Answer:
28.2 gal
$3.12/gal
Step-by-step explanation:
Length of trip:
14,108.6 mi - 13,487.8 mi = 620.8 mi
(620.8 mi)/(22 mpg) = 28.218 gal
She used 28.2 gallons.
price per gallon = $88.04/(28.218 gal) = $3.12/gal
Keith sold half of his comic books and then bought nine
more. He now has 20. How many did he begin with?
Answer:
22 comic books.
Step-by-step explanation:
(20 - 9) * 2 First subtract 9 from 20
11 * 2 Multiply 11 by 2
22 is the product
A report on Americans' attitudes toward teachers' pay found that 82% of the respondents to the survey upon which the report is based think that teachers don't make enough money. Which factor is most relevant when evaluating this report? A. 49% of the respondents were women. B. 78% of the respondents were married. C. 51% of the respondents were men. D. 62% of the respondents were educators.
Answer:
I think the answer is A. 49% of the respondents were women
Use the quadratic formula to solve for x.
3x2-x-8=0.
Consider the following planes. x + y + z = 5, x + 3y + 3z = 5A) Find parametric equations for the line of intersection of the planes. B) Find the angle between the planes.
Answer:
Step-by-step explanation:
Consider the following planes. x + y + z = 5, x + 3y + 3z = 5
the parametric equations for the line of intersection of the planes are determined as follows:
From the first plane, the normal of the first plane is [tex]n_1 = (1,1,1)[/tex]
from the second plane, the normal of the second plane is [tex]n_2 = (1,3,3)[/tex]
[tex]n_1 \times n_2 = \begin {vmatrix} \left \begin{array}{ccc}i&j&k\\1&1&1\\1&3&3 \end{array}\right \end {vmatrix}[/tex]
= i(3-3) -j(3-1)+k(3-1)
= i(0) - j(2) + k(2)
= -2j +2k
Suppose z = 0
x+y + 0 = 5 ---(1)
x+3y + 3(0) = 5 (2)
subtracting by elimination
-2y = 0
y = 0/-2
y = 0
The intersection on point of the plane is (5,0,0)
The equation of plane is r (t) =(5, 0, 0) + t(0, -2, 2)
∴
(x(t), y (t), z(t) ) = (5, -2t, 2t)
B) Find the angle between the planes
The angle between the planes can be represented by the equation:
[tex]cos \theta = \dfrac{a_1a_2+b_1b_2 + c_1c_2}{\sqrt{a^2_1+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}[/tex]
[tex]cos \theta = \dfrac{1 \times 1+1\times 3 +1 \times 3}{\sqrt{1^2+1^2+1^2}\sqrt{1^2+3^2+3^2}}[/tex]
[tex]cos \theta = \dfrac{1+ 3 +3}{\sqrt{3}\sqrt{19}}[/tex]
[tex]cos \theta = \dfrac{7}{\sqrt{3}\sqrt{19}}[/tex]
[tex]\mathbf{\theta = cos ^{-1} (\dfrac{7}{\sqrt{57}})}[/tex]
Need help on this one. Sort of confused.
Answer:
I'm just as confused as you lol
Which graph represents the inequality 3y-5x<-6?
Answer:
First Graph
Step-by-step explanation:
3y-5x<-6
3y<5x-6
y<5/3x-6/3
y<5/3x-2
plug in the coordinates (0,0)
0<0-2
0<-2
0 is not less than -2
therefore the graph would be shaded opposite of (0,0)
Twice a number is at most 36.
Answer:
18?
Step-by-step explanation:
which equation can be represented by the number line
Answer:
B
Step-by-step explanation:
The arrow is going left four units. Since it's going left, we know that we are adding a negative number and since it's going left 4 units, we know that we are adding -4 in our equation. This narrows it down to options B and D. However, the arrow usually represents the second number being added, hence, the answer is B.
3. Determine if the equation represents y as a function of x.
9x + 3y = 12
The perimeter of the original rectangle is 16 feet. A small rectangle has a length of 6.2 feet and width of 1.8 feet. A larger rectangle has a length of 12.4 feet and width of blank. Not drawn to scale What is the perimeter of the enlarged rectangle? Round to the nearest tenth if necessary.
Answer:
32 ft
Step-by-step explanation:
The length of the larger rectangle is double that of the smaller one. If we assume the rectangles are similar, the perimeter will be double as well:
2·(16 ft) = 32 feet . . . . perimeter of larger rectangle
__
The width of the larger one is 2·1.8 ft = 3.6 ft.
Answer:
C) 32 feet
Step-by-step explanation:
＼(ﾟｰﾟ＼)
Determine whether each set {p1,p2} is a linearly independent set in P3.
1. The polynomials p1 (t) = 1 + t2 and p2(t) = 1 - t2.
2. The polynomials p1 (t) = 2t + t2 and p2(t) = 1 + t.
3. The polynomials p1(t) = 2t - 4t2 and p2(t) = 6t2 - 3t.
Answer:
1) The polynomials [tex]p_{1}(t) = 1 +t^{2}[/tex] and [tex]p_{2}(t) = 1-t^{2}[/tex] are linearly independient, 2) The polynomials [tex]p_{1}(t) = 2\cdot t +t^{2}[/tex] and [tex]p_{2}(t) = 1+t[/tex] are linearly independent, 3) The polynomials [tex]p_{1}(t) = 2\cdot t - 4\cdot t^{2}[/tex] and [tex]p_{2}(t) = 6\cdot t^{2}-3\cdot t[/tex] are linearly dependent.
Step-by-step explanation:
A set is linearly independent if and only if the sum of elements satisfy the following conditions:
[tex]\Sigma_{i=0}^{n} \alpha_{i} \cdot u_{i} = 0[/tex]
[tex]\alpha_{0} = \alpha_{1} =...=\alpha_{i} = 0[/tex]
1) The set of elements form the following sum:
[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]
[tex]\alpha_{1}\cdot (1+t^{2})+\alpha_{2}\cdot (1-t^{2}) = 0[/tex]
[tex](\alpha_{1}+\alpha_{2})\cdot (1) +(\alpha_{1}-\alpha_{2})\cdot t^{2} = 0[/tex]
From definition this system of equations must be satisfied:
[tex]\alpha_{1} + \alpha_{2} = 0[/tex] Eq. 1
[tex]\alpha_{1}-\alpha_{2} = 0[/tex] Eq. 2
From Eq. 2:
[tex]\alpha_{1} = \alpha_{2}[/tex]
In Eq. 1:
[tex]2\cdot \alpha_{1} =0[/tex]
[tex]\alpha_{1} = 0[/tex]
[tex]\alpha_{2} = 0[/tex]
The polynomials [tex]p_{1}(t) = 1 +t^{2}[/tex] and [tex]p_{2}(t) = 1-t^{2}[/tex] are linearly independient.
2) The set of elements form the following sum:
[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]
[tex]\alpha_{1}\cdot (2\cdot t+t^{2})+\alpha_{2}\cdot (1+t) = 0[/tex]
[tex]\alpha_{2}\cdot (1) +(2\cdot \alpha_{1}+\alpha_{2})\cdot t +\alpha_1 \cdot t^{2} = 0[/tex]
From definition this system of equations must be satisfied:
[tex]\alpha_{2} = 0[/tex]
[tex]2\cdot \alpha_{1}+\alpha_{2} = 0[/tex]
[tex]\alpha_{1} = 0[/tex]
The polynomials [tex]p_{1}(t) = 2\cdot t +t^{2}[/tex] and [tex]p_{2}(t) = 1+t[/tex] are linearly independent.
3) The set of elements form the following sum:
[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]
[tex]\alpha_{1}\cdot (2\cdot t-4\cdot t^{2})+\alpha_{2}\cdot (6\cdot t^{2}-3\cdot t) = 0[/tex]
[tex](2\cdot \alpha_{1}-3\cdot \alpha_{2})\cdot t + (-4\cdot \alpha_{1}+6\cdot \alpha_{2})\cdot t^{2} = 0[/tex]
From definition this system of equations must be satisfied:
[tex]2\cdot \alpha_{1}-3\cdot \alpha_{2} = 0[/tex] (Eq. 1)
[tex]-4\cdot \alpha_{1}+6\cdot \alpha_{2} =0[/tex] (Eq. 2)
It is easy to find that each coefficient is multiple of the other one, that is:
[tex]\alpha_{1} =\frac{3}{2}\cdot \alpha_{2}[/tex] (From Eq. 1)
[tex]\alpha_{1} = \frac{6}{4}\cdot \alpha_{2}[/tex] (From Eq. 2)
[tex]\alpha_{1} = \frac{3}{2}\cdot \alpha_{2}[/tex]
Which means that polynomials [tex]p_{1}(t) = 2\cdot t - 4\cdot t^{2}[/tex] and [tex]p_{2}(t) = 6\cdot t^{2}-3\cdot t[/tex] are linearly dependent.
Andre and Morgan are both headed to Florida for vacation. Andre will drive 70 miles per hour. Morgan will drive 55 miles per hour but will leave 3 hours earlier than Andre. How many hours will Morgan have been driving before Andre catches up with her?
Answer:
14hours
Step-by-step explanation:
Since Andre and Morgan are both heading to the same location i.e Florida, they will have the same distance.
Distance = Speed × Time
For Morgan:
His speed = 55mi/hr
Let his time = x
Distance covered by Morgan = 55x
For Andre
His speed = 70mi/hr
Time = x-3 (since morgan leaves 3 hours earlier than Andre)
Distance covered = 70× (x-3) = 70(x-3)miles
Since they are driving towards the same location;
55x = 70(x-3)
55x = 70x-210
55x-70x = -210
-15x = -210
x = 210/15
x = 14
Hence Morgan will have been driving 14hours before Andre catch up
A race car driver completes 30 laps and 15 minutes at a constant speed. What is the drivers speed?
Answer:
60 mph
Step-by-step explanation:
It takes two minutes to drive one mile at 30 mph. You are planning on covering two total miles. If your average speed is 60 mph, it would take two minutes to cover these two miles. So you have to go 60 mph.
Hope This Helps :)
The driver's speed is 30 miles per hour.
One mile is approximately 4 laps so 30 laps would be:
= 30 / 4
= 7.5 miles
The driver drove 7.5 miles in 15 minutes.
15 minutes in hours is:
= 15 / 60
= 0.25 hours
The speed of the driver is therefore:
= 7.5 miles / 0.25 hours
= 30 mph
The driver was therefore driving at a speed of 30 mph
Find out more at https://brainly.com/question/19940635.
Write a number (in standard form) that has the digit 7 in the thousands place. Use the digit 7 only once.
Answer:
7123
Step-by-step explanation:
The only requirement is to have 7 in the thousands place, which I've done, and the rest of the numbers can be any number you choose!
L1 : y = 2x , (2) find the equation of the line L2 perpendicular to L1 passing through the point P = (1, 2).
Answer:
2y+x = 5Step-by-step explanation:
Given the line L1 as y = 2x perpendicular to an unknown line L2 passing through the point P = (1, 2), we are to find the equation of line L2. to find the equation of the line L2, we will use the point-slope equation of a line expressed as y-y₀ = m(x-x₀)
m is the slope of the unknown line
(x₀, y₀) is the given point.
First is to get the slope of the known line:
comparing the line L1: y = 2x with the standard equation of the line y = mx+c, it can be seen that m = 2
Then we will calculate the slope of the required line.
Since L1 is perpendicular to L2, the product of their slope will be -1 i.e
mm₁ = -1 where m₁ is the slope of the required line L2.
Given m =2
m₁ = -1/m
m₁ = -1/2
Finally we will calculate the equation of line L2 by substituting the slope of line L2 and the point in the point slope equation above;
y-y₀ = m(x-x₀)
Given (x₀, y₀) = (1,2) and m₁ = -1/2
y-2 = -1/2(x-1)
open the parenthesis
y-2 = -x/2+1/2
multiply through by 2:
2y-4 = -x+1
2y+x = 1+4
2y+x = 5
Hence the equation of the line L2 is 2y+x = 5
Select the relationship that does represent a function.
Answer:
Picture number 3 is the answer
Step-by-step explanation:
A function is a relation in which each element in the domain is paired with exactly one element in the range not 2.
Picture number one has a range left with no domain so it's not a function
Picture number 2 is showing an element in the domain which paired 2 elements in the range so it's not a function
Picture 3 is correct because each element in the domain macthes one element in the range.
Picture 4 is wrong because it's showing elements in the domain that matches 2 elements in the range. Hope it makes sense.
The required relationship that represents a function is given by 3rd image. Option C is correct.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
The first image has a range with no domain, hence it is not a function. In 2nd image depicts an element in the domain that paired two elements in the range, indicating that it is not a function. In 3rd image, it is valid because each element in the domain corresponds to one element in the range. In picture 4, it is incorrect since it depicts domain components that match two range elements.
Thus, the required relationship that represents a function is given by 3rd image. Option C is correct.
Learn more about function here:
brainly.com/question/21145944
#SPJ2
9 pencils cost 7.74 what is the equation of the cost of 6 pencils
Answer:
6 pencils cost $5.16.
Step-by-step explanation:
1. Find the cost of one pencil.
Divide: $7.74 ÷ 9 = $0.86 for one pencil
2. Multiply 0.86 by 6
$0.86 × 6 = $5.16
Answer:
2/3 multiply with 7.74
=5.16
Find the volume of the shipping box using the two methods and show your work: Packing cubes Using the volume formula Explain how both methods provide the same measurement of volume for the shipping box.
Answer:
Volume is the measure of how big an object is in three dimensions, so the volume of a box measure how much room there is inside of the box. To find it, you need to make a few simple measurements of length, width, and height, and then multiply them.
Step-by-step explanation:
{6} E { {6}, {14} } true or false
Answer: true and stop deleting my answers im right im in collage
and I dont need to explain again when i already did so STOP and trust me
A SNACK THAT SMILES BACK®
I need help with this pls ASAP
What is the value of the expression when y = 2? StartFraction 2 minus y Over 4 plus y EndFraction plus StartFraction 3 (y plus 2) Over y EndFraction
Answer:
12
Step-by-step explanation:
Answer:
2.4
Step-by-step explanation:
Give two points with integer coordinates that have a slope of 2/5 between them.
Answer:
yes
Given a 2D line e.g. (3,10) -> (8.3,16.5), how can I find any point on that line that has has whole-number coordinates?
I can easily iteratively walk along one of the axis in integer steps, seeing if the value on the other axis is integer, but this is slow for very very long lines.
From the site a certain ramp has a right triangular shape its height is 30 cm and it’s horizontal length is 3 m what calculation will give us the estimated length of the ramp in meters
Answer:
[tex]a^{2} +b^{2} =c^{2}[/tex]
Step-by-step explanation:
C is the horisontal and a or b can be the height, plug in the numbers and you solve for length.
Answer:
(sqr) 30^2/100^2+3^2
Step-by-step explanation:
graph h(t)=-2(t+5)^2+3, find h(-8)
Answer:
h(-8)=-15
Step-by-step explanation:
Substitute t=-8
h(-8) =-2(-8+5)^2+3
=-2(-3)^2+3
=-2(9)+3
=-18+3
=-15
h(-8) = - 15
Step-by-step explanation:h(t) = - 2(t + 5)² + 3
replace t with - 8
h(-8) = - 2(- 8 + 5)² + 3
h(-8) = - 2(-3)² + 3
h(-8) = -2×9 + 3
h(-8) = - 18 + 3
h(-8) = - 15
7.
A dental office starts the month with 2,258 latex examination gloves. At month's end,
784 gloves remain. How many gloves were used?
I need some help with this question. "A scale drawing of a school bus has a scale of an inch to 5 feet. If the length of the school bus is in inches on the scale drawing, what is the actual length of the bus?"
Answer:
45 Feet
Step-by-step explanation:
4.5 divided by 0.5=9
9 times 5=45
Hoped this helped!
4(6c+5) - 2(3c - 5) = 120
Answer:
[tex]c=5[/tex]
Step-by-step explanation:
[tex]4(6c+5)-2(3c-5)=120[/tex]
Use the distributive property to expand the equation:
[tex]4(6c)+4(5)-2(3c)-2(-5)=120\\\\24c+20-6c+10=120[/tex]
Combine like terms to simplify the equation:
[tex]24c-6c+20+10=120\\\\18c+30=120[/tex]
Subtract 30 from both sides:
[tex]18c+30-30=120-30\\\\18c=90[/tex]
Isolate the variable c. Divide both sides by 18:
[tex]\frac{18c}{18}=\frac{90}{18}\\\\ c=5[/tex]
So, c is equal to 5.
:Done
A square has the following vertices. Find the area of the square.
(-7,-5), (-4,-2), (-1,-5), (-4,-8)
(1 point)
O V18 square units
O 18 square units
O V6 square units
O 6 square units
Answer:
18 square units
Step-by-step explanation:
Since the shape is a square lets find the distance between two close point then square the distance to find the answer.
Lets take the point (-7,-5), (-4,-2)
Distance= √((y2-y1)²+(x2-x1)²)
Distance= √((-2--5)²+(-4--7)²)
Distance= √((-2+5)²+(-4+7)²)
Distance= √((3)²+(3)²)
Distance= √(9+9)
Distance= √18 units
Area= distance ²
area= √18²
Area= 18 square unit
Express the given quantity in terms of the indicated variable.
The area (in ft) of a rectangle that is eight times as long as it is wide;
w = width of the rectangle (in ft)
ft2
X
Need Help?
Read it
Watch It
Master it
Answer:
X = 8W²Step-by-step explanation:
Area of a rectangle is expressed as Length * Width
X = L*W where X is the area of the rectangle in fe²
If the triangle is eight times as long as it is wide, then L = 8W
Substitute L = 8W into the formula for calculating the area of a triangle, we will have;
X = L*W
X = (8W)*W
X = 8W²
The expression X in terms of W is therefore X = 8W²
Sofia invests her money in an account paying 7% interest compounded semiannually. What is the effective annual yield on this account? Enter your response as a percentage rounded to two decimal places and omit the percentage sign
Answer:
7.12
Step-by-step explanation:
The formula for the effective annual yield is given as:
i = ( 1 + r/m)^m - 1
Where
i = Effective Annual yield
r = interest rate = 7% = 0.07
m= compounding frequency = semi annually = 2
i = ( 1 + 0.07/2)² - 1
i = (1 + 0.035)² - 1
= 1.035² - 1
= 1.071225 - 1
= 0.071225
Converting to percentage
0.071225 × 100
= 7.1225%
Approximately to 2 decimal places = 7.12
Therefore, the annual effective yield = 7.12