5x+4y=-30
3x-9y=-18
how do I do an elimination
Answers
Consequently, x = -6 and y = 0 provide the system of equations answer. The response gathering yields "(-6,0)" as the outcome.
What is an elimination sentence?She came back to compete in the meeting's final event, winning the knockout race. Their quick removal is the letdown. Take pride in your quick removal.
To solve this system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the equations. Here's how to do it:
To find: multiply the second solution by 4.
12x - 36y = -72
Eliminate x by combining the two equations:
5x + 4y + 12x - 36y = -30 - 72
Simplify and combine like terms:
17x - 32y = -102
Solve for x:
17x = 32y - 102
x = (32/17)y - 6
Substitute this expression for x into one of the original equations, and solve for y:
5x + 4y = -30
5[(32/17)y - 6] + 4y = -30
Simplify and solve for y:
(160/17)y - 30 = -30
(160/17)y = 0
y = 0
Substitute this value for y back into either of the original equations and solve for x:
3x - 9y = -18
3x - 9(0) = -18
3x = -18
x = -6
So the solution to the system of equations is x = -6 and y = 0. Therefore, the solution set is {(-6,0)}.
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Related Questions
Pe un teren de sport,fetele reprezinta un sfert din numarul baietilor.Daca pleaca 8 baieti si vin acelasi numar de fete,raportul va fi de 1 la 2.Cate fete si cati baieti sunt?
Answers
Answer:
the girls be 12 and boys be 48 respectively
Step-by-step explanation:
The computation of the number of boys and number of girls is shown below:
Let us assume A be girls
And, b be boys
According to the question
b = 4 × a
b - 8 = 2 × (a + 8)
b - 8 = 2 × a + 16
4 × a -8 = 2 × a + 16
4 × a - 2 × a = 16 + 8
2 × a = 24
a = 12
Now
b = 4 × a
= 4 × 12
= 48
Hence, the girls be 12 and boys be 48 respectively
What’s the description of the ridged motions
Answers
What’s the description of the ridged motions
There is a spinner game in a fair. The player has to spin the spinner. If the spinner lands on the white sections, the player will win $10. Otherwise, the player will lose the entry fee which is $2. Check the fairness of the game.A)the game is fair B) the game is not fair, but favorable to the player.C) the game is not fair and not favorable to the player D) can’t be determined
Answers
We have a question about probability. Our approach is to obtain the mean amount that can be obtained for the possible outcomes.
Probability is derived as:
\(\text{Probability = }\frac{\#\text{ of desired outcome}}{\#\text{ of total outcomes}}\)The probability, P of obtaining a white can be derived knowing:
# of desired outcome = 2
# of total outcome = 16
\(P=\frac{2}{16}=\frac{1}{8}\)The average amount obtainable for spinning a white is:
\(\mu=\frac{1}{8}\times\text{ \$10=\$1.25}\)The probability, Q of obtaining any other color can be derived knowing:
# of desired outcome = 14
# of total outcome = 16
\(P=\frac{14}{16}=\frac{7}{8}\)The average amount obtainable for spinning any other color is:
\(\mu=\frac{7}{8}\times\text{ \$2=\$1.75}\)Net gain on average: Average amount gained - Average amount lost
\(\text{ Net gain = \$1.25 - \$1.75 = -\$0.50}\)On average, the player loses 50 cents. That makes it unfavorable for him.
OPTION C
james took a survey to show that baskitball is the favorite sport for 18 out of 25 students which percent is the closet to the probility that a person favorite sport will not be baskitball
Answers
The closest to the probability that a person's favorite sport is 28%.
What is probability?Probability of an event happening is the ratio of the number of required outcome to that of the total number of possible outcomes. while the probability of the event not happening is one minus the event happening.
From the question, the number of required outcome is 18 and the number of possible outcomes is 25.
So the probability of the event that a person's favorite sport is not basketball = 1 - (18/25)
probability of the event that a person's favorite sport is not basketball = (25 - 18)/25 [simply to a single fraction]
probability of the event that a person's favorite sport is not basketball = 7/25
probability of the event that a person's favorite sport is not basketball = 28/100 [convert to percentage]
probability of the event that a person's favorite sport is not basketball = 38%
Therefore, the probability that a person's favorite sport will not be baskitballbis 38%.
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Will make brainiest if 2 people answer :3
Answers
Answer:
1.6
Step-by-step explanation:
12.8/8 = 1.6
15.2/9.5 = 1.6
Scale factor = 1.6
50 POINTS An airplane is traveling at a speed of 240 miles/hour with a bearing of 110°. The wind velocity is 56 miles/hour at a bearing of 325°. What are the plane's actual speed and direction angle? (hint: the direction angle is measured from the positive x-axis in a counter-clockwise direction)
A.
The speed is 179.82 miles/hour, and the direction angle is 100.60°.
B.
The speed is 179.82 miles/hour, and the direction angle is 349.40°.
C.
The speed is 196.77 miles/hour, and the direction angle is 115.60°.
D.
The speed is 196.77 miles/hour, and the direction angle is 349.40°.
Answers
Answer:
the speed is 179.82 miles/hour .and the direction angle is 100.60
The total revenue function for a product is given byR=640xdollars, and the total cost function for this same product is given byC=16,500+60x+x2,where C is measured in dollars. For both functions, the input x is the number of units produced and sold.a. Form the profit function for this product from the two given functions.b. What is the profit when24units are produced and sold?c. What is the profit when39units are produced and sold?d. How many units must be sold to break even on this product?a. Write the profit function.
Answers
For both functions, the input x is the number of units produced and sold. Therefore, 75 units must be sold to break even on this product.
Thus, we have:
P(x) = R(x) - C(x) = 640x - (16,500 + 60x + x^2)
where x is the number of units produced and sold.
To find the profit when 24 units are produced and sold, we substitute x = 24 into the profit function:
P(24) = 640(24) - (16,500 + 60(24) + 24^2) = $5,136
To find the profit when 39 units are produced and sold, we substitute x = 39 into the profit function:
P(39) = 640(39) - (16,500 + 60(39) + 39^2) = $10,161
To find the number of units that must be sold to break even on this product, we set the profit function equal to zero and solve for x:
640x - (16,500 + 60x + x^2) = 0
x^2 + 60x - 16,500 = 0
Using the quadratic formula, we find that the solutions are x = 75 and x = - 235. Since x represents the number of units produced and sold, we take x = 75 as the answer.
Therefore, 75 units must be sold to break even on this product.
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a magazine includes a report on the energy costs per year for 32-inch liquid crystal display (lcd) televisions. the article states that 14 randomly selected 32-inch lcd televisions have a sample standard deviation of $3.90. use a 99% level of confidence. (
Answers
We can conclude that with 99% confidence, the true population mean energy cost per year falls between $13.38 and $19.62.
A report in a magazine contains information on energy costs per year for 32-inch liquid crystal display (LCD) televisions. According to the report, a sample of 14 randomly selected 32-inch LCD televisions have a sample standard deviation of $3.90. Using a 99% level of confidence, the confidence interval for the true population mean energy cost per year can be calculated. A 99% level of confidence indicates that there is only a 1% chance that the true population mean energy cost per year falls outside the interval.Confidence Interval for Mean = $\bar{X}±t_{\frac{\alpha}{2},n-1}\frac{S}{\sqrt{n}}$Where, $\bar{X}$ is the sample mean,S is the sample standard deviation,n is the sample size,t is the critical value of t-distributionα is the level of significancet= 3.71 (using t-distribution table for 99% level of confidence with n - 1 degrees of freedom)Mean = $16.50 ± 3.71 × \frac{3.90}{\sqrt{14}}$=$16.50 ± 3.12$The 99% confidence interval for the true population mean energy cost per year is (13.38, 19.62). Therefore, we can conclude that with 99% confidence, the true population mean energy cost per year falls between $13.38 and $19.62.
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Tara bought one share of Apple stock in 2018 for $43.75. Then, three years later, she sold it for $136.76. How much money did she gain/lose with this stock? What was her return on investment?
Answers
Answer:
Gain= $93.01
ROI= 212.59%
Step-by-step explanation:
Given data
Cost of apple share in 2018 = $43.75
Sale price of apple share= $136.76
1. Her gain is
Gain= Sales price- Cost price
Gain = 136.76-43.75
Gain= $93.01
2. ROI is
ROI= Gain/cost*100
ROI= 93.01/43.75*100
ROI=2.1259*100
ROI= 212.59%
4÷13 helppppppp plssssssssssssssssssssssssssssssssss
Answers
Answer:0.307692308
Step-by-step explanation:
Answer: 0.30769230769
The Jackson's dinner cost $125. They left $21.25 as a tip. What was the percentage of the tip? Please explain and help me! THANK YOU!!!
Answers
Answer:
17%
Step-by-step explanation:
to find the percentage of something, you have to fill out the following formula:
x/100 = 21.25/125. Basically that is saying that some percent out of 100 is equal to 21.25 out of 125. To solve that, you have to cross multiply:
125x = 2125
then you have to divide, to single out x:
the answer is 17
so it is 17%
Divide the tip by the amount dinner was and you get your percentage for the tip
mention about angles of a triangle
Answers
which number is closest to -31
A: -28 B: -27 C: -34 D: -33
Answers
Answer:
D) -33
Step-by-step explanation:
Answer:
D: -33 as it is like if it was positives just oppositite.
For what value of 'k will (x - 1) be a factor of 4x^3 +kx^2 - 7x - 10?
Answers
Answer:
k = 13
Step-by-step explanation:
If (x-1) is a factor, then f(1) = 0
4*1 + k*1 - 7*1 - 10 = 0
4 + k - 7 - 10 = 0
k - 13 = 0
k = 13
a committee of four is chosen at random from a group of 6 women and 3 men. find the probability that the committee contains at least one man.
Answers
The probability that the committee contains at least one man is 1 - (probability of selecting only women).
To find the probability, we need to determine the total number of possible committee combinations and the number of combinations with at least one man. There are 9 people (6 women + 3 men) to choose from, and we want to choose a committee of 4.
Total combinations = C(9,4) = 9! / (4!(9-4)!) = 126
Combinations of only women = C(6,4) = 6! / (4!(6-4)!) = 15
To find the probability of at least one man, we'll subtract the probability of selecting only women from 1:
P(at least one man) = 1 - (15/126) = 1 - 0.119 = 0.881
The probability that the committee contains at least one man is approximately 0.881, or 88.1%.
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Find the moment of inertia about the origin I0 of a lamina occupying the region enclosed by one loop of the four-leaved rose r = cos 2θ. Assuming the density function is p(x,y) = 1.
Answers
The moment of inertia about the origin I0 for a lamina occupying the region enclosed by one loop of the four-leaved rose r = cos 2θ with density function p(x,y) = 1 is I0 = 1/4 * π/4.
To find the moment of inertia, follow these steps:
1. Convert the polar equation to Cartesian coordinates: x = rcosθ, y = rsinθ.
2. Find the area of one loop of the rose using the formula A = 1/2 * ∫(r^2)dθ, where θ ranges from 0 to π/2.
3. Determine the mass of the lamina using the density function p(x,y) = 1 and the area calculated in step 2.
4. Find the moment of inertia using the formula I0 = ∫(x² + y²)p(x,y)dA, where dA is the infinitesimal area element in polar coordinates.
5. Evaluate the integral to obtain the final expression for I0.
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What is the area of the region on the xy-plane which is bounded from above by the curvey=e*, from below by y = cos x and on the right by the vertical line X = ? (a) 2 cos(e* - 5) (b) 14.80 (c) 27/3 (d) 22.14 (e) 31.31
Answers
The area of the region bounded by the curves is d) 22.14.
To find the area of the region bounded by the curves y = \(e^x\), y = cos(x), and x = π on the xy-plane, we need to integrate the difference between the upper and lower curves with respect to x over the specified interval.
The upper curve is y = \(e^x\), and the lower curve is y = cos(x). The vertical line x = π bounds the region on the right.
To find the area, we integrate the difference between the upper and lower curves from x = 0 to x = π:
A = ∫[0, π] (\(e^x\) - cos(x)) dx
To evaluate this integral, we can use the fundamental theorem of calculus:
A = [\(e^x\) - sin(x)] evaluated from 0 to π
A = (\(e^\pi\) - sin(π)) - (\(e^0\) - sin(0))
A = (\(e^\pi\) - 0) - (1 - 0)
A = \(e^\pi\) - 1
Calculating the numerical value:
A ≈ 22.14
Therefore, the area of the region bounded by the curves y = \(e^x\), y = cos(x), and x = π on the xy-plane is approximately 22.14.
The correct answer is (d) 22.14.
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what is the result of 2.130 x 10³ - 6.6 x 10² =
Answers
Answer:
The answer you're looking for is 1470.
Step-by-step explanation:
The method I used was PEMDAS
Since there was no parenthesis, I simplified the exponents.
2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?
After that, I multiplied all terms next to each other.
2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?
The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.
1470 = ?
I hope this was helpful!
the point a(-2, 3) is translated using t: (x,y) → (x 4, y 2). what is the distance from a to a'?
Answers
The distance from point A(-2, 3) to its translated point A' is 2√5 units.
To find the distance between point A(-2, 3) and its translated point A', after the translation given by t: (x, y) → (x + 4, y + 2), we can use the distance formula. The distance formula is defined as:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance: cordinates of A: (x1, y1) = (-2, 3)
Coordinates of A' after translation: (x2, y2) = (-2 + 4, 3 + 2) = (2, 5)
Substituting these values into the distance formula:
Distance = √((2 - (-2))^2 + (5 - 3)^2)
= √(4^2 + 2^2)
= √(16 + 4)
= √20
= 2√5
Therefore, the distance from point A(-2, 3) to its translated point A' is 2√5
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Find the volume.
7 ft
25 ft
18 ft
Answers
Answer:
3150 ft³ or 89.1981 m³ or 116.6667 yd³
Step-by-step explanation:
The scale drawing car length is 3 cm. If the scale is 1 cm:4 ft, what is the actual car length?
O 16 feet
0 10 feet
12 feet
ОО
0 4 feet
Answers
-1/3(x-15)=-4 what is the correct sequence of operations
Answers
Answer:
x = 3
Step-by-step explanation:
The steps I show will be listed from first-to-last.
-1/3x + 5 = -4 (Distribute)
-1/3x = -9 (Subtract 5 from both sides)
x = 3 (Multiply both sides by -3)
Marian Plunket owns her own business and is considering an investment. if she undertakes the investment, it will pay $28,000 at the end of each of the new 3 years. the opportunity requires an initial investment of $7,000 plus an additional investment at the end of the second year of $35,000. what is the NPV of this opportunity if the interest rate is 8% per year? Should Marian take it?
Answers
The NPV is positive, it is worth taking the Investment.
Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.
This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:
NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.
The given problem can be solved by using the following steps:
Calculate the present value (PV) of the expected cash inflows:
Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82
Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39
Since the NPV is positive, it is worth taking the investment.
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whats the surface area of the box 4in. 10in. 8in.
Answers
Answer:
320in
Step-by-step explanation:
Brainliest?
Answer:
surface area of the box = l×w×h
surface area = 10× 8 × 4 = 320in
Which table of values represents the exponential function f(x)=0.1x−4?
Answers
Answer:
for the 1 one is: ___________Find the x and y Intercepts___________
for the 2 one it is a: ________Graph_________
Step-by-step explanation:
BRAINLYLIST will highly appreciated
HAVE A GOD LIKE DAY
if 2.4 j of work is needed to stretch a spring from 15 cm to 19 cm and another 4 j is needed to stretch it from 19 cm to 23 cm, what is the natural length (in cm) of the spring?
Answers
The natural length of the spring is approximately 3.97 cm.
The natural length (in cm) of the spring can be found by the following steps:
Given that 2.4 J of work is needed to stretch a spring from 15 cm to 19 cm and 4 J is needed to stretch it from 19 cm to 23 cm.
We know that the work done in stretching a spring is given by the formula;
W = ½ k (x₂² - x₁²)
Where,W = work done
k = spring constant
x₁ = initial length of spring
x₂ = final length of spring
Let the natural length of the spring be x₀.
Then,
2.4 = ½ k (19² - 15²)
Also,4 = ½ k (23² - 19²)
Expanding and solving for k gives:
k = 20
Next, using the value of k in any of the equations to solve for x₀,
x₀² - 15² = (2 × 2.4) ÷ 20
x₀² = 15² + (2 × 2.4) ÷ 20
x₀² = 15.72
x₀ = √15.72
x₀ ≈ 3.97
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Find the sum a + B of the two angles a E 48°49° and B= 16°19
Answers
To find the sum of two angles a and B, we can simply add the values of the angles together. In this case, a = 48°49' and B = 16°19'.
To add the angles, we start by adding the degrees and the minutes separately.
Adding the degrees: 48° + 16° = 64°
Adding the minutes: 49' + 19' = 68'
Now we have 64° and 68' as the sum of the two angles. However, since there are 60 minutes in a degree, we need to convert the minutes to degrees.
Converting the minutes: 68' / 60 = 1.13°
Adding the converted minutes: 64° + 1.13° = 65.13°
Therefore, the sum of the angles a = 48°49' and B = 16°19' is approximately 65.13°.
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A first-time home buyer is given the choice of two loans: Loan A Loan B $390,000 15 year-fixed 4 discount points M = $3,509.71 $390,000 15 year-fixed 0 discount points M = $3,659.86 How much does the home buyer save in total by choosing Loan A? $27,027.00 $11,427.00 $26,351.02 $42,627.05
Answers
The home buyer saves $26,289 by choosing Loan A. The closest answer choice is $26,351.02.
Calculating the amount the home buyer saves by choosing loan AFrom the question, we are to determine the amount the home buyer saves in total by choosing loan A
To calculate the savings, we need to find the total amount paid for both loans and then subtract the total paid for Loan A from the total paid for Loan B.
For Loan A:
M = $3,509.71
Total amount paid = 15 years x 12 months/year x $3,509.71/month = $631,748.20
For Loan B:
M = $3,659.86
Total amount paid = 15 years x 12 months/year x $3,659.86/month = $658,037.20
The difference between the two is:
$658,037.20 - $631,748.20 = $26,289.00
Hence, the amount the home buyer saves is $26,289
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Answer:
B. 11,427.00
Step-by-step explanation:
got it right on test
-4<=2(x-1)<10 inswer in interval notation. Use decin
Answers
The solution to the inequality -4 ≤ 2(x-1) < 10 in interval notation is [-1, 6).
To solve the inequality -4 ≤ 2(x-1) < 10, we can start by isolating the expression (x-1) in the middle.
-4 ≤ 2(x-1) < 10
Divide each part of the inequality by 2:
\(-4/2 \leq (x-1) < 10/2-2 \leq (x-1) < 5\)
Next, we add 1 to each part of the inequality:
\(-2 + 1 \leq (x-1) + 1 < 5 + 1-1 \leq x < 6\)
The solution to the inequality -4 ≤ 2(x-1) < 10 in interval notation is [-1, 6).
In interval notation, we use brackets [ ] for inclusive bounds and parentheses ( ) for exclusive bounds.
The interval [-1, 6) represents all real numbers x such that -1 is included, but 6 is not included. This means that x can be any value from -1 up to, but not including, 6. The inequality is satisfied when x lies between -1 and 6, inclusive of -1 but excluding 6.
To summarize, the solution to the inequality -4 ≤ 2(x-1) < 10 in interval notation is [-1, 6).
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What is 24/240 as a decimal
Answers
Answer:
0.1
Step-by-step explanation:
Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator