there were n signers of the declaration of independence. the oldest was benjamin franklin, who was y years old. 7 is 10% of y. what was franklins age

Answer:

The rate of change of relationship 'b' is 2.5 times greater than the rate of change of relationship 'a'

Step-by-step explanation:

The given parameters are;

The function representing relationship 'a' is y = 9·x

Some values of relationship 'b' are;

(0, 0), (3, 34.5), (5, 57.5), and (8, 92)

For direct proportionality of relationship 'b' we have;

y = k₂·x

∴ k₂ = y/x

∴ k₂ = 34.5/3 = 23/2

57.5/5 = 23/2

92/8 = 23/2

k₂ = 23/2

Therefore, the direct proportionality relationship of relationship 'a' is y = 9·x

∴ k₁ = 9

Therefore, the rate of change of relationship 'b' is k₂ - k₁ = (23/2) - 9 = 2.5 times greater than the rate of change of relationship 'a'.

The value of h(a -4) is -a² + 8a - 8

A function can be defined as an expression or rule that explains the relationship between a dependent and an independent variable.

Given the functions;

To determine  h(a-4), we substitute the value of x as a - 4 in the h(x) function, we have;

h(a - 4) =- (a - 4)² + 8

expand the bracket

h(a - 4) = - ( a - 4)(a - 4) + 8

h(a - 4) = - (a²- 4a - 4a + 16) + 8

collect like terms

h(a - 4) = - a² + 8a -16 + 8

h(a - 4) = -a² + 8a - 8

Thus, the value of h(a -4) is -a² + 8a - 8

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Answer:

She will need 9 baskets.

(The exact answer is 8.84 but you can't have an eighth of a basket)

Answer:

one side would be 11 inches and the other side would be 7  

Step-by-step explanation:

7 is 4 inches shorter than 11 and the board is 18 inches so when you add 11 and 7 you get 17

Answer:

18 divided by 2= 9

Take one out if the two 9's and minus 4 from only one of them.

9-4=5

Now you have the answer!

Answer: 9 and 5

Hope this helped! :)

Answer:

a) 1.6

b)1.875

Step-by-step explanation:

Answer:

a) 5/8, 0r 0.625

b)15/8, or. 1.875, or 1 7/8

Answer:

it should be 15

Step-by-step explanation:

Answer:

15 units

Step-by-step explanation:

Since the x- coordinates of both points are the same, then calculate the distance between the y- coordinates using the absolute value, that is

d = | - 8 - 7 | = | - 15 | = 15 , or

d = | 7 - (- 8) | = | 7 + 8 | = | 15 | = 15

Answer: 72

Step-by-step explanation: 6*2=12 6*10=60 Normally you would divide by 2 to get triangles but since there are two of each, you don't.

Answer:

Solution given:

diagonal 1=AC=6+6=12units

diagonal 2=BD=2+10=12units

area of polygon (rhombus)=½*(diagonal 1*diagonal 2)

=½(12*12)=12*6=72square units

Area=72square units

Answer:

A=750

B=1250

Step-by-step explanation: I got it right on edge.

Answer: 16

Add all the matches

Answer:

There will be 17 sticks

Step-by-step explanation:

Answer:

80 cm^3 = V

Step-by-step explanation:

The volume of a rectangular pyramid of base area A and height h is

V = (1/3)(base)(height).

Given that the dimensions of the base are L = 10 cm and W = 4 cm, the base area is 40 cm^2.

The height of the pyramid is h = 6 cm.

Therefore the volume of this particular pyramid is

V = (1/3)(40 cm^2)(6 cm), or V = 80 cm^3

hope it helps

im not sure about it

Answer:

y= -x+4

4= 2x-8

Answer:

Shoot I'm down. what you wanna talk about

Answer:

17 wraps

Step-by-step explanation:

Given data

let the  number of vegetarian wraps be x

and chicken wraps be y

so

x+1.5y= 149------------1

and

x+y= 105----------------2

the systems of equation for the problem is

x+1.5y= 149

x+y= 105

from 2

x= 105-y

put this in 1

105-y+1.5y= 149

105-0.5y= 149

-0.5y= 149-105

-0.5y=44

y= 44/0.5

y= 88

put y = 88 in 2

x+88= 105

x= 105-88

x= 17

Answer:

The value in 2006 is 366,025

Step-by-step explanation:

Here, we want to get the value of y in 2006

what we have to do here is to find and substitute the missing value of x

The missing value x is the difference between the number of years in 2002 and 2006

we have this as 2006-2002 = 4

so we have to substitute 4 here for x

Thus, we have this as;

y = 250,000(1.1)^4

y = 366,025

Answer:

± 6

Step-by-step explanation:

Given

[tex]\sqrt{32+4}[/tex]

= [tex]\sqrt{36}[/tex]

= + 6 or - 6 , that is ± 6

Answer:

√{32+4}=√36=√6²=±6 is your answer

Answer:

your answer is correct its option B

Step-by-step explanation:

hope it's helpful...

have a great day

Answer:

distance

Step-by-step explanation:

Point B must be the same distance from the origin as point A​.

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

Given that,

Point B is the image of the point A when A is rotated 90° counterclockwise around the origin.

A point P(x, y) after the rotation of 90°counterclockwise around the origin is P'(-y, x).

So the x coordinate changes to the negative of y coordinate and y coordinate changes to x coordinate.

Distance between P(x, y) from origin (0, 0) is √(x² + y²)

Similarly the distance P'(-y, x) from origin (0, 0) is √((-y)² + x²) = √(x² + y²)

Hence they are at the same distance.

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Answer:

Step-by-step explanation:

Diameter (d) = 5cm

Radius ( r) = d/2 = 5 / 2 = 2.5

Now

Area

= πr²

= 3.14 * (2.5)²

= 19.625 m²

Circumference

= πd

= 3.14 * 5

= 15.7 m

Hope it will help :)

Answer:

[-5,1] or [-4,5]

Step-by-step explanation:

Here, we want to get the intervals over which there is an average rate of change of zero for f

For this to happen, over the given interval, there will not be a change in the y-axis value

What this mean is that the y-axis value will remain the same over this given interval

for x = -5 to x = 1, we have this

for x = -4 to x = 5 , we have this

Answer:

I am not sure , but my answer would be 42.5° .

Answer:

Step-by-step explanation:

Exponential equations have the form of a geometric sequence

[tex]y=ar^x\text{ y=final value, a=initial value, r=common ratio, x=term number}\\ \\ \text{The common ratio is found by dividing any term by the previous term, in this case}\\ \\ r=\frac{1}{3},\ a=27\\ \\ f(x)=27\left(\frac{1}{3}\right)^x[/tex]

Answer:

Step-by-step explanation:

See the attached

All given details are reflected in the diagram (not to scale)

Use the law of sines:

Answer:

We know that Amber decided to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, and after this, the function representing the photo shares is:

f(x) = 3*(4)^x + 45

We do not know the initial function, but with the given information we can assume that the original equation is:

g(x) = 3*(4)^x

Then the new function is:

f(x) = g(x) + 45.

This is a vertical translation, remember that for a function h(x), a vertical translation of N units is written as:

k(x) = h(x) + N

if N is positive, we have a translation of N units up

if N is negative, we have a translation of N units down.

in this case we have;

f(x) = g(x) + 45

This means that f(x) is a vertical translation of 45 units of g(x), then:

the graph of the new function is 45 units above the original function.

Answer: I think it is 10364 or 10248 because when i put it in a calculator I got 8803.4 or 10296

Step-by-step explanation:

Answer:

t=-19/7

Step-by-step explanation:

you need to isolate for t which means you need to get t all alone on one side of the equation. Do do that you can divide both sides by 7. This gives you -19/7=7t/7

we know that anything divided by itself is 1 so we get -19/7=t

This is the simplest for because 19 and 7 are both prime numbers, so you can't simplify them.

Answer:

28.4 kg

Step-by-step explanation:

F = ma

F is 25 N and a is 0.88 m/s^2

25 = 0.88m

Divide both sides by 0.88

m = 28.4 kg

The mass of an object is 28.4 kg.

It is required to find the mass of an object.

The capacity to do work or cause physical change; energy, strength, or active power. The push or pull on an object with mass causes it to change its velocity. Force is an external agent capable of changing a body's state of rest or motion. It has a magnitude and a direction.

Given:

Net force = 25 N

Acceleration=0.88 m/s^2

According to given question we have,

F = ma

25 = 0.88m

Divide both sides by 0.88

m = 28.4 kg

Therefore, the mass of an object is 28.4 kg.

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Answer:

10[tex]\sqrt{3}[/tex], or 17.32050

Step-by-step explanation: