Which equation when graphed has a maximum value at x = −2? A) y = −x2 − 20x − 16, B) y = −x2 − 16x − 12, C) y = −4x2 − 20x − 16, D) y = −4x2 − 16x − 12
Answers
Answer:
Option D. [tex]y=-4x^{2} -16x-12[/tex]
Step-by-step explanation:
using a graphing tool
Graph and determine the vertex in each case
we know that
If the equation has a maximum value at x=-2, then the x-coordinate of the vertex must be equal to -2 and the parabola open downward
case A) [tex]y=-x^{2} -20x-16[/tex]
The vertex is the point [tex](-10,84)[/tex]
case B) [tex]y=-x^{2} -16x-12[/tex]
The vertex is the point [tex](-8,52)[/tex]
case C) [tex]y=-4x^{2} -20x-16[/tex]
The vertex is the point [tex](-2.5,9)[/tex]
case D) [tex]y=-4x^{2} -16x-12[/tex]
The vertex is the point [tex](-2,4)[/tex] -------> is the answer
see the attached figure
The equation with a maximum value at x = -2 is D) y = -4x^2 - 16x - 12, determined by finding the vertex of each quadratic equation and identifying the one with the vertex x-coordinate at -2.
The given equations are all in quadratic form, which can have a maximum value at their vertex point if the leading coefficient is negative. To find the equation that has a maximum value at x = -2, we need to put the equations in vertex form, which is y = a(x - h)^2 + k, where (h, k) is the vertex. By transforming the given equations, we seek the equation that has its vertex at x = -2. This is done by completing the square or using the formula h = -b/(2a) to find the x-coordinate of the vertex.
Let's apply the formula h = -b/(2a) to each equation:
For A) y = -x^2 - 20x - 16, we have a = -1, b = -20, so h = -(-20)/(2 × -1) = 10, which is not equal to -2.For B) y = -x^2 - 16x - 12, using the same approach, we find h = -(-16)/(2 × -1) = 8, again not equal to -2.For C) y = -4x^2 - 20x - 16, with a = -4, b = -20, h = -(-20)/(2 × -4) = 2.5, which is not equal to -2.For D) y = -4x^2 - 16x - 12, we find h = -(-16)/(2 × -4) = -2, which matches the required vertex x-coordinate.Therefore, the correct equation with a maximum value at x = -2 is D) y = -4x^2 - 16x - 12.
Related Questions
The numbers −1 and 3 are plotted on the number line. Absolute Value Which expression could help you find the distance between –1 and 3 on the number line? |–1| + |–3| |–1| + |3| |1| + | –3| |1| + |3|
Answers
Hope this helped.
Answer:
b
Step-by-step explanation:
i did the test
Can somebody help me with this and explain the procedures?
Answers
Answer: 2.35 square miles.
Step-by-step explanation:
To solve this exercise you must apply the formula for calculte the area of a sector in a circle, which is shown below:
[tex]A=r^2\pi(\frac{C}{360})[/tex]
Where C is the central angle in degrees and r is the radius.
Therefore, knowing that:
[tex]C=30\°\\r=\frac{6mi}{2}=3mi[/tex]
When you substitute values, you obtain the following result:
[tex]A=(3mi)^2\pi(\frac{30\°}{360})[/tex]
[tex]A=2.35mi^2[/tex]
Answer:
Area of sector = 2.355 miles²
Step-by-step explanation:
Formula:
Area of circle = πr²
Where r is the radius
Area of sector = πr²(C/360)
Where C is the angle of sector
It is given that radius of circle is 6 miles
To find the are of circle
Here diameter = 6 miles,
radius r = diameter/2 = 3 miles
Area = πr² = 3.14 * 3² = 28.26 miles²
To find area of sector
Here r = 3 and C = 30°
Area of sector = πr²(C/360) = 28.26*(30/360)
= 2.355 miles²
Solve the equation. −5 = c7
Answers
Answer:
[tex] c = - \frac { 5 } { 7 } [/tex]
Step-by-step explanation:
We are given the following equation and we are to solve it for [tex]c[/tex]:
[tex] - 5 = c7 [/tex]
Switching the sides of the equation we get:
[tex] c \times 7 = -5 [/tex]
Then dividing both sides of the equation by 7 to get:
[tex] \frac { c \times 7 } { 7 } = \frac { - 5 } { 7 } [/tex]
[tex] c = - \frac { 5 } { 7 } [/tex]
I(5,3), j(5,-3), and L(-4,3) are three vertices of rectangles ljkL. What are the coordinates of the fourth vertex,of rectangle ljkL
Answers
Check the picture below.
find the polynomial standard form of -5q^2(-q-5)
Answers
Answer:
5q^3+25q^2
Step-by-step explanation:
another name for temporary worker is
a. contingent employment
b. service employment
c. unskilled labor
Answers
Another name for temporary worker is contingent employment.
So the correct answer is A.
Hope this helps,
Davinia.
which sentence is true about a ray?
A. a ray is formed by lines that do not cross each other.
B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.
C. a ray is formed by two lines that cross at one point.
D. a ray is formed when two points on a line are labeled
Answers
Answer:
B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.
Step-by-step explanation:
Given choices are :
A. a ray is formed by lines that do not cross each other.
B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.
C. a ray is formed by two lines that cross at one point.
D. a ray is formed when two points on a line are labeled
Now we need to determine about which sentence is true about a ray.
We know that a ray has one fixed end point and other point moves infinitely then correct choice is :
B. A ray is formed by an endpoint and a line is starting at the endpoint and going to forever in one direction.
The width of a picnic table is 3 times its length. If the length is 5/6 yd long, what is the area of the picnic table in square feet?
Answers
Answer:
The area of the picnic table is [tex]18.75\ ft^{2}[/tex] or [tex]18\frac{3}{4}\ ft^{2}[/tex]
Step-by-step explanation:
we know that
[tex]1\ yd= 3\ ft[/tex]
Let
L-----> the length of the table
W----> the width of the table
the area of the table is
[tex]A=LW[/tex]
Convert yards to feet
[tex]L=\frac{5}{6}\ yd=\frac{5}{6}*3=\frac{5}{2}\ ft[/tex]
[tex]W=3L[/tex]
[tex]W=3(\frac{5}{2})=\frac{15}{2}\ ft[/tex]
substitute in the formula
[tex]A=\frac{5}{2}(\frac{15}{2})=\frac{75}{4}=18.75\ ft^{2}[/tex]
To calculate the area of the picnic table, convert the length to feet and multiply by the width, also in feet, to find the area in square feet.
Explanation:The student is asking about the area of a picnic table in square feet when the width is 3 times the length and the length is given as 5/6 yard. To find the area, first, calculate the width by multiplying the length of 5/6 yard by 3, which gives 5/2 yards (or 2.5 yards).
Since there are 3 feet in a yard, we convert the measurements to feet: 5/6 yard is equal to 5/6 * 3 feet, and the width is 2.5 * 3 feet. Next, multiply the length and width in feet to find the area.
It is important to note that converting measurements should retain unit consistency throughout the calculation.
Plz, help with this! Find the area of the parallelogram.
Answers
Answer:
192 cm²
Step-by-step explanation:
The area (A) of a parallelogram is calculated using the formula
A = bh ( b is the base and h the perpendicular height )
here b = 24 and h = 8, hence
A = 24 × 8 = 192 cm²
What would be the coordinates of the image if this pre-image is reflected across the x-axis?
(-2, 2), (1, 1), (3, 1), (2, 4)
(2, -2), (-1, 1), (-3, -1), (-2, -4)
(-2, 2), (1, -1), (3, 1), (2, 4)
(-2, -2), (-1, 1), (-3, -1), (-2, -4)
Answers
Answer:
The vertices of the pre-image are (-2, -2), (1, 1), (3, -1), and (2, -4).
Since the pre-image is reflected across the x-axis, leave each x-coordinate the same, and change the sign of each y-coordinate.
The vertices of the new image are (-2, 2), (1, -1), (3, 1), and (2, 4).
The table shows the number of calories in for males in the cost of each meal which best describes the strength of the model
Answers
Answer: A WEAK NEGATIVE CORRELATION
Step-by-step explanation:
TOOK THE TEST
For every five flowers, there are 10 yellow flowers. There are a total of 75 yellow and red flowers in her garden how many red flowers are in her garden
Answers
Answer:
Yellow: 50
Red: 25
Step-by-step explanation:
5:10
5 times 5 = 25
10 times 5 = 50
what is the solution for x^2+64=0
Answers
Answer:
If we consider real numbers, there is no solution.
If we take into account imaginary numbers, there are 2 solutions. [tex]x=8i, -8i[/tex]
Step-by-step explanation:
We can take 64 to the other side and then take the square root.
Thus, we have:
[tex]x^2+64=0\\x^2=-64\\x=\sqrt{-64}[/tex]
We CANNOT take the square root of a negative number, so there is no solution.
BUT, if we take into account Imaginary Numbers, we can solve:
[tex]x=\sqrt{-64} \\x=\sqrt{(-1)(64)} \\x=\sqrt{-1} \sqrt{64} \\x=8i[/tex]
Where [tex]\sqrt{-1} =i[/tex]
AND, we can take the positive and negative versions of 8i, since squaring would take it back to original.
So the answer would be 8i and -8i
Answer:
So the answer would be 8i and -8i
what is 4 is to 3 as x is to 20
Answers
Answer:
Step-by-step explanation:
Better write, "Solve '4 is to 3 as x is to 20' for x."
x = 80/3
Writing out this equation of ratios, we get:
4 x
------ = -----
3 20
Cross multiplication here yields:
3x = 80, and then x = 80/3.
To solve this proportion problem, set up the equation 4/3 = x/20. Cross multiply and solve for x to get x = 80/3.
Explanation:This is a proportion problem. We can set up the equation:
4/3 = x/20
To solve for x, we can cross multiply:
4 * 20 = 3 * x
80 = 3x
Divide both sides by 3 to solve for x:
x = 80/3
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An observatory is shaped like a cylinder standing on one of its bases with a dome on top. The
diameter of the floor of the observatory is 64 feet, as shown in the diagram.
Which measurement is closest to the circumference of the base of the observatory in feet?
F 200.96 ft
G 3,215.36 ft
H 100.48 ft
J 401.92 ft
3 A classroom is arranged with 8 seats in the front row, 10 seats in the mid
Answers
Answer:
Option F. [tex]200.96\ ft[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
in this problem
[tex]D=64\ ft[/tex]
substitute
[tex]C=\pi (64)=64\pi\ ft[/tex] -----> exact value of the circumference
Find the approximate value of the circumference
assume
[tex]\pi=3.14[/tex]
[tex]64\pi\ ft=64(3.14)=200.96\ ft[/tex]
The correct answer is option F. The measurement is closest to the circumference of the base of the observatory is 200.96 ft.
To find the circumference of the base of the observatory, we use the formula for the circumference of a circle, which is [tex]\( C = \pi \times d \)[/tex], where [tex]\( C \)[/tex] is the circumference and [tex]\( d \)[/tex] is the diameter of the circle.
Given that the diameter of the floor of the observatory is 64 feet, we can plug this value into the formula:
[tex]\( C = \pi \times 64 \) feet[/tex]
Using the approximation [tex]\( \pi \approx 3.14159 \)[/tex], we calculate the circumference as follows:
[tex]\( C \approx 3.14159 \times 64 \)[/tex] feet,
[tex]\( C \approx 200.96 \)[/tex] feet.
The complete question is:
An observatory is shaped like a cylinder standing on one of its bases with a dome on top. The diameter of the floor of the observatory is 64 feet, as shown in the diagram.
Which measurement is closest to the circumference of the base of the observatory in feet?
F 200.96 ft
G 3,215.36 ft
H 100.48 ft
J 401.92 ft
Write a story problem about 40 apples and 17 peat
Answers
Answer:
Lets say you have 40 apples and 17 "peats". You decide to give your friend, Timmy, 2/3's of the apple, because you know that he loves apples! You also give him 2/7 of your "peats". How many apples and peats, combined, does that leave you with?
Step-by-step explanation:
There really is none.
Can you please help me with number eight please please help me with number eight I need your help and begging you for your help please help me
Answers
Answer:
Step-by-step explanation:
its B! Hope this helps
The answer is B.
Hope this helps.
Which method is the most efficient method to use to solve x^2+5x-6=0
Answers
Answer:
Factoring x=1 x=-5
Step-by-step explanation:
I would factor the equation
-1 *6 = -6
-1+6 =5
(x-1) (x+5) =0
Using the zero product property
x-1 =0 x+5 =0
x=1 x=-5
1. For the carnival, the park rented a dunking booth shaped as a rectangular prism. The booth is 3 1/2 ft wide, 3 1/2 ft long, and 8 ft tall. (a) What is the total volume of the dunking booth? (b) If they are only going to fill the dunking booth 6/7 full, how many cubic feet of water will they need?
Answers
Answer:
Part a) The total volume is [tex]98\ ft^{3}[/tex]
Part b) [tex]84\ ft^{3}[/tex]
Step-by-step explanation:
Part a)
Find the total volume
we know that
The volume of a rectangular prism is equal to
[tex]V=LWH[/tex]
we have
[tex]L=3\frac{1}{2}\ ft=\frac{3*2+1}{2}=\frac{7}{2}\ ft[/tex]
[tex]W=3\frac{1}{2}\ ft=\frac{3*2+1}{2}=\frac{7}{2}\ ft[/tex]
[tex]H=8\ ft[/tex]
substitute in the formula
[tex]V=(\frac{7}{2})(\frac{7}{2})(8)=98\ ft^{3}[/tex]
Part b) If they are only going to fill the dunking booth 6/7 full, how many cubic feet of water will they need?
Multiply the total volume by 6/7
so
[tex]98(6/7)=84\ ft^{3}[/tex]
HELP ME PLZ AS SOON AS POSIBLE
IS THIS RIGHT
Answers
YES IT IS RIGHT.YOU ARE RIGHT
Answer:
Should be A pretty sure
Step-by-step explanation:
The adult population of a town in 2000 was 400. The child population of the town in 2000 was 120. Both the adult and child populations increased by the same percent from 2000 to 2010. If the adult population in 2000 was 500, how many children lived in the town then?
Answers
Answer:
150
Step-by-step explanation:
500 is 125% of 400 (500/400) so you need to get what 125% of 120 is
120 x 1.25 =150
^number of children ^125% as a decimal
To find the number of children after the same percent increase in population as the adults, calculate a 25% increase based on the adult growth from 400 to 500. Applying this to the original child population (120), there were 150 children in 2010.
The question pertains to the percent increase in population and requires finding the number of children in a town given the increase in adult population. Specifically, the child population in 2000 was 120, and the adult population increased from 400 to 500 from 2000 to 2010. Assuming that the child population increased by the same percent as the adult population, we need to calculate this percentage increase and then apply it to the number of children to find the updated child population in 2010.
To find the percentage increase in the adult population:
Calculate the increase by subtracting the original number from the new number (500 - 400 = 100).Divide the increase by the original number (100 / 400 = 0.25).Convert the decimal to a percentage by multiplying by 100 (0.25 × 100 = 25%).Since the child population increased by the same percentage, we then:
Apply the 25% increase to the original child population (120).Multiply 120 by 0.25 to find the increase (120 × 0.25 = 30).Add the increase to the original child population (120 + 30 = 150).Therefore, there were 150 children in the town in 2010.
5(3x+4)=15x+20
Is this associative,commutative,identity,Or a distributive property?
Answers
[tex]\bold{Hey\ there!} \\ \bold{\ Assoviative \ property\ looks\ looks\ like\ this:(2+3)+4;2+(3+4)}\\ \bold{\ Commutative\ property\ looks\ like\ this:b+c;c+b} \\ \bold{\ Distributive\ property\ looks\ like\ this:a(b+c);a(b)+a(c)}\\ \bold{5(3x+4)=15x+20}\\ \\ \bold{5(3x))=15x} \\ \bold{5(4)=20} \\ \\ \bold{Answer:distributive\ property}\checkmark[/tex]
[tex]\bold{Reason:\ because\ it\ almost\ similar\ to\ the\ example\ shown\ above\ as\ to\ how\ solve\ it!} \\ \bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\\frak{LoveYourselfFirst:)}[/tex]
equivalent expressions 36 + 18x
Answers
Answer:
An equivalent expression is 18(2 + x)
Step-by-step explanation:
To find this, look for the greatest common factor. Since both terms are divisible by 18 equally, we take 18 out of each term. Then we divide both terms by 18 and express in a parenthesis.
18(2 + x)
The answer is there
A person can run 2/5 of an mile in 1/4 an hour what is their rate in miles per hour
Answers
Answer: i think its 1.6 but i could be wrong if im not im glad to help
Step-by-step explanation:
A survey asked a group of students to choose their favorite type of snack. The results of the survey are shown in the graph. Based on the graph, how many students in a class of 192 students would be expected to choose cheese that crackers?
Answers
10 students choose cheese that crackers
Answer:
Step-by-step explanation:
It's either 160 or 5 don't ask
a drone costs 300 plus 25 for tax for each set of extra propellers. what is the cost of a drone and 4 extra set of propellers
Answers
4 Extra Set Of Propellor = 4(25$) = $100
Answer:
400
Step-by-step explanation:
The cost is arrived to by adding the initial cost of the drone to the total cost of all the extra propellers. The cost of per propeller due to tax being 25 we get the following expression.
That is: 300+ 4(25)
=400
Can you help me find the answer please
Answers
the answer is 1 / 12 I got this because I know that 1/2 equals a half so half of 12 is 6 so 6/12 is simply 1/2
Answer:
[tex]x=\frac{1}{12}[/tex]
Step-by-step explanation:
Let the unknown number be [tex]x[/tex].
The given equation then becomes;
[tex]\frac{5}{12} +x=\frac{1}{2}[/tex]
Group similar terms
[tex]x=\frac{1}{2}-\frac{5}{12}[/tex]
Collect the LCM on the Right Hand Side.
[tex]x=\frac{6-5}{12}[/tex]
This implies that;
[tex]x=\frac{1}{12}[/tex]
Which container has the greatest surface area? (Use 3.14 for π .)
cone
cylinder
square pyramid
rectangular prism
Answers
Answer:
It is the Rectangular Prism.
Step-by-step explanation:
Sry, I don't have enough time to write out an explanation. Hope the answer helped!
Answer:
the cylinder container has the greatest surface area.
Step-by-step explanation:
The volume of cone is calculated by [tex]v=\frac{1}{3}\times\pi\times r^{2}\times h[/tex]
The volume of cylinder is calculated by [tex]v=\pi\times r^{2}\times h[/tex]
The volume of square pyramid is calculated by [tex]v=\pi\times r^{2}\times h[/tex]
The volume of rectangular prism is calculated by [tex]v=\frac{1}{3}\times B\times h[/tex]
The radius of cone is [tex]\frac{6}{3}[/tex]=[tex]2in[/tex], and slant height is 10 in.
height is calculated as h² = l²- r²
h² = l²- r²
h² = 10²- 3²
h² = 100- 9
h² =91
h= 9.54
The volume of cone is [tex]=\frac{1}{3}\times 3.14\times 3^{2}\times 9.54[/tex]
[tex]=\frac{1}{3}\times 3.14\times 9\times 9.54[/tex]
v=89.8668
The volume of cylinder is [tex]=3.14\times 3^{2}\times 10[/tex]
[tex]=3.14\times9\times 10[/tex]
v=282.6
The volume of square pyramid
The height of pyramid is calculated as h² = l²- r²
h² = 10²- 3²
h² = 100- 9
h² =91
h= 9.54
[tex]v=3.14\times 3^{2}\times 9.54[/tex]
[tex]v=3.14\times 9\times 9.54[/tex]
[tex]v=269.60[/tex]
The volume of rectangular prism[tex]v=\frac{1}{3}\times 6\times 10[/tex]
[tex]v=20[/tex]
Hence, the cylinder container has the greatest surface area.
PLEASE HELP ASAP
In the figure, line m is parallel to line n. The measure of angle 2 is 40 degrees and the measure of angle 3 is 68 degrees. What is the measure of angle 5? Explain how you found the answer using the relationships of angles.
Answers
Answer:
∠1 - 40°
Step-by-step explanation:
∠1 - 40°
b/c it's a right triangle and we have two angles given, 50° and 90°. Add them and subtract by 180° and get 40°.
∠2 - 140°
b/c an exterior (outside) angle is equal to the two most isolated / farthest angles added. The two most is angles are 105° and 35°, add them and get 140°.
∠3 - 40°
b/c ∠'s 1 and 3 are vertical angles meaning they're equal so since ∠1 is 40°, so is ∠3.
∠4 -
b/c ∠' s 2 and 4 are vertical angles meaning they're equal so since ∠2 is 140°, so is ∠4.
∠5 - 35°
b/c we have two angles, 105° and 40°. Add them and subtract by 180° and get 35°.
~~
I hope that helps you out!!
The measure of angle 5 is 72°.
What is angle?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
Given that,
Lines m and n are parallel,
Also, value of ∠2 = 40°, ∠3 = 68°
First determine the value of angle 5 First determine the value of angle 1,
Since, angle of a line = 180°
∠1 + ∠2 + ∠3 = 180°
∠1 + 40 + 68 = 180
∠1 + 108 = 180
∠1 = 72
Since, lines m and n are parallel,
∠1 = ∠5
∠5 = 72°
So, the value of angle 5 is 72°.
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What is the length of the diagonal of the square shown below?
Answers
Answer:
sqrt(50)
Step-by-step explanation:
Since it is a right triangle, we can apply the Pythagorem Theorem.
a^2 + b^2 = c^2
25 + 25 = c^2
50 = c^2
c = sqrt(50)
The length of the diagonal of the square is 5 [tex]\sqrt{2[/tex]
The length of the diagonal of a square is equal to the square root of 2 times the length of a side. In this case, the side length is 5, so the diagonal of the square is 5√2
Let's break down the steps to find the square root of 50:
1. **Given**: We have a right triangle with side lengths:
[tex]- \(a = 25\)\\ - \(b = 25\)2. Apply the Pythagorean Theorem: \[a^2 + b^2 = c^2\] \[25^2 + 25^2 = c^2\] \[50 = c^2\]3. Solve for \(c\): \[c = \sqrt{50}\]4. Calculate the square root of 50: \[c \approx 7.07\][/tex]
Therefore, the length of the hypotenuse (\(c\)) in this right triangle is approximately 7.07 units
.