The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x) = 9x – 2. Which expression represents the profit, (k – h)(x), of producing soccer balls?
A job is shared by 4 workers, w, x, y, and z. worker w does 1/4 of the total hours. worker x does 1/3 of the total hours. worker y does 1/6 of the total hours. what fraction represents the remaining hours allocated to person z?
For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}
Answer:
[tex]x_{n+1}=-\frac{x_{n}}{4}[/tex]
Step-by-step explanation:
We can get geometric sequence dividing each term by -4
So we will have:
[tex]x_{n+1}=\frac{x_{n}}{-4}=-\frac{x_{n}}{4}[/tex]
We can prove it putting the first value in this recursive equation:
x₁=-80
n = 1
[tex]x_{2}=-\frac{x_{1}}{4}=-\frac{-80}{4}=20[/tex]
If x₂ = 20, the next value will be:
[tex]x_{3}=-\frac{x_{2}}{4}=-\frac{20}{4}=-5[/tex]
I hope it helps you!
Match the following items by evaluating the expression for x=-3.
x^-3 1/9,-3,-1/3,9,1
x^-1 -1/3,1,9,1/9,-3
x^0 -3,9,-1/3,1/9,1
x^1 1/9,-3,-1/3,1,9
x^2 -3,1,9,1/9,-1/3
Answer:
The values of given expression at x=-3 are [tex]x^{-3}= -\frac{1}{27}[/tex], [tex]x^{-1}=-\frac{1}{3}[/tex], [tex]x^{0}=1[/tex], [tex]x^{1}=-3[/tex] and [tex]x^{2}=9[/tex].
Step-by-step explanation:
We need to find the value of each expression at x=-3.
The given expression is
[tex]x^{-3}[/tex]
It can be written as
[tex]x^{-3}=\frac{1}{x^3}[/tex] [tex][\because x^{-n}=\frac{1}{x^n}][/tex]
Substitute x=-3 in the above expression.
[tex]x^{-3}=\frac{1}{(-3)^3}\Rightarrow -\frac{1}{27}[/tex]
Similarly,
[tex]x^{-1}=\frac{1}{x}\Rightarrow -\frac{1}{3}[/tex]
[tex]x^{0}=1[/tex] [tex][\because x^{0}=1][/tex]
[tex]x^{1}=(-3)^1=-3[/tex]
[tex]x^{2}=(-3)^2=9[/tex]
Therefore the values of given expression at x=-3 are [tex]x^{-3}= -\frac{1}{27}[/tex], [tex]x^{-1}=-\frac{1}{3}[/tex], [tex]x^{0}=1[/tex], [tex]x^{1}=-3[/tex] and [tex]x^{2}=9[/tex].
Assume that y varies inversely with x. If y=12 when x=5, find y when x=3
When y varies inversely with x, they follow the rule y = k/x. If y=12 when x=5, the constant 'k' is found to be 60. Using this constant, when x=3, y is found to be 20.
Explanation:In mathematics, when we say that y varies inversely with x, it means that as x increases, y decreases proportionally, and vice-versa. Y and x follow the rule y = k/x, where k is a constant number.
Given that y = 12 when x = 5, we can find the constant by multiplying x and y together, so: k = x * y = 12 * 5 = 60.
Now that we have our constant, we can find y when x = 3 by rearranging the formula to y = k / x which gives us: y = 60 / 3 = 20. So, when x is 3, y is 20.
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Subtract 11a2+42a-6 from 14a2-24a+7
The values of subtraction of 11a²+42a-6 from 14a²-24a+7 is
3a² - 66a + 1.
What is Expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
We have to Subtract 11a²+42a-6 from 14a²-24a+7.
So, the subtraction is as follows
= 14a²-24a+7 - ( 11a²+42a-6)
= 14a²-24a+7 - 11a² - 42a + 6
= 14a²- 11a² -24a - 42a + 7- 6
= 3a² - 66a + 1
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On an up hill hike Ted climbs at 3 mph. Going back down, he runs at 5 mph. If it takes him forty minutes longer to climb up than run down, then what is the length of the hike?
Answer: He hiked 10 miles.
Step-by-step explanation:
3mi/hr x 1 2/3 hr = 5 miles. 5 mi/hr x 1 hr = 5 miles.
Rewrite each of the following linear equation in equivalent y=mx+b
what's the slope and the y-intercept
HELP ME PLZZ
How many terms are in the polynomial abcd + e - h 2? two three five six
Answer:
The number of terms in the polynomial are:
Three.
Step-by-step explanation:
We are given a polynomial expression in terms of variable a,b,c,d , e and h as:
[tex]abcd+e-h^2[/tex]
We know that in any algebraic expression the number of terms are the number of unlike expressions that are separated by a minus or plus i.e. addition sign.
Hence here by looking at our polynomial expression we see that there are three terms in the expression :
1) [tex]abcd[/tex]
2) [tex]e[/tex]
3) [tex]h^2[/tex]
Which of the following is unnecessary when multiplying these polynomials?
(2x^3+2x^2-3x)(9x^2-4x+5)
A)use of the distributive property
B)use of the multiplication property of exponents
C)combine like terms
D)find the GCF
Noa drove from the Dead Sea up to Jerusalem, and her altitude increased at a constant rate of 740 meters per hour. When she arrived in Jerusalem after 1.5 hours of driving, her altitude was 710 meters above sea level.
Let A(t) denote Noa's altitude relative to sea level A (measured in meters) as a function of time t (measured in hours).
She stared at -400 meters below sea level and the equation is A(t)=740t-400
Functions and valuesFunctions are written in terms of variables
From the given question;
Let a₀ is the initial height or the height she started at
Required
Initial height
After 1.5 hours, she was 710 meters above sea level
Substitute the given time into the function
A(1.5)=740(1.5)+a₀=710
740(1.5)+a₀=710
1110+a₀=710
a₀=-400
This shows that she stared at -400 meters below sea level and the equation is A(t)=740t-400
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In a programming team of 20 persons, 1/4 are women and 3/4 are men. to obtain a team with 40% women, how many women should be hired?
To obtain a team with 40% women in a programming team of 20 people, we need to find out how many women should be hired. Currently, there are 5 women in the team (1/4 of 20). By setting up an equation and solving for x, we find that 5 women should be hired.
Explanation:To obtain a team with 40% women in a programming team of 20 people, we need to find out how many women should be hired. We know that currently 1/4 of the team are women, which means there are 5 women in the team (20 * 1/4 = 5). To find out how many women should be hired, we subtract the number of women in the team from the target number of women in the team:
Number of women to be hired = Target number of women - Current number of women
Number of women to be hired = 0.4 * (20 + x) - 5
Where x is the number of women to be hired. Now we can solve for x:
0.4 * (20 + x) - 5 = x
Distribute and simplify:
8 + 0.4x - 5 = x
Combine like terms:
0.4x - x = 5 - 8
0.6x = 3
Divide both sides by 0.6:
x = 3 / 0.6
x = 5
So, 5 women should be hired to obtain a team with 40% women.
Solve the quadratic equation -x^2=4
If the diagonals of a quadrilateral do not bisect each other then the quadrilateral could be a
The diagonals of a quadrilateral do not bisect each other then the quadrilateral could be a scalene trapezoid
What is a trapezoid?
The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
For a scalene trapezoid ,
The four sides are of unequal length
The angles of the scalene trapezoid are not equal
The shortest distance between two parallel sides is known as the altitude
The sides of the scalene trapezoid does not bisect each other
Hence , the diagonal is a scalene trapezoid
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Order of operations? How to do?
Thanks
parenthesis first (8+5) = 13
35/5 = 7
13x7 +6
13x 7 = 91 +6 = 97
What is the solution to the system of equations graphed below?
a. (2,-3)
b. (-3,2)
c. (-2,3)
d. (3,-2)
Find the zeros of the function. F(x)= cube root of x
If it rained on 3 days out of 20 days,on what percent of the days did it rain
how are the rules of signs for multiplication and division related
if H(x)=4x-8 and j(x) = -x solve h{j(3)}
Darren drank 2 liters of water.How much millilliters of water did he drank
in a batch of 280 water purifiers 12 were found to be defective. What is the probability that a water purifier chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary. A. 4.3% b. 5.6% c. 95.7% d. 71.8%
the answer would be 4.3 percent
which figure has both line of symmetry and rotational symmetry
Answer:
A line of symmetry is when you can put a line through a shape and you can fold it and it is identical on both sides, and rotational is when you can rotate it and at some point it is in the same spot as it was before, so yes, you are right. the octogon.
Step-by-step explanation:
Three times the greater of two consecutive odd integers is five less than four times the smaller. find the two numbers.
five friends go out to lunch and they decide to split the bill evenly the bill comes out to 57.25 how much does each person owe?
the volume of a square pyramid with height 2.4cm is 3.2cm. what is the width of the base of the pyramid?
Simplify (−34.67)0. I'm not really understanding how to do this so please someone help me.
(02.06 LC)
The figure below shows parallel lines cut by a transversal:
Which statement is true about ∠1 and ∠2?
A. ∠1 and ∠2 are complementary because they are a pair of corresponding angles.
B. ∠1 and ∠2 are congruent because they are pair of corresponding angles
C.∠1 and ∠2 are complementary because they are a pair of alternate interior angles.
D.∠1 and ∠2 are congruent because they are pair of alternate interior angles.
If the measure of angle is 38 what is the measure of its complement
What is the equation of the blue graph?
since the blue graph is 2 lines to the left of the red graph, that would mean it moved -2
so the equation needs to include -2
the correct answer is C