Answer:
2 (x^3 - x^2 + 2 x + 1)
Step-by-step explanation:
Simplify the following:
-(2 x^2 - 3 x^3 + 1) - x^3 + 4 x + 3
Factor -1 out of -3 x^3 + 2 x^2 + 1:
--(3 x^3 - 2 x^2 - 1) - x^3 + 4 x + 3
(-1)^2 = 1:
3 x^3 - 2 x^2 - 1 - x^3 + 4 x + 3
Grouping like terms, 3 x^3 - x^3 - 2 x^2 + 4 x - 1 + 3 = (-x^3 + 3 x^3) - 2 x^2 + 4 x + (3 - 1):
(-x^3 + 3 x^3) - 2 x^2 + 4 x + (3 - 1)
3 x^3 - x^3 = 2 x^3:
2 x^3 - 2 x^2 + 4 x + (3 - 1)
3 - 1 = 2:
2 x^3 - 2 x^2 + 4 x + 2
Factor 2 out of 2 x^3 - 2 x^2 + 4 x + 2:
Answer: 2 (x^3 - x^2 + 2 x + 1)
Answer:
Step-by-step explanation:
4x - x^3 + 3 - 2x^2 + 3x^3 - 1
2x^3 - 2x^2 + 4x + 2 is the solution
You are working with a quadratic equation and construct the following table.
Answer:
a) Vertex is at (-3, -1)
b) y-intercept is at (0,8)
c) x intercept is at (-4,0) and (-2,0)
d) x=-3
Step-by-step explanation:
We know the vertex is the lowest or highest part of a parabola meaning all the points are reflected across. It is the only y value without a matching pair
E.x. -1 and 1, -3 and 3
The only point without a corresponding y value is (-3,-1) therefore the vertex is at (-3,-1)
The y-intercept is where the parabola meets the y axis or the x value is equal to 0, we just have to find when x = 0 to find the y intercept
y intercept: (0,8)
For the x intercept's it is just the reverse, you need to find where the parabola crosses the x axis or when y = 0
x intercept 1:(-4,0)
x intercept 2: (-2,0)
The axis of symmetry is also the x coordinate of the vertex which is 3 so
x = 3
The function h(x) = 5x2 – x – 6 is the result of combining two functions using multiplication. Which functions could have been combined? f(x) = 5x – 6 and g(x) = x + 1 f(x) = 5x – 2 and g(x) = x + 3 f(x) = 5x3 + 14x2 – 9x – 18 and g(x) = x + 3 f(x) = 25x3 – 15x2 – 28x + 12 and g(x) = 5x – 2
Answer:
f(x) =5x -6 and g(x) = x + 1
Step-by-step explanation:
5x^2 - x - 6
finding the product of AC where A is 5 and C is -6 equals -30
factors of -30 whose sum eqjals -1 are +5 and -6
substitute into the expression
5x^2 + 5x -6x - 6
group the expression
(5x^2 + 5x) (-6x - 6)
take out the common factors in each bracket
5x(x + 1) -6 (x + 1)
(5x - 6) (x + 1)
Answer:a
Step-by-step explanation:
10,13,16,19
What is the 30th term?
Step-by-step explanation:
An=A1+(n-1)d
A30=10+(30-1)3
A30=10+(29)3
A30= 10+87
A30=97
it takes me a centuary to type
Does the point (–3, 2) lie inside, outside, or on a circle with center (4, 0) and radius 5 units?
Answer:
The point (-3, 2) lies outside of the circle centered at (4, 0) with radius 5.
Step-by-step explanation:
The distance between two points (x₁, y₁) and (x₂, y₂) on the x-y plane can be calculated with:
√((x₁ - x₂)² + (y₁ - y₂)²)
So in this case, with the points (-3, 2) and (4, 0), the distance is:
√((-3 - 4)² + (2 - 0)²)
√(49 + 4)
√(53) ≈ 7.28
Since 7.28 > 5, the point (-3, 2) lies outside of the circle centered at (4, 0) with radius 5.
The spinner below shows 5 equally sized slices. Tammy spun the dial 25 times and got the following results. Fill in the table below. Round your answers to the nearest thousandths.
Answer:
a) 4/25, or 0.16, or 16%
b) 1/5, or 0.2, or 20%
c) The first option - the theoretical and experimental values should become closer the more trials that are performed.
Step-by-step explanation:
a) 4 of Tammy's 25 spins landed on black, so the experimental probability is 4/25, or 0.16, or 16%.
b) The spinner is split into 5 equal sections. Assuming it is fair, the chance of landing in any given section for a single spin is 1/5, or 0.2, or 20%.
c) The theoretical and experimental values should get closers the more trials you do.
For example, consider 1 coin flip vs 100. The theoretical probability of landing on a given side of a coin is 1/2, or 0.5, or 50%. With a single flip, your experimental probability will either be 0% or 100%, both off of the theoretical probability by 50%. After 100 flips however, the experimental and theoretical probabilities will be much closer to each other.
Which of the following is equivalent to √8?
A.2
B.√2
C.2 √2
D.2 + √2
Answer:
[tex]C.2\sqrt{2}[/tex]
Step-by-step explanation:
Step 1: Know you can split 8 into factors of 4 and 2
[tex]\sqrt{(4)(2)}[/tex]
Step 2: Recognize 4 is a square number
[tex]\sqrt{(2^{2})(2) }[/tex]
Step 3: Because [tex]2^{2}[/tex] is squared you can move it out
[tex]2\sqrt{2}[/tex]
Therefore the answer is C
What is the inverse of y =
1-7
?
4
Answer:
2
Step-by-step explanation:
i need help on this!!
Answer:
1, -0.5, -6.25
Step-by-step explanation:
The number in the left box is the leading coefficient. The coefficient of x^2 is 1, so that goes in the first box.
__
The number in the second box is half the coefficient of x, divided by the leading coefficient:
(1/2)(-1)/1 = -1/2
__
The number in the third box (k) is the number required to make the rewritten g(x) match the original g(x). So far, we have ...
g(x) = 1(x -1/2)^2 + k = x^2 -x -6
x^2 -x +1/4 +k = x^2 -x -6 . . . . . expand the square
1/4 +k = -6 . . . . . . . . . . . . . . . . . subtract the x-terms from both sides
k = -6 1/4 . . . . . . . . . . . . . . . . . . subtract 1/4
So, you have ...
[tex]g(x)=\boxed{1}(x+\boxed{-0.5})^2+\boxed{-6.25}[/tex]
I need help with expressions
Find the percent of increase to the nearest whole from 12 to 20
Answer:
The answer is
[tex]67\%[/tex]Step-by-step explanation:
To find the percentage increase we use the formula
[tex]Percentage \: change = \frac{change}{original \: \: quantity} \times 100\%[/tex]From the question
The original value = 12
To find the change we subtract the smaller value from the larger one
That's
Change = 20 - 12 = 8
So the percentage increase is
[tex] \frac{8}{12} \times 100 \%\\ = \frac{2}{3} \times 100\% \\ = 66.67\%[/tex]We have the final answer as
[tex]67\%[/tex] to the nearest whole number
Hope this helps you
Which simplified fraction is equal to 0.1ModifyingAbove 7 with bar? StartFraction 9 Over 17 EndFraction StartFraction 8 Over 45 EndFraction StartFraction 17 Over 9 EndFraction StartFraction 16 Over 90 EndFraction Please help i will give you brainliest
Answer:
8/45
Step-by-step explanation:
Define x to be the value of your fraction:
[tex]x=0.1\overline{7}\\\\10x=1.7\overline{7}\qquad\text{multiply by 10}\\\\10x-x=1.7\overline{7}-0.1\overline{7}=1.6\\\\x=\dfrac{1.6}{9}=\dfrac{8}{45}\qquad\text{divide by 9; put in lowest terms}[/tex]
____
When in doubt, you can use your calculator to see which fraction gives you 0.1777777778.
_____
We multiplied by 10^1 above, because there is 1 repeating digit. The power of 10 we use matches the number of repeating digits.
Answer:
8/45
Step-by-step explanation:
and have a good day
Wich expression is equivalent to 0.33b+b+0.31b?
A.b+0.64
B.1.64b
C.1.02b
D.1+0.64b
Answer:
B. 1.64b
Step-by-step explanation:
0.33b+1b+0.31b
=1.64b
Could the given matrix be the transition matrix of a regular Markov chain?
[Start 2/2 Matrix 1st Row 1st Column 0.3 2nd Column 0.7 2nd Row 1st Column 0 2nd Column 1 EndMatrix ]
Answer:
Following are the answer to this question:
Step-by-step explanation:
Matrix:
[tex]A=\left[\begin{array}{cc}0.3&0.7\\1&0\end{array}\right][/tex]
[tex]A^2=\left[\begin{array}{cc}0.79&0.21\\0.3&0.7\end{array}\right][/tex]
In the above-given matrix, all entries of the matrix A² will be positive and the matrix A will be the transition of the matrix A, that regulates the Markov chain.
Find the 9th term using the general term a subscript n equals 4 (n minus 5 ).
Answer: The 9th term is 16.
Step-by-step explanation:
Given formula : [tex]a_n=4(n-5)[/tex], where n is a natural number using for determine the terms.
To find the 9th term , we substitute n= 9 in the above expression, we get
[tex]a_9=4(9-5)\\\\\Rightarrow\ a_9=4(4)\\\\\Rightarrow\ a_9=16[/tex] which is the 9th term.
Hence, the 9th term is 16.
Kadir, Chandran and Ping Wei participated in a Science quiz. The number of questions they had answered was in the ratio 4:6:3. Chandran had answered 30 questions. Calculate the total number of questions Kadir amd Ping Wei had answered.
Answer:
35
Step-by-step explanation:
We can call the amount of questions they answered as 4x, 6x and 3x respectively. Since Chandran answered 30 questions, we know that 6x = 30 so x = 5. The total number of questions Kadir and Ping Wei answered was 4x + 3x = 7x and since we know that x = 5, the answer is 7 * 5 = 35 questions.
What slope is perpendicular to m=3/4
Answer:
The slope of the perpendicular line is -4/3
Step-by-step explanation:
Perpendicular lines have slopes that multiply to -1
m * 3/4 = -1
Multiply by 4/3
m * 3/4 * 4/3 = -1 * 4/3
m = -4/3
The slope of the perpendicular line is -4/3
How many rectangles are there?
Answer:
8 (read below)
Step-by-step explanation:
There is 8 if you re counting the bottom, light turqoise one. If not, then 7.
Answer:
17 or 18
Step-by-step explanation:
When two lines cross itis found that the angles opposite each other are the same size. They are known as
Answer:
"vertical angles"
Step-by-step explanation:
Those are "vertical angles."
Jessie leaves home at 7:30 am and rides his bike to school at a speed of 9 miles per hour. If his school is 3 miles from his house, what time will he get to school?
Step-by-step explanation:
d =r*t
d=3 mi
r =9 mi/hr
3=9t
t=1/3 hr
Convert hour to min
t=20 min added to 7:30
The time will he get to school is 7:50 AM
A, B and C together can finish a piece of work in 4 days, A alone can do it in 12 days and B alone in 18 days. How many days will be taken by C to do it alone?
Answer:
9 days
Step-by-step explanation:
Let x = days taken by C to do it alone
In one day, A can do: 1/12 (part of the whole work)
In one day, B can do: 1/18 (part of the whole work)
In one day, C can do: 1/x (part of the whole work)
In one day,together A, B and C can do: 1/4 (part of the whole work)
we have this equation:
1/x + 1/12 + 1/18 = 1/4
--> 1/x = 1/4 - 1/12 - 1/18 = 1/9
--> x = 9 (days)
(9,5) and (4,-7) find the distance between two points
Answer:
13 units
Step-by-step explanation:
Use the distance formula, d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex], where (x2, y2) and (x1, y1) are two different points on the line.
Plug in the values:
d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
d = [tex]\sqrt{(9 - 4)^2 + (5 + 7)^2}[/tex]
d = [tex]\sqrt{5^2 + 12^2}[/tex]
d = [tex]\sqrt{25 + 144}[/tex]
d = [tex]\sqrt{169}[/tex]
d = 13
The length of the shadow of a pole on level ground increase 90m, when the angle of elevation of the sum changes from 58-38.calculate the height of the pole, correct to 3sf
Answer: h = 137.4 metres
Step-by-step explanation:
Given that the length of the shadow of a pole on level ground increase 90m, that is, (x + 90)m will be the total length of the shadow. Also we are given that the angle of elevation of the sum changes from 58-38.
To calculate the height, we will employ trigonometry ratio. SohCahToa which are: tan 58 and tan 38.
Please find the attached files for the solution
ANSWER 4 BRAINLIEST !!!!!!!!!!!!!!!!
the sum of twice a number and 15 less than the number is the same as the difference between -19 and the number. What is the number?
Answer:
-1
Step-by-step explanation:
Twice a number: 2n.
15 less than the number: n-15.
The sum of those: (2n) +(n-15) = 3n-15.
__
The difference between -19 and the number: -19-n
__
These values are the same, so we have ...
3n -15 = -19 -n
4n = -4 . . . . . . . . add n+15 to both sides
n = -1 . . . . . . . . . divide by -4
The number is -1.
cos2A is equivalent to: A. sin2A−cos2A B. sin2A+cos2A C. cos2A−sin2A D. cosA−sinA
Formatted Options:
A. sin²A−cos²A
B. sin²A+cos²A
C. cos²A−sin²A
D. cosA−sinA
Answer:
C. cos²A−sin²A
Step-by-step explanation:
From the double angle formulas, we know that:
cos (A + B) = cosAcosB - sinAsinB
So, if B = A, then the above equation becomes;
cos(A + A) = cosAcosA - sinAsinA [i.e replacing B with A]
=>cos(2A) = (cosA)² - (sinA)²
=> cos(2A) = cos²A - sin²A
Therefore,
cos(2A) is equivalent to cos²A - sin²A
The perimeter of a rectangle is 38 units. The length is 13 units longer than the width. What are the dimensions of the rectangle?
A 18 by 5
B. 12 by 7
Oc is by a
0.16 by
Answer:
D (Presumably)
16 by 3
Step-by-step explanation:
The perimeter of a rectangle is the two lengths added with the two widths. In a formula, this is:
[tex]P=2l+2w[/tex]
Where l is the length and w is the width.
We are told the length is 13 units longer than the width. In other words:
[tex]l=w+13[/tex]
We also already know that the perimeter is 38 units. So, let's substitute P for 38 and l for (w+13) to solve for w:
[tex]P=2l+2w\\38=2(w+13)+2w[/tex]
Distribute:
[tex]38=2w+26+2w[/tex]
Combine like terms:
[tex]38=4w+26[/tex]
Subtract 26 from both sides:
[tex]12=4w[/tex]
Divide both sides by 4:
[tex]w=3[/tex]
Thus, the width is 3 units.
Since the length is 13 units longer than the width, the length is 16 units.
Katie is making chocolate candies for her classmates' Valentine's Day gifts. She melts 12.8 ounces of chocolate and divides it among 40 candy molds. If Katie divided the melted chocolate evenly, how much would each candy weigh?
Answer:
0.32 ounces of chocolate per mold
Step-by-step explanation:
Answer:
the correct answer is 3.125
Step-by-step explanation:
Yolanda is filling her bathtub. The table shows the number of gallons of water in the bathtub at different times since she started filling it. Time (minutes) Water (gallons) 1 16.50 1.5 24.75 2 33 Answer the following questions based on the information in the table. Part A Find the constant of proportionality (in gallons per minute) using the values in the first row of the table.
Answer:
Constant of proportionality
K= 16.5 gallons per minute
Step-by-step explanation:
Time t (minutes) Water g (gallons)
For t= 1, g= 16.50,
for t= 1.5 ,g= 24.75
For t= 2,g= 33
Let the function be
Gallons g= k(time t)
Where k is the constant of proportionality
16.5= k(1)....for when t= 1
24.75= k(1.5) ..for when t= 1.5
Solving gives
8.25=k(0.5)
8.25/0.5= k.
16.5 = k
K= 16.5 gallons per minute
what number should be placed in the box to help complete the division calculation
Answer:
15
Step-by-step explanation:
12 X 15 is 180, which is closest to 187, we have to add a 5 in the space next to 71 and 180 under 187
Finding the Constant of Proportionality from a Graph
Hi there! :)
Answer:
[tex]\huge\boxed{8}[/tex]
Find the constant of proportionality using
rise ( y value) / run ( x value):
Therefore:
8 / 1 = 8 = constant of proportionality
We can go ahead and check our work as well:
16 / 2 = 8
24 / 3 = 8
32 / 4 = 8
Therefore, 8 is the correct constant of proportionality.