Answer:
Fuel efficiency of first car = 30 miles/gallon
Fuel efficiency of second car = 25 miles/gallon
Step-by-step explanation:
Given that:
Fuel consumed by first car = 40 gallons
Fuel consumed by second car = 15 gallons
Total distance drove by the two cars combined = 1575 miles
Sum of their fuel efficiencies = 55 miles/gallon
To find:
The fuel efficiencies of each of the cars = ?
Solution:
Fuel efficiency of a car is defined as the ratio of distance traveled in miles to the number of gallons used by the car.
Let the distance traveled by first car = [tex]x[/tex] miles
So, the distance traveled by other car = (1575 - [tex]x[/tex]) miles
Fuel efficiency of first car = [tex]\frac{x}{40}[/tex] miles/gallon
Fuel efficiency of second car = [tex]\frac{1575-x}{15}[/tex] miles/gallon
As per given question statement:
[tex]\frac{x}{40}+\frac{1575-x}{15}=55\\\Rightarrow 15x+1575\times 40-40x=55\times 40 \times 15\\\Rightarrow 25x=30000\\\Rightarrow x =1200\ miles[/tex]
Distance traveled by first car = 1200 miles
Fuel used by first car = 40 gallons
So, fuel efficiency of first car = [tex]\frac{1200}{40} = \bold{30\ miles/gallon}[/tex]
Distance traveled by second car = 1575 - 1200 = 375 miles
Fuel used by second car = 15 gallons
So, fuel efficiency of second car = [tex]\frac{375}{15} = \bold{25\ miles/gallon}[/tex]
13 points answer this asappppp
Find the value of the function below for the given x-value
F{x} = -5x-1 when x=-3
A.15
B 14
C-16
D-14
Five cubic meters of copper has a mass of 44,800 kilograms. What is the density of copper?
Density = mass / volume
Density = 44,800 kg/ 5m^3
Density = 8,960 km/m^3
Write the equation of the quadratic function whose graph passes through [tex](-3,2)[/tex], [tex](-1,0)[/tex], and [tex](1,6)[/tex].
Answer:
[tex]f(x)=x^2+3x+2[/tex]
Step-by-step explanation:
We want to write the equation of a quadratic whose graph passes through (-3, 2), (-1, 0), and (1, 6).
Remember that the standard quadratic function is given by:
[tex]f(x)=ax^2+bx+c[/tex]
Since it passes through the point (-3, 2). This means that when [tex]x=-3[/tex], [tex]f(x)=f(-3)=2[/tex]. Hence:
[tex]f(-3)=2=a(-3)^2+b(-3)+c[/tex]
Simplify:
[tex]2=9a-3b+c[/tex]
Perform the same computations for the coordinates (-1, 0) and (1, 6). Therefore:
[tex]0=a(-1)^2+b(-1)+c \\ \\0=a-b+c[/tex]
And for (1, 6):
[tex]6=a(1)^2+b(1)+c\\\\ 6=a+b+c[/tex]
So, we have a triple system of equations:
[tex]\left\{ \begin{array}{ll} 2=9a-3b+c &\\ 0=a-b+c \\6=a+b+c \end{array} \right.[/tex]
We can solve this using elimination.
Notice that the b term in Equation 2 and 3 are opposites. Hence, let's add them together. This yields:
[tex](0+6)=(a+a)+(-b+b)+(c+c)[/tex]
Compute:
[tex]6=2a+2c[/tex]
Let's divide both sides by 2:
[tex]3=a+c[/tex]
Now, let's eliminate b again but we will use Equation 1 and 2.
Notice that if we multiply Equation 2 by -3, then the b terms will be opposites. So:
[tex]-3(0)=-3(a-b+c)[/tex]
Multiply:
[tex]0=-3a+3b-3c[/tex]
Add this to Equation 1:
[tex](0+2)=(9a-3a)+(-3b+3b)+(c-3c)[/tex]
Compute:
[tex]2=6a-2c[/tex]
Again, we can divide both sides by 2:
[tex]1=3a-c[/tex]
So, we know have two equations with only two variables:
[tex]3=a+c\text{ and } 1=3a-c[/tex]
We can solve for a using elimination since the c term are opposites of each other. Add the two equations together:
[tex](3+1)=(a+3a)+(c-c)[/tex]
Compute:
[tex]4=4a[/tex]
Solve for a:
[tex]a=1[/tex]
So, the value of a is 1.
Using either of the two equations, we can now find c. Let's use the first one. Hence:
[tex]3=a+c[/tex]
Substitute 1 for a and solve for c:
[tex]\begin{aligned} c+(1)&=3 \\c&=2 \end{aligned}[/tex]
So, the value of c is 2.
Finally, using any of the three original equations, solve for b:
We can use Equation 3. Hence:
[tex]6=a+b+c[/tex]
Substitute in known values and solve for b:
[tex]6=(1)+b+(2)\\\\6=3+b\\\\b=3[/tex]
Therefore, a=1, b=3, and c=2.
Hence, our quadratic function is:
[tex]f(x)=x^2+3x+2[/tex]
In 2016 Jane was 14 years old. At that time she was 7 times as old as her brother, Jim. In what year will Jane be twice as old as Jim will be then?
Answer:
Step-by-step explanation:
Mary will be twice as old as her brother when the age of her brother is equal to the ... Add this value of 8 to Mary's & her brother's present age. ... In three years time I will be half my brother's age. ... In 4 years, she will be four times as old as her son was 9 years ago
GEW has angle measures given by m<=5x+6 m<=3x and m
Answer:
(D) 24°
Step-by-step explanation:
(5x + 6)° + (3x)° + (142 - 4x)° = 180°
5x + 6 + 3x + 142 - 4x = 180
4x + 148 = 180
4x = 32
x° = 8°
m∠E = 3×8° = 24°
Is there a triangle whose angles have these measures in degrees?
A) Yes
B) No
Answer:
No
Step-by-step explanation:
The sum of all internal angles on a triangle must equal 180°
[tex]28 + 64 + 100 = 192[/tex]
Your friend has $100 when he goes to the fair.he spends $10 to enter the fair and $20 on food.rides at the fair cost $2 per ride.which function can be used to determine how much money he has left over after x rides
Answer:
The answer is A f(x)=-2x + 70
Step-by-step explanation:
What is the 100th term of the sequence with a1 = 222 and d = -5
Answer:
-273
Step-by-step explanation:
222- (99*5)
222-495
-273
Answer:
-273
(next time if their is options maybe also try and put them, it would help a lot)
PLEASE HELP ILL GIVE BRAINLIEST!
Answer: Image #1: C. Distributuve Property Image #2: A. n + 2(7)
Step-by-step explanation: For Image #1, they used the Distributive Property because the number 3 was (distributed) and multiplied to both x and 7. The equation is saying that 3x + 21 = 42, and that we’re trying to solve for x. For Image #2, the answer is A. n + 2(7) because after you solve the expression, the answer would be 14n. When you look at the four options, (A. B. C. D.), letter A. would be the answer because it equals to 14n.
Subtract 2.53 x 105 from 1.3 x 108
Answer:
125.2 is your answer dear
Answer:
Step-by-step explanation:
2.53 x 105 is 265.65
1.3 x 108 is 140.4
now, Subtract 2.53 x 105 from 1.3 x 108
140.4 - 265.65
= -125.25
Hope this helps
plz mark as brainliest!!!!!!
If a line on a graph is horizontal, what kind of slope does it have?
a.) undefined slope
b.) negative slope
c.) zero slope
d.) positive slope
Answer:
Zero Slope
Step-by-step explanation:
Hope this helps!
Find the measure of angles 1,2 and 3
Answer:
1-75 2-105 3-35
Step-by-step explanation:
1- 180-75-30=75
2- 180-75=105
3- 180-105-40=35
CAN U GUYS HELP ME WITH THIS?!! 11 POINTS AND BRAINLY PLEASEEEE!!!????
Answer: X=-6
Step-by-step explanation:
Answer:
B. -6
Step-by-step explanation:
Melanie deposits $8200 in a bank account paying 4.4% simple interest. How much money will be in her account after 5 years and 6 months?
Answer:
8200+1894.40 = $10,094.40
Step-by-step explanation:
The formula we'll use for this is the simple interest formula, or:
I = P x r x t
Where:
P is the principal amount, $8200.00.
r is the interest rate, 4.4% per year, or in decimal form, 4.4/100=0.044.
t is the time involved, 5.5....year(s) time periods.
So, t is 5.5....year time periods.
To find the simple interest, we multiply 8200 × 0.044 × 5.5 to get that:
The interest is: $1984.40 + add to Investment ($8000) and you'll get the answer.
Solve for bbb. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. 30b+53 \geq 18b -8330b+53≥18b−8330, b, plus, 53, is greater than or equal to, 18, b, minus, 83
Answer:
b ≥ - 34 / 3
Step-by-step explanation:
Given the inequality :
30b+53≥18b−83
Collect like terms
30b - 18b ≥ - 83 - 53
12b ≥ - 136
Divide both sides by 12
12b / 12 ≥ - 136 / 12
b ≥ - 34 / 3
Hence, b ≥ - 34/3
Answer:
b≥− 34/3
Step-by-step explanation:
help will mark brainliest if correct :)
Answer:
Step-by-step explanation:
x= 0.079
y=-0.169
Answer: x= 0.079
y=-0.169
Step-by-step explanation:
what is the cube root of -27
Answer:
-3
Step-by-step explanation:
[tex]\sqrt[3]{-27}[/tex] is -3 and can be proven by doing [tex]-3^{3}[/tex] as -3 x -3 x -3 of itself will give you -27, as [tex]\sqrt[3]{-27}[/tex] is just -27/-3/-3
1l) HAO WENT TO A HOBBY SHOP AND SAW A DISPLAY OF TOY TRAINS. THE SIGN IN FRONT OF
THE DISPLAY SAID THAT THE TOY TRAINS WERE A REPLICA OF THE LONG ISLAND RAILROAD
TRAINS. HAO ESTIMATED THAT ONE OF THE RAILROAD CARS WAS APPROXIMATELY 15
INCHES LONG AND 4 INCHES WIDE. THE SIGN IN FRONT OF THE DISPLAY STATED
"SCALE- 2 /9".
WHAT IS THE LENGTH OF THE RAILROAD CAR ON HE LONG ISLAND RAILROAD?
WHAT IS THE WIDTH OF THE LONG ISLAND RAILROAD CAR?
Answer:
Length = [tex]57.5\ \text{inches}[/tex]
Width = [tex]18\ \text{inches}[/tex]
Step-by-step explanation:
The scale of the toy train is [tex]\dfrac{2}{9}[/tex]
So, the dimensions of the toy train is [tex]\dfrac{2}{9}[/tex] times the actual dimensions of the train.
The dimensions of actual train is [tex]\dfrac{1}{\frac{2}{9}}=\frac{9}{2}[/tex] times the toy train's dimensions.
Length
[tex]15\times \dfrac{9}{2}=57.5\ \text{inches}[/tex]
Width
[tex]4\times \dfrac{9}{2}=18\ \text{inches}[/tex]
The length of the railroad car on the long island railroad is 57.5 inches.
The width of the railroad car on the long island railroad is 18 inches.
Find the unit rate. Round your answer to the nearest hundredth.
3500 calories for 6 servings of pie
I have been asking and asking for help and not one hleped me all they did was troll and say dumb stuff that has nothing to do with the question plss hlep me I can't do this
Answer:
Try 120
Step-by-step explanation:
There are five dashes in between 100 and 200. Count up by 20s
#1: Solve the linear system below using the elimination method. Type your
answer as an ordered pair in the form (#,#).*
5x + 3y = 1
-5x – 7y = 31
The given linear system is:
[tex]\displaystyle \left \{ {{5x+3y=1} \atop {-5x-7y=31}} \right.[/tex]
Linear systems can be solved using either elimination or substitution. However, the question is asking to solve using elimination, so I will use that method.
When eliminating, you can either eliminate x or y. In this system, x is much easier to eliminate. The x variable in the first equation is 5x, and in the second equation, it is -5x. Since 5 and -5 cancel each other out, you don't need to do anything other than add.
[tex]5x+3y=1\\-5x-7y=31[/tex]
[tex]\displaystyle 3y-7y=1+31\\-4y=32[/tex]
Lastly, you need to leave the variable y alone. The variable is currently -4y or -4 times y. To remove it, you need to do the opposite of it, which is dividing by -4.
Divide both sides by -4:
[tex]\displaystyle\frac{-4y}{-4} =\frac{32}{-4}[/tex]
[tex]\displaystyle y=-8[/tex]
Now that you have the value of y, substitute it into one of the equations to find x. I will be substituting it into the first equation.
[tex]\displaystyle 5x+3y=1 \rightarrow 5x+3(-8)=1[/tex]
Open the parentheses and multiply:
[tex]5x-24=1[/tex]
Move 24 to the other side to leave the variable alone:
[tex]5x-24+24=1+24[/tex]
You will be adding since you're "removing" it by doing the opposite of it.
[tex]5x=25[/tex]
Lastly, divide both sides by 5 to leave x alone.
[tex]\displaystyle \frac{5x}{5} =\frac{25}{5}[/tex]
[tex]x=5[/tex]
[tex]\displaystyle (x,y) \rightarrow (5, -8)[/tex]
The answer is (5, -8).
2) The value of y is directly proportional to the value of x. Given y = 12 when x = 36.
What is the value of y when x = 60? Show your work to receive full credit.
Answer:
I believe the answer is 20
Step-by-step explanation:
An element with mass 570 grams decays by 18% per minute. How much of the element is remaining after 13 minutes, to the nearest 10th of a gram?
9514 1404 393
Answer:
43.2 grams
Step-by-step explanation:
The exponential equation for the decay can be written as ...
amount remaining = (initial amount)(1 -decay rate)^t
= 570(1 -0.18)^t
We want to find the amount remaining after 13 minutes. Evaluating this equation for t=13, we have ...
amount remaining = 570(0.82^13) ≈ 43.2 . . . grams
Is 4 x 2/3 greater than 4?
Answer:
No
Step-by-step explanation:
4 is larger than 1, and 2/3 is less than 1, so if you multiply 4 by anything less than 1 you get a product that is less that the first factor.
Answer:
No
Step-by-step explanation:
g(x)=f(x-1)-5
Describe the transformation to f(x) that results in g(x).
1
2
f(x) has been
translated to the left
one and down five.
f(x) has been
translated to the
right one and down
five.
f(x) has been
translated to the
right one and up five.
f(x) has been
translated to the left
one and up five.
Answer:
f(x) has been translated to the right one and down five.
Step-by-step explanation:
Given
[tex]g(x)=f(x-1)-5[/tex]
Required
Determine the transformation
Taking the analysis one at a time
The relationship between f(x) and f(x - h) is that f(x) is translated h units to the right
So, when f(x) becomes f(x-1), it is as a result of f(x) being translated 1 unit to the right
The relationship between f(x) and f(x) - h is that f(x) is translated h units downwards
So, when f(x - 1) becomes f(x - 1) - 5, it is as a result of f(x - 1) being translated 5 units downwards.
Hence, option 2 answers the question
In the equation 0.5x-8=1.5 the decimal coefficient is
Answer:-9.5
Step-by-step explanation:
Answer:
0.5
Step-by-step explanation:
The coefficient is the number that multiply the variable, in this case x.
HURRY PLEASE HELP Missy borrowed $5900 for seven years at an annual rate of 8%. What is the TOTAL AMOUNT that Missy will need to pay after 7 years? (principal AND interest)
Answer: $5933.04
Step-by-step explanation:
Principal = $5900
Rate = 8%
Time = 7 years
Simple interest = PRT/100
= (5900 × 8% × 7)/100
= (5900 × 0.08 × 7) / 100
= 3304/100
= $33.04
Total amount = Principal + Interest
= $5900 + $33.04
= $5933.04
Add, subtract, multiply or divide all for of these numbers to get a result equal or close to 51.
Numbers: 7, 8, 5, 6
You cannot add any new numbers. Please help i've been stuck on this for an hour now. :(
Estimate 7 x 522 ns
3.866 microseconds? 7 x 522 nano seconds = 3.86600 ms
5-3(2x-7)=2(7-3x)
What is true for the equation x=0, x=28, the equation has no solution or the equation has infinitely many solutions
Step-by-step explanation:
Part 1: 4x + 7 = 3(2x - 5)4x+7=3(2x−5)
4x+7=6x-154x+7=6x−15
7=6x-15-4x7=6x−15−4x
7=2x-157=2x−15
7+15=2x7+15=2x
22=2x22=2x
22=2x / 222=2x/2
x=11x=11
Part 2: Sam is not correct because he messed up the second step. He added 2x on both sides to get 7x, instead he should have subtracted.