Combining the like terms, the equivalent expressions are given as follows:
-15a - 3b + 16a + 4b = a + b.2a - 4b - 3a + 6b + 6 = -a + 2b + 6.2a + 2b - 6a -3 - 2b + 6 = -4a + 3.3a - 6b - 6 + 2a + 6b + 2 = 5a - 4.3a + 4a + 2b - 4 - 5b - 10 = 7a + 7b - 14.How do we add and subtract symbolic expressions?To add or subtracted symbolic expressions, in which the terms are accompanied by letters, we combine the like terms, that is, we add or subtract terms that have the same letter.
One example is:
a + b + 3a + 20b = 4a + 21.
As 1 + 3 = 4, 1 + 20 = 21.
Hence the equivalent expressions for the first space is:
-15a - 3b + 16a + 4b = a + b.
For the second space, it is:
2a - 4b - 3a + 6b + 6 = -a + 2b + 6.
For the third space, it is:
2a + 2b - 6a -3 - 2b + 6 = -4a + 3.
For the fourth space, it is:
3a - 6b - 6 + 2a + 6b + 2 = 5a - 4.
For the fifth space, it is:
3a + 4a + 2b - 4 - 5b - 10 = 7a + 7b - 14.
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Lesson 10: Connecting Equations to Graphs
(Part 1)
Cool Down: Kiran at the Carnival
Kiran is spending $12 on games and rides at another carnival, where a game costs $0.25
and a ride costs $1.
1. Write an equation to represent the relationship between the dollar amount Kiran is
spending and the number of games, , and the number of rides, , he could do.
2. Which graph represents the relationship between the quantities in this situation?
Explain how you know.
The equation to represent the relationship between the dollar amount Kiran is spending and the number of games and the number of rides is 0.25x + y = 12
The graph that represents the relationship between the quantities in this situation is graph C.
How to illustrate the information?It should be noted that the equation will be:
25x + 100y = 1200 in cents
or 0.25 x + y = 12 in dollars
where
x= games
y= rides
The graph that will connect the x axis and y axis at the points where x= 48 and y= 12, Only graph C seems to have a line that may end at x=48. Therefore, the correct option is C.
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Divide. Rationalize all denominators. ∛6 x² y⁴ / 2∛5 x⁷y
The value of the expression [tex]\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex] after rationalizing the denominator is [tex]\frac{5^{\frac{2}{3}}y^{3}}{10x^{5}}[/tex].
A finite collection of symbols that is well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.
Rationalizing the denominator is the process of shifting a root, such as a cube root or a square root, from the fraction's denominator to its numerator (numerator).
The numerator is the part of a fraction that comes before the vinculum.
The denominator of a fraction is the phrase that comes before the vinculum.
Consider the expression,
[tex]\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex]
Now, let [tex]a=\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex]
[tex]a=\frac{(x^{2}y)(y^{3})}{2\sqrt[3]{5} (x^{2}y)(x^{5})}[/tex]
[tex]a=\frac{y^{3}}{2\sqrt[3]{5} {~}x^{5} }[/tex]
To rationalize the denominator we multiply and divide the expression by ( ∛5 )².
[tex]a=\frac{y^{3}}{2\sqrt[3]{5} {~}x^{5} } \times \frac{(\sqrt[3]{5})^{2}}{(\sqrt[3]{5})^{2}}[/tex]
[tex]a=\frac{5^{\frac{2}{3}}y^{3}}{10x^{5}}[/tex]
The value of the expression when rationalized [tex]\frac{x^{2}y^{4}}{2\sqrt[3]{5} x^{7}y}[/tex] is [tex]\frac{5^{\frac{2}{3}}y^{3}}{10x^{5}}[/tex].
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13 divided by 10 5/6 in fraction
Answer:
6/5 or 1 1/5
Step-by-step explanation:
Hope this helps. Please mark me Brainliest!
As a math citizen, why is it important to be able to interpret and analyze graphs?
The name of the figure below is ___ ___.
[ Brainliest + easy points ]
Answer: A line or GH
Step-by-step explanation:
Answer: ray
Step-by-step explanation:
What do I do for the final mark?!?!!?
, The graphical solution of the simultaneous equation is
x = 3 and y = 3.What are simultaneous equations?Simultaneous equations are pairs of equations that contain two unknowns.
How to solve simultaneous equations?Simultaneous equations are solved by any three (3) of the following methods.
Substiution method, Elimination method and Graphical methodHow to solve the given simultaneous equations by graphical methods?Given the simultaneous equations
x + y = 6 and y = x
We first confirm the solution by using the substitution method.
Substiutitng y = x into the first equation, we have
x + y = 6
x + x = 6
2x = 6
x = 6/2
x = 3
Since y = x. So, y = 3.
So, the solution is x = 3 and y = 3.
So, for a graphical solution, plotting the graph of
y = x and x + y = 6 on the x and y axis, their point of intersection is at the point (3, 3)So, the graphical solution of the simultaneous equation is
x = 3 and y = 3.This is seen in the intersection on the graph attached.
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HELP!!! There is a photo please quickly!!
Answer:
∆y = 9
∆x = 6
Slope = 3/2 or 1.5
It looks like you erased it, but you had the answer correct on your paper.
Step-by-step explanation:
describe number patterns: 1, -4, 9, 16
Answer: least to greatest is -4,1,9,16
greatest to least is 16,9,1,-4
Step-by-step explanation: it's common thinking to me
I am stuck. The questions are numbered so please type the number of the question by the answer. Please and thank you.
Answer:
#1 = -1/3
2# = -6/5
3# = 2/9
4# = 2
#5 = -2/3
Step-by-step explanation:
The slope formula is (y2 - y1) / x2 - x1. With (x1, x2) and (x2, y2) be points on the line.
In eight years, Pete will be twice as old as he
was two years ago. How old is he today?
Answer:
10
Step-by-step explanation:
8 + 2 = 10
3(4-2(8+5))
Can someone show me what to do first?
Answer:14
Step-by-step explanation:
14
Answer:
18
Step-by-step explanation:
addition is always before subtraction so you add 8 plus 5 is 13 then 4 minus 2 is 2 so add all together and its 18
Find the distance between C & D.
C = (8, -3) and D = (-9, -6)
Round to the nearest tenth.
Answer: 17.3
Step-by-step explanation:
First answer gets brainliest!!!!!!!!!!!!!!!!!!!!
The following relationships between linear equations are shown below:
12 - (1 / 2) · r → [13 - (3 / 2) · r] - (1 - r) r - 13 / 6 → (7 · r - 3 / 2) - (2 / 3 + 6 · r) 13 · r + 20 → (6 · r + 7) + (13 + 7 · r) - 12 + r → (- 8 - r) + (2 · r - 4)How to match an expression with its simplified form
In this problem we find four cases of linear equations whose relationship with simplified forms, that is, linear equations of the a · r + b, where a, b are constants, must be found. Each relationship can be determined by using algebra properties. Now we proceed to present the conclusion for each case:
Choice A
(6 · r + 7) + (13 + 7 · r)
(6 · r + 7 · r) + (7 + 13)
(6 + 7) · r + 20
13 · r + 20
Choice B
[13 - (3 / 2) · r] - (1 - r)
[13 - (3 / 2) · r] + (- 1 + r)
[- (3 / 2) · r + r] + (13 - 1)
[- (3 / 2) + 1] · r + 12
(- 1 / 2) · r + 12
12 - (1 / 2) · r
Choice C
(- 8 - r) + (2 · r - 4)
(- r + 2 · r) + (- 8 - 4)
(- 1 + 2) · r - 12
r - 12
- 12 + r
Choice D
(7 · r - 3 / 2) - (2 / 3 + 6 · r)
(7 · r - 3 / 2) + (- 2 / 3 - 6 · r)
(7 · r - 6 · r) + (- 3 / 2 - 2 / 3)
r + [- (9 + 4)] / 6
r + [- 13] / 6
r - 13 / 6
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I need help with number 2
What is the question?
The expression 53(1+x) represents the total cost of a meal including the tip.
Answer:
53 + 53x
Step-by-step explanation:
Multiply each term in the parentheses by 53 and you get 53 + 53x
I hope that helps!!
NEED CORRECT ANSWER RN PLS
PLSS HELP :((
will mark brianlist if its the correct answer ty
Please help me with this question
Simplifying the given expression ( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴) gives a result of 0.
Evaluating the expression gives?Given the expression in the question;
( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴)
First, perform the operations inside the parenthesis
( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴)
( (-9(2)³ )/4 ) + ((1/2)(6)² )/( 4²÷2⁴)
Raise 2 to power 3, 6 to power 2, 4 to power 2 and 2 to power 4
( (-9(8) )/4 ) + ((1/2)36 )/( 16 ÷ 16)
Perform the operations in the parenthesis
-72/4 + 18/1
Divide -74 by 4
-72/4 + 18/1
-18 + 18
Negative 18 and positive 18 cancels out each other.
-18 + 18
0
Therefore, simplifying the given expression ( (-9(8-6)³ )/4 ) + ((1/2)(10-4)² )/( 4²÷2⁴) gives a result of 0.
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PLEASE HELP ME
look at the pic down below
Answer: (1) Deena and Eduardo, (2) (A) or cube root of 343
Step-by-step explanation:
Number 1 : Deena and Eduardo are correct,
16 x 16 = 256
4 x 4 x 4 = 64
Number 2 : (a) the cube root. of 343 will give Patel the correct answer,
h^3 = 343
cube root of both sides
so, h. = cube root of 343
Using Company A's calling plan, the cost of an overseas phone call is a $0.95 connection fee plus 18 cents per minute. If the total cost of the call is $2.75, how long is the phone call?
The total duration of the phone call was 10 minutes.
Given that, by using Company A's calling plan, the cost of an overseas phone call is a $0.95 connection fee plus 18 cents per minute. If the total cost of the call is $2.75 and we have to calculate the time how long was the phone call.
Let the number of minutes a phone call held be x.
Now, we will be representing the above given information in terms of linear equation and then solve for the value of x which will give us the number of minutes the phone call held.
Total cost = $0.95 + $0.18x
$2.75 = $0.95 + $0.18x
2.75 = 0.95 + 0.18x
2.75 - 0.95 = 0.18x
1.8 = 0.18x
1.8/0.18 = x
10 = x
Therefore, the call will go 10 minutes long.
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explain why when you divide both sides of an inequality by a negative number, you must reverse the inequality sign.
Suppose a population of 160 crickets doubles in size every month. The function
f(x) = 160:2* gives the population after x months. How many crickets will there be after 2
years?
O2,684,354,560 crickets
O640 crickets
07,680 crickets
O655,360 crickets
Answer:
1. no
2. 2,684,354,560 crickets
3. $9,200
4. b
5. 7.5
6.b
One less than four times a number is 11.
(Could you also help me solve the question too?)
Answer:
3
Step-by-step explanation:
Let's put that number as x.
It says that one minus 4 times x is 11.
So the equation is 4x - 1 = 11.
Add one on both sides to get 4x = 12.
Divide by four on both sides to get x = 3.
Since x is what we are looking for, the answer is 3!
(Hope this helps!)
Anna ordered 200 party favors. she
received only 1/10 of the party favors
she ordered. how many party favors
did anna receive?
Answer: 20
Step-by-step explanation: She received 1/10 of the party favors, and 1/10 of 200 is 20.
Anna ordered 200 party favors, she received only 1/10 of the party favors
she ordered, i.e., Anna received 20 party favors.
Here, given that, Anna ordered 200 party favors. she received only 1/10 of the party favors she ordered.
Now, we have to find out how many party favors Anna received,
we need to calculate 1/10 of the total number of party favors she ordered.
Anna ordered 200 party favors, and she received only 1/10 of that amount.
As, we know that, 'of' indicates 'multiplication'
so, we have to find 1/10 of 200, so that, we multiply 200 by 1/10:
1/10 * 200
= 200/10
= 20
i.e. She received 1/10 of the party favors, and 1/10 of 200 is 20.
So, Anna received 20 party favors.
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Please HELP!
Write an algebraic expression for this word phrase:
Seven less than the product of five and a number.
I know that you have to do (5xn) but how do you do seven less?
Answer:
5n - 7
Step-by-step explanation:
The product of five and a number is 5n
Seven less than the product of five and a number means 5n - 7
Given:
2x + 30 = -4(5x- 2); Prove: x=-1
Answer:
so x=-1
Step-by-step explanation:
substitute "-1" for x
so, 2(-1)+30=28
and, -4(5(-1)-2)>>-4(-5-2)>>20+8
so, 28=28
well i want to know how to spell the word 90
Answer: Ninty
Step-by-step explanation:
determine whether descriptive or inferential statistics were used in the statement. 67% of cell phone users check their phone even though it is not ringing or vibrating. (source: pew research center)
Inferential Statistics
Inferential Statistics is the part of statistical analysis that helps you to determine or predict further steps from the data studied according to Statistical methods. It is helpful in understanding people's perspectives or analyzing data from the samples obtained from it. It can be defined as the analytical tool used to draw conclusions about a population by analyzing random samples.
Descriptive Statistics are used to describe the data and make generalizations about the studies. It is used the define the characteristics of the data obtained.
In the given situation, the statistical analysis is done and it has been inferred from the studies that 67% of people check their cell phone even when it is not ringing or vibrating.
Hence, It is a case of Inferential Statistics.
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What are the answers and how do you write it out
Just use a calculator.
First substitute in the numbers and make sure to use ( ) when plugging in negative values. For example, the first one says n=4, you can substitute n from the expression to 4. So n^2 + 3n + 8 will turn into 4^2 + 3(4) + 8 which is 16 + 12 + 8 = 36. You can do this with the other questions.
Number 10 is -213.
Simplify each expression. Rationalize all denominators. 5√2/ √7 -√2
The rationalization of all denominators is 5.74165.
A fraction is represented inside the form of 'x/y', wherein 'x' is the numerator and 'y' is the denominator. The numerator represents the entire variety of parts taken into consideration. whereas, the denominator represents the full quantity of equal components in a fraction. The pinnacle quantity in a fragment is usually taken into consideration as a numerator.
Another phrase for a denominator is the divisor. both of those words check with the range beneath the road in a not unusual fraction. similarly, while you're speakme approximately statistical values, a denominator refers back to the whole number or population from which samples are taken.
In a fallacious fraction, the numerator is extra than or the same as the denominator and the denominator must not be the same as zero. In an incorrect fraction, the numerator is less than the denominator and the numerator is extra than 0. In an unsuitable fraction, the numerator is constantly more than the denominator.
[tex]5\sqrt{2} /\sqrt{7}- \sqrt{2}[/tex]
[tex]\frac{5\sqrt{2} }{\sqrt{7}-\sqrt{2} }[/tex]
Multiply by the conjugate
[tex]\frac{5(\sqrt{7}+\sqrt{2})\sqrt{2} }{(\sqrt{7} -\sqrt{2} )(\sqrt{7} +\sqrt{2} }[/tex]
Expand [tex](\sqrt{7} -\sqrt{2} )(\sqrt{7} +\sqrt{2} ): 5[/tex]
Factor out the common term 5
[tex]\frac{(5\sqrt{7}+5 \sqrt{2})\sqrt{2} }{5}[/tex]
Cancel the common factor: 5
[tex](\sqrt{7} +\sqrt{2}) \sqrt{2}[/tex]
[tex]= \sqrt{14} +2[/tex]
= Decimal:5.74165
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2. The official Olympic swimming pool measures about 50 m x 25 m x 2.5 m (LWH). If a
box measuring 50cm x 70cm x 25cm (LWH) can hold 315 tennis balls, then what would
be a reasonable estimate for a number of tennis balls that can fit in the swimming pool?
Answer:
the answer isssssssssssssssssss