The equation (D) y - 6 = 4(x+8) represents the line passing through the points (-8, 6) and (-11, -6).
What is the point-slope form of a line?The point-slope form can be used to get the equation of a straight line that traverses a specified point and is inclined at a particular angle to the x-axis. A line exists if and only if each point on it fulfills the equation for the line. This suggests that a linear equation in two variables can represent a line.
The given points are
(x₁, y₁) = (-8, 6)
(x₂, y₂) = (-11, -6)
So, the slope is given by
m = (y₂- y₁)/ (x₂- x₁)
= (-6 -6)/ (-11 -(-8)
= -12/ -3
= 4
Put (x₁, y₁) = (-8, 6) in the equation (y - y₁) = m (x- x₁)
y - 6 = 4(x-(-8)
y - 6 = 4(x+8)
So, the correct option is (D).
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A farmer bought a number of pigs for $168. However, 7 of them died before he could sell the rest at a profit of 5 per pig. His total profit was $36. How many pigs did he originally buy?
Answer:
15$
Step-by-step explanation:
the population of the world in 2010 was 7 billion and the annual growth rate was estimated at 1.2 percent per year. assuming that the world population follows an exponential growth model, find the projected world population in 2044. round your answer to one decimal place.
With annual growth rate of 1.2% per year, the projected world population in 2044 is 10.5 billion
The formula for the exponential growth model is:
X(t) = Xo (1 + r)^t
Where:
X(t) = value of X at time t
Xo = initial value
t = time interval
r = growth rate
Parameters given:
Xo = 7 billion = 7 x 10⁹
t = 2044 - 2010 = 34
r = 1.2% = 0.012
Hence,
X(t) = 7 x 10⁹ (1 + 0.012)³⁴
X(t) = 10.5 x 10⁹ = 10.5 billion
Therefore,
The projected world population in 2044 = 10.5 billion
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a machine makes 36 trophies every hour. The machine makes trophies for 8 and a half hours each day, on 5 days of the week. The trophies are pack into boxes. Each box holds 8 trophies.
How many boxes are needed for all the trophies made each week?
Answer: 1530
Step-by-step explanation: First, you would want to calculate how many are made in one day. 36 trophies are made per hour, for 8 1/2 hours. 36 x 8.5(8 and a half) is 306, so in one day, 306 are made. Then, all you have left is to multiply it by 5, for five days, and that would be 1530. Hope This Helps.
Half of A's money plus one, fifth of B's makes #100. Two
Thirds of A's money plus two-fifth of B's makes # 150.
How much money has each?
The money A has is #150 and the money B has is #125.
According to the question,
We have the following information:
Half of A's money plus one-fifth of B's makes #100. Two-thirds of A's money plus two-fifth of B's makes # 150.
So, we will convert these verbal phrases into expression.
Now, let's take the amount of A to be #x and the amount of B to be #y.
x/2 + y/5 = 100
Using the least common factor of 2 and 5:
5x+2y = 1000
5x = 1000-2y ...(1)
2x/3 + 2y/5 = 150
Adding the fractions using the least common multiple of 3 and 5:
(10x+6y)/15 = 150
Using the cross multiplication method:
10x+6y = 2250
Now, putting the value of 5x from equation 1:
2(1000-2y)+6y = 2250
2000-4y+6y = 2250
2y = 2250-2000
2y = 250
y = 250/2
y = #125
Now, putting this value of y in equation 1:
5x = 1000-2y
5x = 1000-2*125
5x = 1000-250
5x = 750
x = 750/5
x = #150
Hence, the money A has is #150 and the money B has is #125.
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use your knowledge of angle relationship to solve for X in the diagram below. By your solution by name in the geometric relationship.
Answer:
Solution
Here ,
5x +7 = 9x-63 (Corresponding angle)
or, 5x-9x =-63-7
or, -4x =-70
or, X=17.5
Hence the value of X is 17.5 degree.
five and five-sixths minus three and three-fourths plus two and one-half equals blank line.
Answer:
4 7/12
Step-by-step explanation:
The U.S. Bureau of the Census
predicted that the population of
Florida would be about 17.4 million in
2010 and then would increase by
about 0.22 million per year until 2015.
Which of the following linear models
predicts the population, y, of Florida
(in millions) in terms of x, the number
of years since 2010.
A. y = 17.4x + 0.22
B. y = -0.22x + 17.4
C. y = 0.22x + 17.4
D. y = -17.4x + 0.22
The linear model that predicts the population, y, of Florida (in millions) in terms of x, the number of years since 2010 is y = 17.4+0.22x.
According to the question,
We have the following information:
The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2015.
Now, y is the population.
So, we will have the total population in 2010 and 0.22 times the number of years.
So, the expression will be:
y = 17.4+0.22x
Hence, the correct option is C.
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compare adding and subtracting to multiplying and dividing bases with different exponents.
Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.
Define exponents.A number written as a superscript over another number is known as an exponent. In other words, it means that the base has been elevated to a particular level of power. Other names for the exponent are index and power. mn indicates that m has been multiplied by itself n times if m is a positive number and n is its exponent.
Given,
Adding and subtracting to multiplying and dividing bases with different exponents.
Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.
The exponents and variables must match in order to add exponents. The exponents are left constant while the variable coefficients are added. The addition only includes terms with the same variables and powers. Exponents can be multiplied and divided according to this rule.
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What constant would be added to the expression x^2+8/3x in order to make it a perfect square
Answer:
Hence, the value of y = b^2 = (-3/2)^2 = 9/4 is your answer
Step-by-step explanation:
only if your answers are
A) 3/2
B) 9/4
C) 6
D) 9
WHAT DOES Y EQUAL PLS HELP ASAP
The standard form of quadratic function is f(x) = 1(x-2)2 - 6
A quadratic function is a two-degree function. A parabola is the graph of a quadratic function. A quadratic function has the general form f(x)=ax2+bx+c, where a, b, and c are real numbers and a0. A quadratic function has the standard form f(x)=a(xh)2+k. The vertex (h,k) has the coordinates h=-b2a,k=f(h)=f(b2a).
Given points (5,3) and (2,-6)
We know that the General form of a quadratic function is
f(x) = ax2+bx+c
Standard form = a(x-h)2 + k
Here point(x,y) = (5,3) and vertex (h,k) = (2,-6)
y = a(x-h)2 + k
3 = a(5-2)2 – 6
3 = a(3)2 – 6
3 + 6 =9a2
9= 9a2
a2 = 9/9
a2=1
a=1
Now substitute a value in standard form
f(x) = 1(x-2)2 – 6
Therefore the standard form of quadratic function is f(x) = 1(x-2)2 – 6
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Can you help me, please?
Answer: 19
Step-by-step explanation:
Find slope intercept form
Answer: y=x+4
Step-by-step explanation:
The formula for slope-intercept form is y=mx+b where
m is the slope and b is the y-intercept.
Formula for working out the slope: y2-y1/x2-x1
Put the values in the equation: 4-3/0-(-1). Answer is 1/1 which is 1.
y-intercept: put one of the x and y values from the graph into the equation y=mx+b. Here, I'm going to choose the point (0,4).
The equation is now 4=1(0) + b
Working out for equation:
4=0+b
4=b
The final equation is y=x+4.
You can also use the graph to help you find the y-intercept! First, look at the y-axis. Then the point that passes it is your y-intercept!(Remember it's the y value not the x)
Challenge In basketball, some baskets are worth two points. Others are worth three points. In one game, the ratio of three-point baskets to three-point tries for one team was 2:5. If the team scored 24 points from three-point baskets, how many three-point tries did the team have?
Answer:
20
Step-by-step explanation:
3-point shots made : 3-point shots attempted = 2 : 5
If the team made 24 points out of 3-point baskets, then since 24/3 = 8, it made 8 3-point baskets.
Proportion:
8 made is to 2 as x attempted is to 5
8/2 = x/5
2x = 40
x = 20
A line that includes the point (5, –10) has a slope of 0. What is its equation in slope -intercept form?
Answer:
0
Step-by-step explanation:
Slope = (y-y1)/(x-x1)
0
-4(5x - 3) + 12
equation answer pls
Answer:
72
Step-by-step explanation:
Determine the measure of each missing angle:
Angle f= 69
Angle g= 69
Angle h= ??
I found G and F but I’m stuck on H please help me!!
Answer:
Angle f = 69°Angle g = 69°Angle h = 125°Step-by-step explanation:
Angles f and g are congruent as opposite sides are congruent. Therefore:
g = f = (180° - 42°)/2 = 138°/2 = 69°Angles h, 76°, g and the right angle all together form 360°:
h + 76 + g + 90 = 360h + 166 + 69 = 360h + 235 = 360h = 360 - 235h = 125Solve: 9l5n - 8l - 3 < 15
Answer:
9l^5n-8l-3<15
Step-by-step explanation:
Here is a scatterplot showing the relationship between the number of turnovers and the number of points scored for players in a recent NBA season. The correlation for these data is r = 0.92.
Interpret the correlation
Yes.There is a strong , positive association,so an increase in turnovers causes an increase in points for NBA players..
Given that,
This scatterplot illustrates the correlation between a player's turnover rate and their points scored during a recent NBA season. 3000 2500 2000 Points 1500 and r= 0.92
r = 0.92 A strong positive (upward sloping) linear relationship
While a correlation of 0.10 would be a modest positive correlation, a correlation of 0.97 is a significant negative correlation.
Hence, Yes. Because there is a significant positive correlation, more turnovers result in more points for NBA players.
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Solve this system of 3 variables with elimination. Once you eliminate 1 variable to get down to only 2, you can use Desmos but show all work/steps first.
3x − 4y + z = 2
−9x + 12y − 3z = − 6
4x − 2y − z = -16
The value of the x, y, and z for the given system of equations are; x = -2/3, y = -1/2, and z = 1.
First, let us understand the equation:
An equation is an expression that shows the relationship between two or more numbers and variables.
We are given the system of equations;
3x − 4y + z = 2 ...........equation 1
−9x + 12y − 3z = − 6 ...........equation 2
4x − 2y − z = -16 ...........equation 3
Add equation 1 to equation 3, we will get;
(3x − 4y + z ) + (4x − 2y − z ) = 2 -16
7x - 6y = -14 ...........equation 4
Multiply equation 3 by 3 and subtract from equation 2, we will get;
3(4x − 2y − z) - (−9x + 12y − 3z ) = -48 + 6
12x - 6y - 3z + 9x - 12y + 3z = 42
21x - 18y = 42 ...........equation 5
Multiply equation 4 by 3 and add it to equation 4, we will get;
3(-3x + 3z) + (9x + 4z) = 5×3 - 2
-9x + 9z + 9x + 4z = 15 -2
13z = 13
z = 1
Put z = 1 in equation 5, we will get;
-3x + 3×1 = 5
-3x + 3 = 5
-3x = 5 - 3
x = -2/3
y = -1/2
Thus, the value of the x, y, and z for the given system of equations are; x = -2/3, y = -1/2, and z = 1.
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Reduce 4hours 20minutes by 12%
Step-by-step explanation:
by 12 % seconds
Express this equation:
Answer:
(14x +49)^2
Step-by-step explanation:
PLEASE GIVE BRAINLIEST THANK YOU!!!
Sophie and Addison work at a dry cleaners ironing shirts. Sophie can iron 20 shirts per hour, and Addison can iron 30 shirts per hour. Sophie and Addison worked a combined 11 hours and ironed 260 shirts. Determine the number of hours Sophie worked and the number of hours Addison worked.
The number of hours Sophie worked and the number of hours Addison worked are 7 and 4 hours respectively.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x and y be the number of hours for Sophie and Addison:
x + y = 11
20x + 30y = 260
After solving the above two linear equations by substitution:
x = 7 hours
y = 4 hours
Thus, the number of hours Sophie worked and the number of hours Addison worked are 7 and 4 hours respectively.
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2 ( X + 9 ) - 15 = -3
Answer:
x = -2
Step-by-step explanation:
2(x + 9) - 15 = -3 Distributive property
2(x) + 2(9) -15 = -3
2x +18 - 15 = -3 Combine like terms
3x + 3 = -3 Subtract 3 from both sides
3x = -6 Divide both sides by 3
x = -2
Sal has already finished startfraction 5 over 9 endfraction of the 45 math problems he was assigned. If each math problem took him three-fifths of a minute to finish and this pace continues, which expression can be used to determine the amount of time it will take him to finish his remaining homework? 45 times startfraction 5 over 9 endfraction times three-fifths 45 times startfraction 5 over 9 endfraction divided by three-fifths 45 times startfraction 4 over 9 endfraction times three-fifths 45 times startfraction 4 over 9 endfraction divided by three-fifths.
The correct expression to determine the amount of time is 45 times startfraction 4 over 9 endfraction times three-fifths.
Sal has finished = 5/9 of 45 maths problems
So, the remaining number of maths problems = 1 - 5/9
The remaining number of maths problem = (9 - 5)/9
The remaining number of maths problem = 4/9 of 45
Amount of time to solve 1 problem = 3/5 of a minute
Amount of time to solve 4/9 problems = 45×4/9 × 3/5 of a minute.
Hence, 45 times startfraction 4 over 9 endfraction times three-fifths is the correct expression to find the time.
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HELP ME PLS!!!!!!!!!
Answer:
It's a positive correlation.
Step-by-step explanation:
It's gradually going up, even if there's a few points that are a bit uncorrelated.
Graph the solution of the inequality 2x - (3-x) > x + 1 on the number line.
Ο Α.
-5 -4 -3 -2 -1 0 1
OB.T
0 с.
2
+
-5 -4 -3 -2 -1 0 1 2
F
OD. |▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
+ +
3
10Ø|||
-5 -4 -3 -2 -1 0 1 2 3
-5 -4 -3 -2 -1 0 1 2
+43
3
4 5
14
4 5
++
4 5
+
4 5
The solution of the inequality is x>2 and the graph is attached below.
What is inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. When two values are compared, an inequality shows whether one is higher, lower, or simply not equal to the other.
The given inequality is 2x - (3-x) > x + 1,
Now, solving the inequality by opening the bracket,
2x - (3-x) > x + 1
[tex]2x - 3 + x > x + 1[/tex]
3x - 3 > x + 1
Subtracting x from both sides and adding 3 on both sides,
2x > 4
x > 2
So, the graph is attached below and Option D is correct.
Therefore, after solving the given inequality, we get x > 2 and the graph is attached below.
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If an additional worker can produce an additional 20 units of output which can be sold for $4 per unit, what is the maximum wage that this perfectly competitive firm should pay to hire this worker?.
The maximum wage that this perfectly competitive firm should pay to hire this worker = $80
The options for this question
A) $80 minus the firm's profit markup
B) It depends on what the going wage rate is in the labor market.
C) $80
D) There is insufficient information to answer the question.
now, we need to find the maximum wage that this perfectly competitive firm should pay to hire this worker
given that
the additional worker can produce an additional 20 units of output and that can be sold for$4 per unit
maximum wage = additional units × sold per unit
= 20 × 4 = 80
the maximum wage = $80
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The table below shows the number of hours the Carrera family has been driving and the number of miles they’ve driven. Which of the following equations best represents this relationship?
*
Captionless Image
y = 84x
y = 56x
y = 1.5x
Not here
The equation that best represents this relationship given in the table is y = 56x.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have a table below that shows the number of hours the Carrera family has been driving and the number of miles they’ve driven.
We can find the slope of the line from the table as follows -
m = (168 - 84)/(3 - 1.5)
m = 56
Now, we can write -
y = 56x + c
84 = 56 x 1.5 + c
c = 0
So, the equation would be -
y = 56x
Therefore, the equation that best represents this relationship given in the table is y = 56x.
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Simplify your answer as much as possible please.
Answer:
3/5=w
Step-by-step explanation:
the 2 onthe numerator and the 2 on the denominator cancel each other out leaving w byitself.
Answer:
16/5
Step-by-step explanation:
10x3/5=10x w-2/2
Find the length of the third side. If necessary, write in simplest radical form.