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3 years ago

One number is five more than twice another. If their sum is decreased by ten, the result is twenty-two. Find the numbers.

Mathematics

2 answers:

Angelina_Jolie [31]3 years ago

8 0

(x+2x+5)-10=22
3x+5=32
3x=27
x=9
So, the numbers are 3 and 11

saveliy_v [14]3 years ago

4 0

X = 2y + 5
(x + 2y + 5) - 10 = 22
(2y + 5 + 2y + 5) = 4y + 10
(4y + 10) - 10 = 22
4y = 22 y = 5.5
x = 2(5.5) + 5 x = 16
x = 16 y = 5.5

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stich3 [128]

6) $\sqrt[4]{16} = 2;$

3 0

4 years ago

For ΔABC, ∠A = 3x - 8, ∠B = 5x - 6, and ∠C = 4x + 2. If ΔABC undergoes a dilation by a scale factor of 1/2 to create ΔA'B'C' wit

Snezhnost [94]

Answer:

D. ∠B = ∠B' = 74° and ∠C = ∠C' = 66°

Step-by-step explanation:

Given,

$\angle A=3x-8\\\angle B=5x-6\\\angle C=4x+2$

We know,sum of all 3 angles of a triangle is $180$ °

Doing so ,

$\angle A+\angle B+\angle C=180\\3x-8+5x-6+4x+2=180$

Simplifying all like terms,

$12x-12=180\\12x-12+12=180+12\\12x=192$

Dividing both side by 12

$x=\frac{192}{12}$

$x=16$

Now we plug this in each angles and find their exact values.

$\angle A=3x-8=(3\times16)-8=48-8=40$ °

$\angle B=5x-6=(5\times16)-6=80-6 =74$ °

$\angle C=4x+2 = (4\times16)+2=64+2=66$ °

Now substituting the $x=16$ in angles of dilated triangle.

$\angle A'=(2\times16)+8=32+8= 40$ °

$\angle B'=90-16=74$ °

$\angle C'=(5\times16)-14=80-14=66$ °

We see that all the corresponding angles are equal and as far as the options are concerned only option (D) matches.

8 0

4 years ago

I can't get the answer!!!! >:(

Rasek [7]

Answer:

The scale factor of the smaller rectangle to the larger rectangle is 3/2

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem

To find out the scale factor of the smaller rectangle to the larger rectangle. set up a proportion

$\frac{9}{6}=\frac{3}{2}$ ----> ratio of corresponding heights

$\frac{12}{8}=\frac{3}{2}$ ----> ratio of corresponding bases

therefore

The scale factor of the smaller rectangle to the larger rectangle is 3/2

7 0

3 years ago

Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. The triangle was dilated using a s

victus00 [196]

Answer:

$A'(-0.25,0.75)\\\\B'(1.75,-0.25)\\\\C'(-1,-0.25)$

Step-by-step explanation:

A Dilation is defined as a transformation in which the image and the pre-image have the same shape, but their sizes are different.

When the scale factor is greater than 1, the image obtained after the dilation is greater than the pre-image and it is an "Enlargement".

When the scale factor is is between 0 and 1, the image obtained after the dilation is smaller than the pre-image and it is an "Reduction".

In this case you know that the triangle ABC was dilated by this scale factor:

$scale\ factor=\frac{1}{4}$

With the origin as the center of dilation.

Since:

$0$

It is a Reduction.

You can identify that the vertices of the triangle ABC are:

$A(-1,3)\\\\B(7,-1)\\\\C(-4,-1)$

So you need to multiply the coordinates of each vertex of the triangle ABC by $\frac{1}{4}$ , in order to get the coordinates of the triangle A'B'C. Then, you get:

$A'=(\frac{1}{4}(-1),\frac{1}{4}(3))=(-0.25,0.75)\\\\B'(\frac{1}{4}(7),\frac{1}{4}(-1))=(1.75,-0.25)\\\\C'(\frac{1}{4}(-4),\frac{1}{4}(-1))=(-1,-0.25)$