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3 years ago

Find the value of x and the unknown angle in each problem

Mathematics

1 answer:

Gnom [1K]3 years ago

4 0

Hello!

Angle POQ and angle MON are vertical which means they are congruent

x - 28 = 149

Add 28 to both sides

x = 177

Angle NOQ and angle NOM are supplementary meaning they add to 180

NOQ + NOM = 180

Put in the known angle

NOQ + 149 = 180

Subtract 149 from both sides

NOQ = 31

The answers are x = 177 and angle NOQ = 31

Hope this helps!

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An architect wants to draw a rectangle with a diagonal of 13 centimeters. The length of the rectangle is to be 3 centimeters mor

butalik [34]

Answer:

The rectangle is 3.2 cm by 12.6 cm

Step-by-step explanation:

See attached image for a diagram.

Choose w to represent the width because the length is described by referring to the width: it's 3 more than (add 3) triple (multiplied by 3) the width.

Length = 3w + 3

The diagonal forms two right triangles, each with leg = w, other leg = 3w + 3, hypotenuse = 13.

The Pythagorean Theorem says $(\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2$ so

$w^2+(3w+3)^2=13^2\\\\w^2+9w^2+18w+9=169\\\\10w^2+18w-160=0\\\\5w^2+9w-80=0\\$

Now solve using the Quadratic Formula with $a=5,\,b=9,\,c=-80$ .

$w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-9\pm\sqrt{81+1600}}{10}\\\\w=\frac{-9\pm\sqrt{1681}}{10}\\\\w=\frac{-9\pm41}{10}\\\\w=-5\text{ or }w=3.2$

The negative root makes no sense as a distance, so the width of the rectangle is 3.2 cm. The length is 3(3.2) + 3 = 12.6 cm.

5 0

3 years ago

The San Andreas fault separates the pacific plates from the North America plate. The pacific plate moved northward relative to t

lesantik [10]

Answer:

The time, t it will take LA and San Francisco to be next to each other is 8,245,614.04 years which is over 8 million years

Step-by-step explanation:

The given parameters are;

The speed with which the pacific plate moved northward relative to the North American plate = 5.7 cm/year = 5.7 × 10⁻⁵ km/year

The distance between current LA and San Francisco = 470 km

From the formula for speed, s, we have

Speed = Distance/Time

Therefore, Time, t = Distance/Speed

The time, t it will take LA and San Francisco to be next to each other is given as follows;

t = (Distance between LA and San Francisco)/(The speed with which the pacific plate)

t = (470 km)/(5.7 cm/year) = 470/(5.7 × 10⁽⁻⁵⁾) = 8245614.04 years

Therefore, the time, t it will take LA and San Francisco to be next to each other is 8245614.04 years.

6 0

3 years ago

Find the measure of angle A.

ioda

-30 i believe. If it’s wrong sorry

4 0

3 years ago

Let V be the volume of the pyramid of height 11 whose base is a square of side length 6. Find a formula for the area A of the ho

Rainbow [258]

Answer:

Base area = 36

Volume of the pyramid = 132

Step-by-step explanation:

Volume of a pyramid = Base Area × Height/3

Base area = Length × Length (since base of the pyramid is a square)

Given the side length of the square = 6

Base area = 6×6

Base area = 36

Given height of pyramid =11

Volume of the pyramid = 36×11/3

Volume of the pyramid = 12×11

Volume of the pyramid = 132

7 0

3 years ago

F(x)=-2x+6 f(-5) step by step

zaharov [31]

Answer:

f(x=16

Step-by-step explanation:

f(-5)=-2(-5)+6

f(-5)=10+6

f(-5)=16

4 0

3 years ago