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3 years ago

For what value of a is (a,9) a solution for the equation y=2x+1?

Mathematics

1 answer:

Ivahew [28]3 years ago

5 0

Answer:

Step-by-step explanation:

(a,9).......we dont know " a " (or x) but we do know y...it is 9

so sub in 9 for y and solve for x

y = 2x + 1

9 = 2x + 1

9 - 1 = 2x

8 = 2x

8/2 = x

4 = x <======= ur answer is D

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This question is from the similarity chapter. It would be really kind of you if you would answer this question.

katen-ka-za [31]

Answer:

a) 1650 m

b) 1677.05 m

Step-by-step explanation:

Hi there!

1) Determine what is required for the answers

For part A, we're asked for solve for the horizontal distance in which the road will rise 300 m. In other words, we're solving for the distance from point A to point C, point C being the third vertex of the triangle.

For part B, we're asked to solve for the length of the road, or the length of AB.

2) Prove similarity

In the diagram, we can see that there are two similar triangles: Triangle AXY and ABC (please refer to the image attached).

How do we know they're similar?

Angles AYX and ACB are corresponding and they both measure 90 degrees
Both triangles share angle A

Therefore, the two triangles are similar because of AA~ (angle-angle similarity).

3) Solve for part A

Recall that we need to find the length of AC.

First, set up a proportion. XY corresponds to BC and AY corresponds to AC:

$\frac{XY}{BC}=\frac{AY}{AC}$

Plug in known values

$\frac{2}{300}=\frac{11}{AC}$

Cross-multiply

$2AC=11*300\\2AC=3300\\AC=1650$

Therefore, the road will rise 300 m over a horizontal distance of 1650 m.

4) Solve for part B

To find the length of AB, we can use the Pythagorean theorem:

$a^2+b^2=c^2$ where c is the hypotenuse of a right triangle and a and b are the other sides

Plug in 300 and 1650 as the legs (we are solving for the longest side)

$300^2+1650^2=c^2\\300^2+1650^2=c^2\\2812500=c^2\\1677.05=c$

Therefore, the length of the road is approximately 1677.05 m.

I hope this helps!

3 0

3 years ago

A new skateboard cost $150. You have a 30% off coupon how much money did you save with your coupon?

insens350 [35]

150 x .30 = 45

You saved $45 if you use the coupon for the skateboard

5 0

3 years ago

Katie has read 32% of a book. If she has read 80 pages, how many more pages does Katie have left to read? Please explain

yawa3891 [41]

Keep note of these things before we start:
-Of is a keyword that tells us multiplication is being done
-x = total number of pages
-32% = 32/100 = .32

Okay, here we go:
32% of total number of pages = 80
.32 of x = 80
.32*x = 80
.32x = 80
.32x/.32 = 80/.32
x = 250

There are 250 pages in total in Katie's book.
To find out how many pages she has to read (y), subtract the pages read from the total:
TOTAL - PAGES READ = PAGES LEFT TO READ
250 - 80 = y
170 = y

Katie has 170 pages left to read
Hope this helps!

8 0

3 years ago

Last question of my homework pls <3

dimaraw [331]

Answer:

J(2, 5 )

Step-by-step explanation:

Using the section formula

$x_{J}$ = $\frac{1(-2)+2(4)}{2+1}$ = $\frac{-2+8}{3}$ = $\frac{6}{3}$ = 2