Given :
Two equation [tex]x_1 +5x_2 =7[/tex] and [tex]x_1 - 2x_2 = -2[/tex] .
To Find :
The point of intersection of these lines .
Solution :
We will use elimination method :
From equation 1 :
[tex]x_1=7-5x_2[/tex]
Putting value of [tex]x_1[/tex] in equation 2 we get :
[tex](7-5x_2)-2x_2=-2\\\\7-7x_2=-2\\\\x_2=\dfrac{9}{7}[/tex]
Putting value of [tex]x_2[/tex] in equation 1 we get :
[tex]x_1+5\times \dfrac{9}{7}=7\\\\x_1=\dfrac{4}{7}[/tex]
Therefore , point of interaction is [tex](\dfrac{4}{7},\dfrac{9}{7})[/tex] .
Hence , this is the required solution .
The point is: [tex]\left(x_{1},x_{2}\right)=\left(\frac{4}{7},\frac{9}{7}\right)[/tex]
We will solve the given system of equations.
Subtract the second equation from the first one:
[tex]\left(x_{1}+5x_{2}\right)-\left(x_{1}-2x_{2}\right)=7-\left(-2\right)\\x_{1}+5x_{2}-x_{1}+2x_{2}=7+2\\7x_{2}=9\\x_{2}=\frac{9}{7}[/tex]
Then we plug [tex]x_{2}=\frac{9}{7}[/tex] in the given first equation.
[tex]x_{1}+5x_{2}=7\\x_{1}+5\left(\frac{9}{7}\right)=7\\x_{1}+\frac{45}{7}=7\\x_{1}=7-\frac{45}{7}\\x_{1}=\frac{4}{7}[/tex]
So the point is: [tex]\left(x_{1},x_{2}\right)=\left(\frac{4}{7},\frac{9}{7}\right)[/tex]
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Solve each system of equations of equations.
x + y = -6
2x - y = 3
Answer:
x = -1, y = -5
Step-by-step explanation:
x + y = -6
2x - y = 3
Add the two equations together to eliminate y
x + y = -6
2x - y = 3
------------------
3x = -3
Divide by 3
3x/3 = -3/3
x = -1
Now find y
x+y = -6
-1+y = -6
Add 1 to each side
-1+1 +y = -6+1
y = -5
Evaluate81−−√4 help ......................
Answer:
=81e^2lva^2ut-2
Step-by-step explanation:
Samara Park gets $0.25 for each pound of apricots she dries. How much will she be paid if she dries 16.4 pounds?
Samara will be paid $4.10 for drying 16.4 pounds of apricots.
How to calculate payment?To calculate the payment for the purchase of the item, we can use the formula:
Payment = Rate × Amount
Here, the rate is the amount paid per pound and the amount is the total number of pounds item.
To calculate Samara's payment for drying apricots, we can use the formula:
Payment = Rate × Amount
As per the question, the rate is $0.25 per pound, and the amount is 16.4 pounds.
So, substitute these values into the formula:
Payment = $0.25 × 16.4
Multiply $0.25 by 16.4:
Payment = $4.10
Therefore, Samara will be paid $4.10 for drying 16.4 pounds of apricots.
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Which is the best estimate for the percent equivalent to 3/8?
A.) 26% B.) 27% C.) 37% D.) 38%
Answer:
C.) 37%
Explanation:
To find this out, turn 3/8 into decimal form, (0.375).
Now, turn each percent into standard form. (Also decimal form)
26% = 0.26, 27% = 0.27, 37% = 0.37, and 38% = 0.38.
The decimal closest to 0.375 is 37%.
Hope this helped! ♥♥
Mark Me as Brainliest Please! :3
Answer:
D.) 38%
Step-by-step explanation:
Convert the fraction into a decimal:
[tex]\frac{3}{8}=0.375[/tex]
Convert the decimal into a percent:
[tex]0.375*100=37.5[/tex]
0.375 = 37.5%
Round the percent:
37.5% ≈ 38%
Option D is the best answer.
Hope this helps.
Dr. Gordon has a scale drawing of a building site. The drawing uses the scale 2 in. on the drawing for every 100 ft on the building site. Dr. Gordon marks a 6 in. -by-3.2 in. section of the drawing to show the section she will search. What is the area of the section she will search? Show your work.
Answer:
48000
Step-by-step explanation:
6÷2= 3 in.
3×100= 300 in.
3.2÷2=1.6 in.
1.6×100= 160 in.
A= 160×300= 4800 in.
The required area of the section marked by Dr. Gordon is 48,000 feet².
Given that
Dr. Gordon has a scale drawing of a building site.
The drawing uses the scale 2 in. on the drawing for every 100 ft on the building site.
Dr. Gordon marks a 6 in. -by-3.2 in.
The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Here,
Dr. Gordon marks a 6 in. -by-3.2 in
Length = 6 in
Length= 300 ft (since 2 in = 100 ft)
Width = 3.2 in
Width = 160 ft
Now the required area of the section is = length x width
= 300 * 160
= 48000 feet²
Thus, the required area of the section marked by Dr. Gordon is 48,000 feet².
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Now, look at the set of integers. Complete the table for the closure property if integers under the four operations.
Answer:
See below.
Step-by-step explanation:
Addition: closed
Example: -5 + 10 = 5, and -5, 10, and 5 are all integers
Subtraction: closed
Example: 10 - 8 = 2, and 10, 8, and 2 are all integers
Multiplication: closed
Example: -4 * 7 = -28, and -4, -7 and -28 are all integers
Division: not closed
Example: 5/2 = 2.5, and 2.5 is not an integer, although 2 and 5 are integers
The set of integers is closed under addition, subtraction, and multiplication because any addition, subtraction, or multiplication of integers always results in an integer.
The set of integers is not closed under division because a division of integers does not always result in an integer.
What is the median of 6.5, 4.5, 6.5, 4.5, 5, 4.5, 9, 3.5
4.75 is the answer list from least to greatest find the number in the middle
Use the ogive to approximate (a) the number in the sample, (b) the location of the greatest increase in frequency.
Answer:
Step-by-step explanation:
A). Number of samples given in the ogive = Number of points given n the graph
Number of points plotted on the graph = 16
Therefore, number of samples given = 16
B). Frequency at a point where weight of the pumpkins is 23.5 = 10
Frequency at a point where weight of the pumpkin is 24.5 = 23
Increase in frequency = 23 - 10 = 13
None other points have the increase more than the given points.
Location of the greatest increase in the frequency is between the weights 23.5 - 24.5 pounds.
The number of samples is 16, and the location of greatest increase in frequency is 23.5 to 24.5.
We are provided with an ogive curve. In the x-axis, we have weight in pounds and y-axis represents frequency.
(a).
Now, the number of points on the ogive represents the number of sample.
So, the number of points on the curve is 16 which is also the number of samples.
(b).
The greatest increase in frequency is represented in the range 23.5 to 24.5.
The greatest hike in frequency is about 10.
Therefore, the number of samples is 16, and the location of greatest increase in frequency is 23.5 to 24.5.
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When did the United States first establish its measuring system, and who was responsible for
picking the system?
Answer:
1975 Thomas Jefferson
Step-by-step explanation:
7/5 mile / 2/3 hour worked out please
Steps to solve:
7/5 ÷ 2/3
~Dot
7/5 * 2/3
~Flip
7/5 * 3/2
~Multiply
21/10
Best of Luck!
Answer:
21/10 = 2.1 mile/hour
Step-by-step explanation:
(a/b) ÷ (c/d) = (a*d) ÷ (b*c)
then:
(7/5) ÷ (2/3) = (7*3) ÷ (5*2) = 21/10 mile/hour
For 50 points x³+y³+z³=8
Answer:
x = 2
y = - z (for example 2)
Step-by-step explanation:
2³+2³+(-2)³= 8+8-8=8
Answer:
arrg
Step-by-step explanation:
plss help asap im on a time limit
Answer: the first one
Step-by-step explanation: just trust me ;)
Solve the following system of equations algebraically:
y= 16x2 + 9x – 5
y = –2 – 6
Step-by-step explanation:
Is the x between 16 and 2 for multiplication or are you using it as a variable??
A group of 23 friends gets together to play a sport. First, people must be divided into teams. Each teams has to have exaclty 4 players, and no one can be on more than one team. How many teams can they make?
Answer:
5
Step-by-step explanation:
What is 24.541 divided by 6
A computer software company conducted a telephone survey asking its customers how the software could be improved. Assume the survey was conducted by asking the questions below. Each of the questions defines a variable of interest to the company. Classify the data generated for each variable as quantitative or qualitative. Justify your classification.
Required:
a. Is the variable of interest defined by the question "How many hours per week do you use our software?" quantitative or qualitative?
b. Is the variable of interest defined by the question "For how many years have you been using our software?" quantitative or qualitative?
Answer:
Quantitative
Quantitative
Step-by-step explanation:
Given the following research questions to classify:
a. Is the variable of interest defined by the question "How many hours per week do you use our software?
This is a quantitative variable, because the question requires a numerical response such as 5. 10, 2 4 and so on upon which numerical or statistical calculations such as addition, subtraction, range, mean and so on can be performed.
B.) For how many years have you been using our software?
This is also a quantitative variable as the question expects a response of Numeric characteristic such as 2, 3 and so on depending on the number of years the respondent has been using the software
What value of q makes the equation true? -8=32-5q
Answer:
8
Step-by-step explanation:
There is a number such that four times the number plus 3 is equal to 19. Find the number.
An equation is formed of two equal expressions. The number is 4.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that there is a number such that four times the number plus 3 is equal to 19.
Let the number be M.
Given that there is a number such that four times the number plus 3 is equal to 19. Therefore, We can write it as,
4M + 3 = 19
Now, we can write,
4M + 3 = 19
Subtract 3 on both sides
4M + 3 - 3 = 19 - 3
4M = 16
Divide both sides by 4,
4/4 M = 16/4
M = 4
Thus, the number is 4.
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O produtor rural Ricardo Antunes Peixoto, 55 anos, teve uma surpresa enquanto perfurava um poço artesiano em sua fazenda, na zona rural de Brasília de Minas (MG). "Não saiu água, mas saiu fogo", diz, espantado. Uma equipe com cinco operários de uma empresa especializada trabalhou durante dois dias na propriedade para abrir o poço de água, mas, após escavarem 204 metros, o que encontraram foi um produto inflamável, que seria gás natural. O dono da fazenda Lagoa Misteriosa espera lucrar com a descoberta da reserva de gás. "Pelo menos, que se têm notícias no estado, este é o primeiro caso. Agora, com o dinheiro que eu vender o gás, vou abrir [um novo poço] para ter a minha água". Disponível em: . Acesso em: 12 abr. 2013. Considerando a combustão completa do metano, nas CNTP, determine a energia liberada na queima de 224 L de metano que foi em encontrado no poço desse agricultor. Dados: C–H = 416 kJ/mol C?O = 805 kJ/mol O?O = 498 kJ/mol O–H = 464 kJ/mol A. –2 660 kJ/mol B. –8 060 kJ/mol C. –1 220 kJ/mol D. –4 030 kJ/mol E. –2 600 kJ/mol
O produtor rural Ricardo Antunes Peixoto, 55 anos, teve uma surpresa enquanto perfurava um poço artesiano em sua fazenda, na zona rural de Brasília de Minas (MG). "Não saiu água, mas saiu fogo", diz, espantado. Uma equipe com cinco operários de uma empresa especializada trabalhou durante dois dias na propriedade para abrir o poço de água, mas, após escavarem 204 metros, o que encontraram foi um produto inflamável, que seria gás natural. O dono da fazenda Lagoa Misteriosa espera lucrar com a descoberta da reserva de gás. "Pelo menos, que se têm notícias no estado, este é o primeiro caso. Agora, com o dinheiro que eu vender o gás, vou abrir [um novo poço] para ter a minha água". Disponível em: . Acesso em: 12 abr. 2013. Considerando a combustão completa do metano, nas CNTP, determine a energia liberada na queima de 224 L de metano que foi em encontrado no poço desse agricultor. Dados: C–H = 416 kJ/mol C?O = 805 kJ/mol O?O = 498 kJ/mol O–H = 464 kJ/mol A. –2 660 kJ/mol B. –8 060 kJ/mol C. –1 220 kJ/mol D. –4 030 kJ/mol E. –2 600 kJ/mol
How to do this?
No 5
Answer:
M=24
Step-by-step explanation:
because 2+3+6x2=24
A 12-ft ladder leaning against a house makes a 64 degree angle with the ground. Will the ladder reach a window sill that is 10.5 ft up from the base of the house?
Answer:
Yes, it will
Step-by-step explanation:
Given
Length of Ladder = 12 ft
Angle = 64
Required
Determine if it'll reach a height of 10.5ft from the base
See attachment for proper illustration.
From the attachment, we want to determine that x be greater than 10.5
Using sin formula:
[tex]Sin\ 64 = \frac{x}{12}[/tex]
Multiply through by 12
[tex]x = 12 * sin\ 64[/tex]
[tex]x = 12 * 0.8988[/tex]
[tex]x = 10.79[/tex] (Approximated)
Since 10.79 is greater than 10.5, then the ladder will reach the window
sin64 = x/12
x = 12* sin64
Marcie wants to find the total number of students with black hair in the freshman class at her school. She has observed 5 of the 9 freshman homerooms. The graph shows the number of students
with black hair she has counted so far. Based on this information, which is the best protection of the total number of students with black hair and then 9 freshman homerooms at Marcie's school?
Answer: 1/8
Step-by-step explanation: 9/5 = 1/8
what is the answer to d = -f + 2/3a
Answer:
For f = -d +2/3a
Step-by-step explanation:
Five people are tossing a coin in turn and agree that the first one to get a head wins. What's the probability that the first person who tosses the coin wins the game? a. 8/15 b. 16/31 c. 1/2 d. 1/5
(Select all that Apply)
Which of the following is an equation?
O 11=11
6+5=11
6 +5 – 11
06-5=11
rational or irrational 0.135135135135
Answer: it is a rational
Step-by-step explanation:
Which is not a way to solve 5 ÷ 1/2
Answer:
5 divided by 1/2 = 5/1 times 2/1 = 10
Step-by-step explanation:
Answer:la 2.5
Step-by-step explanation:
Solve for y in terms of x. Determine if y is a function of x. If it is, rewrite using f(x) notation. If not, enter ND in the answer field.
7x-5y=2
Answer:
y = (7x-2)/5Step-by-step explanation:
Given the expression 7x-5y = 2, we are to write y in terms of x. to do that, we will have to make y the subject of the formula from the given expression as shown;
7x-5y = 2
subtract 7x from both sides of the equation
7x-5y-7x = 2-7x
-5y = 2-7x
Multiply through by minus sign
-(-5y) = -(2-7x)
5y = -2+7x
5y = 7x-2
Divide both side by 5;
5y/5 = (7x-2)/5
y = (7x-2)/5
Hence the expression y as a function of x is given as y = (7x-2)/5
write the equation of the parabola in vertex form vertex (0,0) passes through (2,1)
Answer:
[tex]f(x)=\frac{1}{4}x^2[/tex]
Step-by-step explanation:
Recall the vertex form of a quadratic equation:
[tex]f(x)=a(x-h)^2+k[/tex]
Where (h,k) is the vertex.
We are told that the vertex is (0,0). Therefore:
[tex]f(x)=a(x-0)^2+(0)[/tex]
Simplify:
[tex]f(x)=ax^2[/tex]
So, to finish the equation, we need to find a.
We know that a point is (2,1). Thus, substitute 1 for f(x) and 2 for x:
[tex]1=a(2)^2[/tex]
Square:
[tex]1=4a[/tex]
Divide both sides by 4:
[tex]a=\frac{1}{4}[/tex]
So, our a value is 1/4.
And we can thus complete our equation:
[tex]f(x)=\frac{1}{4}x^2[/tex]
And we are done :)
write an equation to represent the relationship, and find the amount of peanut butter used to make 25 cracker packages. the table is peanut butter (tbsp) 1/2,5/8,3/4,7/8, the bottom is cracker packages 2,2 1/2,3,3 1/2.
We are given 4 points.
[tex](\frac{1}{2},2)[/tex]
[tex](\frac{5}{8},\frac{5}{2})[/tex]
[tex](\frac{3}{4},3)[/tex]
[tex](\frac{7}{8},\frac{7}{2})[/tex]
Using this, we can make an equation.
[tex]y=4x[/tex]
I got [tex]m=4[/tex] by using the slope formula.
[tex]m=\frac{2.5-2}{0.625-0.5}[/tex]
[tex]m=\frac{0.5}{0.125}[/tex]
[tex]m=4[/tex]
So the equation we have is [tex]y=4x[/tex]
Now, we can solve for how much peanut butter is used to make 25 packages by plugging in 25 for [tex]y[/tex], which is the number of cracker packages.
[tex]25=4x[/tex]
[tex]x=\frac{25}{4}[/tex]
We need to use [tex]\frac{25}{4}[/tex] teaspoons of peanut butter to make 25 packages of crackers.
Hope this helps.
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