Answer:
(3x2−2)⋅(2x−3)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(((6 • (x3)) - 32x2) - 4x) + 6
STEP
2
:
Equation at the end of step
2
:
(((2•3x3) - 32x2) - 4x) + 6
STEP
3
:
Checking for a perfect cube
3.1 6x3-9x2-4x+6 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 6x3-9x2-4x+6
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -4x+6
Group 2: 6x3-9x2
Pull out from each group separately :
Group 1: (2x-3) • (-2)
Group 2: (2x-3) • (3x2)
-------------------
Add up the two groups :
(2x-3) • (3x2-2)
Which is the desired factorization
Trying to factor as a Difference of Squares:
3.3 Factoring: 3x2-2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 3 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Final result :
(3x2 - 2) • (2x - 3)
What is the decimal expansion of 2/3
Answer:
[tex]0.\overline{6}[/tex]
Step-by-step explanation:
It is a repeating decimal fraction:
[tex]\dfrac{2}{3}=0.6666...=0.\overline{6}[/tex]
__
You can see this if you do the long division. Each step is the same as the one before.
Ice is placed around a bowl of water to lower the temperature. The equation D=−75t+22 shows the time, t, measured in minutes and temperature, D, measured in degrees Celsius. Which statement is correct?
Answer:
d) Before cooling begins, the temperature of the water is 22°C
Step-by-step explanation:
Option A
If t=7 minutes
D=-7/5t+22
=-7/5(7)+22
=-49/5+22
=-49+110/5
=61/5
=12.2°C
Change in temperature=12.2°C-22°C
=-9.8°C
Option B
If t=5 minutes
D=-7/5t+22
=-7/5*5+22
=-7+22
=15°
Change in temperature=15°-22°
=-7°
Option C
The temperature of the ice must be less than 22°C
Option D
D=-7/5t+22
When ice is not placed, t=0
D=-7/5t+22
=-7/5(0)+22
=0+22
=22
Temperature of the water before cooling=22°
Answer:
D
Step-by-step explanation:
Solve for x 3 x − 2 = 2 x − 4
Answer:
x= -2
Step-by-step explanation:
Answer: x=-2
Step-by-step explanation: first subtract 2x from both sides leaving you with x-2=-4
Then add 2 to both sides, leaving you with x=-2
please help,
These prisms have different shapes as end faces.
a) Complete this table.
Shape of end face No. of faces No. of edges No. of vertices
Triangle (3 sides) 5
9
6
Rectangle (4 sides)
00
Triangle
Pentagon (5 sides)
15
10
Hexagon (6 sides)
8
18
b) How many edges and vertices does a prism
with a 100-sided end face have?
edges
vertices
Pentagon
Answer:
Step-by-step explanation:
E=300.
V=200.
Which statement illustrates the distributive property?
3 (4 + 5) = 3 (4) + 5
3 (4 + 5) = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = Left-bracket 3 (4) right-bracket + Left-bracket 3 (5) Right-bracket
Answer:
B. 3(4 + 5) = 3(4) + 3(5)
3 left-bracket (4) (5) right-bracket = 3 (4) + 3 (5)
3 left-bracket (4) (5) right-bracket = Left-bracket 3 (4) right-bracket + Left-bracket 3 (5) Right-bracket
Step-by-step explanation:
Distributive property of multiplication over addition:
a(b + c) = ab + ac
You have
3(4 + 5), so following the pattern above, you should get:
3(4 + 5) = 3(4) + 3(5)
Answer:
b
Step-by-step explanation:
I took the test
. Find the measure of angle A.
A
160°
Answer:
20°
Step-by-step explanation:
A= 360°- (160°+2*90°)= 20°
CD=17 AM=5 CD=? I've tried everything but I can't figure it out.
Answer:
We can prove that ΔTMB ≅ ΔTMD and ΔTMA ≅ ΔTMC by ASA. This means that BM = MD = BD / 2 = 8.5 and that AM = CM = 5 which means that CD = MD - CM = 8.5 - 5 = 3.5.
The length of a shadow of a building is 31 m. The distance from the top of the building to the tip of the shadow is 37 m. Find the height of the building. If
necessary, round your answer to the nearest tenth.
m
?
DOO
IDO
32
Answer:
20.2m
Step-by-step explanation:
the shadow becomes the base and the hypotenuse becomes 37,it forms a right angled triangle and using the Pythagoras theorem you take 37squared minus 31 squared,the answer you get you squareroot to get the answer
Which of the following are possible rational roots of the polynomial function?
Check all that apply.
F(x) = 5x2 - 3x+3
Answer: "possible" rational roots: ±1/5, ±3, ±1
Step-by-step explanation: Take plus or minus the factors of the constant divided by the factors of the leading coefficient.
In this case, the constant is 3, so the factors are 1 and 3, and the leading coefficient is 5, so the factors are 5 and 1.
1/5, 3/5, 1/1 and 3/1 are possibilities, simplify and attach the ± to each.
The possible rational roots of the polynomial function f(x) = 5x² - 3x + 3 are; ±1/5, ±3/5, ±1, ±3
What are roots of a polynomial?Root, in mathematics, a solution to an equation, usually expressed as a number or an algebraic formula.
It is a solution to an equation.
Given that a polynomial f(x) = 5x²-3x+3, we need to find the rational roots of the polynomial,
f(x) = 5x²-3x+3
The rational root theorem states that for a polynomial to have any rational roots, then the roots must be of the form;
± (Factors of coefficient of constant term/factors of the coefficient of the highest power)
Now, the coefficient of the highest power is 5 and the constant term is 3.
Factors of 5 = 1, 5
Factors of 3 = 1, 3
Thus, the possible rational roots are; ±1/5, ±3/5, ±1, ±3
Learn more about roots click;
https://brainly.com/question/16932620
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The sum of four consecutive numbers is 186. What is the
second smallest number?
Answer:
Need more info
Step-by-step explanation:
Answer:
46 is the second smallest number of the sequence
Step-by-step explanation:
Let's write the sum of 4 consecutive numbers (starting at the value x) as:
x + (x + 1) + (x + 2) + (x + 3) = 186
Now group all the unknowns:
x + x + x + x + 1 + 2 +3 = 186
4 x + 6 = 186
4 x = 186 - 6
4 x = 180
x = 180/4
x = 45
Then the sequence was: 45, 46, 47, 48
and the second smallest number of the sequence s: 46
there were 7 little cherries for every 2 big cherries. if there were 630 cherries in the box, how many little cherries were there? (please also answer the question in the picture)
Answer:
1)2205little cherries
2)0.5.
Step-by-step explanation:
1)7little=2big
?=630big
7×630=2205little cherries
2
2)²/5x=¹/10what is the value of 10x-2
first find the value of x that is ¹/10÷²/5=¼
so x is ¼
insert the value ie 10×¼-2
=2.5-2
=0.5
Anyone know please help!!
Answer:
only the inverse is a function
Four-digit numerical codes are issued for an ATM. If no integer can be repeated in a code, how many different codes can be formed using only odd integers?
Answer:
The answer is "120".
Step-by-step explanation:
The assuming numbers:
[tex]0, 1,2,3,4,5,6,7,8,9[/tex]
The odd number are=[tex]1,3,5,7,9[/tex]
Now we have four places:
In the first place we have 5 option
In second place we have 4 option
In third place, we have 3 option
In fourth place, we have 2 option
So, the value is [tex]5 \times 4 \times 3\times 2 \times 1= 120[/tex]
So, we have 120 different codes, which form the code.
PLSSSSSSSSSSSSSSSSSS HELP I JUST DONT GET IT write in standard form a) 456000 b) 0.00034 c) 16×10with a seven in the right corner of the 10
Answer:
A) 4.56000 x 10^5
B) 3.4 x 10^-4
C) 160000000
Step-by-step explanation:
Please mark me the brainliest answer!
Answer:
Step-by-step explanation:
a) 456000 = 4.5* 10⁵
b) 0.00034 = 3.4 *10⁻⁴
c) 16 *10 = 1.6 * 10²
The radius of a circle is 2 feet. What is the area of a sector bounded by a 180° arc?
Answer:
[tex]\boxed{Area = 3.14 ft^2}[/tex]
Step-by-step explanation:
Radius = r = 2 feet
Angle = θ = π/2 (In radians) = 1.57 radians
Area of Sector = [tex]\frac{1}{2} r^2 \theta[/tex]
Area = [tex]\frac{1}{2} (4)(1.57)[/tex]
Area = 2 * 1.57
Area = 3.14 ft²
Answer:
[tex]\bold{2\pi\ ft^2\approx6,28\ ft^2}[/tex]
Step-by-step explanation:
360°:2 = 180° so the area of a sector bounded by a 180° arc is a half of area of a circle of the same radius.
[tex]A=\frac12\pi R^2=\frac12\pi\cdot2^2=\frac12\pi\cdot4=2\pi\ ft^2\approx2\cdot3,14=6,28\ ft^2[/tex]
Subtract 15mn – 22m +2n from 14mn – 12m +7n.
Answer: -1mn + 10m +5n
Step-by-step explanation:
14 - 15 = -1
-12 + 22 = 10
7 - 2 = 5
<!> Brainliest is much appreciated! <!>
Answer:
If it just needs to be subtracted it simplify's to -mn+10m+5n
Renting a trailer for 4 days costs $84. Renting the trailer for 5 days costs $100. Which of the following linear equations represents the (days, cost)?
Answer:Y=16x+20
Step-by-step explanation:
Y=16x+20 thats tthe one that worked for me
Please answer this question now
Answer:
hope it will help uh.....
Answer:
Here is a hint: use the exterior angle theorem. That third angle is equal to the two...
Step-by-step explanation:
Find the values of the variables and the measures of the angles
Answer:
Add each given variable
(6x + 10) + (x + 2) + x = 8x + 12
The sum of all the angles equals 180ᴼ
8x + 12 = 180
Subtract 12 from both sides
8x = 168
Divide by 8 on both sides
x = 21
Now plug in 21 for each x to find the measure of each angle.
(6[21] + 10) = 126 + 10 = 136ᴼ
(21 + 2) = 23ᴼ
x = 21ᴼ
A small community organization consists of 20 families, of which 4 have one child,8 have two children, 5 have three children, 2 have four children, and 1 has fivechildren. If one of these families is chosen at random, what is the probability it has`children,`= 1,2,3,4,5?
Answer and Step-by-step explanation:
According to the situation, The probabilities for each one is given below:
As there are 20 families
So the probabilities for each one is
For four families have one child is
[tex]= \frac{4}{20}\\\\ = \frac{1}{5}[/tex]
For eight families have two children is
[tex]= \frac{8}{20}\\\\ = \frac{2}{5}[/tex]
For five families have three children is
[tex]= \frac{5}{20}\\\\ = \frac{1}{4}[/tex]
For two families have four children is
[tex]= \frac{2}{20}\\\\ = \frac{1}{10}[/tex]
For one family have five children is
[tex]= \frac{1}{20}[/tex]
The points (-2,4), (0,8), (1,10), and (3,14) are on a line. Which of the following statements are true?
Answer: y = 2x+8
Check out this graph I supplied you with!
ASAP! A boat travelling at top speed upstream moves at 15km/hr. When it travels downstream, again at top speed< it moves at 25km/hr. What is the boat's top speed in still water?
Answer: 20km/h
Step-by-step explanation:
20km/h. Simply average 15 and 25 by doing (15+25)/2
Hope it helps <3
Suppose the lengths of the pregnancies of a certain animal are approximately normally distributed with mean mu equals 247 days and standard deviation sigma equals 16 days. Complete parts (a) through (f) below.
Answer:
The answer is given below
Step-by-step explanation:
a) What is the probability that a randomly selected pregnancy lasts less than 242 days
First we have to calculate the z score. The z score is used to determine the measure of standard deviation by which the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that Mean (μ) = 247 and standard deviation (σ) = 16 days. For x < 242 days,
[tex]z=\frac{x-\mu}{\sigma}=\frac{242-247}{16}=-0.31[/tex]
From the normal distribution table, P(x < 242) = P(z < -0.3125) = 0.3783
(b) Suppose a random sample of 17 pregnancies is obtained. Describe the sampling distribution of the sample mean length of pregnancies.
If a sample of 17 pregnancies is obtained, the new mean [tex]\mu_x=\mu=247,[/tex] the new standard deviation: [tex]\sigma_x=\sigma/\sqrt{n} =16/\sqrt{17} =3.88[/tex]
c) What is the probability that a random sample of 17 pregnancies has a mean gestation period of 242 days or less
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{17} }=-1.29[/tex]
From the normal distribution table, P(x < 242) = P(z < -1.29) = 0.0985
d) What is the probability that a random sample of 49 pregnancies has a mean gestation period of 242 days or less?
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{242-247}{16/\sqrt{49} }=-2.19[/tex]
From the normal distribution table, P(x < 242) = P(z < -2.19) = 0.0143
(e) What might you conclude if a random sample of 49 pregnancies resulted in a mean gestation period of 242 days or less?
It would be unusual if it came from mean of 247 days
f) What is the probability a random sample of size 2020 will have a mean gestation period within 11 days of the mean
For x = 236 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{236-247}{16/\sqrt{20} }=-3.07[/tex]
For x = 258 days
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{258-247}{16/\sqrt{20} }=3.07[/tex]
From the normal distribution table, P(236 < x < 258) = P(-3.07 < z < 3.07) = P(z < 3.07) - P(z < -3.07) =0.9985 - 0.0011 = 0.9939
Find the value of x. Round the length to the nearest tenth.
Answer:
[tex] x = 5.1 yd [/tex]
Step-by-step Explanation:
Angle of depression is congruent to angle of elevation.
Therefore, angle of elevation of the given figure, which is opposite to x is 25°.
Adjacent length = 11 yd
Opposite length = x
Trigonometric ratio formula for finding x is shown below:
[tex] tan(25) = \frac{opposite}{adjacent} [/tex]
[tex] tan(25) = \frac{x}{11} [/tex]
Multiply both sides by 11 to solve for x
[tex] 11*tan(25) = x [/tex]
[tex] 5.129 = x [/tex]
[tex] x = 5.1 yd [/tex] (to the nearest tenth)
An equilateral triangle has sides 8 units long. An equilateral triangle with sides 4 units long is cut off at the top, leaving an isosceles trapezoid. What is the ratio of the area of the smaller triangle to the area of the trapezoid? Express your answer as a common fraction.
Answer:
1:3
Step-by-step explanation:
Please study the diagram briefly to understand the concept.
First, we determine the height of the isosceles trapezoid using Pythagoras theorem.
[tex]4^2=2^2+h^2\\h^2=16-4\\h^2=12\\h=\sqrt{12}\\ h=2\sqrt{3}$ units[/tex]
The two parallel sides of the trapezoid are 8 Inits and 4 units respectively.
Area of a trapezoid [tex]=\dfrac12 (a+b)h[/tex]
Area of the trapezoid
[tex]=\dfrac12 (8+4)*2\sqrt{3}\\=12\sqrt{3}$ Square Units[/tex]
For an equilateral triangle of side length s.
Area [tex]=\dfrac{\sqrt{3}}{4}s^2[/tex]
Side Length of the smaller triangle, s= 4 Units
Therefore:
Area of the smaller triangle
[tex]=\dfrac{\sqrt{3}}{4}*4^2\\=4\sqrt{3}$ Square units[/tex]
Therefore, the ratio of the area of the smaller triangle to the area of the trapezoid
[tex]=4\sqrt{3}:12\sqrt{3}\\$Divide both sides by 4\sqrt{3}\\=1:3[/tex]
A power line stretches down a 400-foot country road. A pole is to be put at each end of the road, and 1 in the midpoint of the wire. How far apart is the center pole from the left-most pole?
Answer:
The distance between the center pole and the left most pole = 200 ft
Step-by-step explanation:
Given that a power line has a length of 400 ft.
Three poles are to be put, two on each end and one at the midpoint of the wire.
Let us represent this using the number line as shown in the attached diagram.
To find:
The distance between the center pole and the left most pole ?
Solution:
Please refer to the attached diagram for the number line representation of the given situation.
Point A refers to the starting of the road.
Point B refers to the mid point of the road and
Point C refers to the other end point of the road.
So, point A is a at 0.
Point C is at 400.
The mid point will be at:
[tex]AB = \dfrac{A's\ position+C's\ position}{2}\\\Rightarrow AB = \dfrac{0+400}{2}\\\Rightarrow AB = 200\ ft[/tex]
The distance between the center pole and the left most pole = 200 ft
Which one of the following numbers is divisible by 11?
A. 924711
B. 527620
C. 320793.
D. 435854
Answer:
320793
Step-by-step explanation:
320793 / 11 = 29163
The diagram represents 6x2 – 7x + 2 with a factor of 2x – 1. A 2-column table with 2 rows. First column is labeled 2 x with entries 6 x squared, negative 4 x. Second column is labeled negative 1 with entries negative 3 x, 2. Both rows are labeled with a question mark. What is the other factor of 6x2 – 7x + 2? 3x – 2 3x – 1 3x + 1 3x + 2
Answer:
( 3x -2)
Step-by-step explanation:
6x^2 – 7x + 2
We know that the constant only has factors of 1 and 2
Since the middle term is negative we know that that we are subtracting
A negative times a negative is positive for the final term
A negative plus a negative is negative for the middle term
( -1 ) ( -2)
We have to determine how to break up 6x^2
1x * 6x
2x*3x
3x*2x
6x*1x
We are given that one factor is 2x-1
( 2x -1 ) ( -2)
That means the other factor of 6x^2 is 3x ( 2x*3x)
( 2x -1 ) ( 3x -2)
Answer:
3x-2
Step-by-step explanation:
6x² – 7x + 2= 6x² -3x- 4x + 2= 3x(2x-1)- 2(2x-1)= (2x-1)(3x-2)Factors are:
2x-1 and 3x-2--------------
3x – 2 correct3x – 1 incorrect3x + 1 incorrect3x + 2 incorrectHelppp!!!! please!!!
Answer:
your answer is b
hope this helps
Step-by-step explanation:
Answer:
B. m<DYZ = 90 deg
Step-by-step explanation:
There's a mistake in this problem. DY is a radius, so D is the center of the circle, but the circle is called circle O. Is the center D or O?
In any case, a radius that intersects a tangent at 90 degree angles.
m<DYZ = 90 deg
Which ordered pair is a solution for 3x - 1 = y?
Answer: A (2,5)
Step-by-step explanation: Remove Parenthesis
y = 3 (2) - 1
Simplify 3 (2) - 1
Multiply 3 by 2
y = 6 - 1
Subtract 1 from 6
y = 5
Use the x and y values to from the ordered pair.
(2,5)
Answer:
(2.5)
Step-by-step explanation:
Simply because if we tried it it works : 3*2-1=6-1=5y=5 so it's true