Aljan and Bella are both driving from Cleveland to Chicago. Aljan leaves at
7:40 and averages 60 mph (miles per hour on the way. Bella leaves at 8:00
and averages 65 mph on the way. The situation is modeled by this system,
where x is the number of hours after Bella leaves and y is the distance each
will travel:
y = 60x + 20
y = 65x
How long after Bella leaves will she pass Aljan, and how far will they each
have traveled?
Answer:
Bella will pass Ajjan after 4h and they will have travelled 260 miles.
Step-by-step explanation:
In order to calculate the number of hours, "x", that it'll take for Bella to pass Aljan, we need to find the value of "x" that makes both equations equal. Therefore,
[tex]60*x + 20 = 65*x\\65*x - 60*x = 20\\5*x = 20\\x = \frac{20}{5} = 4[/tex]
In order to calculate the distance they traveled, we must use this value for "x" in any of the equations, as done below:
[tex]y = 65*4\\y = 260[/tex]
Bella will pass Ajjan after 4h and they will have travelled 260 miles.
Answer:
Bella will pass Ajjan after 4h and they will have travelled 260 miles.
Step-by-step explanation:
If A = {2, 3, 4, 5} and B = {5, 6, 7, 8}, what is A U B?
{2, 3, 4, 5, 6, 7, 8)
{5}
Hey!!!!
Here's your answer:
Solution:
A={2,3,4,5}
B={5,6,7,8}
A U B={2,3,4,5} U {5,6,7,8}
={2,3,4,5,6,7,8}
In case of Union,we have to list all the elements which are present in both sets.
Hope it helps...
Good luck on your assignment
The numerator of a rational number is less that it’s denominator by 7.If the new number becomes 3/2 when the numerator is tripled and the denominator is increased by 16, find the original number
Pls help me with this question
Answer:
[tex]\frac{23}{30}[/tex]
Step-by-step explanation:
let the denominator of the original fraction be x, then
[tex]\frac{x-7}{x}[/tex] ← is the original fraction
After the given changes, that is
[tex]\frac{3(x-7)}{x+16}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )
6(x - 7) = 3(x + 16) ← distribute parenthesis on both sides
6x - 42 = 3x + 48 ( subtract 3x from both sides )
3x - 42 = 48 ( add 42 to both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Thus
[tex]\frac{30-7}{30}[/tex] = [tex]\frac{23}{30}[/tex] ← the original rational number
anyone help me please?
Answer:
The angle is 36.87°
Step-by-step explanation:
To find the missing angle, we will have to use inverse SOH-CAH-TOA.
Looking at the angle, as well as the two sides, we can infer that the opposite of the unknown angle is 24. Since the given side is not the hypotenuse but the adjacent, we know that we will be using inverse tangent (TOA).
[tex]tan^{1}[/tex] (x) = [tex]\frac{24}{32}[/tex]
x = [tex]tan^{-1}[/tex] ([tex]\frac{24}{32}[/tex])
x = 36.87°
Answer:
≈ 36.9
Step-by-step explanation:
You are given the opposite and adjacent side, leading you to use tan. However, since you're trying to find the angle measurement, and not the side, you use the inverse of tan: [tex]tan^-1[/tex]
Set it up like this:
[tex]tan^-1 (\frac{24}{32})=?[/tex]
When you solve, you get:
36.86
Round to the nearest tenth:
36.9
A rectangular street sign has an area of 40 square inches and a perimeter of 28 inches. What are the dimensions of the sign?
inches by inches
Answer: 4 inches by 10 inches
Step-by-step explanation:
The area of a rectangle can be written as b*h, while perimeter is equal to (2b +2h).
A = b*h = 40
P = 2b + 2h = 28
P = 2b + 2h
28 = 2b + 2h
28 = 2(b+h)
14 = b + h
What two numbers add to 14 and multiply to 40?
4 * 10 = 40
4 + 10 = 14
Answer:
10 and 4
Step-by-step explanation:
The solid glass award that Jillian was given has a total height of 15 inches as shown. A rectangular pyramid with a base of 6 inches by 4 inches and a height of 15 inches. A rectangular prism with a length of 6 inches, width of 4 inches, and height of 2 inches. What is the total volume of glass used to make the award? 120 inches cubed 152 inches cubed 168 inches cubed 204 inches cubed
Answer:
204inches i think
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
edge
If a wave has a velocity of 24 m/s and a period of 3.0 s. what is he frequency of the wave in Hz?
Answer:
Step-by-step explanation:
8hz
Which of the following statements is true? A. sin(j)>cos(L) B. sin(L)
Answer:
a
Step by step explanation:
maybe
Someone help me please !!
13 points
Answer:
idk
Step-by-step explanation:
2) The sum of two numbers is 100. Their difference is 4. What are the two numbers?
Answer: 48, 52
Step-by-step explanation:
The sum of the two numbers (x, y) is 100. This means that;
x+y=100
Their difference is 4, so;
y=x+4
Now, you can substitute that in for y;
x+(x+4)=100
Simplify;
2x+4=100
2x=96
x=48
Now, we plug in the value of x to the second equation;
y=48+4
y=52
Answer:
48 and 52
Step-by-step explanation:
We have a pair of simultaneous equations and will solve these using substitution.
x + y = 100 (1)
x - y = 4 (2)
Solve for x:
x+y=100 , x - y = 4
x=52
Substitute x with 52
(52) + y = 100 , (52) - y = 4
Simplify:
y = 48
Solve for x. Your answer must be simplified. x/-8 ≥−5
Answer:
x ≤ 40
Step-by-step explanation:
Given
[tex]\frac{x}{-8}[/tex] ≥ - 5
Multiply both sides by - 8 to clear the fraction, reversing the symbol as a result of multiplying by a negative quantity.
x ≤ 40
Solve for y.
212-y=282
Answer:
y = -70
Step-by-step explanation:
212 - y = 282
212 - 282 = y
-70 = y
y = -70
PLZ HELP ME! I NEED HELP ON THIS
Answer: D (-/ 13 - -/11) those are supposed to be square root signs lol^^
Step-by-step explanation:
In order to inscribe a circle in a triangle, which line must you construct?
Answer:
You must construct an angle bisector. The point where two angle bisectors meet is the center of the circle.
The correct answer is D. angle bisector.
Hope this helps =)
Find the measure of ∠G
So the right answer is 71 degree
Look at the attached picture
Hope it will help you
good luck on your assignment
Morgan's grandmother orders her groceries online and has them delivered to her house.
Her bill is $120. She has a coupon for 20% off and plans to give the delivery driver a
15% tip.
Answer: The total price of the groceries, including discount and tips $110.4
Step-by-step explanation:
write a table to show your steps for calculating the standard deviation and then use your table to calculate the standard deviation of the values listed:
10, 11, 12, 10.5, 11.25, 12.25, 10
Answer:
The standard deviation for the given data set is 1.65.Step-by-step explanation:
The Standard Deviation is defined as
[tex]\sigma =\sqrt{\frac{\Sigma (x_{i} -\mu)^{2} }{N-1} }[/tex]
Where [tex]\sigma[/tex] is the standard deviation, [tex]\mu[/tex] is the mean and [tex]N[/tex] is the total number of data.
So, first, we need to find the mean of the data set.
[tex]\mu = \frac{10+11+12+10.5+11.25+12.25+10}{7} =11[/tex]
Now, we have to subtract each data with the mean to then elevate the differnece to the square power.
[tex]10-11 = -1 \implies (-1)^{2}=1\\ 11-11 = 0 \\12-11 = 1 \implies 1^{2}=1\\ 10.5-11 = -0.5 \implies (-0.5)^{2} =0.25\\11.25 - 11 = 0.25 \imples (1.25)^{2}=0.0625\\12.25 - 11 = 1.25 \implies (1.25)^{2}=1.5625\\10-11 = -1 \implies (-1)^{2}=1[/tex]
Then, we sum all these results.
[tex]\Sigma (x_{i}- \mu )^{2}=1+0+1+0.25+0.0625+1.5625+1=16.278[/tex]
Next, we divide the sum by [tex]N-1=7-1=6[/tex]
[tex]\frac{\Sigma (x_{i}-\mu )^{2} }{N-1}=\frac{16.278}{6} \approx 2.713[/tex]
Finally, we apply the square root.
[tex]\sigma = \sqrt{2.713} \approx 1.65[/tex]
Therefore, the standard deviation for the given data set is 1.65.
What is the volume of a rectangular prism with the dimensions base 3 1/4 cm height2 1/2 cm and the length 4 1/2 cm?
Answer:
36.5625 cm^2
Step-by-step explanation:
To find volume, you multiply the three dimensions.
Answer:
36.56 cu. cm
Step-by-step explanation:
Volume = base x height x length
hi what s the answer
Answer:
a) 60%
b) 55%
Step-by-step explanation:
a) Count the shaded boxes: 6
Count the total: 10
6 / 10 = 60%
b) Count the shaded boxes: 11
Count the total: 20
11 / 20 = 55%
Answer:
Hey!
a) 60%
b) 55%
Step-by-step explanation:
how do you get a??
we have to c ount the shaded boxes: 6 boxes
6 divided by 10 = 0.6 (multiply by 100 to get 60%)
Now...
We have to count the shaded boxes: 11 boxes in total
Count the total available boxes: 20
11 divided by20 = 0.55 (multiply by 100 to get 55%)
HOPE THIS HELPS!!
Factor the algebraic expression -18y - 27
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
-18y = (-1) * 3 * 3 * 2 * y
-27 = (-1) * 3 * 3 * 3
Common factors = (-1) * 3 * 3 = - 9
-18y - 27 = -9*2y - 9 * 3
=(-9) [2y + 3]
Find the value of b. Round your answer to the nearest tenth.
Step-by-step explanation:
Try using Pythagoras theorem. a^2+b^2=c^2. in this triangle c would be the length you are finding. substitute the other lengths into the equation.
7 ∙ 15 can be written as _____.
5(7 + 10)
10(7 + 5)
7(10 + 5)
Answer:
7(10+5)
Step-by-step explanation:
40 points
What are the slope and the y-intercept of the linear function that is represented by the table?
x
y
Negative three-fourths
Negative StartFraction 1 Over 30 EndFraction
Negative one-half
Negative StartFraction 2 Over 15 EndFraction
One-fourth
Negative StartFraction 13 Over 30 EndFraction
Two-thirds
Negative three-fifths
The slope is Negative two-fifths, and the y-intercept is Negative one-third.
The slope is Negative one-third, and the y-intercept is Negative two-fifths.
The slope is One-third, and the y-intercept is Negative two-fifths.
The slope is Two-fifths, and the y-intercept is Negative one-third.
Answer:
c
Step-by-step explanation:
did the exam on edge and got 100
The slope is Negative two-fifths, and the y-intercept is Negative one-third. Hence, the correct option is A.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The slope of the linear function that is represented by the table,
Slope, m = [(-3/5) - (-13/30)]/[(2/3)-(1/4)]
= [(-18+13)/30] / [(8-3)/12]
= -(12/30)
= -(2/5)
The y-intercept of the linear function that is represented by the table can be found by substituting the coordinate of any one point in the equation of the line.
[tex]y = mx + c\\\\-(\dfrac{2}{15}) = -(\dfrac{2}{5})(-\dfrac12) + C\\\\-\dfrac{2}{15} = \dfrac15 + C\\C = -\dfrac5{15}\\\\C = -\dfrac13[/tex]
Hence, The slope is Negative two-fifths, and the y-intercept is Negative one-third. Hence, the correct option is A.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ2
A)50ft2
B)104ft2
C)54ft2
D)208ft2
Answer:
77
Step-by-step explanation:
PLs help me with this it is really quick!!
Answer:
It's the first one.
Step-by-step explanation:
The first one cannot be folded into a square because of its shape. This question is more of an IQ question so it's not really something you can teach to someone else, but I hope this helps and that you will get it!
Identify the sets as integers,natural numbers or whole numbers {0,5,10,15}
Answer: They are all of the above.
Step-by-step explanation: A integer is a whole number, a whole number is a integer and a natural number is a whole number. The definition of a whole number is a number with no fractions, the definition of a integer is a number with no fractions, and the definition of a natural number is a positive number.
2
Select the correct answer.
In an axiomatic system, which category do points, lines, and planes belong to?
A
theorems
B.
axioms
C.
undefined terms
D.
definitions
Solve by substitution
y=2x-3
-x-8y=7
Answer & Step-by-step explanation:
y = 2x - 3
-x - 8y = 7
Since, we have a equation for y, then we can substitute this equation for y to solve for x.
-x - 8(2x -3) = 7
-x - 16x + 24 = 7
-17x + 24 = 7
-17x = -17
x = 1
So, since we know that x is equal to 1, then we can plug in this number for the equation of y to find y.
y = 2(1) - 3
y = 2 - 3
y = -1
So, the solution is (1, -1). X equals 1 and y equals -1.
At the Math Club awards ceremony,
8 guests sat at each table. All of the
17 tables were filled. If each guest
received 2 awards, how many awards
were given out at the ceremony?
Answer:
272
Step-by-step explanation:
8 people on 1 table * 2 awards= 16 awards per table
16 awards per table * 17 tables = 272
Hope that breaks it down for you. Good luck with homework
Answer:
272 awards
Step-by-step explanation:
Step 1: 8 x 17= 136 (Find how many guest arrived)
Step 2: 136 x 2= 272 (Multiply guest by awards per guest)
Enjoy the answer.
9. You have a globe that has a diameter of 22 inches. Find the volume of
your globe. Use 3.14 for pi and round your answer to the nearest whole
number.
A) 523 cubic inches
B) 44,580 cubic inches
C) 7,235 cubic inches
D) 5,572 cubic inches
Answer:
D
Step-by-step explanation:
4/3 * pi * r^3 is the formula.