A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?

A.
-3x + 4y = 3

B.
-1.5x − 3.5y = -31.5

C.
2x + y = 20

D.
-2.25x + y = -9.75

This is a PLATO math question, will give 15 pts to the best answer

Answer:

  a) area of sidewalk: 346.5 ft²

  b) 278 bags

Step-by-step explanation:

The formula for the area of a circle is ...

  A = π·r² . . . . . where A is the area and r is the radius of the circle. (The radius is half the diameter.)

There are a couple of ways to find the area of a "washer" (a circle with a hole in the middle). One is to subtract the area of the hole from the area of the larger circle. Another way is to find the circumference of the circle whose radius is the average of the inner and outer radii, and multiply that by the width of the washer (the difference of the outer and inner radii).

For the latter purpose, the formula for the circumference of a circle is ...

  C = π·d . . . . . or, since the diameter is twice the radius, ...

  C = 2π·r

___

a) Here, the diameter of the circle that is the center of the walkway is ...

  28 ft + 3.5 ft = 31.5 ft

So, the circumference of that circle is ...

  C = π·d = (22/7)·(31.5 ft) = 99 ft

Then the area of the walkway is ...

  (99 ft)·(3.5 ft) = 346.5 ft²

__

b) 0.8 bags of concrete are required for each square foot, so we can find the number of bags by multiplying 0.8 times the number of square feet:

  bags = 0.8 × 346.5 = 277.2

If only whole bags are available, then 278 bags of concrete will be the minimum number needed.

_____

Comment on the two methods of doing this calculation

If r1 and r2 are the inner and outer radii of the circles, then the area of the washer is π(r2² -r1²).

The centerline diameter will be (2r2 +2r1)/2 = r1 +r2, and the width of the washer will be (r2 -r1). Then the washer area will be π·(r1 +r2)·(r2 -r1). This latter expression can be "simplified" to π(r2² -r1²), a formula for the washer area that is identical to the one above.

Answer:

$95.48 was his commission

Step-by-step explanation:

First we need to find what the retail cost of the chest is.  If it's marked up 150%, we use 763.84 + 1.5(763.84) which gives us a retail price of $1909.60.  If Ben makes 5% on the sale as his commission, then we take 5% of 1909.60 which, in algebraic terms, looks like this:  .05(1909.60) which is $95.48

Answer:

9 units²

Step-by-step explanation:

A differential of area is ...

dA = ((2y -y²) -(y² -4y))·dy = (-2y² +6y)·dy

The indefinite integral of this will be ...

a = -2/3y³ +6/2y²

Then the definite integral over the limits [0, 3] will be ...

(-2/3·3³ +3·3²) - 0 = 9 . . . . square units

Answer:

Step-by-step explanation:

Pick any point that is clearly on the line. (g, c) = (12, 40) is the end point, so will do nicely. The value of r (the constant of proportionality) is the slope of the line, which is the ratio of the y-value of the point to the x-value (or c to g, in this case).

  r = c/g = 40/12 = 10/3  . . . . . . the exact value of the constant r

Then your equation is ...

  c = 10/3g . . . . . . put the value of r where r is in the equation you are given

Answer:

  28. [A] x² -2x +1 r -16

  29. [D] -x² -2x -5 -12/(x-2)

Step-by-step explanation:

In both cases, the answers can be chosen on the basis of the value of the remainder. That value can be found by evaluating the numerator expression at the value of x that makes the denominator zero.

___

28. The root of the denominator is x=-2. The value of the numerator there is ...

  (5(-2)³ -6 -15(-2) = -40 -6 +30 = -16 . . . . points to answer choice [A]

__

29. The root of the denominator is x=2. The value of the numerator there is ...

  -(2)³ -2 -2 = -8 -2 -2 = -12 . . . . points to answer choice [D]

Answer:

  $2880

Step-by-step explanation:

I = Prt

= $3600·8%·10 = 0.80·$3600 = $2880

The simple interest on $3600 over a 10-year period is $2880.

The answer is:

The area of the rectangle is equal to [tex]12units^{2}[/tex]

To find the area of the rectangle shown on the coordinate plan, first, we need to calculate the distance between the points that conforms two of the sides of the rectable (base and height).

We can use any of the four vertex points shown on the coordinate plane, so, we will use the points:

1 - (-4,1)

2 - (-1,-2)

3 - (-3,-4)

Then, calculating the length of the sides, we have:

Base:

[tex]Base=distance(FirstPoint,SecondPoint)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}[/tex]

[tex]Base=\sqrt{(-1-(-4))^{2}+(-2-1)^{2}}\\\\Base=\sqrt{(3)^{2}+(-3)^{2}}\\\\Base=\sqrt{(9+9)}=\sqrt{18}units[/tex]

Height:

[tex]Height=distance(SecondPoint,ThirdPoint)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}[/tex]

[tex]Height=\sqrt{(-3-(-1))^{2}+(-4-(-2))^{2}[/tex]

[tex]Height=\sqrt{(-2)^{2}+(-2)^{2}[/tex]

[tex]Height=\sqrt{4+4}[/tex]

[tex]Height=\sqrt{8}units[/tex]

Therefore, calculating the are of the rectangle, we have:

[tex]Area=base*height\\\\Area=\sqrt{18unis}*\sqrt{units}=\sqrt{144}=12units^{2}[/tex]

Hence, the area of the rectangle is equal to [tex]12units^{2}[/tex]

Have a nice day!

Aswer:

The area of the rectangle is 12 sq. units

step-by-step explanation:

From the question :

we first find the length and width of the rectangle using the distance formula.

For the length we use the points

(-1,-2) and (-4,1)

[tex]l = \sqrt{( {x - x_1)}^{2} + ( {y - y_1)}^{2} } [/tex]

[tex]l = \sqrt{( { - 1 - ( - 4))}^{2} +{(-2 - 1)}^{2} } [/tex]

[tex]l = \sqrt{{3}^{2} +{( - 3)}^{2}}[/tex]

[tex]l = \sqrt{9 + 9} [/tex]

[tex]l = \sqrt{18} = 3\sqrt{2} \: units[/tex]

For the width, let us take the points (-6,-1) and (-4,1)

[tex]w = \sqrt{ {( - 6 - ( - 4))}^{2} + {(-1 - 1) }^{2} }[/tex]

[tex]w = \sqrt{ {2}^{2} + {( - 2)}^{2} }[/tex]

[tex]w = \sqrt{4+4}[/tex]

[tex]w = \sqrt{8 } = 2 \sqrt{2} \: units[/tex]

The area of the rectangle

[tex] = l \times w[/tex]

[tex]A = 3 \sqrt{2} \times 2\sqrt{2} [/tex]

[tex]A = 3 \times 2 \times 2[/tex]

[tex]A =12 \: sq.units[/tex]

Answer:

C. n + n + 1 = 37; n = 18; n + 1 = 19

Step-by-step explanation:

If we let n represent the smaller integer, then the larger one is n+1. Their sum is 37, so you have ...

n + (n+1) = 37

When you subtract 1 and collect terms, you have ...

2n = 36

Dividing by 2 gives you ...

n = 18

Then the larger integer is ...

n+1 = 19

The matching choice is C.

In this sequence, the first term is [tex]a_1[/tex] and every successive term is determined by

[tex]a_n=a_{n-1}+d[/tex]

where [tex]d[/tex] is the common difference between terms. We have

[tex]a_{11}=a_{10}+d=a_{9}+2d=\cdots=a_5+6d[/tex]

so that

[tex]41=11+6d\implies6d=30\implies d=5[/tex]

Then

[tex]a_5=a_4+5=a_3+2\cdot5=\cdots=a_1+4\cdot5[/tex]

[tex]\implies11=a_1+20\implies a_1=-9[/tex]

Answer:

The first term is -13.

Step-by-step explanation:

The general rule of an arithmetic sequence is the following:

[tex]a_{n+1} = a_{n} + d[/tex]

In which d is the common diference between each term.

This is the case going from one term to the next. However, when, as in this problem, we have the fifth and the tenth term, this formula can be expanded, as the following way:

[tex]a_{n + m} = a_{n} + m*d[/tex]

So

[tex]a_{10} = a_{5} + 5*d[/tex]

[tex]41 = 11 + 5d[/tex]

[tex]5d = 30[/tex]

[tex]d = 6[/tex]

The common diference is 6.

To find the first term, we do:

[tex]a_{5} = a_{1} + 4*d[/tex]

[tex]11 = a_{1} + 4*6[/tex]

[tex]a_{1} = -13[/tex]

The first term is -13.

Answer:

  24 cm²

Step-by-step explanation:

We assume that is a circumscribing quadrilateral, rather than one that is circumscribed. It is also called a "tangential quadrilateral" and its area is ...

  K = sr

where s is the semi-perimeter, the sum of opposite sides, and r is the radius of the incircle.

  K = (12 cm)(2 cm) = 24 cm²

_____

A quadrilateral can only be tangential if pairs of opposite sides add to the same length. Hence the given sum is the semiperimeter.

Answer:

x² = 12y, or y = x²/12

Step-by-step explanation:

The most basic formula for the parabola in vertex form is

x² = 4py, where p is the distance (3) between vertex (0, 0) and focus (0, 3).

Thus we have x² = 4(3)y, or x² = 12y, or y = x²/12

Based on the graph, an equation of the parabola in vertex form is [tex]x^2=12y[/tex].

In Mathematics and Geometry, the vertex form of the equation of a vertical parabola that opens either upward or downward can be modeled by the following mathematical equation:

[tex](x - h)^2 = 4p(y - k)[/tex].

Where:

Based on the graph, we can logically deduce that the vertex of this parabola is located at (0, 0), the focus would be at (0, p) and the directrix would be represented by a horizontal line at y = -p.

In this context, the equation of this parabola in vertex form is given by;

[tex](x - h)^2 = 4p(y - k)\\\\(x - 0)^2 = 4(3)(y - 0)\\\\x^2=12y[/tex]

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Answer:

  the correct choice is marked

Step-by-step explanation:

Expressing the difference over a common denominator, we have ...

  (sec(θ)² -1)/sec(θ) = tan(θ)²cos(θ) = tan(θ)·(sin(θ)/cos(θ))·cos(θ)

  = tan(θ)sin(θ)

_____

We have used the following identities:

Answer:

  (3)  y = 12

Step-by-step explanation:

The circle is centered at (x, y) = (-5, 2) and has a radius of 10. Hence the most positive y-value is y = 12.

___

Complete the squares of x-terms and of y-terms.

  (x^2 +10x) + (y^2 -4x) = 71

  (x^2 +10x +25) + (y^2 -4x +4) = 71 + 25 + 4

  (x +5)^2 +(y -2)^2 = 10^2 . . . . . . . a circle centered at (-5, 2) with radius 10.

Answer:

The length of the cable is [tex]1,173\ ft[/tex]

Step-by-step explanation:

Let

x-----> the length of the cable

we know that

[tex]sin(43\°)=\frac{800}{x}[/tex]

[tex]x=\frac{800}{sin(43\°)}\\ \\x=1,173\ ft[/tex]

The length of the cable between the top and bottom of the ski lift can be determined using trigonometry. Applying the sine function, which is the ratio of the length of the opposite side to the length of the hypotenuse, to the given angle of depression and vertical distance, we obtain the length of the cable to be approximately 1172 feet.

The student is asking for the length of the cable between the top and bottom of a ski lift. Given the angle of depression and the vertical distance, we can use the concept of trigonometry to solve this. In this problem, we treat the vertical distance as the opposite side, the cable as the hypotenuse and the angle between them is the depression angle.

If we apply this to the problem, we use the sine function, which is defined as the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we have the equation sin(43°) = 800 feet / length of the cable.

To solve for the length of the cable, we rearrange the equation to get: length of the cable = 800 feet / sin(43°). Hence, with the sine of 43° approximately equals to 0.682, the length of the cable is approximately equal to 1172 feet.

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Answer:

Step-by-step explanation:

The easiest way for me to answer your question is just to do it. If we agree, all well and good. If we don't, then you have the way I did it.

A = (4.75*x + 125)/10000

A = (4.75*10000 + 125) / 10000

A = (47500 + 125) / 10000

A = 47625/10000

A = 4.76

So it looks like we both think it is A.

The question is deceptive because the 125 is really quite small compared to 47500.

Answer:

A. $4.76

Step-by-step explanation:

This case is fairly typical of average cost problems. There is some fixed cost that is amortized over the number of T-shirts produced, and there is some variable cost associated with each item.

Here, if you divide out the equation, you get ...

A = 4.75 + 125/x

Then for x=10,000, the value of A is ...

A = 4.75 +125/10,000 = 4.75 +0.0125 ≈ 4.76

_____

Once you see that the fixed cost of $125 is divided by 10,000, you can look for an answer choice that is very slightly higher than $4.75.

Answer:

C. 1.4x + 1.8y = 79.8

x + y = 53

Step-by-step explanation:

The problem statement gives rise to two equations, one for the amount of money made, and one for the number of items sold. If x and y represent the numbers of items, and if 53 items were sold, then one of the equations will be ...

x + y = 53

This is sufficient to let you choose the correct answer.

___

Since "x" items were sold for $1.40 and "y" items were sold for $1.80, the sales revenue will be the sum of products of price and quantity:

1.40x +1.80y = 79.80

This confirms the choice of answer.

Answer:

• Lateral area is the area of the sides of a 3-dimensional object, excluding the top and bottom bases. (Those bases are generally parallel to each other.) In the case of a cone or cylinder, it is the area of the curved surface. In the case of a pyramid, it is generally the area of the triangular faces. In the case of a cuboid, it is the area of the sides, excluding the top and bottom.

• Some examples are shown in the first attachment. An ambiguous case is shown in the second attachment. (For the ambiguous case, you would need to talk to the poser of the question to see what area they intend by "lateral area.")

Step-by-step explanation:

The total surface area of an object is the total area you would paint if you were to paint all surfaces of the object. The lateral area is the area you would paint if you did not paint the top or bottom surfaces (bases) of the object. For a pyramid or cone, the top base is a point, so has no area.

Some formulas are used for lateral area:

LA = πrs . . . . . cone with base radius r and slant-height s

LA = 2πrh . . . . cylinder with base radius r and height h

LA = Ph . . . . . . prism with base perimeter P and height h

LA = 1/2Ps . . . . pyramid with base perimeter P and slant height s

___

About the ambiguous case in the second attachment

Generally, we take the "lateral area" of a pyramid to be the total area of its triangular faces. Here, the figure appears to be resting on one of its triangular faces, and the square base is uncovered at the side. This orientation suggests that the "lateral area" should include the area of the square, and exclude the area of one of the triangles.

Further adding to the ambiguity is the fact that the top flat surface might also be considered a "base" and excluded from the area calculation.

I don't have a definitive answer for this situation except to say that whoever posed the problem certainly had something in mind when they asked for the "lateral area" of this figure. They should be consulted as to their intent. (When this question was answered on Brainly, the square was included and one triangle was excluded. No feedback was provided to indicate whether that choice was "correct.") Personally, I might say this is a square pyramid and its lateral area is that of the four triangles: 352 m².

Final answer:

The lateral area is the sum of the areas of all the sides of a 3D geometric figure excluding the base(s). For example, the lateral area of a cylinder with height h and radius r is calculated as 2πrh. To understand the concept further, comparing the areas of two squares and using scale for area measurements were demonstrated.

Explanation:

The term lateral area refers to the surface area of the sides of a three-dimensional geometric figure, excluding the area of its bases (top and bottom faces). In other words, it is the sum of the areas of all the faces of the figure that are not its base(s).

To illustrate, let's consider a cylinder as an example. If the cylinder has a height (h) and the radius of its base (r), the lateral area (Alateral) is calculated by the formula Alateral = 2πrh. This is because the lateral surface of a cylinder is essentially a rectangle wrapped around the circular base, the length of the rectangle being the circumference of the base (2πr) and the width being the height (h).

Now let's compare two areas. Suppose you have two squares, one with a side length twice the size of the other. If the smaller square has a side length of 's', then its area is s². The larger square, with sides twice as long, will have an area of (2s)², which equals 4s². The ratio of their areas is therefore 4s² to s², which simplifies to 4:1, showing that the larger square has four times the area of the smaller one.

Similarly, we can use a scale to find the area of a space. By determining the length and width, we can perform the necessary calculations to find the area. When we have two areas to compare, proportions are used to compare their sizes. The area is computed using the dimensional formula L² (length times width for rectangles or 2πr for the circumference and πr² for the area of a circle).

Answer:

  Bagel

                                       plain                          

Tuna Eggs Chicken salad Cream cheese butter

                                      Poppy

Tuna Eggs Chicken salad Cream cheese butter

                                      Wheat

Tuna Eggs Chicken salad Cream cheese butter

3b

There are 15 combinations because tuna, eggs, chicken salad, cream cheese, and butter = 5

there are 3 different types of bagels plain poppy and wheat. with this information you can tell that the 5 combinations x 3 bagel types equal 15 total

Answer:

Step-by-step explanation:

I think the first part of that is asking for the equation for the line of symmetry, although I do not have access to your drop down menu to know for sure!  The axis of symmetry is the equation that splits the parabola into 2 parts that are mirror images of each other.  In this type of parabola, it will be an "x = " equation.  The line that splits the parabola in half is the line x = -2.  The function is increasing where the y values are going up.  This happens in the interval  (-∞, -2].

The function is decreasing where the y values are going down.  This happens in the interval [-2, ∞)

The function y = x^2 – 14x + 58 is written in vertex form by completing the square as y = (x - 7)^2 + 9. The function y = –x^2 – 6x – 20 is written in vertex form as y = - (x + 3)^2 -11. The first function has a minimum of 9 and second has a maximum of -11.

The given functions are quadratic, which are in the form y = ax^2 + bx + c. Converting these functions to vertex form, which is y = a(x - h)^2 + k, can be done by completing the square.

A. The function y = x^2 – 14x + 58 can be rewritten by completing the square:

B. The function y = –x^2 – 6x – 20 can also be rewritten by completing the square:

C. The vertex form of a quadratic function y = a*(x - h)^2 + k allows you to see that the function has a minimum if a is positive and a maximum if a is negative. The value for that extremum is k. Therefore, y = (x - 7)^2 + 9 has a minimum of 9 and y = - (x + 3)^2 -11 has a maximum of -11.

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3wx^2

The third choice is the answer.

Answer :C

Answer:

3wx^2

Step-by-step explanation:

Answer:

The perimeter of one of the trapezoids is equal to [tex](16+8\sqrt{2})\ in[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The perimeter of a square is

[tex]P=4b[/tex]

where

b is the length side of the square

step 1

Find the length side of the smaller square

[tex]16=4b[/tex]

[tex]b=16/4=4\ in[/tex]

step 2

Find the length side of the large square

[tex]48=4b[/tex]

[tex]b=48/4=12\ in[/tex]

step 3

Find the height of one trapezoid

The height is equal to

[tex]h=(12-4)/2=4\ in[/tex]

step 4

Remember that in this problem, one trapezoid is equal to one square plus two isosceles right triangles.

Find the hypotenuse of one isosceles right triangle

Applying Pythagoras Theorem

[tex]c^{2}=4^{2} +4^{2} \\ \\c=4\sqrt{2}\ in[/tex]

step 5

Find the perimeter of one of the trapezoid

The perimeter is equal to

[tex]P=(4\sqrt{2} +4+4\sqrt{2}+12)\\ \\P=(16+8\sqrt{2})\ in[/tex]

Answer:

27.3 Inches

Step-by-step explanation:

Answer:

The first one, the one with A' at -4,5

Step-by-step explanation:

To find which graph shows the translation you first find a point that is easy to follow, ideally one that is along an axis.

Point A would be easy to follow, since it's roughly at (0,3) initially.

Then we apply the translation. T (-4,2) means the X value is moved to the left, subtracted 4 units... while the Y value is moved up, adding 2 units.

So, the point A that was at (0,3) becomes A' at (0 - 4, 3 + 2), or (-4,5).

ANSWER

B. [tex](x,y)\to (0.5x,0.5y)[/tex]

EXPLANATION

From the diagram, MN=6 units.

and M'N'=3 units.

The quadrilateral KLMN was dilated to obtain K'L'M'N'

We can observe that,

[tex] |M'N'| = 0.5|MN| [/tex]

This means that the scale factor of the dilation is 0.5.

The mapping for the dilation is :

[tex](x,y)\to (0.5x,0.5y)[/tex]

The correct answer is B.

Answer:

Step-by-step explanation:

In the attached spreadsheet, I elected to model each shot of each game. The model only covers 50 games, so cannot give the desired probability with much accuracy.

The cell that models the outcome of a shot has the formula ...

  =IF(RAND()<=0.3;1;0)

The RAND() function in this NeoOffice spreadsheet program returns a number uniformly distributed between 0 and 1. We have elected to make numbers of 0.30 or less correspond to shots that are made. (On average, 30% of shots are made.) Each line of 20 shots models one game.

Column B adds the "Shot Successful" numbers to determine the total number of successful shots in that game. Cell B53 finds the total number of games with at least 7 shots made, and divides that number by 50 to find the probability of making 7 or more shots in a game.

I suspect one would need to model several thousand games to determine the probability with any confidence. (The probability based on the binomial distribution is about 0.392. A few different simulations (recalculating the spreadsheet) have given results ranging from 0.24 to 0.62.)

Answer:

  0.5 cm

Step-by-step explanation:

You are given angles B and C and side b, so you can put those values into the given equation:

  sin(105°)/(2 cm) = sin(15°)/c

Multiply this equation by c·(2 cm)/sin(105°) and you get ...

  c = (2 cm)·sin(15°)/sin(105°) ≈ 0.535898 cm

  c ≈ 0.5 cm

_____

Comment on the given equation

When using the Law of Sines to find side lengths, I prefer to write the proportion in a form with the side length of interest in the numerator:

  b/sin(B) = c/sin(C)

or

  c/b = sin(C)/sin(B)

Using either of these forms, it is one step to find the value of c: Multiply the equation by the inverse of the coefficient of c.

  c = b·sin(C)/sin(B)

Answer:

  3

Step-by-step explanation:

The function is undefined when its denominator is zero. The value of x that makes the function undefined is the solution to

  10x -30 = 0

  x - 3 = 0 . . . . . divide by 10

  x = 3 . . . . . . . . add 3

The value of x that is not in the domain of the function is x=3. The function is not defined for that value of x.

Answer:

x = 61

Step-by-step explanation:

Supplementary angles add to 180°, so we have ...

(2x) + (x -3) = 180

3x = 183 . . . . . . . . . add 3

x = 61 . . . . . . . . . . . divide by 3

The value of x is 61.

_____

The angles are m∠P = 122°, m∠Q = 58°. Their sum is 180°.

Answer:

60

Step-by-step explanation:

<H + <T = 180

2x+ 60 + x + 30 = 180

3x + 90 = 180

3x = 90

 x = 30

<T = x + 30 = 30 + 30 = 60

Answer

<T = 60

Answer:

0

Step-by-step explanation:

f(x) = -3x^2 + 6x

Let x=2

f(2) = -3*(2)^2 + 6(2)

       =-3(4) +12

      = -12+12

     =0