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where:
[tex]\begin{gathered} m\angle GK=9x-22 \\ m\angle GH=61 \\ m\angle HJ=5x-7 \\ m\angle KJ=34 \\ so\colon \\ 9x-22+61+5x-7+34=360 \\ \end{gathered}[/tex]add like terms:
[tex]14x+66=360[/tex]Solve for x:
[tex]\begin{gathered} 14x=360-66 \\ 14x=294 \\ x=\frac{294}{14} \\ x=21 \end{gathered}[/tex]Hence:
[tex]\begin{gathered} m\angle GK=9x-22=9(21)-22=167 \\ m\angle HJ=5x-7=5(21)-7=98 \end{gathered}[/tex]Related Questions
For the following find the Range:{(₁-2, 4), (3,-2), (1,0), (-2, -2), (0, 6)}
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Explanation
The range represents the y-value of the given points
Answer:
[tex]Range=(-2,0,4,6)[/tex]Complete the statement with < >, or =. 25 نتانا
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Given
[tex]\frac{3}{2}\text{?}\sqrt[]{\frac{25}{4}}[/tex]Procedure
[tex]\begin{gathered} \sqrt[]{\frac{25}{4}}=\frac{5}{4} \\ so, \\ \frac{3}{2}<\frac{5}{2} \end{gathered}[/tex]Suppose logex = 3, log y = 7, and logz= -2.Find the value of the following expression.loga42
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Therefore,
[tex]\begin{gathered} \log _ax^3+\log _ay-\log _az^4=\log _a(\frac{x^3y}{z^4}) \\ 3\log _ax^{}+\log _ay-4\log _az=3(3)+7-4(-2)=9+7-8=8 \end{gathered}[/tex]Two squares are shown in the diagram . The larger square has sides of length 5x units. The smaller square has an area equal to ⅑ of the larger square . Find the length of the sides or the smaller square. Give your answer in the form a/b where a,b ∊ ℕ
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From the information given,
length of side of the larger square = 5x units
The area of a square is calculated by the faormula,
area = length of side^2
Thus,
Area of larger square = (5x)^2 = 25x^2
The smaller square has an area equal to ⅑ of the larger square. This means that the area of the smaller square is
Area of smaller square = 1/9 * 25x^2 = 25x^2/9
Length of the side of square = square root of area
Thus,
Length of the sides of the smaller square = square root of (25x^2/9)
Length of the sides of the smaller square = 5x/3
I get a whole number so I’m not taking steps correctly
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The sum of the given matrices is not possible to calculate as the order of both the matrix are different.
To add two matrices both matrices must be of the same order.
[3 -8] is of order 1 × 2
[4 -5 -6] is of order 1 × 3
Since the two matrices are of different orders it is not possible for the two matrices to be added.
Although direct sum or Kronecker sum could be used to add the matrices but the correct symbol for them is not used.
Hence the required result is impossible .
A matrix, also spelled "matrices," is a rectangular table or array of characters that are arranged in rows and columns to represent a mathematical object or a property of one.
Matrix representations of linear mappings in linear algebra allow for explicit computations. Because of this, matrices are studied extensively in linear algebra, and most properties and actions of abstract discrete mathematics may be explained in terms of matrices.
To learn more about matrix visit:
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can u help me with this by using inverse trig.ratios. Find angle A and angle B.
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The hypotenuse is 39 because is opposite to the angle of 90 degrees.
So, angle A is given by
[tex]\measuredangle A=\sin ^{-1}\frac{7}{39}[/tex]Then, we have
[tex]\measuredangle A=\sin ^{-1}(0.17948)[/tex]which gives
[tex]\measuredangle A=10.339\text{ degre}es[/tex]Now, angle C is equal to 90 degrees and angle B is given by
[tex]\begin{gathered} \measuredangle B=\cos ^{-1}(\frac{7}{39}) \\ \measuredangle B=\cos ^{-1}(0.17948) \\ \measuredangle B=79.66\text{ degr}ees \end{gathered}[/tex]Therefore, the answer is
[tex]\begin{gathered} \measuredangle A=10.339\text{ degre}es \\ \measuredangle B=79.669\text{ degre}es \\ \measuredangle C=90\text{ degre}es \end{gathered}[/tex]the sum of two numbers is 70 and their difference is 30 ,Find the two numbers using the process of substitution let x=the first number and y=the second number.
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Let the first number be x and the second number be y.
Since the sum of the numbers is 70, it follows that the equation that shows the sum of the numbers is:
[tex]x+y=70[/tex]The difference between the two numbers is 30, hence, the equation that shows the difference is:
[tex]x-y=30[/tex]The system of equations is:
[tex]\begin{cases}x+y={70} \\ x-y={30}\end{cases}[/tex]Make x the subject of the first equation:
[tex]x=70-y[/tex]Substitute this into the second equation:
[tex]\begin{gathered} 70-y-y=30 \\ \Rightarrow70-2y=30 \\ \Rightarrow-2y=30-70 \\ \Rightarrow-2y=-40 \\ \Rightarrow\frac{-2y}{-2}=\frac{-40}{-2} \\ \Rightarrow y=20 \end{gathered}[/tex]The second number is 20.
Substitute y=20 into the equation x=70-y to find x:
[tex]x=70-20=50[/tex]Answers:
The equation that shows the sum of the numbers is x+y=70.
The equation that shows the difference between the numbers is x-y=30.
The numbers are x=50 and y=20.
Emiliano sold half of his comic books and then bought 16 more.He now has 36. How many did he begin with? Write and equation to represent the problem.
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N = original number of comic books
N/2 = number of comic books after he sold half of his collection
N/2 + 16 = number of comic books after he bought 16 more
N/2 + 16 = 36
Solving for N:
[tex]\frac{N}{2}+16\text{ = 36}\Longrightarrow\frac{N}{2}=36-16\text{ = 20 }\Longrightarrow\frac{N}{2}=20\Longrightarrow N\text{ = 20 }\cdot\text{ 2=40}\Longrightarrow\text{ N = 40}[/tex]Answers:
He began with 40 comic books
Equation to represent the problem: N/2 + 16 = 36
Given {(-1,4),(-1,9),(-1,15),(-1,0)}Find the following.Domain=Range-Determine if it is a Function or Not?
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Given the relation:
[tex]\left\{ \left(-1,4\right),\left(-1,9\right),\left(-1,15\right),\left(-1,0\right)\right\} [/tex]The domain of the relation is the set of all values of x.
Therefore:
[tex]\text{Domain}=\left\lbrace -1\right\rbrace [/tex]The range of the relation is the set of all values of f(x) or y. The range is:
[tex]\text{Range}=\left\lbrace 0,4,9,15\right\rbrace [/tex]For a relation to be a function, it must have no more than one y value for each x value.
Since the given relation has more than one y value for each x value, it is NOT A FUNCTION.
A stack of 30 science flashcards includes a review card for each of the following 10 insects, 8 trees, 8 flowers and 4 birds. What is the probability of randomly selecting an insect and then a tree???
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The probability (P) of event A occurring is:
[tex]P(A)=\frac{\text{ number of favorable outcomes to A}}{\text{ total number of outcomes}}[/tex]The probability of 2 consecutive events A and B occur is:
[tex]P=P(A)*P(B)[/tex]Then, let's calculate the probability of selecting an insect:
Favorable outcomes: 10
Total outcomes: 30
[tex]P(insect)=\frac{10}{30}=\frac{1}{3}[/tex]Now, let's calculate the probability of selecting tree:
If the insect card is replaced:
Favorable outcomes: 8
Total outcomes: 30
[tex]P(B)=\frac{8}{30}=\frac{4}{15}[/tex]If the insect card is not replaced:
Favorable outcomes: 8
Total outcomes: 29
[tex]P(B)=\frac{8}{29}[/tex]The probability of randomly selecting an insect and then a tree is:
With replacement:
[tex]\begin{gathered} P=\frac{1}{3}*\frac{4}{15} \\ P=\frac{4}{45} \end{gathered}[/tex]Without replacement:
[tex]\begin{gathered} P=\frac{1}{3}*\frac{8}{29} \\ P=\frac{8}{87} \end{gathered}[/tex]Answer:
With replacement: 4/45
Without replacement: 8/87
the vertex of this parabola Is at parabola is at (2,-4)
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Answer:
[tex]A=3[/tex]
Explanation: We are given two points, P1 is vertex and P2 is another point on the parabola:
[tex]\begin{gathered} P_1(2,-4) \\ P_2(3,-1) \end{gathered}[/tex]The general form of the equation of a parabola is:
[tex]y(x)=A(x\pm B)^2+C[/tex]Where A is the Coefficient of the parabola function which is responsible for compression and stretch, likewise B is responsible for the translation along the x-axis and C is responsible for translation along the y-axis.
We know that our function is translated 2 units towards the right and 4 units downwards:
Therefore:
[tex]\begin{gathered} B=-2 \\ C=-4 \end{gathered}[/tex]And this turns the parabola equation into:
[tex]y(x)=A(x-2)^2-4[/tex]Using P2 we can find the constant-coefficient as:
[tex]\begin{gathered} y(x)=A(x-2)^2-4_{} \\ P_2(3,-1) \\ \\ \\ \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} y(3)=A(3-2)^2-4=-1\rightarrow A-4=-1 \\ \because\rightarrow \\ A=3 \end{gathered}[/tex]Please help me with this rectangle problem they always give me trouble
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Hello there. To solve this question, we'll have to remember some properties about rectangles.
A rectangle is a quadrilateral polygon (that is, it has 4 right angles in its corners) and two parallel sides.
The special cases of quadrilaterals are the parallelogram, that has two parallel sides but the angles might not be right angles and the square, in which the sides are equal.
In the case of the rectangle, it has a side with length L and other side, that we call its width, with length W, as in the following drawing:
Its area A can be calculated taking the product between the length and the width, therefore:
[tex]A=L\cdot W[/tex]With this, we can solve this question.
It says that a rectangle is 15 ft longer than it is wide. Its area is 2700 ft². We have to determine its dimensions.
Say this rectangle has width W.
If this rectangle is 15 ft longer than it is wide, it means that
[tex]L=15+W[/tex]Now, we plug this values for the formula of area, knowing that A = 2700:
[tex]\begin{gathered} A=L\cdot W=(15+W)\cdot W \\ \end{gathered}[/tex]Apply the FOIL
[tex]2700=15W+W^2[/tex]In this case, we have a quadratic equation in W.
We'll solve it by completing the square, that is, finding a perfect trinomial square such that we can undo the binomial expansion and solve a simpler quadratic equation.
The binomial expansion (a + b)² gives us
[tex]a^2+2ab+b^2[/tex]So to find the b we need to complete the square, we start dividing the middle term by 2.
In the case of our equation, the middle term has coefficient 15, hence
[tex]b=\dfrac{15}{2}[/tex]Square the number and add it on both sides of the equation, such that
[tex]\begin{gathered} 2700+\left(\dfrac{15}{2}\right)^2=\left(\dfrac{15}{2}\right)^2+2\cdot\dfrac{15}{2}\cdot W+W^2 \\ \\ 2700+\dfrac{225}{4}=\dfrac{11025}{4}=\left(W+\dfrac{15}{2}\right)^2 \end{gathered}[/tex]Take the square root on both sides of the equation, knowing that 11025 = 105²
[tex]W+\dfrac{15}{2}=\sqrt{\dfrac{11025}{4}}=\sqrt{\left(\dfrac{105}{2}\right)^2}=\dfrac{105}{2}[/tex]Subtract 15/2 on both sides of the equation
[tex]W=\dfrac{105}{2}-\dfrac{15}{2}=\dfrac{105-15}{2}=\dfrac{90}{2}=45[/tex]Then we plug this value in the expression for L, hence we get:
[tex]L=15+W=15+45=60[/tex]Notice that multiplying the numbers, we'll get:
[tex]L\cdot W=60\cdot45=2700[/tex]That is exactly the area we had before.
Hence we say that its width equals 45 ft and its length equals 60 ft.
How do I solve this problem Lucy plans to spend between 50$ and 65$, inclusive, on packages of breads of charms. If she buys 5 packages of breads at $4.95 each, how many packages of charms at $6.55 can Lucy buy while staying within her budget?
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so she can buy 6 packages of charms
Explanation
Step 1
Let
x= money Lucy spends
Lucy plans to spend between 50$ and 65$, replacing we have
[tex]50she buys 5 packages of bread at $4.95Step 2
find the money spent for buying 5 packages of bread
[tex]\begin{gathered} \text{cost}=\text{ 5 mu}ltipliedby4.95 \\ \text{cost}=5\cdot4.95=24.75 \\ \end{gathered}[/tex]Step 3
after, that she will have spent 24.75, the maximum budget is 65
then , she has
[tex]\begin{gathered} \text{balance}=65-24.75 \\ \text{balance}=40.25 \end{gathered}[/tex]Step 4
to find how many packages of charms at $6.55 she can buy,, just divide
[tex]\begin{gathered} \text{total of packages of charm= }\frac{40.25\text{ usd}}{6.55\frac{usd}{\text{pack}}} \\ \text{total of packages of charm=6.14 } \\ \end{gathered}[/tex]she can not buy 0.14 package, so she can buy 6 packages of charms
When rolling a pair of dice, find the probability that the sum is less than five and even.
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In order to obtain the solution for this question, we need to find the sample space for 2 dice, which is given by:
As we can note, there are 36 events and there are 4 events which sum is less than five and even:
Since the probability is defined as the number of possible outcomes divided by the total number of outcomes, we have
[tex]P(\text{ sum less than 5 and even\rparen=}\frac{4}{36}[/tex]By simplifying this result, the answer is:
[tex]P(\text{ less than 5 and even\rparen=}\frac{1}{9}[/tex]Solve for all values of x in simplest form.
|8x| = 64
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Answer: x=8
Step-by-step explanation:
Choose each conversion factor that relates cups to fluid Ounces.A. 8 fl oz/ 1cB. 8c/ 1 fl ozC. 1 fl oz/ 8 cD. 1 c/ 8 fl oz
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Answers:
A. 8 fl oz/ 1c
D. D. 1 c/ 8 fl oz
Explanation:
1 cup is equal to 8 fluid ounces, so the conversion factors that relate these units are factors that keep the same equivalence. So, the conversion factors are:
A. 8 fl oz/ 1c
D. D. 1 c/ 8 fl oz
The area of a circle is 100 square millimeters. What is the circumference?
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9. Marty wants to buy a gallon of lemonade, and a gallon jug costs $3.89, while a pint costs $0.59. He wants to know how much money he would save by buying the gallon jug instead of multiple pints. (3 points: Part I - 1 point; Part II - 1 point; Part III - 1 point)Part I: How many pints are in a gallon?Part II: How much money would Marty spend if he bought multiple pints?Part III: How much money would Marty save by buying the gallon jug instead of multiple pints?
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Part I. In a gallon, there are 8 pints.
Part II. If Marty bought multiple pints, he will spend:
[tex]8\text{ pints}\cdot0.59=\text{ \$4.72}[/tex]Part III. Marty would save:
[tex]4.72-3.89=\text{ \$0.83}[/tex]Marty would save $0.83 by buying the gallon jug instead of multiple pints.
need help with a question
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Let's go over each of the expressions and see if they are equal to 1/8
[tex]2^{-3}=\frac{1}{2^3}=\frac{1}{8}[/tex]So A is equivalent
[tex](-8)^1=-8[/tex]So B is not equivalent
[tex](\frac{32}{4})^{-1}=\frac{1}{\frac{32}{4}}=\frac{4}{32}=\frac{1}{8}[/tex]So C is equivalent
[tex]8^8-8^9=-117440512[/tex]So D is not equivalent
[tex]\frac{8^8}{8^9}=8^{8-9}=8^{-1}=\frac{1}{8}[/tex]So E is equivalent
[tex]undefined[/tex]find an equation of the line passing through the pair points. write the equation in the form ax+by=c (-7,5),(-8,-9)
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Given the pair of coordinates;
[tex]\begin{gathered} (-7,5) \\ (-8,-9) \end{gathered}[/tex]We would begin by first calculating the slope of the line.
This is given by the formula;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The variables are as follows;
[tex]\begin{gathered} (x_1,y_1)=(-7,5) \\ (x_2,y_2)=(-8,-9) \end{gathered}[/tex]We will now substitute these into the formula for finding the slope as shown below;
[tex]\begin{gathered} m=\frac{(-9-5)}{(-8-\lbrack-7)} \\ \end{gathered}[/tex][tex]\begin{gathered} m=\frac{-14}{-8+7} \\ \end{gathered}[/tex][tex]\begin{gathered} m=\frac{-14}{-1} \\ m=14 \end{gathered}[/tex]The slope of this line equals 14. We shall use this value along with a set of coordinates to now determine the y-intercept.
Using the slope-intercept form of the equation we would have;
[tex]y=mx+b[/tex]We would now substitute for the following variables;
[tex]\begin{gathered} m=14 \\ (x,y)=(-7,5) \end{gathered}[/tex][tex]5=14(-7)+b[/tex][tex]5=-98+b[/tex]Add 98 to both sides of the equation;
[tex]103=b[/tex]We now have the values of m, and b.The equation in "slope-intercept form" would be;
[tex]y=14x+103[/tex]To convert this linear equation into the standard form which is;
[tex]Ax+By=C[/tex]We would move the term with variable x to the left side of the equation;
[tex]\begin{gathered} y=14x+103 \\ \text{Subtract 14x from both sides;} \\ y-14x=103 \end{gathered}[/tex]We can now re-write and we'll have;
[tex]-14x+y=103[/tex]Note that the coefficients of x and y (that is A and B) are integers and A is positive;
Therefore, we would have;
[tex]\begin{gathered} \text{Multiply all through by -1} \\ 14x-y=-103 \end{gathered}[/tex]The equation of the line passing through the points given expressed in standard form is;
ANSWER:
[tex]14x-y=-103[/tex]Tiffany has volunteered 65 hours at a local hospital.This is 5 times the number of hours her friend Mario volunteered. Let m represent the number of hours that Mario volunteered. Which equation below can be used to determine the actual number of hours Mario volunteered?A 65 x 5 = mb 5 x m= 65C m +5=65d 5 ÷ m= 65e 5+ m =65
Answers
5 x m = 65
Explanations:The number of hours Tiffany volunteered = 65
The number of hours Mario volunteered = m
Tiffany volunteered 5 times the number of hours mario voluntered
Number of hours Tiffany volunteered = Number of hours Mario volunteered x 5
65 = m x 5
This can also be written as:
5 x m = 65
Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. cos 67° = ____
Answers
Answer: 0.39
The decimal form of cos 67° rounded to the nearest hundredth is 0.39.
Daniel's BAC, B, after drinking can be determined using the formula B - 0,08 - 0.016Nhere N is the number of hours that have elapsed since drinking, What is Daniel's BACNer 3 hours and 15 minutes?
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1) Firstly, We need to convert 3 hours and 15 min into decimal. So, we can write out the following:
[tex]\begin{gathered} 3+\frac{15}{60} \\ 3\frac{1}{4}=3.25 \end{gathered}[/tex]2) As our second step, we can plug into the formula the number we just found:
[tex]\begin{gathered} B=0.08-0.016N \\ B=0.08-0.016(3.25)\Rightarrow B=0.08-0.052 \\ B=0.028 \end{gathered}[/tex]So Daniel's BAC after 3 hours and 15 minutes drinking is
what is the slope when the rise is -10 and the run is 2
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Slope intercdpt form of line
Then
Rise means elevation over y axis
Run means displacement along X axis
Now the Slope m = ( Rise/Run ) = (-10/2) = -5
So its a line directed down with slope -5
(when slope is negative, line goes down)
Find the area of the shape shown below. 7 3
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To find the area of the figure you can divide the figure into to smaller shapes
calculate the area of each of the smaller figures.
for the square
[tex]\begin{gathered} A=s\cdot s \\ A=3\cdot3 \\ A=9 \end{gathered}[/tex]For the triangle the base is the difference between the longest side which is 7 and the side on the square which is 3
[tex]7-3=4[/tex]find the area of the triangle
[tex]A=b\cdot\frac{h}{2}[/tex][tex]\begin{gathered} A=4\cdot\frac{3}{2} \\ A=\frac{12}{2} \\ A=6 \end{gathered}[/tex]Add both areas to find the area of the figure
[tex]\begin{gathered} A_T=9+6 \\ A_T=15 \end{gathered}[/tex]Select the best answer for the question. 3. What is 996 times 32? O A. 29,880 B. 31,680 C. 31,872 D. 51,792
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First, write the factors 996 and 32 in the following arrangement:
Next, take the last digit of 32, which is 2, and multiply it by 996. To do so, first, multiply 2 times 6:
[tex]2\times6=12[/tex]Write the units below the column of the 6, and save the remaining 10 units to be added in the next step.
Next, multiply 2 by the next digit from right to left of 996, which is 9:
[tex]2\times9=18[/tex]Add 1 to the result, since it was a remainder from the last operation:
[tex]18+1=19[/tex]Write a 9 below the second colum, and save the remaining 10 units to be added on the next step.
Repeat the procedure for the third digit of 996 from right to left, which is 9.
[tex]2\times9=18[/tex][tex]18+1=19[/tex]Since there are no more digits from the upper number, write 19 below the third colum.
Now, repeat the procedure with the next digit from the lower number (32), which is 3. Write the result one place shifted to the left.
[tex]3\times6=18[/tex]Next, move to the next digit from right to left of the upper number, which is 9:
[tex]3\times9=27[/tex][tex]27+1=28[/tex]Next, move to the next and last digit from right to left of the upper number, which is 9:
[tex]\begin{gathered} 3\times9=27 \\ 27+2=29 \end{gathered}[/tex]Fill the blank space at the right of the last row with a 0 and add both numbers:
[tex]1992+29880=31872[/tex]Therefore:
[tex]996\times32=31872[/tex]Find the slope & y-intercept: x + 2y –9= 0
Answers
Explanation
we have
[tex]x+2y-9=0[/tex]to know the slope and the y-intercept the easiest way is by isolating y to get the slope-intercept form
Step 1
isolate y
[tex]\begin{gathered} x+2y-9=0 \\ add\text{9 in both sides} \\ x+2y-9+9=0+9 \\ x+2y=9 \\ \text{subtract x in both sides} \\ x+2y-x=9-x \\ 2y=9-x \\ \text{divide both sides by 2} \\ \frac{2y}{2}=\frac{9}{2}-\frac{x}{2} \\ y=-\frac{1}{2}x+\frac{9}{2} \end{gathered}[/tex]Hence
[tex]\begin{gathered} y=-\frac{1}{2}x+\frac{9}{2}\rightarrow y=mx+b \\ m\text{ is the slope} \\ b\text{ is the y intercept} \end{gathered}[/tex]therefore
[tex]\begin{gathered} \text{slope}=-\frac{1}{2} \\ y-\text{intercept =}\frac{9}{2} \end{gathered}[/tex]I hope this helps you
Let the Universal Set, S, have 52 elements. A and B are subsets of S. Set A contains 26 elements and SetB contains 14 elements. If the total number of elements in either A or B is 27, how many elements are inA but not in B?
Answers
ANSWER
Number of elements in A but not in B = 13
EXPLANATION
Step 1: Given that:
n(S) = 52
n(A) = 26
n(B) = 14
n(A U B) = 27
Step2: Using the Venn Diagram
Step 3: Determine the value of n(A n B)
n(A U B) = n(A) + n(B) - n(A n B)
27 = 26 + 14 - n(A n B)
n(A n B) = 40 - 27
n(A n B) = 13
Step 4: Determine the number of elements in A but not in B
n(A - B) = n(A) - n(AnB)
n(A - B) = 26 - 13
n(A - B) = 13
Hence, number of elements in A but not in B = 13
A coach buys a uniform and a basketball for each of the 12 players on the team. Each basketball costs $15. The coach spends a total of $756 for uniforms and basketballs. Write an equation that models the situation with u, the cost of one uniform.Find the cost of one uniform
Answers
Equation: 180 + 12u = 756
the cost of one uniform is $48
Explanation:Total number of players = 12
The cost per basketball = $15
Total cost for uniform and basket balls = $756
let the cost of each uniform = u
The equation becomes:
Total number of players(The cost per basketball ) + Total number of players( cost of each uniform)
12($15) + 12(u) = $756
180 + 12u = 756
To get u, we subtract 180 from both sides:
180 - 180 + 12u = 756 - 180
12u = 576
u = 576/12
u = 48
Hence, the cost of one uniform is $48
3. Lin is solving this system of equations:S 6x – 5y = 343x + 2y = 83. She starts by rearranging the second equation to isolate the y variable: y = 4 -1.5%. She then substituted the expression 4 - 1.5x for y in the first equation, asshown below:--6x – 5(4 – 1.5x) = 346x – 20 – 7.5x = 34-1.5x = 54x = -36y = 4 – 1.5xy = 4 - 1.5 • (-36)y = 58.
Answers
We are given the following system of equations:
[tex]\begin{gathered} 6x-5y=34,(1) \\ 3x+2y=8,(2) \end{gathered}[/tex]We are asked to verify if the point (-36, 58) is a solution to the system. To do that we will substitute the values x = -36 and y = 58 in both equations and both must be true.
Substituting in equation (1):
[tex]6(-36)-5(58)=34[/tex]Solving the left side we get:
[tex]-506=34[/tex]Since we don't get the same result on both sides this means that the point is not a solution.
Now, we will determine where was the mistake.
The first step is to solve for "y" in equation (2). To do that, we will subtract "3x" from both sides:
[tex]2y=8-3x[/tex]Now, we divide both sides by 2:
[tex]y=\frac{8}{2}-\frac{3}{2}x[/tex]Solving the operations:
[tex]y=4-1.5x[/tex]Now, we substitute this value in equation (1), we get:
[tex]6x-5(4-1.5x)=34[/tex]Now, we apply the distributive law on the parenthesis:
[tex]6x-20+7.5x=34[/tex]This is where the mistake is, since when applying the distributive law the product -5(-1.5x) is 7.5x and not -7.5x.