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Tomtit [17]
3 years ago
9

Given ΔDEF : ΔRST, find the scale factor.

Mathematics
2 answers:
LekaFEV [45]3 years ago
8 0

Answer:  The value of x is 12 units and the scale factor is \dfrac{4}{3}.

Step-by-step explanation:  Given that the triangle DEF is similar to the triangle RST.

We are to find the value of x and the scale factor of the dilation.

We know that the corresponding sides of the similar triangles are proportional.

So, we must have

\dfrac{DE}{RS}=\dfrac{EF}{ST}\\\\\\\Rightarrow \dfrac{3}{x}=\dfrac{4}{16}\\\\\\\Rightarrow \dfrac{3}{x}=\dfrac{1}{4}\\\\\Rightarrow x=3\times4\\\\\Rightarrow x=12.

The scale factor is given by

S=\dfrac{\textup{length of a side of the dilated triangle}}{\textup{length of the corresponding side of the original triangle}}\\\\\\\Rightarrow S=\dfrac{RS}{DE}\\\\\\\Rightarrow S=\dfrac{4}{3}.

Thus, the value of x is 12 units and the scale factor is \dfrac{4}{3}.

Grace [21]3 years ago
5 0
The scale factor of DEF : RST is 3/4.

X = 12
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3 years ago
K(t)=10t−19 k=-7 k=-7=<br> Please help
igomit [66]

Answer:

t = 6/5

Step-by-step explanation:

Step 1: Define

k(t) = 10t - 19

k(t) = -7

Step 2: Substitute and Evaluate

-7 = 10t - 19

12 = 10t

t = 6/5

6 0
3 years ago
Richard is given one of four pieces of equal-sized fabric. After using some of his fabric for a project, he has 5/6 of a square
ValentinkaMS [17]

Answer:

Richard used 2\frac{1}{12}\ yd ^2 of fabric for his project.

Step-by-step explanation:

Given:

Total amount of fabric = 11\frac23\ yd^2

Now To convert a mixed fraction to an improper fraction, Multiply the whole number part by the fraction's denominator,  Add that to the numerator,Then write the result on top of the denominator.

11\frac23\ yd^2 can be Rewritten as \frac{35}{3}\ yd^2

Number of pieces fabric was cut = 4

Richard is given one of four pieces of equal-sized fabric.

Amount of fabric Richard was given = \frac14 \times \frac{35}{3}=\frac{35}{12}\ yd^2

Amount of fabric left with Richard = \frac56 \ yd^2

We need to find the amount of fabric Richards used for his project.

Solution:

Now we can say that;

amount of fabric Richards used for his project is equal to Amount of fabric Richard was given minus Amount of fabric left with Richard.

framing in equation form we get;

amount of fabric Richards used for his project = \frac{35}{12}-\frac56

Now we will make the denominator common using LCM we get;

amount of fabric Richards used for his project = \frac{35}{12}-\frac{5\times2}{6\times2} = \frac{35}{12}-\frac{10}{12}

Now Denominator is same so we will solve the numerator.

amount of fabric Richards used for his project  = \frac{35-10}{12}= \frac{25}{12}\ yds^2

\frac{25}{12}\ yds^2 can be rewritten as 2\frac{1}{12}\ yd ^2

Hence Richard used 2\frac{1}{12}\ yd ^2 of fabric for his project.

7 0
3 years ago
Considerando √2=1,4 caculando o valor de 5√2
Stells [14]
The answer would be
8 0
3 years ago
SOMEONE PLEASE HELP ASAP​
zmey [24]

Answer:

The answer would be 15yd^2.

Step-by-step explanation:

The area of a triangle is found by...

A = (L*H) / 2

L = length

H = height

3 0
3 years ago
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