Answer:
[tex]x = - 2[/tex]
[tex]10x + 8 < - 2 \\ 10x < - 2 - 8 \\ 10x < - 20 \\ \frac{10x}{10} < \frac{ - 20}{10} \\ x < - 2 [/tex]
The terms 1/64, 1/32, 1/16 form a geometric progression (GP) If the sum of the GP is (2^36 – 2^-6), find the number of terms
If [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio of the series, then the sum of the first [tex]n[/tex] terms is
[tex]S_n = a + ar + ar^2 + \cdots + ar^n[/tex]
Multiply by [tex]r[/tex] on both sides, then subtract that from and solve for [tex]S_n[/tex].
[tex]rS_n = ar + ar^2 + ar^3 + \cdots + ar^{n+1}[/tex]
[tex](1-r)S_n = a - ar^{n+1}[/tex]
[tex]S_n = \dfrac{a(1-r^{n+1})}{1-r}[/tex]
Use the given first and second terms of the sequence to find [tex]a[/tex] and [tex]r[/tex].
[tex]a = \dfrac1{64}[/tex]
[tex]ar = \dfrac1{32} \implies \dfrac r{64} = \dfrac1{32} \implies r = \dfrac{64}{32}=2[/tex]
Solve for [tex]n[/tex].
[tex]S_n = \dfrac{1-2^{n+1}}{64(1-2)} = 2^{36} - 2^{-6}[/tex]
[tex]\dfrac{2^{n+1} - 1}{2^6} = 2^{36} - 2^{-6}[/tex]
[tex]2^{n-5} - 2^{-6} = 2^{36} - 2^{-6}[/tex]
[tex]\implies n-5 = 36 \implies \boxed{n = 41}[/tex]
A Web music store offers two versions of a popular song. The size of the standard version is 2.8 megabytes (MB). The size of the high-quality version is 4.4 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 3840 MB. How many downloads of the standard version were there?
Step-by-step explanation:
s = number of standard downloads
2s = number of high-quality downloads
2.8s + 4.6(2s) = 2760
2.8s + 9.2s = 2760
12s = 2760
s = 230
The standard version was downloaded 230 times and the high-quality version was downloaded 460 times.
For a normal distribution, find the probability of being (a) Between −1 and +1 (b) Between 3 standard deviations below the mean and 2 standard deviations above the mean (c) More than 3.5 standard deviations away from the mean Use the Standard Normal Table in your textbook or Excel to obtain more accuracy.
Using the normal distribution, the probabilities are given as follows:
a) 0.6826 = 68.26%.
b) 0.9759 = 97.59%.
c) 0.0004 = 0.04%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Item a:
The probability is the p-value of Z = 1(0.8413) subtracted by the p-value of Z = -1(0.1587), hence:
0.8413 - 0.1587 = 0.6826
Item b:
The probability is the p-value of Z = 2(0.9772) subtracted by the p-value of Z = -3(0.0013), hence:
0.9772 - 0.0013 = 0.9759.
Item c:
This probability is P(|Z| > 3.5), which is 2 multiplied by the p-value of Z = -3.5, which is of 0.0002.
Hence:
2 x 0.0002 = 0.0004 = 0.04%.
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Hence, write down the smallest integer value of x that satisfies 7(6+x) -x>0
Answer:
-6
Step-by-step explanation:
[tex]7(6+x)-x > 0[/tex]
[tex]42 + 7x-x > 0[/tex]
[tex]42+6x > 0[/tex]
[tex]6x > -42[/tex]
[tex]x > -7[/tex]
The smallest integer that satisfies the condition, [tex]x > -7[/tex], is -6.
The system of equations is graphed on the coordinate plane.
y=x−1
y=−2x−4
Enter the coordinates of the solution to the system of equations in the boxes.
Answer:
(-1,-2)
Step-by-step explanation:
Hello!
The solution to the system is at the intersection between the two graphed lines.
Remember that a coordinate is written in (x,y) format, so we take the x-value of the points and the y-value of the point.
The coordinate is (-1, -2).
What is the length of BC?
Answer:
75/4
Step-by-step explanation:
Assuming BA and ED are parallel, we know thay the two triangles are similar.
So,
[tex]\frac{25-x}{x}=\frac{36}{12} \\ \\ \frac{25-x}{x}=3 \\ \\ 25-x=3x \\ \\ 4x=25 \\ \\ x=\frac{25}{4} \\ \\ BD=25-\frac{25}{4}=\frac{75}{4}[/tex]
The rectangular part of the field shown below is 160 yd long and the diameter of each semicircle 12 yd. How much will it cost to fertilize the field at 0.25 per square yard? Use π = 3.14 and round to the nearest cent.
It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.
Given that the field is 160 yards long and the diameter is 12 yards and charge of 1 square yard of fertilizing is $0.25.
We are required to find the total cost of fertilizing the field.
The total cost of fertilizing the field will be the product of the cost of 1 square yards and the area of the field.
When we will observe the field carefully then we will say that the diameter of the semi circle is equal to the breadth of the rectangle. There are two semicircles so we have to just find the area of 1 circle and the area of 1 rectangle.
Area of the field=Area of rectangle+Area of circle
=length* breadth+π[tex]r^{2}[/tex]
=160*12+3.14*[tex]6^{2}[/tex]
=1920+3.14*36
=1920+113.04
=2033.04 [tex]yards^{2}[/tex]
Cost of fertilzing the field=2033.04*0.25
=$508.26
Hence It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.
Question is incomplete as the figure which is attached should be included.
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If you spend $50 (including shipping) at an online store, you recieve a $10 gift card. You want to purchase CDs that cost $12 each. If shipping cost $5, write and solve an inequality to find the number of Cds you must to receive the giftcard.
Four CDs must be bought to receive a gift card from an online store.
How to determine the least number of CDs to be bought to receive a gift card
The total costs are equal to the sum of the shipping cost and the total related to the number of acquired CDs (n). The number of gift cards (m) is equal to the total costs divided by minimum spent money, that is, $ 50. We need to solve the following inequation to find the minimum quantity of CDs:
(12 · n + 5)/50 > 1
12 · n + 5 > 50
12 · n > 45
n > 45/12
n > 3.75
Four CDs must be bought to receive a gift card from an online store.
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If f(x) = 3x4 + 2x3 - x + 15,
what would be the list of
possible rational roots?
Answer: A. ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
Step-by-step explanation:
± [tex]\frac{1, 3, 5, 15}{1, 3}[/tex]
= ± [tex]1, 3, 5, 15, 1/3, 5/3, 5[/tex]
Rearranging, we get:
= ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
The table below gives the completion percentage and interception percentage for five randomly selected NFL quarterbacks. Based on this data, consider the equation of the regression line, yˆ=b0+b1x, for using the completion percentage to predict the interception percentage for an NFL quarterback. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Table
6 steps
The regression equation is y = -0.42647x + 29.11471 and the correlation coefficient is -0.9607
How to determine the regression equation?The table of values is given as:
Completion Percentage 57 59 62 63 64
Interception Percentage 5 3.5 3 2.5 1.5
Next, we enter the above values in a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 305Sum of Y = 15.5Mean X = 61Mean Y = 3.1Sum of squares (SSX) = 34Sum of products (SP) = -14.5r = -0.9607Regression Equation = ŷ = bX + a
b = SP/SSX = -14.5/34 = -0.42647
a = MY - bMX = 3.1 - (-0.43*61) = 29.11471
So, the regression equation is
y = -0.42647x + 29.11471
And the correlation coefficient is -0.9607
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At a cost of R55 per box how much would it cost to tile the training room
The total cost needed to tile the training room with an area of 100 m² is R110.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let assume that the area of the trainig room is 100 m² and one box can complete 50 m², hence:
number of box needed = 100 m² / 50 m² = 2
Total cost = R55 per box * 2 box = R110
The total cost needed to tile the training room with an area of 100 m² is R110.
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A text message plan costs $9 per month plus $0.39 per text. Find the monthly cost for x text message The monthly cost of x messages is dollars. (Use integers or decimals for any numbers in the expression.) *
Answer:
The monthly cost = $9 + $0.39x
Step-by-step explanation:
This is multiple choice pls help
Answer: b and e
Step-by-step explanation:
b - the slope is positive
the slope is 8 not negative 8 because, 4+4/2-1 = 8/1 = 8 since subtracting 4 and -4 makes it 4+4
e - it is possible for x to be positive and for y to be negative
please give answer to these fractions give STEPS
no scam 30 points + BRAINLIEST
1/2 × 3/5 ÷ 9/15 - 6/4 ÷ 4/1
Answer:
1/8
Step-by-step explanation:
Look at the screen shots
Question 2: 11 pts
A coin is tossed three times. Find the probability that 2 heads and 1 tail turn up in any order.
Answer:
3/8 or 0.375 or 37.5%
Step-by-step explanation:
So since the coin is tossed three times, it's not to hard to write out every scenario since there will only be 2^3 combinations or 8 combinations. But we can also use Binomial Distribution Formula.
Binomial Distribution Formula:
[tex]P(x)=(^n_x)p^xq^{n-x}[/tex]
Where p = probability of success and q=probability of failure, x=how many successes, and n=total number of trials
Combination Formula:
[tex](^n_x) = \frac{n!}{x!(n-x)!}[/tex]
So let's define the variable values, since it's a coin, the probability of heads/tails should be 50/50 so p=0.50 and q=0.50. Since we want 2 heads then x=2, and since the total number of trials is 3, n=3.
So let's plug the values into the equation:
[tex]P(x)=\frac{3!}{2!}*(0.50)^2*(0.50)^1[/tex]
Rewrite 0.50 as a fraction
[tex]P(x)=\frac{3*2*1}{2*1}*(\frac{1}{2})^2*(\frac{1}{2})^1[/tex]
Cancel out values in fraction, and also square the fraction
[tex]P(x)=3*\frac{1}{4}*\frac{1}{2}[/tex]
Multiply fractions
[tex]P(x)=3*\frac{1}{8}[/tex]
Multiply the two values
[tex]P(x)=\frac{3}{8}[/tex]
This means the probability is 3/8 or 0.375 or 37.5%
I also provided a diagram on how to just draw out each scenario/combination
he graph of f(x) = log x + 3 is the graph of
g(x) = log x translated 3 units
We conclude that the graph of f(x) is the graph of g(x) translated 3 units upwards.
How do relate the graphs of f(x) and g(x)?Here we have the functions:
[tex]f(x) = log(x) + 3\\\\g(x) = log(x)[/tex]
And we want to find a relation between them.
Remember that a vertical translation of N units (the sign of N defines the direction of the translation) is written as:
[tex]f(x) = g(x) + N[/tex]
In this case, we can see that N = 3, it is positive, so the translation is upwards. (This means that the whole graph of the function f(x) is translated upwards 3 units in the coordinate axis)
Then we conclude that the relation between the graphs of the given functions is that the graph of f(x) is the graph of g(x) translated 3 units upwards.
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Evaluate the given algebraic expressions replacing x with -2 and y with 1
3x^2
Answer:
12
Step-by-step explanation:
3x^2
because the information provided states that x = -2, that is what we are going to replace x with.
3(-2)^2
the next step is to evaluate the power because that is next in PEMDAS.
(-2)^2 = 4
that leaves us with:
3 * 4 = 12 ( the " * " represents the multiplication sign)
hope this helps!
oscar bought some markers notebooks and packs of sticky notes for his office he bought the same number of markers as notebooks he bought three more packs of sticky notes than markers and notebooks combined he paid $1.05 for each marker $2.25 for each notebook, and the packs for sticky notes were $1.95. how many of each kind of office supply did oscar buy if he paid $49.05 in all?
The number of each kind of office supply oscar bought is = markers= (43.2 - 4.2y)/3 notebooks = (43.2-3x)/4.2, sticky notes = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3.
Calculation of total office supplyThe number of markers he bought = X
The number of notebooks he bought= y
The number of sticky notes he bought= z= 3 + X+y
The amount he paid for markers = $1.05*X
The amount he paid for notebooks = $2.25*y
The amount he paid for sticky notes= $1.95 (3 + X+y)
The total amount he paid is = $49.05
That is;
$49.05 = $1.05x + $2.25y + $1.95 (3 + X+y)
$49.05 = $1.05x + $2.25y + $5.85 + $1.95x + $1.95y
$49.05 - $5.85 = 3x + 4.2y
$43.2 = 3x + 4.2y
Make X the subject of formula,
3x = 43.2 - 4.2y
X = (43.2 - 4.2y)/3
y= (43.2-3x)/4.2
z = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3
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What is the domain of y = 4 log5 (x - 3)?
A. all real numbers
B. all real numbers greater than 4
C. all real numbers greater than 5
D. all real numbers greater than 3.
The domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.
How to determine the domain?The function is given as:
[tex]y=4\log_5(x-3)[/tex]
Set the expression in bracket greater than 0
x -3 > 0
Add 3 to both sides
x > 3
Hence, the domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.
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Question about a rational expression
The equation is -9=6/v
In the explanation, it tells me to multiply v on both sides. My question is why do you multiply v on both sides and not 6?
When I did the problem I multiplied 6 on both sides and got -54=v, but apparently the answer is -2/3 so I’m confused as to why you multiply v on both sides and not 6.
Rational expressions are often used in combining rates of work.
Rational expressions are often used in combining rates of work. Therefore, it's true.
What is rational expression?It should be noted that a rational expression is simply defined by a rational fraction.
They're are used in combining rates of work. Fir example, if Mr John performs 1/2 of his work and does 1/3 on another day. This can be expressed as:
= 1/2 + 1/3
= 5/6
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To save $5,000 for a vacation in 3 years, how much money must be invested each
year if the investment earns 5% interest compounded annually? Round to the
nearest dollar.
$15,762
$1,586
$3,000
$1,667
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]5000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 5000=P(1.05)^3 \\\\\\ \cfrac{5000}{1.05^3}=P\implies 4319\approx P[/tex]
The amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
How are annual payments or cash flows calculated?The annual payments represent the periodic cash outflows invested in accumulating a future value using an interest rate compounded for a period.
This can be achieved using the future value and present value formulas or factors.
We can also use an online finance calculator, as follows:
Data and Calculations:Future value = $5,000
Investment period = 3 years
Annual compound interest = 5%
N (# of periods) = 3 years
I/Y (Interest per year) = 5%
PV (Present Value) = $0
FV (Future Value) = $5,000 ($4,531.56 + $468.44)
Results:
PMT = $1,510.52
Sum of all periodic payments = $4,531.56 ($1,510.52 x 3_)
Total Interest = $468.44
Thus, the amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.
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which expression is equivalent to 7x^2 sqrt 2x^4 times 6 sqrt 2x^12 if x ≠ 0
The equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]
How to determine the equivalent expression?The expression is given as:
7x^2 sqrt 2x^4 times 6 sqrt 2x^12
Rewrite properly as:
[tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex]
Evaluate the product
[tex]7 * 6x^2 \sqrt{2x^4*2x^{12 }[/tex]
This gives
[tex]42x^2 \sqrt{4x^{16}[/tex]
Take the square root of 4
[tex]2*42x^2 \sqrt{x^{16}[/tex]
Take the square root of x^16
[tex]2*42x^2 *x^8[/tex]
So, we have:
[tex]84x^{10[/tex]
Hence, the equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]
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Answer:
Step-by-step explanation:
The equivalent expression of is
How to determine the equivalent expression?
The expression is given as:
7x^2 sqrt 2x^4 times 6 sqrt 2x^12
Rewrite properly as:
Evaluate the product
This gives
Take the square root of 4
Take the square root of x^16
So, we have:
Hence, the equivalent expression of is
When first hired, Deondre was earning $5.85 per hour. He has worked his way up in the business and is currently making $12.30 an hour. What is the absolute and relative change in Deondre's hourly pay from when he was first hired to now?
Answer:
$6.45/hour
110.26%
Step-by-step explanation:
The absolute change is the difference between salaries now ands then.
12.30 - 5.85 = 6.45
The relative change in the percent increase.
percent increase = (new number - old number)/(old number) × 100%
percent increase = (12.3 - 5.85)/(5.85) × 100%
percent increase = 110.26%
A shoe repair operation uses a two-step sequence that all jobs in a certain category follow. All jobs can be split in half at both stations. For the group of jobs listed: JOB TIMES (minutes) A B C D E Workstation A 27 18 70 26 15 Workstation B 45 33 30 24 10 Click here for the Excel Data File a. Find the sequence that will minimize total completion time. b. Determine the amount of idle time for workstation B.
1. The sequence that will minimize the total completion time is sequence 4. B-A-C-D-E.
2. The determination of the amount of idle time for Workstation B is 37 minutes.
Johnson's Sequencing Rule:According to Johnson's sequencing rule, start listing jobs with minimum completion time first.
If the job occurs at Workstation A, list it on the left side. If the job occurs at Workstation B, list it on the right side, as below:
Data and Calculations:JOB TIMES (minutes) A B C D E
Workstation A 27 18 70 26 15
Workstation B 45 33 30 24 10
The first job with a minimum completion time is Job E at Workstation B.
The second job with a minimum completion time after Job E is Job B at Workstation A.
The third job with a minimum completion time after Job B is Job D at Workstation B.
The fourth job with a minimum completion time after Job D is Job A at Workstation A.
The last job is Job C at Workstation B.
The sequence that minimizes total completion time is as follows:
B A C D E
A B
Calculation of Idle Time at Workstation B:Job Workstation A Workstation B Idle Time
In Out In Out Workstation B
B 0 0+18 = 18 18 18+33 = 51 18
A 18 18+27 = 45 51 51+45 = 96 19
C 45 45+70 = 115 115 115+30 = 145 0
D 115 115+26 = 141 145 145+24 = 169 0
E 141 141+15 = 156 169 169+10 = 179 0
Total Idle Time at Workstation B = 37 (18 + 19)
Thus, the sequence that minimizes the total completion time is sequence 4, while the idle time at Workstation B is 37 minutes.
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Question Completion with Answer Options:1. A-B-C-D-E
2. E-D-B-C-A
3. D-C-B-A-E
4. B-A-C-D-E
5. C-A-B-D-E
Express the following function, F(x), as a composition of two functions, f and g:
Answer:
There are many different answers to this question but here is one that I thought of.
g(x)=x^2
f(x)=x/(x+4)
f(g(x))=F(x): plug in x^2 into each of the x in f(x) and and answer should equal F(x)
Step-by-step explanation:
since the function F(x) had 2 x^2 in it, I thought that g(x) could easily be x^2 that way u can subsitute the x in f(x) later to x^2 and get the right answer.
The lengths of the sides of a pentagons are 2'', 6'', 10'' , 14'', and 24''. calculate the lengths of the sides of a similar pentagon if the shortest side is 5'' .
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"How to get the lengths of the sides of a similar pentagon?
All the measures must be multiplied by the same scale factor to get a similar pentagon.
If in the original pentagon the shortest side measures 2", and in the similar pentagon the shortest side measures 5", then we have:
5" = k*2"
5"/2" = k = 2.5
Then the scale factor is 2.5
To get the other sides of the pentagon, we just need to multiply the other sides of the original pentagon by 2.5
The other sides measure:
6"*2.5 = 15"10"*2.5 = 25"14"*2.5 = 35"24"*2.5 = 60"If you want to learn more about similar figures:
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What is the probability of flipping a coin once and getting heads if you have gotten 5 tails in a row before that?
a. 1/32
b. 1/5
c. 1/4
d. 1/2
Answer:
Answer is..... D
Step-by-step explanation:
every single flipping may two results, head or tail.So last one has equal chance.
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Finding the inverse function of [tex]f(x) = 5\sqrt{x + 3} - 2[/tex], it is best described by graph B.
How to find the inverse of a function?Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.
In this problem, the function is:
[tex]f(x) = 5\sqrt{x + 3} - 2[/tex]
[tex]y = 5\sqrt{x + 3} - 2[/tex]
Exchanging x and y:
[tex]x = 5\sqrt{y + 3} - 2[/tex]
Working through the function to isolate y:
[tex]5\sqrt{y + 3} = x + 2[/tex]
[tex]\sqrt{y + 3} = \frac{x + 2}{5}[/tex]
[tex](\sqrt{y + 3})^2 = \left(\frac{x + 2}{5}\right)^2[/tex]
[tex]y + 3 = \frac{(x + 2)^2}{25}[/tex]
[tex]y = \frac{(x + 2)^2}{25} - 3[/tex]
[tex]f^{-1}(x) = \frac{(x + 2)^2}{25} - 3[/tex]
Which is best represented by graph B.
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Write the equation in slope-intercept form of the line that has slope
3 and y-intercept (0,1)
Answer:
y = 3x + 1
Step-by-step explanation:
The formula for equation of a line in slope intercept form is;
y = mx + c
Where;
m is slope
c is y-intercept
Now, since we have coordinates, we will get the equation as;
(y - y1)/(x - x1) = m
(y - 1)/(x - 0) = 3
y - 1 = 3x
y = 3x + 1