Monday
Ms. Paulsen had 80 paper clips in her desk drawer. She used 39 of them on
papers.
How
many paper clips does Ms. Paulsen have in her desk drawer now?

Using Gaussian elimination, the solution to the given system of equations is given as follows:

x = 5, y = -11, z = 3.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are x, y and z, and the system is given as follows:

There are multiple ways in which a system can be solved, and for this one, Gaussian elimination will be used.

The first step is writing the augmented matrix of the system, as follows:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]

Then, the first column, which is equivalent to be coefficient of y, has to be of zero on the second and on the third row, hence:

The updated matrix will be given by:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]

Then, the second column, equivalent to the coefficient of y, on the third row has to be zero, hence:

R3 -> 11R2 + 5R3.

Then the matrix is:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]

From each row of the system, from bottom up, we find the variables, as follows:

40z = 120

z = 120/40

z = 3.

5y - 10z = -85

5y - 30 = -85

5y = -55

y = -11.

2x - y + 4z = 33

2x + 11 + 12 = 33

2x = 10

x = 5.

Hence the solution for the system is:

x = 5, y = -11, z = 3.

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

we don't have enough information to conclude if the triangles are similar, thus, the correct option is C.

Two figures are similar if the figures have the same shape, but different size.

So, one figure is a dilation/contraction of the other figure.

In this case of the triangles, two are similar if and only if all the correspondent internal angles have the same measure.

For the case of the image, the triangles:

RST and RUV

would be similar if and only if line ST and line UV are parallel, in that case we would get that the angles at S and U are equal, and the same for the angles at T and V.

In this particular case, there is no indication that ST and UV are parallel. (they may be, the may not be)

So we don't have enough information to conclude if the triangles are similar, thus, the correct option is C.

If you want to learn more about similar figures:

https://brainly.com/question/14285697

#SPJ1

dam n bro uglier den a redneck on a sunday

Step-by-step explanation:

Answer: it would be 18/3 or

Step-by-step explanation:

2/3 x 9 = ?

1) You multiple both numerator and denominator: 2x9 / 3x1 = 18/3

2) Find the GCF ( greatest common factor) for both numbers. Which is

3) Then divide both the numerator and denominator by 3 to simplify to it's lowest term: 18÷3= 6 and 3÷3= 1 which gives a fraction of 6/1 or

The Lagrangian is

[tex]L(x,y,\lambda) = x^2 + y^2 - \lambda (x + y - 1)[/tex]

Find its critical points.

[tex]\dfrac{\partial L}{\partial x} = 2x - \lambda = 0 \implies x = \dfrac\lambda2[/tex]

[tex]\dfrac{\partial L}{\partial y} = 2y - \lambda = 0 \implies y = \dfrac\lambda2[/tex]

[tex]\dfrac{\partial L}{\partial\lambda} = -(x+y-1) = 0 \implies x + y = 1[/tex]

From the first two conditions, [tex]x=y[/tex], so

[tex]x + y = 2x = 1 \implies x = y = \dfrac12[/tex]

At the point (1/2, 1/2), compute the Hessian determinant of [tex]f(x,y)[/tex].

[tex]H(x,y) = \begin{bmatrix} \dfrac{\partial^2f}{\partial x^2} & \dfrac{\partial^2f}{\partial x \partial y} \\\\ \dfrac{\partial^2f}{\partial y\partial x} & \dfrac{\partial^2f}{\partial y^2} \end{bmatrix} = \begin{bmatrix}2&0\\0&2\end{bmatrix}[/tex]

[tex]H(x,y)[/tex] is positive definite for all [tex]x,y[/tex], which indeed indicates a local minimum at (1/2, 1/2), so that

[tex]\min\left\{x^2+y^2 \mid x+y=1\right\} = f\left(\dfrac12,\dfrac12\right) = \dfrac14+\dfrac14 = \boxed{\dfrac12}[/tex]

Answer:

375

Step-by-step explanation:

Let the number of hamburgers sold be x. Then, x-66 cheeseburgers were sold.

[tex]x+x-66=684 \\ \\ 2x=750 \\ \\ x=375[/tex]

Answer:

See picture below.

Step-by-step explanation:

The 48 inches allowable minimum height of a rider and the 52 and 2.5 mean and standard deviation of the height of the children in the camp of 140 campers, by the Z–Score gives the number of campers allowed as approximately 132 campers.

The required height of riders is at least 48 inches.

The mean height of the children = 52 inches

The standard deviation of the children's height = 2.5 inches

The number of campers at the camp, n = 140

Required: The number of the 140 campers that will be allowed on the ride

Solution:

The Z–Score of the allowable campers is found using the equation;

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

Which gives;

[tex]z = \frac{48 - 52}{2.5} = - 1.6[/tex]

From the Z–Score table, the probability (proportion) of a camper's height to be less than 48 inches is P(x < 48) = 0.05480

Therefore;

The probability that the height of a camper is more than 48 inches is given by the equation;

P(x > 48) = 1 - P(x < 48) = 1 - 0.05480

Which gives;

P(x > 48) = 1 - 0.05480 = 0.9452

Which gives;

The number of campers allowed, c, is given by the equation;

c = n × P(x > 48)

c = 140 × 0.9452 = 132.328 ≈ 132

Learn more about the Z–Score of a normal distribution here:

https://brainly.com/question/24213960

#SPJ1

Betsy needs to  invest $32,000 in the B-rated bonds paying 13% interest and $28,000 in the certificate of deposit paying 3% interest.

Interest is calculated by multiplying the rate with the principal.

Let x = the amount Betsy will invest in the B-rated bonds paying 13% per annum. The remaining amount, $60,000-x , she will invest in the certificate of deposit paying 3% per annum.

We can express the earnings on these two investments, after converting the percentages to their decimal equivalents, as: 0.13x+0.03(60000-x) and this is to earn a total of $5,000

Now we can write the necessary equation to solve for x.

or, 0.13x+0.03(60000-x) = 5000

or, 0.13x+1800-0.03x = 5000

or, 0.1x+1800 = 5000

or, 0.1x = 3200

or, x = 32000

So Betsy needs to invest $32,000 in the B-rated bonds paying 13% interest and the remainder ($60,000-$32,000 = $28,000) in the certificate of deposit paying 3% interest to obtain $5,000 in interest per annum.

To learn more about interest:

https://brainly.com/question/13324776

#SPJ9

Answer:

-3

Step-by-step explanation:

Hope this helps!

Answer:

-3

Step-by-step explanation:

if its negative then it will continue to be unless 7 is added into -6. So, adding 3 to that would make it -3

Answer:

The total amount of apples sold is 63.  There were 49 red apples and 14 green apples

Step-by-step explanation:

red: green : total

7          2       7+2

7          2          9

When we use the ratios, the total is 9

We are given the total is 63

63 divided by 9 is 7

We need to multiply each number by 7

red: green : total

7*7      2*7       9*7

49       14             63

The total amount of apples sold is 63.  There were 49 red apples and 14 green apples

Answer:

the answer is red apples 49 and green apples 14.

Answer:

3x+4x-1+x+2=73

8x+1=73

8x=73-1

8x=72

8x/8=72/8

x=9

Perimeter (p) of a triangle:

[tex]p = a + b + c[/tex]

P = 73 units

To find the value of x

[tex]73 = 3x + 4x - 1 + x + 2[/tex]

→[tex]73 = 8x + 1 \\ 73 - 1 = 8x[/tex]

→[tex]8x = 72[/tex]

→[tex] \frac{8x}{8} = \frac{72}{8} [/tex]

[tex]x = 9[/tex]

Answer:

The slope of the line is -1.

We can find this by using the slope formula, where [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]. Substitute in our points; [tex]\frac{7-4}{6-9} =\frac{3}{-3}[/tex]. Remember that a negative in either the numerator or the denominator of a fraction makes the entire fraction negative, so [tex]\frac{3}{-3}=-\frac{3}{3}[/tex] Remember that an identical numerator and denominator is equal to 1. Same rule applies here, except it's negative, so the slope of the line is -1. You can see this in action if you were to use a graphing tool. I recommend checking out desmos graphing calculator.

Answer:

32

Step-by-step explanation:

That is a weird question. Usually questions like that include a variable. Its like saying n = 32. It just gives the answer. Assuming you didn't miss anything, this is the answer.

Answer:

[tex]x=-11[/tex]

Step-by-step explanation:

We know that GE = [tex]x+21[/tex] = [tex]2x+23+9[/tex]

Calculate accordingly!

[tex]x+21=2x+23+9[/tex] ( minus [tex]2x[/tex] and minus 21 )

[tex]x-2x=-21+23+9[/tex]

[tex]-x=11[/tex]

Therefore,

[tex]x=-11[/tex]

( You can test this out by substituting the values )

Answer:

B and D

Step-by-step explanation:

The wording in the answer choices make a huge difference. It is possible implies that there is a possibility

A is false. The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)

A good example is a constant function such as g(x) = 7. Here, whatever the value of x, the y value is always 7. This represents a horizontal line passing through y = 7. So the range is just a single number {7}

B can be true. It is possible but not a certainty that f(a) = 4 for some value of a. For example, consider the function g(x) = x + 3.

At x = 4, g(4) = 4 .1 + 3 = 7

At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output

C is false. A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.

D is true. Since at x =4, y = g(x) = 7, this corresponds to a point on the graph. The point will be (x=4, y =7) or (4,7)

E is false. The x, y coordinates have been interchanged in this answer choice

The true statements are B and D.

The wording in the answer choices make a huge difference.

It is possible implies that there is a possibility

A. 4 is in the range of g.

A is false.

The range of a function is the output value of the function for the input value in the domain of the function. So we can say with certainty that 7 is in the range since it is an output. But we cannot state that 4 is in the range because we have only one output value 7 for g(4)

A good example is a constant function such as g(x) = 7.

Here, whatever the value of x, the y value is always 7.

This represents a horizontal line passing through y = 7.

So the range is just a single number {7}

B. For a value a, it is possible that g (a) = 4.

B can be true.

It is possible but not a certainty that f(a) = 4 for some value of a.

For example, consider the function g(x) = x + 3.

At x = 4, g(4) = 4 .1 + 3 = 7

At x = 1, g(1) = 1 + 3 = 4 so it is possible for 4 to be an output.

C. For a value y, it is possible that g (4) = y.

C is false.

A well-defined function has only a unique value for a specific input of x. So we cannot get two different values for a single x value.

D. The point (4,7) is on the graph of y = g (x).

D is true.

Since at x =4, y = g(x) = 7, this corresponds to a point on the graph.

The point will be (x=4, y =7) or (4,7)

E. The point (7, 4) is on the graph y = g(x).

False. The statement doesn't provide any information about g(7), and we cannot determine whether the point (7, 4) lies on the graph of the function y = g(x) based solely on the given information.

To learn more on function click:

https://brainly.com/question/29204088

#SPJ7

Answer:

(n ÷ 4) + 6 = 8

Step-by-step explanation:

Quotient means The answer when you divide' So we are working in the division.

n ÷ 4 is the division part

It says 'and' which can also mean addition. So we add 6. So far our equation is: (n ÷ 4) + 6 (Brackets are needed as we are dividing n by 4 and not dividing n by 4+6)

Lastly it says the answer must be 8 so we add that at the end. So the answer is:

(n ÷ 4) + 6 = 8

The value of the given expression is equivalent to -3

Linear equations are equation that has a linear degree of 1.

The statement three eighths times the quantity 1 plus the square root of 49 end quantity squared minus the quantity four minus one end quantity cubed is written mathematically as:

3/8(1+√49)² - (4-1)³

Expand to have:

3/8(1+7)² - 3³

3/8(8)² -27

3/8(64) - 27

3(8) - 27

24 - 27

-3

Hence the value of the given expression is equivalent to -3

Learn more on linear expression here: https://brainly.com/question/14323743

#SPJ1

Answer: Point B will be at (4,-3)

Point C will be (-2,-3)

Point D will be (6,3)

The cost to carpet this room area is $2764.8.

What is the area?

Area of room = 32*24 (product is equal to the area of carpet)

Cost of carpet per square foot = $3.6 (three. six)

Cost of carpet = Area of carpet * Cost of carpet per square foot (product)

 = 32 x 24 x 3.6

 = 2764.8

The cost to carpet this room area is $2764.8.

Learn more about the area here:

https://brainly.com/question/25292087

#SPJ9

This range defines that the babies delivered weigh between 6.9 and 9.5 pounds.

Part 1.

Given inequality is  | x − 8.1 |  ≤ 1.3

Simplifying this inequality as

x - 8.2 ≤ 1.3 or x - 8.2 ≥ -1.3

Solving x - 8.2 ≤ 1.3  we get, x ≤ 9.5

And

Solving x - 8.2 ≥ -1.3 we have, x ≥ 6.9

Now combining the ranges we get,

6.9 ≤ x ≤ 9.5

Part 2.

This range defines that the babies delivered weigh between 6.9 and 9.5 pounds.

Hence, This range indicates that the babies' weights fall within the range of 6.9 to 9.5 pounds.

Learn more about inequality here:

https://brainly.com/question/20383699

#SPJ9

Answer:

Number of 12$ Shares? 25

Number of 14$ Shares? 57

Step-by-step explanation:

Let x = number of $12 shares.

Let y = number of $14 shares.

"Ivan has $1098 worth of $12 and $14 stock shares."
12x + 14y = 1098

The number of $14 shares is seven more than twice the number of $12 shares.

y = 2x + 7

We have a system of equations.

12x + 14y = 1098

y = 2x + 7

We can use the substitution method since the second equation is already solved for y. Substitute 2x + 7 for y in the first equation.

12x + 14(2x + 7) = 1098

12x + 28x + 98 = 1098

40x = 1000

x = 25

There are 25 $12 shares.

y = 2x + 7 = 2(25) + 7 = 57

There are 57 $14 shares.

Check:

25 × $12 + 57 × $1`4 = $300 + $798 = $1098

The total value is correct, so the answer is correct.

Answer:  27. 10 < x < 20

29. 10 < x < 20

Step-by-step explanation:

The equation of a line perpendicular to the line is y = (-1/2)x - 9

Slope of the line perpendicular to y = 2x - 1, m =-1/2;

Therefore, equation of line perpendicular to given line in slope- intercept form is; y = (-1/2) x + c;

This line passes through (-8, -5); therefore;

-5 = (-1/2)(-8) + c;

c = -9;

Therefore, equation of required line is y = (-1/2)x - 9;

Perpendicular lines are two non-vertical lines in the same plane that intersect at a right angle. Horizontal and vertical lines are perpendicular to one other, forming the coordinate plane's axes. Negative reciprocals are the slopes of two perpendicular lines.

Vertical and horizontal lines are parallel to each other. In this scenario, the slope of the perpendicular line is equal to the slope of a horizontal line, which is 0. The slope of the parallel line is 0 while the slope of the perpendicular line is unknown.

To learn more about perpendicular line ; visit: https://brainly.com/question/18271653

#SPJ9

Taking into account the definition of a system of linear equations, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:

[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]

where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

On the other hand, you know:

So, the system of equations to be solved is

[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]

Among the different existing methods to solve the system of equations, it is decided to solve it using the substitution method. This method consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first one you get:

2.50×2R+4.75R=48.75

Solving:

5R+4.75R=48.75

9.75R=48.75

R= 48.75÷ 9.75

R= 5

Remembering that G=2R, you obtain that G=2×5= 10

In summary, the system of equations that could be used to determine the number of games Kadeesha played and the number of rides Kadeesha went on is:

[tex]\left \{ {{2.50G+4.75R=48.75} \atop {G=2R}} \right.[/tex]

where G is the number of games Kadeesha played and R is the number of rides Kadeesha went on.

Finally, the number of games played is 10 while the number of rides she went on is 5.

Learn more about system of equations:

brainly.com/question/17924725

brainly.com/question/14429662

brainly.com/question/14323743

brainly.com/question/1365672

#SPJ1

The distance between the two points rounding to the nearest tenth is

9.2 units.

Given that the two points are (-1,4) and (8,2).

We are required to find the distance between two given points.

Distance is basically a numerical or occasionally qualitative measurement of how far apart objects or points are.

The points are (-1,4) and (8,2).

The formula to calculate the distance between two points (x,y),(,a,b) is as under:

Distance=[tex]\sqrt{(a-x)^{2} +(b-y)^{2} }[/tex]

Distance=[tex]\sqrt{(8+1)^{2} +(2-4)^{2} }[/tex]

=[tex]\sqrt{(9)^{2} +(-2)^{2} }[/tex]

=[tex]\sqrt{81+4}[/tex]

=[tex]\sqrt{85}[/tex]

=9.2195

After rounding off to nearest tenth we will get 9.2.

Hence the distance between the two points rounding to the nearest tenth is 9.2 units.

Learn more about distance at https://brainly.com/question/17273444

#SPJ9

Answer:

40°

Step-by-step explanation:

At point C, the angle is shown as 110°.
Since a line is 180°, you now know that the other side of point C is 70°.
Line A-B and A-C are equal (shown by the short lines), meaning the angle at point B is also 70°,
A triangle is 180° in total, so the equation would be 180° - 2(70°) = 180° - 140° = 40°

Answer:
y = x - 4

Step-by-Step Explanation:

Perpendicular lines have slopes that are negative reciprocals—multiplying their slopes result in -1.Given the slope of a line m = -1, then it means that the slope of the other line must be 1 (because multiplying the slope of line 1  (m1 = -1), and the slope of the other line (m2 = 1) results in: -1 × 1 = -1).Therefore, given the slope of line 2 (m2 = 1), and the point (2, -2), we could plug these values into the slope-intercept form and solve for the y-intercept (b):y = mx + b-2 = 1(2) + b-2 = 2 + bSubtract 2 from both sides to solve for b:-2 - 2 = 2 - 2 + b-4 = bTherefore, the y-intercept (b) = -4.Hence, the equation of the perpendicular line is: y = x - 4

Please mark my answers as the Brainliest if you find my explanation helpful :)

Answer:

Domain: [-2, infinity)

Range: [-4, infinity)

Step-by-step explanation:

There's only one graph I see.

Domain is how far the graph extends on the x axis.

Range is how far the graph extends on the y axis.