Choose the correct graph of the given system of equations. y + 2x = −1 3y − x = 4 Group of answer choices graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1 graph of two lines that intersect at the point 1, 1, with text on graph that reads One Solution 1, 1 graph of two parallel lines with positive slopes with text on the graph that reads No Solution graph of two lines on top of each other with text on graph that reads Infinitely Many Solutions

Answer:

x =  ± [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

9x² − 16 = 0

9x² = 16

x² = [tex]\frac{16}{9}[/tex]

x = ± √[tex]\frac{16}{9}[/tex]

x =  ± [tex]\frac{4}{3}[/tex]

So, the answer is:  x = [tex]\frac{4}{3}[/tex] , - [tex]\frac{4}{3}[/tex]

Answer: 12.57

Step-by-step explanation:

the radius is 2 so you 2 times pi squared

a.) The position of the train moving from station A to station B after 10 minutes 20 km east

b.)  The position of the train moving from station A to station B after 10 minutes, if station B is assumed to be the origin is 50 km west

c.) The position of the train moving from station A to station B after 10 minutes, if station C is assumed to be the origin is 80 km west

we have that:

Railway station -     A            B              C

Distance(km) -       0            30             60

Starts from A , train reaches B be in 15 minutes

Starts from A , train reaches C be in 30 minutes

a.)

If A is origin

As train covers 30km = 15 minutes

⇒ 15 minutes = 30 km

   1 minute =  km

⇒ 10 minutes = 2×10 = 20 km

The position of the train moving from station A to station B after 10 minutes = 20 km east

b.)

If B is origin then , the position of  the train moving from station A to station B after 10 minutes = 30 + 20  = 50 km west

c.)

If C is the origin then , the position of  the train moving from station A to station B after 10 minutes = 60 + 20  = 80 km west

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#possible complete question:

Three railway stations, A, B, and C, are situated on a straight railway route. Station B is at 30 km in the east from station A and station C is at 60 km in east from station A. A train, with a constant average velocity, starts from A and reaches B in 15 minutes, and reaches C in 30 minutes. Assuming that station A is the origin, find the following:

a. The position of the train moving from station A to station B after 10 minutes.

b. The position of the train moving from station A to station B after 10 minutes, if station B is assumed to be the origin.

c. The position of the train moving from station A to station B after 10 minutes, if station C is assumed to be the origin.

Step-by-step explanation:

Let A(x1,y1)=(-3,1), B(x2,y2)=(5,6)  be the points of a line segment.

Mid point = [tex]\sf{ \dfrac{x1+x2}{2} , \dfrac{y1+y2}{2} }[/tex]

Mid point = [tex]\sf{ \dfrac{-3+1}{2} , \dfrac{1+6}{2} }[/tex]

Mid point = [tex]\sf{ \dfrac{-2}{2} , \dfrac{7}{2} }[/tex]

Answer:c. F(x)=2x

Step-by-step explanation:

The two questions should you ask are:

The given answers to the above questions, one can be able to know the ranges of values that the four numbers have, as well as their relative positions.

In the event that we know the smallest and biggest numbers, we can be ready to mark those points on the number line and after that put the other two numbers in between them agreeing to their relative positions.

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Answer:

2) The smallest amount of fabric Amy can buy is 78 inches = 2 1/6 yards, so she will need 2 1/4 yards of fabric.

3) $2.25(5) + $0.35(2) + $0.25(3) + $0.60 = $13.30 before sales tax

Sales tax is $13.30 × .08 = $1.06

Total is $13.30 + $1.06 = $14.36

The GCF of 84 and 36 is 12.

The GCF of two non-zero integers, x(36) and y(84), is the greatest positive integer m(12) that divides both x(36) and y(84) without any remainder.

GCF of 36 and 84 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

There are 6 common factors of 36 and 84, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 36 and 84 is 12.

Rewrite in the form of a(b + c), a is the greatest common factor of 84 and 36

84/ 12 = 7

36/12 = 3

So, 12(84 + 36)

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The marginal revenue curves for the given demand curves are: MR = -0.5  Q + 12 In a monopoly market, the marginal revenue curve is always below the demand curve. This is because a monopolist can only increase their revenue by decreasing the price of their product, and therefore they must lower the price for all units sold, not just the last one.

For the first demand curve, P = -5Q + 25, the marginal revenue curve can be found by taking the derivative of the demand curve with respect to Q. This gives us:

MR = dP/d Q = -5

So the marginal revenue curve is a horizontal line at MR = -5. Adding the intercept of the demand curve at P = 25, we get:

MR = -5Q + 25

For the second demand curve, P = -0.5Q + 12, the marginal revenue curve can be found in the same way:

MR = dP/dQ = -0.5

So the marginal revenue curve is a horizontal line at MR = -0.5. Adding the intercept of the demand curve at P = 12, we get:

MR = -0.5Q + 12

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A cone with a height of 9 in and a base diameter of 6 in has the volume 84.78 cubic inches.

The formula for the volume of a cone is:

V = (1/3)π[tex]r^{2}[/tex]h, where r is the radius of the base and h is the height.

In the question it is given height = 9 in and a base diameter = 6 in.

Radius = diameter/2

r = d/2 = 6/2 = 3 inches

Substituting the values in the formula:

V = (1/3)π[tex](3\ in)^2[/tex](9 in)

Simplifying the expression:

V ≈ 84.78 [tex]in^3[/tex]

Rounding to the nearest hundredth, we get:

V ≈ 84.78 [tex]in^3[/tex]

Therefore, the approximate volume of the cone is 84.78 cubic inches.

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A plane is an infinite two-dimensional figure.

We have,

When two planes intersect, they form a line.

The vector equation for the line of intersection is given by

r = r₀ + tₓ

where r₀ is a point on the line

tₓ is the cross product of the normal vectors of the two planes.

The parametric equations for the line of intersection are given by

x = a , y = b and z = c

where a, b and c are the coefficients from the vector equation

r = a (i) + b (j) + c (k)

The line of intersection will be perpendicular to the normal of both the planes

The line of intersection lies on both the planes

Therefore , a line is observed at the intersection of two planes

Given data ,

A line is one-dimensional, a segment is a part of a line and is also one-dimensional, and a point is zero-dimensional.

A plane, on the other hand, is a flat, two-dimensional surface that extends infinitely in all directions.

It has length and width, but no thickness, and can be thought of as an infinitely large sheet of paper.

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complete question:

Which of the following is an infinite two-dimensional figure?

A. A line

B. A plane

C. A segment

D. A point

1. 7 x^2 - 9 y^2 = 343 is a hyperbola

2. x^2 + y^2 - 4 x + 6 y - 5 = 1 is a circle

3. 4 x^2 + 9 y^2 = 1 is a ellipse

4. x^2 - 6 y = 0 is a parabola

A conic section conic or a quadratic curve is described as  a curve obtained from a cone's surface intersecting a plane.

The three types of conic section are :

All conics are  written in terms of the following equation:

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0.

In conclusion, a conic is the intersection of a plane and a right circular cone.

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#Complete question:

Match the following equations with the conic sections formed by them. 1. x 2 + y 2 - 4x + 6y - 5 = 0 hyperbola 2. x 2 - 6y = 0 circle 3. 4x 2 + 9y 2 = 1 ellipse 4. 7x 2 - 9y 2 = 343 parabola

The equation using the parent function y = √x that has a domain of 3≤x<∞ and a range of -2≤y<∞ is y = √(x - 3) - 2.

An equation is a mathematical statement that indicates the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields of mathematics, science, engineering, and economics. They can be written in various forms, such as standard form, slope-intercept form, point-slope form, and more.

Here,

To shift the parent function y = √x to the right by 3 units and down by 2 units, we use the transformation:

y = √(x - 3) - 2

This equation has a domain of 3 ≤ x < ∞, since we subtract 3 from x inside the square root function. The range is -2 ≤ y < ∞, since we subtract 2 from the square root function.

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Step-by-step explanation:

f(x) = - 2 (x+1)^2 + 8     is already in vertex form

quadratic form can be found by expanding it :

f(x) = -2 ( x^2 + 2x +1)  + 8

f(x0 = -2x^2 -4x -2 + 8  

f(x) =  - 2x^2 - 4x + 6     <=====quadrtaic form

Answer:6

Step-by-step explanation:

The  explicit formula for nth term geometric sequence is aₙ = a x rⁿ⁻¹.

let a geometric series is of the form

a, a², a³, a⁴ a⁵, ....

where a₁ = a = first term and other terms are obtained by multiplying by

r.

Now, each term is r times of previous term.

So, to get the nth term we have to multiply (n-1) by r.

Thus, the explicit formula for nth term geometric sequence is

aₙ = a x rⁿ⁻¹

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the width of the previous image is 9.5mm.

     The widthh can be defined as the horizontal measurement or distance measured from side to side.

       In geometry, the shorter side of an object is frequently referred to as its "width". For instance, both of the given rectangles are identical rectangles, but one of them has been rotated to demonstrate that the shorter side of the rectangle is referred to as its width.

In the given problem,

         if the width of the previous image is x,

                            4x=38

                        ⇒x=9.5mm

So, the width of previous image is 9.5mm.

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The trend line for the y = 0.5x + 2 is attached accordingly. Note that the the predicted gas price for month 13 would be $8.50.

a. To draw a trend line on a scatter plot, you need to perform a linear regression analysis. This involves finding the line of best fit that passes through the data points. The equation for a linear regression line is typically of the form y = mx + b, where y is the dependent variable (gas price in this case), x is the independent variable (month), m is the slope of the line, and b is the y-intercept.

Once you have the equation for the line of best fit, you can plot it on the scatter plot to visualize the trend. The slope of the line will tell you the direction and steepness of the trend (i.e., whether prices are increasing or decreasing, and how quickly).

b. To predict future values using the trend line, you can simply plug in the value of the independent variable (month) for the month you want to predict, and solve for the dependent variable (gas price). For example, if the equation for the trend line is y = 0.5x + 2, and you want to predict the gas price for month 13, you would plug in x = 13 and solve for y:

y = 0.5(13) + 2

y = 6.5 + 2

y = 8.5

So the predicted gas price for month 13 would be $8.50.

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according to the question the actual distance between Chattanooga and Nashville is 133 miles.

Distance is an object's total, aimless movement. Without regard to whether anything has a beginning or an end, distance can be defined as the amount of space that something has traversed. Distance is referred to be the breadth or magnitude of the gap between two locations. It should be highlighted that the distance between two points and the length travelled between the two are not the same thing. The total length of a path connecting two locations counts as the distance travelled. Distance is the distance in reality that a body travels. It also goes by the name "path length." For instance, the length of a path for the thing passing via point O and arriving at position P would be OP = 360 m.

given,

If 1 inch on the map represents 38 miles in reality, then 3.5 inches on the map would represent:

3.5 inches * 38 miles/inch = 133 miles

Therefore, according to the scale on the map, the actual distance between Chattanooga and Nashville is 133 miles.

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Answer: 2/3

Step-by-step explanation: 1/2 converted to 6ths is 3/6 add them together and it’s 4/6 simplify that and it’s 2/3

Answer:7

Step-by-step explanation: you divide 49 by 7 which gives you 7

Answer:

7

Step-by-step explanation:

1/7 of 49 would be equal to divided 49 by 7 to find 1 seventh of 49

49/7 = 7

so 1/7 of Chesters 49 CDS is equal to 7 CDS that Tony has.

hope this helps :)

The two solutions to the system of equations are (x,y) = (7/5,-3) and (x,y) = (144/65,-12/13).

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x.

We can use substitution to solve this system of equations.

First, we solve the second equation for one of the variables, say x:

5x + 12y + 13 = 0

5x = -12y - 13

x = (-12/5)y - (13/5)

Next, we substitute this expression for x into the first equation:

x² + y² = 1

[(-12/5)y - (13/5)]² + y² = 1

Expanding the square and simplifying, we get:

y² + [(144/25)y² + (312/25)y + (169/25)] + y² = 1

(26/5)y² + (312/25)y + (144/25) = 0

Multiplying both sides by 25 to eliminate the fractions:

26y² + 312y + 144 = 0

Dividing by 4 to simplify:

6.5y² + 78y + 36 = 0

Using the quadratic formula:

y = (-b ± sqrt(b² - 4ac)) / 2a

where a = 6.5, b = 78, and c = 36.

Plugging in these values:

y = (-78 ± sqrt(78² - 4(6.5)(36))) / 2(6.5)

y = (-78 ± sqrt(4761)) / 13

y = (-78 ± 69) / 13

y = -3 or -12/13

If y = -3, then substituting into the equation for x gives:

x = (-12/5)(-3) - (13/5) = 7/5

So one solution is (x,y) = (7/5,-3).

If y = -12/13, then substituting into the equation for x gives:

x = (-12/5)(-12/13) - (13/5) = 144/65

So another solution is (x,y) = (144/65,-12/13).

Therefore, the two solutions to the system of equations are (x,y) = (7/5,-3) and (x,y) = (144/65,-12/13).

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A sample size of at least 1,521 Internet users would be necessary to estimate the proportion of interest (the proportion of Internet users who are willing to pay fees for website access) to within 2 percent in a 95 percent confidence interval.

To calculate the sample size required to estimate a proportion with a certain level of confidence and margin of error, we can use the following formula:

[tex]n = (Z^2 \times p \times (1 - p)) / E^2[/tex]

where:

n is the required sample size

Z is the Z-score for the desired level of confidence (95% confidence corresponds to a Z-score of 1.96)

p is the estimated proportion of interest (the proportion of Internet users who are willing to pay fees for website access)

E is the desired margin of error (2% in this case, expressed as a decimal)

We are given that out of a sample of 13,000 Internet users surveyed in 1995, 2,938 were definitely not willing to pay fees for website access. This means that the proportion of interest (p) is:

p = (13,000 - 2,938) / 13,000 = 0.774

Now we can plug in the values and solve for n:

[tex]n = (1.96^2 \times 0.774 \times (1 - 0.774)) / 0.02^2[/tex]

n ≈ 1,521

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Answer:

When 2.7 is multiplied by 10 to the 2nd power, it becomes 270. The digit 7 is in the ones place, so the value of the digit 7 is 7.

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) Given statement: skipped : I'm not sure what statement you're referring to, as there is no statement labeled "a" in  question.

Hence answer provided.

b) As the degrees of freedom increase, the t distribution curve does become more similar to the standard normal curve.

True. Because the t distribution resembles the normal distribution when the degrees of freedom are high.

c) The two mean non-pooled test is used for 2 independent populations under the assumption that the two populations have different standard deviations.

False - Because the non-pooled t-test can be used to compare the means of the two populations when the assumption of equal variances is true.

d) The standard error is the standard deviation of the sampling distribution and is calculated by dividing the sample standard deviation by the square root of the sample size.

False - Because the standard error, which is determined as the sample standard deviation divided by the square root of the sample size, is a measure of the variability of the sample mean.

a)  Given statement: skipped : I'm not sure what statement you're referring to, as there is no statement labeled "a" in  question.
b) Given statement : As the degrees of freedom increase, the t distribution curve does become more similar to the standard normal curve.

The given statement is true.

Because, When the degrees of freedom are large, the t distribution approaches the standard normal distribution.
c) Given statement: The two mean non-pooled test is used for 2 independent populations under the assumption that the two populations share the same standard deviation.

The given statement is true.

Because, When the assumption of equal variances is met, the non-pooled t-test can be used to compare the means of the two populations.
d)  Given statement: The standard error is not always equal to the sample standard deviation.  

The given statement false.

Because, The standard error is a measure of the variability of the sample mean, and it is calculated as the sample standard deviation divided by the square root of the sample size.

The sample standard deviation is a measure of the variability within the sample itself.

The standard error tends to be smaller than the sample standard deviation because it accounts for the effect of the sample size on the variability of the sample mean.

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Answer: y = -5

Step-by-step explanation:

We move the constants to one side to get y^3 = -125.

Then, we cube root both sides to get y = -5.

Ben's house will be worth $490,523.96 in 9 years if the value continues to increase at a rate of 7% per year.

We can use the formula for compound interest, which is:

A = P × (1 + r)ⁿ

Where:

A = final amount

P = principal (starting value)

r = annual interest rate (expressed as a decimal)

n = number of compounding periods

In this case, the principal is $281,320, the annual interest rate is 7% (or 0.07 as a decimal), and the number of compounding periods is 9 years. Plugging in these values, we get:

A = $281,320 × (1 + 0.07)⁹

A = $281,320 × 1.743

A = $490,523.96

Therefore, Ben's house will be worth approximately $490,523.96 in 9 years if the value continues to increase at a rate of 7% per year.

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