To simplify the fraction we will need to facto
help meeeee pleaseeeee!!!
thank you
The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.
According to the question,
We have the following information:
f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]
Now, to find the value of f(0), we will put 0 in place of x.
f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]
f(0) = 0+7*0-0+12
(When a number has some power then it means that in order to solve this we have expand the expression and multiply the number as many times as the power is given. For example, in the case of 3 as power, we will multiply any number 3 times and in case of 2 as power, we will multiply the given number 2 times.)
f(0) = 0+0-0+12
f(0) = 12
Now, to find the value of f(2), we will put 1 in place of x:
f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]
f(2) = -8+7*4-4+12
f(2) = -8+28-4+12
f(2) = 40 -12
f(2) = 28
Now, to find the value of f(2), we will put -2 in place of x:
f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]
f(-2) = -(-8) + 7*4+4+12
f(-2) = 8+28+4+12
f(-2) = 52
Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.
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If you roll a die 96 times, approximately how many times could you expect it to land on 3 or 4?
Given:
It is given that you roll a die 96 times.
Required:
We have to find the expectation of landing on 3 or 4.
Explanation:
If you roll a die then there are 6 possibilities (1-6) and the possibility of landing on 3 or 4 is 2.
Then the probability of landing on 3 or 4 is
[tex]\frac{2}{6}=\frac{1}{3}[/tex]If you roll the die 96 times then the probability of landing 3 or 4 is
[tex]\frac{1}{3}\times96=32[/tex]Final answer:
Hence the final answer is:
You could expect it to land on 3 or 4 is
[tex]32[/tex]Is the graph of the distance a person has driven over time an example of a continuous or discrete graph?
Let us first understand what are discrete and continuous variables.
Discrete variable:
A discrete variable is countable in a finite amount of time.
For example:
The number of coins in your pocket
The number of trees in the garden
It is not possible to have 2.5 coins or 7.3 trees
Continuous variable:
A continuous variable can take any numeric value.
For example:
The height of the tree
The room temperature
These values can be in decimal like 7.3, 0.23 etc
Now let us come to the question, the distance a person has driven can take any value
for example, it can be 50 miles or 23.4 miles or 120.5 miles
So, decimal values are possible
This means that it must be a continuous graph
The distance a person has driven over time an example of a continuous graph.
Hello! I'm hitting a bit of a snag on this. I think I'm reading it too many times
The solution:
Given:
[tex]\begin{gathered} \text{ A sphere of radius 4m.} \\ \\ A\text{ cube of side 6.45m} \end{gathered}[/tex]Required:
To compare the volume and area of bot shapes.
The Sphere:
[tex]\begin{gathered} Area=4\pi r^2=4(4)^2\pi=64\pi=201.062m^2 \\ \\ Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\times\pi\times4^3=268.083m^3 \end{gathered}[/tex]The Cube:
[tex]\begin{gathered} Area=6s^2=6\times6.45^2=249.615m^2 \\ \\ Volume=s^3=6.45^3=268.336m^3 \end{gathered}[/tex]Clearly, we can see that:
Both shapes have approximately the same volume.
But the cube has a greater volume than that of the sphere.
Therefore, the correct answer is [option 4]
You have the option of loaning money to one friend who promises to pay simple interest or to another friend who promises to pay the same APR but compound the interest. Which would you choose, and why?
I would loan my money to the one who pays the compound interest.
This is because more money would be generated from the compound interest as it is based on the principal (Amount loaned) and also the interest generated from the loan. Unlike simple interest that is only based on the principal.
9×2=2×9 what is the property of this problem?
The property involved is called "commutative property of product"
SInce we are flipping the oerder of the factors and arrive at the same result.
The "flipping is called "commuting" in Math terms.
2. In the xy-plane above, ABCD is a square and point E is the center of the square. The coordinates of points C and E are (7,2) and (1,0), respectively. Write an equation of the line that passes through points A, E, and C. B 1 2 -С E X -6 2 4. 16 A -2
Ready
Points A = (-5, -2) C = (7, 2) E = (1, 0)
1.- Find the slope
m = (y2 - y1) / (x2 - x1)
m = (2 + 2) / (7 + 5)
m = 4/ 12
m = 1/3
2.- Find the equation of the line
y - y1 = m(x - x1)
y + 2 = 1/3(x + 5)
y + 2 = 1/3x + 5/3
y = 1/3x + 5/3 - 2
y = 1/3 x + 5/3 - 6/3
This is the equation:
y = 1/3 x - 1/3
my pleausre
The days high temperature in Detroit , Michigan was recorded as 41 degrees F . Use the formula C = 5/9 ( F- 32) to write 41 degrees F as degrees celsius
Step 1
Given;
Step 2
[tex]\begin{gathered} C=\frac{5}{9}(F-32) \\ F=41 \\ C=\frac{5}{9}(41-32) \\ C=\frac{5}{9}(9) \\ C=5^{\circ}C \end{gathered}[/tex]Answer;
[tex]5^{\circ}C[/tex]Refer to your equation for the line that models the association between latitude and temperature of the cities: Yours y = -12 + 120 Computer calculated y = -1.07 + 119 What does the slope mean in the context of this situation?
The slope in the equations represent the change in temperature by the change in lattitude. This means that for each unit change in the latitude the temperature will decrease by an amount given by the slope.
What is the slope and y-intercept?
y=7x+2
Options:
Blank # 1
Blank # 2
Answer:
Step-by-step explanation:
18098
How do you solve the y-intercept of y = 9x + 9 and what is it simplified?
to know y -intercept we only need to replace x by 0. And we get
[tex]y=9\cdot0+9=9[/tex]so the y-intercept is 9
Is the number -3.7 a natural number, a whole number, an integer, a rational number, an irrational number or a real number?
ANSWER
Rational number and Real number
EXPLANATION
We want to identify what type of number -3.7 is.
A natural number is a number that is a positive integer, used in counting things. Examples are 4, 7 and 55.
A whole number is a number that is used in counting, including 0 i.e. natural numbers including 0.
An integer is a whole number but the difference is that an integer can be positive, negative or zero.
A rational number is a number that can be expressed as a fraction of two integers i.e. a/b while an irrational number is one that cannot be expressed as a fraction of two integers.
A real number is any number that can be found as a distance between two points on the number line.
From the definitions above, we see that we can classify -3.7 as a rational number and a real number.
It is not a natural number, whole number, irrational number or an integer.
To produce g, function f was reflected over the x-axis andFunction g can be defined as
The graph of the functions f and g are given.
It is required to complete the statement concerning how to produce g.
The graph of the parent function f is shown:
Reflect the graph of f across the x-axis:
Translate the function 5 units vertically upwards:
The given parent function is y=f(x).
Reflect the graph across in the x-axis to get the equation y=-f(x).
Translate the graph 5 units up to get y=-f(x)+5
Answers:
To produce g, the function f was reflected over the x-axis and shifted up 5 units.
Function g is defined as g(x)=-f(x)+5.
Which of the following tools did the Greeks limit themselves to in their
The Greeks limited themselves to using only compass and ruler in their formal geometric constructions.
Answer: Options B and D.
ten B В 15 cm А 20 cm С C
Tangent segment, of a circle
Apply formulas
20^2 - 15^ 2 = AB^2
Also
15^2 = 20•( 20 - AB)
225 = 400 - 20AB
Then
20AB = 400-225= 175
AB = √ 175= 13 + 6/25 =13.24
Help please and thank you
If f(x) is a linear function and gives f(3) = 3 and f(9) = -2
Part a
The slope of the line = -5/6
Part b
The y-intercept = 11/2
Part c
f(x) = (-5/6)x + 11/2
The values of
f(3) = 3
f(9) = -2
The points are (3,3) and (9,-2)
Part a
The slope of the line is the change in y coordinate with respect to the change in x coordinate.
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{-2-3}{9-3}[/tex]
=-5/6
Part b
The slope intercept form of the line
y = mx+b
b is the y intercept
Substitute the values in the equation
3 = (-5/6)×3 + b
3= -5/2 + b
b = 11/2
Part c
Then the linear function f(x) = (-5/6)x + 11/2
Hence, if f(x) is a linear function and gives f(3) = 3 and f(9) = -2
Part a
The slope of the line = -5/6
Part b
The y-intercept = 11/2
Part c
f(x) = (-5/6)x + 11/2
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The perimeter of the rectangle is 19.4 centimeters.What is the width in centimeters,of the rectangle Length is 6cm
SOLUTION
From the question, the Perimeter of the rectangle is 19.4 cm and we want to find the width. The perimeter of a rectangle is given by
[tex]\begin{gathered} P=2\left(l+w\right) \\ where\text{ P =perimeter = 19.4} \\ l=length\text{ of rectangle = 6 cm} \\ w=width=? \end{gathered}[/tex]Applying this, we have
[tex]\begin{gathered} P=2\left(l+w\right) \\ 19.4=2\left(6+w\right) \\ 19.4=12+2w \\ 2w=19.4-12 \\ 2w=7.4 \\ w=\frac{7.4}{2} \\ w=3.7 \end{gathered}[/tex]Hence the width is 3.7 cm, option C
Macky Pangan invested ₱2,500 at the end of every 3-month period for 5 years, at 8% interest compounded quarterly. How much is Macky’s investment worth after 5 years?
Compound interest with addition formula:
[tex]A=P(1+\frac{r}{n})^{nt}+\frac{PMT(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}[/tex]where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
PMT = Regular contributions (additional money added to investment)
in this example
P = 2500
r = 8% = 0.08
n = 4
t = 5 years
PMT = 2500
[tex]A=2500(1+\frac{0.08}{4})^{4\cdot5}+\frac{2500\cdot(1+\frac{0.08}{4})^{4\cdot5}-1}{\frac{0.08}{4}}[/tex]solving for A:
[tex]A=189408.29[/tex]Therefore, his investment after 5 years will be
$189,408.29
Which of the following equations represents a line that passes through thepoints (6,-5) and (-6, -7)?
Problem
Which of the following equations represents a line that passes through the
points (6,-5) and (-6, -7)?
Solution
For this case the equation for a line is given by:
y= mx +b
And we can find the slope m with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And replacing we got:
[tex]m=\frac{-7+5}{-6-6}=\frac{-2}{-12}=\frac{1}{6}[/tex]Then we can find the intercept with this formula:
-5 = 1/6 (6)+b
And solving for b we got:
b= -5-1 =-6
And our equation would be:
y= 1/6 x -6
And the best option would be:
I.
can someone please help me find the mesauser of the following?
Answer:
The measure of the given arcs are;
[tex]undefined[/tex]Given the figure in the attached image.
we want to find the measure of the given arcs.
For arc ED.
The measure of arc ED is equal to the measure of arc AB;
[tex]\begin{gathered} ED=AB=\measuredangle AOB=50^{\circ} \\ ED=50^{\circ} \end{gathered}[/tex]To get the measure of BC, we can see that AB, BC, and CD will sum up to 180 degrees.
[tex]\begin{gathered} AB+BC+CD=180^{\circ} \\ 50^{\circ}+BC+40^{\circ}=180^{\circ} \\ BC=180^0-(50^{\circ}+40^{\circ}) \\ BC=90^{\circ} \end{gathered}[/tex]To get arc BED;
[tex]\begin{gathered} \text{BED}=BE+ED \\ \text{BED}=180+50 \\ \text{BED}=230^{\circ} \end{gathered}[/tex]What interest will be earned if $11,000.00 is invested for 3 years at 11% compounded semi-annual?You would earn $ in interest. (Round to 2 decimal places.)
Answer:
$4,167.27
Explanation:
The amount, A(n) in an account for a Principal invested at compound interest is calculated using the formula:
[tex]\begin{gathered} A(n)=P(1+\frac{r}{k})^{nk}\text{ }where=\begin{cases}P=Prin\text{cipal} \\ r=\text{Annual Interest Rate} \\ k=\text{Compounding Period}\end{cases} \\ n=nu\text{mber of years} \end{gathered}[/tex]In the given problem:
• P = $11,000.00
,• r=11% = 0.11
,• n= 3 years
,• k=2 (semi-annual)
Substitute these into the formula:
[tex]\begin{gathered} A(n)=11,000(1+\frac{0.11}{2})^{2\times3} \\ =11,000(1+0.055)^6 \\ =11,000(1.055)^6 \\ =\$15,167.27 \end{gathered}[/tex]Next, we find the interest earned.
[tex]\begin{gathered} \text{Interest}=\text{Amount}-\text{Prncipal} \\ =15167.27-11000 \\ =\$4,167.27 \end{gathered}[/tex]You would earn $4,167.27 in interest (rounded to 2 decimal places).
which function has an inverse that is also a function horizontal line test
If the graph of a function y = f(x) is such that no horizontal line intersects the graph at more than one point, then f has an inverse function.
A. The absolute value function f(x) = | x | is intersected twice by any horizontal line at y > 0. Thus this function does not have an inverse
B. The quadratic function f(x) = x^2 has a graph called parabola. If we plot any horizontal line at y>0, that line will intersect the function twice. This function has no inverse function
1. As part of a summer internship, five people -- Cindy, Damaris, Eugenio, Fareed, and Guzal -- are to be assigned to floors 1-5 in a dormitory. Each person will occupy his or her own entire floor and no other people will be in the dormitory. The assignment of people to floors must follow the following rules:Eugenio lives immediately above Damaris.Cindy is not on the first floor.Fareed does not live immediately below Damaris.Guzal lives either on the first floor or the fifth floor.Which one of the five people could be assigned to live on any of the five floors in the dormitory? A. Cindy B. Damaris C. Eugenio D. Fareed E. Guzal2. If Fareed lives neither directly above nor directly below Cindy in the dormitory, which one of the following people must live on the fourth floor? A. Cindy B. Damaris C. Eugenio D. Fareed E. Guzal
SOLUTION
(1) From the question, if Eugene lives immediately above Damaris, then Eugene can only live between floors 1 to 4.
And Damaris can only live between floors 2 to 5.
Guzal can only live on floors 1 or 5
Siince Cindy cannot live on the first floor, she can only live between floors 2 to 5, Since Fareed does not live immediately below Damaris. Fareed can live between floors 1 to 5.
Hence the answer is Fareed, option D
Write the slope intercept equation through the point (1,2) and it’s parallel to the line y=1+4x
Given:
Line equation, y=1+4x
The point, (1,2)
To find the slope intercept form:
The general slope intercept form is, y=mx+b.
First to find m:
From the line equation,
y=4x+1
We have, m=4
Next to find b:
Substitute m=4, and (1,2) in the general intercept form is,
[tex]\begin{gathered} (2)=4(1)+b \\ 2=4+b \\ b=-2 \end{gathered}[/tex]Now, substitute m=4 and b=-2 in the slope intercept form
Thus, the slope intercept form is,
[tex]y=4x-2[/tex]Find the value of b if it is known that the graph of y=-3x+b goes through the point_
M(-2, 4)
Answer:
b = -2
Step-by-step explanation:
y = mx + b; (-2, 4)
y = -3x + b (x₁, y₁)
m = -3
y - y₁ = m(x - x₁)
y - 4 = -3(x -( -2))
y - 4 = -3(x + 2)
y - 4 = -3x - 6
+4 +4
------------------------
y = -3x - 2
I hope this helps!
If the coordinates of a are (3,4) and the coordinates of b are (-3,3) then the length of an is
The length of the line segment from a to b is 6.08 units or [tex]\sqrt{37}[/tex] units.
What is the length of a line segment and what is the role of coordinates?The length is described as the distance between the two points in a line. The coordinate usually refers to the dimensions of the point with respect to the two dimension graph.
Relation between the coordinates and length: [tex]\sqrt{(x_{1} -x_{2}) ^{2} +(y_{1} -y_{2} )^{2} }[/tex]
Now let point a be ([tex]x_{1},y_{1}[/tex]) and point b be ([tex]x_{2},y_{2}[/tex])
Thus putting values,
length = [tex]\sqrt{(3-(-3))^{2}+(4-3)^{2} }[/tex]
length = [tex]\sqrt{36+1}[/tex]
length = [tex]\sqrt{37}[/tex]
Hence the length of ab is [tex]\sqrt{37}[/tex] or 6.08 units.
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The figure is not drawn to scale. Find the unknown angle.
ThereforeGiven the image, we can find the missing angle using the sum of angles at a point rule.
The sum of angles at a point is known to be 360 degrees.
Therfore,
[tex]\begin{gathered} a^0+315^0=360^0 \\ a^0=360^0-315^0 \\ a^0=45 \end{gathered}[/tex]Therefore, the measure of "a" is
Answer:
[tex]45^0^{}[/tex]14) A positive number is two fifths of another positive number. The sum of the numbers is 49. What arethe two numbers?
Let's use the variable x to represent the second number. The first number is two fifths of x, so the first number is 2x/5.
If the sum of the numbers is 49, we can write the following equation:
[tex]\frac{2}{5}x+x=49[/tex]Now, solving the equation for x, we have:
[tex]\begin{gathered} \frac{2}{5}x+\frac{5}{5}x=49\\ \\ \frac{7}{5}x=49\\ \\ \frac{1}{5}x=7\\ \\ x=7\cdot5\\ \\ x=35 \end{gathered}[/tex]Let's calculate the first number:
[tex]\frac{2}{5}x=\frac{2}{5}\operatorname{\cdot}35=2\cdot7=14[/tex]Therefore the numbers are 14 and 35.
Esmeralda rents a car from a company that rents by the hour. she has to pay an initial fee of $50, and they charge her $8 per hour. she has $150 available to spend on car rental. what is the greatest number of hours for which she can rent the car?A. 18 hoursB. 12.5 hoursC. 12 hoursD. 13 hours
Let the number of hours be x,
Initial fee is $50,
Amount charged per hour is $8
The charge for a number of x hours is'
[tex]x\times8=8x[/tex]The total amount Esmeralda has is $150,
Therefore,
[tex]8x+5\leq150[/tex]Solving for x to find the greates number of hours,
[tex]\begin{gathered} 8x+50\leq150 \\ \text{Collect like terms,} \\ 8x\leq150-50 \\ 8x\leq100 \\ \text{Divide both sides by 8} \\ \frac{8x}{8}\leq\frac{100}{8} \\ x=12.5\text{ hours} \end{gathered}[/tex]Hence, the greates number of hours is 12.5 hours.
Option B is the right answe
4. The relationship between temperature expressed in degrees Fahrenheit(F) and degrees Celsius (C) is given by the formula F= (9/5)C + 32. If the temperature is 5 degrees Fahrenheit, what is it in degrees Celsius ?
To calculate which value in Celsius the temperature of 5 Fº equates to, we first need to rewrite the expression isolating the "C" variable on the left side.
[tex]\begin{gathered} F=\frac{9}{5}\cdot C+32 \\ \frac{9}{5}\cdot C=F-32 \\ 9\cdot C=5\cdot F-160 \\ C=\frac{5}{9}\cdot F-\frac{160}{9} \\ \end{gathered}[/tex]We now need to replace F by 5.
[tex]\begin{gathered} C=\frac{5}{9}\cdot5-\frac{160}{9} \\ C=\frac{25}{9}-\frac{160}{9} \\ C=\frac{-135}{9} \\ C=-15 \end{gathered}[/tex]The temperature is -15 degrees in Celsius.
