A figure is dilated by a factor of 3. which statement about the mesurements of the image is true

Zach worked 1,040 hours this year and made $9 per hour. How much money did he earn over the course of the year?

loris [4]

Answer:

$9,360

Explanation:

$9 per hour, rewrite: 1 hour he earned $9

so for 1040 hours, he earned:

$9 * 1,040

$9,360

7 0

3 years ago

Read 2 more answers

If 5x + 2 = 17, then 12x =____?

tensa zangetsu [6.8K]

36

Step-by-step explanation:

5x is 15

x is 3

12 times 3 is 36

7 0

2 years ago

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A geometric progression has a third term of 20 and a sum of infinity which is 3 times the first term. Find the first term

Anna007 [38]

Answer: the first term is 45

Step-by-step explanation:

Step 1: The formular for the nth term is ar^n-1 and since we're solving for the third term ar^3-1 = ar² which is equal to 20

So ar²= 20 and we make this equation i

Step 2: the formular for the sum of infinity is Sn = a/(1-r) and according the question the sum of infinity is equals to 3 *A ( A means the first term)

Further simplification gives us

3a= a/(1-r)

We simplify Futher by multiplying both sides by (1-r)

3a.(1-r) = a/(1-r).(1-r)

3a(1-r)=a

= 3a-3ar=a

Make 3ar the subject of the formula

3ar= 2a and lets make this equation (ii)

Step 3: From the first equation since ar²=20, let's make a the subject of the formula by dividing both sides by r²

Ar²/r² = 20/r²

A=20/r²lets make this equation (iii)

Step 4: subtitle a as 20/r² into equation (ii)

Since 3ar=2a

Then 3.(20/r²).r = 2. 20/r²

= (60/r²) .r = 40/r²

60/r = 40/r2

Multiplying both sides by r² gives us

60r = 40

Divide both sides by 20 gives us

= 3r= 2

Divide both sides by 3 gives us

= r = 2/3

Step 5: substitute r for 2/3 in equation i

ar²= 20

a. (2/3)2 = 20

= a.4/9 = 20

= 4a = 180

= a = 180/4

a = 45

5 0

3 years ago

What is the value of x? Please show step by step.

3241004551 [841]

Start by using trig to find the length of the line LJ

The triangle KJL (big right angled triangle) has been given the following dimensions

Hypotenuse = $8 \sqrt{2}$
The adjacent angle is 30 degrees

Since we have the hypotenuse and the angle we must use the equation
opposite = Sin(angle) x Hypotenuse

Opposite= sin30 x $8 \sqrt{2}$

Opposite= $4 \sqrt{2}$

Therefore line LJ is $4 \sqrt{2}$

Now look at the smaller right angled triangle (LMJ)

Hypotenuse is the line LJ which is $4 \sqrt{2}$

The adjacent angle is 45

Since we have hypotenuse and angle we must use the equation opposite = sin(angle) * h

therefore
x= $4 \sqrt{2}$ * sin45= 4

3 0

3 years ago

Cindy took her five grandchildren to the movies, where she offered to buy all of them popcorn and candy. A popcorn bag costs $4.

Svetradugi [14.3K]

Answer:

She buys 5 boxes of popcorn and 6 boxes of candy

Step-by-step explanation:

this is because 5 times 4.00 is 20$ and 2.50 times 6 is 15$

15 + 20 is 35

so your answer is 5 boxes of popcorn and 6 boxes of candy

hope this helped :D

6 0

3 years ago