The points (4, -3) and (x, 3) lie on the same straight line.

If the slope of the line is 2, what is the value of x ?

Answer:

y=1/4x+3

Step-by-step explanation:

To write an equation, let's infer we need to write it in slope-intercept form. We need the y-intercept. We can plug 1/4 and (-4,2) into y=mx+b, to solve for b. We have:

2=1/4*-4+b

2=-1+b

3=b

Since we have the slope, 1/4, we can create our equation:

y=1/4x+3

Solve for b in (y=mx+b):

b=y-mx

b=2-(1/4)(-4)

b=2+1

b=3

So the equation is y= (1/4)x + 3

One method is to determine the average hourly rate for all employees, regardless of where they work in your company, what they do, or how many hours they work.

To begin, calculate the total number of hours worked by multiplying the number of weeks in a year by the number of hours worked per week. Divide this figure by the annual salary. For example, if an employee earns $50,000 per year and works 40 hours per week, his or her hourly rate is $50,000/2,080 (40 x 52) = $24.04.

When budgeting for future projects, keep in mind that if you pay Bill $18 per hour, Lisa $16, and Hank and Jake $14, your labor costs will vary depending on who you send to the job site.

However, if you can use Bill less frequently each week and Hank or Jake more frequently, you might be able to budget for next month using the $15.82 per hour figure.

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Answer:

2 3/5

Step-by-step explanation:

First, change all terms to improper fraction

We have;

13/2÷5/2

13/2 ×2/5

13/5

Change to mixed fraction, we have;

2 3/5

Hope it helps.. Please mark brainliest

The simplest simplified form of the given expression is 3 9/10.

First, let us understand the mixed number;

A mixed number is made up of three components: a whole number, a numerator, and a denominator. The numerator and denominator are both components of the appropriate fraction that results in the mixed number.

Change all the given terms to improper fractions, we will get;

6 1/2 = (6 * 2 + 1) / 2 = 13 / 2

1 2/3 = (1 * 3 + 2) / 3 = 5 / 3

We are given;

13/2 ÷ 5/3

= 13/2 × 3/5

= 39/10

Change to mixed fraction, we will get;

39/10 = 3 9/10

Thus, the simplest simplified form of the given expression is 3 9/10.

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Solution of the inequality 4|x + 2| < 8 is given by x > -4 and x<0.

Solution from the given graph is option B where open interval x<0 and open interval x > -4 is shown.

As given in the question,

Given inequality is :

4|x + 2| < 8

Divide by 4 both the side of inequality we get,

⇒(4|x + 2|)/ 4 < 8/4

⇒|x+2| < 2

⇒ (x+2) < 2  or (x+2) >-2

⇒ x< 2-2 or x > -2 -2

⇒ x < 0 or x > -4

Solution of its graph is shown by option B number line where open interval -4 is greater than and less than open interval 0.

Therefore, solution of the inequality 4|x + 2| < 8 is given by x > -4 and x<0.

Solution from the given graph is option B where open interval x<0 and open interval x > -4 is shown.

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The equations that can be used to solve for y, the length of the room

First and foremost, we can begin solving this equation by noting the formula for calculating the area of a rectangle. This formula is given as follows:

Area of a rectangle = Length × Width

Since the width of the room is 5 feet less than the length of the room, we will have the resulting equation as the area of the rectangle:

y( y - 5) = 750

When this equation is fully expressed, we will get the following equations:

Therefore, options, B, C, and E are correct.

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Answer:

I think it is y = -3x + 2

Step-by-step explanation:

The value of j based on the equation d = j + 3.16 if d = 158 is 154.84 meters.

d = j + 3.16

substitute the value of d into the equation

d = j + 3.16

158 = j + 3.16

substract 3.16 from both sides

158 - 3.16 = j

j = 154.84

So therefore, based on the given equation d = j + 3.16, j = 154.84

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The value of j in the equation = 154.84

Distance

Distance is the length of space covered by the car when it moves from one location to another

Given;

Equation d=j+3.16 represent the situation

distance travelled by the car= 3.16meters

d=158

Step 1: Substituting the value of d into the equation d=j+3.16

158= j +3.16

Step 2: Subtract 3.16 from both sides

158-3.16 = j + 3.16 -3.16

Step 3: Add the equation

j= 154.84

Therefore, the value of j in the equation = 154.84

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Answer:

The distance between [tex](-5,-6),(-9,-4)[/tex] is [tex]6 units[/tex].

Step-by-step explanation:

Distance Formula :

[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]

Given,

The two points are

[tex](-5,-6),(-9,-4)[/tex]

To calculate the distance between two points, use the distance formula.

[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]

Substitute the actual values of the points into the distance formula.

Distance[tex]=\sqrt{((-9)^{2} -(-5)^{2}) +( (-4)^{2} -(-6)^{2})}[/tex]

[tex]=\sqrt{(81-25)+(16-36)}[/tex]

[tex]=\sqrt{36}[/tex]

[tex]=6[/tex]

The slope-Intercept form of the given line is y=1.5x.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

The given line passes through (4, -2) and (2, 3). Therefore, the slope of the given line can be written as,

Slope of the line, m = (-2 - 3)/(4 - 2)

                                = 3 / 2

                                = 1.5

Now, the equation of the line passing through (2, 3) can be written as,

y = mx + c

(3) = 1.5(2) + C

3 = 3 + C

3 - 3 = C

C = 0

Substitute all the value in the equation of the line,

y = m(x) + c

y = 1.5(x) + 0

y = 1.5x

Hence, the equation of the given line is y=1.5x .

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[tex]\displaystyle \boxed{\text{First Attachment, 14}}[/tex]

Answer:

x = 30

y = 60

Step-by-step explanation:

      First, vertical angles are congruent. This helps us fill in more of the angles so we can find x and y.

      Next, supplementary angles add up to 180°, aka a line. We can use this to fill out even more of the diagram given.

      Lastly, corresponding angles on parallel lines are congruent.

      By using the information above, we can decide that x = 30 and y = 60. See the first attachment for all the angle values filled out.

[tex]\displaystyle \boxed{\text{Second Attachment, 12}}[/tex]

Answer:

x = 65

Step-by-step explanation:

      From the above explanation, we will be using vertical angles and supplementary angles to solve this question. See the second attachment.

      We also know there are 180 degrees in a triangle.

      Lastly, we know that alternate interior angles are congruent.

      Using this knowledge, we can decide that x = 65.

[tex]\displaystyle \boxed{\text{Third Attachment, 13}}[/tex]

Answer:

x = 30

Step-by-step explanation:

      Again, we will be using vertical angles, supplementary angles, and corresponding angles to solve this question. See the third attachment.

      After placing vertical angles down from the given information, we can fill in more using corresponding angles.

      Lastly, we know there are 360 degrees in a circle. We can create an equation from this and solve.

      Using this information, we can decide that x = 30.

(Excuse me if this doesn't make sense).

Your formula would be (4,1)

Your zero is (0,0)

To graph it:

If your y is 1, your x is 4

If your y is 2, your x is 8.

There's a video for this if my explanation and photo doesn't help

Answer:

2

Step-by-step explanation:

If the doors for the small cabinets are 17.5 in long, and the doors for the large cabinets are 3.5 times longer, find the length of the large cabinet doors by multiplying the length of the small cabinet doors by 3.5:

⇒ Length of large cabinet doors = 17.5 × 3.5 = 61.25 in

1 foot = 12 inches

⇒ 12 foot = 12 × 12 = 144 inches

To find how many large doors can be cut from a board that is 12 feet long, divide 144 inches by the found length of the large door:

⇒ 144 ÷ 61.25 = 2 r 21.5

Therefore, 2 large doors can be cut from a board that is 12 feet long.

(There will be 21.5 inches of board left over).

Final answer: 3[tex]b^{2}[/tex] + 8b + 2

12(3y + 6) = 12 x 3(y + 2) // Factor out 12 = 36(y + 2) // Simplify the multiplication Final answer: 36(y + 2)

An equation is a statement that two mathematical expressions are equal. It consists of two expressions separated by an equal sign (=), where one expression is on the left side and the other expression is on the right side of the equal sign. An equation represents a balance or equivalence between the two expressions, and it can be solved for the unknown variable(s) by applying mathematical operations to both sides of the equation.

Given by the question.

3b (b+4) - 4 (b-5)

= 3[tex]b^{2}[/tex] + 12b - 4b + 20 // Distribute the terms.

= 3[tex]b^{2}[/tex] + 8b + 20 // Simplify the like terms.

Final answer: 3[tex]b^{2}[/tex]+ 8b + 20

12(3y + 6)

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1000/x - 1000/(x + 1) = 4.5 is an equation in terms of x that simplifies to this quadratic equation 9x² + 9x - 2000 = 0 as shown below.

In Mathematics, the standard form of a quadratic equation is given by this mathematical expression:

ax² + bx + c = 0.

Since Winston changed 1000 rand into euros in both 2014 and 2015, this can be represented by this mathematical expression:

1000/x - 1000/(x + 1) = 4.5

Taking the lowest common multiple (lcm), we have:

1000/x(x + 1) = 4.5

1000/(x² + x) = 4.5

Cross-multiplying, we have the following:

1000 = 4.5(x² + x)

1000 = 4.5x² + 4.5x

Multiplying both sides of the equation by 2, we have:

2 × (1000 = 4.5x² + 4.5x)

2000 = 9x² + 9x

Rearranging the terms and equating to zero, we have:

9x² + 9x - 2000 = 0.

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The values of the three integers are:

x= -9, y=66, z= -25

In French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.

In order to solve an equation with variables, you must first determine which variables' values make the equality true. Unknowns are the variables for which the equation must be solved, and equation solutions are the values of the unknowns that satisfy the equality..

Given,

Sum of three integers= 32

x+ y+ z=32  →1

And also given that,

x+ y= z+82 →2

z+16=x →3

By solving equation 1, we get

z+16+y+z=32

2z+y=16 →4

By solving equation 2, we get

z+16+y= z+82

y=82-16

y=66

By solving equation 4, we get

2z+66=16

2z=-50

z=-25

By solving equation 3, we get

x=z+16

x=-25+16

x=-9

Therefore, the three integers are x=-9, y=66, z=-25

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a) The margin of error for an 80% confidence interval in Arkansas is 0.1041

b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

n = 3600

standard deviation = 399.876

Confidence Interval = 80%

a) α = 0.20

The margin of error = Zα/2 (σ / √n)

Zα/2 = 1.4395 --- (From the tabular value)

The margin of Error = 1.4395 + 399.876 / √3600

Therefore, the Margin of Error = 8.1041

b) Margin of Error = 0.07 = 7%

α = 0.20

Critical Value = 1.2816

Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²

n = [(1.2816 * 399.876) / 0.07]²

n = 53599358.98

Therefore, Sample size, n = 53599359

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Ana and Bonita were born nn year apart and its value of nn is 12.

Here we have to find nn which difference in the year in which Ana and Bonita were born.

Let x be the age of Ana and y be the age of Bonita.

It is given that last year Ana was 5 times as old as Bonita so from this statement we get the first equation:

x - 1 = 5(y -1)

x -1 = 5y - 5

5y -x = 4--------(1)

The second statement is Ana is square of Bonita's age. From this we get another equation:

x = y²-----------(2)

Putting equation 2 in equation 1 we get:

5y - y² = 4

y² - 5y +4 = 0

y² - 4y - y + 4 = 0

y(y-4) -1(y -4) = 0

(y - 4)(y -1) = 0

y = 4,1

As x = y²

x = 4² = 16 or x = 1² =1

We cannot take 1 as there is a difference in their age

So we get x = 16 and y =4

So the difference in their age = 16-4= 12

Therefore we get the value of nn as 12.

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He covers 15 miles on the bike, 9 miles by running and 1.5 miles while swimming which sum up to 25.5 miles which is his total training distance.

Distance is defined as an object's entire movement without regard for direction. Distance may be defined as how much ground an item has traversed regardless of its starting or finishing place. Distance is a scalar number that indicates "how much ground an item has covered" while moving. Displacement is a vector variable that describes "how far out of place an item is"; it represents the total change in position of the object. Distance is the length along a line or line segment between two locations on the line or line segment.

Here,

He rides 15 miles, which is ten times as far as he swims.

He runs 9 miles, which is half the distance he rides (15/2=7.5). Plus the additional 1.5 miles, totaling 9.

He swims.10 of what he bikes, for a total of 15x.10 = 1.5. As a result, he swims 1.5 miles.

15 miles = bike

9 miles= run

1.5 mile =swim

Add them all together and you get 25.5 miles.

He rides his bike for 15 miles, runs for 9 miles, and swims for 1.5 miles, for a total training distance of 25.5 miles.

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Answer:

The new mean is 3.6

Step-by-step explanation:

Since each piece of data is now doubled that means the data is now

4.8, 3.2, 6.4, 0.6, 3

Add up all of the data which comes out to 18

Divide 18 by the number of numbers there are which is 5

This will get you 3.6 which is the new mean of the data

(i) Relative growth rate, k = 48 million people/ year

(ii) Population in 2020 is given by 5920 million people.

Given that in 1950, the population of world was 2560 million.

In 1960, the population of world was 3040 million people.

Also it is mentioned that,  world population grows in constant relative proportion.

So, the difference between time = 1960 – 1950 = 10 years

The growth in population = 3040 mil – 2560 mil = 480 million

So the relative growth rate of population is = 480/10 = 48 million/year

Now N be the new population, k be the relative population growth rate, all figures in millions. And t be the time in years passes since 1950.

Then the mathematical model is,

N = 2560 + kt

So for 2020, t = 2020-1950 = 70

k = 48

So, N = 2560+48*70 = 5920

So the population in 2020 is 5920 million people.

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Using the concepts of statistics, we got that  if the per capita death rate increased, then the exponential growth model would decrease the initial population size.

We know very well, the set up of a differential equation relating instantaneous population growth with respect to the time to the per capita population growth rate and the current population size at an arbitrary time is as follows:

dN / dt = rN

Now, we are told that the constant, r, is  per capita population growth rate. N is  current size of the population at some time. "r" is the "organisms added per reproductive period" divided by  total population at that time. For instance, if the 10 rabbits are born per month and the current population is 100 rabbits, then r value  = 0.1.

Hence, the exponential growth model  would decrease the initial population size  if the per capita death rate increased.

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Answer:

Step-by-step explanation:

f(x)=5x2+xf(x)=5x2+xWrite f(x)=5x2+xf(x)=5x2+x as an equation.y=5x2+xy=5x2+xInterchange the variables.x=5y2+yx=5y2+ySolve for yy.Tap for more steps...y=−1−√1+20x10y=-1-1+20x10y=−1+√20x+110y=-1+20x+110Replace yy with f−1(x)f-1(x) to show the final answer.f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110Verify if f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110 is the inverse of f(x)=5x2+xf(x)=5x2+x.Tap for more steps...f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110

Answer:

$1097.46

Step-by-step explanation:

Assume P is the finall price.  The markup of 26% can be written in decimal form as 0.26.  This is in additon to the full price paid for the gold ring, so we can add 1.00 to 0.26 to arrive at the factor 1.26.  Multiply 1.26 times the store cost of $871 to find the amount after 26% markup:

 ($871)*(1.26) = $1097.46

Answer:

7x+40=180

Step-by-step explanation:

(5x+40)+(2x)=180

7x+40=180

if you were to solve

subtract 40 from each side

7x=140

divide both sides by 7

x=20

check your answer

5(20)+40+2(20)=180

100+40+40=180

this is correct

hope this helps..and with future questions if you need to solve it

To find BCD

we know that C is 40 degrees and we know that  triangle is also 180

we can also see that B is a right triangle or 90 degree

so 90+40+A=180

130+A=180

subtract 130 from 180

A=50

In writing the equations that describe each of the colonies A ad B we have;

We know that the increase or decrease of population are exponential problems. We such, we must be able to look at the problem form the exponential perspective. This is how we would be able to know how to write the appropriate equation that would be able to be used in each of the cases that have been shown in the problem.

We are told  that; a scientist is observing two ant colonies. The colonies each have 800 ants when he begins observing them. The population of Colony A increases by 25% each week. The population of Colony B decreases by 25% each week. In each equation, y represents the ant population with respect to a number of weeks, x.

Thus;

For colony A we can write;

y = 800e^0.25x

For colony B we can write;

y = 800e^-0.25x

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Answer:

200 cm²

Step-by-step explanation:

Find the areas of all of the faces

17 × 2 = 34 (Top Face)

8 × 15 = 120 (Both Triangles)

15 × 3 = 30 (Bottom Face)

8 × 2 = 16 (Back Face)

Add them all together

120 + 34 + 30 + 16 = 200 cm²

Thus, 72 is divided into 32 and 40 in a 4:5 ratio. A ratio expresses the number of times one number contains another.

Given:

The given ratio is 4:5.

To find: We have to divide 72 in this ratio.

To divide 72 in the 4:5 ratio, we must perform the following steps:

The ratio is 4:5.

We can write the number of the ratio as 4x and 5x by multiplying a constant x.

The total ratio is 4x+5x=9x.

So, 9x is equal to 72.

We can write-

9x=72

x=8.

So, putting the value of x we get-

4×8 and 5×8

So, the numbers are 32 and 40.

Thus 72 divides itself as 32 and 40 in 4:5 ratio.

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