Which is the best first step and explanation for solving this system of equations?
Answers
Answer:
Subtract equation 1 from equation 2
Step-by-step explanation:
Solve the following system:
{3 x + 4 y = 12 | (equation 1)
3 x = 2 y - 8 | (equation 2)
Express the system in standard form:
{3 x + 4 y = 12 | (equation 1)
3 x - 2 y = -8 | (equation 2)
Subtract equation 1 from equation 2:
{3 x + 4 y = 12 | (equation 1)
0 x - 6 y = -20 | (equation 2)
Divide equation 2 by -2:
{3 x + 4 y = 12 | (equation 1)
0 x+3 y = 10 | (equation 2)
Divide equation 2 by 3:
{3 x + 4 y = 12 | (equation 1)
0 x+y = 10/3 | (equation 2)
Subtract 4 × (equation 2) from equation 1:
{3 x+0 y = (-4)/3 | (equation 1)
0 x+y = 10/3 | (equation 2)
Divide equation 1 by 3:
{x+0 y = (-4)/9 | (equation 1)
0 x+y = 10/3 | (equation 2)
Collect results:
Answer: {x = -4/9 , y = 10/3
Related Questions
Mary had back surgery and was given a prescription with instructions to take 4 tablets twice a day for pain. How many tablets will Mary take in 7 days
Answers
Answer:
56
Step-by-step explanation:
4 x 2 = 8
8 x 7 = 56
Answer = 56
For 7 days-8x7=56
Mary will take 56 tablets in 7 days
Dean is comparing prices on ground beef. Store A is selling 5 pounds of ground beef for $23.49. Store B is selling 8 pounds of ground beef for $36.96.
Which store is offering the better deal on ground beef?
Answers
Store B is offering the better deal on ground beef
Step-by-step explanation:
Dean is comparing prices on ground beef
Store A is selling 5 pounds of ground beef for $23.49Store B is selling 8 pounds of ground beef for $36.96We need to know which store is offering the better deal on ground beef
To find the better deal we must to find the unit price of each store
The unit price = total price ÷ number of pounds
∵ Store A is selling 5 pounds of ground beef for $23.49
∴ The unit price of Store A = 23.49 ÷ 5 = $4.698
∴ The unit price of Store A is $4.698 per pound
∵ Store B is selling 8 pounds of ground beef for $36.96
∴ The unit price of Store B = 36.96 ÷ 8 = $4.620
∴ The unit price of Store B is $4.620 per pound
∵ $4.620 < $4.698
∴ The unit price of Store B is less than the unit price of Store B
∴ Store B is cheaper than Store A, then it is offering the better deal
Store B is offering the better deal on ground beef
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1. y = 4x + 3 for x = -1, 0,1
Answers
Answer:
-1, 3, 7
Step-by-step explanation:
y = 4(-1) + 3
y = -4 + 3
y = -1
y = 4(0) + 3
y = 0 + 3
y = 3
y = 4(1) + 3
y = 4 + 3
y = 7
To solve the linear equation y = 4x + 3, substitute the given x values (-1, 0, 1) into the equation to find the corresponding y values. The results are -1, 3, and 7 respectively.
Explanation:The question asks to solve the equation y = 4x + 3, for the values of x being -1, 0, and 1. This is a linear equation where y depends on x. To find the corresponding y values for each x value:
Substitute x = -1 into the equation. The calculation becomes: y = 4(-1) + 3 = -4 + 3 = -1.Substitute x = 0 into the equation. The calculation becomes: y = 4(0) + 3 = 0 + 3 = 3.Substitute x = 1 into the equation. The calculation becomes: y = 4(1) + 3 = 4 + 3 = 7.Hence, the values for y when x equals -1, 0, and 1 respectively are -1, 3, and 7.
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5. Describe the pattern below.
9, 12, 15, 18, 21, 24
Answers
Answer:
The numbers increase by 3
Step-by-step explanation:
The difference between all the numbers in the sequence have a gap of 3
9 and 12 --gap of 3
12 and 15--gap of 3
18 and 21--gap of 3
21 and 24--gap of 3
Answer
y=3+ before
Step-by-step explanation:
you add 3 to every number
A new car is listed at 27,000. A prospective buyer would incur initial expenses that consist of 4%. sales tax and a license fee of $36. what would the total amount in dollars of the incurred initial expenses be?
Answers
Answer:
$28,116
Step-by-step explanation:
27,000/100*104 = 28,080 + 36 = $28,116
There are 482 studemts in the school and there are two Grade 4 classes: Ms.Ashley's and Mr.Ben's classes. Mrs. Aheley's class had 15 boays and 6 girls. Mr Ben's class ahd 14 girls and 10 boys. In Ms. Ashley's class, 2/3 of the students wear glasses.
In Mr. Ben's class, 1/4 of the kids have others siblings in the school.
1. What fraction of the students in the school are in grade 4?
2. What fraction of the grade 4 students are boys?
3. What fraction of the grade 4 students are in Ms. Ashley's class?
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
Answers
Answer:
1. 45/482 of the students are in grade 4.
2. 5/9 of the students of the grade 4 are boys.
3. 7/15 of the grade 4 students are in Ms. Ashley's class
4. 3/4 of the students in Mr. Ben's class do not have siblings in the same school.
5. There are 14 students with glasses and 7 without glasses.
Step-by-step explanation:
1. Let's review the information given to us for solving the questions:
Number of students in the school = 482
Ms. Ashley's Grade 4 class = 21 students
Ms. Ashley's Grade 4 class boys = 15 students
Ms. Ashley's Grade 4 class girls = 6 students
Ms. Ashley's Grade 4 class with glasses = 2/3 * 21 = 42/3 = 14 students
Mr. Ben's Grade 4 class = 24 students
Mr. Ben's Grade 4 class boys = 10 students
Mr. Ben's Grade 4 class girls = 14 students
Mr. Ben's Grade 4 class with siblings in the school = 1/4 * 24 = 24/4 = 6 students
2. Let's answer all the questions:
1. What fraction of the students in the school are in grade 4?
(Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)/ Number of students in the school
21 + 24 / 482 = 45/482
2. What fraction of the grade 4 students are boys?
(Ms. Ashley's Grade 4 boys + Mr. Ben's Grade 4 boys)/ (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
15 + 10 / 21 + 24
25 / 45 = 5/9
3. What fraction of the grade 4 students are in Ms. Ashley's class?
Ms. Ashley's Grade 4 class / (Ms. Ashley's Grade 4 class + Mr. Ben's Grade 4 class)
21 / 21 + 24
21 / 45 = 7/15
4. What fraction of the students in Mr. Ben's class that do not have siblings in the same school?
(Mr. Ben's Grade 4 class - Mr. Ben's Grade 4 class with siblings in the school)/ Mr. Ben's Grade 4 class
24 - 6 / 24
18 / 24 = 3/4
5. In Ms. Ashley's class, are there more students that wear glasses or do not wear glasses?
There are 14 students with glasses and 7 without glasses.
For which discriminant is the graph possible
b2-4ac=0
b2-4ac=-1
b2-4ac=4
Answers
Answer:
"[tex]b^2-4ac=4[/tex]"
Step-by-step explanation:
By looking at the value of the discriminant in a quadratic, we can find the nature of roots.
Let the value of the discriminant be "D", so we can say:
D > 0 [2 distinct real roots]D = 0 [2 same real roots]D < 0 [no real roots]Graphically, we can write the points in order as:
D > 0, 2 cutting point in x-axisD = 0, 1 touching point in x-axisD < 0, NO cutting/touching point in x-axisLooking at the graph, we clearly see that there is 2 cutting points in the x-axis, so there are 2 roots. This means the value of the discriminant should be greater than 0 (positive value).
Out of the 3 choices given with discriminant formula, the last one has a value that is greater than 0:
4 > 0
Hence, last answer choice is right.
The discriminant determines whether a quadratic equation has real solutions and affects the appearance of the graph.
Explanation:The discriminant is calculated using the formula Δ = b² - 4ac. In order for the graph to be possible:
If Δ = 0, the quadratic equation will have one real root. The graph will touch the x-axis at one point.If Δ < 0, the quadratic equation will have no real roots. The graph will not intersect the x-axis and will be entirely above or below it.If Δ > 0, the quadratic equation will have two distinct real roots. The graph will intersect the x-axis at two points.Therefore, for the discriminant values given:
For Δ = 0, the graph is possible.For Δ = -1, the graph is not possible.For Δ = 4, the graph is possible.How do you Graph this
Y = 5x + 12
y = 2x - 4
Answers
Please help meeeeeeeeeee!!!!!!!!!!!!
DUE TONIGHT!!!!!!!!!
Answers
Np i gotchu my dude
1. represents
2. Each y value
3. to exactly
4. x value
Hope this helps my dude ^^
Answer:
Explain wether the graph represents a function.The graph represents a function because each x-value corresponds to exactly one y-value.
For example, in the given graph you see that for x=2 there's only one corresponding value, which is, y=40, that's what defines a function. If you have a graph where a certain value of x has to y values, that means is not a function, because for one x-value would be more than one y-values, so that would be only a relation, not a function.
It's important to specify the right order, that is, if we say each y-value corresponds to exactly one x-value, that's not exactly de definition of a function, because it actually happens, because in a quadratic expression, 2 and -2 would be the same result 4, so one y-vale has two x-value, but it's still a function.
So, the right order is The graph represents a function because each x-value corresponds to exactly one y-value.
Name one point on the line y - 4 = 3(x + 2)
Please help!!
Answers
A)-124
B)-18
C)-36
D)-96
Answers
Answer:
It's Either B Or D
Step-by-step explanation:
only because They Only number that are closer so you can reverse it is 18 or 96
What value represents the vertical translation from the graph of the
(x+5)2+3?
0 -5
O-3
Answers
Answer:
The value 3 represents the vertical translation upwards of [tex]f(x)[/tex] to [tex]g(x)[/tex]
Step-by-step explanation:
The question is incomplete or missing data.
The correct question
What value represents the vertical translation from the graph of the parent function [tex]f(x) = x^2[/tex] to the graph of the function
[tex]g(x) = (x + 5)^2 + 3[/tex]?
Given functions:
Parent function
[tex]f(x) = x^2[/tex]
Translated function
[tex]g(x) = (x + 5)^2 + 3[/tex]
Translation rules
For horizontal shift
[tex]f(x)\rightarrow f(x+c)[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the left.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the right.
For vertical shift
[tex]f(x)\rightarrow f(x)+c[/tex]
If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the up.
If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the down.
From the functions given the translation rule can be given as:
[tex]f(x)\rightarrow f(x+5)+3[/tex]
[tex]g(x)=f(x+5)+3[/tex]
This shows the graph is shifted left by 5 units and upwards by 3 units.
Thus the value 3 represents the vertical translation of [tex]f(x)[/tex] to [tex]g(x)[/tex]
One number is four more than four times another. If their sum is increased by five, the result is thirty-nine. Find the numbers.
Answers
Answer:
(6, 28) or x=6, y=28 or The numbers are 6 and 28.
Step-by-step explanation:
4x+4=y
x+y+5=39
--------------
4x+4=y
x+y=39-5
----------------
4x+4=y
x+y=34
------------
x+(4x+4)=34
x+4x+4=34
5x+4=34
5x=34-4
5x=30
x=30/5=6
4(6)+4=y
24+4=y
y=28
x=6, y=28
What is the value of f(x) = 2/3 x + 1/4 when x = 6?
Answers
Answer:
4 1/4
Step-by-step explanation:
f(x) = 2/3(6) + 1/4
f(x) = 4 + 1/4
f(x) = 4 1/4(4.25)
choose all that are correct given the equation:
y= 1/4 x + 9
A) y = 7.25 when x = –7
B) y = 7 when x = –8
C) y = 8.5 when x = –4
D) y = 10.25 when x = 5
Answers
Answer:
A), B) & D).
Step-by-step explanation:
Answer:
A) y = 7.25 when x = –7
C) y = 8.5 when x = –4
D) y = 10.25 when x = 5
What is the length of the side opposite angle B?
3 units
4 units
5 units
6 units
Answers
Answer:
B
Step-by-step explanation:
4 units is the answer. i got an 100% on the quiz
The triangle missing from the question has attached and the opposite side of angle B is 4 units.
What is a traingle?A triangle is a three sides lines geometry in which the sum of all angles is 180°.
Given that a triangle ABC and has sides as
AB = 4
BC = 3
AB = 5
It's clearly visible that the opposite side of angle B is AC which has length as 4 units.
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Swami packed 28 oranges and 52 apples in boxes. He packed oranges and apples in separate boxes. If he put equal number of fruits in each box, find the maximum number of fruits he put in
each box.
Answers
Answer:
4
Step-by-step explanation:
Find the greatest common factor (GCF) of 28 and 52. First, write the prime factorization of each:
28 = 2² × 7
52 = 2² × 13
The GCF is 2² or 4. So the most fruits per box is 4.
write an inequality and that represents the graph.
Answers
Answer:
Part 16) [tex]y\leq -x+2[/tex]
Part 17) [tex]y>\frac{1}{3}x-1[/tex]
Step-by-step explanation:
Part 16) we know that
The solution of the inequality is the shaded area below the solid line
The slope of the solid line is negative
The y-intercept of the solid line is the point (0,2)
The x-intercept of the solid line is the point (2,0)
The slope of the solid line is
[tex]m=(0-2)/(2-0)=-1[/tex]
The linear equation of the solid line in slope intercept form is
[tex]y=-x+2[/tex]
therefore
The inequality that represent the graph is
[tex]y\leq -x+2[/tex]
Part 17) we know that
The solution of the inequality is the shaded area above the dashed line
The slope of the dashed line is positive
The y-intercept of the dashed line is the point (0,-1)
The x-intercept of the dashed line is the point (3,0)
The slope of the dashed line is
[tex]m=(0+1)/(3-0)=\frac{1}{3}[/tex]
The linear equation of the dashed line in slope intercept form is
[tex]y=\frac{1}{3}x-1[/tex]
therefore
The inequality that represent the graph is
[tex]y>\frac{1}{3}x-1[/tex]
What is another way to write this number:
300+70+5/10+8/100
Answers
Answer:
18529/50 or 370.58
Step-by-step explanation:
5/10=1/2
8/100=2/25
300+70+1/2+2/25
370+1/2+2/25
370+29/50
18529/50 or 370.58
Step-by-step explanation:
370 + 50/100 + 8/100
37000/100 + 58/100
37058/100 = 370 58/100 = 370 29/50
Use Newton's method to approximate the roots
of f(x) = 3x3 – 4x2 + 1 to six digits.
Answers
Answer:
Step-by-step explanation:
14
Find the 2nd term of (2x+3y)^3
Answers
Answer:
The 2nd term is 3y
Step-by-step explanation:
2x + 3y
__ __
1 2
term term
Answer:
3y
Step-by-step explanation:
Marcela estimates the distance between the library and town hall is 735 ft. The actual distance is 612 ft.
What is the percent error in Marcela's estimate?
Round your answer to the nearest tenth of a percent.
Enter your answer in the box.
Answers
Answer:
The error percentage in estimation is 20 %
Step-by-step explanation:
The estimated distance between library and town = 735 ft
The actual distance = 612 ft
The Error in estimation = Estimated Distance - Actual Distance
= 735 ft - 612 ft = 123 ft
So, the error in the estimation is 123 ft.
Now, [tex]\textrm{ Percentage in Error Estimation} = \frac{\textrm{The estimated Error}}{\textrm{The estimated value}} \times 100[/tex]
= [tex]\frac{123}{612} \times 100 = 20.098[/tex]
or, The error percentage in estimation is 20.09%
Now, rounding off the value to the nearest tenths of a %, we get:
The error percentage in estimation is 20 %
Write the decimal as a fraction or a mixed number in simplest form.
5.76
Answers
Answer:
Step-by-step explanation:
it is 145/25 which is reduced to 29/5
Answer:
5 19/25
Step-by-step explanation:
How many Oxygen atoms are in the following equation Pb(C2H3O2)2
Answers
write an expression with 4.3,-1.07 and 2.971. Use only subtraction and addition to come out with a negative number
Answers
Step-by-step explanation:
You could add (-1.07 + 2.971) to get (1.901)
Then do (1.901 - 4.3) to get a negative number; (-2.399)
I would double check this all with a calculator
What is the slope of the line that passes through the points (-6, -7) and
(-24, -7)? Write your answer in simplest form.
Answers
Slope of the line is 0.
Step-by-step explanation:
Given points are,
(-6, -7) and (-24, -7)
Here,
[tex]x_{1} = -6\ \ \ \ \ y_1=-7\\x_2=-24\ \ \ \ \ y_2=-7[/tex]
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]Slope = \frac{-7-(-7)}{-24-(-6)}\\Slope=\frac{-7+7}{-24+6}\\Slope=\frac{0}{-18}\\Slope= 0[/tex]
Slope of the line is 0.
Keywords: slope, line
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Final answer:
The slope of the line that passes through the points (-6, -7) and (-24, -7) is calculated using the slope formula and is found to be 0, indicating that the line is horizontal.
Explanation:
The question asks for the slope of the line that passes through the points (-6, -7) and (-24, -7). To calculate the slope, we use the formula slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in our values, we get the slope = (-7 - (-7)) / (-24 - (-6)) = 0 / -18 = 0. Therefore, the slope of the line through these two points is 0, which means the line is horizontal.
If 3(r+300)=6, then what would be the value of r+300-2?
Answers
Answer:
The value of r+300-2 is 0.
Step-by-step explanation:
3(r+300)=6
r+300=6/3
r+300=2
r=2-300
r=-298
---------------
r+300-2=-298+300-2=2-2=0
Please check my work and if any answers wrong or you feel like it is not good enough feel free to correct me and let me know, Greatly appreciated.
Question 1
Is the expression x3•x3•x3 equivalent to x3•3•3? Why or why not? Explain your reasoning.
No, Because the given numbers have different value.
Question 2
Rewrite in simplest radical form
1
x
−3
6
. Show each step of your process.
If the symbols of the radicals are given by
It is possible to perform the simplification as well,
Question 3
Rewrite in simplest rational exponent form √x • 4√x. Show each step of your process.
Since these are both x terms and 4x= x*x*x*x, I can simply write 5x.
Question 4
Rewrite in simplest radical form
x
5
6
x
1
6
. Show each step of your process.
Question 5
Which of the following expressions are equivalent? Justify your reasoning.
A. 4√x3
B. 1
x−1
C. 10√x5•x4•x2
D.x^{\frac{1}{3} } multiply by
x^{\frac{1}{3} } multiply by
x^{\frac{1}{3} }
Answers
Question 1:
No, \(x^3 \cdot x^3 \cdot x^3\) equals \(x^9\), while \(x^3 \cdot 3 \cdot 3\) equals \(9x^3\), representing different operations and values.
Question 2:
Incomplete. The expression \(1/x^3\) can be rewritten as \(x^{-3}\) using negative exponents.
Question 3:
Incorrect. The product of \(\sqrt{x}\) and \(4\sqrt{x}\) equals \(4x\), not \(5x\). Use exponents to simplify.
Question 4:
The expression \(x^{5/6} \cdot x^{1/6}\) simplifies to \(x\). Show the steps of exponent addition.
Question 5:
Unjustified. Determine equivalent expressions by simplifying each and comparing results. Justify based on mathematical properties.
Here's a review of your work:
Question 1:
Your reasoning is incorrect. The expressions are not equivalent because they represent different operations. \( x^3 \cdot x^3 \cdot x^3 \) means \( x \) multiplied by itself 3 times, which is \( x^9 \). \( x^3 \cdot 3 \cdot 3 \) is a multiplication of constants, which equals \( 9x^3 \). So, the expressions are not equivalent because they result in different values.
Question 2:
Your answer is incomplete. It seems like you've provided a template for simplifying radicals, but you haven't actually applied it to the given expression. To simplify \( \frac{1}{x^3} \), you can rewrite it as \( x^{-3} \).
Question 3:
Your answer is incorrect. The product of \( \sqrt{x} \) and \( 4\sqrt{x} \) is not simply \( 5x \). To rewrite it in simplest rational exponent form, you should use the property of exponents which states that \( \sqrt{a} = a^{1/2} \). So, \( \sqrt{x} \) is equivalent to \( x^{1/2} \), and \( 4\sqrt{x} \) is equivalent to \( 4x^{1/2} \). Multiplying these expressions together, you get \( 4x^{1/2} \cdot x^{1/2} = 4x^{1/2 + 1/2} = 4x^1 = 4x \).
Question 4:
You haven't shown your process for simplifying \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} \). To simplify, use the property of exponents which states that when you multiply two terms with the same base, you add their exponents. So, \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} = x^{\frac{5}{6} + \frac{1}{6}} = x^{\frac{6}{6}} = x^1 = x \).
Question 5:
You haven't justified which expressions are equivalent. To determine equivalence, you need to simplify each expression and compare them to each other.
165 as a percent from 4,125
Answers
Answer:
$100\%=165$100%=165.
Step-by-step explanation:
Answer:
4%
Step-by-step explanation:
165 is what % of 4125.
Let x represent the % in decimal form
4125*x = 165
Isolate x by dividing both sides by 4125
x = 0.04
0.04 = 4%
You find this by moving the decimal two places to the right
Priya and Han are biking in the same direction on the same path.
Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after hours.
Priya started riding a half hour before Han. If Han has been riding for hours, how long has Priya been riding?
Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for hours.
Use your expressions to find when Han and Priya meet.
Answers
I copy the complete questions again to make them clearer:
Priya and Han are biking in the same direction on the same path.
a. Han is riding at a constant speed of 16 miles per hour. Write an expression that shows how many miles Han has gone after [tex]t[/tex] hours.
b. Priya started riding a half hour before Han. If Han has been riding for [tex]t[/tex] hours, how long has Priya been riding?
c. Priya is riding at a constant speed of 12 miles per hour. Write an expression that shows how many miles Priya has gone after Han has been riding for [tex]t[/tex] hours.
d. Use your expressions to find when Han and Priya meet.
Answer:
a) [tex]H=16t[/tex]b) [tex]t+0.5[/tex]c) [tex]P=12(t+0.5)[/tex]d) Han and Priya meet 1.5 hours after Han started riding.Explanation:
a. Since Han is riding at a constant speed of 16 miles per hour, the number of miles that he has gone is proportional to the number of hours, t, that he has been riding, the constant of variation is 16, and the expression for the number of miles he has gone is:
[tex]H=16\times t=16t[/tex]Where, H is the number of miles Han has gone, and t is the number of hours.
b. Since Priya started riding a half hour before Han, you have to add 1/2 or 0.5 to the time of Han, which is t, to express how long Priya has been riding:
[tex]t+0.5[/tex]c. Since, Priya is riding at a constant speed of 12 miles per hour, the number of miles that she has gone is proportional to the number of hours, t + 0.5, that she has been riding, the constant of variation is 12, and the expression for the number of miles she has gone is:
[tex]P=12\times (t+0.5)=12(t+0.5)[/tex]Where P is the number of miles Priya has gone, and t is the number of hours since Han is riding.
d. To find when Han and Priya meet, you just need to solve the sytem of equations, making H = P, which means that the number of miles that both Han and Priya rides is equal:
[tex]H=P\\ \\ 16t=12(t+0.5)\\ \\ 16t=12t+6\\ \\ 4t=6\\ \\ t=6/4=3/2=1.5[/tex]
Which means that they meet when it has passed 1.5 hours since Han started riding.