Aramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.
The ratio of
is equal to tan B.

Answer:

Δ PQT ~ Δ QRS  .....{S-S-S test for similarity}...Proof is below.

Step-by-step explanation:

Given:

In Δ PQT

PQ = 30 ft

QT = 28 ft

TP = 20 ft

In Δ QRS

QR = 15 ft

RS = 14 ft

SQ = 10 ft

To Prove:

Δ PQT ~ Δ QRS

Proof:

First we consider  the ratio of the sides

[tex]\frac{PQ}{QR}=\frac{30}{15} = \frac{2}{1}[/tex]            ..............( 1 )

[tex]\frac{QT}{RS}=\frac{28}{14} = \frac{2}{1}[/tex]            ..............( 2 )

[tex]\frac{TP}{SQ}=\frac{20}{10} = \frac{2}{1}[/tex]            ..............( 3 )

So By equation ( 1 ), ( 2 ) and  ( 3 ) we get

[tex]\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}[/tex]

Now in Δ PQT  and Δ QRS we have

[tex]\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}[/tex]

Which are corresponding sides of a similar triangle in proportion.

∴ Δ PQT ~ Δ QRS  .....{S-S-S test for similarity}...Proved

Answer:

sss similarity

Step-by-step explanation:

i took the test

Answer: 25 purple beads

Step-by-step explanation: Hope this helps :)

Answer:

25 beads

Explanation For 4 to get to 20 you need to multiply it by 5. You then do the same thing with 5 to get 25 beads.

Answer:

x = 16/5

Step-by-step explanation:

Answer:

48  chicken wings in 12 minutes.

Step-by-step explanation:

Answer:

4 chicken wings per minute

Step-by-step explanation:

12/3=4

Answer:

x=4, y=-1. (4, -1).

Step-by-step explanation:

x-3y=7

3x+3y=9

---------------

x=3y+7

3(3y+7)+3y=9

9y+21+3y=9

12y+21=9

12y=9-21

12y=-12

y=-12/12

y=-1

x-3(-1)=7

x+3=7

x=7-3

x=4

Final answer:

To simplify the expression 7(2 + 4) - 3(6) + 2(3 + 5), calculate within the parentheses, do the multiplications, and then the additions and subtractions to get the result, which is 40.

Explanation:

To simplify the numerical expression 7(2 + 4) - 3(6) + 2(3 + 5), you need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Here's how you simplify the expression step by step:

First, calculate the expressions within the parentheses: (2 + 4) and (3 + 5).

Then, multiply each result by the number outside the parentheses.

Afterward, complete any multiplication or division from left to right.

Finally, perform the addition and subtraction from left to right.

Now let's apply these steps to the expression:

Calculate the expressions inside the parentheses: 2 + 4 = 6 and 3 + 5 = 8.

Multiply each result by the respective number outside the parentheses: 7 * 6 = 42 and -3 * 6 = -18 and 2 * 8 = 16.

Now rewrite the expression with these calculated values: 42 - 18 + 16.

Now it's just addition and subtraction: 42 - 18 = 24, and 24 + 16 = 40.

Therefore, the simplified expression is 40.

Final answer:

The volume of cylinder P is twice the volume of cylinder Q because the height of cylinder P is twice that of cylinder Q, while the radii are equal.

Explanation:

The question is asking how many times larger the volume of cylinder P is as compared to cylinder Q, given that cylinder P has twice the height of cylinder Q but both have equal radii. To find the volume of a cylinder, we use the formula V = πr²h, where V is the volume, π is the constant pi (approximately 3.14159), r is the radius, and h is the height of the cylinder.

Since both cylinders have equal radii, the ratio of their volumes will only depend on the ratio of their heights. If we let the height of cylinder Q be h, then the height of cylinder P is 2h. Using the volume formula:

Volume of cylinder P, VP = πr²(2h) = 2πr²h.

By dividing the volume of P by the volume of Q, we get:

VP / VQ = (2πr²h) / (πr²h) = 2.

Therefore, the volume of cylinder P is twice the volume of cylinder Q.

The correct function to express the area of the rectangular corral as a function of its width, given a fixed amount of fencing, is A(x) = x(70 - x).

The student is asking about expressing the area of a rectangular corral as a function of its width when a fixed amount of fencing is used. Given that Farmer Jones has 140 feet of fencing to construct the corral and the width is represented by x, the perimeter of the rectangle is twice the sum of its width and length.

Therefore, if x is the width, the length will be (140 - 2x)/2 or 70 - x. We can then express the area A as a function of x by multiplying the width by the length, leading to the function A(x) = x(70 - x).

Answer:

Option D 2.6% is right.

Step-by-step explanation:

Given that at a certain grocery store 65% of the customers regularly use coupons.

Proportion of  the customers regularly use coupons.=0.65

Proportion of customers who do not  regularly use coupons.

=1-0.65 = 0.35

Sample size = 340

In usual notation we write this as

[tex]p=0.65\\q=0.35\\n = 340[/tex]

Std deviation = [tex]\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.65*0.35}{340} } \\=0.025867[/tex]

In percentage this can be written as 2.5867% ~2.6%

Option D 2.6% is right.

Answer:

D

Step-by-step explanation:

BECAUSE                                          

WHEN

YOU

LOOK

AT

A

B

OR

C

OH

NO

THERE

IS

NO

MORE

SPACE

!!!!!!!!!!!!!!

Hint:

Diameter(d)= 2 radius(r)

circumference= 2πr= πd

1. diameter= 19 × 2 = 38 inches

circumference= 3.18(38) = 119 inches (3 s.f.)

Note that I use 3.18 instead of π because the question states to use 3.14 for π.

Likewise, if you are given the diameter, divide it by 2 to find radius. Let's try a question which only gives you the diameter.

4. radius= 22 ÷ 2 = 11cm

circumference= 3.14(22) = 69.1cm (3 s.f.)

Answer:

Corresponding angles of similar triangles are congruent.

The true statement is (c) one pair of congruent corresponding angles is sufficient to determine similar triangles

From the complete question (see attachment), we have:

∠

�

�

�

≅

∠

�

�

�

∠NOP≅∠NML

This means that:

Angles NOP and NML are congruent

When the corresponding angles of similar triangles are congruent, then the triangles can be assumed to be similar.

Answer:

-14

Step-by-step explanation:

6(-7/3)=-42/3=-14

Option A: 6x^2+75x+200 is the correct answer

Step-by-step explanation:

The profit is obtained by subtracting the cost from the revenue.

Given

[tex]R(x) = 6x^2+100x+300\\C(x) = 25x+100[/tex]

The Profit function will be obtained by subtracting the cost function from the revenue function

So,

[tex]P(x) = R(x) - C(x)\\= (6x^2+100x+300)-(25x+100)\\=6x^2+100x+300-25x-100\\=6x^2+100x-25x+300-100\\P(x)=6x^2+75x+200[/tex]

Hence,

Option A: 6x^2+75x+200 is the correct answer

Keywords: Functions, function operations

Learn more about functions at:

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Answer:

The area of all faces of the cuboid is 94 square units

Step-by-step explanation:

Given:

Length = 5

Breadth = 4

Height = 3

To Find :

The area of all faces = ?

Solution:

The area of all the faces  =  surface area of the cuboid

The surface area of the cuboid  =  2(LB + BH + HL)

where

L is the length

B is the breadth

H is the height

Now substituting the values,

The surface area of the cuboid

=> [tex]2(5 \times 4 + 4\times 3 + 3\times 5)[/tex]

=> [tex]2(20 + 12+ 15)[/tex]

=> [tex]2(47)[/tex]

=>94 square units

Answer:

i think IV.

Step-by-step explanation:

Answer:

The cost of 5 gallons of fuel would be 5x assuming the cost of 1 gallon to be x.

Step-by-step explanation:

An old truck has a fuel efficiency rating of 12 mpg.

We have to find the cost of gasoline that will be used up after we drive 60 miles.

To drive 60 miles , it uses 5 gallons.

let the cost of 1 gallon of fuel be x.

We have to find the cost of 5 gallons of fuel.

So the cost of 5 gallons of fuel = 5[tex]\times coat of 1 gallon of fuel[/tex]

                                                      = 5x

[tex]\frac{105}{8}[/tex] inches of snowfall measured for entire month

Solution:

Given that first week she measured [tex]3\frac{3}{4}[/tex] inches of snow

Second week she measured twice as much snow, and the third week she measured half as much snow as the first week

It did not snow at all in the fourth week

To find: Amount of snowfall measured for entire month

First week:

[tex]\text{ first week } = 3\frac{3}{4} = \frca{4 \times 3 + 3}{4} = \frac{15}{4} inches[/tex]

Second week:

She measured twice as much snow as the first week

[tex]\text{ second week } = 2 \times \frac{15}{4} = \frac{15}{2} inches[/tex]

Third week:

The third week She measured half as much snow as the first week

[tex]\text{ third week } = \frac{1}{2} \times \frac{15}{4} = \frac{15}{8} inches[/tex]

Fourth week:

It did not snow at all in the fourth week

fourth week = 0

Total snowfall for entire month:

Total snowfall = first week + second week + third week + fourth week

[tex]\rightarrow \frac{15}{4} + \frac{15}{2} + \frac{15}{8} + 0\\\\\rightarrow 15(\frac{1}{4} + \frac{1}{2} + \frac{1}{8} )\\\\\rightarrow 15(\frac{2+4+1}{8})\\\\\rightarrow 15 \times \frac{7}{8} = \frac{105}{8}[/tex]

Therefore [tex]\frac{105}{8}[/tex] inches of snowfall measured for entire month

Inconsistent

Step-by-step explanation:

When you graph a system of equations then ;

They are consistent and independent, they have exactly one solution

If they are consistent and dependent, they have infinite number of solutions

If they there is no solution, the system is inconsistent

In this case, the lines are parallel, no intersecting for a solution.

Learn More

Consistent equations :https://brainly.com/question/548583

Keywords: equations, independent, consistent, dependent, inconsistent

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Answer:

inconsistent

Step-by-step explanation:

because they dont cross eachother

Answer:

Here's what I get.

Step-by-step explanation:

When you dilate an object by a scale factor, you multiply its coordinates by the same number.

If the scale factor is 4, the rule is (x, y) ⟶ (4x, 4y)

Your table then becomes

[tex]\begin{array}{lcl}\textbf{Vertices of}& \, & \textbf{Vertices of}\\\textbf{VWXY}& \, & \textbf{V'W'X'Y'}\\V(-1 ,1) & \quad & V'(-4, 4)\\W(-1, 2) & \quad & W'(-4, 8)\\X(2, -1) & \quad & X'(8 ,-4)\\Y(2, 2) & \quad & Y'(8, 8)\\\end{array}[/tex]

The diagram below shows figure VVXY as a green bow-tie and its image V'W'X'Y' in orange.

The scale factor is greater than one, so the dilation is an enlargement.

Answer:

Exact Form:

y  =  − 25 /8

Decimal Form:

y  = − 3.125

Answer:

1- false; 2- true; 3- true; 4-false

Final answer:

The statements about drawing a card higher than 6 and certain to draw an even or odd number are true. It's false that drawing a multiple of 3 is unlikely and that drawing a card less than 8 is unlikely.

Explanation:

The question involves determining the likelihood of drawing a specific card from a shuffled deck of 10 cards numbered 1-10. Let's assess each of the four statements provided.

Card greater than 6: There are 4 cards greater than 6 (7, 8, 9, 10), so the probability is 4 out of 10 or 0.4. This means it is likely, making the statement true.

Multiple of 3: There are 3 multiples of 3 (3, 6, 9), so the probability is 3 out of 10 or 0.3. This is less than half, but not very small, so the statement is subjective; however, we would not generally describe a 30% chance as 'unlikely', hence the statement might be considered false.

Even or odd number: Every card is either even or odd, so it is certain that an even or odd card will be drawn, making the statement true.

Number less than 8: There are 7 cards less than 8 (1 through 7), so the probability is 7 out of 10 or 0.7. This means it's more likely to draw a card less than 8, which means the statement is false.

Final Answer:

The area of the screen cleared  IS 9900/7 cm² or about 1414.29 cm².

Explanation:

The question asks about finding the area cleared by a windscreen wiper that sweeps out an angle of 180 degrees (or a semi-circle) with a length (or radius) of 30 cm. We can calculate the area cleared using the formula for the area of a circle, A = πr², but since the wiper covers only half the circle, we'll divide the result by 2.

Given the radius (r) is 30 cm, and using π as 22/7, we calculate the area as follows:

First, calculate the area of the full circle: A = πr² = (22/7) * (30)²

Then, since the wiper clears half the circle, we divide this result by 2.

Substituting the values:

A = (22/7) * 900 = 19800/7 cm²

Half of that area is 19800/7 / 2 = 9900/7 cm²

Therefore, the area of the screen cleared by the windscreen wiper is 9900/7 cm² which is approximately 1414.29 cm².

The area cleared by the windscreen wiper is approximately 86 square centimeters.

To find the area cleared by the windscreen wiper, we first need to determine the area of the sector formed by the angle cleared (108°) and then subtract the area of the triangle formed by the radius of the wiper (30 cm) and the two radii that define the angle cleared.

Given:

- Radius of the wiper,  r = 30  cm

- Angle cleared by the wiper, [tex]\( \theta = 108° \)[/tex]

- Value of π, [tex]\( \pi = \frac{22}{7} \)[/tex]

Let's break down the solution step by step:

1. Calculate the area of the sector:

  The formula to calculate the area of a sector of a circle is:

  [tex]\[ \text{Area of sector} = \frac{\theta}{360°} \times \pi r^2 \]\\[/tex]

  where [tex]\( \theta \)[/tex] is the angle in degrees,[tex]\( \pi \)[/tex] is the constant pi, and  r  is the radius of the circle.

  Substituting the given values:

 [tex]\[ \text{Area of sector} = \frac{108°}{360°} \times \frac{22}{7} \times (30)^2 \][/tex]

2. Calculate the area of the triangle:

  The area of a triangle can be calculated using Heron's formula, which states:

  [tex]\[ \text{Area of triangle} = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]

  where  s  is the semi-perimeter of the triangle, and  a ,  b , and  c  are the lengths of its sides.

  In this case, the sides of the triangle are all equal to the radius of the wiper,  r = 30  cm, so  a = b = c = 30  cm.

  The semi-perimeter  s  can be calculated as [tex]\( s = \frac{3r}{2} \).[/tex]

3. Subtract the area of the triangle from the area of the sector:

  [tex]\[ \text{Area cleared} = \text{Area of sector} - \text{Area of triangle} \][/tex]

Let's perform the calculations:

1. Calculate the area of the sector:

  [tex]\[ \text{Area of sector} = \frac{108}{360} \times \frac{22}{7} \times (30)^2 \][/tex]

  [tex]\[ = \frac{108}{360} \times \frac{22}{7} \times 900 \][/tex]

  [tex]\[ = \frac{108}{360} \times 286 \][/tex]

  [tex]\[ = 102 \text{ cm}^2 \][/tex]

2. Calculate the area of the triangle:

  [tex]\[ s = \frac{3r}{2} = \frac{3 \times 30}{2} = 45 \text{ cm} \][/tex]

  [tex]\[ \text{Area of triangle} = \sqrt{45(45 - 30)(45 - 30)(45 - 30)} \][/tex]

  [tex]\[ = \sqrt{45 \times 15 \times 15 \times 15} \][/tex]

  [tex]\[ = \sqrt{506250} \][/tex]

 [tex]\[ = 225 \text{ cm}^2 \][/tex]

3. Subtract the area of the triangle from the area of the sector:

  [tex]\[ \text{Area cleared} = 102 \text{ cm}^2 - 225 \text{ cm}^2 \][/tex]

  [tex]\[ = -123 \text{ cm}^2 \][/tex]

The negative value indicates that the area of the triangle is greater than the area of the sector. This suggests an error in calculation or reasoning. Let's recheck the calculations.

Upon reviewing, it seems there was a mistake in the calculation of the area of the triangle. We should not have taken the square root of the semi-perimeter. Instead, we should have used the correct Heron's formula without the square root. Let's correct this:

[tex]\[ \text{Area of triangle} = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]

[tex]\[ = \sqrt{45(45 - 30)(45 - 30)(45 - 30)} \][/tex]

[tex]\[ = \sqrt{45 \times 15 \times 15 \times 15} \][/tex]

[tex]\[ = 337.5 \text{ cm}^2 \][/tex]

Now, let's subtract the corrected area of the triangle from the area of the sector:

[tex]\[ \text{Area cleared} = 102 \text{ cm}^2 - 337.5 \text{ cm}^2 \][/tex]

[tex]\[ = -235.5 \text{ cm}^2 \][/tex]

It seems that there is an error in the calculation, as the area cannot be negative. Let's reassess the approach and correct any errors.

Upon reevaluation, it appears that we should not subtract the area of the triangle from the area of the sector, as the triangle represents the area covered by the wiper itself, not the area cleared on the windscreen. Instead, we should calculate the area of the sector and use it as the area cleared by the windscreen wiper.

Let's correct the approach and recalculate the area of the sector:

1. Calculate the area of the sector:

  [tex]\[ \text{Area of sector} = \frac{\theta}{360°} \times \pi r^2 \][/tex]

  [tex]\[ = \frac{108°}{360°} \times \frac{22}{7} \times (30)^2 \][/tex]

  [tex]\[ = \frac{108}{360} \times \frac{22}{7} \times 900 \][/tex]

  [tex]\[ = \frac{108}{360} \times 286 \][/tex]

  [tex]\[ = 86 \text{ cm}^2 \][/tex]

So, the corrected area cleared by the windscreen wiper is[tex]\( 86 \, \text{cm}^2 \).[/tex]

In summary, the area cleared by the windscreen wiper is [tex]\( 86 \, \text{cm}^2 \).[/tex]

The Correct Question is:

A windscreen wiper of a vehicle of length 30 cm clears out an angle of 108° as shown in the diagram below. What is the area of 6 the screen cleared? (Take π =22/7)?

Answer:

Explained.

Step-by-step explanation:

The graph of a line on the coordinate system represents the points that are on the graph that will satisfy the equation of the line.

Now, if two lines on the coordinate plane are graphed and they pass through the same point (h,k) that means the point satisfies both the equations of the lines.

Let us have two curve equations [tex]y = 2^{(- x)}[/tex] and [tex]y = 4^{x} + 3[/tex] and they pass through the same point (h,k) on the coordinate plane.

Then we can write [tex]k = 2^{(- h)}[/tex] ......... (1) and  

[tex]k = 4^{h} + 3[/tex] .......... (2)

Now, solving equations (1) and (2) we get

[tex]2^{(- h)} = 4^{h} + 3[/tex] ........... (3)

Therefore, we have to solve the above equation (3) to get the value of h i.e. the x-coordinate of the point/s where the graph of the equations (1) and (2) intersect.

Now, converting h to x we will get the same result. (Answer)

Answer:

y=-2x

Step-by-step explanation:

Parallel means same slope.

y-y1=m(x-x1)

y-(-8)=-2(x-4)

y+8=-2x+8

y=-2x+8-8

y=-2x

Answer: The maximum revenue is $7482 . To get a maximum yield , The number of trees per acre needed is 43.

Step-by-step explanation:

Solution:

Let x represent the extra tree

So for an additional tree the yield of each tree will decrease by 4 bushels.

(80 +x)(26-4x) by expanding

2080 - 320x +26x -4x^2

Using x= -b/2a

X= 294/ -8

X= - 36.75

So apparently he currently has far too many trees per acre. To get the maximum yield , she needs to reduce the number of trees per acre by 36.75

So the number of trees per acre for maximum yield is

80-36.75

=43.25

Approximately x=43

So by reducing he get extra bushel in the tune of 174.

Total revenue= 174 ×43× 1$

=$7482

Answer:

11:55

Step-by-step explanation:

Answer:

-1/2.

Step-by-step explanation:

( - 3 + 2) / 2

= -1 / 2.

The midpoint of a line segment with endpoints -3 and 2 is -0.5. This is calculated by adding the endpoints and dividing by 2.

The midpoint of a line segment is the average of its endpoints. We can find it by adding the two endpoints and dividing by 2. So, for the line segment with endpoints -3 and 2, we would calculate

(-3 + 2) / 2

The answer to this calculation is -0.5. Therefore, the midpoint of the line segment with endpoints -3 and 2 is -0.5.

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Answer:

Use a spreadsheet.

Step-by-step explanation:

If you mean a household budget you could use a spreadsheet.

The columns would be  months and the rows would be  items of expenditure and income.

You use  formulae ( provided by the spreadsheet)  to  do additions, subtractions and so on.

Answer:

91.6

Step-by-step explanation:

Answer:91.6

Step-by-step explanation:

Answer:

32 meters

Step-by-step explanation:

we know that

The scale is [tex]\frac{2}{16} \ \frac{cm}{m}[/tex]

That means ----> 2 cm on a map represent 16 m in the actual

so

using proportion

Find out the distance between union and sun valley if they are 4 cm apart on a map

[tex]\frac{2}{16} \ \frac{cm}{m}=\frac{4}{x} \ \frac{cm}{m}\\\\x=16(4)/2\\\\x=32\ m[/tex]