If f(x) = 3x³ + 5x² + 5, then what is the remainder when f(x) is divided by
x - 4?
By the remainder theorem, the remainder upon dividing a polynomial [tex]p(x)[/tex] by a linear factor [tex]x - c[/tex] is exactly [tex]p(c)[/tex].
Then the remainder upon dividing [tex]f(x)[/tex] by [tex]x - 4[/tex] is
[tex]f(4) = 3\times4^3 + 5\times4^2 + 5 = \boxed{277}[/tex]
the radius of a circle measures 7 inches. a central angle of the circle measuring 4pi/15 radians cuts off a sector. what is the area of the sector? Enter your answer as simplified fraction in the box.
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =\frac{4\pi }{15} \end{cases}\implies A=\cfrac{ ~~ \frac{4\pi }{15}(7)^2}{2}\implies A=\cfrac{98\pi }{15}[/tex]
Steve travels two times as fast as you. Traveling in opposite directions, they are 120 miles apart after 2.5 hours. Find the rate of travel
PLEASE HELPP!!! I WILL MARK AS BRAINLIEST!!!
Which expression represents the area of the rectangle?
130x
130x + 3
130x2 + 30x
Answer:
130x+3
Step-by-step explanation:
The area is (10x)*(13x+3). 10x*13x=130x squared. So, it is 130x+3.
Answer: C: 130x2 + 30x
Step-by-step explanation:
√-11
please solve this perblom
Answer:
3.31662479
Step-by-step explanation:
3.31662479
The graph of the parent function y = x cubed is horizontally stretched by a factor of One-fifth and reflected over the y-axis. What is the equation of the transformed function?
y = (5 x) cubed
y = (negative 5 x) cubed
y = (one-fifth x) cubed
y = (negative one-fifth x) cubed
The equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = (5x)³.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Here, Horizontal shift (also called phase shift):
Left shift by c units: y = f(x + c)
Right shift by c units: y = f(x - c)
For this case, we're specified that:
Original function: y = x³
Transformation: horizontal stretch by a factor of 1/5
Assuming the horizontal axis is having input variable x, and vertical axis having output variable y = x³, and the fact that a function y = f(x) if is horizontally stretched by a factor k, becomes y = f(x/k) , we have:
y = f(x)
y = x³
y = f (5x)
y = (5x)³
Thus, The equation of the transformed version of the function y = x³ when the transformation is horizontal stretch by a factor of 1/5, is y = (5x)³.
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Answer: It's D
Step-by-step explanation:
y = [-1/5x]^3 on edge
Given the function f(x) = 2x, evaluate ƒ(3).
Answer:
f(3) = 6
Step-by-step explanation:
you substitute 3 for x.
So you have 2(3) which is 2 multiplied by 3 which is 6
Pls I do not know how to rotate without tracing paper
Answer:
Point A:
(1, 3) ------> (3, -1)
Point B:
(3, 3) ------> (3, -3)
Point C:
(3, 2) ------> (2, -3)
Step-by-step explanation:
To find the coordinates of a 90° clockwise rotation, use the following:
[tex](x, y)[/tex] -----> [tex](y, -x)[/tex]
This means you will switch the x and y coordinates of the point and then take the opposite of the x coordinate (if it is positive make it negative and if it is negative make it positive).
Point A:
(1, 3) ------> (3, -1)
Point B:
(3, 3) ------> (3, -3)
Point C:
(3, 2) ------> (2, -3)
please answer will give brainly
Answer:
Step-by-step explanation:
The volume of a cube is given by the formula :
a³ (where a is the side length )
So now we have to cube these lengths :
Part A :
(3x²y)³ =
(3x²y)(3x²y)(3x²y) =
(9x^4y²)(3x²y) =
27x^6y³ (This is now fully simplified so our final answer for a)
Part B:
(5y²)³ =
(5y²)(5y²)(5y²) =
(25y^4)(5y²) =
125y^6 (This is now fully simplified so our final answer for b)
Hope this helped and have a good day
How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain.
Step-by-step explanation:
in a management information system, the quality of information is determined by its usefulness to users, and its usefulness determines the success of the information system.
A circle has a diameter that extends from (4.-6) to (-8,10). What are the coordinates the center of the circle?
============================================================
Reason:
For now we'll only focus on the x coordinates. They are 4 and -8. Plot them on a number line and find the midpoint. To do this, add those values up and divide by two
(4 + (-8))/2 = -4/2 = -2
The value -2 is right in the middle of 4 and -8; hence it's the midpoint.
Repeat those steps for the y coordinates
(-6+10)/2 = 4/2 = 2
These two midpoints help lead to (x,y) = (-2, 2) which is the midpoint the given endpoints. By extension, it is the center of the circle.
Visual confirmation is shown below. I used the midpoint command in GeoGebra. Desmos is another graphing tool you can use.
What is the missing term?
+1 4x -3
3x 12x²?
4x - 3
Answer:
83
Step-by-step explanation:
41 plus 36 plus 36 is 83 is the answer for me
The Yasuda family bought a toy that cost t dollars and a game that cost g dollars. Both were on sale. Which of these methods could the clerk use to calculate their total bill?
The equation that the clerk can use to calculate their total bill is t + g.
How to illustrate the equation?From the information given, Yasuda family bought a toy that cost t dollars and a game that cost g dollars.
The equation to calculate their total bills will be:
= t + g
where,
t = cost of toy
g = cost of game.
In this case, the equation that the clerk can use to calculate their total bill is t + g .
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please help will mark brainliest
Answer:
[tex]k > 3~~~\text{or}~~ k < -5[/tex]
Step-by-step explanation:
[tex]~~~~~|3k+3| > 12\\\\\implies 3k+3 < -12~~~~~~\text{or}~~~~~~~~~~3k+3 > 12\\\\\implies 3k < -12-3~~~~~~\text{or}~~~~~~~~~~3k > 12-3\\\\\implies 3k < -15~~~~~~~~~~~\text{or}~~~~~~~~~~3k > 9\\\\\implies k < -\dfrac{15}3~~~~~~~~~~~~\text{or}~~~~~~~~~~k > \dfrac 93\\\\\implies k < -5~~~~~~~~~~~~~~\text{or}~~~~~~~~~~k > 3[/tex]
The diameter of a semicircle is 8 kilometres. What is the semicircle's perimeter?
Answer:
4pi + 8 km
Step-by-step explanation:
the circumference of teh circle is d*pi = 8pi. since this is a semicircle the circumference is 4pi. then the perimeter is 4pi + 8
How many right angles are formed by two perpendicular lines in Euclidean geometry?
A.
3
B.
8
C.
4
D.
1
Answer:
Option c 4
Step-by-step explanation:
The mass, Q, of a sample of Tritium (a radioactive isotope of Hydrogen), decays at a rate of 5.626% per year. Given a
uantity of 726 grams, determine the graph that best models the decay of this radioactive substance.
In ten years' time, the mass of tritium would become 406.87 g. That's almost half of the original mass.
The mass, Q, of a sample of Tritium (a radioactive isotope of Hydrogen), decays at a rate of 5.626% per year.
How to find the decay of the radioactive substance?To make a graph, we need to establish which is the independent and dependent variables.
The independent variable (x-axis) is time in years and the dependent variable (y-axis) is the mass of tritium in grams.
At year 1,
726(1 - 0.05626) = 685.16 g
At year 2,
685.16 (1 - 0.05626) = 646.61 g
At year 3,
646.61 g (1 - 0.05626) = 610.23 g
The final graph is shown in the attached figure.
In ten years' time, the mass of tritium would become 406.87 g. That's almost half of the original mass.
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The weights of steers in a herd are distributed normally. The standard deviation is 200lbs and the mean steer weight is 900lbs. Find the probability that the weight of a randomly selected steer is between 1220 and 1320lbs. Round your answer to four decimal places.
Answer:
0.0369
Step-by-step explanation:
normalcdf (1220,1320,900,200) is 0.0369
If line m and n are parallel and line p is the transversal, Find out the angles a, b and c from the
Answer:
∠A = 55°∠B = 55°∠C = 125°Wxndy~~
the graph of the function f(x) = (x +2)(x + 6) is shown below. On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0). What is true about the domain and range of the function? The domain is all real numbers, and the range is all real numbers greater than or equal to –4. The domain is all real numbers greater than or equal to –4, and the range is all real numbers. The domain is all real numbers such that –6 ≤ x ≤ –2, and the range is all real numbers greater than or equal to –4. The domain is all real numbers greater than or equal to –4, and the range is all real numbers such that –6 ≤ x ≤ –2.
Answer: Choice A
Domain = all real numbers
Range = real numbers greater than or equal to -4
=====================================================
Explanation:
The domain is the set of allowed x inputs of a function.
We can replace x with any number we want to get some output for y = f(x)
This tells us the domain is the set of all real numbers.
-----------
The range is the set of numbers y such that [tex]y \ge -4[/tex]
In other words, we can have y = -4 or y > -4
This is because y = -4 is the lowest output possible, as indicated by the vertex point.
Answer:
b
Step-by-step explanation:
Evaluate:
6-(2/3)^2
A. 17/3
B. 52/3
C. 49/9
D. 50/9
Answer:
The correct answer is: "Option [D]".
Step-by-step explanation:
Hi student, let me help you out!
....................................................................................................................................
Let's use the acronym PEMDAS. With the help of this little acronym, we will not make mistakes in the Order of Operations! :)
[tex]\dag\textsf{Acronym \: PEMDAS}[/tex]
P=Parentheses,
E=Exponents,
M=Multiplication,
D=Division,
A=Addition,
S=Subtraction.
Now let's start evaluating our expression, which is [tex]\mathsf{6-(\cfrac{2}{3})^2}[/tex]
According to PEMDAS, the operation that we should perform is "E-Exponents".
Notice that we have a fraction raised to a power. When this happens, we raise both the numerator (2 in this case) and the denominator (3 in this case) to that power, which is 2. After this we obtain [tex]\mathsf{6-\cfrac{4}{9}}[/tex].
See, we raised both the numerator and the denominator to the power of 2.
Now what we should do is subtract fractions.
Note that 6 and -4/9 have unlike denominators. First, let's write 6 as a fraction: [tex]\mathrm{\cfrac{6}{1}-\cfrac{4}{9}}[/tex]. Now let's multiply the denominator and the numerator of the first fraction times 9: [tex]\mathrm{\cfrac{54}{9}-\cfrac{4}{9}}[/tex].
See, now the fractions have the same denominator. All we should do now is subtract the numerators: [tex]\mathrm{\cfrac{50}{9}}[/tex].
∴, the answer is Option D.
Hope this helped you out, ask in comments if any queries arise.
Best Wishes!
[tex]\star\bigstar\underline{\overline{\overline{\underline{\textsf{Reach \: far. Aim \: high. Dream \: big.}}}}}\bigstar\star[/tex]
[tex]\underline{\rule{300}{5}}[/tex]
Calculate 2/3, to the power of 3, therefore
[tex]\bf{\left(\dfrac{2}{3}\right)^{2}=\dfrac{2\times2}{3\times3}=\dfrac{4}{9} }[/tex]
[tex]\bf{6-\dfrac{4}{9} }[/tex]
Convert 6 to the fraction 54/9.
[tex]\bf{\dfrac{54}{9}-\dfrac{4}{9} }[/tex]
Since 54/9 and 4/9 have the same denominator, join their numerators to subtract them.
[tex]\bf{\dfrac{54-4}{9} \ \ \to \ \ \ Subtract }[/tex]
Subtract 4 from 54 to get 50.
[tex]\bf{\dfrac{50}{9} \ \ \to \ \ \ Answer }[/tex]
Therefore, the correct alternative is "D".
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Urgent help……………………:::::::::::
Answer:
The percentage of people enjoy New years Eve only = 3%
Step-by-step explanation:
The data indicates, The percentage of people enjoy New years Eve = 28%
The percentage of people enjoy New years Eve and Memorial Day = 12%
The percentage of people enjoy New years Eve and Forth of July = 18%
The percentage of people enjoy Enjoy all the three = 5%
The percentage of people enjoy New years Eve only
= The percentage of people enjoy New years Eve
- The percentage of people enjoy New years Eve and Memorial Day
- The percentage of people enjoy New years Eve and Forth of July
+ The percentage of people enjoy Enjoy all the three
= 28% - 12% - 18% + 5%
= 3%
A distribution has the five-number summary shown below. What is the
interquartile range (IQ) of this distribution?
Answer:
tiookvgvc. jbjvth kivtcth jjvf h. bkbgv
Answer:
The IQR of the given distribution is
Step-by-step explanation:
The given distribution has the five-number
28, 34, 43, 59, 62
Divide these numbers in two equal parts.
(28, 34), 43,( 59, 62)
Now divide each parenthesis in two equal parts.
(28), (34), 43,( 59), (62)
It means first quartile is the average of 28 and 34. Third quartile is the average of 59 and 62.
The interquartile range (IQR) of this distribution is
Therefore the IQR of the given distribution is 29.5.
evalute the expression (64)1\2
Answer:
32
Step-by-step explanation:
64×1÷2
64is divided by 2 =32
and 32×1=32
[tex]-6 + 3x - 9x^{2}=-16[/tex]
The solution of x in -6 + 3x - 9x^2 = -16 is [tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]
How to solve the equation?The equation is given as:
-6 + 3x - 9x^2 = -16
Add 16 to both sides
10 + 3x - 9x^2 = 0
Rewrite as:
9x^2 - 3x - 10 = 0
Solve for x using the quadratic formula
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
So, we have:
[tex]x = \frac{3 \pm \sqrt{(-3)^2 - 4 * 9 * -10}}{2 * 9}[/tex]
Evaluate
[tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]
Hence, the solution of x in -6 + 3x - 9x^2 = -16 is [tex]x = \frac{3 \pm \sqrt{369}}{18}[/tex]
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what is the percent increase of 42 from 30?
Answer:
40%
Step-by-step explanation:
your answer is *dun dun dun*
30 + 40% = 42
I need some more text apparently so that drumroll at the top and this will hopefully suffice
What is the area of the following figure if a = 13, b = 5, and c = 12?
Answer:
[tex]A(\triangle)=30\: units^2[/tex]
Step-by-step explanation:
Measures of the sides of the triangle are given as:a = 13, b = 5 and c = 12 Now, find semi perimeter (s) of the triangle, it is given as below:[tex] s=\frac{a+b+c}{2}=\frac{13+5+12}{2}=\frac{30}{2}=15[/tex]Formula for area of triangle is given as:[tex]A(\triangle)=\sqrt{s(s-a)(s-b)(s-c)}[/tex][tex]\implies A(\triangle)=\sqrt{15(15-13)(15-5)(15-12)}[/tex][tex]\implies A(\triangle)=\sqrt{15(2)(10)(3)}[/tex][tex]\implies A(\triangle)=\sqrt{900}[/tex][tex]\huge{\orange{\implies A(\triangle)=30\: units^2}}[/tex]help..and give the right reasons and statement
The triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.
What is the SAS similarity theorem?ΔABC is similar to ΔDEF only if the ratio of two sides of ΔABC and the corresponding two sides of ΔDEF is equal and the angle included on both sides are congruent.
Suppose the two sides of ΔABC are AB and BC, and that of DEF is DE and EF, then for SAS similarity, we need
and
∠ABC = ∠DEF
In triangles ΔAED and ΔCGF,
AE = CF
AD = CG
∠E = ∠G = 90°
Then the triangles ΔAED and ΔCGF are similar to each other. Then angle ∠A is congruent to angle ∠C.
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The average profit on each car sold was $2430, correct to the nearest $10. Calculate the lower bound for the total profit. Write down the exact answer.
The lower bound for the profit is $2425.
What is the lower bound?When a number of rounded off to the nearest $10, it means that the value of the number in the units place, if greater than 5 becomes zero and one is added to the $10 number. If the number is less than 5, there is no change in the $10 number and the units number becomes 0
The possible values of the average profit are 2425, 2426, 2427, 2428, 2429, 2430. 2431. 2432, 2433, 2434
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Solve, using the substitution method.
3m − n = 2
2m + n = − 7
(−1, −5)
(–10, –1)
(–2, –5)
(−5, 1)
Step-by-step explanation:
Hello there!
Here is the solution to our problem:
To begin with, we give our equations labels as below;
3m − n = 2 ...................eq.1
2m + n = − 7 ..................eq.2
Then, Let's manipulate eq.2
2m + n = − 7
n = -7 - 2m ...............eq3
And finally substitute the manipulated eq.3 into eq.1
3m − n = 2
3m − (-7 - 2m) = 2
3m + 7 + 2m = 2
5m = -5
m = -1
Substitute the value of m into eq.3
n = -7 - 2(-1)
= -5
In terms of x and y;
(x,y) : (m, n) => (-1, -5)
Therefore (m, n) = (-1, -5)
I hope this helps.
Have a nice studies.