Answers
Answer:
1. f(4) = 4
2. g(2) = -4
3. f(-5) = -14
4. g(-3) = 21
5. f(0) = -4
6. g(0) = 0
7. f(3) - 1 = 1
8. f(1/4) = -3.5 or -7/2
9. g(1/4) = -0.9375 or -15/16
10. f(a^2) = 2a^2 - 4
11. f(k+1) = 2k - 2
12. g(2n) = 2n^2 - 8n
13. f(3x) = 6x - 4
14. f(2) + 3 = 3
15. g(-4) = 32
Step-by-step explanation:
here’s a pic of my work:
Related Questions
The difference of seven times a number and five is one hundred find the number
Answers
Let the number be x
seven times the number = 7x
The difference of seven times a number and five is one hundred. It means that
7x - 5 = 100
7x = 100 + 5
7x = 105
x = 105/7
x = 15
The number is 15
Don buys a shirt for $24.85. His friend Daryl spends $3.15 more for his shirt. Sean paid the same price as Daryl for his shirt but bought 2. How much did Sean spend for his 2 shirts?
Answers
Solution
- Don buys a shirt for $24.85.
- Daryl spends $3.15 more for his shirt. This means that Daryl spends
[tex]\$24.85+\$3.15=\$28[/tex]- Thus, Daryl spends $28 on his shirt.
- Sean paid the same price as Daryl, that is, he paid $28 for each shirt.
- Sean bought two shirts, thus, Sean spends:
[tex]\$28+\$28=\$56[/tex]Final Answer
Sean spends $56 on his 2 shirts
X Consider lines L and M on the graph below. Which of the following BEST describes the slope of these two lines? y L М. 10 9 8 7 6 5 3 2 1 X 0 1 2 3 4 5 6 7 8 9 10 L has a greater slope than M. Land M have the same slope. M has a greater slope than L.
Answers
since they are parellel lines, we conclude that they have the same slope, the second option is the correct one.
One weekend, 5,780 people saw a new movie at 17 different theaters. Each theater sold tickets at $7.50 a piece. If each theater received the same number of moviegoers, how much did each theater make?
Answers
The amount that each theater make if they received the same number of moviegoers will be $2550.
How to calculate the amount?From the information, 5,780 people saw a new movie at 17 different theaters and each theater sold tickets at $7.50 a piece.
Therefore, the amount that each theater make if they received the same number of moviegoers will be:
= (5780 × $7.50) / 17
= $43350 / 17
= $2550
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The variables x and y vary directly. Write an equation that relates the variable. Then find x when y=16.
Answers
7) We know that x = 5 and y = 2
We can write an equation that relates this values as a proportion.
Let's say there is a number r such as:
x*r=y
That's a equation that relates x and y. Let's solve for the values given.
[tex]5\cdot r=2[/tex]Now solve for r:
[tex]r=\frac{2}{5}[/tex]The relation we found is:
[tex]x\cdot\frac{2}{5}=y[/tex]Now to find the value of x when y = -6, we replace it in the equation:
[tex]\begin{gathered} x\cdot\frac{2}{5}=-6 \\ x=-6\cdot\frac{5}{2}=-15 \end{gathered}[/tex]Then with this relation, x = -15 when y = -6
An inverse variation includes the points (10, 2) and (n, 4). Find n.
Answers
SOLUTION
An inverse variation is given as
[tex]\begin{gathered} a\text{ }\propto\text{ }\frac{1}{b} \\ \text{Introducing a constant k, we have } \\ a\text{ = }\frac{k}{b} \end{gathered}[/tex]Putting a = 10 and b = 2, we have;
[tex]\begin{gathered} 10\text{ = }\frac{k}{2} \\ k\text{ = 10 x 2 = 20 } \end{gathered}[/tex]The relationship becomes
[tex]\begin{gathered} a\text{ = }\frac{20}{b} \\ \text{Putting a = n, and b = 4, we have } \\ n\text{ = }\frac{20}{4} \\ \\ n\text{ = 5} \end{gathered}[/tex]Therefore, n = 5
The country of Latveria has a population of 11.2 million at the start of 1988, which grows at 4.4% per year.A) Write a recursive equation for the population of Latveria.B) Write an explicit equation for the population of Latveria.C) To the nearest tenth of a million, what is the population of Latveria at the start of 1994.
Answers
A) The recursive formula takes into account the previous term. For each term, the next term is expressed in respect to it
Looking at the given scenario, the popularion is increasing by 4.4%. This means that the common ratio is
1 + 4.4/100 = 1.044
Given that the initial population is 11200000, the recaursive formula or equation would be
[tex]\begin{gathered} f_n=\text{ 1.044}f_{n\text{ - 1}} \\ \text{where f}_1=\text{ 11200000} \end{gathered}[/tex]B) For the explicit formula, the general formula for a geometric sequence is
an = a1 * r^(n - 1)
a1 = first term = 11200000
r = common ratio = 1.044
The explicit equation would be
an = 11200000 * 1.044^(n - 1)
C) At the start of 1994, the number of terms, n = 7
We would find a7 by substituting n = 7 into the explicit equation. We have
a7 = 11200000 * 1.044^(7 - 1)
a7 = 11200000 * 1.044^6 = 14501770
the answer choices area. y = 1/3x +2b. y = 2x + 1/3c. y = -1/3x. + 2d. y = -2x - 1/3
Answers
We have to find the line equation of the function shown. We see that passes through the points:
[tex](0,2)\text{ and }(3,1)[/tex]For doing so, we will find the slope and the y-intercept. The slope is given by the expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x₁,y₁) and (x₂,y₂) are two points of the line. In this case, replacing we obtain:
[tex]m=\frac{1-2}{3-0}=\frac{-1}{3}=-\frac{1}{3}[/tex]And thus, the slope is - 1/3. Now, for the y-intercept, we remember that when the x-coordinate is 0, the y-intercept is the y-coordinate.
As the line passes through the point (0,2), the y-intercept will be 2.
Putting those two together, the equation of the line will be:
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{3}x+2 \end{gathered}[/tex]How much grain can a farmer hold in this silo? Use π = 3.14.A. 2,093.3 ft³B. 11,513.3 ft³C. 9,420 ft³D. 12,560.2 ft³
Answers
To find out how much grain the farmer can hold we need to find the volume of the silo. The silo is made from a circular cylinder and half a sphere.
The volume of the cylinder is given by:
[tex]V=\pi r^2h[/tex]In this case r=10 and h=30, plugging this values in the equation above we have that the volume of the cylinder is:
[tex]\begin{gathered} V=(3.14)(10)^2(30) \\ V=9420 \end{gathered}[/tex]Hence the volume of the cylinder is 9420 cubic feet.
Now we need to find the volume ot half the sphere, the volume og an sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]Plugging the radius we have that:
[tex]\begin{gathered} V=\frac{4}{3}(3.14)(10)^3 \\ V=4186.6 \end{gathered}[/tex]Now, we only need half this volume then the volume of the top of the silo is:
[tex]V=2093.3[/tex]Finally we add the volume of the cylinder and half the sphere, therefore the volume of the sylo is:
[tex]11513.3[/tex]and the answer is B.
Ms.Macncheese has 7 plates of fish sticks if she ate 4 how many dose she have left?
A. 3
B. 2
C.1
D.11
Answers
Answer:
3
Step-by-step explanation:
7 - 4 is 3
HELP PLSSSSSSSSSSSSSS
Answers
Answer: 64
Step-by-step explanation:
Length x width x higth= volume
4 x 8 x 2 = 64
Answer:
4 cm
Step-by-step explanation:
First, find the volume of the rectangular prism.
4*8*2=32*2=64 cm^-3
Now, the formula for the volume of the cube is:
Volume = side ^ 3
We know the volume is 64 cm^3, so plug it in to the equation:
64 = side ^ 3
take the cube root of both sides
4 = side
Write the equation for the graph below.Tomato Prices108Price (In dollars)01 2 3 4 5 6 7 8 9 10Weight(in pounds)
Answers
The form of the linear equation is
y = m x + b
m is the slope of the line
b is the y-intercept
The rule of the slope is
[tex]m=\frac{y2-y1}{x2-x1}[/tex](x1, y1) and (x2, y2) are two points on the line
Since (0,0) and (10, 12) are two points on the line
x1 = 0 and y1 = 0
x2 = 10 and y2 = 12
Now substitute them in the rule to find m
[tex]m=\frac{12-0}{10-0}=\frac{12}{10}=1.2[/tex]The slope of the line is 1.2
Substitute it in the form of the equation
y = 1.2 x + b
b is the y-intercept which means value y at x = 0
Since at x = 0, y = 0
Then b = 0
The equation of the line is
y = 1.2 x
3. Solve the absolute inequality |2x + 3| < x + 6
Answers
Answer
The solution is
-3 < x < 3
Explanation
To solve an expression with the absolute value symbol. we obtain two solutions for it.
We first solve when the other side of the equation to the absolute value symbol has positive sign.
Then, we obtain another solution by setting that other side (the right-hand side) to negative. For equations involving inequality signs, the second solution usually changes the inequality sign.
| 2x + 3 | < x + 6
First solution
2x + 3 < x + 6
2x - x < 6 - 3
x < 3
Second solution
2x + 3 > -(x + 6)
2x + 3 > -x - 6
2x + x > -6 - 3
3x > -9
Divide both sides by 3
(3x/3) > (-9/3)
x > -3
So, the solution written together,
x > -3 and x < 3
together, it is
-3 < x < 3
Hope this Helps!!!
Your friend has a coln that is not fair. It comes up heads 70% of the time and talls 30% of the time. You flip it twice. Let Xbe the number of heads that come up. Find the probability distribution for X
Answers
Let X be the number of heads that come up
[tex]\begin{gathered} \text{Probability of head = 70\% = }\frac{70}{100} \\ \text{Probability of tail = 30\% = }\frac{30}{100} \end{gathered}[/tex]Step 1: Write out the formula for the binomial probability distribution
[tex]P_x=^nC_xp^xq^{n-x}[/tex][tex]undefined[/tex]a cylinder had a radius of 3 and height of 2 need answer quick
Answers
To find the volume of a cylinder with radius 3 and height 3
we will use the formular below:
[tex]V=\pi r^2h[/tex]where r is the radius and h is the height
From the question, r=3 and h = 2
substitute the value into the formula
[tex]V=\pi(3)^2\times2[/tex][tex]V=18\pi[/tex]If we substitute the value of pie = 22/7
Then,
[tex]V=18\times\frac{22}{7}[/tex][tex]V\approx56.57\text{ cubic unit}[/tex]solve the equations and verify the answer
Answers
Answer:
See below
Step-by-step explanation:
I THINK what you wrote is:
2(x-2) - 3(x-3) = (5x-5) - 4(x-8)
2x -4 -3x+9 = 5x-5 -4x+ 32
2x-3x-5x+4x = 4 -9 -5 +32
-2x = 22 *** EDITED ***
x = - 11
Trevor's bonus last year with $6720 and this was 12% of his base salary. what is his base salary?
Answers
Answer:
$56,000.
Explanation:
Let his base salary = s
12% of his base salary = $6720
Thus, we have:
[tex]12\%\text{ of s=6720}[/tex]Next, solve for s:
[tex]\begin{gathered} \frac{12}{100}\times s=6720 \\ 12s=6720\times100 \\ s=\frac{6720\times100}{12} \\ s=56,000 \end{gathered}[/tex]His base salary is $56,000.
1. In 2003, the U.S. imported one million, eight hundred seventy thousand 2 barrels of crude oil per day. In 1988. the U.S, imported only nine hundred eleven thousand barrels per day. How many fewer barrels per day did the U.S. import in 1988? Write the equation.
Answers
Let's begin by identifying key information given to us:
Import (2008) = 1,870,000 bbl
Import (2008) =
Use the sketch tool to mark the picture with the given information. Then choose what postulate proves the triangles congruent.
Answers
We choose ASA Postulate to prove this triangle congruent.
In the given question given that
[tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].
[tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].
Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].
So [tex]m\angle BAC\cong m\angle DAC[/tex]
Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].
So [tex]m\angle BCA\cong m\angle DCA[/tex]
Then [tex]AC\cong AC[/tex]
Then [tex]\triangle BAC\cong \triangle DAC[/tex]
There given postulate are AAS, ASA, SSS, SAS.
We have proved using the ASA postulate.
Now describing the ASA postulate.
ASA means Angle-Side-Angle Postulate.
According to ASA Postulate, two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.
Hence, we choose ASA Postulate to prove this triangle congruent.
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Please solve for x using steps 1/3x= 1/3+6/x
Answers
You have the following algebraic equation:
1/3x = 1/3 + 6/x
In order to solve the previous equation you first multiply both sides of the equation by x, thus, you can quit x denominators in the equation. Proceed as follow:
1/3x = 1/3 + 6/x multiply by x both sides
1/3 = x/3 + 6 multiply by 3 both sides
1 = x + 18 subtract 18 both sides
1 - 18 = x + 18 - 18
-17 = x
-17 = x is the same as x = -17. The solution to the given equation is x = -17.
How much hectares is 61,230 km²
Answers
Answer:
6 hecters in the khlathmandu
Jose invests $8,216 in a savings account with a fixed annual interest rate of 7% compounded 12 times per year. What will the account balance be after 11 years?
Answers
After 11 years, the account balance is $17,704.987. (approx.)
Compound interest is defined.The principle of the first loan is multiplied by the annual interest rate multiplied by the number of compound periods minus one to calculate compound interest.
The principal of the loan plus compound interest will then be what is left.
Given,
P = $8,216 for the principal value.
Interest rate, r = 7% or 0.07.
Period, with t = 11.
Interest applied n times every time period, or 12 times.
As far as we are aware, A = P(1 + r/n) n*t
where A is the whole sum.
Fill out the formula with the values,
=> A = 8216(1 + 0.07/12) ^ 11*12
= 8216((12 + 0.07)/12) ^ 132
Upon calculation, we obtain,
≅ $17,704.987
As a result, after 11 years, the account will have a balance of $17,704.987 (about).
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How do you do this step by step?
-7 + 9 + (-8)
Answers
Step-by-step explanation:
-7 + 9 + (-8)
2 + (-8)
-6
Hope this helps! :)
Step-by-step explanation: Remove parenthesis. If there is a "+" in front of an expression in parenthesis, the expression remains the same.
-7+9-8. Calculate the sum or difference. You should get -6.
write down in terms of n, an expression for the nth term of the following sequences
-7,-12,-17,-22,-27
Answers
The expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2
The sequence is -7, -12, -17, -22, -27...
The first term = -7
The common difference = The second term - The first term
= -12 - (-7)
= -12+7
= -5
The nth term of the sequence = a+(n-1)d
Where a is the first term
d is the common difference
n is the n terms
Substitute the values in the equation
The nth term of the sequence = -7+(n-1)-5
= -7-5n+5
= -5n-2
Hence, the expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2
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(04.01 LC)The graph shows a system of equations:y = x + 433y = -2x + 2-3-4-5What is the solution to the system of equations?0 1-2, 2)(2, 2)(2,-2)O(-2,-2)
Answers
Explanation:
We have two equation of line. Both lines intersect at a point.
The point of intersection of two graphs, is the solution of the graph.
At this point, both will have same x and y values
Tracing the graph:
The point of intersection occurs at x = -2, y = 2
Hence, the solution is at (-2, 2)
At the nearest wholesale store, 3 bags of cereal cost $21.75. Which equation represents the proportional relationship?
Answers
The cost of the 5 bags using proportionality method is: $36.25
What is proportionality?
In mathematics, the term proportionality can be defined by considering a two quantities in constant ratio. And the two quantities can be recognized as the variable y and x. Where, the variable y is defined as directly proportionate to the changes in the variable x which is based on its constant ratio.
According to the question, the given data states that 5 bags will cost $36.25.
By using proportionality method to solve the given statement. Put the price over the number of bags
21.75 x
---------- = ---------
3 bags 5 bags
Using cross products defined in standard mathematics,
21.75 * 5 = 3x
108.75 = 3x
Divide each side by 3
108.75/3 = 3x/3
36.25 =x
5 bags will cost 36.25
Hence, the cost of the 5 bags using proportionality method is: $36.25
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Correct Question:
At the nearest wholesale store, 3 bags of bulk cereal cost $21.75. At this rate, how much would 5 bags of bulk cereal cost?
Together, Nora and Addison own 152 shares of stock. Nora has 4 less than three times Addison's amount. How many shares does each girl have?
Answers
Dora have 144 shares of stocks while Addison have 37 shares of stocks.
Let us say that Addison own X shares of stock.
According to the situation provided,
The number of shares of stocks own by Dora are 4 less than 3 times of the Stocks owned by Addison.
Stocks Owned by Dora = 3x - 4
The total shares of stocks are 152.
So, we can write the relation between the stocks as,
x + 3x - 4 = 152
4x - 4 = 152
The above formed relations between the stocks is in the form of linear equation in one variable. A linear equation has highest power of variable equal to 1 and only one variable.
Now, solving the equation further,
4x - 4 = 152
4x = 148
x = 37
The total numbers of stocks owned by Addison are 37.
Shares of stocks owned by Dora are 3(37)-4.
The share of stocks owned by Dora are 144.
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If Y (-7, -4) and Z (5, 2), find the slope of a line perpendicular to YZ
Answers
Answer:
slope of perpendicular line = - 2
Step-by-step explanation:
calculate the slope of YZ using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = Y (- 7, - 4 ) and (x₂, y₂ ) = Z (5, 2 )
[tex]m_{YZ}[/tex] = [tex]\frac{2-(-4)}{5-(-7)}[/tex] = [tex]\frac{2+4}{5+7}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2
A shopper pushes a grocery cart with a force F of 50 N downward and to the right, as shown in the figure below. The anglethe handle makes with the horizontal is 37°, and the cart is moved 14 m. Find the work W done, in joules (1).Ed
Answers
Solution
For this case we can create the following plot:
We want to find the work so we can use this formula:
[tex]W=Fd\cos \theta[/tex]Replacing we got:
[tex]W=50\cdot14m\cdot\cos 37=559.04J[/tex]A= hlba)10. The volume of a large can of tuna fish can be calculated using the formula V = ar?h.Write an equation to find the radius, r, in terms of V and h. Determine the diameter, tothe nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and aheight of 3.3 inches.
Answers
Given the formula for volume:
[tex]V\text{ = }\pi r^2h[/tex]Let's rewrite the formula in terms r, V and h.
i) Rewriting for r in terms of V and h :
[tex]\begin{gathered} V\text{ = }\pi r^2h \\ \frac{V}{h}=\pi r^2 \\ \\ \sqrt[]{\frac{V}{\pi h}}=r \\ \\ r\text{ = }\sqrt[]{\frac{V}{\pi h}} \end{gathered}[/tex]2) Given:
Volume, V = 66 cubic inches
height, h = 3.3 inches
We know that diameter is radius multiplied by 2.
To find the diameter, first find the radius.
Therefore, we have:
[tex]\begin{gathered} r\text{ = }\sqrt[]{\frac{V}{\pi h}} \\ \\ r\text{ = }\sqrt[]{\frac{66}{3.3\pi}} \\ \\ r\text{ = }2.52\text{ inches} \end{gathered}[/tex]Since the radius is 2.52 inches, the dia,eter will be:
D = r x 2 = 2.52 x 2 = 5.04 inches
To the nearest inch = 5 inches
ANSWER:
diameter = 5 inches