Here are two patterns made using identical rhombuses. Without using a protractor, determine the value of a and b. Explain or show your reasoning in your workbook.

Answer:

[tex]\displaystyle f(x)=-\frac{1}{24}\left(x-12\right)^2+6[/tex]

Where f(x) models the height, in inches, of the frog's leap after it had leapt x inches.

Step-by-step explanation:

We are given that a frog leaps two feet, with the highest point in the jump being six inches.

Assuming the frog starts at (0,0), we want to find a quadratic function in vertex form for the path of the jump.

First, we will convert the length of the jump to inches. Two feet is equivalent to 24 inches.

Next, since the frog started at (0, 0), in order to jump a length of 24 inches, it must have ended at (0, 24). These two points will also be our two roots: x = 0 and x = 24. We can use the factored form of a quadratic:

[tex]f(x)=a(x-p)(x-q)[/tex]

Where p and q are the roots.

Substitute in the roots:

[tex]f(x)=a(x-0)(x-24)=ax(x-24)[/tex]

Now, since the frog reached a maximum height of six inches, the y-coordinate of the function at its vertex point is 6.

Since a parabola is symmetrical along its axis of symmetry, the axis of symmetry is always halfway between the two roots.

Therefore, the x-coordinate of our vertex is:

[tex]\displaystyle x=\frac{24-0}{2}=12[/tex]

So, when x = 12, f(x) = 6. Substitute:

[tex]6=a(12)(12-24)[/tex]

Solve for a:

[tex]\displaystyle- 144a=6\Rightarrow a=-\frac{1}{24}[/tex]

Therefore, our function is:

[tex]\displaystyle f(x)=-\frac{1}{24}x(x-24)[/tex]

Now, we can place this into vertex form:

[tex]\displaystyle f(x)=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

Our leading coefficient is -1/24, and the vertex is (12, 6). Hence, our function is:

[tex]\displaystyle f(x)=-\frac{1}{24}\left(x-12\right)^2+6[/tex]

Where f(x) models the height, in inches, of the frog's leap after it had leapt x inches.

Answer:

2(30+x)

Step-by-step explanation:

[tex]55+2x+5\\=60+2x\\=2(x+30) or 2(30+x)[/tex]

Answer: 2 ( 30 + x )

Answer:

41 feet

Step-by-step explanation:

For a radius r, the circumference is [tex]2\pi r[/tex] and the diameter is [tex]2r[/tex], so to get diameter, we can just divide the circumference by pi and we get the answer. Using 3.14 for pi we get:

[tex]127.74 / 3.14 = 41[/tex]

Answer: f(x) = 64 * (3/4)^x

Step-by-step explanation: f(x)=ab^x

When x=0 f(x) = 64

64 = ab^0

b^0 =1 so

64 =a

f(x)=64 b^x

When x=1 f(x) = 48

48 = 64 *b

Divide by 64

48/64 =b

6/8 =b

3/4 =b

f(x) = 64 * (3/4)^x

Answer:

27

Step-by-step explanation:

5(6)-6/2

Answer:

8x^3+2x^2-3x+4

Step-by-step explanation:

8x³ +2x² -3x+4 is the standard form of the  (7x³ + 7x² – 4) + (x³ – 5x² – 3x + 8)

An expression is combination of variables, numbers and operators.

The given expression is  (7x³ + 7x² – 4) + (x³ – 5x² – 3x + 8)

7x³ + 7x² – 4+x³ – 5x² – 3x + 8

In the given expression x is the variable

Plus and minus signs are the operators of the given expression.

Add the like terms in the given expression

8x³ +2x² -3x+4

Hence, 8x³ +2x² -3x+4 is the standard form of the  (7x³ + 7x² – 4) + (x³ – 5x² – 3x + 8)

To learn more on Expressions click:

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Answer:

40.56 in.

Step-by-step explanation:

8 × 3.14 × 1/2 = 12.56 (perimeter for the half circle)

12.56 + 10 + 8 + 10 = 40.56

Answer:

Perimeter = 40.56 inches

Explanation:

The perimeter of a shape is all side lengths added up, so, we know there are sides with the lengths 10 inches, 10 inches, 8 inches, and a semicircle.

To find the perimeter of a semicircle, the formula is

C = πd/2, circumference equals pi times diameter divided by 2 OR C = πr, circumference equals pi times radius.

The diameter is 8, so, filling out the formula, it's

C = 3.14 x 8 /2

C = 25.13/2

C = 12.56

So, adding all the sides up, it's 10 in. + 10 in. + 8 in. + 12.56 in.

Therefore, the answer/perimeter/circumference is 40.56 inches.

This is my second answer so far, I hope it helped!

Answer:

its c

Step-by-step explanation:

Answer: Should be 130

Step-by-step explanation:

A is 80 180-80 is 100. Since it’s an isosceles you can divide by 2 and the two angles would be the same. 100/2 is 50 because two remote interior angles is equal to the exterior angle, 50+80 is 130, d is 130

Answer:

Angle D is 130 degrees

Step-by-step explanation:

180-80=50

Angles b and c are the same and will both be 50 degrees.

The angle of a straight line is 180 degrees.

Since angle c is 50 degrees, then the other angle (d) will have to be 130, so that together the total of the two is 180 degrees.

I hope this helps :)

Answer: Well the image looks like a square so what does not appear to describe this quadrilateral is B; trapezoid. I just don’t know how to explain this but I think it is B. Sorry if I’m wrong but hope this helps.

Answer:

x = 1.5

Step-by-step explanation:

2x = 3

divide both sides by 2

x = 3/2

3 divided by 2 is 1.5 so

x = 1.5

Answer:

1.5

Step-by-step explanation:

[tex]2x = 3 \\ \frac{2x}{2} = \frac{3}{2 } \\ two \: cancle \: by \: two \: then \\ x = \frac{3}{2 } \\ x = 1.5[/tex]

Answer:

[tex]\frac{7}{22}[/tex], the total sum of the money is    

Step-by-step explanation:

1- [tex]\frac{5}{11}[/tex]= [tex]\frac{6}{11}[/tex]

[tex]\frac{6}{11}[/tex]*[tex]\frac{7}{12}[/tex]= [tex]\frac{7}{22}[/tex]

x* [tex]\frac{7}{22}[/tex]= 4500

4500/[tex]\frac{7}{22}[/tex]= about 14142.85

this is what I got out.

Answer:

it is 26

Step-by-step explanation:

hope it helps

Answer:

1= 64 2= 16,536

Step-by-step explanation:

Answer:

It is 16m² because 8 x 2 = 16. And  78 x 212 = 16,536km² because base x height = area.

Step-by-step explanation:

Hello! I see you need help with this problem. I will be giving the answers for each of them from top to bottom!

1. 12

2. 32

3. 7

4. 1

5. 14

Hope this helped:)

Answer:

ok put me brainliest  please

its 215$

Step-by-step explanation:

24-1 = 23

6-1/4 = 5 3/4

23/5 3/4 = 4

The constant is 4, so Vanessa is correct

The answer is:

D. Vanessa is correct because the quotient when dividing the values in the bottom row by the values in the top row is always 4.

Answer:

9300 inches squared

Step-by-step explanation: trust me :)

Answer:

c. no solution

Step-by-step explanation:

i hope this helps :)

Answer:

c

Step-by-step explanation:

they are parallel so they won't intercept. therefore they won't have a solution

Answer:

Step-by-step explanation:

Answer A is not correct because if the kite moves both right and up, the x and y coordinates will change

Answer B is the same as answer A. The kite moved so the coordinates will change.

Answer D is also the same. If the kite moves both on the x and y axis, any angle and distance will change.

Answer C is correct. Since C does not rely on the coordinates, it will always be the same. The position of a shape does not change it´s perimeter.

Answer:

4

Step-by-step explanation: