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Given the system of linear equations:
{y= -5 y=3x -2
Part A: Graph the system of linear equations.
Part B: Use the graph created in Part A to determine the solution to the system.
Part C: Algebraically verify the solution from Part B.
QUESTION 1
the solution is (-1,-5)
To verify the solution algebraically, we need to multiply the first equation with -1 and then sum them up
-y=5
y=3x-2
0=3x+3
3x=-3
x=-3/3
x=-1
Then, we use this value to find the other one
y=3x-2
y=3(-1)-2
y=-3-2
y=-5
Therefore, the solution is (-1,-5), which is the same showed graphically.
QUESTION 2.
Using the same process as we did in the QUESTION 1. The image attached shows both lines and the interception point which is the solution. So, the solution is (6,0).
To verify the solution algebraically, we must multiply the second equation by -6
x+6y=6
-6y=-2x+12
x=-2x+18
x+2x=18
x=18/3
x=6
Then, we use this value to find the other one
x+6y=6
6+6y=6
6y=6-6
y=0/6
y=6
Therefore, the solution is (6,0),
A consumer survey conducted in two consecutive years found that a fixed basket of goods and services cost $36.00 in year 1 and $36.75 in year 2 the inflation rate from year 1 to year 2 is
Answer:
2.08 %
Step-by-step explanation:
(36.75 - 36.00) / 36.00 = .0208 = 2.08 %
Logan calculated the mean absolute deviation of the points he earned throughout the year in four of his classes: geography, math, English, and theat geography: MAD of 3.5
math: MAD of 1.36
English: MAD of 1.8
theater, MAD of 3.15
In which class were his scores the closest together?
geography
math
theater
English
Using it's concept, it is found that due to the lowest Mean Absolute Deviation, his scores were closest together in Math.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation(MAD) of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean. Hence, lower values of the MAD means that the distribution is closer together.Of the four classes, Math was the lower MAD, hence it has the scores that are closest together.
More can be learned about the Mean Absolute Deviation at https://brainly.com/question/3250070
50 points each question. Please help. How do I solve?
[tex]\text{Given that,}\\\\~~~1+ \ln (3xy) = e^{3x-y}\\\\\\\implies \dfrac d{dx} \left[1 + \ln (3xy) \right] = \dfrac{d}{dx} \left(e^{3x-y} \right)\\\\\\\implies \dfrac{1}{3xy} \cdot 3 \dfrac{d}{dx}(xy) = e^{3x-y} \cdot \left(3 - \dfrac{dy}{dx} \right)\\ \\\\\implies \dfrac 1{xy} \left( x \dfrac{dy}{dx} + y \right)= e^{3x-y} \cdot \left(3 - \dfrac{dy}{dx} \right)\\\\\\\implies \dfrac 1y \dfrac{dy}{dx} + \dfrac 1x = 3e^{3x-y}- e^{3x -y} \dfrac{dy}{dx}[/tex]
[tex]\implies \dfrac 1y \dfrac{dy}{dx} + e^{3x-y} \dfrac{dy}{dx} = 3e^{3x-y} - \dfrac 1x\\\\\\\implies \left( \dfrac 1y+ e^{3x-y} \right)\dfrac{dy}{dx} = 3e^{3x-y} - \dfrac 1x\\\\\\\implies \dfrac{dy}{dx}=\dfrac{3 e^{3x-y} -\dfrac 1x}{\dfrac 1y+ e^{3x-y} }\\\\\text{At point}~ (x,y) = (1/3, 1), \text{slope of the tangent line,}\\\\m=\dfrac{dy}{dx} = 0\\\\\text{Hence the equation of tangent line,}\\\\~~~y-1 =0\\\\\implies y=1[/tex]
The point (3,6) is represented on the graph. Which point also belongs on this graph?
Line graph. Line starts at (0, 0). One point plotted: (3, 6).
Answer:
Your answer would be (36,72)
Step-by-step explanation:
1. Daniel needs to add a fence around the apartment swimming pool. The pool is 25 ft. by 20 ft., and the owner wants the fence to be 4 feet from the poolside. How many feet of fencing will Daniel need? (1) 45 (2) 90 (3) 98 (4) 106 (5) 122
Answer:
(5) 122 feet
Step-by-step explanation:
Perimeter of fencing:
[tex]2((25 + 4 + 4) + (20 + 4 + 4))[/tex]
[tex]2(33 + 28) = 2(61) = 122[/tex]
The drug Lipitor is meant to lower cholesterol levels. In a clinical trial of 800 patients, 5% reported headaches.
Construct a 90% confidence interval estimate of the proportion of Lipitor users who will report headaches as a side effect. NO explanation needed or will be reported.
Using the z-distribution, it is found that the 90% confidence interval estimate is given by (0.0373, 0.0627).
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The sample size and the estimate are given, respectively, by [tex]n = 800, \pi = 0.05[/tex].
Hence, the bounds of the interval are given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 - 1.645\sqrt{\frac{0.05(0.95)}{800}} = 0.0373[/tex]
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 + 1.645\sqrt{\frac{0.05(0.95)}{800}} = 0.0627[/tex]
The 90% confidence interval estimate is given by (0.0373, 0.0627).
More can be learned about the z-distribution at https://brainly.com/question/25890103
Use the Multiplication Law of Exponents to solve the expression below.
6 1/2 . 6 1/2=
The base of 6 is the same, so add 1/2+1/2 =1
6^1 = 6
Answer:
The asnwer is
The base of 6 is the same, so add 1/2+1/2 =1
6^1 = 6
Step-by-step explanation:
I hope i helped you very much
In the triangle, angle RST is 90°. RS= 4cm and ST=3 cm. What is the length of RT? R 4 cm S T 3 cm
Step-by-step explanation:
RT^2=RS^2+ST^2
RT^2=16+9=25
RT=√25=5
The answer is 5
Raheem runs five times a week. His route is 4 1/3 miles long. How many miles does he run each week?
Answer:
21.6666666667
If you have to round it up it is 22.
Step-by-step explanation:
If he runs 5 times a week and his route is 4 1/3 then he runs that five times a week you do 5x4 1/3 and that is how you get your answer
Find the volume will give brainlest
Passengers on many commercial flights may make calls from a telephone provided
by the airline. On a certain airline, a call costs $3 to connect plus $2 for each
minute. Which linear equation best represents c, the total cost for a call that lasts m
minutes?
Answer:
c = 3 + 2m
Step-by-step explanation:
Let c = total cost of call (in dollars)
Let m = number of minutes
Given:
Connection fee = $3Cost per minute = $2⇒ c = 3 + 2m
To advance in a computer game, players need to open a door by choosing one number
on each of the dials. What is the probability that
the combination starts with 8?
Answer:
1/3 or 33.3333...%
Step-by-step explanation:
My understanding of this situation is that each dial represents a number in the combination. In order for the combination to start with 8, the first dial needs to land on 8. Since there are three numbers on the dial, the probability that the combination starts with 8 is 1/3. Hope I helped :)
Which fractions are equivalent to the value of
2
10
+
20
100
? Drag and drop the fractions into the box.
Lets see
2/10+20/1002/10+2/102+2/104/102/5Answer:
thanks just needed points
Step-by-step explanation:
Izzie bought 6 hoodies that
each cost the same amount
and a pair of shorts that
cost $23. The items she
bought cost a total of $194
before tax was added. What
was the cost of each
hoodie? (set up an equation
to solve)
Answer:
$ 28.50
Step-by-step explanation:
6 hoods + 23 = 194
6 hoods = 171
hood = $ 28 . 50
ILL GIVE BRAINELST
If the area of C is
400 ft2 and the
perimeter of B is 64 ft,
what is the side length
of square A?
Answer:
A = 12 ft
Step-by-step explanation:
Perimeter ( of SQUARE) B = 64
then each side = 64/4 = 16
AREA of SQUARE C = 400
side X side = 400
then side = sqrt 400
Now use Pyhtagorean Theorem to find leg of right triangle that is
side A Side B hypotenuse Side C
A^2 + 16^2 = (sqrt 400)^2
A^2 = 400 - 256
A^2 = 144 then A = 12 Ft
what is the sum of two numbers is "-7." Two times the first number equals 4 the second number. Find the two numbers.
Answer:
[tex]\sf \text{The numbers are $\dfrac{-14}{3} $ and $\dfrac{-7}{3}$}[/tex]
Step-by-step explanation:
Let the numbers be x , y
Sum of two numers = -7
x + y = -7------------(I)
Two times the first number equals 4 the second number.
2x = 4y ----------(II)
Divide both sides by 2
[tex]\sf \dfrac{2x}{2}=\dfrac{4y}{2}[/tex]
x = 2y
Subtitute x = 2y in equation (I)
2y + y = -7
3y = -7
y = -7/3
Plugin y = -7/3 in equation (II)
[tex]\sf 2x = 4*\dfrac{-7}{3}\\\\2x = \dfrac{-28}{3}\\\\x =\dfrac{-28}{3*2}\\\\x = \dfrac{-14}{3}[/tex]
If you know the volume of a rectangular prism and the area of the base, how can you find the height?
How to solve 8x+y=23
-10x-y=-27
Here,
8x + y = 23 - 10x - y = - 27
10(8x + y) = 23 × 10 8 (- 10x - y) = - 27 × 8
80x + 10y = 230 ---> (i) - 80x - 8y = - 216 ----> (ii)
By elimination method,Equation (i) - (ii)(80x + 10y) - (-80x - 8y) = 230 - (-216)
=> 80x + 10y + 80x + 8y = 230 + 216
=> 10y + 8y = 446
=> 18y = 446
=> y = 446/18
=> y = 24.7
Putting the value of "y" in Equation (i)80x + 10y = 230
=> 80x + 10 × 24.7 = 230
=> 80x + 247 = 230
=> 80x = 230 - 247
=> 80x = -17
=> x = -17/80
=> x = - 0.21
Therefore the values of "x" and "y" arex = -0.21 and y = 24.7
Hope it helpsFind the value of angle W
Answer:
w = 73°
Step-by-step explanation:
The relations involved in solving this figure are ...
linear pairs are supplementarythe angle sum for the quadrilateral is 360°__
The linear pair at lower left gives us a relation we can solve for x:
x +(3x -24) = 180
4x = 204
x = 51
Then the sum of angles inside the quadrilateral is ...
w +(x +15) +(2x -10) +(3x -24) = 360
w +(51 +15) +(2(51) -10) +(3(51) -24) = 360
w +66 +92 +129 = 360
w = 360 -287 = 73
Angle W is 73°.
_____
Additional comment
The remaining angles are supplementary to those inside the quadrilateral:
v = 180° -w = 107°
y = 180° -92° = 88°
z = 180° -66° = 114°
x = 51°
The figure shows the dimensions for a birthday gift. Find the minimum amount of wrapping paper, in square inches, needed to cover the gift. Round your answer to the nearest whole inch.
sqauare inches
The minimum amount of wrapping paper, in square inches, needed to cover the gift shown in the figure is 614 square inches.
What is of total surface area of the rectangular prism?The total surface area of the rectangular prism is the space occupied by each of the face of it. It is the sum of area of all the faces of prism.
Total surface area of the rectangular prism is calculated with the following formula.
[tex]A=2(lb+bh+lh)[/tex]
Here, (b) is the breath of the base (l) is the length and (h) is the height of the rectangular prism.
The minimum amount of wrapping paper required to cover the gift is equal to the surface area of the figure.
The figure is made with different sides, The area of all the sides is equal to the surface area of the figure. The surface area of it is,
[tex]A=2(5\times8)+(15\times8)+(15\times10)+2(\dfrac{1}{2}3\times8)+(15\times5)+(15\times11)\\A=614\rm\;in^2[/tex]
Thus, the minimum amount of wrapping paper, in square inches, needed to cover the gift shown in the figure is 614 square inches.
Learn more about the total surface area of a rectangular prism here;
https://brainly.com/question/15456870
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Jenna surveyed her friends, asking each of them, "How many times have you been to the aquarium?" The resulting data set has a distribution that can be described several ways.
Select from the drop-down menus to correctly complete the statements about the distribution.
The distribution can be described by its shape. If there are more higher values than lower values, the distribution is skewed
Choose...
.
The distribution can be described by its center. If the distribution is skewed left or right, the
Choose...
is an accurate measure of center.
The distribution can be described by its spread. If the data set does not have an outlier, the
Choose...
is an accurate measure of spread.
In the research, the distribution is described by its shape. If there are more higher values than lower values, the distribution is skewed left.
How to illustrate the research?It should be noted that when the distribution of data is skewed to the left, the mean is less than the median.
The distribution can be described by its center. If the distribution is skewed left or right, the median is an accurate measure of center.
The distribution can be described by its spread. If the data set does not have an outlier, the interquartile range is an accurate measure of spread.
Learn more about research on:
https://brainly.com/question/25257347
Answer:
left, median, and range or the IQR
Step-by-step explanation:
Help me asap …………..p
Answer:
1.) Tan C = [tex]\frac{12}{5}[/tex]
2.) Sin Z = [tex]\frac{24}{26}[/tex] or [tex]\frac{12}{13}[/tex] if reduced
3.) Cos A = [tex]\frac{15}{17}[/tex]
4.) Cos A = [tex]\frac{12}{37}[/tex]
Step-by-step explanation:
Let's keep in mind that;
Sin = [tex]\frac{opposite}{hypotenuse}[/tex]
Cos = [tex]\frac{adjacent}{hypotenuse}[/tex]
Tan = [tex]\frac{opposite}{adjacent}[/tex]
Hope this helps!
what is 5/12 - 1/3 = in simplest form
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
See picture below for explanation:
Find the length of the unknown side round your answer to the nearest 10th
Triangle in picture above ☝️
Answer:
72.8
Step-by-step explanation:
A 12 sided die is rolled find the probability of rolling a two
Answer:
1/12
Step-by-step explanation:
so we know the total you have is a 12 dice cube yes? yes.
there fore you denomanator is the the total of everything-12.
there's only 1 #2 on the 12 sided dice this cause you to get 1/12
What is the value of(-4)(-4)(-4)
Answer:
-64
Step-by-step explanation:
-4x-4x-4
[tex] \large \red{\frak{ Question}}[/tex]
The sum of 3/4th of A’s salary and 5/3rd of B’s salary is ₹16,000. The difference of their salaries is ₹2000. If B’s salary is less than that of A, then what is the salary of B (in ₹)?
(a) 8000 (b) 2000
(c) 6000 (d) 12,000
[tex] \pink{ \dag \: \large\sf{ With \: Explanation }}[/tex]
[tex] \blue{ \dag \: \large\sf{No Spam }}[/tex]
Answer:
[tex] \sf \: \fbox{Option C) \: The salary of B is 6000₹}[/tex]
Step-by-step explanation:
Let the salary or A is x and salary of B is y.
now,
Condition one,The sum of 3/4th of A’s salary and 5/3rd of B’s salary is ₹16,000.
writing above statement in equation form,
[tex] \sf \frac{3x}{4} + \frac{5y}{3} = 16000[/tex]
Multiplying above equation with twelve,
[tex] \sf \frac{3x}{4} + \frac{5y}{3} = 16000 \\ \sf \frac{12 \times 3x}{4} + \frac{12 \times 5y}{3} = 16000 \times 12 \\ \sf \fbox{9x + 20y = 192000} \rightarrow eq. 1[/tex]
and condition two,
The difference of their salaries is ₹2000
[tex] \sf \: x - y = 2000[/tex]
Multiplying above equation with 20
[tex] \sf \fbox{\: 20x -20y = 40000} \rightarrow eq.2[/tex]
On adding equation 1 and equation 2,
[tex] \sf9x + \cancel{20y} = 192000 \\ \sf 20x - \cancel{20y} = 40000 \\ \hline \sf 29x + 0y = 232000 \\ \sf x = \frac{232000}{29} \\ \sf \: \fbox{x = 8000₹}[/tex]
Substituting the value of x in,
[tex] \sf \: x - y = 2000 \\ \sf \: 8000 - y = 2000 \\ \sf \: y = 8000 - 2000 \\ \sf \fbox{y = 6000₹}[/tex]
[tex] \sf \: \fbox{The salary of B is 6000₹}[/tex]
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What type of triangle can an equilateral be?
isosceles triangle
right triangle
acute triangle
obtuse triangle
Answer:
Acute triangle
Step-by-step explanation:
Nevada is almost twice the size of which country?
A. Algeria
B. Mauritania
C. Kenya
D. Democratic republic of the Congo
Please help me