Use the diagram to answer the question.
Which of the following statements is true?
lines and line t Intersect
O lines and line t Intersect at Point P
Point Pis on linet and on lines
all of the above are true

A) Here, We'll use "Pythagoras Theorem" which tells:

a² + b² = c²

So, PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

In short, Your Answer would be 16.64 Feet

B) Again, Use the Pythagoras Theorem,  

c² - a² = b²

18² - 14² = b²

b² = 324 - 196

b = √128

b = 11.31

In short, Your Answer would be 11.31 Feet

Part A: Using the Pythagorean Theorem. a^2 + b^2 = c^2

PQ^2 + QR^2 = PR^2  (The rods make a right triangle, where PR would be the hypotenuse, and QR and PQ would be legs a and b.)

14^2 + 9^2 = PR^2

196 + 81 = PR^2

Square root of 277 = PR 

16.64 = PR

So, the hypotenuse would be equal to 16.64 ft.

Part B: Using the Pythagorean Theorem. a^2 + b^2 = c^2

PR^2 - PQ^2 = QR^2 (Trying to find the height of QR this time, not the hypotenuse, since we know what it is already. Subtracting the value of leg a from the hypotenuse will give us the value of leg b, QR.)

18^2 - 14^2 = QR^2

324 - 196 = QR^2

Square root of 128 = QR

So, the new height of QR would be 11.31 ft.

Answer:

cot α = 1/tan α = 1/2.4 = 0.42

Step-by-step explanation:

cot α=0.42

sin α = 0.92

we know that  cot α = 1/tan α

thus,

cot α = 1/tan α = 1/2.4 = 0.42

we know that

sin(x)=tan(x)1+tan2(x)√

[tex]\ sin(\alpha )=tan(\alpha )/\sqrt{ 1+tan^2(\alpha )} \\sin(\alpha )= 2.4/\sqrt{1+2.4^2} = 2.4/\sqrt{1+5.76}\\sin(\alpha )= 2.4/\sqrt{6.76} = 2.4/2.6 = 12/13 = 0.92[/tex]

sin α = 0.92

Answer:

(a) 40

(b) 15% per week, to the nearest percent.

Step-by-step explanation:

Given:

old production,

P(w) = 230(1.1^w)

(a) At week 0, w=0, so

P(0) = 230(1.1^0) = 230

Difference (old - new) = 230-190 = 40

(b) about 15% per week

(c) from the 4th week on

approximate growth rate of new factory

N(w) = 190(R^w)

we know

w=0, N(0) = 190

w=7, N(7) = 505

so R=(505/190)^(1/7) = 1.1499 = 1.15 approx.

(c)

The old production tabulated:

w P(w) New

0 230 190

1 253 220

2 278 252

3 306 290

4 337 337

5 370 380

6 407 440

7 448 505

So we see that at the end of the 4th week, the two productions match, and new factory begins to exceed old production.

Answer:

slope - (2x)

y-intercept - (-1)

Step-by-step explanation:

-8x + 4y = - 4

4y = 8x - 4

y = 2x - 1

Answer:

Step-by-step explanation:

[tex](5^{-2}[/tex] × [tex]4^{-4}[/tex] [tex])^{-2}[/tex]

=[tex](5^{-2}[/tex][tex])^{-2}[/tex] x [tex](4^{-4})^{-2}[/tex]                            ∴[tex](a.b)^{n} =a^{n} .b^{n}[/tex]

=[tex]5^{-2.-2}[/tex] x [tex]4^{-4 . -2}[/tex]                              ∴[tex](a^{n} )^{m}[/tex] = [tex]a^{nm}[/tex] // here m is an exponent of [tex]a^{n}[/tex].

=[tex]5^{4}[/tex] x [tex]4^{8}[/tex]

Answer:

30-100/1000*120

Step-by-step explanation:

Source: Khan Academy

Answer:

30 - 100/1000 x 120

Step-by-step explanation:

Answer:

The answer is A f(x) = -2x + 40

Step-by-step explanation:

it has a negative 2 because the dumps are decreasing by 2 every week and x is the amount of weeks and + 40 because that is the amount you started with.

Answer:

x - y - 2 ≥ 0

Step-by-step explanation:

Answer:

4x - 6y -3

Step-by-step explanation:

4x−2(3y)−3

Distribute

4x - 6y -3

Answer:

4x−6y−3

Step-by-step explanation:

All you really have to do is multiply -2 time 3y and  thats it.

Answer:

  37.5 mi/h

Step-by-step explanation:

  time = distance / speed

On the trip 'going', the time was (150 mi)/(50 mi/h) = 3 h.

On the return trip, the time was (150 mi)/(30 mi/h) = 5 h.

__

  speed = distance / time

The average speed for the whole trip was ...

  speed = (150 mi +150 mi)/(3 h +5 h) = (300 mi)/(8 h) = 37.5 mi/h

His average rate of speed was 37.5 miles per hour.

Step-by-step explanation:

x+3/x-2-1-x/x=17/4find the LCM of the denominators (x-2)x=x^2-2x

(x^2-2x)4=4x^2-8x divide the denominator by the LCM and then multiply x to the numerator

(x+3)4=4×+3

(1-x)(4x-8)

1(4x-8)-x(4x-8)

4x-8-4x^2-8x=4x

Answer:

15

Step-by-step explanation:

half of 30 is 15

he used all the numbers upto 30 once

all the numbers in between arent integers but decimals

Answer:

Distance D = √ [(2 - x)^2 + (3 - 4x^3)^2].

Step-by-step explanation:

Use the distance formula:

D = √[(x2 - x1)^2 + (y2 - y1)^2].

So here it is

D = √[(2 - x)^2 + (4 - y)^2]    where x,y is any point on the curve.

D = √[2 - x)^2 + (4 - (4x^3 + 1))^2]

D = √ [(2 - x)^2 + (3 - 4x^3)^2]

Answer:

1) one and two-thirds hour

2) 2.4 miles

Answer:

not a term

Step-by-step explanation:

There is a common difference between consecutive terms in the sequence, that is

d = 11- 5 = 17 - 11 = 23 - 17 = 6

This indicate the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 5 and d = 6, thus

[tex]a_{n}[/tex] = 5 + 6(n - 1) = 5 + 6n - 6 = 6n - 1

Equate this to 301 and solve for n

6n - 1 = 301 ( add 1 to both sides )

6n = 302 ( divide both sides by 6 )

n = 50.333....

Since n is not an integer value then 301 is not a term in this sequence.

Answer:

4.331507 x 10⁶

Step-by-step explanation:

you move the decimal place 6 times to the right, so 10⁶

Answer:

Step-by-step explanation:

4,331,507=4.331507×10^6

Answer:

D

Step-by-step explanation:

Just did it

A function assigns the values. The equation that represents the function shown on the graph is y=4x.

A function assigns the value of each element of one set to the other specific element of another set.

Given that the graph represents revenue in dollars as a function of greeting cards sold. Therefore, we can write the function as,

Revenue ∝ Number of cards sold

Since the Number of Cards Sold on the x-axis and Revenue in dollars on the y-axis. Therefore, we can write,

y ∝ x

Removing the proportionality, we will get,

y = k x

Now, substitute any point through which the graph of the function passes to get the value of k,

20 = k × 5

20/5 = k

k = 4

Thus, the function can be represented as,

y = kx

y = 4x

Hence, the equation that represents the function shown on the graph is y=4x.

Learn more about Function here:

https://brainly.com/question/5245372

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Answer:

C

Step-by-step explanation:

They all have and addition and subtraction pattern in each cube, thank me later - PrObLeM OcCuReD

Answer:

The answer is none.

Step-by-step explanation:

Hope this helps....

Have a nice day!!!!

Answer: 4

Step-by-step explanation:

Answer:

Part A: The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' is 1/4

Part B:

P''(-1, 0)

Q''(0, -1)

R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are not congruent

Step-by-step explanation:

The coordinates of triangle PQR are;

P(4, 0)

Q(0, 4)

R(-8, -4)

The coordinates of triangle P'Q'R' are;

P'(1, 0)

Q'(0, -1)

R'(-2, -1)

Part A:

The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' can be found from the ratio of the respective coordinates as follows;

The ratio of the x, and y coordinates of the points are;

P'/P  = x'/x = 1/4, y'/y =0/0

R'/R = x'/x = -2/-8 = 1/4, y'/y =-1/-4 = 1/4

Therefore, the scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R' = 1/4

Part B: For reflection across the y-axis, we have;

Pre-image (x, y) becomes the image, (-x, y)

Therefore, we have;

Reflection of P'(1, 0) about the y-xis becomes P''(-1, 0)

Reflection of Q'(0, -1) about the y-xis becomes Q''(0, -1)

Reflection of R'(-2, -1) about the y-xis becomes R''(2, -1)

Part C:

The two Triangles PQR and P''Q''R'' are similar but they are not congruent as the dimensions of PQR are larger than the dimensions of the sides of triangle P''Q''R''.

(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/4

(B) Coordinates of Δ P"Q"R"

P" (-1,0)

Q"(0,-1)

R"(2,-1)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (4,0),

Q(0,-4)

R(-8,-4)

Coordinates of P'Q'R' are

P'(1,0)

Q'(0,-1)

R'(-2,-1)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula = [tex]D= \sqrt{(X_2-X_1)^2+(Y_2-Y_1)^2 }[/tex]

Where D = Distance between two points [tex](X_1.Y_1) \; and\; (X_2.Y_2)[/tex]

from distance formula we can write that

[tex]PQ = \sqrt{(0-4)^2+ (-4-0)^2} }\\[/tex]

PQ = [tex]4\sqrt{2}[/tex]

Similarly

P'Q'= [tex]\sqrt{2}[/tex]

PQ /P'Q' = 4

hence the scale factor of dilation is 1/4 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

[tex](x,y ) \; as \; (-x,y)[/tex]

So the Coordinated of Δ P"Q"R" can be written as

P" (-1,0)

Q"(0,-1)

R"(2,-1)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

For more information please refer to the link below

https://brainly.com/question/12413243

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▹ Answer

You can use a graphing calculator.

▹ Step-by-Step Explanation

Attached is a screenshot.

Hope this helps!

CloutAnswers ❁

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Answer:

See explanation and picture attached

Step-by-step explanation:

We can break down this expression into it's core components:

Since the constant here is -4, the y intercept is -4.

Since the value we are multiplying x by is [tex]\frac{2}{3}[/tex], the slope is  [tex]\frac{2}{3}[/tex]. This means for every time we go horizontal 3 units, the line increases by 2.

The graph is attached.

Hope this helped!

Answer:

Yes, you are correct.

Step-by-step explanation:

You are substituting the measure of angle x as the measure of angle a since they are congruent to each other.

Answer:

Times

first part   x  =  1,33 h       second part  y =  0,66 h

distances  d₁ (first part ) d₁ = 4 miles    d₂  (second part )  d₂ = 0,999 miles

Step-by-step explanation: IMPORTANT NOTE: EVEN PROBLEM STATEMENT DID NOT ASK ANY QUESTION WE WILL ASSUME QUESTION ARE: LENGTH ( IN MILES ) AND SPENT TIME  OF EACH PART OF THE HIKE

We formulate a two-equation system according to:

x = time for the first part

y = time for the second part

then      x  +  y  =  2           or      y = 2 - x

And 3 m/h * x(h)   +  1,5 m/h * y (h)  = 5

3*x  +  1,5*y  = 5

3*x + 1,5 * ( 2 - x )  = 5

3*x  + 3  - 1,5*x  =  5

1,5*x  = 2

x  = 2/1,5 (h)

x = 1,33 (h)

And  y  =  2 -  1,33       y  =  0,66 (h)

Distances are

first part  d₁ = 3*1,33          d₁ =  4 miles

second part  d₂ = 1,5*0,66        d₂  = 0,999 miles

Answer:

3x +10y  is greater than or equal to 250.

Step-by-step explanation:

The question asks us to write an inequality which shows that both nylon and canvas added should be greater than or equal to 250.

Since we don't know the number of nylon backpacks and canvas backpacks the company makes, we used the variables "x" and "y" to represent the number of backpacks they made from each style.

Answer:

3n + 10c > 250

Step-by-step explanation:

I confirmed it in grandpoint

Answer:

35 cm squared

Step-by-step explanation:

Triangle area = bxh 2 = 5.75 x 8 / 2 = 23

Trapezium Area  = a+b /2 x h = 8 + 4 /2 x 2 = 12

23 + 12 = 35

Hope that helped!!! k

0.75x+0.8(x + 10) = 101

Answer:

0.75x+0.8(x+10)=101

Step-by-step explanation:

Jared attempted x shots and made 75% of them, or 0.75x. Zach attempted 10 more shots than Jared did, which is represented as x + 10. He made 80% of them, or 0.8(x + 10). Together, they made 101 shots. So, add the two expressions and set the sum equal to 101:

0.75x + 0.8(x + 10) = 101.

Answer: [tex]x=-3/4[/tex]

Subtract 36x from both sides

[tex]20x-2-36x=36x+10-36x\\-16x-2=10[/tex]

Add 2 to both sides

[tex]-16x-2+2=10+2\\-16x=12[/tex]

Divide both sides by -16

[tex]\frac{-16x}{16} =\frac{12}{-16} \\x=\frac{-3}{4}[/tex]

Answer:

x = - [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given

20x - 2 = 36x + 10 ( subtract 36x from both sides )

- 16x - 2 = 10 ( add 2 to both sides )

- 16x = 12 ( divide both sides by - 16 )

x = [tex]\frac{12}{-16}[/tex] = - [tex]\frac{3}{4}[/tex]

As a check

Substitute this value into the equation and if both sides are equal then it is the solution.

left side = 20 × - [tex]\frac{3}{4}[/tex] - 2 = - 15 - 2 = - 17

right side = 36 × - [tex]\frac{3}{4}[/tex] + 10 = - 27 + 10 = - x17

Since both sides are equal then x = - [tex]\frac{3}{4}[/tex] is the solution

Answer:

i.1832 ii.-56

Step-by-step explanation:

using BODMAS for the first question we solve for what's in the bracket after we go with the division and after multiplication next addition and subtract in doing all that we get

35+25*72-51/17

35+25*72-3

35+1800-3

1835-3

1832

you can also use your calculator to verify answer

ii.-6*9+7-4-5

-54+7-4-5

-47-4-5

-56

Answer:

1,120

Step-by-step explanation:

Find the volume of the larger figure. This can be represented using the formula for volume.

V = lwh

V = 5*18*18

V = 1620

Now, find the volume of the cut out piece of the wood. We will subtract this from the larger block.

V  = lwh

V = 5*10*10

V = 500

Subtract, and you will have your answer.

1620 - 500 = 1,120