The container that holds the water for the football team is 7/10 full. after pouring out 3 gallons of water, it is 1/2 full. how many gallons can the container hold?
If f(x)=x+8 and g(x) = -4x - 3, find (f+g)(x)
(f + g) (x)= -3 x+ 5
(f + g)(x) = -3x + 5
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."For given question,
We have been given two functions.
f(x) = x+8 and g(x) = -4x - 3
We need to find the value of (f + g)(x)
This means, we need to find the addition of functions f(x) and g(x)
⇒ (f + g)(x) = f(x) + g(x)
⇒ (f + g)(x) = (x + 8) + (-4x - 3)
⇒ (f + g)(x) = x - 4x + 8 -3
⇒ (f + g)(x) = -3x + 5
Therefore, (f + g)(x) = -3x + 5
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A line with a slope of 2 passes through (3,9). Which choice is an equation of this line?
Answer:
y - 9 = 22(x - 3)
Step-by-step explanation:
Extra points! Write the equation for the vertical line that contains point E(10, –3).
A) y=(3/10)x-3
B) x=10
C) Other (please write the equation)
What is the area of a triangle with vertices at (0, −2) , (8, −2) , and (9, 1) ? Enter your answer in the box
Answer:
12 square unit.
Step-by-step explanation:
Since, the area of a triangle having vertices [tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] is,
[tex]A=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Here, the vertices of the triangle are (0, −2), (8, −2) and (9, 1),
Hence, area of the given triangle is,
[tex]A=\frac{1}{2}|0(-2-1)+8(1+2)+9(-2+2)|[/tex]
[tex]=\frac{1}{2}| 0+24+0|[/tex]
[tex]=\frac{24}{2}[/tex]
[tex]=12\text{ square unit}[/tex]
Consider the probability distribution of a random variable x. is the expected value of the distribution necessarily one of the possible values of x?
Answer:
No. The expected value can be a value different from the exact value of x.
33 is 75% of what number?
Solve the inequality
-8x - 10 > 7x + 20
A.) x < - 30
B.) x > - 2
C.) x > - 30
D.) x < - 2
To solve the inequality -8x - 10 > 7x + 20, combine like terms, isolate the variable term, and solve for x. The correct answer is D) x < -2.
Explanation:We need to solve the inequality -8x - 10 > 7x + 20.
First, let's combine like terms by adding 8x to both sides. This gives us -10 > 15x + 20. Next, subtract 20 from both sides to isolate the variable term. This gives us -30 > 15x. Finally, divide both sides by 15 to solve for x. This gives us x < -2.Therefore, option D.) x < -2 is the correct answer.
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Find the value of k
given that the line through (−1, k)
and (−7,−2)
is parallel to the line y = x+1
.
Given two lines are parallel, their slopes are equal. After calculating the slopes of the two lines and solving the equation, we find that the value of 'k' in the question is 4.
Explanation:In the realm of Mathematics, when two lines are parallel, their slopes are equal. The line y = x + 1 has a slope of 1. To find the slope of the line through (−7,−2) and (−1, k), use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Here, (x1,y1) is (−7,−2) and (x2,y2) is (−1, k). Hence, the equation for slope would look like this: m = (k - (-2)) / (-1 - (-7)).
As the slopes are equal, we can form an equation 1 = (k + 2) / 6. Solving this equation will give us the value of k. By multiplying both sides by 6, we obtain 6 = k + 2. Consequently, subtracting 2 from both sides, we get k = 4.
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Find the product (x-y) (3x-4y)
you pay $14.82 for 1.5 pound of ham. you buy 2.25 pounds of roast beef for $12.40 per pound. How much less does ham cost per pound than roast beef?
solve and graph |2x+10|>26
need help.... what is half of 1 3/4 IN A FRACTION plzzzzz
We _____ when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.
We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
The average deviation is calculated by taking the absolute value of the deviations from the mean, summing them, and then dividing by the total number of observations.
This gives us a measure of the average distance between each observation and the mean.
The formula for the average deviation is:
average deviation = Σ |x - mean| / n
where x is an observation, mean is the mean of the observations, and n is the total number of observations.
By taking the absolute value of the deviations, we ensure that negative and positive deviations do not cancel each other out when we sum them.
Thus,
We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.
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The glee club has a set of 48 classical cds and a set of 42 show tune cds. each set can be divided equally among the club members. what is the greatest possible number of club members?
The greatest possible number of club members that we can divide 48 classical CDs and 42 show tune CDs is 6.
What is HCF?HCF is the highest common number or factor that divides two or more than two given numbers completely.
These types of questions can be solved by the concept of HCF.
Given that the glee club has a set of 48 classical CDs and a set of 42 show tune CDs and we have to determine the highest number of club members so that we can distribute these two types of CDs to the club members equally.
∴ The HCF of 42 and 48 is 6, we know 2 and 3 also divides 42 and 48 but they are not the largest number.
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Long Beach California has an elevation of -7 ft New Orleans Louisiana is 8 feet below sea level which city has lower elevation
New Orleans has the lower elevation at -8 feet compared to Long Beach, which is at -7 feet, since a lower numerical value below zero indicates a further drop below sea level.
To determine which city has the lower elevation, we need to compare the elevations of Long Beach, California and New Orleans, Louisiana. A lower elevation means that it is further below sea level. Long Beach is at an elevation of -7 feet, while New Orleans is at 8 feet below sea level. In numerical terms, New Orleans’ elevation can be considered as -8 feet because the word 'below' indicates a negative elevation.
Comparing the two elevations:
Long Beach, California: -7 feet
New Orleans, Louisiana: -8 feet
Since -8 is less than -7, we determine that New Orleans has the lower elevation compared to Long Beach.
He area of a rectangle is 27 m2 , and the length of the rectangle is 3 m less than twice the width. find the dimensions of the rectangle.
The width of the rectangle is 4.5 meters, and the length is 6 meters.
Let's denote the width of the rectangle as [tex]\( w \)[/tex] and the length as [tex]\( l \)[/tex].
1. The area [tex]\( A \)[/tex] of a rectangle is given by the product of its length and width, so we have the equation:
[tex]\[ A = l \times w \][/tex]
Since the area is given to be 27 square meters, we can write:
[tex]\[ l \times w = 27 \][/tex]
2. The length of the rectangle is 3 meters less than twice the width.
This relationship can be expressed as:
[tex]\[ l = 2w - 3 \][/tex]
This is our second equation.
Now we have a system of two equations with two variables:
[tex]\[ \begin{cases} l \times w = 27 \\ l = 2w - 3 \end{cases} \][/tex]
We can substitute the expression for [tex]\( l \)[/tex] from the second equation into the first equation:
[tex]\[ (2w - 3) \times w = 27 \][/tex]
Expanding the equation, we get:
[tex]\[ 2w^2 - 3w - 27 = 0 \][/tex]
To solve this quadratic equation, we can factor it:
[tex]\[ (2w - 9)(w + 3) = 0 \][/tex]
Setting each factor equal to zero gives us two possible solutions for [tex]\( w \)[/tex]:
[tex]\[ 2w - 9 = 0 \quad \text{or} \quad w + 3 = 0 \][/tex]
Solving for [tex]\( w \)[/tex], we get:
[tex]\[ w = \frac{9}{2} \quad \text{or} \quad w = -3 \][/tex]
Since the width of a rectangle cannot be negative, we discard [tex]\( w = -3 \)[/tex].
Thus, [tex]\( w = \frac{9}{2} \)[/tex] meters, which simplifies to [tex]\( w = 4.5 \)[/tex] meters.
Now we can find the length [tex]\( l \)[/tex] by substituting [tex]\( w = 4.5 \)[/tex] into the second equation:
[tex]\[ l = 2(4.5) - 3 \][/tex]
[tex]\[ l = 9 - 3 \][/tex]
[tex]\[ l = 6 \][/tex]
1.For the function y = f(x), what is the ordered pair for the point on the graph when x = b - 2? (3 points)
a. (b - 2, f(b -2))
b. (x, f(b))
c. (x, b - 2)
d. (b - 2, f(b))
Answer:
A
Step-by-step explanation:
BIG BRAIN
What form would you use to write the equation of a line if you knew the slope and x-intercept? Explain.
The form used to write the equation of a line if you knew the slope and x-intercept y=mx−k/m
What is slope?The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it
According to the given situation we have given :a slope of 'm' and an x-intercept of 'k'
we can write
y=mx−k/m
and generally, To find the x-intercept, set y = 0 and solve for x.
For example,
Let k be some constant such that
y=mx + k
where
m is the slope.
m=3/4 and the x-intercept is 4
If the x-intercept is 4 this means that x=4 when y=0
So equation:
y=mx + k becomes
0=3/4+ k
k=−3
and our equation is
y=3/4x−3
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A man rides a bicycle a distance of 48 miles in a certain amount of time. If the man increased his speed by 2 miles per hour, he reaches his destination four hours earlier. Find his usual speed. Show Work!
-6 ,4 but speed can't go negative so the answer would be 4.
The standard error of the mean is calculated using which two quantities:
Question 21 the ratio of men to women working for a company is 2 to 3 . if there are 140 employees total, how many women work for the company?
Write an expression that is equivalent to 3/5 (3y+15)
3/5y +9, 3/5y+15, 9/5y+9, 9/5y + 15?
An aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour. Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? Recall the formula d = rt. 0.75(x + y) = 120 x − y = 120 0.75(x − y)= 120 x + y = 120 120(x + y) = 0.75 120(x − y) = 1 120(x − y) = 0.75 120(x + y) = 1 Mark this and return
Answer:
System of equation: 0.75(x+y)=120 and x-y=120
A is correct
Step-by-step explanation:
An aircraft travels with the wind for 120 miles in 0.75 of an hour.
The return trip is flown against the wind and takes exactly 1 hour.
Let speed of aircraft be x mph and speed of wind y mph
Formula:
[tex]speed=\dfrac{Distance}{Time}[/tex]
Case 1: When aircraft along with wind
Speed = x+y
Time = 0.75
Distance = 120
[tex]x+y=\dfrac{120}{0.75}[/tex]
[tex]0.75(x+y)=120[/tex]
0.75(x+y)=120
Case 2: When aircraft against with wind
Speed = x-y
Time = 1
Distance = 120
[tex]x-y=\dfrac{120}{1}=120[/tex]
x-y=120
Hence, The system of equation are 0.75(x+y)=120 and x-y=120
How do I work out 5x+2+3x
Write an equivalent expression using the multiplicative identity property
For an expression equivalent to, let's say, -8, you could do: -2 + -6.
Kim learned in her science class that every 2 minutes she spends in the shower, she uses 17 gallons of water. This rate is constant
The rate of using water per minute will be 8.5 gallons per minute.
What is the rate of flow?The rate of flow of water is defined as the amount of water or any liquid flowing in a unit of time. If the gallons of water are flowing in some minutes the rate will be measured in the gallons of water.
Given that Kim learned in her science class that every 2 minutes she spends in the shower, she uses 17 gallons of water.
The rate of flow of water will be calculated as:-
Rate of flow = Volume of water / Time
Rate of flow = 17 / 2
Rate of flow = 8.5 gallons per minute
Therefore, the rate of using water per minute will be 8.5 gallons per minute.
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How is volume calculated given mass and density?
Sum of mass and density
Mass divided by density
Mass multiplied by density
Difference of mass and density
Answer:
B.
Step-by-step explanation:
when trying to calculate the volume when being given the M or the mass, and the D or density, hears is the calculations needed for that: P=M/V, which also means volume is the mass divided by the volume, or density. Hence, the answer would be mass divided by density. hope this helps!!! (also, please give me brainliest.)
Volume is calculated given mass and density is Mass divided by density.
What is volume?
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic meter and liter) or by various imperial units (such as the gallon, quart, cubic inch).
Mass is the quantity of matter in a physical body. It is also a measure of the body's inertia, the resistance to acceleration (change of velocity) when a net force is applied.
Density is defined as a measure of how compact the mass in a substance or object is.
Since, density of a substance is measure as the ratio of its mass to its volume,
Density = Mass/Volume
or, Density x volume = mass
or, Volume = Mass/Density
Hence,Volume is calculated given mass and density is Mass divided by density.
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Samuel recorded the number of different types of pets his friends have in the table shown below: Cats 5 Dogs 3 Rabbits 1 Guinea Pigs 3
Answer:
Samuel's friends have a total of 12 pets.
Explanation:
To find the total number of pets Samuel's friends have, we simply add up the number of each type of pet:
Number of Cats: 5
Number of Dogs: 3
Number of Rabbits: 1
Number of Guinea Pigs: 3
Total number of pets = 5 (cats) + 3 (dogs) + 1 (rabbits) + 3 (guinea pigs) = 12
So, Samuel's friends have a total of 12 pets.
The area of a garden is 12.9 square feet. Each square foot of the garden needs to have 2.6 pounds of soil.How many pounds of soil are needed for the garden?