Answer: YES
Step-by-step explanation:
Convert liters to gallons. Need to show 2 half gallons ≥ 3 liters
[tex]\frac{3(liters)}{} * \frac{1(gallon)}{3.785(liters)} = 0.7926 gallons[/tex]
[tex]2*\frac{1}{2} gallons = 1 gallon[/tex]
2 half gallons ≥ 3 liters
1 gallon ≥ 0.7926 gallons
TRUE
Worth 20 points!! If you answer wrong or something not related to the question I will report you! Thanks :)
If f: 2x+1 and g: x^2 find
A) f(3)
B) g(7)
C) fg(3)
D gf(3)
E) fg(7)
F) fg(x)
A
f(x) = 2x + 1
f(3) = 2*3 + 1 = 7
B
g(x) = x^2
g(7) = 7^2
g(7)= 49
C
f(g(x)) = 2(g(x) + 1
f(g(x)) = 2 x^2 + 1
f(g(3) = 2* 3^2 + 1
f(g(3) = 19
D
g(f(x)) = (f(x))^2
g(f(x)) = (2x + 1)^2
g(f(3)) = (2*3 + 1)^2 = (6 + 1)^2 = 49
E
f(g(x)) = 2*g(x) + 1
f(g(x)) = 2*x^2 + 1
f(g(3)) = 2*3^2 + 1
f(g(3)) = 2 * 9 + 1
f(g(3)) = 18 + 1
f(g(3) = 19
F
f(g(x)) = 2(g(x)) + 1
f(g(x)) = 2*x^2 + 1
Solve for x: 3x^2+13x=10
The first thing you would do is "bring" the 10 over by subtracting 10 from both sides
[tex]3x^2+13x-10=0[/tex]
Now, you would want to factor
[tex](3x-2)(x+5)=0[/tex]
Then, set each factor equal to zero, and solve
3x-2 = 0
3x = 2
x = 2/3
AND
x+5 = 0
x=-5
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The determinant is given as:
D = -b ±√(b² - 4ac) / 2a
The values of x are:
x = (-13 + √17) / 6
x = (-13 - √17 ) / 6
What is an equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
x + 3 = 4 is an equation.
3x + 4x = 4 is an equation.
We have,
3x² + 13x = 10
This can be written as:
3x² + 13x - 10 = 0
Using the Middle term factorization.
3x² + (10 + 3)x - 10 = 0
3x² + 10x + 3x - 10 = 0
This is not possible so,
Using determinant.
3x² + 13x - 10 = 0
a = 3, b = 13 and c = -10
Now,
Determinant is given as:
D = -b ±√(b² - 4ac) / 2a
D = -b + √(b² - 4ac) / 2a
D = [-13 + √(169 + 120)] / 6
D = (-13 + √17) / 6 _____(1)
D = -b - √(b² - 4ac) / 2a
D = -13 - √(169 + 120) / 6
D = (-13 - √17 ) / 6 ______(2)
Thus,
The values of x are:
x = (-13 + √17) / 6
x = (-13 - √17 ) / 6
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a plumber's fees f are $75 fora house call and $60 per hour h for each hour worked. Write a function rule
The function for the given situation is f=60h+75.
Given that, a plumber's fees f are $75 for house calls and $60 per hour h for each hour worked.
We need to model a function for the given situation.
What is a function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.
According to the question, we can model function as follows:
f=60h+75
Therefore, the function for the given situation is f=60h+75.
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Un cheatah puede recorrer 20 kilometros en 10 minutos. Si pudiera mantener esta velocidad durante una hora ,? cuantos kilometros recorreria
Answer:
If you can maintain this speed you will travel 120 km in 1 hour.
Explanation:
The translated question is, A cheetah can travel 20 kilometers in 10 minutes. If I could maintain this speed for one hour, how many kilometers would you travel?.
Let us find the speed of cheetah
Distance traveled = 20 km
Time taken = 10 minutes = 10/60 = 1/6 hours
So speed = [tex]\frac{20}{\frac{1}{6} } =120[/tex]km/hr.
So speed of cheetah = 120 km/hr, which means cheetah will travel 120 km in 1 hour.
If you can maintain this speed you will also travel 120 km in 1 hour.
Which inequality has –12 in its solution set?
a. X+6<-8
b. X+4>)-6
c. X-3>-0
d. X+5<)-4
Answer:
option d
Step-by-step explanation:
Solve each inequality and check which inequality has -12 as a solution
a. [tex]x+6<-8[/tex]
Subtract 6 from both sides
[tex]x<-14[/tex]
b. [tex]x+4>-6[/tex]
Subtract 4 from both sides of the inequality to get x alone
[tex]x>-10[/tex]
c.[tex]x-3>-0[/tex]
Add 3 on both sides
x>3
d. [tex]x+5<-4[/tex]
Subtract 5 from both sides
x<-9
-12 lies below -9. So x<-9 has -12 in its solution
Sweet T purchased a new pair of jeans to wear to the Battle of the Bands on sale at 40% off. He saved $ 20. What was the regular price of the jeans?
The regular price of the jeans was $50. We know this because he saved $20 when the pants were 40% off so for every 10% percent it is $5, so 100% is $50 if that makes sense, if you need more thorough explanation let me know. :)
Triangle MNO is rotated 180 using the origin as the center of rotation .Which sequence of transformations will produce the same results?
180° rotation about the origin changes the signs of the coordinates.
(x, y) → (-x, -y)
It is a reflection over the y-axis and a reflection over the x-axis (in either order).
You did not provide the options so hopefully you can figure out the answer based on the information I provided.
Answer:
The transformation of the triangle MNO will be first a reflection respect to the x-axis and second a reflection over the y-axis.
Step-by-step explanation:
By definition a coordinate transformation from 180° rotation round the origen can be expressed as:
(x,y) ---> (-x,-y)
On the other hand, the coordinate transformation of the reflection over x- axis is:
(x,y) ---> (x,-y)
And the reflection over the y-axis of the this transformation is:
(x,-y) ---> (-x,-y)
That result the same transformation than the 180° rotation.
Why did the queen have the king measure the rug
The queen might've asked the king to measure the rug to demonstrate humility, responsibility, highlight practical skills, or grasp the concept of measurement. Without specific context, however, it's hard to pinpoint an exact reason.
Explanation:Without specific context, it's difficult to provide an exact reason for the queen asking the king to measure a rug. However, in general, English literature often showcases rulers partaking in ordinary tasks as a means of demonstrating humility, responsibility, or attention to detail. For instance, the queen might have wanted the king to measure the rug in order to prove that he can attend to ordinary matters as well as royal duties, or perhaps to prove himself practical and not merely ceremonial. It could also be a ploy to make the king grasp the concept of measurement, size or area, by doing the task himself.
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A large bag of marbles contains an equal amount of red, orange, yellow, blue, and green marbles. Jaden randomly selects 1 marble from the bag. Which of the following represents the probability of selecting a red, blue, or yellow marble?
A. 0.5
B. 0.4
C. 0.3
D. 0.6
Answer:
Option D
0.6
Step-by-step explanation:
Given that there are 5 colour marbles in a large bag.
The colours are red, orange, yellow, blue and green.
Also given that there are equal amounts of each colour
Let n be the no of marbles of each colour.
Then total no of marbles = 5(n) = 5n
No of red,blue and yellow marbles = n+n+n = 3n
Prob of drawing a red or blue or yellow = P(red)+P(blue)+P(yellow)
= [tex]\frac{n}{5n} +\frac{n}{5n} +\frac{n}{5n} = \frac{3n}{5n}[/tex]
= 0.60
PLZ HELP NOW!!!!!!!!!!
Use the regression line for the data in the scatterplot to answer the question. On average, how many more goals will a player score for every additional hour of practice?
A. 1/2 of a goal
B. 3/4 of a goal
C. 1 goal
D. 4/3 of a goal
Answer:
B
Step-by-step explanation:
I got it correct on edg
Answer:
b
Step-by-step explanation:
A DVD store charges $4.70 for each day, a DVD is rented. The store also gives you a dollar off if the DVD is returned before 5 days. a.Write a rule to represent the rental charges. b. How much will you pay if you return the DVD after 4 days? 7 days?
Answer:
For four days it would be $19.8. For seven days it would be $24.9
Step-by-step explanation:
4 days:
$4.70 x 4 + 1= 19.8
7 days:
$4.70 x 7 = $24.9
I took away 1 from the 4 day equation because the question said you get a dollar off if you return the dvd before 5 days.
Hope this helps!
~Starr
Andy has won 12 out of the last 24 tennis matches he has played. If he wants to improve his win record to 70%, which equation could he use to determine how many matches he would have to win in a row? A) 12 + x 24 + x = 0.70 B) 24 + x 12 + x = 0.70 C) 0.70 24 + x = 12 + x D) 0.70 12 + x = 24 + x
Answer is A
12+x
____. =0.70
24+x
Answer:
A
Step-by-step explanation:
Currently, Andy has a winning record of 50%.
12 /24 = 0.50
To determine a winning record of 70%: add x matches to 12, x matches to 24, and set equal to 0.70.
12 + x /24 + x = 0.70
x = 16
Therefore, Andy would need to win 16 matches in a row.
Jennifer’s grandmother buys carrots at the farm stand.She and her 3 grandchildren equally share the carrots. How many kilograms of carrots will jennifer gets
According to picture Jennifer’s grandmother buys = 28 kg of carrots.
Total number of grandchildren = 3.
Number of kilograms of carrots are distributed equally.
In order to find the Number of kilograms of carrots are distributed, we need to divide total Kgs of carrots by total number of grandchildrens.
Therefore ,
28 ÷ 3 .
On dividing 28 by 3, we get 7.
Therefore, Jennifer will get 7 kilograms of carrots.
A mans hourly wage increased from 12.50 to 13.50. What percent raise did he get
Answer:
The man got a 8% raise.
Step-by-step explanation:
Percentage change = [Increase or decrease in value / Original Value]*100
Increase in hourly wage = [tex]13.5-12.5[/tex]
=[tex]1[/tex]
Percentage raise = [Increase in hourly wage / Initial hourly wage]*100
=[tex]\frac{1}{12.5} *100[/tex]
= [tex]8[/tex]%
The man got a 8% raise.
The man's hourly wage increased from $12.50 to $13.50 which, following the formula for calculating percentage change, indicates that he received an 8 percent raise in his hourly wage.
Explanation:Given that the man's hourly wage increased from $12.50 to $13.50, we can use the formula for calculating the percentage change to find out what percent raise he got.
The formula for calculating the percentage change is as follows:
[(change in quantity)/(original quantity)] × 100
In this case, the change in quantity (the man's wage increase) is $1.00 (13.50 - 12.50), and the original quantity (the man's original wage) is $12.50.
Plugging these values into the formula, we get:
[1.00/12.50] × 100
This calculates to an 8 percent wage increase. Therefore, the man got an 8 percent raise in his hourly wage.
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Mrs. Hill asked her students to express the sum 1 + 3 + 5 + + 7 + 9 + ... + 39 using sigma notation. What is the answer?
The sum 1 + 3 + 5 + + 7 + 9 + ... + 39 in sigma notation is represented as ∑(from n=1 to n=20)[1 + (n-1)*2]. This notation communicates the series' progression and key characteristics.
Explanation:The sum 1 + 3 + 5 + + 7 + 9 + ... + 39 can be represented in sigma notation as follows: Let the general term of this arithmetic series be a_n = 1 + (n-1)*2, where n is the term number. This formula is for a sequence where the difference between each number is 2 (an arithmetic sequence). Thus, the series 1 + 3 + 5 + + 7 + 9 + ... + 39 in sigma notation can be written as ∑(from n=1 to n=20)[1 + (n-1)*2]. Here, n = 1 is the starting point, n = 20 is the end point which is calculated by (39-1)/2 + 1 because the sequence is an arithmetic sequence with common difference 2 and first term 1, and 1 + (n-1)*2 is the formula for the nth term.
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The sum 1 + 3 + 5 + ... + 39 can be written in sigma notation as Σ(1 + (i - 1)2) for i from 1 to 20.
To express the sum 1 + 3 + 5 + 7 + 9 + ... + 39 in sigma notation, we first need to realize that this is an arithmetic series where each term increases by 2. The first term a1 is 1, and the common difference d is 2. We can find the number of terms n in the series by using the formula for the nth term of an arithmetic sequence, which is an = a1 + (n - 1)d.
Since 39 is the last term, we have 39 = 1 + (n - 1)2, which simplifies to n = 20.Now we know our series goes from the 1st term to the 20th term, and the formula for the ith term is ai = 1 + (i - 1)2. Therefore, the series in sigma notation is written as: Σ(1 + (i - 1)2) for i from 1 to 20.
When is a car lease better than a car loan? A. When you want to change cars frequently B. When you want to keep a car for several years C. When you like the idea of owning a car
Answer:
The answer is A) When you want to change cars frequently.
Step-by-step explanation:
Answer with explanation:
Car lease means you don't want to buy the car , you want to use it for various Purposes or you love riding or driving different cars.
⇒Changing cars completely ,means you are interested in distinct brand of cars that is in leasing.
⇒When you want to keep a car for several years , it means you love that thing and either you don't have enough money to buy or you are in two minds ,so either you lease it or take a loan for that thing.
⇒When you like the idea of owning a car, it means you take loan for it,not to lease it.
¬Option A is most appropriate.
When you want to change cars frequently
What is the value for x when solving the equation
−x + (−3) = x + 3 using algebra tiles?
-3.
Hope this helped.
Answer:
x = -3
Step-by-step explanation:
Solving for value of x
−x + (−3) = x + 3
-x -3 = x + 3 [subtract x from both side]
-x -3 -x = x + 3 -x
-2x -3 = 3 [add 3 to both side]
-2x -3 + 3 = 3 + 3
-2x = 6 [divide both side by -2]
[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{6}{-2}[/tex]
x = -3
Create an equation with slope of -3/5 and y intercept of 4
Afaik you just plug these into y=mx+b (slope intercept form)
I would think the answer to be y = (-3/5)x + 4
Answer:
y=-3/5x+4
Step-by-step explanation:
y=mx+b
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
What number needs to be added to both sides of the equation in order to complete the square?
x^2 − 18x = 17
Answer:
81
Step-by-step explanation:
x^2 − 18x + 9^2 = 17 + 9^2
=> x^2 − 18x + 81 = 17 + 81
Use the diagram and the following equation to solve for x.
(Insert diagram below)
113 + (2x + 5) = 180
x=___
Starting with 113+ (2x+5)=180, combine like terms and to get 118+2x=180. Subtract 180-118, which gives you 62. Then you have 2x=62. Divide both sides by 2 to get a final answer of x=31.
Hey there!!
Given :
... 113 + ( 2x + 5 ) = 180
Subtract 113 on both sides
... 2x + 5 = 180 - 113
... 2x + 5 = 67
Subtract 5 on both sides
... 2x = 62
Divide by 2 on both sides
... x = 31
The value of x is 31.
Hope my answer helps!!
Which is a shorter way to write 10 divided by 5?
10 -:- 5. This is the answer. Hope this helps:)
Multiply. (9x−2)(3x−8) Enter your answer, in standard form, in the box. show how to if possible plz and thanks <3
So, the product of (9x - 2)(3x - 8) in standard form is: [tex]27x^2 - 78x + 16[/tex]
What is the MultiplicationTo multiply the expressions (9x - 2) and (3x - 8)
Step 1: Use the distributive property
(9x - 2)(3x - 8) = 9x * (3x) + 9x * (-8)
(9x - 2)(3x - 8) = -2 * (3x) - 2 * (-8)
So , perform the multiplications:
Multiply the terms:
[tex]9x * 3x = 27x^2[/tex]
9x * (-8) = -72x
-2 * 3x = -6x
-2 * (-8) = 16
Combine like terms:
[tex]27x^2 - 72x - 6x + 16[/tex]
Simplify further by combining like terms:
27x^2 - 78x + 16
So, the product of (9x - 2)(3x - 8) in standard form is: [tex]27x^2 - 78x + 16[/tex]
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[(25-11)+(15-9)]÷5 numerical expression ;)
Answer: 100
Step-by-step explanation:
[(25 - 11) + (15 - 9)] * 5
=[ 14 + 6 ] * 5
= 20 * 5
= 100
Is (0,0) a solution to this system?
Uan earns $11 per hour and works at most 30 hours per week. Identify the independent and dependent quantity in the situation, and find reasonable domain and range values. amount of money earned; hours worked; $0 to $330; 0 to 30 amount of money earned; hours worked; 0 to 30; $0 to $330 hours worked; amount of money earned; $0 to $330; 0 to 30 hours worked; amount of money earned; 0 to 30; $0 to $330
Answer:
hours worked; amount of money earned; 0 to 30; $0 to $330
Step-by-step explanation:
Let
y ----> the amount earned per week
x ----> the number of hours worked by week
In this problem
the amount earned per week (variable y) represent the dependent quantity
the number of hours worked by week (variable x) represent the independent quantity
therefore
The domain is the interval -----> [0,30] (the maximum number of hours per week is 30)
The range is the interval -----> [0,11*30] ----> [0,330] (the maximum amount earned per week is $330)
therefore
independent quantity is hours worked
dependent quantity is amount of money earned
domain is 0 to 30
range is $0 to $330
Final answer:
The independent quantity is hours worked and the dependent quantity is the amount of money earned, with a domain of 0 to 30 hours and a range of $0 to $330.
Explanation:
In the given scenario where Uan earns $11 per hour and works at most 30 hours per week, the independent quantity is the hours worked, and the dependent quantity is the amount of money earned. This is because the money earned depends on the number of hours worked.
The domain represents the possible values of the independent variable, which is the hours worked. In this case, it is reasonable to assume that Uan could work anywhere from 0 to 30 hours per week. Therefore, the domain is 0 to 30 hours.
The range represents the possible values of the dependent variable, which is the amount of money earned. Since Uan earns $11 per hour, working 0 hours would yield $0, and working the maximum of 30 hours would yield $330 (30 hours × $11 per hour). Thus, the range is $0 to $330.
The correct answer to the student's question, based on the information, would be: hours worked; amount of money earned; 0 to 30; $0 to $330.
Match each equation with the correct solution
Item bank: 0.8x+5=0.2(40-x) 2(x-5)+7=x+8 3x+3=2(x+7) 5(x-1)-6x=-11x 6(x+2)-x=4(x+4)+7 1/2(x+8)+3/2x=10 1/2x+1/4=x
Drag and drop answer here:
x=11
x=3
x=1/2
The Equation ( x= 11): 3x + 3 = 2(x + 7) and 6(x + 2) - x = 4(x + 4) + 7
The Equation ( x= 3): 0.8x + 5 = 0.2(40 - x), 2(x - 5) + 7 = x and
½(x + 8) + 3/2x = 10
The Equation ( x= 1/2): 5(x - 1) - 6x = -11x and ½x + 1/4 = x
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
1. 0.8x + 5 = 0.2(40 - x)
Solving for x, we get
0.8x + 5 = 0.2(40 - x)
0.8x + 5 = 8 - 0.2x
x + 5 = 8
x = 3
2. 2(x - 5) + 7 = x
Solving for x, we get
2(x - 5) + 7 = x
2x - 10 + 7 = x
2x - 3 = x
-3 = -x
3 = x
3. 3x + 3 = 2(x + 7)
Solving for x, we get
3x + 3 = 2(x + 7)
3x + 3 = 2x + 14
3x = 2x + 11
x = 11
4. 5(x - 1) - 6x = -11x
Solving for x, we get
5(x - 1) - 6x = -11x
5x - 5 - 6x = -11x
5x - 6x = -11x + 5
5x - 6x + 11x = 5
10x = 5
x = 1/2
5. 6(x + 2) - x = 4(x + 4) + 7
Solving for x, we get
6(x + 2) - x = 4(x + 4) + 7
6x + 12 - x = 4x + 16 + 7
5x + 12 = 4x + 23
5x = 4x + 11
x = 11
6. ½(x + 8) + 3/2x = 10
Solving for x, we get
½(x + 8) + 3/2x = 10
½x + 4 + 3/2x = 10
½x + 3/2x = 6
2x = 6
x = 3
7. ½x + 1/4 = x
Solving for x, we get
½x + 1/4 = x
1/4 = ½x
½ = x
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Justify each step in solving the equation 4x=7(x-3) by writing a reason for each statement.
Answer:
Statement Reason
1. 4x=7(x-3) 1. given
2. 4x=7x-21 2.
3. -3x=-21 3.
4. x=7 4.
1. 4x = 7(x - 3) GIVEN
4x = (7)(x) + (7)(-3)
2. 4x = 7x - 21 DISTRIBUTIVE PROPERTY
4x - 7x = 7x - 7x - 21
3. -3x = -21 SUBTRACTION PROPERTY OF EQUALITY
-3x : (-3) = -21 : (-3)
4. x = 7 DIVISION PROPERTY OF EQUALITY
1. Given
2. Distributive Property
3.Subtraction Property of Equality
4. Division Property of Equality
what is the value of f(3)
Its x^2 if x > -1
x = 3 so the answer is 3^2 = 9
The ratio of blue paint to yellow paint in a green paint mixture is 2:3.If you use 16 ounces of blue paint,how many ounces of yellow paint do you need?
Answer:
24 ounces.
Step-by-step explanation:
Given that the ratio of blue paint to yellow paint in a green paint mixture is 2:3.
Actual ounces used for blue paint = 16
By ratio and proportion property we have
2:3 = 16:x where x is the actual ounces of yellow paint used.
Simplify using ratio rules
if a:b = c:d then ad = bc
We get
2x=3(16) = 48
Divide by 2
x = 24
Hence 24 ounces of yellow paint to be used.
Answer:
24 ounces. to be exact
Step-by-step explanation:
On a trip to the movies a family spent 35 on tickets and another 25 on popcorn. They alsp spent 10 on drinks. The oldest son spent some money on candy. Altogether the family spent 76. How much did the oldest son spend on candy
$6 dollars on candy because 35+25+10=70, 76-70=$6