Find the length of the missing side:

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To factor each expression, we apply the given concepts, that is, greatest common factor, difference of squares and perfect squares.

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Expression 1:

The expression is:

[tex]2a^3 + 4a^2 + 8a[/tex]

First, we find the gcf of the numbers 2, 4 and 8, which is 2.

Of the exponents, the gcf between 3, 2 and 1 is 1, so:

[tex]2a^3 + 4a^2 + 8a = 2a(\frac{2a^3}{2a} + \frac{4a^2}{2a} + \frac{8a}{2a}) = 2a(a^2 + 2a + 4)[/tex]

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Expression 2:

The expression is:

[tex]6y^4 - 294y^2[/tex]

The gcf of 6 and 294 is 6.

The gcf of the exponents 2 and 4 is 4.

Thus:

[tex]6y^4 - 294y^2 = 6y^2(\frac{6y^4}{6y^2} - \frac{294y^2}{6y^2}) = 6y^2(y^2 - 49)[/tex]

Then, applying the difference of squares:

[tex]y^2 - 49 = (y - 7)(y + 7)[/tex]

Thus, the factored expression is:

[tex]6y^2(y^2 - 49) = 6y^2(y - 7)(y + 7)[/tex]

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Expression 3:

The expression is:

[tex]5x^2 + 50x + 125[/tex]

The gcf of the coefficients, 5, 50 and 125 is 5, so:

[tex]5(\frac{5x^2}{5} + \frac{50x}{5} + \frac{125}{5}) = 5(x^2 + 10x + 25)[/tex]

Applying the perfect square, we get that:

[tex]x^2 + 10x + 25 = (x + 5)^2[/tex]

Tus, the factored expression is:

[tex]5(x^2 + 10x + 25) = 5(x+5)^2[/tex]

A similar question is given at https://brainly.com/question/11930822

Answer:

97

Step-by-step explanation:

76+83+89+95+100=443

there are all 6 tests.

we consider marks of last lest as "X"

x should be added to total mark

to obtain average mark, total marks should divided by no. of tests.

(443+x)/6=90

443+x=90*6

443+x=540

x=540-443

x=97

Answer:

15 / 1

hope that helps uh...☺

Answer:

Hello,

[tex]\begin{bmatrix}\dfrac{-1}{5} &0\\\dfrac{-1}{10}&\dfrac{1}{4}\end{bmatrix}[/tex]

Step-by-step explanation:

See jointed file

The inverse of the matrix A is

[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]

A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.

We have,

[tex]A = \left[\begin{array}{cc}-5&0\\-2&4\end{array}\right][/tex]

The matrix A is a square matrix and its determinant is not zero.

So the inverse exist.

The inverse of matrix A.

We will change the rows into columns and columns into rows.

So,

[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]

Thus,

The inverse of the matrix A is given above.

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9514 1404 393

Answer:

  D.  180°

Step-by-step explanation:

The letter S is symmetrical about its center. The letter looks the same when it is rotated 180° about its center.

Answer:

-7

Step-by-step explanation:

x + 5 = -2

Answer:

3 chocolate bars and 2 graham crackers

Step-by-step explanation:

8 times 3 equals 24

12 times 2 equals 24

Step-by-step explanation:

you're going to solve for y in the first equation and then substitute it in for the second equation and solve.

Let the perimeter be 100cm

Then value of x = 100/4

x = 25cm

Answered by Gauthmath must click thanks and mark brainliest

Hey there! I'm happy to help!

First, let's find the volume of the cylindrical tank.

To find the volume of a cylinder, take the area of the circle base and multiply it by the height of the cylinder.

To find the area of a circle, you square the radius and multiply it by pi (we will use 3.14).

The diameter is always twice the radius, so we divide by two to find the radius.

1.4/2=0.7

We square this.

0.7²=0.49

And we multiply by 3.14.

0.49×3.14=1.5386

Now that we have the area of the circle, we multiply by the height (length in our case since the cylinder is sideways).

1.5386×4.5=6.9237

Now, we see that we will be losing 1.7 feet every minute. To see how many times 1.7 feet goes into our cylinder, we just divide!

6.9237÷1.7= 4.07276470588

So we see that it will take just over 4 minutes for the tank to empty.

Have a wonderful day and keep on learning! :D

Answer:

7/12

Step-by-step explanation:

3*4=12. 4/12+3/12=7/12.

Answer:

5/12

Step-by-step explanation:

you find the common factor of 12, divide 12 by the denominator, multiply the numerator by that, add the new numerators, put it on the denominator of 12, subtract it from 12/12

Answer:

Step-by-step explanation:

Answer:

(0,-5) and (-4,3) are the points to the equations.

Step-by-step explanation:

Solution:

Step 1: Make an equation for y to substitute to the first equation.

x^2+y^2=25

y=-2x-5

Step 2: Substitute the y-value to the first equation.

x^2+(-2x-5)^2=25

x^2+4x^2+20x+25=25

Our x-values would be 0, and -4.

Step 3: Solve for the y-values by substituting 0 and -4 to the equation y=-2x-5.

y=-2(0)-5=-5 and makes the ordered pair (0,-5)

y=-2(-4)-5=3 and makes the ordered pair (-4,3)

Therefore our answers would be (0,-5) and (-4,3)

Answer:

(-4;3), (0;-5)

Step-by-step explanation:

Answer: Sheldon has made 50 cookies

Step-by-step explanation: for the first test because there are 5 rows and 4 cookies on each row you would multiply 4 times 5. That equals 20. The first tray has twenty and all trays are the same size so if the second one is completely full then it also has twenty. The third one is only half way full meaning twenty divided by two equals ten. Ten is the amount of cookies on the third tray. If you add that all together that is 20+20+10=50

The number of cookies made by Sheldon will be equal to 50.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

For the first test, you would multiply 4 by 5 because there are 5 rows and 4 cookies on each row. 20 is the result.

Since all trays are the same size and the first tray has twenty, if the second tray is totally filled, it will also have twenty.

Twenty divided by two equals 10 because the third one is only half full.

There are ten cookies on the third tray.

The total is,

20+20+10 = 50.

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Answer:

≈ 5.51 hours

Equation: 4.25h + 10

The number of hours Amanda rented the bike is 5.5 hours.

The equation used to solve this problem is 33.38 = 10 + 4.25h.

The rent cost for the helmet is $10.

The rent cost for the bike per hour is $4.25.

We need to find the number of hours Amanda rented the bike as she paid $33.38 in total.

We also have to make an equation that would solve this problem.

Consider h = number of hours Amanda rented the bike.

The cost for renting the helmet = $10.

And rent cost for the bike per hour = $4.25.

Amanda's total cost = Helmet rent cost + bike rent cost

Since we do not know the number of hours the bike was rented we will denote bike rent cost  = $4.25 x h

We have,

$33.38 = $10 + $4.25 x h

33.38 = 10 + 4.25 x h

33.38 - 10 = 4.25 x h

23.38 = 4.25 x h

h = 23.38 / 4.25

h = 5.5011

Rounding to the nearest tenths we get,

h = 5.5 hours

The number of hours Amanda rented the bike is 5.5 hours.

The equation used to solve this problem is 33.38 = 10 + 4.25h.

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Step-by-step explanation:

answer is 10 am i right plzz correct it

Answer:

50

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180 degrees

since one of the angle is given as 80 the remaining is 100

The given is an isosceles triangle which means two of its side length and so its angles are equal in measure so 100/2 = 50

Answer:

4/5 t

Step-by-step explanation:

why?

80%xt by definition of p%=p/100

80/100t

80/100t reduce the fraction with 20

so the answer is;

4/5 t

Hope it helps

Given:

Fixed cost = $150

Additional cost = $22.50

To find:

The equation that showing the cost of the gala depends on the number of attendees.

Solution:

Let x be the number of attendees and y be the cost of the gala.

Total cost = Fixed cost +Variable cost

We have,

Fixed cost = $150

Variable cost = Additional cost × Number of attendees

                      = [tex]22.50\times x[/tex]

                      = [tex]22.50x[/tex]

Total cost of gala is:

[tex]y=150+22.50x[/tex]

Therefore, the required equation is [tex]y=150+22.50x[/tex].

Answer:

65

Step-by-step explanation:

Because its a triangle,

P + Q + R = 180

So,

P + 70 + 45 = 180

P + 115 = 180

Subtract 115 on both sides

P = 65

Answer:

Slower trains: 123 km/h

Faster train: 134 km/h

Step-by-step explanation:

In order to solve this problem, one must know the following formula:

[tex]speed*time=distance[/tex]

The problem gives one the following information:

Let ([tex]speed_1[/tex]) represent the speed of the slower train and ([tex]speed_2[/tex]) represent the speed of the faster train.

One can form an equation, let (x) represent the speed of the slower train. Using the distance equation, one can state that the speed of each train times the travel time equals the distance. Since the trains met each other in (6) hours, and the combined distance traveled between the two trains is (1542 km); one can use this information to form an equation.

[tex](travel\ time)(speed_1)+(travel\ time)(speed_2)=distance[/tex]

Substitute,

[tex]6(x)+6(x+11)=1542[/tex]

Simplify, distribute, multiply every term inside of the parenthesis by the term outside of it. Then combine like terms,

[tex]6x+6x+66=1542[/tex]

[tex]12x+66=1542[/tex]

Inverse operations,

[tex]12x+66=1542[/tex]

[tex]12x=1476[/tex]

[tex]x=123[/tex]

Solve for the speed of the faster train. It is given that it is (11 km/h) faster than the slower train.

[tex]speed_1+11=speed_2\\123+11=speed_2\\134=speed_2[/tex]

Answer:

8 lb box

Step-by-step explanation:

Find which laundry detergent has a lower unit price

The unit price is how much something costs for a single unit

In this case, it is how much the detergent costs for 1 pound

7.4/8 lbs = 0.925 dollars per lb

5.38/4 lbs = 1.345 dollars per lb

Since 1.345 > 0.925, the 8 lb box is a better buy

Case 1

Cost of 8 pound detergent = $7.40

So, cost of 1 pound detergent

= $7.40 ÷ 8

= $0.925

Case 2

Cost of 8 pound detergent = $5.38

So, cost of 1 pound detergent

= $5.38 ÷ 4

= $1.345

$0.925 < $1.345

$0.925 < $1.345So, cost per pound in 8 pound box < cost per pound in 4 pound box

So, buying the 8 pound box is better.

Answer:

yes

Step-by-step explanation:

f(x) = x^2 -1

Hope it helps!!

Answer:

ur answer is 199 thank me later

Answer:

194 ft²

Step-by-step explanation:

Area of rectangle R1 = length * width

                                  = 8 * 5

                                  = 40  square feet

Area of rectangle R2 = 14 * 11

                                    = 154 square feet

Area of the figure = 40 + 154 = 194 ft²

Answer: B

Step-by-step explanation:

The transformation that took place to form A'B'C' is Shifted 4 units left and 2 units down.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, a triangle ABC has undergone a transformation to form A'B'C' we need to identify the steps of transformation

So, considering the point B and B', we see, that, x-coordinate of B is at 5 and that of B' is at 1, that mean there is a shift of 4 units left,

Now, consider the y-coordinate, we see, that B is at 9 and B' is at 7 that gives a downward shifting of 2 units.

Hence, the transformation that took place to form A'B'C' is Shifted 4 units left and 2 units down.

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Answer:

[tex]13\ units[/tex]

Step-by-step explanation:

One is asked to find the distance between two points on a coordinate plane. The easiest way to do so is to use the distance formula, this formula is the following:

[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2[/tex]

Where ([tex](x_1,y_1)[/tex]) and ([tex](x_2,y_2)[/tex]) are the points which one needs to find the distance between. In this case, these points are as follows:

[tex]k\ (-3,5)[/tex]

[tex]j\ (-8, -7)[/tex]

Substitute these points into the formula and solve for the distance between these points,

[tex]D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2[/tex]

[tex]D=\sqrt{((-3)-(-8))^2+((5)-(-7))^2[/tex]

Simplify,

[tex]D=\sqrt{((-3)-(-8))^2+((5)-(-7))^2[/tex]

[tex]D=\sqrt{(-3+8)^2+(5+7)^2[/tex]

[tex]D=\sqrt{(5)^2+(12)^2[/tex]

[tex]D=\sqrt{25+144}[/tex]

[tex]D=\sqrt{169}[/tex]

[tex]D=13[/tex]

Answer:

y=4x/5-44/5

Step-by-step explanation:

First, we know that we can write any linear equation in the form y=ax+b, where a is the slope. This means that y=(4/5)x+b. Now, it has the point (1, -8). Plugging in x=1 and y=-8 gives us -8=(4/5)+b, which means that b=-44/5. Plugging this in gives us y=(4/5)x-44/5. Hope it helped!

Answer:

-23 = - 23

Step-by-step explanation:

there you go...hopefully it makes sense :)

Answer:

59.5

Step-by-step explanation:

Half dozen = $4.25

Full Dozen = 2 X (4.25)

= 8.5

7 Dozens price = 7 X 8.5 =

= $59.5

Answered by Gauthmath