Answer:
Route A is 0.75 km longer than route B.
Step-by-step explanation:
Length of route A is 1.5 times the length of route B.
a = 1.5b
[tex]\frac{a}{b}=\frac{15}{10}[/tex]
[tex]\frac{a}{b}=\frac{3}{2}[/tex] --------(1)
Here, a = Length of route A
b = Length of route B
Length of route A is [tex]\frac{3}{4}[/tex] of route C.
a = [tex]\frac{3}{4}c[/tex]
[tex]\frac{a}{c}=\frac{3}{4}[/tex] ------(2)
Here, c = Length of route C
Length of route C = 3 km
Length of route A = [tex]\frac{3}{4}\times 3[/tex] [From equation (2)]
= 2.25 km
Length of route B = [tex]\frac{2}{3}\times 2.25[/tex] [From equation (1)]
= 1.5 km
Difference in route A and route B = 2.25 - 1.5
= 0.75 km
Therefore, route A is 0.75 km longer than route B.
A history teacher is writing a test worth 100 points. She uses multiple-choice questions worth 6 points
each and true/false questions worth 2 points each. She wants the test to have three times as many
multiple-choice questions as true/false questions. Let m represent the number of multiple-choice
questions on the test, and let t represent the number of true/talse questions. Which system of
equations can be used to find how many each type of question she should write?
6m + 2t = 100
m=t+3
6m + 2t = 100
m = 3t
3m+t=100
m=31
6m + 2t = 100
t = 3m
Answer:6m + 2t= 100
t=3m
Step-by-step explanation:
A parabola has its minimum point at (3,-5) and the y coordinate of the y-intercept is -2.
What is the equation of the parabola?
Answer:
y = [tex]\frac{1}{3}[/tex] x² - 2x - 2
Step-by-step explanation:
x-coordinate of the vertex of a parabola is ( [tex]- \frac{b}{2a}[/tex] )
y = f(x) = ax² + bx + c
(x, y) ∈ f(x)
~~~~~~~~~
{ (0, - 2), (3, - 5) } ⊂ { (x, y): y = ax² + bx + c }
a(0)² + b(0) + c = - 2 ⇒ c = - 2
a(3)² + b(3) + ( - 2) = - 5
9a + 3b - 2 = - 5 ⇒ 3a + b = - 1
[tex]- \frac{b}{2a}[/tex] = 3 ⇒ b = - 6a
[tex]\left \{ {{3a+b=-1} \atop {b=-6a}} \right.[/tex]
3a + ( - 6a) = - 1
a = [tex]\frac{1}{3}[/tex]
b = - 2
y = [tex]\frac{1}{3}[/tex] x² - 2x - 2
The equation of the parabola for the given values is y = x²/3 - 2x - 2.
What is a parabola?A parabola is the part of the conic section of which the points are equidistant from a fixed line called as directrix and a fixed point known as focus.
The general equation for the parabola is given as,
y = ax² + bx + c
Where c is the y-intercept.
Substitute c = -2 as per the question to obtain,
y = ax² + bx - 2
At (3,-5) the parabola has minimum value which implies y' = 0 as below,
y' = 2ax + b = 0
Substitute x = 3 to obtain,
2a × 3 + b = 0
=> -6a = b
And, y = -5 at x = 3 which gives,
-5 = 3²a + 3b - 2
=> 9a + 3b = -3
Substitute b = -6a to get,
9a - 18a = -3
=> a = 1/3
Which implies b = -6 × 1/3 = -2
Now, the equation for the parabola becomes as below,
y = x²/3 - 2x - 2
Hence, the required equation of the parabola is obtained as y = x²/3 - 2x - 2.
To know about parabola click on,
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I need help solving this system
Answer:
x=3 and y=-7
Step-by-step explanation:
just cause lol
Answer:
(x, y) = (3, -7)
Step-by-step explanation:
[tex]\left \{ {{x - 3y = 24} \atop {5x + 3y = -6}} \right.[/tex]
[tex]\left \{ {{x-3y=24} \atop {3y=-6-5x}} \right.[/tex]
[tex]x-(-6-5x)=24[/tex]
[tex]x=3[/tex]
[tex]3y=-6-5(3)[/tex]
[tex]y=-7[/tex]
[tex](x,y)=(3,-7)[/tex]
CHECKING IF ANSWER IS CORRECT:
[tex]\left \{ {{3-3(-7)=24} \atop {5(3)+3(-7)=-6}} \right.\\\left \{ {{24=24} \atop {-6=-6}} \right. \\(x,y)=(3,-7)[/tex]
There is your answer with steps :)
Is the mean of 5 negative numbers positive or negative? explain
Answer: Always negative
David had $30 to spend on three gifts.He spent 10 ¼ dollars on gifts A and 5 ⅘ dollars on gifts B.How much money did he have left for gifts C.
Answer: $13.95
Step-by-step explanation:
1/4 of a Dollar is 25 cents
4/5 of a Dollar is 80 cents
30 - 10.25 = 19.75
19.75 - 5.80 = 13.95
David has $13.95 to spend of Gift C
What is the domain of the function Y = 3 In * graphed below?
Answer:
(0, infinity)
Step-by-step explanation:
Keep in mind that the input to the ln function can never be 0 or below. The coefficient 3 has no effect on the domain. The domain of the function shown is (0, infinity).
The domain of the function y = 3 log x is x > 0.
Option A is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
y = 3 log x
The domain of the function y = 3 log x can never be less than zero.
So,
The domain is from 0 to ∞.
Thus,
The domain is (0, ∞).
Learn more about functions here:
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Please help i need this
Answer:7
Step-by-step explanation:
Craig collects stamps. He collected a total of 225 stamps. If 68% of the stamps he collected were foreign, how many other stamps did he collect
PLEASE HELP ME ITS MY LAST QUESTION
Answer:
30 degrees
Step-by-step explanation:
yes
yesterday 50 bakery customers muffins and 11 of those customers bought bran muffins if 150 customers buy muffin's tomorrow how many bran muffins will the bakery need to bake
Answer:
33 banana muffins
Step-by-step explanation:
11/50 = x/150
50x=1650
50x/50=1650/50
x=33 !
Thank you so much :)
Answer:
b
Step-by-step explanation:
PLANTS The table shows the heights of
sixteen corn stalks.
3. What were the heights of the shortest
and tallest stalks?
Answer: blue, to love me, to nice, to i love you, to be a good boy and suck.
Step-by-step explanation:
hi I am girl
Sally has 2 cats and each cats eats 1/4 tin of cat food every day
Sally buys 9 tins of cat food
For how many days will the cat food feed her 2 cats?
Answer:
18 days
Step-by-step explanation:
Given, Amount of cat food eaten by each cat per day = 1/4 th of a tin
Amount of cat food eaten by 2 cats per day = 1/4 × 2 part of a tin = 1/2 of a tin No. of days 9 tins will last = 9 × 2 = 18
4 people are going to a dinner party. Each person at
the party will eat pound of cake. If you can only buy
whole pounds of cake, how many pounds should you
buy?
Answer:
92 pounds
Step-by-step explanation:
Here is the complete question ;
4 people are going to a dinner party. Each person at the party will eat 23 pound of cake. If you can only buy whole pounds of cake, how many pounds should you buy?
total pounds to be bought = number of people at the party x total pounds they would eat
4 x 23 = 92 pounds
ASAP question in the picture
Answer:
try answer C 33ft
Step-by-step explanation:
A family had 1/3 of pizza left over. Later 3 people shared the remaining 1/3 equally. What fractional part of the whole pizza did each get
Answer: 1/9 pizza portions
Step-by-step explanation:
The pizza was left with only 1/3 of it and 3 people shared this.
The fractional part of the whole pizza that each of the three people ate is therefore:
= Percentage of who pizza left / Number of people
= 1/3 ÷ 3
= 1/3 * 1/3
= 1/9 pizza portions
Juan is solving the problem 7 divided by 1/3. What related multiplication fact will he use to solve?
HELP.....to support the high school the local business will donate five dollars for every ticket sold at the homecoming game. If 121 students, 158 home, and 47 visitors tickets were sold, how much money did they donate?
Answer:
2130 but see the note below
Step-by-step explanation:
Remark
It does not matter whether the home team or the visiting team got the support. All that matters is the total number of tickets. Just eye balling it looks like about 1500 dollars.
Equation
Total Donation = 5 * (121 students + 158 + 47)
Solution
Total Donation = 5(426)
Total Donation = 2130
Note:
There is a problem with with. 121 students cannot be included in the 158 or in the 47. If they are, there is no way to be sure what the answer is. I have solved it as though there were 3 separate categories. If that isn't so, you will get it wrong.
does the graph below represent y as alinear function of x. yes or no
9514 1404 393
Answer:
No
Step-by-step explanation:
The graph is not a straight line with define slope, so does not represent a linear function.
__
The graph has segments that are straight lines. It is what we call "piecewise linear."
The table of values shows the height of a buoy compared to the sea floor over time as the tide goes in and out. This can be modeled by a sinusoidal function.
Which statements are true?
Select EACH correct answer
The maximum value of the function is 5.8
The amplitude of the function is 5.8
The period of the function is 24
The frequency of the function is 24
Answer:
1st statement is true
2nd is false (amplitude is (max - min) ÷ 2 so (5.8 - 4.6) ÷ 2 = 0.6)
3rd is true
4th is false (frequency is the reciprocal of period, they can't be the same)
plz help me fast Thomas goes out to eat at a restaurant and orders fajitas for $12.95 and orders a soft drink for $1.50. Tax is 7% on his total order, and thomas plans to leave with a 20% tip on the entire bill including tax. How much will his dinner cost including tax and tip.
Answer:
$18.55
Step-by-step explanation:
I added the meal and drink then used a calculator and addded that total plus 7% of it then I added 20% of that to get 18.55
12.95+1.50 = x
x + 7% = y
y+ 20%
Which system of equations could be represented by the graph?
Find the missing measure of the arc formed by the endpoints of a central angle.
Answer:
The missing measure of the arc is 125°.
Step-by-step explanation:
Since the circle is 360°, you would first subtract 360 by the degrees given: 360-115-35-85 and the sum is 125. Then, you would set 125 equal to -32x-3 to solve for x.
[tex]125=-32x-3[/tex]
[tex]+3[/tex] [tex]+3[/tex]
-----------------------
[tex]\frac{128}{-32} =\frac{-32x}{-32}[/tex]
[tex]x=-4[/tex]
The missing measure of the arc is 125°.
Micheal and his family are at a basketball game. Micheal decides that he is buying. He buys pretzels and sodas. The pretzels cost $3 and the sodas cost $2. His purchase of 5 items totaled $12. How many pretzels and how many sodas did Michael purchase?
Question 1
1. Which expression is equivalent to 4(2x + 3)?
A. 4 + 2x + 4 +3
B. 8x + 12
C. 8x + 3
D. 4 + 2x + 12
СА
OB
oc
CD
Answer:
B.) 8x + 12
Step-by-step explanation:
Using the Distributive Property the 4 is multiplied by each number inside the parentheses
4*2x = 8x
4*3 = 12
8x+12
Answer: it’s B
Step-by-step explanation: lol I didn’t want to do the math
In a race a cyclist travels 3/8 of the distance in the first hour and 1/3 of the distance in the second hour. What fraction of the total distance has he travelled? What fraction of the total distance does he need to travel in the third hour to complete the race.
Answer:
7/24
Step-by-step explanation:
Answer:
Distance traveled:
3/8 + 1/3 = 9/24 + 8/24 =17/24Remaining distance:
1 - 17/24 = 24/24 - 17/24 =7/24PLEASE CLICK THE INAGE I NEED HELP PLEEEAAASSSE!!!
Answer:
Question 3: There are 12 boys in the class.
Question 4: 120 cookies were not oatmeal raisin.
Question 5: Target offers the best deal.
Step-by-step explanation:
If the ratio of girls to boys is 3:2, and there are 18 girls, that means there will be [tex]\frac{18}{3}[/tex] * 2 = 6 * 2 = 12 boys.
Because there are 200 cookies total, and [tex]\frac{2}{5}[/tex] of them are oatmeal raisin, that means that [tex]\frac{3}{5}[/tex] of the cookies aren't oatmeal raisin. 200 * [tex]\frac{3}{5}[/tex] = 40 * 3 = 120 cookies that aren't oatmeal raisin.
The cookies at Kroger have a unit rate of $0.45 per cookie, the cookies at Meijer have a unit rate of $0.50 per cookie, the cookies at Walmart have a unit rate of $0.38 per cookie, and the cookies at Target have a unit rate of $0.20 per cookie. So Target has the better buy.
Steve earned $7.40 per hour working his paper route. The first week, he worked 16 hours. After getting paid, he put $105 in the bank and spent the rest on rides at the carnival. Each ride cost $0.75. How many rides did Steve ride at the carnival?
Answer:17
Step-by-step explanation: Multiply Steve’s hourly wage ($7.40) by the hours he worked in a week (16 Hours) that would give you your weekly earnings which would be (7.40x16=$118.40) Then subtract what he saved in the bank from your total (118.40-105=$13.40) then you would divide $13.40 (his leftover money) by $0.75 to find the total number of carnival rides he could ride (13.40/0.75=17.86 rides and because he cannot ride 17 and 86 hundredths of a ride he would be able to ride 17 carnival rides.
What is the slope? Please help..
Answer:
its 3, bae
Step-by-step explanation:
trust me on this one
A car travels 160 miles in 4 hours. How many miles per hour does the car
travel?
Answer:
40 mph
Step-by-step explanation:
160÷4 = 40 miles per hour
Answer:
40miles per hour
Step-by-step explanation:
distance traveled/time spent=speed(velocity)
160/4=speed (velocity)
40mph
