Mathematics High School

Two cars leave the same location at the same time but one car is heading north and the other is heading south. After 3 hours, the cars are 360 miles apart. If the car heading north is traveling 10 miles per hour slower than the car heading south, what are the two speeds of the cars?

SHOW THE EQUATION

Answers

Answer 1

3x +3(x-10) = 360

3x +3x-30 =360

6x-30 =360

6x=390

X = 390/6 = 65

65-10 =55

 One car was driving 65 mph

 The other was 55 mph


Answer 2
[tex]d=vt[/tex]
[tex]360=(v_{s})(3)+(v_{n})(3)[/tex]
[tex]360=(v_{s})(3)+((v_{s}-10)(3)[/tex]
[tex]360=3v_{s}+3v_{s}-30[/tex]
[tex]390=6v_{s}[/tex]
[tex]v_{s}=\frac{390}{6}=65[/tex]
[tex]v_{n}=v_{s}-10=65-10=55[/tex]

The south car is traveling at 65mph. The north car is traveling at 55mph. 

Related Questions

If you are throwing a dart at the circular target pictured below, and it is equally likely to hit any point on the target, what is the probability that the dart will hit the rectangle?
Use 3.14 for ,and round your answer to the nearest tenth of a percent.

Answers

The area of the circle is 100pi in^2, and the area of the rectangle is 48in^2. This means 48/100pi of the circle is the target area, which is 15.3% of the total area, so D is the correct answer.

simplify the expression and enter your answer below (19^1/9) ^9

Answers

Multiply 9 by 1/9.

19^1 so in other words, 19.

The simplified expression is 19.

What is expression?

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

some terms are:

Constant: A constant is a fixed numerical value.Variable: A variable is a symbol that doesn't have a fixed value.Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

given:

(1*9^1/9) ^9

Multiply 9 and 1/9

we get

9*1/9 = 1

and 19* 1= 19

Hence, the simplified expression is 19.

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What number must you add to complete the square? X^2 +12x=40

Answers

You halve the linear coefficient, square it, then add that to both sides.  In this case:

(12/2)^2=6^2=36 so you would add 36 to both sides

x^2+12x+36=76  so that the left side is now a perfect square

(x+6)^2=76

Answer:

36

Step-by-step explanation:

(x+6)^2=76

Line K is parallel to line L
What angle is congruent to angle 4.

Answers

∠1 and ∠4 are vertical angles (the angles opposite each other when two lines cross).

Vertical angles are congruent, so ∠1 = ∠4

Answer:

Its A, I took the test..

A rope 18 feet long is cut into two pieces. one piece is used to form a circle and the other used to form a square. find a function representing the area of both square and circle as a function of the length of one side of the square.

Answers

Please give me a brainliest for this, it was so much work. The answer is

f(x)=x^2 + (4x^2 -18x +81)/pi

Write an equation that has a hole at x = 4 and a vertical asymptote at x = -3.

Answers

This has to be a rational equation in order to have those characteristics...in other words a fraction. One such equation would look like this:
x^2 - 2x - 8/x^2 - x - 12.  When you factor both the numerator and the denominator you get (x-4)(x+2)/(x-4)(x+3).  Because the (x-4) is in both the top and the bottom of the fraction, you can cancel them out, which makes that (x-4) a removable discontinuity.  The (x+3) exists as a vertical asymptote.

Find the area of the following shape. A(-5,-8) B(1,-8) C(3,-5) D(1,0) E(-5,-3) F(-3,-6). You must show work to receive credit.

Answers

check the picture below.

now... notice the left-side of the picture. that's the points and shape... ok.. notice the left-side, is really just two rectangles and and four triangles stacked up to each other at the edges.

so.. .just get the area of each rectangle and each triangle, sum them up, and that's the area of the shape.

you can pretty much get the length, width and height of the rectangles and triangles from the grid.

recall area of a triangle = 1/2 bh

A lab found that 670 rats could run through a maze in a mean time of 4.7 seconds. What is the 99% confidence interval for the population mean? Use the formula for margin of error: z•σ/√n. Please explain each step, particularly how to find the population standard deviation.

Answers

Using the formula for margin of error as

MOE = z * σ / √n

would be very difficult since we are not given the value of the standard deviation. Standard deviation value must be given since it is obtained from the experiment.

However, we use another formula for MOE in the form of:

MOE = z sqrt [p (1 – p) / n]

where p is the proportion at 99% confidence interval at z crit value. From the standard distribution tables, this corresponds to a p value of:

z crit = 2.58

p = 0.9951

Therefore the margin of error is:

MOE = 2.58 sqrt [0.9951 (1 – 0.9951) / 670]

MOE = 6.96 x 10^-3 = 0.00696 s

 

We can see that at 99% Confidence interval, the Margin of Error is extremely small (almost 0). For the sake of calculation:

Confidence interval = 4.7 s ± 0.00696 s

Confidence interval = 4.69304, 4.70696

Find the quotient of 5+4i/6+8i , and express it in the simplest form

Answers

remember: i² = -1

[tex] \frac{5+4i}{6+8i}= \frac{(5+4i)(6-8i)}{(6+8i)(6-8i)}= \frac{30-40i+24i-32i^2}{36-64i^2}= \frac{30-16i-32(-1)}{36-64(-1)}= \\ \\ = \frac{30-16i+32}{36+64}= \frac{62-16i}{100}=0.62-0.16i[/tex]

Hope this helps

An electrical heating element produces heat depending on the resistance of the element and the current passed through it. The heat produced can be given by the formula h = I2R where h is the heat generated, I is the current, and R is the resistance. If the element has a fixed current of 2 amps passing through it and a variable current of x amps, it is able to produce a heat of 10x3 + 80, depending on the variable resistance for different additional values of current x. Determine the formula for the variable resistance.

Answers

The heat produced by current I is
H = I²R
where
R =  resistance.
According to the formula, heat produced is proportional to the square of the current.

When a current of I = 2 amps is applied, the heat produced is 
H = 10x³ + 80.
This heat includes heat due to a fixed current of 2 amps, and heat due to a variable current of x amps.

Because the heat produced is proportional to the square of the current, write the expressions as
H = (10x)*(x²) + 20*(2²)

The second term on the right is heat due to the fixed current of 2 amps, written as
20*(2²).
Therefore the fixed resistance is R = 20 ohms, and the square of the fixed current is 2².

The first term represents heat due to variable resistance, written as
(10x)*(x²).
Therefore the variable resistance is 10x, and the square of the variable current is x².

Answer:
The variable current is  10x.

Answer:

(10x - 40) + 120 / (x+2)

Simplify the expression sin^2x-1/cos(-x)

Answers

Use the Pythagorean identity [tex]sin ^{2} x+cos ^{2} x=1[/tex]
to simplify the numerator.
[tex]sin ^{2} x-1=-cos ^{2} x[/tex]
Now use that fact that
[tex]cos(-x)=cos(x)[/tex] to set up the equivalent fraction:
[tex] \frac{sin ^{2}x-1 }{cos(-x)} = \frac{-cos ^{2}x }{cos(x)} [/tex]
Now reduce between the numerator and denominator to get -cos(x)

an ostrich that is 78 inches tall is 15 inches taller than 3 times the height of a kiwi. What is the height of a kiwi in inches

Answers

Turn this into an expression. The height of a kiwi is (k).
78=15+3k
Minus 15.
63=3k
Divide by 3.
21=k
A kiwi is 21 inches tall.
21 inches , because 78 inches minus 15 equals 63 which if divided by 3 equals 21

The bear population increases at a rated of 2% each year. There are 1573 bears this year. What is the growth factor, b?

Answers

that would be 1 + 0.02

Growth factor = 1.02.
Final answer:

To find the growth factor, b, we can use the formula for exponential growth: n = ln(M)/ln(b), where n is the number of years, M is the final population, and b is the growth factor.

Explanation:

To find the growth factor, b, we can use the formula for exponential growth: n = ln(M)/ln(b), where n is the number of years, M is the final population, and b is the growth factor. In this case, the final population is 1573 bears. Let's solve for b: n = ln(1573)/ln(b). To isolate b, we can take the exponential of both sides: b^n = 1573. Now we can solve for b by taking the nth root of 1573. The growth factor, b, is the value that, when raised to the power of the number of years, gives us the final population of bears.

If a coin is tossed twice what is the probability of getting two heads

Answers

25% because the first FLIP, it was a fifty-fifty chance. FLIP again and the chances are divided by two since you can only get 2 things, either heads or tails.

Write 7x-2-7x+6 in simplest form.

Answers

7x - 7x = 0
-2 + 6 = 4

So, the answer is 4. 

Find all the points, if any, where the graph of 12x-5y=0 intersects (x+12)^2+(y-5)^2=169.

A. There are no points of intersection.

B. (0,0)

C. (4.5, 10.9)

D. (0,0) and (4.5, 10.9)

Answers

I: 12x-5y=0
II:(x+12)^2+(y-5)^2=169

with I:
12x=5y
x=(5/12)y
-> substitute x in II:
((5/12)y+12)^2+(y-5)^2=169
(25/144)y^2+10y+144+y^2-10y+25=169
(25/144)y^2+y^2+10y-10y+144+25=169
(25/144)y^2+y^2+144+25=169
(25/144)y^2+y^2+169=169
(25/144)y^2+y^2=0
y^2=0
y=0

insert into I:
12x=0
x=0

-> only intersection is at (0,0) = option B

Answer:

(0,0)

Step-by-step explanation:

If you graph [tex]12x-5y=0[/tex] and [tex](x+12)^2+(y-5)^2=169[/tex] along with the points (0,0) and (4.5, 10,9) you with see that the equations intersect at (0,0)

The sum of two numbers is 70. one number is 8 more than the other. what's the smaller number?

Answers

x=8+y
x+y=70

Rewrite the first equation to x-y=8
Copy the second equation   x+y=70

Add the two equations and you get 2x=78
Therefore, x=39. Since this is the bigger number the smaller number(y) would have to be 31 because you subtract 8 from x which is 39. 39 is your answer. 

Over the weekend, Statton and Tyler drove to Montana to go hunting. Now they're preparing to go home. Tyler needs gas for his jeep, which gets 22 miles per gallon for gas mileage. When he stops at the gas station, he already has 5 gallons of gas in his tank. he buys more gas for $1.25 per gallon if Tyler spends 22 on gas what is the total distance the boys could travel round if necessary to the nearest tenth

Answers

he bought : 22/1.25 = 17.6 gallons

17.6 +5 = 22.6 gallons total

22 * 22.6 =497.2 miles total he can drive

Answer:

The answer would be 497.2

Step-by-step explanation:

Proof I hope you do well on the test .

Given cos B = 11/18 find angle B in degrees. Round your answer to the nearest hundredth.

Answers

[tex]B = cos^{-1}(\frac{11}{18}) \approx 52.33^\circ[/tex]

Answer:

[tex]B\approx 52.33^{\circ}[/tex]

Step-by-step explanation:

We have been given that [tex]\text{cos}(B)=\frac{11}{18}[/tex]. We are asked to find the measure of angle B.

We will use inverse cosine or arccos to solve for the measure of angle B as:

[tex]B=\text{cos}^{-1}(\frac{11}{18})[/tex]

[tex]B=52.33011303567^{\circ}[/tex]

Upon rounding our answer to nearest hundredth, we will get:

[tex]B\approx 52.33^{\circ}[/tex]

Therefore, the measure of angle B is 52.33 degrees.

Find the three arithmetic means in this sequence. 12 __ __ __ 40

Answers

To answer this question first you have to count the difference between the highest number with the lowest number.
In this case, the difference is: 40-12=28

After that, you need to determine the leaps in the sequence. In this case, there are 4 leaps.  
After that divide the difference with the leaps : 28:4=7
Therefore the sequence will be 12 , 19, 26, 33, 40

a nutrition label indicates that one serving of apple crisp oatmeal has 2.5 grams of fat. how many grams of fat . how many grams of fat how many grams of fat arew there in 3.75 sevings?

Answers

2.5x3.75=9.375 grams of fat!

Find a formula expressing the radius r of a sphere as a function of its surface area

Answers

The surface area of a sphere :
[tex]A=4 \pi r^2[/tex]

Solving this equation for r:

A/(4* pi) = r^2          apply sqrt to both sides:

r = sqrt [A/(4 pi)]

Then the radius of a sphere as a function of its surface area :
[tex]r= \sqrt{ \frac{A}{4 \pi } } [/tex]

Hope you got the idea

A car travels 2/5 mile in 1/2 minute. what is the cars speed in miles per hour?

Answers

So a car travels 2/5 mile in 1/2 minute. This means a car travels 4/5 mile in one minute. Then multiply by 60 to find how many miles it travels in 60 minutes, and you can see that you have 240/5, which is equal to 48. Therefore the speed of the car in miles per hour is 48 miles an hour. Hope this helps. Feel free to ask more questions, and ask questions about my explanation.
Final answer:

The speed of the car is 48 miles per hour, based on the given information that the car travels 2/5 miles in 1/2 minute.

Explanation:

To solve this problem, we first need to recognize that the car has traveled 2/5 miles in 1/2 minute. To calculate the speed in miles per hour (mph), we need to find how far the car would go in 1 hour. In other words, how many 1/2 minutes are there in an hour? An hour has 60 minutes, so there are 2*60=120 half-minutes in an hour. If the car travels 2/5 mile in each half minute, then in one hour (or 120 half-minutes), the car would travel 2/5*120=48 miles. Consequently, the car's speed is 48 miles per hour.

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Complete the solution of the equation. find the value of y when x equals 11 8x+6y=28

Answers

If x is 11, then we replace x with 11 in the equation.
8(11) + 6y = 28
88 + 6y = 28
We will subtract 88 from both sides to get rid of the constant.
6y = -60
To isolate the variable, we will divide both sides by 6.
y = -10
In this equation, y equals -10.
First, substitute the value of x back into the equation.

8x + 6y = 28 becomes 8(11) + 6y = 28

Now solve for y.

8(11) + 6y = 28
88 + 6y = 28
6y = -60 <-- Subtract 88 from each side
y = -10 <-- Divide both sides by 6

So, y is equal to -10.

If your front lawn is 24.0 feet wide and 20.0 feet long, and each square foot of lawn accumulates 1050 new snow flakes every minute, how much snow (in kilograms) accumulates on your lawn per hour? assume an average snow flake has a mass of 1.70 mg.

Answers

First find the area of the front lawn:
Area = length * width
Area = 24.0ft * 20.0ft
Area = 480ft^2

Next, find the weight in kilograms of the snow per square foot per hour per ft^2:
[tex]weight\ per\ ft^{2}=\frac{1050\ snowflakes}{minute}\\\\weight\ per\ ft^{2}=\frac{1050\ snowflakes}{minute}*\frac{1.70\ milligrams}{snowflake}*\frac{1\gram}{1000\milligrams}*\frac{1\kilogram}{1000\grams}* \frac{60\minutes}{1\hour}\\\\weight\ per\ ft^{2}=\frac{1050*1.70}{1000*1000*60}*\frac{kg}{hour}=2.975*10^{-5}\ \frac{kg}{hour}\\\\weight=2.975*10^{-5}\ \frac{kg}{hour*ft^{2}}[/tex]

Now multiply the area of the lawn by the weight of the snow per hour per ft^2:
[tex]weight\ of\ snow=lawn\ area*weight\ per\ hour\ per ft^{2}\\\\weight=480\ ft^{2}*2.975*10^{-5}\ \frac{kg}{hour*ft^{2}}\\\\weight=0.01428\ \frac{kg}{hour}[/tex]



Thus your answer is .01428 kg.

Which of the following is true of the location of the terminal side of an angle 0 who's sine value is 1/2?
0 has a reference angle of 30° and is in quadrant one or two
0 as a reference angle 30° and is in quadrant one or four
0 has a reference angle of 60° and is in quadrant one or two
0 as a reference angle of 60° in is in quadrant one or four

Answers

Answer:

A) 0 has a reference angle of 30° and is in quadrant one or two

Step-by-step explanation:

Given :

Terminal side of an angle = 0

Therefore, the terminal side is the x-axis.

sin = 1/2

Sin value is 1/2 when it is 30 degrees.

In the quadrant I and II, the sine value must be positive.

Therefore, the answer is A) 0 has a reference angle of 30° and is in quadrant one or two

Hope this will helpful.

Thank you.

The true statement of the location of the terminal side of an angle is that 0 has a reference angle of 30° and is in Quadrant I or II

What is Standard Position?

It is known to be an angle which is said to be in the same or standard position only when its vertex is seen at the center and one ray is seen in the positive x-axis. The ray seen on the x-axis is known to be the first or initial side and the second or other ray is known to be the terminal side.

Based on the above, the Terminal side of an angle is known as 0

and Sin (theta) =  ½

The Basic angle was given as 30

So we say 180-30 = 150

We say that the terminal side is the x-axis = sin = 1/2

So therefore, Sin as 1/2 only if it is 30 degrees and In the quadrant I and II, the sine value have to be positive value.

Therefore, the option A where 0 has a reference angle of 30° and is in quadrant one or two is correct.

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A= (4,5) B= (7,-9) what is AB ?

Answers

If you are needing to find the distance between the two points, you must use a simple formula, cleverly named, the distance formula. Since I can't input special characters into the answer box, I'll explain it the best I can.

( The square root of (  (x - x)^2 + (y - y)^2 )  )

First, we need to find the first x subtracted from the second x, as so:
(4,5) and (7,-9)

4 - 7 = -3

Now, we square the -3.

-3^2 = 
-3 * -3 = 9

Next, we have to find the first y subtracted from the second y.
(4,5) and (7,-9)

5 - (-9) = 14

Now, we square the 14.

14^2 =
14 * 14 = 196

Let's see how the numbers fit in the formula:

sqrt((x - x)^2 + (y - y)^2)

sqrt((4 - 7)^2 + (7 - (-9))^2)

sqrt((-3)^2 + (14)^2)

sqrt( 9 + 196 )

This is where we currently are in the formula, all we have to do now is square root the total of 9 + 196.

sqrt( 9 + 196 )
sqrt( 205 )

The square root of 205 = 14.31782106...

There are a few answers you can consider:

1) sqrt(205)
2) 14.32 units
or
3) 14.31782106

Depending on the answer you desire, use the one that sounds the most correct to you. Although all three are correct, it may not be the answer you require. 

Hope I could help! If my math is incorrect, or I provided answers you were not looking for, please let know! However, if my answer is correct and well explained, please consider marking my answer as Brainliest! :)

Have a good one.
God bless!

is this answer right

Answers

B IS YOUR ANSWER HOPE IT HELPS
The answer should be B.

Fourteen divided by a number is 14/x, but we're looking for a number divided by 14 which is x/14.
You should use minus rather than less than because less than implies the use of the < symbol.

Write the equation is logarithmic form

33 = 27




A.
log 27 = 3


B.
log327=27


C.
log327 = 3


D.
log 27 = 3 · 3

Answers

We use the log rule logₐ b = x   ⇒   aˣ = b

Given (3)³ = 27

Following the rule, we can write (3)³ = 27 as

log₃ 27 = 3

Correct Answer: C

Final answer:

The correct logarithmic form of the equation 3³ = 27 is log3(27) = 3, which matches option C, showing that the exponent to which the base 3 must be raised to get 27 is 3.

Explanation:

The question asks to express the equality 3³ = 27 in logarithmic form. By definition, the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number.

Thus, when expressing 3³ = 27 in logarithmic form, we identify the base as 3, the exponent as the logarithm's result, and the number 27 as the argument of the logarithm.

Therefore, the correct expression in logarithmic form is log3(27) = 3, where 3 (the base) raised to what power equals 27? The answer is 3, making option C correct.

570 people die from smoking related diseases everyday ?
A) how many die form related diseases every hour?
B) how many die form related diseases every week?
C) has many die form related diseases every year?

Answers

(570 people/ 1 day)* (1 day/ 24 hours)= 23.75 people/hour.


The rate of people who die from smoking is 23.75 people die per hour.

The rate of people who die from smoking is 3,990 people die per week.

The rate of people who die from smoking is 207,408 people die per year.

Hope this helps and if your feeling generous leave a rate, thanks, and brainliest it would really help me reach expert and I would greatly appreciate ;)

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