Solve the system of equations using the linear combination method.

{9x+5y=35
{2x+5y=0



Enter your answers in the boxes.

x =_

y =_

Answer:

given rational function is undefined for x = 2

Step-by-step explanation:

The given rational function is

[tex]\frac{x^2-4}{2-x}[/tex]

The rational function is undefined if the denominator is zero.

Hence, the given rational function is undefined if

[tex]2-x=0[/tex]

Solve the equation for x

[tex]x=2[/tex]

Therefore, the given rational function is undefined for x = 2

Answer:

y ≤ 31 students

Step-by-step explanation:

The rental cost is a fixed cost that will be incurred irrespective of the number of students embarking on the class field trip. This cost added to the total ticket cost must be less than or equal to the budget.

the total ticket cost for y number of students

= 9.5y

Hence the total cost = 9.5y + 600 ( measured in $)

In inequality form,

9.5y + 600 ≤ 900 (all in $)

9.5y ≤ 900 - 600

9.5y ≤ 300

y ≤ 300/9.5

y ≤ 31 students

Answer:

-3

Step-by-step explanation:

right on edge

Answer:

Step-by-step explanation:

If this net folds into a cube, then, when we form the cube, side B and side E becomes opposite sides, because side D and side F would be placed next to side B, having side E as opposite.

Therefore, the right answer is the last choice. Sides B and E appear on opposite sides.

Answer:

The third diagram.

Step-by-step explanation:

When we have two parallel lines cut by a transversal, vertical angles are congruent; alternate interior angles are congruent; alternate exterior angles are congruent; corresponding angles are congruent; and same-side interior angles are supplementary.

In the first diagram, we have two angles on the same side of their respective parallel lines and the same side of the transversal.  These are by definition corresponding angles.  Since they are not congruent, these lines are not truly parallel.

In the second diagram, we have two angles on opposite sides of the transversal and outside the block of parallel lines.  These are by definition alternate exterior angles.  Since they are not congruent, these lines are not truly parallel.

In the third diagram, we have two angles inside the block of parallel lines and on the same side of the transversal.  These are by definition same-side interior angles.  Since they are congruent, these are parallel lines.

Answer:

All values of x make the equation true. It is an infinite solution.

Answer:

Step-by-step explanation:

Let x = the number of hamburgers

Let y = the number of hotdogs

Let us first represent the amount of food:

10x + 5y ≤ 60

This means x packages of $10 hamburgers plus y packages of $5 hotdogs is greater than or equal to $60.

However, we have also been given another important piece of information and that is that he must buy at least three packages of hotdogs.

y ≥ 3

this means that the packages of hotdogs must be no less than 3.

Hence or two inequalities are 10x + 5y ≤ 60 & y ≥ 3.

This also means that the least he can spend on hotdogs is $15. The most he can spend on hamburgers is $45, meaning the most packages of hamburgers he can get is 4

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Answer:

£1.31

Step-by-step explanation:

5+7+12=24

216÷24=9

Small=9x5=45

Medium=9x7=63

Large=9x12=108

2x= Medium, Large= 3x, Small=x

Small=45x, Medium= 63x2=126x, Large=108x3=324x

45x+126x+324x=495x

£648.45=495x

£648.45÷495=x

£1.31=x

The profit for one small cake will be £ 1.31. The profit of the one small cake is the amount of benifit obtained to sell one cake.

When money generated from a commercial activity exceeds the expenses, costs, and taxes involved in maintaining the activity in question, profit is earned.

The ratio of the small :medium: large cake is 5:7:12.

Let the cake is considered to be x;

The sum of alll the cakes is;

5x+7x+12x=24 x

The total no of cake is 216

Each no of cake is found as;

[tex]\rm 24 x = 216 \\\\ x = 9[/tex]

The number of the small cake;

N(s) = 9 ×5 =45

N(m)=9×7=63

N(l)=9×12=108

Let the small cake is x

The profit for one medium cake is twice the profit for one small cake;

P(m)=2x

P(l)=3x

P(s)=x

The small medium and the large cake according to the new condition will be 45 x,126x,324x respectively.

The sum of all the cakes according to the new condition is found as;

[tex]4s x +126 x+324 c \\\\ 495 x=648.45 \\\\ x=\£ \ 1.31[/tex]

Hence the profit for one small cake will be £ 1.31.

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From the graph of given function, we have vertex (1, -6). Therefore, option A is the correct answer.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is y=(x-1)²-6.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex: (1, -6)

Focus: (1, -23/4)

Axis of symmetry: x=1

Directrix: y=-25/4

The coordinate points to plot are (-1, -2), (0, -5), (1, -6), (2, -5) and (3, -2).

Therefore, option A is the correct answer.

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Answer:

its b

Step-by-step explanation:

Answer:constant of variation = 1.2

Step-by-step explanation:

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The approximate speed of model 5's 148-foot blade travels at 0.18 miles per revolution converted to feet is approximately 385.8 revolutions per hour.

To find the number of revolutions per minute for Model 5 with a blade length of 148 feet and a tip speed of 0.18 miles per revolution,

use the following calculation:

First, convert the tip speed from miles to feet:

0.18 miles × 5280 feet per mile = 950.4 feet per revolution

Now, divide this by the length of the blade in feet:

950.4 feet per revolution / 148 feet = 6.43 revolutions per minute

Finally, multiply this by 60 minutes per hour to get the number of revolutions per hour:

6.43 revolutions per minute × 60 minutes per hour = 385.8 revolutions per hour

Therefore, the required speed of model 5 has a blade that makes approximately 385.8 revolutions per hour.

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By solving the equations through linear combination method we are going to get the values of p and q are -6 and three.

It is a bit like elimination method of solving equations within which one variable is eliminated so we'll get the worth of another variable.

We are having two equations:

5p-3q=-39-------------1

-2p-3q=3---------------2

equation1 * 2 and equation 2 *5

10p-6q=-78

-10p-15q=15

Now add both equations

10p-6q-10p-15q=-78+15

-21q=-63

q=3

Put the worth of q in 1

5p-3(-3)=-39

5p+9=-39

5p=-30

p=-6

Hence the system of equations have the worth of p=-6 and q=3.

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When a horizontal plane passes through the center of a sphere with a radius of 26 inches, the cross-section formed is a circle with a radius of 26 inches.

let's break down the problem into two parts:

Describe the cross-section: We'll describe the shape formed when a horizontal plane passes through the center of the sphere.

Calculate the dimensions of the cross-section: We'll calculate the dimensions of the cross-section, such as its radius or diameter.

1. Describe the cross-section:

When a horizontal plane passes through the center of a sphere, it divides the sphere into two equal halves. The cross-section formed by this plane and the sphere will be a circle. Since the plane passes through the center of the sphere, the circle will be perfectly centered.

2. Calculate the dimensions of the cross-section:

Since the radius of the sphere is given as 26 inches, the radius of the cross-section (which is also the radius of the circle formed) will also be 26 inches.

So, the cross-section formed by the plane and the sphere is a circle with a radius of 26 inches.

The linear function f (x) hat the agency could use to determine its daily rental charges will be;

⇒ f (x) = 0.2x + 20

Where, f (x) is in dollars and x is in miles.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Heidi rented a car for one day and paid $58 for 190 miles.

And, On another day she paid $86 for 330 miles.

Now,

We find the linear function for f (x), where f (x) is in dollars and x is in miles as;

Here the two situations are given for miles and dollars as;

(190, 58) and (330, 86)

Thus, The linear function with two points (190, 58) and (330, 86) is defined as;

⇒ y - y₁ = (y₂ - y₁)/(x₂ - x₁) (x - x₁)

⇒ y - 58 = (86 - 58) / (330 - 190) (x - 190)

⇒ y - 58 = 28 / 140 (x - 190)

⇒ y - 58 = 1/5 (x - 190)

⇒ y - 58 = 0.2 (x - 190)

⇒ y - 58 = 0.2x - 38

⇒ y = 0.2x - 38 + 58

⇒ y = 0.2x + 20

⇒ f (x) = 0.2x + 20

Thus, The linear function f (x) hat the agency could use to determine its daily rental charges will be;

⇒ f (x) = 0.2x + 20

Where, f (x) is in dollars and x is in miles.

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To determine the daily rental charges at a car rental agency based on fixed and per mile fees, the linear function f(x) is found to be $40 + $0.15 per mile.

Linear function f(x):