Answer:
[tex]h(g(x))=x^2+x-2[/tex]
[tex]h(g(f(x))= x^2-19x+88[/tex]
Step-by-step explanation:
Composite Function
Suppose f(x) and g(x) are real functions, the composite function named [tex](f\circ g)(x)[/tex] is defined as:
[tex](f\circ g)(x)=f(g(x))[/tex]
The composite function can be found by substituting g into f.
We are given these functions:
[tex]f(x)=9-x[/tex]
[tex]g(x)=x^2+x[/tex]
[tex]h(x)=x-2[/tex]
Find:
a) h(g(x))
Substituting g into h:
[tex]h(g(x))=x^2+x-2[/tex]
b) h(g(f(x))
First we find g(f(x)):
[tex]g(f(x))=(9-x)^2+(9-x)[/tex]
Operating:
[tex]g(f(x))=81-18x+x^2+9-x[/tex]
Simplifying:
[tex]g(f(x))=90-19x+x^2[/tex]
Now find h(g(f(x)) replacing the above equation into h:
[tex]h(g(f(x))= 90-19x+x^2-2[/tex]
Simplifying and rearranging:
[tex]h(g(f(x))= 88-19x+x^2[/tex]
[tex]h(g(f(x))= x^2-19x+88[/tex]
write the decimal expansion of 16 by 3125
Answer:
That will be 0.00512
how would you substitute this equation?
If y = x and y = z, then by substitution we can say x = z.
In this case, substitution gives us
-1/2 x - 2 = -3/2 x + 2
and we can solve for x :
3/2 x - 1/2 x = 2 + 2
x = 4
then solve for y :
y = -1/2 x - 2
y = -1/2 * 4 - 2
y = -2 - 2
y = -4
An expert diver is looking for a particular species of fish along the coast line. He dives 25 feet below the surface of the ocean. Then he dives down 10 more feet. He swims back up 7 feet and down another 3 feet before he finds the species of fish he is looking for. What was the depth at which the diver finds the fish?
Answer:
31
Step-by-step explanation:
Depth Changes:
1. down 25 feet
2. down 10 feet
3. up 7 feet
4. down 3 feet
If we form this into an equation, we get:
25+10-7+3 = 31
Please help!
Four more than twice a number is –10.
(I have 15 mins!)
Answer: -7
Step-by-step explanation:
2X + 4= -10
2X= -10 -4
2X= -14
X= -7
3sinA=4cosA so find tansquareA_sinsquareA
Step-by-step explanation:
Do you mean?
[tex] \frac{ { \tan(x) }^{2} }{ \ { \sin(x) }^{2} } [/tex]
If so:
[tex]3 \sin(x) = 4 \cos(x) \\ \frac{3 \sin(x) }{ \cos(x) } = 4 \\ \frac{ \sin(x) }{ \cos(x) } = \frac{4}{3} \\ \tan(x) = \frac{4}{3} [/tex]
Did the question specify which quadrant? I'm just going to assume that it's the first
(as tangent = opp/adj)
hence
Hypotenuse:
[tex] \sqrt{{3}^{2} + {4}^{2} } = 5[/tex]
[tex] \sin(x) = \frac{4}{5} [/tex]
Finally,
[tex] \frac{ { \tan(x) }^{2} }{ { \sin(x) }^{2} } = \frac{ { \frac{4}{3} }^{2} }{ { \frac{4}{5} }^{2} } \\ = 2 \frac{7}{9} [/tex]
I have to finish this by midnight and I forgot how to do this
Sara reduced the time it takes her to run a mile from 8
minutes to 6 minutes. What was Sara's percent decrease
in the time it takes her to run a mile?
A. 14%
B. 25%
C. 33%
D. 75%
Answer:
25%
Step-by-step explanation:
if a and b are integers,what conditions would make a×b > 0?
Answer:
a and b must be positive integers
Step-by-step explanation:
for example- a= (+1)x(+2)
= (+2)
= (+2)>0
= axb>0
Thank U
An object is thrown off a 256-foot-tall building, and the distance of the object from the ground is measured every second. The function that models the height, h, of the object after t seconds is h(t) = –16t2 + 96t + 256. Determine the time when the object hits the ground
Answer:
The object hits the ground 8 seconds after launch.
Step-by-step explanation:
Let [tex]h(t) =-16\cdot t^{2}+96\cdot t + 256[/tex], where [tex]h[/tex] is the height of the object above the ground, measured in feet, and [tex]t[/tex] is time, measured in seconds. We notice that given expression is a second-order polynomial and hence, there are two roots, one of them corresponding to the instant when the object hits the ground. If [tex]h(t) = 0[/tex], we get the following expression:
[tex]-16\cdot t^{2}+96\cdot t +256 = 0[/tex] (Eq. 1)
Roots are found by applying the Quadratic Formula:
[tex]t_{1,2} = \frac{-96\pm\sqrt{96^{2}-4\cdot (-16)\cdot (256)}}{2\cdot (-16)}[/tex]
[tex]t_1 = 8\,s[/tex] or [tex]t_{2} = -2[/tex]
Only the first root offer a solution that is physically reasonable. Thus, the object hits the ground 8 seconds after launch.
What property is 6m•1=6m
Answer:
This equation is a tautology (Something which is always true)
Step-by-step explanation:
2x + y = 7
this is my first day in algebra and i have no clue how to solve a literal equation
Answer:
y = 7 - 2x
Step-by-step explanation:
Step 1:
2x + y = 7 Equation
Step 2:
y = 7 - 2x Subtract 2x on both sides
Answer:
y = 7 - 2x
Hope This Helps :)
Arbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165. The equation represents the $495 total cost that Barbara paid to Dance Unlimited. 495 = 165 + 55m How many months, m, did Barbara receive dance lessons from Dance Unlimited?
Given:
Per month fee = $55
One-time recital fee = $165
The equation represents the $495 total cost that Barbara paid to Dance Unlimited.
[tex]495=165+55m[/tex]
To find:
We need to find the number of month Barbara receive dance lessons from Dance Unlimited.
Solution:
We have,
[tex]495=165+55m[/tex]
Here, m is number of months. We need to isolate m.
Subtract 165 from both sides.
[tex]495-165=55m[/tex]
[tex]330=55m[/tex]
Divide both sides by 55.
[tex]\dfrac{330}{55}=m[/tex]
[tex]6=m[/tex]
The value of m is 6. So, the required number of month Barbara receive dance lessons from Dance Unlimited is 6.
What is the value of the expression x2+(2+x5) when x=15.
Answer:
759,602
Step-by-step explanation:
Evaluate (x^5 + 2) + x^2 where x = 15:
(x^5 + 2) + x^2 = 15^2 + (15^5 + 2)
| 1 | 5
× | 1 | 5
| 7 | 5
1 | 5 | 0
2 | 2 | 5:
225 + 2 + 15^5
15^5 = 15×15^4 = 15 (15^2)^2:
225 + 2 + 15 (15^2)^2
| 1 | 5
× | 1 | 5
| 7 | 5
1 | 5 | 0
2 | 2 | 5:
225 + 2 + 15×225^2
| | 2 | 2 | 5
× | | 2 | 2 | 5
| 1 | 1 | 2 | 5
| 4 | 5 | 0 | 0
4 | 5 | 0 | 0 | 0
5 | 0 | 6 | 2 | 5:
225 + 2 + 15×50625
| 5 | 0 | 6 | 2 | 5
× | | | | 1 | 5
2 | 5 | 3 | 1 | 2 | 5
5 | 0 | 6 | 2 | 5 | 0
7 | 5 | 9 | 3 | 7 | 5:
225 + 2 + 759375
| | | | 1 | 1 |
| 7 | 5 | 9 | 3 | 7 | 5
| | | | 2 | 2 | 5
+ | | | | | | 2
| 7 | 5 | 9 | 6 | 0 | 2:
Answer: 759602
Answer:
759,602
Step-by-step explanation:
In this problem you would replace the x with 15 and break down the answer.
[tex]x^{2} +(2 + x^{5} )[/tex] = [tex]15^{2} + (2 + 15^{5} )[/tex]
Now that you know the equation, break it down.
15² = 225
225 + (2 + [tex]15^{5}[/tex])
After rewriting the equation, do the work inside the parenthesis.
(2 + [tex]15^{5}[/tex]) = (2 + 759,375) = 759,377
The equation will now look like this.
225 + (759,377)
Solve!
759, 602
Use the distributive property to remove the parentheses -8(3v-w-4)
2. JI. has coordinates J(-6, 1) and Z(-4, 3). Find the coordinates of the midpoint.
Answer:
(- 5, 2 )
Step-by-step explanation:
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
Here (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (- 4, 3) thus
midpoint = [tex]\frac{-6-4}{2}[/tex], [tex]\frac{1+3}{2}[/tex] ) = ( [tex]\frac{-10}{2}[/tex], [tex]\frac{4}{2}[/tex] ) = (- 5, 2 )
PLS HELPPP
Are the triangles similar? If they are, identify the similarity ratio.
Divide the corresponding sides
3/6 = 0.5
5/4 = 1.25
6/8 = 0.75
We get different results, so the sides are not in the same ratio or proportion.
The triangles are not similar.HELP PLSSS 15 points
Big Mitch held 500 pounds in a weightlifting competition. To win the
competition, Big Mitch must add 50 pounds to his best lift. If the variable w
stands for the amount of additional weight Mitch can hold, which of the
following units could apply to that variable?
A. meters
B. gallons
C. pounds
D. inches
80+1246√16
What is the answer please I only have 10 minutes left
Answer:
7556
Step-by-step explanation:
Can You Please give me a Brainlies or how ever you spell it
Answer:
5304
Step-by-step explanation:
80+1246√16
= 1326√16
= 5304.
Choose all the number sentences that have a difference less than 7,650?
A) 12,355 – 4,575
B) 19,345 – 12,000
C) 21,675 – 13,055
D) 24,356 – 18,560
E) 10,500 – 3,560
Are BD and CE congruent? Explain.
Answer:
The answer is D: Yes, BD = 7 and CE = 7
Step-by-step explanation:
B--> -5
D --> 2
-5 + BD = 2
BD = 7
C--> 0
E --> 7
0+CE=7
CE = 7
The answer is D
Susan received $27 for 6 hours of work. Ricky received $14.25 for 3 hours of work. Which statement is true about there hourly rate? Answer choices: A:Susan's rate was closer to $5.00 B:Susan's rate was $0.70 more per hour C: Rickys rate was 0.25 more per hour D:Ricky was paid at half Susan's rate
Answer: C. Rickys rate was 0.25 more per hour" .
Step-by-step explanation:
Susan received $27 for 6 hours of work. Susan's rate we hour will be:
= $27/6
= $4.5
Ricky received $14.25 for 3 hours of work. Ricky's rate will be:
= $14.25/3
= $4.75
From the option given, the correct option is C "Rickys rate was 0.25 more per hour" .
This is because $4.75 - $4.5 = $0.25
which word most closely means: how many parts are out of the whole *
which of the following shows the correct meter reading consumed? a.2419KW b.2491KW c.2548KW d.2584KW pls answer thank you
Answer:
c.2548KW
Step-by-step explanation:
The correct reading of the meter is;
First meter,---2000
Second meter----500
Third meter ------40
Fourth meter -------8
Total 2000+500+40+8 = 2548 kilo watts.
The answer option A,B, and D are not correct because the answers have incorrect meter reading values.
The sum of two numbers is 14 and their product is 45. Represent an equation that could find the two numbers
On a snowy day, only 7/12 of the students attended Calvin Middle School. Among the students that missed school, about 4/5 students call the school to inform the school office. What was the fraction of all students that called in to inform the school about missing school this day?
Answer:
1/3 of all the students called in to inform the school about missing school this day
Step-by-step explanation:
4/5 = students that call the school to inform the school office
only 7/12 attended Calvin Middle School
To get the number of students that missed Calvin Middle School = 1 - number of students that attended Calvin Middle School
= 1 - 7/12 = (12-7) / 12
= 5 /12
The fraction of all students that called in to inform the school about missing school this day is:
5/12 x 4/5 = 1/3
Put in order from least to greatest {-6, 8, 10, 15}
Answer:
-6 , 8 , 10 , 15
Negatives are less than positives so they're first
Solve for the indicated variable.
L = M - N for N
SHOW WORK AND I WILL GIVE BRAINIEST!!! Lisa is making some spiced tea for her mom. The recipe calls for 2.5 cups of sugar for each cup of tea. If she only uses 3/4 cups of tea, how much sugar should she use?
Answer:
She should use 1.875 cups of sugar
Step-by-step explanation:
Find the ratio by cross multiplying
Answer:
I think it is 0.3
Step-by-step explanation:
Because, 3/4 divided by 2.5= 0.3
1. The county fair charges $1.25 per ticket for the rides. Jermaine bought 25 tickets for the rides and spent a total of $43.75 at the fair. Jermaine spent his money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets
Answer:
Y= 12.5+X
Step-by-step explanation:
Y=43.75
X=1.25x25=31.25
so 43.75 minus 31.25= 12.5
he spent 12.5 on fair addmition
At the Sunshine Bakery, 351 loaves of seven-grain bread were baked in six hours and 15 minutes. Estimate how many loaves were baked in one hour.
60
55
65
70
Answer:
B
Step-by-step explanation:
We know that 351 loaves were baked in six hours and 15 minutes.
First, let's convert the time to minutes. 6 hours is 360 minutes, so 6 hours and 15 minutes is 360 + 15 = 375 minutes.
Therefore, we can write the following ratio:
[tex]\frac{351\text{ loaves}}{375\text{ minutes}}[/tex]
We want to estimate how many loaves were baked in one hour or 60 minutes. So, we can write the following proportion:
[tex]\frac{351\text{ loaves}}{375\text{ minutes}}=\frac{x\text{ loaves}}{60\text{ minutes}}[/tex]
Note that the loaves and time align horizontally, while the rates align vertically.
Since we're estimating, let's change 351 to 350 (I'm also going to remove the words, since they're not necessary). So:
[tex]\frac{350}{375}=\frac{x}{60}[/tex]
We can reduce the left by dividing by 25. This yields:
[tex]\frac{14}{15}=\frac{x}{60}[/tex]
Cross multiply:
[tex]15x=60(14)[/tex]
Multiply and solve for x. So:
[tex]15x=840\\\Rightarrow x=56\approx55\text{ loaves}[/tex]
Therefore, approximately 55 loaves were baked in one hour.
So, our answer is B.
And we're done!
Answer:
B) 55Step-by-step explanation:
given
351 loaves baked in 6 hrs and 15 min.
15 min x (1 hr / 60 min) = 0.25 hr
find:
Estimate how many loaves were baked in one hour.
its a ratio and proportion:
351 loaves = x loaves ( just cross multiply)
6.25 hr 1 hr.
x loaves = 351 loaves ( 1 hr.)
6.25 hr.
= 56 ------->>> say 55