Answer:
its easy
Step-by-step explanation:
so basically,
Part A:
To find (f + g)(x), we need to add the two functions together.
(f + g)(x) = f(x) + g(x)
= 3x + 10 + x + 5 (substitute the given functions)
= 4x + 15 (combine like terms)
Therefore, (f + g)(x) = 4x + 15.
Part B:
To evaluate (f + g)(6), we substitute x = 6 in the (f + g)(x) function.
(f + g)(6) = 4(6) + 15
= 24 + 15
= 39
Therefore, (f + g)(6) = 39.
Part C:
The value of (f + g)(6) represents the total number of animals adopted by both shelters in 6 months. The function (f + g)(x) gives us the combined adoption rate of the two shelters at any given time x. So, when x = 6, the combined adoption rate was 39 animals.
(f + g)(6) = 39 represents the total number of animals adopted by both shelters in 6 months, based on the combined adoption rates of the two shelters.
Part A:
To find (f + g)(x), we add the functions f(x) and g(x):
(f + g)(x) = f(x) + g(x)
= (3x + 10) + (x + 5) (substitute the given functions)
= 4x + 15 (combine like terms)
Therefore, (f + g)(x) = 4x + 15.
Part B:
To evaluate (f + g)(6), we substitute x = 6 into the (f + g)(x) function:
(f + g)(6) = 4(6) + 15
= 24 + 15
= 39
Therefore, (f + g)(6) = 39.
Part C:
The value of (f + g)(6) represents the combined number of animals adopted by both shelters after 6 months. The function (f + g)(x) gives us the total adoption rate of the two shelters at any given time x. When x = 6, the combined adoption rate was 39 animals.
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help me for ez brainlist
Answer:
C. 80in^2
Step-by-step explanation:
12*3 for the area of both sides of the H. 12*3= 36, and since there are two we multiply 36*2= 72
For the middle we multiply 4*2=8
72+8= 80
my head is empty for now, i rly can't with online classes
so anyone wanna help me?
Answer:
The Y intercept is (0,7)
Step-by-step explanation:
If it is a y intercept, there will be a number in the y coordinate. For example, (x,y) if the point said (7,0) that would be the x intercept. Because it it (0,7) and in the y place that makes it a y intercept. I hope this helped :)
a tank contains 1700 gallons of diesel fuel. a fuel mixture containing a lubricity additive is pumped into the tank through two inlets. the mixture flowing in through the first inlet contains 0.28oz of additive per gallon, and is being pumped in at a rate of 25gal/min. meanwhile, the mixture being allowed in by the second inlet at a rate of 10gal/min contains 14.9oz of additive per gallon. the mixture in the tank is continuously and thoroughly mixed and drained out at the rate of 20gal/min. if there should be 14oz of additive for every 120 gallons of diesel fuel, how long will it take to reach the right mixture? round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to three decimal places.
The time taken for the mixture to find the right amount of additive per gallon is 12.869 minutes.
The total amount of diesel into the tank = 1700 gallons
The mixture is added at the rate of 0.28 ounces per gallon.
The mixture is added at the rate of 25 gallon per minute.
Let us consider that the time taken is t minutes.
A mixture is a substance made up of two or more distinct chemical components that are not chemically bonded together. A mixture is a mixture of two or more substances that retain their identities while being mixed in the form of solutions, suspensions, and colloids.
Now in t minutes the mixture = 25 × .28 ×t = 7t
Now we will use the second part of the equation as:
The rate of 20gal/min. if there should be 14oz of additive for every 120 gallons of diesel fuel, how long will it take to reach the right mixture
Now we will use the mixture formula to calculate the e amount of diesel in the mixture.
Hence 0.20 × 14×120=336 × 65.11 = 21877.3
Now the diesel mixture will have
Therefore the equation formed is :
336t +7t = 21877.3
Solving we get t=21877.3.
Hence the time taken for the mixture to find the right amount of additive per gallon is 12.869 minutes.
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Using the Table below find the common difference. Write the number in
the answer box. Only write the number!
х
3
5
7
9
у
1
5
9
13
Find a 15
Type the number answer in the blank provided.
Answer:
9
Step-by-step explanation:
if a user adds a new column to a table that already has rows, the existing rows will default to a value of _____ for the new column.
if a user adds a new column to a table that already has rows, the existing rows will default to a value of null for the new column.
When a column is added to a table that has existing rows, the values of the new column will be set to null for all existing rows. This is because the user has not yet specified any values for the new column.
Adding a new column to a table with existing rows will cause the new column values to be set to null for every existing row. This is because the user has not yet specified any values for the new column. This is a default behavior when creating a new column, and it allows the user to specify different values for each row as needed. This is beneficial because it allows the user to easily specify different values for the new column without having to manually enter them for each row.
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Expand and simplify: 2(x-4^2)+7
inverso aditivo de +3x
Answer:
inverso aditivo de +3x
Ok so wala ko kasabot nimo baah
Solve the following ODE from \( x=0 \) to \( x=1 \) using a step size of \( h=0.25 \) with Euler's Method, where \( y(0)=2 \) and \( y^{\prime}(0)=0\left(y^{\prime}=\frac{d y}{d x}\right) \). Make sur
The solution of the given ODE is y = 2, 2.5, 3.34375, 4.26172, 5.27344 from x = 0 to x = 1 using a step size of h=0.25 with Euler's method.
As per data ODE is:
\($y^\prime=y-x+1$\)
Given initial conditions are:
y(0) = 2y'(0) = 0
Using Euler's method to solve the above ODE:
\($$y_{i+1}=y_i+h f(x_i,y_i)$$\)
Here the step size h = 0.25 So, the value of
\($x_1 = 0+0.25 = 0.25$\)
We can evaluate the slope,
\($f(x_i, y_i)$\)
by using the given ODE
\($y^\prime=y-x+1$\)
Substituting \($y = y_i$ \\\) and \($x = x_i$\) we get,
\($f(x_i, y_i) = y^\prime_i = y_i - x_i + 1$\)
Therefore, \($y_{i+1} = y_i + h(y_i-x_i+1)$\)
Now we can use the given initial conditions to find the first approximation.
\($x_0=0, y_0=2$\)
Then,
\($y_1 = y_0 + h(y_0-x_0+1)$\\\)
\($y_1 = 2 + 0.25(2-0+1)$\\\)
\($y_1 = 2.5$\)
Now,
\($x_1=0.25, y_1=2.5$\)
Then,
\($y_2 = y_1 + h(y_1-x_1+1)$\\\)
\($y_2 = 2.5 + 0.25(2.5-0.25+1)$\\\)
\($y_2 = 3.34375$\)
Next,
\($x_2=0.5, y_2=3.34375$\)
Then,
\($y_3 = y_2 + h(y_2-x_2+1)$\\\)
\($y_3 = 3.34375 + 0.25(3.34375-0.5+1)$\\\)
\($y_3 = 4.26172$\)
Next,
\($x_3=0.75, y_3=4.26172$\)
Then,
\($y_4 = y_3 + h(y_3-x_3+1)$\\\)
\($y_4 = 4.26172 + 0.25(4.26172-0.75+1)$\\\)
\($y_4 = 5.27344$\)
Finally,
\($x_4=1, y_4=5.27344$\)
Therefore, the solution of the given ODE is y = 2, 2.5, 3.34375, 4.26172, 5.27344 from x = 0 to x = 1 using a step size of h=0.25 with Euler's method.
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A manufacturing machine has a 2% defect rate. If 10 items are chosen at random, what is the probability that at least one will have a defect
Answer:
2%
Step-by-step explanation:
Unit:transformations homework 5 identifying transformations
The transformation given as A(-8,7) → A'(-8,-7) represents a reflection over x-axis .
In the reflection of the point (x,y) over x-axis transformation ,the x-coordinate of each point remains the same, but the y-coordinate is negated (changes sign).
Let's consider the coordinates of point A that is (-8, 7).
The transformation takes this point to A' (-8, -7).
We can see that the x-coordinate of the point remains the same which is -8. but , the y-coordinate changes from 7 to -7.
We know that in a reflection over the x-axis, the x-coordinate remains the same while the y-coordinate changes sign.
Therefore , the transformation that takes A to A' is a reflection over the x-axis.
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The given question is incomplete , the complete question is
Identify the Transformation given as A(-8,7) → A'(-8,-7)?
What equations for x=-3 is a possible solution?
Answer:
2,4,5
Step-by-step explanation:
a rectangular storage container with a lid is to have a volume of 16 m3. the length of its base is twice the width. material for the base costs $8 per m2. material for the sides and lid costs $16 per m2. find the dimensions of the container which will minimize cost and the minimum cost.
The minimum cost of the container is $576, and the dimensions that minimize the cost are a width of 2 meters, length of 4 meters, and height of 2 meters.
To minimize the cost, we need to find the dimensions of the container that minimize the total cost, taking into account the cost of the base, sides, and lid.
Let's start by defining the dimensions of the rectangular container:
Let the width of the base be "w" meters.
The length of the base will be twice the width, so the length is "2w" meters.
The height of the container is "h" meters.
The volume of the container is given as 16 m³, so we can write the equation:
Volume = Length × Width × Height
16 = 2w × w × h
16 = 2w²h
w²h = 8 ----(Equation 1)
Now, let's find the cost of the base, sides, and lid.
Cost of the base:
The base is a rectangle with dimensions of length = 2w and width = w.
Area of the base = length × width
Area of the base = (2w) × w = 2w²
Cost of the base = Area of the base × Cost per m² = 2w² × $8 = 16w²
Cost of the sides and lid:
The container has two sides with dimensions of length = 2w and height = h.
The container has two sides with dimensions of width = w and height = h.
The container has a lid with dimensions of length = 2w and width = w.
Area of each side = length × height = 2w × h = 2wh
Area of each side = width × height = w × h
Area of the lid = length × width = 2w × w = 2w²
Total area of the sides and lid = 2(2wh) + 2(wh) + 2w² = 4wh + 2wh + 2w² = 6wh + 2w²
Cost of the sides and lid = Total area × Cost per m² = (6wh + 2w²) × $16 = 96wh + 32w²
Now, we need to express the cost in terms of one variable, either w or h, so we can find the minimum value. Since Equation 1 relates w, h, and the volume, we can express h in terms of w.
From Equation 1:
w²h = 8
h = 8/w²
Now, substitute h in the cost equation:
Cost = 16w² (cost of the base) + (96wh + 32w²) (cost of the sides and lid)
Cost = 16w² + 96w(8/w²) + 32w²
Cost = 16w² + 768/w + 32w²
Cost = 48w² + 768/w ----(Equation 2)
To find the minimum cost, we differentiate Equation 2 with respect to w and set it equal to zero:
d(Cost)/dw = 96w - 768/w² = 0
96w = 768/w²
w³ = 8
Taking the cube root of both sides:
w = 2
Substituting w = 2 back into Equation 1:
w²h = 8
(2)²h = 8
4h = 8
h = 2
Therefore, the dimensions of the container that minimize the cost are:
Width (w) = 2 meters
Length = 2w = 4 meters
Height (h) = 2 meters
The minimum cost can be found by substituting the values of w and h into Equation 2:
Cost = 48w² + 768/w
Cost = 48(2)² + 768/2
Cost = 48(4) + 384
Cost = 192 + 384
Cost = $576
So, the minimum cost of the container is $576, and the dimensions that minimize the cost are a width of 2 meters, length of 4 meters, and height of 2 meters.
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What is the value of k?
Answer:k=2.4
Step-by-step explanation:
If Paul is older than Bill and Fred is younger than Bill, then Bill's age is between Paul's and Fred's.
Write the To Prove statement:
Fred < Bill < Paul
Paul is older and Fred is younger
A man keeps birds in a big cage in his garden.
2
of the birds are brown.
5
4 of the birds are black.
The rest of the birds are white.
The man takes a bird out of the cage at random.
The probability that this bird is black is 0.2.
How many of the birds in the cage are white?
Find the value of x
Show the work please thank you
Answer:
x=19
Step-by-step explanation:
(x+14)+(57)=90
x+71=90
x=19
The area of a rectangular garden is 1200 square feet. The width of the garden is 24 feet. Which equation can be used to find the length, l, of the garden?
The equation for finding the length of the garden is l = 1200/24
How to determine the equationIt is important to note that the formula for calculating the area of a rectangle is expressed as;
A = lw
We have that;
A is the area of the rectanglel is the length of the rectanglew is the width of the rectangleFrom the information given, we have the values as;
Area = 1200 square feet
Width = 24 feet
Now, substitute the values of both the area and width of the garden into the formula, we have;
1200 = 24l
Make 'l' the subject of formula by dividing both sides by the coefficient
We have;
1200/24 = 24l/24
Find the ratio, we get;
l = 60 feet
Hence, the equation is l = 1200/24
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Answer:D
Step-by-step explanation:
Triangle UML has coordinates U (-3, -4), M(-1, -1) , and L(-2, -5). If the triangle is translated 5 units up and 1 unit left to form triangle U’M’L’, what will be the coordinates of L’?
After the translation the coordinates of L' are (-3, 0) for the new triangle of U’M’L’.
What is defined as the translation?In geometry, translation refers to a function which moves an object a specified distance. The object is not elsewhere altered. It is not rotated, mirrored, or resized.Every location of the object should be moved within the same direction for the same distance during a translation.When performing a translation, this same initial object is referred to as the pre-image, and also the object just after translation is referred to as the image.The coordinates of triangle are-
U (-3, -4), M(-1, -1) , and L(-2, -5).
The triangle is translated 5 units up and 1 unit left to its original place.
Thus, for the 5 units up translation 5 units will get added to the y-coordinates.
New y-coordinate of L' is -5 + 5 = 0.
For 1 unit left , 1 units will get reduced from the original x-coordinate.
New x-coordinate = -2 - 1 = -3
Thus, the new coordinates L' becomes (-3, 0).
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tyler reades 2/15 pages on monday 1/3 on tuesday and 2/9 on wendsday and 3/4 on thursday .and has 14 pages left on friday how many pages are in the book
The number of pages that are in the book is 1 31/45 pages.
How to illustrate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Tyler reads 2/15 pages on Monday 1/3 on Tuesday and 2/9 on Wednesday and 3/4 on thursday .and has 14 pages left on friday how many pages are in the book.
The fraction for pages will be:
= 2/15 + 2/9 + 1/3 + 3/4 + 1/4
= 2/15 + 5/9 + 1
= 6 / 45 + 25/45 + 1.
= 1 31/45
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Complete question
tyler reades 2/15 pages on monday 1/3 on tuesday and 2/9 on wendsday and 3/4 on thursday .and has 1/4 pages left on friday how many pages are in the book
Help and explain !!!!!
Answer:
yeah the answer is one of those just pick one
Let h be a function where y = h(z)
How to find the size of angle x in a triangle
Answer:
it depends on the question
Usually if it a triangle with 2 angles and an x
you will add the 2 angles and rearrange to give the answer
Step-by-step explanation:
Hope this helps!!!
Answer:
A right triangle has one angle measuring 90 degrees. The side opposite this angle is known as the hypotenuse (another name for the longest side). The length of the hypotenuse can be discovered using Pythagoras's theorem, but to discover the other two sides, sine and cosine must be used. These are trigonometric functions of an angle.
In the diagram below, one of the angles is represented by the Greek letter θ. (pronounced "the - ta"). Side a is known as the "opposite" side and side b is called the "adjacent" side because of their positions relative to the angle θ.
The vertical lines "||" around the words below mean "length of."
So sine, cosine and tangent are defined as follows:
Step-by-step explanation:
So sine, cosine and tangent are defined as follows:
sine θ = |opposite side| / |hypotenuse|
cosine θ = |adjacent side| / |hypotenuse|
when a single card is drawn from a standard 52-card deck, what is the probability that it will be a king or a diamond?
The probability that it will be a king or a diamond is 4/13
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here, we have
There are 52 cards, of which 4 are kings.
There are 52 cards, of which 13 are diamonds.
But there are only 3 cards that are kings which are not diamonds, and only 12 cards that are diamonds but not kings, there’s one card that is both a king and a diamond.
So, there are 3/52+12/52=15/52 chances of drawing a card that is king or diamond but not both.
There are 3/52+12/52+1/52=16/52 chances of drawing a card that is king or diamond or both.
Hence, the probability that it will be a king or a diamond is 4/13.
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Andre was trying to write 7⁴/7⁻³ with a single exponent and wrote 7⁴/7⁻³=7⁴⁻³. Explain to Andre what his mistake was.
I need this by today please help
Answer:
Answer
see explanation
Step-by-step explanation:
Using the rule of exponents
= , then
=
His mistake was in subtracting 3 rather than - 3
A newspaper collected information on schools in its circulation area in order to compare their quality. Two measures the newspaper collected for each school, mean class size and mean score on a statewide reading exam, are shown in the scatterplot. One school in the report, Springside Elementary, is labeled in the graph.
Which is a true statement regarding Springside?
Springside does not affect the correlation.
Springside weakens the correlation shown in the scatterplot.
Springside strengthens the correlation shown in the scatterplot.
Removing Springside would increase the value of the correlation coefficient.
Interpreting the scatterplot, it is found that the correct option is:
Springside weakens the correlation shown in the scatterplot.
In the scatterplot, the mean test score is plotted as function of the mean class-size.From this, we can verify that as the mean class size increases, the mean score decreases, that is, there is a negative correlation between the mean class size and the mean test score.However, for Springside, the mean test score is greater than most other schools with smaller class sizes, which is a different result than expected, thus, it weakens the correlation, and the correct option is:Springside weakens the correlation shown in the scatterplot.
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What is the value of the missing angle?
150*
95
95
105
145
0120°
O 1300
O 1550
0720
Answer:
b) 130
Step-by-step explanation:
The total of the internal angles of any simple hexagon (six sides) is 720°.
720 = 150+95+105+145+95+x
720= 590 + x
720 - 590 = x
130 = x
A bag contains 3 red. 3 white and 3 green balls. One ball is taken out of the bag
at random. What is the probability that the ball drawn is -
(1) red. (2) not red (3) either red or white.
Answer:
1. 3/9 = 0.3% 2. 6/9= 0.6% 3.6/9=0.6℅
Step-by-step explanation:
1.) 3 red and 9 balls
therefore, 3/9
2.) 3 white, 3 green
6/9 balls
3.) 3 red, 3 white
6/9
The midpoint of AB is M (4, 4). If the coordinates of A are (2, 1), what are the
coordinates
of B?
Answer:
(6,7)
Step-by-step explanation:
Let B(x,y).
By the midpoint formula,
4 is the average of 2 and x, so x = 6.Similarly, y = 7.So, the coordinates of B are (6,7).
Solve each equation by factoring. x²-x-20=0 .
The solutions to the equation x² - x - 20 = 0 are x = 5 and x = -4.
To solve the equation x² - x - 20 = 0 by factoring, follow these steps:
Step 1: Rewrite the equation in the form ax² + bx + c = 0.
In this case, the equation is already in the correct form.
Step 2: Factor the quadratic expression on the left side of the equation.
To factor the quadratic expression x² - x - 20, we need to find two numbers whose product is -20 and whose sum is -1 (the coefficient of the x term).
The numbers that satisfy these conditions are -5 and 4.
Step 3: Rewrite the equation using the factored form.
The factored form of the equation x² - x - 20 = 0 is (x - 5)(x + 4) = 0.
Step 4: Set each factor equal to zero and solve for x.
Setting (x - 5) = 0, we find x = 5.
Setting (x + 4) = 0, we find x = -4.
Therefore, the solutions to the equation x² - x - 20 = 0 are x = 5 and x = -4.
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