Two cars leave an intersection at the same time. One drives east while the other travels south at 15 miles per hour faster than the other. After 3 hours, the cars are 225 miles apart. How fast is the southbound car driving?

Answer:

Step-by-step explanation:

x^2-6x=7 is our equation

x^2-2*3*x= 7

So the term we will be adding is 3^2 since 3 the second term is 2*3*x

x^2-6x+9=7-9

We added 9 and substract it to keep the equation

(x+3)^2 = -2

Wich is impossible since a squared number is always positive

Answer:

Step-by-step explanation:

Given,

Perpendicular ( p ) = 8 units

Base ( b ) = 3 units

Hypotenuse ( h ) = ?

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

plug the values

[tex] {h}^{2} = {8}^{2} + {3}^{2} [/tex]

Evaluate the power

[tex] {h}^{2} = 64 + 9[/tex]

Calculate the sum

[tex] {h}^{2} = 73[/tex]

Squaring on both sides

[tex]h = \sqrt{73} [/tex]

Calculate

[tex]h = 8.54[/tex] units

Hope this helps..

Best regards!

Answer:

TEST ANSWER: q1:C q2:a q3:b q4:c

Step-by-step explanation:

i got it right on the test 100%

Answer:

See below.

Step-by-step explanation:

In all triangles, the three interior angles will add up to 180°. Therefore:

[tex](9x+6)+(5x)+(90)=180[/tex]

Remember that the little square means a right angle.

Now, solve for x.

[tex]9x+6+5x+90=180\\14x+96=180\\14x=84\\x=6[/tex]

Now, plug x back into the equations to find each angle:

1)

[tex]\angle ABC = \angle B = 9(6)+6=60\textdegree[/tex]

2)

[tex]\angle BCA = \angle C = 90\textdegree[/tex]

3)

[tex]\angle CAB = \angle A=5(6)=30[/tex]

Answer:

1. angle ABC = 60

2. angle BCA = 90

3. angle CAB = 30

Step-by-step explanation:

Since we know the right angle =90 degrees, we just need to do simple algebra. (We also know the all three angles added together equals 180.)

5x+9x+6+90=180.

Now let's simplify. We can simplify by adding like terms:

14x+96=180

Now we just need to do simple algebra. First we'd subtract the 96 from both sides:

14x+96=180

      -96  -96

14x = 84

Now we just need to divide 14 from both sides to separate the 14 from the x.

[tex]\frac{14x}{14}[/tex] = [tex]\frac{84}{14}[/tex]

x = 6

Now that we know what x equals, we just need to fill it into the equations which shouldn't be too hard. :)

Extra hint: to check your answer just add all three angles together and if you get 180 your answer is correct. :)

HOPE THIS HELPS!! <3 :D

Answer:

Length 37 cm, width 25 cm.

Step-by-step explanation:

Let the original dimensions be length x and width x - 12 cms.

The new dimensions will be length (x - 2) and width (x - 12 - 2) = x-14 cm.

So , from the areas, we have:

x(x - 12) - (x - 2)(x - 14) = 120

x^2 - 12x  - (x^2 - 16x + 28) = 120

-12x + 16x - 28 = 120

4x = 148

x = 37 cms

So the length was 37 cm and the width was 37-12 = 25 cm.

Answer:

The amount of fiber in the entire tomato is approximately 1 g

Step-by-step explanation:

A tomato is cut into 8 slices.

1 slice contains 012 g of fiber

8 slices will contain;

[tex]\frac{8 * 0.12}{1}[/tex] g = 0.96g which equals to 1 g when rounded up nearest  gram.

So the amount of fiber in the entire tomato is 0.96g ≈ 1g

hey mate, here is ur answer in the attachment!

Answer:

x = 27

Step-by-step explanation:

2/3x - 1/9x + 5 = 20

Subtract 5 from each side

2/3x - 1/9x + 5 -5= 20-5

2/3x - 1/9x  = 15

Get a common denominator on the left side

2/3 *3/3 x - 1/9x = 15

6/9x - 1/9x = 15

5/9 x = 15

Multiply each side by 9/5

9/5 * 5/9x = 15 * 9/5

x = 15/5 *9

x = 3*9

x = 27

Answer:

x=27

Step-by-step explanation:

2/3 x -1/9 x+5=20

2/3x -1/9 x=20-5 common denominator

(6x-1x)/9=15 multiply each side by 9

(5x)=135

5x=135

x=135/5=27

x=27

Answer:

Hey there!

The ratio of ducklings to adult ducks is 5:1.

This means for every six ducks, five are ducklings and one is an adult.

If there are 24 ducks, then 5 times 4 = 20 ducklings and 4 adults.

Thus, there are 20 ducklings.

Hope this helps :)

Answer:

20 ducklings.

Step-by-step explanation:

Answer:

Number of flowers planted planted by Charlie per day = 72

Step-by-step explanation:

Given:

Dora can plant 150 flowers and Charlie plants 120 flowers in same time.

Dora can plant 18 flowers more per day than that of Charlie.

To find:

Flowers that can be planted by Charlie per day = ?

Solution:

Let the time taken by Dora to plant 150 flowers = T days

So, T will be the time taken by Charlie to plant 120 flowers.

Number of flowers planted by Dora per day = Total Number of flowers planted by Dora divided by number of days

Number of flowers planted by Dora per day = [tex]\frac{150}{T}[/tex]

Similarly, Number of flowers planted by Charlie per day = Total Number of flowers planted by Charlie divided by number of days

Number of flowers planted by Charlie per day = [tex]\frac{120}{T}[/tex]

As per condition given:

[tex]\dfrac{150}{T} = \dfrac{120}{T} +18[/tex]

Solving the above equation by taking LCM:

[tex]\Rightarrow \dfrac{150}{T} = \dfrac{120 +18T}{T}\\\Rightarrow 150=120+18T\\\Rightarrow 18T = 30\\\Rightarrow T = \dfrac{30}{18}\\\Rightarrow T = \dfrac{5}{3}\ days[/tex]

Number of flowers planted by Charlie per day = [tex]\frac{120}{T}[/tex] = [tex]\frac{120\times 3}{5} = 72[/tex]

So, answer is:

Number of flowers planted planted by Charlie per day = 72

Answer:

The correct option is;

∠MKL

Step-by-step explanation:

From the construction of the line LKJ to form the exterior  angle ∠JKM, we have that the segment MK of triangle KML forms two adjacent angles on JKL which are ∠JKM and ∠MKL, therefore, the adjacent interior angle to angle ∠JKM is angle ∠MKL

PLease find attach The drawing of triangle KML showing the extended point J

Answer:

B) ∠MKL

Step-by-step explanation:

Took the quiz on edge

Answer:

The fraction of corn is 4/10 of the garden.

Step-by-step explanation:

5/10 + 1/10 = 6/10

10/10 - 6/10 = 4/10 or 2/5

Answer:

i think its 67600

Step-by-step explanation:

100*26=2600

2600*26=67600

Answer:

Step-by-step explanation:

If side OL is perpendicular to ON i.e OL ⊥ ON, then angle  ∠LON = 90°. If the is another line OM projecting from O with ∠LOM= (3x+38)° and ∠MON= (9x+28)°, then ∠MON +  ∠LOM =  ∠LON

Substituting the given angles int the expressions above to calculate the value of x;

(9x+28)° + (3x+38)° = 90°

12x+66 = 90°

12x = 90-66

12x = 24

x = 2°

Since ∠LOM= (3x+38)°, to get the value of the angle, we will substitute x = 2° into the expression as shown;

∠LOM= (3(2)+38)°

∠LOM= 6+38

∠LOM= 44°

Hence the measure of angle LOM is 44°

Answer: LOM = 44°

Step-by-step explanation: it’s right on khan academy (picture for proof)

Answer: 1,300 students went on the trip

Step-by-step explanation: So we know that 65% filled the seats so let's turn that into a fraction.  [tex]\frac{65}{100}[/tex] . Now we know that there are 2,000 seats in total so let's put that into a fraction. [tex]\frac{x}{2,000}[/tex]  The x represents the students that went on the trip.

               [tex]\frac{65}{100} = \frac{x}{2,000}[/tex]  we have to cross multiply

   65(2,000) = 100 (x)

    130,000   =  100 (x)          

    130,000   ÷  100                            

        1,300    =   x          So now we know that 1,300 went to the trip students

Question

If the CP of 15 articles equals to the SP of 12 articles, find the gain percent.

Answer:

gain percent = 25%

Step-by-step explanation:

To solve the question given, we will follow the steps below:

gain%  =   [tex]\frac{s.p - c.p}{c.p}[/tex]  ×    100%

But from the question;

"CP of 15 articles equals to the SP of 12 articles", this implies that

15 c.p  =  12 s.p

s.p = 15c.p  /   12

s.p  = [tex]\frac{15 c.p}{12}[/tex]       =   [tex]\frac{5c.p}{4}[/tex]

s.p  =  [tex]\frac{5c.p}{4}[/tex]

substitute  s.p  =  [tex]\frac{5c.p}{4}[/tex]   into the formula

gain%  =   [tex]\frac{s.p - c.p}{c.p}[/tex]  ×    100%

      =[tex]\frac{\frac{5c.p}{4} - c.p }{c.p}[/tex]     ×    100%

       =  [tex]\frac{\frac{5c.p - 4c.p}{4} }{c.p}[/tex]      ×    100%

  =   [tex]\frac{c.p}{4}[/tex]   ÷   c.p      ×    100%

= [tex]\frac{c.p}{4}[/tex]     ×   [tex]\frac{1}{c.p}[/tex]    ×    100%

=   [tex]\frac{1}{4}[/tex]  ×    100%

=  25 %

The answer is- D. 324 pi units squared

The volume of the cone is 324π cubic units, option C is correct.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

We have to find the volume of cone whose height is 12 units, radius is 9 units

Volume = πr²h/3

Now let us plug in values of r and h which are radius and height respectively

Volume of cone = π × 9² ×12 /3

= π × 81×4

=324π cubic units

Hence, the volume of the cone is 324π cubic units, option C is correct.

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ5

Answer:

P(X ≤ 94) =  0.09012

From what we observe; There is a probability  of less than 94 people who voted for the referendum is 0.09012

Comment:

The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.

Step-by-step explanation:

From the information given :

An exit poll of 200 voters finds that 94 voted for the referendum.

How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52​? Based on your​ result, comment on the dangers of using exit polling to call elections.

This implies that ;

the Sample size n = 200

the probability p = 0.52

Let X be the random variable

So; the Binomial expression can be represented as:

X [tex]\sim[/tex] Binomial ( n = 200, p = 0.52)

Mean [tex]\mu[/tex] = np

Mean [tex]\mu[/tex]  = 200 × 0.52

Mean [tex]\mu[/tex]  = 104

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{np(1-p)}[/tex]

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(1-0.52)}[/tex]

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(0.48)}[/tex]

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{49.92}[/tex]

The standard deviation [tex]\sigma[/tex] = 7.065

However;

P(X ≤ 94) because the discrete distribution by the continuous normal distribution values lies in the region of 93.5 and 94.5 .

The less than or equal to sign therefore relates to the continuous normal distribution of X < 94.5

Now;

x = 94.5

Therefore;

[tex]z = \dfrac{x- \mu}{\sigma}[/tex]

[tex]z = \dfrac{94.5 - 104}{7.065}[/tex]

[tex]z = \dfrac{-9.5}{7.065}[/tex]

z = −1.345

P(X< 94.5) = P(Z < - 1.345)

From the z- table

P(X ≤ 94) =  0.09012

From what we observe; There is a probability  of less than 94 people who voted for the referendum is 0.09012

Comment:

The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.

Answer:

63 kids

Step-by-step explanation:

We can add up the number of students who went home sick, hiked, and swam to find the total amount of people.

[tex]4+18+41 = 63[/tex]

Therefore, 63 kids started their day at Camp Sunshine.

I get that feeling I oversimplified this one, let me know if I did. I'm not sure if this is right.

Answer:

63 kids

Step-by-step explanation:

We know that there are some kids who went home sick, some went hiking and some went swimming.

The total number of kids that started the day at Camp Sunshine can be found by adding the number who went home sick, went hiking and went swimming.

sick + hiking + swimming

4 went home sick, 18 went hiking and 41 went swimming.

4+ 18 + 41

Add the numbers together

22+ 41

63

63 kids started the day at Camp Sunshine.

Answer:

Theres no solution ._.

Step-by-step explanation: Bc you have the 2 lines

Answer: No solution

Step-by-step explanation:

There are no values of x that make the equation true

Answer:

C: as the size increases the amount decreases. this means as the x-value increases, the y-value decreases, which is shown by graph C.

Answer:

your answer is c )c and where are you live

Answer:

Step-by-step explanation:

Given the value 78247 a s a stable number because at least one of its digits has the same value  as its position in the number. The 4th number in the value is 4, this makes the number a stable number.

The following are the 3-digits stable numbers that appears in 78247

The first number is 824. This digits are stable numbers because 2 as a number is situated in the same place as the number (2nd position).

Hence, there are only 1 stable 3-digit numbers in the value 78247 since only a value exists as 2 in the value and there is no 1 and 3 in the value.

Answer:

388.6 yd²

Step-by-step explanation:

the missing angle in triangle is 180 - 32 - 38 = 110

Law of sines: 31/sin 38 = VT/sin 32

VT = 26.68

area = 1/2ab sinC

A = 1/2 (31)(26.68) sin 110

388.6 yd²

Answer:

No

Step-by-step explanation:

data provided in the question

Long = 2 miles

distance = [tex]\frac{2}{11}[/tex]

based on the above information,

We can conclude that

there is not more than one relay as if we divide the 2 by 11 so it comes 0.18 which is greater than 0.1

i.e

0.18 > 0.1

So there is no need for more than one relay i.e to be exchanged between two consecutive mile

Answer:

6 miles.

Step-by-step explanation:

Since Miguel is walking 3 miles per hour, 3 times 2 is equal to 6.

Hope that Helped!

Answer:

6mi

Step-by-step explanation:

1hr = 3mph

So , 2hr = 2 × 3mph =6 mi

Hope this helps and pls make as brianliest :)

Answer:

y = -2x + 8

Step-by-step explanation:

y = mx + b

-8 = -2(8) + b

-8 = -16 + b

8 = b

y = -2x + 8

oof i read the question and done goofed frick my add

Answer:

y=2 or y-2=0

Step-by-step explanation:

to find the equation first find the slope m points (-1,2) and (5,2)

m=y2-y1/x2-x1 =2-2/5-(-1)=0/6=0

y=mx+b  the slope is zero then y=b=2

Answer:

[tex]0.2 = \frac{x}{5} - 1.4[/tex]

Move 1.4 to the left side of the equation

That's

[tex]0.2 + 1.4 = \frac{x}{5} \\ \\ \frac{x}{5} = 1.6[/tex]

Convert the decimal to fraction

That's

1.6 = 8/5

[tex] \frac{x}{5} = \frac{8}{5} [/tex]

Multiply through by 5

We have

[tex] \frac{x}{5} \times 5 = \frac{8}{5} \times 5 \\ \\ \\ x = 8[/tex]

Hope this helps you

Answer:

A. -146

Step-by-step explanation

46th term = -11 + ( 46 -1) (-3)

= -11 + (45)(-3)

=-11 -135

= - 146

Answer:

Hello There!

`~~~~~~~~~~~~~~~~~~~~`

4th root of 256 is 4, and 240/4 = 60, and 360/4 = 90, so the 4 roots are

4(cos 60 + i sin 60)

4(cos 150 + i sin 150)

4(cos 240 + i sin 240)

4(cos 330 + i sin 330)

Hope this helped you. Brainliest would be nice!

Answer:

Statement 3: A cone is one-third the size of a cylinder with the same height and radius.

Statement 4: A cone has a circular base.

Step-by-step explanation:

Statement 3: A cone is one-third the size of a cylinder with the same height and radius.

Statement 4: A cone has a circular base.

The true statement is:

Statement 3: A cone is one-third the size of a cylinder with the same height and radius.

Statement 4: A cone has a circular base.

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top . A cone has one face . There are no edges for a cone.

Properties of Cone

As, from the properties of cone we can say that.

A cone is one-third the size of a cylinder with the same height and radius. and, : A cone has a circular base..

Learn more about cone here:

https://brainly.com/question/16394302

#SPJ2