ANSWER:
Angle x is 103 degrees
EXPLANATION
The sum of all the angles in a triangle is 180 degrees
Hence, Let angle A = 27 degrees
Angle B = 50 degrees
Angle C = x degrees
Triangle sum theorem state that
50 + 27 + x = 180
77 + x = 180
x = 180 - 77
x = 103 degrees
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Question
Each equation represents a proportional relationship. Choose the equations for which the constant of proportionality is 14.
Responses
A y = 0.25xy = 0.25x
B 4y = x4y = x
C y = 4xy = 4x
D 32y = 8x32y = 8x
E 14y = 2x
Answer:
its B
Step-by-step explanation: just took the test
A carpenter is working with a beam that is 10 feet long and in the shape of a rectangular prism. He cuts the beam in half. What happens to the surface area and the volume of the beam?
For this problem, we are provided with the image of a beam and its dimensions, we are then informed that the beam was cut in half, and we need to compare the surface area and volume of the beam before and after the cut.
The surface area of a rectangular prism can be calculated with the following expression:
[tex]A_{\text{surface}}=2\cdot(\text{width}\cdot\text{height}+\text{width}\cdot\text{length}+\text{height}\cdot\text{length)}[/tex]The volume of a rectangular prism can be calculated with the following expression:
[tex]V=\text{width}\cdot\text{height}\cdot\text{length}[/tex]We can use these formulas to calculate the characteristics of the beam before the cut:
[tex]\begin{gathered} A_{\text{surface}}=2\cdot(10\cdot1+1\cdot1+1\cdot10)=42\text{ square ft} \\ V=10\cdot1\cdot1=10_{}\text{ cubic ft} \end{gathered}[/tex]Now we can calculate the characteristics of the beam after the cut:
[tex]\begin{gathered} A_{\text{surface}}=2\cdot(5\cdot1+1\cdot1+1\cdot5)=22\text{ square ft} \\ V=5\cdot1\cdot1=5\text{ cubic ft} \end{gathered}[/tex]With this, we can conclude that:
The surface area of the cut beam is 20 sq ft smaller than the original beam.
The volume of the cut beam is half the volume of the original beam.
Which point is located at (-1, -3)?A.point AB.point DC.point ED.point F
SOLUTION
We are asked which point is located at (-1, -3)
From the diagram given, the point located on (-1, -3) is point E.
Hence option C is the correct answer
Evaluate. Assume u > O when In u appears. (In x)96 1 dex X O 96(In x)95+C (In x97 97x +C O (In x)97 +C O (In x)97 97 +
EXPLANATION
[tex]\int \frac{(\ln x)^{96}}{x}dx[/tex]Applying subtitution: u=ln(x)
By integral substitution definition
[tex]\int f(g(x))\cdot g^{^{\prime}}(x)dx=\text{ }\int f(u)du,\text{ u=g(x)}[/tex]Substitute: u=ln(x)
[tex]\frac{du}{dx}=\frac{1}{x}[/tex][tex]\frac{d}{dx}=(\ln (x))[/tex]Apply the common derivative:
[tex]\frac{d}{dx}(\ln (x))=\frac{1}{x}[/tex][tex]\Rightarrow du=\frac{1}{x}dx[/tex][tex]\Rightarrow dx=xdu[/tex][tex]=\int \frac{u^{96}}{x}\text{xdu}[/tex]Simplify:
[tex]\frac{u^{96}}{x}x[/tex]Multiply fractions:
[tex]a\cdot\frac{b}{c}=\frac{a\cdot b}{c}[/tex][tex]=\frac{u^{96}x}{x}[/tex]Cancel the common factor: x
[tex]=u^{96}[/tex][tex]=\int u^{96}du[/tex]Apply the Power Rule:
[tex]\int x^adx=\frac{x^{(a+1)}}{a+1},\text{ a }\ne\text{ -1}[/tex][tex]=\frac{u^{96+1}}{96+1}[/tex]Substitute back u=ln(x)
[tex]=\frac{\ln ^{96+1}(x)}{96+1}[/tex]Simplify:
[tex]\frac{\ln ^{96+1}(x)}{96+1}[/tex]Add the numbers: 96+1=97
[tex]=\frac{\ln ^{97}(x)}{97}[/tex][tex]=\frac{1}{97}\ln ^{97}(x)[/tex]Add a constant to the solution:
[tex]=\frac{1}{97}\ln ^{97}(x)\text{ + C}[/tex]The answer is D:
[tex]\frac{(\ln x)^{97}}{97}+C[/tex]Sarah is saving money to go on a trip. She needs at least $1975 in order to go. Sarah is mowing lawns and walking dogs to raise money. She charges $25 each time he mows a lawn and $15 each time she walks a dog. I have to Define the variables for the problem and Write an inequality to model this problem
We're told from the question that Sarah needs atleast $1975, that means that she can either have exactly $1975 or more but not less;
Let x represent the number times she mows a lawn;
Let y represent the number of times she walks a dog;
The inequality can be modelled thus;
[tex]25x+15y\ge1975[/tex]Hans cell phone plan cost $200 to start, then there is a $50 charge each month.a. what is the total cost ( start-up fee and monthly charge) to use the cell phone plan for one month? b. what is the total cost for x months?c. graph the cost of the cell phone plan over a. Of 2 years using months as a unit of time. Be sure to scale your access by labeling the grid line with some numbers.(pt2 to letter c) what are the labels for the axes of the graph (for x and y)d. is there a proportional relationship between time and the cost of the cell phone plan?Explain how you know!e. Tyler cell phone plan cost $350 to start then there is a $50 charge each month on the same grid as Hans plan in part C above graph the cost of Tyler cell phone plan over Of 2 yearslastly, describe how hans and Tyler's graphs are similar and how they are different..
We know that
• The cost is $200 to start and $50 per month. This can be expressed as follows.
[tex]C=200+50m[/tex](a) The cost for one month would be
[tex]C=200+50\cdot1=200+50=250[/tex](b) The cost for x months is
[tex]C=200+50x[/tex](c) To graph the equation, we use the month as a unit of time, the table values would be
m C
1 250
2 300
3 350
4 400
5 450
6 500
7 550
8 600
9 650
10 700
11 750
12 800
Now, we graph all of these points.
The x-axis label is Months, and the y-axis label is Cost.
(d) The given situation does not show a proportional relationship because a proportional relationship is modeled by the form y = kx, which we do not have in this case.
(e) If the initial fee is $350, the equation is
[tex]C=350+50m[/tex]Let's graph it.
The graphs are similar because they have the same slope but they are different because they have different y-intercepts.
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Frankie and Gus swam for 10 minutes. When the time was up, Frankie had completed 10 7/10 laps and Gus 10 4/5 had completed laps. Frankie wrote the inequality 10 7/10 > 10 4/5 to show who swam the longest distance. Was he correct? Explain your answer by describing where the numbers would be positioned on a number line.
Answer:
Frankie is incorrect.
Step-by-step explanation:
Change 4/5 to 8/10.
You are comparing 10 7/10 to 10 8/10.
10 4/5 (which is also 10 8/10) can be written as 10.8
10 7/10 can be written as 10.7
10.8 > 10.7, so 10 4/5 > 10 7/10 is correct,
and 10 7/10 > 10 4/5 is incorrect.
Frankie is incorrect.
On a number line, show 10 and 11.
Make 10 equal spaces between 10 and 11. Each space is 1/10.
10 7/10 is one space to the left of 10 4/5, so 10 7/10 is less than 10 4/5.
i need help with math
A. ∠4 is congruent to ∠5; True.
B. Two lines are parallel; True.
C. The measure of ∠6 = 90.5°; False.
D. ∠2 and ∠3; True.
What are the properties of angles of parallel lines?On a common plane, two parallel lines do not intersect.As a result, the characteristics of parallel lines with respect to transversals are given below.Angles that correspond are equal.Vertical angles are equal to vertically opposite angles.Interior angles that alternate are equal.The exterior angles that alternate are equal.For the give question;
Two line are cut by the transversal.
∠1 = 90.5° and ∠7 = 89.5°
Thus the result for the given statement are-
A. ∠4 is congruent to ∠5 because they are alternate interior angles; True.
B. Two lines are parallel; True.
C. The measure of ∠6 = 90.5°; False.
∠6 = ∠7 = 89.5°.(correct)
D. ∠2 and ∠3 are supplementary because they are same-side exterior Angeles; True.
Thus, the result for the given statement are found.
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-8-2y=10Hi I'm having a lot of trouble with problems like these.First when I go to solve this how do I know whether to add or subtract the -8 from the 10 or the 10 from the -8Also on problems like these how do I know either to add or subtract?
To solve an equation for a variable, we mean to "isolate" the variable on one side of the equation ( right or left), in order to solve for the variable we add and subtract constant terms, like 7, 8, 10, or any other constant.
In this case, we have the equation -8-2y=10, so the first step to take is to take the -8 "away" and put it to the other side of the equation ( this is the shortest way but you can take the -2y to the other side of the equation first or perform any other operation that you want that does not alter the equation, but the point is to isolate y), to put -8 in the other side of the equation we have to add it to both sides of the equation because -8+8=0:
[tex]\begin{gathered} -8-2y+8=10+8, \\ -2y=18. \end{gathered}[/tex]Now, notice that y still has a constant next to it, but the goal is to leave y alone, so we check what is it that this constant is doing to y, well -2 is multiplying y so in order to take to the other side of the equation we divide all the equation by -2, because -2/-2=1:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{18}{-2}, \\ y=-9. \end{gathered}[/tex]That is how one solves an equation for a variable.
Alternative solution:
[tex]\begin{gathered} -8-2y=10, \\ -8-2y-10=10-10, \\ -18-2y=0, \\ -18-2y+18=0+18, \\ -2y=18, \\ y=\frac{18}{-2}, \\ y=-9. \end{gathered}[/tex]Solve x+1=3, for x: first I choose on which side of the equation I want x, I want x on the left side ( could be the right side, it is up to you), second, I observe the equation and notice that there is a number being added to x, the constant is +1, to get rid of the constant I must subtract the constant on both sides of the equation:
[tex]x+1-1=3-1.[/tex]The last step is to simplify:
[tex]\begin{gathered} x+(0)=3-1, \\ x=2. \end{gathered}[/tex]Select all the values that are equivalent to (25+9.05×10^2)/3.
We have the following:
[tex]\frac{25+9.05×10^{2}}{3}[/tex]solving:
[tex]\frac{25+9.05\cdot100}{3}=\frac{25+905}{3}=\frac{930}{3}=310[/tex]The expression is equivalent to 310
Solve the system of linear equations using the substitution method. 4x+4y=12x=-2y+8
Hello there. To solve this question, we'll need to isolate a variable, substitute its expression into the other equation and find both values.
4x + 4y = 12
x = -2y + 8
Plug x = -2y + 8 in the first equation. Before doing so, divide both sides of the first equation by a factor of 4
x + y = 3
-2y + 8 + y = 3
Subtract 8 on both sides of the equation and add the values
-2y + y = 3 - 8
-y = -5
Multiply both sides of the equation by a factor of (-1)
y = 5
Plug this value into the expression for x
x = -2 * 5 + 8
Multiply the values
x = -10 + 8
Add the values
x = -2
These are the values we're looking for.
The solution for this system of equation is given by:
S = {(x, y) in R² | (x, y) = (-2, 5)}
Answer:
x = -2
y = 5
Step-by-step explanation:
Solving system of linear equations by substitution method:4x + 4y = 12
Divide the entire equation by 4,
x + y = 3 -------------(I)
x = -2y + 8 ------------(II)
Substitute x = -2y + 8 in equation (I)
-2y + 8 + y = 3
-2y + y + 8 = 3
Combine like terms,
-y + 8 = 3
Subtract 8 from both sides,
-y = 3 - 8
-y = - 5
Multiply the entire equation by (-1)
[tex]\sf \boxed{\bf y = 5}[/tex]
Substitute y= 5 in equation (II),
x = -2*5 + 8
= - 10 + 8
[tex]\sf \boxed{\bf x = -2}[/tex]
the store bought a bike from the factory for$ 99 and sold I to Andre for $117 what percentage was the markup?
EXPLANATION
Let's see the facts:
Bike Price: $99
Sold Price: $117
The percentage is given by the following relationship:
[tex]\text{Percentage: }\frac{\text{Selling price per unit}-Cost\text{ price per unit}}{Cost\text{ price per unit}}\cdot100[/tex]Replacing terms:
[tex]\text{Percentage =}\frac{117-99}{99}\cdot100[/tex][tex]\text{Percentage = 18.18\%}[/tex]Answer: The markup was 18.18%
Convert the following expressions to simplify fraction or integer. If it is not a real number, enter none
We are given the expression:
[tex]8^{\frac{2}{3}}[/tex]To get the answer, we will have to apply exponents rules
The rule is:
[tex]a^{\frac{b}{c}}=\sqrt[c]{a}^b[/tex]Thus
we will have
[tex]8^{\frac{2}{3}}=\sqrt[3]{8^2}=\sqrt[3]{64}=4[/tex]Therefore,
The answer is 4
The selling price of a refrigerator is $548.90. If the markup is 10% of the dealer's cost, what is the dealer's cost of the refrigerator?
Answer
Dealer's cost = $499
Explanation
The markup percent is given as
[tex]\text{Markup percent = }\frac{(Selling\text{ Price) - (Cost)}}{Cost}\times100\text{ percent}[/tex]Markup percent = 10%
Selling Price = 548.90 dollars
Cost = ?
[tex]\begin{gathered} \text{Markup percent = }\frac{(Selling\text{ Price) - (Cost)}}{Cost}\times100\text{ percent} \\ \text{10 = }\frac{548.90\text{-(Cost)}}{Cost}\times100\text{ percent} \\ 0.1=\frac{548.90-\text{Cost}}{\text{Cost}} \\ \text{Cross multiply} \\ 0.1(\text{Cost) }=548.90-\text{Cost} \end{gathered}[/tex]0.1 (Cost) + Cost = 548.90
1.1 (Cost) = 548.90
Divide both sides by 1.1
Cost = (548.90/1.1)
Cost = 499 dollars
Hope this Helps!!!
A triangle has sides measuring 5 inches and 8 inches. If x represents the length in inches of the third side, which inequality gives the range of possible values for x? OA. 3< x< 13 B. 5< x< 8 OC. 3
Explanation
Step 1
then
If a,b,c are the sides of a triangle it MUST exist these equality:
each side must be less then the sum of the others sides.
[tex]\begin{gathered} then \\ x<5+8 \\ x<13 \\ \end{gathered}[/tex]Also
[tex]\begin{gathered} x+5>8 \\ x>8-5 \\ x>3 \end{gathered}[/tex]then,the answer is
[tex]3I need help. I have no idea how to respond this question
An angle with its vertex on a circle and chord-shaped sides is said to be inscribed. The arc that is inside the inscribed angle and whose endpoints are on the angle is known as the intercepted arc.
A triangle's internal angles are always divisible by 180 degrees.
The central angle of one radian (s = r) subtends an arc length of one radius. One radian has the same value for all circles because they are all alike. The central angle of a circle is measured by its arc, which is 360 degrees, and its radian measure, which is 2π.
Circles:
A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the center. The radius of a circle is measured from the center to the edge. The line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.
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Find the difference: 8.02 - 0.003A) 7.990B) 8.017C) 8.019D) None of these choices are correct.
Given:
[tex]8.02-0.003[/tex][tex]8.02-0.003=8.017[/tex]Option B is the final answer.
evaluate the expression given sin u = 5/13 and cos v = -3/5 where angle u is in quadrant 2and angle v is in quadrant 2sin ( u - v )
We are given the following information
sin u = 5/13
cos v = -3/5
Where the angle u and v are in the 2nd quadrant.
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \sin\theta=\frac{opposite}{hypotenuse} \end{gathered}[/tex]Let us find cos u
Apply the Pythagorean theorem to find the 3rd side.
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2=c^2-b^2 \\ a^2=13^2-5^2 \\ a^2=169-25 \\ a^2=144 \\ a=\sqrt{144} \\ a=12 \end{gathered}[/tex]Cos u = 12/13
Now, let us find sin v
Apply the Pythagorean theorem to find the 3rd side.
[tex]\begin{gathered} a^2+b^2=c^2 \\ b^2=c^2-a^2 \\ b^2=5^2-(-3)^2 \\ b^2=25-9 \\ b^2=16 \\ b=\sqrt{16} \\ b=4 \end{gathered}[/tex]Sin v = 4/5
Recall the formula for sin (A - B)
[tex]\sin(A-B)=\sin A\cos B-\cos A\sin B[/tex]Let us apply the above formula to the given expression
[tex]\begin{gathered} \sin(u-v)=\sin u\cdot\cos v+\cos u\cdot\sin v \\ \sin(u-v)=\frac{5}{13}\cdot-\frac{3}{5}+\frac{12}{13}\cdot\frac{4}{5} \\ \sin(u-v)=\frac{33}{65} \end{gathered}[/tex]Therefore, sin (u - v) = 33/65
From the entrance, most people will go straight to the roller coaster or straight to the tower. The distance from the entrance to the roller coaster is 461m, and the distance from the entrance to the tower is 707 m. If the paths to these two attractions are separated by a 41o angle, how far apart are the roller coaster and the tower?
The given situation can be illustrated as follow:
In order to determine the distance x between the roller coaster and the tower. Use the law of cosines, as follow:
[tex]x^2=(461)^2+(707)^2-2(461)(707)\cos 41[/tex]By simplifying the previous expression, you obtain:
[tex]\begin{gathered} x^2=220409.5413 \\ x=\sqrt[]{220409.5413} \\ x\approx469.5 \end{gathered}[/tex]Hence, the distance between the tower and the roller coaester is approximately 469.5m
Is there enough information to prove the quadrilateral is a parallelogram if so what property proves it
To solve this problem we remember the following statement: a quadrilateral that has opposite sides that are congruent and parallel can be a parallelogram, rhombus, rectangle or square.
From the figure, we see a quadrilateral with congruent opposite sides. Relating this information to the statement above, we see that this quadrilateral can be a parallelogram, rhombus, rectangle or square. So we conclude that there is not enough information to conclude that the quadrilateral is a parallelogram.
Answer
d. Not enough information
what's the equation of the line that passes through the points (-9,-8) and (-6,6) in point slope form
The equation of the line passing through the given points in the point slope form is;
[tex]y-6\text{ = }\frac{14}{3}(x\text{ + 6)}[/tex]Here, we want to find the equation of the line that passes through the given points
Mathematically, we can write the equation of a line as follows in point slope form;
[tex]y-y_1=m(x-x_1)[/tex]m here represents the slope of the line
To calculate m which is the slope, we use the slope equation as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ m\text{ = }\frac{6-(-8)}{-6-(-9)}\text{ = }\frac{6\text{ + 8}}{-6\text{ + 9}}\text{ = } \\ =\text{ }\frac{14}{3} \end{gathered}[/tex]To write the equation, we use any of the two given points.
Thus, we have;
[tex]\begin{gathered} y-6\text{ = }\frac{14}{3}(x-(-6)) \\ \\ y-6\text{ = }\frac{14}{3}(x\text{ + 6)} \end{gathered}[/tex]A rental car company charges 23.95 per day to rent a car and $0.08 for every mile driven. Nathan wants to rent a car, knowing that:He plans to drive 400 miles.He has at most $440 to spend.Which inequality can be used to determine x, the maximum number of days Nathan can afford to rent for while staying within his budget?
Answer
Explanation
The total charge on the car = (Charge based on number of days) + (Charge based on the number of miles)
Charge based on number of days = (23.95) (x) = (23.95x) dollars
Charge based on the number of miles = (0.08) (400) = 32 dollars
(The total charge on the car) ≤ 440
23.95x + 32 ≤ 440
23.95x + 32 - 32 ≤ 440 - 32
23.95x ≤ 408
Divide both sides by 23.95
(23.95x/23.95) ≤ (408/23.95)
x ≤ 17.04
Hope this Helps!!!
For the piecewise function, find the values g(-2), g(2), and g(8).g(x)=X+7, for xs28- x, for x>2.9(-2)=0
g(x) = x + 7 when x =< 2
g(x) = 8 - x when x > 2
g(-2) Evaluate the first function
g(-2) = -2 + 7
g(-2) = 5
g(2) Evaluate the first function
g(2) = 2 + 7
g(2) = 9
g(8) Evaluate the second function
g(8) = 8 - 8
g(8) = 0
3a + 9 > 21 or -2a +4 > 16
We will look at how to evaluate inequalities in terms of a number line solution.
We have the following two inequalities:
[tex]3a\text{ + 9 > 21 or -2a + 4 > 16}[/tex]We will first solve each inequality separately for the variable ( a ) as follows:
[tex]\begin{gathered} 3a\text{ > 12 or -2a > 12} \\ \textcolor{#FF7968}{a}\text{\textcolor{#FF7968}{ > 4 or a < -6}} \end{gathered}[/tex]Now we will plot the solution on a number line as follows:
Hello! I need help solving and answering this practice problem. Having trouble with it.
In this problem, we have an arithmetic sequence with:
• first term a_1 = -22,
,• common difference r = 5.
The terms of the arithmetic sequence are given by the following relation:
[tex]a_n=a_1+r\cdot(n-1)\text{.}[/tex]Replacing the values a_1 = -22 and r = 5, we have:
[tex]a_n=-22+5\cdot(n-1)=-22+5n-5=5n-27.[/tex]We must compute the sum of the first 30 terms of the sequence.
The sum of the first N terms of a sequence is:
[tex]\begin{gathered} S=\sum ^N_{n\mathop=1}a_n=\sum ^N_{n\mathop{=}1}(5n-27) \\ =5\cdot\sum ^N_{n\mathop{=}1}n-27\cdot\sum ^N_{n\mathop{=}1}1 \\ =5\cdot\frac{N\cdot(N+1)}{2}-27\cdot N. \end{gathered}[/tex]Where we have used the relations:
[tex]\begin{gathered} \sum ^N_{n\mathop{=}1}n=\frac{N\cdot(N+1)}{2}, \\ \sum ^N_{n\mathop{=}1}1=N\text{.} \end{gathered}[/tex]Replacing the value N = 30 in the formula for the sum S, we get:
[tex]S=5\cdot\frac{30\cdot31}{2}-27\cdot30=1515.[/tex]Answer
sum = 1515
What is the simplest form of the radical expression? 3 3 √ 2 a − 6 3 √ 2 a
Please show the steps to help me understand this process.
Simplest form of the radical expression 3 ∛2 a − 6 ∛2 a is given by -3∛2 a.
As given in the question,
Given radical expression is equal to :
3 ∛2 a − 6 ∛2 a
Simplify the given 3 ∛2 a − 6 ∛2 a radical expression to get the simplest form ,
3 ∛2 a − 6 ∛2 a
Write all the prime factors of the number we have,
= 3∛2 a - ( 3 × 2) ∛2 a
Take out the common factor from the given radical expression we have,
= 3∛2 a ( 1 - 2 )
= 3∛2 a (- 1)
= -3∛2 a
Therefore, simplest form of the radical expression 3 ∛2 a − 6 ∛2 a is given by -3∛2 a.
The complete question is:
What is the simplest form of the radical expression? 3 ∛2 a − 6 ∛2 a
Please show the steps to help me understand this process.
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Can you please give me a step by step explanation/solution. Thanks
The Perimeter of a Rectangle
Given a rectangle of width w and length l, the perimeter is calculated as the sum of the side lengths, that is:
P = w + w + l + l
Or, equivalently
P = 2w + 2l
Hermann was calculating the perimeter of a rectangle and built the expression:
P = x + x + 4x + 4x feet
Note this expression is similar to the first one. This means that the width of the rectangle is x and the length is 4x.
a) We'll draw a rectangle with such dimensions:
b) Assuming the base is the length and the height is the width, the relationship between the base and the height is
4x / x = 4
This means the base is four times the height
c) We are given the perimeter as P = 60 feet.
We need to solve the equation
x + x + 4x + 4x = 60
Simplifying:
10x = 60
Dividing by 10:
x = 60/10
x = 6 feet
The base is 4x = 24 feet.
The base of Herman's rectangle is 24 feet
The height of Herman's rectangle is 6 feet
The function y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-8 and x=-5. Use the line segment to determine the average rate of change of the function f(x) on the interval −8≤x≤−5.
The formula for calculating the rate of change of a function is expressed as:
[tex]f^{\prime}(x)=\frac{f(b)-f(a)}{b-a}[/tex]Using the connecting points x = -8 and x = -5 on the graph, this means:
a = -8 = x1
b = -5 = x2
f(b) is f(-5) which is the corresponding y-values at x = -8
f(a) is f(-8) which is the corresponding x-values at x = -5
From the graph;
f(b) = f(-5) = -20 = y2
f(a) = f(-8) = -10 = y1
Determine the change in y and change in x
[tex]\begin{gathered} \triangle y=y_2-y_1=-20-(-10) \\ \triangle y=-20+10=-10 \\ \triangle x=x_2-x_1=-5-(-8) \\ \triangle x=-5+8=3 \end{gathered}[/tex]Find the average rate
[tex]\begin{gathered} Average\text{ rate of change}=\frac{f(b)-f(a)}{b-a}=\frac{\triangle y}{\triangle x} \\ Average\text{ rate of change}=-\frac{10}{3} \end{gathered}[/tex]For the grah , draw a line connecting the coordinate point (-5, -20) and (-8, -10)
Emma has money into savings accounts. One rate is 8% and the other is 12%. If she has $450 more in the 12% account and the total interest is $220, how much is invested in each savings account?
A account 8% B account 12%
A+$450 = B (1)
Ax8% +Bx12%= $220
Ax0.08 + Bx0.12 = 220
Now we replace (1) on B:
Ax0.08 + (A+450)x0.12 = 220
Ax0.08 + Ax0.12 + 54 = 220
Ax0.2 = 166
A= 830.
Now we replace the value of A on equation (1):
830 + 450 = B
B = 1280
Use the Distributive Property to simplify the following expression.8(x+4)
Given the expression:
8(x + 4)
Let's simplify using distributive property.
Use distributive property to distribute 8 into x + 4:
8(x) + 8(4)
Evaluate:
8x + 32
ANSWER:
8x + 32