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2 years ago

Plz help me answer this

Mathematics

1 answer:

timofeeve [1]2 years ago

4 0

Answer:

(-2, -8)

x = -2

y = -8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define systems

13x - 6y = 22

x = y + 6

Step 2: Solve for y

Substitution

Substitute in x: 13(y + 6) - 6y = 22
Distribute 13: 13y + 78 - 6y = 22
Combine like terms: 7y + 78 = 22
Isolate y term: 7y = -56
Isolate y: y = -8

Step 3: Solve for x

Define original equation: x = y + 6
Substitute in y: x = -8 + 6
Add: x = -2

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The figure above shows a square inscribed in a rectangle.

Debora [2.8K]

Answer:

31 units ²

Step-by-step explanation:

Area of a rectangle = length × width

Length = 8 units

Width = 5 units

Area of a rectangle = length × width

= 8 units × 5 units

= 40 units ²

Area of of the blue square = length ²

Length = 3 units

Area of of the blue square = length ²

= (3 units) ²

= 9 units ²

Area of the orange colored part of the figure = Area of a rectangle - Area of of the blue square

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6 0

2 years ago

A libary has 2000 books. there are 3 times as many non fiction books as fiction books. write and solve a system of equations to

Andru [333]

A: number of nonfiction books
b: number of fiction books
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4 0

2 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

2 years ago

Statistics question; please help.

Alex_Xolod [135]

Answer:

Does this sample provide convincing evidence that the machine is working properly?

Yes.

Step-by-step explanation:

Normal distribution test:

$z=\frac{x- \mu }{ \frac{\sigma}{\sqrt{n}} }=\frac{ (x-\mu)\sqrt{n}}{\sigma}$

Where,

$x: \text{ sample mean}$

$\sigma: \text{ standard deviation}$

$n: \text{ sample size determination}$

$\mu: \text{ hypothesized size of the screw}$

$z=\frac{(1.476-1.5)\sqrt{200} }{0.203 }$

$z=\frac{(-0.024)10\sqrt{2} }{0.203 }$

$z \approx -1.672$

Once the significance level was not given, It is usually taken an assumption of a 5% significance level.

Taking the significance level of 5%, which means a confidence level of 95%, we have a z-value of $\pm 1.96$

Therefore, we fail to reject the null. It means that the hypothesis test is not statistically significant: the average length is not different from 1.5!

7 0

2 years ago

3.2666 rounded to the nearest hundredth

enyata [817]

Answer:

3.27

Step-by-step explanation:

Hope it helps!!!

5 0

2 years ago