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3 years ago

GIVING BRAINLIEST Explain your reasoning. 3(n + 2) = 9(6 - n)

Mathematics

1 answer:

irga5000 [103]3 years ago

8 0

Answer: n = 4

Step-by-step explanation:

Divide both sides by 3

n+2=3(6−n)

Expand

n+2=18−3n

Subtract 2 from both sides

n=18−3n−2

Simplify 18−3n−2 to −3n+16.

n=−3n+16

Add 3n to both sides

n+3n=16

Simplify n+3n to 4n

4n=16

Divide both sides by 4

n= 4/16

Simplify 16/4 to4

n=4

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What are the measures of < 1 and < 2. Show your work or explain your answer.

VashaNatasha [74]

Answer:

m<1 = 105°

m<2 = 75°

Step-by-step explanation:

Since lines c and d are parallel to each other, therefore:

m<2 = 75° (corresponding angles are congruent)

m<1 + m<2 = 180° (linear angle pair)

Substitute

m<1 + 75° = 180°

Subtract 75 from both sides

m<1 = 180° - 75°

m<1 = 105°

4 0

3 years ago

Complete the proof please

____ [38]

Answer:

Step-by-step explanation:

ΔQTU ≅ ΔRSU (congruent triangles)

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

these is the case because in the case the triangle is turned, there is equal sides and angles.

7 0

3 years ago

24 , Factor: x²-9 A (x + 3XX-3) B (x+3)2 с (x-3) (x+3)(x+3)

Katarina [22]

Answer:

(x-3)(x+3)

Step-by-step explanation:

We are given the expression $\displaystyle \large{x^2-9}$ :—

To factor this expression, we have a formula for it which is difference of two squares:—

$\displaystyle \large{a^2-b^2=(a+b)(a-b)}$

You can also swap from $\displaystyle \large{(a+b)(a-b)}$ to $\displaystyle \large{(a-b)(a+b)}$ via multiplication property.

From the expression, factor using the formula above:—

$\displaystyle \large{x^2-9=(x^2)-(3)^2}\\\displaystyle \large{x^2-9=(x-3)(x+3)}$

Therefore, the factored expression is:—

$\displaystyle \large{\boxed{(x-3)(x+3)}}$

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If you have any questions regarding the problem or need clarification of my answer/explanation, do not hesitate to ask in comment!

5 0

2 years ago

Canine hip dysplasia is a degenerative disease that causes pain in many dogs. Sometimes advanced warning signs appear in puppies

nordsb [41]

<h2>Answer with explanation:</h2>

Formula for plus-four confidence interval :

$\hat{p}\pm z^* \sqrt\dfrac{\hat{p}(1-\hat{p})}{n+4}}$

, where n= Sample size.

$\hat{p}$ = Sample proportion and $\hat{p}=\dfrac{x+2}{n+4}$

z* = Critical z-value.

Let p be the proportion of puppies area found with early hip dysplasia.

As per given , we have

n= 42

$\hat{p}=\dfrac{5+2}{42+4}=0.1522$

Since confidence interval is not given , so we assume it as 95% .

z-critical value for 95% confidence is 1.96.

Then, the required confidence interval will become :

$0.1522\pm (1.96)\sqrt{\dfrac{0.1522(1-0.1522)}{42+4}}\\\\ 0.152\pm (1.96)\sqrt{0.002805112173}\\\\ 0.152\pm 0.1038\\\\ =(0.1522- 0.1038 ,\ 0.152+ 0.1038)\approx(0.0484,\ 0.256)$

Hence, the plus four confidence interval for p = (0.0484, 0.256)

Interpretation: We are 95% sure that the true proportion of puppies area found with early hip dysplasia lies in (0.0484, 0.256).

7 0

3 years ago

What is the y-intercept of f(x)=-4x^2+6x-5

Olegator [25]

Answer:

(0, -5)

Step-by-step explanation:

The y-intercept is a point on the y-axis, which is otherwise known as "x=0." Given f(x)=-4x^2+6x-5, replace x with 0 to obtain the y-intercept, (0, -5).

4 0

3 years ago