Answer:
Q1.
Perimeter = 2(Length + Width)
Perimeter = [tex]2((2x-7)+(x^2-5))[/tex]
[tex]2\left(2x-7\right)+2\left(x^2-5\right)[/tex]
[tex]4x-14+2x^2-10[/tex]
[tex]2x^2+4x-24[/tex]
Q2.
[tex](-9x^2+3x-10)-(-15x^2-5x+11)[/tex]
[tex]-9x^2+3x-10+15x^2+5x-11[/tex]
[tex]6x^2+8x-21[/tex]
A racetrack charges $80 for each seat in the lower section, $60 for each seat in the upper section, and $40 for field tickets. There are three times the amount of seats in the upper section as the lower section. The revenue from selling all 24,200 tickets is $1,140,000. write a system to represent the situation. How many seats are in each section
Answer:
The seats in the lower section are x= 1720 , in the upper section are 3x= 5160 and y=24,200 - 4x= 24,200 - 6880= 17320 tickets in the field.
Step-by-step explanation:
Let x represent the number of seats in the lower section then the number of seats in the upper section is 3x and y the number of seats in the field.
The equation can be written as
80x + 60 (3x) + 40 y= $1,140,000-----1
And x+ 3x+ y= 24,200------2
4x+ y= 24,200
or y= 24,200-4x----3
Solving Eq 1
80x + 180x + 40 y= $1,140,000
260x+ 40 y=$1,140,000-----4
Putting Eq 3 in Eq 4
260x+ 40 y=$1,140,000
260x+ 40(24,200-4x-)=$1,140,000
260x + 968,000- 160x= $1,140,000
100x= $1,140,000-968,000
100x= 172,000
x= 1720
The seats in the lower section are x= 1720 , in the upper section are 3x= 5160 and y=24,200 - 4x= 24,200 - 6880= 17320 tickets in the field.
Putting the values of x and y in Eq 1 we get the same revenue.
80x + 60 (3x) + 40 y= $1,140,000
80(1720) + 60 (5160) + 40( 17320)= $1,140,000
137600 + 309600 + 692800= $1,140,000
137600 + 1002400= $1,140,000
The total number of seats in the upper section is 5160, in the lower section is 1720 and the total number of seats in the field is 17320.
Given :
A racetrack charges $80 for each seat in the lower section, $60 for each seat in the upper section, and $40 for field tickets.There are three times the amount of seats in the upper section as the lower section. The revenue from selling all 24,200 tickets is $1,140,000.The following steps can be used in order to determine the total number of seats in each section:
Step 1 - In the lower section let the total number of seats be 'x'. So according to the given data, in the upper field, the total number of seats is '3x'. Now, let the total number of seats in the field be 'y'.
Step 2 - The linear equation that represents total revenue from the tickets.
[tex]\rm 80x + 60(3x)+40y = 1140000[/tex]
260x + 40y = 1140000 --- (1)
Step 3 - The linear equation that represents the total number of tickets is:
x + 3x + y = 24200
y = 24200 - 4x --- (2)
Step 4 - Substitute the value of y in equation (1).
260x + 40(24200 - 4x) = 1140000
x = 1720 tickets
Step 5 - Substitute the value of 'x' in equation (2).
y = 24200 - 4(1720)
y = 17320 tickets
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What is the simplified value of the expression below?
4.2 + 0.6 divided by 3 minus 5(0.9 minus 0.5)
Answer:The simplified value: 4.8 divided by 3 or the answer you’ll get from that is 1.6
Step-by-step explanation:
4.2+0.6=4.8 0.9-0.5=0.4 5*0.4=2 3-2=1 4.8 divided by 3
Answer:
The answer is 2.4
Step-by-step explanation:
4.2 + 0.6 divided by 3 minus 5(0.9 minus 0.5) = 2.4
I got it right and used a calculater.
A car dealership manager has determined that the profit, in thousands of dollars, of the dealership can be determined by the expression LaTeX: x^2-4xL a T e X : x 2 − 4 x, where LaTeX: xL a T e X : x is the number of cars sold. A different manager states that the profit of the dealership can be determined by the function LaTeX: 5xL a T e X : 5 x. What number of cars sold makes the equation LaTeX: x^2-4x=5xL a T e X : x 2 − 4 x = 5 x true? Select all that apply.
Answer:
The number of cars that brings the same profit is 9 and 0
Step-by-step explanation:
Given
[tex]x^2 - 4x = 5x[/tex]
Required
Determine the possible values of x
[tex]x^2 - 4x = 5x[/tex]
Subtract 5x from both sides
[tex]x^2 - 4x - 5x = 5x - 5x[/tex]
[tex]x^2 - 9x = 0[/tex]
Factorize
[tex]x(x - 9)= 0[/tex]
Split the equation
[tex]x = 0[/tex] or [tex]x - 9 = 0[/tex]
[tex]x = 0[/tex] or [tex]x = 9[/tex]
Hence, the number of cars that brings the same profit is 9 and 0
Candy Mazer earns $90 a day at her part-time job. She works 2 days each week
Her husband, Jon, earns a salary of $450 a week. What total gross gay de Cards
and Jon get every week? (1 point)
Below is a set of dates taken from 50 coins found in the drawer of the person who wrote this question. Which histogram best portrays the data in the set of numbers? NOTE: the answer choices assume that thex-axis is years, so newer coins would be to the right. (You may want to use the TI-83 to help you.)
Answer:
The fourth graph in the second image.
Step-by-step explanation:
After plotting all the points in a calculator, the fourth graph matches the calculator.
APEX
5th graph with the large spike on the second to last bar
Please solve......... thanks
Answer: 54 teaspoons of oregano
Step-by-step explanation: 1 can is 6 teaspoons so 9 cans would be 54 teaspoons because 9 x 6 = 54.
Hope this helps!
The equation shown has a missing value. -2(2x-?)+1=17-4x. For what missing value(s), if any, does the equation have exactly one solution?For what missing value(s), if any does the equation have no solution?
Answer:
8
Step-by-step explanation:
There are no values for which the equation has only one solution for no solution the missing value can be anything except 16.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The equation shown has a missing value.
-2(2x - ?) + 1 = 17 - 4x
Applying the distributive property:
-4x + ? + 1 = 17 - 4x
? + 1 = 17
There are no values for which the equation has only one solution or unique solutions.
For no solution the missing value can be anything except 16
? + 1 = 17
? = 17 - 1
? = 16
Thus, there are no values for which the equation has only one solution for no solution the missing value can be anything except 16.
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Vincent goes to the gym for 30 minutes every day. He starts a new exercise routine on a Monday and uses a function to model the amount of calories he has used, f\left(d\right)f(d), as a function of the number of days, dd, he has exercised with the new routine.
Complete question is;
Vincent goes to the gym for 30 minutes every day. He starts a new exercise routine on a Monday and uses a function to model the amount of calories he has used, f(d), as a function of the number of days, d, he has exercised with the new routine.
Which statement represents a correct interpretation of f(d) ?
A. f(5) = 150 means Vincent has exercised for a total of 150 minutes after the fifth day of exercising with his
new routine
B. f(10) = 3500 means Vincent will use 3,500 calories on day 10 of exercising with his new routine.
C. f(15) = 5250 means after 15 days of exercising with his new routine, Vincent has used 5,250 calories.
D. f(30) = 10500 means the number of calories Vincent has used times 30 is equal to 10,500
Answer:
Option A: f(5) = 150 means Vincent has exercised for a total of 150 minutes after the fifth day of exercising with his
new routine .
Step-by-step explanation:
We are told that f(d), is a function of the number of days, d, he has exercised with the new routine.
We are also told that he goes to the gym for 30 minutes daily.
Thus;
For option A, f(5) means that he went to the gym for 5 days. At 30 minutes per day means he exercised for a total of: 30 × 5 = 150 minutes. So option A is correct
For option B, f(10) means that he went to the gym for 10 days. At 30 minutes per day means he exercised for a total of: 30 × 10 = 300 minutes. Thus, option B is wrong
For option C, f(15) means that he went to the gym for 15 days. At 30 minutes per day means he exercised for a total of: 30 × 15 = 450 minutes. Thus, option C is wrong.
For option D, f(30) means that he went to the gym for 30 days. At 30 minutes per day means he exercised for a total of: 30 × 30 = 900 minutes. Thus, option D is wrong.
Put these numbers in order from least to greatest.
-8/20, 3/5, -16/32.
Answer:
least to greatest: -16/32, -8/20, 3/5
Step-by-step explanation:
Solve for the indicated variable. 6y + 5x = 7 for x
Answer:
[tex]x = \frac{-6y+7}{5}[/tex]
Step-by-step explanation:
[tex]6y + 5x = 7[/tex]
Isolate x ;
[tex]5x = 7-6y\\\\5x =-6y+7[/tex]
Divide both sides of the equation by 5
[tex]\frac{5x}{5} = \frac{-6y+7}{5} \\\\x = \frac{-6y +7}{5}[/tex]
0.12345 is it rational or irrational number
Answer:
it is a rational number
The figure below is made of two identical triangular prisms what is the value of the figure
Answer:
I will tell you in the explanation...
Step-by-step explanation: God created us and god knows the answer. :)
Find the slope-intercept form for the line passing through (2,7) and parallel to the line passing through (3,8) and (-3,4).
The slope-intercept form for the line passing through (2,7) and parallel to the line passing through (3,8) and (-3,4) is y = ___
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Answer:
[tex]y = \frac{2}{3} x + 5 \frac{2}{3} [/tex]
Step-by-step explanation:
Please see the attached pictures for the full solution.
7+4(2a+15)=-13
Please help
Answer:
a = -10
Step-by-step explanation:
Simplifying
7 + 4(2a + 15) = -13
Reorder the terms:
7 + 4(15 + 2a) = -13
7 + (15 * 4 + 2a * 4) = -13
7 + (60 + 8a) = -13
Combine like terms: 7 + 60 = 67
67 + 8a = -13
Solving
67 + 8a = -13
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-67' to each side of the equation.
67 + -67 + 8a = -13 + -67
Combine like terms: 67 + -67 = 0
0 + 8a = -13 + -67
8a = -13 + -67
Combine like terms: -13 + -67 = -80
8a = -80
Divide each side by '8'.
a = -10
Simplifying
a = -10
suppose 35 gallons of water came out of a pipe in 7 minutes. what was the rate in gallons per minute
Answer:
6 gallons per minute
Step-by-step explanation:
35÷7=6
Please help me! I will mark brainliest! Thanks!
Answer: Group 12
Step-by-step explanation: The element is Mercury.
A fisher caught a large boat load of salmon. She decided to donate some of his fish to the local community, 1,672 people in all. To each person over the age of 50 she gave 16 fish and to each person under 50 she gave 96 fish. Only 3/4 of the over 50s collected their salmon and only 1/8 of the under 50s collected their fish. How many fish did the fisher distribute it total
Answer:
74 fishes
Step-by-step explanation:
Total number of people = 1672
Let us represent:
Number of people over the age of 50 = a
Number of people below the age of 50 = b
People over the age of 50 she gave = 16 fish
People below 50 she gave = 96 fish. Only 3/4 of the over 50s collected their salmon
= 3/4a collected fish = 0.75a
If a should collect = 96 fishes
0.75a =
Cross Multiply
=0.75a × 96 fishes/ a
= 72 fishes
Therefore, 3/4 of the over 50s collected 72 fishes.
1/8 of the under 50s collected their fish.
= 1/8b collected fish = 0.125b
If b people should collect = 16 fishes
0.125b people =
Cross Multiply
0.125b × 16 fishes/b
= 2 fishes.
Therefore, the total number of fishes shared
= 72 fishes + 2 fishes
= 74 fishes
8
Round to nearest hundred thousand.
755,787
What is the quotient of 1/6 divided by 2?
Answer:
1/12 or 0.083
Step-by-step explanation:
A 15-ounce package of pistachios cost 5.99. What is the cost per ounce?
Answer:
$0.39
Step-by-step explanation:
39¢
5.99 ÷ 15 = 0.39
Question 1 (1 point)
Eric is baking a cake. The recipe calls for 2 1/2 pounds of flour for every 1/4 cup of sugar. How many pounds of flour per sugar should Eric use?
5/8
8
4
10
Od
1/10
Answer:
10
Step-by-step explanation:
2 1/2 ÷ 1/4 reduce
5/2 × 4/1 = 20/2
20 ÷ 2 = 10 pounds of flour per sugar
(I'm not very good at math so this might be wrong)
Which of the following shows the union of the sets? {4, 8, 12, 16, 20, 24, 28} {2, 4, 6, 8, 10, 12} A. {4, 8, 12} B. {4, 8, 12, 16} C. {6, 8, 10, 12} D. {2, 4, 6, 8, 10, 12, 16, 20, 24, 28}
What is the volume?
7ft
4ft
1ft
How much will a person pay for 13.5 pounds of bananas at a price of $1.68
Answer:$15.18
Step-by-step explanation:
what is the simplified for the expression below?
Answer:
Option 1: [tex]-2x+3[/tex]
Step-by-step explanation:
[tex]-\frac{1}{5}\left(5x+20\right)-\frac{1}{4}\left(4x-28\right)[/tex]
Expand:
[tex]-\frac{5x+20}{5}-\frac{4x-28}{4}[/tex]
[tex]-\left(x+4\right)-\left(x-7\right)[/tex]
Remove brackets:
[tex]-x-4-x+7[/tex]
Group similar terms together:
[tex]-x-x-4+7[/tex]
[tex]-2x+3[/tex]
Let x stand for the number of calories in each individual snack. 25 snacks are sampled at a time. The population mean is 95 calories and the population standard deviation is 2.5 calories. What is the mean and standard deviation of the sampling distribution of sample means
Answer:
mean = 95, standard deviation of sampling distribution = 0.5
Step-by-step explanation:
sample space n = 25 snacks
mean = bar x = 95 calories
population standard deviation = 2.5 calories
the mean is already given as 95 calories
standard deviation of the sampling distribution = s.d/√n
= 2.5/√25
= 2.5/5
= 0.5
Therefore we have the mean = 95, and standard deviation of sampling distribution = 0.5
In order for Brady to earn a B in his biology course, his test scores must average at least 80%. On the first 5 tests, he has an average of 77%. There is one test remaining in the course. What is the minimum score Brady needs to earn on the last test to receive a B in the class? Can you give a step by step explanation?
Hey there! I'm happy to help!
There were 5 tests needed to make an average of 77. These numbers have to add up to 385 (77×5) because that is what you divide by 5 to find the average which is 77.
Now, we want to find an average of 80 with 6 numbers. We multiply 80 and 6, showing us that the sum of these 6 numbers must be 480. Since 5 of these numbers are the same as with the 77 average, we know that one test score (the one Brady needs to get) is added to 385 to give us 480.
480-385=95
Therefore, Brady needs to earn a 95% on the last test to receive a B in the class.
What kind of distribution is the t-distribution?
Answer:
The t-distribution is a kind of probability distribution that is bell-shaped (like the normal distribution) but has a good number of values at the tails, making the tails fatter and the curve flatter.
Step-by-step explanation:
The t-distribution is a kind of probability distribution that is bell-shaped (like the normal distribution) but has a good number of values at the tails, making the tails fatter and the curve flatter.
The smaller the sample size n, the flatter the t-distribution curve but the larger the sample size n, the closer in identity to the normal distribution, the t-distribution will be.
How do you do this question?
Answer:
∫ₑ°° 1 / (x (ln x)¹⁰) dx
∫₁°° x⁻³ dx
Step-by-step explanation:
A p-series 1 / xᵖ converges if p > 1.
∫ₑ°° 1 / (x (ln x)¹⁰) dx
If u = ln x, then du = 1/x dx.
When x = e, u = 1. When x = ∞, u = ∞.
= ∫₁°° 1 / (u¹⁰) du
p = 10, converges
∫₁₀°° x^(-⅔) dx
= ∫₁₀°° 1 / (x^⅔) dx
p = ⅔, diverges
∫₁°° 2 / x^0.5 dx
= 2 ∫₁°° 1 / x^0.5 dx
p = 0.5, diverges
∫₁°° x⁻³ dx
= ∫₁°° 1 / x³ dx
p = 3, converges
∫₂°° 1/(3x) dx
= ⅓ ∫₂°° 1/x dx
p = 1, diverges
Your answer should be in the form p(x)+\dfrac{k}{x-1}p(x)+
x−1
k
p, left parenthesis, x, right parenthesis, plus, start fraction, k, divided by, x, minus, 1, end fraction where ppp is a polynomial and kkk is an integer.
\dfrac{x^2+2}{x-1}=
x−1
x
2
+2
Answer:
Step-by-step explanation:
the answer i got was -57
Functions can be rewritten is several forms.
The new form of the function is: [tex]\mathbf{f(x) = \frac{x^2}{x - 1} + \frac{2}{x-1}}[/tex]
The function is given as:
[tex]\mathbf{f(x) = \dfrac{x^2+2}{x-1}}[/tex]
Split
[tex]\mathbf{f(x) = \frac{x^2}{x - 1} + \frac{2}{x-1}}[/tex]
The form is given as:
[tex]\mathbf{f(x) = p(x) + \frac{k}{x - 1}}[/tex]
So, by comparison
[tex]\mathbf{p(x) = \frac{x^2}{x - 1}}[/tex]
[tex]\mathbf{k =2}[/tex]
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