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4 years ago

Find the measure of

Mathematics

1 answer:

Sonbull [250]4 years ago

8 0

Answer: 77°

Step-by-step explanation:

First we are going to find x and then insert it in 18x +5 to be able to get our <WZX

But to find x, we will have to apply the the exterior angle theorem

The exterior angle theorem state that : the exterior angle is equal to the sum of the two opposite interior anges

Using this theorem, then from the diagram above ;

18x + 5 = 48 + 8x - 3

we collect like term

18x - 8x = 48-3-5

10x = 40

Divide bothside by 10

10x/10 = 40/10

x = 4

but <WZX = 18x + 5

Then we substitute x=4

<WZX = 18(4) + 5

<WZX = 72 +5

<WZX =77

Therefore the measure of <WZX is 77°

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A glacier in Alaska moves about 29.2 meters a day.

Leto [7]

Answer:

29,100

Step-by-step explanation:

29.1 × 10 = 291

29.1 × 100 = 2,910

29.1 × 1000 = 29,100

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3 years ago

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Semmy [17]

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3 years ago

Kyle is making a frame for a rectangular piece of art. The length of the frame is 3 times the width, as shown below.

NeX [460]

Answer:

3.75 feet

Step-by-step explanation:

The length of the frame is 3 times the width.

Let the width be x.

The length will be 3x.

Kyle uses 10 feet of wood to make the frame. This means that the perimeter is 10 feet.

The perimeter of a rectangle is:

P = 2(L + W)

=> 10 = 2(3x + x)

=> 10/2 = 4x

5 = 4x

=> x = 5/4 = 1.25 feet

The width is 1.25 feet. The length is therefore:

1.25 * 3 = 3.75 feet

5 0

3 years ago

Which equation has infinitely many solutions? A) 4x + 3 3 = 4x + 5 B) 10x + 8 2 = 5x + 4 C) 8x − 5 3 = 2x − 2 D) 8x − 5 2 = 4x −

abruzzese [7]

Answer: If the left side and the right side of the equation are equal, the equations has infinitely many solutions.

Step-by-step explanation:

The options are not clear, so I will give you a general explanation of the procedure you can use to solve this exercise.

The Slope-Intercept form of the equation of a line is the following:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

For this exercise you need to remember that, given a System of Linear equations, if they are exactly the same line, then the System of equations has Infinitely many solutions.

If you have the following system:

$\left \{ {{y=2x+1} \atop {y=\frac{12}{6}x+1}} \right.$

You can simplify the second one:

$y=2x+1$

Then, both equations are the same line.

By definition you can also write the systemf making both equations equal to each other:

$2x+1=2x+1$

So, if the left side and the right side are equal, the equations has infinitely many solutions.

3 0

3 years ago

in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Nimfa-mama [501]

Answer:

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

Step-by-step explanation:

Let $\vec u$ and $\vec a$ , from Linear Algebra we get that component of $\vec u$ parallel to $\vec a$ by using this formula:

$\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a$ (Eq. 1)

Where $\|\vec a\|$ is the norm of $\vec a$ , which is equal to $\|\vec a\| = \sqrt{\vec a\bullet \vec a}$ . (Eq. 2)

If we know that $\vec u =(2,1,1,2)$ and $\vec a=(4,-4,2,-2)$ , then we get that vector component of $\vec u$ parallel to $\vec a$ is:

$\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

Lastly, we find the vector component of $\vec u$ orthogonal to $\vec a$ by applying this vector sum identity:

$\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}$ (Eq. 3)

If we get that $\vec u =(2,1,1,2)$ and $\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$ , the vector component of $\vec u$ is:

$\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

$\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

4 0

3 years ago