A) The slope of the line is 2.
B) the linear equation is y = 2x - 7
C) y-intercept = -7
x-intercept = 3.5
How to find the linear equation?A general linear equation can be written as:
y = m*x + b
Where m is the slope.
If the line passes through two points (x₁, y₁)and (x₂, y₂), then the slope is:
m = (y₂ - y₁)/(x₂ - x₁)
In this case these points are (-3, 7) and (2, -3), then the slope is:
m = (-3 - 7)/(2 + 3) = 2
Then the line is something like:
y = 2x + b
To find the value of b we can replace the values of the point (2, -3), we will get:
-3 = 2*2 + b
-3 - 4 = b
-7 = b
y = 2*x - 7
C) the y-intercept is the value of y when x = 0.
y = 2*0 - 7
y = -7
The x-intercept is the value of x when y = 0.
0 = 2*x -7
7 = 2x
7/2 = x
3.5 = x
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Hector spent $26.75 for 2 DVDs that cost the same amount. The sales tax on his purchase was $4.15. Hector also used a coupon for $1.00 off his purchase.
The cost of one DVD to Hector is $11.8.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Hector spent $26.75 for 2 DVDs that cost the same amount.
The sales tax on his purchase was $4.15.
That means,
the cost of 2 DVDs = 26.75 - 4.15 = $22.6
Hector also used a coupon for $1.00 off his purchase.
That means,
the cost of 2 DVDs = $23.6
The cost of one DVD = 23.6 /2 = $11.8
Therefore, the cost of one DVD is $11.8.
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11. Randy is painting part of a wall, excluding the two corners shown in white. A gallon of paint will cover 100 square feet. How many gallons of paint will Randy need to purchase?
970
-
T
6 ft
1
20 ft
Answer: The wall that Randy is painting is 20 feet long and 6 feet high. The two corners that he is not painting are triangular in shape and are each 6 feet high and 4 feet wide.
So the area of the wall that Randy is going to paint is:
20 ft * 6 ft = 120 sq ft
The area of the two corners that Randy is not painting is:
(1/2) * 4 ft * 6 ft = 12 sq ft
Therefore, the total area that Randy needs to paint is:
120 sq ft - 12 sq ft = 108 sq ft
One gallon of paint will cover 100 square feet.
So Randy will need to purchase 108 sq ft / 100 sq ft/gallon = 1.08 gallons of paint.
Randy will have to purchase 1.08 gallons of paint.
Step-by-step explanation:
If the number of tickets sold is 125, what will be the total sales?
Answer:
I don't know????????....................
The classic 60° triangle has a hypotenuse of length 2. An opposite side of length v3 and an adjacent
side of length 1:
60°
V3 - 1732
What is the value of costo
A 0. 5
B 0. 572
C 0. 866
ОА
The value of cosθ = 0.5
The correct option is (A).
Now, According to the question:
Basic Trigonometric Function Formulas:
By using a right-angled triangle as a reference, the trigonometric functions and identities are derived: sin θ = Opposite Side/Hypotenuse. cos θ = Adjacent Side/Hypotenuse. tan θ = Opposite Side/Adjacent Side.
Remember that in a right triangle, we have that:
cos(θ) = (adjacent cathetus)/(hypotenuse)
Here we have:
θ = 60°adjacent cathetus = 1hypotenuse = 2Replacing all that in the equation we get:
cos(60°) = 1/2 = 0.5
Hence, the value of cosθ = 0.5
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2. Bryan owns a clothing store. Determine whether his costs are fixed or
variable. Use F for fixed and V for variable.
Insurance
Internet bill
Clothes
Employees' salaries
Bryan owns a clothing store, Insurance: F , Internet bill: F , Clothes: V ,Employees' salaries: F
F is for fixed and V is for variable used .
Fixed cost :
Regardless of production output, fixed costs remain constant. Lease and rental payments, insurance, and interest payments are examples of fixed costs. Costs that are not affected by volume are known as fixed costs. Costs that are usually based on time rather than on how many products or services your company sells or produces are known as fixed costs. Rent and lease payments, salaries, utility bills, insurance, and loan repayments are all examples of fixed costs.
Costs that do not change when production or sales volumes increase or decrease are known as fixed costs. This is because they are not directly involved in providing a service or manufacturing a product. Consequently, fixed costs are regarded as indirect costs.
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Answer:
Step-by-step explanation:
A recipe for sparkling grape juice calls for 1 quarts of sparkling water and
quart of grape juice.
a. How much sparkling water would you need to mix with 9 quarts of grape juice?
18
b. How much grape juice would you need to mix with quarts of sparkling water?
c. How much of each ingredient would you need to make 100 quarts of sparkling
grape juice?
Please answer all no need for a step by step I just need the answers thanks :)
a. 9 quarts of sparkling water
b. 1 quart of grape juice
c. 50 quarts of sparkling water and 50 quarts of grape juice
What is the rational behind these values?The rationale behind the values above are as explained below:
a. If the recipe calls for 1 quart of sparkling water to be mixed with 1 quart of grape juice, then to mix with 9 quarts of grape juice, you would need 9 quarts of sparkling water.
b. If the recipe calls for 1 quart of sparkling water to be mixed with 1 quart of grape juice, then to mix with 1 quart of sparkling water, you would need 1 quart of grape juice.
c. To make 100 quarts of sparkling grape juice, using the 1:1 ratio in the recipe, you would need 50 quarts of sparkling water and 50 quarts of grape juice.
Therefore, the correct answers are as given above
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A shop assistant sells goods to the value of $3400 during a certain week. If she is
paid 7.5% commission on these sales, calculate the amount of commission earned.
If she is paid a basic wage of $450, calculate her total wage for that week.
Answer:
$705
Step-by-step explanation:
($3400)(0.075) = $255 commission earned
Total wage for that week = $450 + $255 = $705
note: this answer assumes that $450 is the weekly basic wage, not daily
Determine whether the variable is qualitative or quantitative: Explain your reasoning_ State of residence Is the variable qualitative or quantitative? Explain your reasoning a. The variable is quantitative because state of residence describes an attribute or characteristic. b. The variable is qualitative because state of residence describes an attribute or characteristic c. The variable is qualitative because state of residence is found by measuring or counting d. The variable is quantitative because state of residence is found by measuring or counting:
To determine whether the variable is qualitative or quantitative, the reasoning for the following question will be:
a) qualitative, State of residence describes an attribute or characteristic, making the variable qualitative. Because the state of residence can be determined through measurement or counting, the variable is qualitative.
b) quantitative, The state of residence serves as a description of an attribute or characteristic, so the variable is quantitative. Since determining the state of residence requires measuring or counting, the variable is quantitative.
c) qualitative, Your variable will be quantitative if it is something like, say, your age or salary, which is typically something that can be discovered by counting or using mary-screw analysis. However, in this case, the state of residence is obviously a qualitative factor.
d) qualitative, If your variable is something like, say, your age or salary, or if it's something that is typically discovered by counting or Mary, then these kinds of variables are quantitative. But in this case, the state of residence is categorically important for this question.
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Find the value of x, y, and z in the rhombus below.
104°
(10y+6)°
(z+7)
(-x-10)°
The value of x, y, and z in the rhombus are -114, 7 and 59 respectively
How to find the value of x, y, and z in the rhombus?Since the opposite angles of a rhombus are equal to each other. We can write:
(-x-10)° = 104°
-x-10 = 104
-x = 104 + 10
x = -114
Since the adjacent angles in rhombus are supplementary. We have:
114 + (z + 7) = 180
121 + z = 180
z = 180 -121
z = 59
104 + (10y + 6) = 180
110 + 10y = 180
10y = 180 - 110
10y = 70
y = 70/10
y = 7
Thus, the value of x, y, and z are -114, 7 and 59
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per's debate team at thunderbird high sclusel, 20% of the members are sophomores, 39% arts and the closing argent, the team has a probability of 0 253 of winning the debute. if a junior gives that closing argument, the probabilay of if or cloons, the probability of winning is 083 (4) find the probability that the tests wins the debate (b) describe the design of a simulation to estimate the probability that a sophomore is never selected to give the closing argument in the next 3 debutes explain clearly how you would use a table of random digits to carry out the simulation (e) the dotplot below shows the number of sophomores chosen in 50 simulated sets of 5 debates in which 20% of the time a sophomore is selected and 80% of the time a junior or senice is selected to give the closing argument for the team in the next 5 debates, a sophomore was never chosen to give the closing argument. the sophomores on the team claim that they were purposely ignored. use the results of the simulation to determine if there is convincing evidence that the sophomores were purposely ignored.
Here to solve the probability of this sum, it is difficult to say that the probability without no information.
(a)The probability that the team wins the debate with a junior giving the closing argument is 0.083.
(b) To design a simulation to estimate the probability that a sophomore is never selected to give the closing argument in the next 3 debates, one could randomly assign a closing argument speaker for each debate using a table of random digits. The table would have two columns: one for sophomores and one for juniors and seniors. The probability of a sophomore being selected would be 20%, and the probability of a junior or senior being selected would be 80%. The simulation would be run for 3 debates and the number of times a sophomore is never selected would be recorded. This process would be repeated a number of times to estimate the probability of a sophomore never being selected. (e) Based on the dot plot, it appears that there is some evidence that the sophomores were purposely ignored, as there are several simulated sets of 5 debates where a sophomore was not selected to give the closing argument. However, without more information, it is difficult to say for certain if this is enough evidence to support the claim that the sophomores were purposely ignored.
A larger sample size or a more detailed analysis of the simulation results may be needed to make a more convincing determination.
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Each of the s swimmers on the relay team swam an equal number of the 8 laps in a race. Write an expression that shows how many laps each swimmer swam.
Answer: If each of the s swimmers on the relay team swam an equal number of the 8 laps in a race, the expression that shows how many laps each swimmer swam would be 8/s.
This expression shows that each swimmer swam 8 laps, divided by the total number of swimmers on the team, s.
So, if there are 's' swimmers on the relay team, each swimmer swam 8/s laps.
Step-by-step explanation:
rewrite in simplest form
Use the equation to answer the question.
12a+9b=k(2a+32b)
Which value of k makes the equation true?
a. 6
b. 2
c. 4
d. 3
The value of k that makes the equation true is given as follows:
a. 6.
How to obtain the value of k?The equation for this problem is defined as follows:
12a + 9b = k(2a + 3/2b).
The equation will be true is both sides are equal.
Applying the distributive property to the right side, we have that:
12a + 9b = 2ak + 3kb/2.
Taking one of the terms, the value of k is obtained as follows:
2ak = 12a
k = 12a/2a
k = 6.
Meaning that the correct option is given by option A.
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please help me with this geometry question
Answer:
Step-by-step explanation:
a)
Because if you visualize the formation of it size x will fit perfectly on the 6cm side therefore x = 6cm
b)
6 x 9 = 54cm
Your height i 3 1/2 in and you ue a cale of 1 inch on the portrait repreent 20 inche on the decal what i the height of the decal if your actual height i 55 inche
The height of the wall decal when my actual height is 5.5 inches, is equals to the 110 inches.
We have, My height in the portrait measures = 3 1/2 inches = 7/2 = 3.5 inches
According to the scale used by company,
one inch measurement on portrait = 20 inches on the wall decal. That is portrait measurement / wall decal = 1/20 ( in inches) . We have to determine the height on the wall decal if my actual height is 5.5 inches. Let the height of wall decal be "h inches" when my actual height is 5.5 inches. Write the proportion like this to calculate the value of h , 1/20 = 5.5/ h
Cross multiply we get,
=> 1× h = 5.5 × 20
=> h = 110.0
Hence, the required height of the decal is 110 inches.
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Complete question:
Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal if your actual height is 5.5 inche?
When compared to my actual height of 5.5 inches, the wall decal's height is 110 inches.
We've got My height in the image is 3 1/2 inches plus 7/2, which is 3.5 inches.
On the basis of the scale:
20 inches are equal to one inch in a portrait on the wall decal. That is a portrait measurement divided by a 20-inch wall decal. If my real height is 5.5 inches, we must determine the height on the wall decal. Let the wall decal's height be "h inches" even though my height is 5.5 inches. To compute the value of h, write the ratio as 1/20 = 5.5/h.
When we cross multiply,
1× h = 5.5 × 20
h = 110.0
Therefore, 110 inches is the minimum height for the decal.
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Note: The complete question would be as bellow,
Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal if your actual height is 5.5 inche?
it takes country a 30 minutes to produce a car and 20 minutes to produce a tank. it takes country b 12 minutes to produce a car and 10 min to produce a tank. it is true that
Country B is more efficient than Country A when it comes to producing cars and tanks.
Country A takes twice as long to produce a car (30 minutes) than Country B (12 minutes). However, Country A takes 20 minutes to produce a tank while Country B takes 10 minutes, cutting the amount of time in half.
We can measure the efficiency of each country by calculating the number of cars and tanks each country can produce in an hour. We can do this using the following formula:
Cars per hour = (60 minutes/minutes to produce car)
Tanks per hour = (60 minutes/minutes to produce tank)
For Country A, the number of cars produced in an hour is (60 minutes/30 minutes) = 2 cars per hour and the number of tanks produced in an hour is (60 minutes/20 minutes) = 3 tanks per hour.
For Country B, the number of cars produced in an hour is (60 minutes/12 minutes) = 5 cars per hour and the number of tanks produced in an hour is (60 minutes/10 minutes) = 6 tanks per hour.
Therefore, Country B is more efficient than Country A when it comes to producing cars and tanks.
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A. The ratio of triangles to squares is 2 to 4.
B. The ratio of squares to smiley faces is 6 : 4.
C. The ratio of smiley faces to triangles is 6 to 4.
D. There are two squares for every triangle.
E. There are two triangles for every smiley face.
F. There are three smiley faces for every triangle.
Sarah took the advertising department from her company on a round trip to meet with a potential client. Incluc trip. She was able to purchase coach tickets for $200 and first class tickets for $1290. She used her total bud $11,720. How many first class tickets did she buy? How many coach tickets did she buy?n took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 15 people took the She was able to purchase coach tickets for $200 and first class tickets for $1290. She used her total budget for airfare for the trip, which was $11,720. How many first class tickets did she buy? How many coach tickets did she buy?
6 coach tickets and 9 first-class tickets were bought, totaling the number of tickets purchased.
Explain about the expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
A mix of operators, constants, and variables make up an expression. An expression can yield a value by using one or more operands and one or more operators.
An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
The algebraic expression that results from multiplying two variables, x and y, is xy.
Let's say that x coach tickets were purchased.
And y is the total number of first-class tickets bought.
Now,
15 people in total, including Sarah, made the journey.
Thus,
x + y = 15(1)
Coach and first-class tickets are priced at $200 and $1290, respectively.
The trip's total spending for air travel is $11,720.
Therefore,
200x + 1290y = 11720
20x + 129y = 1172
We obtain by resolving both equations.
x = 6
y = 9
Consequently, 6 coach tickets and 9 first-class tickets were acquired, making up the total number of tickets.
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Hank bought a four family residence for a rental property he put 20% down on 300,000 rental unit how much will he be able to depreciate using the class recovery period for residential rental. Properties each year
The amount he will be able to depreciate using the class recovery period for a residential rental property each year is D. $10,909.09.
The term depreciation defines as an accounting method used to allocate the cost of a tangible or physical asset over its useful life.
It also represents how much of an asset's value has been used, and allows companies to earn revenue from the assets they own by paying for them over a certain period of time.
Using this formula:
Depreciation=Rental unit amount/ MACRS residential rental property recovery period
Where:
Rental unit amount=$300,000
MACRS Residential rental property recovery period=27.5 years
Let's plug in the formula
Depreciation=$300,000/27.5
Depreciation=$10,909.09
In conclusion, the amount he will be able to depreciate using the class recovery period for a residential rental property each year is: D. $10,909.09
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Plane A is flying according to the relation = − 2 + 10 and plane B is flying
according to the relation 2 − 3 = − 6 . They are both heading towards the airport and
will meet there. Determine the position of the airport on the grid.
Show your method of graphing by writing down the information you used to graph each line
in the space provided. Plane A: Plane B:
Answer: plane a is faster than plane b because it has more speed than plane b
Step-by-step explanation:
Could someone please help? Thanks
what do you want help with?
given f(x)=x^2+2x-5 and the values of the linear function g(x) in the table, what is the range of (f+g)(x)
x: -6 -3 -1 4
g(x): 16 10 6 -4
Answers:
(infinity,1]
[-1,1]
R
The range of the function (f+g)(x) = x² - 1 will be ( -1, ∞ ). The correct option is B.
What are a domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
Given that the function is f(x) = x²+2x-5. The function g(x) will be calculated by the data given in the table.
x -6 -3 -1 4
g(x) 16 10 6 -4
The function g(x) will be:-
g(x) = mx + c
m = ( 10 - 16 ) / ( -3 + 6 )
m = -6 / 3
m = -2
c = y - mx
c = 10 - 6
c = 4
g(x) = -2x + 4
The function ( f + g)(x) will be:-
( f + g)(x) = f(x) + g(x)
( f + g)(x) = x²+ 2x - 5 - 2x + 4
( f + g)(x) = x² - 1
At x = 0, the value ( f + g)(x) is -1. The range of the function is ( -1, ∞).
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put -x+3y<6 into cordinates
The inequality -x+3y < 6 passes through the points (-6, 0) and (0, 2).
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
We have an inequality,
-x+3y < 6.
The graph of the inequality is given in the attached image.
And inequality passes through the points (-6, 0) and (0, 2).
Therefore, the graph of the inequality is given in the attached image.
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A string is placed on the outside of a clock going clockwise from 12to 9. The clock has a radius of 6 inches. What is the length of the string
Answer:
9π inches
Step-by-step explanation:
we know clock start from 12 o'clock to 9 o'clock, it will be 270 degree. Then we convert it to radian is 3π/2. We get the radian and the radius. So we can apply the formula of the lenghth of an arc.
l = rθ
l=6*3π/2=9π inches
Before the baseball season begins, a field manager outlines the "on-deck" circle with chalk and covers the area with dirt.
If the "on-deck" circle has a diameter of 6 feet, about how long is the chalk outline?
The length of the chalk outline is 19 feet.
The field is circular and the line drawn by chalk is the length of the rim of the circular field and is called the circumference. It can be calculated from the radius(or diameter) of the circle.
The formula of the circumference of a circle:
Circumference of circle [tex]= 2 * \pi * r = \pi * d[/tex]
where r means the radius of the circle and d means the diameter of the circle.
The diameter d = 2 times of radius
Thus, we have:
Length of a chalk outline [tex]= \pi * d = \pi * 6 = 3.14 * 6 = 18.84 = 19 feet[/tex]
So, the length of the chalk outline is 19 feet.
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Refer to the problem #16,which system of linear equations represent the problem?
Answer:x=y=200
x-y=100
Which angle pair forms corresponding angles?
The angle pairs that forms corresponding angles are angles 1 and 5. Option B
What are corresponding angles?Corresponding angles are defined as angles formed when two parallel lines are both intersected by a transversal.
They are also described as any pair of angles in which each of the angles are on the same side of one of two lines that is cut by another line and on the same side of that other line.
The types of corresponding angles are;
Corresponding angles formed by transversal and parallel lines. These angles are equalCorresponding angles formed by transversal non-parallel lines. These angles are not equalHence, the pairs that are corresponding are 1 and 5
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How much of the circle is shaded? Write your answer as a fraction in simplest form.
Answer:
5/18
Step-by-step explanation:
1. to get to the fractions you need to subtract make them have the same denominator. make 1/2=9/18 and 2/9=4/18
2. 9/18-4/18=5/18
what is (3√6) (3√6)
regular milk has 4% butterfat. how many litres of regular milk must be mixed with 90 l of milk with 1% butterfat to have milk with 2% butterfat?
20 litres of regular milk must be mixed with 90 l of milk with 1% butterfat to have milk with 2% butterfat.
From the data given,
Let us assume that the x litres of regular milk which have 4% butterfat is mixed.
The amount of butterfat in 40 L of milk with 1% butterfat will be = (40*.01)=0.4 L
The amount of butterfat in x L of milk with 4% butterfat will be =x *0.04=0.04 x
The amount of butterfat in (40+x) L (when both are mixed) of milk with 2% butterfat will be =(40+x)*(0.02)=0.02(40+x)
Since we are aware that the total quantity of butterfat in each type's individual milk will match the total amount of butterfat in the final milk.
Therefore we can set up the equation which will be like this:
0.4+0.04 x=0.02(40+x)
Now solving the above equation for getting the value of "x"
0.4+0.04 x=0.02(40+x)
=>0.4+0.04x=0.8+0.02x
=>0.04x-0.02x=0.8-0.4
=>0.02x=0.4
=>x=(0.4/0.02)=20
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To make milk with 2% butterfat, 20 liters of ordinary milk must be combined with 90 liters of 1% butterfat milk.
Assume that 4% butterfat normal milk in an amount of X litres is combined. 40 L of milk with 1% butterfat will contain (40 x 0.01)=0.4 L of butterfat. In X L of milk containing 4% butterfat, the amount of butterfat is equal to =(X liter) x (0.04)=0.04 X.
When both are combined, (40+X) L of milk with 2% butterfat will contain =(40+X)*(0.02)
=0.02(40+X) grams of butterfat.
We know that the overall amount of butterfat in each type's individual milk will be the same as the total amount of butterfat in the finished milk.
As a result, we may construct the equation, which looks like this:
0.4+0.04X = 0.02(40+X)
To find the value of "X," solve the equation above.
0.4+0.04 X=0.02(40+X)
= 0.4+0.04X=0.8+0.02X
= 0.04X-0.02X=0.8-0.4
= 0.02X=0.4
= X=(0.4/0.02)
= 20
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