2. A pole casts a shadow that is 15 feet long. A 6-foot tall man casts a shadow that is 5 feet long.
What is the height of the pole?

14 feet
17 feet
12.5 feet
6 feet

Answer:

[tex]\frac{4\sqrt{6}-\sqrt{15}}{27}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{6} }{8+\sqrt{10} } \\\\\mathrm{Multiply\:by\:the\:conjugate}\:\frac{8-\sqrt{10}}{8-\sqrt{10}}\\=\frac{\sqrt{6}\left(8-\sqrt{10}\right)}{\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)}\\\\\sqrt{6}\left(8-\sqrt{10}\right)=8\sqrt{6}-2\sqrt{15}\\\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)=54\\\\=\frac{8\sqrt{6}-2\sqrt{15}}{54}\\\\\mathrm{Factor}\:8\sqrt{6}-2\sqrt{15}:\quad 2\left(4\sqrt{6}-\sqrt{15}\right)\\\\=\frac{2\left(4\sqrt{6}-\sqrt{15}\right)}{54}\\[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4\sqrt{6}-\sqrt{15}}{27}[/tex]

Answer: The car travels 97.5 miles in 1.5 hour.

Step-by-step explanation:

Given: A car is traveling down a highway at a constant speed, described by the equation , described by the equation [tex]d=65t[/tex], where represents the distance, in miles, that the car travels at this speed in t hours.

To find : Number of miles car travel in 1.5 hour.

Simply put t= 1.5 in the given expression , we get

65(1.5)= 97.5

That means , the car travels 97.5 miles in 1.5 hour.

Answer:Answer:

d=√

−2x2+y

900f4i2n2x

or d=−√

−2x2+y

900f4i2n

Step-by-step explanation:

Let's solve for d.

y=2x2+9xfindf(10)findf(10)

Step 1: Flip the equation.

900d2f4i2n2x+2x2=y

Step 2: Add -2x^2 to both sides.

900d2f4i2n2x+2x2+−2x2=y+−2x2

900d2f4i2n2x=−2x2+y

Step 3: Divide both sides by 900f^4i^2n^2x.

900d2f4i2n2x

900f4i2n2x

=

−2x2+y

900f4i2n2x

d2=

−2x2+y

900f4i2n2x

Step 4: Take square root.

d=√

−2x2+y

900f4i2n2x

or d=−√

−2x2+y

900f4i2n2x

2x

Answer:

d=√

−2x2+y

900f4i2n2x

or d=−√

−2x2+y

900f4i2n

The value of f(10) for function f(x) = 2x² + 9x is 290.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given function is,

f(x) = 2x² + 9x     (1)

To find the value of f(10),

Substitute x = 10,

f(10) = 2(10)² + 9(10)

f(10) = 2 x 100 + 90

f(10) = 200 + 90

f(10) = 290

The required value of f (10) is 290.

To know more about Algebraic expression on:

https://brainly.com/question/19245500

#SPJ3

Answer:

59

Step-by-step explanation:

the inside of a triangle is 180° so add 57+64 which brings u to 121 and then take 180-121 to get the answer of 59

Answer:

they are all equivilent

Step-by-step explanation:

Answer:

B. 0.8, 0.80, 0.800

Step-by-step explanation:

Answer: I do think the answer is C

Step-by-step explanation: I agree with your choice.

Answer:

(-3, -2)

Step-by-step explanation:

Please see the attached pictures for the full solution.

Answer:

who knows what is the whole question

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

(4 +3) ×(7-1) =

7 ×6 =

42

Answer:

Exact Form:

2/45

Decimal Form:

0.04 (4 being repeated)

Answer:

B

Step-by-step explanation:

So we want to find the value of x.

Note that the entire segment (JK) is the sum of the segments JI and IK. In other words:

[tex]JK=JI+IK[/tex]

We know that JK is (2x-1), JI is (2), and IK is (x+3). Substitute:

[tex]2x-1=(2)+(x+3)[/tex]

On the right, add:

[tex]2x-1=x+5[/tex]

Add 1 to both sides:

[tex]2x=x+6[/tex]

Subtract x from both sides. The right cancels:

[tex]x=6[/tex]

And the value of x is 6.

Our answer is B.

Answer:

What work are you referring to

Answer:

Yes, that is true, and x=45.

Step-by-step explanation:

Yes, that's how you set up the equation I also listed the sets to solve it below:

3x+15=2x+60

-2x.     -2x

--------------------

x+15=60

  -15 -15

------------------

x=45

You can also plug it in to check your work.

3(45)+15=2(45)+60

135+15=90+60

150=150

Answer:the answer is 1/10

Step-by-step explanation:

Answer:

y= 4(x) + 3(5x)

$19

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

H.

f = 3x + 31

c = 12x - 1

3x + 31 + 12x - 1 = 180

15x + 30 = 180

15x = 150

x = 10

same-side interior, supplementary

R.

b = x - 10

g = 4x + 60

x - 10 + 4x + 60 = 180

5x + 50 = 180

5x = 130

x = 26

same-side exterior, supplementary

E.

d = 2x + 13

e = 7x + 5

2x + 13 + 7x + 5 = 180

9x + 18 = 180

9x = 162

x = 18

same-side interior, supplementary

I.

a = 10x - 30

e = 8x + 20

10x - 30 = 8x + 20

2x = 50

x = 25

corresponding, congruent

G.

b = x + 30

h = 5x - 14

5x - 14 = x + 30

4x = 44

x = 11

alternate exterior, congruent

Answer:

750 miles

Step-by-step explanation:

Ronald

Rental fee = fixed cost + variable cost

= $25 + $0.05x

Where x = number of miles

Dixon

Rental fee = fixed cost + variable cost

= $40 + $0.03x

How many miles must they both drive for their rental fees to be the same?

Equate the two equations

$25 + $0.05x = $40 + $0.03x

Collect like terms

0.05x - 0.03x = 40 - 25

0.02x = 15

Divide both sides by 0.02

x = 15 / 0.02

= 750 miles

Answer:

0.8

Step-by-step explanation:

"percent" means "per 100" which is the same as "divide by 100."

To change a percent to a decimal, divide the percent by 100.

80% = 80/100 = 0.8

Answer:

Step-by-step explanation:

Exact Form:

565

32

Decimal Form:

17.65625

Mixed Number Form:

17 21/32

Answer:

Step-by-step explanation:

If an elephant charged 13.3 meters in 15 seconds, to calculate the distance charged by the elephant in one minute, the following steps will be arried out.

15 seconds = 13.3 meters

1minute (60 seconds) = x

cross multiply

15 * x = 13.3 * 60

15x = 798

Divide both sides by 15

15x/15 = 798/15

x = 53.2metres

Hence the elephant will charge 53.2 meters for 1 minute

Answer:

5 weeks its 40 divided by 8

Step-by-step explanation:

Answer:

147 maybe?

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

A = s × s = s²

Given s = 7 , then

A = 7² = 49 in²

Answer:

XW since it matches the same as IH  

Step-by-step explanation:

example if it asked another question saying what corresponds with XY. XY is on the last part of the statement so it would  correspond with IJ

Answer:

this is probably a trick question but it should be 6 feet deep

Step-by-step explanation:

sorry if it's wrong but good luck :)

Answer:

6ft

Step-by-step explanation:

Assuming you are starting at ground level and not inside another hole, if you dig 6ft, then that hole will be 6ft.

Cheers.

Answer:

A=3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

itttttttttttttt isssssssssss =3