Consider the following graph of two functions.(8-1-2)Step 3 of 4: Find (8.5(-2)Enable Zoom/Pan866) = -3010-35SG) = x + 3
Answers
The question requires that we evaluate the value of:
[tex](g\cdot f)(-2)[/tex]Recall that:
[tex]\left(g\cdot \:f\right)\left(x\right)=g\left(x\right)\cdot \:f\left(x\right)[/tex]Therefore, we have that:
[tex]\left(g\cdot\:f\right)\left(-2\right)=g\left(-2\right)\cdot\:f\left(-2\right)[/tex]We can get the values of g(-2) and f(-2) from the graph as shown below:
Therefore, we have:
[tex]\begin{gathered} g(-2)=5 \\ f(-2)=1 \end{gathered}[/tex]Hence, we can calculate the composite function to be:
[tex]\begin{gathered} (g\cdot f)(-2)=5\times1 \\ (g\cdot f)(-2)=5 \end{gathered}[/tex]
Related Questions
What is the y-intercept of the graph of y = 2.5x?a. 2.5b. 0c. 1d. -1
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Solution
- We are asked to find the y-intercept of the graph of:
[tex]y=2.5x[/tex]- In order to find the y-intercept, we need to know the definition of the y-intercept.
- The y-intercept is the y-value where the graph crosses the y-axis.
- An implication of this definition is that whenever the graph crosses the y-axis, the x-value at that point is zero. This means that we simply need to substitute x = 0 into the equation given to us to find the y-intercept of the graph.
- The y-intercept can thus is gotten as follows:
[tex]\begin{gathered} y=2.5x \\ \text{put }x=0 \\ y=2.5(0) \\ \\ \therefore y=0 \end{gathered}[/tex]Final Answer
The y-intercept of the graph is y = 0 (OPTION B)
A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measure the angle of depressionto the Groveburg soccer fields to be 20° 15'. To the right side of the balloon, the balloonist measures the angle ofdepression to the high school football field to be 62° 30'. The distance between the two athletic complexes is 4 miles.What is the distance from the balloon to the football field?a.b.>3.6 miC.~6.2 mi>2.2midy1.4 miPlease select the best answer from the choices providedOAOBOCOD
Answers
The distance from the balloon to the football field will be 1.4 miles.
Angle of depression to the Grove burg soccer fields = 20° 15'.
Use 1' = 1 / 60° :
15' = 1 / 4 ° = 0.25 °
20° 15' = 20.25°
Angle of depression to the high school football field = 62° 30'.
30' = 0.5°
62° 30' = 62.5°
the distance from the balloon to the football field will be:
Let the distance be a
a / sin a = c / sin c
a / sin (20.25) = 4 / sin (97.5)
a = 4 sin (20.25) / sin (97.5)
a = 1.4 miles.
Therefore, we get that, the distance from the balloon to the football field will be 1.4 miles.
Learn more about distance here:
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Determine the independent and dependent quantities in each scenario include when possible Part A: A lamp manufacturing company produces 750 lamps per shift Part B:a grocery store sells pears by the pound. A customer purchases 3 pounds by $5.07
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Here, we want to establish the independent and independent quantities in each of the parts
The independent quantities are simply the quantities that do not depend on the dependent quantity. The dependent quantity are the quantities that depend on the independent quantity
a) Here, we have 750 lamps produced per shift
This is obtained by dividing the number of lamps produced by the number of shifts it took to produce them
In this case, the number of lamps produced is dependent on the number of shifts'
Number of shifts is the independent variable while the number of lamps is the dependent variable
b) Here, the cost per pair is 5.07/3 = 1.69
So here, the cost is dependent on the number of pears
The number of pears is the independent variable while the cost of the pears is the dependent variable
suppose we spin the following spinner with the first spin giving us the numerator and the second spin giving the denominator of a fraction. What is the probability that the fraction will be less than or equal to 5/6?
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numerator = top number
denominator = bottom number
numerator less than or equal to 5
total numbers = 4
numbers less than or equal to 5 = 2 ( 5 and 4)
Denominator
5, 6 or 7 = 3
Possible fractions = 4/5, 4/6, 4/7, 5/6 and 5/7
5 out of 16 possible fractions
probability = 5/16
how do u knwo which way to face the inequality sign in the answer of these questions like 1>x<3 how do u know which way to face them. i put some examples os u cna use them to explain
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Using the graph identify the intervals:
a) Function being less than or equal to 0: In which x interval is the graph under the x-axis (the functions are less than 0 when they are under x-axis)
As the ineqaulity sing is less than or equal to 0, the interval includes those x-values for which the function is 0:
Solution: Interval from x=1 to x=3
[tex]\begin{gathered} x^2-4x+3\leq0 \\ 1\leq x\leq3 \\ \lbrack1,3\rbrack \end{gathered}[/tex]b) Function being greater than or equal to 0: In which x interval is the graph over the x-axis.
As the ineqaulity sing is greater than or equal to 0, the interval includes those x-values for which the function is 0:
Solution: Interval from - infinite to 1 and from 3 to infinite
[tex]\begin{gathered} x^2-4x+3\ge0 \\ 1\ge x\ge3 \\ (-\infty,1\rbrack\cup\lbrack3,\infty) \end{gathered}[/tex]c) Function being greater than 0: In which x interval is the graph over the x-axis.
As the ineqaulity sing is greater than to 0, the interval does not include those x-values for which the function is 0.
[tex]\begin{gathered} x^2-4x+3>0 \\ 1>x>3 \\ (-\infty,1)\cup(3,\infty) \end{gathered}[/tex]d) Function being less than 0: In which x interval is the graph under the x-axis.
As the ineqaulity sing is less than 0, the interval does not include those x-values for which the function is 0:
[tex]\begin{gathered} x^2-4x+3<0 \\ 1In the diagram of \bigtriangleup△GKJ below, LH KJ, GL=6, LK=30, and GH=3. What is the length of GJ?
Answers
From the given figures
Since LH // KJ, then
[tex]\frac{GL}{LK}=\frac{GH}{HJ}[/tex]GL = 6, LK = 30
GH = 3, HJ = y
Substitute them in the ratio above
[tex]\frac{6}{30}=\frac{3}{y}[/tex]By using cross multiplication
[tex]\begin{gathered} 6\times y=30\times3 \\ 6y=90 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6y}{6}=\frac{90}{6} \\ y=15 \end{gathered}[/tex]Since GJ = GH + HJ
[tex]\begin{gathered} GJ=3+15 \\ GJ=18 \end{gathered}[/tex]The answer is 36
The line M is parallel to the line y=-2x+2 and goes through the origin. Which of these points is on the line M? (-2,-4)(1,1)(2,-2)(-2,4)
Answers
Answer:
(-2,4)
Explanation:
Two lines are said to be parallel if their slopes are the same.
Comparing the line y =-2x+2 to the slope-intercept form y=mx+b, the slope of the line is -2.
Therefore, the slope of line M that is parallel to it is also - 2.
Since the line M goes through the origin, the y-intercept of line M is 0.
Therefore, the equation of line M is:
[tex]y=-2x[/tex]Therefore, the point which is on line M is the point that satisfies the equation above.
This point is (-2,4).
Check
[tex]\begin{gathered} \text{When }x=-2,y=4 \\ y=-2x \\ 4=-2(-2) \\ 4=4 \end{gathered}[/tex]1 block: 11 houses = 2 blocks : ??? houses
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Write the expression and simplifyThe difference of -10 and the product of p and q
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We start with a subtraction, where we want to subtract the second term from - 10. The second term consists in a multiplication between p and q. Writing this as a mathematical expression we have
[tex]-10-pq[/tex]This expression is already on simplest form.
Find the general solution to dy/dx = 2y passing through the point (5, 1)
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We will have the following:
[tex]\frac{\partial y}{\partial x}=2y\Rightarrow\frac{1}{2y}\partial y=\partial x[/tex][tex]\Rightarrow\int (\frac{1}{2y})\partial y=\int \partial x\Rightarrow\frac{\log (y)}{2}=x+c[/tex]Then we find "c":
[tex]\frac{\log(1)}{2}=5+c\Rightarrow c=-5[/tex]Thus, the general solution passing through (5, 1) is:
[tex]\frac{\log(y)}{2}=x-5[/tex]You are going to paint your door on the outside. Your door is 7 feet 2 inches tall and 32inches wide. You need to know the surface area of the front of your door to determine howmuch paint to buy. The hardware store sells paint by how much covers a square foot. What isthe surface area you should report to the hardware store?
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Data
height = 7 ft 2 in
width = 32 in
1.- Convert height into inches
1 ft ------------ 12 in
7 ft ------------ x
x = 84 in
total height = 84 + 2
= 86 in
2.- Calculate the area
Area = height x width
Area = 84 x 32
Area = 2688 in 2
find all real solutions[tex](2x + 17) \div (x + 1) = x + 5[/tex]
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We have the next equation
[tex]\frac{2x+17}{x+1}=x+5[/tex][tex]2x+17=(x+5)(x+1)[/tex][tex]\begin{gathered} 2x+17=x^2+x+5x+5 \\ 2x+17=x^2+6x+5 \end{gathered}[/tex]Then we sum similar terms
[tex]\begin{gathered} x^2+(6x-2x)+(5-17)=0 \\ x^2+4x-12=0 \end{gathered}[/tex]then we solve the quadratic equation
We can factorize the equation
[tex](x+6)(x-2)=0[/tex]so the solutions are
x=-6
x=2
Solve the system of equations.y = x2 - 2y = -2x + 1A. (-3,7) and (-1,3)B. (-3,7) and (1, -1)C. (1.-1) and (3,-5)D. (-1,3) and (3, -5)
Answers
Answer
Option B is correct.
the solutions to the system of equations include
(-3, 7) and (1, -1)
Step-by-step Explanation
The question is to solve the system of equations
y = x² - 2 ..... equation 1
y = -2x + 1 ..... equation 2
To solve this, we can just equate the expression given for y in equation 1 to the expression given for y in equation 2.
y = x² - 2
y = -2x + 1
Since
y = y
x² - 2 = -2x + 1
x² + 2x - 2 - 1 = 0
x² + 2x - 3 = 0
This gives a quadratic equation which we will now solve
x² + 2x - 3 = 0
x² + 3x - x - 3 = 0
x (x + 3) - 1 (x + 3) = 0
(x - 1) (x + 3) = 0
So,
x - 1 = 0 or x + 3 = 0
x = 1 or x = -3
If x = 1,
y = x² - 2
= 1² - 2
= 1 - 2
= -1
x = 1, y = -1
If x = -3
y = x² - 2
= (-3)² - 2
= 9 - 2
= 7
x = -3, y = 7
So, the solutions to the system of equations include
x = -3, y = 7, that is, (-3, 7)
And
x = 1, y = -1, that is, (1, -1)
Hope this Helps!!!
Write the equation in slope-intercept form through the point (2, -1) and is perpendicular to the line y = -5x + 1 and graph.
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First, we are going to calculate the perpendicular slope. The condition for perpendicular lines is the following:
[tex]m1m2=-1[/tex]First, m1 = -5
[tex]m2=\frac{-1}{m1}=\frac{-1}{-5}\rightarrow m2=\frac{1}{5}[/tex]Now, for b
[tex]b=y-m2x[/tex]For the point (2,-1)
[tex]b=-1-\frac{1}{5}\cdot(2)[/tex][tex]b=-\frac{5}{5}-\frac{2}{5}=\frac{-7}{5}[/tex][tex]y=\frac{1}{5}x-\frac{7}{5}[/tex]1. Sue uses 2.59 pounds ofstrawberries and 0.65 poundof blueberries to make fruitsalad. She serves the sameamount of salad in each of 9bowls. What is the weight,in pounds, of each serving tothe nearest tenth?
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Problem:
Sue uses 2.59 pounds of strawberries and 0.65 pounds of blueberries to make a fruit salad. She serves the same amount of salad in each of 9
bowls. What is the weight, in pounds, of each serving to
the nearest tenth?
Solution:
The total weight of the fruit salad is:
2.59 pounds + 0.65 pounds = 3.24 pounds.
Now, if she serves the same amount of salad in each of 9 bowls, we have that the weight in each serving is:
[tex]\frac{3.24}{9}=\text{ 0.36 pounds}[/tex]Then, we can conclude that the correct answer is:
0.36 pounds.
l A golf ball is hit in the air. The table shown describes y, the height of the ball, in feet, given the time elapsed, x, in seconds, since the time the ball was hit.Based on the information in the table, which statements are true? Select each correct statement.
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Given:
y is the height of the ball in feet
x is the time in seconds
In the given table you can identify the next maximum:
x=3
y=30
The ball has height 0 when it is in the earth so it is hit at second 0 and will be back in the earth at second 6
Then, from the given statements the next are true:
The maximum height of the ball was 30 feetThe ball was in the air for only 6 secondsA. Step 1B. Step 2C. Priya did not make a mistake
Answers
We will have the following:
[tex]\frac{f}{0.25}=16\Rightarrow f=16\cdot0.25[/tex][tex]\Rightarrow f=4[/tex]From this we can see that there was no mistaky on Priya's side. [Option 3]
Determine the probability of being dealt 4 Aecs of cards, from a deck of 52 playing cards, with a replacement.
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Given:
4 Aces of cards from a deck of 5 playing cards.
[tex]\begin{gathered} \text{Probability of drawing 4 Aces }=\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times\frac{4}{52}\times4! \\ \text{Probability of drawing 4 Aces }=\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times\frac{1}{13}\times24 \\ \text{Probability of drawing 4 Aces }=\frac{24}{28561} \end{gathered}[/tex]A circle has area 36 cm². What is the diameter?
Answers
Answer:
6.77 cm
Explanation:
Given that the area of a circle = 36 cm²
We want to find the diameter of the circle.
The area of a circle of radius r is calculated using the formula:
[tex]A=\pi r^2[/tex]Substitute A=36 and π=3.14:
[tex]\begin{gathered} 36=3.14r^2 \\ \text{ Divide both sides by 3.14} \\ \frac{36}{3.14}=\frac{3.14r^2}{3.14} \\ r^2=\frac{36}{3.14} \\ \text{ Take the square root of both sides} \\ r=\sqrt{\frac{36}{3.14}} \\ r=3.3845 \end{gathered}[/tex]Finally, to get the diameter, multiply the radius by 2.
[tex]\begin{gathered} Diameter=Radius\times2 \\ =3.3845\times2 \\ =6.769 \\ Diameter\approx6.77\;cm \end{gathered}[/tex]The diameter of the circle is approximately 6.77 cm.
find the value of the term in the arithmetic sequence 1,6,11,16...(8th term)
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We need to find the 8th term of the following arithmetic sequence:
[tex]1,6,11,16,...[/tex]The formula to find the n-th term an of aₙ arithmetic sequence is:
[tex]a_n=a_1+(n-1)d[/tex]where a₁ is the first term and d is the difference between two consecutive terms.
The first term of this sequence is a₁ = 1, and d is given by:
[tex]\begin{gathered} d=a_2-a_1 \\ \\ d=6-1 \\ \\ d=5 \end{gathered}[/tex]Then, for n = 8, we obtain:
[tex]\begin{gathered} a_8=1+(8-1)5 \\ \\ a_8=1+7(5) \\ \\ a_8=1+35 \\ \\ a_8=36 \end{gathered}[/tex]Answer:
The 8th term is 36.
write a polynomial function in standard form with the given zeros x= -1,-2,-3,-4
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Explanation: For this question we have 4 zeros so x can be as follows
x = -1 or x = -2 or x = -3 or x = -4
We can turn the equalities above into factors as follows
[tex]\begin{gathered} x=-1\rightarrow x+1=0 \\ x=-2\rightarrow x+2=0 \\ x=-3\rightarrow x+3=0 \\ x=-4\rightarrow x+4=0 \end{gathered}[/tex]Step 1: Now that we have the factors we can build a function and simplify it as follows
[tex]\begin{gathered} y=(x+1)(x+2)(x+3)(x+4) \\ y=(x^2+2x+x+2)(x^2+4x+3x+12) \\ y=(x^2+3x+2)(x^2+7x+12) \\ y=x^4+7x^3+12x^2+3x^3+21x^2+36x+2x^2+14x+24 \\ y=x^4+7x^3+3x^3+12x^2+21x^2+2x^2+36x+14x+24 \\ y=x^4+10x^3+35x^2+50x+24 \end{gathered}[/tex]Final answer: So the final answer is
[tex]y=x^4+10x^3+35x^2+50x+24[/tex].
Hi, can you help me answer this question please, thank you!
Answers
Given that
[tex]\begin{gathered} \mu_1=sample\text{ of soda in the coke can} \\ \mu_2=sample\text{ of soda in the pepsi can} \end{gathered}[/tex]Therefore, in the first statement, we are to test how accurate the companies package these cans.
Mathematically it can be expressed as,
[tex]H_0\colon\mu_1\leq\mu_2[/tex]In the second statement, we wish to test the claim that the mean of the amount of liquid in coke cans is greater than the amount of liquid in pepsi cans. This can be expressed mathematically as,
[tex]H_a\colon\mu_1>\mu_2[/tex]Hence, the correct option is Option 1.
katie has 5.455 apples and sadie has 10.31 how many apples do they have in all
Answers
Katie has 5.455
Sadie has 10.31
To find how many apples they have in all add the two numbers
They have = 5.455 + 10.31
They have = 5.455 + 10.310
0 + 5 = 5
1+ 5 = 6
3 + 4 = 7
10 + 5 = 15
They have = 15.765 apples in all
Justin earned $600 last week fixing computers.Is it possible to determine how many hours Justin worked?explain
Answers
Since Justin earned $600 last week
If we want to find the number of hours that he worked, we must have how much he earned per hour
But we do not have how much did he earn per hour, so
It is impossible to find how many hours did he work from the given information
The answer is
No, it is impossible to find that
True or false the function f(x) = -3(x+10)^2 has a minimum
Answers
Notice that:
[tex]\begin{gathered} f^{\prime}(x)=-6(x+10), \\ f^{\prime\prime}(x)=-6. \end{gathered}[/tex]Since for all x, f''(x)<0, by the second derivative criteria we get that f(x) reaches a maximum.
Answer: False.
Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.
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Step 1
Given;
Determine the equation of the line that passes through the point (1/8,2) and is perpendicular to the line 5y+2x=2.
Step 2
Find the slope of the new line based on a perpendicular relationship
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \end{gathered}[/tex][tex]\begin{gathered} 5y=2-2x \\ y=\frac{2-2x}{5} \\ y=\frac{2}{5}-\frac{2}{5}x \\ -\frac{2}{5}=-\frac{1}{m_2} \\ 2m_2=5 \\ m_2=\frac{5}{2} \end{gathered}[/tex]Thus the equation will be;
[tex]\begin{gathered} (\frac{1}{8},2) \\ y=\frac{5}{2}x+b \\ b=y-intercept \\ 2=\frac{5}{2}(\frac{1}{8})+b \\ 2=\frac{5}{16}+b \\ b=2-\frac{5}{16} \\ b=\frac{27}{16} \end{gathered}[/tex][tex]y=\frac{5}{2}x+\frac{27}{16}[/tex]Answer;
[tex]y=\frac{5}{2}x+\frac{27}{16}[/tex]Triangle A'B'C' is apparently - у А A' B C С B' O A clockwise 90 degree rotation of Triangle ABC O A reflection across the y-axis of Triangle ABC O A translation of Triangle ABC right 7 units O A clockwise 270 degree rotation of Triangle ABC
Answers
Since all coordinates of the transformated triangle are changed like this:
[tex](x,y)\rightarrow(y,-x)[/tex]Triangle A'B'C' is a clockwise 270 degree rotation of triangle ABC
A counterclockwise rotation of 90º is the same that a clockwise rotation of 270º
The product of two whole numbers is 592 and their sum is 53. What are the two numbers?
Answers
To solve this problem, we have to build two equations with the given information. Using x and y to represent the two numbers:
• Equation 1
[tex]x\times y=592[/tex]• Equation 2
[tex]x+y=53[/tex]Now that we have to equations, we have to isolate one variable from one equation and replace it in the other.
[tex]x=53-y[/tex]Then, we will replace this value of x in Equation 1:
[tex](53-y)\cdot y=592[/tex]Solving for y we get:
[tex]53y-y^2=592[/tex][tex]-y^2+53y-592=0[/tex]As we got this expression, we will have to use the General Quadratic Formula. With the help of a calculator, we get both values:
[tex]y_1=16[/tex][tex]y_2=37[/tex]Finally, we have to replace these values in Equation 1 to evaluate which meets the condition:
[tex]x_1=\frac{592}{y_1}[/tex][tex]x_1=\frac{592}{16}=37[/tex][tex]x_2=\frac{592}{y_2}[/tex][tex]x_2=\frac{592}{37_{}}=16[/tex]We have to evaluate the values in each equation:
[tex]\begin{gathered} 37+16=53 \\ 53=53 \end{gathered}[/tex][tex]37\cdot16=592[/tex]The first numbers meet the condition.
Answer: 37 and 16
Draw the image of the figure under thegiven transformation.6.reflection across the x-axis7. (X,y) - (x - 4, y + 1)8. reflection across the y-axis
Answers
6.
While transformation with the reflection across the x-axis, the absicssa (x-coordinate) remains the same but ordinate (y-coordinate) changes its sign.
The coordinate of point A is (3,0), coordinate of point B is (1,4) and the coordinate of point C is (5,3).
After transformation the, coordinate with the image can be shown as,
Thus, the coordinates of the image after transformation is A'(3,0), B'(1,-4) and C'(5,-3).
How to do 2 step equations Can you solve 2x + 5=21?
Answers
Given
The equation,
[tex]2x+5=21[/tex]To find the value of x or to solve for x.
Explanation:
It is given that,
The equation is,
[tex]2x+5=21[/tex]That implies,
[tex]\begin{gathered} 2x+5=21 \\ 2x=21-5 \\ 2x=16 \\ x=\frac{16}{2} \\ x=8 \end{gathered}[/tex]Hence, the value of x is 8.