The slope or gradient of a line is a number that describes both the direction and the steepness of line. The equation in point slope form if (-1,2) is a point on the line and 1/4 is the slope is y-2=[tex]\frac{1}{4}x+\frac{1}{4}[/tex].
What is a slope?A number that identifies the direction and steepness of a line is its slope or gradient. Letter m is frequently used to represent the slope.
The ratio of "vertical change" to "horizontal change" between (any) two unique points on a line is used to compute slope. Occasionally, the ratio is written as a quotient (also known as a "rise over run"), which produces the same number for every two unique points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
Given,
x1= -1
y1= 2
slope= 1/4
Substituting the values in the equation,
y-y1= m(x-x1)
y-2= [tex]\frac{1}{4}[/tex](x+1)
y-2= [tex]\frac{1}{4}x+\frac{1}{4}[/tex]
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A(6-1) , В(2,3)
help pls
what is the answer to this?? lmk asap pls and i need the right answer
Answer: no, no, no, yes
Step-by-step explanation:
Hello!
Just take each value of "u" and multiply it by 4. If the answer is smaller than 32, it is a solution. If not, it isn't a solution.
For which equations below is x = -3 a possible solution? Select three options
x = -3 a possible solution for |x| = 3, |–x| = 3 and –|x| = –3.
Here, we are given 6 equations and we need to check for which of the following, x = -3 is a solution.
Let us look at each equation one by one,
1. |x| = 3
if x = -3
|-3| = 3
3 = 3
Hence, -3 is a solution to this equation.
2. |x| = –3
if x = -3
|-3| = -3
3 ≠ -3
Hence, -3 is not a solution to this equation.
3. |–x| = 3
if x = -3
|3| = 3
3 = 3
Hence, -3 is a solution to this equation.
4. |–x| = –3
if x = -3
|3| = -3
3 ≠ -3
Hence, -3 is not a solution to this equation.
5. –|x| = –3
if x = -3
-|3| = -3
-3 = -3
Hence, -3 is a solution to this equation.
4. –|x| = 3
if x = -3
-|3| = 3
-3 ≠ 3
Hence, -3 is not a solution to this equation.
Thus, equations |x| = 3, |–x| = 3 and –|x| = –3 are correct.
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Your solution was incomplete. Check for full content below-
For which equations below is x = –3 a possible solution? Check all that apply.
|x| = 3
|x| = –3
|–x| = 3
|–x| = –3
–|x| = –3
–|x| = 3
Each of the positive integers from 1 to 100 are written on a sheet of paper.
Some of these integers are erased. The product of those integers still on the paper leaves a remainder of 4 when divided by 5. Find the least number of integers that could have been erased.
Answer:
9 14 19 24 29 34 39 44 49 54 59 64 69 74 79 84 89 94 99
Question 3(Multiple Choice Worth 5 points)
(01.03 MC)
Which number has a 4 that is 10 times greater than the 4 in 542?
A. 5,420
B. 54.2
C. 5.42
D. 0.542
Answer:5.42
Step-by-step explanation:maybe it is maybe is not
500 values are normally distributed with a mean of 125 and a standard deviation of 10 which percent of the values lies between 115-125
The percent that the value is between 115 - 125 is 34.13%.
What is defined as the standard normal distribution?A standard normal distribution is a symmetric probability distribution with equal mean, mean, and mode values. The value of the probability of a standard normal distribution is achieved from a statistical table or computer software.For the given question;
The total number of the sample is 500.
The mean of the sample is; μ = 125.
The standard distribution is; σ = 10.
The percentage of the values must lie between 115-125.
Thus,
P(115 < X < 125) = P[(115 - 125)/10 < (x - μ)/ σ < (125 - 125)/10]
= P[-1 < Z < +0]
Z for +0 = 0.50000 and z for -1 = 0.15866 obtained from Z-score table.
P(115 < X < 125) = [0.50000 - 0.15866]
P(115 < X < 125) = 0.34134
P(115 < X < 125) = 34.13%
Therefore, the probability for percent of the values lies between 115-125 is 34.13%.
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evaluate 3^2018 + 3^2015 / 3^2017 + 3^2016
The simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3
How to evaluate the expression?The expression is given as:
3^2018 + 3^2015 / 3^2017 + 3^2016
Factor out 3^2015 in the expression
So, we have
3^2015(3^3 + 1)/3^2015(3^2 + 3)
Cancel out the common factor
(3^3 + 1)/(3^2 + 3)
Evaluate the exponents
(27 + 1)/(9 + 3)
This gives
28/12
Simplify
7/3
Hence, the simplified value of the expression given as 3^2018 + 3^2015 / 3^2017 + 3^2016 is 7/3
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Part 2 of 2
You invested $15,000 in two accounts paying 4% and 7% annual interest, respectively. If the total interest earned for
the year was $960, how much was invested at each rate?
$3000 and $12000
If you know the principal amount, the rate of interest, and the time periods, you can use the simple interest formula to calculate the interest.
The following is a simple interest formula:
SI = P *R * T /100
Where SI = simple interest
Principal (P)
interest rate, or R (in percentage)
T is the time period (in years)
The following formula is used to determine the overall sum:
Sum (A) = Principal (P) + Interest (I)
Where,
The entire amount repaid at the conclusion of the borrowing period is indicated by the letter (A).
You can also write the total amount formula for simple interest as follows:
A = P(1 + RT)
X+Y = $15000
0.04x + 0.07y = 960
0.04x + 0.07 ( 15000 - x) = 960
0.04x + 1050 - 0.07x = 960
0.03x = 90
x = $3000
y= $12000
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For 24 points?
Maths
Estimate the value of:
73.182 x 3.473
Answer:
answer is 251.5
Mark as branliest if helped a bit
Given: A= {2, 4, 6, 8}
B= {1, 3, 5, 7}
C= {3, 6, 9}
7. (A intersection to B) union C =
Please Answer pls I need it tomorrow
Wrong question.....................
The results of a survey of students about whether they attended the dance are shown in the table. What is the best estimate of the probability that a randomly selected boy attended the dance?
a. 7/20
b. 7/15
c. 7/9
d. 7/8
Answer:
7/9 the answer is C
Step-by-step explanation:
Scott rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 92 cents for each mile driven. Scott had to pay $150.55 when he returned the truck. For how many miles did he drive the truck?
I need to find how many miles
Answer:
143 miles
Step-by-step explanation:
Let x = number of miles
Let y = total cost
150.55 = .92x + 18.99 Multiply all the way through by 100 to clear the decimal
15055 = 92x + 1899 Subtract 1899 from both sides
13156 = 92x Divide both sides by 92
143 = x
−4x+2y+z=1;x−y+3x=−5;3x+y−4z=10 Solve each system, HELP!
Answer: x = [tex]\frac{-31}{23}[/tex], y = [tex]\frac{-9}{23}[/tex], z = [tex]\frac{-83}{23}[/tex]
Step-by-step explanation :Solving system of equations
Given the following system of equation below
- 4x + 2y + z =1 .......(1)
x − y + 3x = −5 ........(2)
3x + y − 4z = 10.........(3)
first we solve eq 1 and eq 3:
we get, -13x + 9y = 14 ..........(4)
Now we solve eq 2 and eq 4 and get value of x and y:
we get, x = [tex]\frac{-31}{23}[/tex] and y = [tex]\frac{-9}{23}[/tex]
finally we put value of x and y in eq 1 and get the value of z:
-4(-31/23) + 2(-9/23) + z = 1
106/23 + z = 1
z = 1 - 106/23
z =[tex]\frac{-83}{23}[/tex]
Hence the solution of equation is ([tex]\frac{-31}{23}[/tex], [tex]\frac{-9}{23}[/tex], [tex]\frac{-83}{23}[/tex])
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The table below models a particular physical situation.
x −9 −3 4 10
y 9 1 −7 10
Find the piecewise linear equation that models the data above. Round to three decimal places if needed.
y={
___ x + ___. −9 ≤ x ≤ −3
___ x + ___. −3 < x ≤ 4
___ x + ___. 4 < x ≤ 10
The piecewise linear function that models the situation is given as follows:
y = -4/3x + b, −9 ≤ x ≤ −3,y = -8/7x - 17/7, −3 < x ≤ 4,y = 17/6x - 110/6, 4 < x ≤ 10.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.A piecewise function is a function that has different definitions based on the input.
For x between -9 and -3, the function decreases by 8 when x increases by 6, hence the slope is given by:
m = -8/6 = -4/3, hence:
y = -4/3x + b.
When x = -9, y = 9, hence we use it to find b as follows:
9 = -4/3(-9) + b
9 = 12 + b
b = -3.
Thus the first definition is:
y = -4/3x + b, −9 ≤ x ≤ −3
For x between -3 and 4, the function decreases by 8 when x increases by 7, hence the slope is given by:
m = -8/7
y = -8/7x + b.
When x = -3, y = 1, hence we use it to find b as follows:
1 = -8/7(-3) + b
1 = 24/7 + b
b = -17/7
Thus the second definition is:
y = -8/7x - 17/7, −3 < x ≤ 4.
For x between 4 and 10, the function increases by 17 when x increases by 6, hence the slope is given by:
m = 17/6
y = 17/6x + b.
When x = 10, y = 10, hence we use it to find b as follows:
10 = 17/6(10) + b
b = 10 - 170/6
b = -110/6
Thus the third definition is:
y = 17/6x - 110/6, 4 < x ≤ 10
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Angel owns 10 more DVDs than Philip. Choose an equation
that represents the number of DVDs Philip owns (p) as a
function of the number of DVDs Angel owns (a).
The function of the number of DVDs Angel owns (a) will be a = p + 10
How to calculate the value?From the information, Angel owns 10 more DVDs than Philip.
The number of DVD that Philip owns was represented asp.
Therefore, the function of the number of DVDs Angel owns (a) will be:
a = p + 10
Therefore the function is a = p + 10
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Suppose the Kalamazoo Brewing Company (KBC) currently sells its microbrews in a seven-state area: Illinois, Indiana, Michigan, Minnesota, Mississippi, Ohio, and Wisconsin. The company’s data analytics department has collected data from its distributors in each state. This data consists of the quantity and price (per case) of microbrews sold in each state, as well as the average income (in thousands of dollars) of consumers living in various regions of each state. The data for each state are available via the link below--please note there are multiple tabs at the bottom of the spreadsheet, each refers to one of the seven states selling the Kalamazoo Brewing Company’s microbrews. Excel Data File Assuming that the underlying demand relation is a linear function of price and income, use your spreadsheet program to obtain least squares estimates of Ohio’s demand for KBC microbrews.
Let's say that the Kalamazoo Brewing Company (KBC) now distributes its microbrews across a region that includes seven states: Illinois, Indiana, Michigan, Minnesota, Mississippi, Ohio, and Wisconsin. Data from the company's distributors in each state has been gathered by the data analytics division. This information includes the volume and cost of microbrews (per case) sold in each state as well as the average annual income (in thousands of dollars) of customers residing in various states' areas. Please notice that there are several tabs at the bottom of the spreadsheet, each of which corresponds to one of the seven states where the microbrews of the Kalamazoo Brewing Company are sold. The statistics for each state are available via the link below. Data File in Excel Using the supposition that the fundamental demand relationship is a linear function of price and income, utilize
With your spreadsheet application, you may predict Ohio's demand for KBC microbrews using least squares.
Ohio's demand for KBC microbrews is estimated using least squares as follows: Price + Income = 1.57 times the quantity.
Note: Sheet1 of the attached Excel document has a replication of the data from the question, and Sheet2 contains the results of the regression analysis.
Rounding to two decimal places, we find the following coefficients in the second column of the third table in Sheet2:
Price: $1.57 Profit: $15.00
Because a zero intercept was used for the analysis, the intercept is zero.
Based on the information above, the following is how the least squares estimations of Ohio's demand for KBC microbrews may be expressed:
Quantity = Price + Income + 1.57
To do the regression starting with Sheet1 to acquire
the results in Sheet, then replicate his steps:
Select the "Data Analysis" tab from the "Data" menu. Scroll down in the new window to "Regression," select it, then click "OK."
Select the column holding the Quantity data as the dependent variable by clicking in the "Input Y Range" box in the new window. Select the column holding the Price and Income data as the independent variables by clicking on the "Input X Range" box in the new window. Add "Labels," "Confidence level (95%)," and "Constant is Zero" to your selections. After that, click "OK" to get the results in Sheet2.
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Square LMNO has vertices, L(−4, 2), M(1, 2), N(1, −3), and O(−4, −3). Square LMNO is translated 3 units left and 4 units up to produce square L′M′N′O′.
Which coordinates describe the vertices of the image?
L′(−7, 6), M′(−2, 6), N′(−2, 1), and O′(−7, 1)
L′(−1, 6), M′(4, 6), N′(4, 1), and O′(−1, 1)
L′(0, −1), M′(5, −1), N′(5, −6), and O′(0, −6)
L′(0, 5), M′(5, 5), N′(5, 0), and O′(0, 0)
PLS HELP ME IS ANYONE SPAMS I WILL REPORT YOU AND BAN YOU IMMEDIATLEY BUT IF CORRECT I WILL GIVE BRAINLIESTPLS HURRRY THIS IS DUE TODAY
The coordinate of the square L'M'N'O' will be L′(−7, 6), M′(−2, 6), N′(−2, 1), and O′(−7, 1). Then the correct option is A.
What is a transformation of a point?Each higher dimensional space mapping to itself constitutes a spatial transformation, which preserves some spatial link between the figures.
Square LMNO has vertices, L(−4, 2), M(1, 2), N(1, −3), and O(−4, −3). Square LMNO is translated 3 units left and 4 units up to produce square L′M′N′O′.
The transformation rule will be given as,
(x', y') = (x - 3, y + 4)
Then the coordinate of the square L'M'N'O' will be
L′(−7, 6), M′(−2, 6), N′(−2, 1), and O′(−7, 1)
Then the correct option is A.
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19. 9a2b = c + 4a, for a
Answer:x/5 + 2b/5
Step-by-step explanation:
9a-2b=c+4a solve for a
9a-2b=c+4a
add -4a to both sides
9a-4a-2b=x+4a-4a
5a-2b=x
add 2b to both sides
5a-2b+2b=x+2b
5a= x+2b
divide by 5
5a/5 = x/5 +2b/5
a= x/5 + 2b/5
Measure the length and width of a rectangular room in your house/apartment in feet. Determine the area of the room in square feet. Convert the area to both square inches and square yards. Explain how you made these conversions. When would you want to have the area in square feet? Square inches? Square yards?
Then measure the height of the room in feet. Calculate the volume of the room in cubic feet. Convert the volume to both cubic inches and cubic yards. Explain how you made these conversions. When would you want to have the area in cubic feet? Cubic inches? Cubic yards?
1) The area of the room in square feet, square inches, and square yards is as follows:
Area = 120 ft²
Area = 1,440 in²
Area = 40 yards²
2) The volume of the room in cubic feet, cubic inches, and cubic yards is as follows:
Volume = 1,440 ft³
Voluem = 17,280 in²
Volume = 480 yards²
What are the conversion rates?The conversion rates are:
1 foot equals 12 inches 3 feet are equivalent to 1 yard.The mathematical operations of multiplication and division are used.
Data and Calculations:Let the length = 12 feet
Let the width = 10 feet
Let the height = 12 feet
1 foot = 12 inches
3 feet = 1 yard
Area = 120 ft² (12 x 10)
Area = 1,440 in² (120 x 12)
Area = 40 yards² (120/3)
Volume = 1,440 ft³ (12 x 10 x 12)
Voluem = 17,280 in² (1,440 x 12)
Volume = 480 yards² (1,440/3)
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A local company has K2,500 to set up an annuity to be paid quarterly for 5 years. The payments of that annuity are to be increased in line with the current interest rate. The account pays interest at 10% p.a. compounded quarterly,
a) Calculate the size of each payment during the first year.
b) What is the size of the final payment (payment at the end)?
Answer:
Step-by-step explanation:
(a).
Within 1 year, there would be 4 payments to be made.
therefore, PMT= [tex]\frac{P(1+i)}{n} = \frac{2500(1+0.025)}{4*5} =\frac{2562.5}{20} = $128.125[/tex]
(i) 1st payment will be :PMT $128.125
(ii) 2nd payment will be :128.125*(1.025)^1= $131.33
(iii) 3rd payment will be :128.125*(1.025)^2=$134.61
(iv) 4th payment will be :128.125*(1.025)^3=$137.98
Hence the payments are: $128.125, $131.33, $134.61, and $137.98.
(b).
The size of the final payment [tex]PMT(1+i)^{m-1}[/tex] where m 4 *5= 20
[tex]=128.125(1+0.025)^{20-1} \\=128.125(1.025)^{19} \\=$204.83[/tex]
An open cylindrical tank is 150 feet in diameter and 180 feet high. The lateral surface area of the tank (no top and no bottom) is to be painted with paint that covers 225 square feet per gallon. When filled each cubic foot of the tank holds approximately 7.5 gallons of gasoline valued at $2.75 per gallon.
a) Find the number of gallons of paint required for a single coat of paint.
b) Find the total value of the gasoline in the filled tank.
In linear equation, the total value of the gasoline in the filled tank = $65605290
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.
Radius = 150/2 = 75 feet
height = 180 feet
A)
lateral surface area = 2 *pi*r*h = 2*pi* 75 *180 =84823
number of gallons of paint=84823/225 = 377 gallons
B)
Volume of cylinder= pi*r²h= pi*75^2*180 =3180862.5618
total value of the gasoline in the filled tank =3180862.5618 *7.5 *2.75 =$65605290
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What is the answer to 0.038 ounces to mg
Answer:
1,077.281879 mg is the answer
help pleaseeeeeeeeee its difficult I will slide brainiest
Answer: hope this help
step-step explanation:
On September 22, 2021, the market value of the investments contained in the Martindale Balanced Fund, a mutual fund, was $39,400,000, Liabilities for the
fund were $3,940,000.
If the fund had 1,380,000 shares outstanding, calculate the net asset value per share. Round your answer to the nearest cent.
Answer:
$25.70 (nearest cent)
Step-by-step explanation:
Given:
Market value = $39,400,000Liabilities = $3,940,000Outstanding shares = 1,380,000[tex]\begin{aligned} \textsf{Net Asset Value}_{\textsf{(Per Share)}} & =\dfrac{\textsf{Fund Assets}-\textsf{Fund Liabilities}}{\textsf{Total number of Outstanding Shares}}\\\\\implies \textsf{Net Asset Value}_{\textsf{(Per Share)}} & = \dfrac{\$39,400,000-\$3,940,000}{\$1,380,000}\\\\& = \dfrac{\$35,460,000}{\$1,380,000}\\\\& = \$25.69565217...\\\\\end{aligned}[/tex]
Therefore, the Net Asset Value (NAV) per share is $25.70 (nearest cent).
The given information is,
→ x = $39,400,000
→ y = $3,940,000
→ z = 1,380,000
Formula we use is,
→ (x - y)/z
Now the net asset value per share is,
→ (x - y)/z
→ (39400000 - 3940000)/1380000
→ 35460000/1380000
→ 25.6956521739
→ ≈ $25.70
Hence, the net asset value is $25.70.
PLEASE ANSWERING THIS QUESTION!!!
Solve the quadratic equation by completing the square: [tex]\sf{z^2+8z-44=20}[/tex]
Give the equation after completing the square, but before taking the square root. Your answer should look like: [tex]\sf{(z-a)^2=b}[/tex]
The equation is: (blank)
List all solutions to the equation in simplest radical form, separated by commas. The solutions are:
z= (blank)
Rules answering these questions:
Explain your answer!
Do not spam answers!
Show your work!
Nonsense answers will be reported and delete your answers.
Thanks!
The equation after completing the square is (z + 4)² = 80
The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5
Completing the squareFrom the question, we are to solve the given quadratic equation by completing the square
The given equation is
z² +8z - 44 =20
First, add 44 to both sides of the equation
z² +8z - 44 + 44 = 20 + 44
z² +8z = 64
Now, divide the coefficient of z by 2, square the value and add to both sides
The coefficient of z is 8
Dividing
8/2 = 4
Squaring
4²
Now, add this to both sides
That is,
z² +8z +4² = 64 + 4²
(z + 4)² = 64 + 16
(z + 4)² = 80
The equation after completing the square is
(z + 4)² = 80
Continuation
(z + 4)² = 80
Take the square root of both sides
√(z + 4)² = ±√80
z + 4 = ±√80
z = -4 ± √80
z = -4 ± 4√5
z = -4 + 4√5 and z = -4 - 4√5
Hence,
The equation after completing the square is (z + 4)² = 80
The solutions to the given equation in the simplest radical form are z = -4 + 4√5 and z = -4 - 4√5
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3. What is one question you can ask yourself if you find you are making an irrational
decision because of the endowment effect?
Answer:
Asking yourself how much you'd be willing to spend if someone else offered you a similar product.
A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower
to a metal stake in the ground. After placing the pole, Violet measures the distance
from the pole to the stake and from the pole to the tower, as shown in the diagram
below. Find the length of the guy wire, to the nearest foot.
The length of the guy wire, to the nearest foot is 48 ft.
What is mean by foot of Maths?A unit of length (or distance) in US units equal to 12 inches. The abbreviation is: ft. Or sometimes the single quote mark: ' Example: 10 feet can be written 10 ft, or just 10' A foot is exactly 0.3048 meters in the Metric System (the foot is defined that way).
Step-by-step explanation:
Here, we want to find the length of the wire
from the diagram, we can identify two similar triangles
The smaller one and a bigger one
Mathematically, when two triangles are similar, the ratio of their corresponding sides are equal
We can start by getting the height of the tower
we have this as:
8/11 = 28/x
8 * x = 28 * 11
8x = 308
x = 308/8
x = 38.5 ft
So as we can see, the wire represents the hypotenuse of the larger triangle that measures 28 ft base and 38.5 ft height
So we can use the Pythagoras’ theorem to get the hypotenuse
Let us call this g mathematically;
According to the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
thus, we have it that;
g^2 = 38.5^2 + 28^2
g^2 = 2,266.25
g = √2,266.25
g = 47.61 which is approximately 48 ft
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Solve the calculation
Answer:
83° 59'
Step-by-step explanation:
The numbers given refer to degrees and minutes for two angles
We read them as follows
62° 18' ==> 62 degrees and 18 minutes
21° 14' ==> 21 degrees and 41 minutes
60 minutes make up 1 degree
We simply add the individual components together. If the number of minutes is 60 or greater then we have to convert those minutes to degree and minutes and add to the total degrees
In this case it is a simple addition since 18' + 41' = 59' and is less than 60
So 62° 18' + 21° 14'
==> Add the degrees separately ==> 62 + 21 = 83°
==> Add the minutes separately ==> 18' + 41' = 59'
Put the two components together to get
83° 59'
Which may be a cost of inflation?
Higher prices
Consumer panic
Higher pay for workers
Increased business profits
Answer:
consumer panic
Step-by-step explanation:
Kevin drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hoursWhen Kevin drove home, there was no traffic and the trip only took 4 hours. his average rate was 40 per hour faster on the trip home, how far away does Kevin live from the mountains? Do not do any rounding
Answer:
288 miles
Step-by-step explanation:
Kevin's trip took 9 hours one way, and 4 hours the other way, driving 40 mph faster. You want to know the one-way length of Kevin's trip to the mountains.
SetupThe relation between time, speed, and distance is ...
speed = distance/time
Using d to represent the one-way distance Kevin drove, we can relate his speeds with ...
d/4 = 40 +d/9 . . . . . . speed coming home was 40 mph more than going
SolutionMultiplying by 36 to clear fractions, we have ...
9d = 1440 +4d
5d = 1440 . . . . . . . subtract 4d
d = 288 . . . . . . . divide by 5
Kevin lived 288 miles from the mountains.
