Answer:
y = 3x - 13
Step-by-step explanation:
We are given the points (7,8) and (3,-4)
We want to write an equation of the line that passes through those 2 points.
There are 3 ways to write the equation of the line:
Slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y intercept.Standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0 and a cannot be negative. 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.Although while any one of these options work, the most common way is to use slope-intercept form, so let's do it that way.
First, we need to find the slope of the line.
The slope (m) can be found using this formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are points.
Even though we already have 2 points, let's label their values to avoid any confusion.
[tex]x_1=7\\y_1=8\\x_2=3\\y_2=-4[/tex]
Now substitute these values into the formula.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-4-8}{3-7}[/tex]
Subtract.
m=[tex]\frac{-12}{-4}[/tex]
Divide.
m = 3
The slope of the line is 3.
Here is the equation of the line so far:
y = 3x + b
We now need to find b.
As the equation passes through (7,8) and (3,-4), we can use either one of the points to help us solve for b.
Taking (7,8) for instance:
Substitute 7 as x and 8 as y in the equation.
8 = 3(7) + b
Multiply
8 = 21 + b
Subtract 21 from both sides
-13 = b
Substitute -13 as b in the equation.
y = 3x - 13
Topic: finding the equation of the line
See more: https://brainly.com/question/27951490
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line that passes through the points (7,8) and (3,-4) is y=3x-13.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The slope of the equation will be,
Slope, m = (-4-8)/(3-7) = -12/-4 = 3
Substitute one of the points in the equation of the line,
-4 = 3(3) + C
C = -13
Hence, the equation of the line that passes through the points (7,8) and (3,-4) is y=3x-13.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ1
Match each problem to its solution 8,8.2,9,56.25
The computation shows that the amount will be:
$56.25.$988.2 poundsHow to compute the values?Jonah earns $12.50 per hour
He works for 4.5 hours
Amount he earned will be:
= 12.50 × 4.5 = $55.25
Items worth is $41.23
Amount paid is $50.23
Extra amount paid will be:
= 50.23 - 41.23
= $9
Length of cloth available is 20 m
Length of one long-sleeved blouse is 2.5m
Number of blouses that can be made will be:
= 20/2.5 = 8
Potatoes weight is 3.2 pounds
Oranges weight is 2.3 pounds
Onions weight is 2.7 pounds
Total weight of the purchase will be:
= 3.2 + 2.3 + 2.7 = 8.2 pounds
Learn more about the computation of amount on:
https://brainly.com/question/20038451
#SPJ1
Complete question:
Match each problem to its solution. 8 8.2 9 56.25 Jonah earns $12.50 per hour as a marketing intern. If he works for 4.5 hours, how many dollars does he earn? arrowRight Jessica purchased items worth $41.23 at the local grocery store. The cashier made a mistake while ringing up her items, and Jessica ended up paying $50.23. How many extra dollars did she pay? arrowRight Josie has 20 meters of cloth. She needs to make long-sleeved blouses with that cloth. If one long-sleeved blouse requires 2.5 meters of cloth, how many blouses can she make with the material? arrowRight Jeremy bought 3.2 pounds of potatoes, 2.3 pounds of oranges, and 2.7 pounds of onions. How many pounds does his purchase weigh? arrowRight
Solve for x. Round to the nearest tenth, if necessary.
K
Answer:
0.5
Step-by-step explanation:
The sides opposite and adjacent to the given angle are shown in this right triangle. The relation between them is given by the tangent trig function:
Tan = Opposite/Adjacent
tan(63°) = 1/x
Solve for xWe can multiply this equation by x/tan(63°) to find the value of x:
x = 1/tan(63°) ≈ 1/1.96261 ≈ 0.509525
The length x is about 0.5 units.
I need help please. Trying to get my HS diploma. I did not graduate :(
Which of the following is the graph of f(x)+1?
The graph of f(x) + 1 is the graph in the option C.
Which is the graph of f(x) + 1?
For a given function f(x), a vertical translation is written as:
g(x) = f(x) + N
If N > 0, then the translation is upwards.If N < 0, then the translation is downwards.Here we have g(x) = f(x) + 1, so we have a translation of 1 unit upwards, the graph of f(x) + 1 is the graph of f(x) but translated one unit upwards.
From that, we conclude that the correct option is C.
If you want to learn more about translations:
https://brainly.com/question/24850937
#SPJ1
If the width of the dining room table is w feet, and the length is 3w - 2 feet, write an
algebraic expression that represents the perimeter of the table.
Answer:
2(w)+2(3w-2), or, 8w-4Step-by-step explanation:
The formula for finding the perimeter is 2w+2L (2*width + 2*length)
So, since we know the width is "w" and the length is "3w-2", we can just substitute those into the equation.
2(w)+2(3w-2)
From there, if needed, you can simplify to:
2w + 6w-4
Add like terms:
8w - 4
Hope that helps.
What is the least
common multiple of 12 and 16?
Answer: 48
Explanation: 16 x 3 = 48, 12 x 4 = 48
1. (y + x) = 4; use x = 2 and y = 2
2. x + y ÷ 6; use x = 5 and y = 6
3. y(x + 5); use x = 1 and y = 4
4. q-m+q; use m = 3 and q = 6
Step-by-step explanation:
1-)2+2=4
2-)5+6÷6=6
3-)4(1+5)=24
4-)6-3+6=9
pleasee help!!!!
20 points
The function with the same end behavior of f(x) is the last option:
[tex]g(x) = (-\frac{1}{3} )*x[/tex]
Which function has the same end behavior of f(x)?
By looking at the graph, we can see that the end behavior of f(x) is:
as x → ∞; f(x) → -∞
as x → -∞; f(x) → ∞
Then we just want a function that depends linearly with x and that has a negative coefficient.
The correct option is the last one:
[tex]g(x) = (-\frac{1}{3} )*x[/tex]
Where clearly, when x tends to infinity the function tends to negative infinity, and when x tends to negative infinity, the function tends to infinity.
If you want to learn more about end behavior:
https://brainly.com/question/1365136
#SPJ1
Use the Empirical Rule to determine the percentage of candies with weights between 0.7 and 0.98 gram. Hint: x=0.84
Using the Empirical Rule, it is found that 95% of the candies have weights between 0.7 and 0.98 gram.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Researching this problem on the internet, we have that:
The mean is of 0.84.The standard deviation is of 0.07.Then 95% of the candies have weights between 0.7 and 0.98 gram, as:
0.7 = 0.84 - 2 x 0.07.0.98 = 0.84 + 2 x 0.07.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
#SPJ1
A student hypothesized that in the US adult population, women drank the same amount of water per day as men per kg of body weight as the null hypothesis. The probability value for her null hypothesis was 0.02. Assume the alpha level was 0.05. Which conclusion is justified?
The conclusion that is justified based on the research is that he rejected the null hypothesis that women drank the same amount of water per kg of body weight per day as men.
How to illustrate the research?It should be noted that a research is simply used to get information about a topic.
In this case, it can be deduced that a type 1 error is committed. This implies the rejection of the null hypothesis when it's true.
Learn more about research on:
brainly.com/question/25257437
#SPJ1
15 people were asked to measure their pulse rates after completing a 3 km run. The sample data are given below and are assumed to be normally distributed. Use a TI-83, TI-83 plus, or TI-84 calculator to construct a 98% confidence interval for the mean of the population. Round your answers to two decimal places and use increasing order.
Using the t-distribution, the 98% confidence interval for the mean of the population is (99.21, 110.79).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.Researching the problem on the internet, the data-set is given as follows:
104, 102, 103, 105, 125, 106, 107, 110, 110, 95, 108, 86, 112, 101, 101.
The parameters are given as follows:
[tex]\overline{x} = 105, s = 8.54, n = 15[/tex].
The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 15- 1 = 14 df, is t = 2.6245.
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 105 - 2.6245\frac{8.54}{\sqrt{15}} = 99.21[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 105 + 2.6245\frac{8.54}{\sqrt{15}} = 110.79[/tex]
More can be learned about the t-distribution at https://brainly.com/question/16162795
#SPJ1
The surface area of a cone with radius r units and slant height s units is shown below:
30 points
Surface area = 3.14(rs + r2)
Part A: If r = 3 units and s = 5 units, write an expression that can be used to calculate the surface area of the cone. (4 points)
Part B: What is the surface area of the cone? Show your work. (6 points)
Step-by-step explanation:
part A:
[tex]Area_{_{surface}}=3.14*(3*5+3^2);[/tex]
part B:
[tex]Area_{_{surface}}=3.14*(15+9)=3.14*24=75.36[units^2].[/tex]
Identity the x-intercept of the liner equation 3x + y -9=0
Answer:
The x intercept is 3
(3,0)
Step-by-step explanation:
3x+y -9 =0
To find the x intercept, set y=9 and solve for x.
3x+0-9=0
3x -9=0
Add 9 to each side
3x-9+9=9
3x =9
Divide by 3
3x/3 = 9/3
x =3
The x intercept is 3
(3,0)
Which of the following is equivalent to 6^2/5
Where are the options?
Select the equation of the line that passes through the point (–2, 1) and has slope 3 in point-slope form.
(x – 2) = 3(y + 1)
(y + 1) = 3(x – 2)
(y – 1) = 3(x + 2)
(x + 2) = 3(y – 1)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Select the equation that passes through (-2,1) and has slope 3
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
Formula used, here [tex]\bf{y-y1=m(x-x1)}[/tex]
[tex]\bf{y-1=3(x-(-2)}[/tex] | put in the values, then, simplify
[tex]\bf{y-1=3(x+2)}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=y-1=3(x+2)}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic \not1\theta l}}[/tex]
∞
What is the base of the expression ? 3 11 12 21
Answer:
[tex]11[/tex]
[tex]a {}^{b} [/tex]
a is the base and b is the exponent.
Step-by-step explanation:
HOPE THIS HELPS.
On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform B and zip to the other platform. What is the coordinate when you reach half way?
what is the midpoint
The distance from Platform B to Platform C is 26.926 units
The given parameters are;
The zip-line course distance from platform A to platform F is given;
On the given graph of the path of travel we have;
Coordinates of the point B = (-25, -20) and the coordinates of the point C = (-15, 5).
What is the distance formula?
The distance between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by the formula
[tex]l=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Therefore, the distance between B and C is found by substituting (-25, -20) = (x₁, y₁) and (-15, 5) = (x₂, y₂)
Which gives
[tex]l=\sqrt{(5-(-20))^2}+((-15)-(-25))^2\\l=26.926 units[/tex]
The distance from points B to C = 26.926 units. The distance from Platform B to Platform C is 26.926 units.
To learn more about the distance visit:
https://brainly.com/question/2854969
#SPJ1
which of the fallowing is a mononial
Answer:
A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with a single term but can have multiple variables and a higher degree too. For example, 9x3yz is a single term, where 9 is the coefficient, x, y, z are the variables and 3 is the degree of monomial.
A summer camp cookout is planned for the campers and their families. there is room for 450 people. each adult costs $7, and each camper costs $4. there is a maximum budget of $1,150. write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers. x y ≤ 1,150 7x 4y ≤ 450 x y ≤ 450 7x 4y ≤ 1,150 x y ≤ 1,150 4x 7y ≤ 450 x y ≤ 450 4x 7y ≤ 1,150
Hence, the required inequality is x+y≤4, 7x+4y≤1150
What is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
How to solve?Let x be the number of adults and y be the number of campers.
There are rooms for 450 people, so
x+y≤450.
Each adult costs $7, then x adults cost $7x.
Each camper costs $4, then y campers cost $4y.
There is a maximum budget of $1,150, so
7x+4y≤1,150
Hence, you get the system of two inequalities:
x+y≤4
7x+4y≤1150
to learn more about inequality: https://brainly.com/question/16562548
#SPJ4
Answer:
x + y [tex]\leq[/tex] 450
7x + 4y [tex]\leq[/tex] 1,150
Step-by-step explanation:
X and Y is the amount of people it can fit.
7 and 4 is the amount of money for each person.
7x is the amount per adult, 4y is the amount per camper.
Hope this helps.
whats the rule (-2,-7) (0,-1) (7, 22)
The rule of the points is y = 3.2x - 0.7
How to determine the rule?The points are given as:
(-2,-7) (0,-1) (7, 22)
The above points form an approximate linear equation.
So, we make use of a linear regression to determine the rule
When the above points are entered in a statistical calculator, we have the following summary:
Sum of X = 5Sum of Y = 14Mean X = 1.6667Mean Y = 4.6667Sum of squares (SSX) = 44.6667Sum of products (SP) = 144.6667The regression equation is then represented as:
y = bx + a
Where
b = SP/SSX = 144.67/44.67 = 3.23881
a = MY - bMX = 4.67 - (3.24*1.67) = -0.73134
This gives
y = 3.23881x - 0.73134
Approximate
y = 3.2x - 0.7
Hence, the rule of the points is y = 3.2x - 0.7
Read more about regression at:
https://brainly.com/question/17844286
#SPJ1
QUICK PLEASE. George invested $1000 for 4 years. If the investments earned 5.5% compounded weekly, how many compounding period would occur and what is the interest rate?
The number of compounding period is 52.
The interest rate is 0.11%.
What is the compounding period and interest rate?The compounding period is the number of times the investment would earn a compound interest in a year. Because interest is compounded weekly, the compounding period would be equivalent to the number of weeks in a year. This is 52.
Interest rate = yearly interest / compounding period
5.5 / 52 = 0.11%
To learn more about compound interest, please check: https://brainly.com/question/26367706
#SPJ1
Which expressions are equivalent to √1,120y? Select three options.
√√2-2-2-2-5-7-y-y
√2² √2² √2² √5² √7²√√
√2² √2² √2. √5.17.√7.SY
02.2.y√2-5-7-y
4y√70y
The expression that is equivalent to √1,120y is: 4√70y.
What are Equivalent Expressions?Expressions are said to be equivalent when the value of one is the same as the value of the other when evaluated or simplified.
Given the expression, √1,120y, we can simplify as shown below:
√(16 × 70 × y)
= 4√70y
Thus, 4√70y is equivalent to √1,120y .
Learn more about equivalent expressions on:
https://brainly.com/question/22365614
#SPJ1
Use the function below to find F(1)
Answer:
[tex]B: \frac{1}{2}[/tex]
Step-by-step explanation:
Plug 1 in as t
[tex]F(1) = 4 * \frac{1}{2^{3(1)}}[/tex]
Simplify the exponent 3*1
[tex]F(1) = 4 * \frac{1}{2^{3}}[/tex]
Cube the 2
[tex]F(1) = 4 * \frac{1}{8}[/tex]
Multiply:
[tex]F(1) = \frac{4}{8}[/tex]
Simplify:
[tex]F(1)=\frac{1}{2}[/tex]
WHAT IS THE VALUE OF THE EXPRESSION 8 MORE THEN 3 TIMES THE DIFFRENCE OF 4 AND A NUMBER WHEN N=3
The value of the expression as described in the task content is; 11.
What is the value of the expression?The expression as described in the task content is; 3(4 - N) +8.
However, the value of N in this scenario is; 3.
Therefore, the value of.the expression is;
3(4 - 3) +8
= 3(1) + 8
= 3+8
= 11.
Read more on value of expressions;
https://brainly.com/question/625174
#SPJ1
The equation 5x2 30x 15 = 0 is being rewritten in vertex form. fill in the missing step. given 5x2 30x 15 = 0 step 1 ✔ step 2 5(x2 6x 9) 15 − 45 = 0 step 3 5(x 3)2 − 30 = 0 5(x2 30x ___) 15 ___ = 0 5(x2 30x ___) − 15 ___ = 0 5(x2 6x ___) − 15 ___ = 0 5(x2 6x ___) 15 ___ = 0
The missing step in making the equation in vertex form is option D which is
[tex]5(x^{2} +[/tex]6x____)+15.
Given Equation [tex]5x^{2} +30x+15=0[/tex]
Parabola in vertex form. Equation is a relationship between two or more variables which is expressed in equal to form. It is solved to find the variables.
To express the equation of a parabola in vertex form we must complete squares. The equation is given as
[tex]5x^{2} +30x+15=0[/tex]
The first step is to factor 5 and leave space to complete the third term in the parenthesis, along with a space outside it to compensate. This should look like
([tex]5(x^{2} +6x............)+15..........=0[/tex]
Those spaces need to be filled out like shown in the step 2. Thus the correct step is D.
Hence the correct step in vertex form is D which is
[tex]5(x^{2} +6x[/tex]___-)+15____=0.
Learn more about equations at https://brainly.com/question/2972832
#SPJ4
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.Find the probability that the person has an IQ score between 92 and 108.
Using the normal distribution, it is found that there is a 0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
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.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 100, \sigma = 15[/tex].
The probability that the person has an IQ score between 92 and 108 is the p-value of Z when X = 108 subtracted by the p-value of Z when X = 92, hence:
X = 108:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{108 - 100}{15}[/tex]
Z = 0.53
Z = 0.53 has a p-value of 0.7019.
X = 92:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{92 - 100}{15}[/tex]
Z = -0.53
Z = -0.53 has a p-value of 0.2981.
0.7019 - 0.2981 = 0.4038.
0.4038 = 40.38% probability that the person has an IQ score between 92 and 108.
More can be learned about the normal distribution at https://brainly.com/question/4079902
#SPJ1
Which of the following models the context "A plumber who charges $50 for a
house call and $85 per hour"?
Answer:
a. y = 85x + 50
Step-by-step explanation:
a. y = 85x + 50
Please answer this question
Answer: B
Step-by-step explanation:
The factors of 1 are [tex]\pm 1[/tex]
The factors of 20 are [tex]\pm \{1, 2, 4, 5, 10, 20\}[/tex].
By the rational root theorem, we see that the answer is B.
A family has to travel 380 miles to reach their vacation spot. They plan to stop for lunch after driving 2/5 of the distance. How far will they have traveled when they stop for lunch?
Answer:
152 miles
Step-by-step explanation:
380/5 = 76
76*2 = 152
as they will have traveled 2/5, you would need to divide your miles by 5 then multiply by 2!
Tony made 14 { L}14 L14, start text, space, L, end text of lemonade for a party. His guests drank 9,500 { mL}9,500 mL9, 500,m, L, end text of the lemonade.
How many milliliters of lemonade did Tony have left over?
Unit conversion is a way of converting some common units into another without changing their real value. The lemonade left with Tony is 4500ml.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
One litre is equal to 1000 millilitres. Tony made 14 Liter of lemonade, therefore, Tony made 14,000 millilitres of lemonade. His guest drank 9500 millilitres. Therefore, the lemonade left with Tony is,
Lemonade left = 14,000 - 9,500 = 4,500 ml
Hence, the lemonade left with Tony is 4500ml.
Learn more about Units conversion:
https://brainly.com/question/4736731
#SPJ1
Dwight Donovan, the president of Finch Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of five years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $103,000 and for Project B are $41,000. The annual expected cash inflows are $34,441 for Project A and $12,522 for Project B. Both investments are expected to provide cash flow benefits for the next five years. Finch Enterprises’ desired rate of return is 8 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.)
1. The computation of the net present value of each project is as follows:
Project A Project B
NPV $36,523 $9,000
2. Based on the net present value approach, Project A should be adopted, instead of Project B.
What is the net present value?The net present value is the difference between the costs and the annual cash inflows discounted to their present values.
Data and Calculations:Project A Project B
Initial costs $103,000 $41,000
Annual cash inflows $34,441 $12,522
Project live 5 years 5 years
Rate of return 8% 8%
Annuity factor 3.993 3.993
PV of cash inflows $139,523 $50,000
NPV $36,523 $9,000
Question Completion:1. Compute the net present value of each project.
2. Which project should be adopted based on the net present value approach?
Thus, based on the net present value approach, Project A should be adopted.
Learn more about the net present value at https://brainly.com/question/13228231
#SPJ1