What is the slope of a trend line that passes through the points (1, 3) and (10, 25)?
15
2
O
O
O
0
2
22
24

The Area of Rectangle would be Decreased by 16% of the original Area. Now the Area of Rectangle is 84%.

Let the Length of rectangle be ‘x’

And width of rectangle be ‘y’

Area of Rectangle = Length X Width

Original Area of rectangle = x X y = xy square units

As the length is increased by 40% then, the new length would be 1+40% i.e 1.4 and,

The width is decreased by 40% then, the new width would be 1-40% i.e  0.6

New Length = 1.4x

New Width = 0.6y

Now , New Area of Rectangle = 1.4x X 0.6y

                    = 0.84xy square units

The effect is that the New Area of the rectangle is 84% of the original area. There is a decrease of 16% in the area.

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The division equation is x * 3/8 = 5/4 and there are (10/3) times 3/8s there in 5/4.

Let's assume that x times 3/8 are in 5/4.

So, calculating a division equation for the value of x.

x * 3/8 = 5/4

=> x = 5/4 * 8/3

=> x = 40/12

Dividing the numerator and denominator by 4.

We get, the value of x equal to

=> x = 10/3

Division equation: A division equation is a mathematical expression containing a division operator. Division equations are useful not only in math class but also in everyday life.

For example, if we want to share a bundle of papers equally with our friends, we can use this solution to find the given question. 100 papers and we have 10 friends. To find out how many papers each person gets, divide 100 by 10. The solution is 10. This means that each friend receives 10 papers.

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(x+2)(3x+1)

x(3x+1)+2(3x+1)

3x²+x+6x+2

3x²+7x+2

(3x²+7x+2)(x-3)

x(3x²+7x+2)-3(3x²+7x+2)

3x³+7x²+2x-9x²-21x-6

3x³+7x²-9x²+2x-21x-6

3x³-2x²-19x-6

Nathan can drive 83 miles without exceeding the budget.

Let us assume the number of miles Nathan can go in $75 budget be x. Now forming the equation based on the mentioned information -

The total budget = daily rental charge + number of miles × cost per mile

Keep the values in formula -

75 = 29.50 + 0.55x

Rewriting the equation according to variable x

0.55x = 75 - 29.50

Performing subtraction on Right Hand Side of the equation

0.55x = 45.5

x = 45.5 ÷ 0.55

Performing division on Right Hand Side of the equation

x = 82.7

As 0.7 will be counted a mile, thus, Nathan can drive 83 miles.

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The numeric value of the expression 8n at n = 6 is different of 56, hence n = 6 is not a solution to the expression 8n = 56.

A number a is a solution to an expression if the numeric value of the expression at input a generates an identity with the expression.

In this problem, the expression is given as follows:

8n = 56.

We want to verify if the number six is a solution to the presented expression.

The numeric value of the expression at n = 6 is found replacing the lone instance of n by 6, hence it is obtained as follows:

8n = 8 x 6 = 48.

(the product of 8 and 6 is 48).

Then the equality would be of:

48 = 56.

Which is a contradiction, hence n = 6 is not a solution to the expression 8n = 56.

The problem is:

Explain how to determine if the number is a solution to the equation. 56 = 8n for n = 6

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Answer:

Original equation

distributive property

subtract 5x from both sides

add 12 to both sides

Divide both sides by 14

Step-by-step explanation:

The expression represents the time she spent driving is       [tex]\frac{228.95}{x}[/tex]

The expression represent the time she spent driving can be calculated as follows:

We know that

Time = [tex]\frac{distance}{ speed}[/tex]

Let x be her speed on the first half of the trip.

Then for first half , the tiime she takes is

T1= [tex]\frac{150}{x}[/tex]

while in a second half the time taken by her is

T2= [tex]\frac{150}{1.9x}[/tex]

T2= [tex]\frac{78.95}{x}[/tex]

the total time she spent on driving is

T1 + T2 =    [tex]\frac{150}{x}[/tex] + [tex]\frac{78.95}{x}[/tex] =    [tex]\frac{228.95}{x}[/tex]

Hence, the expression represents the time she spent driving is       [tex]\frac{228.95}{x}[/tex]

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Step-by-step explanation:

the slope is the inclination of a line, or of the tangent (also a line) on a point of a bent curve.

it is expressed as ratio (y coordinate change / x coordinate change) when going from one point on the line or curve to another point on the line.

it tells us how many units y changes when x changes a certain number of units (like 1).

it is positive, if the line goes up (when going from left to right). the larger the value, the steeper the line goes up.

it is negative, if the line is going down (again, going from left to right). the lower the value, the steeper the line goes down.

a horizontal line has a slope of 0/x = 0.

a vertical line has a slope of y/0, which is undefined, or sometimes expressed as infinite.

The graph that represents the solutions of the given system of equations is attached below.

We are given a system of equations. The first equation is a quadratic polynomial. The second equation is linear in nature. The equations are given below.

x² - y = -2

4y - 8 = x

We need to find the solution to the equations using a graph. The graph of the equations is attached below. The graph of the first equation is represented by an upward parabola. The graph of the second equation is represented by a straight line. The intersection points of the two curves are the solutions to the given system of equations.

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Step-by-step explanation:

we know, the area of a rectangle is

length × width

so, we have here

length × (x - 5) = x² - 7x + 10

therefore,

length = (x² - 7x + 10) / (x - 5)

so, just by looking at it (with experience) I see that length is (x - 2).

but let's do the actual polynomial division, which seems to be the desired exercise here.

x² - 7x + 10 ÷ x - 5 =

it is very similar to actual number divisions.

we go from left to right.

we start with the first term (x²) and see how many times (x - 5) would fit into it. for that we look only at the first term in x - 5 (that is x).

x² / x = x

that is already our first term of the result (quotient) :

x² - 7x + 10 ÷ x - 5 = x

now, we multiply that result with the divisor (x - 5) and subtract that from the dividend.

x² - 7x + 10 ÷ x - 5 = x

- x² - 5x

--------------

0 - 2x

and now we pull down the next term from the dividend :

x² - 7x + 10 ÷ x - 5 = x

- x² - 5x

--------------

0 - 2x + 10

and we repeat the process with that new dividend :

-2x / x = -2

that is our next term of the quotient.

x² - 7x + 10 ÷ x - 5 = x - 2

- x² - 5x

--------------

0 - 2x + 10

we repeat the process of multiplying that term (-2) with the divisor (x - 5) and subtracting that result from the dividend :

x² - 7x + 10 ÷ x - 5 = x - 2

- x² - 5x

--------------

0 - 2x + 10

- -2x + 10

-------------

0 0

there is no remainder, and there is no more term to pull down. we are finished.

the result of the division is (as expected) : x - 2

the expression to describe the length is therefore

x - 2

The equation that represents the relationship between m and n is written as: n = 7m.

A proportional relationship between two variables have a slope of constant of proportionality, k, which is y/x.

The equation that represents a proportional relationship is expressed in slope-intercept form as y = kx.

In this situation m = x, and n = y.

The constant of proportionality, k = n/m.

Find the constant of proportionality, k, using a pair of values from the given table, say (3, 21):

k = 21/3

k = 7

To write the equation, substitute k = 7 into n = km:

n = 7m.

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Answer: -1

Step-by-step explanation:

Answer:

By counting, to go from one point to another, we go down 4, over 4. This means the slope is -4/4. This can then be simplified.

-4/4 = -1

So, the slope is -1

By using the distance formula, The distance between the points (−6, −3) and (0, 5) is 10 units.

In geometry, we use the distance formula to evaluate the distance between two points whose coordinates are given,

The coordinates of the points are given as [tex](x_{1} ,y_{1})( x_{2} ,y_{2} )[/tex]

Then, the distance (D) between them is given by :

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

Now, the given points are  (−6, −3) and (0, 5).

Putting these values in the distance formula, we have

[tex]D = \sqrt{(-6-0)^{2}+ (-3 -5)^{2} }\\ \\D = \sqrt{36 +64 \\\\ \\D = 10[/tex]

Hence, the distance between the points (−6, −3) and (0, 5) is 10 units.

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Answer: 10 units

Step-by-step explanation: i took the test and got it right

Answer:

320 pounds sterling

Step-by-step explanation:

All you have to do is $380.80 divided by $1.19 which is equal to one pound sterling. Hope this helps!

x = 1.53347526

Take the log of both sides of the equation.

[tex]ln(2^{3x-1} ) = ln(3^{x-2} )[/tex]

Expand [tex]ln(2^{3x-1} )[/tex] by moving 3x-1 outside the logarithm

[tex](3x-1)ln(2)= ln(3^{x-2} )[/tex]

Move x-2 outside the logarithm      [tex]ln(3^{x-2} )[/tex]

[tex](3x-1)ln(2) = (x-2)ln(3)[/tex]  

Solve the equation for x

[tex]x = -[\frac{{2ln(3)-ln(2)}}{3ln(2)-ln(3)} ][/tex]

The value of x is 1.53347526(After applying the log values)

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The system that models the equation is m = 2.5 lb.

This is a mixed-up issue.  The combination of

80% almonds and 20% peanuts make up combination A.

Completely peanuts in mixture B

both the

As a combination, use 60% peanuts and 40% almonds.

Since mixture C is created by combining mixtures A and B, we may calculate its combined weight in pounds to be 5 pounds.

Hence, we

Let m be the weight in pounds of mixture A (20% peanuts, 80 % almonds).

and

50-m is the quantity of mixture B in pounds.

Consequently, the set of equations that models this circumstance is:

0.20m + 1(50-m) = 0.60(5) (5)

0.80m + 0(50-m) = 0.40(5)

Equation 2's solution for m gives us

m = 2.5 lb.

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The maximum height of the diver as calculated from the function is   14.54 feet.

The function that represents the position of the diver is

h(t) = -16t² + vt + 10

The diver is at a height of 10 feet.

So at t=0 , h=10

Now we will find the rest of the solutions from the graph which follows the path of a parabola .

at t=1.42 , h(t)=0

Therefore 0 = -16(1.42)² + 1.42t + 10

or, V =15.68 ft/s

Again:

For h(t) to be maximum we have to find t for which h'(t)=0 , so we diff

h'(t) = -32t +15.68

or, t = -15.68 / 32

or, t = 0.49 seconds

Now h(0.49) =  16(0.49)² + 1.42 × 0.49 + 10 = 14.54 feet

Hence the maximum height of function is 14.54 feet

Therefore the diver has an initial velocity of 15.68 ft/sec and the diver reached a height of 14.54 feet at the maximum point.

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Answer: [-1, ∞)

Step-by-step explanation:

     First, we will simplify the equation.

     Given:

t - 1/3 ≥ -12/9

     Add 1/3 to both sides of the equation:

t ≥ -1

     Next, we know that a bracket is used when representing greater than or equal to and less than or equal to. Here, it's greater than or equal to so we will use a bracket on the left side.

     Then, t can be any value to infinity above -1, so we will use ∞) on the right side.

[-1, ∞)

The number of polio vaccinations is 32  and measles vaccination is 28

Let p represent the number of polio vaccines and let m represent the number of measles vaccines.

We know that each polio vaccine consists of 4 doses, and each measles vaccine consists of 2 doses.

Dr. Potter gave a total of 60 vaccinations last year. Therefore, the sum of the number of polio vaccines and measles vaccines must total 60. Therefore:

p+m=60

Together, they consisted of 184 doses.

Since each polio vaccine has 4 doses, the amount of doses for p polio vaccines is 4p.

And since each measles vaccine has 2 doses, the amount of doses for m measles vaccines is 2m.

So:

4p+2m=184

We now have a system of equations:

p+m=60

4p+2m=184

We can solve using elimination. Let’s multiply the first equation by -2. So:

-2p-2m=-120

Now, we can add this to the second equation. Hence:

(-2p+4p)+(-2m+2m)=(-120+184)

2p=64

p=32

Therefore, Dr. Potter gave out 32 polio vaccinations

p+m=60

By the first equation:

p+m=60

Substitute 32 for p to get

32+m=60

m=60-32

m=28

So, 28 measles vaccinations were given out.

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Answer:

64

Step-by-step explanation:

Hope this helps!

Answer:

2nd answer is the right one

Step-by-step explanation:

the square root of 9 is 3. The square root of 8 is a little smaller because 8 is smaller than 9.

Answer:

See attachment...

Hope this helps! :)

Using the range idea, the following scenario is represented by the inequality 0 ≤ y ≤ 2000. Here option D is the correct answer.

A function's range is the set that contains all of the output values that the function can take. In the context of this problem, the following input and output are provided:

Input the number of crates that have been loaded into the vehicle. Total weight of the crates loaded into the vehicle as output.

Because the weight of an amount can never be negative, and the greatest weight is 2,000 pounds, as stated in the issue, the range in this context is reflected by the following inequality: 0 ≤ y ≤ 2000.

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Based on heads and feet of chicken and rabbits, there are 12 rabbits in the cage.

Let us represent chicken by x and rabbit by y. So, we all know that chicken and rabbit have 1 head each. We also know that chicken has 2 feet and rabbit has 4 legs. Now forming the equation accordingly.

Equation for head -

x + y = 35 : Equation 1

Equation for feet -

2x + 4y = 94 : Equation 2

Rewriting equation 1 according to x

x = 35 - y : Equation 3

Keep the value of x from equation 3 in equation 2

2(35 - y) + 4y = 94

Preforming multiplication on Left Hand Side

70 - 2y + 4y = 94

Performing subtraction

2y = 94 - 70

2y = 24

y = 24 ÷ 2

Performing division

y = 12

Thus, there are 12 rabbits in the cage.

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The expression that could represent the amount of sodium per serving, in milligrams, in the new soup recipe is y = 0.67x

From the information, the new soup recipe contains 33% less sodium per serving than the old soup recipe.

Let's say Sodium in an old soup recipe per serving = x mg

Let's say Sodium in a new soup recipe per serving = y mg

The new soup recipe contains 33% less sodium per serving than the old soup recipe

y = x  - (33/100)x

100y = 100x  - 33x

100y = 67x

Divide through by 100

y = 0.67x

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Answer:

1.35⁷ = 8.1722 (to 5sf)

Answer:

Step-by-step explanation:

In the given triangle AED, segments GB and FC are parallel to base ED. Points G and F are on segment AE in that order. Lengths AG=2, GF=5, FE=3, GB=6, and CD=7 are given. You want the lengths of AB, BC, FC, and ED.

Segments of transversals crossed by parallel lines are proportional:

  AG : GF : FE = AB : BC : CD

  2 : 5 : 3 = AB : BC : 7

Multiplying the first ratios by 2 1/3 will give the second ratios:

  2 : 5 : 3 = 4 2/3 : 11 2/3 : 7

This lets us conclude ...

  AB = 4 2/3

  BC = 11 2/3

Corresponding segments of similar triangles are proportional:

  AG : GB = FA : FC = AE : ED

  2 : 6 = (5+2) : FC = (5+2+3) : ED

We notice the second number in the first ratio is 3 times the first number. That means these ratios are ...

  2 : 6 = 7 : 21 = 10 : 30

This lets us conclude ...

  FC = 21

  ED = 30

The lengths of the missing sides are calculated to be

The parallel lines in the figure created similarity between the dimensions, this makes the ratio of the dimensions equal

The given dimensions that is used to find the missing sides

Solving for AB

AB / CD = AG / FE

AB / 7 = 2 / 3

cross multiplying

3 * AB = 7 * 2

AB = 14/3 = 4.667

Using AB, GF is calculated

AB / BC = AG / GF

14/3 / BC = 2 / 5

cross multiplying

BC = (5 * 14/3) / 2

BC = 35/3 = 11.667

Solving for FC

GB / FC = AG / A'F

6 / FC = 2 / (2 + 5)

cross multiplying

2 * FC = 6 * 7

FC = 42/2 = 21

Solving for ED

GB / ED = AG / AE

6 / ED = 2 / (2 + 5 + 3)

cross multiplying

2 * ED = 6 * 10

ED = 60/2 = 30

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The gal in the first mixes is nine-halves, the constant of proportionality is one-twelfth and the white paint required in 7 gals is seven twelfths

Given:

White paint = 3/8 gal

Blue paint =  2 7/8 gal

Red paint = 5/4 gal

Gallons of  first mixes = White paint + Blue paint + Red paint

Gallons of first mixes = 3/8 + 2 7/8 + 5/4 = 9/2 gal

The constant of proportionality of white paint to gallons of mixed paint:

constant of proportionality = white paint volume/ mixed paint volume

constant of proportionality = (3/8) / (9/2) = 1/12  

The constant of proportionality of white paint to gallons of mixed paint gives the fraction of white color in the total volume

In order to make 7 gallons of the same color paint, the quantity of white paint he will need is:

White paint in 7 gallons = 1/12 x 7 =  7/12

Therefore, blank one is nine-halves, blank two is  one-twelfth and blank three is seven twelfths

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Answer:

The coordinates of B are (4, 2)

Step-by-step explanation:

The coordinates of B can be calculated as follows ?

The midpoint of line AB is M(3,-3)  is derived from the formula

[tex]M=(\frac{x_{1}+x_{2}}{2} ,\frac{y_{1}+y_{2}}{2})[/tex]

Where [tex]x_1[/tex] and [tex]y_1[/tex] are the coordinates of A and [tex]x_{2}[/tex] and [tex]y_{2}[/tex] are the coordinates of B

Since the coordinates of A are (2, -8), then the value of [tex]x_1[/tex] is 2 and the value of [tex]y_{1}[/tex] is -8.

Since the [tex]x[/tex]-coordinate of M is 3, then the equation to follow is

[tex]\frac{x_{1}+x_{2}}{2}=3[/tex]

Substitute 2 for [tex]x_{1}[/tex], then it follows that

[tex]\frac{2+x_{2}}{2}=3[/tex]

Multiply both sides of the equation by 2

[tex]\frac{2+x_{2}}{2}\times 2=3\times 2[/tex]

Simplify both sides of the equation

[tex]2+x_{2}=6[/tex]

Substract 2 from both sides of the equation

[tex]2-2+x_{2}=6-2[/tex]

Simplify the equation

[tex]x_{2}=4[/tex]

Since the [tex]y[/tex]-coordinate of M is -3, then the equation to follow is

[tex]\frac{y_{1}+y_{2}}{2}=-3[/tex]

Substitute -8 for [tex]y_{1}[/tex], then it follows that

[tex]\frac{-8+y_{2}}{2}=3[/tex]

Multiply both sides of the equation by 2

[tex]\frac{-8+y_{2}}{2}\times 2=-3\times 2[/tex]

Simplify both sides of the equation

[tex]-8+y_{2}=-6[/tex]

Add 8 to both sides

[tex]-8+8+y_{2}=-6+8[/tex]

Simplify the equation

[tex]y_{2}=2[/tex]

Since the value of [tex]x_{2}[/tex] is 4 and the value of [tex]y_{2}[/tex] is 2, then the coordinates of B are (4,2).

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Answer:6978

Step-by-step explanation:304585

Answer:

∴ x = 90

Step-by-step explanation:

(180 - x)° = x° (vertically opposite angles)

  180 - x = x

        -2x = -180

         2x = 180

        ∴ x = 90