What is f(g(x) of f(x)=9x+2 and g(x)=x-2 over 9
The value of the composite function f(g(x)) is calculated as f(g(x)) = 65.
What is termed as the composite function?Composite functions is one in which one function is placed within another.
A composite function defines one that is reliant on another. A composite function is defined whenever one function is replaced for another. For example, the composite function constituted by substituting g(x) for x in f is f(g(x)) (x).f(g(x)) is spoken as "f оg(x)."For, the given values in the question;
f(x) = 9x+2 and g(x) = x-2
We have to find the value of f(g(x)) for x = 9.
First estimate the value of g(x) by substituting x = 9 in it.
g(x) = x-2
g(9) = 9-2 = 7
Now,
f(x) = 9x+2 and
f(g(x)) = f(7) = 9x+2, (substitute x = 7)
f(g(x)) = 9×7 + 2
f(g(x)) = 65.
Thus, the value of the composite function f(g(x)) = 65.
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Buster's dog house is 3 feet long, 2 feet wide, and 2 feet high. how much space would there be if buster's house were twice as long
there woldbe 96 volume
Step-by-step explanation:
to find the volume you have to multiply width x lenghth x height
so set up your equation like this -
3 x 2 x 2
the times everything by 2 so it will now look like this -
6 x 4 x 4
then solve and get the answer 96
It is the end of the budgeting period for John Smith, and he has $500 left in his budget for car rental expenses. He plans to spend this budget on a sales trip throughout the country. He will rent a car that costs $50 per day and $ 0.50per mile, and he can spend no more than 500
The number of miles that John Smith can travel with his budget if he has $500 left in his budget for car rental expenses is 900 miles.
How to calculate the expression?Amount left in the budget = $500
Since he will rent a car that costs $50 per day and $ 0.50per mile, the expression will be:
50 + 0.50m = 500
where m = number of miles
Collect like terms
0.5m = 500 - 50
0.5m = 450
Divide
m = 450/0.5
m = 900
Therefore, the number of miles that John Smith can travel with his budget is 900 miles.
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which statements about doubling in investment are true check all that apply an investment of $5000 will double in six years at an annual compound interest rate of 12% An investment of $1000 will double at an annual compound interest rate of 18% in six years an investment of $350 will double in nine years At a compound interest rate of 8% an investment of $2000 will double at a simple interest rate of 5% in 20 years and investment of $700 will double in 12 years at a simple interest rate of 6%
The following statement are true:
An investment of $5,000 will double in 6 years at an annual compound interest rate of 12%.An investment of $350 will double in 9 years at a compound interest rate of 8%. An investment of $2000 will double at a simple interest rate of 5% in 20 years.What is rule 72?It's an easy way to calculate just how long it's going to take for your money to double. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.
Using the formula
time for doubling money= 72/R
First, An investment of $5,000 will double in 6 years at an annual compound interest rate of 12%.So, 72/12 = 6 years
Thus, It will take 6 years to double the investment. This statement is true.
Second, An investment of $1000 will double at an annual compound interest rate of 18% in 6 years.So, 72/18 = 4 years
Thus, It will take 4 years to double the investment. This statement is not true.
Third, An investment of $350 will double in 9 years at a compound interest rate of 8%.so, 72/8= 9 years.
Thus, It will take 9 years to double the investment. This statement is true.
Fourth, An investment of $2000 will double at a simple interest rate of 5% in 20 years.So, interest = PRT/100
I = (2000 × 0.05 × 20)
I = $2000
Thus, This statement is true.
Fifth, An investment of $700 will double in 12 years at a simple interest rate of 6%Interest = ( 700 × 0.06 × 12 ) = $504
Amount after 12 years
=700 + 504
= $1204.
Thus, This statement is not true.
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1. The price of one kg grapes is 60p, find the total price of 30 kg grapes in pounds.
2. The price of one kg carrots is 35p, find the total price of 40-kg carrots in pounds.
3. The price of one kg grapes is 60p and the price of one kg bananas is 40p per kg, find the total price of 30 kg grapes and 40kg bananas in pounds.
4. The price of one kg oranges is 90p and the price of bananas is 30p per kg, find the total price of 30 kg oranges and 40kg bananas in pounds
Maths:
Round 1
1) Grapes cost £1.50 per kg and carrots cost £1.00 per kg. How much would it costs for 3kg of
grapes and half a kilogram of carrots? £5
2) Jenny decides to share her sweets between herself and her 3 friends. She has 212 green
sweets, 310 blue sweets and 502 yellow sweets. How many sweets will Jenny and her friends
get each? 256
3) Large chocolate bars come with 32 pieces. Medium chocolate bars come with 24 pieces.
Barry buys 8 large bars of chocolate and 6 medium bars. How many pieces of chocolate will he
have altogether? 400
4) A flower shop sells roses for £1.79, carnations for £1.25 and buttercups for £1.30. Holly
decides to buy 3 roses and a buttercup. How much does she spend? £6.67
5) Pencils come in packs of 12 and each pack costs £1.19. Mr Green needs to buy a pencil for
each of the 50 children in his class. How much will he spend on pencils? £5.95
Round 2
1) Mrs Orange decides to share her savings between her six grandchildren. She has £350 in
her savings tin and £1450 in her savings account. How much will each of her grandchildren get?
£300
2) Green lollipops come in packs of 5, yellow lollipops come in packs of 6 and blue lollipops
come in packs of 4. A school buys 32 packs of blue lollipops and 18 packs of green lollipops.
How many lollipops will they buy altogether? 218
3) The baker’s oven can bake 28 loaves of bread at a time. In a day, it can go through 30 full
bakes. How many loaves of bread would be baked after 1 week? 5880
4) Ms Purple sells cars for a living. In one day, she sells 2 blue cars (at £4500 each), 7 yellow
cars (at £6000 each) and 12 black cars (at £8000 each). How much money does she take in car
sales in that one day? £147,000
5) Coaches carry 58 people. A school decides to take its 300 pupils and 38 staff on a visit to the
beach. A single coach costs £128. How much will the total cost of the coaches come to? £768
Topic:
Fruit Veg
Quince
raspberry
Lettuce
garlic
tomato
strawberry
grape
pumpkin
blackberries
nashi
kiwi
chilli
pear
passion fruit
cantaloupe
fig
eggplant/aubergine
cucumber
lemon
peach
lime
watermelon
pineapple
Zucchini/courgette
grapefruit
persimmons
mango
plum
cauliflower
Broccoli
Leeks
Fennel
Carrots
Coriander
Silverbeet
Snow peas
Beans
Celery
Beetroot
Peas
Artichoke
Sweet potato
Draw LMN with vertices L(2,-2), M(7,-3), and N(5,2). Find the coordinates of the vertices after a 90 degree rotation about the origin and about each of the points L, M, and N.
The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.
How does rotation by 90 degrees changes coordinates of a point if rotation is with respect to origin?Let the point be having coordinates (x,y).
If the point is in first quadrant:
Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
We know that the rotation of a point (x,y) about the origin by 90° is (-y,x).
Given vertices of ΔLMN are L(2,-2), M(7,-3), and N(5,2).
Let consider the rotations of L, M, and N are L', M', and N' respectively.
The rotation of a point L(2,-2) about the origin by 90° is L'(-2,-2).
The rotation of a point M(7,-3) about the origin by 90° is M'(-7,-3).
The rotation of a point N(5,2) about the origin by 90° is N'(5,2).
Hence, the points L'(-2, -2), M'(-7, -3), and N'(5, 2) are the rotation of vertices.
Therefore, L, M, and N of ΔLMN about the origin by 90°.
Hence, The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.
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Tony's Used Car Dealership is selling a car for $12,000. This price represents a 20%
reduction from the original price of the car. What was the original price of the car?
The original price of the car is $15,000
Let us assume the original price of car be x. So, forming the equation to find the value of x and hence the original price of the car.
Equation -
x - 20% × x = 12000
x - 20/100×x = 12000
Cancelling zero as common in both numerator and denominator, on the left hand side of the equation
x - x/5 = 12000
Taking LCM on Left Hand Side of the equation
(5x - x)/5 = 12000
Rewriting the equation
4x = 12000 × 5
Performing multiplication on Right Hand Side of the equation
4x = 60,000
x = 60,000 ÷ 4
Performing division
x = 15,000
Therefore, the original price of the car is $15,000.
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THE TRIANGLE SHOWN HERE IS REFLECTED IN X-AXIS AND THEN IN Y-AXIS. WRITE THE FINAL COORDINATES OF TRIANGLE:
Answer:
Option 4
Step-by-step explanation:
This is the same as a rotation of 180° about the origin, which means we can negate the x and y coordinates of the preimage to get the coordinates of the image.
Select the lesser of The two given numbers -152, 12
Answer:
-152
Step-by-step explanation:
-152 < 12
-152 is negative, which means it is less than 1.
12 is positive, which means it is greater than 1.
Therefore, -152 is the lesser of the two given numbers.
Have a great rest of your day! :)
Hi!
-152 is less than 12, because:
It's negative, and 12 is positive!It's to the left of 12 on the number line![tex]\mathbb{NUMBER \ LINE}[/tex]
[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]
[tex]-152[/tex] [tex]12[/tex]
Cheers!
Have a nice day!
I hope this helps!
what is an equation of the line that passes through the points (0,8) and (5,2)
Wheat Corporation pays for shares to acquire % common stock of Grain Investments, Inc. on January 5, 2018. Wheat Corporation sells shares for on January 6, 2018. Which of the following is the correct journal entry for the transaction on January 6, 2018? (Round any intermediate calculations to two decimal places, and your final answer to the nearest dollar.)
Marketable securities are 63,360 credits (refer to the table below for journal entries).
What are journal entries?A journal entry is an act of keeping or making records of any economic or non-economic transaction.An accounting journal, which shows a company's debit and credit balances, records transactions. The journal entry can be made up of multiple recordings, each of which is either a debit or a credit. Otherwise, the journal entry is considered unbalanced if the total of the debits does not equal the total of the credits.So,
The following can be deduced from the information provided in the question:
The purchase price per share will be as follows:
= $528,000/100,000= $5.28The share price will be as follows:
= $54,000/12,000 = $4.50The following is the loss on the sale of marketable securities:
= 12,000 x (4.50 - 5.28)= 12,000 × 0.78= $9,360Then, the journal entries are: (Refer to the table below)
Therefore, marketable securities are 63,360 credits (refer to the table below).
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The correct question is given below:
Wheat Corporation pays $ 528 comma 000 for 100,000 shares to acquire 45% common stock of Grain Investments, Inc. on January 5, 2018. Wheat Corporation sells 12 comma 000 shares for $ 54 comma 000 on January 6, 2018. What is the correct journal entry for the transaction on January 6, 2018? (Round any intermediate calculations to two decimal places, and your final answer to the nearest dollar.)
How long does it take $450 to double at a simple interest rate of 14%? Express your answer in months. Round to the nearest whole number.
The number of months so that the investment gets double will be 86 months.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on. The amount is given as,
A = P + (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
The principal amount is $450 and if the amount gets doubled, then the value of the amount will be $900. The simple interest rate is 14%. Then the time is given as,
A = P + (PRT)/100
900 = 450 + [450 x 14 x T] / 100
450 = 450 x 14 x T / 100
T = 100 / 14
T = 7.14 years
T = 7.14 x 12
T = 85.7 ≈ 86 months
The number of months so that the investment gets double will be 86 months.
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(e) For what value(s) of x is f(x) = 0?
Step-by-step explanation:
For the value of x = 0 then the f(x) will became f(o) = 0
In the word grapefruit , the ratio of vowels to consonants is 2 : 3
Answer:
pineapple: 4:5strawberry: 3:7Step-by-step explanation:
You want the ratio of vowels to consonants in each of the words "pineapple" and "strawberry."
RatioTo form the reduced ratio vowels:consonants, we need to identify the type of letter each is. Here we use bold to identify the vowels.
pineapple ⇒ 4:5
strawberry ⇒ 3:7 . . . . counting "y" as a vowel
Write the expression. Then, check all that apply.
twice the difference of a number and six
The algebraic expression for the given statement is: 2(n - 6).
How to Write an Algebraic Expression?To translate the statement, "twice the difference of a number and six", follow the steps below:
The two operations we would use are multiplication and subtraction.
The constants are 2 and 6.
Twice is translated as 2 ×, (-) is "difference".
Let the number be "n" .
The difference of a number, n, and 6, would be: n - 6.
Therefore, we would have the following algebraic expression: 2(n - 6).
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expressions that have 2\3 as a product.
The expression that have 2\3 as a product are 4/5 × 5/6 and 6/7 × 7/9 which is option (a) and (e) .
An expression in maths could be a sentence with a minimum of 2 numbers/variables and a minimum of one maths operation in it.An expression could be a combination of terms that are combined by victimization mathematical operations like subtraction, addition, multiplication, and division.(a) 4/5 × 5/6 = 20/30
= 2 /3
(b) 7/8 × 9/10 = 63 / 80
(c) 1/3 × 2/3 = 2 /9
(d) 3/4 × 7/12 = 21 / 48
= 7 / 16
(e) 6/7 × 7/9 = 42 /63
= 6 / 9
= 2 / 3
Only the expression (a) and (e) have 2\3 as a product.
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The complete question is given below :
Choose all the expressions that have 2\3 as a product.
(a) 4/5 × 5/6
(b) 7/8 × 9/10
(c) 1/3 × 2/3
(d) 3/4 × 7/12
(e) 6/7 × 7/9
Vicente is investing money into a savings account that pays 3% simple interest, and plans to leave it there for 10 years. Determine what Vicente needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years.
The amount Vicente needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years is $15,384.62
What is simple interest?
The simple interest on the savings is determined as the deposit multiplied by the annual interest rate and the number of years that deposit would last in the account
I=PRT
I=simple interest
P=principal=deposit=unknown
R=annual simple interest=3%
T=number of years=10
A(amount in 10 years)=P+PRT
A=P(1+RT)
$20,000=P(1+3%*10)
$20,000=P*1.30
P=$20,000/1.30
P=$15,384.62
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Please help solve number 24
express the following as percents a)15 girl out of 75 pupils
At the movie theatre, child admission is $5.90 and adult admission is $9.00. On Saturday, 137 tickets were sold for a total sales of $1003.60. How many adult tickets were sold that day?
The number of adult tickets, that were sold that day at the movie theatre was 62
What are simultaneous equations?
Simultaneous equations are two or more equations that must be solved concurrently in order to derive the values of the unknown, the total sales, as well as the total number of tickets sold, can be modeled into equations as below:
let x be the number of adult tickets
let y be the number of children's tickets
9x+5.90y=1000.60....... equation 1
x+y=137.................. equation 2
solve for y in equation 2
y=137-x
substitute for y in equation 1
9x+5.90(137-x)=1000.60
9x+808.30-5.90x=1000.60
9x-5.90x=1000.60-808.30
3.10x=192.30
x=192.30/3.10
x=adult tickets=62
children tickets=137-62
children tickets=75
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If a family has 5 children, in how many ways can the parents have 2 boys and 3 girls as children?
Considering the definition of combination, if a family has 5 children, in 10 ways the parents can have 2 boys and 3 girls as children.
What is combinationCombinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.
To calculate the number of combinations, the following expression is applied:
[tex]mCn=\frac{m!}{n!(m-n)!}[/tex]
where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.
Ways the parents have 2 boys and 3 girlsIf a family has 5 children, you can know that:
Among the 5 children, 3 are boys = 5C3 = [tex]\frac{5!}{3!(5-3)!}[/tex]= [tex]\frac{5!}{3!2!}[/tex]Among the 5 children, 2 are girls = 5C2 = [tex]\frac{5!}{2!(5-2)!}[/tex]= [tex]\frac{5!}{2!3!}[/tex]So, you can observe that 5C3 is equal to 5C2. Then:
5C3 = 5C2 = [tex]\frac{5!}{3!2!}[/tex]= 10
Finally, if a family has 5 children, in 10 ways the parents can have 2 boys and 3 girls as children.
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Ronnie is playing a card game where the goal is to get the lowest possible score. In
the first round, Ronnie scored -6 points. In the second round, he scored -12 points.
What is Ronnie's total score
Jackie buys 6 packs of 100 post-its, 4 packs of 10 post-its, and 4 fancy post-its by themselves.
Then, her friend gives her 3 more fancy post-its. How many post-its does she have now?
Step-by-step explanation:
Number of post-it's = 6*100=600+4*10+4+3=647post-its
Construct an angle of measure 45° with the help of a protractor. Bisect it and find the measure of the bisected angles .
Answer:
See attachment
Step-by-step explanation:
Draw a 45o angle
Bisecting means dividing the angle into 2 halves, which is 22.5o each
Identify the y-intercept for each function and determine which function has the greater y-intercept. Please help me!
Answer for this please see image attached m
Answer:
angle A=125 angle B= 114 angle C= 121
Step-by-step explanation:
first you have to find x so that you can find each angle
the interior angles of a triangle is equal to 360
add the angles together x+x+7+x+11=360
combine like terms 3x+18=360
subtract 18 on both sides 3x=342
divide by 3 on both sides x=114
to find angles:
plug in X to each side
(114)+7 = angle C
(114)+11= angle A
114= angle B
How to solve x+5/-6= -4
x+5/-6= -4
multiply each side by -6
x-5/6= -4
*-6 *-6
x+5=24
subtract 5 from each side
x=19
A rental car company charges $71.02 per day to rent a car and $0.12 for every mile
driven. Lily wants to rent a car, knowing that:
She plans to drive 475 miles.
. She has at most $390 to spend.
.
What is the maximum number of days that Lily can rent the car while staying within
her budget?
Answer:
Step-by-step explanation:
4 is the maximum number of days.
Using Inequality, the maximum number of days that Lily can rent the car while staying within her budget is 4 days.
How to find the maximum number of days she can rent the car?The rental car company charges $71.02 per day to rent a car and $0.12 for every mile driven.
Lily wants to rent a car and she plans to drive 475 miles. She has a budget of $390.
Therefore, the maximum number of days that Lily can rent the car while staying within her budget can be calculated as follows:
Using inequality,
total cost = 71.02(x) + 0.12(y)
where
x = number of days
y = number of miles
Therefore,
71.02x + 0.12(475) ≤ 390
71.02x ≤ 390 - 57
71.02x ≤ 333
x ≤ 333 / 71.02
x ≤ 4.68882005069
Therefore,
she can drive maximum of 4 days.
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100 POINTS!!! Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Multiply or divide as indicated. Leave your answer with no factors in the denominator.
p^-4 q^5 r^6 / p^-3 qr^-2
Answer:
[tex]\dfrac{q^{4} r^8}{p}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}[/tex]
Separate the variables:
[tex]\implies\dfrac{p^{-4}}{p^{-3}} \times \dfrac{q^5}{q} \times \dfrac{r^6}{r^{-2}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies p^{(-4-(-3)} \times q^{(5-1)} \times r^{(6-(-2)}[/tex]
[tex]\implies p^{(-4+3)} \times q^{(5-1)} \times r^{(6+2)}[/tex]
[tex]\implies p^{-1} \times q^{4} \times r^8[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{1}{p} \times q^{4} \times r^8[/tex]
Simplify:
[tex]\implies \dfrac{q^{4} \times r^8}{p}[/tex]
[tex]\implies \dfrac{q^{4} r^8}{p}[/tex]
How long does it take to ride a bicycle 100 miles at each of the following speeds: 5 mph, 10 mph, 15 mph, 20 mph, 25 mpb? What is always true about the product speed x time?
The times associated with each speed are:
20 h10 h6.667 h5 h4 hIt is always true that the speed is inversely proportional to time.
How to analyze the motion of a bicycle at constant speed
In this case we find the situation of bicycle moving at constant speed, where the traveled distance (s), in miles, is equal to the following expression:
s = v · t (1)
Where:
v - Speed, in miles per hour.t - Time, in hourNow we proceed to calculate time needed for each speed:
t = s / v
Case 1
t = 100 mi / 5 mi / h
t = 20 h
Case 2
t = 100 mi / 10 mi / h
t = 10 h
Case 3
t = 100 mi / 15 mi / h
t = 6.667 h
Case 4
t = 100 mi / 20 mi / h
t = 5 h
Case 5
t = 100 mi / 25 mi / h
t = 4 h
According to the model for rectilinear uniform motion, the speed is inversely proportional to time.
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