Translation involves changing the position of a function.
The equation that represents the new function is: [tex]\mathbf{g'(x) = |x| - 7}[/tex]
The parent function is given as:
[tex]\mathbf{g(x) = |x|}[/tex]
The rule of translating a function down is:
[tex]\mathbf{(x,y) \to (x,y-h)}[/tex]
Where: h is the number of units translated down
i.e. h = 7
So, we have:
[tex]\mathbf{g'(x) = g(x) - h}[/tex]
Substitute [tex]\mathbf{g(x) = |x|}[/tex]
[tex]\mathbf{g'(x) = |x| - h}[/tex]
Substitute 7 for h
[tex]\mathbf{g'(x) = |x| - 7}[/tex]
Hence, the required function is: [tex]\mathbf{g'(x) = |x| - 7}[/tex]
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The equation that represents the given situation is g(x) = |x|-7
To write an equation that represents a vertical translation 7 units down of the graph of g(x) = |x|, we need to modify the original function accordingly.
A vertical translation can be represented by adding or subtracting a constant to the function. In this case, since we are translating the graph downward by 7 units, we subtract 7 from the original function:
g(x) = |x| - 7
Thus, the equation that represents this vertical translation is g(x) = |x| - 7.
This results in each point on the graph of g(x) = |x| shifting 7 units downward, creating the new graph of g(x) = |x| - 7.
The formula for a trapezoid relates the area A, the two bases, a and b, and the height, h. A=h ( a+b ) 2 Solve for b.
B= 2a/ h - a
Hope it helps!
please help!
create an expression equal to 6/5
what you have to work with:
1/16, (7/10, -, 5/8), ÷
What is the measure of an exterior angle of a regular 7-sided polygon? The answer must be a decimal.
hamburger selling $1.25 a pound contains 30% fat. how much does the consumer pay for the meat without the fat?
For a quadrilateral to be a parallelogram, its opposite sides and _____ must be congruent.
For a quadrilateral to be a parallelogram, its opposite sides and angles must be congruent.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral. The word "quadrilateral" is derived from the Latin "quadra" (four) and "latus" (sides).
For a quadrilateral to be a parallelogram, its opposite sides and angles must be congruent.
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Percy works two part-time jobs to help pay for college classes. On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50. On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50. His hourly wage at the library, x, and hourly wage at the coffee cart, y, can be determined using the system of equations below. 3x + 2y = 36.50 2x + 5y = 50.00 At which job does Percy earn the greater hourly wage? How much does Percy earn each hour at this job? Percy earns a greater hourly wage of $7.00 at the library. Percy earns a greater hourly wage of $7.00 at the coffee cart. Percy earns a greater hourly wage of $7.50 at the library. Percy earns a greater hourly wage of $7.50 at the coffee cart.
Answer:
Percy earns a greater hourly wage of $7.50 at the library.
Step-by-step explanation:
What is the name of this angle?
A.
acute
B.
right
C.
obtuse
D.
straight
2 more than twice a number w
1. You will use 25% of your budget to rent business space and pay for utilities. Write an algebraic expression that indicates how much money will be spent on business space and utilities. Do not include commas for large numbers. Do not solve.
2. How much money will rent and utilities cost? Enter your answer as a number, without any commas or dollar signs.
An online weather report says the temperature is between 40 degrees and 50 degrees, when it is really 54.4 degrees outside. Which of the following is true?
In the inequality 3x + 14 ≤ 44, x represents the cost of CDs Tim bought. Which phrase most accurately describes the cost of CDs?
Answer:
The cost of the cd is at most 10$
Step-by-step explanation:
Please Help! I don't want an exact answer, just a brief explanation of what the question actually means.
IF THE STUDENTS HIKE AT A SPEED OF 4 KM/H, WHAT IS THE TOTAL DISTANCE THE STUDENTS WILL HIKE?
Answer:
21km i beileve srry im late
Step-by-step explanation:
Rectangle EFGH is translated according to the rule T–5, 9(x, y). If the coordinates of the pre-image of point H are (–2, –3), what are the coordinates of H'?
Answer:
(-7,6)
Step-by-step explanation:
Just took test on edgen
Which of the following are valid names of triangles below click all that apply
Answer
pic?
Step-by-step explanation:
Find the equation of the line in the xy-plane that contains the point (4, 1) and that is perpendicular to the line whose equation is y = 3x + 5.
10 POINTS FOR SIMPLE QUESTIONS!
What is the value of z in the equation 2(4z − 6 − 6) = 170 − 46?
12.5, 15.5, 16.5, 18.5
How many solutions does the equation 5x + 3x − 4 = 10 have?
Zero, One, Two, Infinitely many
What is the value of z in the equation 4(2z + 3) = 12?
−13, 12, 0, 12
What is the solution to the following equation?
5(2x − 6) + 20 = 10
9, 5, 3, 2The steps below show the incomplete solution to find the value of x for the equation
5x − 2x − 3 = −2 + 15:
Step 1: 5x − 2x − 3 = −2 + 15
Step 2: 5x − 2x − 3 = 13
Step 3: 3x − 3 = 13
Which of these is most likely the next step?
3x = 16, 3x = 10, 3x = 39, 3x = 3
BRAINLIEST TO BEST ANSWER THAT SHOWS ALL WORK, YOU MIGHT NEED TO WRITE THIS OUT ON PAPER.
5. You are given the following equation: 24+6=−18
5a. Identify the x-intercept of the equation.
5b. Identify the y-intercept of the equation.
5c. Graph the equation.
My number has 2 digits and is even, the sum of my numbers digits is 10, the difference of the two digits of my number is 6, my number has 4 factors,what am i
For high school wrestling competitions, the wrestling mat must be a square with an area of 1444 square feet. _ feet is the length of each side of the wrestling mat.
The length of each side of the wrestling mat is, 38 feet.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
For high school wrestling competitions, the wrestling mat must be a square with an area of 1444 square feet.
Let the length of each side of the wrestling mat is, x
Hence, We get;
⇒ x² = 1444
⇒ x = √1444
⇒ x = 38 feet
Thus, The length of each side of the wrestling mat is, 38 feet.
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Find the real or imaginary solutions of the equation by factoring. X^4-10x^2=-9
Test scores are normally distributed with a mean of 100 and a standard deviation of 15. an individual's iq score is found to be 90. find the z-score corresponding to this value.
The z-score corresponding to this value will be negative 0.6667.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
Test scores are typically conveyed with a mean of 100 and a standard deviation of 15. A singular's level of intelligence score is viewed as 90.
The z-value is given as,
z = (90 - 100) / 15
z = - 10 / 15
z = - 0.6667
The z-score relating to this worth will be negative 0.6667.
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A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 330330 yd of fencing is available, find the largest total area that can be enclosed.
HELP, I NEED SOMEBODY
2. Solve the equation p^2 + 4p = 1 by completing the square. Show your work
The solutions to the equation [tex]p^2+4p=1[/tex] using completing the square method are [tex]-2- \sqrt{5}[/tex] and [tex]-2+ \sqrt{5}[/tex]
The given equation is:
[tex]p^2+4p=1[/tex]
Add [tex](\frac{4}{2})^2[/tex] to both sides of the equation
[tex]p^2+4p+(\frac{4}{2})^2= 1 + (\frac{4}{2})^2\\\\p^2+4p+2^2=1+2^2\\\\(p+2)^2=1+4\\\\(p+2)^2=5\\\\[/tex]
Find the square root of both sides
[tex]p+2 = \pm\sqrt{5}\\\\p=-2\pm sqrt{5} \\\\p = -2 - sqrt{5}\\\\p=-2+ \sqrt{5}[/tex]
The roots of the equation are [tex]-2- \sqrt{5}[/tex] and [tex]-2+ \sqrt{5}[/tex]
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The equation p² + 4p = 1 can be solved by first rearranging to p² + 4p - 1 = 0, completing the square, simplifying and taking square roots. The solutions are p = -2 + sqrt(5) and p = -2 - sqrt(5).
Explanation:To solve the quadratic equation p² + 4p = 1 by completing the square, we first arrange the equation with the quadratic and linear terms on one side and the constant on the other:
p²+ 4p - 1 = 0.
Next, we complete the square by adding the square of half the coefficient of p to both sides of the equation. The coefficient of p is 4, so half of it is 2, and squaring it gives 4. So, we have:
p² + 4p + 4 = 1 + 4
This simplifies to:
(p + 2)² = 5
Then, we take square roots of both sides:
p + 2 = ± sqrt(5)
Which further simplifies to:
p = -2 ± sqrt(5)
So, the solutions for this quadratic equation are p = -2 + sqrt(5) and p = -2 - sqrt(5).
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Write 5 equations where the difference is equal to 3
Answer:
5-2
28 - 5²
17 - 7 × 2
[tex]\frac{28}{4}-4[/tex]
5 × 3 - 4 × 3
Step-by-step explanation:
Let x and y be any two numbers,
Such that,
y - x = 3,
⇒ y = 3 + x
Where, x is any positive real number.
Thus, we can find such equation by using this,
Such equations could be,
5 - 2, 28 - 25, 17 - 14, 7 - 4, 15 - 12
or
5-2, 28 - 5², 17 - 7 × 2, [tex]\frac{28}{4}-4[/tex], 5 × 3 - 4 × 3
Five equations where the difference is equal to 3 are, respectively:
(i) [tex]y - x = 3[/tex]
(ii) [tex]y + 9\cdot x = 3[/tex]
(iii) [tex]y -5\cdot x = 3[/tex]
(iv) [tex]y +2\cdot x = 3[/tex]
(v) [tex]y -11\cdot x = 3[/tex]
Reminder - Statement is incomplete. After some research, we determine that complete form is: "Write 5 linear equations where the difference is equal to 3".
From Analytical Geometry, a Linear Equation is an expression of the form:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.[tex]y[/tex] - Dependent variable.[tex]m[/tex] - Slope.[tex]b[/tex] - Intercept.Based on the question, we need to write 5 expressions so that:
[tex]y - m\cdot x = b[/tex]
If we know that [tex]b = 3[/tex], then we get the following expressions:
(i) [tex]y - x = 3[/tex]
(ii) [tex]y + 9\cdot x = 3[/tex]
(iii) [tex]y -5\cdot x = 3[/tex]
(iv) [tex]y +2\cdot x = 3[/tex]
(v) [tex]y -11\cdot x = 3[/tex]
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You can buy an item for $20 at a store within walking distance. You can buy the same item online for $12 with $10 for shipping. Which is the better deal?
What is the unit rate for $1 for 12lbs
2c/11= c-3/4 what is the solution
20 pts. Involves Triangle Centroids
What are 6 centimeters equal to?
A. 600 meters
B.
1/6 of a millimeter
C. 60 millimeters
D. 600 millimeters
What is one benefit to lifelong physical activity? healthier diet lower risk of stroke organized daily schedule lower chance of injury