use the elimination method to solve the system of equations. Choose the correct ordered pair.
2y=x+2
x-3y=-5
The concept of solving a problem by elimination is to solve for one variable, by getting rid of the other.
Let's solve [2y = x + 2, x - 3y = -5] in terms of y.
Start by transforming the second equation into one of the same form as the first (y = x + c).
x-3y = -5
x = -5 + 3y
3y = x+5
Now we have two equations that are in the same form:
3y = x+5
2y = x+2
To solve in terms of y, we need to get rid of x -- so subtract the first equation from the second equation - this will yield the following:
y = 3 [[ 3y - 2y = y, x - x = 0, 5 - 2 = 3 ]]
Now take this information and solve for x:
2(3) = x+2
6 = x+2
x = 4
Now we have the solution, just make it a coordinate point:
(4, 3)
Answer:
Apex Answer (4,3)
Step-by-step explanation:
Just did the apex quiz yall add me julius_rob
Are the solutions correct?
Answer:
First one is wrong. x should be 16.
Second one is not completely visible, so cannot say.
Step-by-step explanation:
In the last step, the divison by 4 yields:
x/16 = 1, so x = 16
what is equivalent to the expression 4 / -3 to the square root of 64
[tex]\sqrt{a}=b\iff b^2=a\ for\ a\geq0\ and\ b\geq0\\\\\dfrac{4}{-3\sqrt{64}}=\dfrac{\not4^1}{-3(\not8_2)}=-\dfrac{1}{6}[/tex]
Which of the following expression is equal to 6-4(x+3)?
Answer:
-3
Step-by-step explanation:
6-4 (x+3)
2(x+3)
2x+6=0
2x=-6
2x/2= -6/2
x=-3
Members of a movie rental club pays a minimum of $15 annual membership fee and $2 for new release movies. Nonmembers pay $3 for new release movies. Write a system of linear equations that represents this situation
Answer:
The system of linear equations are
y = 15 + 2x
y = 3x
Step-by-step explanation:
Let us assume that the number of new release movies be x.
Let us assume that the total cost be y.
As given
Members of a movie rental club pays a minimum of $15 annual membership fee and $2 for new release movies.
Than the equation becomes
y = 15 + 2x
As given
Nonmembers pay $3 for new release movies.
y = 3x
Therefore the system of linear equations are
y = 15 + 2x
y = 3x
You will be Brainiest Answered if answered.
Thanx
Answer:
9R30
Step-by-step explanation:
9
36)354
324
30
What is y=-2/3x written in standard form?
Answer:2x−3y=6
Step-by-step explanation:Standard form: Ax + By = C
Just take 2/3x to the other side.
So the answer would be
−23x+y=−2
In standard form
x
can't be negative and A, B and C need to be an integers (whole numbers)
(I multiplied the whole equation by -3)
2x−3y=6
So the final answer would be: 2x−3y=6
Cecily is comparing two checking accounts. Checking account A has a monthly fee of $16 and a per-check fee of $0.08, while checking account B has monthly fee of $14 and a per-check fee of $0.12. She want to know how many checks she would need to write per month for the accounts to charge the same amount in fees.
Part 1: If x represents the number of checks Cecily writes per month, what expression represents the monthly fee in dollars charged by checking account A?
Part 2: What equation can be set up to solve for the number of checks Cecily would need to write per month for the accounts to charge the same in fees?
Answer:
Total charge per month = $ 16 + (0.08) * x
equation for having same charge
0.08 x - 0.12 y = 8
Step-by-step explanation:
Part 1:
Monthly fee = $ 16
Per check fee = $ 0.08
Checks signed in month = x
Total Charge monthly = Monthly fee + Checks fee
Putting the values
Total charge per month = 16 + (0.08) * x ...........(i)
Part 2: Let she signs y checks for account B
Monthly fee of B = $ 14
per check fee = @ 0.12
Total Charge = monthly fee + checks fee
= $ 14 + y *(0.12) ..................(ii)
For having same value in the bank then equation (i) and (ii) shuld be equal to each other
i.e.
16 + 0.08x = 24 + 0.12y
0.08 x - 0.12 y = 24-16
0.08 x - 0.12 y = 8
this will be the equation
Triangles △ABC and △DEF are similar. Find the angles of these triangles if
m∠A=100°, m∠B=30°.
Answer:
angle A and angle D equals 100 degrees, angle B and angle E equals 30 degrees, and angle C and angle F equal 50 degrees.
Step-by-step explanation:
a triangle has to equal 180 degrees, and since they are similar, it should equal the same. Hope this helped you. :))
The angles of triangles △ABC and △DEF, which are similar, are 100°, 30°, and 50°. This is calculated using the properties of similar geometry and the fact that the sum of all angles in a triangle equals 180°.
In Triangle Similarity, the corresponding angles are equal due to the property of similarity in geometry.
Since we know that △ABC and △DEF are similar and we have m∠A=100° and m∠B=30°, we can determine that angles A and B in triangle △DEF are also 100° and 30°, respectively.
The third angle in both triangles can be calculated using the property that the sum of all angles in a triangle equals 180°.
Hence, in △DEF and △ABC we can calculate the measure of the third angle by 180° - (100°+30°) = 50°.
So for triangles △ABC and △DEF, the angles are 100°, 30° and 50° respectively.
Learn more about Triangle Similarity here:
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solve the system by substitution 2x+y=10 x-3y=-2 state whether the system had one solution infinite solutions or no solution
Answer:
System has only one solution. x= 4 and y = 2.
Step-by-step explanation:
We have given two equations :
2x + y = 10 ----------(1)
x - 3y = -2 ----------(2)
From equation (2), we can write:
x - 3y = -2
or x = -2 + 3y , substitute this in equation (1).
We get, 2x + y = 10
2*(-2 + 3y) + y = 10
-4 + 6y + y = 10
7y = 10 + 4
y = 14/7 = 2
And x = -2 + 3*2 = -2 + 6 = 4
Hence we get x= 4 and y = 2. System has only one solution
The system of equations 2x+y=10 and x-3y=-2 has one solution, which is found by solving for y in terms of x using the first equation, substituting into the second equation, and solving for x, then solving for y. The solution is (4, 2).
To solve the system by substitution, we can express one variable in terms of the other using one of the equations and then substitute this into the second equation. Starting with the system:
2x + y = 10
x - 3y = -2
We can solve the first equation for y:
y = 10 - 2x
Next, we substitute this expression for y into the second equation:
x - 3(10 - 2x) = -2
Solving this equation for x:
x - 30 + 6x = -2
7x = 28
x = 4
Now we substitute x = 4 back into the equation y = 10 - 2x to find y:
y = 10 - 2(4)
y = 2
So the one solution to the system is (4, 2).
Since we found a unique solution, the system of equations has exactly one solution and is therefore consistent and independent.
Together, teammates Pedro and Ricky got 2677 base hits last season. Pedro had 275 more hits than Ricky. How many hits did each player have?
Answer:
Ricky = 1201
Pedro = 1476
Step-by-step explanation:
Assign variables
let p be the number of Pedro's base hits
let r be the number of Ricky's base hits
Create a system of equations
p + r = 2677 <= Pedro and Ricky got 2677 base hits
p = r + 275 <= Pedro had 275 more hits than Ricky
Solve using the substitution method (replace a variable with an expression)
p + r = 2677
Substitute "p" with "r + 275"
r + 275 + r = 2677
Combine like terms to simplify
2r + 275 = 2677
Isolate "r" by moving everything else to the right side.
2r = 2677 - 275 Subtract 275 from both sides
2r = 2402
2r/2 = 2402/2 Divide both sides by 2
r = 1201 Ricky's base hits
To find Pedro's hits, substitute "r" into any equation.
p = r + 275
p = 1201 + 275 Substitute r = 1201, then add
p = 1476 Pedro's base hits
∴ Ricky had 1201 base hits and Pedro had 1476 base hits.
Final answer:
By setting up an equation where R represents Ricky's hits, and calculating R + 275 for Pedro's hits, we can solve for R and then find the number of hits for each player. Ricky had 1201 hits, while Pedro had 1476 hits.
Explanation:
To solve the problem of determining how many base hits Pedro and Ricky each had last season, we can use algebra. Let's let the variable R represent the number of hits Ricky had. Since Pedro had 275 more hits than Ricky, we can express Pedro's number of hits as R + 275. According to the question, the sum of their hits is 2677, so the equation will be R + (R + 275) = 2677.
Now, let's solve the equation:
R + R + 275 = 2677
2R + 275 = 2677
2R = 2677 - 275
2R = 2402
R = 2402 / 2
R = 1201
So, Ricky had 1201 hits. To find Pedro's hits, we substitute R into the expression R + 275:
Pedro's hits = R + 275 = 1201 + 275 = 1476
Therefore, Ricky had 1201 hits and Pedro had 1476 hits.
You had 15 text messages, deleted 2 then got 5 more, you responded to 4,
and whats your total? a, b, or c?
A. 12
B. 14
C. 18
Answer: The answer is C
Step-by-step explanation: 15 - 2 = 13 13+5=18
Hope this helps :)
Dr. Peterson works about 178 hours each month. Which of the following is the best estimate of the number of hours she works in a year?
Answer:
Option B.
Step-by-step explanation:
Dr. Peterson works about 178 hours each month.
There are 12 months in one year.
So Dr. Peterson works in a year = 178 × 12 = 2,136 hours
We will go through all the options to find which is the closest to the answer.
Option A : 200 × 20 = 4,000 hours
Option B : 180 × 10 = 1,800 hours
Option C : 100 × 12 = 1,200 hours
Option D : 100 × 10 = 1,000 hours
Therefore, Option B is the best estimate of the number of the hours she works in a year.
Della by tree seedling that was 2 1/4 feet tall during the first year it grew 1 1/6 ft after two years it was 5 ft tall how much did the seedling grow during the second year
Answer:
[tex]\frac{19}{12}[/tex] feet
Step-by-step explanation:
First, we need to find the height after one year:
2.25 + 1 1/6 = [tex]\frac{41}{12}[/tex]
Now to find the amount in the second year, we can subtract the above amount from 5:
5 - [tex]\frac{41}{12}[/tex] = [tex]\frac{19}{12}[/tex]
So in the second year it grew [tex]\frac{19}{12}[/tex] feet
I am a number between 80 and 100 my ones digit is two less than my tens digit I am a prime number what number am I
The number you are looking for is 89.
Explanation:The number you are looking for is 89.
Here is how we can find it:
Since the number is between 80 and 100, we know it must have a tens digit of 8. The ones digit is two less than the tens digit, so it would be 6. Now we have the number 86, but we need to check if it is a prime number. A prime number is a number that is only divisible by 1 and itself. We can check if 86 is divisible by any number less than itself.Since we can divide 86 by 2 and get 43, it is not a prime number.Therefore, we have to keep increasing the ones digit by 1 until we find a prime number.The next number is 87, but it is divisible by both 3 and 29. Finally, we arrive at 89, which is only divisible by 1 and itself, making it a prime number.Learn more about Prime numbers here:https://brainly.com/question/35915729
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What is the surface area, in square inches, of a sphere with a diameter of 8 in.? and round to the nearest whole number. Enter only the number.
Answer:
SA = 201 in^2
Step-by-step explanation:
The formula for surface area of a sphere is
SA = 4pi r^2
We know that the diameter is 8
To find the radius we cut the diameter in half.
r = d/2
r = 8/2 =4
Substitute in what we know.
SA = 4 *pi *4^2
= 4*pi*16
= 64*pi
Letting pi = 3.14
= 200.96 in^2
We want to round to the nearest whole number
SA = 201 in^2
Functions and graphs
Answer:
f(x) = -8 x + 34
Step-by-step explanation:
First, normalize the equation 8y = x-16 into y = ... form (divide by 8):
y = 1/8 x - 2
So the slope of this line is 1/8. The slope of a perpendicular line is the negative reciprocal, which means you swap numerator and denominator and add a minus sign. So the slope of our line is -8 and our function will look like f(x) = -8x + b
Now all we have to do is find b such that f(x) goes through (5,-6).
So f(5) = -8*5 + b = -6, and solve it for b:
-40 + b = -6 =>
b = 34.
So f(x) = -8x + 34
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}.\\\\\text{We have}\ 8y=x-16\qquad\text{divide both sides by 8}\\\\y=\dfrac{1}{8}x-2\to m_1=\dfrac{1}{8}.\\\\\text{Let}\ y=mx+b.\ \text{It's perpendicular to given line. Therefore}\ m=-\dfrac{1}{\frac{1}{8}}=-8.\\\\y=-8x+b.\\\\\text{The line passes through point (5, -6)}.\ \text{Put the coordinates of the point}\\\text{to the equation of a line:}[/tex]
[tex]-6=-8(5)+b\\-6=-40+b\qquad\text{add 40 to both sides}\\34=b\to b=34\\\\Answer:\ \boxed{f(x)=-8x+34}[/tex]
Someone please help me solve this
Answer:
First, you have to get all of the variables on one side of the equation.
x15 on both sides
8 + a = 15+15a/6
x6 on both sides
48 + 6a=15+15a
Subtract 15 on both sides and Subtract 6a on both sides
33=11a
a=3
Step-by-step explanation:
Can you help me to determine the y-intercept of 7 and slope please
Answer:
slope = 2.5 and the y intercept is 3
Step-by-step explanation:
To find the slope we can use the formula
m = (y2-y1)/(x2-x1)
I will use the point (2,8) (6,18) We can pick any 2 point we want.
= (18-8)/(6-2)
= (10/4)
= 2.5
To find the y intercept we need to find the equation of the line.
We will use the point slope form
y-y1= m(x-x1)
y-8 = 2.5(x-2)
Distribute the 2.5
y-8 = 2.5x-5
Add 8 to each side
y-8+8 = 2.5x-5+8
y = 2.5x+3
This equation is in slope intercept form y = mx+b
where the slope is 2.5 and the y intercept is 3
Hi There!
-----------------------------------
Find The Slope:
[tex]m = \frac{13 - 8}{4 - 2} = \frac{5}{2} or 2.5[/tex]
-----------------------------------
Find The Y-Intercept:
Substitute using x = 2 and y = 8
Use y = mx + b
Substitute: 8 = 2.5(2) + b
Simplify: 8 = 5 + b
Subtract 5 too both sides: 8 - 5 = 5 + b - 5
Simplify: 3 = b
Y-Intercept = 3
-----------------------------------
Point Slope Form: y - 8 = 2.5(x - 2)
Slope Intercept Form: y = 2.5x + 3
-----------------------------------
Hope This Helps :)
325 Students and adult Will be riding the buses .Each buses hold 48 people.how many buses are needed .
Answer:
7 buses are needed.
Step-by-step explanation:
There are 325 students and adults.
Each bus holds 48 people.
The number of buses needed = [tex]\frac{325}{48}[/tex] = 6.770833333
Since we cant have 0.770833333 buses, we accept that only 7 buses are needed here and that;
325 - (48 × 6) = 37 people will not fill the last bus.
Simplify the expression left parenthesis (3/5)2
Answer:
9/25
Step-by-step explanation:
The answer is 9/25
find the unit rate off $1.29 for 3pens
Answer:
$.43 per pen
Step-by-step explanation:
To find the unit rate, we take the price of the pens and divide by the number of pens
$1.29/3
$.43 per pen
Answer: $0.43
Step-by-step explanation:
Unit rate is how much each pen costs.
If the total amount is $1.29 for all three pens, then the price for one pen should be calculated by 1.29/3, therefore, the answer is $0.43
Lee bought a couch for $600. He made equal payments of 10% of the total cost. How much was each payment?
$6
$10
$60
$100
Answer:
$60
Step-by-step explanation:
Each payment was 10% of $600.
You need to find what 10% of $600 is.
To find a percent of a number, multiply the percent by the number. Change the percent to a decimal by moving the decimal point of the percent two places to the left.
10% of $600 =
= 10% * $600
= 0.10 * $600
= $60
Answer:
60
Step-by-step explanation:
600 * .10= 60
Peter calculated that the theoretical probability of obtaining exactly two heads when flipping six coins is 23.4%. What number of heads also has a 23.4% theoretical probability of coming up when 6 coins are flipped?
Answer:
4 heads
Step-by-step explanation:
Assuming the coins are properly weighted such that each side is equally likely, this means that getting heads is the same probability as getting tails. We're told that getting 2 heads and 4 tails is a 23.4% chance. If we somehow fool our brains into thinking heads and tails swap, then it would be 4 heads and 2 tails. The swap is simply changing the labels for each coin. It really doesn't matter. This symmetry is useful to help simplify larger problems.
If the coins were altered so that the chances of getting heads on any single coin toss was something like 60%, then swapping the labels wouldn't work because the two sides would be different.
what is the domain of the function in this table? X 3 4 5 6 Y 4 4 2 5
Answer:
The domain is {3,4,5,6}
Step-by-step explanation:
Because all your x - values is ur domain and ur y - values is ur range
isabell is mixing red paint with blue paint to make purple paint.she adds 3/10 of a fluid ounce of red to 11/15 of a fluid ounce of blue to make 1 1/30 fluid ounces of blue to make 1 1/30 of purple.how many fluid ounces of red will she need to make 3 fluid ounces of purple paint
Answer:
We will need 27/31 of an ounce of red
Step-by-step explanation:
3 /10 red + 11 /15 blue makes 1 1/30 purple
Get a common denominator of 30
3/10 * 3/3 = 9/30 red
11/15 *2/2 = 22/ 30 blue
1 1/30 = 31/30 purple
So the ratio of red to purple is
9/30
-------- = 9/ 31
31/30
Keeping this ratio, we want 3 ounces purple
9 red x red
-------- = --------------
31 purple 3 purple
Using cross products,
9*3 = 31 *x
27 = 31x
Divide each side by 31
27/31 = x
We will need 27/31 of an ounce of red
What is the coefficient of q in the sum of these two expressions? (23q – 34) and (–16q – r) NEED HELPPP
The coefficient of q in the sum of (23q - 34) and (-16q - r) is 7.
Explanation:In mathematics, a coefficient is a numerical factor or constant that multiplies a variable or term in an algebraic expression. It determines the scale or magnitude of the term and is often used in equations, polynomials, and linear expressions.
The sum of the two expressions is (23q - 34) + (-16q - r).
To find the coefficient of q in this sum, we need to combine the like terms.
Combining the q terms, we have 23q - 16q = 7q.
Therefore, the coefficient of q in the sum of the two expressions is 7.
That u have to find the distance between the pair of points
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (1, 3) and (3, 1). Substitute:
[tex]d=\sqrt{(3-1)^2+(1-3)^2}=\sqrt{2^2+(-2)^2}=\sqrt{4+4}=\sqrt8\approx2.8[/tex]
Answer: C. 2.8PLEASE HELP ASAP! I don’t know how to do this can someone please help.
Answer: 2.50
Step-by-step explanation: your answer is 2.50
What is the vertex form of the quadratic y = 3x^2 + 18x - 4?
Answer:
y = 3(x + 3)² - 31
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h. k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square
take out a common factor of 3 from the first 2 terms
y = 3(x² + 6x) - 4
add/subtract ( half the coefficient of the x-term)² to x² + 6x
y = 3(x² + 2(3)x + 9 - 9 ) - 4
y = 3(x + 3)² - 27 - 4
y = 3(x + 3)² - 31 ← in vertex form