-Determine the equation of the line that passes through the point (9, -42)and is parallel to the line y = -5x + 1.Enter your answer in slope-intercept form.Pls see picture
Answers
Two parallel lines have the same slope. Given the equation of one of the lines, you can determine the slope of the other line:
[tex]y=-5x+1[/tex]The slope of the line is the coefficient of the x-term, in this case, that coefficient is -5. Then the slope of both parallel lines is m= -5.
The line you have to find must cross through the point (9,-42). Using the point-slope form you can determine the equation of the parallel line:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of one point of the line:
[tex]\begin{gathered} y-(-42)=-5(x-9) \\ y+42=-5(x-9) \end{gathered}[/tex]To write the equation in slope-intercept form, the first step is to distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y+42=(-5)\cdot x+(-5)\cdot(-9) \\ y+42=-5x+45 \end{gathered}[/tex]Subtract 42 to both sides of the expression to pass the term to the right side of the equal sign:
[tex]\begin{gathered} y+42-42=-5x+45-42 \\ y=-5x+3 \end{gathered}[/tex]The equation of the line is y= -5x + 3
Related Questions
12:36=21 :
Fill in the blank I don't understand it ?
Answers
Answer:
63
Step-by-step explanation:
12:36
36/12=3
21(3)=63
Write a quadratic equation to match the relationship given in the table
Answers
In order to find the quadratic equation, let's use the standard form of a quadratic equation:
[tex]y=ax^2+bx+c[/tex]Using the point (0, 2) from the table, we have:
[tex]\begin{gathered} 2=a\cdot0^2+b\cdot0+c \\ c=2 \end{gathered}[/tex]Now, using the points (-1, -2) and (1, 22):
[tex]\begin{gathered} -2=a(-1)^2+b(-1)+2 \\ a-b=-4 \\ 22=a(1)^2+b(1)+2 \\ a+b=20 \end{gathered}[/tex]Adding both equations, we can solve for a:
[tex]\begin{gathered} a-b+(a+b)=-4+(20) \\ 2a=16 \\ a=8 \\ a+b=20 \\ 8+b=20 \\ b=12 \end{gathered}[/tex]Therefore the equation is y = 8x² + 12x + 2
What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (−6, 9)?
y equals negative one-third times x plus 3
y equals negative one-third times x plus 7
y = 3x − 33
y = 3x + 27
Answers
Answer:
y=-1/3x+7
Step-by-step explanation:
put it in y-y1=m(x-x1)
perpendicular means the slope is opposite
slope is -1/3
y-9=-1/3 (x+6)
y-9=-1/3x -2
+9 +9
y=-1/3x +7
slope of p=
slope of q=
slope of r=
slope of m=
*PLEASE HELP*
Answers
P= - 5/2
Q = - 5/2
R= 5/2
M= 2/5
Step by step
Slope can be found using the formula
y2 - y1 over x2 - x1
P = (-4,8) and (4, -12)
-12 -8 over 4 - -4
-20/8
= -5/2
Q= (6.8, 13) and (12, 0)
0 - 13 over 12 - 6.8
-13/5.2
= - 5/2
R= ( .4, -3) and (6.8, 13)
13 - -3 over 6.8 - .4
16/6.4
= 5/2
M= (-15.5, 0) and (0, 6.2)
6.2 - 0 over 0 - -15.5
6.2 / 15.5
= 2/5
I just want the answer :)
Answers
Answers ↓
angle 1 → 90°
angle 2→ 44°
angle 3 → 90°
angle 4 → 46°
I hope this helps u
(1 - 3k) - 4(2 + 2.5k)
HELP!! Quick answer pls
Answers
The answer is -13k - 7
Answer:
1 - 3k - 8 + 10k
1 - 3k + 10k - 8
1 - 13k - 8
1 - 8 - 13k
-7 - 13k or -7 + (-13k)
Set up a system of equations and solve using substitution or elimination. You must show all work You have 258 coins in a jar. They are a combination of dimes and quarters. If the money in the jar equals $36.75, how many of each type of coin is there?
Answers
Answer:
185 dimes and 73 quarters
Step-by-step explanation:
q + d = 258
25(q) + 10(d) = 3675
y=2 and x=-10 what is the value of k the constant
Answers
Answer:
- 164/4+50y/3+ify=0
Step-by-step explanation:
hope it helps
Mark says, '81 is a square number. Therefore, 810 is a square number.'
Is Mark correct? Explain your answer.
Answers
Answer:
mark is right
Step-by-step explanation:
3+5x5 =13
Answer:
Mark is not correct , becouse squared number Is number which can be after "=" when you times same numbers for example: 4*4=16 so 16 is squared number,is this make sense?
the question is in the image
Answers
For the given opens down parabola, ordered pair of the vertex (h, k) = (1, -4) , the maximum value of the parabola is y = -4.
As given,
Graph of parabola shows it open down parabola.
Vertex is the highest point on the graph of parabola.
it is known as the maximum value.
Let (h, k) be the vertex of the given parabola.
From the graph value of the vertex is equal to :
(h ,k)=(1, -4)
h represents the x-coordinate.
k represents the y-coordinate.
y-coordinate represents the maximum value of the parabola.
y =-4 is the maximum value.
Therefore, for the given opens down parabola, ordered pair of the vertex (h, k) = (1, -4) , the maximum value of the parabola is y = -4.
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Use these two representations of reflection at the right to sort each each statement below as the or false
Answers
The statements that are true are:
Statement A: Figure A was reflected from the third quadrant to the second quadrant
Statement B: Triangle DEF was reflected over the x-axis
The False statements are:
Statement C: The image of DEF is in quadrant 3
Statement D: The reflection of A can be represented by (-x, y)
Statement E: The reflection of DEF can be represented by (-x, y)
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution.
Answers
The standard normal distribution becomes smaller.
What is standard deviation?
Your dataset's average level of variability is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.Think about the following data: 2, 1, 3, 2, 4. The average and the sum of squares representing the observations' variances from the mean will be 2.4 and 5.2, respectively. This means that (5.2/5) = 1.01 will be the standard deviation.As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution
becomes smaller.
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A 25-foot ladder is leaning against the side of a house so that the bottom of the ladder is 15 feet from the base of the house. Will the ladder reach a window that is 21.5 feet above the ground?
Answers
The ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
From the data:
The right angle triangle can be drawn:
From the diagram:
Applying Pythagoras' theorem:
BC² = AB² + AC²
25² = 15² + AC²
After solving
AC = 20 feet
AC < 21.5 feet
Thus, the ladder will not reach a window that is 21.5 feet above the ground if the length of the ladder is 25 feet.
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Answer:
No, because the ladder will only reach 20 feet high
Step-by-step explanation:
I go it right on my quiz :]
a dietician is planning a snack package of fruit and nuts. each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, 2 units of fat and will contain 20 calories each. each ounce of nuts will supply 3 units of protein, 2 units of carbohydrates and 4 units of fat, and will contain 50 calories. Every package must provide at least 9 units of protein, at least 18 carbohydrates, and no more than 22 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least amount of calories. What is the least number of calories?
ANSWER ASAP PLEASE
Answers
The number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least amount of calories is
3 ounces of nut5 ounces of fruitThe least number of calorie is 250 calories
How to find the number of ounces of fruit and number of ounces of nuts with the least amount of calories.given data
1. each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, 2 units of fat and will contain 20 calories
2. each ounce of nuts will supply 3 units of protein, 2 units of carbohydrates and 4 units of fat, and will contain 50 calories
3. Every package must provide at least 9 units of protein, at least 18 carbohydrates, and no more than 22 units of fat
To get at least 9 units of protein, we take at least 3 ounces of nut
3 ounces of nut will give 3 times each unit, and they are as follows
3 * 3 = 9 units of protein2 * 3 = 6 units of carbohydrates4 * 3 = 12 units of fat50 * 3 = 150 caloriesAnother restriction is no more than 22 units of fat and we have 12 already remaining 10 units of fat
fruits has lesser calories hence we use it to get the required fats
10 units of fat ÷ 2 units of fat in fruit = 5
5 ounces of fruit will give 5 times each unit, and they are as follows
5 * 3 = 15 units of carbohydrates5 * 2 = 10 units of fat 5 * 20 = 100 caloriesCombining 3 ounces of nut and 5 ounces of fruit will give
9 + 0= 9 units of protein6 + 15 = 21 units of carbohydrates12 + 10 = 22 units of fat150 + 100 = 250 caloriesAbove maintains the requirements stated in the question with the minimal calorie
the required calorie is 250
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verify that real number can be a complex number but a complex number can not be a real number. Also verify that the lengths of the complex number and its conjugate are equal but the converse is not necessarily true.
Answers
real number can be a complex number but a complex number can not be a real number, verified.
the lengths of the complex number and its conjugate are equal but the converse is not necessarily true., verified.
Not all complex numbers are real numbers, despite the fact that every complex number is a real number.
In fact, determining whether the complex number z = a + bi is real is one of the complex conjugate's most useful applications. If and only if z = a + 0i, a complex number is real. In other words, a complex number is real if it contains an imaginary part.
Mathematical proof:
Let z = a+bi, where a and b = real numbers.
Let z* =complex conjugate of z.
Then the magnitude (absolute value) of z is:
|z| = √(a²+b²).
And the value of z* is:
|z*| = √[a²+(-b)²] = √(a²+b²).
So |z| = |z*|.
This Completes the Proof.
what are real numbers?
its a quantity whose decimal expansion has an endless range. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are utilised in measurements of continuously altering quantities such as size and time.
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A disco ball is shaped like a sphere with diameter of 60 inches to the nearest square inch what is the surface area of the disco ball
Answers
To calculate the surface area of a sphere, you have to use the following formula:
[tex]SA=4\pi r^2[/tex]Where "r" is the radius of the sphere.
We know that the diameter of the sphere is d = 60 inches and that the radius is half the diameter, then the radius can be determined as follows:
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{60}{2} \\ r=30in \end{gathered}[/tex]Once the radius is calculated, you can determine the surface area of the sphere:
[tex]\begin{gathered} SA=4\pi(30^2) \\ SA=4\pi\cdot900 \\ SA=3600\pi\approx11309.73in^2 \end{gathered}[/tex]The surface area of the sphere is 3600π in², expressed as a decimal value, the surface area is equal to 11309.73 in²
The school store has 2000 pencils in stock and sells an average of 50 pencils per day. The manager reorders when the the number of pencils in stock is 950 let d= the number of days
Answers
we make a equation depending of the days
[tex]T=2000-50d[/tex]Where T is the total of pencils
In this equation we are going to subtract 50 pencils for each day from the original 2000
to know the days where are 950 pencils we replace the total by 950 and solve d
[tex]\begin{gathered} 950=2000-50d \\ 50d=2000-950 \\ 50d=1050 \\ d=\frac{1050}{50} \\ \\ d=21 \end{gathered}[/tex]the number of days is 21
someone help me with the last two problems
Answers
Here is the completed table:
x /AM/
14 16
3 13
11 33
10 40
What are the values?/AM/ + /AC/ = /AC/
(x + 2) + (3x - 9) = 6x - 21
4x - 7 = 6x - 21
6x - 4x = 21 - 7
2x = 28
x = 28 / 2
x = 14
/AM/ = 14 + 2 = 16
/AM/ + /MW/ = /AW/
(2X + 7) + (3x - 4) = 18
5x + 3 = 18
5x = 18 - 3
5x = 15
x = 15/5
x = 3
/AM/ = (2 X 3) + 7 =
= 6 + 7 = 13
x + x + x + x = 44
4x = 44
x = 44 / 4
x = 11
/AM/ = 11 x 3 = 33
/AG/ + /GM/ = /AM/
2(x + 10) = 3x + 10
2x + 20 = 3x + 10
20 - 10 = 3x - 2x
10 = x
/AM/ = (3 x 10) + 10
= 30 + 10
= 40
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Find the nth term of this quadratic sequence
2, 8, 18, 32, 50,
Answers
Step-by-step explanation:
+6,+10,+14,+18
+4+4+4
therefore quadratic 4/period function=2
[tex]y = 2{x}^{2} + bx + c[/tex]
y=2 x=1
[tex] 0 = b + c[/tex]
y=8 x=2
8=8+2b+c
0=2b+c
y=18 x=3
0=3b+c
therefore
the equation is 2x^2=y
NEEED HELPPP ASAPPPPPP
Answers
The inverse of the function → f(x) = [tex]\sqrt{11x+12}[/tex] is
f⁻¹(x) = (x² - 12)/11
We have -
y = f(x) = [tex]\sqrt{11x+12}[/tex]
We have to find its inverse function.
What is the procedure to find inverse of function ?Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace 'y' with 'x' and vice - versa.
Step 2 - Rewrite the equation by solving for 'y'.
Step 3 - Replace 'y' with f⁻¹(x).
According to the question -
y = f(x) = [tex]\sqrt{11x+12}[/tex]
x = [tex]\sqrt{11y+12}[/tex]
x² = 11y + 12
x² - 12 = 11y
y = (x² - 12)/11
f⁻¹(x) = (x² - 12)/11
Therefore, the inverse of the function → f(x) = [tex]\sqrt{11x+12}[/tex] is
f⁻¹(x) = (x² - 12)/11
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explain which of the following is better to but
Answers
X
x=-4y
The slope is -4, and
the y-intercept is O.
Answers
The description of the error in finding the slope and y-intercept, of the graph of the equation is given by the option:
To be in slope-intercept form, the equation needs to be solved for y, not x
The equation in slope-intercept form is, [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]
What is the slope-intercept form of a straight-line equation?The slope-intercept form of the equation of a straight line is an equation of the form, y = m·x + c
The slope-intercept form of a straight-line equation is of the form, y = m·x + c, where:
m = The slope of the equation
c = The y-intercept
The given equation is x = -4·y
The given equation is not in the slope and intercept form given that the subject of the equation is x, rather than y
The error is therefore, in making x, the subject of the equation rather than y, that is the equation needs to be solved for y, not x
The correction of the error is performed as follows:
x = -4·y
-4·y = x
[tex]\displaystyle{y = \frac{x}{-4} = -\frac{1}{4} \cdot x[/tex]
Which gives: [tex]\displaystyle{y = -\frac{1}{4} \cdot x[/tex]
The slope of the graph of the equation is [tex]-\frac{1}{4}[/tex], the y-intercept, c, is 0
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Marie’s age is 12 less than triple Carl's’s age. When you add Marie's age to Carl’s age, you get 68. How old is Marie and how old is Carl? Show work.
A.) Use x to represent Carl's age. If x is Carl's age, write an expression for Marie's age using Carl's age x.
B.) Write an equation for the situation.
C.) Solve the equation from part a. Show your work. What is Marie's age and Carl's age.
30 Points for answering!
Answers
Find each sum:
1. 4j+k, -3k+7, 5-2j, and j+k-8
2. 5x^2-9x+3 and -2x^3+4x^2+7
Answers
1. The sum for the algebraic expression 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4
2.The sum for the algebraic expression 5x^2-9x+3 and -2x^3+4x^2+7 is -2x³+9x²-9x+10
What is algebraic addition?The addition of two or more numbers or quantities taken with regard to their signs according to the rules of addition in algebra.
First we will find the sum of 4j+k, -3k+7, 5-2j, and j+k-8
0i + 4j + k + 0
0i + 0j - 3k + 7
0i - 2j + 0k + 5
0i + j + k- 8
So the sum of 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4
First we will find the sum of 5x²-9x+3 and -2x³+4x^2+7
0x³ + 5x² - 9x + 3
-2x³ + 4x² + 0x+ 7
So the sum of 5x²-9x+3 and -2x³+4x²+7 is -2x³+9x²-9x+10
Therefore, the sum of the given algebraic expressions 4j+k, -3k+7, 5-2j, and j+k-8 is 3j-k+4 and 5x²-9x+3 and -2x³+4x²+7 is -2x³+9x²-9x+10.
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Here is a linear equation: y = 2/3x + 1 Are (6, 5) and (9, 8) solutions to the equation? Explain or show your reasoning.
Answers
A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given linear equation, y = 2/3x + 1
To be a point of its solution the point must satisfy the given equation.
Substitute (6,5)
5 = (2/3)6 + 1
5 = 2(2) + 1 = 5
Therefore, the (6,5) is the solution of the equation.
Substitute,(9,8)
(2/3)9 + 1 = 7
8 ≠ 7
So,(9,8) is not the solution of the equation.
Hence "A linear equation is a mathematical form of a line segment the point (6,5) satisfies the equation y = 2/3x + 1 so it is the solution of the equation but (9,8) is not the solution".
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3) Speedy Car Rental charges a flat fee of 30$ plus $.15 for each mile
a) write an equation for the cost as a function of the number of miles driven.
b) how much would the cost be if you drove 80 miles?
Answers
Answer:
a) C(m) = flat rate + rate per mile
b) $42
Step-by-step explanation:
a) C(m) = flat rate + rate per mile*No. of miles => 30+.15x
b) 30+.15*80 = 42
What is the difference between the values of |-
10 and 19 ?
Answers
Answer: 9
Step-by-step explanation:
the value of -10 is 10 and the value of 19 is 19 s0 19 - 10
Write the sentence as an equation.
341 is the same as the product of k and 273, minus 79
Answers
Answer:
341 = 273k - 79 or 273k - 79 = 341
The table shows the linear relationship between the distance in feet below sea level and the time in seconds traveled by a submarine What is the rate of change of the distance in feet below sea level with respect to time that the submarine traveled? Record your answer
Answers
The rate of change of the distance in feet below the sea level over time is: 8 ft/sec.
What is the Rate of Change of a Linear Relationship?The rate of change of a linear relationship between variables x and y is calculated as:
Rate of change = change in y / change in x.
From the table given, we have:
x = time (in seconds)y = distance below sea level (in feet)Using any two points from the table, (0, 460) and (18, 604):
Rate of change of the linear relationship = change in y / change in x = (604 - 460)/(18 - 0)
Rate of change of the linear relationship = 144/18
Rate of change of the linear relationship = 8 ft/sec.
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For a given week, Tammy's Coffee House has available 1584 ounces of A grade coffee and 1536 ounces of B grade coffee. These are blended into 1-pound
packages as follows: an economy blend that contains 3 ounces of A grade coffee and 8 ounces of B grade coffee, and a superior blend that contains 9 ounces of
A grade coffee and 3 ounces of B grade coffee. (The remainder of each blend is made of filler ingredients.) There is a $3 profit on each economy blend package
sold and a $2 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of
each blend should it make to maximize its profit for the week?
Note that the ALEKS graphing calculator can be used to make computations easier.
Economy blend:
Superior blend:
package(s)
package(s)
X
S
Answers
There is a requirement of 176 packets of economy blend and 96 packets of a superior blend to make maximum profit for the week.
Using the given data, calculate the x number of packages of the economy blend as well as the y number of packages of the superior mix.
3x + 11y =1584
6x + 4y = 1440
From the graph of these two equations, three extreme points are deduced: (240,0), (0,144), and (176,96).
The maximum (2x +4y) is the goal function.
Determine the aim function's value at all these extreme points,
The objective function value for (240,0) is 2 × 240 = 480
The objective function value for (0,144) is 4 × 144 = 576
The value of the objective function for (176,96) is 2 × 176 + 4 × 96 = 736
∴ The optimal point is (176,96) where x = 176 and y = 96.
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