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2 years ago

Find angle sqr and pqr

Mathematics

1 answer:

steposvetlana [31]2 years ago

8 0

Answer:

The answer is number C

Step-by-step explanation:

$(2x + 6) + (10x - 5) = 61 \\ 12x + 1 = 61 \\ 12x = 60 \\ x = 5 \\ then \\ m < sqr = 2 \times 5 + 6 = 16 \\ m < pqr = 10 \times 5 - 5 = 45$

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Layla emptied out her change jar to buy a new binder for school. She found 147 coins consisting of dimes and nickels that totale

den301095 [7]

Answer:

d + n = 147

0.10d + 0.05n = 11.65

d = 86, n = 61

Step-by-step explanation:

Let

Number of dimes = d

Number of nickels = n

Total coins = 147

Total value = $11.65

d + n = 147 (1)

0.10d + 0.05n = 11.65 (2)

From (1)

d = 147 - n

Substitute d = 147 - n into

0.10d + 0.05n = 11.65

0.10(147 - n) + 0.05n = 11.65

14.7 - 0.10n + 0.05n = 11.65

- 0.10n + 0.05n = 11.65 - 14.7

-0.05n = -3.05

n = -3.05 / -0.05

= 61

n = 61

Substitute n = 61 into

d + n = 147

d + 61 = 147

d = 147 - 61

d = 86

6 0

2 years ago

Look at the graph of the linear function. On a coordinate plane, a line goes through 4 points. Point A is (negative 2, negative

kondor19780726 [428]

Using it's concept, the rate of change between point C and point D is of 2.

<h3>What is the average rate of change of a function?</h3>

The average rate of change of a function is given by the <u>change in the output divided by the change in the input</u>. Hence, over an interval [a,b], the rate is given as follows:

$r = \frac{f(b) - f(a)}{b - a}$

Considering the points of the given linear function, we have that:

Point C: f(1) = 2.

Point D: f(2) = 4.

Hence the rate of change between point C and point D is given by:

r = (4 - 2)/(2 - 1) = 2.

More can be learned about the average rate of change of a function at brainly.com/question/24313700

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4 0

7 months ago

Question:

aivan3 [116]

Answer:

part A) The scale factor of the sides (small to large) is 1/2

part B) Te ratio of the areas (small to large) is 1/4

part C) see the explanation

Step-by-step explanation:

Part A) Determine the scale factor of the sides (small to large).

we know that

The dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

z ----> the scale factor

$\frac{CB}{C'B'}=\frac{CD}{C'D'}=\frac{BD}{B'D'}$

The scale factor is equal to

$z=\frac{CB}{C'B'}$

substitute

$z=\frac{4}{8}$

simplify

$z=\frac{1}{2}$

Part B) What is the ratio of the areas (small to large)?

<em>Area of the small triangle</em>

$A=\frac{1}{2}(2)(4)=4\ units^2$

<em>Area of the large triangle</em>

$A=\frac{1}{2}(4)(8)=16\ units^2$

ratio of the areas (small to large)

$ratio=\frac{4}{16}=\frac{1}{4}$

Part C) Write a generalization about the ratio of the sides and the ratio of the areas of similar figures

In similar figures the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In similar figures the ratio of its areas is equal to the scale factor squared

4 0

3 years ago

2x^3-x^2+x-2 factorize

bekas [8.4K]

Answer:

$(x-1)(2x^2+x+2)$

Step-by-step explanation:

Factorize:

$f(x)=2x^3-x^2+x-2$

<u>Factor Theorem</u>

If f(a) = 0 for a polynomial then (x - a) is a factor of the polynomial f(x).

Substitute x = 1 into the function:

$\implies f(1)=2(1)^3-1^2+1-2=0$

Therefore, (x - 1) is a factor.

As the polynomial is cubic:

$\implies f(x)=(x-1)(ax^2+bx+c)$

Expanding the brackets:

$\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c$

$\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c$

Comparing coefficients with the original polynomial:

$\implies ax^3=2x^3 \implies a=2$

$\implies (b-a)x^2=-x^2 \implies b-2=-1 \implies b=1$

$\implies -c=-2 \implies c=2$

Therefore:

$\implies f(x)=(x-1)(2x^2+x+2)$

Cannot be factored any further.

4 0

2 years ago

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Seclate all the numbers that are solutions to the inequalitt w>1.

natima [27]

Answer:

The numbers should be A. 5 and C. 0.

Hope I Helped

6 0

2 years ago

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