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Stephen, Paul & Bridget share some money in the ratio 3 : 4 : 2. In total, Stephen and Bridget receive £50. How much does Paul get?

y = 2x

Step-by-step explanation:

The linear functions are given by:

y = mx+b

To find the slope, we have to find the change in x and y

The change in x is:

[tex]-14-(42) =-14+42 =28\\14+14= 28[/tex]

The change in y is:

[tex]-28-(-84) = -28+84 = 56\\28-(-28) = 28+28 = 56[/tex]

The slope is:

[tex]Slope = \frac{change\ in\ y}{Change\ in\ x}\\=\frac{56}{28}\\= 2[/tex]

Putting slope in equation of linear function

[tex]y =2x+b[/tex]

To find the value of b, we will put any pair of input and output in the slope-intercept form

So, putting (14,28)

[tex]28 = 2(14) + b\\28 = 28+b\\b = 28-28\\b = 0[/tex]

Hence,

the linear equation for function is:

y = 2x

Keywords: Linear function, slope intercept form

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Answer:

The answer is yes :)

Step-by-step explanation:

Answer:

Step-by-step explanation: If you add 19 and 17 together you get 36.

Hope this helps! :)

Answer:

y = -2x + 3

Step-by-step explanation:

Slope-intercept equation of a line is:

y = mx + b

where m is the slope and b is the y intercept.

Here, m = -2 and b = 3.

y = -2x + 3

Answer:

y = 7

Step-by-step explanation:

The straight line which is perpendicular to the y-axis will be either x-axis or parallel to the x-axis.

Now, the general equation for all straight line which is either x-axis or parallel to x-axis are given by y = c ........... (1), where c is any constant.

For c = 0 the line will be x -axis. therefore, y = 0, is the equation of x-axis.

Now, if the line (1) passes through the point (-2, 7), then the equation will be y = 7. (Answer)  

{Since, the point (-2,7) will satisfy the equation (1) and then c will be equal to 7.}

Answer:

Step-by-step explanation:

If [tex]y[/tex] is inversely propotional to the square of [tex]x[/tex], then the relation would be like

[tex]y=\frac{K}{x^{2} }[/tex]

Where [tex]K[/tex] is the constant of propotionality.

Now, we need to use a pair from the table to find the constant of proportionality, we are gonna use [tex](1,4)[/tex]

[tex]y=\frac{K}{x^{2} }\\4=\frac{K}{(1)^{2} } \\K=4[/tex]

Replacing this constant, the expression between variables is

[tex]y=\frac{4}{x^{2} }[/tex]

Which is the answer to a).

Now, if [tex]y=25[/tex] the value of [tex]x[/tex] would be

[tex]y=\frac{4}{x^{2} }\\25=\frac{4}{x^{2} }\\x^{2} =\frac{4}{25}\\ x=\sqrt{\frac{4}{25} }\\ x=\frac{2}{5}[/tex]

Therefore, the answer to b) is [tex]x=\frac{2}{5}[/tex]

In an inverse variation, y is inversely proportional to the square of x. To express y in terms of x, the equation is y = k/(x^2). To find the positive value of x when y = 25, the equation is 25 = k/(x^2), and x = sqrt(k/25) is the solution.

In an inverse variation, a variable is inversely proportional to another variable if their product is a constant. In this case, y is inversely proportional to the square of x. We can write this relationship as y = k/x^2, where k is the constant of variation.

To express y in terms of x, we can rearrange the equation as y = k/(x^2).

To find the positive value of x when y = 25, we can substitute these values into the equation and solve for x. We have 25 = k/(x^2). Rearranging the equation gives us k = 25x^2. Since we want to find the positive value of x, we can take the square root of both sides to get x = sqrt(k/25).

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Answer:

[tex]630.36\ ft^2[/tex]

Step-by-step explanation:

we know that

To find out the area of the sidewalk, multiply the length by the width of the sidewalk

The width of the sidewalk is equal to

[tex]113.4\ ft-110\ ft=3.4\ ft[/tex]

or

[tex]75.4\ ft-72\ ft=3.4\ ft[/tex]

The area is equal to

[tex]113.4(3.4)+72(3.4)\\385.56+244.8\\630.36\ ft^2[/tex]

Answer:

10s^2-15s+20

Step-by-step explanation:

because 5(2s^2)=10s^2, 5(-3s)=-15s, and 5(4)=20

hope it helps:)

Answer:102−15+20

Step-by-step explanation:that’s that answer because I just did the question on imagine math

Answer:

The answer should round up to 40 minutes. Do it to make sure the answer is 4 which in this case = 40

Step-by-step explanation:

[tex]22 - 7 \div 3.50[/tex]

Answer:

Computer can be rented for  42.85 minutes using $22

Step-by-step explanation:

Given:

Setup charge =  ​$ 7

Additional charge for every 10 minutes = ​$ 3.50

To find:

The time for which the computer can be rented for  ​$ 22

Solution:

Let the additional time be x

for  additional charge for 10 minutes =3.50

for 1 minute , additional charge = [tex]\frac{3.50}{10}[/tex]= $0.35

According to the question

setup cahrge + additional charge= $22

[tex]7+(0.35\times x)=22[/tex]

[tex](0.35\times x)=22-7[/tex]

[tex](0.35\times x)=15[/tex]

[tex]x=\frac{15}{035}[/tex]

x=42.85

Answer:

The answer is option A. 117

Step-by-step explanation:

The general solution of the quadratic equation is:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

The given equation is x2 + 9x − 9 is expressed as minus 9 plus or minus the square root of r, all over 2

Comparing to the general solution

∴ r = determinant = b² - 4 a c  

From the given equation: a = 1 , b = 9 and c = -9

∴ r = 9² - 4 * 1 * (-9) = 81 + 36 = 117

The answer is option A. 117

Answer:

117

Step-by-step explanation:

Answer:

Yes, it's an arithmetic sequence.

Step-by-step explanation:

Each term in this sequence is 4 more than the previous term.  Therefore we have an arithmetic sequence.

Answer:

Step-by-step explanation:

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ ||\ k\iff m_1=m_2\\\\\text{We have}\ k:y=4x-1\to m_1=4.\\\\\text{Therefore}\ m_2=4.\\\\l:y=4x+b\\\\\text{Put the coordinates of the point (-3, 7) to the equation of a line:}\\\\7=4(-3)+b\\7=-12+b\qquad\text{add 12 to both sides}\\19=b\to b=19\\\\\text{Finally:}\\\\y=4x+19[/tex]

Answer:

y = 2 over 3 x + 5

Step-by-step explanation:

m= y2-y1/x2-x1

m= (9-7)/(6-3)

m=2/3

y=mx+b

y= 2/3x+b

(3,7)

7=2/3(3)+b

7=6/3+b

7=2+b

5=b

b=5

y=2/3x+5

The Fendley family is planning a vacation, and they are trying to choose which resort they will stay in. Mrs. Fendley has created the table below showing their four options. They want to spend no more than $250 per night for the resort. Which resorts will fit into their budget? Select two that apply.

Resort Amount Charged

A $550 for 2 nights

B $694 for 3 nights

C $1028 for 4 nights

D $1153 for 5 nights

A no

Resort A $275 per night

B maybe

Resort B $231.33 per night

C no

Resort C $257 per night

D maybe

Resort D $230.60 per night

the answer is b or d you choose which one you would like to choose

Answer:

a = - 10

Step-by-step explanation:

Given

[tex]\frac{a}{5}[/tex] = - 2

a is divided by 2. The inverse operation to division is multiplication, thus

Multiply both sides by 5 to clear the fraction

a = 5 × - 2 = - 10

Answer:

The Value of x= 7.

m∠A= 21°

m∠B= 80°

m∠C= 79°

Step-by-step explanation:

Given:

m∠A = 2x+7

m∠B = 10x+10

m∠C = 8x+23

We need to find the value of x and measures of each angle.

Now by angle sum property which states that sum of all angles of a triangle are 180°.

Hence from above statement we can say in ΔABC;

m∠A+m∠B+m∠C=180

Now substituting the given values in above equation we get;

[tex]2x+7+10x+10+8x+23=180\\2x+10x+8x+7+10+23=180\\20x+40=180\\20x=180-40\\20x=140\\\\x=\frac{140}{20} =7[/tex]

Hence value of x is 7.

Substituting the value of x in all angles we get;

m∠A=[tex]2x+7=2\times7+7=14+7=21\°[/tex]

m∠B=[tex]10x+10=10\times7+10=70+10=80\°[/tex]

m∠C=[tex]8x+23= 8\times7 +23 = 56+23=79\°[/tex]

Final answer:

To find the value of x and the measure of each angle in triangle ABC, set up an equation using the given angle measures. Solve for x and substitute it back in to find the measures of each angle. Then : m<A = 2(7) + 7 = 21 degrees

m<B = 10(7) + 10 = 80 degrees

m<C = 8(7) + 23 = 79 degrees

Explanation:

To find the value of x and the measure of each angle in triangle ABC, we need to set up an equation using the given angle measures. Since the sum of the angles in a triangle is 180 degrees, we can write the equation as:

m<A + m<B + m<C = 180

Substituting the given angle measures, we have:

(2x + 7) + (10x + 10) + (8x + 23) = 180

Simplifying the equation:

20x + 40 = 180

Subtracting 40 from both sides:

20x = 140

Dividing both sides by 20:

x = 7

Now that we know the value of x, we can find the measure of each angle by substituting x into the respective expressions:

m<A = 2(7) + 7 = 21 degrees

m<B = 10(7) + 10 = 80 degrees

m<C = 8(7) + 23 = 79 degrees

Answer:

[tex]6.5 \times 10^{-9}[/tex]

Step-by-step explanation:

The scientific notation of a number is to express the number in the form [tex]x\times 10^{y}[/tex] where x is the base of ten.

So, if we want to express the number 0.0000000065, then we can write it as

[tex]\frac{6.5}{1000000000} = 6.5 \times 10^{-9}[/tex].

So, we can write 0.0000000065 as [tex]65\times 10^{-10}[/tex] or [tex]0.65 \times 10^{-8}[/tex] but those are not the scientific notation.  

Therefore, [tex]6.5 \times 10^{-9}[/tex] is the scientific notation of 0.0000000065. (Answer)

Answer:  x = -13

=========================

Work Shown:

19 = 38/2

19 & 1/2 = 19 + 1/2

19 & 1/2 = 38/2 + 1/2

19 & 1/2 = (38+1)/2

19 & 1/2 = 39/2

-------

In the original equation, replace the "19 & 1/2" with "39/2" to get

(5/2)x + (1/2)x = 39/2 + (9/2)x

Each term involves a fraction with a denominator of 2. If we multiply both sides by the common denominator, then the fractions will cancel out

For example: 2*(5/2)x = (10/2)x = 5x

So after multiplying both sides by 2, you should have this new equation

5x + 1x = 39 + 9x

--------

Let's solve that latest equation for x

5x + 1x = 39 + 9x

6x = 39 + 9x

6x-9x = 39 + 9x-9x ... subtract 9x from both sides

-3x = 39

-3x/(-3) = 39/(-3) .... divide both sides by -3

x = -13

Answer:44 cents

Step-by-step explanation:

7/16 = .4375

Answer:

Step-by-step explanation: To find the unit price you could divide 7 by 16

Answer:

B)

Step-by-step explanation:

16.24/14=1.16

33.3/30=1.11

1.16-1.11=0.05

The correct statement is The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

14 pound bag cost = 16.24

cost of 1 pound bag = 16.24/14

                                  = $1.16

and,

another bag which is of  30 pound costs = 33.30

                                                                    = 33.30 / 30

                                                                    = $1.11

Hence, The unit rate per pound of a 14 pound bag is $0.05 more than the unit rate of a 30 pound bag.

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Answer:

f(x) = -|x| + 1

Step-by-step explanation:

f(x) = |xl when reflected over the x-axis is f(x) = -|x|.

When reflected over x-axis a graph becomes negative in y value.

f(x) = -|x| then translate 1 unit to the right is f(x) = -|x| + 1. Adding 1 translates the graph towards the right because the positive x-axis is on the right.

Answer:

30 Oranges!

Step-by-step explanation:

Given that for every 2 apples there are 3 oranges.

How many oranges would be there in a basket of 20 apples?

Since for every couple of apples we have 3 oranges we will calculate how many couples of apples are there in the basket.

Given there are 20 apples. This means that there are [tex]$ \frac{20}{2} $[/tex] = 10 pairs of apples.

Since for one pair we have three oranges, for 10 pairs we would have 3 X 10 = 30 oranges.

Therefore, we can conclude that the number of oranges in the bigger basket would be 30.

Answer:

4.213

Step-by-step explanation:

Answer:

HL

Step-by-step explanation:

HL is used for right triangles that are congruent. These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.

The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

Here, we have,

A triangle is a polygon that has three angles and three sides. The sum of angles in a triangle is 180 degrees.

Types of triangles are isosceles, scalene and equilateral triangles.

Two angles are said to be complementary if their sum is 90 degrees.

Two triangles are said to be congruent if all their corresponding sides and angles are congruent.

This means that the triangles have equal angles and equal sides.

here, we have,

HL is used for right triangles that are congruent.

These two triangles are congruent(the same) and they happen to be right triangles, therefore, HL.

The postulate that proves the triangle are congruent is hypotenuse-leg (HL) congruency theorem.

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Answer:

Yes

Step-by-step explanation:

Another way of stating the question:  Does the Pythagorean Theorem apply here?  Does 6^2 + 8^2 = 10^2?

           Does 36   + 64   = 100?   YES

Yes, this is a right triangle.

Answer: Yes. That is because it fits the requirements of the Pythagoream Therom:

6^2+8^2    10^2

36+64        100

100      =    100  :)

Answer:

0.5

Step-by-step explanation:

-5 2/5=-27/5

9 8/11=107/11

-3 5/6=-23/6

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

-27/5+107/11-23/6

-27/5-23/6+107/11

-162/30-115/30+107/11

-277/30+107/11

-3047/330+3210/330=163/330=0.493=0.5

After converting all measurements to the same format (decimals), we can see that the shortest piece of wood Jimmy measured is 4.02 ft.

To find the shortest piece of wood, we first need to convert all the lengths to the same format, preferably in decimals for easier comparison. The lengths of the wood pieces given are 4.2 ft, 9/2 ft, 4.02 ft, and 4 2/9 ft.

Let's break it down:

So, we have pieces of wood that are 4.2 ft, 4.5 ft, 4.02 ft, and 4.22ft. Looking at these numbers, it is clear that the piece of wood that measures 4.02 ft is the shortest.

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Answer:

4/3*100^3*π

Step-by-step explanation:

V = 4/3*π*r^3

= 4/3*π*100^3

≈ 4.18879*10^6

To minimize production cost, we need to find the dimensions of the package that will satisfy the volume equation and minimize the cost equation. Taking the partial derivatives of the cost equation with respect to the variables 'r' and 'h', and setting them equal to zero, we can find the critical points. Solving these equations, we find that the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.

To find the dimensions of the package that will minimize production cost, we need to consider the cost of the sides and bottom made of styrofoam and the cost of the top made of glued paper. Let's denote the radius of the base of the cylinder as 'r' and the height of the cylinder as 'h'.

The volume of a cylinder is given by the formula V = πr²h. We know that the volume of the package needs to be 350 cubic centimeters, so we can write the equation as πr²h = 350.

The cost of the sides and bottom of the container is given by the formula C1 = 0.03 * (2πrh + πr²), and the cost of the top is given by the formula C2 = 0.08 * πr².

To minimize the cost, we need to find the values of 'r' and 'h' that satisfy the volume equation and minimize the cost equation.

Since this is a calculus problem, we will differentiate the cost equation with respect to 'r' and 'h', and set the derivatives equal to zero to find the critical points.

Taking the partial derivatives of C1 and C2 with respect to 'r' and 'h', we get:

Solving these equations, we find that h = 7 cm and r = 2.5 cm. Therefore, the dimensions for the package that will minimize production cost are a height of 7 cm and a radius of 2.5 cm.

The function through the points (10, 18), (14, 24), and (18, 30) is a direct variation function with a constant of variation of 1.8.

In this case, we have a linear function. We can determine this by checking if the changes between the x-values and the y-values are consistent. For the change in x-values: (14-10 is 4) and (18-14 is also 4), the change is constant. Similarly, check the change in y-values: (24-18 is 6) and (30-24 is also 6), thus the change is constant. Hence, the function is linear.

More so, this function is a direct variation function because it passes through the origin. In direct variation functions, the ratio of y to x remains constant. In this case, the y divided by x at each point [(18/10=1.8), (24/14=1.71), (30/18=1.67)] is approximately 1.8, which is almost constant.

So, the best description of this function is: 'The function is a direct variation function with a constant of variation of 1.8'.

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Answer:

The function is linear but not a direct variation function.

Step-by-step explanation: