Solution:17.Graph each system and determine the number of solutions that it has. If it has one solution,name it.A. X +2y=4y= -1/2x+2B. 2x-y=1y=-3
Answers
Systems of Equations
Given the system:
[tex]\begin{gathered} x+2y=4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]It's required to graph and find the solutions of the system.
Solving the first equation for y:
[tex]\begin{gathered} 2y=-x+4 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]We can see both equations are exactly the same, so there is only one equation and one line.
Let's give x some values and graph the line.
x = 0:
[tex]\begin{gathered} y=-\frac{1}{2}\cdot0+2 \\ y=2 \end{gathered}[/tex]x = 2
[tex]\begin{gathered} y=-\frac{1}{2}\cdot2+2 \\ y=1 \end{gathered}[/tex]With the points (0, 2) and (2, 1) we graph the line as follows.
Since the number of equations is greater than the number of unknowns, the system has infinitely many solutions. For example, (0, 2) and (2, 1) are solutions for the system.
Related Questions
How many liters each of a 55% acid solution and a 80% acid solution must be used to produce 50 liters of a 60% acid solution? (Round to two decimal places if necessary.)
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Given:
Let x denote the number of liter solutions.
[tex]\begin{gathered} \text{acid}+\text{acid}=\text{acid} \\ 55\text{ \%x+80 \%( 50-x)=}60\text{ \%}\times50 \end{gathered}[/tex]Solve the equation for x,
[tex]\begin{gathered} 55\text{ \%x+80 \%( 50-x)=}60\text{ \%}\times50 \\ \frac{55}{100}x+\frac{80}{100}(50-x)=\frac{60}{100}\times50 \\ 0.55x+0.8(50-x)=30 \\ 0.55x+40-0.8x=30 \\ -0.25x=30-40 \\ x=-\frac{10}{-0.25} \\ x=40 \end{gathered}[/tex]It gives,
[tex]\begin{gathered} 40\text{ liters of 55 \% acid will be n}eeded \\ (50-x)=(50-40)=10\text{ liters of 80 \% acid will be n}eeded \end{gathered}[/tex]Answer: 40 liters of a 55% acid solution and 10 liters of 80% acid solution must be used to produce 50 liters of a 60% acid solution
Type the correct answer in the box. Use numeral instead of words. If nessary, use / for fraction bar. The data set represents the number of cups of coffee sold in a Cafe
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4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 12, 12, 14, 15,
The first quartile is 6 and the third is 12
So the difference is 12- 6 = 6 (answer)
Sharon baked 72 cookies for herclassmates. Her brothers ate some ofthe cookies and 54 cookies remain.Find the percent of decrease.
Answers
Answer
Percent decrease = 25%
Explanation
Percent decrease is given as
[tex]\text{Percent decrease = }\frac{Amount\text{ decreased}}{\text{Original amount}}\times100\text{ percent}[/tex]For this question,
Amount decreased = (Original amount) - (Amount remaining)
Amount decreased = 72 - 54 = 18 cookies
Original amount = 72 cookies
Percent decrease = (18/72) × 100%
Percent decrease = 25%
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Sole the following problem by using the 4 measurements given
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The symbol Σ (called sigma) means "sum up". So, in this case, the expression indicates the sum of the (xᵢ)², where i goes from 1 to 4, which is 1, 2, 3 and 4. Then, we have:
[tex]\sum_{i\mathop{=}1}^4(x_i)^2=(x_1)^2+(x_2)^2+(x_3)^2+(x_4)^2[/tex]From the word problem, we know the value of each xᵢ.
[tex]\begin{gathered} x_1=5 \\ x_2=13 \\ x_3=19 \\ x_4=16 \end{gathered}[/tex]Finally, we operate.
[tex]\begin{gathered} \sum_{i\mathop{=}1}^4(x_i)^2=(x_1)^2+(x_2)^2+(x_3)^2+(x_4)^2 \\ \sum_{i\mathop{=}1}^4(x_i)^2=(5)^2+(13)^2+(19)^2+(16)^2 \\ \sum_{i\mathop{=}1}^4(x_i)^2=25+169+361+256 \\ \sum_{i\mathop{=}1}^4(x_i)^2=811 \end{gathered}[/tex]AnswerThe result of computing the given expression is 811.
Clara scores 24 points per coin. In all, how many coins does Clara have to collect to score a total of 48 points?
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Convert 0.03 inches to days to grow 3 inches
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Answer: 700
Step-by-step explanation:
i am smart
Find the variance and the standard deviation of the following set,(5,6,7,8,9)
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To find the variance, and standard deviation, calculate first for the mean.
[tex]\begin{gathered} \mu=\frac{\sum x_i}{n} \\ \mu=\frac{5+6+7+8+9}{5} \\ \mu=\frac{35}{5} \\ \mu=7 \end{gathered}[/tex]Now that we have the mean, we can now solve for the variance.
[tex]undefined[/tex]solve for y y - 2x = 15
Answers
Starting with the equation:
[tex]y-2x=15[/tex]Add 2x to both sides of the equation:
[tex]y-2x+2x=15+2x[/tex]Since -2x+2x=0, then:
[tex]y=15+2x[/tex]solve the literal equation for x.v= x• y•zx=
Answers
v = x• y•z
v/(y•z) = x• y•z/(y•z) (dividing by (y•z) on both sides of the equation)
v/(y•z) = x (simplifying)
The answer is x=v/(y•z)
One option in a roulette game is to bet $20 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) Ifthe ball lands on red, you get to keep the $20 you paid to play the game and youare awarded $20. If the ball lands elsewhere, you are awarded nothing and the $20that you bet is collected. Find the expected payback for this roulette game if you bet $20 on red.The expected payback is $ (Round to the nearest cent as needed.)
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In order to calculate the expected value, we need to calculate the sum of products of every possibility (the product of its pr
Eliminate factors equivalent to 1 and rewrite the right side of this equation
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You deposit $1,200 in an account that earns 5% interest compounded monthly. Estimate how long it would take for the investment to double.
Answers
17.5 years.
It takes 17.5 years to double the investment of $1200.
What is compound interest?Compound interest simply means that the interest on a bank account, loan, or investment grows exponentially over time rather than linearly.Given ,
P = $1200
r = 5 % = 0.05
n = 12
A = $2400( Since double of p)
Equation ,
A = [tex]P ( 1 + r / n)^{nt}[/tex]
2400 = [tex]1000 ( 1 + .05/ 12)^{12t}[/tex]
2.4 = [tex](1 + .05/12)^{12t}[/tex]
log both sides,
log 2.4 = log[tex]( 1 + .05/ 12)^{12t}[/tex]
log 2.4 = 12t . log ( 1 + .05/ 12)
(log 2.4) / (12 log (1 + .05/ 12)) = t
t = 17.5 years.
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Can someone help me asap
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Answer:
A) 670
B) 192 and 670
C) 192
an astronsut weighs 174 pounds on earth and 29 pounds on the moon if his daughter weighs 108 pounds on earth what is the daughters weight on the moon in pounds
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Answer:
Step-by-step explanation:
18 pounds
Stella is a scientist. She observes and counts 210 bacteria in a culture. Later, Stella counts again and finds the number has increased by 30%. How many bacteria are there now? There are bacteria now.
Answers
Answer:
273
Step-by-step explanation:
you just need to find 30% of 210 which is 63
Then you do 210 + 63 which is 273 bacteria
Corbin begins calculating the volume of a cylinder, in cubic meters, using the following steps. V = Bh V = (113.04) x 20 Which model could represent Corbin's cylinder? 120 m 113.04 m 20 m 36 m A 20 m 6 m 20 m *50.52 m
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Given the following expression:
[tex]\begin{gathered} V=Bh \\ \Rightarrow V=(113.04)\cdot(20) \end{gathered}[/tex]Notice that the value of the area of the base is the following:
[tex]B=\pi\cdot r^2=113.04[/tex]with pi = 3.14, we can solve for r to find the radius of the cylinder:
[tex]\begin{gathered} 3.14r^2=113.04 \\ \Rightarrow r^2=\frac{113.04}{3.14}=36 \\ \Rightarrow r=\sqrt[]{36}=6 \\ r=6 \end{gathered}[/tex]therefore, the cylinder has radius 6 and height 20 (the correct model is C)
A bank deposit slip shows a total of $441 in $1 loonies and $2 coins. If the number of $2 coins was 3 times the number of $1 loonies, how many of each are there?
Answers
The number of $1 loonies are 63 and the number of $2 coins are 189
Let x be the number of $1 loonies and y be the number of $2 coins.
A bank deposit slip shows a total of $441 in $1 loonies and $2 coins.
so, we get an equation,
x + 2y = 441 .................(1)
The number of $2 coins was 3 times the number of $1 loonies.
so, we get an equation,
y = 3x .............(2)
Substitute the above value of in equation (1),
x + 2(3x) = 441
x + 6x = 441
7x = 441
x = 63
Substitute above value of x in equation (2),
y = 3 * 63
y = 189
Therefore, the number of $1 loonies are 63 and the number of $2 coins are 189
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Sales are $500,00 and variable cost are $350,00. What is the contribution margin ratio
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If Sales are $500,000 and variable cost are $350,000. The contribution margin ratio is 30%.
What is contribution margin ratio?Contribution margin ratio can be determine or find by substracting or deducting the variables cost form the sales and then dividing it by the sales.
Now let find the contribution margin ratio using this formula
Contribution margin ratio = Sales - Variable cost / Sales
Where:
Sales = $500,000
Variable costs = $200,000
Let plug in the formula
Contribution margin ratio = $500,000 - $350,000 / $500,000
Contribution margin ratio = $150,000 / $500,000
Contribution margin ratio = 0.3 × 100
Contribution margin ratio = 30%
Therefore we can conclude that 30% is the contribution margin ratio .
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A can of beans has surface area 329 cm². Its height is 14 cm. What is the radius of the circular top?
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radius = 1/2 x (square root of 14^2 + 2 x 329 / pi) - 14 / 2
radius = 3.07 to 2dp
Lionfish are considered an invasive species, with an annual growth rate of 65%. A scientist estimates there are 7,000 lionfish in a certain bay after the first year.Write the explicit equation for f (n) that represents the number of llonfish in the bay after in years. Show all necessary math work.
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
Lionfish:
growth rate: 65%
time = 1 year
amount (1) = 7000
Step 02:
explicit equation:
f(1) = 7000
n = time
r = 65% = 0.65
f(n) = f(1) * r ^ (n - 1)
f(n) = 7000 * (0.65) ^ (n - 1)
[tex]f(n)\text{ = 7000 }\cdot(0.65)^{(n-1)}[/tex]The answer is:
f(n) = 7000 * (0.65) ^ (n - 1)
Solve quadratic equations by finding square roots (2r-5)^2=81
Answers
r
=
7
r
=
−
2
Explanation:
(
2
r
−
5
)
2
=
81
or
2
r
−
5
=
±
√
81
or
2
r
−
5
=
±
9
or
2
r
=
5
±
9
or
r
=
5
±
9
2
or
r
=
5
+
9
2
or
r
=
14
2
or
r
=
7
-------------Ans
1
or
r
=
5
−
9
2
or
r
=
−
4
2
or
r
=
−
2
------------Ans
2
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Find S20 given -4,8,20,32, ... Precalc Series and sequences, will give brainliest.
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Solution
Step 1
Given -4, 8, 20, 32....
Common difference
8- (-4)=12
20 -8= 12
32- 20= 12
The common difference (d) is 12
Step 2
We are finding the sum of the first 20th term
[tex]S_{20}=\frac{n}{2}(2a+(n-1)d)[/tex]where n is 20
d is 12
a is -4
[tex]\begin{gathered} S_{20}=\frac{20}{2}(2\times-4\text{ +(20-1)12)} \\ S_{20}=10(-8+(19)12) \\ S_{20\text{ }}=10(-8+228) \\ S_{20}=10(220) \\ S_{20}=2200 \end{gathered}[/tex]Which of the following is equivalent to the expression below?
√28-√63+√112
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The value of given expression is 3√7.
What is the expression?
An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
F(x) = √28 - √63 + √112
F(x) = 2√7 - 3√7 + 4√7
F(x) = 3√7
Option A is right answer.
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Need help ASAP thank you
Answers
Domain and range of a function is the set of values that we are allowed to enter into our function. This set consists of the x values for a function like f. (x). The set of values that a function can accept as input is known as its range.
answer -2< = x< = 3.
What are some illustrations of the domain and range of a function?
A simple function, such f(x) = x2, can only have the counting numbers 1, 2, 3, etc. as its domain (what goes in) and the set of numbers 1, 4, 9, etc. as its range (what comes out). Another function, g(x) = x2, may have a range of..., and an integer domain of..., -3, -2, -1, 0... 1, 2, 3.
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I need help breaking it down to understand the answer.
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SOLUTION
Each amount in the situation with the expression that represents it will be shown below
Situation Expression
The centimeters of rain on Thursday r
How many more centimeters of rain fell on Saturday 0.15r
than on Thursday
The centimeters of rain on Saturday 1.15r
what is the error and how do I explain it
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When we do multiplications of polynomials we have to multiply every term of the first expression with every term of the second expression, then:
[tex]\begin{gathered} (k+4)^2=(k+4)(k+4) \\ =k\cdot k+4k+4k+4\cdot4 \\ =k^2+8k+4^2 \\ =k^2+8k+16 \end{gathered}[/tex]Now, the error in the expression given is that they did not do all the possible multiplications, they only squared the two terms.
10 POINTS
The given table of values represents a linear equation. What is the slope?
x 3 4 5 6
y 1 5 9 13
Responses
2,
3,
5,
4
Answers
The slope of the linear equation is 4.
We are given a table which has the values of the "x" column and the corresponding "y" column.The values in the "x" column are 3, 4, 5, and 6.The values in the "y" column are 1, 5, 9, and 13.The values represent the linear equation as given.We need to find the slope of the linear equation.We can form the data into coordinate form.The points are (3, 1), (4, 5), (5, 9), and (6, 13).Let us consider the first (3, 1) and the last point (6, 13) to cover the whole range of the data that is given to us.The slope is given by the ratio of the change in the y-coordinates to the change in the x-coordinates.The slope is Δy/Δx.The slope is (13 - 1)/(6 - 3).The slope is 12/3.The slope is 4.To learn more about equations, visit :
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In ADEF below, mZD=3x+5, mZE = 4x-15, and mZF = 2x+10. Which statement is1) DF=FE2) DE = FE3) m
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Therefore:
[tex]DF=FE[/tex]properties of chords. leave answer in simplest form. DONT TAKE FOREVER TO ANSWER
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Let's put more details in the figure to better understand the problem:
To be able to determine DC, let's treat this as two similar triangles and apply ratio and proportion.
We get,
[tex]\text{ }\frac{\text{ AB}}{\text{ OB}}\text{ = }\frac{\text{ EF}}{\text{ OE}}[/tex][tex]\frac{18}{12}\text{ = }\frac{x}{\text{ 10}}[/tex][tex]\frac{18\text{ x 10}}{12}\text{ = }x[/tex][tex]\frac{180}{12}\text{ = }x[/tex][tex]15\text{ = }x[/tex][tex]\text{ FE = 15}[/tex]If a diameter or radius is perpendicular to a chord, then it bisects the chord and its arc. Therefore, we can say that FE = ED.
Determining the length of FD, we get:
[tex]\text{ FE + ED = FD}[/tex][tex]\text{ FE + FE = FD}[/tex][tex]\text{ 15 + 15 = FD}[/tex][tex]\text{ FD = 30}[/tex]Therefore, FD = 30
please help asap! will give brainliest
Answers
Answer:
See below
Step-by-step explanation:
It'll look like this (but you will need to change the + - signs on the x and y axes !)
Step by step
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
Your coordinates and the new coordinates after 180 degree rotation
(4, 4) ➡️ (-4, -4)
(4, 1) ➡️ (-4, -1)
(2, 1) ➡️ (-2, -1)
(2, 3) ➡️ (-2, -3)
So with each rule in transformations, you change the sign and/or the x and y change places. In the 180 degree rotation, we simply change the x and y sign, taking the shape from a positive x and y location in quadrant I to a negative x and y location in quadrant 3.
See my attachment below
