The fraction equivalent to -84/-90 in the least common terms is 14/15, as both the numerator and the denominator can be divided by the common factor 6, resulting in a simplified positive fraction.
To find which fraction is equivalent to -84/-90 in the least common terms, we need to simplify the fraction by canceling out any common factors in the numerator and the denominator. We observe that both numbers are divisible by 6. When we divide the numerator and the denominator by 6, we get:
-84 / -90 = (-84 / 6) \/ (-90 / 6) = 14 / 15
Since a negative divided by a negative results in a positive number, we eliminate the negative signs and get the fraction in its least common terms as 14/15.
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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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
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
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
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
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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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
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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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
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
A conjecture and the flowchart proof used to prove the conjecture are shown.
Drag an expression or phrase to each box to complete the proof
Here are the answers below that I got. Hope this helps mate. Cheers.
Answer:
As mention in the explanation steps.
Step-by-step explanation:
The following expression or phrase to each box are helpful to complete the proof.
(1). We say that ∠ACB and ∠BCD are supplementary, from linear pair of postulate.
(2). ∠ACB + ∠BCD =180°, because ∠ACB and ∠BCD are supplementary (from the difinition of supplementary angles).
(3). ∠ACB +45° = 180° because ∠BCD =45°(substitute).
(4).Subtraction properties of equality ( because we subtract 45 degree from both sides of the previous equation).
(5). ∠ABC is obtuse, because m∠ABC grater than 90°.
(6). From the definition of obtuse triangle (ΔACB is an obtuse triangle because ∠ACB =135 degree which is grater than 90 degree).
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
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:
John recieves £173 per week after working for 25 hours. How much does he get per hour
Answer:
Amount John gets paid per hour [tex]6.92[/tex] Dollars per hour ,
Step-by-step explanation:
To find how much he gets paid per hour we need to divide the total payment he received by the total number of hours he worked.
Amount John gets paid per hour = [tex]\frac{173}{25}[/tex] Dollars per hour.
=[tex]6.92[/tex] Dollars per hour
Is (0,0) a solution to this system?
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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Please Help! <3 Which relation is a function?
Apply the vertical line test. Think of a vertical line moving from left to right in the graph. If the graph of the relation intersects the vertical line in more than one point in any position of the vertical line, then the relation is not a function.
The only graph that passes the vertical line test is the graph at the bottom right.
The graph at the bottom right is a function. All others are not.
what is the value of f(3)
Its x^2 if x > -1
x = 3 so the answer is 3^2 = 9
Yul has lunch at a resterant if his bill was $14.50 and yul wants to leave a 20% tip what is the amount he should leave for the tip
14.50 times 0.20 = 2.9
He would give a $2.90 as a tip of 20% from a bill of $14.50
I need halpp can ya'll folks help ma plez.What is 2.5x=15 thank you
place x to the other side of the equation
x=15/2.5
x=6
Answer:
6
Step-by-step explanation:
If you take 15 and divide it. by 2.5 you. get 6
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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The ticket price for the hockey match was 14.50. The price has increased by 7%. How much is a ticket after the increase
Answer:
15.5
Step-by-step explanation:
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
Will mark brainliest please help , worth 30 points need answers too both
(18)
2.5% of 129,500 is
$129500 * 0.025 = $3237.50 is the commission on the sale
(19)
sales $3012
commission 3.5% of sales: 0.035 * 3012 = $105.42
Raquelle's total earnings: $290 + 105.42 = $395.42
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:
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.
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:)
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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