Answer:
B
Step-by-step explanation:
What is the equation of the line that is parallel to the line defined by the equation y = 3x−7 and goes through the point (4, 2)?
Answer:
[tex]y-2=3(x-4)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given a line contains the point (4, 2).
We also know that the line is parallel to y= 3x - 7.
We want to write the equation of this line.
Parallel lines have the same slopes.
First, let's find the slope of y = 3x - 7.
3 is in the place of where m (the slope) is, so that means it is the slope of that line.
It is also the slope of the line whose equation we want to write.
The equation of the line can be written in three ways:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept. Standard form, which is ax+by=c, where a, b, and c are free integer coefficients. a and b cannot be 0, and a is usually non-negative as well. Point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point.All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.
SolvingSubstitute 3 as m in [tex]y-y_1=m(x-x_1)[/tex].
[tex]y-y_1=3(x-x_1)[/tex]
Now, substitute 4 as [tex]x_1[/tex] and 2 as [tex]y_1[/tex].
[tex]y-2=3(x-4)[/tex]
Topic: parallel and perpendicular lines
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An AP has first term as 3 and Common difference of 2 how many terms are needed to make the sum to 99
Answer:
9
Step-by-step explanation:
The [tex]n[/tex]term is [tex]2n+1[/tex].
[tex]S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)[/tex]
The number of terms that needed to make the sum to 99 is 9
The first term of the arithmetic progression = 3
The common difference = 2
The sum of n term is = (n/2) [2a+(n-1)d]
Where a is the initial term
d is the common difference
Substitute the values in the equation
(n/2) [2(3)+(n-1)2] = 99
(n/2) [6 + 2n - 2] = 99
(n/2)[4+2n] = 99
n(2 + n) = 99
2n + [tex]n^2[/tex] = 99
[tex]n^2[/tex] + 2n - 99 = 0
Split the terms
[tex]n^2[/tex] - 9n +11n - 99 =0
n(n -9) + 11(n - 9) = 0
(n + 11)(n - 9) = 0
n = -11 or 9
Since n cannot be a negative number, therefore n = 9
Hence, the number of terms that needed to make the sum to 99 is 9
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Give two examples of functions that include an absolute value expression and have a vertex of (-1,3).
Select all that apply.
A. f(x)= |x-1| +3
C. f(x)=2x+1| +3
DE. f(x)= |x-1|-3
G. f(x)=2x+11-3
B. f(x)=x+1-3
D. f(x)=2|x-1| +3
OF. f(x)=x+1| +3
H. f(x)=2x-1|-3
Answer:
B and G
Step-by-step explanation:
f(x) = a|x-h|+k
The number inside the absolute value argument "h" represents the x-value of the vertex. For -1, the number inside has to be +1.
k represents the y-value of the vertex, in this case 3.
The only two expressions that have an h value of 1 and k value of 3 are B and G.
what's the next number 2 7 8 3 12 9 (ITS NOT 4!!!! 4 IS NOT AN OPTION!!!!!)
I'm not sure but I'd say 31
the value of 5/32 ÷ 25/4
Answer: [tex]\frac{1}{40}[/tex] or 0.025
Step-by-step explanation:
[tex]\frac{5}{32}[/tex] ÷ [tex]\frac{25}{4}[/tex] = [tex]\frac{5}{32}*\frac{4}{25} =\frac{5}{4(8)} *\frac{4}{5(5)} =\frac{1}{40}[/tex]
Help with this one please x Thankyou x
the measure of one angle of a triangle is 66°. of the remaining two angles, one is twice the measure of the other. how could you find the measures of the two unknown angles?
Answer:
below
Step-by-step explanation:
x = one angle and the other = 2x
solve this to find 'x' and '2x'
x + 2x + 66 = 180 because all of the angles of a triangle = 180
Find the term named in the problem and the explicit formula.
13) 18,14,10,6,
14) 30,0,-30,-60,
Find a₂₂
Find a₃₇
15) -34,-31,-28,-25,
Find a₂₃
The named terms in the sequence are a₂₂ = -66, a₃₇ = -1050 and a₂₃ = 32
How to determine the named term in the sequence?Sequence 1
From the question, we have the following sequence that can be used in our computation:
18,14,10,6,
In the above sequence, we can see that the 4 is subtracted from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₁ = 18
d = -4
The nth term can be represented as
aₙ = a₁ + (n - 1)d
For the 22nd term, we have
a₂₂ = 18 + (22 - 1) * -4
Evaluate
a₂₂ = -66
Sequence 2
Here, we have
30,0,-30,-60,
In the above sequence, we can see that the 30 is subtracted from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₁ = 30
d = -30
The nth term can be represented as
aₙ = a₁ + (n - 1)d
For the 37th term, we have
a₃₇ = 30 + (37 - 1) * -30
Evaluate
a₃₇ = -1050
Sequence 3
Here, we have
-34,-31,-28,-25,
In the above sequence, we can see that the 3 is added from the previous term to get the current term
Using the above as a guide,
So, we have the following representation
a₁ = -34
d = 3
The nth term can be represented as
aₙ = a₁ + (n - 1)d
For the 23rd term, we have
a₂₃ = -34 + (23 - 1) * 3
Evaluate
a₂₃ = 32
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Multiple Choice You are taking guitar
•lessons. The cost of the first lesson is twice the cost of each additional lesson. You spend $360 for 8 lessons. How much did the first
lesson cost'7
A $40
(C $50
(E $80
B) $45
(D $60
The cost of the first lesson based on the information is E. $80.
How to calculate the cost?From the information, the cost of the first lesson is twice the cost of each additional lesson. Let the others lesson b represented by x.
The first lesson will be: = 2 × x = 2x
Since there are 8 lessons, this will be:
First lesson + Other lesson = Cost
2x + (7 × x) = 360
2x + 7x = 360
9x = 360
Divide
x = 360/9
x = 40
Therefore, first lesson will be:
= 2x
= 2 × 40
= 80
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Pre-Calculus A
Which of the following graphs is a function?
The graph represents a function is graph a
What is a function?A function is a relationship between two sets or groups that maps each one of the elements contained in the first set to exactly one of the elements of the second set.
The graph a is a linear function, in which when we take any x value or y value, it gives the x and y value.
Hence, The graph that is a function is graph a.
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what can be used to show the rank order and shape of a data set simultaneously
A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a stem-and-leaf display. The Option C is correct.
What is the stem-and-leaf display?This is a device used for presenting quantitative data in a graphical format to assist in visualizing the shape of a distribution. They evolved in the early 1900s and are very useful in exploratory data analysis.
Also known as stem-and-leaf plot, was invented by John Tukey (but the idea can be traced back to the work of Arthur Bowley in the early 1900s.) in his work titled “Some Graphic and Semigraphic Displays” in 1972.
Missing options "a. relative frequency distribution b. pie chart c. stem-and-leaf display d. pivot table
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Emilia invests $10,000 in an account that compounds continuously. She plans to leave it in the account untouched. The table shows the balance of the account over 30 years. Enter the data into the graphing tool to plot these values on a scatter plot, with x representing the number years invested and f(x), or y, representing the account balance. Time Invested (years) Account Balance 5 $12,840 10 $16,487 15 $21,170 20 $27,183 25 $34,903 30 $44,817 Which equation most likely represents the curve of best fit for this data set? Select the correct answer.
The scatter plot is given by the image at the end of the answer, and the exponential function of best fit is given by:
y = 10000(1.0513)^x.
How to built the scatter plot?The scatter plot is built inserting all the points of the data-set in a graph, which are in the following input-output format:
(time in years, balance in dollars).
Hence the points for this problem are given as follows:
(5, 12840), (10, 16487), (15, 21170), (20, 27183), (25, 34903), (30, 44817).
From the graph given at the end of the answer, we can see that the function is exponential.
The exponential function of best fit is found inserting the points into a calculator, and is given as follows:
y = 10000(1.0513)^x.
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Anna is buying a house selling for $285,000. To obtain the mortgage, Anna is required to make a 15 % down payment. Anna obtains a 25 -year mortgage with an interest rate of 5 %. Click the icon to view the table of monthly payments.
a) Determine the amount of the required down payment.
b) Determine the amount of the mortgage.
c) Determine the monthly payment for principal and interest.
a) Determine the amount of the required down payment.
a) The amount of the required down payment is $42,750.
b) The mortgage amount after the down payment is $242,250.
c) The monthly payment for both principal and interest is $1,416.17.
What is the down payment?The down payment refers to the upfront cash payment made to reduce the cost of the home.
After deducting the down payment from the home price the result is the loan amount.
Monthly payments pay part of the loan amount the computed interest.
The monthly payments and the down payment can be determined with an online finance calculator.
Home Price = $285,000
Down Payment = 15%
Loan Term = 25 years
Interest Rate = 5%
Monthly Pay: $1,416.17
Loan Amount $242,250 ($285,000 - $42,750)
Down Payment = $42,750 ($285,000 x 15%)
Total of 300 Mortgage Payments = $424,851 ($1,416.17 x 300)
Total Interest = $182,601
Thus, after making a down payment of $42,750 cash, Anna will be making monthly payments of $1,416.17 for 300 months.
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