Write the slope-intercept form of the equation of the line through the given points13) through: (5, 3) and (5, 4)14) through: (0, 4) and (2, 3)15) trough: (-1, 4) and (-4,-5)16) through: (-1, -2) and (-3,0)
The slope-intercept form of the linear equation is
y = m x + b, where
m is the slope
b is the y-intercept
If the x-coordinates of the two points are equal, that means the line is vertical
A vertical line has no slope
Its equation is x = a, where a is the x-coordinate of any point on the line
13) The two points are (5, 3) and (5, 4)
They have the same x-coordinates, then its equation is
x = 5
The rule of the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex](x1, y1) and (x2, y2) are two points on the line
The line passes through points (0, 4) and (2, 3)
x1 = 0 and y1 = 4
x2 = 2 and y2 = 3
Substitute them in the rule above to find m
[tex]m=\frac{3-4}{2-0}=-\frac{1}{2}[/tex]The equation is
[tex]y=-\frac{1}{2}x+b[/tex]b is the value of y at x = 0
at x = 0 y = 4
b = 4
The equation of the line is
[tex]y=-\frac{1}{2}x+4[/tex]draw a model to represent 2 1/4 and write it as an improrer frrcation
The improper fraction equivalent of the fraction 2 1/4 is 9/4.
Improper fraction:
Basically, the improper fraction is also the fraction where the numerator is greater than or equal to the denominator.
Given,
Here we have the mixed fraction 2 1/4.
And we have to convert this mixed fraction into improper fraction.
The conversion from mixed fraction to an improper fraction will follow the following formula,
numerator = (denominator × whole number) + numerator of mixed fraction
Based on the this rule, the numerator of the improper fraction is,
=> numerator = (4 x 2) + 1
=> numerator = 8 + 1
=> numerator = 9
The denominator will remain same.
Therefore, the resulting improper fraction is 9/4.
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what is the slope of any line parallel to the line 8x+9x=3 in the standard (x,y) coordinate plane ?
The slope of the line that is parallel to 8x + 9x = 3 is: -8/9.
What is the Slope of Parallel lines?If two lines are parallel to each other, their slope values is equal to each other. This means the value of "m" in their equation expressed in slope-intercept form as y = mx + b, is the same.
Given the equation of a line in standard form as, 8x + 9y = 3, rewrite this in slope-intercept form:
8x + 9y = 3
8x + 9y - 8x = -8x + 3 [subtraction property of equality]
9y = -8x + 3
9y/9 = -8x/9 + 3/9 [division property of equality]
y = -8/9x + 1/3
The slope of the equation is -8/9. Therefore, the slope of the line that is parallel to the equation 8x + 9y = 3 will also be: -8/9.
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A group of friends wants to go to the amusement park. They have no more than $760 to spend on parking and admission. Parking is $17.75, and tickets cost $33.50 per person, including tax. Which inequality can be used to determine x x, the maximum number of people who can go to the amusement park?
The net of a rectangular prism is shown below. The surface area of each face is labeled.
We will have the following:
Inferring from the information presented in the diagram we can conclude that the measurements will be:
Base: 3ft * 12ft = 36f t^2
Side1: 3ft * 2ft = 6 ft^2
Side 2: 12ft * 2ft = 24 ft^2
So, the values that would represent the dimension will be:
Length: 12 ft.
Width: 3 ft.
Height: 2 ft.
What is the rate of change (slope) and the initial value (y-axis) for this table?
Answer: m = 24
Step-by-step explanation:
The right side of the table is the x value, and the left side is the y value.
Pick two points, I will pick (1,35) and (3,83).
Once you pick the points, input them in the rise over run formula:
y2-y1/x2-x1
83-35/3-1 = 48/2 = 24
Whats the answer to x + 23 12
A.8
B.-11
C.-6
D.6
Answer:
-11
Step by step explanation:
-11+23=12
Mrs. Doctor made a pot of hot chocolate in the teacher’s lounge. She wants to put 2/3 cup of hot chocolate into mugs to share with the other teachers. The pot holds 10 cups. How many mugs will Mrs. Doctor be able to fill?
Using the mathematical operation of division, Mrs. Doctor can fill 15 mugs using 10 cups.
What is the division operation?The division operation is one of the basic mathematical operations.
The division operation involves using the divisor to divide the dividend, which results in a quotient.
For instance, since the pot holds 10 cups and the distribution is 2/3 cups for each mug, we can divide 10 cups by 2/3 cups to get 15 mugs.
The quantity of hot chocolate for each mug = 2/3 cups
The total number of cups that the pot holds = 10 cups
The number of mugs that can be filled from 10 cups = 15 (10 ÷ 2/3)
Thus, we can divide 10 cups by 2/3 cups to get the number of mugs Mrs. Doctor can fill.
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for rayleigh winds with an average wind speed of 8 m/s: a. how many hours per year do the winds blow at less than 13 m/s? (5') b. how many hours per year are wind speeds above 25 m/s? (5')
A. 7658.8 hr/year
B. 4.082 hr/year
C. 99206 kwh
Moreover, The annual average wind speed was calculated directly at 4.56 m/s. Using the Weibull distribution, the annual wind speed is 4.55 m/s, while using the Rayleigh distribution it is 4.523 m/s. The annual wind power density was directly calculated to be 114.54 W/m2.
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write the following number in standard form: nine hundred twenty-eight
In this kind of problem is better to work backwards. We have the number nine hundred twenty-eigh.
This means that the two last digits are a 2 and a 8, becasue we have a "twenty-eight" = 28
And then, we have "nine hundred" = 900
The number whole, then, is:
[tex]928[/tex]What is r + s + t when r = 25, s = –11, and t = –7?
Answer:
7
Step-by-step explanation:
a finite sequence of three-digit integers has the property that the tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term. for example, such a sequence might begin with the terms 247, 475, and 756 and end with the term 824. let be the sum of all the terms in the sequence. what is the largest prime factor that always divides ?
The largest prime factor that always divides the sum of the terms in the sequence is 37.
The sequence is finite and consists of three-digit integers.
The tens and units digits of each term are, respectively, the hundreds and tens digits of the next term, and the tens and units digits of the last term are, respectively, the hundreds and tens digits of the first term.
From the above property of the sequence, we can see that each digit at the units, tens as well as hundreds place will appear the same number of times in the sequence.
Let "x" be the sum of the digits at unit place in all the terms.
The sum of all the terms is "S".
S = 111*x
S = 3*37*x
We can clearly see that the sum "S" is divisible by 37.
Hence, the largest prime factor that always divides the sum of the terms in the sequence is 37.
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which plan will result in the prive of feed reaching 12 faster
In plan B the price rises by 10%.
Thus the price rise is per week is $0.8
In plan A the price rise per week is $0.1
In plan C the price rise per week is
[tex]\frac{12-8}{8}=\frac{4}{8}=0.5[/tex]In plan D the price rise per week is $0.25
Considering all the plan the maximum price rise for each week is 0.8.
So the plan that would lead to $12 fastest is plan B.
The answer is plan B.
Sigma notation for 22, 28, 34, 40, 46
The sigma notation for the sequence 22, 28, 34, 40, 46 is as follows:
[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]
How to represent a notation in sigma notation?A sequence is represented in sigma notation according to the following rule:
[tex]\sum_{n = 0}^{n = N-1} a + bn[/tex]
In which the parameters are described as follows:
N is the number of terms in the sequence.a is the first term of the sequence.b is the common difference between the terms of the sequence.In the context of this problem, the sequence is:
22, 28, 34, 40, 46.
Hence the values of these parameters are given as follows:
N = 5, as there are 5 terms in the sequence.a = 22, which is the first term of the sequence.b = 6, as the difference between each term of the sequence is.Hence the sigma notation of the sequence is given by:
[tex]\sum_{n = 0}^{n = 4} 22 + 6n[/tex]
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for this I already did the first part and I got f(x)=2.5x+1so can you help me with the second part
suppose that marv and patricia will each take a covid test, and that the probability that both will test positive is 0.15. what is the probability that one or more of them tests negative?
The probability that one or more of them tests negative is 0.85.
Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.
If Marv and Patricia will each take a Covid test, then the events that will occur are : both will test positive, both will test negative, or one of them will test negative.
Based on the given information, the probability that both will test positive is 0.15. Subtract it from 1 to and get the probability that one or more of them tests negative.
probability = 1 - 0.15
probability = 0.85
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6. If f(x) = x2 - 1, which of the following is equal to g(x) = f(x - 3)?
A.g(x) = x/ +8
B.g(x) = x2 + 6x+8
C.g(x)= x2 - 6x + 8
D.g(x) = x2 + 6x- 10
( x - 2) ( x - 4 ) is function which is equal to g(x) .
In the simplest terms, what is a function?
As a set of inputs with one output for each, a function is defined as a relationship between them. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.f(x) = x² - 1
f( x - 3 ) = ( x - 3 )² - 1
= x² + 9 - 6x -1
= x² -6x + 8
= x² -4x -2x + 8
= x( x - 4 ) -2( x - 4)
= ( x - 2) ( x - 4 )
g(x) = f(x - 3)
= ( x - 2) ( x - 4 )
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Find the square root. V100
for the square root you must look for a number that multiplied with itself gives you the indicated value
for this case a number that multiplied by itself gives you 100
[tex]10\times10=100[/tex]sothe square root of 100 is:
[tex]10[/tex]Which of the following properly describe
"slope"? Select all that apply.
0
A)
ratio of the change in y-values
(rise) for a segment of the graph to
the corresponding change in x-
values (run)
OB) x₂-x₂
y₂-M1
C) ₂-₁
x₂-x₂
D) run/rise
☐ E) rise/run
Please Help i will give brainliest Its a emergency please help with this equation i am not sure what to do its a math problem
Answer:
the last choice is the 6th term of expression
Step-by-step explanation:
all the work and steps is in the pic go check it out sorry if wrong and have a wonderful day:)
Amy has a piece of wood that measures 42 inches. The model shows the length remaining after she cut a piece from the 42-inch piece of wood. About how many inches did Amy cut from the 42-inch piece of wood? 2 3 4 5 6 7 8 10 12 inches
Given data
Ammy has a piece of wood that measures 42 inches
Ammy cut from the 42-inch piece of wood is calculated as
[tex]42-9=33\text{ inches}[/tex]Thus, Amy cut from the 42-inch piece of wood is 33 inches
Karl drove 40 miles in 50 minutes. Teresa drove 35 miles in 42 minutes. Who had a higher average speed?
The person that has the higher average speed is Teresa.
How to find average speed?Average speed is calculated by dividing the total distance that something has travelled by the total amount of time it took it to travel that distance.
Therefore, Karl drove 40 miles in 50 minutes and Teresa drove 35 miles in 42 minutes.
The person that has the higher average speed can be calculated as follows;
average speed of Karl = distance / time
average speed of Karl = 40 / 50
average speed of Karl = 4 / 5 miles per minutes
average speed of Teresa = distance / time
average speed of Teresa = 35 / 42
average speed of Teresa = 5 / 6 miles per minutes
Therefore, Teresa had the higher average speed.
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Arianys is driving to a concert and needs to pay for parking. There is
an automatic fee of $11 just to enter the parking lot, and when she
leaves the lot, she will have to pay an additional $3 for every hour she
had her car in the lot. How much total money would Arianys have to
pay for parking if she left her car in the lot for 4 hours? How much
would Arianys have to pay if she left her car in the lot for t hours?
Cost of parking for 4 hours:
Cost of parking for t hours:
Pls help me
Answer:
c = 3t + 11
t = time in the lot
c = total cost
4 hours the cost will be $23
Step-by-step explanation:
Cost for 4 hours.
c = 3t + 11
c = 3(4) + 11
c = 12 + 11
c= $23
Every computer that a business owner purchases will lose most of its value after 5 years of use. The owner plans to purchase a computer for $2,100 and replace it after 4 years.Part BMethod 2 of determining the computer's value is to reduce its value by 30% after each year of use.Which function, g(n), represents the value of the computer after years of use for Method 2?g(n) = 0.3n(2,100)g(n) = 0.7 (2.100)g(n) = 2.100(0.3)^ng(n) = 2.100(0.7)^n
Answer:
D. g(n)=2100(0.7)^nD. g(n)=2100(0.7)^
Explanation:
• The purchase price, i.e. the initial value of the computer = $2100.
,• The rate at which its value reduces = 30%.
To determine the computer's value after n years of use, we use the depreciation formula below:
[tex]A(n)=P(1-r)^n[/tex]In this case:
• The Principal, P = $2100
,• The rate, r = 30%
Substitute these values into the formula.
[tex]\begin{gathered} g(n)=2100(1-30\%)^n \\ =2100(1-\frac{30}{100})^n \\ =2100(1-0.3)^n \\ \implies g(n)=2100(0.7)^n_{} \end{gathered}[/tex]The function g(n) that represents the value of the computer after n years of use is Option D.
Find the Value of X in each case. RSM geo Lesson 9, 24d
The value of x in the triangle is 17 degrees.
How to find angle in a triangle?A triangle is a polygon with three sides and angles.
The sum of angles in a triangle is 180 degrees.
Therefore, ABC is a triangle and CDE is a also a triangle.
Let's find the angle x in the triangle CDE.
Hence,
∠ACB = 180 - 4x - 49 (sum of angles in a triangle is 180 degrees)
∠ACB = 180 - 49 - 4x
∠ACB = 131 - 4x
Therefore,
180 = ∠DCE + ∠DEC + ∠CDE
∠CDE = 100°
∠DEC = x
∠DCE = ∠ACB = 131 - 4x
Hence,
180 = 131 - 4x + x + 100
180 = 231 - 4x + x
180 - 231 = -3x
-51 = -3x
divide both sides by -3
x = -51 / -3
x = 17
Therefore,
x = 17
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What is 7h+(-9.1d)-13+6d-3.5h simplified
After simplification, 7h+(-9.1d)-13+6d-3.5h is 3.5h-3.1d-13.
According to the question,
We have the following expression:
7h+(-9.1d)-13+6d-3.5h
Now, we will simplify it by adding or subtracting the numbers or the numbers with the same variable together. For example, 3.5h can only be subtracted from 7h because both of them h as a variable. And 6d can be subtracted from 9.1d.
(More to know: when a positive and a negative number is multiplied then the result is always negative. In this case, we will multiply +1 into -9.1d.)
Now, let's simplify the given expression:
7h-3.5h-9.1d+6d-13
3.5h-3.1d-13
Hence, the expression obtained after solving the given expression is 3.5h-3.1d-13.
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7. Find the area of the figure. 112 cm2 384 cm2 88 cm2
88cm² is the area of the trapezoid in the diagram.
This question is incomplete, the missing diagram is uploaded along the answer below below.
What is the area of the trapezoid?A trapezoid is simply a quadrilateral with at least one pair of parallel sides.
The area of a trapezoid is expressed as;
A = 1/2 × ( a + b ) × h
Where a is length of base a, b is length of base b and h is the height.
Given the data in the diagram;
Length of base a = 8cmLength of base b = ( a + 6cm ) = 8cm + 6cm = 14cmHeight h = 8cmArea A = ?To determine the area of the trapezoid, plug the given lengths into the above formula and solve for A.
A = 1/2 × ( a + b ) × h
A = 1/2 × ( 8cm + 14cm ) × 8cm
A = ( 8cm + 14cm ) × 1/2 × 8cm
A = ( 22cm ) × 4cm
A = 88cm²
Therefore, the area is 88 square centimeters.
Option C is the correct answer.
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29 + 17w = 624
w =
Help
Answer:
w = 35
Step-by-step explanation:
To solve this problem, you will need to undo it in reverse order. The first thing done to w is to multiply it by 17 and then add 29 to it. You need to undo the addition of 29 with subtraction first.
624-28=595
Next, you need to undo the multiplication by 17 with division.
[tex]\frac{595}{17} =35[/tex]
Therefore, your answer is 35
-
у
0
1
1
3
2
9
3
27
{(2, 1), (-7, -1), (-5, -5), (9, -4), (-3, -3) }
Domain:
Range: