Cora and Leroy went out to lunch. Leroy's bill
was $8.59 less than three times Cora's bill. If
their combined bill total was $68.29. how much
more did Leroy pay than Cora?
Let
x -------> Leroy's bill
y -------> Cora's bill
we have
x=3y-8.59 ------> equation A
x+y=68.29 ------> equation B
solve the system
substitute equation A in equation B
(3y-8.59)+y=68.29
solve for y
4y=68.29+8.59
4y=76.88
y=19.22
Find the value of x
xc=3(19.22)-8.59
x=49.07
therefore
Leroy's bill was $49.07Cora's bill was $19.22hi how do you find the area of this figuer
we can divide the figure in two parts, a triangule and a square. So the area is sum of the area fo each figure
[tex]A=3\cdot3+\frac{2\cdot3}{2}=9+3=12[/tex]therefore the area is 12m^2
Marshall has a rectangular garden that he wants to enclose with a fence. To calculate the perimeter, he used the expression below; where w represents the width and I represents the length of the garden. 2w + 2L Which other expression could Marshall use to calculate the perimeter?A. wLB.2wLC.2(w+2L)D.2(w+L)
by factoring the expression, you can also write
[tex]\begin{gathered} 2w+2l \\ 2(w+l) \end{gathered}[/tex]Find the measure of angle A associated with the following ratios and round to the nearest degree.
For, CosA = 0.2785 value of angle m∠A = 73.8293° ≈ 74°
Inverse Cosine function:
The inverse cosine function is written as cos^-1(x) or arccos(x).
CosA = 0.2785
A = [tex]Cos^{-1}[/tex](0.2785)
A = 73.8293°
thus by calculation we can say,
m∠A = 73.8293°
≈ 74°
Thus,
For, CosA = 0.2785 value of angle m∠A = 73.8293°
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Round to the nearest tenthRound to the nearest hundredthRound to the nearest whole number
Round to the nearest tenth
15. 7.953 is equal to 8.0 rounded to the nearest tenth.
16. 4.438 is equal to 4.4 rounded to the nearest tenth.
17. 5.299 is equal to 5.3 rounded to the nearest tenth.
18. 8.171 is equal to 8.2 rounded to the nearest tenth.
Round to the nearest hundredth
19. 5.849 is equal to 5.85 rounded to the nearest hundredth.
20. 4.484 is equal to 4.48 rounded to the nearest hundredth.
21. 0.987 is equal to 0.99 rounded to the nearest hundredth.
22. 0.155 is equal to 0.16 rounded to the nearest hundredth.
Round to the nearest whole number
23. 98.55 is equal to 99 rounded to the nearest whole number.
24. 269.57 is equal to 270 rounded to the nearest whole number.
25. 14.369 is equal to 14 rounded to the nearest whole number.
26. 23.09 is equal to 23 rounded to the nearest whole number.
Express the fraction as a percentage use the bar notation if necessary
We have to express the fraction as a percentage.
We can think of the percentage as a fraction with denominator 100.
This means that 25% is equivalent to 25/100.
This is because 100% is the unit, then 100/100 = 1.
We can use this to convert a fraction to a percentage by transforming the denominator into 100.
In this case, the fraction is 2/5.
The denominator is 5, so to convert it to 100 we have to multiply it by 100/5 = 20.
Then, we apply this both to the numerator and denominator:
[tex]\frac{2}{5}*\frac{20}{20}=\frac{2*20}{5*20}=\frac{40}{100}=40\%[/tex]Answer: 2/5 = 40%
Similar PcIn this session, you will apply your knowledge of similar polygons to real-lifesituations.An artist plans to paint a picture. He wants to use a canvas that is similar to aphotograph with a height of 8 in, and a width of 10 in. If the longer horizontalsides of the canvas are 30 in. wide, how high should the canvas be?
24 in
Explanation / Steps:
Since the aim of the artists is to duplicate the photograph on a different scale canvas:
8 * 30 / 10 = 24 in
More details:
Since for a side of 8 in is requires a side of 10 in => a side of 1 in requires 8/10 ~ 0.8 in
then a side of 30 in requires 30 *0.8 = 24 in
In a right triangle, cos (2x) = sin (8x + 5)'. Find the smaller of the triangle's two
acute angles.
According to the given problem,
[tex]\cos (2x)^{\circ}=\sin (8x+5)^{\circ}[/tex]Consider the formula,
[tex]\sin (90-\theta)=\cos \theta[/tex]Apply the formula,
[tex]\sin (90-2x)=\sin (8x+5)[/tex]Comparing both sides,
[tex]\begin{gathered} 90-2x=8x+5 \\ 8x+2x=90-5 \\ 10x=85 \\ x=\frac{85}{10} \\ x=8.5 \end{gathered}[/tex]Obtain the value of the two angles,
[tex]\begin{gathered} 2x=2(8.5)=17 \\ 8x+5=8(8.5)+5=73 \end{gathered}[/tex]It is evident that the smaller angle is 17 degrees, and the larger angle is 73 degrees.
Thus, the required value of the smaller acute angle of the triangle is 17 degrees.
Joe’s parents are making sandwiches for the class picnic they have 7230 size is 48 two slices and 96 tomato sauce is Y
We have to calculate the maximum common divisor of these 3 numbers in order to know what is the maximum ammount of sandwiches they can make.
We can list the factors of each number:
72: 1, 2, 3, 4, 6, 8, 12, 18, 24, 36, 72.
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 96.
To calculate this factors, we start by dividing by 2 and 3, and so on, and checking if the result is a whole number. If it is, the denominator is a factor.
The maximum common divisor is 24, so they can make 24 sandwichs, each one with 72/24=3 slices of turkey, 48/24=2 slices of cheese and 96/24=4 slices of tomatoes.
George's boxes
He has bought boxes at different prices.
3 boxes at $3.50 and 4 boxes at $3.00.
The cost of the first group of boxes is 3 boxes x 3.50 $/boxes = $10.50.
The cost of the second group is 4 boxes x 3.00 $/boxes = $12.
Then, if we add the cost, it is 10.50 + 12 = $22.50.
If we write it in the blanks we have:
3 boxes * 3.50 = 3 * 3.50
4 boxes * 3.00 = 4 * 3.00
(3 * 3.50) + (4 * 3.00) = 22.50
(underlined is what goes in the blanks)
c(t)=2(t-4)(t+1)(t-6)
Question: find the x- or t intercepts of the polynomial function:
c(t)=2(t-4)(t+1)(t-6).
Solution:
the t-intercept (zeros of the function) of the given polynomial function occurs when c (t) = 0, that is when:
[tex]c(t)\text{ = 0 = }2\mleft(t-4\mright)\mleft(t+1\mright)\mleft(t-6\mright)[/tex]this can only happen when any of the factors of the polynomial are zero:
t-4 = 0, that is when t = 4
t + 1 = 0 , that is when t = -1
and
t-6 = 0, that is when t = 6.
then, we can conclude that the t-intercept (zeros of the function) of the given polynomial are
t = 4, t = -1 and t = 6.
Of the following real functions of real variable it calculates: a) the domain, b) the intersections with the axes c) the limits at the ends of the domain. d) Draw the graph e) calculates the first derivative and identifies the minimum or maximum points of the function
Given:
[tex]g(x)=\frac{x+\sqrt{x}}{x+1}[/tex]Find-: Domain, intersection with axis, limit at end the domain, draw the graph, first derivative the minimum and maximum of the point is:
Sol:
Domain:
The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.
[tex]\begin{gathered} g(x)=\frac{x+\sqrt{x}}{x+1} \\ \\ Domain:x>0 \end{gathered}[/tex]The domain is greater than the zero "0" because the negative value of "x" is create undefine form inside the square root.
Intersection with axis:
For x-intersection value of "y" is zero so,
[tex]\begin{gathered} g(x)=\frac{x+\sqrt{x}}{x+1} \\ \\ 0=\frac{x+\sqrt{x}}{x+1} \\ \\ 0=x+\sqrt{x} \\ \\ \sqrt{x}(\sqrt{x}+1)=0 \\ \\ x=0,\sqrt{x}=-1 \\ \\ \sqrt{x}=-1\text{ Not possible } \\ x=0 \end{gathered}[/tex]For y intersection value of "x" is zero then,
[tex]\begin{gathered} y=\frac{x+\sqrt{x}}{x+1} \\ \\ y=\frac{0+\sqrt{0}}{0+1} \\ \\ y=0 \end{gathered}[/tex]Graph of function is:
The first derivative is:
[tex]\begin{gathered} g(x)=\frac{x+\sqrt{x}}{x+1} \\ \\ g^{\prime}(x)=\frac{(x+1)(1+\frac{1}{2\sqrt{x}})-(x+\sqrt{x)}}{(x+1)^2} \\ \\ g^{\prime}(x)=\frac{x+\frac{\sqrt{x}}{2}+1+\frac{1}{2\sqrt{x}}-x-\sqrt{x}}{(x+1)^2} \\ \\ g^{\prime}(x)=\frac{1+\frac{1}{2\sqrt{x}}-\frac{\sqrt{x}}{2}}{(x+1)^2} \\ \\ \end{gathered}[/tex]For maximum is:
[tex]\begin{gathered} g^{\prime}(x)=0 \\ \\ 1+\frac{1}{2\sqrt{x}}-\frac{\sqrt{x}}{2}=0 \\ \\ \frac{2\sqrt{x}+1-x}{2\sqrt{x}}=0 \\ \\ x-1=2\sqrt{x} \end{gathered}[/tex]Square both side then:
[tex]\begin{gathered} (x-1)^2=2\sqrt{x} \\ \\ x^2+1-2x=4x \\ \\ x^2-6x+1=0 \\ \\ x=\frac{6\pm\sqrt{36-4}}{2} \\ \\ x=\frac{6\pm\sqrt{32}}{2} \\ \\ x=5.83,x=0.17 \end{gathered}[/tex]For the maximum or minimum point are
(5.83) and 0.17
A line that includes the point (10,5)and has a slope of 1.What is its equation in slope intercept form?
The line equation is y = x - 5
EXPLANATION
Given:
Point (10, 5)
x=10 and y=5
slope (m)=1
We need to first find the intercept(b).
Substitute x=10 , y=5 and m=1 into y=mx + b and solve for intercept(b).
That is;
5 = 1(10) + b
5 = 10 + b
5 - 10 = b
-5 = b
Form the equation by substituting m=1 and b=-5.
Hence, the line equation is y = x - 5
what is the slope of y=x-7
The given equation is in slope-intercept form, which means the coefficient of x is the slope.
Therefore, the slope is 1.How to know if you have the slope-intercept form?
The slope intercept-form is y = mx + b, as you can observe, the variable y is completely isolated, and the other side of the equation has two terms. Whenever you have a linearGrea equation like this, it means you have a slope-intercept form where the slope is m, and the y-intercept is b.
Find the missing side length and angles of ABC given that m B = 137º, a = 15, and c = 17. Round to the nearest tenth.(Find angles A and C and side b)
Given the triangle ABC and knowing that:
[tex]\begin{gathered} a=BC=15 \\ c=AB=17 \\ m\angle B=137º \end{gathered}[/tex]You need to apply:
• The Law of Sines in order to solve the exercise:
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]That can also be written as:
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]Where A, B, and C are angles and "a", "b" and "c" are sides of the triangle.
• The Law of Cosines:
[tex]b=\sqrt[]{a^2+c^2-2ac\cdot cos(B)}[/tex]Where "a", "b", and "c" are the sides of the triangle and "B" is the angle opposite side B.
Therefore, to find the length "b" you only need to substitute values into the formula of Law of Cosines and evaluate:
[tex]b=\sqrt[]{(15)^2+(17)^2-2(15)(17)\cdot cos(137\degree)}[/tex][tex]b\approx29.8[/tex]• To find the measure of angle A, you need to set up the following equation:
[tex]\begin{gathered} \frac{a}{sinA}=\frac{b}{sinB} \\ \\ \frac{15}{sinA}=\frac{29.8}{sin(137\degree)} \end{gathered}[/tex]Now you can solve for angle A. Remember to use the Inverse Trigonometric Function "Arcsine". Then:
[tex]\frac{15}{sinA}\cdot sin(137\degree)=29.8[/tex][tex]\begin{gathered} 15\cdot sin(137\degree)=29.8\cdot sinA \\ \\ \frac{15\cdot sin(137\degree)}{29.8}=sinA \end{gathered}[/tex][tex]A=\sin ^{-1}(\frac{15\cdot sin(137\degree)}{29.8})[/tex][tex]m\angle A=20.1\degree[/tex]• In order to find the measure of Angle C, you need to remember that the sum of the interior angles of a triangle is 180 degrees. Therefore:
[tex]m\angle C=180º-137º-20.1\degree[/tex]Solving the Addition, you get:
[tex]\begin{gathered} m\angle C=180º-137º-20.1\degree \\ m\angle C=22.9\degree \end{gathered}[/tex]Therefore, the answer is:
[tex]undefined[/tex]the post office and city hall are marked on a coordinate plane. write the equation of the line in slope intercept form that passes through these two points.
The given points are (1,6) and (-5,-3).
First, we have to find the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing given points, we have
[tex]m=\frac{-3-6}{-5-1}=\frac{-9}{-6}=\frac{3}{2}[/tex]Now, we use the point-slope formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=\frac{3}{2}(x-1) \\ y=\frac{3}{2}x-\frac{3}{2}+6 \\ y=\frac{3}{2}x+\frac{-3+12}{2} \\ y=\frac{3}{2}x+\frac{9}{2} \end{gathered}[/tex]Therefore, the equation would be y = 3/2x + 9/2You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friendr walks 220 yards due west from your position and takes a bearing on the cabin of N 21.2°E. How far are you from the cabin?A. 638 yardsB. 608 yardsC. 567 yardsD. 589 yards
In the given right triangle
we have that
[tex]\begin{gathered} tan(21.2^o)=\frac{220}{x}\text{ -----> by TOA} \\ \\ solve\text{ for x} \\ \\ x=\frac{220}{tan(21.2^o)} \\ \\ x=567\text{ yrads} \end{gathered}[/tex]The answer is option Con which of the following lines does the point (1,6) lie
It is required to determine which line the point (1,6) lies on.
To do this, substitute the point into each equation and check which of the equations it satisfies.
Check the first equation:
[tex]\begin{gathered} y=x+5 \\ \text{ Substitute }(x,y)=(1,6): \\ \Rightarrow6=1+5 \\ \Rightarrow6=6 \end{gathered}[/tex]Since the equation is true, it follows that the point lies on the line.
Check the second equation:
[tex]\begin{gathered} y=-x+7 \\ \text{ Substitute }(x,y)=(1,6): \\ \Rightarrow6=-1+7 \\ \Rightarrow6=6 \end{gathered}[/tex]Since the equation is true, it follows that the point also lies on the line.
Check the third equation:
[tex]\begin{gathered} y=2x-1 \\ \text{ Substitute }(x,y)=(1,6): \\ \Rightarrow6=2(1)-1 \\ \Rightarrow6=1 \end{gathered}[/tex]Notice that the equation is not true. Hence, the point does not lie on the line.
So the given point only lies on lines a and b.
The answer is option D.
Convert the following Quadratic Equations from Vertex Form to Standard Form.
4)
Given:
The vertex form is given as,
[tex]y=-\frac{1}{3}(x+6)^2-1[/tex]The objective is to convert the vertex form to standard form.
The standard form can be obtained as,
[tex]\begin{gathered} y=-\frac{1}{3}(x+6)^2-1 \\ =-\frac{1}{3}(x^2+6^2+2(x)(6))-1 \\ =-\frac{1}{3}(x^2+36+12x)-1 \\ =-\frac{x^2}{3}-\frac{36}{3}+\frac{12x}{3}-1 \\ =-\frac{x^2}{3}-12+4x-1 \\ =-\frac{x^2}{3}+4x-13 \end{gathered}[/tex]Here,
[tex]\begin{gathered} a=-\frac{1}{3} \\ b=4 \\ c=-13 \end{gathered}[/tex]Hence, the required standard form of the equation is obtained.
6.[–/1 Points]DETAILSALEXGEOM7 8.3.006.MY NOTESASK YOUR TEACHERIn a regular polygon, each interior angle measures 120°. If each side of the regular polygon measures 4.6 cm, find the perimeter of the polygon in centimeters. cm
Given:
Measure of each interior angle = 120 degrees
Length of each side = 4.6 cm
Let's find the perimeter of the polygon.
Since the measure of each interior angle is 120 degrees, let's find the number of sides of the polygon using the formula below:
[tex]120=\frac{(n-2)*180}{n}[/tex]Let's solve for n.
We have:
[tex]\begin{gathered} 120n=(n-2)*180 \\ \\ 120n=180n-180(2) \\ \\ 120n=180n-360 \\ \\ 180n-120n=360 \\ \\ 60n=360 \end{gathered}[/tex]Divide both sides by 60:
[tex]\begin{gathered} \frac{60n}{60}=\frac{360}{60} \\ \\ n=6 \end{gathered}[/tex]Therefore, the polygon has 6 sides.
To find the perimeter, apply the formula:
Perimeter = number of sides x length of each side
Perimeter = 6 x 4.6
Perimeter = 27.6 cm
Therefore, the perimeter of the polygon is 27.6 cm
ANSWER:
27.6 cm
Evaluate x^1 - x^-1 + x^0 for x = 2.
The value of x^1 - x^-1 + x^0 for x = 2 is 5
we need to evaluate x¹ - x⁻¹ + x⁰
A positive exponent tells us how many times to multiply a base number, while a negative exponent tells us how many times to divide a certain base number. Negative exponents can be re written. x⁻ⁿ as 1 / x
x¹ - 1/x + x⁰
(any number or variable which is raised to the power zero is considered as 1)
x¹ - 1/x + 1
x² - 1 + x
x² + x - 1
The value of this expression for x = 2
2² + 2 - 1
4 + 2 - 1
5
Therefore,the value of x^1 - x^-1 + x^0 for x = 2 is 5
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1. According to a recent poll, 4,060 out of 14,500 people in the United States were clas-sified as obese based on their body mass index. What’s the relative frequency of obe-sity according to this poll?
The relative frequency of obesity is the ratio between obese people in the sample and total people in the sample:
[tex]\frac{4060}{14500}=0.28[/tex]The relative frequency is 0.28
(G.12, 1 point) Which point lies on the circle represented by the equation (x-4)2 + (y - 2)2 = 72? O A. (-1,4) B. (8,3) O C. (9,0) O D. (-2, 2)
To know if a point lies on a circle you use the (x,y) of each point in the equation and prove it that correspond to a mathematical congruence.
A. (- 1 , 4)
[tex]\begin{gathered} (-1-4)^2+(4-2)^2=7^2 \\ -5^2+2^2=49 \\ 25+4=49 \\ 29=49 \end{gathered}[/tex]As 29 is not equal to 49, this point doesn't lie in the circle
B. ( 8 , 3)
[tex]\begin{gathered} (8-4)^2+(3-2)^2=7^2 \\ 4^2+1^2=49 \\ 16+1=49 \\ 17=49 \end{gathered}[/tex]As 17 is not equal to 49, this point doesn't lie in the circle
C. (9 , 0)
[tex]\begin{gathered} (9-4)^2+(0-2)^2=7^2 \\ 5^2+(-2)^2=49 \\ 25+4=49 \\ 29=49 \end{gathered}[/tex]As 29 is not equal to 49, this point doesn't lie in the circle
D. (-2 , 2)
[tex]\begin{gathered} (-2-4)^2+(2-2)^2=7^2 \\ -6^2+0^2=49 \\ 36=49 \end{gathered}[/tex]As 36 is not equal to 49, this point doesn't lie in the circle
None of the points lies on the circle.The next graph represents the circle and the 4 given points:
Barry Bonds holds the major league home run record with 73 in one season. If Pete Alonso wants to break his record, how many homeruns would he have to hit on average over 162 games to break Bonds' record?
73 homeruns in one season
162 games Pete Alonso must do at least 74 homeruns
He must do 74 homeruns and 88 will not be homeruns.
On average he must do 74/162 = 0.45 homeruns per game
If we start with 5 people that have the coronavirus, and the number of cases increases by 26% each week. How many cases of coronavirus will there be
in 36 weeks?
Answer:
6600 new cases
Step-by-step explanation:
00:00Drag a tile to each number to classify it as rational or irrational.rationalirrational9.682.010010001...✓ 64-57
the numbers are
[tex]undefined[/tex]Joaquin has been working on homework for 3 1/2 hours. If each assignment takes him of 1/4 an hour, how many assignments has he completed? Select one OA. 13 O B. 14 OC. 15 OD. 16
The total amount of time he has spent doing homework:
[tex]3\frac{1}{2}[/tex]And the time it takes to complete each assignment:
[tex]\frac{1}{4}[/tex]To find the number of assignments he has completed in that time, we divide the total time 3 1/2 by the time for each assignment 1/4:
[tex]3\frac{1}{2}\div\frac{1}{4}[/tex]To make this division we need to convert 3 1/2 to a fraction as follows:
[tex]3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{6+1}{2}=\frac{7}{2}[/tex]We multiply the whole number by the denominator 3x2 and we add to that the numerator 1, and divide that by the original denominator 2.
Now instead of 3 1/2 we use 7/2 for our division:
[tex]\frac{7}{2}\div\frac{1}{4}[/tex]And we use the formula to divide two fractions, which is:
[tex]\frac{a}{b}\div\frac{c}{d}=\frac{a\times d}{b\times c}[/tex]Applying this to our division:
[tex]\frac{7}{2}\div\frac{1}{4}=\frac{7\times4}{2\times1}[/tex]Solving the operations:
[tex]\frac{7}{2}\div\frac{1}{4}=\frac{28}{2}=14[/tex]Answer: 14 assignments
20. Monroe's teacher wants each student to draw a sketch of the longest specimen. Which specimen is the longest? 21. Seen through the microscope, a specimen is 0.75 cm long. What is its actual length?
20)
The sketch of the given data is
By observing the sketch, the longest line is A.
Hence the specimen A is the longest.
21)
In the microscope, the size of the specimen is 0.75cm long.
It is given that the microscope enlarges the actual length 100 times.
[tex]\text{Size =100}\times Actual\text{ length}[/tex][tex]\frac{\text{Size }}{100}\text{=}Actual\text{ length}[/tex]Substitute Size=0.75, we get
[tex]\frac{0.75}{100}=\text{Actual length}[/tex][tex]\text{Actual length=0.0075 cm}[/tex]Hence the actual length of the specimen is 0.0075cm.
the problem was sent in a picture
The vertex of the given parabola is (h, k)=(0,0).
(x, y)=(2, -4) is a point on the parabola.
The vertex form of a parbola is,
[tex]y=a(x-h)^2+k\text{ ------(1)}[/tex]Here, (h, k) is the vertex of parabola.
Put h=0, k=0, x=2 and y=-4 in the above equation.
[tex]\begin{gathered} -4=a(2-0)+0 \\ \frac{-4}{2}=a \\ -2=a \end{gathered}[/tex]Put a=-2, h=0, k=0 in equation (1) to find the function.
[tex]y=-2x^2[/tex]Put y=0 to obtain a quadratic function and solve for x.
[tex]\begin{gathered} 0=-2x^2 \\ x=0 \end{gathered}[/tex]So, there is only one solution to the graph.
Short cut:
Since the parabola touches the x axis when the x intercept is zero, the solution of the quadratic function of the parabola is x=0. So, there is only one solution to the graph.
How many different 5 card hands can be dealt from a deck of 52 cards if the hand consists of exactly 2 aces?
Solution
We need to remember that in a standard deck we have 4 aces and 48 other types of cards
For this case we can solve the problem with the follwoing operation:
[tex](4C2)\cdot(48C3)=\frac{4!}{2!2!}\cdot\frac{48!}{45!3!}=6\cdot17296=103776[/tex]So then we have 103776 ways to create the combination required
Question: Jack has an old scooter. He wants to sell it for 60% off the current price. The market price is $130.
What should his asking price be? Explain your reasoning.
The asking price for the scooter is $78.
How to calculate the price?From the information, Jack has an old scooter. He wants to sell it for 60% off the current price and the market price is $130.
In this case, the asking price will be:
= Percentage × Market price
= 60% × $130
= 0.6 × $130
= $78
The price is $78.
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use the first derivative test to classify the relative extrema. Write all relative extrema as ordered pairs
The given function is
[tex]f(x)=-10x^2-120x-5[/tex]First, find the first derivative of the function f(x). Use the power rule.
[tex]\begin{gathered} f^{\prime}(x)=-10\cdot2x^{2-1}-120x^{1-1}+0 \\ f^{\prime}(x)=-20x-120 \end{gathered}[/tex]Then, make it equal to zero.
[tex]-20x-120=0[/tex]Solve for x.
[tex]\begin{gathered} -20x=120 \\ x=\frac{120}{-20} \\ x=-6 \end{gathered}[/tex]This means the function has one critical value that creates two intervals.
We have to evaluate the function using two values for each interval.
Let's evaluate first for x = -7, which is inside the first interval.
[tex]f^{\prime}(-7)=-20(-7)-120=140-120=20\to+[/tex]Now evaluate for x = -5, which is inside the second interval.
[tex]f^{\prime}(7)=-20(-5)-120=100-120=-20\to-[/tex]As you can observe, the function is increasing in the first interval but decreases in the second interval. This means when x = -6, there's a maximum point.
At last, evaluate the function when x = -6 to find the y-coordinate and form the point.
[tex]\begin{gathered} f(-6)=-10(-6)^2-120(-6)-5=-10(36)+720-6 \\ f(-6)=-360+720-5=355 \end{gathered}[/tex]Therefore, we have a relative maximum point at (-6, 355).