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2 years ago

If your bike 8 miles south and then 6 miles east, what is the distance you are from your starting point?

Mathematics

1 answer:

Lady bird [3.3K]2 years ago

8 0

Answer:

<em>14 miles</em>

Step-by-step explanation:

It's still 14 miles no matter which way you go.

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What is the future value of $845 a year for seven years at an interest rate of 11.3 percent? $6,683.95 $6,075.69 $8,343.51 $8,00

k0ka [10]

The future value of cash whose initial value is $845, at the rate of 11.3% for 7 years will be calculated using the compound interest rate, that is:
A=p(1+r/100)^n
where:
A=future amount
r=rate=11.3%=0.113
time=7 years
thus the future value of our cash will be:
A=845(1+0.113)^7
A=845(1.113)^7
A=$1,787.82

7 0

3 years ago

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What are the vertex and xintercepts of the graph of the function below?<br> y=(x + 4)(x-2)

erik [133]

Yo sup??

y=(x+4)(x-2)

to find the x intercept put y=0

0=(x+4)(x-2)

so either x=-4 or x=2

Therefore the graph intersects the x axis at -4 and 2

Lenght of x intercept=|-4-2|=6 units

y=(x+4)(x-2)

=x^2+2x-8

This is an upward opening parabola

To find the coordinates of the vertex we can apply the formula

(-b/2a,-D/4a)

b=2

a=1

D=b^2-4ac

=4-4*1*(-8)

=4+32=36

Vertex=(-2/2*1,-36/4*1)

=(-1,-9)

Hope this helps.

3 0

3 years ago

-6x-4+5x=4<br> What is "x". Please show your work.

4vir4ik [10]

Answer:

first thing to do is combine like terms

now you would have -x-4=4

this is because you added -6x+5x

now you would add 4 to each side

now you would have-x=8

then you would divide the negative because x has to be positive

now you would have x= -8

that is your answer. if you any questions just ask :D

Step-by-step explanation:

5 0

3 years ago

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Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest fo

agasfer [191]

From the recursive rule

$a_n = a_{n-1}-13$

it follows that

$a_{n-1}=a_{n-2}-13 \implies a_n = a_{n-2} - 2\times13$

$a_{n-2}=a_{n-3}-13 \implies a_n = a_{n-3} - 3\times13$

and so on. Notice how the subscript on a on the right side and the coefficient multiplied by 13 add up to n (n - 2 + 2 = n; n - 3 + 3 = n; and so on). If we continue the pattern, we'll end up with

$a_n = a_1 + (n-1)\times13$

so that the explicit rule for the n-th term in the sequence is

$a_n = -2 + 13(n-1) \implies a_n = \boxed{13n-15}$

6 0

2 years ago

On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negativ

worty [1.4K]

Answer:

The rule of the reflection is rx-axis(x, y) → (x, –y) ⇒ 3rd answer

Step-by-step explanation:

Let us revise the reflection on the axes

If point (x , y) reflected across the x-axis , then its image is (x , -y) , the rule of reflection is rx-axis (x , y) → (x , -y)

If point (x , y) reflected across the y-axis , then its image is (-x , y) , the rule of reflection is ry-axis (x , y) → (-x , y)

In Δ LMN

∵ L = (-4 , 2)

∵ M = (-5 , 4)

∵ N = (-2 , 3)

In ΔL'M'N'

∵ L' = (-4 , -2)

∵ M' = (-5 , -4)

∵ N' = (-2 , -3)

The signs of y-coordinates of the vertices of Δ LMN are changed, that means Δ LMN are reflected across the x-axis

∵ The y-coordinate of L is 2 and the y-coordinate of L' is -2

∵ The y-coordinate of M is 4 and the y-coordinate of M' is -4

∵ The y-coordinate of N is 3 and the y-coordinate of N' is -3

∴ Δ LMN is reflected across the x-axis

∴ The image of point (x , y) is (x , -y)

The rule of the reflection is rx-axis(x, y) → (x, –y)

7 1

3 years ago

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