The point M on the line of equation 3x + y + 4 = 0 that is closest to the point (-3, 2) is (-21/10, 23/10) or (-2.1, 2.3).
To find the point M on the line 3x + y + 4 = 0 that is closest to the point (-3, 2);
1. First, find the slope and the y-intercept of the given line. Rewrite the equation in slope-intercept form (y = mx + b):
y = -3x - 4
The slope (m) of the line is -3 and the y-intercept (b) is -4.
2. The slope of a perpendicular line is the negative reciprocal of the original slope. So, the slope of the perpendicular line is 1/3.
3. The point (-3, 2) lies on this perpendicular line. Use the point-slope form (y - y1 = m(x - x1)) to find the equation of the perpendicular line:
y - 2 = (1/3)(x + 3)
4. Solve the equation for y:
y = (1/3)x + 3
5. Now, we have two lines:
Original line: y = -3x - 4
Perpendicular line: y = (1/3)x + 3
6. To find the point M where these lines intersect, set the equations equal to each other:
-3x - 4 = (1/3)x + 3
7. Solve for x:
-3x - (1/3)x = 3 + 4
-10x/3 = 7
x = -21/10
8. Substitute x back into either equation to find the corresponding y-coordinate. We will use the original line equation:
y = -3(-21/10) - 4
y = 63/10 - 4
y = 23/10
9. The point M is (-21/10, 23/10) or (-2.1, 2.3).
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angle 1 and angle 2 are complementary angles. If measure angle 1 =6x - 15 and measure angle 2= 3x + 6, find measure angle 2.
Answer:
39
Step-by-step explanation:
Complementary angles add up to 90.
(6x - 15) + (3x + 6) = 90
9x - 9 = 90
9x = 99
x = 99/9 = 11
m∠2 = 3(11) + 6 = 39
What is the slope of a line that passes through the points (4, - 3) and (- 2, 9)
Answer:
-2
Step-by-step explanation:
slope = y2 - y1 / x2 - x1
= 9 - (-3) / -2 -4
= 12 / -6
= -2
evaluate each function at the given value using synthetic substitution
1-4
vikas ranks 9th in the class. how many students are there in the class? statements : 1) his friend got the 35th rank which is the last rank. ii) his rank from the last is 27th
There are total 35 students in the class.
Given that,
Vikas ranks 9th in the class,
Assume that there are 'n' number of students in the class
Therefore,
There are 8 students who have scored better than him.
So, The total number of students with a rank better or equal to Vikas,
= 8 + 1 (Vikas himself)
= 9.
Now, his friend got the 35th rank which is the last rank
This means that there are a total of 35 students in the class.
Also, also given that,
Vikas's rank from the last is 27th,
This means that there are 26 students who have scored lower than Vikas.
So, the total number of students with a rank worse or equal to Vikas,
= 26 + 1 (Vikas himself)
= 27.
Therefore, The total number of students in the class = 35.
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COULD SOMEONE HALP MEH PLS!?!?
I’ll give brainliest! =-=
Answer:
its clearly 74
Step-by-step explanation:
are you gay or sum
Answer: g 26
Step-by-step explanation: 100-48= 52
52/2=26
1. s = 1/2(u+v)t
make u the subject and show the steps plz
2. p/2 = √t +r /9
make t the subject and show the steps plz
WHATS THE ANSWER PLS TELL ME
The linear equation in the given graph is.
y = 40x
How to write the linaer equation?We know that the general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept, these two values are constants, and the variables are x and y.
First, notice that the line intercepts the y-axis at the point (0, 0), then b = 0.
So we can write:
y = a*x
Also notice that the line passes through the point (1, 40), then:
40 = a*1
40/1 = a
The linear equation is.
y = 40x
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Solve A=1/2(bh) for h
Answer: 2A/b = h
Step-by-step explanation: First, get rid of the fraction by multiplying both sides of the equation by 2. That gives us 2A = bh.
Don't be thrown off by the capital A in this problem.
Just treat it like any other variable.
To get h by itself on the right side of the equation, we now simply
divide both sides of the equation by b and our answer is 2A/b = h.
Take a look back at the formula now in the
original problem, A = 1/2bh, does that look familiar?
What should be added to a⁴+a²+1 to make it a perfect square
Answer:
\(a ^{2} \)
a^4 + a^2 + 1
a^4 + a^2 + x + 1
a^2 ( a^2 + 1) + 1 ( x + 1)
so, here clearly we can see that If wee add a^2 in place of x it would be a perfect square..
Hope it helpz~
A stream of crude oil has a molecular weight of 4.5x10² kg/mol and a mean average boiling point of 370 °C. Estimate the followings: 1. The crude specific gravity at 60 °F? 2. The crude gravity (API°) at 60 °F? 3. Watson characterization factor? 4. Refractive index? 5. Surface tension? 6. Is this crude oil paraffinic, naphthenic or aromatic? Explain, briefly and qualitatively.
The crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.
Specific gravity at 60 °F: 0.88
API° at 60 °F: 28
Watson characterization factor: 1.014
Refractive index: 1.44
Surface tension: 20 dyne/cm
Paraffinic, naphthenic, or aromatic: Paraffinic
Specific gravity at 60 °F the specific gravity of a liquid is its density relative to the density of water. The specific gravity of crude oil is typically between 0.8 and 1.0. A specific gravity of 0.88 means that the crude oil is 88% as dense as water.
API° at 60 °F: The API°, or American Petroleum Institute gravity, is a measure of the lightness or darkness of crude oil. A higher API° indicates a lighter crude oil. A crude oil with an API° of 28 is considered to be a medium-heavy crude oil.
Watson characterization factor the Watson characterization factor is a measure of the aromaticity of crude oil. A higher Watson characterization factor indicates a more aromatic crude oil. A crude oil with a Watson characterization factor of 1.014 is considered to be a paraffinic crude oil.
Refractive index the refractive index of a liquid is a measure of how much light is bent when it passes through the liquid. The refractive index of crude oil is typically between 1.4 and 1.5. A refractive index of 1.44 indicates that the crude oil is slightly more refractive than water.
Surface tension the surface tension of a liquid is a measure of the force that acts at the surface of the liquid, tending to minimize the surface area. The surface tension of crude oil is typically between 20 and 30 dyne/cm. A surface tension of 20 dyne/cm indicates that the crude oil has a relatively high surface tension.
Based on the estimated values, the crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.
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Justine wants to go to the school dance next week, but only if her friend kelly goes. she asks her mom to go, saying she will complete all her homework on time. her mom says she can go to the dance as long as she completes all her chores for the week. using this situation, describe the concepts of conditional probability and independent and dependent events and how they relate to justine’s situation.
Justine only goes when her friend goes [Conditional probability].
Mom going to PROM and Justine going to PROM are separate events. [Independent events].
Mom can't go until she finishes the housework is dependent on events
independent events. [Dependent events]
What is probability?The probability exists in the analysis of the possibilities of happening of a result, which exists acquired by the ratio between favorable cases and possible cases.
Conditional probability directs to the possibility that some outcome happens given that another possibility contains also occurred.
Justine only goes when her friend goes [Conditional probability]
Independent events exist as those possibilities whose occurrence exists not dependent on any other event.
Mom going to PROM and Justine going to PROM are separate events. [Independent events]
Dependent events exist that depend upon what occurred before.
Mom can't go until she finishes the housework is dependent on events
independent events. [Dependent events]
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The diagram shows a sector of a circle radius 10cm
angle=135 degrees
find the perimeter and area of the sector , giving your answer correct to 1 decimal place
Area of the sector = 117.75 sq.cm and Perimeter = 43.55 cm.
What is a Circle ?A circle is a round shaped figure , All the points of the plane lie in the same plane.
It is given that the radius of the sector of the circle is given by 10cm
Angle of the sector is 135 degree
Perimeter = ?
Area = ?
\(\rm Area \; of\; the \; sector = \dfrac{\theta}{360} \pi r^2\)
\(\rm \theta =\) 135 degree
Area of the sector = (135/360) * π *(10)²
Area of the sector = 117.75 sq.cm
The Perimeter = (\(\rm \theta\)/360) *π *d +r+r
Perimeter = (135/360) *3.14 *20 + 10+10
Perimeter = 43.55 cm
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Roll a number cube. If the number cube comes up odd, you win the same number of points as the number on the cube. If the number comes up even, you lose 4 points. What is the expected number of points per roll?.
Answer:
-0.5
Step-by-step explanation:
Expected value is found by multiplying the probabilities of each roll by the amount won or lost with each roll.
The odd rolls are 1, 3 and 5. The probability of rolling a 1 is 1/6, and the value is 1; this gives us 1/6(1) = 1/6.
The probability of rolling a 3 is 1/6, and the value is 3; this gives us 1/6(3) = 3/6.
The probability of rolling a 5 is 1/6, and the value is 5; this gives us 1/6(5) = 5/6.
Rolling any even number gives us the same value. The probability of rolling an odd number is 3/6, and the value is -4; this gives us 3/6(-4) = -12/6.
Together we have
1/6+3/6+5/6-12/6 = 4/6+5/6-12/6 = 9/6-12/6 = -3/6 = -0.5
(look at the image) can i get help with these 2 questions?
Answer:
18. ∠AED= ∠BEC (vert. opp. ∠s)
2x -11= 105
2x= 105 +11
2x= 116
x= 116 ÷2
x= 58
∠AEB= 180° -105° (adj. ∠s on a str. line)
∠AEB= 75°
∠BEC= 105° (vert. opp. ∠s)
∠CED= ∠AEB (vert. opp. ∠s)
∠CED= 75°
∠AED= 105° (given)
19. ∠AEB +∠BEC= 180° (adj. ∠s on a str. line)
6x +19 +x= 180
7x +19= 180 (simplify)
7x= 180 -19 (-19 on both sides)
7x= 161 (simplify)
x= 161 ÷7
x= 23
∠AEB= 6(23) +19
∠AEB= 157°
∠BEC= 23°
∠CED= ∠AEB (vert. opp. ∠s)
∠CED= 157°
∠AED= ∠BEC (vert. opp. ∠s)
∠AED= 23°
find the measure od abc
1.- The sum of the internal angles in a triangle equals 180°.
8x + 5x + 6x = 180°
19x = 180
x = 180/19
x = 180/19
2.- Calculate angle ABC
ABC = 8x
ABC = 8(180/19)
ABC = 1440 / 19
ABC = 75.8°
Please explain how to do this!
Answer:
0.05 hours
Step- by- step explanation:
2.75 - 2.00 = 0.75 Time(Hours)
45 - 30 = 15 Area (Square meters)
0.75 ÷ 15 = 0.05 hours
Hope this helps ^◇^
assume that a customer shops at a local grocery store spending an average of $ a week, resulting in a retailer profit of $ each week from this customer. assuming the shopper visits the store all 52 weeks of the year, calculate the customer lifetime value if this shopper remains loyal over a 10-year life span. also assume a percent annual interest rate and no initial cost to acquire the customer.
"The customer yields $780 per year in profits for this retailer."
Customer lifetime value (CLV) is a prediction of the total value a customer will bring to a business over their entire relationship with the company. Retailer profits refer to the financial gain a retailer makes after subtracting all costs, including the cost of goods sold, operating expenses, and taxes, from the revenue generated by their retail sales.
The customer spends $250 a week, so the retailer profits:
= $250 - $235= $15 from each visit.If the shopper visits the store every week for a year, the retailer profits:
= $15 x 52= $780 per yearIf this shopper remains loyal for a 10-year lifespan, the retailer profits:
= $780 x 10= $7,800This is the CLV without considering inflation or any other factors. To consider inflation, we can apply the 8% annual interest rate to calculate the present value of the future profits. The present value of $7,800 over 10 years with an 8% interest rate is approximately $5,100 (the exact value will depend on the method used to calculate the present value).
This question should be provided as:
Assume that a customer shops at a local grocery store spending an average of $250 a week, resulting in a retailer profit of $15 each week from this customer. Assuming the shopper visits the store all 52 weeks of the year, calculate the customer lifetime value if this shopper remains loyal over a 10-year life span. Also assume a 8 percent annual interest rate and no initial cost to acquire the customer.
The customer yields $_____ per year in profits for this retailer.
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Today’s weather report states that it is highly likely to snow today. Which probability best represents the chance of snow today?
A.
0.05
B.
0.50
C.
0.95
D.
1.00
Assume a standard Normal distribution. Draw a​ well-labeled Normal curve for each part.
a. Find the​ z-score that gives a left area of 0.6768.
b. Find the​ z-score that gives a left area of 0.1332.
a. The z-score is approximately 0.43.
Draw the Normal curve and shade the area to the left of the z-score.
b. The corresponding z-score is approximately -1.10.
Draw the Normal curve and shade the area to the left of the z-score.
A standard Normal distribution means that we have a bell-shaped curve with a mean of 0 and a standard deviation of 1. A Normal curve, we can use a graphing calculator or a standard Normal distribution table.
a. The z-score that gives a left area of 0.6768, we need to look up the value in the Standard Normal distribution table. A printed table or an online calculator to find that the z-score is approximately 0.43.
Draw the Normal curve and shade the area to the left of the z-score.
b. To find the z-score that gives a left area of 0.1332, we can again use the Standard Normal distribution table.
This time, we look up the area that corresponds to 0.1332 and find that the closest value is 0.1335.
The corresponding z-score is approximately -1.10.
We can then draw the Normal curve and shade the area to the left of the z-score.
To draw a well-labeled Normal curve for each part, we first need to find the corresponding z-score using a Standard Normal distribution table.
The z-score to shade the area to the left of the curve and label the mean and standard deviation on the x-axis.
Drawing the Normal curve helps us visualize the distribution and calculate probabilities for various events.
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During each week of piano lessons, Nate learns to play 1 new piece. Is the total number of piano pieces Nate learns proportional to the number of weeks he takes lessons?
Answer:
Yes
Step-by-step explanation:
1 piece per week can be written as a 1:1 ratio
$\bullet$ $\$2.41$ for the first pound $\bullet$ $\$0.41$ per additional pound for the next six pounds $\bullet$ $\$0.39$ per additional pound after that for example, a two-pound package costs $\$2.82$ to send by media mail. if a package full of books costs $\$7.99$ to send by media mail, how many pounds does the package weigh? explain your work in complete sentences.
The package weighs approximately 10.9 pounds.
Let's assume the weight of the package in pounds is "x". We can break down the cost of sending the package by media mail into three parts:
1. The cost for the first pound: $2.41.
2. The cost for the additional pounds up to six pounds: $0.41 per pound.
3. The cost for the additional pounds beyond six pounds: $0.39 per pound.
To determine the weight of the package, we need to solve the equation based on the given information:
Cost = $2.41 + $0.41 * (x - 1) + $0.39 * (x - 7)
We know that the cost of sending the package is $7.99, so we can set up the equation as follows:
$7.99 = $2.41 + $0.41 * (x - 1) + $0.39 * (x - 7)
Now, we can solve this equation to find the value of "x," which represents the weight of the package.
$7.99 - $2.41 = $0.41 * (x - 1) + $0.39 * (x - 7)
$5.58 = $0.41x - $0.41 + $0.39x - $2.73
$5.58 = $0.8x - $3.14
$0.8x = $8.72
x ≈ 10.9
Therefore, there are around 10.9 pounds in the bundle.
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Answer:10.9
Step-by-step explanation:
A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.
Answer)
a
hope this helps
Please Help Me Guys :)
Answer:
5. x=80°, y= 80°
Step-by-step explanation:
5.x=80 (Vertically opposite angle V.O.A)
y=80 (alternate angle)
Help me out with this question!! 50 points
C
The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C
The correct answer is D) The first inequality should be s + h ≤ 1800.
The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.
The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.
i need help with this asap
dexide whether pait of angles
1 and 2
4 and 3
5 and 6
arw alternate interior angles
alternate exterior angles
corresponding anglws
same side intetior angles
Answer:
1 and 2 is corresponding angles
4 and 3 is alternate interior angles
5 and 6 corresponding angles
Factorise x^2 + x - 12
Answer:
(x+4)(x-3)
Step-by-step explanation:
I'm italian. I used a formula that we Italians call "somma e prodotto". Tell me if it's correct.
- 71 = x/64
One step
Answer:
x=-4544
Step-by-step explanation:
- 71 = x/64
Multiply each side by 64
- 71 *64 = x/64 *64
x=-4544
Answer:
x=−4544
Step-by-step explanation:
0.1 (0.5 + 6) = 2
I thank you a million who ever helps me
Answer:
m = 28
Step-by-step explanation:
Simplifying
0.1(0.5m + 6) = 2
Reorder the terms:
0.1(6 + 0.5m) = 2
(6 * 0.1 + 0.5m * 0.1) = 2
(0.6 + 0.05m) = 2
Solving
0.6 + 0.05m = 2
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '-0.6' to each side of the equation.
0.6 + -0.6 + 0.05m = 2 + -0.6
Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 0.05m = 2 + -0.6
0.05m = 2 + -0.6
Combine like terms: 2 + -0.6 = 1.4
0.05m = 1.4
Divide each side by '0.05'.
m = 28
Simplifying
m = 28
LOL WAS I CORRECT EXPLANATION= BRAINLIST CROWN
Answer:
yes, it is correct. Why weren't you sure?
HELP PLEASE GIVING BRAINLIEST!!!
Answer:
161
Step-by-step explanation: