x - 3y = 17
x = 2y + 13
What are the steps for solving these?
Answers
Answer:
(x, y) = (5, -4)
Step-by-step explanation:
The second equation gives you an expression for x that can be substituted into the first equation.
(2y +13) -3y = 17 . . substitute for x in the first equation
-y = 4 . . . . . . . . . . . subtract 13 and simplify
y = -4
x = 2(-4) +13 = 5 . . . use the second equation to find the value of x
The solution is (x, y) = (5, -4).
_____
Additional comment
When faced with a system of linear equations, the first step is to look at them and observe where the variable terms are, and any relationships between coefficients. Several options are generally open to you for solving the equations. Methods generally taught first are ...
substitutioneliminationSubstitution is handy when one of the variables or variable terms can be written (easily) in terms of the other variable. Elimination is handy when some simple multiple of one of the equations can be added to the other equation to cancel one of the variable terms (eliminate it).
Other available methods include matrix methods, Cramer's rule, and graphing. Working knowledge of all of these methods will help you identify the one that will be easiest to use in any given situation.
The availability of calculators able to use these methods greatly simplifies the task of finding a solution. It is simply a matter of entering the equations in the appropriate form.
One of my favorites is the graphing calculator, which only requires you type in the given equations and click on the solution point to find its coordinates.
Related Questions
if f (x) =3(x+3)^2 - 10 then calcutlate f (2)
pls answer todayyy i need help
Answers
Answer:
x
=
−
8
−
√
13
3
,
−
8
+
√
13
3
I dont know why the answer is spacing out like this
16.A company sells calculators for $35 each. Businesses
must order a minimum of 100 calculators, and they
must pay a shipping cost of $50. Which amount of
money represents a reasonable sum that a business
might spend to purchase calculators?
F $750
H $2990
G $1070
I $3585
Answers
Answer: $3550 or letter: I
Step-by-step explanation: 35*100= $3,500 + $50 (tax)= $3,550 or in your case it is closest to letter i
URGENT! WILL MARK BRAINLIEST!!
Write an inequality that represents the graph.
(it’s #4)
Answers
Hope this helps! :)
y > 2
Explanation:
- The dot is open, indicating that the inequality symbol must be greater than or less than (nothing with equal too).
- Since the graph is shaded to the right, that would mean that the inequality symbol would be greater than (>)
- The dot is placed at the value 2, therefore the solutions to the inequality would be all numbers greater than 2, or y > 2
Hope that helped!
A baseball traveled 330 feet in 5 seconds. Which rate is equivalent to the rate at which the baseball traveled?
Answers
Answer:
the baseball traveled 66 feet per second if that helps
Step-by-step explanation:
List the ordered pairs
Answers
Step-by-step explanation:
C. in descending order by weight<br /><br />
What is the greatest common factor of 8, 28, and 48?
Answers
[tex] \: \: \: \: \: \: \: [/tex]
the GCF of 28,48 are GCF OF 281 , 2, 4, 7, 14, 28GCF OF 48
1 , 2, 3, 4, 6, 8, 12, 16, 24, 48 hope it helpsThe greatest common factor of 8, 28, and 48 is 4.
Greatest Common FactorThe largest common factor out of all the numbers in the given set is known as Greatest Common Factor.
How to evaluate Greatest Common Factor?Factors of 8, [tex]8=2\times 2\times 2[/tex]
Factors of 28, [tex]28=2\times 2\times 7[/tex]
Factors of 48, [tex]48=2\times 2\times 2\times 2\times 3[/tex]
The common factors in the above set of numbers are 2and 2.
So, the Greatest Common Factor of 8, 28, and 48 is [tex]2\times 2=4[/tex].
Learn more about Greatest Common Factor here: https://brainly.com/question/11444998
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What is the image of O(1,4) after two reflections, first across the line y = 4, and then across
the line x = -2?
(-5,4)
(-2, 4)
(-1,8)
(1,4)
Answers
Answer:
A. (-5,4)
Step-by-step explanation:
A reflect on y=4 does not affect point (1,4) since it is on y=4
So a reflect on itself is the same
A reflection of x= -2 is trickier
Since the distance between x=-2 and (1,4) is 3 (I am only counting x-axis the distance between -2 and 1 is 3)
So we have to start at (-2,4) (Since the y-axis, "4" didn't change) and move it 3 points to the left
Which is (-5,4)
Thus A
Hope this helps!
the table shows the height of the sage bush at each of 2 ages. what was the bushes average rate of growth per year during this time period. pls answer quick
Answers
Answer:
2.4 inches a year
Step-by-step explanation:
It took 5 years for the bush to grow 22 inches, and it went up by 12 inches in 5 years. So, the easiest thing to do is 12 / 5 = 2.4 inches a year. :)
(Brainliest ??)
2x2 cuantos porfasss
Answers
Answer:
4
Step-by-step explanation:
Answer:
2 x 2 = 4
Step-by-step explanation:
if you count 2 2 times then you would get 4. EASY
9000 dollars is placed in an account with annual interest rate of 7.75 how much will be in the account in 18 year nearest cent
Answers
Answer:
9139.50
Step-by-step explanation:
since it didn't mention any withdraws from the account or any charges, its just a matter of multiplying 7.75 by 18 and adding it to the original balance.
Answer:
9139.50
Step-by-step explanation:
evaluate each expression if r=12 s= -4 t= -6
rs divided by 16
Answers
Answer:
-3
Step-by-step explanation:
r = 12
s = -4
t = -6
Equation
rs ÷ 16
12(-4) ÷ 16
-48 ÷ 16
-3
The value of the expression rs ÷ 16 at r = 12, s = -4, and t = -6 will be negative 3.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ rs ÷ 16
The value of the expression at r = 12, s = -4, and t = -6 will be given as,
⇒ [12 × (-4)] ÷ 16
Simplify the expression, then we have
⇒ [12 × (-4)] ÷ 16
⇒ - 48 / 16
⇒ - 3
The worth of the articulation rs ÷ 16 at r = 12, s = - 4, and t = - 6 will be negative 3.
More about the value of the expression link is given below.
https://brainly.com/question/23671908
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The Wilsons are storing water in case there is a natural disaster. They have 12 small bottles of water that hold 8 ounces each. They also have 4 large bottles of water that hold 24 ounces each. They estimate that they have around 2,000 ounces of water in total. Is that a good estimate?
Answers
100 pts. & will give brainliest! answer asap
every year in delaware there is a contest where people create cannons and catapults designed to launch pumpkins as far in the air as possible. the equation y = 15 + 110x - 16x^2 can be used to represent the height, y, of a launched pumpkin, where x is the time in seconds that the pumpkin has been in the air. what is the maximum height that the pumpkin reaches? how many seconds have passed when the pumpkin hits the ground? (hint: if the pumpkin hits the ground, its height is 0 feet)
a. the pumpkins maximum height is 204.06 feet and it hits the ground after 7.01 seconds.
b. the pumpkins maximum height is 3.44 feet and it hits the ground after 7.01 seconds.
c. the pumpkins maximum height is 204.06 feet and it hits the ground after 3.44 seconds
d. the pumpkins maximum height is 3.44 feet and it hits the ground after 204.05 seconds.
Answers
First we need to differentiate y
[tex]\\ \sf\Rrightarrow \dfrac{dy}{dx}[/tex]
[tex]\\ \sf\Rrightarrow \dfrac{d}{dx}(-16x^2-110x+15)[/tex]
[tex]\\ \sf\Rrightarrow -32x-110[/tex]
Now let it be 0
[tex]\\ \sf\Rrightarrow -32x-110=0[/tex]
[tex]\\ \sf\Rrightarrow -32x=110[/tex]
[tex]\\ \sf\Rrightarrow x=|110/-32[/tex]
[tex]\\ \sf\Rrightarrow x=3.44s[/tex]
Put it in y
[tex]\\ \sf\Rrightarrow y=15-110(3.44)-16(3.44)^2[/tex]
[tex]\\ \sf\Rrightarrow y=204.05ft[/tex]
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand contains 11% vinegar. The chef wants to make 380 milliliters of a dressing that is 7% vinegar. How much of each brand should she use?
Answers
Answer: To make a 310mL mixture that contains 8% vinegar, use 186mL of the first brand and 124mL of the second brand.
Step-by-step explanation:We want the total mixture to be 310mL so: F + S = 310
Also, you want the total mixture to contain 8% vinegar so: .06F + .11S = .08(310)
Now, we can solve the system of equations using substitution.
F + S = 310
.06F + .11S = .08(310)
F = 310 - S [solve 1st equation for F]
.06(310 - S) + .11S = .08(310) [substitute into 2nd equation]
18.6 -.06S +.11S = 24.8
.05S = 6.2
S = 124
F + 124 = 310 [substitute answer for S back into original equation]
F = 186
The price of an item has been reduced by 20% The original price was $32 find the price of the item now.
Answers
Answer:
25.6
Step-by-step explanation:
32-(32*20%)=32-6.4=25.6
Jeremy brought a sandwich and a drink that cost him $7. His drink cost $1.75. Solve the equation 7=s + 1.75 to find s, the cost of Jeremy’s sandwich.
Answers
Answer:
the answer is 5.25
Step-by-step explanation:
subtract the amount from the drink and should give you the cost of the sandwich
What is the slope of the line containing (-2, 5) and (4, -4)?
Answers
Answer:
B. - 3 / 2
Step-by-step explanation:
Let,
( x1, y1 ) = ( - 2, 5 )
So,
x1 = - 2
y1 = 5
( x2, y2 ) = ( 4, - 4 )
So,
x2 = 4
y2 = - 4
Formula : -
Slope = ( y2 - y1 ) / ( x2 - x1 )
Slope = ( - 4 - 5 ) / ( 4 - ( - 2 ) )
= - 9 / ( 4 + 2 )
= - 9 / 6
Slope = - 3 / 2
Answer:
B
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (4, - 4 )
m = [tex]\frac{-4-5}{4-(-2)}[/tex] = [tex]\frac{-9}{4+2}[/tex] = [tex]\frac{-9}{6}[/tex] = - [tex]\frac{3}{2}[/tex] → B
First to get it will get Brainly and 20 points. Good luck
Answers
[tex] \frac{1}{2} [/tex]
Answer:
the correct answere is 1:2
Step-by-step explanation:
my sister is working on the same thing and I helped her and she got it right.
A bakery sells glazed donuts for $1.09 each. Cinnamon bagels and onion bagels are $1.59 each. Max buys x donuts, y cinnamon bagels, and z onion bagels. Which expression represents the total amount Max spent at the bakery?
A.
1.09x + 1.59yz
B.
1.09x + 1.59y + 1.59z
C.
1.09x + 3.18(y + z)
D.
(1.09 + 1.59)(x + y + z)
Answers
Answer:
B
Step-by-step explanation:
For each glazed donut, Max spends $1.09. Therefore, if he buys x donuts, he pays $1.09 x times, or $1.09 * x. Similarly, for cinnamon bagels, he pays $1.59 * y, and for onion bagels, he pays $1.59 * z. Adding these up, we get
1.09x + 1.59y + 1.59z
It requires 350 joules to raise a certain amount of a substance from 10. 0°C to 30. 0°C. The specific heat of the substance is 1. 2 J/g°C. What is the mass of the substance? 12 g 15 g 18 g 30 g.
Answers
The correct option is B which is 15 g.
Given to us:
the heat [tex]Q= 350\ Joules[/tex],
the specific heat [tex]c= 1.2\ J/g\ ^o C[/tex],
the lower temperature [tex]t_1= 10^o C[/tex],
the higher temperature [tex]t_2= 30^o C[/tex],
Formula for specific heat:
[tex]Q=mc(\Delta T)[/tex]
where,
[tex]m[/tex] is the mass,
[tex](\Delta T)[/tex] is the temperature difference,
Putting in the values;
[tex]350=m\times 1.2\times (30-10)\\\\m= \dfrac{350}{1.2\times (30-10)} \\\\m=14.5833 grams[/tex]
Hence, the mass is 14.5833 grams. therefore, the correct option is B which is 15 g.
To know more visit:
https://brainly.com/question/1209542
2.
In a box of 80 glasses, 3 are broken.
Work out the percentage of broken glasses in the box.
Answers
Answer: the answer is 3.7%
Step-by-step explanation:
We know there’s total 80 glasses and if 3 are broken we can represent it in a fraction which is 3/80
3/80=0.0375
to find percentage take 0.0375 and multiply it by 10 to get 3.7
therefor the answer is 3.7%
Daniela listened to a popular radio station for 1 hour. Then she made a circle graph to summarize what she had heard.
Complete the table to show the angle measure for each section and the number of minutes that section represents.
Answers
Answer:
1.50
Step-by-step explanation:
divide 2 add 5 divide 2 again
Someone plz help me! I’m begging!! :(
Answers
Answer:
Option D
Step-by-step explanation:
Expanding option A equations:
8 + (3 * y) = 8 + 3y
(8 + 3) * y = 11y
∴ not equivalent.
Expanding option B equations:
(7 - 3) * y = 4y
7 - (3 * y) = 7 - 3y
∴ not equivalent.
Expanding option C equations:
(6 ÷ y) + 13 = [tex]\frac{6}{y} + 13[/tex]
13 + (y ÷ 6) = [tex]13 + \frac{y}{6}[/tex]
∴ not equivalent.
Expanding option D equations:
7 + (y * 5) = 7 + 5y
7 + (5 * y) = 7 + 5y
∴ equivalent.
Hope this helps!
What is the range of this graph?
Answers
The range is the y value of where the dots are located.
Answer: (3,4,5,6)
this question is kind of confusing and i need help, please and thank you! :)
Answers
ummmmmmmm a lot and alot
1 year = 365 days
6 years = (365x6) = 2190 days
2190 days x 0.5 (half) = 1095
answer = 1095 pounds
Ricardo wants to cover a shelf with shelf
liner. The shelf is 4 feet wide and feet
deep. What is the area of the shelf?
Answers
Answer:
16 also th8s needs to be 16 letters long lol
Step-by-step explanation:
4 times 4 is 16
Pls answer this problem
Answers
Aaron noticed that he caught 8 pidgeys for every Squirtle when he played Pokémon Go. If Aaron caught 104 Pidgeys how many Squirtles did he catch?
Answers
Answer:
He caught 13 squirtles
Step-by-step explanation:
104/8 = 13 squirtles
Squirtles divided by pidgeys
What does geometric progression mean?
Answers
Step-by-step explanation:
[tex] \large\tt\underline\blue{a} \underline\pink{n} \underline\green{s} \underline\red{w}\underline \purple{e} \underline\orange{r}[/tex]
A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.
What is the domain and range ?
Answers
Answer: domain are the ones that go side to side or the x range is the ones that go up and down or the y
Step-by-step explanation: