Two cars leave an intersection at the same time. One drives east while the other travels south at 25 miles per hour faster than the other. After 2 hours, the cars are 250 miles apart. How fast is the southbound car driving?
Step-by-step explanation:
Pythagoras :
c² = a² + b²
c is the Hypotenuse (side opposite of the right angle), which is in our case the distance of the 2 cars.
after 2 hours the east car was driving x miles. and the south car was driving x + 2×25 = x + 50 miles.
x² + (x + 50)² = 250²
x² + x² + 100x + 2,500 = 62,500
2x² + 100x = 60,000
x² + 50x = 30,000
x² + 50x - 30,000 = 0
the solution for a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 50
c = -30,000
x = (-50 ± sqrt(2500 - 4×1×-30000))/(2×1) =
= (-50 ± sqrt(2500 + 120000)/2 =
= (-50 ± sqrt(122500))/2 = (-50 ± 350)/2 =
= -25 ± 175
x1 = -25 + 175 = 150 miles
x2 = -25 - 175 = -200 miles.
negative distances don't make any sense here in our scenario, so the solution is x = 150 miles.
therefore, the east car was going 75 mph (traveled in 2 hours 150 miles).
and the south car was going 75 + 25 = 100 mph (traveled in 2 hours 200 miles).
Use the table from a random survey about the preferred service for streaming movies. Out of 750 people, how many would you expect to prefer Company B?
Answer:
The correct answer option is 192
Step-by-step explanation:
We are given the results of a random survey about the preferred service for streaming movies.
We are to find the number of people we would expect to prefer Company B.
Number of people using service B = 32
Total number of people = 125
Number of people expected to prefer Company B =32/125 x 750 = 192
15)
Solve for X
X\42=6
A)
7
B)
252
C)
260
D)
332
Answer:
b)252 is the answer
Step-by-step explanation:
x\42=6
x=6*42
x=252
Which of the following statements is meaningless?
A.There was a 3% decrease in the price of sugar.
B.There was a 200% increase in the population of a town.
C.There was a 120% decrease in the amount of water in a dam. D.There was a 0% change in the temperature in the room after 1 hour.
Answer:
(C)
Step-by-step explanation:
If can't have a meaning as something can't decrease more than 100% of itself.
The statement that is meaningless is
There was a 120% decrease in the amount of water in a dam.
Option C is the correct answer.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
A percentage increase can be of any number.
A percentage decrease can not be below 100%.
Now,
A.
There was a 3% decrease in the price of sugar.
This is possible.
B.
There was a 200% increase in the population of the town.
This is possible.
C.
There was a 120% decrease in the amount of water in a dam.
This is not possible.
The highest percentage decrease can be up to 100%.
D.
There was a 0% change in the temperature in the room after 1 hour.
This is possible.
Thus,
There was a 120% decrease in the amount of water in a dam is meaningless.
Learn more about percentages here:
https://brainly.com/question/11403063
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proportion margin of error equation when proportion is negative
Step-by-step explanation:
1.Find the sample size, n, and the sample proportion. The sample proportion ρ is the number in the sample with the characteristic of interest, divided by n.
2. Multiply the sample proportion by 1 - ρ.
3. Divide the result by n.
4. Take the square root of the calculated value. You now have the standard error
If one of the roots of the equation x² – 4x + k = 0 exceeds the other by 2, then find the roots and determine the value of k.
Step-by-step explanation:
the solutions for a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -4
c = k
x = (4 ± sqrt(16 - 4k))/2 = 2 ± sqrt(4 - k)
x1 = 2 + sqrt(4 - k)
x2 = 2 - sqrt (4 - k)
x1 = 2 + x2
2 + sqrt(4 - k) = 2 + 2 - sqrt(4 - k)
2×sqrt(4 - k) = 2
sqrt(4 - k) = 1
4 - k = 1
k = 4 - 1 = 3
x1 = 3
x2 = 1
Answer:
The roots are 1 and 3.
k = 3.
Step- by-step explanation:
We use the facts that if α and β are the roots of ax^2 + bx + c = o then α+ β = -b/a and α β = c/a.
The roots are written as α and α+2, then:
α + α + 2 = -(-4)
2α + 2 = 4
α + 1 = 2
α = 1
also
α (α + 2) = k
Substituting for α:
1(1 + 2) = k
k = 3.
The roots are 1 and 1 + 2 = 3.
PLEASE HELP!!!!! 100 points!!!
The angle of elevation from an anchor to the top of a flag pole is 22 If the pole is
10 meters high, how long does the wire connecting the anchor to the pole must be?
(Round answer to the 1st decimal place.)
Answer:
26.7 mStep-by-step explanation:
The 22 degree angle is opposite to the 10 m side of the right triangle.
We need to find the length x of the hypotenuse.
Use trigonometry:
sine = opposite/hypotenusesin 22° = 10/xx = 10 / sin 22° x = 26.7 m (rounded)Answer:
PLEASE HELP!!!!! 100 points!!!
The angle of elevation from an anchor to the top of a flag pole is 22 If the pole is
10 meters high, how long does the wire connecting the anchor to the pole must be?
(Round answer to the 1st decimal place.)
Which of the following is a nonlinear function
Answer:
Linear functions are equations where the greatest power of the variable (typically x) is 1;
They are graphed as straight lines;
So, any function that has the following format:
f(x) = ax + b;
Nonlinear functions would be any equation that has a variable to a power greater than 1;
This could be a quadratic equation or an exponential equation
What force must be applied to a truck of mass 300kg for it to accelerate at 5m/s2
Answer:
mass=300kg
acceleration=5m/S2
force=?
Now,
force= m×A
=300kg×5
=1500 Newton answers
Step-by-step explanation:
hop this may help you
Which inequality is graphed on the number line?
Number line from 0 to 10. Start at 0. Count up by 1. Point t is depicted by an arrow from 6 to 0
A. t > 9
B. t < 0
C. t < 6
D. t > 6
Answer:
C
Step-by-step explanation:
If the line goes from 6 to 0 then that means it is decending and that T is LESS than 6
use substitution method (y = 2x-10 (2y=x-8
Answer:
(4, -2)
Step-by-step explanation:
Use the expression for y given by the first equation to substitute for y in the second equation.
2(2x -10) = x -8 . . . substitute for y
4x -20 = x -8 . . . . . eliminate parentheses
3x = 12 . . . . . . . . add 20-x
x = 4 . . . . . . . . .divide by 3
y = 2(4) -10 = -2 . . . substitute for x in the first equation
The solution is (x, y) = (4, -2).
[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\blue{S}\green{W}\red{E}\purple{R:-}}}[/tex]
We've been given to find out the values of x & y from the two given linear equations by substitution method.
Here we have,
y = 2x - 10 - - - - - (1) 2y = x - 8 - - - - - (2)As we have given the value of y i.e (y = 2x - 10) placing this value of y in the second equation we get,
[tex]:\implies\tt{2(2x - 10) = x - 8}[/tex]
[tex]:\implies\tt{4x - 20 = x - 8}[/tex]
[tex]:\implies\tt{4x - x = - 8 + 20}[/tex]
[tex]:\implies\tt{3x = 12}[/tex]
[tex]:\implies\tt{x = \frac{12}{3} }[/tex]
[tex]:\implies\tt{x = 4}[/tex]
Placing x = 4 in equation (1) we get,
[tex]:\implies\tt{y = 2x - 10}[/tex]
[tex]:\implies\tt{y = 2 \times 4 - 10}[/tex]
[tex]:\implies\tt{y = 8 - 10}[/tex]
[tex]:\implies\tt{y = - 2}[/tex]
The solution of the given system for linear equation is (x,y) = (4,-2)solve 4/6 x 2/5(PLEASE HELP I'M FAILING MATH!!!!!!!!!!!!!!!!!!!!!!!!!!)
[tex] \frac{4}{6} \times \frac{2}{5} \\ = \frac{4 \times 2}{6 \times 5} \\ = \frac{8}{30} \\ = \frac{4}{15} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
PLEASE HELP ME ASAP this is very important to me IT WILL RAISE MY GRADE and if you help me god bless you
Answer:
1/5 so the first option
Step-by-step explanation:
slope
(y2-y1)/(x2-x1)
Solve the system of equations 4x – 5y = –6 and -6x + 7y = 12 by
combining the equations.
Answer:
x=-9, y=-6. (-9, -6).
Step-by-step explanation:
4x-5y=-6
-6x+7y=12
----------------
6(4x-5y)=6(-6)
4(-6x+7y)=4(12)
-----------------------
24x-30y=-36
-24x+28y=48
-----------------------
-2y=12
y=12/-2
y=-6
4x-5(-6)=-6
4x+30=-6
4x=-6-30
4x=-36
x=-36/4
x=-9
please help!! (only correct answers and no links)
Four transformations of the function f(x) are given below.
For each transformation, drag the graph that shows the result of that transformation into the box under it.
Answer:
f(x) - 3 : the ones that move the graph down
f(x -3) : the ones that move the graph to the RIGHT
Step-by-step explanation:
graph transformations:
f (x-3):
if the number is inside the "()" sign with the x -> you will have to move the graph sideways (left or right), but it has a little twist: if the number is negative (i.e: f(x)-3), you will move the graph to the right, and if it is positive, you will move it to the left.
f (x) -3:
if the number is outside the "()" -> you will have to move the graph up or down. there is no twist here: if its negative, it goes down, if its positive, it goes up.
hope i could help:)
Write the expanded form of the expression.
3(4x - 6) =
Answer:
12x - 18
Step-by-step explanation:
3 x 4x = 12x
3 x -6 = -18 (Negative and positive make a negative.)
12x - 18
please answer, click on file, thank you
Answer:
3x²
im lazy to solve right now
hope it helps
Answer:
Step-by-step explanation:
half of the circle is 180 degrees
so x + 3x = 180
4x = 180
x = 45
Write the equation of the line with a slope of 3 and passes through the point (0,5).
Answer can be in either slope-intercept
form or point-slope
form
Answer:
y=3x+5
Step-by-step explanation:
y-y1=m(x-x1)
y-5=3(x-0)
y-5=3(x)
y-5=3x
y=3x+5
Note that the slope intercept form is y=mx+b where m=slope and b=y-intercept.
If you're satisfied with the answer, then please mark me as Brainliest. Thank you.
Can someone plz help me? :(
the answer to your question is B.) 12x
Rewrite this problem combining like terms!!
2 m − 3 m + 4
please help ASAP! A circular plate has a radius of 13 centimeters.
What is the area of the plate?
Use 3.14 for π.
Answer:
area = PI x r^2
area = 3.14 x 13^2
area = 3.14 x 169
area = 530.66
Step-by-step explanation:
Plz Mark as brainliest hope this helps
BRAINLIEST FOR CORRECT ANSWER
Two friends rent an apartment together. They agree that one person will pay 3 times what the other person pays. If the rent is $850, then what equation could be used to determine how much each person pays?
Answer:
n+3n=$850 n is one person and 3n is the other represented by n
Step-by-step explanation:
At the store one pack of pencils are on sale 4 for $1.25. Another pack has 8 pencils for $2.50 with 20% off. Which is the better deal?
Answer:
second pack
Step-by-step explanation:
1.25÷4= 0.31 so for the first pack 1 pencil cost $0.31
2.50×20%= 0.5 so its ¢50 off. 2.50-0.50= 2. 2÷8= 0.25. so for the second pack 1 pencil costs $0.25 which is lower than the 1st pack.
I hope it wasn't too confusing
I need helppp
It’s for math and I’m clueless
Answer:
14
Step-by-step explanation:
x=4 y=1
Substitute them into the equation 3x-4yy+6
3(4)-4(1)+6
12-4+6
=
The line y = 4x + 3 crosses the y-axis at A.
1) What is the coordinates of point A?
Answer:
A(0,3)
Step-by-step explanation:
the line crosses y-axis so its x-coordinates must be zero,
so we subistitute by x=0 in the equation of the line, from this we get y=3
then the coordinates of point A will be (0,3)
Solve the proportion
x/10=9/5
Answer:
X = 10*9/5
= 2*9
= 18
Answer = 18
Answer:
[tex]x=18[/tex]
Step-by-step explanation:
First way (equivalent fractions):
[tex]\frac{x}{10}=\frac{9}{5}[/tex]
[tex]\frac{x}{10}=\frac{18}{10}[/tex]
[tex]x=18[/tex]
Second way (cross multiplication):
[tex]\frac{x}{10}=\frac{9}{5}[/tex]
[tex]5x=90[/tex]
[tex]x=18[/tex]
8) The height of a stack of CD cases is Proportional to the number of CDs in the stack. A stack of 6 CDs is 66mm high.* Find the unit rate**
a) How high is a stack of 10 CDs?
b) Write an equation that relates the height (y) of a stack of CDs and the number of CD cases(x) in the stack.
please help I will mark your answer as brainliest
Answer:
a) 110 mm
b) y = 11x
Step-by-step explanation:
The unit rate for 6 CD at 66 mm is
66mm / 6 CD = 11 mm per CD
a) 10 CD's
66 mm x mm
--------- = ------------
6 CD 10 CD
Using cross products
66 * 10 = 6x
660 = 6x
Divide by 6
660/6 = x
110 mm for 10 CD's
b) y = 11 x
We use the rate and multiply by the number of cases to get the height
Please help me , correct answer will get brainiest!
answer is probably just 4
4/1 rise over run
Matthew wants to buy a new pair of jeans. If the jeans were originally $65.00, but are on sale with a 10% discount, how much will Matthew have to pay for the jeans?
10% off means the jeans will sell for 90% of the original price ( 100% - 10% = 90%)
Multiply the original price by 90%
65.00 x 0.90 = 58.50
He will pay $58.50
Please help ASAP. Trigonometry
Write TWO different equations that you could use to solve for x. You don't need to solve.
Answer:
cos(52°) = 18/x
x = 18·sec(52°)
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Cos = Adjacent/Hypotenuse
In this geometry, that means ...
cos(52°) = 18/x
You can use the relation sec(x) = 1/cos(x) to rewrite this as ...
x = 18·sec(52°)
_____
You can also use the complementary angle and the complementary trig function.
sin(90° -52°) = 18/x