Given a modelled account balance for the period of d days as shown below:
[tex]\begin{gathered} f(d)=d^3-2d^2-8d+3 \\ \text{where,} \\ f(d)\text{ is the account balance} \\ d\text{ is the number of days} \end{gathered}[/tex]Given that the account balance is $38, we would calculate the number of days by substituting for f(d) = 38 in the modelled equation as shown below:
[tex]\begin{gathered} 38=d^3-2d^2-8d+3 \\ d^3-2d^2-8d+3-38=0 \\ d^3-2d^2-8d-35=0 \end{gathered}[/tex]Since all coefficients of the variable d from degree 3 to 1 are integers, we would apply apply the Rational Zeros Theorem.
The trailing coefficient (coefficient of the constant term) is −35.
Find its factors (with plus and minus): ±1,±5,±7,±35. These are the possible values for dthat would give the zeros of the equation
Lets input x= 5
[tex]\begin{gathered} 5^3-2(5)^2-8(5)-35=0 \\ 125-2(25)-40-35=0 \\ 125-50-75=0 \\ 125-125=0 \\ 0=0 \end{gathered}[/tex]Since, x= 5 is a zero, then x-5 is a factor.
[tex]\begin{gathered} d^3-2d^2-8d-35=(d-5)(d^2+3d+7)=0 \\ (d-5)(d^2+3d+7)=0 \\ d-5=0,d^2+3d+7=0 \\ d=0, \end{gathered}[/tex][tex]\begin{gathered} \text{simplifying } \\ d^2+3d+7\text{ would give} \\ d=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=1,b=3,c=7 \end{gathered}[/tex][tex]\begin{gathered} d=\frac{-3\pm\sqrt[]{3^2-4\times1\times7}}{2\times1} \\ d=\frac{-3\pm\sqrt[]{9-28}}{2} \\ d=\frac{-3\pm\sqrt[]{-17}}{2} \end{gathered}[/tex]It can be observed that the roots of the equation would give one real root and two complex roots
Therefore,
[tex]d=5,d=\frac{-3\pm\sqrt[]{-17}}{2}[/tex]Since number of days cannot a complex number, hence, the number of days that would give a balance of $38 is 5 days
Graph the line with the given slope m and y-intercept b.
m = 4, b = -5
Answer:
Step-by-step explanation:
What we know:
m = 4, b = -5
y = mx + b where m is the gradient/slope and b is the y-intercept
Substitute m and b values:
y = 4x + -5 which is the same as y = 4x - 5
Substitute all x values to find y coordinate:
When x = -7, y = (4 x -7) - 5 = -33
When x = -6, y = (4 x -6) - 5 = -29
When x = -5, y = …
Continue for all x values
A rectangular board is 1200 millimeters long and 900 millimeters wide what is the area of the board in square meters? do not round your answer
Answer: Area of the rectangular board is 1.08 square meters
The length of the rectangular board = 1200 milimeters
The width of the rectangular board = 900 milimeters
Area of a rectangle = Length x width
Firstly, we need to convert the milimeter to meters
1000mm = 1m
1200mm = xm
Cross multiply
x * 1000 = 1200 x 1
1000x = 1200
Divide both sides by 1000
x = 1200/100
x = 1.2 meters
For the width
1000mm = 1m
900mm = xm
cross multiply
1000 * x = 900 * 1
1000x = 900
Divide both sides by 1000
x = 900/1000
x = 0.9m
Length = 1.2 meters
Width = 0.9 meter
Area = length x width
Area = 1.2 x 0.9
Area = 1.08 square meters
A restaurant offer 7 appetizers and 10 main courses.In how main ways can a person order a two-course meal
Take into account that there are 7 chices for the first course, and there are 10 choices for the entree.
The total number of choices is given bye:
total_choices = Choices_for_first_course x choices_fro_entree
Then, by replacing the values of the previous parameters you get:
total_choices = 7 x 10 = 70
There are 70 ways a person can order a two-course meal
n is equal to 30% of 600
Given:
[tex]n=\frac{30}{100}\times600[/tex]Solve the expression,
[tex]\begin{gathered} n=\frac{30}{100}\times600 \\ n=30\times6 \\ n=180 \end{gathered}[/tex]Answer: n = 180
I want to know how to determine whether the x or r in cos A = -2/5 is negative so when im using cos A's values in the x^2+y^2=r^2 equation I dont use the wrong number
INFORMATION:
STEP BY STEP EXPLANATION:
ANSWER:
Jane needs $20 to buy her radio.She has saved $15.What precent of the cost of the radio has she saved?
Let's begin by listing out the information given to us:
Cost of Radio (c) = $20
Jane's saving (s) = $15
% of radio cost saved = (Jane's saving / Cost of Radio) * 100%
[tex]\begin{gathered} x=\frac{s}{c}\cdot100 \\ x=\frac{15}{20}\cdot100=75 \\ x=75 \end{gathered}[/tex]Jane has saved 75% of the radio cost
W L is tangent to circle O at point W. If mW H A = 260 degrees , find m< AWL
Answer:
[tex]m\angle AWL\text{ = 130}\degree[/tex]Explanation:
Here, we want to get the measure of the angle marked AWL
The measure of this angle is simply half the measure of the big arc WHA
Mathematically, we have the measure of the angle as:
[tex]\begin{gathered} m\angle AWL\text{ = }\frac{1}{2}\text{ }\times\text{ mWHA} \\ \\ =\text{ }\frac{1}{2}\times\text{ 260 = 130}\degree \end{gathered}[/tex]Construct a pair of parallel lines with a set of alternate interior angles that measure X degrees.X=60 degrees
Given:
An angle is x= 60 degrees.
Required:
Construct a pair of parallel lines with a set of alternate interior angles that measure X degrees.
Explanation:
First, draw a line then construct an angle of 60 degrees.
Now take a point B on the line that is making an angle of 60 degrees cut the arc from point B with the same measure of arc A.
Now cut the arcs from point A that join the line l and from C that joins m as with the same arc. Draw a line with the intersecting arc.
Thus the angle
[tex]\theta[/tex]will be an interior angle of measures 60 degrees.
Final Answer:
The figure is attached in the explanation part.
How long will it take until the diver enters the water? How do you know?
Given:
The equaiton that model height of the driver jumps from the ledge.
[tex]h=-t^2+8t+115[/tex]Requried:
We need to find the time taken by driver to enter the water.
Explanation
Three commercials are played in a row between songs on the radio. The three commercials fill exactly 3 minutes of time. If the first commercial uses 1 – minutes, and the second uses 3 minute, how long is the third commercial? The third commercial is minutes long.
3 commercials
3 minutes
3 = 1st commercial + 2nd commercial + 3rd commercial
3 = 1 1/5 + 3/4 + 3rd commercial
3rd commercial = 3 - 6/5 - 3/4
= 60/20 - 24/20 - 15/20
= 21/20
The third commercial last = 21/20 or 1 1/20.
A sphere has a radius that is 2.94 centimeters long. Find the volume of the sphere. Round to the nearest tenth.
The volume of a sphere is given as
[tex]V=\frac{4}{3}\pi r^3^{}[/tex]Where r = 2.94 cm
π = 3.14
Substituting values,
[tex]\begin{gathered} V=\frac{4}{3}\times3.14\times2.94^3=1.33\times3.14\times25.41 \\ V=106.12 \end{gathered}[/tex]The volume to the nearest tenth is 106.1 cubic centimeters.
15= x/6-1 help me with this im just using it to study so show step by step because i forgot
The value of x after solving the expression, 15 = (x/6)-1, step by step is 96.
According to the question,
We have the following expression:
15 = (x/6)-1
Now, we can change the sides because it will not make any difference to the overall answer.
(x/6)-1 = 15
Now, we will move 1 from the left hand side to the right hand side. So, the sign will change from minus to plus.
x/6 = 15+1
x/6 = 16
Now, we will move 6 from the left hand side to right hand side. 6 is in the division on the left hand side then it will be in multiplication on the right hand side.
x = 16*6
x = 96
Hence, the value of x after solving the expression step by step is 96.
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What is the average rate of change over the interval [1,2]Type the numerical value for your answer as a whole number, decimal, or fractionMake sure answers are completely simplified
To calculate the average rate of change over the interval [1,2] we need to identify the points in the extremes of the interval.
This points are (1,50) and (2,25).
We calculate the average rate of change as the slope:
[tex]r=\frac{y_2-y_1}{x_2-x_1}=\frac{25-50}{2-1}=-\frac{25}{1}=-25[/tex]Answer: the rate of change over [1,2] is -25.
Identify the domain and range and tell whether the relation is a function
For a function, every element in the domain must have a unique image in the range.
On checking the domain and range provided in the question, we can see that there are two images for the range when the domain equals -2:
[tex](-2,3)\text{ and (}-2,7)[/tex]Therefore, the given domain and range violate the property of a function.
The relation is NOT a function.
Which of the following polar coordinates would not be located at the point?
Explanation
We are asked to select the option that would not be located at the given point
To do so, let us find the original coordinates of the given polar point
The point is located 6 units away from the origin in a direction of 270 degrees
The equivalent coordinates are
[tex]\begin{gathered} (6,\frac{3\pi}{2}) \\ (6,\frac{-\pi}{2}) \\ (-6,90^0) \end{gathered}[/tex]Thus, we are to eliminate any option that is not equivalent to the above, we are left with
[tex](6,\frac{-3\pi}{2})[/tex]Thus, the answer is option A
(1 3/4 - 1/8)+(5/6 ÷ 2/3)
ANSWER
23/8
EXPLANATION
To solve this, first, we have to do the operations in the parenthesis. The first one is a subtraction between a mixed number and a fraction, so before doing the subtraction, we have to convert the number to an improper fraction by adding the parts,
[tex]1\frac{3}{4}=1+\frac{3}{4}=\frac{7}{4}[/tex]So the subtraction is,
[tex]1\frac{3}{4}-\frac{1}{8}=\frac{7}{4}-\frac{1}{8}=\frac{2\cdot7-1}{8}=\frac{14-1}{8}=\frac{13}{8}[/tex]Then we divide the second term using the KCF rule:
• K,eep the first fraction
,• C,hange the division sign for a multiplication sign
,• F,lip the second fraction
[tex]\frac{5}{6}\div\frac{2}{3}=\frac{5}{6}\times\frac{3}{2}=\frac{15}{12}=\frac{5}{4}[/tex]Now, we add these two results,
[tex]\frac{13}{8}+\frac{5}{4}=\frac{13+5\cdot2}{8}=\frac{13+10}{8}=\frac{23}{8}[/tex]Hence, the answer is 23/8.
Take a look at the graph below. In the text box provided, describe to the best of yourability the following characteristics of the graph:Domain & RangeIs it a function?InterceptsMaximum/Minimum• Increasing/Decreasing intervals
we know that
The domain is the set of all possible values of x and the range is the set of all possible values of y
so
In this problem
The domain is the interval {-6,5}
[tex]-6\leq x\leq5[/tex]The range is the interval {-2,1}
[tex]-2\leq y\leq1[/tex]Intercepts
we have
x-intercepts (values of x when the value of y is equal to zero)
x=-5,x=0 and x=3
y-intercepts (values of y when the value of x is equal to zero)
y=0
Maximum value y=1
Minimum value y=-2
Increasing intervals
{-6,4}, {2,3}
Decreasing intervals
{-1,2} and {3,5}
Solve the system using addition. Use pencil and paper. Explain why the addition method is a good choice for solving the system. If you wanted to solve for x first, is the addition method still a good choice? Explain. X-4.6y = - 8.8 -x+2.9y = 3.7 The solution is. (Type an order
5. Jeannette has $5 and $10 bills in her wallet. The number of fives iseight more than five times the number of tens. Let t represent theNumber of tens. Write an expression for the number of fives.
The number of fives is eight more than five times the number of tens.
Therefore,
[tex]F=5\cdot T+8[/tex]where F represents the number of fives and T the number of tens
Graph the line with slope -2 passing through the point (3,5)
To graph the line, you need to know at least two points of it.
Knowing its slope and one point you can determine the equation of the line by using the point-slope form:
[tex]y-y_1=m(x-x_1_{})[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of one point of the line
For m=-2 and (x₁,y₁)=(3,5) the equation of the line is:
[tex]y-5=-2(x-3)[/tex]Next, replace the equation for any value of x and solve for y, for example, use x=2
[tex]y-5=-2(2-3)[/tex]-Solve the difference within the parentheses then the multiplication
[tex]\begin{gathered} y-5=-2(-1) \\ y-5=2 \end{gathered}[/tex]-Add 5 to both sides of the equation
[tex]\begin{gathered} y-5+5=2+5 \\ y=7 \end{gathered}[/tex]The coordinates for the second point are (2,7)
Plot both points and link them with a line
Write this algebraic expression into a verbal expression: 1/3 ( h - 1 )
Answer:
One-third of the difference of h and 1
quien me puede ayudar a resolver estos ejercicios porfa de ecuaciones
3x^2 -5x +1 =0
Aplica la formula cuadrática:
[tex]\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]Donde:
a = 3
b= -5
c= 1
Reemplazando:
[tex]\frac{-(-5)\pm\sqrt[]{(-5)^2-4\cdot3\cdot1}}{2\cdot3}[/tex][tex]\frac{5\pm\sqrt[]{25-12}}{6}[/tex][tex]\frac{5\pm\sqrt[]{13}}{6}[/tex]Positivo:
(5+√13) /6 = 1.43
NEgativo:
(5-√13) /6 = 0.23
help meeeeeeeeee pleaseee !!!!!
The value of the composite function is as follows:
(gof)(5) = 6How to find composite function?The composite function can be solved as follows:
Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is a function that depends on another function.
f(x) = x² - 6x + 2
g(x) = -2x
Therefore,
(gof)(5) = g(f(5))
So we need to find g(f(x)) first.
Therefore,
g(f(x)) = -2(x² - 6x + 2)
g(f(x)) = - 2x² + 12x - 4
Therefore,
g(f(x)) = - 2x² + 12x - 4
(gof)(5) = g(f(5)) = - 2(5)² + 12(5) - 4
(gof)(5) = g(f(5)) = -50 + 60 - 4
(gof)(5) = g(f(5)) = 6
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Convert degrees to radians:288° = __ πEnter your answer to the tenths place
Given:
[tex]288^{\circ}[/tex]To convert degrees into radians:
We know that,
[tex]\text{Radian}=\theta\times\frac{\pi}{180}[/tex]So, we get
[tex]\begin{gathered} \text{Radian}=288\times\frac{\pi}{180} \\ =\frac{144\pi}{90} \\ =\frac{16\pi}{10} \\ =\frac{8\pi}{5} \end{gathered}[/tex]Thus, the answer is,
[tex]\frac{8\pi}{5}[/tex]a package of 8 count AA batteries costs 6.40 a package of 20 count AA batteries costs 15.80 which statement about the unit price is true?the 20 count pack of AA batreries has a lower unit price of 0.80 per batterythe 8 count pack of AA batteries has a lower unit price 0.79 per batterythe 8 count pack of AA batteries has a low unit price of .80 per batterythe 20 count pack of AA batteries has a lower unit price of .79 per battery
Notice that for the $6.40 package each battery costs:
[tex]\frac{6.40}{8}=0.80.[/tex]For the $15.80 package each battery costs:
[tex]\frac{15.80}{20}=0.79.[/tex]Therefore, the 20 count pack of AA batteries has a lower unit price of $0.79 per battery.
Answer: Last option.
4(px+1)=64The value of x when p is -5 is ?
Answer:
x = -3
Explanation:
Given the equation:
[tex]4\left(px+1\right)=64[/tex]We are required to find the value of x when p is -5.
[tex]\begin{gathered} 4\left(px+1\right)=64\colon p=-5 \\ 4\left(-5x+1\right)=64 \\ -20x+4=64 \\ -20x=64-4 \\ -20x=60 \\ \text{Divide both sides by -20} \\ x=\frac{60}{-20} \\ x=-3 \end{gathered}[/tex]Find the most important variable in the problem. A bag of marbles is full with 20 marbles, 12 of which are yellow. How many are not yellow? A. the total number of marbles B. the number of yellow marbles C. the number of marbles that are not yellow
Since there are 20 marbles and 12 of them are yellow; the marbles that are not yellow is not the same number as the marbles, and neither the number of Yellow marbles because they are yellow. So the answer is C.
Bc is included between
Answer:
A. angle B and angle C
Step-by-step explanation:
Line segments are named after the two points where they begin and end.
which expression is equivalent to 5^-2 x 5^5
Given the expression:
[tex]5^{-2}\ast5^5[/tex]To find the equivalent expression, let's simplify the expression using power rule.
[tex]a^m\ast a^n=a^{m+n}[/tex]Since they have the same base, we are to add the exponents.
We have:
[tex]5^{-2}\text{ }\ast5^5=5^{-2+5}=5^3[/tex]Therefore, the eqivalent expression is 5³
ANSWER:
[tex]5^3[/tex]We a
A certain Greenland shark is 37 cm long at birth and grows 0.75 cm / year. A certain spiny dogfish shark is 22 cm long at birth and grows 1.5 cm/year. When will the sharks be equal in length? Let x = time in years Let y = length of the sea creatures
In 20 years the length of shark will be equal.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
A certain Greenland shark is 37 cm long at birth and grows 0.75 cm / year.
. A certain spiny dogfish shark is 22 cm long at birth and grows 1.5 cm/year.
Let x = time in years Let y = length of the sea creatures
So, the equation can be written as
For Green land shark: y= 37+ 0.75x
For Spiny Dogfish: y= 22 + 1.5x
When both equation are equal
37+ 0. 75x = 22 + 1.5x
37- 22 = 1.5x - 0.75x
15 = 0.75x
x= 15/0.75
x= 20
and, y= 22 + 1.5(20)= 52
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