Answers
The equation of the given linear function passing through two points is
y = 6 -2x.
What is equation of a linear function passing through given two points?Let (x₁, y₁) and (x₂, y₂) be two points on the given linear function whose equation in variables x and y is given by formula below.
(y - y₁) = {(y₂ -y₁)/(x₂-x₁)} (x -x₁)
Given that f is a linear function ,
f(-3) = 12
f(6) = -6
⇒(x₁, y₁) = ( -3,12)
(x₂, y₂) = ( 6,-6)
Thus the equation of the linear function is :
⇒ y - 12 = { ( -6-12)/(6-(-3))} ( x - (-3))
⇒ y - 12 = { -18/ 9} ( x +3)
⇒ y - 12 = -2 ( x+3)
⇒ y = 12 -2x - 6
⇒ y = 6 -2x
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Related Questions
An electrician leans an extension ladder against the outside wall of a
house so that it reaches an electric box 28 feet up. The ladder makes an
angle of 71° with the ground. Find the length of the ladder. Round your
answer to the nearest hundredth of a foot if necessary.
Answers
Answer:
30 feet
Step-by-step explanation:
i used a ruler, mm side. 1 mm = 1 foot
draw a horizontal line.
draw a vertical line 28mm high
use a protractor to find a line that connects to the base and top of vertical line.
measure said line
Answer:
Step-by-step explanation:
\text{sin }\color{purple}{71}=\frac{\color{green}{\text{opposite}}}{\color{#EB0000}{\text{hypotenuse}}}=\frac{\color{green}{28}}{\color{#EB0000}{x}}
sin 71=
hypotenuse
opposite
=
x
28
\text{sin }71=
sin 71=
\,\,\frac{28}{x}
x
28
\frac{\text{sin }71}{1}=
1
sin 71
=
\,\,\frac{28}{x}
x
28
x\text{ sin }71=
x sin 71=
\,\,28
28
Cross multiply.
\frac{x\text{ sin }71}{\text{ sin }71}=
sin 71
x sin 71
=
\,\,\frac{28}{\text{ sin }71}
sin 71
28
Divide both sides by sin 71
x=\frac{28}{\text{ sin }71}=29.613379...\approx29.61
x=
sin 71
28
=29.613379...≈29.61
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Find the time-and-a-half pay rate by multiplying the hourly wage, $22 by
by 1-1/2
When the hourly wage is $22, the time-and-a-half pay rate is $
(Simplify your answer.)
Answers
consequently, the time and a half rate will be 33 dollars per hour according to the query.
What is the logic behind time and a half pay rate and how tocalculate it?A higher rate of pay known as "time and a half" is normally only applied to hours that are over 40 in a workweek or that are worked extra.
Companies have different overtime pay practices, with time and a half as a typical rate.
Simply said, it means that for each hour performed within the time and a half window, the employee will receive payment in addition to their regular hourly rate of one half of that amount.
Time and a Half Rate = Hourly Rate * 1.5
According to the given question:
Time and a half rate =22$*1-1/2
=22$*1.5
=33$ per hour
Therefore, According to the question given the Time and a pay half rate will
be 33$ per hour.
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The quadratic equation [tex]( k - 1 )x^{2} + 2x + ( 2k - 3 ) = 0[/tex] , where k is R, has real distinct roots.
Find the range of possible values for k.
Answers
The possible values of k such that the quadratic equation has real distinct roots are 1 / 2 and 2.
What are the possible values of k associated to quadratic equation?
In this problem we find the case of a quadratic equation, of which the values of a variable k must be found such that the polynomial have real distinct roots. This can be done by using the discriminant of the quadratic formula, which is defined below:
For a · x² + b · x + c = 0, the discriminant is:
b² - 4 · a · c > 0
Then, if we know that a = k - 1, b = 2 and c = 2 · k - 3, then the possible values of k are:
2² - 4 · (k - 1) · (2 · k - 3) > 0
4 - (4 · k - 4) · (2 · k - 3) > 0
4 - (8 · k² - 8 · k - 12 · k + 12) > 0
8 · k² - 20 · k + 8 > 0
Whose form form is shown below:
8 · (k² - (20 / 8) · k + 1) = 0
8 · (k² - (5 / 2) · k + 1) = 0
8 · (k - 2) · (k - 1 / 2) = 0
The possible values of k are 1 / 2 and 2.
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A woman bought some large frames for $10 each and some small frames for $5 each at a closeout sale. If she bought 23 frames for $160, find how many of each type she bought
Answers
A woman purchased 12 little frames and 10 large frames.
We create an algebraic equation in this question.
Algebraic equation: what is it?An algebraic equation is a mathematical statement that makes two expressions equal to one another.
In most circumstances, an algebraic equation consists of a variable, coefficients, and constants.
According to question, the equation will be
Let x = large frame
y = small frame
x + y = 22 ---(1)
10x + 5y = 160 ---(2)
Now, solve the eq(1) and eq(2),
we get, x = 10
and, y = 12
If you want to cross-check you can do like that,
large frame price = $10
and, x = 10 (means 10 large frames women bought)
so the price will be = $ 10 * 10
= $100
Now, for the small frame price = $5
and, y = 12 (means 10 large frames women bought)
so the price will be = 12 * $5
= $60
Now total price is given = $160
and if we add both the prices of large and small frames = $100 + $60
we get, same as total price = $160
Therefore, we can say that woman bought 10 large frames and 12 small frames.
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A pile of sand has a weight of 65 kg.
Some of the sand is put into a small sack.
The rest of the sand is put into a large sack.
The sand in the large sack weighs 15 kg more than the sand in the small sack.
What is the weight of the sand in the small sack?
Answers
Answer:
25kg
Step-by-step explanation:
65=x+x+15
65-15=2x
50=2x
25=x
I NEED HELP!!!
50 POINTS!!!
Answers
slope is 3;
rise/run = y/x
6/2 = 3/1
Complete the two-way frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in a particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How many students are enrolled in either algebra or physics?
Awnsers:
33
38
2
5
Answers
1. The frequency table will be:
Physics - Not in algebra = 9
Not in physics (Algebra) = 24
Not in physics (Not in algebra) = 2
Total (Not in physics) = 26
Total = 11
2. The students are enrolled in either algebra or physics is B. 38.
How to calculate the value?It was found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both.
Not in physics for algebra = 24
Not in physics = 2
The Total for the value will be:
= 24 + 2= 26
The students enrolled in either will be:
= Algebra + Physics - Both
= 29 + 14 - 5
= 43 - 5
= 38
This illustrates the concept of addition and subtraction of numbers.
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Answer:
Its B. 38
Step-by-step explanation:
Hope this helps :)
PLEASE HELP
Lanny goes to the bank and puts $4000 in a savings account. He earns a simple interest of 2.5%. If he leaves the money in the account for five years, what is the total amount in the account after the five years?
Answers
The total amount in the account after interest will be about $4525.63 .
In the fields of finance and economics, interest is the additional sum that is paid by a borrower or deposit-taking financial institution to a lender or depositor at a certain rate (the amount borrowed).
The borrower may be obliged to pay fees to the lender or another entity, but interest is different.Interest also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve but not at a set rate or proportionally;It is a share of the reward or interest received by risk-taking businesspeople when income is generated that exceeds all expenses.Interest when the principal is $4000 , time is 5 years and rate is 2.5%.
We know that from compound interest:
Amount = principal (1 + rate)ⁿ
Therefore
Amount = 4000 (1 +0.025)⁵
Amount = $4525.6328...
Amount ≈ $4525.63
Therefore adding interest the sum would be worth $657.51
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I need the right answer so please be correct
Answers
Answer: 8
Step-by-step explanation:
found slope
Mr. Giordano's drove 4.5 miles in 5 minutes. Mr. Baras drove 6.3 miles in 8 minutes. Who drove faster? Explain using unit rates for both teachers.
Answers
If Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove faster because the speed of the Mr. Giordano greater than Mr. Baras
Total distance traveled by the Mr. Giordano = 4.5 miles
The time taken = 5 minutes
Speed = Distance / Time
Speed = 4.5/5
= 0.9 miles per minutes
Total distance traveled by the Mr. Baras = 6.3 miles
The time taken = 8 minutes
Speed = Distance / Time
Speed = 6.3/8
= 0.78 miles per minutes
Hence, if Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove faster because the speed of the Mr. Giordano greater than Mr. Baras
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Solve the question on the image attached. It is not the first option.
Answers
Answer:
Option 2
Step-by-step explanation:
Even though there is a hole at x=2, the graph still approaches 3 from both sides. (We only consider the behavior around the point, not the point itself)
Simplify 5^3 times 5^4
a: 5^12
b: 5^7
c: 5^9
d: 25^7
Answers
Answer:
b
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then
[tex]5^{3}[/tex] × [tex]5^{4}[/tex]
=[tex]5^{(3+4)}[/tex]
= [tex]5^{7}[/tex]
44+400 divided by (4+62)-24
Answers
Answer:
10.57
Step-by-step explanation:
44+400=444
(4+62)-24=
66-24=42
444/42=10.57
Help me please!! due at 8pm tonight 10/12/22
Answers
Answer:
y=3x+3
Step-by-step explanation:
Use rise/run
Answer:
y=-9x+5
Step-by-step explanation:
Students make 97.5 ounces of liquid soap for a craft fair. They put the soap in 6.5-ounce bottles and sell each bottle for $5.50$. How much do the students earn if they sell all the bottles of liquid soap? Explain.
Answers
The students will earn $82.5 if they sell all the bottles of liquid soap.
What is a unitary method?The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.
Given that,
Total amount of liquid soap prepared by the students for a craft fair =
97.5 ounces
Weight of each bottle in which students poured the soap = 6.5 ounces
Let us first calculate the number of bottles, each contains 6.5 ounces of soap from 97.5 ounces of soap.
So, Number of bottles = [tex]\frac{97.5}{6.5}[/tex] = 15
It means, 15 bottles are prepared which contains 6.5 ounces of soap from 97.5 ounces of soap.
The amount at which each bottle is sold = $5.50
The total amount earned by selling all the bottles of liquid soap = 15×$5.50 = $82.5
Hence, The students will earn $82.5 if they sell all the bottles of liquid soap.
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Please help! Please and thank you
Answers
Answer:
8 divided by 2
Step-by-step explanation:
URGENTTTY PLS PLS HELP !! GRAPH TOO PLS !!
Answers
Write the equations for the line parallel and the line perpendicular to the given
line passing through the given point.
10. y = 2x + 7; (0, 1)
Answers
The equation of line which is parallel and the line perpendicular to the given line passing through the given point as y = 2x + 7; (0, 1) is y = (-1/2)x + 1.
What is perpendicular line?
The definition of a perpendicular line in geometry is a pair of lines that meet or intersect at right angles (90°). The Latin word "perpendicularis," which denotes a plumb line, is where the word "perpendicular" first appeared.
[tex](y-1) = -\frac{1}{2} (x-0)[/tex]The equation of the line given in the question is:
y = 2x+7
On comparing with the equation y = mx + a
where, m is slope
we get slope of the line as m = 2.
Since the line we have to find is parallel to given line, they have equal slope.
Now, we know that the equation of perpendicular line is given by:
[tex](y-y_1) = -\frac{1}{m} (x-x_1)[/tex]
given points are (0,2) which is represented by (x1,y1)
On putting the value in the equation, we get
[tex](y - 1) = -\frac{1}{2}(x-0)[/tex]
After simplifying it we get the final equation as:
[tex]y = -\frac{1}{2} x + 1[/tex]
Above equation is the equation of line which is parallel and the line perpendicular to the given line passing through the given point as y = 2x + 7; (0, 1).
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Drag the tiles to the boxes to form correct pairs.Match the palrs of equivalent expressions.(-14 +30)–(1+36)46+13(5+26)+(26+)86-15(56–3)–(8+66)16–11(-10+6)+(76–5)– 15 - 26
Answers
Kindly check below.
1) Examining the expressions inside the tiles, we can tell that:
[tex]\begin{gathered} (-14+\frac{3}{2}b)-(1+\frac{8}{2}b)=-\frac{5}{2}b-15 \\ 4b+\frac{13}{2} \\ (5+2b)+(2b+\frac{3}{2})=4b+\frac{13}{2} \\ 8b-15 \\ (\frac{7}{2}b-3)-(8+6b)=\frac{7}{2}b-3-8-6b\rightarrow-11-\frac{5}{2}b \\ -\frac{5}{2}b-11 \\ (-10+b)+(7b-5)=8b-15 \\ -15-\frac{5}{2}b \end{gathered}[/tex]2) Based on this we can tell the following relationship of equivalence:
Write an inequality to represent the following. Five less than twice a number is less than 14.
Answers
Answer:
2x-5< 14 is the answer
Step-by-step explanation:
Answer:
2x-5<14
I hope this helps!
Describe the translation from AB to A’B’
Answers
The translation from AB to A’B’ is (x, y) → (x + 9, y + 2).
What is Translation in Math?The translation is a type of transformation in mathematics. When a shape is transformed, the original shape is referred to as the preimage, and the translated shape is referred to as the image.In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to have the same size as the original shape, and hence the shapes are congruent. They were simply relocated in one or more directions.Given:
The coordinates of A(preimage) are (-5,1).
The coordinates of A'(image) are (4,3).
From the coordinates of the translated image, A'B' we can determine the transformations.
The translation applied to the point (-5,1) are (x, y) → (x + 9, y + 2).
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Mrs. Scott rented a jeep. The rental charge is a flat fee of
$115 plus $12.50 per hour. Her bill is $152.50, not
including tax. Write and solve an equation that could be
used to find the number of hours she rented the jeep
Answers
Step by step
Using y intercept form
y = mx + b
Flat fee of $115 is y intercept or “b”
The $12.50 per hour is the rate or “m”
$152.50 is the total
So your equation is
$152.50 = $12.50x + $115
To solve subtract $115 from both sides to isolate x
$152.50 - $115 = $12.50x + $115 -$115
$152.50 = $12.50x
Divide both sides by $12.50 to solve for x
x = 12.2 hours
3. Toby randomly interviewed 70 patrons at a country music concert to determine their favorite type of music. Based on the results of his survey, he made the following claim:
Two out of three concert-goers prefer country music.
Which of the following statements best describes why this is not a valid claim?
O Only people on the floor level were surveyed.
Not enough patrons at the concert were surveyed.
The concert-goers were not randomly surveyed.
Toby only surveyed patrons at a country music concert who are probably biased toward country music.
Al changes se
Answers
Answer: Two out of three concert-goers prefer country music.
Step-by-step explanation:
Toby is interviewing country music concert participants, and therefore isn't getting a diverse spread of interviewees and isn't getting accurate data.
How many positive integer pairs (x,y) satisfy 4x+12y=640?
Answers
The number of positive pairs that satisfy the given linear function is given by: 161.
When a function is positive and when it is negative?We have to look at the graph of the function relative to the x-axis, more specifically if the function is above or below the x-axis, as follows:
A function is positive when it is above the x-axis.A function is negative when it is below the x-axis.In the context of this problem, the function is defined as follows:
4x + 12y = 640.
Which is a linear function, as both x and y have exponents of 1. The ordered pairs on the function are the values above the line. With integer numbers, that is, numbers that have no decimal parts, from the graph of the function given at the end of the answer, the values of x for which the function is positive is given by:
0 ≤ x ≤ 160.
Containing 161 values of x. Since this represents a function, each of the 161 values of x is associated to a value of y, meaning that there are 161 positive integer pairs (x,y) that satisfy the equation 4x + 12y = 640.
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what are the steps of simplifying the fraction 1244/2000 to its lowest term?
Answers
Explanation: Find the GCD (or HCF) of numerator and denominator
GCD of 1244 and 2000 is 4
Divide both the numerator and denominator by the GCD:
1244 ÷ 4
2000 ÷ 4
Reduced fraction:
311/500
Therefore, 1244/2000 simplified to lowest terms is 311/500.
Write an
equation of the line passing through point P(-1,-4) that is parallel to
y = -6x + 8.
Answers
y = -6x -25 is equation of slope intercept .
What exactly does slope intercept mean?
A method of expressing a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line is drawn the y-axis is known as the y-intercept, and the slope refers to how steep the line is.The equation is y = -6x + 8
compare with equation y=mx+b
slope m = -6
Use the point-slope method
y = -6x + 8
point P(-1,-4) point given (x1,y1)
y-y1=m(x-x1) point-slope form
y - ( -1 ) = -6 ( x - (-4))
y + 1 = -6 ( x + 4 )
y + 1 = -6x - 24
y = -6x -25
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what does it mean translate the figure 5 units up
Answers
By definition. a Translation is a transformation in which a figure is moved a fixed distance in a fixed direction.
The Image is the figure obtained after the transformation and the Pre-Image is the original figure.
In this case, you know that the figure shown in the picture must be translated 5 units up. Therefore, the rule for this transformation is:
[tex](x,y)\rightarrow(x,y+5)[/tex]You can identify that the marked point on the Pre-Image has the following coordinates:
[tex]\mleft(-4,-3\mright)[/tex]Therefore, applying the rule for this transformation, you get that the coordinates of the marked point in the final figure, are:
[tex]\mleft(-4,-3\mright)\rightarrow\mleft(-4,-3+5\mright)\rightarrow(-4,2)[/tex]The answer is:
Coordinates of the marked point in the original figure:
[tex](-4,-3)[/tex]Coordinates of the marked point in the final figure:
[tex]\mleft(-4,2\mright)[/tex]If the water level rises 12 centimeters every 7 minutes and you record the data point of (21,y), what is the value of y? Use slope to justify your answer. please help deadlines at 1200 am sunday
Answers
The value of y-coordinate from the given information is 36.
Given that, the water level rises 12 centimeters every 7 minutes and you record the data point of (21, y).
What is slope of a 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.
According to the question the water rises 12 cm every 7 minutes. Taking x to represent the time in minutes and y to represent the rise in cm then, find the rise y in time x as;
7 minutes = 12 cm
1 minute
(1×12)/7 = 12/7
Hence in 1 minute, the rise is 12/7 cm
Thus in 11 minutes, the rise will be ;
21 × 12/7 = 3 × 12 = 36 cm
So, (x, y) will be (21, 36)
Therefore, the value of y-coordinate from the given information is 36.
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what is the total weight capacity of a bus that can carry 54 passengers with each weighing 50kg
Answers
Answer:
2700 kg
Step-by-step explanation:
54 × 50 kg = 2700 kg
Several years ago, Belle invested in some gold. Gold is currently valued at $2,622 per ounce, which is 90% more than Belle originally paid for it. What was the purchase price of the gold?
Answers
Answer:
262.20
Step-by-step explanation: she originally payed for 10%=.10
2,622x.10=262.2