What are the coordinates of the image of the point after a dilation by a scale factor of 3 with the origin as the center of dilation, followed by a translation over the -axis?

Given:

Three integers, a, b, and c, where c is a positive integer.

The product of a and b is 6.

The product of a and c is -4.

The product of b and c is -6.

To find:

The values of a,b and c.

Solution:

According to the given information:

[tex]ab=6[/tex]        ...(i)

[tex]ac=-4[/tex]       ...(ii)

[tex]bc=-6[/tex]      ...(iii)

From (ii), we get

[tex]a=-\dfrsc{4}{c}[/tex]          ...(iv)

From (iii), we get

[tex]b=-\dfrsc{6}{c}[/tex]         ...(v)

Putting [tex]a=-\dfrsc{4}{c}[/tex]  and [tex]b=-\dfrsc{6}{c}[/tex] in (i), we get

[tex]\dfrac{-4}{c}\times \dfrac{-6}{c}=6[/tex]

[tex]\dfrac{24}{c^2}=6[/tex]

[tex]\dfrac{24}{6}=c^2[/tex]

[tex]4=c^2[/tex]

Taking square root on both sides, we get

[tex]\pm \sqrt{4}=c[/tex]

[tex]\pm 2=c[/tex]

It is given that c is a positive integer. So, it cannot be negative and the only value of c is [tex]c=2[/tex].

Putting [tex]c=2[/tex] in (iv), we get

[tex]a=-\dfrsc{4}{2}[/tex]

[tex]a=-2[/tex]

Putting [tex]c=2[/tex] in (v), we get

[tex]b=-\dfrsc{6}{2}[/tex]

[tex]b=-3[/tex]

Therefore, the values of a,b,c are [tex]a=-2,b=-3,c=2[/tex].

Answer:

81.25%

Step-by-step explanation:

58-32=26

26/32=0.8125

0.8125x100=81.25

Sorry I'm not that good at explaining but here is something that helped me.

Answer: first would be 6 the next would be 12 then the next would be 18 and so on just add 6 for each one and for ten pizzas it would be 6*10 and that equals 60 im sure you get it

Answer:

C

Step-by-step explanation:

You have 2 totals so the number of males + females = 127 so x + y = 127

Then there are 23 more males than females, it did not say 23 times more so B is out, so the female number + 23 = male number so y + 23 = x

Therefore letter C is the answer.

Answer:

D: distance around the edge of the swimming pool

Step-by-step explanation:

perimeter is the distance around something.

Step-by-step explanation:

Perimeter is used to find out the boundary of any thing or figure...So,

Option D Distance around the edge of a swimming pool. is correct answer.

Answer:

I don't think so. Because what if that specific family member never checks their email. I think a good way would have been to email more than one or every person in that family (now since its extended you might not know everyone so just as many as you know of)

Answer:

4 quarts = 1 gallon

Step-by-step explanation:

Hope that hleps

1 quart = 1/4 gallon

Multiply the number of quarts by 4 to find the number of gallons.

Answer:

Answer: 10240

Step-by-step explanation:

640 x 16 = 10240

1 Pound = 16 Ounces

Answer:

he saves 3 dollars. its not worth it.

Step-by-step explanation:

you divide 12 by ten getting you 1.2 which you subtract from 1.50 that then multiply that by 10

Answer:

4

Step-by-step explanation:

She can buy 4 bracelets because 4 x 9.50 = 38 + 12 = 50. So 4 would fit her budget perfectly without going over. LEt me know if you find any fault in my answer! Thanks! Have a good day! Hope this helps!

Answer:

v fggfbfgbfgbgbfgb

Step-by-step explanation:fgfgbgfbfg

Answer:

b=312

g=396

you can use substitution or elimination

Step-by-step explanation:

(b+g=708)10

(15b+10g=8640)1

(10b+10g=7080)-

(15b+10g=8640)

10b-15b=-1560

-5b=-1560

divide both sides by -5

b=312

then substitute

b+g=708

312+g=708

g=708-312

g=396

so b=312

g=396

Answer:

a) 72.25sec

b) 6.25secs

c) after 10.5secs and 2 secs

Step-by-step explanation:

Given the height reached by the rocket expressed as;

s(t)= -4t^2 + 50t - 84

At maximum height, the velocity of the rocket is zero i.e ds/dt  = 0

ds/dt = -8t + 50

0 = -8t + 50

8t = 50

t = 50/8

t = 6.25secs

Hence it will reach the maximum height after 6.25secs

To get the maximum height, you will substitute t - 6.25s into the given expression

s(t)= -4t^2 + 50t - 84

s(6.25) = -4(6.25)^2 + 50(6.25) - 84

s(6.25) = -156.25 + 312.5 - 84

s(6.25)  = 72.25feet

Hence the maximum height reached by the rocket is 72.25feet

The rocket will reach the ground when s(t) = 0

Substitute into the expression

s(t)= -4t^2 + 50t - 84

0 = -4t^2 + 50t - 84

4t^2 - 50t + 84 = 0

2t^2 - 25t + 42 = 0

2t^2 - 4t - 21t + 42 = 0

2t(t-2)-21(t-2) = 0

(2t - 21) (t - 2) = 0

2t - 21 = 0 and t - 2 = 0

2t = 21 and t = 2

t = 10.5 and 2

Hence the time the rocket will reach the ground are after 10.5secs and 2 secs

Answer:

the top answer or A. if it was labeled

Step-by-step explanation:

because my guy it is simple math

Answer:

i honestly dont know

Step-by-step explanation:

Given:

15 is decreased by three times a number, the result is 21.

To find:

The equation for the given statement and solve it.

Solution:

Let n be the unknown number. Then,

Three times of a number = [tex]3n[/tex]

15 is decreased by three times a number = [tex]15-3n[/tex]

It is given given that the result after subtraction is 21. So,

[tex]15-3n=21[/tex]

[tex]-3n=21-15[/tex]

[tex]-3n=6[/tex]

Divide both sides by -3.

[tex]n=\dfrac{6}{-3}[/tex]

[tex]n=-2[/tex]

Therefore, the required equation is [tex]15-3n=21[/tex] and its solution is [tex]n=-2[/tex]. Hence, the correct option is (a).

Answer:

a

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

KL = 12

LM = 9

12 + 9 = 21

KM = 21

Answer:

c

Step-by-step explanation:

Answer:

a,a,d

Step-by-step explanation:

the formula has been given

Answer: The answer is C (sorry if this might be wrong I tried to do the math and I got C)

Step-by-step explanation:

Answer:

The domain represents the time of motion of the meteor as it falls from 100 km height above the Earth's surface at a speed of 20 km

Step-by-step explanation:

The given parameters from the question are;

The elevation of the meteor above the Earth's surface = 100 km

The rate at which the meteor falls = 20 km per second

The 'x' values represent the time in seconds and the 'y' values represent the meteor's height

Therefore, we have;

y = 100 - 20·x

The domain of a function is the set of inputs to the function

Therefore, the domain represent the time it takes the meteor to reach the given 100 km height above the Earth's surface

At the start x = 0 seconds

On the Earth's surface, y = 0, therefore;

0 = 100 - 20·x

x = 100/20 = 5

When the meteor just touches the Earth's surface x = 5 seconds

Therefore, the domain is 0 ≤ x ≤ 5.

Answer:

x = 17.1°

Step-by-step explanation:

tan x = 4/13 = 0.3077

x = 17.1°

The measure of the angle θ from the given triangle is 17.9°.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given triangle, AC=13 and BC=4 units.

We know that, sinθ=Opposite/Hypotenuse

sinθ= 4/13

sinθ= 0.3076

θ=17.9°

Therefore, the measure of the angle θ from the given triangle is 17.9°.

Learn more about the trigonometric ratios here:

brainly.com/question/25122825.

#SPJ2

Answer:

Didn't finish sorry. I wish I could help.