The rate of change of a linear functions is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are points through the graph.
Function 1.
From the table we have that the functions passes through the points (-11,8) and (-7,13), pluggin the values in the formula above we have:
[tex]\begin{gathered} m=\frac{13-8}{-7-(-11)} \\ m=\frac{5}{11-7} \\ m=\frac{5}{4} \end{gathered}[/tex]Therefore the rate of change of functions 1 is 5/4
Function 2.
From the graph we notice that the functions passes through the points (-3,-4) and (1,-1), hence:
[tex]\begin{gathered} m=\frac{-1-(-4)}{1-(-3)} \\ m=\frac{-1+4}{1+3} \\ m=\frac{3}{4} \end{gathered}[/tex]Therefore the rate of change of function 2 is 3/4.
Comparing both rates of change we conclude that Function 1 has the greater change of rate.
The perimeter of rhombus EFGH is 48 cm and the measure of
Given data
Perimeter = 48cm
perimeter of a rhombus is the sum of all length of the outer boundary.
A rhombus has equal length
Perimeter = 4L
4L = 48
L = 48/4
L = 12cm
a) GH = 12cm
b)
c)
To find
Opposite = 6 side facing the given angle
Hypotenuse = 12 side facing right angle
[tex]\begin{gathered} \text{Apply trigonometry ratio formula} \\ \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \sin \theta\text{ = }\frac{6}{12} \\ \sin \theta\text{ = 0.5} \\ \theta\text{ = }\sin ^{-1}0.5 \\ \theta\text{ = 30} \end{gathered}[/tex]Therefore,
Angle
can you please help me with the both of them?
The values of x and angle in triangle STU are 11 and 123, 65, and the values of x and angle in triangle BCD is 3 and 70, 50
The inner of two angles are formed where two sides of a polygon meet are called the interior angle
Given that in two triangles
S = 58, T= 5x + 10 and U = 11x +2
B = 22x + 4, C = 15x + 5 and D =120
In the Triangle STU Formula to find out the value of x is
Sum of interior angles = exterior angle
= 5x + 10 + 58 = 11x +2
= 5x + 68 = 11x + 2
11x -5x = 68 -2
6x = 66
X = 11
Now substitute x value in T & U
T = 5(11) +10 U = 11(11) + 2
T= 55 +10 U = 121 + 2
U = 123 T = 65
In the Triangle BCD Formula to find out the value of x is
Sum of interior angles = exterior angle
22x + 4 + 15x + 5 = 120
37x + 9 = 120
37x = 111
X = 3
Now substitute x value in B & C
B = 22(3) +4 U = 15(3) + 5
T= 66 +4 U = 45 + 5
U = 70 T = 50
Therefore the values of x and angle in triangle STU are 11 and 123, 65, and the values of x and angle in triangle BCD are 3 and 70, 50
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I am still confused on how to solve these problems please help.
Step 1: We have a line segment XZ, with point Y between X and Z.
Therefore, we have:
XY + YZ = XZ
Replacing with the values given:
7a + 5a = 6a + 24
Like terms:
7a + 5a - 6a = 24
6a = 24
Dividing by 6 at both sides:
6a/6 = 24/6
a = 4
Step 2: Now we can find the length of the line segment, this way:
YZ = 6a + 24
Replacing a by 4
YZ = You can finish the calculation
3 373,Consider the complex number z =+22What is 23?Hint: z has a modulus of 3 and an argument of 120°.Choose 1 answer:А-2727-13.5 +23.41-13.5 - 23.41
To answer this question, we can proceed as follows:
[tex]z=-\frac{3}{2}+\frac{3\sqrt[]{3}}{2}i^{}\Rightarrow z^3=(-\frac{3}{2}+\frac{3\sqrt[]{3}}{2}i)^3[/tex][tex](-\frac{3}{2}+\frac{3\sqrt[]{3}i}{2})^3=(\frac{-3+3\sqrt[]{3}i}{2})^3=\frac{(-3+3\sqrt[]{3}i)^3}{2^3}[/tex]We applied the exponent rule:
[tex](\frac{a}{b})^c=\frac{a^c}{b^c}[/tex]Then, we have:
[tex]\frac{(-3+3\sqrt[]{3}i)^3}{2^3}=\frac{(-3+3\sqrt[]{3}i)^3}{8}[/tex]Solving the numerator, we have:
[tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex][tex](-3+3\sqrt[]{3}i)^3=(-3)^3+(3\sqrt[]{3}i)^3+3(-3)(3\sqrt[]{3}i)(-3+3\sqrt[]{3}i)[/tex][tex]-27+81\sqrt[]{3}i^3-27\sqrt[]{3}i(-3+3\sqrt[]{3}i)[/tex][tex]-27+81\sqrt[]{3}i^3+81\sqrt[]{3}i-27\cdot3\cdot(\sqrt[]{3})^2\cdot i^2[/tex][tex]-27+81\sqrt[]{3}i^2\cdot i+81\sqrt[]{3}i-81\cdot3\cdot(-1)[/tex][tex]-27+81\sqrt[]{3}(-1)\cdot i+81\sqrt[]{3}i+243[/tex][tex]-27-81\sqrt[]{3}i+81\sqrt[]{3}i+243[/tex][tex]-27+243=216[/tex]Then, the numerator is equal to 216. The complete expression is:
[tex]=\frac{(-3+3\sqrt[]{3}i)^3}{8}=\frac{216}{8}=27[/tex]Therefore, we have that:
[tex]z^3=(-\frac{3}{2}+\frac{3\sqrt[]{3}}{2}i)^3=27[/tex]In summary, therefore, the value for z³ = 27 (option B).
The food service manager at a large hospital is concerned about maintaining reasonable food costs. The following table lists the cost per serving, in cents, for items on four menu's. On particular day, a dietician orders 68 meals from menu 1, 43 meals from menu 2, 97 meals from menu 3, and 55 meals from menu 4.Part AWrite the information in the table as a 4x5 matrix M. Maintain the ordering of foods and menu's from the table.M=[__]Part BWrite a row matrix N that represents the number of meals ordered from each menu. Maintain the ordering of menu's from the tableN=[___]Part CFind the product NMNM=[___]1st blank options (average or total)2nd blank (each food, food, or each menu)
Answer and step by step:
a) To write the information in the table as a 4x5 matrix:
b) Write a row matrix N that represents the number of meals ordered from each menu.
c) Find the product NM:
To find the product of two matrices, the matrices have to be the same number of columns and rows. Then it cannot be solved.
What is the slope? y= x+2
The given equation is
[tex]y=x+2[/tex]It is important to know that the slope is the coefficient of x when it's expressed in slope-intercept form like this case.
Hence, the slope is 1.In ∆KLM, l= 56 inches , k =27 inches and < K=10°. Find all possible values of < L, to the nearest degree.
SOLUTION
In this question, we are meant to find the possible values of
This is just an application of SINE RULE, which says that:
[tex]\begin{gathered} \frac{L}{\sin\text{ L}}\text{ = }\frac{K}{\sin \text{ K}},\text{ we have that:} \\ \\ \frac{56}{\sin\text{ L }}\text{ = }\frac{27}{\sin \text{ 10}} \\ \text{cross}-\text{ multiplying, we have that;} \\ 27\text{ x sin L = 56 X sin 10} \\ \sin L\text{ =}\frac{56\text{ X sin 10}}{27} \\ \sin \text{ L = }\frac{56\text{ X 0.1736}}{27} \\ \\ \sin \text{ L = }\frac{9.\text{ 7216}}{27} \\ \sin L\text{ =0.3600} \\ \text{Taking sine inverse of both sides, we have:} \\ L=21.1^0 \\ L=21^{0\text{ }}(\text{correct to the nearest degr}ee) \end{gathered}[/tex]myself and my daughter is having issues with this problem. we keep coming up 11.96 and rounding it to 12 but it saying it is wrong
using trigonometric ratio
[tex]\tan 23^{\circ}=\frac{13}{y}[/tex][tex]\begin{gathered} y=\frac{13}{\tan 23^{\circ}} \\ y=\frac{13}{0.42447481621} \\ y=30.6260807557 \\ y\approx30.6 \end{gathered}[/tex]Note
tan 23 = opposite/adjacent
Agrocery store bought milk for $2.20 perhalf gallon and stored it in two refrigerators. During the night one refrigerator malfunctioned and ruined 13 half gallons. If the remaining milk is sold for $3.96 per half gallon, how many half gallons did the store buy if they made a profit of $121.00
Answer
The store bought 98 half gallon milks
Explanation
Let the number of half gallon nilks they bought be x
They bought each half gallon milk at a rate of 2.2 dollars each
13 half gallons got spoilt.
They then sold the rest of the half gallone (x - 13) gallons at 3.96 dollars per half gallon
Profit = Revenue - Cost
Revenue = (Amount of half gallons sold) × (Price of each one)
Revenue = (x - 13) × 3.96
Revenue = (3.96x - 51.48)
Cost = (Amount of half gallons bought) × (Price of each one)
Cost = x × 2.20
Cost = 2.20x
Profit = 121 dollars
Profit = Revenue - Cost
121 = (3.96x - 51.48) - 2.20x
121 = 3.96x - 51.48 - 2.20x
121 = 1.76x - 51.48
1.76x - 51.48 = 121
1.76x = 121 + 51.48
1.76x = 172.48
Divide both sides by 1.76
(1.76x/1.76) = (172.48/1.76)
x = 98 half gallon milks
Hope this Helps!!!
A rectangle is placed around a semicircle as shown below. The width of the rectangle is 8 yd. Find the area of the shaded regiorUse the value 3.14 for 1, and do not round your answer. Be sure to include the correct unit in your answer.
It is given that,
[tex]\begin{gathered} Radius\text{ of semicircle = width of rectangle = 8 yd} \\ Diameter\text{ of semicircle = length of rectangle = 16 yd} \\ \pi\text{ = 3.14} \end{gathered}[/tex]The area of the semicircle is calculated as,
[tex]\begin{gathered} Area\text{ = }\pi\times r^2 \\ Area\text{ = 3.14 }\times\text{ 8 }\times\text{ 8/2} \\ Area\text{ = 100.48 yd}^2 \end{gathered}[/tex]The area of the rectangle is calculated as,
[tex]\begin{gathered} Area\text{ = Length }\times\text{ Breadth} \\ Area\text{ = 16 yd }\times\text{ 8 yd} \\ Area\text{ = 128 yd}^2 \end{gathered}[/tex]The area of the shaded region is calculated as,
[tex]\begin{gathered} Area\text{ of shaded region = Area of rectangle - Area of semicircle} \\ Area\text{ of shaded region = 128 yd}^2\text{ - 100.48 yd}^2 \\ Area\text{ of shaded region = 27.52 yd} \end{gathered}[/tex]Examine the following graph, where the exponential function P(x) undergoes a transformation.The preimage of the transformation is labeled P(x), and the image is labeled I(x).
Explanation
For the function P(x), the value of x in the function is halved to get the values of x in the image.
This can be seen in the graphs below.
The red line represents the preimage and the blue line represents the image.
Answer: Option 4
Write a rule for the nth term of the sequence, then find a_20. 7, 12, 17, 22, ...
Problem
To find the 20th term of the sequence: 7, 12, 17, 22.
The rule for the nth term of the sequence is addding 5 to the term before to get the next term.
Concept
This is an arithmetic sequence since there is a common difference between each term. In this case .
Common ratio = 5
The term to term rule of a sequence describes how to get from one term to the next.
Final answer
The first term is 7. The term to term rule is 'add 5'.
25% of what number w is 9?=25100
25 % of 36 is 9
Explanation
Step 1
the easy way to find the percentage of any number is:
[tex]\begin{gathered} y\text{ \% of x } \\ total\text{ =x*}\frac{y}{100} \end{gathered}[/tex]so
A) let
25% of what number w is 9?
let
[tex]\begin{gathered} nubmer(x)\text{ = W} \\ percentage\text{ \lparen y\rparen=25 \%} \\ total\text{ =}9 \end{gathered}[/tex]now, replace and solve for w:
[tex]\begin{gathered} y\text{ \% of x } \\ total\text{ =x*}\frac{y}{100} \\ 9=W*\frac{25}{100} \\ 9=W*0.25 \\ divide\text{ both sides by 0.25} \\ \frac{9}{0.25}=\frac{W\times0.25}{0.25} \\ 36=W \end{gathered}[/tex]therefore ,
25 % of 36 is 9
What is the area in simplest form? 5/6 ft 4/6 ft
We are given a rectangle with a length of 5/6 ft and a height of 4/6 ft. To determine the area let's remember that the area of a rectangle is the product of the length by the height. Therefore, the area is:
[tex]A=(\frac{5}{6}ft)(\frac{4}{6}ft)[/tex]Solving the product we get:
[tex]A=\frac{20}{36}ft^2[/tex]Now, we simplify the result by dividing both sides by 4:
[tex]A=\frac{\frac{20}{4}}{\frac{36}{4}}ft^2=\frac{5}{9}ft^2[/tex]Therefore, the area is 5/9 square feet.
4) Identify the LIKE terms: 7y + 5r-4r + 2w 7y and 2w 7y and 5 O -4r and 2w 51 and 41
Problem Statement
We are asked to identify the like terms from the following expression:
[tex]7y+5r-4r+2w[/tex]Concept
When we are asked to identify like terms, the question is asking us to find which terms have the same variables with the same power.
For example:
[tex]\begin{gathered} \text{Given the expression:} \\ x^2+2x+y+yx+y^3+y^2+2y+3x^2 \\ \\ 3x^2\text{ and }x^2\text{ are like terms because they have the same variable (x) and both have a power of 2.} \\ y\text{ and 2y are like terms because they have the same variable (y) and both have a power of 1.} \\ \\ \text{Those are the only like terms in the expression} \end{gathered}[/tex]With the above information, we can solve the question.
Implementation
By the explanation given above, the like terms from the given expression are:
[tex]5r\text{ and }-4r[/tex]Find the probability that a point chosen at random on LP is on MN
The length of LP is 12 units and the length of MN is 3 units; therefore the probability that a point chosen at random falls on MN is
[tex]\frac{MN}{LP}=\frac{3}{12}=0.25[/tex]
Find f (-9) if f (x) = (20+x)/5
The given function is expressed as
f(x) = (20 + x)/5
We want to find f(- 9). To do this, we would substitute x = - 9 into the function. It becomes
f(- 9) = (20 + - 9)/5 = (20 - 9)/5
f(- 9) = 11/5
A professor decided he was only going to grade 8 out of 10 HW problems he assigned. How many different groupings of HW problems could he grade?
Answer:
The number of groupings is 45
Explanation:
Given that the professor decided he was only going to grade 8 out of 10 HW problems he assigned.
We want to calculate the number of ways the professor can grade the HW.
Which is a conbination;
[tex]10C8[/tex]Solving we have;
[tex]\begin{gathered} n=10C8=\frac{10!}{8!(10-8)!} \\ n=45 \end{gathered}[/tex]Therefore, the number of groupings is 45
25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. developed at least tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure. A) how many only got tumors? B) how many didn't get a tumor? C) how many suffered from at least one of these effects?
Explanation:
The total number of mice for the experiment is
[tex]Universalset=25[/tex]How to know how many mice didn't have a tumor?
Identify the total mice who did not have any effects or the effects did not include a tumor.
The number of mice that had respiratory failur is
[tex]n(R)=9[/tex]Based on this, it can be concluded 9 mice did not have a tumor,
Hence,
The number of mice that didnt have a tumor is 9
To figure out the number that got only tutmor, we will consider the number that has both tumors and respiratory failure
[tex]n(T\cap R)=4[/tex]The number that developed tumors is given below as
[tex]n(T)=15[/tex]Hence,
The number that got
Write the translation of point P(2, -9) to point P'(0, -12). [A] (x, y) =(x-3, y – 2) [B] (x, y) = (x+3, y +2) [C] (x, y) = (x+ 2, y + 3) [D] (x, y) = (x-2, y-3)
Applying the transformation (x, y) → (x - 2, y - 3) to point P, we get:
P(2, -9) → (2 - 2, -9 - 3) → P'(0, -12)
Find the terminal point on the unit circle determined by π2 radians.Use exact values, not decimal approximations.
Okay, here we have this:
Considering the provided information, we are going to determine the requested terminal point, so we obtain the following:
So for this we will first calculate how much the given angle is in degrees, from there then we proceed to observe in the unit circle, then we have:
(pi/2)*(180°/pi)=180°/2=90°
We can observe in the image of the unit circle that the terminal point of 90° is (0, 1).
Finally we obtain that the terminal point of pi/2 radians is (x,y)=(0, 1).
tem = 462-5 h 1995. Central High School had a student population of 2250 students. By 2005, the student population was only 1.800 students. What is the percent of decrease in the student population? A 2002 B. 25% C. 75% D. 80% tem = 119766
Central High School had a student population of 2250 students.
By 2005, the student population was only 1.800 students.
What is the percent of decrease in the student population?
A 2002
B. 25%
C. 75%
D. 80%
Percentage of decrease = 100 - 100 * (1800/2250) = 100 - 100 * 0.8 = 100 - 80 = 20%
At its first meeting, the math club had 16 students attend. At its second meeting, 25 students attended. What was the percent of increase?
First, subtract 16 to 25:
25 - 16 = 9
next, calculate the associated percentage of 9 to 16, as follow:
(9/16)(100) = 56.25
Hence, the increase was of 56.25%
True Or False? the y intercept for the line of the best fit for this scatterplot is 5
From the graph of the line we notice that if we prolong the line to the y-axis it will intercept it at approximately 4.5.
Therefore, the stament is False.
The vertices of ABC are A(2,-5), B(-3, - 1), and C(3,2). For the translation below, give the vertices of AA'B'C'. T * - 1) (ABC) The vertices of AA'B'C' are A'B', and c'| (Simplify your answers. Type ordered pairs.)
In order to calculate the translation of <-4, -1> to the triangle ABC, we just need to add these coordinates to all vertices of the triangle, that is, add -4 to the x-coordinate and -1 to the y-coordinate. So we have that:
[tex]\begin{gathered} A(2,-5)\to A^{\prime}(2-4,-5-1)=A^{\prime}(-2,-6) \\ B(-3,-1)\to B^{\prime}(-3-4,-1-1)=B^{\prime}(-7,-2) \\ C(3,2)\to C^{\prime}(3-4,2-1)=C^{\prime}(-1,1) \end{gathered}[/tex]So the vertices after the translation are A'(-2, -6), B'(-7, -2) and C'(-1, 1).
The following data are an example of what type of regression?
x
1
2
4
6
8
10
12
OA. Exponential
OB. Quadratic
O C. Linear
OD. None of the above
Y
1.2
1.4
2.1
3.1
4.3
5.6
7.2
The given data is an example of Option C Linear regression equation,
y = 0.5438x + 0.2169
Given,
The data;
x ; 1 2 4 6 8 10 12
y ; 1.2 1.4 2.1 3.1 4.3 5.6 7.2
We have to find the type of regression of the given data;
Regression equation;
In statistics, a regression equation is used to determine whether or not there is a link between two sets of data.
Lets find regression equation first;
There are 7 number of pairs
The regression equation is;
y = 0.5438x + 0.2169
That is,
The given data is an example of Option C Linear regression equation,
y = 0.5438x + 0.2169
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Which of the following sequences represents an arithmetic sequence with a common difference d = –4? 768, 192, 48, 12, 3 35, 31, 27, 23, 19 24, 20, 16, 4, 0 5, –20, 80, –320, 1,280
The general formula of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)\cdot d[/tex]Where d is known as the common difference and it represents the distance between consecutive terms of the sequence. So we can calculate this distance for each of the four options:
[tex]\begin{gathered} 768,192,48,12,3 \\ 768-192=576 \\ 192-48=144 \end{gathered}[/tex]So in the first sequence the difference between terms is not even constant so this is not the correct option.
[tex]\begin{gathered} 31-35=-4 \\ 27-31=-4 \\ 23-27=-4 \\ 19-23=-4 \end{gathered}[/tex]In the second sequence the distance is -4 so this is a possible answer.
[tex]\begin{gathered} 20-24=-4 \\ 16-20=-4 \\ 4-16=-12 \\ 0-4=-4 \end{gathered}[/tex]In the third sequence the distance is not always the same so we can discard this option.
[tex]\begin{gathered} -20-5=-25 \\ 80-(-20)=100 \end{gathered}[/tex]Here the distance isn't constant so the fourth option can also be discarded.
Then the only sequence with a distance d=-4 is the second option.
36. Let f(x) = x 4 x - 6 and g(x) = x - 2x – 15. Findf(x)•g(x)
f(x) = x^2 + x - 6
g(x) = x^2 - 2x - 15
Process
factor both functions
f(x) = (x + 3)(x - 2)
g(x) = (x - 5)(x + 3)
Divide them:
f(x) / g(x) = [(x + 3)(x - 2)] / [x - 5)(x + 3)]
Simplify like terms
f(x) / g(x) = (x - 2)/ (x - 5)
on the unit circle, in standard position, an angle of which measure is coterminal with an angle that measures pi/4 radians?
Coterminal angles are defined as the angles which possess the same terminal side.
The given angle measure is π/4 radians.
Consider that one full circle constitutes an angle measure of 2π radians.
So if we add 2π to the given angle, the resultant will represent the same terminal side.
[tex]undefined[/tex]y = 2x - 9 y = -1/2x + 1Graph both equations to find the solutionfor this system.
To answer this question, we can graph both lines equations using the intercepts of both lines. The intercepts are the x- and the y-intercepts for both lines.
The x-intercept is the point where the line passes through the x-axis. At this point, y = 0. Likewise, the y-intercept is the point where the line passes through the y-axis. At this point, x = 0.
Therefore, we can proceed as follows:
1. Graphing the line y = 2x - 9First, we can find the x-intercept. For this, y = 0.
[tex]\begin{gathered} y=2x-9\Rightarrow y=0 \\ 0=2x-9 \\ 9=2x \\ \frac{9}{2}=\frac{2}{2}x \\ \frac{9}{2}=x\Rightarrow x=\frac{9}{2}=4.5 \end{gathered}[/tex]Therefore, the x-intercept is (4.5, 0).
The y-intercept is:
[tex]y=2(0)-9\Rightarrow y=-9[/tex]Therefore, the y-intercept is (0, -9).
With these two points (4.5, 0) and (0, -9) we can graph the line y = 2x - 9.
2. Graphing the line y = -(1/2)x +1We can proceed similarly here.
Finding the x-intercept:
[tex]\begin{gathered} 0=-\frac{1}{2}x+1 \\ \frac{1}{2}x=1 \\ 2\cdot\frac{1}{2}x=2\cdot1 \\ \frac{2}{2}x=2\Rightarrow x=2 \end{gathered}[/tex]Therefore, the x-intercept is (2, 0).
Finding the y-intercept:
[tex]\begin{gathered} y=-\frac{1}{2}(0)+1 \\ y=1 \end{gathered}[/tex]Then the y-intercept is (0, 1).
Now we can graph this line by using the points (2, 0) and (0, 1).
Graphing both linesTo graph the line y = 2x - 9, we have the following coordinates (4.5, 0) and (0, -9) ---> Red line.
To graph the line y = -(1/2)x + 1, we have the coordinates (2, 0) and (0, 1) ---> Blue line.
We graph both lines, and the point where the two lines intersect will be the solution of the system:
We can see that the point where the two lines intersect is the point (4, -1). Therefore, the solution for this system is (4, -1).
We can check this if we substitute the solution into the original equations as follows:
[tex]\begin{gathered} y=2x-9 \\ -2x+y=-9\Rightarrow x=4,y=-1 \\ -2(4)+(-1)=-9 \\ -8-1=-9 \\ -9=-9\Rightarrow This\text{ is True.} \end{gathered}[/tex]And
[tex]\begin{gathered} y=-\frac{1}{2}x+1 \\ \frac{1}{2}x+y=1\Rightarrow x=4,y=-1 \\ \frac{1}{2}(4)+(-1)=1 \\ 2-1=1 \\ 1=1\Rightarrow This\text{ is True.} \end{gathered}[/tex]In summary, we found the solution of the system:
[tex]\begin{gathered} \begin{cases}y=2x-9 \\ y=-\frac{1}{2}x+1\end{cases} \\ \end{gathered}[/tex]Using the intercepts of the lines, graphing the lines, and the point where the two lines intersect is the solution for the system. In this case, the solution is (4, -1) or x = 4, and y = -1.