The equation 3x + 2 = 29 is modeled below.
Which is the first step in solving the equation for x?

Answer:

g= (9,8)  f= (-5,1)

Step-by-step explanation:

you're welcome =)

Answer:

3/8

Step-by-step explanation:

the total number of possible results is 4×4=16.

out of these 16 only the results

1 2

1 3

1 4

2 2

2 3

3 2

are desired results. these are 6.

so the probability of a desired result is 6/16 = 3/8

The transformation represents a reflection over the y = × line.

A. (x, y) → (-x, y)

A reflection over the y-axis is a transformation that flips a point or shape across the vertical line y = 0.

This means that points on the right side of the y-axis will be reflected to the left side, and vice versa.

Let's examine each option to determine which one represents a reflection over the y-axis.

A. (x, y) → (-x, y):

This transformation reflects the point across the y-axis.

For example, if we have a point (3, 2), after applying this transformation, it becomes (-3, 2).

This represents a reflection over the y-axis.

B. (x, y) → (-x, -y):

This transformation not only reflects the point across the y-axis but also flips it vertically.

For example, if we have a point (3, 2), after applying this transformation, it becomes (-3, -2).

This represents a reflection over the y-axis.

C. (x, y) → (y, x):

This transformation swaps the x and y coordinates of a point, which does not represent a reflection over the y-axis.

Instead, it represents a 90-degree rotation of the point.

D. (x, y) → (y, -x):

This transformation swaps the x and y coordinates of a point and negates the new x-coordinate.

It does not represent a reflection over the y-axis.

Instead, it represents a 90-degree rotation of the point in the counterclockwise direction.

Based on the explanations above, both options A and B represent a reflection over the y-axis.

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Answer:

2 GB Remaining

Step-by-step explanation:

35 - 4 + 3 = 34

Answer:

50

Step-by-step explanation:

Answer:

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

The slope-intercept form is:

Convert the given equation to the above form.

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Answer:

$880

Step-by-step explanation:

Use the equation:

\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.

220=(1-0.75)x

simplify parenthesis terms

220=0.25x

divide both sides by 0.25

880=x

So, the original price was $880.

Hope this helps! :)

Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

Answer:

Step-by-step explanation:

Since EF = 20 and E is at 4

F is at:

Answer:

No

Step-by-step explanation:

You can if you want, but there is a total of 6 on the dice. And there are 3 odds. Each odd you role you gain 10 cents, but each time a student roles a even they also get 10 cents. So you will get paid and in a game of chance and gambling. You won't gain anything if ALL of the students are together and going against you. Its like 1 vs 25 and you would have to pay a lot of students at one time to play this game. So logically no, because you won't gain money. But also you could if you always get odds, but again. That's a 3/6 or 1/2 each time you role to get a odd number.

Hope that helped, or even made sense xD

Answer:

x = -11.2

Step-by-step explanation:

hope it helps

Answer:

14 students have to retake the test

Step-by-step explanation:

to calculate the mean mark as

sum of ( product of mark and frequency ) ÷ total

mean = \(\frac{14(2)+15(10)+16(2)+17(3)+18(13)}{30}\)

        = \(\frac{28+150+32+51+234}{30}\)

       = \(\frac{495}{30}\)

      = 16.5

students who score less than 16.5 will retake the test , that is

2 scored 16 , 10 scored 15 , 2 scored 14

number who have to retake test = 2 + 10 + 2 = 14

Given :

Actual length of the bolt is 2.5 inches.

Measured length of the bolt is 2.6 inches.

To Find :

The percent error of the bolt.

Solution :

We know, percentage error is given by :

\(\delta =| \dfrac{Actual\ Value - Expected\ Value}{Expected\ Value}|\times 100\\\\\delta =| \dfrac{2.6-2.5}{2.5}|\times 100\\\\\delta = 4 \%\)

Therefore, the percentage error in the bolt is 4% .

Answer:

D) 4%

Step-by-step explanation:

Please trust me!

MAKE SURE TO TAKE BREAKS AND DRINK WATER!

<3

The equation that represents the linear function is y =32x

What is a linear equation explain?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

A linear function is represented as

                    y = mx + c

The slope is calculated as

          m = y₂ - y₁/x₂ - x₁

        m = 576 - 64/18 - 2

        m = 512/16

         m = 32

The linear equation is then calculated as

        y = 32( x - 2 ) + 64

         y = 32x - 64 + 64

          y =  32x

Hence, the equation that represents the linear function is y =32x

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The complete question is -

A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale. Number of Hours (x) 2 6 18

Number of Tickets Sold (y) 64 192 576

1.Write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, x, since the tickets have been on sale.

Given:

A statement is given about the sales of ink cartridges by a family owned ink company ABC.

Find:

we have to find the answers of the questions from part(a) to (e) using given statement.

Explanation:

(a) Let us represent the number of the Xavier set, Yvonne set and Zena set in the form of x, y and z respectively as following

x = the number of Xavier set

y = the number of Yvonne set

z = the number of Zena set

(b) we can write the given data in following way

Blue Black Red

Xavier(x) 1 1 0

Yvonne(y) 2 3 1

Zena(z) 4 5 1

Left refills 11 14 3

Therefore, the system of linear equations can be represented as

x + 2y + 4z = 11

x + 3y + 5z = 14

0x + y + z = 3

(c) Now we will solve the given system of equations by Gauss-Jordon elimination as below

given system of equation is

x + 2y + 4z = 11

x + 3y + 5z = 14

y + z = 3

The matrix of the above set can be formed as below

Answer:

1

Explanation:

Radius = C/2π

C is 6.28 and 2*pi is also 6.28

So 6.28/6.28 = 1.

Answer: the answer is 1

Step-by-step explanation:

The total weight of the liquid in the tank is approximately 12,628 pounds.

To calculate the weight of the liquid, we need to determine the volume of the hemisphere and then multiply it by the density of the liquid. The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius of the hemisphere.

In this case, the diameter of the tank is given as 24 feet, so the radius is half of that, which is 12 feet. Plugging this value into the formula, we get V = (2/3)π(12)³ ≈ 904.78 cubic feet.

Finally, we multiply the volume by the density of the liquid: 904.78 cubic feet * 92.5 pounds per cubic foot ≈ 12,628 pounds. Therefore, the total weight of the liquid in the tank is approximately 12,628 pounds.

In summary, to calculate the weight of the liquid in the tank, we first determine the volume of the hemisphere using the formula V = (2/3)πr³. Then, we multiply the volume by the density of the liquid.

By substituting the given diameter of 24 feet and using the appropriate conversions, we find that the total weight of the liquid is approximately 12,628 pounds.

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Area of a compound figure

A compound figure can generally be divided into smaller figures and its area is the sum of all the smaller areas.

The image provided can be divided into a triangle and a rectangle (see image below):

The total area is the sum of the area of the triangle and the area of the rectangle.

Where B=20 is the base of the triangle and H=10, thus:

The area of the rectangle is

Ar = W*L, where W=20, L=40

Ar = 20*40 = 800

The total area is 100 + 800 = 900

Total area= 900

Answer:

\( - \frac{11}{3} \: \: » \: \: 90\% \: » \: \: 2 \: \: » \: \: \frac{89}{4} \)

Answer:

\(1\frac{3}{5}\) meter is the difference in depths of locations diver dove.

Step-by-step explanation:

All angles are 90 degrees.Rhombus: All sides are of equal length.Square: All angles are 90 degrees and all sides are of equal length

a) To construct a triangle in GeoGebra, we can follow the steps below:

Step 1: Open GeoGebra and select the ‘Polygon’ tool.

Step 2: Select the ‘Triangle’ option.

Step 3: Click three points anywhere on the graph.

Step 4: Once you have drawn the triangle, you can use the ‘Angle’ tool to measure all the angles in the triangle. Similarly, use the ‘Length’ tool to measure the length of each side of the triangle.To identify the type of triangle, we can use the following properties:Acute Triangle: All angles of the triangle are less than 90 degrees.Right Triangle: One of the angles in the triangle is 90 degrees.Obtuse Triangle: One of the angles of the triangle is greater than 90 degrees.Scalene Triangle: All sides of the triangle are of different lengths.Isosceles Triangle: Two sides of the triangle are of the same length.Equilateral Triangle: All sides of the triangle are of the same length.To construct a quadrilateral in GeoGebra, we can follow the steps below:

Step 1: Open GeoGebra and select the ‘Polygon’ tool.

Step 2: Select the ‘Quadrilateral’ option.

Step 3: Click four points anywhere on the graph.

Step 4: Once you have drawn the quadrilateral, you can use the ‘Angle’ tool to measure all the angles in the quadrilateral. Similarly, use the ‘Length’ tool to measure the length of each side of the quadrilateral.To identify the type of quadrilateral, we can use the following properties:Irregular Quadrilateral: All sides and angles of the quadrilateral are of different lengths and measures.Trapezium: Only one pair of opposite sides is parallel.Parallelogram: Opposite sides are parallel.Rectangle:.b) Since we need to add a screenshot of the work done in GeoGebra, we cannot add it here. However, while you construct the triangle and the quadrilateral, you can keep adding the measure of angles and sides to find the properties of the figure. You can then use the Text command available in GeoGebra to describe the type of triangle or quadrilateral that you have constructed. To use the Text command in GeoGebra, follow the steps below:

Step 1: Select the ‘Text’ tool from the toolbar

.Step 2: Click anywhere on the graph to add the text box.

Step 3: Type the text in the text box.

Step 4: Customize the font, color, and size of the text as required.

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For the time period of  the projectile at least 192 feet above the ground is between 2 second and 6 second

Since s=128t-16t2, we want to know the 2 times where 128t-16t2=192, as those two values will be the begin and end times of the interval in question. We can rewrite that equation in standard quadratic equation form:

16t2-128t+192=0 or, simplified, 8t2-64t+96=0

or t2-8t+12=0

since it is now in quadratic form, we can solve using the quadratic formula:

t = 2 and 6

So the time period from approximately 2 second and 6 second has the projectile above 192 feet.

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Answer:

Weight of decaf coffee = 5 pounds.

Weight of regular coffee = 8 pounds.

Step-by-step explanation:

(a) Let x be the weight of decaf coffee and y the weight of regular coffee. Then:

x + y = 13

2x + 3y = 34

(b) From the first equation x = 13 - y, so substituting for x in second equation:

2(13 - y) + 3y = 34

26 - 2y + 3y = 34

y = 34 - 26 = 8.

Substituting for y in the first equation:

x + 8 = 13

x = 5.

\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)

Information : The given ellipse is a horizontal ellipse, and it's centre lies on origin, as the foci are given on x - axis.

The foci of the ellipse can be written in form :

\(\qquad \sf  \dashrightarrow \: ( \pm ae , 0)\)

So,

\(\qquad \sf  \dashrightarrow \: ae = 5\)

and Vertex of the ellipse can be written as

\(\qquad \sf  \dashrightarrow \: (\pm a,0)\)

Now, plug the value in first equation ~

\(\qquad \sf  \dashrightarrow \: ae = 5\)

\(\qquad \sf  \dashrightarrow \: 11e = 5\)

\(\qquad \sf  \dashrightarrow \: e = \cfrac{5}{11} \)

Now, we have to find b (length of semi minor axis)

we can use the formula ~

\(\qquad \sf  \dashrightarrow \: b {}^{2} = {a}^{2} (1 - {e}^{2} )\)

\(\qquad \sf  \dashrightarrow \: b {}^{2} = 121(1 - \frac{25}{121} )\)

\(\qquad \sf  \dashrightarrow \: b {}^{2} = 121( \frac{121 - 25}{121} )\)

\(\qquad \sf  \dashrightarrow \: b {}^{2} = 96\)

Now, we can write the equation of ellipse as :

\(\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1\)

[ plug the values ]

\(\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {121}^{} } + \cfrac{ {y}^{2} }{ {96}^{} } = 1\)

Answer:

\(\dfrac{x^2}{121}+\dfrac{y^2}{96}=1\)

Step-by-step explanation:

General equation of an ellipse:

\(\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1\)

where:

If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.

If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.

Given:

Therefore, the ellipse is horizontal with its center at (0, 0):

⇒ h = 0 and k = 0

⇒ a = 11

⇒ c = 5

To find b², use  c² = a² − b²:

⇒ 5² = 11² − b²

⇒ b² = 11² − 5²

⇒ b² = 96

Therefore, the standard form of the equation of the ellipse is:

\(\implies \dfrac{(x-0)^2}{11^2}+\dfrac{(y-0)^2}{96}=1\)

\(\implies \dfrac{x^2}{121}+\dfrac{y^2}{96}=1\)

For the given equation,4x²−y²−24x−4y+28=0.The center is (h,k)=(3,−2), vertex (h+a,k)=(4,−2) and (h−a,k)=(2,−2), foci is (h+c,k)=(5.23,−2) and (h−c,k)=(0.77,−2)

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation of the hyperbola is,

4x²−y²−24x−4y+28=0

Comparing the equation with the standard equation we get,

Center (h,k)=(3,−2)

Vertex (h+a,k)=(4,−2) and (h−a,k)=(2,−2)

Foci (h+c,k)=(5.23,−2) and (h−c,k)=(0.77,−2)

Asymptotes y=2x−8 and y=−2x+4

Thus, for the given equation,4x²−y²−24x−4y+28=0.The center is (h,k)=(3,−2), vertex (h+a,k)=(4,−2) and (h−a,k)=(2,−2), foci is (h+c,k)=(5.23,−2) and (h−c,k)=(0.77,−2)

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Answer:

Selling Price = Cost + $3.00

c 1, 2, 3, 4, 5,

f(c) 4, 5, 6, 7, 8,

The merchant uses Selling Price = Cost + $3.00 to determine the selling price.

Addition is a process of combining two or more numbers.

A merchant adds $3.00 to his cost to determine his selling price.

The cost is denoted by c.

The selling price is given by f(c).

As there is given add in the sentence, it means we have to use the addition rule.

Selling price is the sum of cost plus three

Selling Price = Cost + $3.00

So the table becomes as below

c 1, 2, 3, 4, 5,

f(c) 4, 5, 6, 7, 8,

Hence, the merchant uses Selling Price = Cost + $3.00 to determine the selling price.

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W be the set of all vectors \(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]\) where b and d are real. If W is a vector space because it can be expressed as W = span {v1,. . . .,vn}. So the option A is correct.

Let W be the set of all vectors

\(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]\)

where b and d are real.

We can write the matrix as;

\(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]=b\left[\begin{matrix}1\\ 5\\ 1\\ 0\end{matrix}\right]+d\left[\begin{matrix}-2\\ 1\\3\\ 1\end{matrix}\right]\)

Remember that if aα + bβ ∈ W, ∀ α, β ∈ W and a, b are scalers, then W is a vector space. Let,

\(\alpha=\left[\begin{matrix}1\\ 5\\ 1\\ 0\end{matrix}\right],\beta=\left[\begin{matrix}-2\\ 1\\3\\ 1\end{matrix}\right]\)

These are independent vectors.

bα + dβ ∈ W. where α, β are independent vectors.

That is WE is a span of {α, β}.

Hence, W is a vector space.

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The complete question is:

Let W be the set of all vectors \(\left[\begin{matrix}b-2d\\ 5b+d\\ b+3d\\ d\end{matrix}\right]\) where b and d are real. Determine if W is a vector space and check the correct answer below.

A. W is a vector space because it can be expressed as W = span {v1,. . . .,vn}.

B. W is a vector space because it contains the zero element.

C. W is not a vector space because it does not have additive closure

D. W is not a vector space because it does not have a zero element.