Write a congruence statement for the pair of triangles. Name the postulate it theorem that justifies your statement.

When asked to find a number one-tenth as large as another number, what operation would you use? What about when asked to find a

kherson [118]

Apply division by 10 when one tenth of a number is required and apply multiplication by 10 when 10 times of a number is required.

<u>Solution:</u>

Need to determine what operation is required to get one-tenth of a number and 10 times of a number

To get one tenth of a number, divide the number by 10.

For example to get one – tenth of 100, divide it by 10, we get 10 as a result.

$\frac{1}{10} \times 100 = 10$

To get ten times of a number, multiply the number by 10

For example 10 times of 10 = 10 x 10 = 100

Hence apply division by 10 when one tenth of a number is required and apply multiplication by 10 when 10 times of a number is required.

6 0

3 years ago

A rectangle has perimeter 28cm. Its area is 42sq.cm. Determine the dimensions of the rectangle. Include a diagram in your soluti

yawa3891 [41]

The dimensions of the rectangle are: b=9.65 cm and h=4.35 cm or b=4.35 cm and h= 9.65 cm.

<h3>Quadrilaterals</h3>

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle is equal to base x height (A=bh). The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter is 2b+2h.

<h3>System of Linear Equations</h3>

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

The question gives:

Perimeter=28cm

Area= 42 cm²

If the perimeter is the sum of all sides of the rectangle, you have:

Perimeter= 2b+2h=28

If the area of the rectangle is 42cm², you have:

Area=bh=42 cm²

You can write a system of linear equations.

2b+2h=28 (1)

bh=42 (2)

From equation 2, you have $b=\frac{42}{h}$ . Then, you can replace it in equation 1.

$2*\frac{42}{h}+2h=28 \\ \\ 84+2h^2=28h\\ \\ 2h^2-28h+84=0 \; dividing\; by\; 2\\ \\ h^2-14h+42=0$

Now, you should solve the quadratic equation.

$h_{1,\:2}=\frac{-\left(-14\right)\pm \sqrt{\left(-14\right)^2-4\cdot \:1\cdot \:42}}{2\cdot \:1}$

$h_{1,\:2}=\frac{-\left(-14\right)\pm \:2\sqrt{7}}{2\cdot \:1}$

$h_1=\frac{-\left(-14\right)+2\sqrt{7}}{2\cdot \:1}=7+\sqrt{7}=9.65 cm$

$h_2=\frac{-\left(-14\right)-2\sqrt{7}}{2\cdot \:1}=7-\sqrt{7}=4.35cm$

If h1=9.65 cm, then $b_1=\frac{42}{9.65} =4.35 cm$ , and if h2=4.35 cm, then $b_1=\frac{42}{4.35} =9.65 cm$ .

Read more about the quadratic function here:

brainly.com/question/1497716

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8 0

2 years ago

The next term of the arithmetic sequence 39,60,81,102,123.....is

Rasek [7]

It is 144 just add 21

6 0

3 years ago

Read 2 more answers

A city official would like to know if there is public support for increasing funding for arts programs. To collect data, the cit

maw [93]

Answer:

I think the answer is either c or d. but i think your answer is good

Step-by-step explanation:

7 0

3 years ago

(−6)^2<br> Need halp please

ziro4ka [17]

This is an EXPONENT.

To do this all we need to do is multiply the base by itself how many times the power says.

(-6)² = (-6) × (-6) = 36

Recall that any negative number times another negative number is positive so that is why this would be positive.

So, (-6)² = 36

Hope I helped ya!!

4 0

3 years ago

Read 2 more answers