y = -2x + 12 is the linear equation of the line that passes through the coordinates of points (1, 10) and (2, 8).
What is the equation of line with the given coordinates?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
The slope of a line is expressed as change in y over change in x.
Slope m = (y₂-y₁)/(x₂-x₁)
Given the data in the question;
Point 1 ( 1, 10 )
x₁ = 1y₁ = 10Point 2 ( 2, 8 )
x₂ = 2y₂ = 8First, we determine the slope of the line.
Slope m = (y₂-y₁)/(x₂-x₁)
Slope m = ( 8 - 10 )/( 2 - 1 )
Slope m = (-2)/( 1 )
Slope m = -2
Now, determine the y-intercept b, by substituting the slope and the coordinates of one point into the equation of line formula.
y = mx + b
10 = -2(1) + b
Solve for b
10 = -2 + b
b = 10 + 2
b = 12
Now that we have the slope m and y-intercept b, plug these into y = mx + b to determine the equation of the line.
y = mx + b
y = -2(x) + 12
y = -2x + 12
Therefore, the equation of the line that goes through the given points is y = -2x + 12.
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The Hike 4 Life company manufactures hiking boots. The production facility has foxed costs of $400 a day and the cost of making 1 pair of boots is $4.75. Which of the following equations
represents the daily production cost based on the number of pairs of boots manufactured each day?
The equation that represents the daily production cost based on the number of pairs of boots manufactured each day is C(x) = 4.75x + 400.
What are linear equations?
Linear equations are a subset of first order equations. Linear equations are defined for lines in the coordinate system. One homogeneous variable of degree one constitutes a linear equation in one variable (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.
Given, the daily production cost (in $) = C(x)
The number of pairs of boots manufactured = x
The cost of making a pair of boots = $ 4.75
The fixed cost of production each day = $ 400
Thus, net cost of making 'x' boots added to the daily fixed production cost will give the daily production cost.
Therefore, C(x) = 4.75x + 400, is the correct equation.
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Determine the value of the trigonometric ratio.
Given,
The measure of side YZ is 21.
The measure of side XY is 20.
The measure of side XZ is 29.
Required:
The value of tanX.
The trigonometric ratio is calculated as,
[tex]tan\theta=\frac{side\text{ opposite to }\theta}{side\text{ adjacent of }\theta}[/tex]Substituting the values,
[tex]\begin{gathered} tanX=\frac{YZ}{XY} \\ tanX=\frac{21}{20} \end{gathered}[/tex]ence, the value of tanX is 21/290.
What value(s) of x in the relation below would create a set of ordered pairs that is not a function? Justify your answer. {(0,5) (1,5) (2, 6) (x, 7)}
First, let's see the points on the coordinate plane:
Now, let's remember that a function has every element of it's domain related with only one element from it's image.
Therefore, x = 2 would create a set of ordered pairs that is not a function. Let's see it in the plane:
As we can see, x = 2 has two values on the image: f(2) = 6 and f(2) = 7, and this never can happen in a function.
Please help me solve this
(a) 291/2020
Divide the total for the 10-14 year column by the total.(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.Quadrilateral IJKL with vertices I( 5,2 ), J( 9,5), K( 5,-2 ), and L( 2,-3 ) : Reflect in the line x=1. What are the coordinates of J’?
The Solution:
Given that the vertices of a quadrilateral are:
[tex]I(5,2),J(9,5),K(5,-2)\text{ and L(2,-3)}[/tex]We are required to find the coordinate of J' when J(9,5) is reflected in the line x=1.
The new x-coordinate will become:
[tex]x=1-9=-8[/tex]So, the required coordinate of J' is:
[tex](-8,5)[/tex]Therefore, the correct answer is J'(-8,5)
It takes 3 1/5 teaspoons
of strawberry syrup
to make 1 3/4
strawberry
milkshakes. How
many teaspoons of
syrup would it take to
make just one
strawberry
milkshake?
The quantity of teaspoons of syrup it would take to make just one strawberry milkshake is 1 29/35 teaspoons
RatioThis is the number which gives the comparison between two quantities. The ratio of teaspoons of strawberry to make strawberry milkshake is the comparison between the two quantities.
It takes 3 1/5 teaspoons of strawberry syrup to make 1 3/4 strawberry milkshakes Number of teaspoons of syrup would it take to make just one strawberry milkshake = xEquate the ratio of teaspoons of strawberry syrup to strawberry milkshakes
Teaspoons of strawberry : make strawberry milkshake
3 1/5 : 1 3/4 = x : 1
16/5 ÷ 7/4 = x/1
cross product
16/5 × 1 = 7/4 × x
16/5 = 7/4x
divide both sides by 7/4x = 16/5 ÷ 7/4
x = 16/5 × 4/7
= (16 × 4) / (5 × 7)
= 64 / 35
= 1 29/35 teaspoons
The teaspoons of syrup would it take to make just one strawberry milkshake is 1 29/35 teaspoons
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Peaches Water (cups)
40
30
400
300
How many peaches are needed for every 1 cup of water? Note: Your answer may be exact or rounded to the nearest hundredth
The table below shows the number of peaches and cups of water used to make fruit punch according to a certain recipe.
The peaches required for every cup of water is 4/3
what is unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
so;
A.T.Q:-
Is there two columns of data and two data points? Like this:
peaches Water
40 30
400 300
If so, then there are two ways to do it.
1) You can set up a ratio like this
40/30 = x
:-Where x is the number of peaches for every cups of water .
So;
x = 40/30 peaches
x = 4/3 peaches
2) Look at the increase from one to the other.
3 cups of water requires 4 peaches.
∵ Hence by unitary method
1 cup of water requires 4 /3 peaches.
:- so; 4/3 peaches are required for every cup of water.
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Customer 1 buys 2 hamburgers and 4 drinks, and his total is $13.00. Customer 2 buys 3 hamburgers and 7 drinks, and his total comes out as $21.00. PART A. You want to buy 8 drinks and 9 hamburgers for you and your friends. How much do you expect to pay?PART B. Show your work or explain how you got your answer.
Answer:
[tex]\text{Total= \$43.5}[/tex]Step by step explanation:
To solve this situation we can create a system of linear equations, with the given information for the customers:
Let x be the price for each hamburger
Let y be the price for each drink
[tex]\begin{gathered} 2x+4y=13\text{ (1)} \\ 3x+7y=21\text{ (2)} \end{gathered}[/tex]To solve for x and y. We can use the substitution method, which consists of isolating one variable in one of the equations and substitute it into the other.
Let's isolate y in (1):
[tex]\begin{gathered} 4y=13-2x \\ y=\frac{13}{4}-\frac{2}{4}x \end{gathered}[/tex]Now, substitute it into equation (2).
[tex]3x+7(\frac{13}{4}-\frac{2}{4}x)=21[/tex]Solve for x:
[tex]\begin{gathered} 3x+\frac{91}{4}-\frac{7}{2}x=21 \\ -\frac{1}{2}x+\frac{91}{4}=21 \\ -\frac{1}{2}x=21-\frac{91}{4} \\ -\frac{1}{2}x=-\frac{7}{4} \\ x=\frac{7\cdot2}{4} \\ x=\frac{7}{2}=\text{ \$3.5 } \end{gathered}[/tex]With the x-value, we can substitute it into the equation (1) to find the price for each drink:
[tex]\begin{gathered} y=\frac{13}{4}-\frac{2}{4}(3.5) \\ y=\frac{13}{4}-\frac{7}{4} \\ y=\frac{6}{4}=\text{ \$1.5} \end{gathered}[/tex]Therefore, the price for each hamburger is $3.5 and for each drink is $1.5.
Now, if we want to buy 8 drinks and 9 hamburgers:
[tex]\begin{gathered} \text{Total}=(8\cdot1.5)+(9\cdot3.5) \\ \text{Total}=12+31.5 \\ \text{Total= \$43.5} \end{gathered}[/tex]159,095 rounded to ten thousands place
Answer:
160,000
Step-by-step explanation:
1/8=?/4 how does this get solved?
Answer: ? = 1/2
Step-by-step explanation:
Your question is a bad example, so let me come up with one.
2/8 = 1/4
This is done by dividing both the numerator and denominator by the same value: 2/8 / 2/2
or
2/2 = 1, 8/2 = 4
We now have 1/4
or 9/36
What can we divide 36 by, 9 by? We need to divide by both for it to work.
9/3 = 3
36/3 = 12
3/12 But we can divide this again
3/3 = 1
12/3 = 4
1/4, we could also have divided 9/36 by 6/6 to get 1/4
For 1/8 to get ?/4, we do
8/? = 4
? = 1/2
, so the answer is 1/2/4 = 1/2*4 = 1/8
I need help with statements 2,4,5, and 7
We know that:
[tex]\begin{gathered} YW\cong YZ,XY\cong VY \\ XZ=XY+YZ \\ XZ\cong VY+YW=VW \\ XZ\cong VW \end{gathered}[/tex]Above, we use the transitive property
6. How many 18k stamps can be bought with #2.00?
By using the method of division, they can buy 11 stamps.
What is division?The procedure or act of dividing the condition of division one of the pieces or groupings into which a whole is divided or is divisible. Distribution can be an act, a process, or an instance of distribution among a number. something that separates, divides, or marks off the act of dividing into portions or the process of being divided. one of the chunks or groups into which a whole can be split up or divided. the action, procedure, or occurrence of distributing among a group. Division is the act or process of splitting something that is already divided.
Given that,
18k stamps can be bought with #2.00
2.00 ÷ 0.18= 11.11
Hence, they can buy 11 stamps.
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The number of cars sold weekly by a new automobile dealership grows according to a linear growth
model. The first week the dealership sold six-cars (Po= 6). The second week the dealership sold
nine cars (P₁ = 9).
Write the recursive formula for the number of cars sold, Pn, in the (n + 1)th week.
P₁ = Pn-1 +
Write the explicit formula for the number of cars sold, Pn, in the (n + 1)th week.
Pn=
If this trend continues, how many cars will be sold in the fourth week?
_____cars
The recursive formula of the function is P(n + 1) = 3 + Pn while the explicit formula is P(n) = 6 + 3(n -1)
The recursive formula of the functionThe given parameters are
Po = 6
P1 = 9
From the question, we understand that the number of cars follows a linear model
This means that the common difference is
d = P1 - Po
So, we have
d = 9 - 6
Evaluate
d = 3
The recursive formula is
P(n + 1) = d + Pn
So, we have
P(n + 1) = 3 + Pn
The explicit formula of the functionFrom the question, we understand that the number of cars follows a linear model
This means that the common difference is
d = 9 - 6
Evaluate
d = 3
The explicit formula is
P(n) = Po + (n -1) * d
So, we have
P(n) = 6 + (n -1) * 3
Evaluate
P(n) = 6 + 3(n -1)
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Types of Posts Cost of Each Post Base Price Posts with Words Only S5 $5 Posts with Pictures Only $10 $25 Posts with Words and Pictures $10 $35 Samuel ordered 2 posts with words only and 2 posts with pictures only. After placing his order, Samuel realized he could have saved money if he, instead, ordered 2 posts with words and pictures. Let y represent Samuel's savings, in dollars, and let x represent the number of posts. Which equation could be used to determine the amount of money Samuel could have saved if he ordered 2 posts with words and pictures, instead of his original order? A y = 5x – 5B. y = 5.r + 65C y = -5r + 25D y = 2
x = Number of posts
y = samuel's savings
If he order 2 posts with words and pictures:
y = 2(10) + 35 = 55
If he order 2 posts with words only and 2 posts with pictures only.
y = 2(5) + 2(10) + 5 + 25 = 10 + 20 + 5 + 25 = 60
Therefore, he could have save 5 dollars
Therefore the equation is:
y = 5x - 5
In a promotion for a local
Subway, every 5th customer will
get a free sandwich and every
3rd customer will get a free
drink. Which customer will be
the first person to get a free
sandwich and drink?
Answer:
15th customer
Step-by-step explanation:
to find the answer to this, you have to find the least common multiple(I think that’s what it is called). In this case, in order to find it, you can just multiply 5*3 to get 15 for the answer
Find the average value of the following numbers: -7,-4.2,-1,0,2,6,10,12
Answer:2.225
Step-by-step explanation:
If you add all the numbers and then divide by the number of numbers given you get the average.
A monument in the form of a marble cylinder has a circular base with a radius 1.5 meters. The altitude of the monument is 3.5 meters. How many cubic meters of marble does this monument contain?
A. 24.74 M 3
B. 6.19 M 3
C. 21.21 M 3
D. 7.07 M 3
If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube
The shape of the monument is cylinder
The base radius of the cylinder = 1.5 meter
The altitude of the monument = 3.5 meters
The volume of the cylinder = [tex]\pi r^{2}h[/tex]
Where r is the radius of the cylinder
h is the height of the cylinder
Substitute the values in the equation
The volume of the cylinder = [tex]\pi (1.5)^{2}(3.5)[/tex]
= 24.74 meter cube
Hence, If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube
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I am having trouble can u help me please
From the given histogram, it is found that Class 4 contains the largest number of exam scores.
What is an histogram?An histogram of a data-set is a graph that shows the number of times each element of x was observed, or elements in each range of x were observed.
From the histogram in the problem, we have that:
Class 1 contains 5 scores.Class 2 contains 3 scores.Class 3 contains 7 scores.Class 4 contains 19 scores.Class 5 contains 15 scores.Class 6 contains 18 scores.All these number of scores are given at the center of the bars on the graph.
The largest number among these number of scores is of 19 in Class 4, hence Class 4 contains the largest number of exam scores.
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12. A company has bought 3.4 acres of land out of the 4
acres of land that it plans to buy. What percent of the land
has the company already bought? Solve the problem with a
math drawing or a percent table, or both, explaining your
reasoning.
Answer:
I think about 3.4/4=.85 or 85% of acreage was bought.
Step-by-step explanation:
Consider a game in which a player rolls one die. If an even number comes up, the player wins the number of dollars showing on the die. If an odd number comes up, the player loses the number of dollars showing on the die. Calculate the expected value for this game. Is the game fair? (Assume that there is no cost to play the game.)
Answer:
Yes
Step-by-step explanation:
Winning numbers: 2, 4, 6
Losing numbers: 1, 3, 5
The even numbers are greater.
The average even (winning) number is 4.
The average odd (losing) number is 3.
You can win half a dollar on average.
Equation: (1/6)(-1)+(1/6)(2)+(1/6)(-3)+(1/6)(4)+(1/6)(-5)+1/6(6) = 0.5
help me please!!!!!!!!
Answer:
First option is correct.
Step-by-step explanation:
Normally, Pete's dad deposits $25 into his bank account every week.
Now, he wants to deposit x extra dollars for 8 weeks. So, the total deposits for these 8 weeks will be:
8*(25 + x)
He wants to keep the total deposits above 500. So
8*(25 + x) > 500
Now we solve the inequality similarly to how we would solve an equality.
8*(25 + x) > 500
200 + 8x > 500
8x > 500 - 200
8x > 300
x > 300/8
x > $37.50
So the first option is correct.
The weekly repair cost Y for a machine has a probability density function given by f(y)=3(1−y)^2, 0
Using integrals, the 90th percentile of the given probability distribution is of $53.58.
What is the 90th percentile of the distribution?The amount exceeded only 10% of the time is the 90th percentile of the distribution, which is the value of p for which:
[tex]\int_0^p f(y) dy = 0.9[/tex]
The integral represents the cumulative density function of the distribution, which is the reason why we use it to find the 90th percentile of the distribution.
The function is given by:
f(y) = 3(1 - y)²
Hence the integral is calculated as follows:
[tex]\int_0^p 3(1 - y)^2 dy[/tex]
Applying the integral of the power of y rule, along with the substitution, it is found that:
[tex]\int 3(1 - y)^2 dy = -(1 - y)^3[/tex]
Hence:
[tex]\int_0^p 3(1 - y)^2 dy = -(1 - y)^3|_{y = 0}^{y = p}[/tex]
Applying the Fundamental Theorem of Calculus, considering the value of the definite integral, it is found that:
-(1 - p)³ + 1 = 0.9
-(1 - p)³ = -0.1
(1 - p)³ = 0.1
Applying the cube root to both sides:
1 - p = 0.4642.
p = 1 - 0.4642
p = 0.5358.
This amount is in hundredths of dollars, hence the 90th percentile of the given probability distribution is of $53.58, as 0.5358 x 100 = $53.58.
What is the missing information?The problem is missing, and is given by the image at the end of the answer.
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HELP ASP ILL GIVE BRAINLIEST AND 50 points
Answer:
1. 12 days
2. more than 200 miles
3. 11 lawns
4. at least 9 hours (about 9.92 hours)
Step-by-step explanation:
1. 20x < 254, so x < 12.7. We need an integer here, so x = 12 days.
2.
[tex]70 + .15x < 50 + .25x[/tex]
[tex]20 < .10x[/tex]
[tex]200 < x[/tex]
[tex]x > 200[/tex]
3. 65x > 699, so x > 10.8. Since fractions of lawns are not accepted here, Mark must mow at least 11 lawns.
4. Assuming that the speed stays constant, 65x = 645, so x = 9.92 hours. The trip will take at least 9 hours, actually close to 10 hours.
find the mean median and mode 85,91,76,85,93
Answer:
mean: 86 median: 85 mode: 85
Step-by-step explanation:
Use the sequence below to complete each task. 972, 324, 108, ... a. Identify the common ratio (r). b. Write an equation to represent the sequence. C. Find the 6th term (ac)
(a),
The common ratio between the terms is
[tex]\frac{972}{324}=\frac{324}{108}=3[/tex](b).
The common ratio found in (a) tells us that every next number is found by dividing the previous number by 3; therefore, the equation for a_n the nth term will be
[tex]a_n=\frac{972}{3^n}[/tex](c).
The sixth term will be at n = 6. Putting n = 6 into the equation in (b) gets us
[tex]a_6=\frac{972}{3^6}=\frac{4}{3}[/tex]A music store is having its "Black Friday" sale. The store will give
$5 off for the second item a customer purchases. Emma wants
buy a pair of headphones for $25 and a CD for $18.50. How
much does she need to pay in total?
Based on the given task content; the amount of money the customer needs to pay if given a discount of $5 off the second item bought is $38.50
The amount paid by the customer after deducting discountItem 1:
Headphones = $25
Item 2:
CD = $18.50
Discount on the second item = $5Amount paid on the second item = original cost - discount
= $18.50 - $5
= $13.50
Total amount the customer needs to pay = cost of item 1 + Amount paid on the second item
= $25 + $13.50
= $38.50
In conclusion, the total amount the customer needs to pay for headphones and CD is $38.50
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Find the surface area (in square units) of the polyhedron. i need help!!
The surface area and volume of the polyhedron are mathematically given as
SA=160 Sqr UnitsV=105 cubic unitsThis is further explained below.
What is surface area?Generally, The surface area of a three-dimensional object is equal to the total of areas of all of its faces, also known as surfaces. A cuboid has six faces that are rectangular in shape.
Add together the areas of each of the cube's six sides to get the surface area of the cube. To get the surface area of the prism, we may additionally label its length (l), width (w), and height (h), and then use the formula surface area = length (l) times width (w) times height (h).
To refresh your memory, the surface area of an item is the entire area of the exterior surfaces of the three-dimensional object or the total sum of the area of the faces of the object.
In other words, the surface area of an object is its "face area." It is expressed in terms of square units as a measurement.
In conclusion, Generally, the Surface area is mathematically given as
SA= 9+35+35+33+36+12
SA=160 Sqr Units
Generally, the equation for Volume is mathematically given as
V=(11*9)+6
V=99+6
V=105 cubic units
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CQ is attached surface area
When Ms. Paul bought a new office phone, she borrowed $1,200 at a rate of 18% for 9 months. How much interest did she pay?
Assuming simple interest, the formula to calculate the interest Ms. Paul paid is:
[tex]Interest=Principal\times Rate\times Time[/tex]In the problem, here are the given information:
Principal (Money borrowed) = $1,200
Rate = 18% or 0.18 in decimal form
Time = 9 months or 0.75 year.
(Take note that the time in the formula is measured in years.)
Let's plug in the given information to the interest formula above.
[tex]Interest=1,200\times0.18\times0.75[/tex]Then, solve.
[tex]Interest=162[/tex]Therefore, Ms. Paul paid interest of $162.
Please
50 POINTS! BRAINLIEST!
The graphs of the conics intersect at two points.
x² + y² = 4
x^2/4 - y^2/9 =1
What are the coordinates of these points of intersection?
Enter your answer by filling in the boxes.
and
( , ) and ( , )
In linear equation, The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .
What are a definition and an example of a linear equation?
A linear equation with one variable is one that contains just one variable. It has the formula Ax + B = 0, with A and B being any two real numbers and x being an uncertain variable with only one possible value. One such linear equation in one variable is 9x + 78 = 18.x² + y² = 4 ..........1
x²/4 - y²/9 = 1
⇒ 9x² - 4y² = 36 ..........2
multiply equation (1) is multiply by 9
9 x² + 9y² = 36 ..............3
equation (3) - (2)
13y² = 0
y = 0
put y =0 in equation 1
x² + 0 = 4
x = ± 2
The co - ordinates of these points of intersection are ( -2,0) ( 2, 0) .
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If
F(x) = f(xf(xf(x))),
where
f(1) = 2, f(2) = 5, f '(1) = 4, f '(2) = 5,
and
f '(5) = 6,
find
F '(1).
F '(1) =
The composite function F(1) has a value of 2
How to evaluate the composite function?The definition of the composite function is given as
F(x) = f(xf(xf(x)))
Also, we have
f(1) = 2, f(2) = 5, f '(1) = 4, f '(2) = 5, and f '(5) = 6,
Substitute 1 for x in the equation F(x) = f(xf(xf(x)))
So, we have
F(1) = f(xf(xf(1)))
From the question
f(1) = 2
So, we have
F(1) = f(xf(2))
From the question
f(2) = 5
So, we have
F(1) = f(5)
As a general rule
If f '(2) = 5 then f(5) = 2
So, we have
F(1) = 2
Hence, the value of the function F(1) is 2
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