Which system of equations represent the matrix shown below?

1 2 -1| 8
-1 0 3| 15
1 -2 4| 18

A. x + 2y + z =8
x + y + 3z =15
x + 2y + 4z =18

B. x + 2y + z =8
x + 3z =15
x + 2y + 4z =18

C. x + 2y - z =8
-x + y + 3z =15
x - 2y + 4z =18

D. x + 2y - z =8
-x + 3z =15
x - 2y + 4z =18

Answer:

(x+2.3)^2 + (y) ^2 = (6/7)^2

Step-by-step explanation:

The equation of a circle can be written as

(x-h)^2 + (y-k) ^2 = r^2  where ( h,k) is the center and r is the radius

(x- -2.3)^2 + (y-0) ^2 = (6/7)^2

(x+2.3)^2 + (y) ^2 = (6/7)^2

Answer:

It will take them 2 2/5 days working together

Step-by-step explanation:

To find the time worked

1/a + 1/b = 1/t

Where a and b are the times worked individually and t is the time worked together

1/4 + 1/6 = 1/t

Multiply each side by 12t to clear the fractions

12t( 1/4 + 1/6 = 1/t)

3t + 2t =12

Combine like terms

5t = 12

Divide by 5

t = 12/5

t = 2 2/5

It will take them 2 2/5 days working together

Answer:

The center is (1,4)

Step-by-step explanation:

The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.

Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:

[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]

So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:

[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]

Answer:

Hey there!

A=1/2bh

14=1/2(28)h

14=14h

h=1

Hope this helps :)

Answer:

Step-by-step explanation:

Area of a triangle is

[tex] \frac{1}{2} \times b \times h[/tex]

where b is the base

h is the height

From the question

Area = 14in²

b = 14 inches

So we have

[tex]14 = \frac{1}{2} \times 28 \times h[/tex]

which is

[tex]14 = 14h[/tex]

Divide both sides by 14

That's

[tex] \frac{14}{14} = \frac{14h}{14} [/tex]

We have the final answer as

h = 1

Therefore the height is 1 inch

Hope this helps you

Answer:

14 Quarters and 28 dimes

Step-by-step explanation: 14 quarters $3.50

28 dimes is $2.80 total is $6.30

Answer:

C.

6a + 18x + 18p

Step-by-step explanation:

3(2a + 6 (x + p)) firs multiply (x + p) with 6

3 (2a + 6x + 6z) now multiply inside the parenthesis with 3 and the answer would be 6a + 18x + 18p

Answer:

Correlation Coefficient

Step-by-step explanation:

Answer:

Option (3)

Step-by-step explanation:

[tex](x-i\sqrt{3})[/tex] is a factor of a polynomial given in the options, that means a polynomial having factor as [tex](x-i\sqrt{3})[/tex] will be 0 for the value of x = [tex]i\sqrt{3}[/tex].

Option (1),

3x⁴ + 26x² - 9

= [tex]3(i\sqrt{3})^{4}+26(i\sqrt{3})^2-9[/tex] [For x = [tex]i\sqrt{3}[/tex]]

= 3(9i⁴) + 26(3i²) - 9

= 27 - 78 - 9 [Since i² = -1]

= -60

Option (2),

4x⁴- 11x² + 3

= [tex]4(i\sqrt{3})^4-11(i\sqrt{3})^2+3[/tex]

= 4(9i⁴) - 33i² + 3

= 36 + 33 + 3

= 72

Option (3),

4x⁴ + 11x² - 3

= [tex]4(i\sqrt{3})^4+11(i\sqrt{3})^2-3[/tex]

=  4(9i⁴) + 33i² - 3

= 36 - 33 - 3

= 0

Option (4),

[tex]3x^{4}-26x^{2}-9[/tex]

= [tex]3(i\sqrt{3})^4-26(i\sqrt{3})^{2}-9[/tex]

= 3(9i⁴) - 26(3i²) - 9

= 27 + 78 - 9

= 96

Therefore, [tex](x-i\sqrt{3})[/tex] is a factor of option (3).

Answer:

[2.5 ,4]

Step-by-step explanation:

The graph in this interval has a vertex while opening up wich means it's a minimum

Answer:

[tex] x = 2 [/tex]

Step-by-step explanation:

Given a right-angled triangle as shown above,

Included angle = 60°

Opposite side length = 3

Adjacent side length = x

To find x, we would use the following trigonometric ratio as shown below:

[tex] tan(60) = \frac{3}{x} [/tex]

multiply both sides by x

[tex] x*tan(60) = \frac{3}{x}*x [/tex]

[tex] x*tan(60) = 3 [/tex]

Divide both sides by tan(60)

[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]

[tex] x = \frac{3}{tan(60} [/tex]

[tex] x = 1.73 [/tex]

[tex] x = 2 [/tex] (approximated to whole number)

Assuming angle A is opposite to side a, B is the opposite to side b, and angle C is the opposite to side c.

Answer:

The right triangle has the following angles:

A = 48.31º, B = 41.69º and C = 90º.

The sides are:

[tex] \\ a = 37.26[/tex], [tex] \\ b = 33.12[/tex] and c = 49.9.

Step-by-step explanation:

The inner sum of a triangle = 180º.

A=48.31º,

C=90º

A + B + C = 180º

48.31º+ B + 90º = 180º

B = 180º - 90º - 48.31º

B = 41.69º

We can apply the Law of Sines to solve for unknown sides:

[tex] \\ \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}[/tex]

We know that sin(90º) = 1.

[tex] \\ \frac{a}{sin(48.31)} = \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

Then, a is:

[tex] \\ \frac{a}{sin(48.31)} = \frac{49.9}{1}[/tex]

[tex] \\ a = 49.9*sin(48.31)[/tex]

[tex] \\ a = 49.9*0.7467[/tex]

[tex] \\ a = 37.26[/tex]

Thus, b is:

[tex] \\ \frac{b}{sin(41.69)} = \frac{49.9}{1}[/tex]

[tex] \\ b = 49.9*sin(41.69)[/tex]

[tex] \\ b = 33.12[/tex]

In any coordinate pair, the first number is the x-value and the second number is the y-value.

To find the slope, simply take the difference of the y values and divide by the difference in the x values: (14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is -5/3.

It is find the slope of the line.

The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

The slope is always calculated from the rise divided by the run. Typically, the equation is presented as:

m = Rise/Run

If you have two points, the points should be [tex]P_{1} (x_{1} ,y_{1} )[/tex] and [tex]P_{2} (x_{2} ,y_{2} )[/tex]  So, the equation would be:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

In any coordinate pair, the first number is the x-value and the second number is the y-value.

The difference of the y values and divide by the difference in the x values:

m=(14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is  -5/3.

Learn more about slope here:

https://brainly.com/question/17114095

#SPJ5

Answer:

Hey there!

The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.

The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.

The circumference of the circle is 50.24 yards.

Hope this helps :)

Answer:

Step-by-step explanation:

If  x and y be real numbers satisfying 2/x=y/3=x/y, then any two of the equation are equated as shown;

2/x = y/3 ... 1 and;

y/3 = x/y... 2

From equation 1, 2y = 3x ... 3

and from equation 2; y² = 3x ... 4

Equating the left hand side of equation 3 and 4 since their right hand sides are equal, we will have;

2y = y²

2 = y

y = 2

Substituting y = 2 into equation 3 to get the value of x;

2y = 3x

2(2) = 3x

4 = 3x

x = 4/3

The value of x³ will be expressed as (4/3)³ = 4*4*4/3*3*3 = 64/27

Answer:

3

Step-by-step explanation:

Use this equation

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute

-6-3/0-3 subtract

-9/-3 simplify

-3/-1 two negitives cansle out

3/1=3

Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.

Have a good day! :)

Answer:

3

Step-by-step explanation:

To find the slope, we use the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -6 -3)/(0 -3)

    = -9/-3

    = 3

Answer: hundredths place

Step-by-step explanation:

The complete question is;

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Answer:

A) P (x < 10) = 0.6700

B) P (x > 5 ) = 0.9406

C) P (8.0000 < x < 15.0000) = 0.6332

Step-by-step explanation:

A) we are given;

Mean;μ = 8.9 minutes

Standard deviation;σ = 2.5 minutes

Normal random variable;x = 10

So to find;P(x < 10) we will use the Z-score formula;

z = (x - μ)/σ

z = (10 - 8.9)/2.5 = 0.44

From z-distribution table and Z-score calculator as attached, we have;

P (x < 10) = P (z < 0.44) = 0.6700

B) similarly;

z = (x - μ)/σ =

z = (5 - 8.9)/2.5

z = -1.56

From z-distribution table and Z-score calculator as attached, we have;

P (x > 5 ) = P (z > -1.56) = 0.9406

C)between 8 and 15 minutes

For 8 minutes;

z = (8 - 8.9)/2.5 = -0.36

For 15 minutes;

z = (15 - 8.9)/2.5 = 2.44

From z-distribution table and Z-score calculator as attached, we have;

P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332

Answers:

sin a=12/15=4/5

step by step explanation:

AB=9, and BC=12

find c: hyp.=√12²+9²=c²

c=15

sin a=opp/hyp.=12/15=4/5 ( convert to degrees)

a=41.10

Answer:

[tex]\sqrt{x-4} +5[/tex]

Step-by-step explanation:

the conjugate of [tex]\sqrt{x-4} -5[/tex]  is the term that completes a²-b² when multiplied by each other

a²-b² = (a+b)(a-b)

Answer:

6[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

y + 1[tex]\frac{1}{6}[/tex] = 7[tex]\frac{5}{6}[/tex]

y + [tex]\frac{7}{6}[/tex] = [tex]\frac{47}{6}[/tex]

y = 40/6 = 20/3 = 6[tex]\frac{2}{3}[/tex]

Answer:

0.40

Step-by-step explanation:

The computation of the probability for the second student be sophomore and the first is a freshman is shown below:

Let us assume

Sophomore = S

Freshman = F

Based on this assumption, the probability is as follows

So,

[tex]= \frac{P(S\cap F)}{P(F)} \\\\ = \frac{P(S) \times P(F)}{P(F)} \\\\ = \frac{16}{40}[/tex]

= 0.40

Hence, the probability for the second student be sophomore and the first student be freshman is 0.40

Answer:

The answer is 4 + √15 .

Step-by-step explanation:

You have to get rid of surds in the denorminator by multiplying it with the opposite sign :

[tex] \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } [/tex]

[tex] = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } [/tex]

[tex] = \frac{ {( \sqrt{5} + \sqrt{3} ) }^{2} }{( \sqrt{5} - \sqrt{3} )( \sqrt{5} + \sqrt{3}) } [/tex]

[tex] = \frac{ {( \sqrt{5} )}^{2} + 2( \sqrt{5} )( \sqrt{3}) + {( \sqrt{3}) }^{2} }{ {( \sqrt{5}) }^{2} - { (\sqrt{3} )}^{2} } [/tex]

[tex] = \frac{5 + 2 \sqrt{15} + 3 }{5 - 3} [/tex]

[tex] = \frac{8 + 2 \sqrt{15} }{2} [/tex]

[tex] = 4 + \sqrt{15} [/tex]

Answer:

h = 7.1 cm

Step-by-step explanation:

To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:

[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:

[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]

So the area of the triangle is:

[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]

[tex]S = 60\ cm^2[/tex]

Now, to find the height, we can use the following equation for the area of the triangle:

[tex]S = base * height/2[/tex]

The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:

[tex]60 = 17 * h/2[/tex]

[tex]h = 120/17[/tex]

[tex]h = 7.06\ cm[/tex]

Rounding to the nearest tenth, we have h = 7.1 cm

Answer:

7.1 cm

Step-by-step explanation:

:D

Answer:

43\ 12 , 35/ 6

Step-by-step explanation:

43\ 12 , 35/ 6

Answer:  B: (3, -7)

Step-by-step explanation:

4x + 4y = -9

         y = 2x - 13

Use Substitution:

4x + 4(2x - 13) = -9

4x + 8x - 52 = -9

       12x - 52 = -9

               12x = 43

                   [tex]x=\dfrac{43}{12}[/tex]

None of the options provided are valid so either there is a typo on your worksheet or you typed in one of the equations wrong.

Plan B: Input the choices into the equation to see which one makes a true statement.

               4x + 4y = -9

A) (x, y) = (-3, -7)

               4(-3) + 4(-7) = -9

                -12   +   -28 = -9

                             -40 ≠ -9

B) (x, y) = (3, -7)

               4(3) + 4(-7) = -9

                12   +   -28 = -9

                             -16 ≠ -9

C) (x, y) = (3, 7)

               4(3) + 4(7) = -9

                12   +   28 = -9

                            40 ≠ -9

D) (x, y) = (-3, 7)

               4(-3) + 4(7) = -9

                -12   +   28 = -9

                              16 ≠ -9

Obviously there is something wrong with the first equation because none of the options provide a true statement.

               y = 2x - 13

A) (x, y) = (-3, -7)

               -7 = 2(-3) - 13

               -7  = -6    -13

                -7 ≠ -19

B) (x, y) = (3, -7)

               -7 = 2(3) - 13

               -7  = 6    -13

                -7 = -7                   this works!!!

C) (x, y) = (3, 7)

               7 = 2(3) - 13

               7  = 6    -13

                7 ≠ -7

D) (x, y) = (-3, 7)

               7 = 2(-3) - 13

               7  = -6    -13

                7 ≠ -19

Option B is the only one that provides a true statement so this must be the answer.

Answer:

yeyyyaya

Step-by-step explanation:

Answer:

b. (10,10,0)

Step-by-step explanation:

r+v can be evaluated if the vectors/matrices have the same dimensions.

These do. They are both 1 by 3 vectors.

Just add first to first in each.

Just add second to second in each.

Just add third to third in each.

Example:

(5,-5,6)+(1,2,3)

=(5+1,-5+2,6+3)

=(6,-3,9)

Done!

In general, (a,b,c)+(r,s,t)=(a+r,b+s,c+t).

r+v

=(7,3,9)+(3,7,-9)

=(7+3,3+7,9+-9)

=(10,10,0)

Done!

Answer:

x=5

Step-by-step explanation:

h (x) = 3

We want the x values where y =3

The values are x = -7 and x=5

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:

[tex]T = 180^{\circ}[/tex] (Period)

[tex]z_{min} = -4[/tex] (Minimum)

[tex]z_{max} = 5[/tex] (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:

1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]

[tex]\Delta z = \frac{5+4}{2}[/tex]

[tex]\Delta z = \frac{9}{2}[/tex]

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]

[tex]z_{m} = \frac{1}{2}[/tex]

The new function is:

[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]

Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:

[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

Answer:

A) $0.11

Step-by-step explanation:

Since a dozen (12) eggs cost $1.35. You will divide $1.35 by 12. And it will equal 0.1125. Round it up it equals to 0.11.

Answer:

Q(1,1), N(3,2) A(2,5)

Step-by-step explanation: