If h(x)=(f o g) (x) and h(x)=3(x+2)^2, find find one possibility for f(x) and g(x)
Answer:
[tex]f(x)= 3x^2[/tex] and [tex]g(x)= x+2[/tex]
Step-by-step explanation:
[tex]h(x)=(f o g) (x)[/tex]
[tex]h(x)=3(x+2)^2[/tex]
[tex](f og)(x) = f(g(x))[/tex]
g(x) is the inside function and f is the outside function
To get g(x) , we need to find the inside function in h(x)
[tex]h(x)=3(x+2)^2[/tex]
Inside function is x+2
So g(x) is x+2
when g(x)= x+2 then f(x) is [tex]3x^2[/tex]
So [tex]f(x)= 3x^2[/tex] and [tex]g(x)= x+2[/tex]
what is the ratio of 3√x4
What two fractions are equivalent to 24/84
Multiply:
453
x 1.1
-------
A) 49.83
B) 56.43
C) 498.3
D) 564.3
use the distributive property to write the following expression in an equivalent form:6× (10+25)
2 to the power of 14
How many solutions can be found for the linear equation? 4(x + 5) - 5 = 8x + 18/ 2
A)no solutions
B)one solution
C)two solutions
D)infinitely many solutions
Answer: The correct option is A.
Explanation:
The given equation is,
[tex]4(x+5)-5=\frac{8x+18}{2}[/tex]
Multiply both sides by 2.
[tex]2[4(x+5)-5]=\frac{8x+18}{2}[/tex]
[tex]8(x+5)+2(-5)=8x+18[/tex]
[tex]8x+40-10=8x+18[/tex]
[tex]8x+30=8x+18[/tex]
Subtract both sides by 8x.
[tex]30=18[/tex]
This statement is false for any value of x, therefore the system of equation have no solution and option A is correct.
Answer:
Option A is correct
No solutions
Step-by-step explanation:
The distributive property says that:-
[tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]
Given the equation:
[tex]4(x+5)-5 = \frac{8x+18}{2}[/tex]
Using distributive property we have;
[tex]4x+20-5 = \frac{8x+18}{2}[/tex]
⇒[tex]4x+15= \frac{8x+18}{2}[/tex]
Multiply both sides by 2 we have;
[tex]8x+30 = 8x+18[/tex]
Subtract 8x from both sides we have;
[tex]30=18[/tex] False.
For any value of x, there is no solutions for the given system of equation
Therefore, No solution can be found for the linear equation
Compare 9.75, 9.7, 9.675
A decimal is a number that consists of a whole and a fractional part.
Comparing the given decimal values from smallest to greatest we get,
9.675 < 9.700 < 9.750
What is a decimal number?A decimal is a number that consists of a whole and a fractional part.
It lies between integers and represents numerical value for quantities that are whole plus some part of a whole.
We have,
9.75, 9.7, 9.675
We can write from smallest to greatest values.
We can make the given decimal values in tenths, hundredths, and thousandths place values.
Let's write all the given decimal numbers till the thousandth place value as:
9.75 can be written as 9.750
9.7 can be written as 9.700
9.675 is already in the thousandth place value.
Comparing from smallest to greatest we have,
9.675 < 9.700 < 9.750
Thus,
Comparing the given decimal values from smallest to greatest we get,
9.675 < 9.700 < 9.750
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a computer repairman charges an initial fee of $100 plus an hourly fee of $75.
Mr. Billings paid the repairman $475. How many hours did the repairman work?
Answer:
The repairman worked 5hours
Step-by-step explanation:
Initial fee = $100
Charge per hour = $75
This simply implies that the repairman charges $100 and charge 75 for every hour worked.
Initial fee = $100
Charge per hour = $75
To find the hours work when his total work fee is 475, we should understand that,
Total work fee = initial fee + total charges
Total charges = charge per hour * hour worked.
Total work fee = initial free + (charge per hour * hour worked.)
475 = 100 + 75*h
Collect like terms
75h = 475 - 100
75h = 375
Divide both side by 75 .
75h/75 = 375/75
h = 5.
Since h represent hour work by the repairman.
The repairman worked 5hours
Describe a Situation with two quantities that have proportional Linear relationship
Let d denote the distance covered(in km) over the time t(in hours) with a speed of 10 km/h.
This means that the with the increasing time the distance covered will also increase.
Hence, the two variables i.e. distance and time are directly proportional to each other and also the equation which describes this relationship is given by:
d=10t
Also, the relationship is Linear.
Since, the equation is linear which relates the two variable.
1/3(−32.48−14.02) Enter your answer, as a decimal to tenths, in the box
1. Translate the variable expression into a word phrase: 4b – 2
Translate the word phrase into a variable expression:
2. the sum of 16 and 4 times a number
3. Write an equation for the following word problem. Use b for the number of boys and g for the number of girls.
There are eight fewer boys than girls in Mrs. Davis' class. How many boys are in the class?
4. Will the standard form 3.2 × 10–4 be more or less than 1? Explain what effect the negative exponent has.
5.Use a five-step plan to solve the following word problem. Show all five steps in your response:
Doug is twice Anne's age. Doug is 34 years old. How old is Anne?
Answer:
1) The difference between four times the number b and 2.
2) 16 + 4*x
3) if there are 8 fewer boys than girls in the class, then g - b = 8, so the number of boys is: b = g - 8
4) 3.2*[tex]10^{-4}[/tex] is less than 1 because of the negative exponent, the expression is equivalent to 3.2/10000 = 0.00032 < 1
5) Ok, Dough is twice Anne's age. so if D is Dough's age, and A is Anne's age:
D = 2*A
and D = 34
then 34 = 2*A
if we divide both sides by 2, we get
34/2 = 2*A/2
17 = A
Anne is 17 years old.
Alexandra earns $125 from her paper route each month, but she spends about $20 each month on personal expenses to pay for a school trip that costs $800 about how many months does she need to save money? Explain
Alexandra will need approximately 8 months to save enough money for the school trip.
To calculate the number of months Alexandra needs to save money for her school trip, we'll first find out how much she saves each month after deducting her personal expenses.
Monthly earnings from paper route: $125
Monthly personal expenses: $20
Monthly savings = Earnings - Expenses
Monthly savings = $125 - $20
Monthly savings = $105
Now, let's determine how many months it will take for Alexandra to save enough money for the trip.
Total cost of the school trip: $800
Number of months needed = Total cost of trip / Monthly savings
Number of months needed = $800 / $105
Number of months needed ≈ 7.62
Therefore, Alexandra will need approximately 8 months to save enough money for the school trip.
Each month, Alexandra earns $125 from her paper route. After deducting her personal expenses of $20, she saves $105 per month. Since the school trip costs $800, we divide the total cost of the trip by her monthly savings to find out how many months she needs to save. The result is approximately 7.62, so we round up to 8 months. Therefore, Alexandra needs 8 months to save enough money for the school trip.
Complete question:
Alexandra earns $125 from her paper route each month, but she spends about $20 each month on personal expenses to pay for a school trip that costs $800 about how many months does she need to save money? Explain
Which of the following equations describe the line (-6, 2) (-1, -4)? (Graph below)
A. y - 4 = -5/6(x - 1)
B. y - 2 = -5/6(x + 6)
C. y + 4 = -6/5(x + 1)
D. y + 4 = -5/6(x + 1)
E. y - 2 = -6/5(x + 6)
F. y - 6 = -6/5(x + 2)
Answer: c.
Step-by-step explanation:
Which is a simplified form of the expression -(z + 1) + 2(z – 2)?
A. -z – 5
B. 3z – 3
C. z – 5
D. 2z – 5
I honestly need help tho.
Answer:
The answer is C
Step-by-step explanation:
A healthy human heart beats about 1,533,000 times in a year. A sparrow's heart beats about 241,776,000 times in a year. About how many times faster does the sparrow's heartbeat compared to the human heart?
A. 2×1082×106=1×102or about 100 times faster
B. 2×1092×106=1×103or about 1,000 times faster
C. 2×1082×105=1×103or about 1,000 times faster
D. 2×1092×105=1×104or about 10,000 times faster
Answer:A
Step-by-step explanation: if you count the places, it’s 10 to the 8th power and 10 to the 6th power so that makes it A
The sparrow's heart beats approximately 158 times faster than a human heart. None of the options provided (A, B, C, or D) match this calculation.
Explanation:To find how many times faster the sparrow's heartbeat is compared to the human heart, you divide the number of times the sparrow's heart beats by the number of times a human heart beats. Thus, you would perform 241,776,000 ÷ 1,533,000. The result of this division is approximately 157.7, which means that the sparrow's heart beats about 158 times faster than a human heart.
None of the options provided in the question (A, B, C, or D) match this result, indicating there may be a mistake. Always remember, the correct way to compare in such circumstances is to do division, and not multiplication or addition.
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Karen can paint a wall in 2.5 hours. Stephanie takes 1.25 hours to paint the same size wall. How many minutes will it take for Karen and Stephanie to paint the same wall?
is 3.02859 is a rational number
If prices increase at a monthly rate of 1.2%, by what percentage do they increase in a year?
Final answer:
To calculate the annual increase from a monthly rate of 1.2%, use the compound interest formula to calculate the compounding effect over 12 months, resulting in an annual increase of approximately 15.47%.
Explanation:
The question asks about the annual percentage increase if prices increase at a monthly rate of 1.2%. The calculation involves compounding the monthly increase over the course of a year. To find the total percentage increase for the year, the formula for compound interest can be used, which is [tex](1 + r)^n[/tex], where r is the monthly increase rate, and n is the number of periods (months in a year).
Steps to Calculate Annual Increase:
Convert the monthly percentage increase to a decimal by dividing by 100: 1.2% / 100 = 0.012.
Add 1 to the monthly rate: 1 + 0.012 = 1.012.
Raise this sum to the power of 12, since there are 12 months in a year: [tex]1.012^{12[/tex].
Subtract 1 from the result to find the annual increase rate in decimal form.
Multiply by 100 to convert back to a percentage.
When we do the math, it turns out the prices increase by approximately 15.47% over the course of a year, when compounded monthly at a rate of 1.2%.
Prices increase by 1.447% in a year when the monthly increase is 1.2%.
Explanation:To calculate the percentage increase in a year, we need to calculate the total increase over 12 months. Since prices increase at a rate of 1.2% per month, we can calculate the total increase over 12 months as follows:
1.012 x 1.012 x ... x 1.012 (12 times) = 1.01447
The total increase is 1.01447, which is equivalent to a 1.447% increase over the course of a year.
A group of 11 people are going to the movies one Saturday. Adults' tickets cost $11.50 each and children's tickets cost $7.25 each. If the total cost for admission to the movies is $105.25, how many children attended the movie?
Answer: 5
Step-by-step explanation:
Let x be the number of adults and y be the number of children going to the movies one Saturday.
Given : A group of 11 people are going to the movies one Saturday.
[tex]x+y=11----------------(1)[/tex]
Adults' tickets cost $11.50 each and children's tickets cost $7.25 each.
The total cost for admission to the movies is $105.25.
i.e. [tex]11.50x+7.25y=105.25-----------------(2)[/tex]
Multiply equation (1) by 11.5 , we get
[tex]11.5x+11.5y=126.5---------------------(3)[/tex]
Subtract equation (2) from (3), we get
[tex]4.25y=21.25\\\\ y=\dfrac{21.25}{4.25}=5[/tex]
Put value of y= 5 in (1), we get
[tex]x+5=11\\\\ x=11-5=6[/tex]
Hence, 5 children attends the movie.
The first four terms of a sequence are shown below 1, 4, 7, 10. Which formula can be used to determine the nth term in the sequence
Final answer:
The nth term of the given arithmetic sequence 1, 4, 7, 10 can be determined using the formula 3n - 2.
Explanation:
The student is trying to find a formula that can be used to determine the nth term of a sequence given its first four terms: 1, 4, 7, 10.
This sequence is arithmetic, meaning each term increases by a constant difference, which in this case is 3.
To find the nth term of an arithmetic sequence, we use the formula an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference between the terms. For this sequence:
a1 is 1 (the first term of the sequence)d is 3 (the difference between successive terms)Substituting these values into the formula, we get:
an = 1 + (n - 1)×3
Therefore, the nth term an can be simplified to 3n - 2. So, the formula 3n - 2 can be used to determine the nth term in the sequence.
Can anyone help me find the slope??
Answer:
The slope is -3/4
Explanation:
To find the slope of a line, you can use the "rise over run" method where you count how many units from one point to the next the line increases or decreases along the y-axis and place this number in the numerator of a fraction; then, count how many units to the left or right that same point is along the x-axis and place this number in the denominator. Simplify if necessary and that becomes the slope.
So, assuming each tick on the axes is 1 unit, to get from the leftmost point to the rightmost point, we go down 3 units on the y-axis ("rise" -3 units) and to the right 4 units ("run" 4 units). Therefore, the slope is -3/4
The method I like to use the most because it involves the actual math of finding a slope is plugging plotted points into the slope formula. The slope formula is [tex]\frac{Y2 - Y1}{X2 - X1}[/tex] where two points along the line (X1, Y1) and (X2, Y2) are used.
Again, assuming, each tick is 1 unit, the plotted points on the line in the image are (-2, 2) and (2, -1). Now, we plug these ordered pairs into the formula and solve:
[tex]\frac{Y2 - Y1}{X2 - X1} = \frac{-1 - 2}{2 - (-2)} = \frac{-3}{2 + 2} = \frac{-3}{4}[/tex]
Therefore, the slope is -3/4
how can you compare fractions with the same denominators
A piece of paper is 0.00075 inches thick. How many sheets of paper will be in a stack that is 2.25 inches high
write a system of equations that has (2,7.5) as its solution
2w + 5 = 4w + 13
What it is w?
each bag of pattern blocks contains 50 block. to make a class pattern, the teacher combines 4 bags of blocks. how many pattern blocks are there?
Sandy is organizing her bedroom she found 6 jar filled with pennies if each gar has 4,560 pennies how many pennies does sandy have in all?
If each jar is full of 4,560 pennies, then the answer is 27,360 pennies in all.
4560*6=27360
Hope this helps.
Answer:
sandy has 4566
Step-by-step explanation:
3. A recipe calls for 1 1/2 cups of flour, 3/4 a cup of white sugar, and 1/8 a cup of brown sugar. (a) How many total cups of ingredients are there? Show your work using a number line. (b) Which of the following mixing bowls can you use to make the recipe: 2-cup, 3-cup, or 4-cup?
Answer:
a) 19/8
b) 3 cup since it's 2.4
My question is up above