which equation shows the quadratic function used to solve 7x^2=9+x for x?

ANSWER

[tex]h= 2 \cos(\pi(t + \frac{1}{2} )) + 5[/tex]

EXPLANATION

The given equation that models the height is

[tex]h(x) = - 2 \sin(\pi(t + \frac{1}{2} )) + 5[/tex]

This is sine a sine function that is reflected in the x-axis.

This function will coincide with the cosine function with the same amplitude, period, phase shift and vertical translation.

The function that can also model this height is

[tex]h= 2 \cos(\pi(t + \frac{1}{2} )) + 5[/tex]

The last choice is correct.

Answer:  [tex]\bold{A)\quad y=5sin\bigg(\dfrac{6}{5}x-\pi\bigg)-4}[/tex]

Step-by-step explanation:

The general form of a sin/cos function is: y = A sin/cos (Bx-C) + D where the period (P) = 2π ÷ B

In the given function, [tex]B=\dfrac{6}{5}[/tex]  →   [tex]P=2\pi \cdot \dfrac{5}{6}=\dfrac{10\pi}{3}[/tex]

Half of that period is: [tex]\dfrac{1}{2}\cdot \dfrac{10\pi}{3}=\large\boxed{\dfrac{5\pi}{3}}[/tex]

Calculate the period for each of the options to find a match:

[tex]A)\quad B=\dfrac{6}{5}:\quad 2\pi \div \dfrac{6}{5}=2\pi \cdot \dfrac{5}{6}=\dfrac{5\pi}{3}\quad \leftarrow\text{THIS WORKS!}\\\\\\B)\quad B=\dfrac{6}{10}:\quad 2\pi \div \dfrac{6}{10}=2\pi \cdot \dfrac{10}{6}=\dfrac{10\pi}{3}\\\\\\C)\quad B=\dfrac{5}{6}:\quad 2\pi \div \dfrac{5}{6}=2\pi \cdot \dfrac{6}{5}=\dfrac{12\pi}{5}\\\\\\D)\quad B=\dfrac{3}{10}:\quad 2\pi \div \dfrac{3}{10}=2\pi \cdot \dfrac{10}{3}=\dfrac{20\pi}{3}[/tex]

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright.  I can't really explain much but i can get your answer.

AS A DECIMAL: 1.047197551196597746154214461093167628065723133125035273658

As a property:

π/3

Sorry if its wrong... I tried lol

Answer:

The answer would be 2

Step-by-step explanation:

I think the answer is 4:24

Answer:

4 : 24

Step-by-step explanation:

1:6

We need to make the 1 a 4, so we will multiply by 4

What we do to one side, we do to the other

1 *4 = 4

6*4 = 24

1: 6  becomes 4: 24

Answer:

0.5

Step-by-step explanation:

Its too hard to explain

Answer:

option b

6 C 2 + 6

Step-by-step explanation:

Given in the question that,

number of pink beans = 87

number of purple beans = 74

number of white beans = 35

number of black beans = 70

number of orange beans = 25

number of green beans = 47

if two beans selected are different

6 C 2

(6 colours of beans)

if two beans selected are same

6 C 1 = 6

(6 colours of beans)

total sample space will be

6 C 2 + 6

In any inequality or equation, a number that does not change is called​ a constant.

A number that does not change in any inequality or equation is called a constant.

Equations are not always balanced on both sides using an "equal to" sign in mathematics. Sometimes it might be about a "not equal to" connection, meaning that something is superior to or inferior to another. In mathematics, an inequality is a connection between two numbers or other mathematical expressions that results in an unequal comparison.

A constant in algebra is a single integer or, occasionally, a letter (such as a, b, or c) that stands in for a fixed number. something constant or unalterable a number that is supposed not to change the value in a particular mathematical discussion, for example, a number that has a fixed value in a certain scenario, globally, or that is distinctive of some substance or instrument

a concept in logic with a predetermined name

Therefore, A constant is a quantity that does not alter in any inequality or equation.

Learn more about inequalities here:

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To find the answer, you have to set each one equal to each other.

(160 + 40x = 55x)

Now, you just solve for X.

55x - 40x = 15x

160 / 15 = 15 / 15x

This means 160/15 = x, or is equal to

10 2/3

Answer:

C is the answer

Step-by-step explanation:

Answer:

[tex]15.23[/tex]

Step-by-step explanation:

First, we can make an equation by adding all the ages together and dividing it by the sum of the frequencies.

[tex](13*7)+(14*12)+(15*18)+(16*9)+(17*5)+(18*4)+(19*2)[/tex]

Now simplify.

[tex](13*7)+(14*12)+(15*18)+(16*9)+(17*5)+(18*4)+(19*2) = 868[/tex]

We can divide this number by the sum of the frequencies.

[tex]\frac{868}{7+12+18+9+5+4+2} \\ \\ \frac{868}{57} \\ \\ 15.23[/tex]

Answer:

Step-by-step explanation:

First you need to find the total number of years of all the people tracked.

The general formula is

Total years = age*frequency for all ages.

Age                 Frequency              Total

13                        7                             91

14                       12                           168

15                       18                           270

16                        9                            144

17                         5                             85

18                         4                             72

19                         2                             38

Totals                 57                            868

The mean is the total number of years / total frequency

mean = 868/57

mean = 15.23

Answer:

The lake's shape is a cylinder. The volume of a cylinder is given as: V=πhr^2 where r equals the radius, and h the depth. Therefre, the volume of the lake is:

V=πhr^2

V=π(20ft)(32,5ft)^2

V=66.364,1875‬ ft^3.

Given that 66.364,1875‬ ft^3 equals 496.44 gallons, we can say that 496.44 gallons of water is required to fill the lake.

Answer: (y-3)(4y-5)

Step-by-step explanation:

4*15= 60. 60= -12 x -5

4(y-12)(y-5)

(y-3)(4y-5)

Answer:

The answer is 4x-3 because all your doing is subtracting 3x from 4x

Answer:

the answer is D:  1800 square in

Step-by-step explanation:

find the area of the triangle

area = 1/2 bh

=1/2 (15 inch) (20 inch)

=150 square inch

***then multiply by 2 which gives you 300 square inch***

find the area of the 3 rectangular faces

A=lw

= (25 in) (15 in)

= 375 square inch

A = lw

= (25 in) (20 in)

= 500 square inch

A = lw

= (25 in) (25 in)

= 625 square inch

then add all 3 rectangular faces which equals to 1500 square inch

then add the triangular and rectangular

300 square inch + 1500 square inch = 1800 square inch

Answer:

The answer for study island would be D. 1,800 in2

hope i helped :)

There are 70 degrees in angle A.

Answer:

1.93 x 10^-15

Step-by-step explanation:

You want to move the decimal just past the first real number and count the spaces moved, which is 15. Since the decimal is being moved to the right the spaces moved will be negative. Therefore you remove the zeroes and get 1.93 times 10 to the negative 15th power.

scientific notation means, moving the dot in a way that only one integer is to its left, namely the in this case it'll look like 1.93, so we'll have to move the dot all the way from the left to the right that many slots.

[tex]\bf 0.00000000000000193\implies \stackrel{\textit{moved }\stackrel{\downarrow }{15} \textit{ slots to the right}}{0000000000000001.93}\implies 1.93\times 10^{\stackrel{\downarrow }{-15}}[/tex]

8+8=16 so 16/5 16÷5=3.2 32%

32% is the answer I think. Hope this helps

Answer:

32%

Step-by-step explanation:

8 + 8 = 16.

16/5

16 ÷ 5

= 3.2

= 32%

hence the numbers are 8 and 13

hope it helps you!!!!!!!!

Final answer:

The two numbers that satisfy the conditions of summing up to 21 and one being 18 less than twice the other are 8 and 13.

Explanation:

To solve the problem, let’s denote the two numbers as x and y. According to the question, the sum of the two numbers is 21, which can be expressed as an equation: x + y = 21. Additionally, we are told that one number is 18 less than two times the other, which gives us another equation: x = 2y - 18.

We can use the method of substitution to solve these equations. First, we will solve the second equation for x, which we already have as x = 2y - 18. Then we will substitute this expression for x in the first equation: (2y - 18) + y = 21. Simplifying we get: 3y - 18 = 21. Adding 18 to both sides gives us 3y = 39. So, dividing both sides by 3 yields y = 13. Now that we have the value of y, we can substitute it back into the equation x = 2y - 18 to get x = 2(13) - 18 which simplifies to x = 8.

Thus, the two numbers in question are 8 and 13.

Answer:

I think the answer is B

Answer:

Cone diameter = 18 m therefore radius = 9 m

Lateral Area = PI * radius * slant height

Lateral Area = 3.14 * 9 * 15 = 423.90 square meters

Step-by-step explanation:

Final answer:

The lateral surface area of a cone with a diameter of 18 meters and a slant height of 15 meters is approximately 423.9 square meters, calculated using the formula LSA = πrl with π approximated as 3.14.

Explanation:

The student is asking about finding the lateral surface area of a cone with a given diameter and slant height, where the diameter is 18 meters and the slant height is 15 meters. To find the lateral surface area (LSA) of a cone, the formula LSA = πrl can be used, where 'r' is the radius of the base and 'l' is the slant height of the cone. Since the diameter is 18 meters, the radius is half of that, which is 9 meters. Using 3.14 as the approximation for π (pi), we can calculate the lateral surface area.

The calculation would be as follows:

Find the radius (r): Diameter / 2 = 18m / 2 = 9m.

Use the formula LSA = πrl: LSA = 3.14 * 9m * 15m.

Calculate the LSA: LSA = 3.14 * 135m².

LSA = 423.9m², which is the lateral surface area of the cone.

Therefore, 423.9 square meters is the closest approximation to the lateral surface area of the given cone.

ANSWER

C) x = −3 or x = 9

EXPLANATION

The given quadratic function is:

[tex]4 {x}^{2} - 24x - 108[/tex]

To find the zeros, we equate to zero.

[tex]4 {x}^{2} - 24x - 108 = 0[/tex]

Divide through by 4

[tex] {x}^{2} - 6x - 27 = 0[/tex]

Factor to get,

[tex] {x}^{2} + 3x - 9x - 27 = 0[/tex]

[tex]x(x + 3) - 9(x + 3) = 0[/tex]

[tex](x + 3)(x - 9) = 0[/tex]

Use the zero product property,

[tex]x = - 3 \: or \: x = 9[/tex]

Answer:

The time at which the ball will reach its maximum height is t= 3 seconds.

Step-by-step explanation:

To find the the time at which the ball will reach its maximum height,  we need to solve the model given - 3x2 + 18x +7

since h(t) is the height given we can re-write the equation as:

h(t)= -3(t)² + 18t +7

Differentiating the above equation

[tex]\frac{dt}{dh} = -6t + 18[/tex]

When the ball is at maximum height [tex]\frac{dt}{dh}=0[/tex]

0=-6t+18

-18 = -6t

=> t= -18/-6

=> t= 3

the time at which the ball will reach its maximum height is t= 3 seconds.

We can find the maximum height by putting value of t in equation:

h(3) = -3(3)²+ 18(3) +7

h(3)= -27 + 54 + 7

h(3)= 34 ft

Answer:

three seconds

Step-by-step explanation:

Answer:

a triangle will always have 0 parallel sides

Step-by-step explanation:

The answer is probably 14, but I don't know how to prove it correctly, I mean by using the mathematical language. So if it will work, I can try to guess how I got this answer. So if you will draw radiuses, like I did on the screenshot, you will get 2 equal to each other triangles, but the thing is that I have no idea why they should be equal. So if the first step is right the value of x should be equal to 14, as the side below is equal to 14 too. That's it, I guess I helped you at least a little!

The value of x in the chord and arc circle figure is 8[tex]\sqrt{2}[/tex] units.

Given:

Find:

Solution:

As it is given that the radius of the circle is 9 units.

So, from here the diameter is 2*9 units = 18 units.

Now, we will draw a line from A to B, we will then Right triangle.

From the right-angled triangle we can calculate the value of x by Pythagoras Theorem, we get;

[tex]x^{2} = (18)^{2} - (14)^{2}[/tex]

[tex]x^{2} = 324 - 196[/tex]

[tex]x^{2} = 128[/tex]

[tex]x = \sqrt{128} = 8\sqrt{2}[/tex]

Hence, the value of x is 8[tex]\sqrt{2}[/tex] units.

To learn more about chords, refer to:

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Answer:

a) Similar

b) Perimeter of rectangle 2 is k times the Perimeter of rectangle 1 (Proved Below)

c) Area of rectangle 2 is k^2 times the Area of rectangle 1 (Proved Below)

Step-by-step explanation:

Given:

Rectangle 1 has length = x

Rectangle 1 has width = y

Rectangle 2 has length = kx

Rectangle 2 has width = ky

(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?

Rectangle 1 and Rectangle 2 are similar because the angles of both rectangles are 90° and the sides of Rectangle 2 is k times the sides of Rectangle 1. So sides of both rectangles is equal to the ratio k.

(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.

Perimeter of Rectangle = 2*(Length + Width)

Perimeter of Rectangle 1 = 2*(x+y) = 2x+2y

Perimeter of Rectangle 2 = 2*(kx+ky) = 2kx + 2ky

                                          = k(2x+2y)

                                          = k(Perimeter of Rectangle 1)

Hence proved that Perimeter of rectangle 2 is k times the perimeter of rectangle 1.

(c) Write a paragraph proof to show that the area of Rectangle 2 is k^2 times the area of Rectangle 1.

Area of Rectangle = Length * width

Area of Rectangle 1 = x * y

Area of Rectangle 2 = kx*ky

                                  = k^2 (xy)

                                  = k^2 (Area of rectangle 1)

Hence proved that area of rectangle 2 is k^2 times the area of rectangle 1.

Final answer:

Rectangles 1 and 2 are similar due to proportional dimensions. The perimeter of Rectangle 2 is proven to be k times the perimeter of Rectangle 1 by factoring out the scale factor. Similarly, the area of Rectangle 2 is k² times the area of Rectangle 1, as shown by multiplying the scaled dimensions.

Explanation:

(a) Yes, Rectangle 1 and Rectangle 2 are similar because the sides of Rectangle 2 are proportional to the sides of Rectangle 1. This means that the two rectangles have the same shape but different sizes, which is the definition of similarity in geometry.

(b) To prove that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1, consider the perimeter of Rectangle 1, which is 2x + 2y. When each dimension is multiplied by k, the new length is kx and the new width is ky, so the perimeter of Rectangle 2 is 2(kx) + 2(ky) = 2kx + 2ky. Factoring out the common factor of k gives k(2x + 2y), which is k times the perimeter of Rectangle 1.

(c) For the area of Rectangle 2, the area of Rectangle 1 is xy. After scaling by k, the new dimensions of Rectangle 2 are kx and ky, so its area is (kx)(ky) = k²(xy), which shows that the area of Rectangle 2 is k² times the area of Rectangle 1.

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (- 4, - 2)

m = [tex]\frac{-2-2}{-4+2}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2

Answer:

The slope can 1/2 or 0.5

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The slope of a line is defined as ...

slope = (change in y)/(change in x)

Given two points, (x1, y1) and (x2, y2), the slope can be computed using ...

slope = (y2 -y1)/(x2 -x1)

It does not matter which points you call point 1 and point 2. You just need to be consistent.

Using the point values in the order given in the problem statement, we have ...

slope = (4 -6)/(1 -5) = -2/-4

slope = 1/2

ANSWER

C. 9

EXPLANATION

We use the Altitude Theorem,to find the value of a.

According to the altitude theorem, the height of the triangle of the triangle is equal to the geometric mean of the two segment it creates on the hypotenuse.

[tex]6 = \sqrt{4a} [/tex]

Square both sides to get,

[tex]36 = 4a[/tex]

[tex]9 = a[/tex]

The correct choice is option C.

Answer:

C

Step-by-step explanation:

the answer is 9

Answer:

B:  g(x) = x^3 + 1

Step-by-step explanation:

Please  use " ^ " to denote exponentiation:  f(x) = x^3.

This graph starts (increasing) in Quadrant III and grows without bound in Quadrant IV.  It passes thru the origin (0, 0).

If we want to translate the graph 1 unit up, then the function f(x) becomes

g(x) = f(x) + 1, or x^3 + 1.

Answer:B:  g(x) = x^3 + 1

Step-by-step explanation:

Answer:

The most reasonable Answer is *D.) the bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.*

Step-by-step explanation:

Answer:

The answer is D) The bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.

Step-by-step explanation:

The bed bug population has increased because the bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.