To eliminate the y-variable in the given system of equations and find the value of x, you can multiply the first equation by 3 and the second equation by 4 to make the coefficients of y equal. Then, add the two equations together to eliminate the y-variable. Finally, solve for x.
Explanation:To eliminate the y-variable and find the value of x in the given system of equations, we can multiply the first equation by 3 and the second equation by 4 to make the coefficients of y in both equations equal. This will allow us to eliminate the y-variable when we subtract the two equations.
Multiplying the first equation by 3, we get: 6x - 12y = 18
Multiplying the second equation by 4, we get: -12x + 12y = 48
Now, we can add the two equations together, and the y-variable will cancel out: (6x - 12y) + (-12x + 12y) = 18 + 48
Simplifying, we have: -6x = 66
Dividing both sides by -6, we find: x = -11
Therefore, the value of x is -11.
Final answer:
To eliminate the y-variable and find the value of x in the system of equations, we can use the method of elimination. We can multiply the equations by coefficients to create opposite coefficients for the y-terms, which will cancel each other out when added together. The resulting equation can then be solved to find the value of x.
Explanation:
To eliminate the y-variable and find the value of x, we can use the method of elimination. In this case, we need to multiply the two equations by coefficients that will create opposite coefficients for the y-terms so that they will cancel each other out when added together. Let's multiply the first equation by 3 and the second equation by 4:
6x - 12y = 18
-12x + 12y = 48
Adding these two equations eliminates the y-variable:
-6x = 66
Solving for x, we divide both sides by -6:
x = -11
Can somebody help/teach me about this please?
“Suppose the equation h=-16t^2 + 35t models the altitude a football will reach t seconds after it is kicked. IS THE GIVEN VALUE POSSIBLE?”
A: h= 16 ft. B: h= 20ft.
The given value h=16 ft is possible based on the quadratic equation model provided. By solving the equation h=[tex]-16t^2 + 35t[/tex] and substituting h=16, we find the possible values of t to be approximately 0.52 seconds or 1.48 seconds.
- For each given value of h, set [tex]\( h = -16t^2 + 35t \)[/tex] and solve for t.
- If you obtain real solutions, the given h is possible. If not, it isn't possible.
Checking for h=16:
1. Set h=16 and solve for t:
[tex]\[ 16 = -16t^2 + 35t \][/tex]
2. Rearrange to form a quadratic equation:
[tex]\[ -16t^2 + 35t - 16 = 0 \][/tex]
3. Solve for \( t \) using the quadratic formula:
[tex]\[ t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where a= -16, b=35, c=16.
- Find the discriminant:
[tex]\[ b^2 - 4ac = 35^2 - 4 \times (-16) \times (-16) = 1225 - 1024 = 201 \][/tex]
Since the discriminant is positive, this quadratic has real roots, indicating that h=16 is possible.
Checking for h=20:
1. Set h=20 and solve for t:
[tex]\[ 20 = -16t^2 + 35t \][/tex]
2. Rearrange to form a quadratic equation:
[tex]\[ -16t^2 + 35t - 20 = 0 \][/tex]
3. Solve for t using the quadratic formula:
[tex]\[ t = \frac{-35 \pm \sqrt{35^2 - 4 \times (-16) \times (-20)}}{2 \times (-16)} \][/tex]
- Find the discriminant:
[tex]\[ 35^2 - 4 \times (-16) \times (-20) = 1225 - 1280 = -55 \][/tex]
Since the discriminant is negative, this quadratic has no real roots, indicating that h=20 is not possible.
Conclusion:
- The value h=16 is possible.
- The value h=20 is not possible.
A parabola has a vertex at (-1, 0) and opens down. What is the equation of the parabola? y = -x2 - 1 y = -(x - 1)2 y = -(x + 1)2
Answer:
The answer is D
Step-by-step explanation:
Carl tells his friend Logan about a new music download service.
Carl says that if you download x collections per month, your monthly cost will be 2(x + 10). Logan says the cost will be 2(x + 5). Who is correct?
A. Only Carl is correct.
B. Only Logan is correct.
C. Both Carl and Logan are correct.
D. Both Carl and Logan are incorrect.
Answer:
caral corect
Step-by-step explanation:
hes wrong not d
Which triangles are congruent by ASA
Answer: ΔHGF≅ ΔABC
Step-by-step explanation:
ASA congruence postulate says that if two angles and the included side of a triangle are congruent to two angles and the included side of next triangle then the triangles are congruent.In the given figure ΔABC and ΔHGF have the pair of two corresponding angles and the included sides are congruent.
i.e.[tex]\angle{C}\cong\angle{F}[/tex]
[tex]\overline{GF}\cong\overline{BC}[/tex]
tex]\angle{G}\cong\angle{B}[/tex]
Therefore , by ASA congruence postulate:-
ΔABC ≅ ΔHGF
In ΔTUV , there is only angle given . So there is no enough information to prove it by ASA.
It costs $6 to take 1 dog to the dog beach. It costs $1 more for each additional dog.
a hiker first hike down into a canyon 345 ft below sea level she then hike on her husband 50 ft of the side of the mountain what was the final altitude of the hiker
Need help with this one!
(Please help me!)
Which type of probability is determined by considering all possible outcomes, without actually testing them?
A. Empirical probability
B. Theoretical probability
C. Unpredictable probability
D. Random probability
Answer: B. Theoretical probability
Step-by-step explanation: Theoretical probability is based on calculations, and not actual tests.
if the area of a square is 225 cm2, what is the length of the diagonal
For the spring festival, the Math Club is selling rulers for $1 and compasses for $2.50. the club would like to sell as many items as they can to raise funds. they need to at least make $15 to break even. write an inequality to represent this situation. let r=#of rulers sold and c=#of compasses sold.... School rules state that the club can sell a maximum of items for the festival. Write another inequality for this constraint (limitation).
Final answer:
To represent the situation, the inequality is 1r + 2.50c >= 15. The constraint on the maximum number of items sold is r + c <= M.
Explanation:
To write an inequality representing the situation, we need to consider the cost and the number of items sold. Let's denote the number of rulers sold as r and the number of compasses sold as c. The cost of the rulers is $1 each and the cost of the compasses is $2.50 each. The Math Club needs to make at least $15 to break even, so the inequality is: 1r + 2.50c >= 15.
Now, let's consider the constraint or limitation on the maximum number of items sold. Let's assume the maximum number of items that can be sold is M. So the inequality for this constraint is: r + c <= M.
Final answer:
The student should write the inequality 1r + 2.5c ≥ 15 to represent the condition of making at least $15 from selling rulers and compasses. An additional constraint can be represented by the inequality r + c ≤ m, with m being the maximum number of items allowed to be sold.
Explanation:
The Math Club is looking to make at least $15 by selling rulers at $1 each and compasses at $2.50 each. To represent this situation as an inequality where r is the number of rulers and c is the number of compasses sold, we use the equation: 1r + 2.5c ≥ 15. This inequality ensures that the combination of rulers and compasses sold will bring in at least $15.
If there is a maximum number of items that the Math Club is allowed to sell, we can represent this as another inequality. Let's say the maximum number of items is m. Then, we can write the inequality as: r + c ≤ m, where m is the given maximum number of items that can be sold.
A student ate 3/20 of all candies and another 1.2 lb. Another student ate 3/5 of the candies and the remaining 0.3 lb. Altogether, what weight of candies did they eat?
Answer:
6 Pounds
Step-by-step explanation:
Above
whats the answer to this question
there are 200 end of the school year dance tickets available students who have perfect attendance are able to personage them in advance if 18 tickets were purchased in advance then what percent of the tickets were purchased in advance
The percentage of the tickets for the dance that were purchased in advance is 9%.
What is the percentage of the tickets that were bought in advance?Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign used to represent percentage is %.
Percent of advance tickets bought = (number of advance tickets / total number of tickets) x 100
(18 / 200) x 100 = 9%
To learn more about percentages, please check: https://brainly.com/question/25764815
If nick bought 5 apples for 4.45 what would be the cost for 7 apples
what decimal is equivalent to 6 %
An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 220 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.
Completely simplify spare root of 24x^6
Answer:
Assuming x ≥ 0:
[tex] \sqrt{24 {x}^{6} } = \sqrt{24} \sqrt{ {x}^{6} } = \sqrt{4} \sqrt{6} \sqrt{ {x}^{6} } = 2 {x}^{3} \sqrt{6} [/tex]
Can anybody correct me if I'm wrong? (I might be mixing my answers / questions up a bit) I also need more to be checked but anyways I'm very thankful for those who read into this.
the measures of two complementary angles have a ratio of 2:7 . what is the measure of the smaller angle
Answer:
The smaller angle is 20 degrees.
Explanation:
Complementary angles are two angles (or more) whose sum is 90 degrees.
If two angles have a sum of 90 degrees and their ratio is 2:7, we must determine which two numbers when added together would yield this proportion?
60 + 30 = 90 but 60:30 is a 6:3 ratio which simplifies to 2:1.
45 + 45 = 90 but 45:45 is a 1:1 ratio.
50:40 = 90 but 50:40 is a 5:4 ratio.
10 + 80 = 90, but 10:80 is a 1:8 ratio. We're getting closer!
20 + 70 = 90, and 20:70 can be simplified to 2:7 when you divide each number in the ratio their greatest common factor (GCF) of 10.
Therefore, the two complementary angles would be 20° and 70°, the smaller of which would be 20°
Rewrite this logarithm as a subtraction of logs
Log11 (29/11)
Final answer:
To rewrite the given logarithm as a subtraction of logs, use the property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.
Explanation:
The given logarithm is log11 (29/11). To rewrite this as a subtraction of logs, we can use the property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.
So, log11 (29/11) can be rewritten as log11 (29) - log11 (11).
WILL MARK BRAINLIST!!!!
Just need question 1 (i) and 2 (i), (ii)
what is the value of 6/x +2x to the second power when x is 3
2(2x+9)=50 simplifyed
What is the height of a rectangular prism that has a volume of 192 cubic feet and a base with an area of 48 square feet? Explain your work.
The height of the rectangular prism is 4 feet.
To find the height of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:
[tex]\[ \text{Volume} = \text{Base Area} \times \text{Height} \][/tex]
Given that the volume of the rectangular prism is 192 cubic feet and the base area is 48 square feet, we can set up the equation as follows:
[tex]\[ 192 = 48 \times \text{Height} \][/tex]
To solve for the height, we divide both sides of the equation by the base area:
[tex]\[ \text{Height} = \frac{192}{48} \][/tex]
[tex]\[ \text{Height} = 4 \][/tex]
Therefore, the height of the rectangular prism is 4 feet.
Which of the following is not a valid probability?
A 0.3
B 1
C 0
B 106
Which statement is true about the distribution? A line ranging from 0 to 120 with boxes between 15 and 28, 28 and 34, 34 and 40, and 40 and 48. The IQR is the best measure of variability because the distribution has an outlier. Either the IQR or the range are good measures of variability because the distribution has an outlier. Either the IQR or the range are good measures of variability because the distribution has no outliers. The range is the best measure of variability because the distribution has an outlier.
Answer: The answer is A. "The IQR is the best measure of variability because the distribution has an outlier."
Step-by-step explanation:
4.5 divided by 0.5+0.1 in computation words
Explanation of dividing 4.5 by 0.5+0.1 in computation words.
4.5 divided by 0.5+0.1 can be written as:
4.5 / (0.5 + 0.1)
To solve this, we first add 0.5 + 0.1 to get 0.6. Then, we divide 4.5 by 0.6 to find the result.
The result of the computation is 7.35.
To compute the given expression[tex]\(14.5 \times 0.5 + 0.1\):[/tex]
Multiplication :
- Multiply [tex]\(14.5\)[/tex] by [tex]\(0.5\).[/tex]
- [tex]\(0.5\)[/tex] represents half, so you're essentially halving 14.5.
Half of [tex]\(14.5\) is \(7.25\).[/tex]
Addition :
- Now add [tex]\(0.1\) to \(7.25\).[/tex]
- The addition gives [tex]\(7.25 + 0.1 = 7.35.[/tex]
Thus, the result of the computation is 7.35.
Complete question : Write the computation in words: 4.5 divided by 0.5+0.1
Jane buys People magazine at Walmart each week for $4.99. A 52 week subscription to the magazine is $203.84. How much would she save each week per magazine if she signed up for the subscription?
please help i will be the happiest person alive
100 points and branliest
Answer:
Q1: The correct option is: 16
Q2: The correct options are: [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]
Q3: The correct option is: [tex]\overline{BC}=12; \overline{EF}=16[/tex]
Step-by-step explanation:
Question 1:
As here [tex]\triangle RST\sim \triangle MNO[/tex], so the ratio of the corresponding sides will be equal. That means.....
[tex]\frac{RS}{MN}=\frac{RT}{MO}\\ \\ \frac{8}{x}=\frac{6.5}{13}\\ \\ 6.5x=8*13\\ \\ x=\frac{8*13}{6.5}=16[/tex]
So, the length of the side [tex]x[/tex] will be 16.
Question 2:
If two triangles are similar, then the ratio of their corresponding sides should be equal. So, here the ratios of the corresponding sides are............
[tex]\frac{AB}{DE}=\frac{1}{3} \\ \\ \frac{BC}{EF}=\frac{2}{6}=\frac{1}{3}\\ \\ \frac{AC}{DF}=\frac{2}{7}[/tex]
So we can see that the ratio of side [tex]AC[/tex] and side [tex]DF[/tex] is not equal with the other ratios.
Thus, the proportions that show the triangles are not similar: [tex]\frac{AB}{DE}=\frac{AC}{DF}[/tex] and [tex]\frac{AC}{DF}=\frac{BC}{EF}[/tex]
Question 3:
Given that, [tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]
The ratio of [tex]AB[/tex] and [tex]DE[/tex] is given as [tex]\frac{3}{4}[/tex]
So, the ratio of [tex]BC[/tex] and [tex]EF[/tex] will be also [tex]\frac{3}{4}[/tex]
Among the four options, if [tex]BC=12[/tex] and [tex]EF=16[/tex], only then the ratio will be [tex]\frac{3}{4}[/tex]
[tex]\frac{BC}{EF} =\frac{12}{16}= \frac{3}{4}[/tex]
So, the lengths of [tex]BC[/tex] and [tex]EF[/tex] could be 12 and 16 respectively.
Answer:
the correct answer is c
Step-by-stepth explanation:
PLEASE HELP, ASAP!
Eumin pays $3.56 for 4 juice boxes.
How much would Eumin pay for 7 juice boxes?
Enter your answer in the box.