4. Here is the graph of a linear equation.
Select all true statements about the line and its equation.
A. One solution of the equation is (3,2).
B. One solution of the equation is (-1,1).
C. One solution of the equation is (1, 3/2).
D. There are 2 solutions.
E. There are infinitely many solutions.
F. The equation of the line is y=1/4x+5/4.
G. The equation of the line is y=5/4x+1/4

To get the equation which combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3) we need to plug the points into each equation choice.

Therefore , this is the first step to solve this equation.

The equations of degree 1 are known as linear equations.

These are the equations which are defined for a straight line in a coordinate system.

A linear equation is one that describes a straight line. The general form of a linear equation is  y= mx + b, where m denotes the slope and b its y-intercept.

Note:

The complete question is ,

A linear equation is graphed to the left. Which of the following equations combines with the graphed equation to create a system of equations whose solution set is comprised of the points (−1,−5) and (3,3)?

WHAT IS THE FIRST STEP IN SOLVING THIS PROBLEM?

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Answer:

Step-by-step explanation:

2. Unit Rate: 1:2

3. A class has 26 kids. Johnny is trying to figure out the number of ears everyone has in total. You can use the ration 1:2. For every kid there are 2 ears. Therefore there are 52 ears total. [tex]\frac{1}{2}=\frac{26}{52}[/tex]

4. Multiplication

5. No, you can't have half an ear

If m∠ 1=(3 x) degrees and m ∠2=(x+48) degrees

The equation to solve the value of x is

3x = x+48

The value of x = 33

The angle 1 = 99 degrees

The angle 2 = 81 degrees

The measure of angle 1 = 3x degrees

The measure of angle 2 = x + 48 degrees

The sum of the angles on a straight line is add up to 180 degrees. Therefore angle 1 and angle 2 are supplementary angles.

∠1 + ∠2 = 180 degrees

Substitute the values in the equation

3x + x + 48 = 180

4x + 48 = 180

4x = 180 - 48

4x = 132

x = 132/4

x = 33

Part b

Then the measure of angle 1 = 3x

= 3 × 33

= 99 degrees

The measure of angle 2 = x + 48

= 33 + 48

= 81 degrees

Therefore, the equation to solve x is 3x = x + 48 and the measure of angles 1 and 2 is 99 degrees and 81 degrees respectively

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there are about millions of multinational and national companies which are working for the better Gross National Product(GNP).

The United States is super power and has multiple resources to maintain itself  and the over all economic system. As, there are about millions of multinational and national companies which are working for the better Gross National Product(GNP). As, there is agriculture, car manufacturer, and the military industry for improving and adding the value to the over all GNP of the United States.

The Oil and gas sector is the one major factor for the development of the United State's GNP(Gross National Product). As, the exports of the region is well known to be very high and generates more revenue for the over all system as well.    

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Answer:

C) inconsistent

Step-by-step explanation:

3x+y=−5

3y+15=−9x

3x + y = -5

9x + 3y = 15

3x + y = -5

3x + y = 5

The system graphs as two parallel lines.

Answer: C) inconsistent

Two correct options are option (C) The speed of the canoe in still water is 4 miles per hour and option (D) The speed of the water current is 3 miles per hour.

A canoe travels 7 miles per hour downstream and 1 mile per hour upstream.

x is the Canoe's speed with no water current in miles per hour

y is the speed of the water current, in miles per hour

The equations are

x + y = 7

x - y = 1

Here we have to use the elimination method

Add both the equation

2x = 7 + 1

2x = 8

x = 8/2

x = 4

Then substitute the value of x in the first equation

4 + y = 7

y = 7 -4

y = 3

Therefore, the correct options are option (C) and option (D)

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Answer:

26

Step-by-step explanation:

One leg measures 7.

One leg measures 8.

a² + b² = c²

7² + 8² = c²

c² = √113 = 10.630 = 11

perimeter = 7 + 8 + 11

perimeter = 26

The value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

-5x - 10y = 30 and - 3x + 3y = 27

Solve by using the elimination method,

Divide the equation - 3x + 3y = 27 by 3 and equation -5x - 10y = 30 by 5 on both sides,

(- 3x + 3y) / 3 = 27 / 3  and (-5x - 10y) / 5 = 30 / 5

-x + y = 9  and -x - 2y = 6

Subtract equation

-x + y = 9 - (-x - 2y = 6)

-x + y - 9 = x - 2y - 6

y = 3

and - x + 3 = 9, x = -6

Therefore, the value of x and y after solving the equation -5x - 10y = 30 and - 3x + 3y = 27 by elimination method is -6 and 3 respectively.

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Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.

Given that,

We have to find applying a coat of paint 0.07cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated volume of paint in cubic centimeters, which may be calculated using a linear approximation.

We know that,

Volume of a sphere = 4/3 πr³

Volume of a hemisphere is

V= 2/3 πr³

dV = 2πr² dr

Here,

dr=0.07cm

r=(1/2)×40m=2000cm

Let plug in the formula

dV = 2×π×(2000²)×(0.07)

dV=1759291.886 cubic centimeters

Therefore, Applying a coat of paint 0.07 cm thick to a hemispherical dome with a diameter of 40 meters will require an estimated 1759291.886 cubic centimeters of paint, using a linear approximation.

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3 is the value of (fog⁻¹)(5) for functions f(x)=7-2x and g(x)=x+3.

A relation is a function if it has only One y-value for each x-value.

Given that the functions are f(x)=7-2x and g(x)=x+3.

We need to find the value of  (fog⁻¹)(5)

g⁻¹(x)=x-3.

By composite functions

f(g⁻¹)(x)=7-2(x-3)

f(g⁻¹)(x)=7-2x+6

Now plug in the value of x as 5

f(g⁻¹)(5)=7-2(5)+6

=7-10+6

=-3+6

=3

Hence, the value of  (fog⁻¹)(5) is 3.

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Multiplication of matrices is not commutative by determining the product matrices ST and TS .

Given :

Consider the matrices

S = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]     and  T = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]

Show that multiplication of matrices is not commutative by determining the product matrices ST and TS.

ST = [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]

[tex]ST_{11[/tex] = 4 * 0 + 1 * -4 = -4

[tex]ST_{12[/tex] = 4 * 4 + 1 * 3 = 19

[tex]ST_{21[/tex] = -3 * 0 + -2 * -4 = 8

[tex]ST_{22[/tex] = -3 * 4 + -2 * 3 = -18

ST = [tex]\left[\begin{array}{ccc}-4&19\\8&-18\end{array}\right][/tex]

TS = [tex]\left[\begin{array}{ccc}0&4\\-4&3\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}4&1\\-3&-2\end{array}\right][/tex]

[tex]TS_{11[/tex] = 0 * 4 + 4 * -3 = -12

[tex]TS_{12[/tex] = 0 * 1 + 4 * -2 = -8

[tex]TS_{21[/tex] = -4 * 4 + 3 * -3 = -25

[tex]TS_{22[/tex] = -4 * 1 + 3 * -2 = -10

TS  = [tex]\left[\begin{array}{ccc}-12&-8\\-25&-10\end{array}\right][/tex]

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The ratio of p:r is 6/5

A ratio can be described as the comparison of two or more numbers which indicates their sizes in relation to one another.

From the information given, we have that;

t: w = 7:2

We have that;

Now, substitute the values into the formula

p = 4t + w

p = 4(7) + 2

expand the bracket

p = 28 + 2

Add the values

p = 30

r = t + 9w

r = 7 + 9(2)

expand the bracket

r = 25

The ratio, p:r

p:r = 30/25

p: r = 6/5

Hence, the value is 6/5

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By using distance formula, it can be calculated that-

Distance between  (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units

What is distance formula?

Distance formula is used to find the distance between two coordinates.

If the points are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex], then distance is calculated by the formula

d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

The points are (-4, -5) and (4, 2)

Distance between  (-4, -5) and (4, 2) = [tex]\sqrt{(-4-4)^2+(-5-2)^2}[/tex]

                                                            = [tex]\sqrt{64 + 49}\\\sqrt{113}[/tex]units

Distance between  (-4, -5) and (4, 2) is [tex]\sqrt{113}[/tex] units

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 2 sin A sin B with two angles A and B, 2 sin A sin B = cos (A-B) - cos (A + B). The 2sinasinb formula is equivalent to the difference between the angle sum and the angle difference of the cosine functions. The formula for two sins is two sins A and two sins B: cos (A-B) - cos (A + B).

What is 2SinASinB Identity?

2SinASinB identity is a trigonometric formula and it is used for the simplification of trigonometric expressions. It is also used for evaluating integrals involving trigonometric functions for easy calculation. We can derive the formula for 2SinASinB using the angle sum and angle difference formulas of the cosine function. Using the 2SinASinB formula, we can derive another trigonometric formula for SinA SinB given by, sinA sinB = (1/2)[cos(A - B) - cos(A + B)].

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Answer: D is  the right answer .The slope of KM is 1 and the slope of NL is –1.

A rhombus is a parallelogram whose all sides are equal. Its diagonals perpendicularly bisect each other.

i.e. product of its slope should be -1.

[∵if one line is perpendicular to the other lines then product of its slope should be -1.]

Slope of  KM= 1

Slope of NL= -1

Product of slope of diagonals=1×-1=-1

∴diagonals of given parallelogram perpendicularly bisect each other.

Therefore, it is a rhombus.

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There is actually enough evidence for the manufacturer to believe that the mean number of hours and mobs will last has actually changed.

We are supposed to use Israel and

significance level  α=.05  to perform hypothesis test on the statement of the manufacturer.

So Let's move into our worksheet, our population is 700, our sample size is 48.

The sample mean is 675

Sample standard deviation is 77.

So the first step is to state the null and alternative hypothesis and we have that our hate notes is based on the fact that μ is a cost of 700.

This is what the manufacturer wants, but she thinks that it might have changed probably lesser than or greater than Saddam is our alternative hypotheses, his meal is not equals to 700. So she is not sure whether it does, it's either decrease or increase but it has actually changed.

So after stating our null and alternative protesters, the next needs to state the decision rule that we will be using to either reject or accept the no like protesters.

So will be making a use of the PVA limited to make the decision. It is your roost is that if our evil is better than alpha we are supposed to accept, protesters and if our pivot is lesser than alpha, We are supposed to reject the null hypothesis is that our alpha is equals deserve .05.

So that being said it's time for us to move to draw our test statistics. Now for our test statistic is going to be AT. Test. Yes, our sample size is greater than 30. There's no issue with that. But we actually don't know the value of the population standard deviation. We are making use of the samples and activation which is 27. So that means it would be better if we use our T. Test as our test statistics. So our test statistic is a teacher has given towards us. T is a cost to extra minus meal divided by S divided by the square root of n. Our expert in this case is 6 75 minus. We have 700 divided by our s is 77 divided by the square root of 48. So let's do the math. 6 75 minus 700. We have a -25 divided by so we have 77 divided by the spirit of 48. We have this to be 11.11399. So uh -25 divided by 11.11399. We have our answer to be -2.249. So they simply implies that our test statistics is manners two points 249. So the next step is for us to get the p value attached to this test statistic scenes, we are using the p value method uh to make our decision. So we need a P value. We already have the level of significance. So to get the P value, we can decide to make itself. It it it's a distribution table but that will only give us a range of values in which the p value is located. It won't give us the actual P value. So most times we decide to use calculator to get the p value the exact p value. So our test is actually a two tailed tests were testing for a T score.

Our degree of freedom is the sample size minus one.

48-1=47

And our T score uh is minus two points 249.

So that we have a miners 2.249. And as you can see our p value here is 0.02 0.0294. T. Value is 0.029 so far. Alright, so there's our p value. So the next thing is to make our decision. So we have that as you can see their .0-9 Too far is actually lesser than 0.05 hands.

We make a decision by saying, we are going to reject the null hypothesis. So the decision is that we're going to be rejected the null hypothesis.

As a result, the manufacturer has sufficient reason to think that the average number of hours and mob duration have altered.

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Cap rate (going in) = 5.6%

The estimated value of this property = 17,85,714.2 $

The needed rate of return is the rate of return that investors are looking for on assets that are similar. The value of the property and the needed rate of return are inversely related. Property value will fall as the needed rate of return rises, and the opposite is also true.

given cash flow is $100,000 and it increases by 5400$ every year hence growth rate would be 5.4 %.

Cash flows = $1,000,00

Growth rate = 5.4%

Required rate of return = 11%

the required rate of the property = cash flow / ( Required rate of return - growth)

the required rate of the property = 100,000 / (11 -5.4 ) = 17,85,714.2 $

Cap rate (going in) = Required rate of return - a growth rate of the property

Cap rate (going in) = (11 - 5.4) %

Cap rate (going in) = 5.6%

Thus, it can be concluded that the decrease in the required rate of return is the cause of the increase in the value of the property.

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Answer:

$800

Step-by-step explanation:

Let's say that Shola's salary is x dollars. This means that Akin's salary is 0.8x dollars, because his salary is 20% less than Shola's salary.

Since Shola spent 45% of his salary on accommodation, he had 0.55x dollars left, or $550. This means that we can write the equation 0.55x = 550.

To solve for x, we can divide both sides of the equation by 0.55 to get x = 1000. This means that Shola's salary is $1000, and since Akin's salary is 20% less than Shola's, his salary is 0.8 * 1000 = $800. Therefore, Akin's salary is $800.

Answer:

4

Step-by-step explanation:

Solve for x over the real numbers:

x^3 = 64

Take cube roots of both sides:

Answer: x = 4

4^2 = 16

4^3 = 64

the dimensions of a rectangle with area 64000 m2 whose perimeter is as small as possible. (give your answers in increasing order, to the nearest meter.)Length: 200 m and Width: 320 m

The area of a rectangle is given by the formula A = lw, where l is the length and w is the width. To find the dimensions of a rectangle with an area of 64000 m2 and a perimeter that is as small as possible, we can use the formula P = 2l + 2w. We can use this to create an equation with the area and solve for l and w: 64000 = lw, and 2l + 2w = P (min). Solving for l and w, we get l = 200 m and w = 320 m. Thus, the dimensions of the rectangle with an area of 64000 m2 and a perimeter that is as small as possible are 200 m by 320 m.

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Answer:

20

Step-by-step explanation:

20.

[tex]\frac{8}{\frac{2}{5} }[/tex]

Check the attached image below.

[tex]\frac{8}{1}* \frac{5}{2}[/tex]

[tex]\frac{8}{1}*\frac{5}{2}=\\\\ \frac{8*5}{1*2} =\\\\ \frac{40}{2}=\\ \\20[/tex]

[tex]\frac{8}{\frac{2}{5} }=20[/tex].

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.

M(x, c) M(x, d) dx is equivalent to = b M(x, c) dx + M(x, d) dx. So, by demonstrating that the two sides of a rectangle are equal, we have established Green's Theorem. The sum of rectangles theorem. Since each region can be as nearly approximated by a sum of rectangles as desired, Green's Theorem must apply to all regions.

It looks like the integral is

[tex]\int\limits^0_c {xy} + x^{2} y^{3} \, dy[/tex]

Let's close the loop by adding a line integral over the line segment joining (1, 4) to (0, 0). Then the closed loop is the triangular region

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x}

Since the integrand has no singularities over or on the boundary of T, we have by Green's theorem

Compute the double integral:

From this result, we subtract the line integral over the extra line segment we added. Parameterize this path by

C' : {(1 - t, 4 - 4t) : 0 ≤ t ≤ 1}

The line integral over C' is

[tex]\int\limits^1_0 {(256t^{5} }+1280t^{4}+ 2560t^{3} - 2564t^{2} + 1288t - 260) \, dt[/tex]

T = {(x, y) : 0 ≤ x ≤ 1 and 0 ≤ y ≤ 4x} so that the line integral over C alone is 60/3 - (-44) = 64.

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Answer:

x = 1, y = -5.

Step-by-step explanation:

X-3y = 16         Equation (1)

4x- y = 9          Equation (2)

We can solve this by the Method of Elimination.

One way is to multiply the second equation by -3, as follows:

-3(4x - y = 9)

= -12x + 3y = -27     Call this equation (3)

Now if we add equation (3) to equation (1) we eliminate the y terms:

    x - 3y  =  16  

-12x + 3y = -27       Adding:

-11x  + 0    = -11

-11x = -11

x = -11/-11 = 1

Finally, we find the value of y by substituting x = 1 into equation (2):

4(1) - y = 9

-y = 9 - 4

-y = 5

y = -5.

So, the answer is x = 1, y = -5.

or we can write it as an ordered pair (1, -5).

Hope this helps.

Answer:

x=1 and

y= -5

Answer:

The inequality form is 0≤x≤9 0 ≤ x ≤ 9 .

Answer:

So the payoff balance of the car loan after 4 years will be approximately $22,169.73.

Step-by-step explanation:

payoff balance after 4 years can be calculated using the following formula:

Payoff balance = Principal * (1 + APR/n)^(nt) - [(Principal * (1 + APR/n)^(nt) * (APR/n)) / (1 + APR/n - 1)]
Where:
Principal is the loan amount, which is $28,550 in this case.
APR is the annual percentage rate, which is 8% in this case.n is the number of times per year that interest is compounded, which is usually 12 for monthly compounding.t is the number of years for which the loan is taken, which is 4 years in this case.
Plugging in the values, we get:
Payoff balance = $28,550 * (1 + 0.08/12)^(124) - [($28,550 * (1 + 0.08/12)^(124) * (0.08/12)) / (1 + 0.08/12 - 1)]
Payoff balance = $28,550 * 1.006669^48 - [$28,550 * 1.006669^48 * 0.006669] / 0.006669Payoff balance = $22,169.73

The desired equation is then y -4 = 12/15 (x -9)

Equations of degree 1 are linear equations. It is the straight line's equation. A linear equation with parameters a and b equal to zero has the conventional form ax+by+c = 0.where a ≠ 0 and b ≠ 0.

We need this line's equation in the point-slope form, y - k = m. (x - h).

The point (h, k) in the point-slope form shown above can be chosen at random from the two points (9, 4) and (-6, -8). In the above point slope form, the other point is thus denoted by (x, y):

Let (x, y) be and (h, k) be (9,4). (-6,-8). Consequently, y - k = m(x - h) becomes

-8-4 = m (-6-9), so that -12 = m(-15), and the slope is thus m = 12/15

The desired equation is then y -4 = 12/15 (x -9) (which is in point-slope form).  

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Kanoi and Ale'a can weed the same garden together in 22.22 minutes

Rate of work refers to amount to of work completed at a given time

Information from the question include

Kanoi can weed a garden in 40 minutes

Kanoi's rate = 1/40 per minute

Ale'a can weed the same garden in 50 minutes

Ale'a rate = 1/50 per minute

When both are working together the rate will be

1/40 per minute + 1/50 per minute

= 9/200 per minute

The time is solved

1 / 9/200

= 200/9

= 22.2222 minutes

= 22.22 minutes to the nearest hundredth

The time it will take both of them to weed is 22.22 minute

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X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X ,,a. X = 16.786 , b. X = 8.014

To find the baby kitten weight corresponding to the given z-scores, we use the formula X = μ + Zσ, where μ is the mean, σ is the standard deviation, and Z is the z-score. For the first z-score of 1.98, we substitute the values and solve for X. X = 12.3 + (1.98)(2.2) = 16.786. For the second z-score of 2.87, we substitute the values and solve for X. X = 12.3 + (2.87)(2.2) = 8.014. Therefore, the baby kitten weights corresponding to the given z-scores are 16.786 and 8.014, respectively.

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