Write the equation that represents the line use exact numbers

Answer:

600,000 mL

Step-by-step explanation:

Since there is 1,000 mL in 1 L, 600 L = 600,000 mL.

If Carmen sold 600 liters of soda, then he would have sold 600000 milliliters of soda. 1 liter= 1000 milliliters

A) To find A in terms of B, we need to find A = xB. One given is A = 12 and B = 3. We substitute, which gives us 12 = x4. Divide both sides by 4, which gives us x = 3. This means that A = 3B.

B) For this, we can just plug in 5 as B in our equation. A = 3*5 -> A = 15.

C) We can plug in A as 36. 36 = 3B -> B = 12.

A.) The formula for A in terms of B is A = 4B. B.) When B = 5, A = 20. C.) When A = 36, B = 9.

A.) To find the formula for A in terms of B, we can set up a proportion using the given values. Since A is directly proportional to B, we can write the proportion as A/B = k, where k is the constant of proportionality. Substituting the values A = 12 and B = 3, we have 12/3 = k. Solving for k, we find k = 4. Therefore, the formula for A in terms of B is A = 4B.

B.) To find the value of A when B = 5, we can substitute B = 5 into the formula A = 4B. A = 4(5) = 20.

C.) To find the value of B when A = 36, we can rearrange the formula A = 4B to solve for B. Dividing both sides by 4, we get B = A/4. Substituting A = 36, we have B = 36/4 = 9.

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Answer:

Solution 1

(x,y) = (-1,3)

Solution 2

(x,y) = (1,5)

Step-by-step explanation:

To easily solve this question, we use a graphing tool, or a calculator to plot each graph.

The solution of the system of equations corresponds to the intersection between both graphs

f(x)=x^2 + 4/4x + 3

g(x)=|x+4|

Please see image below

Solution 1

(x,y) = (-1,3)

Solution 2

(x,y) = (1,5)

Graphical methods or numerical methods such as Newton's method are used to approximate the solution(s) to the system of equations represented by f(x) and g(x) to the nearest tenth of a unit.

To approximate the solution(s) to the given system of equations f(x) = x^2 + 4 / (4x + 3) and g(x) = |x + 4| using technology, one can employ a graphing calculator or graphing software. By plotting both functions on the same set of axes, the point(s) of intersection represent the solution(s) to the system. To find the approximate solution to the nearest tenth, it may be necessary to use the graph's zoom and trace features to accurately determine the x-values where the two graphs intersect.

If this graphical method is insufficient, numerical methods such as Newton's method can provide a more precise approximation.

The map tells you 1 inch = 0.5 miles.

Multiply each dimension on the map by 0.5 to get the miles, then add them together:

House to Sports store = 2 x 0.5 = 1 mile.

Sports store to Jay's house = 3.75 x 0.5 = 1.875 miles.

Jay's house to park = 1.5 + 0.5 = 2 inches x 0.5 = 1 mile.

Total distance = 1 + 1.875 + 1 = 3.875 miles.

The total distance covered in miles is; 3.875 miles

From the map, we see that;

1 inch = 0.5 miles.

Now, total distance in inches is;

D = 2 + 3.75 + 1.5 + 0.5

D = 7.75 inches

Using the given conversion rate to miles, we have;

D = 7.75 * 0.5

D =  3.875 miles.

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Answer:

well if it is parallel it would but 2 lines going in the same direction. it will never touch

Step-by-step explanation:

Answer:

The slope of this line is undefined.

Explanation:

The slope of a line is rise over run, where the rise is the change in y value and the run is the change in x. Since there is no change in x when a line is parallel to the y-axis, any slope would mean you would divide by 0.

[tex]m=\frac{rise}{run}\\m = \frac{rise}{0} \\m= \frac{anything}{0}\\[/tex]

Since you cannot divide by 0 the answer will always be undefined no matter what the numerator is. The slope of any vertical line will be undefined.

The midsegment is half the length of the base.

1) 32 ÷ 2 = 16

So, 16 is the midsegment

2) 11 ÷ 2 = 5.5

So, 5.5 is the midsegment

3) 32 ÷ 2 = 16

So, 16 is the midsegment

4) 14 ÷ 2 = 7

So, 7 is the midsegment

First find out the ares of the square

10×10

100

Square Area = 100

Next, find the length of the sides of the triangle

16-10= 6

10-6= 4

Multiple the sides of the triangle a divide by two

6×4

24

24÷2

12

Add both the area of the square and triangle together

100+12

112

The area of the figure is 112

Answer:

Step-by-step explanation:

10x10=100in (Area of square )

(10-6)x6/2=12in (Area of triange )

100+12=112in

Answer: Off the top of my head, I can see that B is a correct statement.

Step-by-step explanation: 4 x 2 = 8

3 x 2 = 6

this multiplication shows that statement B is true.

4(xsquared -2) thats the answer

So, this is technically (4x×4x)-8. Therefore, the answer is 16x-8.

7 students watch less than 3 hours of tv a day.

Hope this helps.

You should just count the x's in slots 0, 1, and 2, so the answer should be 7 (or however many those 7 x's represents)

Answer:

Step-by-step explanation:

Let p represent the number of calories in a peach and g the number of calories in an orange.  

Then p = g + w.

From this we get g = p - w.

In words:  "The number of calories we get from an orange is equal to p, the number of calories from a peach, less w calories."

Answer:  [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

Let's call the  time he carried the ball: t

You know that he bounced the  ball for 1/3 of his recess.

You also know that he threw the ball in the air and caught it 3/6 of the time.

Therefore, to solve the exercise you only need to add both fractions, as you can see below. Therefore, the result is:

[tex]t=[/tex][tex]\frac{1}{3}[/tex]+[tex]\frac{3}{6}[/tex]

[tex]t=[/tex][tex]\frac{5}{6}[/tex]

Answer:

20

Step-by-step explanation:

Area of Triangle = 1/2b*h

Area of Triangle = 1/2*4 2/3*8 4/7

Area of Triangle = 20

Answer:

complementary angles

Step-by-step explanation:

Adjacent angles form a right angle.

A right angle is 90 degrees.

Two angles that add to 90 degrees are complementary.

The adjacent angles are complementary

Answer:

-2/8

Step-by-step explanation:

Since both numbers are negative we want to find which ever is closer to 0. -2/8 is -1/4 which is closer to 0 then -2/3 so -2/8 is larger

Answer:

18 km/h

Step-by-step explanation:

Let S km be the distance between ports M and N, x km/h be the speed of the motorboat in still water. Then x-2 km/h is the speed of the motorboat upstream and x+2 km/h is the speed of the motor boat downstream.

1. The motorboat traveling downstream covers the distance between port M and port N in 6 hours, then

[tex]\dfrac{S}{x+2}=6[/tex]

2. Once, the motorboat stopped 40 km before reaching N, turned around, and returned to M. This took the motorboat 9 hours. Then

[tex]\dfrac{S-40}{x+2}+\dfrac{S-40}{x-2}=9[/tex]

From the first equation [tex]S=6(x+2)=6x+12.[/tex] Substitute it into the second equation:

[tex]\dfrac{6x+12-40}{x+2}+\dfrac{6x+12-40}{x-2}=9,\\ \\\dfrac{6x-28}{x+2}+\dfrac{6x-28}{x-2}=9.[/tex]

Now

[tex]\dfrac{(6x-28)(x-2)+(6x-28)(x+2)}{(x-2)(x+2)}=9,\\ \\(6x-28)(x-2+x+2)=9(x^2-4),\\ \\(6x-28)\cdot 2x=9x^2-36,\\ \\12x^2-56x-9x^2+36=0,\\ \\3x^2-56x+36=0,\\ \\D=(-56)^2-4\cdot 3\cdot 36=2704,\\ \\x_{1,2}=\dfrac{56+\sqrt{2704}}{2\cdot 3}=\dfrac{56\pm52}{6}=\dfrac{2}{3},\ 18.[/tex]

The speed of the motorboat cannot be less than the speed of the current, thus, x=18 km/h.

The speed of the motorboat in still water if the speed of the current is 2 km/hour is 18 km/hour.

Suppose the distance between port M and N =d

Suppose the speed of the motorboat in still water =x

The speed of the current =2 km/h (given)

So, the downstream speed of the boat = (x+2)

Upstream speed of the boat = (x-2)

Speed is the distance covered in unit time.

According to the question, a motorboat travelling downstream covers the distance between port M and port N in 6 hours.

This means, [tex]\frac{d}{x+2} =6[/tex]

So, [tex]d=6(x+2)[/tex]

Distance covered by the motorboat when the motorboat stopped 40 km before reaching N = d-40

=[tex]6(x+2)-40[/tex]

=[tex]6x-28[/tex]

So, [tex]\frac{6x-28}{x+2} + \frac{6x-28}{x-2} =9[/tex]

So, [tex]x=18[/tex]

[tex]x=\frac{2}{3}[/tex](not possible)

Therefore, the speed of the motorboat in still water if the speed of the current is 2 km/hour is 18 km/hour.

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Answer: [tex]\frac{1}{r^{7} } +\frac{1}{s^{12} }[/tex]

Step-by-step explanation:

With negative powers, [tex]r^{-7}  = \frac{1}{r^{7} }[/tex]

do the same for s too

For this case we have that by definition of power properties:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

We have the following expression:

[tex]r^{-7} + s ^{-12}[/tex]

We can rewrite it as:

[tex]\frac {1} {r ^ 7} + \frac {1} {s ^{ 12}}[/tex]

Finally:

[tex]r ^ {- 7} + s ^ {- 12} = \frac {1} {r ^ 7} + \frac {1} {s ^ {12}}[/tex]

Answer:

Option D

Answer:

12

Step-by-step explanation:

6 + 7n = 90

n = number of book reports

6 + 7n = 90

7n = 84

n = 12

12 book reports

stan needs to report at least 12 books to get passing marks.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given,  stan needs 90 points to get a passing grade in the class. He already has6 points.

Let "x " be the number of books he Reports.

Since each book report is worth 7 points.

Thus, if he reports x books he will get = 7 * x points

Since he already has 6 points

So, the total points stan has for reporting x books = 7x + 6

Thus inequality,

7x + 6 ≥ 90

=> 7x + 6 ≥ 90

=> 7x ≥ 84

=> x ≥ 12

therefore, stan needs to report at least 12 books to get passing marks.

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Answer:

You are looking for your first credit card. You plan to use this credit card only for emergencies and to pay the credit card balance in full each month. Which credit card feature is most important?

b. Low APR

c. Generous rewards program

d. No balance transfer fee

Answer:

[tex]40x-72[/tex]

Step-by-step explanation:

we have

[tex]8(5x-9)[/tex]

Applying the distributive property

taking the outer term and multiplying it by each term inside the parenthesis

so

[tex]8(5x-9)=8*5x-8*9[/tex]

[tex]40x-72[/tex]

Answer:

[tex]8(5x - 9) = 40 x - 72[/tex]

Step-by-step explanation:

Let a, b, and c be any real number. Then

[tex]a(b + c) = ab + bc[/tex]

This is called the distributive property.

The given expression is

[tex]8(5x - 9)[/tex]

Or

[tex]8(5x + - 9)[/tex]

Let a=8, b=5x and c=-9

We apply the distributive property to obtain:

[tex]8(5x - 9) = 8 \times 5 x + 8 \times - 9[/tex]

We simplify to get:

[tex]8(5x - 9) = 40 x - 72[/tex]

Answer:

The answer is 165 in.

Step-by-step explanation:

The first shape (On the right) has a length of 3in. If you look at the top. and the height is 9in. Now you can find the width by looking at the other shape on the left and its width is 3in. Good thing the width on that shape matches the width on the right shape. so now you multiply 3, 3, and 9 and you get 81.

Now you look at the shape on the left. We already know the width which is 3in. and the height is 4in. to find the length don't look at the 10in. the 10 is the 1st and 2nd shape put together. look at the top of the shape on the left and there is a 7. That 7 is your length. now you multiply 7, 3, and 4 and you should get 84. Now you add 84 and 81 and you are left with the answer of 165in squared.

The total surface area of the two cubical figures is A = 224 inches²

A cuboid is defined as a three-dimensional shape, that has six rectangular faces, eight vertices and twelve edges

The total surface area of the cuboid is given by the formula

Surface Area = 2 ( LH + LW + HW )

where ,

Length of the cuboid = L

Width of the cuboid = W

Height of the cuboid = H

Given data ,

Let the surface area of the figure be represented as A

Now , let the surface area of the first cuboid be A₁

And , let the surface area of the second cuboid be A₂

On simplifying the equation , we get

The surface area of the cuboid A₁ = ( 3 x 4 ) + 2 ( 7 x 3 ) + 2 ( 7 x 4 )

The surface area of the cuboid A₁ = 12 + 42 + 56

The surface area of the cuboid A₁ = 110 inches²

And ,

The surface area of the cuboid A₂ = 2 ( 3 x 3 ) + 3 ( 9 x 3 ) + ( 5 x 3 )

The surface area of the cuboid A₂ = 18 + 81 + 15

The surface area of the cuboid A₂ = 114 inches²

So , the total surface area of the figure A = surface area of the cuboid A₁ + surface area of the cuboid A₂

The total surface area of the figure A = 110 inches² + 114 inches²

The total surface area of the figure A = 224 inches²

Hence , the total surface area of the figure A = 224 inches²

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Answer:

The function intersects the y-axis at point (0.9) (vertex)

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex of the parabola

if a>0 then the parabola open upward (vertex is a minimum)

In this problem we have

[tex]y-x^2=9[/tex] -----> [tex]y=x^2+9[/tex]

This is a vertical parabola open upward

The vertex is the point (0,9)

The vertex is a minimum

see the attached figure to better understand the problem

The graph does not intersect the x-axis (the function has no real roots)

The function intersects the y-axis at point (0.9) (vertex)

Answer:

Option B.

Technician A only

Step-by-step explanation:

Since we are talking about the most important function of a piston, the technician A is correct.

A piston is used to transfer force from expanding gas in the cylinder to the crankshaft , in an engine.

In a pump,  its purpose is compressing or ejecting the fluid in the cylinder.

Technician B is not correct, because piston rings are used for creating a seal between piston and cylinder walls.

Answer:

B. Technician A only

Step-by-step explanation:

PENN

The mode would be best because it describes the color used most often.

Answer:

Mode because its the number shown most.

Step-by-step explanation:

Answer:  option C

[tex]x=-10\\y=11[/tex]

Step-by-step explanation:

You can apply the elimination method:

- Multiply the second equation by 3.

- Add both equations to cancel out the variable x.

- Solve for y:

[tex]\left \{ {{-3x+5y=85} \atop {(3)(x+4y)=34(3)}} \right.\\\\\left \{ {{-3x+5y=85} \atop {3x+12y=102}} \right.\\-------\\17y=187\\y=11[/tex]

- Substitute y=11 into any of the original equations ans solve for x. Then:

[tex]x+4(11)=34\\x=34-44\\x=-10[/tex]

The answers are:

[tex]x=-10\\y=11[/tex]

We can solve system of equations using several methods, but the simplest way to solve it, is isolating variables in terms of another variables.

So, isolating "x" from the second equation we have:

[tex]x + 4y =34\\x=34-4y[/tex]

Then, substituting "x" into the first equation, we have:

[tex]-3(34-4y) +5y =85\\-102+12y+5y=85\\17y=85+102\\17y=187\\y=\frac{187}{17}=11\\[/tex]

Now, substituting "y" into the second equation to calculate "x", we have:

[tex]x + 4(11) =34\\x=34-44\\x=-10[/tex]

So, the solutions for the system of equations are:

[tex]x=-10\\y=11[/tex]

Have a nice day!

Answer:

Solve e + 5 = 3e − 11 to find the value of e

Step-by-step explanation:

Let

j------> Jamie's age

e----> Ella's age

we know that

[tex]j=e+5[/tex] -----> equation A

[tex]j=3e-11[/tex] -----> equation B

equate equation A and equation B and solve for e

[tex]e+5=3e-11[/tex]

[tex]3e-e=5+11[/tex]

[tex]2e=16[/tex]

[tex]e=8[/tex]

Find the value of j

[tex]j=8+5=13[/tex]

Jamie's age is 13 years old

Ella's age is 8 years old

100% is always the full number so 113 is your answer

Hope this helps and have a blessed day

Answer:

88.5

Step-by-step explanation:

100:113*100 =

(100*100):113 =

10000:113 = 88.5

The answer is A: 225

Answer: No

Step-by-step explanation:

Pythagorean Theorem goes with a right triangle, the formula is a^2+b^2=c^2.

Let's try this out with your values.

(18*18)+(12*12) = 468

If this is true than c^2 is 468

c^2 or (22*22) is 484 is this is not a right triangle.