Which equation represents the line that passes through the points (-3,7) and (3,3)

Chris baked 95 cookies.

Step-by-step explanation:

Given,

Cookies baked by Haley = 50

Cookies baked by Chuck = 65

Cookies baked by Dana = 90

Average of them = 75

Let,

Cookies baked by Chris = x

Average = [tex]\frac{Sum\ of\ quantites}{No.\ of\ people}[/tex]

[tex]75=\frac{50+65+90+x}{4}[/tex]

Multiplying both sides by 4

[tex]4*75=\frac{50+65+90+x}{4}*4\\300=205+x\\300-205=x\\95=x\\x=95[/tex]

Chris baked 95 cookies.

Keywords: addition, average

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Answer:

There are 110 children total in the sports club

Step-by-step explanation:

To get this answer, its actually easier than it seems. You might need a calculator however.

First you start with the 11 children who play both badminton and squash, then, you divide that by 0.25 (25%) to get 44.

Next you take 44 and divide it by 0.4 (40%) to get 110.

And there you go! If you want to make sure you got it right simply start with 110 and multiply it by 0.4 then multiply the number/decimal you get by 0.25. You should get 11 to confirm your answer :)

Answer:

Principal Invested in Municipal Bonds is $16,000

Principal Invested in Corporate Bonds is $15,000

Step-by-step explanation:

If;

Principal Invested in municipal bonds = a

Principal Invested in corporate bonds = b

then we have;

a + b = $31,000 --------------------------------Equation 1

0.075a + 0.085b = $2,475  ---------------Equation 2

From equation 1 we have;

a = 31,000 - b

By putting the values of a in Equation 2 we get;

0.075 (31,000 - b) + 0.085b = 2,475

2,325 - 0.075b + 0.085b = 2,475

0.01b = 150

b = $15,000

By putting the values of b in equation 1 we get;

a = $16,000

Final answer:

Reggie Means invested $16,000 in municipal bonds at 7.5% interest and $15,000 in corporate bonds at 8.5% interest to earn a total annual interest of $2,475.

Explanation:

Let the amount invested in municipal bonds be $x. Thus, the amount invested in corporate bonds will be $(31,000 - x). The municipal bonds earn 7.5% annual interest and the corporate bonds earn 8.5% interest. The total annual interest from both investments is $2,475.

To calculate the interest from municipal bonds, use the formula Interest = Principal × Rate × Time. The interest from municipal bonds is 0.075x (since 7.5% is the same as 0.075).

Similarly, for corporate bonds, the interest will be 0.085(31,000 - x). The sum of these interests equals $2,475:

0.075x + 0.085(31,000 - x) = 2,475

Solving this equation:

Answer:

The shipping and handling charge that Bryce paid is $109.65

Step-by-step explanation:

Given as :

The online price of the treadmill = $510

The charge of shipping and handling = 21[tex]\dfrac{1}{2}[/tex] % of online price

Let The shipping and handling charge that Bryce paid = $x

Now, According to question

∵ The charge of shipping and handling = 21[tex]\dfrac{1}{2}[/tex] % of online price

So, x = [tex]\dfrac{43}{2}[/tex] % of $510

Or, x = [tex]\dfrac{43\times 510}{100\times 2}[/tex]

Or, x = $109.65

The shipping and handling charge that Bryce paid = x = $109.65

Hence,The shipping and handling charge that Bryce paid is $109.65 Answer

Answer:

Graph is below

Step-by-step explanation:

y>3x+10 is represented by the red line, which is dotted because it's values are not included in the solution. Everything above it is shaded red because it is greater than. y<-3/4x-1 is represented by the blue line, which is dotted because it's values are not included in the solution. Everything beneath is shaded blue, because it is less than. The intersection of the two shaded areas is purple. (8,10) is not part of the solution because it does not have an x value beneath -3.

(this was a hard question, but i'm certain that at least the graph is correct.)

Answer:

(- 3, 1 )

Step-by-step explanation:

Given f(x) then f(x) + c represents a vertical translation of f(x)

• if c > 0 then shift up by c units

• if c < 0 then shift down by c units

Thus for f(x) - 4

(- 3, 5 ) → (- 3, 5 - 4 ) → (- 3, 1 )

Answer:

It would be 5.1942486

Step-by-step explanation:

Becuase the 0 is after the 6 the 6 stays as it is and there is no need to round up or down

We're starting with 5.19424860514, and we need to round to the 6th decimal. 1st, we need to identify the 6th place. In this case, that is 8. Everything before that is the same no matter what. 5.19424 is our base. We need to look at the 860514. More specifically, the 86. 6 is over 4, so the 8 becomes a 9 using basic rounding rules. Therefore, our final answer is 5.194249

Hope this helps!

Answer:

The points for the given two linear equation as

[tex]x_1 , y_1[/tex] = - 2 , - 6

[tex]x_2 , y_2[/tex] = - 2 , 6

The graph so plotted as shown

Step-by-step explanation:

Given as :

The two linear equation are

y = 3 x                 ........A and

y = - x - 8             .........B

Solving equation A and B

Now, Put The value of y from eq A into eq B

So, 3 x = - x - 8

Or, 3 x + x = - 8

Or, 4 x = - 8

∴ x = [tex]\dfrac{-8}{4}[/tex]

I.e x = - 2

Now , Put the value of x into eq A

∵ y = 3 x

∴ y = 3 × (-2)

I.e y = - 6

Again, Put the value of x into eq B

∵ y = - x - 8

∴ y = - 2 - (-8)

I.e y = 6

So, for x = - 2 , y = - 6

And for x = - 2 , y = 6

Hence , The points for the given two linear equation as

[tex]x_1 , y_1[/tex] = - 2 , - 6

[tex]x_2 , y_2[/tex] = - 2 , 6

The graph so plotted as shown . Answer

Answer:

30

Step-by-step explanation:

3x5=15

15x2=30

Answer:

30

Step-by-step explanation:

Multiply 3 by 5 which is 15 and them multiply by 2 which is 30

The liquid started cooling from 194 degrees. This is calculated by determining the rate of cooling, which is 8 degrees per minute, and extrapolating back to find the initial temperature.

The subject of the question is about determining the initial temperature of cooling liquid. To solve this, we have to first identify the rate at which the temperature is decreasing. Given, after 2 minutes it was 178 degrees and after 5 minutes it was 154 degrees. That's a decrease of 24 degrees over 3 minutes, or 8 degrees per minute.

Since the liquid started cooling 2 minutes before it was first observed at 178 degrees, we can estimate that the liquid would have been 16 degrees hotter at the start of the cooling period. So, it would have started cooling at 178 + 16 = 194 degrees.

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Answer: f(3)=11.5

Step-by-step explanation:

In order to solve this equation, all you have to substitute the value inside of the parenthesis with the value of x in the equation after the equals sign. SO...

f(3)=3x+2.5

f(3)=3(3)+2.5

f(3)=9+2.5

f(3)=11.5

Hope this helps!

Answer:

x = 11

Step-by-step explanation:

Vertical angles mean that their values are equivalent, which means that:

5x + 10 = 7x -12

Solve for x

22 = 2x

x = 11

Hope this helps :)

Mei charges $15 per hour as her regular hourly rate before applying a 40% discount to her next door neighbor, resulting in a discounted rate of $9 per hour.

To calculate the regular hourly rate Mei charges before the 40% discount, we set up an equation where the discounted rate is equal to 60% of the original rate, because 100% - 40% = 60%. Mei charges her neighbor $9 per hour after the discount. Let h represent Mei's regular hourly rate before the discount.

So, the equation would be 0.60h = $9. To find h, we divide both sides of the equation by 0.60:

h = $9 / 0.60

h = $15

Thus, Mei's regular hourly rate before the discount is $15 per hour.

Mei's regular hourly rate before the discount is $15.

To find Mei's regular hourly rate before the discount, let's denote it as h .

Given that Mei offers her neighbor a 40% discount, her neighbor pays only 60% of the regular rate. This can be represented as:

[tex]\[ 0.60h = 9[/tex]

To find ( h ), we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.60:

[tex]\[ \frac{0.60h}{0.60} = \frac{9}{0.60} \][/tex]

This simplifies to:

[tex]\[ h = \frac{9}{0.60} \][/tex]

Now, we can calculate:

[tex]\[ h = \frac{9}{0.60} = 15 \][/tex]

So, Mei's regular hourly rate before the discount is $15.

Answer:

1 positive solution

2.87.

Step-by-step explanation:

x^2 + 2x + 7 = 21

x^2 + 2x - 14 = 0

The product of its roots = c/a = -14 so it will have 1 positive solution.

x = -2 +/- sqrt (2^2 - 4*-14) / 2

x = -1 +/- sqrt60/2

= -1 +/- 3.873

GreATest solution is 2.87

Answer:

Step-by-step explanation:

Find the equation of the line thru the points (2,1) and (3,5)

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

This is a 2 step process. First find the slope of the line thru the points.

slope, m = diffy/diffx

m = (5-1)/(3-2)

m = 4

---------

Now use y = mx + b with either point to find b, the y-intercept.

y = mx + b

5 = 4*3 + b

b = -7

-------

Answer:

Step-by-step explanation:

Formula for calculating the equation of a line is expressed as shown below;

y = mx+c OR y-y1 = m(x-x1) where

m is the slope or gradient

c is the intercept (the point where the line cuts the y axis)

m = ∆y/∆x

m = y2-y1/x2-x1

Given the points (-8,8) and (1,-10).

x1 = -8, y1 = 8, x2 = 1, y2 = -10

m = -10-8/1-(-8)

m = -18/9

m = -2

The equation of a line can also be written as a point slope:

y-y1 = m(x-x1)

Substituting the value of x1, y1 and m into the equation we have;

y-8 = -2(x-(-8))

y-8 = -2(x+8)

y-8 = -2x-16

y= -2x-16+8

y = -2x-8

The equation of the line is y = -2x-8

Answer:

The answer is 74%

Step-by-step explanation:

Method One:

1) Un-reduce the fraction to ger 74/100

2) Your answer is 74%

Method 2:

1) Divide 37 by 50

2) You get .74

3) Your answer is 74%

Answer:

1/4

Step-by-step explanation:

There are 7 points from 0 to 7/4. This means each point represents 1/4. Therefore A is 1/4

Answer:

1/4

Step-by-step explanation:

If you count back from the 7/4, A will be at the 1/4 point.

Hope this helps :)

To promote economic growth, countries would most likely act so that inflation "remains at a low level".

Answer: Option c

Explanation:

The Central Bank and the government basically command Inflation or either of them. The monetary policy is helpful from its changing interest rates parameters . Although there are a different types of tools which can control inflation are as follows

Monetary policy: The demand in the economy is reduced by higher interest rates, and result into lower economic growth with lower inflation.

Commanding supply of money: Monetarists debt huge by setting a close bond between the inflation and money supply.

Supply-side Policies: The scheme to hike the efficiency of the economy and competitiveness by declining pressure on long-term costs.

Fiscal policy: The reduction of spending, demand and inflationary pressures resulted from a higher rate of income tax.

Wage controls: Inflationary pressures can be reduced by controlling wages  , but after 1970 such act is rarely performed.

Answer:

Therefore the required sentence into an equation is

[tex]5+(C\times a)=2[/tex]

Step-by-step explanation:

Given:

5 more than a product of a number and a

equals 2

Use a variable C for the unknown number

To Find:

Translate above sentence into an equation . ?

Solution:

Let ' C ' for the unknown number

and ' a ' for the other number.

Then according to given condition we have

5 more Product of ( C and a ) = 2

Therefore the required sentence into an equation is

[tex]5+(C\times a)=2[/tex]

Answer:

Step-by-step explanation:

[tex]\dfrac{5}{6}<\dfrac{w}{8}\Rightarrow\dfrac{w}{8}>\dfrac{5}{6}\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup\cdot\dfrac{w}{8\!\!\!\!\diagup}>8\!\!\!\!\diagup^4\cdot\dfrac{5}{6\!\!\!\!\diagup_3}\\\\w>\dfrac{20}{3}\\\\w>6\dfrac{2}{3}\\\\7>6\dfrac{2}{3}[/tex]

Answer:   D ) 7

Step-by-step explanation:

7 is greater than 5

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The value of x is 10

Step-by-step explanation:

We know that the sum of internal angles of a quadrilateral is 360 degrees

So,

Given

Angle 1 = A1 = 3x+10

Angle 2 = A2 = 9x+50

Angle 3 = A3 = 4x

Angle 4 = A4 = 13x+10

So,

[tex]A_1+A_2+A_3+A_4 = 360\\(3x+10)+(9x+50)+(4x)+(13x+10) = 360\\3x+10+9x+50+4x+13x+10 = 360\\3x+9x+4x+13x+10+50+10 = 360\\29x+70 = 360[/tex]

Subtracting 70 from both sides

[tex]29x+70-70 = 360-70\\29x = 290[/tex]

Dividing both sides by 29

[tex]\frac{29x}{29} = \frac{290}{29}\\x = 10[/tex]

Hence,

The value of x is 10

Keywords: Angles, Quadrilateral

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Answer:

It has no slope because (x2-x1) in the formula [tex]m=\frac{y2-y1}{x2-x1}[/tex] is equal to zero, and the denominator of a fraction cannot be zero

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

the points (7, 10) and (7, 20)

substitute the values

[tex]m=\frac{20-10}{7-7}[/tex]

[tex]m=\frac{10}{0}[/tex] ----> is undefined

The line has a slope undefined ---> is a vertical line (parallel to the y-axis)

Answer:

The shop can cut the cost of production per sandwich to $3.75.  The revenue function would then be defined as R(x)=9x.

Step-by-step explanation:

We want to make as big profit as possible by making as little sandwiches as possible. This means that we want the profit, which is [tex]revenue- production\: cost[/tex] to be as big as possible.

For the first choice the profit per sandwich is [tex]8.25-4=4.25[/tex] dollars.

For the second choice the profit per sandwich is [tex]9-3.75=5.25[/tex] dollars.

For the third choice the profit per sandwich is [tex]8.5-3.5=5[/tex] dollars.

We see here that for the second choice the profit is greatest, therefore this choice is most suitably correct.

Answer:

3/4 * 6 x 10 = 45/1 = 45

Step-by-step explanation:

Multiple: 3/4 * 6 = 3 · 6/4 · 1 = 18/4 = 9 · 2/2 · 2 = 9/2

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(18, 4) = 2. In the following intermediate step, cancel by a common factor of 2 gives 9/2.

In other words - three quarters multiplied by six is nine halfs.

Multiple: the result of step No. 1 * 10 = 9/2 * 10 = 9 · 10/2 · 1 = 90/2 = 45 · 2/1 · 2 = 45

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(90, 2) = 2. In the following intermediate step, cancel by a common factor of 2 gives 45/1.

In other words - nine halfs multiplied by ten is forty-five.

Answer:

[tex]y\leq 2x+4[/tex]

[tex]y\geq -x-6[/tex]

Step-by-step explanation:

step 1

Find the equation of the solid line with positive slope

we have the points

(0,4) and (-2,0)

Find the slope

[tex]m=(0-4)/(-2-0)=2[/tex]

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=2\\b=4[/tex]

substitute

[tex]y=2x+4[/tex]

step 2

Find the equation of the inequality with positive slope

we know that

The solution of the inequality, is the shaded area below the solid line

so

The equation of the inequality is

[tex]y\leq 2x+4[/tex] ----> inequality A

step 3

Find the equation of the line with negative slope

we have the points

(-6,0) and (-4,-2)

Find the slope

[tex]m=(-2-0)/(-4+6)=-1[/tex]

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

we have

[tex]m=2\\point\ (-6,0)[/tex]

substitute

[tex]0=-(-6)+b[/tex]

solve for b

[tex]0=6+b[/tex]

[tex]b=-6[/tex]

so

The linear equation is

[tex]y=-x-6[/tex]

step 4

Find the equation of the inequality with negative slope

we know that

The solution of the inequality, is the shaded area above the solid line

so

The equation of the inequality is

[tex]y\geq -x-6[/tex] ----> inequality B

therefore

The system of inequalities is

[tex]y\leq 2x+4[/tex] ----> inequality A

[tex]y\geq -x-6[/tex] ----> inequality B

Answer:

[tex]12x^2+4x[/tex]

Step-by-step explanation:

The area of a square or rectangle can be found by multiplying the width by the height. Since we now both, we can create an expression.

[tex](3x+1)*(4x)[/tex]

Now we can apply the distributive law/property to expand the expression.

[tex]3x(4x)+1(4x)[/tex]

Finally, we can simplify.

[tex]12x^2+4x[/tex]

Answer:

It will be $7602.3

Step-by-step explanation:

The equation [tex] y = 10000(0.97)^{x}[/tex] gives the purchasing power of $10000 after x years.

Therefore, the sum of money $10000 will value [tex] 10000(0.97)^{x}[/tex] after x number of years.

Now, after 9 years i.e. x = 9 years, the sum value of $10000 will become [tex] y = 10000(0.97)^{9} = 10000 \times 0.76023 = 7602.3[/tex] dollars. ( Answer )

[tex]E(t) = 40(0.65)^t[/tex]

Step-by-step explanation:

Given,

Current quantity of emission, P = 40 millions,

Reduction in emission per year, r = 35% = 0.35,

Thus, the quantity of emission after t years,

[tex]E(t)=P(1-r)^t[/tex]

[tex]E(t) = 40(1-0.35)^t[/tex]

[tex]\implies E(t) = 40(0.65)^t[/tex]

Which is the required function.

To represent Freedonia's carbon-dioxide emissions E(t), t years from now with a yearly reduction of 35%, use the function E(t) = 40 * (0.65)^t, where 40 million tons is the current emission and 0.65 is the remaining percentage of emissions after reduction.

The student is asking to write a function that models the carbon-dioxide emissions of Freedonia in million tons, E(t), t years from today, given that the emissions are being reduced by 35% each year. The current emission level is 40 million tons of carbon-dioxide.

To create this function, we need to take into account the exponential decay of the emissions due to the percentage reduction. The general form for exponential decay is given by the equation E(t) = E_0 × (1 - r)^t, where E_0 is the initial amount, r is the rate of reduction (as a decimal), and t is the time in years. For Freedonia, E_0 is 40 million tons, and r is 0.35. Therefore, the equation becomes E(t) = 40 × (1 - 0.35)^t.

Answer:

1. The lowest point is 9 feet below sea level, and the highest point is 108 feet above sea level.

Step-by-step explanation:

The sea level is considered to be zero levels.

Now, the level +x feet means it is at x feet higher than sea level and the level -x feet means it is at x feet lower than the sea level.

Now, the lowest point of the country lies at −9 feet. The highest point of the country lies at +108 feet.

That means, the lowest point is 9 feet below sea level, and the highest point is 108 feet above sea level. (Answer)