The required values of x and y is 9 and -36, respectively. The correct answer is option a.
Given that the system of equations:
y = -3x - 9 (1)
y = (1/3)x - 39 (2)
Setting the two equations equal to each other since they both equal y:
-3x - 9 = (1/3)x - 39
⇒ -3(3x) - 3(9) = (1/3)(3x) - 39(3)
⇒ -9x - 27 = x - 117
⇒ -9x - x = -117 + 27
⇒ -10x = -90
⇒ x = -90 / -10
⇒ x = 9
Substitute the value of x back in the equation (1),
y = -3(9) - 9
⇒ y = -27 - 9
⇒ y = -36
Hence, the solution to the system of equations is x = 9 and y = -36. The correct answer is option a.
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Ryan made a cd of his favorite songs. There are 42 minutes of time on Cd. He records 14 songs. What is the average length of each song?
felix bought 5/6 pound of peanuts. He ate 3/4 pounds of peanuts. How much did felix hace left
Question: How many 1 8 lb packages of fudge can be sold from 7 pounds of fudge?
Let us assume that it is 1/8 lb packages of fudge.
So, the question is how many 1/8 lbs of fudge can be sold from 7 pounds of fudge
Answer:
Total amount of fudge = 7 pounds
Portions of division = 1/8 pounds
So, number of packages that can be made from 7 pounds are =
[tex]\frac{7}{\frac{1}{8}}[/tex]
= [tex]7\times8=56[/tex]
Hence, 56 packages of 1/8 lbs each can be made from 7 pounds fudge.
Which of the following is a correct interpretation of the expression 6-13?
Answer:
The answer is C
Step-by-step explanation:
Subtraction goes left on the number line
You always start with the first number on the number line
What expression shows the relationship between the value of any term and n, its position in the sequence for the given sequence?
10, 5, 0, -5, -10, ...
A) -5n
B) -5n + 15
C) -3n + 15
D) 5n
Answer:
B
Step-by-step explanation:
These are the terms of an arithmetic sequence with n th term
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d
where d is the common difference and [tex]a_{1}[/tex] the first term
here d = - 10 - (- 5) = - 5 - 0 = 0 - 5 = - 5 and [tex]a_{1}[/tex] = 10, hence
[tex]a_{n}[/tex] = 10 - 5(n - 1) = 10 - 5n + 5 = 15 - 5n → B
How many solutions does this system have!
y = 3x + 5
y = -x + 4
a. one
b. two
c. infinite number
d. no solution
Answer:x=-14y=174
y=3x+5,y=-x+4
3x+5=-x+4
There are infinite number of solutions!
Move all terms containing
x
x to the left side of the equation.
Tap for more steps...
4
x
+
5
=
4
4x+5=4
y
=
−
x
+
4
y=-x+4
Move all terms not containing
x
x to the right side of the equation.
Tap for more steps...
4
x
=
−
1
4x=-1
y
=
−
x
+
4
y=-x+4
Divide each term by
4
4 and simplify.
Tap for more steps...
x
=
−
1
4
x=-14
y
=
−
x
+
4
y=-x+4
Replace all occurrences of
x
x with the solution found by solving the last equation for
x
x. In this case, the value substituted is
−
1
4
-14.
x
=
−
1
4
x=-14
y
=
−
(
−
1
4
)
+
4
y=-(-14)+4
Simplify the right side.
Tap for more steps...
x
=
−
1
4
x=-14
y
=
17
4
y=174
The solution can be shown in both point and equation forms.
Point Form:
(
−
1
4
,
17
4
)
(-14,174)
Equation Form:
x
=
−
1
4
y
=
17
4
x=-14y=174
1. What is the value of x? Show your work to justify your answer.
2. What is the value of the exterior angle? Show your work to justify your answer.
Answer:
x=72 and the exterior angle is 154
Step-by-step explanation:
We will call the unknown angle in the triangle y. Angle y and the angle (2x +10) form a straight line so they make 180 degrees.
y + 2x+10 =180
Solve for y by subtracting 2x+10 from each side.
y + 2x+10 - (2x+10) =180 - (2x+10)
y = 180-2x-10
y = 170-2x
The three angles of a triangle add to 180 degrees
x+ y+ 82 = 180
x+ (170-2x)+82 = 180
Combine like terms
-x +252=180
Subtract 252 from each side
-x+252-252 = 180-252
-x = -72
Multiply each side by -1
-1*-x = -72*-1
x=72
The exterior angle is 2x+10. Substitute x=72 into the equation.
2(72)+10
144+10
154
Answer: x=72 and the exterior angle is 154
Step-by-step explanation:
We will call the unknown angle in the triangle y. Angle y and the angle (2x +10) form a straight line so they make 180 degrees.y + 2x+10 =180Solve for y by subtracting 2x+10 from each side.y + 2x+10 - (2x+10) =180 - (2x+10)y = 180-2x-10y = 170-2xThe three angles of a triangle add to 180 degreesx+ y+ 82 = 180x+ (170-2x)+82 = 180Combine like terms-x +252=180Subtract 252 from each side-x+252-252 = 180-252-x = -72Multiply each side by -1-1*-x = -72*-1x=72The exterior angle is 2x+10. Substitute x=72 into the equation.2(72)+10144+10154
I need help ASAP pleaseSolve for y Y+1.5=7.26
Answer:
5.76
Step-by-step explanation:
If you subtract 7.26 by 1.5 by puting the 1.5 under the 7.26 you would get that and put y=5.76.
Answer:
Y=1.05 = 7.26
Y = 7.26 - 1.05 - 6.21
Step-by-step explanation:
witch multiples of 24 are not factors of 24
Answer:
A factor of 24 is a number that can be multilied by another number (normally whole (not fraction or decimal) numbers) so a factor must be less than the number any multiple of 2 greater than 24 will work so just any even number greater than 24 exg 26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60, and so on.
Step-by-step explanation:
Not all multiples of a number are its factors. In the case of the number 24, only the multiples that can divide evenly into 24, which include 1, 2, 3, 4, 6, 8, 12, and 24, can be considered its factors. Higher multiples like 48, 72 or 96 are not factors as they do not divide into 24.
Explanation:In mathematics, the multiples of a number are obtained by multiplying that number by any integer. The factors of a number, on the other hand, are the numbers that you can evenly divide into that number. Therefore, for the number 24, its multiples include 24, 48, 72, 96, and so on.
However, not all multiples of 24 are factors of 24. A factor must divide into 24 with no remainder, which isn't the case with greater multiples of 24. For instance, 48, 72, 96 etc. are multiples of 24, but they are not factors of 24 because they cannot divide evenly into 24.
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Three hens can lay 3 eggs in 3 days.In how many days can 7 hens lay 7 eggs?
Answer: 3 days
Step-by-step explanation: It would take 3 days for seven hens to 7 lay eggs because each hen lays an egg each day.
1 hen/1 egg = 3 days
7 hens/7 days = 14 eggs
7 hens/3 days = 7 eggs
Answer:
3 days
Step-by-step explanation:
Three hens lay 3 eggs in 3 days
We have to find the days in which 7 hens lay 7 eggs
Hen/egg=[tex]\frac{3}{3}[/tex]
Hen/egg=1
Using unitary method
1 hen lays 1 egg in 3 days
1 hen lays in 1 day =[tex]\frac{1}{3}[/tex]eggs
7 hens lay 7/3 eggs in 1 day
7 hens lay 1 egg=[tex]\frac{3}{7}[/tex]days
7 hens lay 7 eggs=[tex]\frac{3}{7}\times 7[/tex]
7 hens lay 7 eggs=3 days
Hence, 7 hens lay 7 eggs in 3 days
eleanor purchased $2568 worth of stock and paid her broker a 0.5% fee. She sold the stock when the stock price increased to 3928 using an online broker that charged $7 per trade. What are her net proceeds?
Answer:
Eleanor's net proceeds would be $1340.16.
Step-by-step explanation:
If Eleanor purchased $2568 worth of stock and paid a 0.5% broker fee, she would have to pay $12.84 for the service, which is what we get when we multiply her initial purchase by the percentage (0.005). When Eleanor sold the stock at $3928, she had to pay a flat fee of $7 for the trade, decreasing her overall profit by $7, or $3921. Subtracting her initial investment from the overall profit gives Eleanor a net proceed of $1340.16.
Eleanor's net proceeds from her stock sale, after accounting for both the original broker's fee and the online trading fee, are $3908.16.
Explanation:To calculate Eleanor's net proceeds, we first need to calculate the fee she paid to her first broker. At 0.5% of $2568, that comes to $2568 * 0.005 = $12.84.
Next, she sold her stocks for $3928 using an online broker that charges a flat rate of $7 per trade. So, she paid another $7 in fees.
Therefore, the total fees she paid are $12.84 (first broker) + $7 (second broker) = $19.84.
Finally, to find her net proceeds, we subtract the total fees from the amount she sold her stocks for: $3928 - $19.84 = $3908.16.
So, Eleanor's net proceeds from selling her stocks are $3908.16.
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A water yank holds 18,000 gallons. How long will it take for the water level to reach 6,000 gallons if the water is used at an average rate of 450 gallons per day?
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
18,000 - 6000 = 12,000
12,000 ÷ 450 = 26.66 = 26 days 16 hours
Convert 5.4 ⋅ 103 to standard form. 0.0054 0.00054 5,400 54,000
Answer:
The correct option is C. 5,400
Step-by-step explanation:
Consider the provided number.
[tex]5.4\cdot 10^3[/tex]
If the exponent of 10 is a positive number then you need to move the decimal point right as much as the exponent value.
If the exponent of 10 is a negative number then you need to move the decimal point left as much as the exponent value.
Now consider the provided number.
[tex]5.4\cdot 10^3[/tex]
Here the power of 10 is positive, so move the decimal point right as shown.
[tex]5400[/tex]
Hence, the correct option is C. 5,400
Sade found that 75% of 60 is the same as 30% of another number,n.What is the value of n?
The area of a rectangular dog pen is 8 1/2 square feet. If the width is 3 2/5 feet, what is the length ,in feet ?
Answer:
2 1/2 ft
Step-by-step explanation:
Area is given by the formula
A = l*w
We know the area is 8 1/2
Changing this to an improper fraction 8 1/2 = (2*8 +1)/2 = 17/2
The width is 3 2/5 as an improper fraction = (5*3+2)/5 = 17/5
A = l*w
17/2 = l* 17/5
Multiply each side by 5/17
17/2 * 5/17 = l* 17/5 * 5/17
5/2 = l
2 1/2 = l
Please help and show work
Answer:
The ratio is 1:3
Step-by-step explanation:
People can do this in different ways.
Firstly, set some variables for cydlinder A:
Diameter = 18
Height = 1
Radius = 18 ÷ 2 = 9
Area of a cylinder is [tex]\pi r^{2} h[/tex]
Plug values in:
[tex]\pi 9^{2} 1[/tex] = 81π
Diameter = 18 ÷ 3 = 6
Height = 1 * 3 = 3
Radius = 6 ÷ 2 = 3
[tex]\pi3^{2}3 = 27\pi[/tex]
Cylinder b is 3 times less than cylinder a:
81π ÷ 27π = 3
So that means three lots of cylinder b is equal to one of cylinder a.
Meaning the ration is 1:3
what is
[tex]2x + 4 \geqslant 24[/tex]
please help!!!
[tex]2x+4\geq24\qquad\text{subtract 4 from both sides}\\\\2x\geq20\qquad\text{divide both sides by 2}\\\\\boxed{x\geq10\to x\in[10;\ \infty)}[/tex]
HELP PLS 15+ POINTS
Write an equation of the line that has:
a. no slope and passes through the point (4,-5)
b. a slope of 0 and passes tgrough the point (-4,-1)
Patty needs a total of 80$ to buy a bicycle .she has already saved 35$. If she saves 10$ a week. From her earnings ,what is the best number of weeks she must work to have enought money to but a bicycle?
A) 3
B)4
C)5
D)8
Answer:
C) 5 weeks
Step-by-step explanation:
Given :- Cost of bicycle = $80,
Current Savings = $35 and
Saves $10 per week
Additional money that is required to buy the bicycle = $80 - $35
= $45
If she saves $10 per week then the best number of weeks to save $45 is 5 weeks
(Savings in 5 weeks = $10 × 5 = $50)
Please help ASAP!!!
A six-sided number cube is rolled. What is the probability of getting a 3 and then a 4, given that the first number rolled was a 3?
1. 1/3
2. 1/6
3. 1/36
4. 1/2
The probability of getting a 3 and then a 4, given that the first number rolled was a 3 on a six-sided number cube is 1/36.
The probability of getting a 3 and then a 4, given that the first number rolled was a 3 on a six-sided number cube:
Probability of rolling a 3 on the first roll: 1/6
Since each roll is independent, the probability of rolling a 4 after rolling a 3: 1/6
Therefore, the overall probability of getting a 3 and then a 4: 1/6 × 1/6 = 1/36
f(x) = x − 3 and g(x) = 2x + 8 Which ordered pair is a solution for the system?
I put it into Desmos and got (-11, -14)
Write an absolute value inequality that describes the acceptable weights, w, of a 20-ounce bottle of sports drink.
Answer: [tex]0\leq w\leq 20[/tex]
Step-by-step explanation:
Since, Here w represents the weight of the bottle.
And, According to the question, he acceptable weights, w, of a 20-ounce bottle of sports drink.
That is, weight of the bottle can not be higher than 20 or the it can be atleast 20.
Therefore, [tex]w\leq 20[/tex]
And, the weight can not be negative.
Therefore, [tex]0\leq w[/tex]
Thus, the required inequality is,
[tex]0\leq w\leq 20[/tex]
What are the first 4 terms of the arithmetic sequence in the graph?
Look at the picture.
[tex]a_1=4\\\\a_2=6\\\\a_3=8\\\\a_4=10[/tex]
Answer:
Start from bottom to top. They are asking for the y-intercept of the dot. The order is as follows: 4, 6, 8, 10.
Which point is on the graph of f(x)=5^x?
Answer:
B. (0 , 0)
Step-by-step explanation:
Plug in the coordinate into the equation given.
Note that:
x = x
f(x) = y
Also note that in B, x = 0, y = 0
Plug in the corresponding number with the corresponding variable
0 = 5^(0)
Simplify
5^0 = 0
0 = 0 (True)
B. (0 , 0) is your answer
~
Answer:
(1,5)
Step-by-step explanation:
This is the correct answer.
What is the slope-intercept equation for the line below? (0, 4) (4, 1)
Answer:
The equation of the line would be y = 5/4x - 4
Step-by-step explanation:
To find the equation of any line, start by finding the slope using the slope formula.
m(slope) = (y2 - y1)/(x2 - x1)
m = (-4 - 1)/(0 - 4)
m = -5/-4
m = 5/4
Now that we have the slope, use that and either point to get the equation of the line
y - y1 = m(x - x1)
y + 4 = 5/4(x - 0)
y + 4 = 5/4x
y = 5/4x - 4
The equation of the line would be y = (5/4) x - 4. Hence, option B is correct.
What is an equation?An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
To find the equation of any line, start by finding the slope using the slope formula.
m(slope) = (y₂ - y₁)/(x₂ - x₁)
m = (-4 - 1)/(0 - 4)
m = -5/-4
m = 5/4
Now that we have the slope, use that and either point to get the equation of the line.
y - y₁ = m(x - x1)
y + 4 = 5/4(x - 0)
y + 4 = 5/4x
y = 5/4x - 4
Hence, option B is correct.
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given abc with a(-4 -2), b(4,4), and c(18,-8). write the equation of the line that contains the altitude that passes through b in standard form
check the picture below.
so red line of BD is perpendicular to AC, hmmmm let's firstly find the slope of AC, bearing in mind that perpendicular lines have negative reciprocal slopes.
[tex]\bf A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{18}~,~\stackrel{y_2}{-8}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-8-(-2)}{18-(-4)}\implies \cfrac{-8+2}{18+4} \\\\\\ \cfrac{-6}{22}\implies -\cfrac{3}{11} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{11}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{11}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{11}{3}}}\impliedby \textit{BD's slope}[/tex]
so we're really looking for the equation of a line whose slope is 11/3 and runs through B(4,4). Keeping in mind that
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex]\bf B(\stackrel{x_1}{4}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies \cfrac{11}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{11}{3}(x-4)[/tex]
[tex]\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}\textit{ to do away with the denominators}}{3(y-4)=3\left( \cfrac{11}{3}(x-4) \right)\implies 3y-12=11(x-4)} \\\\\\ 3y-12=11x-44\implies 3y=11x-32 \\\\\\ -11x+3y=-32\implies \blacktriangleright 11x - 3y= 32\blacktriangleleft[/tex]
Final answer:
The equation for the altitude passing through point B(4,4) is in standard form as 11x - 3y = 32. This was found by calculating the slope of AC, finding the perpendicular slope, and then applying it with point B to find the equation of the line.
Explanation:
To find the equation of the altitude that passes through point B(4,4) of the triangle ABC with vertices A(-4,-2), B(4,4), and C(18,-8), we need to determine the slope of line AC and then find the perpendicular slope that passes through B.
Firstly, we calculate the slope of AC:
The slope of the altitude will be the negative reciprocal of the slope of AC because the altitude is perpendicular to AC. Hence,
Now we use the point-slope form of the equation of a line using point B:
Rewriting in standard form (Ax + By = C), we get:
So, the standard form of the equation of the altitude passing through point B is 11x - 3y = 32.
PLEASE ANSWER I WILL GIVE YOU BRAINLIEST
Simplify.
What is the value of the expression? 1/5 (-22.38 - 10.12)
Enter your answers, as a decimal to tenths
Answer:
The answer is 7 if you round 6.5
Step-by-step explanation:
1/5(-22.38 - 10.12)
1/5 (-32.5)
= -6.5
Please help me with NUMBER 7 !! Thank you so much! 20 points!! :))
Answer:
x<-3 or x>-1
Step by step explanation:
Start with -5x>15. To get x by itself, we have to divide each side by -5. When we do that we get x<-3. (Don't forget to flip the sign when dealing with negative · and ÷.) Now answer the second equation. x-5>-6 To get x by itself, add 5 to both sides to get x>-1. Now we have x<3 or x>-1.
The linear inequality y ≤ 3/2x + 3/2
is graphed. Determine a solution for the inequality.
A) (0, 2)
B) (1, 3)
C) (-2, 0)
D) (-3, 1)
Answer:
it's (B)
Step-by-step explanation:
To find a solution for the linear inequality y ≤ (3/2)x + (3/2), we need to graph it and find the region that satisfies the inequality. The correct solution for the inequality is (-2, 0).
Explanation:To determine a solution for the linear inequality, y ≤ (3/2)x + (3/2), we need to graph it and find the region that satisfies the inequality. This inequality represents a line with a slope of 3/2 and a y-intercept of 3/2. Starting from the y-intercept, we can draw a line that goes up 3 units vertically and 2 units horizontally, and another line that goes down 3 units vertically and 2 units horizontally. Shade the region below the line to include the points that satisfy the inequality. The correct solution for the inequality is (C) (-2, 0).
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Find the absolute value of |-15|
Answer:
15 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Absolute value is always positive.
Answer:
Step-by-step explanation: Absolute value of -15 is 15. Absolute value is the distance of a number on the number line from 0. Even though it is a negative, it is a positive because it is a number of units from number line. Hope it helps!!☺☻ Please give Brainliest!