The function represented by the graph has an equation of f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we have the following graph that can be used in our computation:
The graph is an absolute value graph
As a general rule, an absolute value is expressed as
y = |x - h| + k
In this case, the vertex is
Vertex = (h, k)
As a general rule, the vertex of a function is the minimum point on the graph
On the given graph, the minimum point is (3, 5)
This means that
(h, k) = (3, 5)
Substitute the values (h, k) = (3, 5) in the equation y = |x - h| + k
So, we have the following representation
y = |x - 3| + 5
Rewrite the equation as a function
f(x) = |x - 3| + 5
Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5
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help meeeeeeeeeeeeeeeeee please
Answer:
I believe it's 4.5 seconds
Change the standard form equation y=x^2-4x+9 to vertex form by completing the square.
Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked how much is Nick share of the money. Nick and Pam are paid ?
Nick got a total of $33.25 for his part of work.
What is the general equation of a Straight line? How it represents a proportional relationship?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked.
Assume that Nick recieved $[x]. Then, Pam will get - (52.25 - x). For direct proportionality -
y₁/x₁ = y₂/x₂
We can write -
x/3.5 = (52.25 - x)/2
2x = 3.5(52.25 - x)
2x = 182.875 - 3.5x
x = 33.25
Therefore, Nick got a total of $33.25 for his part of work.
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In the figure below, o ll m. Find the values of y and x.
The values of y and x is 117 degrees and 28 degrees.
Given:
o ll m
Let angle beside 63 is a.
63 + <a = 180
<a = 180 - 63
<a = 117 degrees.
y = 117 degrees (since alternate interior angles are equal)
y = 4x + 5(vertically opposite angles are equal)
117 - 5 = 4x
4x = 112
divide by 4 on both sides
x = 112/4
x = 28 degrees.
Therefore the values of y and x is 117 degrees and 28 degrees.
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To find the equation of a regression line, y = ax + b, you need these formulas:
Sy
a=rsa
b =ỹ - ax
A data set has an r-value of 0.793. If the standard deviation of the x-
coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772,
what is the slope of the line to three decimal places?
The slope of the line is 0.393.
Define slope.Slope is the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").
Given,
A data set has an r- value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772.
We'll use the following formula for slope if the r- value (or Pearson's coefficient) and the standard deviations of the x and y coordinates are provided:
m = 8ₓ/8ₐ
where m is the slope of the best-fit line.
8ₓ = Standard deviation of the x-coordinates is 5.591,
8ₐ = the standard deviation of the y-coordinates is 2.772.
Slope is:
m = 8ₐ/8ₓ
m = (0.793)(2.772)/5.591
m = 0.393
The slope of the line is 0.393.
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Select all correct answers. which values are part of the solution set based on the result of the inequality? -4x + 24 < -2x + 2 9.5 -10 11.5 15 10 -3
11.5 and 15 are the values that are part of the solution set of the inequality.
Inequality is defined as relationship between non-equal numbers or expressions. The solution of an inequality is the set of values that satisfies the given inequality.
To determine the solution set of the given inequality, isolate the variable to one side and simplify.
-4x + 24 < -2x + 2
-4x + 2x < -24 + 2
-2x < -22
22 < 2x
11 < x
Hence, the solution set of the given inequality is the set of numbers greater than 11. Among the given choices, 11.5 and 15 are both greater than 11.
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Which one is greater 1 1/2 or 1.456
based on the t-test assuming equal variances on the t-testequal worksheet, is the difference in mean mpg between 4 and 8 cylinder cars statistically significant?
Yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.
What is t statistic and critical value of t?
T statistic is ratio of a parameter's estimated value to its standard error when it deviates from its hypothesized value.
Critical t value is a cut-off point in t distribution
In question, the calculated t statistic is 8.1023 and critical t value one tail is 1.7139 and critical t value two tail is 2.0686. So, the value of calculated t statistic is higher than critical t value one tail or two tail. Therefore, we can reject the null hypothesis.
Thus, yes, the difference in mean mpg between 4 and 8 cylinder cars statistically significant because the calculated value of t statistic is higher than the critical t value.
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Make x the subject:
Q1) 9y-5x = 4
Answer:
x = 9/5 y - 4/5
Step-by-step explanation:
Make x the subject:
9y - 5x =4
Subtract 9y from each side
9y-9y - 5x =-9y+4
-5x = -9y +4
Divide each side by -5
-5x/-5 = -9y/-5 + 4/-5
x = 9/5 y - 4/5
Answer:
x = (9/5)y - (4/5)
Step-by-step explanation:
Given equation,
→ 9y - 5x = 4
Solving for the required value of x,
→ 9y - 5x = 4
→ -5x = -9y + 4
→ x = (-9y + 4)/-5
→ [ x = (9/5)y - (4/5) ]
Hence, value of x = (9/5)y - (4/5).
Find the equation of the line passing through the given points. Express the equation in standard form. (4,5) and (-3,-1)
Answer:
y = m x + b equation for a straight line
when x = 4 y = 5
5 = m * 4 + b
m = (5 - b) / 4 solving for m
when x = -3 y = -1
-1 = (5 - b) / 4 * -3 + b = -3 * (5 - b) / 4 + 4 b / 4
-1 = (-15 + 3 b + 4 b) / 4
11 = 7 b b = 11 / 7
Since m = (5 - b) / 4
m = (5 - 11/7) / 4 = 6/7
We then have y = 6 x / 7 + 11 / 7
Or 7 y = 6 x + 11
Check:
when (4 , 5) 35 = 24 + 11 = 35
Two fire towers are 21 miles apart. Tower B is due East of Tower A. The rangers at Tower A spot a fire at 43°north of east. The rangers at Tower B spot the same fire 31° north of west.
How far is Tower B from the fire? Round to the nearest tenth.
Tower B is 14.9 miles away from the fire.
What is the law of sines?
According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides. The sine rule is another name for it.
Here,
According to the law of sines
BC/sin A = AC/sin B = AB/sin C
∠A = 43°, ∠B = 31°, ∠C = 180° - ∠A - ∠B = 106°
AB = 21 miles
So, BC = (AB/SinC)×SinA
BC = 14.9 miles
Hence, Tower B is 14.9 miles away from the fire.
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How do I do this can someone help me plss
Answer:
I think is 50m.
Step-by-step explanation:
AB (3x + 2) cm AC 11 cm BC (2y + 3) In the diagram, ABC is an equilateral triangle. Find the value of (x+y)
For the given triangle ΔABC the value of (x + y) would be 7 cm.
What is an equilateral triangle?
An equilateral triangle is a triangle with the same length on all three sides. An equilateral triangle is also equiangular in Euclidean geometry; that is, all three internal angles are congruent to each other and are each 60°.
Given data:
Length of AB = (3x + 2) cm.
Length of AC = 11 cm.
Length of BC = (2y + 3) cm.
The property of an equilateral triangle says that all sides of an equilateral triangle are equal.
then we can write,
AB = AC
3x + 2 = 11
3x = 11 - 2
3x = 9
x = 9/3
x = 3 cm
Also, BC = AC
2y + 3 = 11
2y = 11 - 3
2y = 8
y = 8/2
y = 4 cm
So the value of (x + y) = 3 +4
= 7 cm.
Hence, For the given triangle ΔABC the value of (x + y) would be 7 cm.
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(-3,-5), perpendicular to x +2y=-4
The equation of the line perpendicular to y = - (1 / 2) · x - 2 and that passes through the point (x, y) = (- 3, - 5) is y = 2 · x + 1.
How to determine an equation of the lineIn this problem we must determine the equation of a line perpendicular to another line, provided that the equation of a line and a point of intersection are given. According to analytical geometry, two lines are perpendicular if and only if the product of the two slopes equals - 1.
The equations of the line are defined by functions of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.And the slope relationship between two perpendicular line:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.First, derive the equation of the line in slope-intercept form:
x + 2 · y = - 4
2 · y = - x - 4
y = - (1 / 2) · x - 2
Second, calculate the slope of the perpendicular line by the slope relationship:
m' = - 1 / (- 1 / 2)
m' = 2
Third, find the y-intercept of the perpendicular line by the equation of line, the slope and the coordinates of the given point:
b = y - m · x
b = - 5 - 2 · (- 3)
b = - 5 + 6
b = 1
Then, obtain the equation of the line in slope-intercept form:
y = 2 · x + 1
The equation of the line is y = 2 · x + 1.
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What is the solution set for ly-9| ≤122
O y23 ory≤21
O
-35y≤21
O y2-3 ory$21
0 35ys21
The solution set for the inequality is.
-113 ≤ y ≤ 131
What is the solution set for the inequality?Here we have the following inequality:
|y - 9| ≤ 122
Any absolute value inequality can just be decomposed as follows:
|y - 9| ≤ 122
to:
-122 ≤ y - 9 ≤ 122
Now we can solve this for y by adding 9 in all places:
-122 + 9 ≤ y - 9 + 9 ≤ 122 + 9
-113 ≤ y ≤ 131
That is the solution set.
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Can somebody please explain what this question is asking, and how I solve it. I can not solve this, need help please.
Answer:
g(10)=-33, x=3
Step-by-step explanation:
g(x)=-4x+7. --------(1)
a) g(10)=?
since we know function x = -4x+7 to find function g(10) we will just place 10 whenever we see x
g(10)=-4(10)+7
g(10)=-40+7
g(10)= -33
b.)find x if g(x)=-5. ---------(ii)
g(x)=-4x+7. we will place (I) in (ii)
g(x)=-5
-4x+7=-5
-4x=-5-7
-4x=-12
cancel the minus(-) sign in both sides
4x=12
x=12/4
x=3
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A plane is 80 miles south and 95 miles east of an airport. How far is the plane from the airport? What bearing should be plane take to fly directly to the airport?
Answer:
124.2 miles
∠310.1°
Step-by-step explanation:
You want to know the bearing and distance to the airport from a plane that is 95 miles east and 80 miles south of it.
DistanceThe Pythagorean theorem or the distance formula can be used to find the distance to the airport.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((95 -0)² +(-80 -0)²) = √(9025 +6400) = √15425
d ≈ 124.197 . . . . miles
The plane is about 124.2 miles from the airport.
BearingThe reference angle with respect to the +y axis can be found using the tangent relation.
Tan = Opposite/Adjacent
tan(α) = 95/80 = 19/16
α = arctan(19/16) ≈ 49.9° . . . . . . CCW from +y axis
The bearing angle is measured clockwise from the +y axis (north), so is ...
bearing = 360° -49.9° = 310.1°
The bearing to the airport is 310.1°.
__
Additional comment
Some navigators would refer to the bearing as N 49.9° W.
Less commonly, it might be referred to as W 40.1° N. Usually, N and S are the reference directions, with the modification being E or W from there. The less common usage might be chosen if an angle less than 45° is wanted.
The bearing is often reported to the nearest degree, without any degree symbol, as N50W.
You have a gift certificate to a book store worth $95. Each paperback books is $10 and each hardcover books is
$17. You must spend at least $20 in order to use the gift certificate. Write and graph a system of inequalities to
model the number of each kind of books you can buy. Let x = the number of paperback books and y = the number
of hardback books
Answer: You make a system of inequality to spend at least $20. The word "at least" means you can spend equal to $20 or higher than $20. Or you can write it as,
⇒ what you buy should be ≥ 20
Input the price to the inequality above
⇒ what you buy should be ≥ 20
⇒ paperback price + hardcover price ≥ 20
⇒ 10x + 17y ≥ 20
Because the number of paperback books and the number of hardcover books can't be negative, make new inequality forms
⇒ x ≥ 0
⇒ y ≥ 0
So this is the summary
10x + 17y ≥ 20
x ≥ 0
y ≥ 0
Step-by-step explanation:
Water pressure can be measured in atmospheres (atm). At 30 meters in depth the water pressure measures 4 (atm). At 50 meters in depth under water the pressure is 6 (atm). Write a linear function for pressure based on the depth in meters. Please show work.
y = 0.1x + 1 is the linear function for pressure based on the depth in meters
How create a linear function for the pressure based on the depth in meters?Given that: At 30 meters in depth the water pressure measures 4 (atm)
At 50 meters in depth under water the pressure is 6 (atm)
We will consider the two given data values as our points 1 and 2 respectively. And that is what we are going to use to create a linear function for pressure
Let the y and x represent the pressure and depth respectively
point 1 (30, 4) and point 2 (50, 6)
slope(m) = y2-y1 / x2-x1
where x1 =30, y1 = 4 and x2 = 50, y2 = 6
slope(m) = 6-4 / 50-30 = 2/20 = 1/10
Linear function are of the form y-y1 = m(x-x1). Thus:
y-4 = 1/10 (x-30)
y-4 = 1/10(x) - 3
y = 1/10(x) + 1 = 0.1x + 1
Therefore, the linear function for pressure based on the depth in meters is y = 0.1x + 1
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8x - 4y = 16
8x+4y= 16
Answer:
X = 2, Y = 0
Step-by-step explanation:
Add the two equations together to cancel out -4y and +4y
leaving you with:
8x = 16
8x = 16
divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)
leaving you with:
x = 2
substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):
8(2) - 4 y = 16
8 x 2 = 16
leaving you with:
16 - 4y = 16
subtract 16 from both sides to get 4y on its own
leaving you with:
-4y = 0
so y = 0, and x = 2
. A cash register contains nickels and dimes. There are 12 nickels in the
cash register. The total amount of money in the cash register is $2.30.
How many dimes are in the cash register?
Answer: 17 Dimes.
Step-by-step explanation:
Help please ty nobody is helpinf i am payint xtra
Answer:
A)- 65
B)- 25
c)- 25
To find A- pay attention to the bottom..add 60+55 then subtract that from 180
yu get 65..now we know that 65+90= 155 subtract that from 180 you get 25. so now we have B..B and C are congruent meaning they are equals
hope this helps
A line passes through point (8, 4) and has a slope of - 3/4 Write an equation in Ax + By = C form for this line. Use integers for A, B, and C.
The equation of the line in the given form Ax + By = C is 3x + 4y = 40
How to determine the equation in the given form?The given parameters from the question are given as
Point = (8, 4)
Slope = -3/4
Start by representing the equation in the slope intercept form
This is calculated as
y = m(x - X) + Y
Where
m, Slope = -3/4
(X, Y), Point = (8, 4)
So, we have
y = -3/4(x - 8) + 4
Multiply through by 4
4y = -3(x - 8) + 16
Evaluate the like terms
4y = -3x + 24 + 16
This gives
3x + 4y = 24 + 16
Evaluate
3x + 4y = 40
Hence, the equation is 3x + 4y = 40
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an airplane is preparing to land at an airport. it is 48,000 feet above the ground and is descending at the rate of 3,200 feet per minute. at the same airport, another airplane is taking off and will ascend at the rate of 2,800 feet per minute. when will the two airplanes be at the same altitude and what will that altitude be?
Answer:
After 8 minutes ; altitude = 22,400 feet
Step-by-step explanation:
s1 = 2800t
s2 = -3200t + 48 000
2800t = -3200t + 48 000
28t = -32t + 480
7t = -8t + 120
7t + 8t = 120
15t = 120
15/15 t = 120/15
t = 8 minutes
s = 8 * (2800) = 22400 feet
suppose goop purchases 150 gallons of raw material. what is the probability that they will run out of raw material?
The probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.
We have following information,
the demand for the polymer is distributed normally .
Mean (μ) = 250 gallons and Standard deviations (σ) = 125 gallons
Selling price of poymer = $25 per gallons
cost price of raw material for polymer= $ 10 per gallons
Salvage value = $(-5)/ gallon
Now, Using the formula for normally distributed sample,
Z = ( X - μ ) /σ
where , X---> sample mean
μ ----> population mean
σ----> standard deviations
Z -----> Z-value
from question it is clear X = 150
putting all the values of variables in above formula we get, Z = ( 150-250)/125 = -100/125
= - 0.8
(-0.8) value of z = 0.21 = 21% , the value of z is measure from normal distribution table.
They will run out of raw material if demands exceds this quantity or
Probability ( out of stock ) = 1 - 0.21 = 0.79 = 79%
So, the probability that they will run out of raw material is 0.78 or 78% if the order quantity is 150 gallons.
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#Complete Question :
Goop Inc needs to order a raw material to make a special polymer. The demand for the polymer is forecasted to be Normally distributed with a mean of 250 gallons and a standard deviation of 125 gallons. Goop sells the polymer for $25 per gallon. Goop's purchases raw material for $10 per gallon and Goop mrust spend $5 per gallon to dispose off all unused raw material due to government regulations. (One gallon of raw material yields one gallon of polymer.) That is to say, the salvage value is $(-5)/gallon. If demand is more than Goop can make, then Goop sells only what they made and the rest of demand is lost. ?
1. Suppose Good purchases 150 gallons of raw material. What is the probability that they will run out of raw material? ?
Beverly is making peanut butter-banana bread. She always doubles the amount of nuts and peanut butter chips. The total amount of chips and nuts after doubling is 412 cups.
Write and solve an equation to find the original amount of nuts, x, in the recipe.
The original amount of nuts, x, in the recipe is 103
The equation for the original amount is 2x + 2x = 412
What is an algebraic expression?An algebraic expression can be defined as an expression made up of terms, factors, constants, coefficients, and variables.
These expressions are also known to be made up of mathematical operations such as;
SubtractionAdditionMultiplicationDivisionBracketParenthesesFrom the information given, we have that;
Beverly doubles the amount of nuts and peanut butter chips
Total number = 412
This is represented as;
2x + 2x = 412
collect like terms
4x = 412
Make 'x' the subject of formula
x = 412/ 4
x = 103
Hence, the value is 103
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A line has a slope of -7 and includes the points (-2, -10) and (-3, h). What is the value of h?
Answer:
-3
Step-by-step explanation:
You can use to find the slope of a line going through and .
I like to line up the points and subtract vertically. Then put 2nd difference over 1st difference.
(6,h)
minus
(7,-10)
------------
-1 h-(-10)
This also said to be equal to -7:
Multiply -1 on both sides:
Subtract 10 on both sides:
[texh=-3[/tex]
So if h=-3 then the slope of the line going through (6,h) and (7,-10) is -7.
Let's test it:
(6,-3)
minus
(7,-10)
----------
-1 7
So the slope is 7/-1=-7. This is the intended goal.
The check is good.
Can anyone write the equation of the graph?
The equation of the absolute value function graph is: y = |x - 3| + 5.
How to Write the Equation of the Graph of Absolute Value Function?The equation, y = a|x – h| + k, represents the equation of an absolute value function in the vertex form, where:
(h, k) = vertex of the graph a = determines if the graph opens up or opens down.h = horizontal translation factor (this determines how far left or right the parent function is translated)k = vertical translation factor (this determines how far up or down the parent function is translated)We are given the following from the graph:
Vertex (h, k) = (3, 5)
Plug in the values of h and k into the equation, y = a|x – h| + k:
y = a|x - 3| + 5
A point on the graph is (5, 7). Find the value of a by substituting (x, y) = (5, 7) into y = a|x - 3| + 5:
7 = a|5 - 3| + 5
7 = a|2| + 5
7 = 2a + 5
7 - 5 = 2a
2 = 2a
2/2 = 2a/2
1 = a
a = 1
Write the equation of the absolute function graph by substituting a = 1 into y = a|x - 3| + 5:
y = |x - 3| + 5
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g in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. calculate the expected value to two decimals.
Using the concepts of probability, we got that 0.4286 is the probability that the battery life for an iPad Mini will be 10 hours or less which is about 42.86%.
From the given information;
Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :
[tex]f_X(x)[/tex] = [tex]\frac{1}{B-A}[/tex] where A<x<B
where A and B are the two parameters of the uniform distribution
From the question;
Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours
So; Let A = 8,5 and B = 12
Therefore; the mathematical expression for the probability density function of battery life is :
[tex]f_X(x)[/tex] = [1 / (12-8.5)]8.5<x<12
[tex]f_X(x)=[/tex](1/3.5)8.5<x<12
The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:
F(x) = P(X ≤x)
F(10)=[tex](x-A)/(B-A)[/tex]
F(10)=(10-8.5)/(12-8.5)
F(10)=1.5/3.5
F(10)=0.4286
Hence, the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286
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(Complete question)
In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the iPad Mini showed a mean life of 10.25 hours (The Wall Street Journal, October 31, 2012). Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?
the distance y (in miles) that train A travels in x amount of time is represented by the equality y=78x. The graph shows the distance that train B travels.
URGENT PLS ANSWER!!!
ty!
We can conclude that train A is moving faster than train B
What is the general equation of a Straight line?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
We have the following problem -
The distance y (in miles) that train A travels in [x] amount of time is represented by the equality y = 78x. The graph shows the distance that train B travels.
Train A is moving with speed s[A] = 78 miles/hour {As slope of the equation is 78}. The train B will move with speed given by -
s[B] = (132 - 66)/(2 - 1) = 66 miles/hour
Therefore, we can conclude that train A is moving faster than train B
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[In the complete question it is asking to find which train is moving faster]