Find the value of two numbers if their sum is 12 and their difference is 4. Systems of equations 8th grade math.
Answers
To solve this problem, we will setup a system.
We know that two numbers have a sum of 12 and a difference of 4.
So let's call our first number x and our second number y.
So we know that x + y = 12.
We can also say that x - y = 4.
Now rewrite the equations on top of each other.
x + y = 12x - y = 4Now we can use addition to solve this system.
When we add the equations together, the y's will cancel.
So we have 2x = 16.
Now divide both sides by 2 and x = 8.
Now plug an 8 back in for x in the first equation to find that y = 4.
So our numbers are 8 and 4.
Related Questions
Write an inequality for the following statement:
The difference between twice a number and 6 is at least 35.
2n−6≤352 n minus 6 is less than or equal to 35
2n−6≥352 n minus 6 is greater than or equal to 35
6−2n≥356 minus 2 n is greater than or equal to 35
6−2n<35
Answers
The inequality for each statement is written as follows:
1. \(2n-6\leq 35\)
2. \(2n-6\geq 35\)
3. \(6-2n\geq 35\)
Let the number be n.An inequality is simply a mathematical relation that can be used to compare two (2) integers or variables in an equation by illustrating any of the following:
Greater than (>).Less than (<).Greater than or equal to the other (≥).Less than or equal to the other (≤).For this exercise, the inequality for each statement is written as:
2n minus 6 is less than or equal to 35:
\(2n-6\leq 35\)
2n minus 6 is greater than or equal to 35:
\(2n-6\geq 35\)
6 minus 2 n is greater than or equal to 35:
\(6-2n\geq 35\)
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Which length of time is between 11.20 am and 2.05 pm ?
Answers
Answer:
2 hours 45 minutes.
Step-by-step explanation:
12.00 - 11.20 = 40 minutes
2. 05 = 14.05
14.05 - 12.00 = 2.05 = 2 hours 5 minutes
Answer = 2 hours 45 minutes.
write an equation in slope-intercept form for the graph shown (i will give brainliest whoever gets it right)
Answers
Answer:
y=-3x+2
Step-by-step explanation:
Solve. Check for extraneous solutions. √2 x+6 - √x-1 =2
Answers
x = 5 is not an extraneous solution of the equation.
✓(2x + 6) - ✓(x - 1) = 2
✓(2x + 6) = 2 + ✓(x - 1)
Squaring both the sides of equation, we get
(✓(2x + 6))² = (2 + ✓(x - 1))²
2x + 6 = (2)² + (✓(x - 1))² + 2(2)(✓(x - 1))
2x + 6 = 4 + x - 1 + 4(✓(x - 1))
x + 3 = 4✓(x - 1)
Squaring again on both the side of the equation, we get
(x + 3)² = (4✓(x - 1))²
x² + 3² + 2×3×x = 16(x - 1)
x² + 9 + 6x = 16x - 16
x² - 10x + 25 = 0
By applying middle term splitting on equation (1), we get
x² - 5x - 5x + 25 = 0
x(x - 5) -5(x - 5) = 0
(x - 5) (x - 5) = 0
x = 5 and 5.
Check for extraneous solutions by putting value of x in original equation -
✓(2×5 + 6) - ✓(5 - 1) = 2
✓16 - ✓4 = 2
4 - 2 = 2
2 = 2
LHS = RHS
x = 5 is not an extraneous solution of the equation.
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. the fraction of the variation in the values of a response y that is explained by the least-squares regression of y on x isquestion 15 options:a) the correlation coefficient.b) the slope of the least-squares regression line.c) the coefficient of determination.d) the intercept of the least-squares regression line.
Answers
The coefficient of determination measures the fraction of variability in the values of y that is explained by the least-square regression of y on x.
The fraction of variance of the regressand y cannot be explained, i.e., which is not correctly predicted by the explanatory variables x.
Fraction of variance forms the ratio of mean squared prediction error over the total variance of the response (except subtracting off an estimate of trial-to-trial variability from both) and subtracts this ratio from one.
Regression involves the determination of the degree of relationship in the patterns of variation of two or more variables through the calculation of the coefficient of correlation, r.
Therefore the fraction of the variation in the values of a response y that is explained by the least-squares regression of y on x is the coefficient of determination.
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Find the explicit formula 13,11,9,7
Answers
-2 pattern
13-2=11-2=9 and so on
n employee randomly selects a chocolate, records their selection and returns the chocolate to the display. They select 10 chocolates in this way. Determine the probability that they select 3 white chocolates.
Answers
The probability of an employee randomly selecting three white chocolates out of ten is 0.25028228759765625 or approximately 0.25. Probability is the possibility that an event will occur.
The formula for calculating probability is as follows: P(A) = n(A) / n(S), where n(A) represents the number of favorable outcomes and n(S) represents the number of possible outcomes.
In the case where an employee randomly selects a chocolate, records their selection, and returns the chocolate to the display, selecting 10 chocolates in this way, the possible number of outcomes is 4 * 10 = 40, where the 4 represents the total number of chocolate types and the 10 represents the total number of chocolate selected.
The formula for the binomial distribution is as follows: P(X = x) = \((nCx) p^x (1 - p)^(n - x)\), where n is the total number of trials, x is the total number of successes, p is the probability of success, 1 - p is the probability of failure, and nCx is the binomial coefficient of x in n.
Using the binomial distribution formula, the probability of selecting three white chocolates is:
P(X = 3) = (10C₃) (1/4)^3 \((3/4)^(10 - 3)\) P(X = 3)
= (120) (1/64) (27/64)P(X = 3)
= 0.25028228759765625
Therefore, the probability of an employee randomly selecting three white chocolates out of ten is 0.25028228759765625 or approximately 0.25.
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- 3x + 3y = 6
x + 3y = 18
solve using substitution
find x and y
Answers
Answer:x = 3 and y = 5
Step-by-step explanation:
We have two equations:
-3x + 3y = 6 ........(1)
x + 3y = 18 ........(2)
We can use the second equation to solve for y in terms of x:
-4x = -12
x = 4
Now we substitute this expression for y into the second equation:
3 + 3y = 18
3y = 15
y = 5
Therefore, the solution to the system of equations is x = 3 and y = 5.
equation 1: - 3x + 3y = 6
equation 2: x + 3y = 18
start with equation 2:
x + 3y = 18
subtract 3y from both sides:
x = 18 - 3y
plug the new equation into equation 1:
- 3x + 3y = 6
- 3 (18 - 3y) + 3y = 6
multiply:
-54 + 9y + 3y = 6
collect like terms:
-54 + 12y = 6
add 54 to both sides, then divide the whole equation by 12:
12y = 60
y = 5
plug the y value into either equation to solve for x. for example, here is equation 2:
x + 3y = 18
x + 3(5) = 18
x + 15 = 18
x = 3
check answer:
x + 3y = 18
3 + 3(5) = 18
3 + 15 = 18
18 = 18 is true
Samantha fills her car's gas tank. It now has 18 gallons of gas. She uses 1/2
of the gas when she drives to the beach. Then, she uses 3/4 of the
remaining gas when she drives to the mall. How many gallons of gas does
Samantha's car have left? *
Answers
Answer:
18 x 1/2 = 9
18 - 9 = 9
9 x 3/4 = 27/4
9 - 27/4 = 2 1/4 or 2.25 gallons
11. Find the measures of 1 and 2
Answers
Answer:
No entiendo lo que dice gracias
5/6 + 3/4 + 2/3 = ?
What is the ?
Answers
Answer:
1/2 + 2/3 + 5/4 = 29/12 = 2 5/12 ≅ 2.4166667
Step-by-step explanation:
In a spot check of cartons of eggs, Matilda found that 6 out of 200 eggs were cracked. If the store has 3,000 eggs for sale, how many can expect to be cracked. (Prediction = Proportion)
Group of answer choices
90
60
600
900
Answers
\(\boxed{\large{\bold{\textbf{\textsf{{\color{gold}{Answer \red{:)}}}}}}}}\)
In a spot check of cartons of eggs, Matilda found that 6 out of 200 eggs were cracked.
In 200 eggs cracked =6
in 1 egg cracked =\(\dfrac{6}{200}\)
According to the question,
If the store has 3,000 eggs for sale, how many can expect to be cracked.
In 3000 eggs cracked=\(\dfrac{6}{200}×3000\)
90 eggs Therefore:-If the store has 3,000 eggs for sale, 90 eggs can expect to be cracked
If the store has 3,000 eggs for sale, 90 eggs can expect to be cracked.
What is Proportion?A proportion is an equation in which two ratios are set equal to each other.
For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4)
Given that :
In a spot check of cartons of eggs, Matilda found that 6 out of 200 eggs were cracked.
In 200 eggs cracked = 6 / 200 in 1 egg cracked
According to the question,
If the store has 3,000 eggs for sale, how many can expect to be cracked.
In 3000 eggs cracked = 6 / 200 x 3000
= 90 eggs
Hence, If the store has 3,000 eggs for sale, 90 eggs can expect to be cracked.
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Hey I really need some help I would appreciate it thank you !! Please answer if you are sure what the answer is this is important. Thanks again!
Here are the answers to choose from
A. 18 cm
B. 15 cm
C. 14 cm
D. 8cm
Answers
Answer:
it looks like 15 cm would be the right answer
Find the power set for the following sets (Write 3 examples of each)
a) Two sets A & B both having any 2 elements
b) Two sets A & B both having any 3 elements
c) Two sets A & B both having any 4 elements
Answers
Given statement solution is :- a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
Set A: {apple, banana}, Set B: {cat, dog}
Power set of A: {{}, {apple}, {banana}, {apple, banana}}
Power set of B: {{}, {cat}, {dog}, {cat, dog}}
Set A: {red, blue}, Set B: {circle, square}
Power set of A: {{}, {red}, {blue}, {red, blue}}
Power set of B: {{}, {circle}, {square}, {circle, square}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}
Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}
Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}
Set A: {red, blue, green}, Set B: {circle, square, triangle}
Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}
Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
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What is the leading coefficient of a third degree function that has an output of 221 when x=2, and has zeros of −15, 3i, and −3i?
Answers
Answer:
1
Step-by-step explanation:
The function with the given zeros will factor as ...
f(x) = a(x +15)(x^2 +9) . . . . with leading coefficient 'a'
You have ...
f(2) = 221 = a(2+15)(2^2+9) = a(17)(13) = 221a
Then a = 221/221 = 1
The leading coefficient is 1.
_____
Additional comment
As you know, a function with zero x=p has a factor of (x -p). The given zeros mean the function has factors (x -(-15)), (x -3i). and (x -(-3i)). The product of the last two factors is the difference of squares: (x^2 -(3i)^2) = (x^2 -(-9)) = (x^2 +9). This is how we arrived at the factorization shown above.
a kit contains 600 letter tiles and 40 number tiles each tile has the same mass and the kit has a total mass of 2400 grams. what equation would represent this
Answers
Answer:
900
Step-by-step explanation:
Sandra makes and sells bracelets. It costs her $2 to make each bracelet, plus a one-time cost of $15 for supplies. She plans to sell each bracelet for $5. Let x represent the number of bracelets. Which equation can be used to find the number of bracelets she needs to sell to break even?
Answers
The equation for breaking even is, 2x + 15 = 5x.
We have, Sandra makes and sells bracelets. It costs her $2 to make each bracelet, plus a one-time cost of $15 for supplies. She plans to sell each bracelet for $5.
Therefore we have,
What is the her total revenue?The number of bracelets that Sandra needs to sell in order to break even can be solved by equating the total cost to her total revenue.
If the x represents the number of bracelets,
The total cost would be, 2x + 15.
Her total revenue from sales is expressed as 5x.
Thus, the equation for breaking even is,
2x + 15 = 5x
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PLEASE ANSWER QUICKLY
Put the following equation of a line into slope-intercept form, simplifying all fractions.
6x+10y= -80
Answers
Answer:
y=-0.6 X-8
Step-by-step explanation:
6x+10y= -80
Subtract the positive 6x from both sides of the equation
This will make your equation look like 10y= -80-6x
(If it helps you can rewrite the equation so it looks like 10y= -6x -80)
Divide both sides of the equation by 10. This will isolate your Y axis
Now your equation will look like y= (-6x -80) / 10
I got y= -0.6x -8
I hope this helps and it is correct :)
help! i need help with this!
Answers
Answer:
it should be 10
Step-by-step explanation:
Answer:
Use pythagoras theorem
Step-by-step explanation:
Square root of 10 Square minus 8 Square. This will be the length of AD and DC. The length of AC will be 6+6 which is 12
Given m n, find the value of x.
m
(5X-11)°
(6x-7)°
Answers
Answer:
x = 18
Step-by-step explanation:
the angles pictured are supplementary angles.
supplementary angles are angles whose sum equals 180°
ex: <1 + <2 = 180°
\(5x - 11 + 6x - 7 = 180\)
\(11x - 18 = 180\)
\(11x = 198\\x = 18\)
Answer:
\(\boxed{\sf{x=18}}\)
Step-by-step explanation:
To find the value of x, you have to use the supplementary angles which is equal to 180°.
Supplementary angles = 180°
5x-11+6x-7=180
Combine like terms.
\(\sf{5x+6x-11-7=180}\)
5x+6x=11x
\(\sf{11x-11-7=180}\)
Subtract the numbers from left to right.
-11-7=-18
\(\sf{11x-18=180}\)
You have to add by 18 from both sides.
11x-18+18=180+18
Solve.
Add the numbers from left to right.
180+18=198
11x=198
Divide by 11 from both sides.
11x/11=198/11
Solve.
198/11=18
\(\rightarrow \boxed{\sf{x=18}}\)
Therefore, the final answer is x=18.
Please help me solve this. With Reasoning
6 2/5 - 4 2/3
Answers
Answer:
1 and 11/15.
Step-by-step explanation:
To solve, we can separate the integers from the fractions.
(6 - 4) + (2/5 - 2/3)
= 2 + (6/15 - 10/15)
= 2 + (-4/15)
= 1 + 15/15 - 4/15
= 1 + 11/15
= 1 and 11/15
Hope this helps!
1. David bought a used Dodge Challenger for $14,000. The value of the car depreciates 11% per year from the time he bought the car. Find a function that represents the value of David’s car, V(t), after t years.
2. How much will David’s car be worth 6 years after he bought it?
Answers
Answer:
V(t) = 14,000(0.89)^t
Step-by-step explanation:
Present value of the Dodge Challenger = $14,000
Present percentage value = 100%
Depreciation value = 11%
Number of years = t
Future value = V(t)
V(t) = Present value of the Dodge Challenger(Present percentage value - Depreciation value)^t
= 14,000(100% - 11%)^t
= 14,000(89%)^t
= 14,000(0.89)^t
V(t) = 14,000(0.89)^t
2x²+10x+12 اريد مساعده
Answers
Answer:
2(x+2)(x+3)
Step-by-step explanation:
The number that is 75% of one less than a number n.
Answers
Answer:
The number is n-0.75
Step-by-step explanation:
Here in this question, we are interested in giving a number which is 75% of 1 less than a number n.
The first thing we do here is to calculate the value of 75% of 1.
That would be;
75/100 * 1 = 0.75
So this value less than n will be;
n- 0.75
Dr. Dobbs is studying the body's response to Robitussin cough syrup and how long it stays in the body after a dose of 1000 mg. Depending on the person, the rate of decay in the body is 55% of the Robitussin is left after each hour that passes. A person needs to have at least 100 mg for the body to feel the effects.
Determine the length of time before another dose of Tylenol will be needed to be taken again. ( How many hours before the amount of Tylenol drops below 100 mg.)
Answers
The requried another dose of Robitussin would need to be taken at least 5 hours after the initial dose in order for the body to maintain the minimum effective amount of 100 mg.
Let t be the number of hours that have passed since the dose was taken, and let A(t) be the amount of Robitussin in the body at time t. We know that A(0) = 1000 mg (the initial dose), and that A(t) = 0.55 A(t-1) (the rate of decay is 55% per hour).
We want to find the value of t such that A(t) = 100 mg. We can use recursive substitution to find A(t) in terms of A(0):
A(1) = 0.55 A(0) = 0.55 * 1000 = 550
A(2) = 0.55 A(1) = 0.55 * 550 = 302.5
A(3) = 0.55 A(2) = 0.55 * 302.5 = 166.375
A(4) = 0.55 A(3) = 0.55 * 166.375 = 91.50625
A(5) = 0.55 A(4) = 0.55 * 91.50625 = 50.3284375
So, after 5 hours, the amount of Robitussin in the body drops below 100 mg.
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A spinner has an equal chance of landing on either red blue or green. You spin six times. What is the probability that spinner lands on red at least two times?
Answers
Answer:
0.8906 ( 4 decimal places)
Step-by-step explanation:
With an equal probability of landing in either blue or red, then
Probability of success, p = 0.5
Number of trials, n = 6
Probability of landing on red atleast twice Can be obtained using a cumulative binomial probability ;
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x ≥ 2) = p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6)
Obtaining the individual probabilities and summing them up or we could use a cumulative probability option on either a calculator, excel or an online binomial probability distribution.
Using an online binomial probability calculator :
P(x ≥ 2) = 0.890625
P(x ≥ 2) = 0.8906 ( 4 decimal places)
Shaquira is baking cookies to put in packages for a fundraiser. Shaquira has made 86 8686 chocolate chip cookies and 42 4242 sugar cookies. Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies. What is the greatest number of identical packages that Shaquira can make?
Answers
Answer: 2
Step-by-step explanation:
Given: Shaquira has made 86 chocolate chip cookies and 42 sugar cookies.
Shaquira wants to create identical packages of cookies to sell, and she must use all of the cookies.
Now, the greatest number of identical packages that Shaquira can make= GCD of 86 and 42
Prime factorization of 86 and 42:
86 = 2 ×43
42 = 2 × 3 × 7
GCD of 86 and 42 = 2 [GCD = greatest common factor]
Hence, the greatest number of identical packages that Shaquira can make =2
A study on the latest fad diet claimed that the amounts of weight lost by all people on this diet had a mean of 23.4 pounds and a standard deviation of 6.8 pounds.
Step 2 of 2 : If a sampling distribution is created using samples of the amounts of weight lost by 63 people on this diet, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Using the Central Limit Theorem, the standard deviation of the sampling distribution of sample means would be of 0.86.
What does the Central Limit Theorem state?It states that the standard deviation of the sampling distribution of sample means is given by:
\(s = \frac{\sigma}{\sqrt{n}}\)
In which:
\(\sigma\) is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
\(\sigma = 6.8, n = 63\).
Hence:
\(s = \frac{\sigma}{\sqrt{n}}\)
\(s = \frac{6.8}{\sqrt{63}}\)
s = 0.86.
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brainliest fir CORRECT answer
Answers
Answer:
y ≈ 5.2
Step-by-step explanation:
∠ F = 180° - (42 + 48)° ← sum of angles in a triangle
∠ F = 180° - 90° = 90°
Thus Δ DEF is right at F
Using the sine ratio in the right triangle
sin48° = \(\frac{opposite}{hypotenuse}\) = \(\frac{DF}{DE}\) = \(\frac{y}{7}\) ( multiply both sides by 7 )
7 × sin48° = y , then
y ≈ 5.2 ( to the nearest tenth )
For the rhombus below, find the measure of 1, 2, 3, and 4.
Answers
Answer:
Angle 1 is 51, Angle 2 is 51, Angle 3 equal 39, Angle 4 is 51
Step-by-step explanation:
A rhombus diagonals are perpendicular so all the angles in the middle of the rhombus measure is 90 degrees. So this means we are dealing with 4 right congruent triangles.
Since a rhombus is a paralleogram, it opposite sides are parallel. Since there is a line that it cuts through the parallel line, Angle 3 and 39 are alternate interior angles.
Alt. interior angles are congruent so Angle 3=39.
In the upper left triangle, angle 3 ,angle 4, and the middle angle form 180 degrees since it a triangle. The middle angle measure 90 degrees. so we can find angle 4.
\(39 + 90 + x = 180\)
\(129 + x = 180\)
\(x = 51\)
so angle 4=51.
Angle 4 and Angle 1 are alt. interior angles so that means Angle 1 also equal 51.
Rhombus also has angle bisectors to angle 1=angle 2.
Angle 2=51.