The solution to the given function is (f-g)(x) = -6x² - x - 7.
What is a function?
Function, in mathematics, an expression, rule, or law that defines a relationship between : one variable (the independent variable) and another variable (the dependent variable).
A function is an equation with a single solution for y for each value of x. Each input of a particular type receives exactly one output when using a function. Instead of y, a function is frequently named f(x) or g(x). When x equals 2, we should determine our function's value because f(2) says to do so.
Given: f(x) = 3x² - 2x
g(x) = 9x² -x + 7
To find: ( f - g )(x)
thus (f-g)(x)= 3x² - 2x - ( 9x² - x + 7)
(f-g)(x) = -6x² - x - 7
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K
A company had 80 employees whose salaries are summarized in the frequency distribution below. Find the mean salary.
Salary ($) Employees
5,001-10,000
10,001-15,000
17
15
15,001-20,000
20,001-25,000
25,001-30,000
OA. $7,376.62
B. $17,625
C. $15,862.50
D. $19,387.50
16
13
19
The mean salary of the employees is $17625.5.
The total number of employees in the company is 80.
The total salary for the first interval is [(5001+10000)/2]*17 = 127508.5.
The total salary for the second interval is [(10001+15000)/2]*15 = 187507.5.
The total salary for the third interval is [(15001+20000)/2]*16 = 280008.
The total salary for the fourth interval is [(20001+25000)/2]*13 = 292506.5.
The total salary for the fifth interval is [(25001+30000)/2]*19 = 522509.5.
In math, a mean is the average of a data collection, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers. The mean salary is the sum of all salaries divided by the total number of employees.
M = (127508.5 + 187507.5 + 280008 + 292506.5 + 522509.5)/80
M = 17625.5
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Please show and explain this please
The graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
What is a graph of a function?Defining a function's graph: The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We could also say that the graph of f is the graph of y = f(x). As a result, the graph of an equation is a particular instance of the graph of a function. We merely select a value for x, then determine the value of y that corresponds. Equations that have been solved for y are graphed as functions! In this instance, the graph of f(x) is the graph of y = x² - 3. Making points for the graph is simple.So, the function with which the given graph matches:
The graph of the option (E) f(x) = (x + 10)(x - 3)²(x + 1) is:(Refer to the graph attached below)We can easily see that coordinates of the given graph and the graph of equation (E) match.Therefore, the graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.
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If the measure of ∠ C A B = 4 x + 14 and ∠ D A E = 6 x − 18 then find the measure of ∠ C A B
CAB and DAE are suplementary
Measure of CAB is 84.4, by using supplementary angle theory.
What is supplementary angle?
In geometry, two angles are referred to as supplementary angles if their sum is 180 degrees. For instance, if A + B = 180°, then A and B are considered supplementary angles. Complementary angles always result in a straight angle when combined (180 degrees).
Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.
We have given, CAB= 4x+14 and DAB = 6x-18
Both are supplementary angle
Therefore, CAB + DAB = 180
4x+14+6x-18=180
10x-4=180
10x=176
x=17.6
hence, CAB = 4(17.6)+14 = 84.4
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A school is organising a fun runThe fun run involves a 5
1
2
mile run around the field, then a 5
4
7
mile run back to the school. Find the total distance of the fun run.Give your answer as a mixed number in its simplest form.
In mixed fraction the total distance of the fun run is 11 1/14
A school is organising a fun run. The fun run involves a 5 1/2
mile run around the field, then a 5 4/7 mile run back to the school.
The total distance is equal to summation of run around the field and run back to school.
total distance = 5 1/2 + 5 4/7
= 11/2 + 39/7
The L. C. M of 2 and 7 is 14
= [tex]\frac{11.7}{2.7} + \frac{39.2}{7.2}[/tex]
(77 + 78)/14
155/14
Upon dividing 155 by 14, the quotient is 11 and the the remainder is 1
In mixed fraction it is 11 1/14
So in mixed fraction the total distance of the fun run is 11 1/14
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I tried doing it but the whole thing is confusing
Given the equation:
y = 828000 - 2700x
Where y is the value of the building and x is the number of months of use.
Let's find when the value of the building will be $666,000.
To find when the value will be $666,000, substitute 666000 for y in the equation and solve for x.
y = 828000 - 2700x
666000 = 828000 - 2700x
Subtract 828000 from both sides:
666000 - 828000 = 828000 - 828000 - 2700x
-162000 = -2700x
Divide both sided by -2700:
[tex]\begin{gathered} \frac{-162000}{-2700}=\frac{-2700x}{-2700} \\ \\ 60=x \\ \\ x=60 \end{gathered}[/tex]The value of the building will be $666,000 after 60 months.
Now, let's convert from months to years.
Where:
12 months = 1 year
[tex]60\text{ months = }\frac{60}{12}=5\text{ years}[/tex]Therefore, the value of the building will be $666,000 after 5 years.
ANSWER:
5 years.
I don’t understand this paper and our sub has no idea, nor the other students so if someone could help me, that would be great.
By Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.
Given two triangles are ABC and A'B'C'.
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
1) Triangle ABC is reduced to triangle A'B'C'
∠ABC=∠A'B'C'=90°
∠BAC=∠B'A'C'
So, by AA similarity
ΔABC≈ΔA'B'C'
2) Triangle ABC is enlarged to triangle A'B'C'
∠ABC=∠A'B'C'
∠BAC=∠B'A'C'
So, by AA similarity
ΔABC≈ΔA'B'C'
Therefore, by Angle-Angle theorem similarity ΔABC is similar to ΔA'B'C'.
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w/2 + 4 is greater than 5
Answer:
I say w is equal to 4, because:
4 divided by 2 = 2
2 + 4 = 6
6 > 5
Step-by-step explanation:
Hope it helps! =D
Can somebody Answer this?
Garry needs 18.4 oz of glue and 9.2 oz of glitter to make 4 bottles.
What is direct proportion?In direct proportion between two or more than two quantities if one quantity is multiplied or divided by some constant k other quantities will also be multiplied or divided by the same constant k.
Given, Making 1 bottle of glitter glue Garyy requires 4.6 oz of glue and 2.3 oz of glitter.
∴ 4 bottles of glitter glue require (4.6×4) = 18.4 oz of glue and (2.3×4) = 9.2 oz of glitter.
As the no. of bottles is multiplied by 4 thus material requirements will also be multiplied by a factor of 4.
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Length is 3x − 4, area is 6x4 − 8x3 + 9x2 − 3x − 12
The width of the given rectangle is 2x²-3x+3.
Given that, area of rectangle = [tex]6x^4-8x^3+9x^2-3x-12[/tex] and the length of rectangle = 3x-4.
What is the area of a rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units. The formula to find the area of a rectangle = Length × Width.
Now, (3x-4) × width = [tex]6x^4-8x^3+9x^2-3x-12[/tex]
⇒ Width = [tex]\frac{6x^4-8x^3+9x^2-3x-12}{3x-4}[/tex]
3x-4|[tex]6x^4-8x^3+9x^2-3x-12[/tex]|2x³-3x+3
[tex]6x^4[/tex] - 8x³
_________________
0+9x²-3x-12
(-) 9x²+12x
_________________
0+9x-12
(-) 9x(+)12
_________________
0
So, width = 2x²-3x+3
Therefore, the width of the given rectangle is 2x²-3x+3.
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find X and Y X - 3 y + 3 15 12
To solve this problem we have to remember that diagonals of a parallelogram bisect each other. This means that they intersect in the midle point of each other. From this we can conclude that
[tex]\begin{gathered} x-3=15 \\ \text{and} \\ y+3=12 \end{gathered}[/tex]Once we have our equations we can solve them. Let's find x
[tex]\begin{gathered} x-3=15 \\ x=15+3 \\ x=18 \end{gathered}[/tex]Now, let's find y
[tex]\begin{gathered} y+3=12 \\ y=12-3 \\ y=9 \end{gathered}[/tex]Then x=18 and y=9,
4626ххXхA school received 46 iPads. The school library took 26 of the iPads and the rest were split equally among 4 teachers to use in theirclassrooms. Using the strip diagram and the letter x to represent the unknown quantity, which equation could be used to find thenumber of iPads each teacher received?A)4x = 46 - 26B)4x +46 +264x - 26 - 46D)4x = 26 + 46
Given data:
The box is given.
The given expression can be written as,
[tex]\begin{gathered} 26+x+x+x+x=46 \\ 4x+26=46 \end{gathered}[/tex]Thus, the option (c) is correct.
a Fill in the blank. If necessary, use the slash mark (/) for a fraction bar. If cosg = then tang =
We can use a right triangle and the below trigonometric ratios.
[tex]\begin{gathered} \cos(\theta)=\frac{\text{ Adjacent leg}}{\text{ Hypotenuse}} \\ \tan(\theta)=\frac{\text{ Opposite leg}}{\text{ Adjacent leg}} \end{gathered}[/tex]In this case, we have:
[tex]\cos(\theta)=\frac{3}{5}=\frac{\text{Adjacent leg}}{\text{Hypotenuse}}[/tex]As we can see, we need to know the value of the opposite leg. Since it is a right triangle, we can use the Pythagorean theorem formula.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where} \\ a\text{ and }b\text{ are the legs} \\ c\text{ is the hypotenuse} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} a=3 \\ b=? \\ c=5 \\ a^{2}+b^{2}=c^{2} \\ 3^2+b^2=5^2 \\ 9+b^2=25 \\ \text{ Subtract 9 from both sides} \\ 9+b^2-9=25-9 \\ b^2=16 \\ $$\text{ Apply square root to both sides of the equation}$$ \\ \sqrt{b^2}=\sqrt{16} \\ b=4 \end{gathered}[/tex]Finally, we have:
Then, we can find the value of tan(θ):
[tex]\begin{gathered} \tan(\theta)=\frac{\text{Opposite leg}}{\text{Adjacentleg}} \\ \tan(\theta)=\frac{4}{3} \end{gathered}[/tex]Answer[tex]\tan(\theta)=\frac{4}{3}[/tex]What is the slope and y-intercept?
y=-5x+6
Options:
Blank # 1
Blank # 2
any whole number is a proper subset or rational number
Answer:
The natural numbers, whole numbers, and integers are all subsets of rational numbers
Step-by-step explanation:
hope it helps
have a good day
State the null and alternative hypotheses for the claimA report from five years ago said that the average income of accountants was $51,497; but nowadays it's more than that.
ANSWER and EXPLANATION
We want to state the null and alternative hypotheses for the claim given.
A null hypothesis is a statement about a population parameter such that the likelihood can be tested to either accept or reject the alternative hypothesis.
An alternative hypothesis on the other hand is a statement that directly contradicts the null hypothesis.
Therefore, going by that, we see that the null hypothesis is:
[tex]\mu=\$51,497[/tex]and the alternative hypothesis is:
[tex]\mu>\$51,497[/tex]8. Use the point-slope formula to write an equationof a line in slope-intercept form using the points(1/2,5) and (5/2,9)
We have the next two points:
- (1/2,5)
- (5/2,9)
And we must use the point-slope formula to write an equation of a line in slope-intercept
First, we need to calculate the slope of the line using the point-slope formula
[tex]\begin{gathered} y_2-y_1=m(x_2-x_1) \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]Where (x1, y1) and (x2, y2) are the two points
Now, replacing the points
[tex]m=\frac{9-5}{\frac{5}{2}-\frac{1}{2}}=\frac{4}{\frac{4}{2}}=\frac{4}{2}=2[/tex]Now, we must replace the slope and one of the two points in the point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]Replacing m = 2 and (1/2, 5)
[tex]y-5=2(x-\frac{1}{2})[/tex]Finally, we must simplify to obtain the slope-intercept form
[tex]\begin{gathered} y-5=2x-1 \\ y=2x-1+5 \\ y=2x+4 \end{gathered}[/tex]ANSWER:
y = 2x + 4
The formula S=
2S-a, n
Oan=- n
n(a₁ + an)
2
2S+ a₁n
an-- n
an-2S+a, n+n
a, 2S-a, n+n
gives the partial sum of an arithmetic sequence. What is the formula solved for a,,?
Answer:
2S-a1n/n
Step-by-step explanation:
S = n(a1 + an)/2
2S = n(a1 + an)
2S = na1 + nan
nan = 2S - na1
an = (2S - n a1)/n
5. Evaluate the following V16
Which of these shows the result of using the first equation to substitute fory in the second equation, then combining like terms? y- 3x 3x+ 2y= 18 OA. 3y 18 B. 9x= 18 OC. 6x= 18 OD. 3x= 18 m
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
74.52
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]
A coordinator will select 5 songs from a list of 8 songs to compose an event's musical entertainment lineup. How many different lineups are possible?
The number of lineups possible is the combination of selecting 5 songs from 8 songs.
8C5 = 56.
What is combination?A combination is a mathematical way that evaluates the number of possible arrangements within a collection of items, leaving behind of the order of selection. A combination can select items in any order. Combinations can be confused with permutations Water is a combination of hydrogen and oxygen. The car interior is available in various color combinations. The formula for combinations is nC_r = n/(r!*(n - r)!), where n is the number of items and r is the number of items selected at once. Let's look at an example of how combinations are calculated. There are 10,000 possible combinations of the numbers 0-9 in a 4-digit codeTo learn more about combination from the given link:
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find the distance from line y= -3x + 4 to line y = -3x - 1
In the accompanying diagram of BCD m
Given:
m∠C = 70°
m∠CDE = 130°
Question 1:
To find ∠CDB, let's use the exterior angle theorem.
The exterior angle theorem states that the sum of 2 opposite interior angles is equal to the exterior angle.
Thus,
m∠C + m∠B = 130
70 + m∠B = 130
Subtract 70 from both sides:
70 - 70 + m∠B = 130 -70
m∠B = 60°
Now, use the triangle angle sum theorem to find ∠CDB.
The triangle angle sum theorem states that the sum of interior angles in a triangle is 180°
∠CDB = 180 - 70 - 60 = 50°
∠CDB = 50°
Question 2:
∠CBA = ∠C + ∠CDB
∠CBA = 70 + 50 = 120°
∠CBA = 120°
ANSWER:
∠CDB = 50°
∠CBA = 120°
Winston is making a model of a statute using a scale where 2 inches equals 6 feet. If the actual height of
the statue is 20 feet, how tall is the model, in inches?
Answer:
6 2/3 inches
Step-by-step explanation:
2 inches / 6 feet * 20 feet = 6 2/3 inches
The length of a rectangle is six times its width.
If the perimeter of the rectangle is 84 m, find its area.
The area when the length of a rectangle is six times its width is 216m².
How to calculate the value?Let the width = w
Let the length = 6 × w = 6w
Therefore the perimeter will be:
= 2(Length + Width) = 84
2(w + 6w) = 84
2 × 7w = 84
14w = 84
Divide
w = 84 / 14
w = 6
Width = 6m
Length = 6w = 6 × 6 = 36m
The area will be:
= Length × Width
= 36m × 6m
= 216m²
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Write an explicit equation for the arithmetic sequence defined byt(n+1)= t(n)-4t(2) = 10
We need to find the explicit equation for the sequence:
[tex]\begin{gathered} t\mleft(n+1\mright)=t\mleft(n\mright)-4 \\ \\ t(2)=10 \end{gathered}[/tex]First, we can complete the given table. Notice that when we subtract 4 from the n-th term, we obtain the next term (n+1).
Then, to find a previous term, we can add 4. Thus. we obtain:
n t(n)
0 14+4 = 18
1 10+4 = 14
2 10
3 10-4 = 6
4 6-4 = 2
5 2-4 = -2
Now, observing the above relations, we need to write an expression for t(n) in terms of n:
n t(n)
0 18 = 18 - 0*4
1 14 = 18 - 1*4
2 10 = 18 - 2*4
3 6 = 18 - 3*4
4 2 = 18 - 4*4
5 -2 = 18 - 5*4
...
n 18 - n*4
Therefore, an explicit equation for the sequence is:
[tex]t(n)=18-4n[/tex]7x — 9y = 12—7x – 7y = -28
In order to solve this system of equations, we can add both equations, this way we can find the value of y and then the value of x:
[tex]\begin{gathered} \begin{cases}7x-9y=12 \\ -7x-7y=-28\end{cases} \\ 7x-9y-7x-7y=12-28 \\ -16y=-16 \\ y=\frac{-16}{-16}=1 \\ \\ 7x-9=12 \\ 7x=21 \\ x=\frac{21}{7} \\ x=3 \end{gathered}[/tex]So the solution to this system is (3, 1).
Given: f(x) =x^2 + 6x + 5Find the x and y value of the vertex (turning point)And what are the zeros of the parabola?
Solution: X-value of vertex=-3
Y-value of vertex=-4
Zeros of the parabola: X=-5 and x=-1
Analysis
We can find the x-coordinate of the vertex, calculating -b/2a. First, we identify the a and b values of y=ax^2+bx+c of your quadratic equation.
b=6
a=1
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{6}{2(1)}=-3 \\ \\ After\text{ we find x-coordinate, we can find y-coordinate of the vertex replacing x-value.} \\ f(x)=x^2+6x+5\text{ = }^^(-3\text{ }^2)+6(-3)+5 \\ f(x)\text{ = 9}-18+5 \\ f(x)=-4 \end{gathered}[/tex]Now, let's find the zeros of the parabola. We factorize the quadratic equation:
[tex]\begin{gathered} f(x)=x^2+6x+5 \\ f(x)=(x+5)(x+1) \\ Let^{\prime}s\text{ equal to zero} \\ (x+5)(x+1)=0 \\ (x+5)=\text{ 0 }(x+1)=0 \\ x=-5\text{ }x=-1 \end{gathered}[/tex]Estimate [tex] \sqrt[3]{20} [/tex] between two integers.
Answer
∛20 is between 2 and 3.
Explanation
The question asks us to find the cube root of 20.
∛20
The key to doing this without the calculator is to take the cube of numbers and the one that has 20 in between them is the answer.
1³ = 1
2³ = 8
3³ = 27
We can see that 20 is between 8 and 27.
So,the cube root of 20 has to be betwen 2 and 3.
The other way to do this with the calculator is to actually find the cube root of 20
∛20 = 2.71
Which is between 2 and 3.
Hope this Helps!!!
A tank has two inlet pipes and one outlet pipe. The inlet pipes can fill the tank in 4 hoursand 10 hours. The outlet pipe can drain the tank in 2 hours. One day the outlet pipe was leftopen as the empty tank was being filled. Will the tank ever be full? If so, how long will ittake to fill the tank? If not, explain why not.
The two inlet pipes can fill the tank in 4 hours and 10 hours.
The work done by the inlet pipes per hour is calculated to be:
[tex]\Rightarrow\frac{1}{4}+\frac{1}{10}=\frac{7}{20}\text{ units per hour}[/tex]The outlet pipe drains the tank in 2 hours. The work done will be:
[tex]\Rightarrow\frac{1}{2}\text{ units per hour}[/tex]Therefore, if both inlet pipes and the outlet pipes are opened at the same time, the work done by the pipes combined will be:
[tex]\Rightarrow\frac{7}{20}-\frac{1}{2}=-\frac{3}{20}\text{ units per hour}[/tex]Since the work done to fill the tank is negative, it means that the tank will never get full as it empties faster than it fills up.