Answer:
the gas mileage would be 21.12 mi/gal
Step-by-step explanation:
The computation of the gas mileage is shown below:
Given that
Driving into a 20-mph
Gas mileage by approx 12%
No wind at 24mi/gal
based on the above information
The deduction would be
= 12% × 24
= 2.88 mi/gal
Now the actual mileage in 20-mph would be
= 24 - 2.88
= 21.12 mi/gal
hence, the gas mileage would be 21.12 mi/gal
Picture a rectangular prism with a volume of 150 cubic units. What is the number of unit cubes that would fill the volume of this prism if they were packed without any gaps or overlaps?
Answer:
150 units woild fill the volume of the prism.
x^2- 11 = 70 I need help on how to solve this
Answer: Add 11 to the other side of the equation, giving you 81. Then, since x is square you are going to need to square root both sides ([tex]\sqrt{x}[/tex] this symbol). When you do that, you should get what x is! Let me know if you still need help!
A triangle has sides which are consecutive odd integers and an
angle of 120°. What is the perimeter of the triangle?
Answer:
Perimeter = 15
Step-by-step explanation:
We are told that the length of each of the 3 sides of the triangle are consecutive odd integers.
Thus means that we can write the 3 terms as;
(x - 2), x, (x + 2)
Thus, perimeter is;
P = (x - 2) + x + (x + 2)
P = 3x
If an angle is 120°, it means that the corresponding side that is directly opposite the angle is the largest side of the triangle.
Thus, this side is (x + 2)
Using cosine rule, we have;
(x + 2)² = x² + (x - 2)² - 2(x(x - 2))cos 120
Expanding, we have;
x² + 4x + 4 = x² + x² - 4x + 4 - (2x² + 4x)(-½)
This reduces to;
4x = x² - 4x + x² - 2x
2x² = 10x
2x = 10
x = 10/2
x = 5
Thus, other sides are;
(x - 2) = 5 - 2 = 3
And (x + 2) = 5 + 2 = 7
So,perimeter is;
P = 3x = 3 × 5 = 15
write the slope intercept-form of the equation of the line through the given points.
Answer:
qs,wdnfm.ew fw v
Step-by-step explanation:
wdmc vw.mv / n,v
In a regular polygon the interior angle is thrice the exterior angle. The number of sides of the polygon is.
Answer:
8
Step-by-step explanation:
Measure of one interior angle of a regular polygon of n sides:
(n - 2)180/n
Measure of one exterior angle of a regular polygon if n sides:
360/n
"the interior angle is thrice the exterior angle"
(n - 2)180/n = 3 * 360/n
(n - 2)180 = 3 * 360
n - 2 = 3 * 2
n = 8
The number of sides is 8.
Unit Test Review Active 1 2 3 Which best describes a model of ? five wholes divided into 12 equal pieces twelve wholes divided into 5 equal pieces a whole divided into 5 equal pieces with 12 pieces shaded in O a whole divided into 5 equal pieces and another whole divided i
Answer:
15%
Step-by-step explanation:
Trust me, i took the K12 test and got it correct :)
A system of equations is shown below: 2x = 5y + 4 3x − 2y = −16 What is the solution to this system of equations? (5 points) (−8, −4) (8, 4) (−4, −8) (4, 8)
Answer:
(-8,-4)
Step-by-step explanation:
Answer:
EASY (-8,-4)
Step-by-step explanation:
factorise the following fully:
6a⁴b⁶-8a³b⁵+12a²b³
Answer:
2a^2 b^3(3a^2 b^3 - 4ab^2 + 6)
When multiplying 1,729 times 308, Clayton got a product of 52,253. Does his answer seem reasonable
Answer:
No, it does not
Step-by-step explanation:
Well first we round off the factors 1790 and 308 to 2000 and 300These are numbers which we are kind of close to our original numbers, but easier to multiply without a calculator or anything of the kindThen we easily multiply and estimate if the answer is rightSo [tex]2000*300=600,000[/tex] Now how close is 600,000 to 52,253? They are way too far apart!So that means the product is not reasonable, it's not even close to our estimation.Estimate 61.26 - 59.593 by first rounding each number to the nearest whole number.
Answer:
1
Step-by-step explanation:
61.26=61
59.593=60
61-60=1
Answer:
1
Step-by-step explanation:
61.26 rounded to the nearest whole number = 61
59.593 rounded to the nearest whole number = 60
61 - 60 = x
61 - 60 = 1
x = 1
Please help Express both quantities in each comparison
using the same units. Write the comparison
as a ratio in fraction form. Then write an
equivalent ratio using whole numbers.
a) 85¢ to $1.20 b) 24 kg to 80 g
Answer:
1a) .85/1.20 = 85/120 = 17/24. 2a) 17:24
1b) 24000/80 = 2400/8 = 300/1. 2b) 300:1
_______________________________
I believe this is what the problem is asking.
Please help!!! Will mark brainliest!
Write a system of equation for each of the descriptions below, and then solve the systems. Hint: you can graph the equations to find the solutions.
13. A number is 7 more than another number. The sum of the numbers is 15. Find the numbers.
14. One number is two times the other, and their sum is 27. What are the numbers?
15. Thirteen is the sum of two numbers and their difference is equal to five. Find the numbers
16. Three times one number is equal to two times the larger one and their difference is 1. What are the numbers?
17. Joseph has 30 coins and they are all either dimes or nickels. The total $2.15. How many dimes does he have?
18. A golfer completed 18 holes with a total of 79 strokes. On each hole he met par, which was either four or five each time. How many holes were played in four strokes?
19. There are two numbers. The difference between them equals six, and one of the numbers is three times the other number. There are two pairs of numbers that satisfy these descriptions, What are they?
20. There is a number that is three-fifths the total of the other number. When four is added to one of the numbers their sum will be equal to the other number. There are two pairs of numbers that satisfy these descriptions. What are they?
Answer:
4, 11
Step-by-step explanation:
Q# 13 :
Let the first number be 'x'
the 2nd number would be ' x + 7'
x + x + 7 = 15
2x= 15-7
x= 8/2
x= 4
2nd number: x + 7
= 4+7
= 11
What is opportunity cost?
1. the limited availability of goods or services
2. a benefit lost when choosing between two options
3. the resources used to produce finished goods or services
4. a system of directly exchanging goods or services for other goods or services
Answer:
the answer is 2
Step-by-step explanation:
Bcz u choseine option and lose the next bet benefit
Mr. Schneider paid $2276.35 to have a landscaper build a patio with the dimension below. How much did the landscaper charge for each square metre of patio? 3.2m 5.4m 1.8m 1.2m
Answer:
Step-by-step explanation:
Since we are not given the dimension. Let us say the shape of the patio is a rectangle with length 30m and width 18m.
Area of the rectangle = Length * Width
Area of the rectangle = 30 * 18
Area of the rectangle = 540m²
This means that 540m² of the patio costs $2276.35. To get the cost of each square metre of patio, we will say;
540m² = $2276.35
1m² = x
cross multiply;
540x = $2276.35
x = $2276.35/540
x = $4.22
Hence each square meter of patio will cost $4.22
Note that the dimension of patio was assumed. Same explanation can be employed for any dimension.
3/5 of Camden's toys are orange. What percentage of Camden's toys are not orange?
Answer:
2/5
Step-by-step explanation:
Answer:2/5
Step-by-step explanation:
A clown sells large balloon animals for $25 each. Small balloon animals sell for $10 each. Jordan is buying 2 large balloon animals and x small balloon animals. Let y represent the total cost Jordan must pay in dollars. Part 1: Write an equation in slope-intercept form to model this description. Part 2: What is Jordan’s total cost if she purchases 4 small balloon animals? Show your work.
Answer: Part 1: y =10x+50
Part 2: Jordan’s total cost = $90
Step-by-step explanation:
Given: Price of each large balloon = $25
Price of each small balloon = $10
Price of 2 large balloons = 2 (Price of each large balloon)
= $2 (25)
= $50
Part 1: Total cost = (Number of small balloons)(Price of each small balloon) + (Number of large balloons)(Price of each large balloon)
Let x = Number if small balloons , y= total cost Jordan must pay in dollars.
Then, y= (x)(10)+(2)(25)
⇒ y =10x+50
Part 2: If she purchases 4 small balloon animals, put x=4
Then, y= 10(4)+50=40+50= 90
i.e. Jordan’s total cost = $90
Which inequalities have no solution? Check all of the boxes that apply. 1. x > x 2. –3x –3x 3. –4 + x > –2 + x 4. x – 2 < x + 3
Answer:
1, 3
Step-by-step explanation:
1. x > x
Technically, one number cannot be more than itself. It can only equal to itself.
3. –4 + x > –2 + x
If you minus x from both sides of the equation, it becomes:
-4 > -2
This is not true no matter what x is, thus it has no solution.
4. x – 2 < x + 3
If you add 2 on both sides, it becomes:
x < x + 5
This inequality is possible and has infinitely many solutions.
Note: I will update this answer and address Question 2 once the inequality sign is given :)
What’s the angles relationship?
Answer:
The relationship between the angles would be parallel because they are the exact same degree now if they were different degrees their relationship would be perpendicular but with them being the same the answer is parallel
Whats the ANSWER GIVING BRAINLIEST TO RIGHT ONE:)
Answer:
C
Step-by-step explanation:
I believe this is the correct one.
Answer:
C
Step-by-step explanation:
C has the point (-2, -3.5) and the point (0.5, -4)
Write an equation of a line through (15, 8) that is perpendicular to the line y =57 x −1.
Answer:
Equation of a line through (15, 8) that is perpendicular to the line y =57 x −1 is [tex]\mathbf{y=-\frac{1}{57}x+\frac{157}{19}}[/tex]
Step-by-step explanation:
We need to write an equation of a line through (15, 8) that is perpendicular to the line y =57 x −1.
The equation will be in slope-intercept form: [tex]\mathbf{y=mx+b}[/tex]
Where m is slope and b is y-intercept.
Finding Slope of new line
We are given equation [tex]y =57x-1[/tex] of line, which is perpendicular to the line whose equation we need to find.
If the lines are perpendicular there slopes are inverse of each other i.e [tex]m_1=-\frac{1}{m_2}[/tex]
Slope of given line is m= 57 ( compare the given equation with standard slope-intercept form the value of m is 57
Slope of new line is m= [tex]-\frac{1}{57}[/tex]
Finding y-intercept of new line
Now finding y-intercept (b) for new line. It can be found using point (15,8) and slope m = [tex]-\frac{1}{57}[/tex]
[tex]y=mx+b\\8=-\frac{1}{57}(15)+b\\8=-\frac{15}{57}+b\\b=8+\frac{15}{57}\\b=\frac{8*57+15}{57}\\b=\frac{471}{57}\\b=\frac{157}{19}[/tex]
So, y-intercept b of new line is: [tex]b=\frac{157}{19}[/tex]
Equation of required line
Equation of line having slope m= [tex]-\frac{1}{57}[/tex] and y-intercept [tex]b=\frac{157}{19}[/tex] is:
[tex]y=mx+b\\\mathbf{y=-\frac{1}{57}x+\frac{157}{19}}[/tex]
So, equation of a line through (15, 8) that is perpendicular to the line y =57 x −1 is [tex]\mathbf{y=-\frac{1}{57}x+\frac{157}{19}}[/tex]
A function f (x)is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x) =
Answer:
f(x) = 2x + 1Step-by-step explanation:
We can see y-intercept is 1 as per point (0, 1)
Using another point to find the slope (-3, -5)
m = (1 - (-5))/(0 - (-3)) = 6/3 = 2So the function is:
f(x) = 2x + 17/2x + 1/2x = 9 + 9/2x
the value of x is
Answer:
Step-by-step explanation:
X is -18
Peter hired a cleaning company to clean his house. The cleaning company charges a fixed fee of $15 plus $17 per hour to clean a house. A second cleaning company charges $20 per hour to clean a house. The second company does not charge a fixed fee in addition to their hourly rate. For what number of hours is the total amount charged for cleaning a house the same for both companies? Show or explain how you got your answer.
Answer:
5 hours
Equations:
first company: 17x+15
second company: 20x
Proof:
17(5)+15 => 85+15 => 100
20(5) => 100
Answer:
5 hours
Step-by-step explanation:
Write the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7. Type your answer in the box provided or use the upload option to submit your solution.
Answer:
y = x - 1
Step-by-step explanation:
If it's parallel to x - y = 7, that means the slope of that equation is the slope for the equation you're looking for.
To get the slope, you need to put the given equation into slope intercept form, so move x to the other side. You should get: -y = 7 - x
Then, to get the y positive, divide by -1: y = -7 + x
Slope intercept form is as follows: y = mx + b, so whatever the number is in front of x is your slope. In this instance, your slope is 1.
You now have your slope, and a point in which your new line passed through. Using slope intercept form, y = mx + b, if you substitute in what you know, you can find your answer. Right now you know y, m, and x, and you're looking for b.
x=1; y=0; m=1.
So, substituting, you'd get 0 = (1)(1) + b
0=1+b Solve
You should get b= -1, leaving your final answer as y = x - 1
y=x+1 is the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We need to find slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7.
The slope will be same as it is parallel.
x - y = 7.
-y=7-x
y=x-7
Slope is 1.
Now equation of line passing through (1,0)
0=1(1)+c
c=-1
y=x-(-1)
y=x+1
Hence y=x+1 is the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7.
To learn more on slope of line click:
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What is the lowest term of 110/33
Answer:
10/3
Step-by-step explanation:
110/33
lowest term of 110/33 is 10/3
4. What is the solution to the system of equations?
Hint: Solve each equation for y first, then graph.
5. What is the solution to the system of equations?
Answer:
4. The solution to the system of equations is: (2,-1)
5. The solution to the system of equations is: (3,5)
Step-by-step explanation:
4. What is the solution to the system of equations?
[tex]2x+3y=1\\-3x+4y=-10[/tex]
Let:
[tex]2x+3y=1--eq(1)\\-3x+4y=-10--eq(2)[/tex]
Multiply eq(1) by 3 and eq(2) by 2 and add both equations
[tex]6x+9y=3\\-6x+8y=-20\\---------\\0x+17y=-17\\y=\frac{-17}{17}\\y=-1[/tex]
So, value of y=-1
Now finding the value of x bu putting value of y in eq(1)
[tex]2x+3y=1\\2x+3(-1)=1\\2x=1+3\\2x=4\\x=\frac{4}{2}\\x=2[/tex]
So, value of x=2
The solution to the system of equations is: (2,-1)
5. What is the solution to the system of equations?
[tex]y=2x-1\\6x-y=13[/tex]
Let:
[tex]-2x+y=-1--eq(1)\\6x-y=13--eq(2)\\------\\4x=12\\x=\frac{12}{4}\\x=3[/tex]
So, value of x=3
Putting value of x in equation 1 to find value of y
[tex]y=2x-1\\y=2(3)-1\\y=6-1\\y=5[/tex]
So, value of y=5
The solution to the system of equations is: (3,5)
Given two sides of a triangle, find a range of possible side lengths for the third side.
9 and 32
Answer: Two sides of a triangle have lengths 2 and 7. Find all possible lengths of the third side. Show Answer. difference $$< x <$$ sum $$7 -2 < x < 7+2$$ Answer: $$5 < x < 9$$ Problem 7. Two sides of a triangle have lengths 12 and 5. Find all possible lengths of the third side
Step-by-step explanation: i hope i helped
A city council consiste of 8 democrats and 6 republicans. If a committee of 4 people is selected,find the probability of selecting 2 democrats and 2 republicans
Answer:
Step-by-step explanation:
8C2 * 6C2
============
14C4
8C2 = 8*7/1 * 2 = 28
6C2 = 6*5 / 1*2 = 15
14C4 = 14*13 *12 * 11 / (1 * 2 * 3 * 4) = 1001
28 * 15 / 1001 = .4195
AB=3x-4 and BC=5x-10
Answer:
Step-by-step explanation:
an isosceles triangle two adjacent sides are equal
so AB = BC
3x-4 = 5x-10
2x = 6
x= 3
so ,
3 ( 3 ) -4 = 5
5 ( 3 ) -10 = 5
Find the missing side length of JK .
Answer:
I'm pretty sure it's 16
Step-by-step explanation:
it measures up with the other triangles side