Graph the equations y = -1/2x + 3 and y = 2x - 2
1After you graph the two lines, be sure to take a screenshot of your work and include it in your answer below.

2) What is the solution to the system of equations?

3) Prove that the answer you provided in part 2 is correct, by substituting the solution into the original equations. Be sure to show all your work.

Answer:

The correct answer is C: Y = -1/2x - 4.The slope of the given line is -1/2, so any line that is parallel to it will have the same slope. In order to find the equation of a line with the same slope that passes through the point (2, -5), we can use the point-slope form of the equation of a line.The point-slope form of the equation of a line is:y - y1 = m(x - x1)where m is the slope of the line, and (x1, y1) is a point on the line.In this case, we can plug in the values m = -1/2, x1 = 2, and y1 = -5 to get:y + 5 = -1/2(x - 2)Solving for y, we get:y = -1/2x - 4Therefore, the equation of the line that is parallel to the given line and passes through the point (2, -5) is Y = -1/2x - 4.

Answer: x = 19

Step-by-step explanation:

Let's start with what we have, we'll let x = the number:

4x - 12 = 64

Then we add 12 to both sides:

4x = 76

Divide by 4 from both sides:

x = 19

Answer: 22%

Step-by-step explanation:

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is [tex]y=-\frac{3}{4}x-17[/tex]

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Step-by-step explanation:

since f(x) = 2×x + 1

therefore f(2.99) = 2×2.99 + 1 = 6.98 ≈ 7

therefore f(2.999) = 2×2.999 + 1 = 6.998 ≈ 7

therefore f(3.01) = 2×3.01 + 1 = 7.02 ≈ 7

therefore f(3.001) = 2×3.001 + 1 = 7.002 ≈ 7

now for the what conclusion can you draw from these results i dont 100% know but i think he wants that

the point x = 3 and the point y = 7

since f(x) = y

and since we have the approximate of x 3

A child of a parent with a mutation in collagen and displaying OI will have 50% probability of also having OI.

Osteogenesis imperfecta (OI) is an inherited or genetic bone disorder which is present at birth. It is also known as brittle bone disease. A child born with OI may have soft bones which fracture easily, bones which are not formed normally, and other problems. Signs and symptoms may range from mild to severe.

Life expectancy for OI babies vary greatly depending on OI type. Babies with Type II generally die soon after birth. Children with Type III may live longer, but mostly only until around age 10.

About 90% of OI cases are caused by autosomal dominant mutations in the type I collagen genes. Mutations in one or the other of these genes cause the body to make either abnormally formed collagen or too little collagen. Mutations in these genes cause OI Types I through IV.

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Answer:

Step-by-step explanation:

m=riserun=ΔyΔx

m=y2−y1x2−x1

m=0−2−2−2

m=−2−4

m=12

The answer is :

m = 0.5

Franklin has 10 granola bars and 6 pieces of dried fruit. The greatest number of snack bags Franklin can make is 2 bags.

The factor shared by at least two numbers is known as the common factor. Each of the given numbers is divided exactly by two or more numbers.

Here given granola bar = 10 and dried fruit = 6.

Then, the common factors of 10 and 6 are

1, 2, 3, and 6 are used to represent factors of 6.

1, 2, 5, and 10 are used to represent factors of 10.

2 is discovered to be the biggest common factor between 6 and 10.

Then, the greatest number of snack bags Franklin can make is 2 bags.

The complete question -

Franklin wants to create a snack bag for a trip he is going on. He has 10 granola bars and 6 pieces of dried fruit. If the snack bag should be identical without any food left over, what is the greatest number of snack bags Franklin can make?

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Answer: Look in the attachment:

Step-by-step explanation: If it was random sampling, it would all be done randomly, barley without doing anything, and NOT doing anything particular, the 4 that are circled (in the attachment) are the ones that I am talking about; they ARE NOT examples of random sampling. If you look at the attachment, you might understand a little more :P

Using a double integral, the area of the region is [tex]\frac{\pi}{12}[/tex].

Consider the following polar equation:

r = 8cos3[tex]\theta[/tex]

This is the process for measuring the intensity of light. Such intensity varies according to how close or far you are from LED light bulbs. Engineers use polar curves to plot the level of the intensity at any given point. In other words, a polar curve tells an engineer how LED light bulbs spread light across a room or surface.

The objective is to find the area of the region using double integral.

The sketch of the curve attached at the end of solution.

The intersection points of the curve with horizontal axis are given by,

8cos3[tex]\theta[/tex] = 0

cos3[tex]\theta[/tex] = 0

[tex]3 \theta & =\pm \frac{\pi}{2}[/tex]

[tex]\theta & =\pm \frac{\pi}{6}[/tex]

Therefore, the loop is given by the region,

[tex]D=\left\{(r, \theta) \mid-\frac{\pi}{6} \leq \theta \leq \frac{\pi}{6}, 0 \leq r \leq \cos 3 \theta\right\}[/tex]

Let A be the area of the curve.

The area of the loop is given by,

[tex]& A(D)=\iint_D d A \\[/tex]

[tex]& =\int_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \int_0^{\cos 3 \theta} r d r d \theta \\[/tex]

[tex]& =\int_{-\frac{\pi}{6}}^{\frac{\pi}{6}}\left[\frac{r^2}{2}\right]_0^{\cos 3 \theta} d \theta \\[/tex]

[tex]& =\frac{1}{2} \int_{\frac{\pi}{6}}^{\frac{\pi}{6}} \cos ^2 3 \theta d \theta \\[/tex]

[tex]& =\frac{1}{2} \int_{-\frac{\pi}{6}}^{\frac{\pi}{6}}\left(\frac{1+\cos 6 \theta}{2}\right) d \theta \\[/tex]

[tex]& =\frac{1}{4}\left[\theta+\frac{1}{6} \sin 6 \theta\right]_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \\[/tex]

[tex]& =\frac{1}{4}\left[\left(\frac{\pi}{6}+\frac{1}{6} \sin \pi\right)-\left(-\frac{\pi}{6}+\frac{1}{6} \sin (-\pi)\right)\right] \\[/tex]

[tex]& =\frac{1}{4}\left(\frac{\pi}{3}\right) \\[/tex]

[tex]& =\frac{\pi}{12} \\[/tex]

Hence, the area of the one loop of the rose [tex]r = 8 \cos(3\theta)[/tex] is [tex]\frac{\pi}{12}[/tex].

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Answer: 11 feet

Step-by-step explanation:

The equation for area of square is

area = s^2

So we just need to take the square root of 121, and we will get the answer is 11 ft!

Answer:

11 ft

Step-by-step explanation:

Since the area of the square is 121 (and squares have all four sides the same length), the sides must be 11 feet. Because

11 × 11 = 121

You could show work by using an equation.

Area = s^2

121 = s^2

Square root both sides.

sqrt121 = sqrt(s^2)

11 = s

The side length is 11 feet.

Refer to the photos taken.

Answer: 96 crayons

Step-by-step explanation:

Take 182 subtract 86 = 96 crayons

96 crayons are not broken

Answer:

It will take 4 Hours

Step-by-step explanation:

5 x 40 equals 200 (So 200 is the total distance needed to be made)

We can now divde the total distance by how fast the car is moving to get the time.

200 / 50 = 4

So the answer is 4 hours

From 1750 to 1900, Europe's strength and dominance over the world grew dramatically.

New western political concepts developed strong, centralized states that directed empires all around the world, while industrialization created unprecedented wealth.

The following are the reasons and impacts of the various revolutions that occurred between 1750 and 1900:

The globe became really autonomous as a result of industrialization.

They were able to push for changes to their terrible working conditions through the formation of unions.

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The axis of symmetry of the parabola would be x = 2

From the question, we have the following parameters that can be used in our computation:

Vertex = (2, 13)

Rewrite the vertex as follows

So, we have the following representation

(x, y) = (2, 13)

Remove the y-coordinates

This gives

x = 2

This represents the axis of symmetry

Hence, the axis of symmetry is x =2

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The equations are 2r + b = 8.40 and 3r + b = 9.35. Then the cost of refill and egg breakfast will be $0.95 and $6.50, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The eatery charge you and your companion got was not organized. You requested 2 beverage tops off and the egg breakfast, for a sum of $8.40. Your companion requested 3 tops off and the egg breakfast for $9.35.

Let 'r' be the cost of refill and 'b' be the cost of egg breakfast. Then the equations are given as,

2r + b = 8.40            ...1

3r + b = 9.35            ...2

From equations 1 and 2, then we have

3r - 2r = 9.35 - 8.4

r = $0.95

Then the cost of the egg breakfast will be given as,

2 (0.95) + b = 8.40

b = $6.50

The equations are 2r + b = 8.40 and 3r + b = 9.35. Then the cost of refill and egg breakfast will be $0.95 and $6.50, respectively.

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The Question is based on concept of Simplification and answer to this question is -19√2

What is Simplification?

Simplification is the process of making a task, problem, or system easier to understand and manage. It involves breaking down a concept or problem into simpler parts in order to better understand the whole. Simplification can help streamline a process, making it more efficient and easier to complete. It can also help to make complex topics more accessible to a wider audience. Simplification can also be used to make a difficult problem more manageable, allowing for easier solutions.

Here we are given question 2√2 - 7√8 we can do some simplifications like:
but we know we can write √8 = 3√2
hence putting back in original eqn
2√2 - 7(3√2)
2√2 - 21√2
-19√2
Hence required answer is -19√2 by simplification

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Answer:

x< 5

Step-by-step explanation:

See the graph below

The number of people who speaks neither of these languages is 8.

Set theory is a branch of mathematical logic that studies sets, which can be described informally as collections of objects. Although any object can be collected into a set, set theory as a branch of mathematics is primarily concerned with those that are relevant to mathematics as a whole.

Sets are well-defined collections that are entirely defined by their elements. In this case, in the group of 42 people, 30 people speak Spanish and 20 people speak French, those who speak neither of these languages will be:

= 20 + 30 - 42

= 8

Therefore, 8 people neither speaks the languages.

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Answer:

6:5 or [tex]\frac{6}{5}[/tex]

Step-by-step explanation:

[tex]\frac{90}{75}[/tex]  Divide by [tex]\frac{15}{15}[/tex]

[tex]\frac{6}{5}[/tex] or 6:5

Expreion have a quotient of 6 is 0. 48 ÷ 0. 08.

What is quotient?

In mathematics, the quotient is the result of performing division operations on two integers. It is essentially the outcome of the division procedure. In arithmetic division, the terms divisor, dividend, quotient, and remainder are employed in four different ways.Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

0. 48 ÷ 0. 8

=0.06

The solution for Long Division of [tex]$\frac{4.8}{8}$[/tex] is 0.6

The solution for Long Division of [tex]$\frac{0.48}{0.08}$[/tex] is 6.

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Answer:

(0,14)  This is the y intercept.

(28,0) This is the x intercept.

Step-by-step explanation:

Let x = 0

x + 2y = 28

0 + 2y = 28

2y = 28  Divide both sides by 2

x = 14

(0,14)  This is the y intercept.

Let y = 0

x + 2y = 28

x + 2(0) = 28

x + 28

(28,0) This is the x intercept.

Answer: C

Step-by-step explanation:

Answer:Y=10X-16

Step-by-step explanation:

y = x3- 2x 2,( 2, 4)( Given)

Find the first outgrowth, calculate the pitch and find the equation.

We should first know the pitch of the wind at(,4)

pitch at any point on the wind is written by its first outgrowth as

dy/ dx = 3x2- 2

pitch at x = 2

m = 3( 2) 2- 2 = 12- 2 = 10

Equation of a digression is given as

c mx = y

Where m is the pitch

Substituting the values

c 10 × 2 = 4

On farther computation

c 20 = 4

c = 16

The equation of the digression is y = 10 x- 16

Thus, the equation of the digression line to the wind is y = 10x-16

Mr. Kenny can complete five projects without running out of clay.

The number of projects that can be completed will be calculated using division.

1/6 of a pound of clay is required for number of project = 1

7/8 pounds of clay will be required for number of project = 7/8 ÷ 1/6

Rewriting the fraction with numerator and denominator

Number of projects = (7×6)÷(8×1)

Performing multiplication in numerator and denominator

Number of projects = 42/8

Performing division

Number of projects = 5.25

Rounding off, we get number of projects = 5

Mr. Kenny can complete 5 projects.

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Answer: 2/12= 16.67% four sig fig

Step-by-step explanation:

Using (mass of sugar)/(total mass)

and total mass equals (mass of sugar) + (mass of water)

get a total mass of 12kg

Therefore percentage is 2/12=1/6=16.666666%

Answer:

The percentage of sugar in the syrup is 16.66...%

Step-by-step explanation:

lmk

There are 324 miles can Mario drive with 9 gallons of gas.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

He can drive 18 miles on ½ a gallon of gas.

Now,

Since, He can drive 18 miles on ½ a gallon of gas.

Let the number of miles cover with 9 gallons of gas = x

So, By definition of proportion, we get;

⇒ 18 / (1/2) = x / 9

⇒ 18 × 2 = x / 9

⇒ 36 × 9 = x

⇒ x = 324 miles

Thus, The number of miles cover with 9 gallons of gas = 324 miles

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