Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

In a paint factory, an old conveyer line has filled 22 barrels of paint and is filling more at a rate of 1 barrel per minute. A worker just switched on a newer line that can fill 12 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How many barrels will each line have filled? How long will that take?

The mean number of points for all 5 games is 4 points.

The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean.

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

As per the question,

Here, n = 5

⇒ ∑x = Sum of Observations

⇒ ∑x = 10 + 3 + 2 + 5 + 0 = 20

Mean = ∑x/n

Mean = 20/5

Mean = 4

Hence, the mean of the given data is 4.

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Answer:

x≥-8

Step-by-step explanation:

Because we don't know the first number mentioned, we can name it as x

Since the problem starts off with "twice a number" so we mark it as 2x and then it states to take the difference of that number and 9. So the new problem we have is 2x-9=?. Now, the answer that we have is at least -25, so the answer is no longer an equal sign, but a greater-than or equal-to sign. Making our new equation 2x-9≥-25. Now we can act as if its a normal equation, adding 9 to both sides making it 2x≥-16, divide both sides by 2 to get x≥-8.

An extra step to ensure our answer is more than or equal to -8 is by plugging in -8 AND another number that is more than -8. 2(-8)-9=? which we would find that ? is -25. A number that is greater than -8 could be -1, which we would test by doing 2(-1)-9=?. ? would be equal to -11 so we know that our final answer of x≥-8 is correct.

Answer: The expression X^2 + _x + 100 is the square of a binomial if the missing number is -b/2 and b^2 - 4ac = 0.

Step-by-step explanation: The general form of the square of a binomial is (x + b)^2 = x^2 + 2bx + b^2.

In this case, the missing number is -b/2, and the expression becomes X^2 - x + 100.

Now to find the value of x, we can use the equation b^2 - 4ac = 0

The equation becomes x^2 - 41100 = 0

Which gives x^2 - 400 = 0

So x = ± 20.

So the possible values for the missing number that make the expression the square of a binomial is -20/2 = -10 and 10.

Answer:

To find the missing number in the given expression, we will see the operation used. Step 1: Recall the concept of addition. We need to find the first addend. Step 2: Think of the number which when added to 3 gives the sum equal to 8. Step 3: 5 + 3 = 8. So, the missing number is 5. Step 4: Write the missing number: 5 + 3 = 8.

Step-by-step explanation:

=================================================

Work Shown:

Plug the first equation into the second equation.

2x - y = 5

2x - (3x-1) = 5

2x - 3x+1 = 5

-x+1 = 5

-x = 5-1

-x = 4

x = -4

Use this to find the value of y.

y = 3x-1

y = 3*(-4)-1

y = -12-1

y = -13

The solution is (x,y) = (-4,-13)

This points to    choice A    as the final answer.

You can use graphing software like Desmos or GeoGebra to confirm that the two lines intersect at (-4,-13).

Answer:

20

Step-by-step explanation:

4 ÷ 1/5  Multiply by the reciprocal (turn the fraction upside down)

4 x 5 = 20

Answer:

D. the experiment

Step-by-step explanation:

The hypothesis becomes the basis of the experiment.

Answer:

D= dependent. T= independent

Step-by-step explanation:

I would say this bc the total distance depends on the amount of time he ran

d is distance

t is time (how long he ran)

The equation [tex]4x^2+12x+9=0[/tex] has only one solution, and the type of solution is rational.

Finding the value of the given equation's unknown variables is a step in the equation-solving process. The value of the variable satisfies the requirement that the two expressions are equal. When a linear equation has one variable, there is only one solution; when there are two variables, there are two solutions. A quadratic equation's solution yields two roots. To solve an equation, a variety of techniques and steps are used. Let's go over each method for solving an equation in detail one by one.

Here steps for solving an equation are given below.

[tex]4x^2+12x+9=0\\4x^2+6x+6x+9=0\\2x(2x+3)+3(2x+3)=0\\(2x+3)(2x+3)=0\\2x=-3\\x=\frac{-3}{2}[/tex]

Here both solutions are same so the equation [tex]4x^2+12x+9=0[/tex] has only one solution and the type of solution is a rational solution.

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Given ,

[tex]\bold\red{zeroes \: of \: a \: cubic \: polynomial \: are \: - 2 \:, \: 0 \: and \: 7} \\ [/tex]

[tex]let \:, \\ \boxed{\alpha \: = - 2} \\ \boxed{\beta \: = 0} \\ \boxed{\gamma \: = 7} [/tex]

Now ,

[tex]sum \: of \: zeroes \: = \alpha \: + \: \beta \: + \: \gamma \: \\ \dashrightarrow \: sum = - 2 + 0 + 7 = \underline{5} \\ \\ sum \: of \: product \: of \: zeroes \: taken \: two \: at \: a \: time \: = \alpha\beta \: + \beta\gamma \: + \: \alpha\gamma \\ \dashrightarrow \: ( - 2)(0) \: + \: (0)(7) \: + \: (7)( - 2) \: = \: \underline{ - 14} \\ \\ product \: of \: zeroes \: = \: \alpha\beta\gamma \\ \dashrightarrow \: ( - 2)(0)(7) = \underline{0}[/tex]

We know that ,

[tex] \boxed{cubic \: polynomial \: = {x}^{3} - (\alpha \: + \: \beta \: + \: \gamma \:) \:{x}^{2} + (\alpha\beta \: + \: \beta\gamma \: + \: \alpha\gamma) \:x \: - \: \alpha\beta\gamma} [/tex]

Plugging in the values , we get

[tex]\boxed{f(x) = {x}^{3} - 5 {x}^{2} - 14x + 0}[/tex]

since this polynomial has degree 3 , it is called a cubic polynomial.

hope helpful! :)

To graph a system of equations, you can first solve each equation for y, and then plot the solutions on the same coordinate plane.

For the first equation, 8x + 8y = 64, we can solve for y by subtracting 8x from both sides, which gives us 8y = 64 - 8x. Then we divide both sides by 8 to get y = (64 - 8x)/8.

For the second equation, 2x - 2y = -4, we can solve for y by adding 2x to both sides, which gives us 2y = 2x - 4.

So the solutions for y in the first equation are:

y = (64 - 8x)/8

and in the second equation are:

y = 2x - 4

We can now plot these two lines on the same coordinate plane. The point of intersection of these two lines will be the solution of the system of equations

Answer is attached in the graph.

Step by step

The easiest way to solve these is to graph on an internet or app graphing calculator.

To graph by hand you need to simplify them and arrange in slope intercept form y=mx + b

(#1)

8x + 8y = 64 all are divisible by 8

8/8x + 8/8y = 64/8

Simplify

x + y = 8

Arrange in slope intercept form

subtract x from both sides to isolate y

x - x + y = -x + 8

y = -x + 8

We plot the first point of y intercept of 8 (0,8) and plot the 2nd point by slope of -1/1 or

( 1, -1). Draw your line

(#2)

2x - 2y = -4 are all divisible by 2

2/2x - 2/2y = -4/2

Simplify

x - y = -2

Arrange in slope intercept form

subtract x from both sides to isolate y

x - x - y = -x -2

Simplify

-y = -x -2

Change the signs by multiplying all by -1

y= x +2

We plot the first point of y intercept

of 2 (0, 2) and plot the 2nd point by slope of 1/1 or ( 1, 1). Draw your line

Now you can find the solution is where the lines intersect. At (3, 5)

See my attached graph for your two line equations below

y = x + 2

y = -x + 8

Answer:

the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together

Step-by-step explanation:

angle addition postulate formula is ∠AOB + ∠BOC = ∠AOC

The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The quadratic regression equation y = –0.1x² + 143.99x – 13,242.84 models expected company profits in terms of the number of pairs of shoes sold.

The profit can the company expect if it sells 400 pairs of shoes will be given as,

y = –0.1(400)² + 143.99(400) – 13,242.84

y = – 16,000 + 57,596 – 13,242.84

y = 28,354

y ≈ 28,400

The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.

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∠3 is congruent to ∠1. Hence, proved.

Two angles are said to be complementary angles if they add up to 90 degrees. In other words, when complementary angles are put together, they form a right angle (90 degrees).

Given that, ∠3 and ∠2 are complementary; m∠2 + m∠3 = 90°---------(I)

From the given figure,

m∠1 + m∠2 = 90°---------(II)

From the given equation (I) and (II), we get

m∠1 + m∠2=m∠2 + m∠3

m∠1 ≅ m∠3

Hence, proved.

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The coordinates of the circumcenter of a triangle with vertices A(0,1),

B(2, 1) , and C(2, 5)  is (1,3).

What is circumcenter of triangle?

The point at which the perpendicular bisectors of a triangle's sides come together is known as the circumcenter of that triangle. The circumcenter is, in other words, the point at which the bisector of a triangle's sides coincides. P serves to indicate it (X, Y).

Given:  A triangle with vertices A(0,1), B(2, 1) , and C(2, 5).

Using distance formula:

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

AB = 2 units

BC = 4 units

AC = √20 units

The midpoint of AC:

[tex]= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )\\= (\frac{2+0}{2}, \frac{5+1}{2}) \\= (\frac{2}{2} , \frac{6}{2})\\ = (1, 3)[/tex]

The midpoint of AC is (1, 3).

Hence, The coordinates of the circumcenter of a triangle with vertices A(0,1),  B(2, 1) , and C(2, 5)  is (1,3).

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The value of j by solving with one-step equation solution method will be of the option C i.e. 2/30.

What are one-step equations?

A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true.

To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself. The inverse operations are:

Addition and subtraction

Multiplication and division

The most important thing to remember is that whatever you do to one side of the equation, you have to do the same thing to the other side.

Now,

given that,

19/30=j+17/30

To find j, subtract 17/30 from both side,  (Using one-step equation method)

19/30-17/30=j+17/30-17/30

2/30=j

Hence, the value of j will be 2/30.

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Answer:

Based on the given information, we know the following:

Solid A is formed by joining one hemisphere to the frustum of a cone.

Solid B is formed by joining the other hemisphere to the small cone that was removed from the large cone.

The volume of solid A is 6 times the volume of solid B.

We can use the formulas for the volume of a hemisphere and a frustum of a cone to represent the volumes of solids A and B.

The volume of a hemisphere is (2/3)πr^3, where r is the radius of the hemisphere.

The volume of a frustum of a cone is (1/3)πh(R^2+r^2+Rr), where h is the height of the frustum, R is the radius of the larger base and r is the radius of the smaller base.

The volume of a cone is (1/3)πr^2h

Let's call the height of the frustum h, the radius of the large base R and the radius of the small base r

We can set up the equation: (2/3)πr^3 = 6((1/3)πr^2h + (1/3)πR^2h + (1/3)πRrh)

After simplifying, we get:

2h = 12r + 12Rh + 6Rr

We know k = (R/r)^(1/3)>(7)^1/3, we can substitute it into the equation:

2h = 12r + 12rk + 6rk^2

Solving for h, we get:

h = 6rk + 6rk^2

So h is expressed in terms of k and r.

Answer:

Step-by-step explanation:

180 total

180-3=177

ratio of angle 1 to angle 2:

2:1

we need to divide 177 by 3 since there are 3 parts in the ratio above

177/3=59

angle 1 = 59x2=118

angle 1=118 degrees

angle 2=59+3=62

angle 2 =62 degrees

we can check by adding 62 and 118

62+118=180

The cost function is  [tex]C(x)=[/tex] [tex]\left \{ {{35} \atop {(0.1t-5)}} \right.[/tex] .

The application of the idea of kinds of functions is the foundation of this issue. We will create and classify the sort of function we have using the provided information.

According to the given information, the cell phone plan has a basic charge of $45 a month. The plan includes 500 free minutes and charges 10 cents for each additional minute of usage.

Let t be the number of minutes the cell phone is used.

So, for 0≤t≤500 it will cost only the basic charge of $45.00

For an additional minute of usage, it costs 10 cents or $0.1 in addition to the basic charge. So, our function looks like:

f(x)=45+0.1(t-500)=45+0.1t-50 = (0.1t-5), for 500 ≤ t ≤ 700.

Thus, the cost function looks like:

C(x) = [tex]\left \{ {{35} \atop {(0.1t-5)}} \right.[/tex]

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Answer: z=23

Step-by-step explanation:

Since the sum of all interior angles of a triangle is 180, let's use that to solve this problem.

First, let's set up an equation.

z+62+95=180

Next step is to simplify the left side of the equation, which leaves us with:

z+157=180

Lastly, subtract 157 from both sides of the equation and we get the final answer:

z = 23

Answer:

[tex]\frac{3}{16}[/tex] f - [tex]\frac{3}{2}[/tex] g

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] ( [tex]\frac{1}{2}[/tex] f - 4g )

multiplying each of the terms inside the parenthesis by [tex]\frac{3}{8}[/tex]

[tex]\frac{3}{8}[/tex] × [tex]\frac{1}{2}[/tex] f

= [tex]\frac{3(1)}{8(2)}[/tex] f

= [tex]\frac{3}{16}[/tex] f

and

[tex]\frac{3}{8}[/tex] × - 4g ( cancel 4 and 8 by 4 )

= [tex]\frac{3}{2}[/tex] × - g

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

combining the 2 products, gives

[tex]\frac{3}{16}[/tex] f - [tex]\frac{3}{2}[/tex] g

Answer:

[tex]\textsf{Orange partial product}=\dfrac{3}{16}\;f[/tex]

[tex]\textsf{Pink partial product}=-\dfrac{3}{2} \;g[/tex]

[tex]\textsf{Product}=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)[/tex]

Calculate the partial products then add these together to find the product of the given expression.

Orange partial product

[tex]\implies \dfrac{3}{8} \times \dfrac{1}{2}f[/tex]

[tex]\implies \dfrac{3 \times 1}{8\times 2}\;f[/tex]

[tex]\implies \dfrac{3}{16}\;f[/tex]

Pink partial product

[tex]\implies \dfrac{3}{8} \times (-4g)[/tex]

[tex]\implies \dfrac{3 \times -4}{8} \;g[/tex]

[tex]\implies \dfrac{-12}{8} \;g[/tex]

[tex]\implies -\dfrac{\diagup\!\!\!\!4 \times 3}{\diagup\!\!\!\!4 \times 2} \;g[/tex]

[tex]\implies -\dfrac{3}{2} \;g[/tex]

Product:

[tex]\implies \dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g[/tex]

To get to the mall, you'll need to find the shortest path from your home to the mall.

The Manhattan Distance formula is an efficient way to calculate the shortest path between two points on a rectangular grid. The formula is as follows:

MD = |x1-x2| + |y1-y2|

Where MD is the Manhattan Distance, x1 and y1 are the coordinates of your home, and x2 and y2 are the coordinates of the mall.

To find the shortest path, simply plug in the coordinates for your home and the mall into the formula and calculate the Manhattan Distance. The result is the shortest number of blocks you need to travel to get to the mall.

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By completing squares in both the variables and try to get the general equation of the form:

(x - a)^2 + (y - b)^2 = R^2

A general circle equation for a circle whose center is (a, b) and the radius is R, is:

(x - a)^2 + (y - b)^2 = R^2

So, if we have an equation like:

x^2 + cx + d + y^2 + h*y + l = m

We just need to complete squares in both x and y, such that we end with an equation of the form of:

(x - a)^2 + (y - b)^2 = R^2

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If a translation of (x,y) → (x+6,y-10) is applied to figure ABCD, the coordinates of D are (1,-12).

What is translation?

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes.

The points of the original image is -

A(-3,4), B(3,4), C(1,-2), D(-5,-2)

The translation of (x,y) → (x+6,y-10) is applied -

A(-3,4) = (-3+6,4-10) = (3,-6)

B(3,4) =  (3+6,4-10) = (9,-6)

C(1,-2) = (1+6,-2-10) = (7,-12)

D(-5,-2) = (-5+6,-2-10) = (1,-12)

Therefore, the new points are -

A'(3,-6), B'(9,-6), C'(7,-12) and D'(1,-12).

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Find the difference between the two lower numbers. If the total is more than the greatest integer, the three numbers can represent the lengths of the triangle's sides.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

Find the sum of the two smaller numbers. If the aggregate is more than the greatest number, the three numbers can represent the lengths of the sides of a triangle.

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The required values of the events are P(Sum > 5) = 0.72 , P (sum is even) = 0.5.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

We have,

According to empirical or relative frequency probability, probabilities are determined by dividing the total number of potential outcomes of an experiment by the number of ways an event could occur.

There are a total of 36 possible results when a fair die is rolled twice consecutively, which is

(1,1), (1, 2), (1,3), (1,4), (1, 5), (1, 6)

(2,1), (2, 2), (2, 3), (2,4), (2,5), (2,6)

(3, 1), (3,2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4,2), (4,3), (4, 4), (4, 5), (4, 6)

(5, 1),(5, 2), (5, 3), (5,4), (5,5), (5, 6)

(6,1), (6, 2), (6,3), (6,4), (6,5), (6,6)

Event A: The total exceeds 5. We find 26 numbers in the table that are bigger than 5, so

P(A) = P(Sum > 5) = 0.72 Event

B: The results of the total are even from the table are 18

P(B) = P (sum is even) = 0.5

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Answer:

Step-by-step explanation:

Distance between top of the tower and point of observation = 100 meters
Angle of Elevation = 45 degrees

Let's draw a right angle triangle with the following specifications.

tan(45 degrees) = x/100

tan(45 degrees) = 1

100(1) = x

x =  100 meters

The height of the tower is 100 meters.

The tablet is 99% effective if used correctly.

However, since individuals make mistakes and it's easy to forget or overlook pills, the actual effectiveness of the pill is only about 93%. Accordingly, 7 out of every 100 women who take pills annually become pregnant.

Depending on the type of pills you're utilizing and when you start taking them. The birth control pill can be started on any day of the month. However, for up to 7 days, you might need to use a backup birth control method, such as condoms, depending on when you start and the type of pill you're taking.

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