what is the function g(x) created from f(x)= x^2 by moving the graph left 4 units, vertically stretching it by a factor of 5, and shifting the graph down 8 units
Answers
As given by the question
There are given that the equation of current graph:
[tex]f(x)=x^2[/tex]Now,
According to the question,
There are also given that graph left 4 units, that means
[tex](x+4)^2[/tex]Then,
Vertical stretching it by a factor of 5 units
So,
The equation will be:
[tex]f(x)=5(x+4)^2[/tex]Then,
And, shifting the graph down 8 units
So,
[tex]f(x)=5(x+4)^2-8[/tex]Hence, the correct option is D
Related Questions
-Quadratic Equations-The sum of two integers is 42 and their product is 432. Write and solve an equation to find the two integers.
Answers
numbersThe first thing to do is to write the exact relations from the question, as follows:
[tex]\begin{gathered} x+y=42 \\ x\times y=432 \end{gathered}[/tex]Where X and Y stand for the unknown integer numbers.
Now, we will isolate Y in the first equation and substitute in the second one. This way, we will be able to find the value of X. From this strategy, we perform the calculation that follows:
[tex]\begin{gathered} y=42-x\to x\times(42-x)=432 \\ 42x-x^2=432\to0=x^2-42x+432 \\ x^2-42x+432=0 \end{gathered}[/tex]Now, it is important to remember the Bhaskara relation. But first, let's remember that any quadratic equation attends to the following generic form:
[tex]y=ax^2+bx+c[/tex]And we use the Bhaskara relation to find the values of X where Y is 0. In the present question, the constants are the following:
[tex]\begin{gathered} a=1 \\ b=-42 \\ c=432 \end{gathered}[/tex]And the Bhaskara relation is:
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Now, we will substitute the values and perform the calculation.
[tex]\begin{gathered} x_{1,2}=\frac{-(-42)\pm\sqrt[]{(-42)^2-4\times1\times432}}{2\times1} \\ x_{1,2}=\frac{-(-42)\pm\sqrt[]{1,764-1,728}}{2}=\frac{42\pm\sqrt[]{36}}{2}=\frac{42\pm6}{2} \\ x_1=\frac{42+6}{2}=\frac{48}{2}=24_{} \\ x_2=\frac{42-6}{2}=\frac{36}{2}=18 \end{gathered}[/tex]As you can see, both numbers, 24 and 18, if summed will result in the number 42. For this reason, we found here, not only the value of X but also the value of Y. Because there is no distinction between X and Y, you say that:
The two number which are integers, their sum is 42 and their multiplication is 432 are the numbers 24 and 18.Write the inequality for this graph. Use x as your variable.
Answers
Notice that the points on the graph are all numbers greater than or equal to zero, therefore the given graph represents the following interval:
[tex]\lbrack0,\infty).[/tex]Zero is part of the graph because the circle is filled.
The above interval as an inequality is:
[tex]x\ge0.[/tex]Answer:
[tex]x\ge0.[/tex]Make an input-output table for the function y = 2x + 4. Use x-values of 1, 2, 3, 4, and 5. 3 4 O 5 Input, x 1 2 Output, y 57 9 11 13 2 3 4 5 O Input, x 1 Output, y6 8 10 12 14 2 3 5 Input, 1 Output, y 6 36 76 156 1 2 3 4 5 Input, 1 Output, y5 6 7 8 9 13 14
Answers
Y = 2x + 4
Substitute the values of x = 1, 2, 3, 4 and 5
when x = 1
y = 2(1) + 4 =6
when x = 2
y=2(2) + 4 = 8
when x = 3
y = 2(3) + 4 = 10
when x = 4
y = 2(4) + 4 = 12
when x = 5
y = 2(5) + 4 = 14
Output, y = 6, 8, 10, 12, 14
There is a line that includes the point (0, 10) and has a slope of 7. What is its equation inslope-intercept form?
Answers
We have that the slope-intercept form is
[tex]y=mx+b[/tex]where
m is the slope
b is the y-intercept, the value of the y-coordinate when x=0
in this case, we have
m=7
b=10
we substitute the values and we find the slope-intercept form
[tex]y=7x+10[/tex]what digit is in the
Answers
The absolute value of |3| is 3.
Using the information below. Find the velocity with which a ball reaches the ground when it is dropped from a height of 64 m. If a ball is dropped on the ground from a height of h m, then the ball reaches the ground with the velocity 4.43 √h m/sec.
Answers
The ball reaches a speed of
[tex]4.43\sqrt[]{h}\text{ }\frac{m}{s}[/tex]when dropped from a height of h meters.
When dropped from a height of 64 meters, the terminal speed would be
[tex]4.43\sqrt[]{64}\rightarrow35.44\text{ }\frac{m}{s}[/tex]The sidewalk hazard marker is shaped like a pyramid,
with a height 2 centimeters greater than the length of
each side of its square base. The volume of the marker
is 297 cubic centimeters. What are the dimensions of
the sidewalk hazard marker?
Answers
Pyramid with a height 2 centimeters greater than the length of
each side of its square base. The volume of the marker is 297 cubic centimeters. Then dimensions length is 29.8 and height 31.8
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given,
The side of square base of pyramid x.
Height 2 centimeters greater than the length of each side of its square base=x+2
Volume of pyramid=297cubic centimeters
We have to calculate the dimensions
Volume=1/3 a²h
a is the side length.
h is height of pyramid.
297=x²(x+2)/3
891=x³+2x²
891=x²(x+2)
x²=891, x+2=891
x=29.8, x+2=891,x=889
Hence length of base the pyramid is 29.8 cm and height is 31.8cm
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Y=-10x-75How do I get the x-intercept of this linear equation
Answers
In order to find the x-intercept, we must make y equal to 0.
[tex]0=-10x-75[/tex]then, clear the equation for x
[tex]\begin{gathered} 10x=-75 \\ x=-\frac{75}{10} \\ x=-7.5 \end{gathered}[/tex]The x-intercept of the linear equation is (-7.5,0)
what is the original price of the tennis racquet if it is 30% off and the sale price is $21
Answers
sale price = $21
30% off is
let
x = original price
[tex]\begin{gathered} \frac{30}{100}x=21 \\ 30x=2100 \\ x=\frac{2100}{30} \\ x=\text{ \$70} \end{gathered}[/tex]The original price = $70
You planted 460 acres in soybeans You treated 2.4 pints per acre the herbicide sells for $101 per 2.5 container How many gallons of herbicide will you use ?
Answers
Since 2.4 pints per acre were used, multiply the total amount of acres (460) times 2.4 to find the total volume of herbicide to be used:
[tex]460\times2.4\text{ pints}=1104\text{ pints}[/tex]Since 1 gallon is equal to 8 pints, divide the number of pints over 8 to find the number of gallons that will be used:
[tex]\frac{1104}{8}=138[/tex]Therefore, 138 gallons will be used.
A map shows a garden with a width of 2 inches and a length of 6 inches. The map uses a scale of 1 inch for 10 yards. What is the actual length and width of the garden? Don't Forget the units.
Answers
Scale
1 inches = 10 yards
Width = 2 inches
2 * 10 = 20 yards
Length = 6 inches
6 * 10 = 60 yards
So, actual :
length = 60 yd
width = 20 yd
.........................answer explanation of another question shown on session....................
2 cake = 9 person
1 person = 2/9th cake
So,
45 person would take up:
45 * 2/9 = 10 cakes
a car's speedometer has a percent error of 5% the speedometer currently shows that the car is traveling at a speed of 60 miles per hour which statement describes the actual speed of a car would be
Answers
We know that the percent error is 5%, so, if the speed shown by the car is 60 miles per hour, then we have to subtract the percentage error to find the actual speed.
[tex]\begin{gathered} 0.05\cdot60=3 \\ 60-3=57 \\ 60+3=63 \end{gathered}[/tex]The actual speed is 57 miles per hour.
Hence, the right statement is C because the speed could be 57 or 63 miles per hour.Silvia manages a sub shop and needs to prepare smoked turkey sandwiches. She has 1- lb of turkey in the cooler, and each sandwich requires001Ib of turkey. How many sandwiches can she make?
Answers
The total amount of turkey available to make the sandwiches is 1 1/2lb. Each sandwich requires 1/2lb of turkey. To determine how many sandwiches can be made you have to divide the total amount by the amount needed per sandwich:
[tex]1\frac{1}{2}\div\frac{1}{2}[/tex]First, you have to express the mixed number as a fraction:
-Divide the whole number by 1 and add 1/2
[tex]\frac{1}{1}+\frac{1}{2}[/tex]-Multiply the first fraction by 2 to express it using the same denominator and add 1/2
[tex]\frac{1\cdot2}{1\cdot2}+\frac{1}{2}=\frac{2}{2}+\frac{1}{2}=\frac{2+1}{2}=\frac{3}{2}[/tex]Now you can write the division as follows:
[tex]1\frac{1}{2}\div\frac{1}{2}=\frac{3}{2}\div\frac{1}{2}[/tex]To divide two fractions, you have to multiply the dividend by the reciprocal (inverse) fraction of the dividend. So, switch 1/2 upside down and multiply both fractions:
[tex]\frac{3}{2}\div\frac{1}{2}=\frac{3}{2}\cdot\frac{2}{1}=\frac{3\cdot2}{2\cdot1}=\frac{6}{2}=3[/tex]Silvia can make 3 sandwiches with the smoked turkey available.
A camera has a listed price of 717.98 before tax, if the sales tax rate is 7.5% find the total cost of the Camera with sales tax included round to the nearest cent as necessary
Answers
To find the total cost of the camera with sales. First, we need to find only the sales tax.
To find this price. First, divide the percentage by 100:
7.5/100 = 0.075
and then, multiply this by the camera listed price.
0.075* 717.98 = 53.8485
Rounded to the nearest cent:
= 53.85
So the sales taxes represents $53.85
Now, the total cost of the camera with sales is given by the listed price plus the sales taxes.
Therefore:
717.98 + 53.85 = 771.83
Hence, 771.83 represents the total cost of the camera with sales taxes.
need help asappppppp
Answers
Ok, so:
Let me draw the situation here below:
We're going to use the pythagorean theorem:
If 9² + 12² = 15², then, the triangle is a right triangle.
So, 81 + 144 = 225
So, the relation is good.
Then, the statement is true.
graph the system of inequalitiesy > -3x + 5y ≤ x - 2
Answers
Solution
The solution therefore, is (1.75, -0.25) and all points beyound the intersection of both lines
Writing and Solving Systems Using Elimination: Tutorial? QuestionType the correct answer in each box. Use numerals instead of woSolve this system of equations using the elimination method.3x – 2y = 02x + y = 7
Answers
We are asked to solve a system of linear equations via the elimination method.
3 x - 2 y = 0
2 x + y = 7
in order to use elimination, we look into finding appropriat factors to use to multiply one (or both) of the equations, so that one of the variables can be eliminated just by adding the equations term by term, thus leaving us with an equation that contains only one unknown, and which we can easily solve.
Looking at our system, we select to multiply the second equation by "2",and that way, eliminate the term in
Find the vertex and write the quadratic function in vertex form (which our OpenStax textbook also calls the standard form).f(x)=x2−12 x + 117
Answers
Given
[tex]f(x)=x^2-12x+117[/tex]To find:
The vertex and the equation in vertex form.
Explanation:
It is given that,
[tex]f(x)=x^2-12x+117[/tex]That implies,
[tex]\begin{gathered} f(x)=x^2-12x+117 \\ f(x)=[(x-6)^2-36]+117 \\ f(x)=(x-6)^2+81 \\ y-81=(x-6)^2 \end{gathered}[/tex]Hence, the vertex is (6,81) and the vertex form of the equation is
[tex]y=(x-6)^2+81[/tex]x + 5y = 12Step 2 of 2: Determine the missing coordinate in the ordered pair (?, -2) so that it will satisfy the given equation.
Answers
given the equation:
x + 5y = 12
given the ordered pair (?, -2)
recall that,
A coordinate is (x, y)
that means from the ordered pairs given,
y = -2
x = ?
let's substitite y = -2 into the given equation
x + 5y = 12
x + 5(-2) = 12
x - 10 = 12
collecting like terms
x = 12 + 10
x = 22
therefore, the coordinate that will satisfy the given eq
a nurse has chlorpromazine for injection that contains 10 mg per 2 ml he must give a patient 0.025 grams. how many ml should he give the patient
Answers
Our data are the following
1. We have an injection that contains 10 mg/ 2ml.
We want to know how many ml should he give if the nurse must give a patient 0.015 gr.
for this purpose we proceed with the so-called rule of 3:
So, we resolve the above rule to x ml, that is:
x ml = (0.025 mg x 2ml ) ÷ 10 mg ,
the above is equivalent to say
x ml = ( 0.05 ml ) ÷ 10 = 0.005 ml
So, we can conclude that
the ml should he give the patient is 0.005 ml
Complete the table below. Provide an answer for each integer division problem, and write a related equation using integer multiplication.
Answers
You need to remember the Sign Rules for Division:
[tex]\begin{gathered} \frac{-}{-}=+ \\ \\ \frac{+}{+}=+ \\ \\ \frac{-}{+}=- \\ \\ \frac{+}{-}=- \end{gathered}[/tex]And the Sign Rules for Multiplication:
[tex]\begin{gathered} -\cdot-=+ \\ +\cdot+=+ \\ -\cdot+=-_{} \\ +\cdot-=- \end{gathered}[/tex]Then, knowing those rules, you can solve the operations given in the exercise:
1. For the Integer Division:
[tex]-36\div(-9)=4[/tex]The result is positive because both numbers have the same sign.
Now, knowing that result, you can set up the following Related Equation using Integer Multiplication:
[tex](-9)(4)=-36[/tex]2. For the second Division, you get:
[tex]24\div(-8)=-3[/tex]Then, its corresponding Related Equation using Integer Multiplication can be:
[tex](-8)(-3)=24[/tex]3. For the next one, you get:
[tex]50\div10=5[/tex]So, its corresponding Related Equation using Integer Multiplication can be:
[tex]10\cdot5=50[/tex]4. For the last Division, you get:
[tex]42\div6=7[/tex]Hence, its corresponding Related Equation using Integer Multiplication can be:
[tex]7\cdot6=42[/tex]Therefore, the answer is:
Solve for x? Round to the nearest whole number
Answers
The solution for x, considering the relations in a right triangle, is given as follows:
x = 924.
Solution for xFor the large triangle, we have that:
The base is of b.The height is of 500.The angle adjacent to the base is of 20º.The value of b is found applying the tangent of the angle, as follows:
tan(20º) = 500/b
0.36397023426 = 500/b
b = 500/0.36397023426
b = 1374.
For the smaller triangle, it is found that:
The base is of a.The height is of 500.The angle adjacent to the base is of 48º.Hence the value of the base is also found with the tangent as follows:
tan(48º) = 500/a
1.11061251483= 500/a
a = 500/1.11061251483
a = 450.
Hence the measure of x is calculated as follows:
x = 1374 - 450 = 924.
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A road sign reads "Speed Limit 30." Which statement best represents the allowed driving speeds (x) on this road?
Answers
hello
this question involves a simple multiplication of numbers
Answer:
Step-by-step explanation:3xp23
x
12. Derek scored a total of 42 points in the first 4 basketballgames. If he continues to score at this rate, how manypoints will he score during the entire 18-game season?
Answers
Given data:
The numbers of points scored in 4 games are 42.
The expression for the given statement is,
[tex]\begin{gathered} 4\text{ games= 42 points} \\ 1\text{ game = 10.5 points} \end{gathered}[/tex]Multiply the above expression by 18 on both sides.
[tex]\begin{gathered} 18(1\text{ game) =18(10.5 points)} \\ 18\text{ games =189 points} \end{gathered}[/tex]Thus, in 18 games 189 points achieved.
i dont understand how to get the answer of this problemThe question is: Using a protractor, draw a linear pair of angles in a 5:1 ratio.My teacher posted the answer key and the picture below is the answer I just don’t understand how to do the problem…
Answers
With a protractor, you can draw angles between 1° and 180°.
We need to draw a pair of angles in a 5:1 ratio, this means that the measure of one of the angles is 5 times the measure of the other. For example, if one angle is equal to 10° the other has to be equal to 50°.
In the image, your teacher suggested you draw a 30° angle and another equal to 150°
[tex]\frac{150}{30}=5[/tex]Then, the 5:1 ratio is preserved.
And remember that a linear pair of angles is the same as saying 'two adjacent angles that add up to 180°'
[tex]150+30=180[/tex]You can even write an equation to find out the angle.
[tex]\begin{gathered} 5x+x=180 \\ \Rightarrow6x=180 \\ \Rightarrow x=30 \end{gathered}[/tex]Then, one angle will be equal to 30° and the other 5*30°=150°
The figure represents a traffic island that has angles measuring 60°, 20°, and 100°. Match each angle with its correct measure. Use the red numbers and DRAG it to the appropriate angles of the triangle. Then Input your answers in the blanke. m 60 20* 100% m
Answers
Based on the given information you can notice:
angle M is greater than 90°, then, it is necessary m
angle P has a lower measure than angle N, moreover, both angles P and N are lower than 90°. Then, it is necessary mand m
mmmJeff works in the Klein Forest cafeteria. When A-lunch begins, he has already prepared 50lunches. He will prepare 10 lunches per minute. Which function can be used to determine thenumber of lunches, L. he has prepared after m minutes?L = 60mL = 10mL = 50m + 10L = 10m + 50
Answers
The function is L = 10m + 50
Here, we want to find out which of the functions is required to determine the number of lunches L prepared after m minutes
In the question, we already had 50 lunches prepared
We also know that he prepares 10 lunches in one minute
So after A-lunch begins, the number of lunches prepared will be 10 * m = 10m
Adding this to the 50 on ground, then we have the total L lunches
Mathematically, that would be;
L = 10m + 50
find the surface area of the prism is __ in squared
Answers
Given
l = 9 in
b = 5 in
h = 12 in
Find
Surface area of the prism
Explanation
surface area of the given prism =
[tex]\begin{gathered} 2(lb+bh+hl) \\ 2(45+60+108) \\ 2(213) \\ 426 \end{gathered}[/tex]Final Answer
Therefore , the surface area of the prism = 426 in ssqaured
HHH NG DOJO 3 2 1 HHH -6-5-4-3-2-1 + 11 2 3 4 5 6 7 8 9 + -2 +-3 -4 OG ACN* -6 If this is the graph of f(x) = a*+h ( + k, then : O A. The domain is (h.), and the range is (-). B. The domain is (-0,), and the range is (k.co). C. The domain is (-0,9), and the range is (h.co). D. The domain is (h.), and the range is (-k.co). O
Answers
Given the graph of an exponential function;
[tex]f(x)=a^{(x+h)}+k[/tex]The domain of exponential functions is all real numbers.
Thus, the domain of the graph is;
[tex](-\infty,\infty)[/tex]
The range of a function is the set of outputs that satisfy the defined function.
Thus, the range of the graph is;
[tex](k,\infty)[/tex]CORRECT OPTION: B
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into thecorrect position in the answer box. Release your mouse button
Answers
Since we have a right isosceles triangle,we have the following:
using the pythagorean theorem, we have:
[tex]\begin{gathered} x^2+x^2=(12)^2 \\ \Rightarrow2x^2=144 \\ \Rightarrow x^2=\frac{144}{2}=72 \\ \Rightarrow x=\sqrt[]{72}=6\cdot\sqrt[]{2} \\ x=6\cdot\sqrt[]{2} \end{gathered}[/tex]therefore, the length of each leg of the isosceles right triangle is 6*sqrt(2)