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).
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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
Write an equation in point slope form for the line through the given point with the given slope.
(-7, 9); m: 4/5
A. y+7=4/5(x-9)
B. y-7=4/5(x+9)
C. y-9=4/5(x-7)
D. y+9=4/5(x-7)
❤︎
Answer:
Ans C
m=4/5
X1= -7
Y1 = 9
Y-Y1=m(X-X1)
Y-9=4/5(X-(-7))
Y-9=4/5(X+7)
A circle has equation x2 + y2 = 25
The circle passes through the points A, B, C and D.
Complete the coordinates for A, B, C and D.
A. (5,_)
B.(_,-5).
C. (_,0)
D(0,_)
Answer: A. (5; 0), B. (0; - 5), C. (-5; 0), D. (0; 5).
Step-by-step explanation:
A. (5; _) [x = 5; y - ?]
x² + y² = 25
5² + y² = 25
25 + y² = 25
25 + y² - 25 = 25 - 25
y² = 0
y = 0
A. (5; 0)
B. (_; -5) [x - ?; y = -5]
x² + y² = 25
x² + (- 5)² = 25
x² + 25 = 25
x² + 25 = 25
x² + 25 - 25 = 25 - 25
x² = 0
x = 0
B. (0; - 5)
C. (_; 0) [x - ?; y = 0]
x² + y² = 25
x² + 0² = 25
x² + 0 = 25
x² = 25
x = ± √25 = ± 5
C. (-5; 0) or (5; 0)
Point A has coordinates (5; 0), which means that
point C has coordinates (-5; 0).
D. (0; _) [x = 0; y - ?]
x² + y² = 25
0² + y² = 25
0 + y² = 25
y² = 25
y = ± √25 = ± 5
D. (0; - 5) or (0; 5)
Point B has coordinates (0; -5), which means that
point D has coordinates (0; 5).
6. Write the equation for the two functions and
compare the rates of change.
Function C
Function D
y
The Used Book
Store will pay $0.50
for each box of
hardcover books.
--2
4
0
2
4
Answer:
the photo is blank for me
Step-by-step explanation:
During swim practice Brand swim six butterfly stroke laps and eight freestyle Laps. What is the ratio of freestyle apps to total laps? A. 6:14 B. 8:6 C. 8:14 D. 14:8
Answer:
C) 8 : 14
Step-by-step explanation:
From the Question, we have
Six butterfly stroke laps
Eight freestyle Laps.
Total number of laps = (6 + 8)laps
= 14 laps
Hence,
The ratio of freestyle laps to total laps is:
Freestyle laps : Total laps
= 8 : 14
Option C is correct.
simplify if possible 3t+2g-t-3g
Answer:
2t-g
Step-by-step explanation:
Collect like terms
3t-t= 2t
2g-3g= -g
2t-g
Write the equation of the line with the given slope and y intercept.
m = 0.25 b = 6
Answer:
y=−2x+6
Step-by-step explanation:
the equation of a line in slope-intercept form is. y=−2x+6 is the equation.
What is the greatest common factor of 26 and 34?
Answer:
Answer is
2
Step-by-step explanation:
Peter is folding brochures for his Dad's new company. After 1 hour, he has 330 brochures left to fold. After 4 hours, he only has 90 brochures left to fold.
(From the above statements you should be able to create two ordered pairs. I will create one for you..... (1,330). Now you create the other ordered pair and continue with the problem.)
Write an equation in slope-intercept form, y=mx+b, that represents the number of brochures Peter has left to fold, , after a given number of hours, x.
Answer:
y = -80x + 410
Step-by-step explanation:
(1,330) is the first point, the other point is (4,90)
m = y2 - y1/x2 - x1
m = 90 - 330/4 - 1
m = -240/3
m = -80/1
m = -80
y - y1 = m(x - x1)
y - 330 = -80(x - 1)
y - 330 = -80x + 80
y = -80x + 80 + 330
y = -80x + 410
The sum of the digits of a given two digits the new numbers is 5 .if the digits are reversed, the new number is reduced by 27 . find the given number
Answer:. The numbers are 41 and 14
Step-by-step explanation: X and Y represent the digits. In the Tens place, the digit has 10× its base value. Therefore we can set up equations to model the information given:
10x+y = 10y + x +27
X + Y = 5
y =5-x rewritten to substitute for y
10x + 5-x = 10(5-x)+x +27
Distribute and then combine like terms:
9x +5 = 50 - 9x +27
Add 9x to both sides; subtract 5 from both sides.
9x +9x = 50+27-5
18x = 72 Combine like terms. Then divide both sides to solve for x.
x = 4
4+y=5 Substitute 4 for x; solve for y.
y=1
Substitute values of x and Y into the original equation and check.
40 +1 = 10 +4 + 27
41 = 14+ 27
True! 41=41
The numbers are 41 and 14.
prove the two triangles congruent.
sas
sss
asa
aas
hl
not congruent
Answer:
SAS because there congruent and each side has the same degree
Step-by-step explanation:
27) Solve: x – 9 = 20
28) Solve: 1/3 x 5/8
29) Solve: 4 x 4 x 4 = ?
Answer:
bghjgkk7686968679
hjkggkhk67896869
ghjkgh
Step-by-step explanation:
hjkh7689
Answer:
29, 5/24 ,64
Step-by-step explanation:
27) x-9=20
x=20+9
x=29
28) 1/3*5/8
1*5/3*8
5/24
29) 4*4*4
4*4=16
16*4
64
what’s the answer and how did you get it? i’m confused
Answer:
The answer is 3.
Step-by-step explanation:
Because you should put the gh with gh, 2 is equivalent to 2 (so the 2 disappeared) and you only have 8-7=1 plus 2=3.
Answer: The given expression is 8g^2h-7gh+2
The degree of 8 g^2 h is 2, 1
The degree of - 7 g h is 1
The degree of 2 is 0
But the degree of expression will the highest degree of the indivisual expression of above i.e 3.
The answer is 3.
Algebra
Please help me
Answer:
Step-by-step explanation:
3) slope is rise over run.. look at the graph and count
from the dot rise=4 run=2 4/2 = 2 slope of 3) is 2
4) rise = -3 run =1 slope of 4) is -3
5) rise =1 run =2 slope of 5) is 1/2
6) rise = ∞ run = 0 slope of 6) is undefined
Animal Kingdom - You won the lottery and decided to buy all of the cats and dogs at a shelter and let them all roam free on a farm. You forgot to ask exactly how many dogs and how many cats they were giving you, but you know that there are 152 animals altogether and there are 3 times as many dogs as there are cats. Write an equation to find out the number of dogs and cats and then solve it.
Answer:
3x=152
Step-by-step explanation:
You know that there are 152 animals intotal so that goes at the end. if we say that the dogs are x because we dont know how many there are, then there are 3 times more cats then there are x.
I need helppp!!!
−50=10s
The cost of renting a boat at a lake is $35 per hour plus $5 for life jackets. Write an
• equation in slope-intercept form that can be used to calculate the total amount you would pay for
renting a boat. (assume only you need a life jacket)
Answer:
y = 35x + 5
Step-by-step explanation:
Slope-intercept form is y = mx + b
m is the slope, b is the constant, or y-intercept.
In this case, 5 is our constant. You pay a one-time fee of $5 for a life jacket. This price doesn't change nor do you have to pay it again, so this is your constant.
35 is our slope. 35 represents the $35 you pay for each hour with the boat. This is our slope because it will change overtime, based on x, or the number of hours you are renting the boat.
y is the total cost, since you have to add up $35 times the number of hours you are renting, plus the $5 for the life jacket.
what is the quotient 5 divided by 30
Answer: 6
Step-by-step explanation:
30÷5=6
I need help ASAP please HElp
Answer: C
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
In triangle QRS, the measure of
angle Q is 70º. Angle R is
congruent to angle S. What is the
measure of angle R in degrees?
Answer:
55 degrees :)
Step-by-step explanation:
all triangles add up to 180 degrees.
we already have 70 degrees and since <S = <R they are the same # of degrees.
subtract 70 from 180 and we get 110.
divide 110 by 2=55
<S 55
<R 55
<Q 70
Answer:
62
Step-by-step explanation:
Please help me if you can
Answer:
7. [tex]r^{19}[/tex]
Step-by-step explanation:
r^11 x r^8 =
r^11 + 8=
2^19
Catherine buys 2.12 pounds of tomatoes, 1.45pounds of chicken and 3.19 20 points
pounds of onions from a supermarket. Find the total weight of the
groceries she bought.
Answer:
The answer is 6.762 pounds.
Step-by-step explanation:
2.12 + 1.45 + 3.19 20 = 6.762.
Carl earns $3.25 per hour walking his neighbor’s dogs. He walks them 1/3 of an hour in the morning and 1/2 of an hour in the afternoon.
a. How much time does Carl spend dog walking every day?
b. How much time does Carl spend dog walking in a week?
c. Ten minutes is equal to 1/6 of an hour. How many minutes does Carl work dog walking each week?
d. How much money does Carl earn each week?
an object is dropped from the too of a tower with a height of 1120 feet. neglecting air resistance, the height of the object at a time t seconds is given by the polynomial
5. Adam spent half of his weekly allowance buying lunch. To earn
more money his parents let him shovel snow for $9.30.
What is his weekly allowance if he ended with $15.10?
Please please help please please ASAP
Answer:
a
Step-by-step explanation:
tan is the opposite divided by the adjecent. The opposite of x is 24 and the adjecent of x is 18, so you would get 24/18 but you have to simplify which simplified is equal to 4/3
i need help can yall help me
Answer:
2{[tex]\frac{1}2}[/tex]t+3}=1
2[tex]\frac{1}{2}[/tex]t+2 * 3=1
t+6=1
t=-5
Step-by-step explanation:
2{[tex]\frac{1}2}[/tex]t+3}=1
2[tex]\frac{1}{2}[/tex]t+2 * 3=1
t+6=1
t=-5
How many miles can a car travel on 15 gallons of gas if it travels 28 miles on 1 gallon of gas?
A. 43 miles
B. 270 miles
C. 405 miles
D. 420 miles
A cylindrical water tank has a diameter of 5.3 meters and a height of 9 meters. What is the maximum volume that the water tank can hold? Use ϖ to approximate the volume to the nearest hundredth.
Answer:
198.56[tex]m^{3[/tex]
Step-by-step explanation:
To find the volume of a cylinder, you need to find the area of the cross-section (one of the circles on the side) and multiply it by the length.
Area of the circle = π[tex]r^{2}[/tex] = π x (5.3/2) x (5.3/2) = π x 2.65 x 2.65 = 7.0225π
Volume of the cylinder = 7.0225π x 9 = 63.2025π = 198.56[tex]m^{3[/tex]
A rectangular fish tank has a base that is 9 inches
by 8 inches. How much water will it take to fill the
tank to a depth of 10 inches?
HELP PLEASE LOOK AT THE PIC ATTACHED
A PAIR OF PARALLEL LINES IS AND
Answer: ↓↓↓
Step-by-step explanation:
a.) DE || CB
b.) AJ ⊥ A F
c.) No, because they don't intersect at a right angle.
a. A pair of parallel lines is BC and GH.