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Alona [7]
3 years ago
14

Find 3 different ratios that are equivalent to 7:3.

Mathematics
2 answers:
ratelena [41]3 years ago
5 0

Answer:

14:6

21:9

28:12

Step-by-step explanation:

Given the initial ratio of 7:3, you can find equivalent ratios by multiplying the two numbers by the same factor:

7 x 2 = 14

3 x 2 = 6

14:6

7 x 3 = 21

3 x 3 = 9

21:9

7 x 4 = 28

3 x 4  = 12

28:12

fgiga [73]3 years ago
4 0

Answer:

jfjgngjgtgjg

Step-by-step explanation:

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Dilate a triangle with vertices (0,0), (0,2) and (2,0) using the scale factor k=3. What is the value of the ratio (new to origin
seropon [69]

Answer:

Part a) The ratio of the perimeters is 3

Part b) The ratio of the areas is 9

Step-by-step explanation:

Part A) What is the value of the ratio (new to original) of the perimeters?

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x-----> the perimeter of the new triangle

y-----> the perimeter of the original triangle

z=\frac{x}{y}

we have

z=3

substitute

\frac{x}{y}=3

Part B) What is the value of the ratio (new to original) of the areas?

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x-----> the area of the new triangle

y-----> the area of the original triangle

z^{2}=\frac{x}{y}

we have

z=3

substitute

\frac{x}{y}=3^{2}

\frac{x}{y}=9}

3 0
3 years ago
Solve the following system of equations by the substitution method.
ruslelena [56]
5x = y + 6 (I)
2x - 3y = 4 (II)
-------------------
We have:
5x = y + 6 → x =  \frac{y+6}{5}

Soon:
2x - 3y = 4 → 2* (\frac{y+6}{5}) - 3y = 4\to \frac{2y+12}{5} - 3y = 4
<span>least common multiple (5)
</span>\frac{2y+12}{5} - 3y = 4\to \frac{2y+12}{\diagup\!\!\!\!\!5} - \frac{15y}{\diagup\!\!\!\!\!5} = \frac{20}{\diagup\!\!\!\!\!5}
2y + 12 - 15y = 20
- 15y + 2y = 20 - 12
- 13y = 8
\boxed{\boxed{y = - \frac{8}{13} }}\end{array}}\qquad\quad\checkmark


4 0
3 years ago
What is (7x)(2+5-10)
algol13
Simplify (2+5-10) and then it's -3 and then (7x)(-3) = -21
5 0
3 years ago
Read 2 more answers
Help me do this …math
Daniel [21]

Step-by-step explanation:

How to find inverse function:

Step 1: Write down equation.

f(x) = 4 \sin(x)  + 3

Remeber Ruler notation that

f(x)=y so we replace y with f(x).

y = 4 \sin(x)  + 3

Next, we must isolate x so first we subtract 3.

y - 3 = 4 \sin(x)

Divide both sides by 4.

\frac{y - 3}{4}  =  \sin(x)

\sin {}^{ - 1} ( \frac{y - 3}{4} )  =  \sin {}^{ - 1} ( \sin(x) )

Remeber that sin^-1x and sin x are inverse functions so they will cancel out to x. So we get

\sin {}^{ - 1} ( \frac{y - 3}{4} )  = x

Swap x and y. So our inverse function is

\sin {}^{ - 1} ( \frac{x - 3}{4} )  = y

If you want another proof: Here's one,

Let plug an a x value for the orginal equation,

4 sin x+3. Let say that

x =  \frac{\pi}{2}

We then would get

4 \sin( \frac{\pi}{2 } )  + 3 = 4 \times (1) + 3 = 4 + 3 = 7

So when x=pi/2, y=7.

By definition of a inverse function, if we let 7 be our input, we should get pi/2. as a output.

So let see.

\sin {}^{ - 1} ( \frac{7 - 3}{4} )  =  \sin {}^{ - 1} ( \frac{4}{4} )  =  \sin {}^{ - 1} (1)  =  \frac{\pi}{2}

So this is the inverse function of 4 sin x+3.

1b. The range of f(x) is [-1,7).

We can use transformations to describe range.

We have

f(x) = 4 \sin(x)  + 3

Parent function is

\sin(x)

with a range of [-1,1].

We then vertical stretch by 4 so we get

4 \sin(x)

and our range will be

[-4,4].

Then we add a vertical shift of 3.

4 \sin(x)  + 3

So our range of 4 sin x+3.

[-1,7].

1c. Domain of a inverse function is the range of the orginal function.

The range of f(x) is [-1,7) so the domain of f^-1(x) is [-1,7].

f(x) domain was restricted to -pi/2 to pi/2 so the range of f^-1(x) is [-pi/2, pi/2]

6 0
2 years ago
You are inviting 30 friends to a party. You know that each person eats, on average,
nika2105 [10]

Answer:

11.25 pizzas

Step-by-step explanation:

We are given that:

There are 30 friends total

Each eat 3 slices

1 pizza has 8 slices

So, with the given information, you can know that

Number of slices pizza that all 30 friends eat = 30*3 = 90 slices

Each pizza have 8 slices so we need 90 slices so we need in total of:

Number of pizzas need = 90/8 = 11.25 pizzas

Hope this help you :3

8 0
3 years ago
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