Answers
In order to solve by elimination, let's multiply the first equation by -2. This way, when we add the equations, the variable y will be canceled out:
[tex]\begin{cases}-6x-2y=-18 \\ x+2y={3}\end{cases}[/tex]Now, adding the equations, we have:
[tex]\begin{gathered} -6x-2y+x+2y=-18+3\\ \\ -5x=-15\\ \\ x=\frac{-15}{-5}\\ \\ x=3 \end{gathered}[/tex]Now, calculating the value of y, we have:
[tex]\begin{gathered} x+2y=3\\ \\ 3+2y=3\\ \\ 2y=0\\ \\ y=0 \end{gathered}[/tex]Therefore the solution is (3, 0).
Related Questions
what is a solution in algebra?
Answers
To understand what is a solution we need to state first what is an equation:
Equation is a mathematical statement that is formed by
Find the equation of the line passing the poin (-7,2) that is perpendicular to line 4x-3y=10
Answers
Explanation
Step 1
find the slope of the given equation:
two lines are perpendicular it the product of the slopes equals -1, so
[tex]\begin{gathered} \text{ line 1 is perpendicular to line 2} \\ L1\parallel L2 \\ \text{if} \\ m_1\cdot m_2=-1 \end{gathered}[/tex]then , let
[tex]\begin{gathered} \text{ Line 1} \\ 4x-3y=10 \end{gathered}[/tex]to know the slope, we need to convert the equation into the form:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}[/tex]to do that, let's isolate y
so
[tex]\begin{gathered} 4x-3y=10 \\ \text{subtract 4x in both sides} \\ 4x-3y-4x=10-4x \\ -3y=10-4x \\ \text{divide both sides by -3} \\ \frac{-3y}{-3}=\frac{10-4x}{-3} \\ y=-\frac{10}{3}+\frac{4}{3}x \\ y=\frac{4}{3}x-\frac{10}{3} \\ y=\frac{4}{3}x-\frac{10}{3}\rightarrow y=\text{ mx+b} \end{gathered}[/tex]hence,
[tex]\text{slope 1=m}_1=\frac{4}{3}[/tex]Step 2
now, let's find the slope of the line 2
[tex]\begin{gathered} \text{let} \\ m_1=\frac{4}{3} \\ \end{gathered}[/tex]replacing
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ \frac{4}{3}\cdot m_2=-1 \\ \text{ to isolate, multiply both sides by 3/4} \\ \frac{4}{3}\cdot m_2\cdot\frac{3}{4}=-1\cdot\frac{3}{4} \\ m_2=-\frac{3}{4} \end{gathered}[/tex]so, the slope 2 is -3/4
Step 3
finally, let's find the equation of the line
use the expression
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \text{where} \\ \text{ m is the slope} \\ \text{and (x}_0,y_0)\text{ are the coordinates of a known point} \end{gathered}[/tex]let
[tex]\begin{gathered} m=m_2=-\frac{3}{4} \\ (x_0,y_0)=(-7,2) \end{gathered}[/tex]replace and isolate y
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-2=-\frac{3}{4}(x-(-7)) \\ y-2=-\frac{3}{4}(x+7) \\ y-2=-\frac{3}{4}x-\frac{21}{4} \\ \text{add 2 in both sides} \\ y-2+2=-\frac{3}{4}x-\frac{21}{4}+2 \\ y=-\frac{3}{4}+\frac{-21+8}{4} \\ y=-\frac{3}{4}x-\frac{13}{4} \\ y=-\frac{3}{4}x-\frac{13}{4} \end{gathered}[/tex]therefore, the answer is
[tex]y=-\frac{3}{4}x-\frac{13}{4}[/tex]I hope this helps you
Mallory Has 26 Yards of fabric that she will cut into pieces wach piece will be 2/3 yards long how many pieces will mallory have?
Answers
Divide the total lenght of the fabric ( 26 yards ) by the length of each piece ( 2/3)
26 / (2/3) = 39 pieces
The image of Rectangle PQRS reflected across the y-axis is Rectangle P'Q'R'S'. If the coordinates of the rectangle are P(-10,3), Q(-6,1), R(-2,6), S(-6,5), what will be the coordinates of P'? (-10,-3) (-3,-10) (3,10) (10,3)
Answers
Reflection across the y-axis means that every point in the figure transforms to
[tex](x,y)\rightarrow(-x,y)[/tex]Therefore, the point P(-10,3 ) will be transformed into
[tex]P(-10,3)\rightarrow P^{\prime}(10,3)\text{.}[/tex]which is the fourth choice.
A game has 3 possible outcomes:The first outcome has a probability of 0.2. The result is winning $30.The second outcome has a probability of 0.2. The result is winning $50.The third outcome has a probability of 0.6. The result is losing $80.Let X be the amount of your winnings. Then E(X) =
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We compute the expected value by multiplying each outcome by the probability of that outcome, next we add up those products.
[tex]E(X)=\text{ 30}\cdot0.2\text{ + 50}\cdot0.2-80\cdot0.6=\text{ 6+10-48=-32}[/tex]Find the distance between the two points rounding to the nearest tenth(if necessary).(-6,0) and (-9, -4)
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Find the distance between the two points rounding to the nearest tenth
(if necessary).
(-6,0) and (-9, -4)
Applying the formula to calculate the distance between two points
[tex]d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}[/tex]substitute the coordinates of the given points
[tex]d=\sqrt[]{(-4-0)^2+(-9+6)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{16+9} \\ d=\sqrt[]{25} \\ d=5\text{ units} \end{gathered}[/tex]1) The number of mice (in millions) is modeled by the function below, where t is measured in years. How many mice are in the culture after 10 year? (round to the nearest whole tenth) n(t) = 12e = 12e^0.012
Answers
The number of mice (in millions) is modeled by the function
[tex]n(t)=12e^{0.012t}[/tex]Since t is measured in years, to find how many mice are in the culture after 10 years we just need to substitute t for 10 in te previous function, obtaining:
[tex]n(10)=12e^{0.012(10)}=12e^{0.12}=13.52996222\approx14[/tex]Then aproximating the answer will be 14 that means that there will be 14 millions of mices after 10 years.
what is the best method to solve 2y=2x+12 y=-2x-3 and why?
Answers
2y = 2x + 12
y = -2x - 3
You have the value of y in the second equation
So you can substitute it in the first equation and find the value of x
2(-2x - 3) = 2x + 12
2(-2x) - 2(3) = 2x + 12
-4x - 6 = 2x = 12
You can add 6 to both sides and subtract 2x from both sides to find x
-4x - 6 + 6 = 2x + 12 + 6
-4x = 2x + 18
-4x - 2x = 2x - 2x + 18
-6x = 18
Divide both sides by -6
x = -3
Substitute x in equation (2) to find y
y = -2(-3) -3
y = 3
The solution is (-3, 3)
Using complete sentence, describe how the variable h and the variable k of the general formula for a cube root function effects the graph. And than here is the general formula,
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The variable k translates the graph of the function vertically, if k is positive then the translation is up; is k is negative the translation is up. Similarly the variable h translates the graph of the function horizontally, if h is positive the translation is to the right whereas if h is negative the translation is to the left.
The points D, E, F and G all lie on the same line segment, in that order, such that the ratio of DE: EF: FG is equal to 1 : 5:5. If DG 11, And DE.
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The ratio of DE: EF: FG of 1: 5 : 5 means that if there are 1+5+5 =11 parts, 1 part is DE, 5 parts is EF, and 5 parts is FG.
The length DG = DE + EF + EF+ FG is 11; therefore, the length of DE (which is 1 part ) is
[tex]DE=\frac{1}{11}[/tex]which is our answer!
describe the transformation of y=-2(x-2)^2 when compared to the parent function y=x^2
Answers
Answer:
Shifted to the right by 2 units
Vertically stretched by a factor of 2
Explanation:
The transformed parabola given is different from the parent function in that is multiplied by 2 and there is 2 subtracted from the x -coordinate.
Subtracting 2 from the x-coordinate shifts the parent function to the right by 2 units.
Multiplying the parent function by 2 stretches it vertical by a factor of 2.
Therefore, when comparing the parent function y = x^2 and its transformed version y = 2 (x-2)^2, the latter can be described as:
The function y = y = 2 (x-2)^2 results when the parent function is
Shifted to the right by 2 units
Vertically stretched by a factor of 2
Algebra 1 Write a system of inequalities to represent the shaded portion of the graph.
Answers
Given: A shaded portion of the graph
Required: System of inequalities to represnt the shaded portion.
Explanation:
Firstly consider the the non-dotted line.
It passes through two points. (0,3) and (-1.5,0)
So write the equation of line using two point form.
[tex]\begin{gathered} y-3=\frac{3-0}{0-(-1.5)}(x-0) \\ y-3=2x \end{gathered}[/tex]so the equation is
[tex]2x-y+3=0[/tex]Since (0,0) lies in shaded region, therefore the inequality is
[tex]2x-y+3\ge0[/tex]Now, consider the dotted line.
It passes through two points. (-3,0) and (0,-1).
Equation of dotted line is
[tex]\begin{gathered} y-0=\frac{0-(-1)}{-3-0}(x+3) \\ y=-\frac{1}{3}(x+3) \end{gathered}[/tex]So the equation is
[tex]\begin{gathered} 3y=-x-3 \\ x+3y+3=0 \end{gathered}[/tex]Now, since (0,0) lies in the shaded portion, therefore the inequality is
[tex]x+3y+3>0[/tex]Final Answer: The system of inequalities are
[tex]\begin{gathered} 2x-y+3\ge0 \\ x+3y+3>0 \end{gathered}[/tex]Question 7 of 10Use the function below to find F(1).F(t)=2..23tO A. 3-Im1O B. 2O C.O D.SUBMIT
Answers
Answer: C. 1/4
Explanation
Given
[tex]F(t)=2\cdot\frac{1}{2^{3t}}[/tex]As we are asked to find F(1), then we have to substitute 1 over t:
[tex]F(1)=2\cdot\frac{1}{2^{3(1)}}[/tex]By multiplying the expression in the exponent we get:
[tex]F(1)=2\cdot\frac{1}{2^3}[/tex]We can rewrite this expression as follows as we have 2 elevated to the third power:
[tex]F(1)=\frac{2}{2\cdot2\cdot2}[/tex]Simplifying;
[tex]F(1)=\frac{1}{2\cdot2}[/tex][tex]F(1)=\frac{1}{4}[/tex]Factor 35r + 40s - 30t. Write your answer as a product with a whole number greater than 1.
Answers
Answer:
5(7r+8s-6t)
Explanation:
Given the expression:
[tex]35r+40s-30t[/tex]The greatest common factor of 35, 40 and 30 = 5
Therefore:
[tex]\begin{gathered} 35r+40s-30t=5\mleft(\frac{35r}{5}+\frac{40s}{5}-\frac{30t}{5}\mright) \\ =5(7r+8s-6t) \end{gathered}[/tex]A2012с16BFind cos(ZBAC + 30°).
Answers
Given:
[tex]\begin{gathered} AC=12 \\ AB=20 \\ BC=16 \end{gathered}[/tex]We know the indentity,
[tex]\begin{gathered} \cos (A+B)=\cos A\cos B-\sin A\sin B \\ \cos (\angle BAC+30^{\circ})=\cos (\angle BAC)\cos 30^{\circ}-\sin (\angle BAC)\sin 30^{\circ} \\ \cos (\angle BAC+30^{\circ})=\cos (\angle BAC)\frac{\sqrt[]{3}}{2}^{}-\sin (\angle BAC)\frac{1}{2} \end{gathered}[/tex]Now,
[tex]\begin{gathered} \cos (\angle BAC)=\frac{AC}{AB}=\frac{12}{20}=\frac{3}{5} \\ \sin (\angle BAC)=\frac{CB}{AB}=\frac{16}{20}=\frac{4}{5} \end{gathered}[/tex]It gives,
[tex]\begin{gathered} \cos (\angle BAC+30^{\circ})=\cos (\angle BAC)\frac{\sqrt[]{3}}{2}^{}-\sin (\angle BAC)\frac{1}{2} \\ \cos (\angle BAC+30^{\circ})=\frac{3}{5}\times\frac{\sqrt[]{3}}{2}-\frac{4}{5}\times\frac{1}{2} \\ \cos (\angle BAC+30^{\circ})=\frac{3}{10}\sqrt[]{3}-\frac{2}{5} \end{gathered}[/tex]Answer:
[tex]\cos (\angle BAC+30^{\circ})=\frac{3}{10}\sqrt[]{3}-\frac{2}{5}[/tex]Which of the following out the algebraic expression is not simplified?
Answers
Solution
- In order for us to figure out which of the options is not simplified, we simply need to check which of the options has more than 1 like term.
- Observing the options, we find out that:
[tex]\begin{gathered} \text{ Option C has more than 1 like terms. They are:} \\ 2p^2q^2\text{ and }-2p^2q^2 \end{gathered}[/tex]- Had the expression been simplified, we would have had:
[tex]\begin{gathered} 2p^2q^2+2p^2q^3-2p^2q^2+xy \\ \text{ Collect like terms} \\ \\ 2p^2q^2-2p^2q^2+2p^2q^3+xy \\ \\ =2p^2q^3+xy \end{gathered}[/tex]Final Answer
The answer is OPTION C
what is the y value of the solution to the system of equations shown below y = 22 - 6 y = 50 – 21
Answers
Given the equation system:
[tex]\begin{cases}y=2x-6 \\ y=5x-21\end{cases}[/tex]To determine the y-value of the solution of the equation system, first, you have to calculate the value of x.
To determine the value of x, equal both expressions:
[tex]2x-6=5x-21[/tex]-Pass the x-term to the left side of the equation and the constant to the right side of the equation by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 2x-5x-6=5x-5x-21 \\ -3x-6=-21 \end{gathered}[/tex][tex]\begin{gathered} -3x-6+6=-21+6 \\ -3x=-15 \end{gathered}[/tex]-Divide both sides by -3 to reach the value of x:
[tex]\begin{gathered} -\frac{3x}{-3}=-\frac{15}{-3} \\ x=5 \end{gathered}[/tex]Now that you have determined the value of x, replace it in either one of the equations to calculate the corresponding y-value, for example, replace the first equation with x=5
[tex]\begin{gathered} y=2x-6 \\ y=2\cdot5-6 \\ y=10-6 \\ y=4 \end{gathered}[/tex]So the corresponding y value for the solution of this equation system is y= 4 (option D)
How to write 4/9 as a decimal using long division
Answers
Using long division:
Answer:
[tex]\frac{4}{9}=0.444[/tex][tex]\frac{5}{8}[/tex]Answer:
[tex]\frac{5}{8}=0.625[/tex]Five scores have the same mean and median. If the four lowest scores are 20, 30, 50, and 60, what is thehighest score?
Answers
Let's call the highest score 'x'.
The scores in the crescent order would be:
20, 30, 50, 60, x.
So the median of those scores is 50.
If the mean and median are equal, we have that the mean is also 50, so we can find the value of x using:
[tex]\begin{gathered} 50=\frac{20+30+50+60+x}{5} \\ 250=20+30+50+60+x \\ 250=160+x \\ x=250-160=90 \end{gathered}[/tex]So the highest score is 90.
Which statements are true about the graph of this line? 1. The slope is increasing 2. y=x-23. The slope is decreasing 4. y=x+2
Answers
Answer:
1. The slope is increasing
2. y=x-2
Explanation:
First we need to get the slope of the line. Using the coordinate points;
(6,4) and (2, 0)
Slope m = y2-y1/x2-x1
m = 0-4/2-6
m = -4/-4
m = 1
Since the slope is a positive value, hence the slope is increasing
Get the intercept
Substitute m = 1 and (2, 0) into y = mx+c
0 = 2(1) + c
0 = 2+c
c = -2
Get the required equation
y - mx+c
y = 1x + (-2)
y = x - 2
Hence the correct option is slope is increasing and y = x-2
A bird bath that is 5.3 ft tall casts a shadow that is 22.3 ft long. Find the length of the shadow that a 6.3 ft car casts.
Answers
Consider that the realtion in between the bird bath and its shadow is proportional, then, you have:
5.3/22.3 = 6.3/x
where x is the length of the shadow. Solve for x the previous equation:
x = (6.3/5.3)(22.3)
x = 26.50
Hence, the length of the shadow is 26.50 ft
dan's cooler holds 5 gallons of water if he pours 1/5 gallons of water into each water bottle how many water bottles will it take to empty the cooler of water
Answers
Solution
For this case we have the following rate:
[tex]\frac{1}{5}\cdot\frac{\text{gallons}}{\text{bottle}}[/tex]The total amount of volume is 5 gallons
Then we can find the number of bottles in the following way:
[tex]\text{Bottles}=\frac{5\text{gal}}{\frac{1}{5}\cdot\frac{\text{gal}}{\text{bot}}}=25\text{bottles}[/tex]Then the total of bottles are 25
Each drop contains 0.14mL. After 6 drop how much liquid has been dropped?
Answers
The total amount of liquid dropped is 0.84 mL
Here, we want to calculate the total amount of liquid dropped
From the question, we are given the amount of each drop
So the total amount of 6 drops will be 6 multiplied by the amount of each drop
Mathematically, that would be;
[tex]0.14\text{ mL }\times\text{ 6 = 0.84 mL}[/tex]Find the number of ground miles from a point directly below the plain to the radar station
Answers
The distance from the place and the radar station is 160 miles and the angle of depression is 34º
The distance of the plane to the ground, the horizontal distance between the plane and the radar station, and the direct distance from the plane to the radar station form a right triangle.
The angle of depression is the angle from the horizontal downward an object (radar station) from the point of view of an observer (plane)
You have to determine the horizontal distance between the plane and the radar station, since that side is opposite to the known angle, use the trigonometric ratio that relates the hypotenuse with the opposite side of an angle. That would be the sine
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypothenuse}}[/tex]Where
θ is the angle
"opposite" refers to the side that does not interact with the angle
"hypothenuse" is the distance between the plane and the radar station
Replace the expression with the known measures
[tex]\sin 34=\frac{x}{160}[/tex]Multiply both sides by 160 to determine the value of x
[tex]\begin{gathered} 160\cdot\sin 34=x \\ x=89.47 \end{gathered}[/tex]The ground distance between the plane and the radar station is 89.47 miles
how many litres are there in 35,853 cm3
Answers
We have first the next equivalence
1 liter = 1000 cm^3
x liter = 35,853 cm^3
x is the number of liters in 35,853 cm^3
x is calculated if we divide
Please solve this, also, pls ignore the part that's scratched/ crossed out :)
Answers
The standard form is given by:
[tex]\begin{gathered} y=Ax^2+Bx+C \\ or \\ x=Ay^2+By+C \end{gathered}[/tex]Therefore:
[tex]x=\frac{y^2}{2}-y+\frac{5}{2}[/tex]The vertex is the point V(h,k) which is given by:
[tex]\begin{gathered} k=\frac{-b}{2a} \\ h=y(k) \\ ---- \\ k=-\frac{-1}{2(\frac{1}{2})}=1 \end{gathered}[/tex][tex]y(1)=\frac{1^2}{2}+-1+\frac{5}{2}=2=h[/tex]Therefore, the vertex is:
[tex]V=(2,1)[/tex]the focus is:
[tex](3,1)[/tex]And the directrix is:
[tex]x=1[/tex]Complete the following statement.a0 -9 = -10
Answers
ANSWER
x = -1
EXPLANATION
Let us replace the box with x:
x - 9 = -10
To solve this, collect like terms by taking the -9 to the other side.
The sign changes:
x = 9 - 10
x = -1
simplify the expression. 1.4z^2 + 5.4 + 6z - 2.1 - 3z. + z^2 =
Answers
1.4z² + 5.4 + 6z - 2.1 - 3z + z² =
Combining similar terms:
= (1.4z² + z²) + (6z - 3z) + (5.4 - 2.1) =
= 2.4z² + 3z + 3.3
An airport shuttle company owns cars that have a maximum capacity of 4 passengers and vans that have a maximum capacity of 9 passengers.They have 11 total vehicles that can combine to carry out 79 passengers. write a system of equations to represent this situation (hint: x=number of cars,y=number of vans)
Answers
Let x represent the number of cars
Let y represent the number of vans
We were told that the maximum capacity of the car is 4 passengers. This means that the number of passengers that x cars would carry is 4 * x = 4x
Also, the maximum capacity of the van is 9 passengers. This means that the number of passengers that y vans would carry is 9 * y = 9y
The total number of vehicles used is 11. It means that
x + y = 11
Also, the 11 vehicles can combine to carry 79 passengers. This means that
4x + 9y = 79
The equations are
x + y = 11
4x + 9y = 79
This question has multiple parts of it you can not do one with out the other
Answers
Part A:
Let:
V = Volume
r = Radius
h = Height = 20 ft
The volume of a cylinder is given by:
[tex]\begin{gathered} V(r)=\pi r^2h \\ so\colon \\ V(r)=20\pi r^2 \end{gathered}[/tex]Answer for part A:
[tex]V=20\pi r^2[/tex]Part B:
From the previous equation, solve for r:
Divide both sides by 20π:
[tex]r^2=\frac{V}{20\pi}[/tex]Take the square root of both sides:
[tex]\sqrt[]{r^2}=\sqrt[]{\frac{V}{20\pi}}[/tex]Answer for part B:
[tex]r=\sqrt[]{\frac{V}{20\pi}}[/tex]Part C:
Using the previous equation:
[tex]r=\sqrt[]{\frac{V}{20\pi(3.14)}}[/tex]Graphing the function: