Mrs. Myles has 54 cookies to give to the 18 students in her class. Write a number sentence using the variable c to represent the number of cookies each student gets. A) 18 = 54c B) 54 × 18 = c C) 54 - 18 = c D) 54 ÷ 18 = c

Answer: $1,624

Step-by-step explanation:

The amount after x-years is given as :

9[tex]x^{2}[/tex] + 50x + 1000

Since x represents number of years , this means that after 6 years , the amount will be :

9([tex]6^{2}[/tex] ) + 50(6) + 1000

⇒9(36) + 300 + 1000

⇒324 + 300 + 1000 =

Therefore, the amount after 6 years will be $1,624

The correct answer is option B, as the solution of  the equation:

[tex]\frac{1}{3 m}+\frac{6 m-9}{3 m}=\frac{3 m-3}{4 m}[/tex]  is [tex]\frac{23}{15}[/tex]

Solving this type of equation containing the fractions involves the mathematical operations like finding a common denominator, combining the fractions, eliminating the fraction denominators, cancelling common terms, distributing, adding/subtracting to both sides, simplifying, and dividing both sides by the same factor.

The Steps of calculation are as follows:

Let's verify the answer:

We had the equation:

[tex]\[\frac{1}{3m} + \frac{6m - 9}{3m} = \frac{3m - 3}{4m}\][/tex]

And we simplified it to:

[tex]\[\frac{6m - 8}{3m} = \frac{3m - 3}{4m}\][/tex]

Next, we cross multiplied:

[tex]\[4m(6m - 8) = 3m(3m - 3)\][/tex]

[tex]\[24m^2 - 32m = 9m^2 - 9m\][/tex]

We then brought all terms to one side:

[tex]\[24m^2 - 9m^2 - 32m + 9m = 0\][/tex]

[tex]\[15m^2 - 23m = 0\][/tex]

Factoring out m:

[tex]\[m(15m - 23) = 0\][/tex]

So, either m = 0 or 15m - 23 = 0.

If 15m - 23 = 0, then [tex]\(m = \frac{23}{15}\)[/tex].

Therefore, the correct answer is: b. [tex]\frac{23}{15}$[/tex].

Answer:

(144.9;145.5) so from 144.9 to 145.5lbs

Answer:

OPtion 3 points

Step-by-step explanation:

See the attached figure.

As shown, we can notice that the coordinates of all the points are (-3,2), (-3,3), (1,4), (1,-4), (2,-2), (2,-4).

The figure will be a function if for each value of x there exist a unique value of y.

In the figure, for each value of x we have two values of y. So it is not a function. We need to remove any of ordered pairs that have same input values.

From (-3,2) and (-3,3), we need to remove one point.

From (1,4) and (1,-4), we need to remove one point.

From (2,-2) and (2,-4), we need to remove one point.

It means total we need to remove 3 points from this graph so that it will be a function.

So, the correct option is 3 points.

Answer:

Step-by-step explanation:

1st year- 7*3=21

2nd year- 21*3=63

Answer:30

Step-by-step explanation:

Answer:

I think the correct answer is

A- 40

B- 40

Answer:

1.3

Step-by-step explanation:

Radius is half of a diameter so you just need to divide 3.6 by 2

Answer:

1.8

Step-by-step explanation:

The formula for diameter and radius is 2r = d, if we solve this equation we get 2r = 3.6 So, divide 3.6 by 2 and you got your answer!

Answer:

The difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds.

Step-by-step explanation:

The first positioned swimmer took 55.98 seconds and the second positioned swimmer took 56.87 seconds to complete the race.

So, the difference is (56.87 - 55.98) = 0.89 seconds.

The second positioned swimmer took 56.87 seconds and the third positioned swimmer took 56.94 seconds to complete the race.

So, the difference is (56.94 - 56.87) = 0.07 seconds.

The third positioned swimmer took 56.94 seconds and the fourth positioned swimmer took 57.17 seconds to complete the race.

So, the difference is (57.17 - 56.94) = 0.23 seconds.

The fourth positioned swimmer took 57.17 seconds and the fifth positioned swimmer took 57.27 seconds to complete the race.

So, the difference is (57.27 - 57.17) = 0.10 seconds.

The fifth positioned swimmer took 57.27 seconds and the sixth positioned swimmer took 57.35 seconds to complete the race.

So, the difference is (57.27 - 57.35) = 0.08 seconds.

Therefore, the difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds. (Answer)

Answer:

Between which two places is the difference in finishing times the shortest?

2 & 3

What is the difference in those times?

0.07

Step-by-step explanation:

i do

Answer:

Part 1) The graph in the attached figure N 1

Part 2) The graph in the attached figure N 2

Step-by-step explanation:

Part 1) we have

Line 1: y-intercept: 3 ordered pair: (3, 4)

we know that

To draw a line we need a minimum of two points

Remember that the y-intercept is the value of y when the value of x is equal to zero

so

In this problem we have

(0,3) and (3,4)

Plot the points on a coordinate plane and connect them to graph the line

see the attached figure N 1

Part 2) we have

Line 2: y=-2x+2

Find the intercepts of the line

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

[tex]y=-2(0)+2=2[/tex]

The y-intercept is the point (0,2)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

[tex]0=-2x+2\\2x=2\\x=1[/tex]

The x-intercept is the point (1,0)

Plot the intercepts and connect them to graph the line

see the attached figure N 2

Answer:

Part 1) The graph in the attached figure N 1

Part 2) The graph in the attached figure N 2

Step-by-step explanation:

Part 1) we have

Line 1: y-intercept: 3 ordered pair: (3, 4)

we know that

To draw a line we need a minimum of two points

Remember that the y-intercept is the value of y when the value of x is equal to zero

so

In this problem we have

(0,3) and (3,4)

Plot the points on a coordinate plane and connect them to graph the line

see the attached figure N 1

Part 2) we have

Line 2: y=-2x+2

Find the intercepts of the line

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

The y-intercept is the point (0,2)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

The x-intercept is the point (1,0)

Plot the intercepts and connect them to graph the line

see the attached figure N 2

The solution of the system of equations is (-7 , 5)

Step-by-step explanation:

The steps of the linear combination method are:

∵ 2x + 3y = 1 ⇒ (1)

∵ y = -2x - 9

- Add 2x to both sides

∴ 2x + y = -9 ⇒ (2)

Multiply equation (2) by -1 to make the coefficients of x opposites

∴ -2x - y = 9 ⇒ (3)

Add equations (1) and (3) to eliminate x

∴ 2y = 10

Divide both sides by 2

∴ y = 5

Substitute the value of y in equation (1) or (2) to find x

∵ 2x + 5 = -9

- Subtract 5 from both sides

∴ 2x = -14

- Divide both sides by 2

∴ x = -7

The solution of the system of equations is (-7 , 5)

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Answer:

10 paperback and 5 hardcover books

Step-by-step explanation:

Please see attached picture for full solution.

Let's check:

total cost= 10(3) + 5(8)= $70 ✓

You could also try to solve the question by assuming John bought all paperback books first instead of all hardcover books. The answer should be the same.

Answer:

1.5

Step-by-step explanation:

Answer:

The person above is right.

Its: T = A^ 1.5

Step-by-step explanation:

Graph the planet data, shown right, using the regression calculator. When you are done, click “Resize window to fit data.”

Mercury and Venus are

✔ closer to

the sun than Earth is.

So, their orbital periods are

✔ shorter

than Earth's orbit.

The further a planet is from the sun, the

✔ longer

its orbit is.

A power regression equation for this data is:

T = A^

1.5

I took it and got it right.

[tex]\text{You're solving the equations:}\\\\4r - 5 = 17\\ 12 - 2s = 2\\\\\text{Solve for r:}\\\\4r-5=17\\\\\text{add 5 to both sides}\\\\4r=22\\\\\text{Divide both sides by 4}\\\\\boxed{r=5.5}\\\\\text{Solve for s:}\\\\12 - 2s = 2\\\\\text{Subtract 12 from both sides}\\\\-2s=-10\\\\\text{Divide both sides by -2}\\\\[/tex]

[tex]\boxed{s=5}[/tex]

An equation is formed when two equal expressions. The product of r and s is 27.5.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation 4r - 5 = 17 can be solved for r as shown below,

4r - 5 = 17

Add 5 on both the sides of the equation,

4r - 5 + 5 = 17 + 5

4r = 22

Divide both the sides of the equation by 4,

4r / 4 = 22 / 4

r = 11/2

r = 5.5

The given equation 12 - 2s = 2 can be solved for s as shown below,

12 - 2s = 2

Subtract 12 from both the sides of the equation,

12 - 2s - 12 = 2 - 12

-2s = -10

Divide both the sides of the equation by -2,

-2s/-2 = -10/-2

s = 5

Now, the product of r and s can be written as,

r × s

= 5.5 × 5

= 27.5

Hence, the product of r and s is 27.5.

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Answer:0.2

Step-by-step explanation: 1/10 and 1/10

Simply means this in maths

1/10+1/10

0.1+0.1= 0.2

Answer:

Step-by-step explanation:

Total cost for trip = 290 + 50 + 95*5 =290+50+ 475 = $ 815

Savings = $143

Money needed = 815 - 143 = $ 672

No. of driveways = 672/48 = 14

14 driveways must she shovel to have enough money to pay for the trip.

Sneha needs to calculate the total cost of her vacation which is $815. After taking into account her savings, she requires an additional $672. As she earns $48 shoveling each driveway, she would need to shovel 15 driveways.

This is a question of basic algebra and problem solving. Sneha needs to calculate the total cost of her vacation first. She will spend $50 on transportation, $290 on food, and $95 per night for the hotel for 5 nights, or $475 ($95 x 5) for the hotel total.

Adding these amounts together, Sneha's vacation will cost $815 ($50 + $290 + $475). She currently has $143 in savings, meaning she needs $672 more dollars ($815 - $143).

As Sneha earns $48 for each driveway she shovels, we divide the total she needs by the earning for each driveway. That gives us 14 driveways. As Sneha can't shovel a fraction of a driveway, she will need to shovel 15 driveways in total.

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Answer:

z = 65°

y= 105°

Step-by-step explanation:

angle z is adjacent to 115° on a straight line, hence they are supplementary angles, i.e they add up to 180°

hence,

z + 115° = 180°

z = 180° - 115° = 65°  

recall that the sum of angles inside a convex quadrilateral always adds up to 360°

i.e z + y  + 102° + 88° = 360°  (we know z from above)

65 + y +102+88=360

y = 360 -65-102-88 = 105°

Answer: 0.5

Step-by-step explanation:

Let the number be x , then

42% of x = 0.21

0.42x = 0.21

divide through by 0.42

x = 0.21/0.42

x = 0.5

Therefore : 42% of 0.5 = 0.21

Answer:

.5

Step-by-step explanation:

.42/1 * x = .21

x = .21/.42

x = .5 or 1/2

Answer:

  B, E

Step-by-step explanation:

It can be helpful to factor the first two terms:

  f(x) = x^2(x -7) +36

This can make it easier to evaluate the function for different values of x.

The answer choices suggest you need to know whether f(5) and f(-14) match the values given here.

  f(5) = 5^2(5 -7) +36 = -50 +36 = -14 . . . . matches choice B (and E)

  f(-14) = (-14)^2(-14-7) +36 = -21(196) +36 . . . . does not match choice A (or D)

__

The one remaining answer choice we need to consider is C. If we look at f(0) for this equation, we find it is (-5)(-10) +14 = 64, which does not match f(0) = 36 for the function given in the problem statement.

The only true answer choices are B and E.

_____

The remainder theorem tells you that f(a) = the remainder from f(x)/(x -a).

6.9 for X and -0.55 for X and 1 for Y

Step-by-step explanation:

The numerical Coefficient is said to be the fixed number that is in multiple with the variable. If the number is not with the variable then it is not taken into account.

STEP 1:

6.9 is the coefficient for X

STEP 2:

-0.55 is the coefficient for x

STEP 3:

1 is the coefficient for y

STEP 4:

343 a 2.65 not considered as the don't have the variables.

390 gallons of 90 % antifreeze must be mixed with 60 gallons of 15% antifreeze to get a mixture that is 80%

Solution:

Let "x" be the gallons of 90 % antifreeze

60 gallons of 15 % antifreeze

Then, (x + 60) is the gallons present in final mixture that is 80 %

Therefore, x gallons of 90 % antifreeze is mixed with 60 gallons of 15 % antifreeze to get a mixture that is (x + 60) gallons of 80 %

Thus, a equation is framed:

90 % of x + 15 % of 60 = 80 % of (x + 60)

Solve the above equation for "x"

[tex]90 \% \times x + 15 \% \times 60 = 80 \% \times (x+60)\\\\\frac{90}{100} \times x + \frac{15}{100} \times 60 = \frac{80}{100} \times (x+60)\\\\0.9x + 0.15 \times 60 = 0.8(x + 60)\\\\0.9x + 9 = 0.8x + 48\\\\0.9x - 0.8x = 48 - 9\\\\0.1x = 39\\\\ x = 390[/tex]

Thus 390 gallons of 90 % antifreeze must be mixed

Answer: r ~= 24.50986

Step-by-step explanation:

This question is done by simply looking at the circumference formula for a circle (2pi r)

154= 2*pi*r

154/(2*pi) = r

r ~= 24.50986

Answer:

Step-by-step explanation:

[tex]circumference=2\pi*r\\\\2\pi*r=154\\\\2*\frac{22}{7}*r=154\\\\r=\frac{154*7}{2*22}\\\\r=\frac{49}{2}=24.5 cm[/tex]

To find the length of the train and its speed, we can use the formula Length = Speed x Time. By setting up and solving equations, we can find that the length of the train is 200 meters and the speed of the train is 20 m/s.

To find the length of the train, we can use the formula:

Length = Speed x Time

Given that the train takes 10 seconds to pass you and 30 seconds to pass the bridge, we can calculate:

Length of train = Speed of train x Time taken to pass you = Speed x 10

Length of train + Length of bridge = Speed of train x Time taken to pass the bridge = Speed x 30

Substituting the values, we have:

Speed x 10 + 100 = Speed x 30

Simplifying the equation, we get:

Speed = 400/20 = 20 m/s

Substituting the value of speed back into the first equation, we have:

Length of train = 20 x 10 = 200 meters

Therefore, the length of the train is 200 meters and the speed of the train is 20 m/s.

Answer:

457

Step-by-step explanation:

I add all the numbers I could see and got 457.... i need more information hope this helps

Answer:

The equations system has multiple solutions for x, y.

Step-by-step explanation:

Let's solve for x and y this equations system:

We can observe that the second equation is a simplification of the first (divided by 2) and therefore, the system has multiple solutions for x and this way:

x           y

-27/5    -5

-21/5    -4

-3         -3

-9/5      -2

-3/5      -1

3/5       0

9/5        1

3           2

21/5      3

27/5     4

33/5     5

Answer:

Up

Step-by-step explanation:

Shifting a graph a number of units up is a vertical translation. So, in a vertical translation, we shift the graph up by adding a constant at the end of the function.

In any function [tex]f(x)[/tex]. If we add the constant [tex]d[/tex] at the end of the function, then this will shift graph of the function [tex]d[/tex] units up.

Answer:

[tex]10 {x}^{2} + 4x[/tex]

Step-by-step explanation:

[tex] \frac{20 {x}^{2} + 8x }{2} = \frac{20x}{2} + \frac{8x}{2} = 10 {x }^{2} + 4x[/tex]

Answer:

Volume of metal piece  = 3680 mm³

Step-by-step explanation:

volume of horizontal cuboid:

V =  l * b * h

= 30 * 8 * 8 = 1920 mm³

Volume of vertical cuboid:

breadth = 10 mm

Length = 14+8 = 22 mm

Height = 8 mm

V = 22 * 10 * 8

=  1760 mm³

Volume of metal piece = 1920 + 1760

   = 3680 mm³

Answer:

3680  

i got  100 on test

Answer:

The difference between a median and altitude of a triangle is given below :

Altitude is the perpendicular line drawn from a vertex of a triangle to its opposite side .But a median of a triangle is a segment connecting a vertex to the midpoint of its opposite side.

Step-by-step explanation:

The difference between a median and altitude of a triangle is given below :

Altitude is the perpendicular line drawn from a vertex of a triangle to its opposite side .But a median of a triangle is a segment connecting a vertex to the midpoint of its opposite side.

Answer: 20%

Step-by-step explanation:

Percentage increase = increase / original value x 100

Increase = $12.00 - $10.00 = $2

Therefore :

% increase = [tex]\frac{2}{10}[/tex] x 100

% increase = 20

Answer:

20%

Step-by-step explanation:

12.00 - 10.00 = 2.00

2 divided by 10 = 0.2

100  multiplied by 0.2 which gives you 20%

Answer:

Step-by-step explanation:

[tex]7x+14=7(x+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\7x+14=(7)(x)+(7)(2)\\\\7x+14=7x+14\qquad\text{subtract}\ 7x\ \text{from both sides}\\\\7x-7x+14=7x-7x+14\\\\14=14\qquad\bold{TRUE}\\\\\bold{CONCLUSION}\\\text{The equation has infinitely many solutions}[/tex]