Answer: y = 4x + 7
Step-by-step explanation:
It's a line, so the formula is y = mx + b.
(x₁, y₁) = (-1, 3)(x₂, y₂) = (-2, -1)Slope(m): [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}} =\frac{-1-3}{-2-(-1)} =\frac{-4}{-1} =4[/tex]
Y-intercept(b):
[tex]y=4x+b\\3=4(-1)+b\\3=-4+b\\b=3+4=7\\[/tex]
Therefore, y = mx + b = 4x + 7.
3(5a+4b)-3a+b I need help with this problem. I just am really confused
Answer:
12a + 13b
Step-by-step explanation:
3(5a + 4b) - 3a + b
multiply 3 by 5a and 4b
15a + 12b - 3a + b
Now add the a terms together and b terms together
15a - 3a + 12b + b
12a + 13b
Answer:
12a + 13b
Step-by-step explanation:
3(5a+4b)-3a+b
To simplify the expression, we need to distribute the 3 to all terms inside the parentheses
3*5a+3*4b-3a+b
15a+12b-3a+b
Combine like terms
12a + 13b
The Watkins family is trying to decide which kind of in-ground pool to install. They are determining whether to put in a saltwater pool or a basic chlorine pool. The graphs below model the average annual cost of owning each type of pool after t years.
If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do you know?
The chlorine pool is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
The saltwater pool is more cost effective because the y-value at 10 years is less on graph A than it is on graph B.
They would be equally cost effective because the vertical asymptotes for each graph are the same.
They would be equally cost effective because the horizontal asymptotes for each graph are the same.
Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
If the family plans to move to their retirement home in 10 years, We need to find which pool would be more cost effective to install.
As in the given graph, the x-axis denotes the year while the y-axis denotes the cost of maintaining the pool in that year.
When we compare the two of the given graph we will find the cost of maintaining a chlorine pool is less as compared to a salt water pool at x=10, therefore, after 10 years.
Hence, the Watkins family should install a chlorine pool because it is more cost effective because the y-value at 10 years is less on graph B than it is on graph A.
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Answer:
a
Step-by-step explanation:edge
1 3/5+(-2 7/10)= what is this
Answer:
-1.1
Step-by-step explanation:
:)
If 4x is one factor of 4x^2 - 12x, what is the other factor?
Answer:
(x - 3)
Step-by-step explanation:
4x² - 12x ← factor out 4x from each term
= 4x(x - 3)
the factors are 4x and (x - 3)
How many solutions are there to the system of equations shown?
Answer:
There are two solutions. The parabola and the line intersect at two different points.
Answer:
Two
Step-by-step explanation:
there are two slope lines, so you need two equations for each lines.
Using the table, give the percentage associated with each unit of standard deviation in the standard normal curve to the nearest hundredth.
Standard Deviation Percentage Area
-2 to -1 ____________%
0 to +1 ____________ %
0 to +2 _____________%
+1 to +3 _____________%
-1 to +2 _____________%
The corresponding standard deviation percentage area for -2 to -1, 0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85%
How to find the percentage associated with standard deviation?To find the Standard Deviation Percentage Area, you have to consider the lower and upper points:
-2 to -1
The gap between -2 and -1 is 1 step, you will subtract -1 from -2:
-2 to -1 => 0.4772 - 0.3413 = 0.1359 = 13.59%
Note: the values for -2 and +2 are the same. The same also applies to -1 and +1 and others
0 to +1
Check the value under 1. That is 0.3413 = 34.13%
0 to +2
Check the value under 2. That is 0.4772 = 47.72%
+1 to +3
The gap between +1 and +3 is 2 steps, you will subtract 1 from 3:
+1 to +3 => 0.4987-0.3413 = 0.1574 = 15.74%
-1 to +2
-1 to +2 is the same as moving -1 to 0 and then moving from 0 to +2, you will add the values for -1 and +2:
-1 to +2 => 0.3413 + 0.4772 = 0.8185 = 81.85%
Therefore, the Standard Deviation Percentage Area for -2 to -1, 0 to +1, 0 to +2, +1 to +3 and -1 to +2 are 13.59%, 34.13%, 47.72%, 15.74% and 81.85% respectively
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How many pounds of chamomile tea that cost $9 per pound must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80?
The number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80 from the algebraic equation is; 12 pounds
How to solve algebraic equations?Let x represent the number of pounds of Chamomile tea needed.
We are told to find the number of pounds of chamomile tea that cost $9 per pound that must be mixed with 8 pounds of orange tea that cost $6 per pound to make a mixture that costs $7.80.
Therefore,
9x + 6(8) = 7.8(8 + x)
9x + 48 = 62.4 + 7.8x
9x - 7.8x = 62.4 - 48
1.2x = 14.4
x = 14.4/1.2
x = 12
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examples of a unit rate
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
A recording studio charges musicians an initial fee of $ 100 to record and album. Studio time also coasts an additional $75 per hour
Write a slope intercept form equitation to model this situation
The linear model that represents the total cost of recording is f(x) = 75x + 50.
The initial fee is $50 for recording an album.
There is an additional cost per hour i.e. $75.
number of hours = x
Now based on the above information, the linear model should be f(x)=75x+50
Here 50 represent the initial fee i.e. equivalent to y-intercept
And, 75 represent the slope
Therefore we can conclude that the linear model that represents the total cost of recording is f(x) = 75x + 50.
what is the answer to 3 2/13 + 7/8
Answer:
the exact form is 419/104
decimal for:4.02884615...
mixed number form: 4 3/104
Step-by-step explanation:
calculator
14. What is the y-intercept on the equation y = 3x - 6*
Answer:
-6 is the y-intercept, as in the point that crosses the y axis
How many natural numbers less than 200 are divisible by 4 but not divisible by 12.
There are 33 numbers that are less than 200 and divisible 4 but not divisible 12. this can be solved with the help of simplification.
What is simplification?
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Main body:
Given that,
To determine how many natural numbers less than 200 are divisible by 4, but not divisible by 12.
Here,
Let the largest number divisible by 4 less than 200 is 198
The total numbers divisible by 4 and less than 200 is,
= 198 / 4 = 49
Similarly
The total number divisible by 12 and less than 200 is,
= 192/ 12 = 16
So the numbers that are less than 200 but divisible 4 not by 12 is,
= 49 - 16
= 33
Hence, there are 33 numbers that are less than 200 and divisible 4 but not divisible 12.
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w+5r use s=2 and b=3
Answer:
Assuming w=2 and r=3, we plug in these values
2+5*3 = 2+15 = 17
Step-by-step explanation:
Help!! Question Solve. 2 1/3−1/2x=−2/3 Enter your answer in the box. x =
Answer:
x = 6
Step-by-step explanation:
2 [tex]\frac{1}{3}[/tex] - [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] ( subtract 2 [tex]\frac{1}{3}[/tex] from both sides )
- [tex]\frac{1}{2}[/tex] x = - [tex]\frac{2}{3}[/tex] - 2 [tex]\frac{1}{3}[/tex] = - 3 ( multiply both sides by - 2 to clear the fraction )
x = - 3 × - 2 = 6
x = 6
the weight of football players is normally distributed with a mean of 210 pounds and a standard deviation of 10 pounds. the probability of a player weighing less than 220 pounds is . a. 0.1587 b. .5000 c. 0.3413 d. 0.8413
Write an equation of the line that passes through (4,-1) and is parallel to the line y = 3x +7
An equation of the parallel line is
Answer:
[tex]y=3x-13[/tex]
Step-by-step explanation:
Parallel lines have the same slope. So, the equation is:
[tex]y+1=3(x-4) \\ \\ y+1=3x-12 \\ \\ y=3x-13[/tex]
Choose the correct numbers from the
box below to complete the subtraction
sentence that follows.
The correct numbers from the box below are 5/6 - 1/3 = 1/2.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A table with five different fractions.
Now, 5/6 - 1/3 we will check and the result must fall in the fractions given in the table.
5/6 - 1/3.
= (5 - 2)/6.
= 3/6.
= 1/2.
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Graph the equation y = 2x + 2 Iready
Answer:
picture it to pixilated
Step-by-step explanation:
The x-intercept and y-intercept of the equation will be (-1, 0) and (0, 2). The graph is given below.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
The linear equation is given below.
y = 2x + 2
Convert the equation into intercept form, then we have
y = 2x + 2
y - 2x = 2
y / 2 - x / 1 = 1
The x-capture and y-block of the situation will be (- 1, 0) and (0, 2). The chart is given beneath.
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Hey! I don’t understand this proof. Can anyone help me thank you!
Proved that the length of AB ≅ the length of CD
The conditions are given that
The line BC and the line AD are parallel lines
The parallel lines are two coplanar straight lines are at equal distance from each other and never intersect each other
Similarly
The measure of angle BAD is equal to the measure of angle DCB
If angle BAD = angle DCB, then we can say that the given shape is a parallelogram
In the parallelogram the opposite sides will be equal
Then the length of the length of AB equal to the length of CD
Hence, proved that the length of AB ≅ the length of CD
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Emma is going to invest $720 and leave it in an account for 18 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Emma to end up with $2,440?
The interest rate that would be required for Emma to end up with $2440 in her bank account is 6.8%
Given,
P = $720
A = $2440
t = 18 years.
r = n[(A/P)^1/nt - 1]
r = 12 × [(2440/720)¹/⁽¹²⁾¹⁸ - 1]
r = 0.06799764
Then convert r to R as a percentage.
R = r × 100
R = 0.06799764 × 100
R = 6.8%/year
Hence the rate of interest is 6.8%
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The value of "y" varies directly with "x" and
y = -8 when x = 20.
Find "y" if x = -4.
Now use the value you found for k, in y=kx to
solve for y when x is -4.
k=-²/
y =
Reduce to simplest form.
Answer:
y = 8/5
Step-by-step explanation:
Formula we use,
→ y = kx
Then the value of y will be,
→ y = kx
→ y = (-2/5) × (-4)
→ y = (-2 × -4)/5
→ [ y = 8/5 ]
Hence, the value of y is 8/5.
Hannah borrows $999 from her parents to buy a phone. She will repay $225 to start, and then another $43 per week.
A. Write an equation that can be used to determine w, the number of weeks it will take for Hannah to repay the entire amount.
B. What number of weeks will it take Hannah to repay the entire amount?
A. The equation that can be used to determine the number of weeks is $999=225+42w
B. The number of weeks it will take Hannah to repay is 18weeks
What is linear equation?An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 3 = 0 has only one solution as x = -2.
the total amount of money Hannah repaid is $225+$43×w, where w is the number of weeks to repay $43.
therefore $999= $225+$43w
$43w=$ (999+225)
$43w= $1224
divide both side by $43
w= $1224/$43
w= 18 weeks
therefore it will take Hannah 18weeks to repay the money.
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2 -3 - > › Solve for x 5(x + 2) = 6x +1 X =
Answer:
the is 20 because you need to multiple
Please help ASAPPPP!!!!!!!!!!!!! It’s due in 3 mins
The ball hits the ground after x = 6 seconds.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equation is h(x) = -2x² + 8x + 24.
(a) when the ball is thrown, the time is t = 0 sec.
Therefore, the height of the ball when it is thrown is,
h(0) = -2(0)² +8(0) +24
h(0) = 24
(b) The derivative of the function is,
h'(x) = -4x + 8
Substitute h'(x) = 0 into the above equation,
0 = -4x +8
4x = 8
x = 2
The second derivative of the function is,
h''(x) = -4
Since the second derivative of the function is negative, the function is maximum at x = 2.
(c) The maximum height of the ball is,
h(2) = -2(2)² + 8(2) +24
h(2) = -8 +16 +24
h(2) = 32
(d) The ball hits the ground when h(x)= 0, therefore,
0 = -2x² +8x +24
0 = -2x² +12x - 4x + 24
0 = -2x(x - 6) - 4(x - 6)
0 = (x - 6)(-2x - 4)
(x - 6) = 0 or (-2x-4) = 0
x = 6 or x = -2
Since time cannot be negative, it follows, x = 6 seconds.
Hence, the ball hits the ground after x = 6 seconds.
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PLEASE HELP FAST
A cylindrical jar has a radius of 6 inches and a height of 10inches. The jar is filled with marbles that have a volume of 20 in3. Use 3.14 for pi. Show work. Complete sentences.
a. What is the volume of the jar?
b. How many whole marbles can fit in the jar? *Each marble has the volume of 20 cubic inches
The volume of the cylindrical jar be 1130.97 in³.
Also, 56 whole marbles can fit in the jar.
Given, a cylindrical jar has a radius of 6 inches and a height of 10 inches.
The jar is filled with marbles that have a volume of 20 in³.
(a) The volume of the cylindrical jar be,
Volume = πr²h
Volume = (3.14)(6)²(10)
Volume = 1130.97 in³
(b) Now, if each marble has the volume of 20 in³
then, the number of marbles that can be fit in the jar be,
The number of marbles = 1130.97/20
The number of marbles = 56.
Hence, the volume of the cylindrical jar be 1130.97 in³.
Also, 56 whole marbles can fit in the jar.
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Aldo purchased a prepaid phone card for $45.75. Calls cost 7 cents a minute using this card. The credit, C (in dollars), left on the card after it is used for x
minutes of calls is given by the following function.
C(x)=45.75-0.07x
How much credit is left on the card after Aldo uses it for 20 minutes of calls?
Answer: 44.35
Step-by-step explanation:
0.07x20=1.4
45.75-1.4
What is the answer to this question
Answer:
Angle 6 is 78 degrees Angle 7 is 102 degrees
Step-by-step explanation:
Since both lines are parallel, you can assume that Angle 6 plus Angle 7 are a linear pair. Angle 1 corresponds to Angle 5 by the corresponding parts. Angle 5 is congruent to Angle 7 by Vertical angles so therefore Angle 7 is 102. Since Angle 6 + Angle 7 equal 180 degrees, you can put the equation like this,
[tex]Angle 6 + 102 = 108. Angle 6 = 78.[/tex]
Therefore you get your two answers
-2(9x-1)=-(x-9) - 7x
Answer:
Step-by-step explanation: 34
Answer:
x = [tex]\frac{11}{26}[/tex]
Step-by-step explanation
Expand 2(9x - 1): 18x - 2
Expand - ( x - 9 - 7x: -8 + 9
Add 2 to both sides 18x - 2 +2 = -8x + 9 + 2
Simplify
18x = -8x + 11
Add 8x to both sides
18x + 8x = -8x + 11 + 8x
Simplify
26x = 11
Divide both sides by 26
[tex]\frac{26x}{26}[/tex] = [tex]\frac{11}{26}[/tex]
Simplify
x = [tex]\frac{11}{26}[/tex]
Help my with this problem please 50 points
Answer:
[tex]-4x^2-4x+20[/tex]
Step-by-step explanation:
Since we're subtracting the entire quadratic, we can place the second equation in parentheses and distribute the subtraction sign.
[tex]2x^2-9x+8-(6x^2-5x-12)\\2x^2-9x+8-6x^2+5x+12\\2x^2-6x^2-9x+5x+8+12\\-4x^2-4x+20[/tex]
Answer:
[tex]-4x^2-4x+20[/tex]
Step-by-step explanation:
To find the difference of the two quadratic expressions, subtract the second expression from the first expression:
[tex]\implies (2x^2-9x+8)-(6x^2-5x-12)[/tex]
Remove the parentheses and apply the distributive law
[tex]-\left(a-b\right)=-a+b[/tex]
[tex]\implies 2x^2-9x+8-6x^2+5x+12[/tex]
Collect like terms:
[tex]\implies 2x^2-6x^2+5x-9x+8+12[/tex]
Combine like terms:
[tex]\implies -4x^2-4x+20[/tex]
Therefore, the difference of the two quadratic expressions is:
[tex]\large \boxed{-4x^2-4x+20}[/tex]
Write an equation of the line passing through the point A (8, 2) that is perpendicular to the line y = 4x - 7.
The equation of line perpendicular to line y = 4x – 7 and passing through point A (8, 2) is y + (1/4)x = 4.
What does the point slope form of a line equation look like?A line's point slope form equation is y - y₁ = m(x - x₁). Consequently, y - 0 = m(x = 0), or y = mx, is the equation of a line passing through the origin with a slope of m.How do you figure out the slope of a line that is perpendicular to another line?The slope of a line that is perpendicular to another line is equal to the negative reciprocal of that line's slope.
Given: A line is perpendicular to line y = 4x – 7 and passes through point A (8, 2).
We know that,
Slope of line perpendicular to another line is negative reciprocal of its slope.
So, m(slope) = -1/4
Equation of line is given as follows:
y - y₁ = m(x - x₁)
y - 2 = -1/4(x - 8)
y + (1/4)x = 4
Therefore, the equation of line perpendicular to line y = 4x – 7 and passing through point A (8, 2) is y + (1/4)x = 4.
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