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Anestetic [448]
2 years ago
5

9 Find the values of r and y. с A 95° B 4x ro D E

Mathematics
1 answer:
Inga [223]2 years ago
4 0

Answer:

  • x = 18°, y = 167°

Step-by-step explanation:

<u>In right triangle sum of two angles is 90°</u>

  • 4x + x = 90°
  • 5x = 90°
  • x = 90°/5
  • x = 18°

<u>Angle y is exterior angle and equals non-adjacent interior angles</u>

  • y = 4x + 95° =
  • 4*18° + 95° =
  • 72° + 95° =
  • 167°
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Simplify using only POSITIVE exponents:
pickupchik [31]

So here are a few rules with exponents that you should know:

  1. Multiplying exponents of the same base: x^m*x^n=x^{m+n}
  2. Dividing exponents of the same base: x^m\div x^n=x^{m-n}
  3. Powering a power to a power: (x^m)^n=x^{m*n}
  4. Converting a negative exponent to a positive one: x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m
<h2>1.</h2>

Firstly, solve the outside exponent:

(2x^3y^7)^{-2}=2^{-2}x^{3*-2}y^{7*-2}=2^{-2}x^{-6}y^{-14}

Next, convert the negative exponents into positive ones:

2^{-2}x^{-6}y^{-14}=\frac{1}{2^2x^6y^{14}}=\frac{1}{4x^6y^{14}}

<u>Your final answer is \frac{1}{4x^6y^{14}}</u>

<h2>2.</h2>

For this, just divide:

\frac{12x^5y^3}{4x^{-1}}=\frac{12}{4}x^{5-(-1)}y^{3-0}=3x^6y^3

<u>Your final answer is 3x^6y^3</u>

<h2>3.</h2>

For this, convert all negative exponents into positive ones:

\frac{r^{-7}b^{-8}}{t^{-4}w}=\frac{t^4}{r^7b^8w}

<u>Your final answer is \frac{t^4}{r^7b^8w}</u>

3 0
4 years ago
Plsss hElpp!!!!! TY!!
kari74 [83]

Given:

A circle with diameter 9 cm.

To find:

The area of the circle.

Solution:

The area of a circle is:

A=\pi r^2                   ...(i)

Where r is the radius.

We know that, the diameter of a circle is twice than its radius.

The diameter of the given circle is 9 cm.

r=\dfrac{9}{2}

r=4.5

Substituting r=4.5, \pi =3.14 in (i), we get

A=(3.14)(4.5)^2

A=(3.14)(20.25)

A=63.585

A\approx 63.6

Therefore, the area of the given circle is 63.6.

4 0
3 years ago
The base of a triangular prism is an isosceles right triangle with a hypotenuse of 72−−√ centimeters. The height of the prism is
Amiraneli [1.4K]

Answer:

Step-by-step explanation:

Surface area = lateral area + 2(area of base)

Lateral area = perimeter of base * height.

Because it is a isosceles right triangle, both sides are equal.

x^{2} +x^{2} = 72

2x^{2} = 72. Divide both sides by 2

x^{2} = 36.  Square both sides.

x = 6.

So the perimeter of the base = 6 + 6 +\sqrt{72} = 20.485281374239

Lateral area = 20.485281374239 * 7 = 143.397 cm^{2}

Area of base is (1/2)base * height.

(1/2)(6)(6) = 18

Using the surface area formula

surface area = 143.397 + 2(18) = 179.4 cm^{3}

4 0
3 years ago
Which of the following is equal to the expression (8x)^-2/3 (27x)¯1/3
LiRa [457]

The equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x

<h3>How to evaluate the expression?</h3>

The expression is given as:

(8x)^-2/3 * (27x)^-1/3

Evaluate the exponent 8^-2/3

(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * (27x)^-1/3

Evaluate the exponent (27x)^-1/3

(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * 1/3(x)^-1/3

Multiply 1/4 and 1/3

(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^-2/3 * (x)^-1/3

Evaluate the exponent

(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-2/3 -1/3)

This gives

(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-1)

So, we have

(8x)^-2/3 * (27x)^-1/3 = 1/12x

Hence, the equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x

Read more about equivalent expression at

brainly.com/question/2972832

#SPJ1

3 0
1 year ago
The combined weight of the people in an elevator is 49% of the 3,025-pound capacity.Which would be the best way to estimate the
klasskru [66]

Answer:

50% of 3000

Step-by-step explanation:

49% is very close to 50% (half).  3,025 pounds is very close to 3,000 pounds.

Half of 3,000 pounds is 1,500 pounds.

3 0
3 years ago
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