Solve the following system of linear equations by graphing:4.Ex+3y54 9- 5858615+cilo=Answer 2 PointsKeypadKeyboard ShortcutsGraph the linear equations by writing the equations in slope-intercept form:y =Ixty =IxtIdentify the appropriate number of solutions. If there is a solution, give thepoint:O One SolutionO No SolutionO Infinite Number of Solutions
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We have a system of equations:
[tex]\begin{gathered} -\frac{4}{5}x+3y=-\frac{58}{5} \\ \frac{4}{3}x+\frac{9}{5}y=\frac{86}{15} \end{gathered}[/tex]We have to write the equations in slope-intercept form.
We start with the first equation:
[tex]\begin{gathered} -\frac{4}{5}x+3y=-\frac{58}{5} \\ 3y=-\frac{58}{5}+\frac{4}{5}x \\ 5\cdot3y=4x-58 \\ 15y=4x-58 \\ y=\frac{4}{15}x-\frac{58}{15} \end{gathered}[/tex]For the second equation we get:
[tex]\begin{gathered} \frac{4}{3}x+\frac{9}{5}y=\frac{86}{15} \\ \frac{9}{5}y=\frac{86}{15}-\frac{4}{3}x \\ y=\frac{5}{9}\cdot\frac{86}{15}-\frac{5}{9}\cdot\frac{4}{3}x \\ y=\frac{86}{9\cdot3}-\frac{20}{27}x \\ y=-\frac{20}{27}x+\frac{86}{27} \end{gathered}[/tex]To graph the equations we need two points. We can easily identify the y-intercept from the equations, but we have to identify one more point for each equation.
We can give a value to x and find the corresponding value of y.
Then, for example we can calculate y for x = 1 in the first equation:
[tex]\begin{gathered} y=\frac{4}{15}(1)-\frac{58}{15} \\ y=\frac{4}{15}-\frac{58}{15} \\ y=-\frac{54}{15} \end{gathered}[/tex]Then, for the first equation we know the points (0, -58/15) and (1, -54/15).
For the second equation we can do the same, by giving a value of 1 to x (NOTE: we can give any arbitrary value to x, it does not have to be the same for both equations) and calculate y:
[tex]\begin{gathered} y=-\frac{20}{27}(1)+\frac{86}{27} \\ y=-\frac{20}{27}+\frac{86}{27} \\ y=\frac{66}{27} \end{gathered}[/tex]Now we know the points of the second equation: (0, 86/27) and (1, 66/27).
With such fractions we can not make an accurate graph in paper, as they don't match the divisions of the grid.
We can use approximate decimals values for the fractions and graph the points.
The approximations for the first equation are:
[tex]\begin{gathered} (0,-\frac{58}{15})\approx(0,-3.9) \\ (1,-\frac{54}{15})=(1,-3.6) \end{gathered}[/tex]and for the second equation:
[tex]\begin{gathered} (0,\frac{86}{27})\approx(0,3.2) \\ (1,\frac{66}{27})\approx(1,2.4) \end{gathered}[/tex]We can then graph the equations as:
If we graph the equations with the exact points, we get an intersection point at (7,-2).
This intersection is the unique solution to both equations at the same time, so it is the only solution to the system of equations.
Answer:
The equations in slope-intercept form are:
y = 4/15 x + (-58/15)
y = -20/27 * x + 86/27
The system has only one solution: (7, -2).
Related Questions
Which answer describes the pattern in this sequence?12) 412, 1, 21OaddO multiply by 2o subtract 1multiply by12
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Answer:
The answer that describes the pattern in this sequence is;
[tex]\text{ multiply by }\frac{1}{2}[/tex]Explanation:
Given the sequence;
[tex]2,1,\frac{1}{2},\frac{1}{4},\ldots[/tex]The sequence shows a Geometric Progression.
The common ratio of the sequence would be;
[tex]\begin{gathered} r=\frac{1}{2}=\frac{\frac{1}{2}}{1}=\frac{\frac{1}{4}}{\frac{1}{2}} \\ r=\frac{1}{2} \end{gathered}[/tex]Therefore, the answer that describes the pattern in this sequence is;
[tex]\text{ multiply by }\frac{1}{2}[/tex]
A park volunteer Plans to work on pallet Stonewall for one hour every Monday one every Wednesday and three hours on Friday
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Solution
For this case we can do the following:
Part a
we can select the points (0,0) and (2,10) and k is given by:
[tex]k=\frac{10-0}{2-0}=5[/tex]Part b
The equation is given by:
y= 8x
Part c
We can replace x= 16 in the equation and we got:
y= 8*16= 128 hours
please help with this i will attach photo of figure
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The variable I=f(w) represents the number of individuals (in thousands) infected w weeks after the epidemic begins.
The value of I=f(2) represents the number of individuals in thousandas infected 2 weeks after the beginning of the epidemic.
From the graph, where I=8, we can conclude that there are 8,000 infected people after 2 weeks of the beginning of the epidemic.
Answer:
f(2) = 8
Means 8,000 people are infected after 2 weeks of the beginning of the epidemic.
Determine the linear equation of the vertical and horizontal line passing through the point (5,8).
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Given:
The horizontal and vertical line psses through the point (5,8).
To find:
Find the equation of vertical and horizontal line passing through the given point.
Equation of vertical line:
[tex]x=5[/tex]Equation of horizontal line:
[tex]y=8[/tex]Which I two triangles are congruent? Complete the congruence statement.
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Answer:
∆vuw≈∆bca∆uvw≈∆cba∆vwu≈∆bac
a. Determine whether the equation x/4-x/3=1 is a linear equation. If yes, identify the equation in standard form.
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The given equation is a linear equation and its standard form is [tex]3x-4y=12[/tex].
The given equation is -
[tex]\frac{x}{4}-\frac{y}{3}=1[/tex] ---- (1)
We have to determine if the given equation is a linear equation. If it is a linear equation, then we have to write it in standard form.
A linear equation is referred to as the equation of a straight line.
A linear equation with two variables can be written in the standard form as
[tex]ax+by=c[/tex]
where a, b, c are constants
and, x, y are variables
So, from equation (1), we can say that -
The equation [tex]\frac{x}{4}-\frac{y}{3}=1[/tex] is a linear equation.
Identifying the equation in standard form, we have
[tex]\frac{x}{4}-\frac{y}{3}=1\\= > \frac{3x-4y}{12}=1\\ = > 3x-4y=12[/tex]
Hence, the standard form of the given linear equation is [tex]3x-4y=12[/tex].
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Determine the correct order of the numbers from least to greatest. 1.3, -2.875, 6.75, -4, -1.67, -3.75, 3.5
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By definition, the Positive numbers are those numbers greater than zero and Negative numbers are those numbers less than zero.
Therefore, you know that the Positive numbers are greater than the Negative numbers.
For this exercise it is also important to remember that the Absolute value of a number tells you its distance from zero on the Number line. The Absolute value of a number is always positive.
Knowing the above, you can set up that:
[tex]-4<-3.75<-2.875<-1.67<1.3<3.5<6.75[/tex]Remember that this symbol means "Less than":
[tex]<[/tex]The answer is:
[tex]-4,-3.75,-2.875,-1.67,1.3,3.5,6.75[/tex]2. Which statement is an example of a transitive relationship? If ctm and m || n, then cin. If x = 2y and 2y 8, then x = 4. If a Il band b || c, then a || o. If min and mlp, then m || p.
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A relationship is said to be transitive, if
a R b, b R c, then → a R c.
Test the given options
For the first option, if x = 2y and 2y = 8, then for transitive relationship,
[tex]\begin{gathered} x=2y \\ 2y=8 \\ then,x=8 \end{gathered}[/tex]the first option is not correct because x ≠ 4
For the second option, If a Il b and b || c, then a || c
[tex]\begin{gathered} a\text{ R b means that a is parallel to b} \\ b\text{ R c means that b is parallel to c} \\ a\text{ R c means that a is parallel to c} \end{gathered}[/tex]Looking at the second option, there is a relationship of parallelism between a, b and c, therefore, this is a transitive relationship
For the third option
If m ⊥ n and m ⊥ p, then m ∥ p.
The statement from the point of view of transitive relationship is incorrect
it should be, n ⊥ p.
Tracy wants to buy some food for her slumber party. Great Foods Grocery Store is selling 2 bags of potato chips for $6.50 and 5 two-liter sodas for $3.00. Best FoodsGrocery Store is selling 2 bags of potato chips for $5.00 and 3 two-liter sodas for $2.00. if p = potato chips and s= two-liter sodas, write a system of equations to model thisproblem2p=5.00 and 3s=2.006.50p + 3.00s= 7 and 5p +2s=52p=6.50 and 5s=3.002p + 5s 9.50 and 2p +39 7.00
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Answer:
[tex]\begin{gathered} \text{ The system that describes this problem:} \\ 2p+5s=9.50 \\ 2p+3s=7.00 \end{gathered}[/tex]Step-by-step explanation:
Let p be the potato chips
Let s be the two-liter sodas
Then, if Great Foods Grocery Store is selling 2 bags of potato chips for $6.50 and 5 two-liter sodas for $3.00:
[tex]2p+5s=9.50[/tex]For Best Foods Grocery Store:
2 bags of potato chips for $5.00 and 3 two-liter sodas for $2.00.
[tex]2p+3s=7[/tex]Three vertices of parallelogram JKLM are J(1, 4), K(5, 3), and L(6,-3). Find the coordinates ofvertex M.The coordinates are MOD.
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Given data:
The coordinate of first vertex is J(1, 4).
The coordinate of second vertex is K(5, 3).
The coordinate of third vertex is L(6,-3).
Assume the coordinate of M is (x, y).
The diagonal of the parallelogram intersect at the mid point, the mid point of the diagonal JL is,
[tex]\begin{gathered} a=\frac{1+6}{2} \\ =\frac{7}{2} \\ b=\frac{4-3}{2} \\ =\frac{1}{2} \end{gathered}[/tex]This is also the mid point of KM diagonal.
[tex]\begin{gathered} \frac{7}{2}=\frac{x+5}{2} \\ x=2 \\ \frac{1}{2}=\frac{y+3}{2} \\ y=-2 \end{gathered}[/tex]Thus, the coordinate of M is (2, -2).
Which of the following has the same value as cos 2pi/3
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First, let's calculate the value of cos 2pi/3:
[tex]\cos\frac{2\pi}{3}=-0.5[/tex]Now, let's calculate the value of each option:
[tex]\begin{gathered} \cos\frac{\pi}{6}=0.866\\ \\ \\ \\ \cos\frac{4\pi}{3}=-0.5\\ \\ \\ \\ \sin\frac{5\pi}{3}=-0.866\\ \\ \\ \\ \sin\frac{7\pi}{6}=-0.5\\ \\ \\ \\ \cos\frac{11\pi}{6}=0.866 \end{gathered}[/tex]Therefore the correct options are B and D.
Not a timed or graded assignment. Need full work shown. Quick answer with work = amazing review
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The Solution:
Given the expression below:
[tex]10\text{ }\sqrt[]{112m^6}[/tex]We are asked to simplified in radical form.
Let's find the factors of 112.
[tex]\begin{gathered} 112=2\times56 \\ =2\times2\times28 \\ =2\times2\times2\times14 \\ =2\times2\times2\times2\times7 \end{gathered}[/tex][tex]\sqrt[]{m^6}=\sqrt[]{m^3\times m^3}[/tex]So,
[tex]\sqrt[]{112m^6}=\sqrt[]{112\times m^3\times m^3}=\sqrt[]{2\times2\times2\times2\times7\times m^3\times m^3}[/tex][tex]10\sqrt[]{112m^6}=10\sqrt[]{2\times2\times2\times2\times7\times m^3\times m^3}=10(2\times2\times m^3)\text{ }\sqrt[]{7}[/tex]Thus,
[tex]10\sqrt[]{112m^6}=\text{ }10(2\times2\times m^3)\text{ }\sqrt[]{7}=10(4)m^3\text{ }\sqrt[]{7}=40m^3\text{ }\sqrt[]{7}[/tex]Therefore, the correct answer is
[tex]40m^3\text{ }\sqrt[]{7}[/tex]I need to know the scale factor and what S is.
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In order to find the scale factor between the triangles, we can compare the sides PR and PT, which are corresponding sides between the triangles.
The side PR has a length of 27 units, and the side PT has a length of 9 units, so we can find the scale factor by dividing one length by the other:
[tex]\text{scale factor}=\frac{PR}{PT}=\frac{27}{9}=3[/tex]Now that we have the scale factor, we can find the length of PS by comparing it with the corresponding side PQ:
[tex]\begin{gathered} \text{scale factor}=\frac{PQ}{PS} \\ 3=\frac{24}{PS} \\ PS=\frac{24}{3}=8 \end{gathered}[/tex]If the length of PS is 8 units and S is above the x-axis to the right, its coordinates will be (8, 0).
Put the following equation of a line into slope-intercept form, simplifying all fractions. Žy 2x = 8 Answer: Submit Answer attempt 1 out of 2 Privacy Policy Terms of Service
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We have the following:
the equation of a line into slope-intercep form is:
[tex]y=mx+b[/tex]now,
[tex]\begin{gathered} 2y-2x=8 \\ 2y=2x+8 \\ y=x+4 \end{gathered}[/tex]therefore, the answer is:
[tex]y=x+4[/tex]Describe two methods you could use to solve for `x` in `1.12^{x}=20`
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EXPLANATION:
Given;
We are given the following equation;
[tex]1.12^x=20[/tex]Required;
We are required to describe two methods which can be used to solve for x in this equation.
Step-by-step solution;
We can solve for the variable x by taking the natural log of both sides of the equation. This is shown below;
[tex]1.12^x=20[/tex]We take the natural log of both sides;
[tex]ln1.12^x=ln20[/tex]Next we apply the log rule;
[tex]\begin{gathered} If: \\ log_bx^a \\ Then: \\ alog_bx \end{gathered}[/tex]Therefore, our equation is now refined and becomes;
[tex]xln1.12=ln20[/tex]Divide both sides by ln(1.12);
[tex]x=\frac{ln(20)}{ln(1.12)}[/tex]A second method is to express it as a logarithmic equation;
[tex]1.12^x=20[/tex]We shall apply the log rule which is;
[tex]\begin{gathered} If: \\ log_bx=a \end{gathered}[/tex][tex]\begin{gathered} Then: \\ b^a=x \end{gathered}[/tex]For example;
[tex]\begin{gathered} If: \\ log_{10}100=2 \end{gathered}[/tex][tex]\begin{gathered} Then: \\ 10^2=100 \end{gathered}[/tex]Therefore, for the equation given;
[tex]\begin{gathered} If: \\ 1.12^x=20 \end{gathered}[/tex][tex]\begin{gathered} Then: \\ log_{1.12}20=x \end{gathered}[/tex]Note that both solutions can be simplified eventually with the use of a calculator.
ANSWER:
(1) By taking the natural log of both sides
(2) By expressing the equation as a logarithmic equation
Help n k oh hi k. Hi hold kb b g g I
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SOLUTION:
[tex]v(n)=(14)\cdot b^n[/tex]The correct answer is;
If b = 1.06, the weekly growth rate of the share's value is 6%
A circle with a radius of 3.9 cm is centered at the vertex of an angle.Suppose the angle has a measure of 175 ____degrees.What is the radian measure of this angle?____ radians What is the length (in cm) of the arc subtended by the angle's rays along the circle?_____ cm Suppose θ represents the varying degree measure of the angle. Write an expression that represents the length (in cm) of the arc subtended by the angle's rays along the circle. (Enter "theta" for θ.) ______cm
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We can draw the following picture:
From the angle-arc relationships, since the vertex is at the center of the circle, then the arc is equal to 175 degrees.
In radians, 175 degrees is equivalent to
[tex]175=175\cdot(\frac{\pi}{180})\text{rad}[/tex]that is
[tex]175=3.054\text{ rad}[/tex]What is the radian measure of this angle? 3.054 radians
The arc-lengh S is given by
[tex]s=r\cdot\theta[/tex]where, r=3.9cm and theta is equal to 3.054 rad (which is 175 degrees but in this formula the number must be written in radians). By sustituting these value, we have
[tex]\begin{gathered} s=(3.9)(3.054) \\ s=11.91\text{ cm} \end{gathered}[/tex]What is the length (in cm) of the arc subtended by the angle's rays along the circle? 11.91 cm
Suppose θ represents the varying degree measure of the angle. Write an expression that represents the length (in cm) of the arc subtended by the angle's rays along the circle.
We wrote the formula above:
[tex]s=r\cdot\theta[/tex]where s is the arc-lenght, r is the radius and theta is the angle (in radians).
In a raffle, one ticket will win a $930 prize, and the other tickets will win nothing. There are 500 in the raffle, each costing $6. If you buy a ticket, what is the expected profit?
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8. The chart below shows the student lunch menu at a school. A lunch consists of onesandwich, one snack, and one drink.Lunch MenuSandwichSnack Drinkturkey apple juicebologna bananamilkpeanut buttercookieshamyogurtHow many different lunch choices does a student have?hirtants and subite or
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We have to find all the different lunch choices that a student have, where one lunch consists of one sandwich, one snack, and one drink.
For doing so, we remember the multiplication principle. As for each option of sandwich, we have _ options for the snacks, and for each snack we have _ options of drinks, we just have to multiply each one of the values. In this case,
Out of 167 randomly selected adults in the United States who were surveyed, 70 exercise on a regular basis. Construct a 90% confidence interval for the proportion of all adults in the United States who exercise on a regular basis. Round to three decimal places
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ANSWER:
(0.356, 0.482)
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the proportion with the data of the statement:
[tex]\begin{gathered} p=\frac{x}{n}=\frac{70}{167} \\ \\ p=0.4192 \end{gathered}[/tex]For a 90% confidence interval, we have that the value of Z is the following:
[tex]\begin{gathered} \alpha=1-90\% \\ \\ \alpha=1-0.9=0.1 \\ \\ \alpha\text{/2}=\frac{0.1}{2}=0.05 \\ \text{ } \\ \text{The corresponding value of Z would be:} \\ \\ Z_{\alpha\text{/2}}=1.645 \end{gathered}[/tex]We calculate the interval as follows:
[tex]\begin{gathered} \text{ Upper limit }=p+Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}}=0.4192+1.645\cdot\sqrt{\frac{0.4192\cdot\left(1-0.4192\right)}{167}}\:=0.482 \\ \\ \text{ Lower limit}=p-Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}}=0.4192-1.645\cdot\sqrt{\frac{0.4192\cdot\left(1-0.4192\right)}{167}}\:=0.356 \end{gathered}[/tex]The 90% confidence interval for the proportion of all adults in the United States is (0.356, 0.482)
write log_4 10 as a quotient of natural logarithms.ln__ln__
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We have to use the change-of-base formula of logarithms to simply write this log.
The logarithm to convert is:
[tex]\log _410[/tex]The change of base formula (using natural logarithms) is:
[tex]\log _ab=\frac{\ln b}{\ln a}[/tex]Matching this with the logarithm, we can write it as:
[tex]\log _410=\frac{\ln 10}{\ln 4}[/tex]Find the surface area of the cylinder below. Use 3.14 for l~l. round your answer to the nearest tenth.
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mmhey again um yea i looked at my notes but thats not really helpful :/
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We have the following:
Since the sides are equal, it means that all the angles are equal, we also know that the sum of the 3 angles within a triangle is always 180°, therefore
[tex]\begin{gathered} 5x+5x+5x=180 \\ \text{solving for x:} \\ 15x=180 \\ x=\frac{180}{15} \\ x=12 \end{gathered}[/tex]The value of x is 12
changing the value of b in f(x)=mx+b results in a translation or reflection?
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what is the slope and the y-intetercept of each problemy= -2x - 3y= -2x + 2
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Answer:
• m=-2, b=-3
,• m=-2, b=2
Explanation:
The slope-intercept form of the equation of a line is:
[tex]y=mx+b\text{ where }\begin{cases}m=\text{slope} \\ b=y-\text{intercept}\end{cases}[/tex]Part A
Given the equation:
[tex]y=-2x-3[/tex]• The slope, m = -2
,• The y-intercept, b=-3
Part B
Given the equation:
[tex]y=-2x+2[/tex]• The slope, m = -2
,• The y-intercept, b=2
Which equation is nonlinear? x=-4 y= 0 y= 2/3x- 2 y= ײ +1
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equationWhich equation is nonlinear?
x=-4
y= 0
y= 2/3x- 2
y= ײ +1
__________________
Linear eqaution form
y = mx +b
x=-4 (Line)
y= 0 (lineon the axis)
y= 2/3x- 2 (This is a linear equation )
_____________________
Answer
y= ײ +1
laws of exponent : multiplication and power to a powerquestion 2)))-2r⁵ • 6r ⁻⁸
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You need to remember the following:
- The Product of powers property states that:
[tex]b^m\cdot b^n=b^{(m+n)}[/tex]- According to the Negative exponent rule:
[tex]b^{-m}=\frac{1}{b^m}[/tex]Given the following expression:
[tex](2r^{5})(6r^{-}^{8})[/tex]You can simplify it as following:
1. Multiply the coefficients.
2. Apply the Product of powers property.
3. Apply the Negative exponent rule.
Then, you get:
[tex](2r^{5})(6r^{-}^{8})=12r^{(5-8)}=12r^{-3}=\frac{12}{r^3}[/tex]The answer is:
[tex]\frac{12}{r^3}[/tex]Identify the vertex, intercepts and whether of the graph of the function below opens up or down. Type your answers as a point (x,y). If an intercept does not exist type "none". If more than one intercept exists you can type either intercept.f(x)= -|x-9|+16 Vertex = Answerx intercept = Answery intercept = Answergraph opens Answer
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The absolute value function :
[tex]f(x)=\pm\lvert x-h\rvert+k[/tex]has a vertex at (h, k) and it opens upward if the sign before the absolute value sign is positive. It open downward if the sign is negative.
From the problem, we have :
[tex]f(x)=-\lvert x-9\rvert+16[/tex]The vertex will be (9, 16)
x intercept is the value of x when f(x) = 0.
Set f(x) = 0 and solve the value of x.
[tex]\begin{gathered} 0=-\lvert x-9\rvert+16 \\ \lvert x-9\rvert=16 \end{gathered}[/tex]In solving absolute values, you will get two values, one for the positive and one for the negative.
[tex]\begin{gathered} x-9=16 \\ x=16+9 \\ x=25 \end{gathered}[/tex][tex]\begin{gathered} x-9=-16 \\ x=-16+9 \\ x=-7 \end{gathered}[/tex]The x-intercepts are (-7, 0) and (25, 0)
y-intercept is the value of f(x) when x = 0.
Set x = 0, and evaluate f(x)
[tex]\begin{gathered} f(x)=-\lvert0-9\rvert+16 \\ f(x)=-9+16 \\ f(x)=7 \end{gathered}[/tex]The y-intercept is (0, 7)
The sign before the absolute value sign is negative, so it opens downward
The graph below shows the solution to which system of inequalities?A. x< 1 and y2 xB. ys 1 and y>xC. x≤ 1 and y> xD. y< 1 and y2
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To answer this question let's look at each line first.
The slant line can be express by the equation:
[tex]y=x[/tex]We notice that the shaded part is above this line, then we have that that inequality is written as:
[tex]y\ge x[/tex]Now, the horizontal line is express as:
[tex]y=1[/tex]since the shaded region is below that line and the line is dashed the inequality is:
[tex]y<1[/tex]Therefore, the system of inequalities is:
[tex]\begin{gathered} y\ge x \\ y<1 \end{gathered}[/tex][tex](1-(-1)*2)x^{2} -1[/tex]
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Answer:
[tex]3x {}^{2} - 1[/tex]
Step-by-step explanation:
(1-(-1)×2) x² - 1
When there is a - in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses.
(1+1x2)x2-1
Any expression multiplied by 1 remains the same
(1+2) x²-1
Add the numbers
3x2-1