1. Consider the following functions. f(x) = 3x2 + x + 2 g(x) = 4x2 + 2(3x – 4) h(x) = 5(x2 - 1) a. Find f (x) - g(x). b. Find g(x) - h(x).
Answers
a.
Let's write function g(x) better:
[tex]g(x)=4x^2+2(3x-4)=4x^2+6x-8[/tex]Now we can do the substraction easier
[tex]f(x)-g(x)=(3x^2+x+2)-(4x^2+6x-8)_{}[/tex][tex]f(x)-g(x)=3x^2+x+2-4x^2-6x+8[/tex][tex]f(x)-g(x)=(3-4)x^2+(1-6)x+2^{}+8[/tex][tex]f\mleft(x\mright)-g\mleft(x\mright)=-x^2-5x+10[/tex]That's answer a
b.
We write h(x) better too:
[tex]h(x)=5(x^2-1)=5x^2-5[/tex]And do the same as before:
[tex]g(x)-h(x)=(4x^2+6x-8)-(5x^2-5)[/tex][tex]g(x)-h(x)=4x^2+6x-8-5x^2+5[/tex][tex]g(x)-h(x)=(4-5)x^2+6x-8+5[/tex][tex]g(x)-h(x)=-x^2+6x-3[/tex]That's answer b
Related Questions
What do you notice about these two expressions? 4 50 8 + 15 50 8 + 7 15 1 They both show subtracting 2 4 They both show adding 3 50 8 They both contain the sum 7 15
Answers
The 3rd option is right as both contain the sum
50/7 + 8/15
what is the volume of a sphere with a radius of 3.3m rounded to the nearest tenth in cubic meters
Answers
For this exercise you need to use the following formula for calculate the volume of a sphere:
[tex]V=\frac{4}{3}\pi r^3[/tex]Where "r" is the radius of the sphere.
In this case you can identify that:
[tex]r=3.3m[/tex]Then, you can substitute this value into the formula:
[tex]V=\frac{4}{3}\pi(3.3m)^3[/tex]Finally, evaluating, you get that the volume of the sphere (rounded to the nearest tenth in cubic meters) is:
[tex]V\approx150.5m^3[/tex]The answer is:
[tex]V\approx150.5m^3[/tex]The total profit (in dollars) from the sale of a espresso machines is P(x) = 160x - 0.85x^2 + 25.Evaluate the marginal profit at the following values to 4 decimal place accuracy if necessary:(A) P'(60) =(B) P'(65) =
Answers
We will have the following:
[tex]\begin{gathered} P(x)=160x-0.85x^2+25 \\ \\ \Rightarrow P^{\prime}(x)=160-1.7x \end{gathered}[/tex]So:
A) P'(60):
[tex]P^{\prime}(60)=160-1.7(60)\Rightarrow P^{\prime}(60)=58[/tex]B) P'(65):
[tex]P^{\prime}(65)=160-1.7(65)\Rightarrow P^{\prime}(65)=49.5[/tex]can someone please help me find the Answer to the following
Answers
First, to find the slant height, we use Pythagorean's Theorem to find the slant height, as the image below shows.
Then,
[tex]\begin{gathered} h^2=10^2+7.5^2 \\ h^2=100+56.25 \\ h=\sqrt[]{156.25} \\ h=12.5ft \end{gathered}[/tex]The slant height is 12.5 feet.Now, the surface area formula is
[tex]SA=2bs+b^2[/tex]Where s = 12.5 and b = 15.
[tex]\begin{gathered} SA=2\cdot15\cdot12.5+15^2 \\ SA=375+225 \\ SA=600ft^2 \end{gathered}[/tex]Hence, the surface area of the pyramid is 600 square feet.During a special one-day sale, 600 customers bought the on-sale sandwich. Ofthese customers, 20% used coupons. The manager will run the sale again the nextday if more than 100 coupons were used. How many coupons were used andshould she run the sale again?80 coupons were used; no, she should not run the sale again140 coupons were used; yes, she should run the sale againOOO115 coupons were used; yes, she should run the sale again120 coupons were used; yes, she should run the sale again
Answers
Answer:
120 coupons were used; yes, she should run the sale again
Explanation:
The total number of customers = 600
The percentage that used coupon = 20%
[tex]\begin{gathered} 20\%\text{ of 600} \\ =\frac{20}{100}\times600 \\ =120 \end{gathered}[/tex]Thus, 120 coupons were used.
Since more than 100 coupons were used, the manager should run the sale again.
I need to know number 6SP please I need to find the mean
Answers
The mean absolute deviation is given by the next formula:
[tex]\text{MAD}=\frac{1}{n}\sum ^{\square}_i|x_i-\bar{x}|[/tex]Where n is the number of points in the data set and x with a bar on top is the mean.
In our case,
[tex]\bar{x}=\frac{1}{25}(5\cdot1+5\cdot2+4\cdot3+4\cdot4+6\cdot5+6\cdot1)=\frac{79}{25}[/tex]and n=25.
Then,
[tex]\text{MAD}=\frac{1}{25}(5|1-\frac{79}{25}|+5|2-\frac{79}{25}|+4|3-\frac{79}{25}|+4|4-\frac{79}{25}|+6|5-\frac{79}{25}|+|6-\frac{79}{25}|)[/tex]Finally,
[tex]\text{MAD}=\frac{862}{625}\approx1.4[/tex]The answer is 1.4 once rounded.
Help me with my Algebra 2 work :) -- (Multiplying and Dividing Rational Expressions)(Drag and Drop question)
Answers
a. For the expression P(x) • Q(x), we multiply the two functions.
[tex]\frac{2}{3x-1}\times\frac{6}{-3x+2}[/tex]When multiplying rational expressions, simply multiply the numerator to the other numerator and the denominator to the other denominator.
Hence, P(x) • Q(x) is equal to:
[tex]\frac{12}{(3x-1)(-3x+2)}[/tex]
b. For the expression, P(x) ÷ Q(x), we multiply P(x) to the reciprocal of Q(x).
[tex]\frac{2}{3x-1}\times\frac{-3x+2}{6}[/tex]As mentioned above, when multiplying rational expressions, simply multiply the numerator to the other numerator and the denominator to the other denominator. The expression becomes:
[tex]\frac{2(-3x+2)}{6(3x-1)}[/tex]Then, simplify 2/6 to 1/3.
Hence, P(x) ÷ Q(x) is equal to:
[tex]\frac{-3x+2}{3(3x-1)}[/tex]Samantha have six times as many fish in her aquarium as Lily. Lily and Samantha have 70 fishes together. how many fish does each girl have?
Answers
The problem indicates that Samantha has 6 times as many fish as Lily.
If we call the number of fishes that Lily has "x", then the number of fishes that Samantha has will be "6x".
Lily: x
Samantha: 6x
Now, since together they have 70 fishes, we need to add the two quantities (x and 6x) and equal them to 70:
[tex]x+6x=70[/tex]To solve this problem we need to solve this equation for x.
The first step is to add the like terms on the left of the equation:
[tex]7x=70[/tex]And then, divide both sides of the equation by 7:
[tex]\begin{gathered} \frac{7x}{7}=\frac{70}{7} \\ \end{gathered}[/tex]As you can see 7 in the numerator and denominator on the left side cancel each other:
[tex]x=\frac{70}{7}[/tex]And on the right side, 70/7 is equal to 10:
[tex]x=10[/tex]Let's remember our initial definitions:
Lily: x
Samantha: 6x
Since we now know that x=10, we conclude that Lily has 10 fishes.
To calculate the amount that Samantha has multiply 6 by 10:
[tex]6x=6(10)=60[/tex]Samantha has 60 fishes.
Answer:
Lily: 10
Samantha: 60
Number of balls madeHow many games had 11 or fewer balls made?
Answers
The number of games that had 11 or fewer balls made = 6
Explanations:The number of games that have 11 or fewer balls made will be the number of games that have between 0 to 11 balls made.
Number of games that had 0-3 balls made = 0
Number of games that had 4 - 7 balls made = 1
Number of games that had 8-11 balls made = 5
The number of games that had 11 or fewer balls made = (Number of games that had 0-3 balls made) + (Number of games that had 4-7 balls made) + (Number of games that had 8-11 balls made)
The number of games that had 11 or fewer balls made = 0 + 1 + 5
The number of games that had 11 or fewer balls made = 6
Answer:
6
Step-by-step explanation:
Benchmark estimate of 6.34 + 3.95
Answers
The value of 6.34 + 3.95 using benchmarks estimating is 10.
BenchmarksBenchmarks to estimate means rounding to the nearest whole number
Step 1: If the value after decimal is 5 or more than round off it to successive whole number other wise round off it to preceding whole number
Step 2: We need to round 6.34 and 3.95 to the nearest whole number
6.34 will be rounded to 6.
3.95 will be rounded to 4.
Since we have gotten the rounded number to be 6 and 4 then;
Benchmark estimate = 6 + 4
= 10
Therefore, Benchmark estimate 6.34 + 3.95 =10.
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Compare the functions f(x) = 20x² and g(x) = 4* by completing parts (a) and (b).(a) Fill in the table below. Note that the table is already filled in for x = 2.(The ALEKS calculator can be used to make computations easier.)f(x)=20x²g(x) = 4*(b) For x ≥ 5, the table suggests that f(x) is (Choose one) ✓ greater than g(x).I need help with this math problem.
Answers
ANSWERS
(a) Table:
(b) For x ≥ 5, the table suggests that f(x
EXPLANATION
(a) First, we have to fill in this table. To do so, we have to substitute x with each value from the first column for each function,
[tex]f(3)=20\cdot3^2=20\cdot9=180[/tex][tex]g\mleft(3\mright)=4^3=64[/tex]Repeat for all the other x-values,
(b) As we can see in the table, for x = 2, x = 3, and x = 4, f(x) is greater than g(x). But, for x = 5 and x = 6, f(x) is less than g(x).
Hence, for x ≥ 5, f(x) is never greater than g(x).
Determine the graph of line with the given y-intercept and slope
Answers
The form of the equation of the line is
y=mx+b
where m is the slope and
b is the y-intercept
In our case
m=3/2
and
b=-5
the equation of the line is
y=3/2 x -5
In order to graph we need at least another point and connect it with the y-intercept
if x=2
y=3/2 (2)-5=3-5=-2
y=-2
The point is
(2,-2)
Then we can graph the line
(0,2)-5The function g(x) = -3x - 6. Compare the slopes.A. The slope of f(x) is the same as the slope of g(x).B. The slope of f(x) is undefined, and the slope of g(x) is negative.Ο ΟC. The slope of f(x) is greater than the slope of g(x).D. The slope of f(x) is less than the slope of g(x).
Answers
To solve the exercise, first we are going to find the slope of the function f(x). Since we have a graph of the function, we can see two points through which the line passes:
[tex]\begin{gathered} (x_1,y_1)=(0,2) \\ (x_2,y_2)=(1,-1) \end{gathered}[/tex]Now we can use this formula to find the slope:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex][tex]\begin{gathered} m_{f(x)}=\frac{-1-2}{1-0} \\ m_{f(x)}=\frac{-3}{1} \\ m_{f(x)}=-3 \end{gathered}[/tex]Then, the slope of the function f(x) is -3.
On the other hand, the function g(x) also describes a line and is written in slope-intercept form, that is:
[tex]\begin{gathered} y=mx+b\Rightarrow\text{ slope-intercept form} \\ \text{ Where m is the slope and} \\ b\text{ is the y-intercept of the line} \end{gathered}[/tex]Then, you can see that the slope of the function g(x) is -3, because
[tex]\begin{gathered} g(x)=-3x-6 \\ m_{g(x)}=-3 \\ \text{and} \\ b=-6 \end{gathered}[/tex]Therefore, the slope of f(x) is the same as the slope of g(x) and the correct answer is option A.
Suppose a charity received a donation of $17.3 million. If this represents 41% of the charity's donated funds, what is the total amount of its donated funds? Round your answer to the nearest million dollars.
Answers
Using the concept of percentage, the total amount that was donated to charity is $42.195 million.
What is meant by percentage?A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. The abbreviation used to represent percentages is the symbol "%". A% has neither a recognized unit of measurement nor any dimensions. Take this as an example: There will be 50 men in the class if there are 100 students total and there are 50 men in the class. There are 250 male students overall, or 250 out of 500.
According to the data, the charity got a donation of $17.3 million, or 41% of its total donations.
Let x serve as a symbol for the total sum.
This will be shown as follows:
41% × x = $17.3million
0.41x = $17.3 million
Divide by 0.41
x = $17.3million / 0.41
x = $42.195 million
The total amount that is donated to charity is $42.195 million
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Find the measureOf an act intercept by and inscribed whose measure is 75°Hent, draw a picture and label it,
Answers
From the arc-angle relationships, we know that the inscribed angle is half of the intercepted arc, that is,
[tex]75=\frac{arcAB}{2}[/tex]Then, by moving the denominator to the left hand side, we get
[tex]\begin{gathered} 2\times75=arcAB \\ \text{arcAB}=150 \end{gathered}[/tex]then, the arcAB measure 150 degrees.
The Jordan family budgeted 16% of their disposable annual income of $44,000 for food, but found they needed $35 more per week. How much of their income should now beadded to their food budget?$1,587.00$1,820.00$1,924.00$2,042.00None of these choices are correct.
Answers
Given:
The percentage of income budgeted for food, R=16%.
The income of the family, I=$44,000.
The extra amount for food needed per week, x=$35.
The amount budgeted by the family for food in an year is,
[tex]\begin{gathered} A=\frac{R}{100}\times I \\ =\frac{16}{100}\times44000 \\ =7040 \end{gathered}[/tex]There are 365 days in an year and 7 days in a week.
The number of weeks per year is,
[tex]N=\frac{365}{7}[/tex]The extra amount added by the family for food is,
[tex]\begin{gathered} A_w=xN \\ =35\times\frac{365}{7} \\ =1825 \end{gathered}[/tex]Hence, the family should add $1825 to their food budget.
So, none of these choices are correct.
use the information to answer the following questionsmr. ramirez purchased 20 concert tickets for a total of $225.the concert tickets cost $15 for adults and $10 for children under the age of 12 part A: write a system of equations to represent the given scenario. use the variables "a" for adults and "c" for children.
Answers
Answer:
a + c = 20
15a + 10c = 225
Explanation:
If 'a' is the number of tickets for adults and 'c' is the number of tickets for children, we can write the following equation:
a + c = 20
Because Mr. Ramirez purchased a total of 20 concert tickets.
In the same way, if the cost of the tickets is $15 for adults and $10 for children, we can write the following equation:
15a + 10c = 225
Because 15a is the total cost for adults, 10c is the total cost for children and 225 is the total cost in general.
Therefore, the system of equations that represents the given scenario is:
a + c = 20
15a + 10c = 225
were would he be at in 6 seconds
Answers
6 seconds later we can say that dwyane was running to the left of zero, because if he was running at 4 meters per second to the right when he passed the zero point, hence 6 seconds later he was on the left of the zero at the point -2.
What are the domain and range of the function f of x is equal to the quantity x squared plus 6x plus 8 end quantity divided by the quantity x plus 4 end quantity?
A. D: {x ∊ ℝ | x ≠ 4}; R: {y ∊ ℝ | y ≠ 0}
B. D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2}
C. D: {x ∊ ℝ | x ≠ 4}; R: {y ∊ ℝ | y ≠ 2}
D. D: {x ∊ ℝ | x ≠ −2}; R: {y ∊ ℝ | y ≠ 0}
Answers
The domain and range of [tex]f(x) = \frac{x^{2}+ 6x+8}{x+4}[/tex] is D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2} .
The domain of a function f(x) is set of the value of x for which it is defied and Range of function is set of values f takes .
The rational number [tex]f(x) = \frac{p(x)}{q(x)}[/tex] where p(x) and q(x) are polynomial in terms of x and q(x) ≠ 0 . The domain of rational number is set of values that do not cause denominator equal to zero .
The given function is :
[tex]f(x) = \frac{x^{2}+ 6x+8}{x+4}[/tex]
we need to find domain and range of function,
For domain put denominator equals to zero
x+4 = 0
x = -4
so, domain is every real number except number making it zero
domain = (-∞,-4)∪(-4,∞) and x ≠ -4
For range ,factoring numerator
x²+6x+8 = x²+2x+4x+8
x(x+2)+4(x+2) = (x+4)(x+2)
Putting numerator back,
[tex]f(x) = \frac{(x+4)(x+2)}{x+4}[/tex]
Cancelling factor (x+4) from numerator and denominator
[tex]f(x) = x+2[/tex]
Putting x+2 = 0
[tex]x +2 = 0\\x = -2[/tex]
range = (-∞,-2)∪(-2,∞) and f(x) ≠ -2
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D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2}
I took the test
Good morning can someone help me with my math
Answers
Part A
Angles 1 and 2 (<1 and <2 ) are alternate angles
Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines
Therefore < 1 and < 2 are equal
Part B
AC and BD are Arc angles
AC = 2 x < 1
BD = 2 x < 2
Since < 1 and < 2 are equal
Then AC = BD
Part C
Parallel lines AB and BC will intercept the AC and BD arcs
Can anyone help me pls this is my last grade for algebra and Ik failing the class right now I need this grade to be able to pass my class pls help
Answers
For every room added, the price increase is $50, therefore the slope is equal to 50.
Since the value for one room is $125 and we know that each room costs $50, then the y-intercept is the value for 1 room minus 50.
[tex]b=125-50=75[/tex]Now we can create the function for this situation:
[tex]f(x)=50\cdot x+75[/tex]Where f(x) is the price and x is the number of rooms to be cleaned. Since the function is linear, the unit rate is equal to the slope, so the unit rate is 50.
The amount charged to drive to the client's home is the fixed part of the price, so it is equal to the y-intercept. The price is $75.
To find the cost of 8 rooms we need to make x = 8 and calculate the value of the expression.
[tex]f(8)=50\cdot8+75=475[/tex]The value would be $475.
Is (5, 1) a solution to the equation y = 1? yes no
Answers
Since the coordinates are written as (x,y), for the point (5,1) we have that:
[tex]\begin{gathered} x=5 \\ y=1 \end{gathered}[/tex]Therefore, this is a solution to the equation y=1.
Then, the answer is yes.
The function g is graphed below. At what numbers in the interval (-4,4) is g discontinuous?
Answers
The graph has discontinuity if the curve or the line is not continuous.
From the graph shown, The graph stopped at (-1, 0) and then starts again at (-1, 4), stopped again at (3, 2)
then gone with (3, 3) and continues up to (4, -2)
So graph g discontinuous at -1 and 3
Rewrite the equation by completing the square.X^2 + 11x + 24 = 0
Answers
Solution
For this case we can complete the square on this way:
[tex]x^2+11x+(\frac{11}{2})^2+24-(\frac{11}{2})^2[/tex]and if we simplify we got:
[tex](x+\frac{11}{2})^2+24-\frac{121}{4}=(x+\frac{11}{2})^2-\frac{25}{4}[/tex]We can use this property:
[tex](a^2+2ab+b^2)=(a+b)^2[/tex]For this case:
[tex]a=x,b=\frac{11}{2}[/tex]Answer:
(x+11/2)^2 = 25/4
did it on khan, hope this helps<3
Find the y - intercept of the equation -7x - 5y = -140
Answers
Given -
-7x - 5y = -140
To Find -
The y-intercept of the equation =?
Step-by-Step Explanation -
The Y-intercept is a point where the graph of the equation cuts the y-axis.
At y-axis x = 0.
So, we know that at y-intercept x = 0
Put x = 0 in -7x - 5y = -140
= -7(0) - 5y = -140
= -5y = -140
= y = 140/4
y = 28
Final Answer -
The y-intercept of the equation = (0, 28)
Answer:
4
Step-by-step explanation:
-7x-5y=-140
Y=4
Because 7 times 5 =35
140 divided by 35=4
5(4)=20
20 times 7=140. So y=4
the function h(t)=-4.9t^2+19t+1.5 describes the height in meters of a basketball t seconds after it has been thrown vertically into the air.what is the maximum height of the basketball? round your answer to the nearest tenth
Answers
we have
h(t)=-4.9t^2+19t+1.5
This function represent a vertical parabola open downward
The vertex represent a maximum
using a graphing tool
see the attached figure
please wait a minute
The vertex is the point (1.94, 19.92)
therefore
the maximum height of the basketball is 19.9 meters
You have $ 24 and you go to the grocery store to buy a Kit Kats snack and a drink You spent $ 1.75 on a drink If each bar of Kit Kat costs $1.49write an inequality that represents how many bars of Kit Kat you can buy
Answers
The inequality that represents the situation is:
[tex]1.49x+1.75\le24[/tex]Where x is the number of Kit Kat we could buy.
I need to find the solution to 5x-2 divided by 6
Answers
Given:
[tex](5x-2)\div6[/tex]To find:
Solve the given expression.
Explanation:
Rewrite the given expression,
[tex]\frac{5x-2}{6}[/tex]Expand the fraction into 2 simpler fractions with common denominator 6,
[tex]\frac{5x}{6}+\frac{-2}{6}[/tex]Simplify the expression, we will get:
[tex]\frac{5}{6}x-\frac{1}{3}[/tex]Final answer:
Hence, the required solution is:
[tex]\frac{5}{6}x-\frac{1}{3}[/tex]
Need help solving this problem This is from my ACT prep guide
Answers
Answer:
[tex]h=101.7\text{ ft}[/tex]Step-by-step explanation:
To approach this situation, let's make a diagram of it;
To solve this problem we can use trigonometric relationships since there are right triangles involved; trigonometric relationships are represented as
[tex]\begin{gathered} \sin (\text{angle)}=\frac{\text{opposite}}{\text{ hypotenuse }} \\ \cos (\text{angle)}=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan (\text{angle)}=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]Then, since we can divide the neighbor building into two parts compounded by two right triangles, use the tan relationship for the 56 degrees triangle, and sin relationship for the 32 degrees triangle:
[tex]\begin{gathered} \tan (56)=\frac{h_1}{150_{}} \\ h_1=150\cdot\tan (56) \\ h_1=22.2\text{ ft} \\ \\ \sin (32)=\frac{h_2}{150} \\ h_2=150\cdot\sin (32) \\ h_2=79.5\text{ ft} \end{gathered}[/tex]Hence, for the total height of the building:
[tex]\begin{gathered} h=h_1+h_2 \\ h=22.2+79.5 \\ h=101.7\text{ ft} \end{gathered}[/tex]Given the equation y = 1.3* Growth a. Does this equation represent growth or decay? 1.3 b. What is the growth or decay factor? e. What is the rate of growth or decay? d. What is the initial value?
Answers
Answer:
a. Growth
b. 1.3
c. 30%
d. 1
Explanation:
The exponential equation given can be written in the form
[tex]y=1.3^x=1(1.3)^x[/tex]From this form, we see that
a. the function represents a growth since 1.3 > 1
b. the growth factor is 1.3
c. The rate of growth is (1.3 - 1) * 100% = 30%
d. the initial value is 1.
Hence, the answers
a. Growth
b. 1.3
c. 30%
d. 1