What are the quotient and remainder of (3x4 - 2x + 7x-4)= (x - 3)?
a. 3x2 + 772 +21x + 70; 206
c. 3x4 + 7%? +21x2 + 70; 206
b. 3x + 77? + 21x + 70; -206
d. 37° +73+ + 21x + 703 76
The quotient of dividing (3x⁴ - 2x³ + 7x² - 4) by (x - 3) is 3x³ + 7x² + 28x + 84 and the remainder is 248
How to determine the quotient and the remainder?The division expression is given as:
(3x⁴ - 2x³ + 7x² - 4) / (x - 3)
Set the divisor to 0
x - 3 = 0
Solve for x
x = 3
Substitute x = 3 in 3x⁴ - 2x³ + 7x² - 4
3x⁴ - 2x³ + 7x² - 4 = 3(3)⁴ - 2(3)³ + 7(3)² - 4
Evaluate
3x⁴ - 2x³ + 7x² - 4 = 248
This means that the remainder is 248
Recall that:
Dividend = Divisor * Quotient + Remainder
So, we have:
3x⁴ - 2x³ + 7x² - 4 = x - 3 * Q + 248
Subtract 248 from both sides
3x⁴ - 2x³ + 7x² - 252 = x - 3 * Q
Divide both sides by x - 3
Q = (3x⁴ - 2x³ + 7x² - 252)/(x - 3)
Factorize the numerator
Q = (x - 3)(3x³ + 7x² + 28x + 84)/(x - 3)
Cancel out the common factors
Q = 3x³ + 7x² + 28x + 84
Hence, the quotient is 3x³ + 7x² + 28x + 84 and the remainder is 248
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747.7 plus a 15% increase
Answer:
[tex]859.855[/tex]
Step-by-step explanation:
You start with the current amount:
[tex]747.7[/tex]
First calculate [tex]15\%[/tex] of [tex]747.7[/tex]:
[tex]747.7 \cdot 0.15 = 112.155[/tex]
Now add that new value back into the original amount:
[tex]747.7 + 112.155 = 859.855[/tex]
As a trick to speed things up, you can calculate it in one expression:
[tex]747.7 \cdot 1.15 = 859.855[/tex]
Use the formula pH = log (1/H*) to find the pH of the substance given its concentration
of hydrogen ions in a liter of acid rain that has a pH. Round your answer to the nearest
ten-thousandth.
10. pH = 3.6
A survey found that 78% of high school freshmen have Internet access at home. OF the 754 freshman at one high school, about how many would be expected to have Internet access at home?
Answer:
About 588 students.
Step-by-step explanation:
78% = 0.78
Therefore, we can conclude the following:
78% of 754 = 754 * 0.78 = 588.12
helpme pleaseee urgentlyyy
The circumference of the given circle.
Solution:In order to find the circumference, first we'll have to find the raduis.
[tex]d = 2r[/tex]
[tex] \frac{8}{2} [/tex]
[tex] = 4 \: ft[/tex]
Now, we can work out the volume.
[tex]\huge\boxed{Fomula: C = 2\pi {r}}[/tex]
[tex] c= 2 \times \pi \times 4[/tex]
[tex]c = 25.13274 \: {ft}[/tex]
[tex]\large\boxed{C = 25.13 \: ft\: (2 \: d.p)}[/tex]
Hence, the circumference of the given circle is 25.13 feets.
in baseball Anthony hit 0.63 of the pitches thrown at him what percent of the pitches did Anthony miss
2 2/3 + 1/5
Could Someone Help??
Answer:
13/15
Step-by-step explanation:
you multiply the numbers by each other like 3×1/5 = 3/15 and 5×2/3 = 10/15
then you add them to get 13/15
can someone help me rn?
Answer:
y = 1
Step-by-step explanation:
Given:
equation of the parabola: [tex]y=a(x-1)^2+q[/tex]points on the parabola: (-1, -9) and (1, 1)Substitute point (1, 1) into the given equation of the parabola to find q:
[tex]\begin{aligned}\textsf{At}\:(1,1)\implies a(1-1)^2+q &=1\\a(0)^2+q &=1\\q &=1\end{aligned}[/tex]
Substitute the found value of q and point (-1, -9) into the given equation of the parabola to find a:
[tex]\begin{aligned}\textsf{At}\:(-1,-9)\implies a(-1-1)^2+1 &=-9\\a(-2)^2+1 &=-9\\4a+1 &=-9\\4a &=-10\\a &=-\dfrac{5}{2}\end{aligned}[/tex]
Therefore, the equation of the parabola is:
[tex]y=-\dfrac{5}{2}(x-1)^2+1[/tex]
The maximum or minimum point on a parabola is the vertex.
Vertex form of a parabola: [tex]y=a(x-h)^2+k[/tex] where (h, k) is the vertex.
Therefore, the vertex of the parabola is (1, 1) and so the maximum value of y = 1
Vertex at (1,q)
There is a point already given from which parabola passes through its (1,1)
So q=1Hence
vertex=(1,1)Equation:-
y=a(x-h)²+ky=a(x-1)²+1Now put (-1,-9)
-9=a(-2)²+1-9=4a+14a=-10a=-5/2a is negative hence parabola is opening downwards
So
vertex is maximum
Max value
y=124. Which point is NOT on the circle with center (-4,3) and radius 6? a. (2,3) b. (2,0) c. (-4,-3) d. (-10,3)
Answer:
Your answer is b. (2,0) is not a point on the circle.
Step-by-step explanation:
Center of the Circle: (h,k) = (-4,3)
Radius of the Circle: r = 6
Find the points on the circle.
(h + r ,k)
(-4 + 6 , 3) = (2,3)(h - r ,k)
(-4 - 6 , 3) = (-10,3)(h , k + r)
(-4 , 3 + 6) = (-4,9)(h , k - r)
(-4 , 3 - 6) = (-4,-3)AXYZ is rotated 180°.
What are the coordinates of point X'?
Reason:
When rotating a point 180 degrees around the origin, you use the rule
[tex](x,y) \to (-x,-y)[/tex]
We flip the sign of each coordinate from positive to negative or vice versa.
The point X is at the location (-4, 1). Rotating this 180 degrees will get us to X'(4, -1)
why are asymptotes important in rational function graphs
Answer:
when sketching the curves of functions.
Step-by-step explanation:
There is a wide range of graph that contain asymptotes and that includes rational functions, hyperbolic functions, tangent curves, and more. Asymptotes are important guides when sketching the curves of functions. This is why it’s important that we know the properties, general forms, and graphs of each of these asymptotes.
Which description matches the algebraic expression 45 n?
the sum of a number and 45
the quotient of a number and 45
the product of a number and 45
the difference of a number and 45
Answer:
The product of a number and 45
Step-by-step explanation:
Answer:
the product of a number and 45
Step-by-step explanation:
i just finished the quiz
if x=3,y=-2(negative 2) and z=6,what is 7xyz
Step-by-step explanation:
x = 3
y = - 2
z = 6
Question:[tex]7xyz[/tex]
Solution,
= 7 × 3 ( - 2 ) × 6
= 21 ( - 2 ) × 6
= - 42 × 6
= - 252
hence the answer is - 252....
Find the height of the tree below to the nearest foot.
I need this answer asap please
Answer:283 awnser is 283
Step-by-step explanation:
Alex has 64 cubes with dimensions in ft like
1/2 x 1/2 x 1/2
He uses all the cubes to fill a box shaped like a larger rectangular prism. There are no gaps.
What is the volume in cubic ft of the larger rectangular prism?
This composite figure is made up of three simpler shapes. What is the area of the figure? 7 cm 4 cm 5 cm 4 CE 8 cm A. 66 square cm R 50 square cm C. 46 square cm D. 80 square cm
The total area of the given figure will be 66 square cm.
What is an area?
The space occupied by any two-dimensional figure in a plane is called the area. Here we have three shapes a triangle, a rectangle and a parallelogram.
Total area = Area of triangle + Area of rectangle + Area of parallelogram
Total area = [(1/2) x 4 x7] + [4 x 5] + [ 4 x 8 ]
Total area = 14+20+32
Total area = 66 square cm
Hence the total area of the given figure will be 66 square cm.
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If ∠1 and ∠2 are vertical angles and m∠1 = 108°, find m∠2.
Answer:
[tex]m\angle 2= 108^{\circ}[/tex]
Step-by-step explanation:
Vertical angles are equal.
Answer:
108°
Step-by-step explanation:
vertical angles are angles opposite each other when two lines cross.
if <1 and <2 are vertical angles, it means that m<1 = m<2
m<1= 108°
therefore, m<2= 108°
Pls ingore all of the questions below, but help me with the attached image
What is the only number that has the same number of letters as it's meaning? ...
What number doesn't have its own Roman numeral? ...
What is the only even prime number? ...
What is the smallest perfect number? ...
What is our current numerical system based on? ...
Is Pi a rational or irrational number?
Answer:
w = 23
Step-by-step explanation:
so the total degree of a triangle is 180,
when you add all 3 it should equal 180.
35 + (5w) + (w + 7) = 180
subtract 35 from both sides, 35 - 35 + (5w) + (w + 7) = 180 - 35
(5w) + (w + 7) = 145
combine like terms (add the w's), (5w + w) + 7 = 145
6w + 7 = 145
subtract 7 from both sides, 6w + 7 - 7 = 145 - 7
6w = 138
divided both sides by 6 to get w alone, 6w / 6 = 138 / 6
w = 23
2. The bases of the trapezoid (x-14) cm and (x+2) cm. its medien is 30 cm lang, how long is the shorter
Answer:
x2-2x=58
Step-by-step explanation:
(x-14)(x+2)=30
x2+2x-14x-28=30
x2+2x-14x=28+30
x2-2x=58
help does anyone know the answer to this!!! ^_^
The exponential function which represent the graph shown in image is f(x)=2.(1/4)ˣ. Option C is correct.
What is an exponential function?Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.
The exponential function with dependent variable y and independent variable x can be written as,
f(x)=a.bˣ
Here, x is the variable in the power of a number, b is a constant which is known as the change factor and a is the initial value of the function.
Here, in the graph, it passes from the (0,2) and (2,0) from x and y axis. it tells us that the initial value of is 2.
a=2
The graph is plotted on right side in opposite way, which tells the value of b is in the reciprocal. Thus,
b=1/4.
Put the values as,
f(x)=a.bˣ
f(x)=2.(1/4)ˣ
Hence, the exponential function which represent the graph shown in image is f(x)=2.(1/4)ˣ. Option C is correct.
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Pls help me this question is bad
Answer:
using law of indices
the answer is 1
These two shapes have the same perimeter.
regular hexagon
square
Not actual size
The length of each side of the hexagon is 8 centimetres.
Calculate the area of the square.
Question
Answer: u can use this to practice and u can also find your awnser in thes pic
Step-by-step explanation:
Please help i really need this i will give a brainliest to the people that answer correctly
1st options: a positive, a negative, no
2nd options: decreases, increases, varies
Answer:
There is a negitve corrilation because as time increases speed decreases
Step-by-step explanation:
Which of the following are based on empirical probability
The empirical probability is Life insurance, Car insurance, and Mortality.
What is empirical probability?
The ratio of the number of outcomes in which a defined event occurs to the total number of trials, not in a theoretical sample space but in a real experiment, is the empirical probability, relative frequency, or experimental probability of an event.
Therefore the empirical probability will be Life insurance, Car insurance, and Mortality.
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What is the length of the segment joining the points at (-6, 8) and (6, 3)?
Enter your answer in the box.
units
Answer:
13 units
Step-by-step explanation:
So the length of those 2 points is 6+6 = 12.
The height would be 8-3 =5
Using pythagoras, you can find out the length of the line joining the 2 points so:
[tex]5^2 + 12^2 = 169[/tex]
[tex]\sqrt{169} = 13[/tex] units
Sandy has built a triangular pool and wants to
add a rectangular deck around it as shown in the
figure. How many square feet of wood does Sandy
need for the deck?
Ten students received their test grades back for Math 171.
80
88
60
52
96
58
66
Find the 5 number summary.
Answer:
5 number summary hulaan mo hhahah 82 56 92 78 68
Select the expression that is equivalent to the given expression: 3(x + 2) - x
A: 5x + 6
B: 2x + 6
C: 2x + 2
D: 9
Answer:
B
Step-by-step explanation:
if you simply 3(x+2)-x, you get 2x+6.
it is not 3x+6 because x already equals 1. 2x+6=2x+6
Noa hopes to pick the winning ticket during her math class’s raffle. The student who picks the ticket with a true statement will win. Which is the winning ticket?
A correct answer is an option a which is 2x = - 23
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
We need to select correct statements from the given options.
2 ( x - 6 ) = - 35
2 x - 12 = - 35
2x=-35+12
2x = - 23
Therefore, 2 ( x - 6 ) = - 35 is equivalent to .2x=-23
8(x-7)=35
8x-556=35
8x=91
Therefore, 8(x-7)=35 is not equivalent to 8x=91.
9(x-6)=-35
9x-54=-35
9x=19
Therefore,9(x-6)=-35 is not equivalent to 9x=19.
4(x-5)=35
4x-20=35
4x=55
Therefore,4(x-5)=35 is not equivalent 4x=55 to .
Hence, the correct answer is an option a which is 2x = - 23
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