An equation of the line containing the given point and parallel to the given line is y = 2x - 19.
The condition for two parallel lines.
In Mathematics, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
Mathematically, the point-slope form of a line is given by this equation:
y - y₁ = m(x - x₁)
Where:
x and y are the points.m represents the slope.Given the following equation:
2x - 56 = 3 ⇒ m₁ = 2
Therefore, m₁ = m₂ = 2.
At point (8, -3), we have:
y - y₁ = m(x - x₁)
y - (-3) = 2(x - 8)
y + 3 = 2(x - 8)
y + 3 = 2x - 16
y = 2x - 16 - 3
y = 2x - 19
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Find the greatest common factor of thefollowing monomials:10x^3y^3 32xy^2
The greatest common factor between the monomials can be determined as,
[tex]\text{GCF}(10x^3y^3,32xy^2)=2xy^2[/tex]Thus, the above expression gives the required greatest common factor.
What’s the frequency?
The total frequency of the particular 5 classes (67, 68, 69, 70, and 71) will be 19.
What is the frequency?The quantity of times a specific data value occurs is known as its frequency. We use f to represent a data value's frequency. For instance, grade A is said to have a frequency of five if five students received an A in science.So, the frequency for 5 classes:
Frequency of 67: 4Frequency of 68: 6Frequency of 69: 4Frequency of 70: 4Frequency of 71: 1The total frequency of these particular 5 classes will be:
4 + 6 + 4 + 4 + 1 = 19Therefore, the total frequency of the particular 5 classes (67, 68, 69, 70, and 71) will be 19.
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If 4−5=−12 and y = 3, what is x ?
Substituting y=3 in 4x-5y=-12 we get:
[tex]4x-5\cdot3=-12.[/tex]Simplifying the above equation we get:
[tex]4x-15=-12.[/tex]Adding 15 to the above equation we get:
[tex]\begin{gathered} 4x-15+15=-12+15, \\ 4x=3. \end{gathered}[/tex]Finally, dividing the above equation by 4 we get:
[tex]\begin{gathered} \frac{4x}{4}=\frac{3}{4}, \\ x=\frac{3}{4}\text{.} \end{gathered}[/tex]Answer: If 4x-5y=-12 and y=3 then:
[tex]x=\frac{3}{4}\text{.}[/tex]The height of Debbie is 85 centimetres. The height of Leo is 90 centimetres. Write the height of Debbie as a fraction of the height of Leo. Give your answer in its simplest form.
To write the height of Debbie as a fraction of the height of Leo in its simplest form is this: 17/18.
What does it mean to write a figure as a fraction of another?Writing one figure as a fraction of another can be done by representing the figures as numerators and denominators. In this case, what we will have is 85/90. That is the height of Debbie divided by the height of Leo.
To express this fraction in its simplest form will mean dividing the figures until they can no longer be divided. Using 5 as a common factor for dividing, we can conclude that the simplest form of the answer is 17/18.
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Please answer this question, I need help.
Answer:3 8 10
Step-by-step explanation:
2x(3x-4)-3x(5x+6)
Can somebody help explain how to get the awnser for this like step by step!
By using basic algebra we get x = 0 and x =[tex]\frac{-26}{9}[/tex]
What is basic algebra ?Algebra is a branch of mathematics that helps translate real-world situations or problems into mathematical truths. Mathematical operations like addition, subtraction, multiplication, and division are needed in addition to variables like x, y, and z to construct a meaningful mathematical expression. All branches of mathematics, such as calculus, trigonometry, and coordinate geometry, employ algebra. A fundamental algebraic equation is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations such as addition, subtraction, multiplication, division, etc. are done on variables and constants.
2x(3x-4)-3x(5x+6)
[tex]6x^{2} -8 -15x^{2} -18x\\-9x^{2} -26x = 0\\9x^{2} +26x = 0\\x(9x +26)=0\\x = 0\\ x = \frac{-26}{9}[/tex]
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Please help me out, I need to turn it in in 15 mins
What is their rate of change (speed) in Section D (Hours 7-10)? Remember to include units.
Step-by-step explanation:
I assume the hours are also in units of 2.
that means in D the distance is -20 miles in 10 hours or
-20 miles / 10 hours = -2 miles / hour
b) 150 g of syrup are needed to make 8 flapjacks.
Find the quantity of oats needed to make 16 of these flapjacks.
Based on the fact that 150g of syrup are needed when making 8 flapjacks, the quantity that is needed to make 16 flapjacks is 300 g.
How to find out quantity needed?The quantity of oats needed to make 8 flapjacks is 150 g.
Assuming direct proportion, the quantity of oats needed to make 16 flapjacks can be found by the formula:
= (Quantity of oats needed for 8 flapjacks x Number of flapjacks to be made) / Number of flapjacks made
Solving for the quantity of oats needed gives:
= (150 x 16) / 8
= 2,400 / 8
= 2,400 x 1/8
= 300 g
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Find the value of x that makes line u parallel to line v
Answer:
x = 10
Step-by-step explanation:
the angles shown are corresponding angles
corresponding angles are equal
12x - 4 = 10x + 16
subtract 10x from both sides
2x - 4 = 16
add 4 to both sides
2x = 20
divide both sides by 2
x = 10
Sales of SUVs (sport utility vehicles) in the United States (in millions) for the years 1990-1999 can be modeled by the quadratic equation shown below.y = 0.016x^2 +0.124x +0.787Here x = 0 represents 1990, x = 1 represents 1991, and so on. Use the model to approximate sales in 1995, Sales in 1995 were approximately ____ million SUVs.(Round to the nearest tenth as needed.)
The sales in 1995 were approximately 1.8 millions.
Explanation:
Since x = 0 is 1995, x = 1 is 1991 and so on, if we want to find the approximate amount of sales, we need to evaluate the expression for x = 5:
[tex]y=0.016x^2+0.124x+0.787[/tex][tex]\begin{gathered} y=0.016\cdot5^2+0.124\cdot5+0.787 \\ y=0.016\cdot25+0.62+0.787 \\ y=0.4+0.62+0.787 \\ y=0.4+0.62+0.787 \\ y=1.807 \end{gathered}[/tex]To the nearest tenth, the sales of SUV were approximately 1.8 millions
A company XYZ issued 30 year bonds with 10% annual coupon rate at their par value of $1000 in 2010. The Bonds had a 7% call premium, with 5 years of call protection. Today XYZ called the bonds. Compute the realized rate of return for an investor who purchased the bonds when they were issued in 2010. Briefly explain why the investor should or should not be happy.
1. Tha rate of return is 11.12%
2. The investor will not be happy in case the market interest rates fall
How to illustrate the information?n is NPER 5 (called back in 5yrs)
Coupon payment / PMT = 1000 * 10% = 100,
Purchase price PV (PV is entered as a negative value) -1000
Called for value is FV Call premium is 7% hence FV = 107% * 1000 = 1070
You can use the RATE function in excel
Rate(nper, PMT, PV,FV, Type)
RATE(5,100,-1000,1070)
= 11.12%
The investor was promised a fixed return rate of 10%, but since the bond was called after 5 years, the actual return was 11.12%, so the investor had good reason to be pleased.
In the event that market interest rates decline, the investor will not be pleased because, had the bond not been called, he would have continued to receive his fixed 10% coupon payments of $100 per year.
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Solve. Todd sold bunches of flowers on a street corner on Friday afternoons. Each bunch sold for $2.75. One Friday he made $71.50. How many bunches of flowers did he sell that day?
Todd sold 26 bunches of flowers on a street corner on Friday afternoon
The selling price of each flower bunch = $2.75
Total money made by Todd on Friday = $71.50
Arithmetic: The foundational subject in mathematics is arithmetic, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the crucial branches of mathematics, arithmetic serves as the cornerstone of the field of mathematics.
Finding the number of flower bunches sold by Todd:
Number of bunches sold by Todd = Total money made by Todd/Selling price of each flower bunch
= 71.50/2.75
= 26
Number of bunches sold = 26
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A coin is weighted so that there is a 58% chance that it will come up "heads" when flipped. The coin is flipped four times. Find the probability of getting two "heads" and two "tails". Round your answer to four decimal places.
P(A) =Probability of heads
P(B) = Probability of tails
P(B)= 1 - P(A) = 1 - 58 = 42%
The events are independent, so, let's assume that we flip the coin and the first two results are heads, so:
P(A) =0.58
Now, let's assume the last two results are tails so:
P(B) = 0.42
Therefore:
[tex]\begin{gathered} P(A\cap A\cup B\cap B)=P(A)\cdot P(A)\cdot P(A)+P(B)\cdot P(B) \\ P(A\cap A\cup B\cap B)=0.58\cdot0.58+0.42\cdot0.42=0.3364+0.1764=0.5128 \end{gathered}[/tex]Find the circumference of a circular swimming pool with a radius of 8.5 yards. Use 3.14 as an approximation for pie. Round your answer to the nearest whole yard. Enter only the number.
Answer:
53 yards
Step-by-step explanation:
Hello!
The circumference formula of a circle is [tex]C = 2\pi r[/tex], where C is the circumference, and r is the radius.
Given that pi is 3.14, solve for the circumference.
Solve for C[tex]C = 2\pi r[/tex][tex]C = 2(3.14)(8.5)[/tex][tex]C = 53.38[/tex]The circumference of the circle is 53.38, but rounded to the nearest whole yard would be 53 yards.
h, the points A(−5, 6), B(2, 6), C(2, -1) and D(-5, -1) are the vert of a square. what is the area of the square?
Answer:
so find dots, then count how many sections are beetween them, so you will find lenght of every side and use formula to find area(S=a²+b²).
Over the last three evenings, Karen received a total of 130 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. How many phone calls did she receive each evening?
CORRECT ANSWERS ONly
Answer first evening she received 130 second evening she received 520 third evening she received 1300
Step-by-step explanation: that's the right one for shure i worked it out
Is trangle ABC ~ trangle XYZ ? if so , what sequence of transformation maps trangle ABC to XYZ
You have the figurew ABC with the following vertices:
A(-2,-4)
B(0,-1)
C(2,-4)
First, multiply all points by 2 (this is the first transformation)
A => A'(-4,-8)
B => B'(0,-2)
C => C'(4,-8)
Next, translate the previous points 6 units upward (which means add 6 units to each y-coordinate).
A' => X(-4,-2)
B' => Y(0,4)
C' => Z(4,-2)
as you can notice, with the previous transformation you obtain the vertices X, Y, and Z and form the figure XYZ.
Answer: a dilation by and a translation
Step-by-step explanation: just did on edge
The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function
R(x) = -3x² + 56x
How many hearing aids need to be produced and sold in order to maximize the revenue? (Round to
the nearest whole number.)
The revenue is at a maximum after
- -
The maximum revenue is $
hearing aids are produced and sold.
What is the revenue? (Round answer to the nearest cent.)
The revenue is at a maximum after x = 9
The maximum is $ 261
9 hearing aids are produced and sold.
The revenue, R(x), of producing and selling 'x' Awesome Hearing Aids is modeled by the function,
R(x) = -3x² + 56x
We need to find the number of hearing aids produced and sold in order to maximize the revenue.
We use the differentiation method to find the maximum of the function R(x).
Differentiate R(x) with respect to x and equate it with 0,
R'(x) = -6x + 56
Then, -6x + 56 = 0
⇒ 6x = 56
⇒ x = 56/6 = 9.33 ≈ 9 [since x is the number of hearing aids]
Now we find the second derivative of R(x) at x = 9.
R''(x) = -6
⇒ R''(9) = -6 < 0
Since R''(9) < 0, the revenue R(x) is maximum at x = 9.
So the maximum revenue is obtained after x = 9.
Therefore maximum revenue = R(9) = -3 x 9²+56 x 9 = $ 261
Hearing aids produced and sold in order to maximize the revenue = 9
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A contractor completed five-ninths of a job before a second contractor completed an additional one-third. What fraction of the job is left undone?
[tex]\frac{1}{9}[/tex] fraction of the job is left undone.
What is fraction?Any number of equal parts is expressed by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, represents how many components of a suitable size there are when stated in ordinary English. fraction, A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction occurs in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. a week ago.
Given Data
A contractor completed five-ninths of a job before a second contractor completed an additional one-third.
Total work done is 1.
Contractor and second contractor completed:
= [tex]\frac{5}{9}[/tex] + [tex]\frac{1}{3}[/tex]
= [tex]\frac{5+3}{9}[/tex]
= [tex]\frac{8}{9}[/tex]
Total work done = 1
Work left undone:
= 1 - [tex]\frac{8}{9}[/tex]
= [tex]\frac{1}{9}[/tex]
[tex]\frac{1}{9}[/tex] fraction of the job is left undone.
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what is -5 x (- 3/9)
Answer:
Step-by-step explanation:
−5(−3/9)
Divide
-5x(-1/3)
Multiply
−5x(−1/3)
x 5/3
combine multiple terms into single fraction
5x/3
Question
Solve: n- 5/11=-1/3
N=?
Answer: 26/33
Step-by-step explanation:
Step-by-step explanation:
app called maple calculator
nine sales representitives for a company are to br chosen at random to participate in a training program. the company has twelve sales representatives, three in each of four regions. what is the probability that the nine sales representatives chosen to participate in the training program will be from only three of the four regions?
The probability is 6/70.
What is probability ?
probability is concerning about numerical description is how likely is an event is occur or how likely it is true.
Sol-
way will be selecting 84 out of eight since representative so 84 which is equal to at 70. And we need that we since we are things. There are two things representing the regions, so the four selected sales representatives are from only two off the regions. So if we select to sales representative from the two regions while we select de o sales representative from the other two regions, so four is it to selected from the four and to select from the two region and to select from two regions on day zero selected from the two regions and they're selected from the two regions. So is equal to four factorial over two factorial, two factorial times two factorial over to Victoria, zero factorial times too times Sorry, that was two factorial over to factory a factory times two factorial zero factorial two factorial which is equal to six for the
Thus,
probability is 6/70 which is equal toe open toe eight 57.
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Point A is at (-1, -9) and point B is at
(2, 4).
What is the midpoint of line segment AB?
-9-8-7 -6 -5 -4 -3 -2
The most appropriate form of midpoint of line segment will be given by-
Coordinate of midpoint of AB = ([tex]\frac{1}{2}, -\frac{5}{2}[/tex])
What is midpoint of a line segment?
At first, it is important to know about section formula. Let the coordinate of end point of a line segment is ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex]) respectively. Let another line intersects the line in the ratio m : n. Coordinate of point of intersection =[tex](\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m + n})[/tex].
If m = n =1, we get the coordinate of midpoint.
Coordinate of midpoint = [tex](\frac{x_1+y_1}{2}, \frac{x_2, y_2}{2})[/tex]
Midpoint of a line segment is that point which is equidistant from both the end points.
Here,
Coordinate of A = (-1, -9)
Coordinate of B = (2, 4)
Coordinate of midpoint of AB = ( [tex]\frac{-1 + 2}{2}, \frac{-9 + 4}{2}[/tex])
= ([tex]\frac{1}{2}, -\frac{5}{2}[/tex])
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a 4x³ - 6x² + 4 para x = -2, 3 y 1.
3
For value 4x³- 6x² + 4 is
If para x = -2
4x³ - 6x² + 4
=4(-2)³ - 6(-2)² + 4
=4(-8) - 6(4) + 4
=-32 - 24 + 4
=-52
If para x = 3
=4x³ - 6x² + 4
=4(3)³ - 6(3)² + 4
=4(27) - 6(9) + 4
=108 - 54 + 4
=58
If para x = 1
4x³ - 6x² + 4
=4(1)³ - 6(1)² + 4
=4 - 6 + 4
=2
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Find the recursive formula. 2, 32, 62, 92, ...
Answer:
122
Step-by-step explanation:
2+30 =32
32+30=62
62+30=92
Answer:
Use the formula
Step-by-step explanation:
I hope it helps
What equation would you set up to solve for X?
How many seven-digit numbers are there when 0 and 8 cannot be the leading number?
There are_____such seven-digit numbers.
Answer:
With the restrictions that 0 or 8 cannot be the leading digit, the leading digit can be one of [1, 2, 3, 4, 5, 6, 7, 9] = 8 choices.
The other six digits can be one of [1, 2, 3, 4, 5, 6, 7, 8, 9, 0] = 10 choices each.
Therefore, there are:
8*10*10*10*10*10*10 = 8*10^6 = 8,000,000 7-digit numbers under the given restrictions.
Step-by-step explanation:
hope this helps
The coordinate 3 has a weight of 1 , and the coordinate 6 has a weight of 2 .
For the coordinates and their weights, the weight average is 5
How to determine the weight average?The given parameters are:
Coordinate 3 has a weight of 1
Coordinate 6 has a weight of 2
The weight average is then calculated as:
Weight average = Sum of (Weight * Coordinate)/Sum of Weights
Substitute the known values in the above equation
So, we have the following equation
Weight average = (3 * 1 + 6 * 2)/(1 + 2)
Evaluate the product in the above equation
So, we have the following equation
Weight average = (3 + 12)/(1 + 2)
Evaluate the sum in the above equation
So, we have the following equation
Weight average = (15)/(3)
Evaluate the quotient in the above equation
So, we have the following equation
Weight average = 5
Hence, the weight average of the coordinates is 5
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Complete question
The coordinate 3 has a weight of 1 , and the coordinate 6 has a weight of 2 .
Find the weighted average.
the equation of a line is y=mx+b. if we know the line passes through (7,8), what does that tell us
The equation of the line is given as y = -2x + 22. This means that when x is equal to zero, y = 22. M also shows how steep the line is, being the gradient.
What is the calculation that justified the above?In order to arrive at a logical solution, we must assume the value of the slope as this is not given.
Assuming the slope of the line is -2, we thus can say:
The equation of a line that passes through a point (x₁,y₁) and a slope m is given by
(y - y1) = m (x - x1)
Recall that the slope, m = -2
While
Point (x1, y1) = (7, 8)
Hence, the equation of the line is:
y-8 = (-2) (x-7)
y-8 = -2x + 14
y = -2x+ 14 + 8
Hence,
y = -2x + 22
Thus, the equation of the line is:
y = -2x + 22
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Find the difference.
(-9ab-4a+8) - (-2ab+4)
Enter the correct answer.
Answer:
-7ab-4a+4
Step-by-step explanation:
simplify the expression
hope this helped
have a great day ^^