For the function, tell whether the graph opens up or opens down, identify the vertex, and tell whether the graph is wider, narrower, or the same width as the graph of y = |x|.
y = 2 - |x – 10|
Question 6 options:
opens down, (10, 2), same
opens down, (-10,- 2), narrower
opens down, (-10,- 2), narrower
opens up, (10, 2), same
Answers
Answer:
opens down; (10, 2); same
Step-by-step explanation:
If the vertex of f(x) is (0, 0) then translating it to (h, k) makes the function look like f(x -h) +k. Changing the sign of f(x) to -f(x) reflects it across the x-axis, so ...
y = 2 - |x -10|
is the function y = |x| reflected across the x-axis and translated 10 units right and 2 units up. Because there is no horizontal or vertical scale factor, the apparent width of the function is the same as the original.
Final answer:
The graph of the function y = 2 - |x – 10| a .opens down with a vertex at (10, 2). It has the same width as the graph of y = |x|, meaning it is not stretched or compressed horizontally, but it is shifted upward and to the right.
Explanation:
To determine whether the graph of the function y = 2 - |x – 10| opens up or down, we must understand the behavior of the absolute value function. Since the absolute value function has a V-shape, the negative sign in front of the absolute value in the given function indicates that the graph opens down, creating an upside-down V-shape. Furthermore, the vertex of the graph is at the point where the expression inside the absolute value equals zero. In this case, x – 10 = 0, so x = 10. Plugging this into the function gives us the y-coordinate of the vertex, which is y = 2 - |10 - 10| = 2. Therefore, the vertex is (10, 2).
Comparing the width of the graph to the graph of y = |x|, we notice that there is no multiplication factor affecting the x inside the absolute value, hence the graph of the given function has the same width as the graph of y = |x|. In other words, the graph is neither stretched nor compressed horizontally. Rather, it is vertically shifted upward by 2 units, and horizontally shifted to the right by 10 units due to the x – 10 part of the function.
Related Questions
Tomas used 3 1/3 cups of flour and now has 1 2/3cups left. Which equation can he use to find f, the number of cups of flour he had to begin with?
f+3 1/3=1 2/3
f-3 1/3=1 2/3
3 1/3f=1 2/3
f/3 1/3=1 2/3
Answers
For this case we have that the variable "f" represents the number of cups of flour that Tomas had initially.
If of that amount Luis used [tex]3 \frac {1} {3}[/tex] of cups of flour, then we have the following expression:
[tex]f-3 \frac {1} {3}[/tex]
If Luis has[tex]1 \frac {2} {3}[/tex] cups of flour left, then we have the following equation:
[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]
Finally, the equation that represents the given situation is:
[tex]f-3 \frac {1} {3} = 1 \frac {2} {3}[/tex]
Answer:
Option B
Catherine likes to go ice fishing she has learned from experience that she stays warm about 15 minutes for every undershirt she wears if she wants to stay out for 75 minutes how many undershirts should she put on
Answers
easch cube inside the rectangle prism has a edge length of 3/4 inch what is the volume of the rectangle prism
Answers
Volume = (edge)^3
Volume = (3/4)^3
Volume = (27/64) inches^3
Done.
Which is a quadratic function?
f(x) = 2x + x + 3
f(x) = 0x2 – 4x + 7
f(x) = 5x2 – 4x + 5
f(x) = 3x3 + 2x + 2
Answers
Answer:
C
Step-by-step explanation:
B isn't right. The 0 makes x^2 go away leaving a linear equation.
A is a linear function.
D is a cubic, so the answer is
C which has an x^2 function
The format of a Quadratic function is
ax2 + bx + c
Which products result in a perfect square trinomial? Check all that apply. (–x + 9)(–x – 9) (xy + x)(xy + x) (2x – 3)(–3 + 2x) (16 – x2)(x2 – 16) (4y2 + 25)(25 + 4y2)
Answers
Answer:
(xy + x)and (xy + x)
(2x - 3) and (-3 + 2x)
(4y² + 25) and (25 + 4y²)
Step-by-step explanation:
* Lets explain the meaning of the perfect square trinomial
- If a binomial multiply by itself, then the answer will be a perfect
square trinomial
- Example: if the binomial (ax + b) multiply by itself, then
(ax ± b)(ax ± b) = (ax)(ax) ± (ax)(b) ± (b)(ax) + (b)(b)
(ax + b)(ax + b) = (ax)² ± 2(axb) + (b)²
∵ (ax + b)(ax + b) = (ax + b)²
∴ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
* From the example above the perfect square trinomial has 3 terms
# 1st term is the square the first term in the binomial
# 2nd term is twice the product of the two terms of the binomial
# 3rd term is the square of the second term of the binomial
* Lets solve the problem
- The product of (-x + 9)and (-x - 9)
∵ -x + 9 ≠ -x - 9
∴ The product of (-x + 9) and (-x - 9) is not a perfect square trinomial
- The product of (xy + x)and (xy + x)
∵ xy + x = xy + x
∴ (xy + x)(xy + x) = (xy + x)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (xy + x) and (xy + x) is a perfect square trinomial
- The product of (2x - 3) and (-3 + 2x)
∵ (-3 + 2x) can be written as (2x - 3)
∴ 2x - 3 = -3 + 2x
∴ (2x - 3)(-3 + 2x) = (2x - 3)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (2x - 3)(-3 + 2x) is a perfect square trinomial
- The product of (16 - x²) and (x² - 16)
∵ 16 - x² can be written as -x² + 16
- If we take -1 common factor from -x² + 16
∴ -x² + 16 = -(x² - 16)
∴ (-x² + 16)(x² - 16) = -(x² - 16)(x² - 16) = -(x² - 16)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∵ -(x² - 16)² = -(x^4 - 32x² + 256) = -x^4 + 32x² - 256
∵ x^4 - 32x² + 256 is perfect square trinomial
∵ -x^4 + 32x² - 256 is not a perfect square trinomial
∴ The product of (16 - x²) and (x² - 16) is not a perfect square trinomial
- The product of (4y² + 25) and (25 + 4y²)
∵ 25 + 4y² can be written as 4y² + 25
∴ 4y² + 25 = 25 + 4y²
∴ (4y² + 25)(25 + 4y²) = (4y² + 25)²
∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial
∴ The product of (4y² + 25) and (25 + 4y²) is a perfect square trinomial
Can someone please help me on the last two empty boxes :( ??!!
Answers
Answer:
trinomial binomialStep-by-step explanation:
mono-, bi-, tri- are prefixes meaning 1, 2, and 3, respectively. A 3-term polynomial is a trinomial; a 2-term polynomial is a binomial.
Which expression is the radical form of m^2.5?
Answers
The expression [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .
What is a Radical form ?
If n is a positive integer greater than 1 and n is a real number, then
[tex]\rm \sqrt[n]{a}[/tex] = aⁿ
Here the index is represented by n, the radicand is represented by a , and the sign is called the radical.
Left side of the equation is called the radical form
Right side of the equation is called exponent form.
The given exponent form is
[tex]\rm m^{2.5}[/tex]
In radical form this will be written as
[tex]\rm \sqrt[2.5]{m}[/tex]
Therefore the expression [tex]\rm m^{2.5}[/tex] in radical form is [tex]\rm \sqrt[2.5]{m}[/tex] .
To know more about Radical form
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Can someone help me?
Thanks-Aparri
Answers
Answer:
10y
Step-by-step explanation:
9y + y = 10y
Answer:
[tex]10y[/tex]
Step-by-step explanation:
[tex]9y + y = y(9 + 1) = y(1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) = y \times 10 = 10y[/tex]
A can can be rented for $50 per day with unlimited mileage, or for $40 per day plus 25 cents per mile . For what daily mileages will be unlimited mileage plan save you money ?
Answers
Please help me !! D is also an option but I couldn't get it in the picture
Answers
Answer: A) (-1, 0) to (1, 2)
Step-by-step explanation:
Complex numbers are written in the form of ai + b ; where "a" represents the x-coordinate and "b" represents the y-coordinate --> (a, b)
-i → -1i + 0 → (-1, 0)
2 + i → 1i + 2 → (1, 2)
Which graph connects those two coordinates? OPTION A
At 350 degrees Fahrenheit, an oven can cook approximately 3 pounds of turkey per hour. At 450 degrees Fahrenheit, it can cook approximately 4.5 pounds per hour. How many more ounces of turkey can the oven cook at 450 degrees than at 350 degrees in 10 minutes? (1 pound = 16 ounces)
A) 4
B) 6
C) 8
D) 12
Answers
Answer:
D
Step-by-step explanation:
Eliminate the parameter.
x = t - 3, y equals two divided by quantity t plus five
Answers
Answer:
y = 2/(x +8)
Step-by-step explanation:
Solve the first equation for t and substitute that expression into the second equation.
x = t -3
x + 3 = t
Then for y, we have
y = 2/(t +5)
y = 2/((x +3) +5) . . . . substitute for t
y = 2/(x +8) . . . . . . . . simplify
Need help with this math question
Answers
Answer:
120
Step-by-step explanation:
If those 2 polygons are similar, then their corresponding angles are the same. The thing that makes them similar as opposed to congruent is that their side lengths exist in proportion to one another instead of being the same.
Answer:
[tex]w = 120\°[/tex]
Step-by-step explanation:
In this case we know that
ABCD and FECG are similar polygons.
This means that their sides are proportional and their corresponding angles are equal.
So if the lines FG and AD are parallel and of proportional length then by definition the angle w is equal to 120 °
Thus
[tex]w = 120\°[/tex]
If f(x)=5x, what is f^-1(x)?
A. f^-1(x)=-5x
B. f^-1(x)=-1/5x
C. f^-1(x)=1/5x
D. f^-1(x)=5x
Thanks!
Answers
Answer:
C. f^-1(x) = 1/5x
Step-by-step explanation:
You know that f^-1(f(x)) = x, so you can try the answers.
A: f^-1(5x) = -25x . . . . not itB: f^-1(5x) = -x . . . . . . not itC: f^-1(5x) = x . . . . . . . correct choiceD: f^-1(5x) = 25x . . . . not it____
You can also solve for f^-1(x). It will be "y" when ...
f(y) = x
5y = x
y = 1/5x . . . . . divide by 5
Graph the function.
y = –2x^2 + 6x – 2
Answers
Answer:
Step-by-step explanation:
Which list shows the numbers in order from least to greatest? A. 53.783 B. 53.65 C. 53.09 D. 53.163 A) A, B, D, C B) C, D, B, A C) D, C, B, A D) B, C, A, D
Answers
Answer:
B) C,D,B,A
Step-by-step explanation:
Graph the system of equations. then determine wheather the system has no solution, one solution, or infinitely many solutions. If the systems has one solution, name it.
y= -x + 5
y= x - 3
A. one solution; (1,4)
B. infinitely many
C. no solution
D. one solution; (4, 1)
Answers
Answer:
See below in bold.
Step-by-step explanation:
If we add the 2 equations we eliminate x and we get 2y =2.
So y = 1.
Substituting y = 1 in the second equation 1 = x - 3.
So x = 4.
A. One solution: (4, 1).
If we drew a graph we would have 2 lines which intersect at the point (4, 1).
Answer:
Step-by-step explanation:
If we add the 2 equations we eliminate x and we get 2y =2.So y =1.
Substituting y = 1 in the second equation 1 = x - 3.So x = 4.
A.
One solution: (4, 1).If we drew a graph we would have 2 lines which intersect at the point (4, 1).
Charlie entered an elevator and ride up 10 floors and then down 2 floors before realizing he had not pressed the button for Floor 1. He then pressed the button for Floor 1 and rode down 14 floors and exited the elevator on Floor 1. On which floor did he begin?
Answers
Answer:
Floor 7
Step-by-step explanation:
He entered the elevator on floor x.
Then he rode up 10 floors. Now he is on floor x + 10.
Then he rode down 2 floors. Now he is on floor x + 10 - 2 = x + 8.
Then he pressed the Floor 1 button and rode down 14 floors to Floor 1. Now he is on floor x + 8 - 14 = x - 6 which is the same as Floor 1.
Floor x - 6 is the same as Floor 1, so we get the equation:
x - 6 = 1
Add 6 to both sides:
x = 7
Since we let x be the floor number he entered the elevator in, he entered the elevator on Floor 7.
Answer:
He began on floor 7
Step-by-step explanation:
This is a question where you have to use the question from the end and work your way backwards if that makes sense.
He had to go down 14 floors to get to floor 1. So 14 + 1 = 15. He was on the 15th floor.
Next he went down 2 floors. Since this is reverse, add two floors to the answer. 15 + 2 = 17. He was on the 17th floor.
And finally, he goes up 10 floors. Doing this in reverse, take away 10 floors to the answer. 17 - 10 = 7
He started on the 7th floor.Now to make sure it is correct, start from 7 and follow the original order of the question.
7 + 10 = 17
17 - 2 = 15
15 - 14 = 1
At the start of the first down, the football was 30 yards from the Tigers' end zone. During three downs, the ball moved 9
yards farther from their end zone, then 14 yards closer to it, and then 2 yards closer to it. How many yards from their end
zone was the ball at the end of the third down?
Answers
Answer:
23
Step-by-step explanation:
30 + 9 = 39.
39 - 14 = 25.
25 - 2
= 23
Answer:
23
Step-by-step explanation:
A chemist wants to mix a 66% alcohol solution with eight liters of 54% alcohol solution to produce a solution that is 65% alcohol. How many liters of the 66% alcohol solution should be used ?
Answers
Answer:
We have 8 liters of 54% alcohol.
We will add "x" liters of 66% alcohol to make "8 +x" liters of 65% alcohol.
54 * 8 + 66 x = 65 (8 + x)
432 + 66x = 520 + 65x
x = 88 liters
Step-by-step explanation:
The coordinates of vertex S are (_,_)
The area of rectangle PQRS is_____square units.
Answers
Answer:
vertex s is -2,-2
Step-by-step explanation:
and with the rectangle is q to p is 4cm coz one box is 1 cm and r to q is 3cm so you multiply them and the answer is 12cm
Find the arc length intercepted by a central angle of radians in a circle whose radius is 18.4 inches. 13.8π 15.2π 24.5π
Answers
Final answer:
The arc length intercepted by a central angle of π radians in a circle of radius 18.4 inches is calculated as arc length = θ × radius, resulting in 18.4π inches.
Explanation:
To find the arc length intercepted by a central angle of θ radians in a circle with radius r, we use the formula:
arc length (s) = θ × r
Given that the central angle θ is π radians and the radius r is 18.4 inches, we can compute the arc length as follows:
arc length (s) = π × 18.4 inches
By multiplying, we get:
arc length (s) = 18.4π inches
Therefore, the arc length intercepted by a central angle of π radians in a circle with a radius of 18.4 inches is 18.4π inches.
Sherina wrote and solved the equation.
x-56=230
x-56-56=230-56
x=174
What was Sherina’s error?
Sherina’s work is correct.
Sherina only needed to subtract 56 from 230.
Sherina made a subtraction error when subtracting 56 from 230.
Sherina should have added 56 to both sides of the equation.
Answers
Answer:
Sherina should have added 56 to both sides of the equation.
Step-by-step explanation:
To solve this equation: x-56=230 you need to add 56 to both sides of the equation:
x-56 + 56=230 + 56 → x = 286.
Therefore, Sherina should have added 56 to both sides of the equation.
Answer:
Last option: Sherina should have added 56 to both sides of the equation.
Step-by-step explanation:
To solve the equation [tex]x-56=230[/tex] Sherina needed to solve for the variable "x".
To calculate the value of the variable "x" it is important to remember the Addition property of equality. This states that:
[tex]If\ a=b\ then\ a+c=b+c[/tex]
Therefore, Sherina should have added 56 to both sides of the equation.
The correct procedure is:
[tex]x-56+(56)=230+(56)\\x=286[/tex]
Determine the principal value of the function: Arc sin(square root of 3/2)
Answers
Answer:
π/3
Step-by-step explanation:
We have to find the principal value of [tex]\text{arc sin}(\frac{\sqrt{3}}{2} )[/tex]
arc sin means sin inverse. The sin inverse is a one to one function with its range between [tex]-\frac{\pi}{2} \textrm{ to } \frac{\pi}{2}[/tex]
The principal value of the arc sin will lie within the above given range.
value of sin (60) or sin([tex]\frac{\pi}{3}[/tex]) is [tex]\frac{\sqrt{3}}{2}[/tex].
[tex]\frac{\pi}{3}[/tex] lies between [tex]-\frac{\pi}{2}\textrm{ and } \frac{\pi}{2}[/tex]
So, from here we can say that the Principal Value of Arc sin(square root of 3/2) is π/3
The principal value of the function Arc sin(√3/2) is,
⇒ π / 3
We have to given that,
⇒ Arc sin (√ 3/ 2)
Since, Value of arc sin lies between - π/2 and π/2.
Hence, The principal value of the function Arc sin(√3/2) is,
⇒ Arc sin(√3/2)
⇒ Arc sin(sin π/3)
⇒ π / 3
Therefore, The principal value of the function Arc sin(√3/2) is,
⇒ π / 3
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A textbook store sold a combined total 440 of physics and sociology textbooks in a week. The number of sociology textbooks sold was 54 less than the number of physics textbooks sold. How many textbooks of each type were sold?
Answers
First subtract the difference of the two by the total:
440 - 54 = 386
Now divide that by 2:
386 / 2 = 193
193 is the number of Sociology books sold.
Now add 54 to 193 for the total Physics books:
193 + 54 = 247 Physics books were sold.
A national study found that a car's value decreases by 15 percent annually. If the car was purchased for $66,000, how much will the car be worth in 10 years? A. $12,993.71 B. $11,768.35 C. $18,429.50 D. $13,792.14
Answers
Answer:
A. $12,993.71
Step-by-step explanation:
Each year, the car's value is multiplied by 1-0.15 = 0.85. After 10 years, the car's value will be ...
$66,000×0.85^10 ≈ $12,993.71
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth.
Answers
Check the picture below.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{27.6}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{30^2-27.6^2}=h\implies \sqrt{138.24}=h\implies 11.76\approx h \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the triangle}}{\cfrac{1}{2}bh\implies \cfrac{1}{2}(27.6)(11.76)}\implies 162.288\implies \stackrel{\textit{rounded up}}{162.3}[/tex]
To find the area of the right triangle with a given hypotenuse and adjacent leg, use the Pythagorean theorem to calculate the other leg. Then, use the base and height (the two legs) in the area formula for a right triangle. The area of the triangle is approximately 148.7 cm².
To find the area of a right triangle, you need two perpendicular sides, known as the legs of the triangle. Since we are given the hypotenuse (30 cm) and one adjacent leg (27.6 cm) which is one of the legs, we need to find the other leg. Using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In mathematical terms, this is expressed as a² + b² = c². Therefore, the length of the other leg (b) can be found using the equation b² = c² - a², where c is the hypotenuse and a is the given adjacent leg.
Substituting the given values, we have b² = 30² - 27.6². Calculating this gives b ≈ 10.8 cm.
Now, the area of the triangle can be calculated using the formula for the area of a right triangle, which is (1/2) × base × height. In this case, the base and height are the two legs of the triangle. Substituting the lengths of the legs we have, Area ≈ (1/2) × 27.6 cm × 10.8 cm. The result is approximately 148.7 cm², which is the area of the triangle rounded to the nearest tenth.
Help with this question, please!
Answers
Answer:
see below
Step-by-step explanation:
Apart from the pictures being drawn with the axis at a funny angle relative to the edges of the solid, it should be pretty clear from the pictures that the figure has both plane and axis symmetry.
Every point on one side of the axis has a matching point on the other side at the same distance. Every point on one side of the plane of symmetry has a matching point on the other side at the same distance.
The airplane was 32,000 feet above sea level. It landed in a valley 100 feet below sea level. Write an integer to express the change in the altitude
Answers
Answer:
- 32,100 ft
Step-by-step explanation:
Initial Altitude = 32,000 ft above sea level = +32,000 feet
Final Altitude = 100 ft below sea level = -100 ft
Altitude change,
= final altitude - initial altitude
= - 100 - (32,000)
= - 32,100 ft
17. Find the value of (+328.62) – (+98.6).
A. –427.22
B. 230.02
C. 427.22
D. –230.02
Answers
For this case we must find the value of the following expression:
[tex](+328.62) - (+ 98.6) =[/tex]
We apply distributive property to the term within the parenthesis taking into account tha:
[tex]- * + = -[/tex]
Rewriting we have:
[tex]+ 328.62-98.6 =[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]+328.62-98.6 = 230.02[/tex]
Answer:
230.02
Option B