Answers
to solve this,
Step 1
the purpose of this method is eliminate a variable by adding the two equations, to do this, you need to be sure that the add will make that variable disappear.
Let's see y
\(\begin{gathered} \frac{y}{3} \\ \text{and} \\ -\frac{y}{2} \end{gathered}\)to eliminate y make
\(\begin{gathered} multiply\text{ the first equation }by\text{ }\frac{1}{2} \\ \\ \frac{5x}{6}+\frac{y}{3}=\frac{4}{3}\text{ by }\frac{1}{2} \\ \frac{1}{2}\cdot\frac{5x}{6}+\frac{1}{2}\cdot\frac{y}{3}=\frac{1}{2}\cdot\frac{4}{3} \\ \frac{5x}{12}+\frac{y}{6}=\frac{2}{3}\text{ equation (3)} \\ \end{gathered}\)Now, multiply the second equation by 1/3
\(\begin{gathered} \frac{2x}{3}-\frac{y}{2}=\frac{11}{6}\text{ by }\frac{1}{3} \\ \frac{1}{3}\cdot\frac{2x}{3}-\frac{1}{3}\cdot\frac{y}{2}=\frac{1}{3}\cdot\frac{11}{6} \\ \frac{2x}{9}-\frac{y}{6}=\frac{11}{18}\text{ equation (4)} \end{gathered}\)Now, add equations 3 and 4
\(\begin{gathered} \frac{5x}{12}+\frac{y}{6}=\frac{2}{3} \\ \frac{2x}{9}-\frac{y}{6}=\frac{11}{18} \\ x(\frac{5}{12}+\frac{2}{9})=\frac{2}{3}+\frac{11}{18} \\ x(\frac{23}{36})=\frac{23}{18} \\ x=\frac{23\cdot18}{36\cdot23} \\ x=\frac{414}{828} \\ \\ x=\frac{1}{2} \\ \end{gathered}\)Now, with this value of x, find y, replacing in the equation 1 or 2
\(\begin{gathered} \frac{2x}{3}-\frac{y}{2}=\frac{11}{6} \\ \frac{2(\frac{1}{2})}{3}-\frac{y}{2}=\frac{11}{6} \\ \frac{1}{3}-\frac{y}{2}=\frac{11}{6} \\ -\frac{y}{2}=\frac{11}{6}-\frac{1}{3} \\ -\frac{y}{2}=\frac{3}{2} \\ y=\frac{3\cdot-2}{2} \\ y=-3 \end{gathered}\)so, the solution is x=0.5 and y =-3
I really hope this helps
Related Questions
5y - 10 = -25A) y = 3 B) y = 7 C) y = -3 D) y = -7
Answers
We want to solve the equation;
\(5y-10=-25\)We start by collecting like terms;
\(\begin{gathered} 5y=-25+10 \\ 5y=-15 \\ y=-\frac{15}{5} \\ y=-3 \end{gathered}\)Which expression shows a way to find 356+495?
A. 300+400+50+90+10
B. 300+50+6+400+5
C. 700+140+11
D. 700+14+11
Answers
The correct way to find the addition is,
356 + 495 = 700 + 140 + 11
Option C is correct.
Addition:The given expression is,
356+495
It can be written in different form.
356+495 = 300 + 400 + 56 + 95
356 + 495 = 300 + 400 + 140 + 11
356 + 495 = 700 + 140 + 11
Hence, above way to find the addition is correct.
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Find the value of x from the given figure.
Answers
The value of x from the given figure is given as follows:
144º.
What is a straight angle?An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.
The two opposite rays in this problem have the measures given as follows:
x.x/4.Hence the equation to find the value of x is given as follows:
x + x/4 = 180
x + 0.25x = 180
1.25x = 180
x = 180/1.25
x = 144º.
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3x the sum of 3 and some number is 24 what is the number
Answers
Answer:
×=8
Step-by-step explanation:
24 divide by 3 is 8
8 x 3 is 24
Which phrases relate to perimeter? Check all that apply.
refers to the distance around a figure
given in square units
used to find the amount of fencing
o used to find the amount of carpeting
estimated by counting the squares inside
calculated by adding the side lengths
Answers
Answer:
(a) refers to the distance around a figure
(c) used to find the amount of fencing
(e) estimated by counting the squares inside
(f) calculated by adding the side lengths
Step-by-step explanation:
In the simplest term, the perimeter of a given figure is the distance around that figure. This also means that the perimeter of a figure can be found by adding the lengths of all its sides.
If perimeter is the distance around a figure, then it could be measured in any specified units of length e.g meter, yard, inch e.t.c.
Perimeter can also be estimated by counting the squares inside a given enclosure.
A practical application of perimeter is that it comes to play when, for example, there is a need to build a fence around an area.
PS:
For other options;
=> Perimeter is not given in square units. That is rather typical of area
=> Perimeter is not used to find the amount of carpeting. That is also typical of area
Answer:
a c f
Step-by-step explanation:
What is the quotient of 20/8 divided by 5/12?
85/12
12
16
25/9
Answers
Answer:
6 (None of the above)
Step-by-step explanation:
Let's solve the problem,
→ 20/8 ÷ 5/12
→ 20/8 × 12/5
→ 240/40 = 6
Hence, the answer is 6.
mary blake is considering whether to buy stocks or bonds. she has a good understanding of the pros and cons of both. the stock she is looking at is trading at $66.75, with an annual dividend of $3.50. meanwhile, the bond is trading at 92.50%, with an annual interest rate of 11.5%.calculate for mary her yield for the stock and the bond.note: round your answers to the nearest tenth percent.
Answers
The yield Mary Blake makes from investing in the stock is about 5.24%, and the yield from the bonds is 11.5%, while the value of the amount the bond yields is $106.375
\({}\) Yield
Stock \({}\) 5.24%
Bond \({}\) 11.5%
What is an investment?An investment is the an input of (financial) capital into the acquisition of assets that will generate future revenue.
The amount at which the stock Mary Blake is looking at is trading = $66.75
The annual dividend of the stock = $3.50
The amount at which the bond is trading = 92.50% of par
The annual interest rate from the bond = 11.5%
Mary Blake's percentage yield from investing in the stock can be found as follows;
Yield percentage = (3.5/66.75) × 100 ≈ 5.24%
The percentage yield from the bond as indicated in the question is 11.5%
The yield amount from the bond is found as follows;
Amount of the bond = $1000 × 92.50 = $925.0
The yield amount = 11.5% × $925.0 = $106.375
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Find the value of x and y variable in the following parallelogram
Answers
Answer:
y + 5 = 3y - 1
2y = 6, so y = 3
4x - 2 = x + 10
3x = 12, so x = 4
A ladder 10 ft long rests against vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.7 of ft/s, now fast (in rad/s) is
the angle (in radians) between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the
angle's rate of change when the bottom of the ladder 8 ft from the wall.)
Wall
Answers
Check the picture below.
\(cos(\theta )=\cfrac{x}{10}\implies \stackrel{chain~rule}{-sin(\theta )\cdot \cfrac{d\theta }{dt}}=\cfrac{1}{10}\cdot \cfrac{dx}{dt} -sin(\theta )\cdot \cfrac{d\theta }{dt}=\cfrac{1}{10}(0.7)\)
\(\cfrac{d\theta }{dt}=\cfrac{0.07}{-sin(\theta )}~\hfill \stackrel{\textit{when the ladder's bottom is 8ft, x = 8}}{sin(\theta )=\cfrac{8}{10}\implies sin(\theta )=\cfrac{4}{5}} \\\\\\ \cfrac{d\theta }{dt}=-\cfrac{0.07}{~~ \frac{4 }{5 } ~~}\implies \implies \cfrac{d\theta }{dt}=-0.07\cdot \cfrac{5}{4}\implies {\Large \begin{array}{llll} \cfrac{d\theta }{dt}=-0.0875~\frac{rad}{s} \end{array}}\)
the rate is negative because the angle is decreasing as the ladder slides outwards.
A bag of 13 marbles contains 5 marbles with red on them. 6 with blue on them, 6 with green on them, and 5 with red and green on them. What is the probability that arandomly chosen marble has either green or red on it? Note that these events are not mutually exclusive. Express your answer as a fraction in lowest terms or a decimalrounded to the nearest millionth.
Answers
Answer:
P = 6/13
Explanation:
There are 13 marbles in total. 5 of them are red and green, there are 5 marbles with red on them and there are 6 marbles with green on them.
Those 5 marbles with red on them are the same 5 marbles with red and green.
And from the 6 marbles with green on them, 5 of them are the same 5 with red and green.
So, the total number of marbles with red or green is 6 because there are:
5 marbles with red and green and 1 marble with red on it.
Therefore, the probability to chose a marble that has either green or red on it is:
\(P=\frac{6}{13}\)So, the answer is 6/13
Why was math created
Answers
SOLUTION:
Step 1:
In this quesdtion, we are meant to explain the topic:
Why was Math created?"
Step 2:
The details of the solution are as follows:
1. Mathematics is a body of knowledge and knowledge and practice, that is derived from the contributions of thinkers throughout the ages and across the globe.
2. It gives us a way to understand patterns, to quantify relationships, and to predict the future.
3. Math helps us understand the world — and we use the world to understand math.
4. Excellent for your brain: Creative and analytical skills are highly desired by employers.
5. It has a lot of real-world applications.
6. It helps in better problem-solving skills.
7. Mathematics is needed in almost every career and profession.
8. Mathematics helps understand the world better.
9. Mathematics is a universal language.
10. Numbers help us understand the world, and Mathematics helps us understand numbers.
The real-life applications of Mathematics are endless.
We are surrounded by numbers, equations and algorithms – especially in this age of data science, with huge data sets that can only be understood through statistical models and analysis.
Answer:
Maths was invented to understand the world and to make measurements, do calculations etc. make and measure shapes, measure angles, and to use these things in real life. The Egyptians used the Pythagoras theorem to accurately make their pyramids.
Find an equation of the vertical line passing through the point (-4, 0).
Answers
The equation of the vertical line passing through the point given as (-4, 0) is x = -4
How to determine the equation of the vertical line passing through the point?The point is given as:
(-4, 0)
Rewrite the point as follows:
(x, y) = (-4. 0)
Vertical lines do not intersect the y-axis.
So, we remove the y coordinate
So, we have
x = -4
Hence, the equation of the vertical line passing through the point given as (-4, 0) is x = -4
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What two numbers add up to -2 and multiple to 10
Answers
There are no two Real numbers that add up to -2 and multiply to 10.
The numbers that add up to -2 and multiply to 10, we can use algebraic methods. Let's denote the two numbers as x and y. Based on the given conditions, we can set up two equations:
Equation 1: x + y = -2
Equation 2: x * y = 10
To solve this system of equations, we can use substitution or elimination methods. Let's solve it using the substitution method:
1. Solve Equation 1 for x:
x = -2 - y
2. Substitute the value of x in Equation 2:
(-2 - y) * y = 10
3. Simplify the equation:
-2y - y^2 = 10
4. Rearrange the equation to standard form:
y^2 + 2y + 10 = 0
5. Since the equation is a quadratic equation, we can apply the quadratic formula:
y = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 2, and c = 10.
6. Calculate the discriminant: b^2 - 4ac:
2^2 - 4(1)(10) = 4 - 40 = -36
7. Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, there are no real numbers that satisfy both conditions of adding up to -2 and multiplying to 10.
In conclusion, there are no two real numbers that add up to -2 and multiply to 10.
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Help please !!!! This is really hard
Answers
Answer:
Option -c :5^ -12 . 2^ 40
Step-by-step explanation:
( 5^6 . 2^8 )( 5^-2 . 2^5 )
( 5^6 . 5^-2 ) ( 2^8 . 2^5 )
5^ -12 . 2^ 40
Option -c : 5^ -12 . 2^ 40
I hope im right!!
A radioactive compound with mass 260 grams decays at a rate of 3.8% per hour. Which equation represents how many grams of the compound will remain after 8 hours?
Answers
Approximately 138.3 grams of the compound will remain after 8 hours. The decay of a radioactive compound is an exponential process, which can be modeled by the equation:
N(t) = N₀ * e^(-λt)
where N(t) is the amount of the compound remaining at time t, N₀ is the initial amount of the compound, λ is the decay constant, and e is the mathematical constant known as Euler's number.
To find the amount of the compound remaining after 8 hours, we need to plug in the given values into the equation above. We know that the initial mass of the compound is 260 grams, and the decay rate is 3.8% per hour, which means that the decay constant λ is equal to 0.038. Therefore, the equation becomes:
N(8) = 260 * e^(-0.038 * 8)
Simplifying this equation gives:
N(8) = 260 * e^(-0.304)
N(8) ≈ 138.3 grams
Therefore, approximately 138.3 grams of the compound will remain after 8 hours.
It's important to note that this calculation assumes that the decay rate remains constant over time, which may not always be the case in reality. Additionally, the actual amount of the compound remaining may vary due to experimental error or other factors.
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Use the figure to answer the questions.
(a) Describe the relationship among the lengths of the segments formed by two secants. You may use words and/or and equation.
(b) Suppose CG = 3 in, CH = 2 in, and GE = 5 in, is it possible to find the length of DH? If so, show how to find the length. If not, explain why not.
Help would be appreciated!
Answers
Based on the intersecting secants theorem:
a. CG*CE = CH*CD
b. length of DH = 10 in.
What is the Intersecting Secants Theorem?When an exterior point is formed by two secant segments to a circle, the product of the length of one secant segment and its external segment will always be equal to the product of the length of the other secant segment and its external segment, according to the intersecting secants theorem.
a. Based on the intersecting secants theorem, the relationship that describes the lengths of the segments formed by the two secants is:
CG*CE = CH*CD
b. Given the following lengths:
CG = 3 in, CH = 2 in, and GE = 5 in
CE = CG + GE = 3 + 5 = 8 in.
CD = CH + DH = 2 + DH
Substitute into CG*CE = CH*CD:
3*8 = 2*(2 + DH)
24 = 4 + 2DH
24 - 4 = 2DH
20 = 2DH
20/2 = DH
DH = 10 in.
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3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
Answers
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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complete the following statements. in general, % of the values in a data set lie at or below the 70th percentile. % of the values in a data set lie at or above the 20th percentile.. if a sample consists of 600 test scores, of them would be at or below the 86th percentile. if a sample consists of 600 test scores, of them would be at or above the 62th percentile.
Answers
If a sample consists of 600 test scores, 516 of them would be at or below the 86th percentile. If a sample consists of 600 test scores, 228 of them would be at or above the 62th percentile.
What is percentile?A percentile is a score that compares a specific score to the scores of the other members of a group. It displays the proportion of other scores that a given score outperformed. For instance, if you have a test score of 75 and are placed in the 85th percentile, it signifies that your score is greater than those of 85% of other test takers.
Given that,
In general, 70 % of the values in a data set lie at or below the 70th percentile.
20 % of the values in a data set lie at or above the 20th percentile.
Generally percentile defines the percentage of a data set that is below or at a value that is being considered.
Hence the percentage of the values of a data set that lies below or at the 16th percentile is 16%
Also the values of a data set that lies below or at the 24th percentile is 24%
Given a sample of 600 test scores , the number of test scores that will be at or below the 86th percentile is 86% of 600 which is mathematically represented as:
K = \(\frac{86}{100}\) × 600
K = 516 test scores
Given a sample of 600 test scores , the number number of test scores that will be above the 62 th percentile is (100 - 62 = 38 )% of 600 which is mathematically represented as:
a = \(\frac{38}{100}\) × 600
a = 228 test scores.
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PLEASE HELP MEEEE MARK BRAINLEST What is the coefficient of the variable in the expression 4 - 3x - 7+ 6? Answers 0-7 O-3 4 06
Answers
2. In triangle ABC, SA is a right angle, and m B = 45°
(1 point)
C
16 ft
A
B.
What is the length of BC? If your answer is not an integer, leave it in simplest radical form.
O 16 ft
O 16.2 ft
O 16.5 ft
O 32 ft
Answers
Answer:
\(16\sqrt{2}\)
Step-by-step explanation:
The given triangle shown is a 45-45-90. We can use this picture attached to figure out BC.
n in this case is 16ft
Based on the picture, we can get BC's length, which is n\(\sqrt{2}\)
BC = \(16\sqrt{2}\)
Among 2165 passenger cars in a particular region, 235 had only rear license plates. Among 330 commercial trucks, 50 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.10 significance level. Identify the P-value. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks. Let a success be a vehicle that only has a rear license plate Group of answer choices
Answers
Using the z-distribution, it is found that the p-value is of 0.0192.
At the null hypothesis, it is tested if commercial trucks owners do not violate laws requiring front license plates at a higher rate than owners of passenger cars, that is, the subtraction is of at most 0, hence:
\(H_0: p_2 - p_1 \leq 0\)
At the alternative hypothesis, it is tested if commercial truck owners violate the laws more, that is, the subtraction is positive, hence:
\(H_1: p_2 - p_1 > 0\)
For each sample, the size, the proportion and the standard error are given by:
\(n_1 = 2165, p_1 = \frac{235}{2165} = 0.1085, s_1 = \sqrt{\frac{0.1085(0.8915)}{2165}} = 0.0067\)
\(n_2 = 330, p_1 = \frac{50}{330} = 0.1515, s_1 = \sqrt{\frac{0.1515(0.8485)}{330}} = 0.0197\)
For the distribution of differences, the mean and the standard error are given by:
\(\overline{p} = p_2 - p_1 = 0.1515 - 0.1085 = 0.043\)
\(s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0067^2 + 0.0197^2} = 0.0208\)
The test statistic is given by:
\(z = \frac{\overline{p} - p}{s}\)
In which \(p = 0\) is the value tested at the null hypothesis.
Hence:
\(z = \frac{\overline{p} - p}{s}\)
\(z = \frac{0.043 - 0}{0.0208}\)
\(z = 2.07\)
The p-value is found using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is more than a value, with z = 2.07.
Using the calculator, the p-value is of 0.0192.A similar problem is given at https://brainly.com/question/15545277
2. A coffee maker and a juice maker are making beverages. The rate at
which the coffee is being made is given by y = 6x, where y represents the
amount of coffee in mL and x represents the time passed in seconds. The
amount of juice that has been made at different times is summarized in
the table.
thing Company
A. At what rate is the coffee maker making coffee?
B. At what rate is the juice maker making juice?
C. Is juice or coffee being made at a faster rate?
Time (s)
0
1
2
3
Juice (mL)
0
8
16
24
Answers
(A) The rate of making coffee by coffee maker is 6 mL/second.
(B) The rate of making juice by juice maker is 8 mL/second.
(C) Juice is being made at a faster rate.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
The rate of coffee made by coffee maker is represented by,
y = 6x (1)
Here, y represents the amount of coffee in mL and x represents the time passed in seconds.
Also, The rate of juice made by juice make can be represented by the given table as,
k = 8h (2)
Here, k represents the amount of juice in mL and h represents the time passed in seconds.
(A)
To find the rate of making coffee, solve the equation (1),
y = 6x
⇒ y/x = 6 mL/second
The rate of making coffee by coffee maker is 6 mL/second.
(B)
To find the rate of making juice, solve the equation (2),
k = 8h
⇒ k/h = 8 mL/second
The rate of making juice by juice maker is 8 mL/second.
(C)
Since, the juice is made at the rate of 8 mL/second and the coffee is made at the rate of 6 mL/second.
Therefore, juice is being made at a faster rate.
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A regular heptagon has an apothem of approximately 5.2 cm and a perimeter of approximately 35.0 cm.Find the area of the heptagon.
Answers
Answer:
\(91\operatorname{cm}^2\)Explanation:
Step 1. The information that we have about the regular heptagon is:
The apothem, which we will call ''a'':
\(a=5.2cm\)The perimeter, which we will call ''P'':
\(P=35cm\)Step 2. The formula to find the area of any regular polygon (in this case a heptagon) is:
\(A=\frac{P\times a}{2}\)Where A is the area, P is the perimeter and a is the apothem.
Step 3. Substitute the values of P and a into the formula:
\(A=\frac{35cm\times5.2cm}{2}\)Solving the operations we find the area:
\(\begin{gathered} A=\frac{182cm^2}{2} \\ \\ A=\boxed{91\operatorname{cm}^2} \end{gathered}\)Answer:
\(91\operatorname{cm}^2\)
¿De qué número 64 es el 80%?
Answers
32 = 25t ^ 2 - 4 round to the nearest tenth
Answers
Answer:
t = 1.2, -1.2
32 + 4 = 25t^2
36 = 25t^2
Root of 36 = root of 25t
6 = 5t
6/5 = t
Therefore t = +-1/2 or +-6/5
Write and solve an equation to find the value of x.
Answers
The value of x for each item is given as follows:
28. x = 5.
29. x = 3.44.
How to obtain the value of x in each item?For item 28, we apply the crossing chord theorem, which states that the products of the parts of the chords are equal, hence the value of x is obtained as follows:
16x = 10 x 8
16x = 80
x = 5.
For item 29, we apply the two secant theorem, hence the value of x is obtained as follows:
10(x + 10) = 12(12 + 25)
10x + 100 = 444
10x = 344
x = 3.44.
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It costs $35 per hour to rent a boat at the lake. You also need to pay a $25 fee for safety equipment. You have $200. For how long can you rent the boat? CLEAR CHECK 6.6 hours 5 hours 313 hours 8 hours
Answers
What type of observation is this?
The cheese looks furry.
Answers
Answer:
This is a qualitative observation
Step-by-step explanation:
It is observing the qualities of the cheese as opposed to quantity which would include numbers or data.
What is the sum of m and the number after it
Answers
The algebraic representation of the expression is (m + n)
AlgebraSum means addition (+)The number after m is nsum of m and the number after it
= m + n
Therefore, the algebraic representation of the expression is (m + n)
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of 30 students , 1/3 play sports. Of those who play sports, 2/5 play soccer. How many students play soccer?
Answers
Answer:
10 ppl play sport. 2/5= 4/10 so 4 ppl play soccer
Step-by-step explanation: