1. Aubrey is driving on a long road trip. She currently has 14 gallons of gas in her car. Each hour that she drives, her car uses up 0.75 gallons of gas. How much gas would be in the tank after driving for 6 hours? How much gas would be left after tt hours?
2. Find the sum of -8x^2+3 and -9x^2+3x-3−
3.Simplify the expression to a polynomial in standard form:
(-3x-5)(-x^2+x-5)
Answer:
See solutions below
Step-by-step explanation:
1) Total amount of gallons = 14 gallons
If she uses up 0.75 gallons of gas each hour then;
1 hour = 0.75gallons
after driving 6 hours, amount of gallons used will be;
6 hours = x
Divide both expressions
1/6 = 0.75/x
x = 6 * 0.75
x = 4.5gallons
Amount of gas left = 14 - 4.5 = 9.5 gallons of gas
Hence 9.5 gallons of gas will be left after 6 hrs
Similarly;
1 hour = 0.75gallons
after driving t hours, amount of gallons used will be;
t hours = x
x = 0.75t
Amount of gas left after t hours = (14 - 0.75t) gallons of gas
2) We are to find the sum of -8x^2+3 and -9x^2+3x-3
-8x^2+3 + (-9x^2+3x-3)
= 8x^2+3 -9x^2+3x-3
Collect like terms
= 8x^2 -9x^2+3x + 3-3
= -x^2 + 3x
Hence the sum is -x²+3x
3) Expressing in standard form;
(-3x-5)(-x^2+x-5)
Expand
= 3x³-3x²+15x+5x²-5x+25
Collect like terms
= 3x³-3x²+5x²+15x-5x+25
= 3x³+2x² + 10x + 25
Hence the product in polynomial form is 3x³+2x² + 10x + 25
Leena lives 1 4/7 miles from school. She walks the first 6/7 mile by herself. Then she
walks the rest of the way with her friend. How far did Leena walk with her friend? Plz help
Answer:
Leena walked 5/7 miles with her friend
Step-by-step explanation:
7/7 = 1
7 +4 =11
Answer:
5/7
Step-by-step explanation:
Select all that apply. Which of the following name an angle in the drawing? ACB CDE ECB BDA
Answer:
ecb and acb
Step-by-step explanation:
Tomas collected 139 cans for recycling on Monday, and twice that number on Tuesday. How many cams did he collect on Tuesday
Answer:
278
Step-by-step explanation:
139x2=278
Given the system of equations. What is the x-value in the solution?
8x+ 3y = 7
4x + 3y = 5
Answer
a) (x + 7)(2x - 1)
b) (3x + 4)(x - 5)
c) (y + 9) (y + 4)
d) (b - 12)(b - 3)
please solve these i’m begging
Answer:
A.) [tex]2x^2 + 13x - 7[/tex]
B.) [tex]3x^2 - 11x - 20[/tex]
C.) [tex]y^2 + 13y + 36[/tex]
D.) [tex]b^2 - 15b + 36[/tex]
Step-by-step explanation:
For all of these you want to multiply the first thingy (Ex. x) in the first parenthesis by the first in the second parenthesis (Ex. 2x) plus the first one in the first (Ex. x) times the second one in the second (Ex. -1) plus the second one in the first one (Ex. 7) times the first one in the second parenthesis (Ex. 2x) plus the second one in the first parenthesis (Ex. 7) times the second one in the second (Ex. -1)
A.) (x + 7)(2x - 1) = (2x * x) + (-1 * x) + (7 * 2x) + (7 * -1) = 2x^2 -x + 14x - 7 = 2x^2 + 13x - 7
B.) (3x + 4)(x - 5) = (3x * x) + (3x * -5) + (4 * x) + (4 * -5) = 3x^2 - 15x + 4x - 20 = 3x^2 - 11x - 20
C.) (y + 9) (y + 4) = (y * y) + (4 * y) + (9 * y) + (9 * 4) = y^2 + 4y + 9y + 36 = y^2 + 13y + 36
D.) (b - 12)(b - 3) = (b * b) + (b * -3) + (-12 * b) + (-12 * -3) = b^2 - 3b - 12b + 36 = b^2 - 15b + 36
A scuba diver dives 10 meters below the surface of the ocean, and then dives down another 8 meters. How many meters down does the diver dive? Show an absolute value equation that can be used to find your answer.
what is x=9 z=2 times?
Answer:
x=9
z=2
Step-by-step explanation:
the measures of the angles of a triangle are shown in the figure below solve for x 46° 2x+20° 72°
Answer:
x = 21
Step-by-step explanation:
Add all the angles to get 138 + 2x = 180. Subtract 138 to get 2x = 42. x = 21
Answer:
x = 21
Step-by-step explanation:
Can I have brainliest?
A circle's circumference is 600 m.
What is a good approximation of the circle's area?
A. 300 m2
B. 3,000 m2
C. 30,000 m2
D. 300,000 m2
Answer:
i think its a but im not sure
3/4 into a percent and a decimal
Answer:
75% and .75
Step-by-step explanation:
Which classification best describes the relationship between <2 and <4?
Answer:
c) because 2*2 =4 and 4 -2 =2
Step-by-step explanation:
The circumference of a circle is 15 ft. find its area writing 3.14 for pi PLS
Answer:
17.9140127389 FT²
Step-by-step explanation:
Circumference is found using the formula 2πr.
15=2πr
r=15/(2*3.14)
r=2.38853503185
Area is found using the formula πr²
A= πr²
=3.14( 2.38853503185²)
=17.9140127389
( I will give brainlist) Mrs. Perkey solved the problem below. Oh no! It looks like she made a mistake! -3/5 + -2/5 = -1/5 What did she do wrong? Please explain how to solve this problem the correct way for full points.
Answer:
It is actually -1.
Step-by-step explanation:
((-3) / 5) + ((-2) / 5) her problem should be set up like this. She just plain out did -3/5+-2/5 and that is not what your supposed to do.
pls mark me brainliest
Answer:
-5/5= -1
Step-by-step explanation:
-3/5 + -2/5 = -5/5
when u have to add 2 minus values it shuld not be subtracted by each other but added instead and put the (-) sign infront of the final value as given above.
Take this decimal and express it in fraction and percentages.
.19
Answer:
0.19 = 19/100
19/100 = 19%
Step-by-step explanation:
take 0.19 x 100 = 19
that's where u get 19% and 19 over 100 from.
Answer:
0.19 = 19/100 = 19%
Step-by-step explanation:
1. Start with 0.19 (the given)
2. Read it out loud "19 hundredths"
3. Write down 19 out of 100 because that's what you said in the last step (if it were "0.3" you would write "3/10" because you read it as "three tenths"
4. Check if you can simplify. In this case you cannont
5. If the fraction is out of 100 (which in this case it is) simply write the numerator as the percent "19" is the numerator and it IS out of 100. You would write 19%
3 points) A fence is to be built to enclose a rectangular area of 240 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 13 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
Answer:
For the rectangular area, we will have a length L, and a width W, such that the two sides with measure L and one with measure W will be made with the material of $4 per ft, and the other side with measure W will be made with the material that costs $13 per ft.
Then the total cost will be:
C = (L + L + W)*$4 + W*$13.
And we know that the area is equal to 240 ft^2, then:
240ft^2 = L*W
To solve this, the first step is to isolate one of the variables in the second equation. I will isolate L:
L = (240ft^2)/W
Now we can replace this in the first equation to get:
C = ( 2*(240ft^2)/W + W)*$4 + W*$13.
C = $4*480ft^2/W + W*$17
Now we want to find the minimum of this function, then we need to look at the zero of the first derivative of C:
C' = - ($4*480 ft^2)/W + W*$17 = 0
- ($4*480 ft^2) + $17*W^2 = 0
Let's solve this for W:
$17*W^2 = ($4*480 ft^2)
W^2 = ($4*480 ft^2)/$17 = 112.94ft^2
W = √(112.94 ft^2) = 10.63 ft.
Then the width must be 10.64 ft, and the length can be obtained with the equation:
L*W = 240 ft^2
L*10.64 ft = 240 ft^2
L = (240 ft^2)/10.64ft = 22.56 ft
The width is 10.64 ft, and the length is 22.56 ft
The owner of a ballroom dance studio has 8 locations in the Houston area. Each studio is a 30 foot by 30 ft. room. If each couple requires 72 inch by 72 inch area, what is a reasonable estimate for the total number of people the dance company can accommodate in the city of Houston for all of it's locations?
Answer: 400
Step-by-step explanation:
Area required by each couple = 72 inch by 72 inch
= 6 feet by 6 feet [ 1 feet = 12 inches and [tex]72\text{ inches}=\dfrac{72}{12}\text{ feet}=6 \text{ feet}[/tex]]
= 36 square feet
Area in each studio = 30 ft by 30 ft = 900 square feet
Then, Area of 8 studios in Houstan = 8 x (900 feet) = 7200feet
Total couple the dance company can accommodate in the city of Houston for all of it's locations = [tex]\dfrac{7200}{36}=200[/tex]
Total people = 2 x (Total couples)= 2 x 200=400
Hence, a reasonable estimate for the total number of people the dance company can accommodate in the city of Houston for all of it's locations = 400
Find the value of m.
Answer:
Step-by-step explanation:
x=2
a=1.25
m=3.75
tell me if u need any steps
Marco sells and ships oranges from the trees in his orange grove for $1.25 per pound plus a shipping fee. One package has a shipping fee of $4.95 and a total cost of $11.20. Write and solve an equation to find the number of pounds of oranges in the package. Show your work.
(Please help )
Answer:
Let x = the number of pounds of oranges in the packet.
The equation: 11.20 = 1.25x + 4.95
11.20 = 1.25x+4.95
6.25 = 1.25x
x = 5
There are 5 pounds of oranges in the packet.
Let me know if this helps!
1/2 + 34 + 2/3
What is the answer!?
Answer:
35 OR 35.1666666667
Step-by-step explanation:
Answer:
the answer rounded to the nearest hundredth is 35.17
Step-by-step explanation:
What values of x solve the equation f (x) = 1
Solve the Equation p - 15 = 30.
Answer:
45
Step-by-step explanation:
add 15 on both sides
a knife is three times the cost of a spoon. 9 spoons and 12 knives cost £82.80. Work out the cost of one knife.
Ben also bought a package of 3 T-shirts for $14.25. What is the unit price, per T-shirt
Answer:
4.75 per T-shirt
Step-by-step explanation:
Divide 14.25 by 3
Jill and Kyle get paid per project. Jill is paid a project fee of $35 plus $8 per hour. Kyle is paid a project fee of $20 plus $16 per hour. Write an expression to represent how much a company will pay to hire both to work the same number of hours on a project.
Answer:
The company will pay $43 project fee and $24 an hour.
Step-by-step explanation:
25 + 10h +18 + 14h
= 25+ 18 + 10h + 14h
=43 + 24h
According the a University Center for Logistics Management, 7% of all merchandise sold in the United States gets returned. A Seattle department store samples 89 items sold in January and found that 10 of the items were returned. H0: p = 0.07 H1: p < 0.07 Calculate the test statistic: Group of answer choices 1.31 2.33 0.99 1.15 1.57
Answer:
The test statistic is 1.57.
Step-by-step explanation:
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
A Seattle department store samples 89 items sold in January and found that 10 of the items were returned.
This means that [tex]n = 89, X = \frac{10}{89} = 0.1124[/tex]
7% of all merchandise sold in the United States gets returned.
This means that [tex]\mu = 0.07[/tex]
For a proportion, the standard deviation is [tex]\sigma = \sqrt{p(1-p)} = \sqrt{0.07*(1-0.07)} = 0.2551[/tex]
Test statistic:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{0.1124 - 0.07}{\frac{0.2551}{\sqrt{89}}}[/tex]
[tex]t = 1.57[/tex]
The test statistic is 1.57.
On a map of North Carolina, the distance between Charlotte and Wilmington is 14.75 inches. If 2 inches
equals 24 miles, what is the approximate distance between the two cities?
Answer:
12
Step-by-step explanation:
I don't really know but good luck I hope it right
Can somebody please help me with this math problem please brainliest if your correct thanks picture is attached !!
Answer:
x = (3, 4)
(I'm assuming the missing sign in the picture is a negative (-))
Answer:
x={3, 4}
Step-by-step explanation:
that may answer po
Moe puts $1500 in a bank certificate that pays an annual rate of 4.5% compounded annually. No withdrawals or deposits are made. How much will the certificate be worth (to the nearest dollar) at the end of 7 years?
Answer:
FV= $2,041.29
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $1,500
Number of periods (n)= 7 years
Interest rate (i)= 4.5% = 0.045
To calculate the future value, we need to use the following formula:
FV= PV*(1+i)^n
FV= 1,500*(1.045^7)
FV= $2,041.29
Identify and locate the symmetry elements in each of the following objects(ignore labeling or writing). Identify the point group for each object.a) A wine bottle (without labels)b) A tennis racquet (without labels)c) A tennis ball with the seams.d) An American footballe) One shoe and a pair of shoes, one on your left foot the other on your rightfoot.
Answer:
hello your question is incomplete attached below is the complete question
answer: attached below
Step-by-step explanation:
1) attached below
2)
a) wine bottle ( without labels ) :
Linear structure with no center of inversion its point group is c ∞ v
b) A tennis racquet ( without labels )
1 C2 axis , 2 бv planes , point group ---- C2v
c) A tennis ball with the seams
3 perpendicular c2 axis , one through the narrow portions of each segment, others through the seams
d)