Let f(x)=x2-2 and g(x)=9-X. Perform the composition or operation indicated.(fg)(-7)
Answers
Given the functions below
[tex]\begin{gathered} f(x)=x^2-2 \\ g(x)=9-x \end{gathered}[/tex]We are to find (fg)(-x)
SOLUTION
First of all, we have to get (fg)(x)
[tex](fg)(x)=(x^2-2)(9-x)[/tex]Expand the function
[tex]\begin{gathered} (fg)(x)=x^2(9-x)-2(9-x) \\ (fg)(x)=9x^2-x^3-18+2x \\ \therefore(fg)(x)=-x^3+9x^2+2x-18 \end{gathered}[/tex]Let us now solve for (fg)(-7)
[tex]\begin{gathered} (fg)(-7)=-(-7)^3+9(-7)^2+2(-7)-18 \\ (fg)(-7)=343+441-14-18=752 \end{gathered}[/tex]Hence,
[tex](fg)(-7)=752[/tex]
Related Questions
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.
Find all solutions in the set of real numbers. Show all your work. cos2θ=−sin2θ
Answers
Equate the given to zero
[tex]\begin{gathered} \cos 2\theta=-\sin ^2\theta\Longrightarrow\cos 2\theta+\sin ^2\theta=0 \\ \\ \text{Use the identity }\cos 2\theta=1-2\sin ^2\theta,\text{ THEN the equation becomes} \\ \cos 2\theta+\sin ^2\theta=0 \\ (1-2\sin ^2\theta)+\sin ^2\theta=0 \\ \\ \text{simplify} \\ (1-2\sin ^2\theta)+\sin ^2\theta=0 \\ 1-2\sin ^2\theta+\sin ^2\theta=0 \\ 1-\sin ^2\theta=0 \\ \\ \text{Add }\sin ^2\theta\text{ to both sides} \\ 1-\sin ^2\theta+\sin ^2\theta=0+\sin ^2\theta \\ 1\cancel{-\sin ^2\theta+\sin ^2\theta}=\sin ^2\theta \\ 1=\sin ^2\theta \\ \text{OR} \\ \sin ^2\theta=1 \\ \\ \text{get the square root of both sides} \\ \sqrt[]{\sin ^2\theta}=\sqrt[]{1} \\ \sin \theta=\pm1 \\ \\ \text{The values for which }\sin \theta\text{ is equal to }+1\text{ or }-1\text{ is} \\ \theta=\frac{\pi}{2}+2\pi n,\theta=\frac{3\pi}{2}+2\pi n \end{gathered}[/tex]Determine whether each equation has a solution. Justify your answer.a. (a + 4) / (5 + a) = 1b. (1 + b)/ (1 - b) = 1c. (c - 5 )/ (5 - c) = 1
Answers
Leave the variable in each equation in one side of the equation to find if it has a solution:
a.
[tex]\begin{gathered} \frac{a+4}{5+a}=1 \\ \\ Multiply\text{ both sides by \lparen5+a\rparen:} \\ \frac{a+4}{5+a}(5+a)=1(5+a) \\ \\ a+4=5+a \\ \\ Subtract\text{ a in both sides of the equation:} \\ a-a+4=5+a-a \\ 4=5 \end{gathered}[/tex]As 4 is not equal to 5, the equation has no solution.b.
[tex]\begin{gathered} \frac{1+b}{1-b}=1 \\ \\ Multiply\text{ both sides by \lparen1-b\rparen:} \\ \frac{1+b}{1-b}(1-b)=1(1-b) \\ \\ 1+b=1-b \\ \\ Add\text{ b in both sides of the equation:} \\ 1+b+b=1-b+b \\ 1+2b=1 \\ \\ Subtract\text{ 1 in both sides of the equation:} \\ 1-1+2b=1-1 \\ 2b=0 \\ \\ Divide\text{ both sides of the equation by 2:} \\ \frac{2b}{2}=\frac{0}{2} \\ \\ b=0 \\ \\ Prove\text{ if b=0 is the solution:} \\ \frac{1+0}{1-0}=1 \\ \\ \frac{1}{1}=1 \\ \\ 1=1 \end{gathered}[/tex]The solution for the equation is b=0c.
[tex]\begin{gathered} \frac{c-5}{5-c}=1 \\ \\ Multiply\text{ both sides by \lparen5-c\rparen:} \\ \frac{c-5}{5-c}(5-c)=1(5-c) \\ \\ c-5=5-c \\ \\ Add\text{ c in both sides of the equation:} \\ c+c-5=5-c+c \\ 2c-5=5 \\ \\ Add\text{ 5 in both sides of the equation:} \\ 2c-5+5=5+5 \\ 2c=10 \\ \\ Divide\text{ both sides by 2:} \\ \frac{2c}{2}=\frac{10}{2} \\ \\ c=5 \\ \\ Prove\text{ if c=5 is a solution:} \\ \frac{5-5}{5-5}=1 \\ \\ \frac{0}{0}=1 \\ \\ \frac{0}{0}\text{ is undefined} \end{gathered}[/tex]As the possible solution (c=5) makes the expression has a undefined part (0/0) it is not a solution.
The equation has no solutionThe school store is running a promotion on school supplies. Different supplies are placed on two shelves.• You can purchase 3 items from shelf A and 2 from shelf B for $26, or• You can purchase 2 items from shelf A and 5 from shelf 8 for $32.Let z represent the cost of an item from shelf A and let y represent the cost of an item from shelf B. Write and solve asystem of equations to find the cost of items from shelf A and shelf B. Show your work and thinking!
Answers
We define the following notation:
• z = cost of an item from shelf A,
,• y = cost of an item from shelf B.
From the statement, we know that:
• 3 items from shelf A and 2 from shelf B cost $26, so we have:
[tex]3z+2y=26,[/tex]• 2 items from shelf A and 5 from shelf B for $32, so we have:
[tex]2z+5y=32.[/tex]We have the following system of equations:
[tex]\begin{gathered} 3z+2y=26, \\ 2z+5y=32. \end{gathered}[/tex]1) To solve this system, we multiply the first equation by 2 and the second equation by 3:
[tex]\begin{gathered} 2\cdot(3z+2y)=2\cdot26\rightarrow6z+4y=52, \\ 3\cdot(2z+5y)=3\cdot32\rightarrow6z+15y=96. \end{gathered}[/tex]2) We subtract equation 1 to equation 2, and then we solve for y:
[tex]\begin{gathered} (6z+15y)-(6z+4y)=96-52, \\ 11y=44, \\ y=\frac{44}{11}=4. \end{gathered}[/tex]We found that y = 4.
3) We replace the value y = 4 in the first equation, and then we solve for z:
[tex]\begin{gathered} 3z+2\cdot4=26, \\ 3z+8=26, \\ 3z=26-8, \\ 3z=18, \\ z=\frac{18}{3}=6. \end{gathered}[/tex]Answer
The cost of the items are:
• z = 6, for items from shelf A,
,• y = 4, for items from shelf B.
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
1) both balloons are red2)neither of the balloons are large
Answers
It is given that there are ballons of different colors in the party pack given by the table.
The total number of red, yellow and blue baloons can be found by adding the respective columns.
The total number of baloons is the sum of all cells combined.
Hence find the total number of red, yellow and blue baloons as follows:
[tex]\begin{gathered} n(R)=12+15+24=51 \\ n(Y)=24 \\ n(B)=25 \end{gathered}[/tex]The total number of baloons is given by:
[tex]\begin{gathered} n(S)=n(R)+n(Y)+n(B) \\ n(S)=51+24+25 \\ n(S)=100 \end{gathered}[/tex]The probability of both red baloons is given by:
[tex]\begin{gathered} P(R,R)=\frac{^{51}^{}C_2}{^{100}C_2} \\ P(R,R)=\frac{17}{66} \end{gathered}[/tex]Hence the probability of both red baloons is 17/66 or 0.2575757....
The function h is a quadratic function whose graph is a translation 7 units left and 8 units up of the function f(x)=x². What is the equation of h in vertex form and in the form y = ax² +bx+c?
Answers
Answer:
The vertex form of a quadratic function is given by f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.
Step-by-step explanation:
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
5 is 100 times? I am not sure.Solve question 1
Answers
Answer:
0.005
0.05
50
Explanation:
For the first question;
Let the number be x.
So let's go ahead and solve for x as shown below;
[tex]\begin{gathered} 10\times x=0.05 \\ x=\frac{0.05}{10} \\ x=0.005 \end{gathered}[/tex]For the 2nd question;
Let the missing number be y.
We can solve for y as seen below;
[tex]\begin{gathered} 100\times y=5 \\ 100y=5 \\ y=\frac{5}{100} \\ y=0.05 \end{gathered}[/tex]For the 3rd question;
Let the missing number be z.
We can solve for z as shown below;
[tex]\begin{gathered} \frac{1}{100}\times z=0.5 \\ \frac{z}{100}=0.5 \\ z=100\times0.5 \\ z=50 \end{gathered}[/tex]what is the factor of 2 and 10
Answers
The factor of 2 and 10 is equal to adding up 10, 2 times:
[tex]2\cdot10=10+10=20[/tex]This way, the factor is 20
What type of wording in a problem statement or description of a situation tells you that you have a rate of change?
Answers
There different types of wording that tells us that we have a rate of change.
For example, when talking about speed, or in general, when talking about any measure per unit of time (meters per second, gallons per minute, miles per hour) all these are rates of change.
Other example, not as common as the first one, is when the statement refers to a slope, which is in other words, a rate of change.
Similar to the first one, when the statement talks about amounts and/or growth over time, for example: On the first day the plant was 10 cm high, on the second day it was 15 cm high, on the fifth day...
Determine if a - 7 is the solution of the equation 2x+10=-4.
Answers
In order to check if x = -7 is the solution of the equation, let's use this value in the equation and check if the final sentence is true:
[tex]\begin{gathered} 2x+10=-4 \\ 2\cdot(-7)+10=-4 \\ -14+10=-4 \\ -4=-4 \end{gathered}[/tex]The final sentence is true, so the value x = -7 is the solution of the equation.
A fair coin is tossed 3 times in succession. The set of equally likely outcomes is (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT). Find the probability of getting a tailon the second toss
Answers
A fiar coin is tossed 3 times in succession.
The results for each experiment is displayed as follows;
[tex]\begin{gathered} \text{HHH} \\ \text{HHT} \\ \text{HTH} \\ \text{THH} \\ \text{HTT} \\ \text{THT} \\ \text{TTH} \\ \text{TTT} \end{gathered}[/tex]On each toss from the above results, the probability of getting a tail would include all results that has a tail come up. That would be;
[tex]P\lbrack\text{Event\rbrack}=\frac{\text{Number of required outcomes}}{Number\text{ of all possible outcomes}}[/tex][tex]P\lbrack\text{tail\rbrack}=\frac{4}{8}[/tex]Note that to get a tail on the "second toss" would mean to get a result with a tail as the second out of three. We have 7 outcomes with tails. However 4 of these has a tail as a second outcome, hence we have the required outcome as 4 out of a total of 8.
ANSWER:
Probability of getting a tail on the second toss is
[tex]P\mleft\lbrace\text{tail}\mright\rbrace=\frac{1}{2}[/tex]What is the equation of the following graph?A. f(x) = 3(2³)OB. f(x) = 5()*Oc. f(x) = ()*D.) = 2(3³)
Answers
From the graph,
when x = 0, y = 2
when x = 1, y = 6
Considering option D,
f(0) = 2(3^0) = 2 * 1 = 2
f(1) = 2(3^1) = 2 * 3 = 6
Thus, the correct option is
D
How do I find the minimum and maximum in a factored quadratic equation
Answers
Supposed you have a quadratic equation
x^
Find the solution to the following equation.4(x - 1) + 11.1 = 7(x - 4)
Answers
Answer: x = -3
Explanation:
The expression we have is:
[tex]4(x-1)+11.1=0.7(x-4)[/tex]Step 1: Use the distributive property, multiply the number outside the parenthesis by the numbers or terms inside the parenthesis
[tex]4x-4+11.1=0.7x-2.8[/tex]Step 2: Move all of the terms with x to the left, and all of the independent terms to the right side of the equation
[tex]4x-0.7x=-2.8+4-11.1[/tex]Note that we we move a term to the other side of the equation they change of sig.
step 3: combine like terms
[tex]3.3x=-9.9[/tex]Step 4: Divide both sides of the equation by 3.3 to solve for x
[tex]\begin{gathered} \frac{3.3x}{3.3}=\frac{-9.9}{3.3} \\ x=\frac{-9.9}{3.3} \\ x=-3 \end{gathered}[/tex]Mia was baking cupcakes for a party. She makes four drops of red food coloring for every six drops of yellow food coloring to dye her icing Orange. What is the ratio that would create the same orange color .
Answers
To find the ratio that would create the same orange color, we need to find the value from the division of the number of drops of each color of the food coloring.
From the present question, we know that Mia uses 4 drops of red for every 6 drops of yellow. It means that, for every 10 drops, 4 is red and 6 is yellow.
The ratio is:
( I will be finishing once I understand the best way to give you the final answer"
What is the second term of the sequence generated by the fo02O 3O 5O 6
Answers
1) Since no other information has been given, we need to assume that the numbers used in this Sequence are whole numbers.
2) Therefore, we can write this:
[tex]undefined[/tex][tex]22y = 11(3 + y)[/tex]I need help with my homework cause I'm sorta slow
Answers
Given the expression:
[tex]22y=11(3+y)[/tex]First we need to get rid of the parenthesis by multiplying 11 by 3 and by y:
[tex]\begin{gathered} 22y=11(3+y) \\ \Rightarrow22y=33+11y \end{gathered}[/tex]Now we solve for y:
[tex]\begin{gathered} 22y=33+11y \\ \Rightarrow22y-11y=33 \\ \Rightarrow11y=33y \\ \Rightarrow y=\frac{33}{11}=3 \\ y=3 \end{gathered}[/tex]Therefore, y=3
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answers
The value of angle is ∠P is 140° and ∠Q is 110°.
What do you mean by the exterior and interior angles of a triangle?
The angle between any two of a triangle's three sides is referred to as the interior angle. Any angle that is created when one of a polygon's sides intersects with a line that extends from another side is considered its external angle.
∠P and ∠Q is the exterior angle of the triangle.
we know that the sum of the exterior angle is the sum of the opposite interior angle.
9is the sum of the opposite interior angles that is (110°+30°) = 140°
∠Q is the sum of the opposite interior angles that are (30°+80°)= 110°
Hence,
∠P is 140° and ∠Q is 110°.
to learn more about the exterior and interior angles of a triangle from the given link,
https://brainly.com/question/21912045
#SPJ1
My question asks; at an ice cream parlor, ice cream cones cost $1.10 and Sundaes cost $2.35. One day the receipts for a total of 172 cones and Sundaes were $294.20. How many cones were sold?
Answers
Data:
ice cream cones: x
sundaes: y
Total receipts :T
[tex]T=1.10x+2.35y[/tex]As the total of cones and sundaes is 178:
[tex]x+y=172[/tex]The total receipts were: $294.20
[tex]294.20=1.10x+2.35y[/tex]1. Solve one of the variables in one of the equations:
Solve x in the first equation:
[tex]\begin{gathered} x+y=172 \\ x=172-y \end{gathered}[/tex]2. Use this value of x in the other equation:
[tex]\begin{gathered} 294.20=1.10x+2.35y \\ 294.20=1.10(172-y)+2.35y \\ \end{gathered}[/tex]3. Solve y:
[tex]\begin{gathered} 294.20=189.2-1.10y+2.35y \\ 294.20-189.2=-1.10y+2.35y \\ 105=1.25y \\ \frac{105}{1.25}=y \\ y=84 \end{gathered}[/tex]4. Use the value of y=84 to find the value of x:
[tex]\begin{gathered} x=172-y \\ x=172-84=88 \end{gathered}[/tex]Then, the ice cream parlor sold 88 cones and 84 sundaesMay I please get help with this problem? for I have got it wrong multiple times and still cannot get the correct answer
Answers
Answer:
x = 61.9°
Step-by-step explanation:
Let's take a closer look at our triangle:
Since we're on a right triangle, we can say that:
[tex]\sin(x)=\frac{15}{17}[/tex]Solving for x,
[tex]\begin{gathered} \sin(x)=\frac{15}{17}\rightarrow x=\sin^{-1}(\frac{15}{17}) \\ \\ \Rightarrow x=61.9 \end{gathered}[/tex]The concession stand sells 3 hot dogs forevery 4 hamburgers they prepare. Howmany hot dogs do they make if theyprepare 24 hamburgers?
Answers
3 Hotdogs are prepared for 4 hamburgers
N Hotdogs. For. 24. Hamburgers
Then make cross multiplication
3 x 24 = N x 4
Now find N
N = (3x24)/4 = 72/4 = 18 HOtdogs
and the missing numbers.
11. 360 ÷ 60 = 36 tens ÷ 6 tens =
Answers
Answer:
360÷60=36÷6=6÷0.6=10 not sure if this is right
Jamele runs a grocery store that sells bar coffee bean blend by the pound. she wishes to mix 40 pounds of coffee to sell for a total cost of $222. to obtain the mixture she will mix coffee that sells for $5.10 per pound with coffee that sells for $6.30 per pound. how many pounds of each coffee should she use
Answers
As per given by the question.
There are given that total mix pounds is 40.
Now,
There is two equation would be needed, one to the acount for money and the other to account for mass.
Then,
x is the pounds of $ 5.10/pound coffee.
y is the pouns of 6.30/pound coffee.
So,
The first equation is;
[tex]5.10x+6.30y=222[/tex]And;
The grocer wants to mixture of 40 pounds of coffee,
So;
[tex]x+y=40[/tex]Now,
From the second equation,
[tex]\begin{gathered} x+y=40 \\ x=40-y \end{gathered}[/tex]Then,
Put the value of x into the first equation.
So,
[tex]\begin{gathered} 5.10x+6.30y=222 \\ 5.10(40-y)+6.30y=222 \\ 204-5.10y+6.30y=222 \\ 204+1.2y=222 \\ 1.2y=18 \\ y=15 \end{gathered}[/tex]Now,
Put the value of y into the second equation;
So,
[tex]\begin{gathered} x=40-y \\ x=40-15 \\ x=25 \end{gathered}[/tex]Hence, the 25 and 15 pounds of each coffee shoud she use.
8th grade math (puzzle clues) (This photo may not show all the questions)
Answers
Answer
Taking all the clues given, one by one, and formulating the correct top 10, we have
1) Gateway Arch in St. Tim, Missouri.
2) San Jacinto Monument in La Porte, Texas.
3) Washington Monument in Washington, DC.
4) Perry's Victory and International Peace Memorial in Put-in-Bay, Ohio.
5) Jefferson Davis Memorial in Fairview, Kentucky.
6) Bennington Battle Monument in Bennington, Vermont.
7) Soldiers and Sailors Monument in Indianapolis, Indiana.
8) Pilgrim Monument in Cape Cod, Provincetown, Massachusetts.
9) Bunker Hill Monument in Boston, Massachusetts.
10) High Point Monument in High Point, New Jersey.
Given the following piecewise function, determine h(x)h(x) = { -x, if x greater than or equal to -2{ 2, if x > -2h(-6) =h(-2) =h(6) =
Answers
Part 1) h(-6)
h(x)=-x
x=-6
so
h(-6)=6
Part 2) h(-2)
h(x)=-x
For x=-2
h(-2)=2
Part 3) h(6)
h(x)=2
x=6
so
h(6)=2
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]Each of these is a pair of equivalent ratios for each pair explain why they are equivalent ratios or draw a diagram that shows why they are equivalent ratios 2:7 and 10,000:35,000
Answers
Given this pair of equivalent ratios:
[tex]\begin{gathered} 2:7 \\ \\ 10,000:35,0000 \end{gathered}[/tex]It is important to remember that equivalent ratios represent the same value, but they have different forms.
Equivalent ratios can be obtained by multiplying both parts of a ratio by a common number.
In this case, you can identify that:
[tex]2\cdot5,000=10,000[/tex][tex]7\cdot5,000=35,000[/tex]Therefore, both parts of the original ratio can be multiplied by 5,000 in order to get the other ratio.
Hence, the answer is: They are equivalent ratios because they have the same value when they are simplified, and the second ratio can be obtained by multiplying both parts of the first ratio by 5,000.
Ms. Wheeler asks her students to look at their desks. What do the desks represent inEuclidean geometry?
Answers
To determine the what desk represents in Euclidean geometry?
Euclidean geometry, sometimes called parabolic geometry, is a geometry that follows a set of propositions that are based on Euclid's five postulates
The most basic terms of geometry are a point, a line, and a plane. A point has no dimension (length or width), but it does have a location
In its rough outline, Euclidean geometry is the plane and solid geometry commonly taught in secondary schools
“A point is that which has no part” and “a line is a length without breadth.” Proceeding from these terms, he defined further ideas such as angles, circles, triangles, and various other polygons and figures.
For example, an angle was defined as the inclination of two straight lines, and a circle was a plane figure consisting of all points that have a fixed distance (radius) from a given centre.
Hence in Euclidean geometry the desk represent the plane