Solve this math problem 20 points

Answer:

The equation of the line is [tex]y + 7 = -\frac{1}{3}(x - 9)[/tex]

Step-by-step explanation:

Equation of a line:

The equation of line, in point-slope form, is given by:

[tex]y - y_0 = m(x - x_0)[/tex]

In which m is the slope and the point is [tex](x_0, y_0)[/tex]

Perpendicular lines:

If two lines are perpendicular, the multiplication of their slopes is -1.

Through (9,-7)

This means that [tex]x_0 = 9, y_0 = -7[/tex]

So

[tex]y - y_0 = m(x - x_0)[/tex]

[tex]y - (-7) = m(x - 9)[/tex]

[tex]y + 7 = m(x - 9)[/tex]

Perpendicular to y = 3x + 4

This line has slope 3, so:

[tex]3m = -1[/tex]

[tex]m = -\frac{1}{3}[/tex]

Thus

[tex]y + 7 = m(x - 9)[/tex]

[tex]y + 7 = -\frac{1}{3}(x - 9)[/tex]

Answer:

The width of the rectangle lies between 12 and 20.

Step-by-step explanation:

Let the width of the rectangle is w.

length of the rectangle,

L = 8 w + 20

116 < L < 180

So,

116 < 8 w + 20 < 180

96 < 8 w < 160

12 < w < 20

So, the width of the rectangle lies between 12 and 20.

Answer:

294 in

Step-by-step explanation:

set a ratio w/l

11/14

set it equal to 231/x

x = length

[tex]\frac{11}{14}[/tex] = [tex]\frac{231}{x}[/tex]

cross multiply

11x = 3234

divide by 11

x = 294

Answer:

please write the question in english than I may help you

[tex]\sf \bf {\boxed {\mathbb {GIVEN:}}}[/tex]

Radius of the circle "[tex]r[/tex]" = 5.5 yd

[tex]\sf \bf {\boxed {\mathbb {TO\:FIND:}}}[/tex]

The area of the given figure.

[tex]\sf \bf {\boxed {\mathbb {SOLUTION :}}}[/tex]

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {b. \:47.5\:sq\:yd.}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

We know that,

[tex]\sf\pink{Area\:of\:a\:semi-circle}[/tex] = [tex]\frac{\pi \: {r}^{2} }{2} [/tex]

Using 3.14 for π, we have

[tex] = \frac{3.14 \times ( {5.5 \: yd})^{2} }{2} \\[/tex]

[tex] = \frac{3.14 \times 5.5 \times 5.5 \: {yd}^{2} }{2}\\ [/tex]

[tex] = \frac{94.985 \: {yd}^{2} }{2} \\[/tex]

[tex] = 47.5 \: {yd}^{2} \\[/tex]

Using [tex]\frac{22}{7} [/tex] for π,

[tex] = \frac{22 \times 5.5 \times 5.5 \: {yd}^{2} }{7 \times 2} \\[/tex]

[tex] = \frac{665.5 \: {yd}^{2} }{14}\\ [/tex]

[tex] = 47.5 \: {yd}^{2} \\[/tex]

Therefore, the area of the semi-circle is [tex]47.5\: yd²[/tex].

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

Answer:

s = 4.28 cm (Answer A)

Step-by-step explanation:

1) The formula for the circumference of a circle of radius r is C = 2(pi)r, and this corresponds to a full circle, with central angle 360 degrees.  

2) Here the circumference is 28 cm.  Therefore, solving for the radius involves the following calculation:   28 cm = 2(pi)r, or

r = (28 cm) / (2 pi), or (28 cm) / 6.28 = 4.46 cm.  

3) The arc length s = r(theta), when the central angle (theta) is 55 degrees, is (55/360) times the circumference of the circle:  (55/360)(28 cm), or

s = 4.28 cm (Answer A)

Answer:

Q3. 9

Q4. 6

Step-by-step explanation:

Answer:

Faces = 6

Vertices = 8

Edges = 12

Step-by-step explanation:

In a solid geometric shape :

         A face is a flat surface : faces = 6

         A vertex (plural: vertices) is a Corner : vertices = 8

         An edge is a particular type of line segment joining

                                                          two vertices : Edges = 12

Answer:

D. -7/8(-8/7)x-3/4=20(-7/8) is the answer.

Answer:

Step-by-step explanation:

48 ft by 60 ft

Answer:

Santino rented the canoe for 8 hours.

Step-by-step explanation:

The total bill is represented by the formula r(h) = $10 + ($7.50/hour)h,

where h is the number of hours over which the canoe is rented.

If the total bill is $70, then $70 = $10 +  ($7.50/hour)h.

Solve this for h.  Start by subtracting $10 from both sides, obtaining:

$60 =  ($7.50/hour)h.

Dividing both sides by ($7.50/hour), we get:

           $60

h = --------------------- = 8 hours

      ($7.50/hour)

Santino rented the canoe for 8 hours.

Answer:

45) 35.75 sq km

46) 24.5 sq km

Step-by-step explanation:

Area of Square:

A= [tex]\frac{(base)(height)}{2}[/tex]

45) A = (11)(6.5) ÷ 2 =

46) A = (10)(4.9) ÷ 2 =

Answer:

45) [tex]35.75[/tex] [tex]km^2[/tex]

46) [tex]24.5[/tex] [tex]km^2[/tex]

Step-by-step explanation:

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

The formula to find the area of a triangle is  [tex]A=\frac{1}{2}bh[/tex] where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.

So, let's solve and find out the answer.

--------------->>>>

45)

[tex]A=\frac{1}{2}(11)(6.5)[/tex]

[tex]A=\frac{1}{2}(71.5)[/tex]

[tex]A=35.75[/tex]

The area of this triangle is [tex]35.75[/tex] [tex]km^2[/tex]

--------------->>>>

46)

[tex]A=\frac{1}{2} (10)(4.9)[/tex]

[tex]A=\frac{1}{2} (49)[/tex]

[tex]A=24.5[/tex]

The area of this triangle is [tex]24.5[/tex] [tex]km^2[/tex]

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

Hope this is helpful

Answer:

4m - 15

Step-by-step explanation:

a( x + y) = ax + ay

[tex]3( m - 5 ) + m\\\\3m - 15 + m \\\\4m - 15[/tex]

Answer:

4m-15

Step-by-step explanation:

Distrubite 3 through the parentheisis

3m-15+m

Collect like terms

4m-15

Answer:

54 m^3

Step-by-step explanation:

this is the answer = 54 m^3

Volume of the rectangular pyramid will be 54[tex]m^{3}[/tex].

Rectangular pyramid has 5 faces where one face is rectangular which is at bases and other 4 faces are triangular which is connected at the one point .

If we assume that l is the length of the base and b is the width of the base and h is height of the rectangular pyramid then we can calculate the volume of the rectangular pyramid using the formula stated below

                 Volume of the rectangular pyramid = V=  (1/3)×l×b×h

According to the asked question

l = 6m

b = 3m

h = 9m

then we can calculate the volume of the rectangular pyramid by using the above formula

= V=  (1/3)×l×b×h

= (1/3)×6m×3m×9m

= 54[tex]m^{3}[/tex]

Learn more about volume of the rectangular pyramid

Here:https://brainly.com/question/924442

#SPJ2

9514 1404 393

Answer:

Step-by-step explanation:

The 3+4 = 7 ratio units represent the total of 490 snacks, so each ratio unit represents 490/7 = 70 snacks.

The number of soda cans is 3·70 = 210.

The number of candy bars is 4·70 = 280.

Marvin bought 210 soda cans and 280 candy bars.

A negative x is to the left of the y axis and a negative y value is below the x axis. Any value to the left and below the axis’ will be in the 3rd quadrant.

Answer: 3rd quadrant

Answer:

48

Step-by-step explanation:

the answer is 48 I got this answer by multiplying 5 by 10 and subtracting is from 2 which gives me 50 - 2 which is 48

Answer:

48

Step-by-step explanation:

5×10-2=50-2

=48

hope it helps!!

Answer:

1. f= 3/5

2. t= 3/5

Step-by-step explanation:

FYI you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Answer:

Below in bold.

Step-by-step explanation:

2(f - 9) = -28

2f - 18 = -28

2f = -28 + 18

2f = -10

f = -5.

-3(2t + 3) = -21

2t + 3 = -21/-3

2t + 3 =  7

2t = 4

t = 2.

Answer:

here is your answer

Step-by-step explanation:

b

c

a answer

Answer:

He traveled at 72km/hr during the rain

Step-by-step explanation:

Question is not well formatted. See comment

Given

[tex]d=400km[/tex] --- distance

[tex]t = 11hrs[/tex] --- total time

Let his speed from city A till the rain starts on his return trip be [tex]s_1[/tex]

Let his speed from city during the rain be [tex]s_2[/tex]

So:

[tex]s_2 = s_1 -20[/tex]

Required

Calculate [tex]s_2[/tex]

From the question, we understand that; he drives the whole 400 km and 2/5 of 400 km at [tex]s_1[/tex]

The distance covered during this period is:

[tex]d_1 = 400 + \frac{2}{5} * 400[/tex]

[tex]d_1 = 400 + 160[/tex]

[tex]d_1 = 560[/tex]

And the time during this period is:

[tex]t_1 = \frac{2}{5} * 11[/tex]

[tex]t_1 = 4.4[/tex]

So, the distance during the rain is:

[tex]d_2 = 2 * 400 - d_1[/tex]

[tex]d_2 = 2 * 400 - 560[/tex]

[tex]d_2 = 800 - 560[/tex]

[tex]d_2 = 240[/tex]

And the time during the rain is:

[tex]t_2 = 11 - t_1[/tex]

[tex]t_2 = 11 - 4.4[/tex]

[tex]t_2 = 6.6[/tex]

So, we have:

[tex]d_1 = 560[/tex] --- distance covered before the rain

[tex]d_2 = 240[/tex] --- distance covered when raining

[tex]s_2 = s_1 -20[/tex]

[tex]t_1 = 4.4[/tex] ---- time spent before the rain

[tex]t_2 = 6.6[/tex] --- time spent in the rain

Speed is calculated as:

[tex]Speed = \frac{distance}{time}[/tex]

Make distance the subject

[tex]distance = speed * time[/tex]

So:

[tex]d_1 + d_2 = s_1 * t_1 + s_2 * t_2[/tex]

Recall that:

[tex]s_2 = s_1 -20[/tex]

Make [tex]s_1[/tex] the subject

[tex]s_1 = s_2 + 20[/tex]

The expression [tex]d_1 + d_2 = s_1 * t_1 + s_2 * t_2[/tex] becomes:

[tex]560 + 240 = (s_2 + 20) * 4.4 + s_2 * 6.6[/tex]

[tex]800 = 4.4s_2 + 88+ 6.6s_2[/tex]

Collect like terms

[tex]6.6s_2 + 4.4s_2 = 880 - 88[/tex]

[tex]11s_2 = 792[/tex]

Solve for [tex]s_2[/tex]

[tex]s_2= \frac{792}{11}[/tex]

[tex]s_2=72km/h[/tex]

The distance and time 400 km and 11 hours as well as the speed

reduction gives the speed during the rainy part as 60 km/h.

Based on the comment in the question, we have;

Given:

Distance between City A and City B = 400 km

Distance travelled at the same speed on his way back = [tex]\mathbf{\frac{2}{5}}[/tex] of the distance

Amount by by which his speed is reduced in the remaining [tex]\frac{3}{5}[/tex] of the distance because of rain = 20 km/h

The duration of the trip = 11 hours

Required:

How fast Mr. Jones was driving during the rainy part of his trip from City

B to City A?

Solution:

Let v represent the constant speed, we have;

[tex]Time = \mathbf{ \dfrac{Distance}{Speed}}[/tex]

The distance for which his speed is v = ([tex]\frac{2}{5}[/tex] + 1) × 400 km = 560 km

Total distance of the round trip = 400 km + 400 km = 800 km

The distance for which the speed = v - 20 = 800 km - 560 km = 240 km

Therefore, we have;

[tex]\mathbf{\dfrac{560}{v} + \dfrac{240}{v - 20}}= 11[/tex]

Which gives;

[tex]\mathbf{\dfrac{560 \times (v - 20) + 240 \cdot v}{v\times (v - 20) } } = 11[/tex]

11 × (v² - 20·v) = 560·v - 20 × 560 + 240·v

11·v² - 220·v - 560·v - 240·v + 11200

11·v² - 1020·v + 11,200 = 0

Using the quadratic formula, to solve the above quadratic equation we have;

[tex]v = \dfrac{1020 \pm\sqrt{(-1020)^2 - 4 \times 11 \times 11200} }{2 \times 11} = \dfrac{1020 \pm740 }{22} = \mathbf{ \dfrac{1020 \pm740 }{22}}[/tex]

v = 80 or v = [tex]12 . \overline{72}[/tex]

The possible value for the constant speed is therefore;

v = 80 km/h

The speed during the rain = v - 20, which gives;

Learn more about quadratic formula here;

https://brainly.com/question/283838

Answer:b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

third side is the hypotenuse since it is opposite to 90 degree.

using pythagoras theorem

a^2 + b^2 = c^2

24^2 + 18^2 = c^2

576 + 324 = c^2

900 = c^2

[tex]\sqrt{900}[/tex] = c

30 = c

therefore third side is 30.

Answer:

30

Step-by-step explanation:

[tex] {24}^{2} + 18 {}^{2} = c {}^{2} \\ 576 + 324 = c {}^{2} \\ \sqrt{900 = \sqrt{c }^{2} } \\ = 30[/tex]

Answer:

P(A or B) = 1.16

Step-by-step explanation:

Given probability:

Probability of event A = P(A) = 0.46

Probability of event B = P(B) = 0.7

P(A and B) = 0.43

Find:

P(A or B)

Computation:

If A is an incident and B is a separate event, P(A or B) is the possibility of either A, B, or both events occurring.

P(A or B) = P(A) + P(B)

P(A or B) = 0.46 + 0.7

P(A or B) = 1.16

Answer:

About 135.

Step-by-step explanation:

As the sample is random the number of monkeys likely to be in the zoo

=  (22/65) * 400

= 135.38

Answer:

21 < x

Step-by-step explanation:

4 > 11 -x/3

Subtract 11 from both sides

4 - 11 > -x/3

-7 > -x/3

Multiply both sides by 3

-7*3 > -x

-21 > -x

Multiply both sides by (-1)  

21 < x

When we are multiplying by negative, then inequality sign changes.

Step-by-step explanation:

ejdjbd x bxbx k wbu y DJ UK j HK JM dz

nb

Answer:

option B

Step-by-step explanation:

[tex]f(x) = 2x^2 + 6x -4\\\\g(x) = 5x^3 - 6x^2 - 3\\\\(f + g)(x) = f(x) + g(x) \\\\[/tex]

               [tex]= (2x^2 + 6x - 4) + ( 5x^3 -6x^2 - 3) \\\\= 2x^2 + 6x - 4 + 5x^3 - 6x^2 - 3\\\\= 5x^3 + 2x^2 - 6x^2 + 6x - 4 - 3 \\\\= 5x^3 - 4x^2 + 6x - 7[/tex]

Answer:

the answer is b

Step-by-step explanation:

hope this helps :)