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musickatia [10]
3 years ago
14

What is the value of z?

Mathematics
1 answer:
Phoenix [80]3 years ago
8 0

Answer:

1.5454

Step-by-step explanation:

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Solve the system by using a matrix equation
Sergeu [11.5K]

Answer:

Option A is correct (17,11).

Step-by-step explanation:

6x - 9y = 3

3x - 4y =7

it can be represented in matrix form as\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right]

A= \left[\begin{array}{cc}6&-9\\3&4\end{array}\right]

X= \left[\begin{array}{c}x\\y\end{array}\right]

B= \left[\begin{array}{c}3\\7\end{array}\right]

i.e, AX=B

or X= A⁻¹ B

A⁻¹ = 1/|A| * Adj A

determinant of A = |A|= (6*-4) - (-9*3)

                                    = (-24)-(-27)

                                    = (-24) + 27 = 3

so, |A| = 3

Adj A=  \left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]

A⁻¹ =  \left[\begin{array}{cc}-4&9\\-3&6\end{array}\right]/3

A⁻¹ =  \left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right]

X= A⁻¹ B

X=  \left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right]

X= \left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right]

X= \left[\begin{array}{c}-4+21\\-3+14\end{array}\right]

X= \left[\begin{array}{c}17\\11\end{array}\right]

x= 17, y= 11

solution set= (17,11).

6 0
3 years ago
Read 2 more answers
Find the volume of a square based pyramid like you see below if the side of the base is 10 inches and the height of the the tria
Mekhanik [1.2K]

Answer:

The volume of a square based pyramid is <u>645.3 cubic inches</u>.

Step-by-step explanation:

Given:

The side of the base is 10 inches and the height of the the triangular face is 20 inches.

Now, to find the volume of square based pyramid.

Base side (a) = 10 inches.

Slant Height (s) = 20 inches.

Now, to get the height of pyramid by using pythagorean theorem:

Leg 1 = \frac{base}{2}=\frac{10}{2}=5\ inches.

Hypotenuse = 20 inches.

So,

Hypotenuse² = (leg 1)² + (leg 2)²

20^2=5^2+leg2^2\\400=25+leg2^2\\Subtracting\ both\ sides\ by\ 25 \ we\ get:\\375=leg2^2

<em>Using square root on both sides we get:</em>

<em />19.36=leg2<em />

<em>leg 2 = 19.36 inches.</em>

Thus, the height of pyramid = 19.36 inches.

Now, to get the volume of square pyramid we put formula:

h = 19.36 inches.

a = 10 inches.

Volume=a^2\frac{h}{3}

Volume=10^2\times \frac{19.36}{3}

Volume=100\times 6.453

Volume=645.3\ cubic\ inches.

<u><em>Hence, the volume to the nearest tenth is 645.3 cubic inches.</em></u>

Therefore, the volume of a square based pyramid is 645.3 cubic inches.

3 0
2 years ago
How many natural numbers?<br> from 78 to 234<br> how many whole numbers <br> from 24 to 721
Vinil7 [7]

Answer:

<u>158 natural numbers from 78 to 234, and 699 whole numbers from 24 to 721.</u>

Step-by-step explanation:

Natural numbers are positive integers (whole numbers), so all numbers from the range of 78 to 234 would be included, including 78 and 234 itself. That is 158 natural numbers. Whole numbers are numbers without a fraction or decimal, they are integers. So all numbers from 24 to 721 would be included, as well as 24 and 721 itself. That is 699 whole numbers from 24 to 721. Hope this helps.

3 0
3 years ago
Read 2 more answers
I’m another normally distributed test score is 80 and the standard deviations is 10. How common are values in the less than 60?
lord [1]

Answer:

<em>The probability of obtaining a score less than 60 is 2.28% </em>

<em>It happens 2 out of 100 times.</em>

Step-by-step explanation:

If the mean μ = 80 and the standard deviation σ = 10, then we need to find the probability that an X value is less than 60.

Then we find

P(X

To find this probability we use the Z statistic.

Z = \frac{X- \mu}{\sigma}

P(\frac{X- \mu}{\sigma}

P(Z

This is the same as

P(Z> 2)

We look for this value in the table for the normal distribution of right queue and we have:

P(X  2) = 0.02275

<em>The probability of obtaining a score less than 60 is 2.28% </em>

<em>It happens 2 out of 100 times.</em>

6 0
2 years ago
- What is the equation of a cirde with a center
wlad13 [49]

Answer:

<h2>C.</h2>

Step-by-step explanation:

The equationof a circle:

(x-h)^2+(y-k)^2=r^2

<em>(h, k)</em><em> - center</em>

<em>r</em><em> - radius</em>

<em />

We have <em>center = (4, -1) → h = 4, k = -1</em>, and <em>r = 9</em>.

Substitute:

(x-4)^2+(y-(-1))^2=9^2\\\\\huge\boxed{(x-4)^2+(y+1)^2=81}

6 0
2 years ago
Read 2 more answers
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