given f(x)=x^3 and g(x)=1-5x^2, find (fog) (x) and its domain
Answer:
answer is b
Step-by-step explanation:
You and your family attend your brother’s championship baseball game. Between innings you decide to go to the snack stand. You go to the snack stand with $15 and find that sodas are $2.50 and that popcorn is $3.75. Write an inequality that models the number of sodas you can buy if you get a bag of popcorn too. What is the maximum number of sodas you can buy in this situation?
The height of a triangle is 4 cm more than twice the length of the base. the area of the triangle is 63 cm2. find the height of the triangle.
Answer:
THE ANSWER COULD BE 14
Hidemi is a waiter. He waits on a table of 4 whose bill comes to $69.98. If Hidemi receives a 20% tip, approximately how much will he receive?
$3.50
$14.00
$84.00
$7.00
Suppose that the length of a certain rectangle is 5 meters less than four times its width. the perimeter of the rectangle is 40 meters. find the length and width of the rectangle.
Complete the expression so it forms a perfect-square trinomial. x² +___ x + 49 A. 14 B. 7 C. 7/2
The expression so it forms a perfect square trinomial is 14x.
We have given that,
The expression so it forms a perfect-square trinomial.
We have to determine the x² +___ x + 49.
What is the factor?
A divisor of an integer n also called a factor of n, is an integer m that may be multiplied by some integer to produce n.
In this case, one also says that n is a multiple of m.
(x + 7)(x + 7)
x^2 + 14x + 49
The expression so it forms a perfect square trinomial is 14x.
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What are the steps for using a compass and straightedge to construct a square? Drag and drop the steps in order from start to finish. Use a straightedge to draw line a and label a point on the line as point P. Without changing the compass width, place the compass point on point S and draw an arc in the interior of ∠SPT . Use the straightedge to draw QS¯¯¯¯¯ and QT¯¯¯¯¯. Construct a line perpendicular to line a through point P. Label a point on this line as point R. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→ . Label the points of intersection as points S and T. Keeping the same compass width, place the compass on point T and draw an arc in the interior of ∠SPT to intersect the previously drawn arc. Label the point of intersection as point Q.
Answer: The steps for using a compass and straightedge to construct a square are as follows :-
1. Use a straightedge to draw line a and label a point on the line as point P.
2. Construct a line perpendicular to line a through point P.
3. Label a point on this line as point R.
4. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→.
5. Label the points of intersection as points S and T.
6. Keeping the same compass width, place the compass on point T and draw an arc in the interior of∠SPT to intersect the previously drawn arc.
7. Label the point of intersection as point Q.
8. Without changing the compass width, place the compass point on point S and draw an arc in the interior of∠SPT .
9. Use the straightedge to draw QS ,QT,SR and RT.
Here we have finished with the square RTQS.
Amelia knits 1/10 of a scarf in 48 minutes. What fraction of a scarf can she knit in an hour? A. 5/24 B. 1/480 C. 1/8 D. 2/25
The law of detachment can be used to draw a conclusion from the following statements: "It will be sunny on Tuesday." "I will always go outside if the weather is nice."
Final answer:
Using the law of detachment, if it is sunny on Tuesday and there is a habit of going outside in nice weather, one can conclude that they will go outside on Tuesday.
Explanation:
The law of detachment is a concept in logic used to form conclusions given a conditional statement and its hypothesis being true. For instance, in the scenario provided:
If it is sunny on Tuesday (hypothesis).
I will always go outside if the weather is nice (conditional statement).
By applying the law of detachment, we can conclude that:
I will go outside on Tuesday (conclusion).
This logical reasoning assumes that a 'nice' weather includes a sunny day. Hence, if it is indeed sunny on Tuesday, the condition for going outside is met.
What type of transformation takes the graph of
f(x)=|x|
to the graph of
g(x)=â3+|x|
?
Â
vertical translation of 3 units up
horizontal translation of 3 units right
vertical translation of 3 units down
horizontal translation of 3 units left
Luigi is an urban planner. as an independent contractor, he charges $140 fee plus $ 25 per hour for each contract with the city.
Write a function to represent this scenario where Y represents the total amount her changes for a project and x represents the number of hours worked on a project
x = hours 25 per hour = 25x
y = total
so y = 25x +140
Answer: y = 140+25x
Step-by-step explanation:
Since According to the question, Luigi initally charged $140.
And, per hour he charged an additional amount $25 for each contract with the city.
Here, x represents the number of hours worked on a project.
Thus the additional amount after x hours = 25x
So, the total amount he charged in x hours= 140+ 25x
And, according to the question y represents the above change.
Thus, we get a function for the given situtaion
which is , y= 140+ 25x , where x is number of hours and y is total amount charged.
anonymous 4 years ago A technical writer makes $45,000 per year and has just begun contributing 8% of her salary to her 401(k) plan. If her employer matches 6% of her contributions, how much will have been contributed to the 401(k) plan after 2 years?
Answer:
$7,632 would have been contributed to the 401(k) plan after 2 years.
Step-by-step explanation:
A technical writer makes salary per year = $45,000
She contributing 8% of her salary to her 401(k) plan = 8% of 45,000
0.08 × 45,000 = $3,600
Her employer matches 6% of her contributions = 6% of 3,600
= 0.06 × 3,600 = $216.00
Total contribution for one year = 3,600 + 216.00 = $3,816
After 2 years = 3,816 × 2 = $7,632.00
$7,632 would have been contributed to the 401(k) plan after 2 years.
In 2010, the national debt of the United States was about 14 trillion dollars. In 2003 it was about 7 x 10 to the 12 dollars. About how many times larger was the national debt in 2010 than 2003? THIS IS SCIENTIFIC NOTATION
Answer: About 2 times.
Step-by-step explanation:
Given : In 2010, the national debt of the United States was about 14 trillion dollars.
We know that 1 trillion [tex]=1,000,000,000,000= 10^{12}[/tex]
then, In 2010, the national debt of the United States was about [tex]14\times10^{12}[/tex]
dollars.
In 2003 it was about [tex]7\times10^{12}[/tex] dollars.
Now, the number of times the national debt was larger in 2010 than 2003 :-
[tex]\dfrac{ 14\times10^{12}}{7\times10^{12}}\\\\=\dfrac{14}{7}\times10^{12-12}\\\\=2\times10^0=2[/tex]
Hence, national debt was about 2 times larger in 2010 than 2003 .
An article with a net weight of 10 lb (pounds) is packaged in a box that weighs ½ lb. If 20 of these boxed articles are put into one freight container that weighs 15 lb, what is the gross weight?
In a school election, 3/4 of the students vote. There are 1464 ballots. Write and solve and equation to find the number of students.
x = total number of students
equation is:
(3/4)x = 1464
to solve for x divide both sides by 3/4
x = 1464 / 3/4 = 1952
x = 1952
there are 1952 total students
if TRAP is an isosceles trapezoid what is the value of x ?
the answer to this question is 19!
The probability of choosing either a girl or a boy is
Amy, who is 17 years old, is 5 years older than twice Moe's age.Write an equation that you could solve to find Moe's age. Solve the equation and describe your steps.
Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation. The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware. The total bill for the catering services is $1,512. Which equation can be used to determine the total number of guests, g, who attend the dinner party? 13.50g + 540 = 1,512 13.50g - 1,512 = 540 5400g + 13.50 = 1,512 540g - 1,512 = 13.50
Answer:
The equation can be used to determine the total number of guests is 13.50g + 540 = 1512 and the total number of guest are 72 .
Step-by-step explanation:
As given
Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation.
The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware.
The total bill for the catering services is $1,512.
Total number of guests, g .
Than the equation becomes
1512 = 540 + 13.50 g
1512 - 540 = 13.50 g
972 = 13.50 g
[tex]g = \frac{972}{13.50}[/tex]
g = 72
Therefore the equation can be used to determine the total number of guests is 13.50g + 540 = 1512 and the total number of guest are 72 .
Solve the equation
5x - 5 = 3x - 9
A. 1
B. -2
C. -3
D. -1
What is the solution of the linear quadratic system or equations?
Y=x^2+5x-3
Y-x=2
The solution to the system of equations are (1, 3) and (-5, -3)
Given the following functions
Y=x^2+5x-3
Y-x=2; y = x + 2
Equating both outputs will give
x^2+5x-3 = x + 2
x^2+5x-3 - x - 2 = 0
x^2 + 4x - 5 = 0
Factorize the equation
x^2 + 5x - x - 5=0
x(x+5) - 1(x+5) = 0
(x-1)(x+5) = 0
x = 1 and -5
Recall that y = x + 2
y = 3 and -3
Hence the solution to the system of equations are (1, 3) and (-5, -3)
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The solution to a linear quadratic system of equations can be found by substitifying one equation into the other and solving. In this case, the solutions are (1,3) and (-5,-3).
Explanation:To find the solution of a linear quadratic system of equations, you need to substitute one equation into the other. In this case, for the equations [tex]Y = x^2 + 5x - 3[/tex] and [tex]Y - x = 2[/tex], you would first isolate Y in the linear equation, resulting in [tex]Y = x+2.[/tex]
Then, you substitute (x + 2) for Y in the quadratic equation, leading to [tex]x + 2 = x^2 + 5x - 3.[/tex]
Next, rearrange the equation to get it in the standard quadratic form: 0 = [tex]x^2 + 5x - x - 3 - 2.[/tex] Simplifying this results in the equation [tex]0 = x^2 + 4x - 5.[/tex]
Finally, solve this equation by factoring or using quadratic formula, which gives the solutions as x = 1, -5. Substituting both 1 and -5 into the equation Y = x + 2 gives the corresponding y-values, Y = 3 and -3. Therefore, the solutions to the system of equations are (1,3) and (-5,-3).
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find the digit that makes 2,72_ divisible by 6
To find the missing digit to make 2,72_ divisible by 6, add the digit 4.
To find the digit that makes 2,72_ divisible by 6, we need to focus on the divisibility rules for 6. In this case, a number is divisible by 6 if it is divisible by both 2 and 3. For 2, the last digit must be even, and for 3, the sum of the digits must be a multiple of 3.
Given the number 2,72_, the blank digit needs to be 4 to make the number divisible by 6. This is because when the digit 4 is added, the number becomes 2,724, which is divisible by both 2 and 3.
What is the greatest common factor of 60x4y7, 45x5y5, and 75x3y? 5xy 15x3y 45x3y5 75x5y7
Answer: 15x3y
Step-by-step explanation:
We rewrite the expressions by using factorisation method of their primes. This will give:
60x4y7= 2×2×3×5×x×x3×y×y6
45x5y5= 3×3×5×x×x4×y×y4
75x3y= 3×5×5×x×x2×y
Common factors= 3 × 5 × x3 × y
= 15x3y
Answer:
its B
Step-by-step explanation:
Richard borrowed $950 from his parents to make some repairs on his car. He promised to repay the loan by giving his parents at least $85 from his paycheck each week. Assuming richard sticks to his promise, which of the following is not a possible scenario for the amount of debt Richard has remaining?
I think it's B but I'm not 100% sure
Answer:
B
Step-by-step explanation:
To solve this, you need to know first how many weeks will take Richard replacing the money.
We will call X the number of weeks so we say
$85 * X =$950
X= 11.17
This means it will take at least ≈12 weeks to pay his debt.
To know which scenario it's not possible, use the equation to choose the right option.
A: $85*5= $425
After 5 weeks, he paid $425, this mean he's $525 in debt.
B: $85*6= $510
After 6 weeks, he paid $510, this means he's $440 in debt.
C. $85*7= $595
After 7 week,s he paid $595, this means he's $355 in debt.
D. $85*8= $680
After 7 weeks, he paid $680, this means he's $270 in debt.
The not possible scenario is B because he will be paying at least $85 or more so he will debt $440 or less al week 6.
Twice a number, increased by one, is between negative three and seven. find all the numbers.
To solve the inequality -3 < 2x + 1 < 7 for the number x, subtract 1 from all parts and then divide by 2. The solution is the range of numbers greater than -2 and less than 3.
Explanation:The problem statement here results in an inequality that can be expressed algebraically. If 'x' represents the unknown number, we can write the inequality as -3 < 2x + 1 < 7.
To solve for 'x', we will isolate the variable on one side by following the rules of inequalities similar to solving equations.
First, subtract 1 from all parts of the inequality to get the pure inequality without a constant.
-4 < 2x < 6
Now, divide all parts of the inequality by 2, which yields:
-2 < x < 3
All numbers greater than -2 and less than 3 satisfy the original problem statement. Therefore, the range of numbers that solve the inequality is from -2 to just below 3.
To determine the number of trout in a lake, a conservationist catches 180 trout, tags them and throws them back into the lake. later, 48 trout are caught; 12 of them are tagged. how many trout would the conservationist expect to be in the lake?
The sum of 4 times mike's age and 3 times susan's age is 79. mike is 1 year more than 3 times as old as susan. find each of their ages.
A mathematical scale in which the concentration of hydrogen ions in a solution is expressed as a number from 0 to 14
parallelogram ESTA has vertices E (10,0), S(14,3),T(6,9) and A (2,6). to calculate its area, Jamal will first determine the equation of the line through point E and perpendicular to ST. What is the equation of this line?
Six times a number decreased by ten is eight. Find the number.
A) 2
B) 3
C) 4
D) 5