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Licemer1 [7]
3 years ago
9

In triangle MNP if the measure of angle R is five more than twice x, and the measure of angle S is one more than x, and the meas

ure of angle T is sixteen less than seven times x, whats x
Mathematics
1 answer:
Dmitrij [34]3 years ago
6 0

Answer:

x = 19

Step-by-step explanation:

Let's convert the given statements into algebraic expressions.

R is five more than twice x:

R = 2x + 5

S is one more than x:

S = x + 1

T is sixteen less than seven times x:

T = 7x - 16

Also, we know, the sum of 3 angles in a triangle is ALWAYS EQUAL to 180 degrees. Thus we can write:

R + S + T = 180

Substituting the expressions, we have:

2x + 5 + x + 1 + 7x - 16 = 180

Now we do algebra and simply solve for x. Shown below:

2x + 5 + x + 1 + 7x - 16 = 180\\10x-10=180\\10x=180+10\\10x=190\\x=\frac{190}{10}\\x=19

Hence, x = 19

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The triangle and the trapezoid have the same area. Base b2 is twice the length of base b1. What are the lenghts of the bases of
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Answer:

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Step-by-step explanation:

The formula of an area of a triangle:

A=\dfrac{bh}{2}

<em>b</em><em> </em>- base

<em>h</em> - height

We have <em>b = 21cm, h = 6cm</em>.

Substitute:

A=\dfrac{(21)(6)}{2}=63\ cm^2

The formula of an area of a trapezoid:

A=\dfrac{b_1+b_2}{2}\cdot h

<em>b₁, b₂</em> - bases

<em>h</em><em> - </em>height

We have <em>b₁ = 2b₂</em>, therefore <em>b₁ + b₂ = 2b₂ + b₂ = 3b₂</em>.

The area of a triangle and the area of a trapezoid are the same.

Therefore

\dfrac{3b_2}{2}\cdot h=63         <em>multiply both sides by 2</em>

3b_2h=126          <em>divide both sides by 3</em>

b_2h=42         <em>divide both sides by h</em>

b_2=\dfrac{42}{h}

b_1=2b_2\to b_1=2\cdot\dfrac{42}{h}=\dfrac{84}{h}

8 0
2 years ago
Read 2 more answers
Which polynomial is prime?<br> Ox+3x²-x²-3<br> Ox4-3x²-x² + 3<br> O 3x²+x-6x-2<br> O 3x²+x-6x + 3
GarryVolchara [31]

Answer:

The polynomial 3x² + x - 6x + 3  is a prime polynomial

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For a polynomial to be prime, it means that the polynomial cannot be divided into factors

From the list of options, the polynomial (D) is prime, and the proof is as follows:

We have:

3x² + x - 6x + 3

From the graph of the polynomial (see attachment), we can see that the function does not cross the x-axis.

Hence, the polynomial 3x² + x - 6x + 3  is a prime polynomial

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8 0
2 years ago
(x + 4)(3x + 2) = ____________ 2. (3x – 1)(2x – 5) = ____________ 3. (5x + 2)(2x + 5) = ____________ 4. (4x – 1)(2x + 7) = _____
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Answer:

Step-by-step explanation:

Use FOIL method

1) (x +4 )(3x +2) = x*3x + x*2 + 4*3x + 4*2

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2 years ago
Anna wanted to buy a camera. The first discount store sold her favorite camera for $95. The second store sold the same camera fo
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The second store offered the better buy at the price of $92.00.

What is better buy?

Better buy refers to the lowest price out of the prices offered by the three stores.

In order to determine the lowest price, the no discount price of the first store needs to be compared to the prices of  two other stores, bearing that after-discount price is the pre-discount price multiplied by 1 minus the discount rate.

First store price=$95.00

Second store after-discount price=pre-tax discount price*(1-discount rate)

pre-discount price=$115

discount rate=20%

Second store after-discount price=$115*(1-20%)

Second store after-discount price=$92.00

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pre-discount price=$105

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Third store after-discount price=$105*(1-10%)

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(3x+4)-(-8-2x) simplified
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