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3 years ago

14

In ΔSTU, m∠S=(11x+3)∘,∠T=(2x+16)∘, and m∠U=(x+7)∘. Find .

1 answer:

frozen [14]3 years ago

6 0

Answer:

x = 11

Step-by-step explanation:

In ΔSTU ,

m∠S = (11x+3)° ; m∠T = (2x+16)° ; m∠U = (x+7)°

According to angle sum property of a triangle , sum of all the interior angles of the triangle is 180°.

So,

$11x + 3 + 2x + 16 + x + 7 = 180$

$= > 14x + 26 = 180$

$= > 14x = 180 - 26 = 154$

$= > x = \frac{154}{14} = 11$

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3 years ago

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Answer: X'(-3, -2), Y'(-5, 1), and Z'(2, -3)

Step-by-step explanation:

Upon reflection across the x-axis, the x-coordinates remain the same while the signs of the y-coordinates flip. So, the coordinates will be X(3, -2), Y(5, 1), and Z(-2, -3).

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3 years ago

Evaluate 2.625-(-6)

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3 years ago

LOTS OF POINTS <br> Simplify the expression by factoring, showing the steps in your work

julia-pushkina [17]

Answer:

$\frac{3x+7}{4x+1}$

Step-by-step explanation:

$\frac{12x^2+31x+7}{16x^2+8x+1}$

First you factor $12x^2+31x+7$ :

$=\left(12x^2+3x\right)+\left(28x+7\right)$

Then you factor out $3x$ from $12x^2+3x$ :

$12x^2+3x$

$=12xx+3x$

$=3\cdot \:4xx+3x$

$=3x\left(4x+1\right)$

Then you factor out 7 from $28x+7$ :

$28x+7$

$=7\cdot \:4x+7$

$=7\left(4x+1\right)$

$=3x\left(4x+1\right)+7\left(4x+1\right)$

Factor out common term $4x+1$ :

$=\left(4x+1\right)\left(3x+7\right)$

$\frac{\left(4x+1\right)\left(3x+7\right)}{16x^2+8x+1}$

Factor $16x^2+8x+1$ :

$=4^2x^2+8x+1$

$=4^2x^2+8x+1^2$

$=\left(4x\right)^2+8x+1^2$

$=\left(4x\right)^2+2\cdot \:4x\cdot \:1+1^2$

Use the perfect square formula:

$=\left(4x+1\right)^2$

$\frac{\left(4x+1\right)\left(3x+7\right)}{\left(4x+1\right)^2}$

Cancel out common factor $4x+1$ :

$=\frac{3x+7}{4x+1}$

8 0

3 years ago

What is the surface area of this triangular prism rounded to the nearest tenth? A) 48.6km2 B) 63.4 km2 C) 72.6 km2 D) 84.4 km2

Mekhanik [1.2K]

Correct option B) $63.4km^2$ .

<u>Step-by-step explanation:</u>

We have the following figure attached as shown below.

Now, this triangular prism have 2 similar right angled surfaces and 3 rectangular surfaces , Let's calculate area for all of them:

2 similar right angled surfaces

We know that area of triangle = $\frac{1}{2} b(h)$

⇒ $area = \frac{1}{2} b(h)$

⇒ $area = \frac{1}{2} (3.6)(7.7)$

⇒ $area = 13.86km^{2}$

But there 2 such surfaces so , $area = 2(13.86) = 27.72km^2$

3 rectangular surfaces

Area of rectangle = $length(breadth)$

⇒ $area_1 = 3.6(1.8)$

⇒ $area_1 = 6.48km^2$

⇒ $area_2= 7.7(1.8)$

⇒ $area_2 = 13.86km^2$

⇒ $area_3 = 8.5(1.8)$

⇒ $area_2 = 15.3km^2$

Total area = $6.48 + 13.86 + 15.3 = 35.64km^2$

Adding area of 2 similar right angled surfaces & 3 rectangular surfaces:

$Area = 27.72+35.64 = 63.36km^2$ = $63.4km^2$

Correct option B) $63.4km^2$ .

4 0

3 years ago

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