Part A - determine the slope of Line MN.

Part B - determine the length of line MN.

​

Answer:

here is your answer

Step-by-step explanation:

cross multiplication

divide

[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]

Speed of Carmen = 40km/h

and speed of Carmella = 60km/h

Step-by-step explanation:

Let the speed of Carmen = x km/h

Carmella speed will be (x + 20)km/h

Distance = 120 km

Time between Carmen and Carmella = 1 hour

[tex] \sf Time= \frac{distance}{speed} [/tex]

Let the time taken by Carmen be T1

and Carmella be T2

[tex] \sf So \: T_1 = \frac{120}{x} \: and \: T_2 = \frac{120}{x + 20} [/tex]

As there is 1 hour difference so

[tex] \sf T_2 - T_1 = \: 1 hour \\ \\ \\ \sf \implies \frac{120}{x } - \frac{120}{x + 20} = 1 \\ \\ \\ \sf \implies \frac{120(x + 20) - 120x}{x(x + 20)} = 1 \\ \\ \\ \sf \implies 120x + 2400 - 120x = {x}^{2} + 20x \\ \\ \\ \sf \implies 2400 = {x}^{2} + 20x \\ \\ \\ \sf \implies 0 = {x}^{2} + 20x - 2400 \\ \\ \\ \sf \implies 0 = {x}^{2} + 60x - 40x - 2400 \\ \\ \\ \sf \implies0 = x(x + 60) - 40(x + 60) \\ \\ \\ \sf \implies 0 = (x + 60)(x - 40) \\ \\ \\ \sf \implies \red{\boxed{x = 40km}}[/tex]

We have not considered 60 as it will become negative value and negative value is not possible in distance

Speed of Carmen = 40km/h

Speed of Carmella = 40 + 20 = 60km/h

we know the angle is between 90° and 180°, 90° < θ < 180°, that means the angle is in the II Quadrant, where the sine is positive and the cosine is negative, with that info, let's find check a few things

[tex]sin(\theta )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2 - 3^2}=a\implies \pm\sqrt{16}=a\implies \pm 4 = a\implies \stackrel{II~Quadrant}{-4=a} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{-4}}{\underset{hypotenuse}{5}} \\\\\\ tan\left(\cfrac{\theta}{2}\right)\implies \cfrac{sin(\theta)}{1+cos(\theta)}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{1-\frac{4}{5}}\implies \cfrac{ ~~ \frac{3}{5} ~~ }{\frac{1}{5}}\implies \cfrac{3}{5}\cdot \cfrac{5}{1}\implies 3[/tex]

Answer: x^2  i think

Step-by-step explanation: "be the roots m = 2, n = 3 Sum of the roots = m + n = 2 + 3 m + n = 5 Product of the roots = mn = (2)(3) mn = 6 Standard form is x^2 - (m + n)"

These same things are present

So

Answer:

[tex]\sf \overline{PQ}=12[/tex]

[tex]\sf \overline{UV}=10[/tex]

[tex]\sf \overline{TV}=7[/tex]

[tex]\sf m \angle T=45^{\circ}[/tex]

[tex]\sf m \angle R=75^{\circ}[/tex]

[tex]\sf m \angle Q=60^{\circ}[/tex]

[tex]\sf m \angle U=60^{\circ}[/tex]

Step-by-step explanation:

≅ sign means that the triangles are congruent, which means they both have the same shape and the same size.

When comparing congruent shapes, inspect the order in which the vertices are given in the statement.

Therefore, if ΔPQR ≅ ΔTUV then:

Similarly:

Therefore, from inspection of the triangles:

[tex]\sf \overline{PQ} \cong \overline{TU}=12[/tex]

[tex]\sf \overline{UV} \cong \overline{QR}=10[/tex]

[tex]\sf \overline{TV} \cong \overline{PR}=7[/tex]

[tex]\sf m \angle T \cong m \angle P=45^{\circ}[/tex]

[tex]\sf m \angle R \cong m \angle V = 75^{\circ}[/tex]

The sum of the interior angles of a triangle is 180°, therefore:

[tex]\sf m \angle Q \cong m \angle U=180^{\circ}-45^{\circ}-75^{\circ}=60^{\circ}[/tex]

Answer:

3.5 m/hr  

Step-by-step explanation:

2 + c   =   5 -c           c = speed of current

2 c = 3      c = current speed = 1.5 m/hr

                         your speed =   5 - 1.5    (or  2 + 1.5)  =  3.5 m/hr

Here's the link to the answer:

https://riverside.rocks/index.php

Answer:

a pendulum consists of a mass hanging at the end of a string which is 18 cm long. find the vertical height through which the mass rises and falls as the pendulum swings through 30°on each side of the vertical.

Answer:

1. P = IRT

T = P/IR

2. A = 2(L + W)

L + W = A/2

W = A/2 - L

3. y = 5x - 6

x = (y +6)/5

4. 2x - 3y = 8

y = (2x - 8)/3

5. (x+y)/3 = 5

x = 5×3 - y

x = 15 - y

6. y = mx + b

b = y - mx

7. ax + by = c

by = c - ax

y = (c - ax)/b

Hope it helps!

Answer:

[tex]32\sqrt{7}-24\sqrt{2}[/tex]

Step-by-step explanation:

[tex]8(4\sqrt{7}-\sqrt{18})\\\\8(4\sqrt{7}-3\sqrt{2})\\\\32\sqrt{7}-24\sqrt{2}[/tex]

Answer:

Area = 28 cm^2

Step-by-step explanation:

Triangle Area = 1/2 * 5 * 4 = 10 cm^2

Big Rectangle = 4 * 3 = 12 cm^2

Small Rectangle = 4 * 1.5 = 6 cm^2

Total Area = 10 + 12 + 6 = 28 cm^2

Answer:

Step-by-step explanation:

Discussion

Area of the Triangle

3 4 5 is the first triangle most people encounter when they begin their study of the Pythagorean Theorem. You can show this to be true by trying it.

c = 5

b = 3

a = 4

c^2 = a^2 + b^2           Equation  Substitute values

c^2 = 3^2 + 4^2           Expand

c^2 = 9 + 16                 Combine

c^2 = 25                       Take the square root of both sides.

√c^2 = √25

c = 5                     Which is exactly what you are given.

A right triangle has the property of Area = 1/2 * a * b using the values given above.

Find the area of the triangle

Area = 1/2 a * b                          

Area = 1/2 3 * 4                                                    

Area =                                                               6

Find the area of the rectangle

L = 3 + 1.5 =4.5                        Just add the two parts of the vertical line together.

w = 8 - 4 = 4

Area of the rectangle = L * w   Substitute values

Area of the rectangle = 4.5 * 4

Area of the rectangle =                                18         Add

Total area                                                      24

Answer

24 cm^2

Answer:

[tex]144^{90}[/tex]

Step-by-step explanation:

sqrt (144^180)   =    (144^180 )^1/2  = 144^90

Answer:

Median = 19

IQR = 11

Third quartile = 25

Step-by-step explanation:

Just caculate it...

Answer:  0.3 feet

Work Shown:

(1 ft)/(150 ft) = (x ft)/(40 ft)

1/150 = x/40

1*40 = 150*x

40 = 150x

x = 40/150

x = 4/15

x = 0.2667 approximately

x = 0.3

Note: 0.3 ft = 0.3*12 = 3.6 inches

Answer:

1. 1119.982

2. 315.266

3. 297.866

Answer:

1. 1119.982

2. 315.266

3. 297.866

Answer:

59.5 miles

Step-by-step explanation:

1 in = 7 mi

7 x 8.5 = 59.5

Answer:

D.

Step-by-step explanation:

it should be the sales tax because you pay a little bit more.

Answer:

36

Step-by-step explanation:

you do 4×9 = 36

she used 36 for each bag

Answer:

x=8

Step-by-step explanation:

Let's say this mystery number is x.

6 times this x is 16 less than the square of x so we can write this as:

[tex]6x = x^2 - 16[/tex]

We can then re-arrange this into a quadratic and simplify it so:

[tex]x^2 -6x-16 =0[/tex]

[tex](x-8)(x+2)[/tex]

x=8, x=-2

And since the question is asking for the positive solution,
x=8

Answer:

D. t < -4 or t > 5

Step-by-step explanation:

Inequality 1

Inequality 2

⇒ t < -4 or t > 5

⇒ Option D

Graph

Answer:

[tex]\sf D. \quad t < -4, t > 5[/tex]

Step-by-step explanation:

Given system of inequalities:

[tex]\begin{cases}5t-1 < -21\\4t+2 > 22\end{cases}[/tex]

Solve the inequalities by isolating t.

Inequality 1

[tex]\sf \implies 5t-1 < -21[/tex]

[tex]\implies \sf 5t-1+1 < -21+1[/tex]

[tex]\sf \implies 5t < -20[/tex]

[tex]\sf \implies 5t \div 5 < -20 \div 5[/tex]

[tex]\sf \implies t < -4[/tex]

Inequality 2

[tex]\sf \implies 4t+2 > 22[/tex]

[tex]\sf \implies 4t+2-2 > 22-2[/tex]

[tex]\sf \implies 4t > 20[/tex]

[tex]\sf \implies 4t \div 4 > 20 \div 4[/tex]

[tex]\sf \implies t > 5[/tex]

Therefore, the solution to the system of inequities is:

[tex]\sf t < -4, t > 5[/tex]

When graphing inequalities:

Therefore, to graph the given system of inequalities:

(Refer to attachment for the graph).

Learn more about inequalities here:

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Answer:

0.4714, a simplified 47%

Step-by-step explanation:

:)

Step-by-step explanation:

2) 8,6,5,3 ,57 7,4,2/8

=92/8

mean =11.5

Arrange the terms in ascending order

2,3, 4, 5, 6, 7, 8, 57

the median of the ascending set= 5.5

3) 72 75 85 82 37 108/ 6

459/6

mean =76.5

Arrange the terms in ascending order

37, 72, 75, 82, 85, 108

the median of the ascending set= 78.5

4) 10 students were asked because there were 10 data values in the list.

5) it should be 55/10 =5.5

so its false

6) Sum first and find the mean number

5+4+3+2+1/5

=3

Answer:

Step-by-step explanation:

Let the number of 1-point shots is x and 2-points shots is y.

The system as per question is

Solve it by elimination, subtract the first equation from the second

Find the value of x

Answer:

It’s If I do not stay home from the concert then it is not raining.

Step-by-step explanation:

it’s the answer that I have because in the question it’s asking what is the same but I guess opposite. Which is why I chose the first answer as my answer since if it’s not raining then they would go to the concert.

The amount of the surface area covered with stickers is 0.6 or 60%

The amount of area to cover is given as:

Covered area = 3/5

Express as percentage

Covered area = 3/5 * 100%

Divide 3 by 5

Covered area = 0.6 * 100%

Evaluate the product

Covered area = 60%

Hence, the amount of the surface area covered with stickers is 0.6 or 60%

Read more about proportions at:

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Answer:

135.93

Step-by-step explanation:

I took the test

The “Volume” in finance means total shares traded during a certain time frame option (B) is correct.

To make a profit, share traders buy and sell the stock of companies listed on the stock exchange.

The number of shares traded in a certain stock, index, or other investment during a given period of time is known as volume.

Thus, the “Volume” in finance means total shares traded during a certain time frame.

Learn more about the share trade here:

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The price that John would pay for the new laptop after accounting for the sales, price coupon and the sales tax is  0.72p.

After the sales price and coupon is applied, the price of the laptop would reduce.

Price after the sales price = (1 - 0.2) x p = 0.8p

Price after the coupon = (1 - 0.15) x 0.8p

0.85 x 0.8p = 0.68p

A tax increases the price of the laptop.

Price after the tax = (1 + 0.06) x 0.68p = 1.06 x 0.68p = 0.72p

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