Answer:
[tex]\boxed {\boxed {\sf (1, 3) \ or \ x=1 \ and \ y=3}}}[/tex]
Step-by-step explanation:
We are given this system of equations:
[tex]4x+y=7\\4x-2y=-2[/tex]
We use elimination to solve to eliminate one of the variables, so we only have to work with one at a time. We do this by adding and subtracting the equations, and sometimes multiplying the entire equation by a number.
Notice how both equations have a 4x. This means they can easily be eliminated, without multiplying the equations by another number first. Let's subtract the 2 equations.
[tex]\ \ \ 4x+y=7\\ -(4x-2y)=-2[/tex]
The 4x will cancel because 4x-4x=0.
[tex]\ \ \ \ y=7 \\ - (-2y) = -2[/tex]
Since there are back to back negative signs, they become addition signs.
[tex]\ \ \ \ y=7 \\+2y=2[/tex]
[tex]3y=9[/tex]
We are solving for y , so we must isolate the variable. It is being multiplied by 3 and the inverse of multiplication is division. Divide both sides by 3.
[tex]3y/3=9/3\\y=3[/tex]
Now we can substitute 3 in for y in the original equations. Let's use the first one.
[tex]4x+y=7\\4x+3=7[/tex]
3 is being added to 4x. The inverse of addition is subtraction. Subtract 3 from both sides.
[tex]4x+3-3=7-3\\4x=4\\[/tex]
x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.
[tex]4x/4=4/4\\x=1[/tex]
x is equal to 1 and y is equal to 3. Coordinate points are written as (x, y). The solution to this system of equations is (1, 3).
Which equation best represents the data in the function table
Answer:
y = x² + 1
Step-by-step explanation:
y = x² + 1
When x = -3
y = -3² + 1
y = 9 + 1 = 10
When x = -1
y = x² + 1
y = -1² + 1
y = 1 + 1 = 2
When x = 0
y = x² + 1
y = 0² + 1 = 1
When x = 2
y = x² + 1
y = 2² + 1
y = 4 + 1 = 5
All of the x and y values have been correct
Answer:
A
Step-by-step explanation:
the others will not produce the correct value for the image ((y)), if you replace the incognito x in the equation by the -3, you can see that you only obtain the result 10 for y in the first equation. you don't even need to test all the cases.
-3.-3 +1 = 10
-3.-3 + 2 = 11
-3.-3 -1 = 8
-3.-3 -3 = 6
There are 6 black marbles, 5 green marbles and 9 yellow marbles. What is the probability that a black
marble will selected. Simplify to lowest terms
Answer:
15
Step-by-step explanation:
easy algebra question below first correct answer gets brainliest, if you put one of those links you will get reported and blocked
Answer:
15^2 = 8^2 + x^2 = 12.69.
Step-by-step explanation:
Find the missing ratio (n) from the two equivalent ratios 6:15 = n:35.
Answer:
Solution :-[tex] \sf \: 6 \times 35 = 15 \times n[/tex]
[tex] \sf \: \dfrac{6 \times 35}{15} = n[/tex]
[tex] \sf \: 14 = n[/tex]
Value of n is 14
can someone help me on number 2 and please ASAP :( will mark brainlist
Answer:
A = 53°
AB = 23.3
BC = 18.6
Step-by-step explanation:
2. Given,
C = 90°
B = 37°
AC = 14
Required:
A, AB, and BC
Solution:
✔️A = 180 - (90 + 37) (sum of triangle)
A = 53°
✔️Find AB and BC using trigonometric function:
Reference angle = 37°
Opp = 14
Hyp = AB
Adj = BC
To find AB, apply SOH:
Sin 37 = Opp/Hyp
Sin 37 = 14/AB
AB = 14/Sin 37
AB = 23.262962 ≈ 23.3 (nearest tenth)
To find BC, apply TOA:
Tan 37 = Opp/Adj
Tan 37 = 14/BC
BC = 14/Tan 37
BC = 18.5786275 ≈ 18.6 (nearest tenth)
6. Select all values of x for which f(x) = g(x).
A.0
B. 1
C.-3
D.4
A rectangle has a length of (3x - 4) units and a width of (2x + 3) units. What is the perimeter of the rectangle in terms of x?
Answer:
(10x-2) units
Step-by-step explanation:
The perimeter of a rectangle is 2*length+2*width.
2(3x-4)+2(2x+3)
=6x-8+4x+6
=10x-2
The perimeter of a rectangle is ( 10x - 2 ).
Here,
The length of rectangle is (3x - 4) units.
The width of rectangle is (2x + 3) units
We have to find the perimeter of a rectangle.
What is the perimeter of a rectangle?
The sum of two times of length and width is called the perimeter of a rectangle.
Now,
The length of rectangle is (3x - 4) units.
The width of rectangle is (2x + 3) units
Since, The perimeter of a rectangle = 2 (length + width)
Hence, The perimeter of a rectangle = 2(3x - 4 + 2x + 3)
= 2 (5x -1)
= 10x - 2
Therefore, The perimeter of a rectangle is ( 10x - 2 ).
Learn more about the perimeter of a rectangle visit:
https://brainly.com/question/17297081
#SPJ2
who ever answer this get a brainliest and a thank you i need it answered asap
Answer:
a = 9
Step-by-step explanation:
For solve the problem we can use the Pythagorean theorem in this way
a^2 + (3√3)^2 = (6√3)^2
If we solve the equation we have
a^2 + 27 = 108
a^2 = 81
a = +/-9
we take only the the positive value because a length can’t be negative
a = 9
are the two lines x+2y=7 and 2x+4y=21 parallel or perpendicular?
Answer:
They are parallel
Step-by-step explanation:
Determine the value of a so that the following system has no solution.
ax+5y=10
6x+2y=7
HURRY PLSSSS
Answer:
z
Step-by-step explanation:
(PLEASE HELP) Find the difference of
(p+7)−(6p2+13p).
Answer:
-(6p^2+12p-7)
Step-by-step explanation:
p+7-6p^2-13p
-12p-6p^2+7
-(6p^2+12p-7)
betty saves 161 a month she saves 141 less than jack how much will jack save in two years
Answer:its 20
Step-by-step explanation:
because it is
Answer:
7248 A year
Step-by-step explanation:
Since the question was poorly described, i can only assume that Jack saves 141 more than betty and since the question didn't have any units i can't safely assume that 161 is (money)
Which statements are true about the toolbox? Select two options.
The shape can be broken into a rectangular prism and a triangular prism.
The shape can be broken into a rectangular prism and a rectangular pyramid.
The formula for the volume of this figure is V = B h + one-third B h.
The volume of the toolbox is 840 inches cubed
The volume of the toolbox is 900 inches cubed
Answer:
Option A and E.
Step-by-step explanation:
It is mentioned that Chiyo has a toolbox having a rectangular prism shape with a length of 8 inches, width of 15 inches, and height of 6 inches.
In addition to this, A triangular prism with a triangular base with base 8 inches and height 3 inches. The prism has a height of 15 inches.
So here the shape can be broken into a triangular prism and rectangular prism
Therefore the first option is correct
Now as we know that
Volume of the rectangular prism is
= l×b× h
= 8 × 15 × 6
= 720
And, the volume of the triangular prism is bh
And, the area of the triangular prism is 1 ÷ 2 × b × h
= 1 ÷ 2 × 8 × 3
= 12
Now the volume is
= 12 × 15
= 180
So, the volume of the tool box is
= 720 + 180
= 900
Hence, the last option is correct
A plane flies 220 miles in an hour with the jet stream. The return flight against the jet stream to the the original hangar takes 2
hours. Which system of linear equations can be used to find the rate of the jet stream and the speed of the plane?
A)
x + y - 440
x - y - 110
B)
x + y = 220
x-y-110
9.
x + y = 220
x+y=110
D)
x + y = 220
x - y = 220
Answer:
B
Step-by-step explanation:
what is the sum of all the integers between square root of 12 and 52? I need to know now pls!
Answer: 7&8
Step-by-step explanation:
If the probability of Megan drawing a flat stone from a bag is and she draws 1 stone at a
time and replaces it, how many times would you expect Megan to get a flat stone if she
tries 306 times?
a. 34
b. 45
C. 53
d. 66
help me plzzzzzzzzzzzzzz
Answer:
−x2+2x−1=0
Step-by-step explanation:
To write an equation in standard form, move each term to the left side of the equation and simplify.
ax2+bx+c=0
Move 1
to the left side of the equation by subtracting it from both sides.
2x−x2−1=0
Reorder the polynomial.
−x2+2x−1=0
Answer and Step-by-step explanation:
Standard form of an equation is as follows:
Ax + By = C
We have 2x, -[tex]x^{2}[/tex], and a 1.
Subtract 1 from both sides.
[tex]-x^{2} + 2x - 1[/tex] = 0 is the equation in standard form.
#teamtrees #PAW (Plant And Water)
Which geometric term best describes each figure
Answer:
Parallel lines
Step-by-step explanation:
parallel lines are lines that dont touch
5) Crystal wants to consolidate her bills into 1 smaller monthly payment. She has a total of
$23,000 worth of debt. If she consolidates with a personal loan, she can choose between a 5
year or 8 year loan at 6.75% APR. How much more interest will she pay if she chooses 8
years instead of the 5 year loan?
Answer:
The amount more in interest she will pay if she choose 8 years instead of 5 years loan is approximately $2,665.92
Step-by-step explanation:
The total worth of debt Crystal has. P = $23,000
The options on the number of years for which the loans for consolidation are available, t = 5 and 8 years
n = 12 × t = The number of monthly payment = 12×5 = 60 or 12 × 8 = 96
The annual percentage rate of the loans, r = 6.75% = 0.0675
The monthly payments, 'M', Crystal pays is given as follows;
[tex]M = \dfrac{P \cdot \left(\dfrac{r}{12} \right )\cdot \left ( 1 + \dfrac{r}{12} \right)^{n} }{\left ( 1 + \dfrac{r}{12} \right)^{n} - 1}[/tex]
When n = 60, we get;
[tex]M = \dfrac{23,000 \times \left(\dfrac{0.0675}{12} \right )\cdot \left ( 1 + \dfrac{0.0675}{12} \right)^{60} }{\left ( 1 + \dfrac{0.0675}{12} \right)^{60} - 1} \approx 452.72[/tex]
The total amount payed, A = M × n
∴ The total amount payed when n = 60 is, A₅ = 452.72 × 60 = 27163.2
A₅ ≈ $ 27,163.2
The interest on the loan, I₅ = A₅ - P
∴ I₅ = $27,163.2 - $23,000 = $4,163.2
When n = 80, we get;
[tex]M = \dfrac{23,000 \times \left(\dfrac{0.0675}{12} \right )\cdot \left ( 1 + \dfrac{0.0675}{12} \right)^{96} }{\left ( 1 + \dfrac{0.0675}{12} \right)^{96} - 1} \approx 310.72[/tex]
∴ The total amount payed when n = 80 is, A₈ = 310.72 × 96 = 29,829.12
A₈ = $ 29,829.12
The interest on the loan, I₈ = A₈ - P
∴ The interest on the loan, I₈ = 29,829.12 - 23,000 = 6,829.12
The interest Crystal pays when takes the loan for 8 years, I₈ = $6,829.12
Therefore, the amount more interest she will pay if she choose 8 years instead of 5 years loan, ΔI = I₈ - I₅
ΔI = $6,829.12 - $4,163.2 = $2,665.92
The amount more interest she pays if she choose 8 years instead of 5 years loan, ΔI = $2,665.92.
What is Pi?
like the numbers
Answer:
3.14159265359
Step-by-step explanation:
Ivan earns $8 each time he walks his neighbor's dog. He already walked the dog 5 times. How many more times does he need to walk the dog to earn enough money to buy a game that costs $88?
Answer: 6 more times!
Step-by-step explanation:
Isaiah collects bags of cans for recycling. After they picnic he collected four bags of cans. How many bags did Isaiah take to the recycling center
Answer:
[tex]x + 4[/tex]
Step-by-step explanation:
The question have missing details.
Because, the question says she collected some cans "after picnic"; This means that she has some cans "before picnic"
So, we assume that she has x bags of can before the picnic.
[tex]After\ Picnic = 4[/tex]
So, the total number of bags collected is:
[tex]Total = Before + After\ Picnic[/tex]
[tex]Total = x + 4[/tex]
If x is 5, then she took 9 bags of can to the recycling center
If x is 2, then she took 6 bags of can to the recycling center
If x is 0, then she took 4 bags of can to the recycling center
Name one attribute that all squares and rhombus always share.
Answer:
equal sides!
Step-by-step explanation:
Answer:
Step-by-step explanation:
Both of them have sides that are equal. The second attribute is both of the shapes are parallel to each other
Which fractions are equivalent to the fraction below check all that apply 12/21 ?
If side 1 is 13, side 2 is 12, and side 3 is 18, can a triangle be made?
Answer:
no
Step-by-step explanation:
Hello how do I do this on a graph. X>-3
Answer:
use desmos i swear its not a virus, like the other links, its a graphing calculator and u dont need to download anything. hope it helps.
Step-by-step explanation:
Choose an integer to represent each situation
A credit of $28: 28 or -28?
A temperature of 11 degrees below zero: 11 or -11?
Graph this function: y =3/4x - 4 (you can just put the cordinants)
Which survey question has the least amount of bias?
a. Why are vegetables good for you?
b. How many hours of sleep do you get?
C. Do you think the media has a negative role in politics?
d. Why are teen drivers dangerous?
I run a business. It costs £54,000 a year. Most of the money goes on paying wages. The ratio of wages to other costs is 2 : 1. How much do I spend on wages every year?
Answer:
2 × 54,000 ÷ (1+2)
£36,000
Step-by-step explanation:
Total cost of the business = £54,000
wages : other costs = 2 : 1
Total ratio = 2 + 1 = 3
How much do I spend on wages every year?
Amount spent on wages yearly = ratio of wages / total ratio × Total cost of the business
= 2 × 54,000 ÷ (1+2)
= 2/3 × £54,000
= £108,000/3
= £36,000
Amount spent on wages yearly = £36,000