The width of a rectangle play area is 5 meters less than the length. The perimeter of the playground is 38 meters. Write a system of equations that represents the dimensions of the play area

Answer:

x = 6, length of the rectangle is 18cm, and width is 21cm

Step-by-step explanation:

To solve this problem, we can use the perimeter of a rectangle formula: P = 2l + 2w.

Here, l = 3x and w = 4x - 9, so the perimeter is P = 2(3x) + 2(4x - 9) = 52.

Solving for x, we get x = 6.

Therefore, the length of the rectangle is 3x = 18 cm, and the width is 4x - 9 = 21 cm.

The null and alternative hypotheses for the above scenario are

H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon

Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon

Given that,

One automaker says that their van gets 57.2 miles per gallon (mpg). An impartial testing business has been hired to evaluate the mpg for this van. They tested 91 vans, and the results showed that the average mileage was 56.9 with a standard deviation of 1.8 mpg. Is there adequate proof that the vans don't meet their mpg rating at the 0.025 level

To find: state the null and alternative hypotheses for the above scenario.

The null and alternative hypotheses for the above scenario are

H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon

Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon

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Answer: ∠1= 75°, ∠2= 105°, ∠3=105°, ∠4=75°, ∠6=105°, ∠7= 105°, ∠8=75°

Step-by-step explanation:

∠1 is corresponding to angle 75° which make them equal.

∠2 is supplementary to ∠1 which means they add up to 180°. Since ∠1 is 75° you would subtract 75° from 180° to get 105°.

∠3 is vertical to ∠2 which makes them equal.

∠4 is vertical to ∠1 which makes them equal.

∠6 is corresponding to ∠2 which makes them equal.

∠7 is vertical to ∠6 which makes them equal.

∠8 is vertical to 75° which makes them equal.

The unit vector that has the same direction as the given vector is[tex]& (3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].

The given vector(v) is -3i+7j

The unit vector is found by dividing the vector by its magnitude

Unit vector of  [tex]$v=\frac{v}{\|v\|}$[/tex]

The formula of unit vector in the direction of a given vector is:

We have to find the magnitude first

So,

[tex]& \|v\|[/tex] =[tex]\sqrt{(3)^{2}+(-7)^{2} } =\sqrt{9+49} =\sqrt{58}[/tex]

[tex]& \|v\|=\sqrt{58}[/tex]

The unit vector is:

The i, j, and k are the unit vectors in the directions of the x-axis, y-axis, and z-axis respectively in a 3-dimensional plane. i.e.,

[tex]$$\begin{aligned}& =(1 / \sqrt{58})(3 \mathrm{i}-7 \mathrm{j}) \\& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}\end{aligned}$$[/tex]

Therefore, the unit vector is [tex]& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].

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option D is correct- The length of quadrilateral of A’D’ is 6. When it is reflected ,the lengths don’t change.

image is attached below,

Quadrilateral

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.

Reflection

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

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Answer:

Answer is in attached photo. (B)

Step-by-step explanation:

The solution is in the attached photo , do note the question might specify the method to use to solve the equations, just like this the question:

1) Substitution Method

2) Elimination Method

The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.

432 hamburgers.

We can write an equation to represent the information given.

Hamburgers + Cheeseburgers = 491

Cheeseburgers = Hamburgers - 59

Substitute the second equation into the first equation:

Hamburgers + (Hamburgers - 59) = 491

Solve for 'Hamburgers':

2Hamburgers - 59 = 491

2Hamburgers = 550

Hamburgers = 275

Since the question asks for the number of hamburgers, the answer is 275 hamburgers.

The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.

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The missing interior angles of the hexagon is as follows:

∠X = 135 degrees

∠Y = 135 degrees

The polygon above has 6 sides. Therefore, the polygon is a hexagon. The sum of interior angles of a polygon is ( n − 2 ) × 180°.

where

The sum of interior angles in an hexagon is calculated as follows:

180(6 - 2) = 180(4) = 720 degrees

Therefore, the angles of x and y are congruent.

Hence,

let

∠x = ∠y = a

Therefore,

2a + 91 + 149 + 100 + 110 = 720

2a  = 720 - 450

2a = 270

a = 270 / 2

a = 135 degrees

Therefore,

∠x = ∠y = 135 degrees.

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Answer:373248

Step-by-step explanation:

72^3 = 373248

Th systems of Linear Inequalities are:

x>=-7,

y<6-2x/3,

y<=-1,

y>3/5x-5,

y<6+5x

Step1:

x>=-7,y<6-2x/3,y<=-1,y> 3/5x-5,y<6+5x: [x>=-7]

[y<6-2x/3]

[y<=-1]

[ y>3/5x-5]

[y<6+5x]

x>=-7

[tex]3y+2x < 6\sy < =-1\sy > \frac{3}{5}[/tex]

x-5\sy-5x<6

Separate y for 3y+2x6 as follows: y6-2x/3 3y+2x6

Step2:

shuffle twice to the right side

Divide both sides by 3 using the formula 3y/6/3-2x/3.

simplify

3y/3<6/32x/3

Simplify 3y/3 by dividing it by y.

3/3=1

simplify 6/3-2x/3: 6-2x/3

6/3-2x/3

Apply the formula a/c + b/c = a+-b/c = 6-2x/3 y 6-2x/3

Identify y for y-5x6: y6+5x y-5x6.

Y=6+5x move the right side by 5x.

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Answer:

which parallelogram?

Step-by-step explanation:

repost it and add a pic

Answer: Number 2

Step-by-step explanation:

Angle 1 + Angle 2 + Angle 3 = 180 degrees because its a straight line, so we immediately eliminate number 1 and 4 (Because it says the angles add up to 270). Next, we look at 2 and 3. 3 is incorrect because with just 1 right angle, QRST might be a rectangle. Therefore, number 2 is correct. :>

The required domain is x ≥ -4.So option(4) is correct.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

From the graph, we can see that curve is starting from -4 to infinity in x direction.

By baby curve method

x ≥ -4

Thus, required domain is x ≥ -4.So option(4) is correct.

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Answer:  To find the point of intersection of two lines without using graph paper, we can use the method of solving a system of equations.

First, we need to find the slope-intercept form of each line. The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of Line A, we can use the slope formula: m = (y2 - y1)/(x2 - x1). Plugging in the given points, we get: m = (-1 - 3)/(-2 - (-4)) = -4/2 = -2.

Therefore, Line A can be written as y = -2x + b. To find the y-intercept, b, we can plug in one of the points, such as (-4,3) and solve for b: 3 = -2(-4) + b, so b = 11.

So, the slope-intercept form of Line A is y = -2x + 11

We can use the same process to find the slope-intercept form of Line B: m = (7 - 4)/(-5 - (-4)) = 3/1 = 3. So Line B can be written as y = 3x + b. Plugging in one of the points, (-4,4), we get 4 = 3(-4) + b, so b = 16.

So, the slope-intercept form of Line B is y = 3x + 16

Now we have two equations: y = -2x + 11 and y = 3x + 16. To find the point of intersection, we need to find the values of x and y that make both equations true. To do this, we can set the two equations equal to each other:

-2x + 11 = 3x + 16

Subtracting 3x from both sides:

-5x = 5

Dividing both sides by -5:

x = -1

Now we can substitute this value of x back into either equation to find the corresponding value of y. Using y = -2x + 11:

y = -2(-1) + 11 = -2 + 11 = 9

So the point of intersection of Line A and Line

Step-by-step explanation:

A) The measure of the central angle is  [tex]\frac{4}{3} \pi[/tex] .

B) The radius of the circle is 55.43 in.

A) We know,

The area of a sector is  [tex]\frac{n}{2\pi } \pi R^{2}[/tex]

where n = the degree of the central angle of the sector

          R = radius of the circle

Suppose, the measure of the central angle is x.

   [tex]\frac{x}{2\pi } .\pi .24^{2} = 384\pi[/tex]

⇒ [tex]\frac{x}{2\pi } = \frac{384\pi }{576\pi }[/tex]

⇒ [tex]x = \frac{384\pi }{576\pi } * 2\pi[/tex]

⇒ [tex]x = \frac{4}{3} \pi[/tex]

So, the measure of the central angle is  [tex]\frac{4}{3} \pi[/tex].

B) Suppose the radius of the circle is r in.

   [tex]\frac{\pi /4}{2\pi } .\pi .r^{2} =384\pi[/tex]

⇒[tex]\frac{1}{8} .\pi .r^{2} =384\pi[/tex]

⇒ [tex]r^{2} = 384\pi / \frac{1}{8} \pi[/tex]

⇒  [tex]r^{2} = 3072[/tex]

As r > 0

So, r = 55.43

Hence, The radius of the circle is 55.43 in.

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The three points that lie on a line y = -2/5x with a slope -2/5 will be:

(0, 0)

(5, -2)

(10, -4)

Given slope = m = -2/5. We suppose the line passes through the origin, so b = 0

substituting m = -2/5 and b = 0 in the slope-intercept form

y = -2/5x + 0

y = -2/5x

Thus, the equation of line with the slope m = -2/5 and passes through the origin (0, 0) will be:

y = -2/5x

As the equation of line passes through (0, 0), thus the point (0, 0) lies on the line.

Putting x = 0 in the equation y = -2/5x

y = -2/5 × (0)

y = 0

Thus, (0, 0) is the point which also passes through the line

Putting x = 5 in the equation y = -2/5x

y = -2/5 × 5

y = -2

Thus, (5, -2) is the point which also passes through the line.

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The point that lies on the function defined by the equation is (2, 7)

From the question, we have the following parameters that can be used in our computation:

y = 2x + 3

The point in the ordered pair that lies on the graph of the equation is the solution set

Take for instance, we set x = 2

So, we have the following representation

y = 2 * 2 + 3

Evaluate the product and the sum

This gives

y = 7

When repesented as an ordered pair, we have

(2, 7)

Hence, the point is (2, 7)

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The MEAN best describes the monthly rents.

The best one is Mean : 898

Now, According to the question:

The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810.

We are required to use the mean, median and mode to explain which measure of central tendency best describes the monthly rent.

The mean, median and mode (as calculated) are the measures of central tendency for the data set given.

This measures which value is closest to the center such that it can conveniently represent every other data. Observe carefully that the least value is 670 while the highest is 1550.

Also, observe that the value which is "more central" to both extremes is the mean.

The median is closer to the lowest value and much farther from the highest value.

The mode is actually at the lowest end of the data set.

However, the mean is safely between both ends. Its farther away from the least value than the median which means its moving closer to the "center" unlike the other two measures.

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The measure of arc RT is: C. 204 degree.

arc ORT = 102° - 90°

arc = 12°

arc ROT = 180° - 2×12°

arc ROT = 180° -  24°

arc ROT = 156°

Hence:

Measure of arc RT

arc RT= 360° - 156°

arc RT = 204°

Therefore the correct option is C.

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If the equation "y = 7400x" represents the number of miles(y) , that satellite space explorer files in x hours , then the rate of change is 7400 miles per hour.

The Rate Of Change is also known as "Slope" ,

The rate of change can be found by taking the derivative of the equation   ⇒ y = 7400x with respect to x.

The derivative of the equation "y = 7400x" with respect to x is  ;

⇒ dy/dx = d/dx(7400x) = 7400 .

Therefore ,  rate of change of the equation "y = 7400x" is 7400 miles per hour , that means the satellite explorer files will cover 7400 miles in 1 hour .

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The roots of the parabola are given as follows:

x = -2 and x = -4.

The quadratic function for this problem is defined as follows:

y = x² + 6x + 8.

Completing the squares, the quadratic function can be factored as follows:

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

As:

Then the roots are obtained as follows:

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Answer: The percent was 12.5%

Angle of depression and elevation:The angle of depression refers to the angle above the hill.The ship is 349.8 feet away from the skyscraper's base horizontally.

You could calculate the angle of elevation, for instance, if you were standing on the ground and were looking up at a mountain's summit.

The angle between a line of sight's horizontal axis and its downward axis is known as the angle of depression.

The ship is 349.8 feet away from the skyscraper's base horizontally.

Angle of depression and elevation:The angle of depression refers to the angle above the hill.

given the aforementioned variables

The harbor is 824 feet tall.

Depression angle is 67 degrees.

SOH CAH TOA identification claims that:

Tan = opp/adj Tan = 824 Tan = 67

d = 824.8/tan67 d = 349.8 feet

Therefore, the vertical distance from the skyscraper's base to the ship is 349.8 feet.

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Answer:

15x-3

Step-by-step explanation:

Recall that parallelograms, as the name implies, have two pairs of parallel sides. In this case, line segments AB and CD are parallel to each other, and then BC and DA are parallel to each other:

Perimeter = AB + BC + CD + DA = (6x-4) + (2x) + (5x+1) + (2x) = 15x - 3

The width of the mural (in feet) when it is finished is equal to 12.25 feet.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Scale factor = 2/5

For the width of the mural (in feet), we have:

2/5 = 4.9/x

x = (5 × 4.9)/2

x = 24.5/2

x = 12.25 feet.

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On dividing the expression [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)], the value obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression is given as - [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)]

Apply the fraction rule, (a/b)/(c/d) = a·d/b·c

= [(x²-9) × (x²-2x-15)]/[(x²-4x-5) × (x²+5x+4)]

= [(x²-9) × (x+3)]/[(x²-4x-5) × (x+1)]

Expand the expression -

= [(x²-9) × (x+3)]/(x³-3x²-9x-5)

= (x³+3x²-9x-27)/(x³-3x²-9x-5)

= 1 + [(6x²-22)/(x³-3x²-9x-5)]

Therefore, the expression obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].

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Answer: 6

Step-by-step explanation:

1. 16/1 × 3/8= 48/8

2. 48/8= 6

When y = 5x the possible outcome of table is 2.8 when x = 4 , 3.88 when x= 7 and 3.33 when x= 4 .

A function's range can refer to one of two closely related ideas: The function's image is its codomain. Given two sets, X and Y, a function is a binary relation between X and Y if, for every x in X, there is exactly one y in Y that corresponds to f. Take a look at the function y = f(x). The range of the function is the spread of all the y values from the lowest to the highest. Substitute all of x's values into the given expression for y to determine whether it is positive, negative, or equal to other values.

if y=5 x

y= 7 and X = 4 , then

                         7= 5(4)

                          7 = 20

                         = 20/7

                      =     2.8

when Y =9 and X = 7 then,

                     9 = 5(7)

                         9 = 35

                          35/9

                      =    3.88

when Y = 6 and X = 4 then,

                          6= 5(4)

                           6= 20

                              20/6

                             = 3. 33

Missing function of table are 2.88 , 3.88,3.33

The range is (0;+∞). The values are all positive (if a positive number is raised to a power, the result cannot be negative), and the value cannot be zero, so the range is (0;+∞).

Incomplete question :

Create a table from y=5x. You can just do numbers like

Y 7. 9. 6

X 4. 7. 4 or sum I just need the table

Complete the table for the given rule.

Rule:y=5x

x, y

5,4,2

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