Answers
Answer:
the equation of a straight line which is of the form y = mx + b, is called the slope intercept form. Here 'm' is the slope of the line and 'b' is the point at which the line intercepts the y - axis. An example for slope intercept form equation is y = 3x + 5.
Step 1: Write equation in slope- intercept form
To start off, let’s write the formula for slope- intercept form. After we know this, we will continue to substitute information.
y= mx+ b
Step 2: Find y- intercept
Let’s begin by finding the y- intercept. This is the point that falls directly on the y- axis. After we find the y- intercept, we will be able to eliminate two of the options; answer A and C state that the y- intercept is positive 4 and answer B and D say that the y- intercept is negative 4.
Since the line crosses 4 on the y- axis on the top part of the graph, the y- intercept is positive 4. Let’s substitute this into the equation.
y= mx+ b
y= mx+4
Step 3: Find slope
Now that we have updated the equation, let’s find the slope. This will be the final part of the equation. Keep in mind that the only remaining options are A and C, in which the slope is said to be either 3 or -3.
To find the slope, let’s find two points, and use the rise/ run formula. For the sake of this problem, we will use (0,4) and (1,1).
In between these two points, there is a difference of 3/1. This can be reduced to 3; however, since the line on the graph reduces, the slope is negative. This will leave our slope as -3. Let’s put this into our equation.
y= mx+4
y= -3x+4
This is the final equation. Hope this helps! Comment below for more questions.
Related Questions
If Roger were 32 years older, he would be three times as old as he is now. How old is
Roger?
Answers
Answer:
16
Step-by-step explanation:
Set up the equation ->
x+32=3x
(you can get this easily by writing the equation down as you read the problem)
--> revisiting x+32=3x
-x on both sides to isolate the number and put the like terms together
We are left with 32=2x
Divide 2 on both sides, and you will get x (his current age) --> x=16
Roger is currently 16 years old.
Answer:
16
Step-by-step explanation:
3x = 32 + x
2x = 32
x = 16
A laptop was originally sold for $975. The laptop is now on sale for $828.75.The percent markdown must have been...
Answers
Answer:
15% markdown
Step-by-step explanation:
To find the percent markdown
Take the original price minus the new price
975-828.75
146.25
Divide by the original price
146.25/975
.15
Change to percent form
15% markdown
Critical Thinking: Empirical/Quantitative Skills
United flight 15 from New York's JFK to San Francisco uses a Boeing 757-200 with 180 seats. Because some
people with tickets don't show up. United will overbook by selling more than 180 tickets. If the flight is not
overbooked, the airline will lose revenue due to empty seats, but if too many tickets are sold and some
passengers are denied seats, the airline loses money from the compensation that must be given to bumped
passengers. Assume that there is a 0.905 probability that a passenger with a ticket will show up for the
flight. Also assume that the airline sells 200 tickets for the 180 seats that are available.
1. When 200 tickets are sold, calculate the probability that exactly 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Show your calculation (ie. what you put in the calculator) and round to 4 decimals.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
Answers
Answer:
1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume that there is a 0.905 probability that a passenger with a ticket will show up for the flight.
This means that [tex]p = 0.905[/tex]
Also assume that the airline sells 200 tickets
This means that [tex]n = 200[/tex]
Question 1:
Exactly, so we can use the P(X = x) formula, to find P(X = 180).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910[/tex]
0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Now we have to use the approximation.
Mean and standard deviation:
[tex]\mu = E(X) = np = 200*0.905 = 181[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15[/tex]
Using continuity correction, this is [tex]P(X \leq 180 + 0.5) = P(X \leq 180.5)[/tex], which is the p-value of Z when X = 180.5. Thus
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180.5 - 181}{4.15}[/tex]
[tex]Z = -0.12[/tex]
[tex]Z = -0.12[/tex] has a p-value of 0.4522.
0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So
[tex]p + 0.4522 = 1[/tex]
[tex]p = 1 - 0.4522 = 0.5478[/tex]
0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Q25 A train travelling at a speed of 30km/h crosses a bridge 25m long in 12 sec. How long will it take to overtake a another train 25m long travelling at 20km/hr? option given 1. 72 sec 2. 74 sec 3. ,75 sec or data insufficient.
Answers
Answer:
WHAT
Step-by-step explanation:
In 5 days she made 80 sandcastles. Each day she made 4 fewer castles than the day before. How many castles did she make each day?
Answers
Answer:
Castles made: N day 1
N - 4 day 2
N - 8 day 3
N - 12 day 4
N - 16 day 5
Total 5 N - 40 = 80
N = 24 total castles day 1
Total castles = 24 + 20 + 16 + 12 + 8 = 80
Which of the following best describes the use of the formula S = (n- 2)180°,
where n is the number of sides?
Answers
Answer:
It is used to find the sum of the interior angles in a regular polygon.
Step-by-step explanation:
A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 110 feet. The smallest path bordering the patch of grass measures 55 feet. The smallest angle formed by the paths bordering the patch of grass measures 29º.
What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest
degree. Show all your work.
Answers
Answer:
76 degrees
Step-by-step explanation:
First, we can draw a picture. Two of the sides are 110 feet and 55 feet. In a triangle, the smallest angle is opposite the smallest side and vice versa. Therefore, if I have my triangle arranged in the way shown, the smallest angle of 29 degrees will be opposite of the smallest side of 55 feet.
The law of sines states that a/sinA=b/sinB=c/sinC , with corresponding angles being opposite of its corresponding side. Therefore, we can say that
55 feet/ sin(29 degrees) = 110 / sin(largest angle).
If we say that the largest angle is equal to x, we can say
55 / sin(29°) = 110/sin(x)
multiply both sides by x to remove a denominator
55 * sin(x)/ sin(29°) = 110
multiply both sides by sin(29°) to remove the other denominator
55 * sin(x) = 110 * sin(29°)
divide both sides by 55 to isolate the sin(x)
sin(x) = 110 * sin(29°) / 55
For an angle, if sin(x) = y, we can say that arcsin(y) = x. Therefore, we can say
x = arcsin(110 * sin(29°)/55)
x ≈ 76 degrees
A manager records the repair cost for 14 randomly selected dryers. A sample mean of $88.34 and standard deviation of $19.22 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the dryers. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answers
Answer:
Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]
Step-by-step explanation:
Given that,
Point estimate = sample mean = [tex]\bar x[/tex] = 88.34
sample standard deviation = s = 19.22
sample size = n = 14
Degrees of freedom = df = n - 1 = 13
Critical value =[tex]t\alpha /2,[/tex] df = 1.771
Margin of error
[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]
Margin of error = E = 9.10
The 90% confidence interval estimate of the population mean is,
[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]
Solve for x, where x > 0 and 84x(x + 2) = 90-13x. Express your answer as a simplified common fraction.
Answers
84x(x+2) = 84x² + 168x
84x² + 168x = 90 - 13x
84x² +181x - 90 = 0
bhaskara formula
[tex]\frac{-181+-\sqrt{181^{2}- 4.84.(-90) } }{168 } }[/tex]
[tex]\frac{-181+-\sqrt{32.761 +30.240} }{168}[/tex]
[tex]\frac{-181+-251}{168}[/tex]
since its a positive number, we can't use the minus
so, [tex]\frac{70}{168}[/tex]
they're both dividable by 14, so
x = [tex]\frac{5}{12}[/tex] is your answer
hope it helps :)
Pleasant help me out explanation need it
Answers
Answer:
for which question???????????????
Answer:
Ok please tell me your question because you forgotten the question your asking dor
11 + box equals 19 find box
Answers
Answer:
8
Step-by-step explanation:
11 + x = 19
Subtract 11 from each side
11+x -11 = 19-11
x = 8
Answer:
8
Step-by-step explanation:
11 + box = 19
=> box = 19 - 11
.°. box = 8
Alex says that the function f(x)=(3x)^2 represents a vertical stretch of the quadratic parent function by a factor of 3. Marta says that it represents a horizontal compression by a factor of 1/3. Decide whether one student is correct, both are correct, or neither is correct.
Answers
9514 1404 393
Answer:
Marta is correct
Step-by-step explanation:
With respect to parent function g(x), the function g(kx) represents a compression by a factor of 1/k. Here we have k=3, so the function f(x) represents a curve that has distances from the y-axis reduced to 1/3 their parent-function values.
The attached graph shows the horizontal compression.
__
If the expression for f(x) were expanded to ...
f(x) = (3x)^2 = 9x^2
we would then recognize it as a vertical stretch of the parent function by a factor of 9. Alex is correct in that the transformation can be interpreted as a vertical stretch, but he is claiming an incorrect stretch factor.
A father's age is thrice the sum of the ages of his two children. After five years, his age will be
twice the sum of their ages. How old is the father?
Answers
Answer: 45 years old
Step-by-step explanation:
Given:
- Father's age is thrice the sum of ages of his two children
- After five years, his age will be twice the sum of their ages
Let x be the two children's current age and 3x be the father's current age
Solve:
Set equation
3x + 5 = 2 ( x + 10 )
Expand parenthesis
3x + 5 = 2x + 20
Subtract 5 on both sides
3x + 5 - 5 = 2x + 20 - 5
3x = 2x + 15
Subtract 2x on both sides
3x - 2x = 15
x = 15
15 × 3 = 45 years old
Hope this helps!! :)
Please let me know if you have any questions
f(x) = −16x2 + 24x + 16
what is the vertex
Answers
Answer:
VERTEX: (0.75,25)
Step-by-step explanation:
the vertex will be at [-b/2a, f(-b/2a)]
−16x2 + 24x + 16
4(-4x^2 + 6x +4)
a = -4, b=6,c=4
-6/-8 = 3/4
f(3/4) = 25
You are planning table decorations for a wedding. You must have at least one thing on the table. You have 5 identical candles, 4 identical pictures, 3 identical flowers, and 4 identical bowls to choose from. How many ways can you decorate?
answer in permutations
Answers
Answer:
You can decorate the weeding in 240 different ways.
Step-by-step explanation:
Since you are planning table decorations for a wedding, and you must have at least one thing on the table, and you have 5 identical candles, 4 identical pictures, 3 identical flowers, and 4 identical bowls to choose from, to determine how many ways can you decorate the following calculation must be performed:
5 x 4 x 3 x 4 = X
20 x 12 = X
240 = X
Therefore, you can decorate the weeding in 240 different ways.
Hans rented a truck for one day. There was a base fee of $15.95, and there was an additional charge of 77 cents for each mile driven. Hans had to pay
$207,68 when he returned the truck. For how many miles did he drive the truck?
Answers
Answer: 249 miles
Step-by-step explanation:
First write a function that represents the amount paid for renting a truck:
Set x as each mile driven.Set y as the total amount paid.$15.95 is the base fee paid no matter the mile, meaning the rent start at $15.95, not 0.Function: y = mx + b
m = slope = amount paid for each mile driven = 77¢ = $0.77b = y-intercept = amount paid when 0 miles driven = base fee = $15.95y = 0.77x + 15.95
He paid a total of $207.68, therefore y = 207.68:
207.68 = 0.77x + 15.95
Solve the equation for x:
207.68 - 15.95 = 0.77x
191.73 = 0.77x
x = 249 miles driven
REVISED 2/3/
the following using the picture below.
4
a) Two pairs of supplementary angles:
b) A pair of complementary angles:
Please explain this! Thank you!
Answers
Supplementary angles are those angles which make a sum of 180°.
Complementary angles are those angles which make a sum of 90°.
The supplementary angles are given by the straight lines making angles of 180°.
There are two straight lines CB and DE
The angles DAF and FAE are the two angles making a straight line DE
The angles CAF and FAB are the two angles making a straight line CB
The complementary angles are given by angles formed between the perpendicular lines making angles of 90°.
Angle BAF is formed by angle BAE and angle AEF
Supplementary Angle given by the straight line DE is formed by the angles DAF and FAE.
Complementary Angle BAF is formed by angle BAE and angle AEF.
https://brainly.com/question/12919120
f(x) = x2
g(x) = (x +4)^2 - 1
We can think of g as a translated (shifted) version of f.
Hurry I am in summer school and almost done I need help ASAP!
Answers
Answer:
down by 1 unit and left by 4 units
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
Then
g(x) = (x + 4)² - 1
is f(x) shifted down by 1 unit and shifted left by 4 units
A driver starts a trip with 30 gallons of gasoline in the tank of his car. The car
burns 4 gallons for every 80 miles. Assuming that the amount of gasoline in the tank decreases linearly, write a linear function that relates the number of gallons G left in the tank after a journey of "d" miles.
Answers
Answer:
Step-by-step explanation:
We have to look at this as something as basic as combining like terms. We know that the driver starts with 30 GALLONS of gas and loses x GALLONS while driving, giving us an equation that says
Gallons of gas used = Gallons in car - gallons used; in other words, if everything is in the same label, you can subtract. We start off with 30 gallons, thus:
Gallons of gas used = 30 G
That's a start, at least. Now we need to figure out how much is burned. Remember, in order to do any subtraction at all we have to have like labels, so we need what goes after that subtraction sign to also be a label in gallons, G. The driver burns 4 gallons per 80 miles times how many miles he drives, so the expression for that is
[tex]\frac{4G}{80mi}*dmi[/tex] and what happens here is that the label of miles cancels out, leaving us with just G, which is what we're after. The whole equation then is
[tex]G=30-\frac{4}{80}d[/tex], choice 1
Using a straightedge and compass, the ancient Greeks were able to construct
many geometric objects.
A. True
B. False
Answers
Answer:
A. True
Step-by-step explanation:
Write down the name of the solid shape that is being described. "When you cut me in half, the number of faces on one of my halves is double the number of faces that I started with.
Answers
Answer:
Cone
Step-by-step explanation:
A cone only has 1 side, and when it's cut in half it has two
The circumference of a
square orchard is 1600
meters. How many square
meters does the orchard
cover? How many hectares
Answers
9514 1404 393
Answer:
160,000 m²16 haStep-by-step explanation:
The side length of a square is 1/4 of the perimeter, so the side length of the square orchard is (1600 m)/4 = 400 m.
The area of a square is the square of the side length, so the area of the orchard is (400 m)² = 160,000 m².
A hectare is 10,000 m², so the area of the orchard in hectares is ...
16·(10,000 m²) = 16 ha
Evaluate the given expression for x = 5 and y=5. 6x2 + 7xy + 3y?
Answers
Step-by-step explanation:
Given, x = 5
y = 5
= 6(5)^2 +7(5)(5) +3(5)
= 6(25)+7(25) +15
= 150+175 + 15
= 150 + 190
=340
Answer:
x = 12 y = 7
Step-by-step explanation:
6x^2 + 7xy + 3y
6(5)^2+ 7(5) + 7(8)y
6(5+5)+25+35 + 7(8)-7y
60+25+35+ 56-7y
y - 5 = 120 + 35 - 5 (+49y)
sqrt 150 + sqrt 49
x = 12 y = 7
Find the value of x and y.
60°
6
Answers
Answer:
b .
x = 3
y = 3[tex]\sqrt3[/tex]
Step-by-step explanation:
Using the pythagorean identities for 30-60-90° triangle,
we know the ratio of the sides is x - x√3 - 2x
Since 2x = 6
Then smallest side is x (opposite ∠30°) = 6/2 = 3
The other side y , opposite ∠60° will be x√3 or 3√3.
9514 1404 393
Answer:
B. x = 3; y = 3√3
Step-by-step explanation:
You only need to use your sense of triangles to choose the correct answer:
x < y < 6
This relation fits only one answer choice:
x = 3, y = 3√3
_____
Additional comment
For multiple choice questions, it isn't always about working the problem. Usually, it is about knowing what the answer has to look like. The usual criteria are (a) is the answer true; (b) does the answer make sense in the context of the problem statement; (c) can you get this answer if you work the problem in detail. More often than not, the first two criteria will let you choose the correct answer without doing any detailed solving.
In the circus, a leopard has been trained to jump through a ring of fire that has a diameter of 8 feet. What is the ring's circumference? Use 3.14 for .
Answers
Answer:
no cap, but am no so sure but all I know is area or circumference of a circle is = to pie r²
Answer:
25.12 ft
Step-by-step explanation:
C= [tex]\pi[/tex] × d
C= 3.14 × 8 ft = 25.12 ft
Please Help!! much appreciated! :D
Find the value of y.
Answers
In the largest triangle, the missing side has length
√((11 + 5)² - x ²) = √(256 - x ²)
But it's also the hypotenuse of the triangle with side lengths 11 and y, so that its length can also be written as
√(11² + y ²) = √(121 + y ²)
so that
√(256 - x ²) = √(121 + y ²)
or, by taking the squares of both sides,
256 - x ² = 121 + y ²
y ² = 135 - x ²
In the smallest triangle, you have
5² + y ² = x ² ==> x ² = 25 + y ²
Substitute this into the previous equation and solve for y :
y ² = 135 - (25 + y ²)
y ² = 110 - y ²
2y ² = 110
y ² = 55
y = √55
Mr. Johnson took up an appointment with Nestle Ghana as an accountant with an annual salary of $164 million. as part of his appointment, he was promised a yearly increment of $24 million. Mr Johnson got promoted to chief accountant after six years of work with an annual salary of $300 million and yearly increment of$36 million.
calculate a) Mr. Johnson's salary in the tenth year of service.
b). Mr. Johnson's total earnings at the end of the tenth year of service.
Answers
Answer:
300 million(1+ 36 million) y
Step-by-step explanation:
Equation?
Slope?
Y-intercept?
Answers
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (4, 2) ← 2 points on the line
m = [tex]\frac{2-(-3)}{4-0}[/tex] = [tex]\frac{2+3}{4}[/tex] = [tex]\frac{5}{4}[/tex]
The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{5}{4}[/tex] - 3 ← equation of line
A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?
Answers
Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.
He wants to end up with a 44 mL solution, so
x + y = 44 mL
Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain
0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL
of acid.
Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives
0.04x + 0.15 (44 mL - x) = 5.28 mL
0.04x + 6.6 mL - 0.15x = 5.28 mL
1.32 mL = 0.19x
x ≈ 6.95 mL
==> y ≈ 37.05 mL
In the figure AB = BC = CD = DA 2 3.2 units. The slope of AB is. What else do
you need to show to prove that the figure is a square?
Answers
Answer:
B) AD = 1/3 is the answer.
