Can someone please help me? I need to get 10 of these right and I don’t understand them
Answers
9514 1404 393
Answer:
(x, y) = (1, 1)
Step-by-step explanation:
About Algebra
All of Algebra is based on a few simple rules:
adding 0 doesn't change anythingmultiplying by 1 doesn't change anythingdoing the same thing to both sides of an equation doesn't change the values of the variablesanything can be substituted for its equalWhen we solve equations by substitution, we make use of these facts.
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About Substitution
Generally, substitution in equation solving is done for the purpose of eliminating a variable from the equation. That usually means you want to write an expression for one variable in terms of other variables.
Finding the Expression to Substitute
In this set of equations, the variables are x and y. We can substitute for y an expression involving x, or we can substitute for x an expression involving y. These equations are written in such a way that either method works as well as the other.
Let's choose to substitute for y. This means we need an equation of the form ...
y = <some expression involving x>
The first equation makes it easy to get that. If we add y (to both sides, see rule 3 above), we get ...
5x -y +y = 4 +y
5x = 4 + y . . . . . . . . . simplified
Subtracting 4 (from both sides) gets us the form we want.
5x -4 = 4 -4 + y
5x -4 = y . . . . . . by rule 4 above, we can use (5x-4) anyplace you see y
Using the Expression to Substitute
Now, we have an expression for y that we can use in the second equation. There, y is multiplied by 4, so we need to be sure to multiply the whole expression by 4:
-x + 4(5x -4) = 3 . . . . . . substituted for y in the second equation
-x +20x -16 = 3 . . . . . use the distributive property to eliminate parentheses
19x -16 = 3 . . . . . . collect terms
This has a constant (-16) where we don't want it, so we can add 16 (to both sides) to get rid of it.
19x -16 +16 = 3 +16
19x = 19 . . . . simplify
Now, we can divide by 19 (to both sides) to get x by itself.
(19x)/19 = 19/19
x = 1 . . . . almost done; we still need to find y
Finishing Up
Using the equation for y that we used for substitution, we can find y from our value of x.
y = 5x -4 = 5×1 -4 = 5-4
y = 1
So, the solution is x = 1, y = 1, or (x, y) = (1, 1).
_____
Additional comment
In this set of equations, both variables (x and y) appear with coefficients of 1 (actually, -1). This makes it easy to solve for an expression that can be substituted for the variable. In systems of equations that you want to solve by substitution, it usually works well to start by looking for a variable with a coefficient of 1 (or -1). Use that to write the substitution expression as we did here.
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Alternate Solution
If you use a variable with a coefficient other than 1 to write the substitution expression, you end up with fractions. That's OK if you're comfortable with arithmetic using fractions. It generally requires more care.
For example, we could solve the first equation for x:
x = (4 +y)/5
Substituting that into the second equation gives ...
-(4 +y)/5 +4y = 3
-4/5 -y/5 +4y = 3
(3 4/5)y = 3 4/5 . . . . . add 4/5 (to both sides), collect terms
Now, you get to divide by 3 4/5 to get ...
y = (3 4/5)/(3 4/5) = 1
Fortunately, in this case, we can see the numerator and denominator are identical, so the division result is 1. If it weren't you'd be faced with dividing mixed numbers--not always a student's first choice of fun math operations.
x = (4 +1)/5 = 1 . . . . finishing up
Related Questions
which graph could represent a function ? ?
Answers
Answer:
The third Graph
Step-by-step explanation:
Using the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
Answer:
The third Graph
Step-by-step explanation:
PLEASE HELP!!
Graph the line with the equation
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Answer:
Step-by-step explanation:
The volume of the world's oceans is nearly 1.5⋅10^9 cubic kilometers. Write this number in scientific notation.
Answers
Answer:
"The World Ocean." The Columbia Encyclopedia. CD-ROM. 2007, 6th Ed. New York: Columbia University Press. "The World ocean has an area of about 361 million sq km (139,400,000 sq mi), an average depth of about 3,730 m (12,230)
Viau, Elizabeth Anne. World Builders: Water on Earth. California State University Los Angeles. 2003.
There are two origins of water: comets (extraterrestrial bombardment) and out gassing (condensation of steam from early volcanism). These processes are continuing today.
Step-by-step explanation:
37.
An express train travelled at a certain average speed from Town X to Town Y which was
150 km away. It then continued its journey to Town Z at an average speed 20 km/h faster than
its initial average speed. Town Ywas 200 km from Town Z. If it took the same time to travel for
both parts of the journey, what was the train's average speed for the first part of the journey?
Answers
Answer:
60 km/hr
Step-by-step explanation:
Let the speed at the initial average speed from Town X to Town Y be a.
We are told that it journeyed to Town Z at an average speed 20 km/h faster than its initial average speed. Thus, its average speed here is (a + 20) km/hr.
Town Y was 200 km from Town Z.
Thus, time spent here is;
t_2 = 200/(a + 20)
Time from X to Y is; t_1 = 150/a
We are told that it took the same time to travel for both parts of the journey.
Thus; t_1 = t_2
150/a = 200/(a + 20)
Cross multiply to get;
150(a + 20) = 200a
150a + 3000 = 200a
200a - 150a = 3000
50a = 3000
a = 3000/50
a = 60 km/hr
What is 4.35 divided by 2.5?
Answers
it’s 1.74
explanation
Answer:
1.74
Step-by-step explanation:
Find the total amount given the original price and tax rate. Round to the nearest cent if necessary.
$15.25,7%
Answers
Given:
Original price = $15.25
Tax rate = 7%
To find:
The total amount.
Solution:
We know that,
Total amount = Original price + Tax
According to the question,
Total amount = 15.25 + 7% of 15.25
[tex]\text{Total amount}=15.25+\dfrac{7}{100}\times 15.25[/tex]
[tex]\text{Total amount}=15.25+1.0675[/tex]
[tex]\text{Total amount}=16.3175[/tex]
Round to the nearest cent (two decimal places).
[tex]\text{Total amount}\approx 16.32[/tex]
Therefore, the total value is $16.32.
Simplify: 5d?(3d - 2)
A
8d8 + 3d2
B.
15d3 + 3d
C 15d3 - 10d2
D 8d3-10d?
Answers
Greatest common factor of 4 and 19?
Answers
Answer:
The greatest common factor of 4 and 19 is 1
Step-by-step explanation:
Answer:
Greatest common factor of 4 and 19 is 1
pls help i’ll give you brainliest
Answers
Step-by-step explanation:
5x and -7x are like terms
5x-7x+9=-2x+9 and there's your equivalent expression
Answer:
i want to say 7x is the answer
Step-by-step explanation:
because if you add 5x to 9 = to 14 the -7 = to 7x
Amy and Ben share £21 between them in the ratio 5 : 2. How much does Amy get?
(Im really sorry I just don't understand ratio.)
Answers
Answer:
✑ [tex] \underline{ \underline{ \sf{First ,\: Let's \: learn \: about \: the \: ratio}}} : [/tex]
Let us consider , there are 30 boys and 40 girls in a school. So, the ratio of number of boys to number of girls = [tex] \sf{ \frac{30}{40} = \frac{3}{4} = 3:4}[/tex] and read as 3 is to 4. We can say , the ratio compares two of more quantities of same unit. Until two quantities have same units , it is meaningless to compare by ratio. So, to find the ratio of two quantities , it is necessary to express them in same unit or of same kind. Since , they are in division form. So ,ratio is unit less quantity. Thus , the ratio is a comparison of two quantities of the same kind in division which doesn't have any units. For example : [tex] \sf{ \frac{a}{b}} [/tex] is a ratio and is read as ' a is to b ' in which ' a : is antecedent and ' b ' is called consequent.
✎ [tex] \underline{ \underline{ \sf{Now \: let's \: solve : }}}[/tex]
☪ [tex] \underline{ \sf{Solution}} : [/tex]
£ 21 is to be divided between Amy and Ben in the ratio 5 : 2. So, let Amy get £ 5x and Ben get £ 2x.
Then , According to the question , [tex] \text{5x +2x = 21}[/tex]
Solve for x :
⇝ [tex] \sf{7x = 21}[/tex]
⇝ [tex] \sf{ \frac{7x}{7} = \frac{21}{7} }[/tex]
⇝ [tex] \sf{x = 3}[/tex]
The value of x is 3. Now , substitute the value of x in 5x :
Amy received £ 5x = 5 × 3 = £ 15 .
☥ [tex] \boxed{ \boxed{ \tt{Our \: final \: answer \: is \bold{£ \: 15}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ♡
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What is the sum of all prime numbers beetween 70 to 80?
What is the product of prime numbers immediately before and after 50?
Answer both plz thx....
Answers
Answer:
Prime numbers between 70 and 80 are 71,73,79
71+73+79=223
50 =2x5x5=2x5^2
the _________ is a number that is multiplied. the number that indicates how many times this number is used as a factor is the ___________
Answers
The base is a number that is multiplied. The number that indicates how many times this number is used as a factor is the exponent
For example, the number 2^3 expands out to 2*2*2. We have three copies of the base '2' being multiplied.
Another example: 5^2 = 5*5.
Answer:
The "Factor" is a number that is multiplied. The number that indicates how many times this number is used as a factor is the "Exponent".
Step-by-step explanation:
Example: 7 • 7 can be written as 72, 7 is the base and 2 is the exponent. The exponent 2 means there are two factors.
Hope it helped : )
to the nearest 50 square feet what is the area of the actual store?
Answers
What is the value of x? B 75° Enter your answer in the box. X=
Answers
Answer:
55
Step-by-step explanation:
75+50=125
180-125=55
4 +14 x 17 x 4 + 3
Orders of operations
Answers
You do 14 times 17 then times that by 4 that add 4 and 3
Conner had 354$ and spent 243 cents. How much did conner have left and how many dollars? please help. If you do, then I will tell you a secret.
Answers
Conner: $354 - 243 cents
243 cents = $2.43 because 100 cents = 1 dollar
Conner: $354 - $2.43 = $351.57
$351.57
He has 351 dollars left.
Answer:
354 - 243 = 111
Step-by-step explanation:
300 - 200 = 100
50 - 40 = 10
4 - 3 = 1
100 + 10 + 1 = 111
3 + 7 Is what
A) 10
B) 18
C) 37
Answers
Answer:
A)10
Step-by-step explanation:
hope it helps u
Which expression is equivalent to 12(4m−2n+4)?
1.2m−n+2
2.2m−2n+4
3.8m−4n+4
4.8m−4n+8
Answers
Answer:
1. 2m - n + 2
Step-by-step explanation:
12×4m - 12×2n + 12×4. ( because 12 is multipled by whole bracket)
48m - 24n + 48.
2m - n + 2. (by finding common factor 24)
Brian has reduced his cholesterol level by 13% after his last check up. If his original level was 240, what is his approximate cholesterol level now?
Answers
Answer:
208.8
Step-by-step explanation:
240 times 0.87 is 208.8
Tell whether the ordered pair (-4,-2) is a solution of the system of linear equations.
Y= 2x+6
Y= -3x-14
Answers
-20 > -2x + 4 inequality
Answers
Step-by-step explanation:
-20 > -2x + 4
2x > 4 + 20
2x > 24
x > 12
or
x ∈ 《12 , + ∞》
-20 > -2x + 4
-20 -4 > -2x
-24 > -2x
-24/-2 < x <inequality changes when you divide by a -ve no. >
12 < x
Write as a power of 10. How did you do it? a) 100 b) 10 000 c) 100 000 d) 10 e) 1000 f) 1 000 000
Answers
Answer: ↓↓↓
Step-by-step explanation:
a.) 100 - 10^2
b.) 10,000 - 10^4
c.) 100,000 - 10^5
d.) 10 - 10^1
e.) 1000 - 10^3
f.) 1,000,000 - 10^6
What I do personally is that I count the number of zeros in the number and that is how many powers the ten powers to. Like a, there are two zeros in 100 so its 10 to the power of 2.
A piece of timber is x cm long. 9 cm is cut off how much is left
Answers
Answer:
x-9cm
Step-by-step explanation:
compute
MATH LOVERS PLS!!!!!!!
Answers
7) C
8) A
9)D
10)B
11x – 2y = 20 in slope intercept form
Answers
Answer:
[tex]y=\frac{11}{2}x-10[/tex]
Step-by-step explanation:
Answer: y= 11/2 x - 10
Step-by-step explanation: I think
CAN SOMEONE HELP ME ON ALL AND THOSE ANSWERS ARE ANSWERS FOR THESE PROBLEMS PLS HELP ME I WILL GIVE BRAINLIST ):
Answers
2. 18
3. 12.56
4. 9.42
5. 8pi
6. 5pi
7. 62.8
8. 7.5
:)
Which of the following correctly uses absolute value to show the distance between -80 and 15? (5 points)
a
|-80 - 15| = |-95| = -95 units
b
|-80 + 15| = |-65| = 65 units
c
|-80 - 15| = |-95| = 95 units
d
|-80 + 15| = |-65| = -65 units
Answers
Answer:
it's answer is b
|-80+15| = |-65| = 65 units
Hope this helps :)
This question is about displacement. Displacement is a set of vectors. So the answer is - can't be + can't be.
so,answer-b
Help In math pls this a slope problem
Answers
Answer:
D
Step-by-step explanation:
A delivery truck drove 52 miles per hour. It took 4 hours to travel between two towns. What is the distance between the two towns? Use the equation dert, where d is distance, r is rate, and t is time. The distance between the two towns is miles.
Answers
Answer:
104?
Step-by-step explanation:
52*4 = 208 ÷ 2 = 104
HELP GIVING BRAINLIEST NUMBER 5!!!!!!
Answers
Answer:
1 solution
Step-by-step explanation:
4x + 5 = 6(x+3) - 20 - 2x
4x + 5 = 6x + 18 - 20 - 2x
4x + 5 = 4x -2
X = 3 therefore, there is only one solution