What does it mean to solve an equation?
Complete the statements.

The variable in the equation is represented by
To solve the equation you must find the
that makes the equation true.

is a solution of the equation because 5 = 5 is a true statement.

Answer:

4 red marbles

Step-by-step explanation:

r is the number of red marbles then green marbles is 9r , so

r + 9r = 40

10r = 40 ( divide both sides by 10 )

r = 4

there are 4 red marbles

Answer:

[tex]\displaystyle 250°[/tex]

Explanation:

When converting from radians to degrees, multiply one hundred eighty by the radian measure, then divide it pi:

[tex]\displaystyle \boxed{250°} = 1\frac{7}{18}\pi[\frac{180}{\pi}][/tex]

I am joyous to assist you at any time.

This function is Exponential

Hope that helps!

[tex]3x + 2y = 6[/tex]

[tex] - 3x + y = 12[/tex]

[tex]3x - 3x + 2y + y = 6 + 12[/tex]

[tex]3y = 18[/tex]

[tex]y = \frac{18}{3} = 6[/tex]

[tex]3x + 2y = 6[/tex]

[tex]3x + 2(6) = 6[/tex]

[tex]3x + 12 = 6[/tex]

[tex]3x = 6 - 12[/tex]

[tex]3x = - 6[/tex]

[tex]x = \frac{ - 6}{3} = - 2[/tex]

[tex]\ln(3x+2) = 3x\\\\\implies \log_e (3x+2) = 3x\\\\\implies e^{3x} = 3x+2[/tex]

[tex]3+3\sqrt[6]{x}~~ = ~~5\implies \stackrel{\textit{1st step,-3 to both sides}}{3\sqrt[6]{x}~~ = ~~2}\implies \sqrt[6]{x}=\cfrac{2}{3} \\\\\\ (\sqrt[6]{x})^6=\left( \cfrac{2}{3} \right)^6\implies x=\cfrac{2^6}{3^6}\implies x=\cfrac{64}{729}[/tex]

The standard equation for a circle is '[tex](x-h)^2+(y-k)^2=r^2[/tex]

      --> Standard form:

              [tex](x - )^2 +(y-(-5))^2=2^2\\x^2+(y+5)^2=4[/tex]

Hope that helps!

Answer:

x^2 + (y + 5)^2 = 4.

Step-by-step explanation:

Standard form is (x - a)^2 + (y - b)^2 = r^2

 - where (a, b) is the center and radius = r.

So our equation is:

(x - 0)^2 + (y - (-5))^2 = 2^2

x^2 + (y + 5)^2 = 4.

The length of the diagonal is the hypotenuse of the fence

The length of the wood is [tex]7\sqrt{ 2[/tex] yards

The dimensions of the fence are:

7 ft by 7 ft

The length (L) of the diagonal is calculated using:

[tex]L = \sqrt{a^2 + b^2[/tex]

This gives

[tex]L = \sqrt{7^2 + 7^2[/tex]

Express as products

[tex]L = \sqrt{7^2 * 2[/tex]

Express as radical

[tex]L = 7\sqrt{ 2[/tex]

Hence, the length of the wood is [tex]7\sqrt{ 2[/tex] yards

Read more about diagonals at:

https://brainly.com/question/10187910

Answer:

The interest earned is $96.60

Step-by-step explanation:

Since we are working the a simple interest problem, we will use the formula

[tex]I=Prt[/tex],

Where P represents the principal, r represents the rate as a decimal, and t represents the time in years. First, we need to change the 4.6% into a decimal by dividing by 100:

[tex]4.6\div 100 = 0.046[/tex]

From our given information and our decimal rate, we have:

[tex]P=1050\\r=0.046\\t=2[/tex]

Substituting these into our equation, we get:

[tex]I=1050(0.046)(2)\\I=96.6[/tex]

We write that as $96.60 in context of the problem.

Answer:

principle (p)=RS 1,050

Rate(R)=4.6

time(T)=2years

we know that

I=P×R×I/100

=1050×4.6×2/100

=9660/100

=96.6

therefore the earned simple interest is RS.96.6

Answer:

x = 9 cm

create proportional equation:

[tex]\sf \dfrac{9}{3x-20} = \dfrac{72+9}{3x-20+56}[/tex]

[tex]\sf \dfrac{9}{3x-20} = \dfrac{81}{3x+36}[/tex]

[tex]\sf 9(3x+36) = 81(3x-20)[/tex]

[tex]\sf 27x+324 = 243x-1620[/tex]

[tex]\sf 27x-243x=-1620-324[/tex]

[tex]\sf -216x=-1944[/tex]

[tex]\sf x = 9[/tex]

Answer:

Step-by-step explanation:

Since parallel lines cut the transversals proportionally, we can set the following equation and solve for x;

Answer:

I think it is point D

Step-by-step explanation:

hope this helps if it is wrong please let me now

Answer:

(-10, 19)

Step-by-step explanation:

Hey there!

In order to find the value of x and y, you need to make a system of equations

Now the question says to use elimination

The elimination method is when you make two values the same and then eliminate them with the proper sign: addition, subtraction, etc.

In this case, the step of making equal values is already done for us since there is 2y in both equations

[tex]-5x-2y=12\\3x+2y=8\\\\-2x=20\\x=-10\\[/tex]

What was done was called elimination

I added both equations together and when you add -2y and 2y, they eliminate each other

Now when you simplify the system, you get that x is equal to -10

Now we can substitute this value into the first or second equation

I am going to do the first equation

[tex]-5(-10)-2y=12\\50-2y=12\\-2y=-38\\y=19[/tex]

So after substituting the x value in the equation, we got the y value

Which is 19

So the solution to this system of equations is:

(-10, 19)

Answer:

573,300.00 to the nearest 10

Step-by-step explanation:

Answer:

Emma began her journey at 7:30 a.m., at 8 a.m. she was 20 miles away, she stayed for an hour and a half, she left at 10 a.m., she was 7.5 miles from her house at 11:45, she traveled 80 miles total

Step-by-step explanation:

please let me know what you don't understand here. because this is really simple.

the distance from home is increasing and then decreasing when she is traveling.

the rate of distance per time would give us even the speed with which she was traveling.

when there is no change in the distance over time, that means she was "stationary" - either at home or at her grandmother's place.

so, let's answer the questions :

(a)

movement started at 7:30am (that is when she began her journey).

(b)

20 miles

you pick 8am on the time scale and move straight up until you hit the curve. and then you check what value is at that point all the way to the left on the distance scale : 20.

(c)

from 8:30am to 10am = 1.5 hours.

we see this by the interval on the time scale for which the curve is totally flat (a horizontal line) = no change in distance from home during that time.

(d)

at 10am

that is when the curve indicates the begin of a change in the distance to home.

(e)

7.5 miles.

this is the point marked by a star on the graph.

down on the time scale this point shows 11:45am, and on the left side in the distance scale it shows 7.5 miles (the middle between 5 and 10 miles).

so, at that time she was still 7.5 miles away from home.

(f)

she traveled 40 miles to her grandmother (the left part of the curve from 0 distance until it turns flat), and then 40 miles back home (the right part of the curve from 40 distance all the way down to 0).

so, in total she traveled

40 + 40 = 80 miles

Answer:

It is neither.

Step-by-step explanation:

A whole number is all numbers is 0, 1, 2, 3, 4.... you get it

An irrational number is a number that cannot be written as a fraction and -2 can be written as -2/1

Answer:

$372

Step-by-step explanation:

12 × 10 = 120

1 foot = $3.10

120 feet = ?

120 feet × $3.10

= $372

$372÷ 1 foot = $372

Step-by-step explanation:

100% = 11.5

20% more means 120%

120% = 100%×1.2 = 11.5×1.2 = 13.8 ounces

if we do a vertical line test on that graph, we'll find that a vertical line will pass by and hit the line only once on its way down, only once meaning the graph is the graph of a function.

well, is really how high and low it goes or namely over the y-axis.

well, it goes up up up to 3 then U-turns and back down it goes, now the graph has arrowheads, meaning the graph keeps on going towards infinity, vertically as well as horizontally since it's a parabola, so the range will be

well, is simply how left and right it goes or namely over the x-axis.

judging from the arrowheads it moves from infinity to infinity, so

Answer:

c = 2.5 , d = - 3

Step-by-step explanation:

f(x) = cx + d

f(4) = 7 ( substitute x = 4 into the equation and equate to 7 )

f(10) = 22 ( substitute x = 10 into the equation and equate to 22 )

4c + d = 7 → (1)

10c + d = 22 → (2)

subtract (1) from (2) term by term to eliminate d

(10c - 4c) + (d - d) = 22 - 7 , that is

6c = 15 ( divide both sides by 6 )

c = 2.5

substitute c = 2.5 into (1) and solve for d

4(2.5) + d = 7

10 + d = 7 ( subtract 10 from both sides )

d = - 3

Answer:

c = 2.5

d = - 3

Step-by-step explanation:

f(x) = cx + d

f(4) = 7

f(10) = 22

4c + d = 7

10c + d = 22

(10c - 4c) + (d - d) = 22 - 7

6c = 15

---    ----

6      6

c = 2.5

4(2.5) + d = 7

10 + d = 7

-10       -10

d = - 3

Answer:

yes i do

Step-by-step explanation:

1/4 x 12= 3

12 divided by 4 = 3

Answer:

x = -5

y = -4

Step-by-step explanation:

5x - 4y = -9

10x - 8y = -18

10x - 7y = -22

-y = 4

y = -4

Substitue y into any equation

5x - (-16) = -9

5x = -25

x = -5

Answer:

1)   area = (x + 3)(2x + 3) ft²

2)   299 ft²

Step-by-step explanation:

Question 1

Area of a rectangle = width x length

Given:

⇒ area = (x + 3)(2x + 3) ft²

Question 2

If x = 10:

⇒ area = (10 + 3)(2(10) + 3)

            = 13 · 23

            = 299 ft²

#1

So

Area:-

#2

Put x=10

Answer:

288 cm^3.

Step-by-step explanation:

The volume of each small  square = 2*2*2 = 8 cm^3

Each rectangular length of end 2*2 is made up of 12/2 = 6 squares.

There are  6 of these rectangular lengths.

So the volume = 6 * 6 * 8 cm^3

288 cm^3.

slope is = (13 - 8) / (17 - 7) = 5/10 = 1/2 or 0,5

slope for A (xa ; ya) and B (xb ; yb) = (yb - ya) / (xb - xa)

Using proportions, it is found that the statement that Tiffany would expect the spinner to land on a color section beginning with the letter "B" roughly 48 times is True.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, out of 8 sections, 4(Blue, Brown, Bronze and Black) begin with letter "B". We want to find the equivalent amount out of 98 trials. Hence, the rule of three is:

8 trials - 4 start with "B".

96 trials - n start with "B".

Applying cross multiplication:

8n = 4 x 96

n = 0.5 x 96

n = 48.

Hence, the statement is True.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

Bottom left = 8

Top right = 15

Middle right = 25

Step-by-step explanation:

Total = 40

3 + 5 = 8

40 / 8 = 5

1 part = 5

5 x 3 = 15

5² = 25

Answer:

45%

Step-by-step explanation:

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Approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.

Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.

A 15-meter by 23-meter garden is divided into two sections. In this rectangle,

Here, a vertical line is drawn from the top to bottom side to split the shape into a square and a rectangle. The length of the left side of the square will be 15 long. Thus, the lenght of its diagonal is,

[tex]d_1=15\sqrt{2}\\d_1=21.213\rm\; m[/tex]

The length of the sidewalk in smaller rectangle in the right side of figure is,

[tex]d_2=\sqrt{15^2+8^2}\\d_2=17\rm\; m[/tex]

Sum of the lengths of the two sidewalks using the pythagoras theorem is,

[tex]S=21.2+17\\S=38.2\rm\;m[/tex]

Thus, approximate sum of the lengths of the two sidewalks, shown as dotted lines in the figure of rectangle garden is 38.2 meters.

Learn more about the Pythagoras theorem here;

https://brainly.com/question/343682

Answer:

D 38.2

Step-by-step explanation:

E2020

Answer:

338 m^2

Hope this helps!

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