Answer:
When the truck is full: [tex]g_{mf} = \frac{m}{8}[/tex]
When the truck is empty: [tex]g_{me} = \frac{m}{9.6}[/tex]
Step-by-step explanation:
When the truck is full for every eight miles traveled by the vehicle, there is a cost of one gallon of fuel, therefore for every mile the cost is one eight of a gallon, with this information we can create the following expression:
[tex]g_{mf} = \frac{m}{8}[/tex]
Where m is the number of miles traveled by the truck.
When the vehicle is empty, it's performance improves by 20 %, which means that for the same amount of fuel it'll travel a distance 120% of the previous one. Therefore we need to multiply 1.2 on the denominator of the last expression:
[tex]g_{me} = \frac{m}{8*1.2}\\\\g_{me} = \frac{m}{9.6}[/tex]
The expression represents the amount of gasoline used (g) is,
When the truck is full (mf) is represented as [tex]m_f = \dfrac{m}{8}[/tex],
And when the truck is empty (me) is represented as, [tex]m_e = \dfrac{m}{9.6}[/tex]
Given that,
A long-distance delivery truck averages 8 miles per gallon when the truck is full.
The miles per gallon improve by 20% when the truck is empty.
We have to determine,
Which expression represents the amount of gasoline used (g) in terms of the number of miles driven when full (mf) and the number of miles driven when empty (me).
According to the question,
The amount of gasoline used (g) in terms of the number of miles driven when full (mf),
And The distance delivery truck averages 8 miles per gallon when the truck is full.
The amount of gasoline when the truck is full is represented as,
[tex]m_f = \dfrac{m}{8}[/tex]
Then,
The miles per gallon improve by 20% when the truck is empty.
The number of miles driven when empty is represented as,
[tex]m_e = \dfrac{m}{8 + 8 \times 0.20}\\\\m_e = \dfrac{m}{8+ 1.6}\\\\m_e = \dfrac{m}{9.6}[/tex]
Hence, The expression represents the amount of gasoline used (g) is,
When the truck is full (mf) is represented as [tex]m_f = \dfrac{m}{8}[/tex],
And when the truck is empty (me) is represented as, [tex]m_e = \dfrac{m}{9.6}[/tex].
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A total of 937 people attended the play admission was two dollars for adults and $.75 for students the total ticket sales amounted to $1109 how many students and adults attended the school play
Answer:
325 adults
Step-by-step explanation:
x=#adults
y=#children
x+y=937
2x+0.75y=1109
2x+2y=1874
-2x-0.75y=1109
1.25y=765
y=612
x=937-612
x=325
pls help for brainliest
Answer:
70cm2
Please mark
Step-by-step explanation:
Answer:
396 cm²
Step-by-step explanation:
The figure is composed of 2 rectangles.
The vertical rectangle on the left has area (A) calculated as
A = 27 × 10 = 270 cm²
The horizontal rectangle on the right has area (A) calculated as
A = 9 × (24 - 10) = 9 × 14 = 126 cm²
Thus area of figure = 270 + 126 = 396 cm²
Please help
Destiny wants to purchase a handbag that is on sale. The regular price is $175 but the discount is currently $20 dollars an item. What will the sales price be?
Answer:
the
Step-by-step explanation:
sale would be $20 for every item, duh
Which is the graph of f(x) = + (4)?
Answer:
Step-by-step explanation:
The graph of f(x) = + (4) is the same as that of g(x) = 4; it's a constant function defined for all x values but its range is just one number: 4.
please help will mark brainliest!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
256
Step-by-step explanation:
<1=<8 -->alt exterior angles
<4=<1 --> vertical angles
= <1=<4=<8(128)
256
what is the equation of the line of best fit for the following data (4,3) (6,4) (8,9) (11,12) (13,17)
Answer:
The table of data is shown below
The equation of line best fit is given in the form y=mx+b
to find the slope 'm', follow these steps:
STEP 1
Mean (X) = \frac{4+6+8+13+11}{5}=8.4
Mean(Y)= \frac{17+12+9+4+3}{5}=9
STEP 2
Refer to Picture 2 and Picture 3 for the working out of ( x_{i} -mean(X)) and ( y_{i} -mean(Y))
( x_{i}-X)( y_{i}-Y) =(-4.4)(8)+(-2.4)(3)+(-0.4)(0)+(2.6)(-5)+(4.6)(-6)
( x_{i}-X)( y_{i}-Y) =(-35.2)+(-7.2)+0+(-13)+(-27.6)=-83
STEP 3:
( x_{i}-X) ^{2} = (-4.4)^{2}+ (-2.4)^{2}+ (-0.4)^{2}+ (2.6)^{2}+ (4.6)^{2}=53.2
STEP 4:
To find slope, divide answer in STEP 2 by the answer in STEP 3
m= \frac{-83}{53.2} =-1.56
STEP 5:
b=Mean(Y)-[slope*mean(X)]
b=9-(-1.56*8.4)=22.105
We have the slope, m=-1.56 and y-intercept of 22.105
The equation of line is
y=22.105-1.560x
Correct answer: Last statement
Step-by-step explanation:
Please help! Correct answer only, please! Find the following product if possible. Explain if it is not possible. A. B. C. D.
Answer:
Option (B)
Step-by-step explanation:
If A = [tex]\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}[/tex] and B = [tex]\begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}[/tex]
Multiplication of these matrices,
A.B = [tex]\begin{bmatrix}1 & 3\\ -2 & 5\end{bmatrix}\times \begin{bmatrix}-2 & 1\\ 3 & 4\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}(1(-2)+3(3) & 1(1)+3(4)\\ (-2)(-2)+5(3) & 1(-2)+5(4)\end{bmatrix}[/tex]
= [tex]\begin{bmatrix}7 & 13\\ 19 & 18\end{bmatrix}[/tex]
Therefore, Option (B) will be the answer.
Find all solutions for a triangle with C = 130°, c = 17, and b = 5. Round to the nearest tenth.
a.A= 37.0°, B = 15.0°, a = 15.2
c.A = 37.0°, B = 13.0°, a = 13.4
b. A= 35.0°, B = 13.0°; a = 15.4
d no solutions
Answer:
C
Step-by-step explanation:
Use sine rule
17/sin130=5/sinB
(5×sin130)÷17=sinB
sinB=0.2253017892
B=sin^-1ans above
=13.4
A=(130+13) subtracted from 180=37°
a/sin37=17/sin130
=13.4
please help me with math
Answer:
6. composite figure
7. 60+432=492
If a ray _______ an angle of a triangle, it divides the opposite side into segments proportional to the lengths of the other two sides. An angle bisector divides an angle into two _______ halves. A perpendicular bisector is the line perpendicular to a segment passing through the segment’s _______.
Answer:
bisects, equal, midpoint
Step-by-step explanation:
According to the "Angle Bisector" Theorem, an angle bisector of a triangle divides the opposite side into segments proportional to the lengths of the other two sides of the triangle.
If a ray bisects an angle of a triangle, it divides the opposite side into segments proportional to the lengths of the other two sides. An angle bisector divides an angle into two equal halves. A perpendicular bisector is the line perpendicular to a segment passing through the segment’s midpoint.
Jack picked 60Apples from an apple tree he uses 12 of them to make applesauce replaces the remaining apples equally into six gift basket which equation can be used to determine the number of Apples place is in to each gift basket?
Answer
60 apples minus how many she picked (12) or 60-12 divided by 6 baskets. The answer will be 60-12=48. 48 divided by 6 equals 8. The ANSWER IS 8
Step-by-step explanation:
The formula used to calculate how many apples should be included in each gift basket is as follows:
6x = 48
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
Jack has 48 apples left after using 12 of the 60 apples he took from the tree to make applesauce.
The leftover apples will be distributed equally among six gift baskets, he said. He puts x apples in each present basket, where x is the number of apples. Then he adds six times as many apples to each of the six gift baskets.
He has to fill the gift baskets with 48 apples, thus we can create an equation:
6x = 48
We may divide both sides of the equation by 6 after finding the value of x:
x = 8
Hence, Jack needs to fill each of the six gift baskets with 8 apples.
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What is the value of this expression when a = 7 and b = -4? | 2a | - b/3 A.) -6 B.) -3 1/3 C.) 3 1/3 D.) 6
The answer to the question what is the value of this expression when a = 7 and b = -4? | 2a | - b/3 it is D.) 6
The value of this expression (|2a| - b)/3 when a = 7 and b = -4 is 6. So, option D is correct.
What is the modulus function?The absolute value of a number or variable is returned by a modulus function. It is defined as
|x| = x, x > 0
= -x, x < 0
= 0, x = 0
How to solve this problem?The given expression is (|2a| - b)/3. Here, we have to put a = 7 and b = -4 to get the value.
Now, (|2a| - b)/3 = (|2×7| - (-4))/3 = (|14| + 4)/3 = (14 + 4)/3 [Since 14 is a positive integer]
i.e. (|2a| - b)/3 = 18/3 = 6
Therefore, the value of this expression (|2a| - b)/3 when a = 7 and b = -4 is 6. So, option D is correct.
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What is the volume of this cylinder?
Use a ~ 3.14 and round your answer to the nearest hundredth.
10 mm
7 mm
Answer:
[tex]1538.6mm^{3}[/tex]
Step-by-step explanation:
[tex]V=\pi r^{2} h[/tex]
[tex]V=3.14*7^{2} *10[/tex]
[tex]V=31.4*49=1538.6[/tex]
A bookstore manager marks down the price of older hardcover books, which originally sell for b dollars, by 42%. Part 1 out of 4 Enter an expression for the markdown using a decimal. The markdown is ..... (Answer this question piece)
Answer:
0.42
Step-by-step explanation:
The original price of the old hardcover books was sold for b dollars. But the manager markdown the hardcover books by 42%.
The expression of the markdown using a decimal can be represented below.
Recall the markdown is 42 %. If you want to convert from percentage to a decimal, you have to move the decimal point two places to the left . The percentage sign is removed at this stage and the value is represent in decimal. Or you can just divide the percentage value by 100.
In our case the percentage value can be solved as 42/100 = 0.42 in decimal or by just simply moving the decimal points two places to the left which is 0.42.
Find the volume of a right circular cone that has a height of 18.8 inches and a base with a diameter of 14.3 inches. Round answer to the nearest tenth of a cubic inch.
Answer:
The volume of the right circular cone is [tex]1005.9\ \text{inch}^2[/tex].
Step-by-step explanation:
It is given that,
Height of a right circular cone is 18.8 inches and its diameter is 14.3 inches. We need to find the volume of the cone. The volume of cone is
[tex]V=\dfrac{1}{3}\pi r^2 h[/tex]
So,
[tex]V=\dfrac{1}{3}\times 3.14\times (\dfrac{14.3}{2})^2\times 18.8\\\\V=1005.9\ \text{inch}^2[/tex]
So, the volume of the right circular cone is [tex]1005.9\ \text{inch}^2[/tex].
Answer:1006.5
Step-by-step explanation:
Hodel just got her driver's license. Her parents offer her two options. 1. They'll buy her a used car that will cost her $0.50 per mile in gas and maintenance fees. 2. They'll buy her a new hybrid car but she'll have to contribute $5,000 to the cost. The new car will then cost her an additional $0.10 per mile in gas and maintenance fees. If she plans to keep the car until she graduates from college in six years and she intends to drive it 10,000 miles each year, which option will cost her less?
Answer:
The second option will cost her less than the first one.
Step-by-step explanation:
In order to solve this problem we will create two functions to represent the cost of the car in function of the miles drove by her.
For the first option we have:
[tex]cost_1(x) = 0.5*x[/tex]
For the second option we have:
[tex]cost_2(x) = 5000 + 0.1*x[/tex]
Since she intends to drive it for 10,000 miles per year for 6 years, then the total mileage she intends to drive her car is 60,000 miles. Applying this to the formula of each car and we have:
[tex]cost_1(60000) = 0.5*60000 = 30000[/tex]
[tex]cost_2(60000) = 5000 + 60000*0.1 = 11000[/tex]
The second option will cost her less than the first one.
If mike reads 50 pages an hour how long would it take him to read 1225 pages
Which of the following options have the same value as %70, percent of 80?
Answer:
A, C and E.
Step-by-step explanation:
[tex]70 \% \times 80[/tex]
[tex]70/100 \times 80[/tex]
[tex]560/10[/tex]
[tex]=56[/tex]
[tex]0.7 \times 80[/tex]
[tex]=56[/tex]
[tex]7/10 \times 80[/tex]
[tex]=56[/tex]
Solve
1. x2 + x - 6 = 0
Answer:
x = -3 x=2
Step-by-step explanation:
x^2 + x - 6 = 0
Factor
What two numbers multiply to -6 and add to 1
3*-2 =-6
3+-2 =1
(x+3) (x-2) = 0
Using the zero product property
x+3 = 0 x-2 = 0
x = -3 x=2
The graph shown here is the graph of which of the following rational functions
Answer:
The answer is 100% B
Step-by-step explanation:
The graph of the polynomial rational function is f ( x ) = x / ( x + 2 ) ( x - 5 )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the polynomial function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = x / ( x + 2 ) ( x - 5 )
The rational function is of the form P ( x ) / Q ( x ) , where Q ( x ) ≠ 0
So , the value of P ( x ) = x
And , the value of Q ( x ) = ( x + 2 ) ( x - 5 )
Therefore , the graph of the rational function is plotted
Hence , the graph of the polynomial is f ( x ) = x / ( x + 2 ) ( x - 5 )
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Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!
Answer:
smaller r = ( 6.5 , 0)
larger r = ( 21.5 , 0)
vertex = ( 14, -56.25)
Step-by-step explanation:
f(r) = (r -14)² -56.25 square (r-14)
f(r) = r² -28r +196 -56.25 simplify
f(r) = r² -28r + 139.75
use quadratic formula
x=−b±√(b²−4ac)/ 2a
a = 1, b =-28, c = 139.75
x=−(−28)±√(−28)2−4(1)(139.75)2(1)
x=(28±√225)/2
x=43/2 or x=13/2
or 21.5 and 6.5
This parabola is given in vertex form f (r) = a(r - h)² + k, where (h, k) is the vertex of the parabola so just write the given numbers ( 14, -56.25)
Simplify
2 * (3 - 1) + 3
7
8.
10
11
Answer:
7.
Step-by-step explanation:
Follow the order of operations.
We do the operation in the bracket first. So we are left with:
2 * (2) + 3
We multiply before we add, so:
4 + 3.
Finally, we add.
7.
I hope this helps!
Zak paid 450 dorllarsfor a motor at discount of 10% find the actual selling price of the motor I need it ASAP
Answer:
hey. Answer is $495 as the actual price of the motor without discount.
Step-by-step explanation:
So you would multiply 450 by .10 and you get 45. So he got $45 off. Then add 450 to 45. Yoy get $495!
A house valued at £210,000 correct to 2 significant figures. A) What is the lowest value of the house? B) What is the highest value of the house?
Answer:
Range could be 205000 to 214999. Any number in this range, when rounded to two signnificant digits will yield 210000.
A virus is spreading around Summerfield. At the moment, 800 people are infected. If the virus is spreading at a rate of 15% each day, how many people in all will have caught the virus in 12 days? Write an equation to
represent the situation. *
A y=800(0.85)^12
B y=800(0.15)^12
C y=800(1.15)^12
D y=0.85(800)^12
E y=0.15(800)^12
F y=1.15(800)^12
G y=(0.85•800)^12
H y=(0.15•800)^12
I y=(1.15•800)^12
Answer:
C y=800(1.15)^12
Step-by-step explanation:
Solve for m.
m − 10 + 6m = 10 + 2m
m =
Answer:
m = 4
Step-by-step explanation:
m−10+6m=10+2m
7m-10=10+2m
Subtract 2m from both sides
5m-10=10
Add 10 to both sides
5m=20
Divide both sides by 5
m=4
Answer:
m=4
Step-by-step explanation:
m − 10 + 6m = 10 + 2m
7m - 10 = 10 + 2m (subtract 2m from both sides)
7m - 10 - 2m = 10
5m - 10 = 10 (add 10 to both sides)
5m = 10 + 10
5m = 20 (divide both sides by 5)
m = 20/5
m = 4
What is the exact value of sin(5π/12)?
(please give steps)
Answer:
0.966053748
Step-by-step explanation:
[tex] \sin \bigg( \frac{5\pi}{12} \bigg) \\ = \sin \bigg( \frac{5 \times 180 \degree}{12} \bigg) \\ = \sin ( 5 \times 15 \degree) \\ = \sin ( 75 \degree) \\ = \sin ( 45 \degree + 30 \degree) \\ = \sin 45 \degree \times \cos 30 \degree + \cos 45 \degree \times \sin 30 \degree \\ \\ = \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2} + \frac{1}{ \sqrt{2} } \times \frac{1}{2} \\ \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } + \frac{1}{2 \sqrt{2} } \\ \\ = \frac{ \sqrt{3} + 1}{2 \sqrt{2} } \\ \\ = \frac{1.732 + 1}{2 \times 1.414} \\ \\ = \frac{2.732}{2.828} \\ \\ = 0.966053748[/tex]
The line AB has midpoint (2, 5).
A has coordinates (1, 7).
Find the coordinates of B.
Answer:
(3,3)
Step-by-step explanation:
Answer:
(3,3)
Step-by-step explanation:
To find the midpoint add the x coordinates together and divide by 2
(1+ xb)/2 = 2
1+ xb = 4
xb = 4-1
xb =3
To find the midpoint add the y coordinates together and divide by 2
(7+ yb)/2 = 5
7+ yb = 10
yb = 10-7
yb =3
I want to know what is 600 minutes to days
Answer:
Not even a whole day. To be exact, it is .416667 of a day
Step-by-step explanation:
Since 60 minutes are in 1 hour, than 600 minutes would be 10 hours.
24 hours in a day, so you are 14 hours short, about 840 minutes.
Answer:
~0.42 days
Step-by-step explanation:
60 minutes in one hour
60 times 24 = 1440 minutes in a day
600 minutes divided by 1440 = 0.4166666667...
Rounded up to 0.42
technically not a whole day but yeah
If the length of AC equals 50, what is the length of the midsegment DE?
Answer:
Length of DE is 25.
Step-by-step explanation:
Right, so this is something called midsegment theorem. ΔDBE is similar (but not congruent) to ΔABC because of the angles they share. Since DE is described as a midsegment, this means BE=EC and BD=DA; so ΔDBE is half the size of ΔABC, meaning its side lengths are also half that of the larger triangle.
(Sorry if this information was unnecessary. Just got an answer deleted because I wasn't detailed enough.)