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2 years ago

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:

Multiplying exponents of the same base: $x^m*x^n=x^{m+n}$
Dividing exponents of the same base: $x^m\div x^n=x^{m-n}$
Powering a power to a power: $(x^m)^n=x^{m*n}$
Converting a negative exponent to a positive one: $x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m$

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>

For this, just divide:

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For this, convert all negative exponents into positive ones:

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

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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

$A=(3.14)(4.5)^2$

$A=(3.14)(20.25)$

$A=63.585$

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Therefore, the area of the given circle is 63.6.

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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

2 $x^{2}$ = 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.

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Using the surface area formula

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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

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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

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1 year ago

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klasskru [66]

Answer:

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3 years ago