Chocolates Price Ratio (Price per chocloate)
Store A 36 pack box 54 54/ 36 = 3/2 = 1.5
Sotre B 6-pack boxes 12 12/ 6 = 2
_____________________________
Store A 1.5
______________________________
Answer
Store A offers a better deal
The square of a negative number
is sixteen more than six times the
negative number. Find the number. The sum of two numbers is
twenty three. And The product of the
two numbers is one hundred
twenty. Find the two numbers.Help me. From: Jessie
The numbers are:
1. The value of x = 5
2. The value of x = 15 or 8 and y = 8 or 15
What is Square?
The word Square means a number multiplied by itself.
The above answers were gotten in the following way:
1. Let the unknown negative number be x
The square of the negative number: x² is
Sixteen more than six times of negative x: 6x+16
It is written as: (x)²=6x+16
Equating to zero, we have:
x²-6x-16=0
Factorizing, we have:
x²-8x+2x-16=0
x(x-8)+2(x-8)=0
x+2=0 and x-8=0
x=-2 and 8
Since the number is negative, x = -2
Therefore, the value of the negative number is -2
2. Given:
Sum of two numbers = 23
Product of two numbers = 120
Calculation:
Let the two numbers be x and y
x+y=23...............equation 1
xy=120..................equation 2
From equation 1, x=23-y
Substitute the value of x in equation 2, we have:
(23-y)y=120
Opening the brackets, we have:
23y-y²=120
Rearranging the equation, we have:
-y²+23y=120
Equating to zero, we have:
-y²+23y-120=0
Multiplying both sides by (-1), we have:
y²-23y+120 = 0
Factorizing, we have:
y²-15y-8y+120=0
y(y-15)-8(y-15)=0
(y-8)(y-15)=0
y=8 or 15
Substituting the values of y in any of the equation. Choosing equation 1, we have:
From Equation 1: x+y=23
When y=8,
x+8=23
x=23-8
x=15
When y=15
x+15=23
x=23-15
x=8
Therefore the values of the two numbers are 15 and 8
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Given the following sequences: I. 2,4,6,8,10... II.2,4,8,16,32... III. a,a + 2, a + 4, a + 6, a +8... Which ones are arithmetic sequences?
ANSWER
The arithmetic sequences are: I and iii
EXPLANATION
The formula for the nth term of an arithmetic sequence is:
[tex]a_n=a_1+d(n-1)[/tex]where a1 is the first term of the sequence and d is the common difference.
For the first sequence I. 2, 4, 6, 8, 10... we can find the common difference by subtracting the first term from the second:
[tex]\begin{gathered} a_2=a_1+d(2-1) \\ a_2=a_1+d \\ d=a_2-a_1 \\ d=4-2 \\ d=2 \end{gathered}[/tex]So the nth term of this sequence is:
[tex]a_n=2+2(n-1)[/tex]Each term of this sequence follows this rule. Therefore this is an arithmetic sequence.
For the second sequence II. 2, 4, 8, 16, 32... there's no common difference because between the first and second term there's a difference of 2, between the second and third there's a difference of 4, and this increases as we move through the sequence. Therefore this is not an arithmetic sequence.
For the third one, III. a, a+2, a+4, a+6, a+8... we can see that there is a common difference:
[tex]\begin{gathered} a_2_{}_{}=a_1+d(2-1) \\ d=a_2-a_1 \\ d=a+2-a \\ d=2 \end{gathered}[/tex]The rule for the nth term is:
[tex]a_n=a+2(n-1)[/tex]Let's find the first 5 terms:
[tex]\begin{gathered} a_1=a+2(1-1)=a \\ a_2=a+2(2-1)=a+2 \\ a_3=a+2(3-1)=a+4 \\ a_4=a+2(4-1)=a+6 \\ a_5=a+2(5-1)=a+8 \end{gathered}[/tex]This shows that each term follows the same rule. Therefore this is an arithmetic sequence.
. Explain in words:
José says the graph represents Terrence skating up a hill and then down a hill What
do you say to José?
from motion detector
A motion sensor, sometimes known as a motion detector, is a piece of technology that use a sensor to find nearby individuals or objects. Any security system needs motion sensors as a crucial part. A sensor will alert your security system and, with newer systems, your cell phone when it senses motion.
How does a motion sensor function?
Active ultrasonic motion detectors emit ultrasonic sound waves, which bounce off surrounding objects and return to the source of emission. The sensor initiates and completes the required action, whether it be turning on a light or sounding an alert, when a moving object interferes with the waves.
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What's the radius of 5?
The formula for radius is
radius = diameter/2
If diameter = 5, then
radius = 5/2
radius = 2.5
Find the slope, x-intercept, and y-intercept for the line 10x-7y + 7 = 0. The slope is The I-intercept is h The y-intercept is Note: Your answers must be decimals. Submit Question Jump to Answer
slope=1.43
y-intercept=1
x-intercept=-1.43
Explanation
Step 1
get the slope intercept form of the equation
[tex]y=mx+b\text{ (slope intercept equation)}[/tex]where
m is the slope and b is the y-intercept
to do this, isolate y
[tex]\begin{gathered} 10x-7y+7=0 \\ \text{subtract 10 x in both sides} \\ 10x-7y+7-10x=0-10x \\ -7y+7=-10x \\ \text{subtract 7 in both sides} \\ -7y+7-7=-10x-7 \\ -7y=-10x-7 \\ divide\text{ both sides by -7} \\ \frac{-7y}{-7}=\frac{-10x}{-7}-\frac{7}{-7} \\ y=\frac{10x}{7}+1 \end{gathered}[/tex]so,
[tex]\begin{gathered} \text{slope}=\frac{10}{7} \\ y-\text{intercept}=1 \end{gathered}[/tex]Step 2
to find the x-intercept replace the y value with zero in the equation
[tex]\begin{gathered} y=\frac{10x}{7}+1 \\ 0=\frac{10x}{7}+1 \\ \text{subtract 1in both sides} \\ 0-1=\frac{10x}{7}+1-1 \\ \frac{10x}{7}=-1 \\ \text{Multiply both sides by 7/10} \\ \frac{10x}{7}\cdot\frac{7}{10}=-1\cdot\frac{7}{10} \\ x=-\frac{7}{10} \end{gathered}[/tex]so, the x intercept is
[tex]-\frac{7}{10}[/tex]I hope this helps you
HELP Please!!!
Bridget worked on her Math homework for 1 ½ hours. Then she worked on her Social Studies homework for ¼ hour. How many hours total did she work on her homework?
Be sure to show all of your work and steps.
Answer: 1 3/4
1/4= 15 minutes
1/2 = 30 minutes
add 1/2 to 1/4 and you get 3/4 because 1/2 is equal to 2/4 if you add the 1/4 to it
heres the actual math:
1/2 = 2/4
2/4 + 1/4 = 3/4
slap that one in front of it so its 1 3/4 and therea your answer
A woman earned wages of $34,600, received $1500 in interest from a savings account, and contributed $2700 to a tax-deferred retirement plan. She was entitled to a personal
exemption of $2900 and had deductions totaling $5090. Find her gross income, adjusted gross income, and taxable income.
If She was entitled to a personal exemption of $2900 and had deductions totaling $5090. her gross income is $36,100, adjusted gross income is $33,400 , and taxable income is $25,410.
Gross incomeGross Income:
Gross Income= Wages + Interest received
Gross Income= 34,600 + $1500
Gross Income= $36,100
Adjusted Gross Income:
Adjusted Gross Income = Income - Tax Def Contribution
Adjusted Gross Income = $36,100- $2,700
Adjusted Gross Income = $33,400
Taxable Income :
Taxable Income = AGI - Deductions - Personal exemption
Taxable Income= $33,400- $5,090 - $2,900
Taxable Income= $25,410
Therefore her gross income is $36,100.
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In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
O Yes
The probability of having female baby is 0.95
What is probability?
Probability is a discipline of mathematics that deals with statistical models of how probable an event is to exist or how likely a statement is to be true. The probability of an occurrence is a value between 0 and 1 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
The probability of having female baby is = 284/(284 + 15) = 0.95
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Simplify the following expression by expanding and collecting like terms.-(7x + 6) + 3(-5x – 3)Give your answer in the form ax + b.Provide your answer below:
ANSWER:
[tex]-22x-15[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]-\mleft(7x+6\mright)+3\mleft(-5x-3\mright)[/tex]We solve and reduce like terms, just like this:
[tex]\begin{gathered} -7x-6-15x-9 \\ (-7x-15x)+(-6-9) \\ (-22x)+(-15)=-22x-15 \end{gathered}[/tex]What is the value of the missing angle
Answer: 105
Step-by-step explanation:
Angles in a triangle add up to 180 degrees always, you already have two angles. Subtract those two angles from 180 then you have 75. A straight line always equals 180, and since we just found one angle on that line which is 75, just subtract 75 from 180 to get the answer.
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y > x + 2y > -2 x - 7I NEED THE CORDINATES
Given:
There are given that the set of inequality is:
[tex]\begin{gathered} y>x+2 \\ y>-2x-7 \end{gathered}[/tex]Explanation:
From the given system of inequality, we need to draw the graph and find the set of points, where both of the graphs will intersect.
Now,
The graph of the given system of inequality is shown below:
Final answer:
Hence, the set of the point from the given system of inequality is shown below:
[tex](-3,-1)[/tex]60x-30/5=18. please help meeeeee. 10 pts worth.
Discount Pricing A wool suit that was originally priced at $700 is on the 30%-off clearance rack. What is the sale price of the suit?
Answer:
Sale Price = $490
Explanation:
After 30% off, the sale price is 100% - 30% = 70% the original price.
70% of the original price is
[tex]\frac{70\%}{100\%}\times\$700=0.7\times\$700[/tex][tex]=\$490[/tex]which is our answer!
Hence, the sale price of the wool suit is $490.
What is the net price of merchandise listing for $5,900 less a trade discount rate of 45%?
A percentage is a number or ratio that represents a fraction of 100.
If there is a trade discount of 45% on the price of the merchandise of $5900, the net price of the merchandise is $3245.
What is a percentage?A percentage is a number or ratio that represents a fraction of 100.
We have,
Merchandise price = $5,900
Discount rate = 45%
45% = 45/100 = 9/20
The net price of the merchandise:
= 5900 - (45% of 5900)
= 5900 - 9/20 x 5900
= 5900 - 9 x 295
= 5900 - 2655
= 3245
Thus,
If there is a trade discount of 45% on the price of the merchandise of $5900, the net price of the merchandise is $3245.
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James spins a basketball on his finger and then passes the ball to his friend.
a. What type of transformation is used when James spins the basketball on
his finger?
b. What type of transformation is used to pass the basketball?
The types of transformations that occur as a result of the motion on the ball are;
A) Rotation
B) Translation
What is the type of transformation?Transformation is a method required to resize or change the orientation of a given shape or figure. The types of transformation are translation, reflection, rotation, and dilation.
Translation is a method of transformation that involves moving an object or shape from one point to another without changing any dimension.
Reflection is a method of transformation that involves flipping a given figure about a given reference point or line. In order words, a mirror image of the original object.
Rotation is a method of transformation that involves turning a given figure at an angle about a reference point.
Dilation is a method of transformation whereby the length of the sides of the figure is either increased or decreased.
A) When James spins a basketball on his finger, it is clear that this transformation is rotation because it involves turning the ball at an angle about a given point.
B) When James passes the basketball, the transformation would be translation because it involves moving the ball from one point to another without changing the dimension of the ball.
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3х-7-(-2х) +9 simplify
Give a brief history about TRIANGLE NUMBERS, including Mathematicians that contributed for its development.
Brief history of triangle numbers
What is Triangle Number?
An equilateral triangle-shaped group of objects is counted using a triangular number or triangle number. Square and cube numbers are two further examples of figurate numbers, which also include triangle numbers.
Students are typically introduced to triangular numbers through the account of Carl Gauss, a well-known mathematician who used the concept of the triangle number formula to aid him with summing consecutive integers as a student. This tale and its applications in many situations are discussed in the article Clever Carl.
Triangular numbers were created by the Pythagoreans, who discovered connections between geometric forms and numbers, giving rise to triangular, square, pentagonal, and other numbers.
After four or five terms, students may recognize that the answer can be discovered by adding consecutive terms, according to our research. As an illustration, you may use the formulas 1+2+3+4+5 or 10 (the preceding term) + 5 to determine the fifth term. However, when students attempt to transition from this to the general formula for triangle numbers of
n(n+1)/2
Drawing triangle numbers is an exercise that could be helpful in establishing a connection between these two concepts.
The nth term and substitution into algebraic expressions can then be discussed using this formula. Sequences, notably quadratic sequences, can also be discussed.
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In a recent year, 31.4% of all registered doctors were female. If there were 47,300 female registered doctors that year, what was the total number of registered doctors?
Proportionately, the total number of registered doctors, based on the ratio of female doctors, is 150,637.
What is proportion?Proportion refers to the quantity relationship of a variable contained in another.
Using proportion, two values are equated to each other.
For instance, we equate the percentage of registered female doctors to the number of registered female doctors.
Proportions, like ratios, are stated as fractions, decimals, or percentages because they depict the portion of a variable in another.
The ratio of registered female doctors = 31.4%
The number of registered female doctors = 47,300
31.4% = 47,300
100% = 47,300/31.4% x 100
The total number of registered doctors = 150,637 (47,300/31.4%)
Thus, the total number of registered doctors is 150,637, given that 47,300 female registered doctors proportionately represent 31.4% of the population.
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What is the unit rate of the graph below make sure you use answer include unit three point
Answer:
have you heard of the genger bread man
Step-by-step explanation:
Let g(x) be the indicated transformation .Write the rule for g(x) Linear function defined in the table vertical translation down 2 units I will send you a picture
You have the following data set:
x 1 0 -3
y 5 4 1
Where y is a function of x. In order to translate the previous function 2 unitd downward, you take into account that you subtract 2 units to the given values for y. Then, you have:
y (5-2) (4-2) (1-2)
which becomes:
y 3 2 -1
Finally, the given table becomes:
x 1 0 -3
y 2 2 -1
What is the solution to the equation 6x - 5 = 25?
Solution
Step 1
Write the equation
[tex]6x\text{ - 5 = 25}[/tex]Step 2
Apply the addition equality theorem
[tex]\begin{gathered} 6x\text{ - 5 = 25} \\ \\ Add\text{ 5 to both sides:} \\ \\ 6x-5+5=25+5 \\ \\ 6x\text{ = 30} \end{gathered}[/tex]Step 3
Use the division equality theorem:
[tex]\begin{gathered} 6x\text{ = 30} \\ \\ Divide\text{ both sides by 6} \\ \\ \frac{6x}{6}\text{ = }\frac{30}{6} \\ \\ x\text{ = 5} \end{gathered}[/tex]Final answer
x = 5
how loud a sound is depending on how far away you are PLEASE !!!!!help asap
distance to sound level dB
85
79
73
67
listener
5
10
20
40
Answer:
2346 dl sheep
Step-by-step explanation:
all well STrxrcgvw'#'zuucrb if ivAr4w3ws4
find the equation of the line
use exact number
y= x+
Answer:
[tex]y=\frac{-1}{3}x+5[/tex]
Answers being -1/3 and 5
Step-by-step explanation:
In slope-intercept form, you seem to be missing your slope and intercept. Luckily, the graph has everything you need.
Recall slope is rise over run or y over x.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
The slope of this line can be determined by counting the x and y movements of the line between two intersections where it evenly collides. For instance, between (0,5) and (3,4), the line moves right three and down one.
This would give you a slope of -1/3.
Another way to find the slope is to choose any two points and use the slope formula above. Using those same two points:
[tex]m=\frac{4-5}{3-0}[/tex]
[tex]m=\frac{-1}{3}[/tex]
Now you have the first part of your answer. The slope is -1/3.
The second part is the y coordinate of the y-intercept. In this case, the graph includes the intercept, which we can clearly determine is (0,5). Therefore, your second answer would be 5.
The full answer being [tex]y=\frac{-1}{3}x+5[/tex].
HELP ME PLEASE !!!
REASONING An absolute value function is positive over its entire domain. How many x-intercepts does the graph of the function have?
● None
01
02
O Infinite
A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.
What is a good x-intercept illustration?Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).
How do you calculate the math x-intercept?We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.
What is an illustration of intercept?This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).
The x-intercept is zero, right?If you can locate the x-intercept of a linear function, finding the zero should be simple. The x-coordinate of the x-intercept is zero.
The x-intercept can be positive or negative, but how do you know?Summary
The location on the graph where our line crosses the x-axis is known as the x-intercept.Positive numbers are to the right of the origin and negative numbers are to the left of the origin on the x-axis.The location on the graph where our line crosses the y-axis is known as the y-intercept.Which side of a graph is negative?Consider the numbers as being on the x-axis to help you remember this. The positive values are located to the right of the origin, and the negative values are located to the left of the origin.
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