Phillip wants to find the width, QP, of his driveway. He walks along the edge of the driveway 45 ft and
marks point R. Then he walks 13 ft further and marks point N. He turns 90° and walks until his location,
point R, and point P are collinear. He marks point M at this location, as shown.
(a) Can Phillip conclude that ΔPQR and ΔMNR are similar? Why or why not?
(b) Suppose MN = 15 ft. Calculate the width of the driveway, QP. Show all your work and round
answer to nearest tenth.

1. 13 cm

2. 27.2 in

3.24x

4. 7 m

radius is half of the diameter

diameter is twice of the radius so

radius=diameter/2,diameter =2x radius

Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

answer

a. 5,8

explanation

use numbers in each answer choice

+5 * -8 = - 40

+5 -8 = -3

Consider the form [tex]x^2+bx+c[/tex]. Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]b[/tex]. In this case, whose product is -40 and whose sum is -3.

[tex]\longrightarrow\boxed{\bold{(-8,5)}}[/tex]

Write the factored form using these integers.

[tex](x-8) \ (x+5)[/tex]

Answer:

A

Step-by-step explanation:

(x+5)(x-1)－(x+1)(x-4)=7x-1

Answer: The slope is -5/4

m=-5/4

Step-by-step explanation:

45 minutes is 3/4 of an hour.

how often does 3/4 fit into 3 ?

3 / 3/4 = 3/1 / 3/4 = (3×4)/(1×3) = 4

so, it will be rung 4 times.

Answer: 4 times.

Step-by-step explanation:

We can divide 3 hours by 45 minutes, to get the number of times the bell will ring in 3 hours:

3 hours ÷ 45 minutes = 4

Therefore, the bell will be rung 4 times in 3 hours.

We can also think of it like this: 3 hours is 180 minutes, and the bell rings every 45 minutes.

So, we can divide 180 by 45 to get the number of times the bell will ring:

180 minutes ÷ 45 minutes = 4

Therefore, the bell will be rung 4 times in 3 hours.

The volume of the prism will be 88 cubic units. Then the correct option is B.

Given that:

Length, L = 4 units

Width, W = 4 units

Height, H = 5.5 units

The volume of the prism is given as,

V = L x W x H

The volume of the prism is calculated as,

V = 4 x 4 x 5.5

V = 88 cubic units

The volume of the prism will be 88 cubic units. Then the correct option is B.

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The complete question is given below.

The perimeter of the regular nonagon will be; 840.7 units

The in-radius of the regular nonagon is given as:

Radius, r =17

The perimeter is then calculated by:

P = 18r/Tan(π/9)

Substitute 17 for r;

P = 18(17)/Tan(π/9)

Evaluate the product of 18 and 17;

P =  306/Tan(π/9)

Evaluate the quotient

P =  840.7

Hence, the perimeter of the regular nonagon = 840.7 units

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The equation for the relationship between the number of bracelets made and the number of beads is y = 21x.

First, the rate of change

= (483 - 210) / (23 - 10)

= 273 / 13

= 21

So, the equation for the relationship between the number of bracelets made and the number of beads used.

(y - 210) = 21 (x-  10)

y - 210 = 21x - 210

y = 21x

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Answer: Answer choice C: -1.3 and 1.3.

Step-by-step explanation:

We can start by using the formula for the distance, D, between the two trains as a function of time, T:

D = 55(T + 2.25) - 120T

Simplifying this equation, we get:

D = 55T + 123.75 - 120T

D = -65T + 123.75

To find the two values of T for which D = 40, we can set this equation equal to 40 and solve for T:

40 = -65T + 123.75

-85 = -65T

T = 1.31

Plugging this value back into the original equation, we can see that D is equal to 40:

D = -65(1.31) + 123.75

D = 40.0375

Therefore, one solution is T = 1.31. To find the other solution, we can plug D = 40 into the equation and solve for T:

40 = -65T + 123.75

-83.75 = -65T

T = 1.29

Plugging this value back into the original equation, we can see that D is equal to 40:

D = -65(1.29) + 123.75

D = 40.0375

Therefore, the two values of T for which D = 40 are approximately 1.3 and 1.3, which rounds to answer choice C: -1.3 and 1.3.

Answer:2.7

Step-by-step explanation:

Formula, divide the value in centimeters by 100 so 1 meter equals 100 centimeters

So 270 centimeters = 270/100 = 2.7

The money Brooke initially invest is  $1.21.

Using the formula for compound interest formula:

A = P(1 + r/n)^(nt)

where:

A = final amount after t years

P = initial investment

r = annual interest rate

n = number of times interest is compounded per year

t = number of years

Substituting the given values:

1.47 = P(1 + 0.10/1)^(1*2)

1.47 = P(1.10)^2

1.47 = P(1.21)

P = 1.47/1.21

P = 1.2148...

Rounding to the nearest cent, Brooke initially invested $1.21.

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answer:

15

step-by-step explanation:

-4x - 6y = 8

+ (6x + 5y = 7)

__________

2x - y = 15

The values of AB and BC are equal and equal to

Information given in the problem includes

DE bisects AC at point B

AC = a + 23

AB = 3a + 4

From  the definition of a bisector, point B divides AC into two equal sides, this means that

AB = BC = (1/2) * AC

Substituting the value of AC and AB

AB = 3a + 4 = (1/2) * (a + 23)

3a + 4 = (1/2) * (a + 23)

solving for a

2 * (3a + 4) = a + 23

6a + 8 = a + 23

6a - a  = 23 - 8

5a = 15

a = 3

Then we have that:

AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13

and, AB = BC

so BC = 13

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A point that represent a striking deviation in the box plot above include the following: C. P.

In Mathematics and Statistics, a box plot can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

In conclusion, we can logically deduce that point P represent a striking deviation in the box plot because it is an outlier (it is significantly far from all of the other data points).

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The three different values of n to demonstrate that 2n + 3n is equivalent to 5n are 1, 4 and 10.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2n + 3n

On simplifying the equation , we get

A = 5n

when n = 1 , we get

2n + 3n = 2(1) + 3(1) = 2 + 3 = 5

5n = 5(1) = 5

Therefore, both expressions give the same result of 5.

when n = 4 , we get

2n + 3n = 2(4) + 3(4) = 8 + 12 = 20

5n = 5(4) = 20

Again, both expressions give the same result of 20.

when n = 10 , we get

2n + 3n = 2(10) + 3(10) = 20 + 30 = 50

5n = 5(10) = 50

Hence , the equation is solved

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The level of significance based on the information will be:

a. F = 4.11, with 3 df between and 30 df within - < 0.05

b. F = 1.12, with 5 df between and 83 df within - > 0.05

c. F = 2.28, with 4 df between and 42 df within - > 0.05

The likelihood of rejecting the null hypothesis when it is true, or the alpha level, is used in statistical tests to evaluate statistical significance.

The significance level, or alpha, for this example is set at 0.05 (5%). This was accurately illustrated above

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Answer:

C. (4, 0)

Step-by-step explanation:

(x, y)

a. (4, 3)

y = 12 - 3x

3 = 12 - 3(4)

3 = 12 - 12

3 = 0  false

b. (-4, 4)

y = 12 - 3x

4 = 12 - 3(-4)

4 = 12 + 12

4 = 24  false

c. (4, 0)

y = 12 - 3x

0 = 12 - 3(4)

0 = 12 - 12

0 = 0  true

d. (0, 4)

y = 12 - 3x

4 = 12 - 3(0)

4 = 12 - 0

4 = 12  false.

Answer:   C   (4, 0)

Step-by-step explanation:

your function y = 12 - 3x

They are asking which of those points are on the line

(x, y)   this is a format of a point where you can plug in x for x and y for y.

a.  (4, 3)  x=4  y=3  substitute and see if your answer is true

   3 = 12 -3(4)

   3 = 0   this is not true so (4, 3) is not a solution

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

  4 = 12 - 3(-4)

  4 = 24  not true

c.  (4, 0)  x=4  y=0

  0 = 12-3(4)

  0 = 0  true      (4,0) is a solution

d. (0, 4)

4 =  12 - 3 (0)

4=12

Applying the leg rule, the length of BC in simplest radical form is: x = x = √390

The leg rule is used to find missing lengths in a right triangle when an altitude intersects the hypotenuse and form segments.

The leg rule is given as:

Hypotenuse / leg = leg / part

Thus, using the image given, we have:

Hypotenuse (AC) = 65

Part (DC) = 6

Leg = x

Plug in the values:

65 / x = x / 6

Cross multiply:

x * x = 6 * 65

x² = 390

x = √390

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If each tile cost $2 then the amount spend by  Nicole’s mother on tiles is $130

Given that Nicole‘s mother put tiles on a section of the kitchen floor.

The section included 5 rows with 13 tiles in each row

Each tile cost $2.

To find the total amount spend by Nicolas mother on tiles we have to find the number of tiles

Number of tiles =5×13

=65 tiles

Now let us find the amount

Total amount on tiles = 2×65

=$130

Hence, if each tile cost $2 then the amount spend by  Nicole’s mother on tiles is $130

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The surface area of the triangular prism is 191 cm².

The surface area (SA) of a triangular prism is given by the formula:

SA = 2A + Ph

where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.

First, we need to find the area of the triangular base.

Using the formula for the area of a triangle:

A = (1/2)bh = (1/2)(5 cm)(4 cm) = 10 square centimeter

Next, we need to find the perimeter of the base:

P = 5 cm + 6 cm + 8 cm = 19 cm

Now we can use the formula for the surface area of a triangular prism:

SA = 2A + Ph

= 2(10 cm²) + (19 cm)(9 cm)

= 20 cm²+ 171 cm²

= 191 cm²

Therefore, the surface area of the triangular prism is 191 cm².

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Step-by-step explanation:

( 11 * x ) + 2     where 'x' is a number

The amount of flour that will be needed for 38 cakes is 912 grams therefore Johan does not have enough amount of flour

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

360 grams is needed for 15 small cakes

therefore for 1 small cake, 369/15 = 24grams will be needed

therefore for 38 small cakes = 38× 24 = 912 grams of flour will be needed.

Johan has 0.85 kg of flours which is equivalent to 0.85 × 1000grams = 850 grams of flour.

Since 912 grams will be needed for 38 small cakes , it shows that Johan does not have enough amount of flour for 38 small cakes.

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The account will be worth approximately $13,268.58 in 20 years if it is opened with an initial deposit of $6,500 and earns 3.6% interest compounded semi-annually.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Principal P = $6,500

Compounded semi-annually n = 2

Time t = 20 years

Interest rate r = 3.6%

Accrued amount A = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 3.6/100

r = 0.036

Plug in the given values into the above formula.

A = P( 1 + r/n )^( n × t )

A = $6,500( 1 + 0.036/2 )^( 2 × 20 )

A = $6,500( 1 + 0.036/2 )^( 40 )

A = $6,500( 1 + 0.018 )^( 40 )

A = $13,268.58

Therefore, the accrued amount in 20 years is $13,268.58.

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Answer:

The answer would be 3.5 in decimal form.

Answer:

The answer is 55/12

Step-by-step explanation:

8-41/12

(8×12+1×(-41))/12

(96-41)/12

55/12

The total number of meals received by the company this month = 40 meals

Given data ,

Let the number of meals received by the company this month be A

Now , the proportion is given as

The number of boxes of meals in the past month = 3 boxes

The number of meals in 3 boxes = 15 meals

The number of boxes in the present month = 8 boxes

So , the proportion is

15 / 3  = A / 8

Multiply by 8 on both sides , we get

A = 5 x 8

A = 40 meals

Hence , the number of meals is A = 40 meals

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The different committees possible are 10,584. Option A is the answer.

Тhe number оf wаys tо choosе 4 men out оf 9 is givеn by 9C4, which is:

9C4 = (9!)/(4!5!)

= 126

Similаrly, the number оf wаys tо choosе 6 wоmen out оf 9 is givеn by 9С6, which is:

9С6 = (9!)/(6!3!)

= 84

So the tоtal number оf wаys tо choosе a committее consisting оf 4 men and 6 wоmen is:

126 * 84 = 10,584

Тherefore, the аnswer is (А) 10,584.

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Answer: im pretty sure the answer is in the pdf, when you scroll down. its 126 cm^2

Step-by-step explanation:

The simplified form of trigonometric functions by trigonometric formulas are listed below:

Case 1: 0.5√(2 - √3)

Case 2: (0.5√2) / (1 + 0.5√2)

Case 3: sin 6x

Case 4: sin θ

In this problem we must simplify and evaluate trigonometric functions by means of trigonometric formulas. The first two expressions must be simplified and evaluated by of half angle formulas:

Case 1

sin 15° = √[(1 - cos 30°) / 2]

sin 15° = √[(1 - √3 / 2) / 2]

sin 15° = √[(2 - √3) / 4]

sin 15° = 0.5√(2 - √3)

Case 2

tan 22.5° = sin 45° / (1 + cos 45°)

tan 22.5° = (0.5√2) / (1 + 0.5√2)

The last two expressions are simplified and evaluated by double angle formulas:

Case 3

2 · sin 3x · cos 3x

sin 6x

Case 4

2 · sin 0.5θ · cos 0.5θ

sin θ

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