Answer:
x = - 3 with multiplicity 2
Step-by-step explanation:
f(x) = (x - 3)(x + 3)(x + 3) = (x - 3)(x + 3)²
Equating each factor to zero and solving for x
x - 3 = 0 ⇒ x = 3 with multiplicity 1
x + 3 = 0 ⇒ x = - 3
x + 3 = 0 ⇒ x = -3
Thus x = - 3 has multiplicity of 2
The fact that the factor is squared gives the multiplicity
(x + 3)³ has root - 3 of multiplicity 3
HURRY PLZ!!!
Solve for x: 1 x − 2 + 1 x + 2 = 4 x2 − 4
A) 0 B) 3 C) −1 D) no solution
Answer:
D) no solution
Step-by-step explanation:
1/ (x-2) + 1/(x+2) = 4/(x^2-4)
x cannot equal 2 or -2 since that would make our fractions equal 1/0 or be undefined
Factor the term on the right
1/ (x-2) + 1/(x+2) = 4/(x-2)(x+2)
Multiply both sides by (x-2) (x+2)
(x-2) (x+2) (1/ (x-2) + 1/(x+2)) = 4/(x-2)(x+2)*(x-2) (x+2)
Distribute
x+2 + (x-2) = 4
Combine like terms
2x = 4
Divide by 2
2x/2 = 4/2
x =2
But this is not a possible solution since that is not in the domain
Which law would you use to simply the expression (p/q)^3
[tex]\text{Hey there!}[/tex]
[tex](\frac{p}{q})^3[/tex]
[tex](\frac{p}{q})^3=\frac{p}{q}\times\frac{p}{q}\times\frac{p}{q}[/tex]
[tex]\text{Numerator: p}\times\text{p}\times\text{p}[/tex]
[tex]\text{Denomintor: q}\times\text{q}\times\text{q}[/tex]
[tex]\frac{p\times p\times p}{q\times q\times q}[/tex]
[tex]p\times p \times p=p^3[/tex]
[tex]q\times q \times q=q^3[/tex]
[tex]\boxed{\boxed{\bf{Answer:\frac{p^3}{q^3}}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic meters? 3.6 3,600,00 360 36
Answer: 3,600,000 cm³
Step-by-step explanation: First you have to convert all the units into centimeters,
2 meters = 200 centimeters
1.5 meters = 150 centimeters
To find the volume of a rectangular prism you multiply all the sides.
120 * 200 * 150 = 3,600,000
The answer is 3,600,000 cubic centimeters.
The volume of a rectangular prism with the given dimensions is 3.6 cubic meters.
The dimensions of a rectangular prism are 120 centimetres(1.2 meters) by 2 meters by 1.5 meters.
What is the formula to find the volume of a rectangular prism?The formula to find the volume of a rectangular prism is l×b×h.
Now, volume=1.2×2×1.5=3.6 cubic meters.
Therefore, the volume of a rectangular prism is 3.6 cubic meters.
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Recycling center a processes aluminum at rate of 100 pounds per hour, while recycling center b processes aluminum at a rate of 2 tons per week. Assuming that both centers operate all day every day, which center processes aluminum faster, and why?
Answer:
Center a processes it faster
Step-by-step explanation:
Center B math: 2 tons as pounds is 4000 pounds.
4000/7=571.43 pounds a day
571.43/24=23.81 pounds a hour
23.81 pounds per hour is less than 100 pounds an hour. so center a is the faster one.
Answer:
Center A process aluminium faster
Because
Center A process 8.4 Tons of aluminium per week while center B processes 2 tons per week
Step-by-step explanation:
Topic: Unit Conversion
Given
Center A Rate of Processing Aluminium
A = 100 pounds per hour
Center B Rate of Processing Aluminium
B = 2 tons per week
To solve this question, the following assumptions will be made
Both centers operate 24 hours a dayBoth centers operate 7 days a weekHaving said that, the first step is to make conversions.
We either convert pounds to tons or tons to pounds.
Converting Center A Rate of Processing Aluminium from Pounds to Tons
1 Pound = 0.0005 Tons
So, 100 Pounds = 0.0005 * 100
100 Pounds = 0.05 Tons.
So, Center A Rate of Processing Aluminium is 0.05 Tons per hour
Before we make comparison, both must be in the same unit.
i.e. either in Tons per hour or Tons per units.
Converting Center A Rate of Processing Aluminium from Tons per hour to Tons per week
There are 24 hours a day;
So, Center A Rate of Processing Aluminium is 0.05 Tons/hr* 24 hr/day
Converting Center A Rate of Processing Aluminium is 1.2 Tons / day
There are 7 days a week;
So, Center A Rate of Processing Aluminium is 1.2 Tons/ day * 7 days / week
Converting Center A Rate of Processing Aluminium is 8.4 Tons / week
At this point, we have the following
Center A Rate of Processing Aluminium = 8.4 Tons / week
Center B Rate of Processing Aluminium = 2 tons per week
By Comparison,
8.4 Tons per week is greater than 2 tons per week; So, Center A process aluminium faster
Bridgette made a graph of her neighborhood on a coordinate grid. The points A(-2, 3), B(-2, -2), C(2, -2), and D(2, 3) represent her daily jogging path. She starts at her house, point A, then she jogs to points B, C, and D before returning home. If each space on the coordinate grid represents 1 block, how many blocks does she jog?
Answer:
[tex]\boxed{\text{18 blocks}}[/tex]
Step-by-step explanation:
Distance travelled on graph = AB + BC + CD + DA
AB = CD = (3 +2) = 5
BC = AD = 2 –(-2) = 4
Distance on graph = 2 × 5 + 2 × 4 = 10 + 8 = 18 spaces = 18 blocks
Bridgette jogs [tex]\boxed{\textbf{18 blocks}}[/tex]each day.
which values from the set{5,7,9,11,13} make the inequality w-4<8 true?
Answer:
5, 7, 9, 11
Step-by-step explanation:
Solve the inequality
w - 4 < 8 ( add 4 to both sides )
w < 12
w ∈ { 5, 7, 9, 11 }
{29, 29, 29, 28, 28, 27}
What is the best measure of center for this data set?
a. mean because there is an outlier
b. mode because there is an outlier
c. median because there is an outlier
d. mean or median because there is no outlier
find the total surface area of this cone. round to the nearest tenth(my last question of my homework and I keep getting it wrong)
Answer:
The surface area is approx. 1017.9 in^2.
Step-by-step explanation:
Total surface area of cone = πrl + πr^2. Since the radius is 12 in. and the slant height is 15 in, substitute 12 for r and 15 for l.
A = π(12)(15) + π(12)^2
= 180π + 144π
= 324π in^2
≈ 1017.9 in^2
Hope this helps!
find the surface area please. teacher checks soon
Answer:
Surface Area= 144
Step-by-step explanation:
To find the area of the triangle you would multiply the base times the height and divide it by 2. 9x6/2=27. For one triangle the area is 27. Since there are 4 you would multiply it by 4. 27x4= 108. This will give you 108. Now all you need to do is add the square which is 6x6= 36. 108+36=144.
help 10 points for correct answer asap
Answer:
Final answer is [tex]S_n=565.5[/tex].
Step-by-step explanation:
Given that [tex]a_1=12[/tex], [tex]a_n=75[/tex], and [tex]n=13[/tex].
Using those values, we need to find the value of [tex]S_n[/tex].
Plug these values into sum formula :
[tex]S_n=\frac{n}{2}\left(a_1+a_n\right)[/tex]
[tex]S_n=\frac{13}{2}\left(12+75\right)[/tex]
[tex]S_n=\frac{13}{2}\left(87\right)[/tex]
[tex]S_n=\frac{1}{2}\left(1131\right)[/tex]
[tex]S_n=565.5[/tex]
Hence final answer is [tex]S_n=565.5[/tex].
Which expression can be used to find 80% of 20
When you say Percent, you really mean per 100. So percentage is the result you get when multiplying a quantity by a percent. To find 80% of 20, we can use the following expression:
[tex]20\times \frac{80}{100}=16[/tex]
That is the product of 80 and 20 divided by 100, which is 16.
Answer:
The correct answer is
80% of 20 = 16
Step-by-step explanation:
points to remember
x% of y is given by
(x/100) * y
To find 80% of 20
Let 'x' be the 80% of 20 then we can write,
x = (80/100) * 20
x = (8/10) * 20
= 8 * 2 = 16
Therefore 80% of 20 is 16
The correct answer is 16
HELP ME PLEASEEE ASAPPPPPPPP!
Answer: upper quartile - 163
Lower quartile - 184
Step-by-step explanation:
97,163,169,175,184,199
[97,163,169] [175,184,199]
Upper. Lower.
163. 184.
Answer: 102
Step-by-step explanation: get the largest and smallest number which is 199 and 97 then subtract then 199-97 which you get 102 :D
Evaluate the cube root of 125/1000
Answer:
5/10
Step-by-step explanation:
The cube root of 125 is 5 and the cube root of 1000 is 10.
Final answer:
The cube root of 125/1000 simplifies to 5/10 or 0.5. This is determined by taking the cube root of both the numerator and the denominator separately, or by understanding properties of exponents and simplification of fractions.
Explanation:
To evaluate the cube root of 125/1000, we can simplify this expression by looking for cube roots of the numerator and the denominator separately. The cube root of 125 is 5 because 5³ equals 125. Similarly, the cube root of 1000 is 10 because 10³ equals 1000. Therefore, the cube root of 125/1000 is 5/10, which simplifies to 1/2 or 0.5.
Another way to approach this is by using the fact that 125 is a “125–like” number, which helps us recognize that 125 is one eighth of 1000, as 1000 multiplied by the reciprocal of 8 (which is 1/8) is 125. This intuitive understanding confirms that the cube root of 125/1000 simplifies to a small number like 0.5.
What is the value of x in the solution to the system of equations below?
2x + y = 1
2x + 3y = 11
a.) x = - 2
b.) x = 3
c.) x = - 1
d.)x = 5
Answer:
A) X=-2
Step-by-step explanation:
by multiplying the first term by -3 then -6X-3y=-3
and 2X+3y=11
then by adding = -4X=8
then X=8/-4=-2
The value for x in the given system of equations is found by using the method of elimination, resulting in x = -2. The value of y was found first, namely y = 5, and was then substituted into the first equation to find x.
Explanation:The system of equations given is:
2x + y = 1 2x + 3y = 11To find the value of x, we can use the method of elimination or substitution. Let’s use elimination. First, subtract the first equation from the second.
That gives us: 2x + 3y - (2x + y) = 11 - 1
Which simplifies to: 2y = 10
Then divide both sides by 2: y = 5
Now substitute y = 5 into the first equation: 2x + 5 = 1, which simplifies to 2x = -4, and lastly x = -2.
So the solution for x in the system is x = -2 (option a.).
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The figure above shows a store’s supply-demand graph for lawn chairs if the stores make $800 by selling lawn chairs which of the following is possible valid price for them?
a.) $50
b.) $40
c.) $25
d.) $20
Answer:
d.) $20
Step-by-step explanation:
Answer: Option 'b' is correct.
Step-by-step explanation:
Since we have given the figure showing store's supply demand graph for lawn chairs.
Profit made by selling lawn chairs by the store = $800
Using the graph , we conclude that
Demand curve and supply curve intersect at (25,40)
Here, y- axis denotes the price of commodity.
x - axis denotes the quantity of commodity.
So, the possible valid price for them would be $ 40.
Hence, Option 'b' is correct.
ANSWER ASAP Which system of linear inequalities is represented by the graph
X+2y<4; 2y<-x+4; y<(-x/2)+2
Option 3
what is the slope of line that passes through the points (8, -9) and (14, -9)
Answer:
Step-by-step explanation:
[tex]\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{14}~,~\stackrel{y_2}{-9}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-9-(-9)}{14-8}\implies \cfrac{-9+9}{6}\implies \cfrac{0}{6}\implies 0[/tex]
2) Jamie has twice as much money as Kristen. Together they have $36. How much money does each have?
Answer:
jamie has 24 and kristen is 12
Step-by-step explanation:
jamie is twice kristan which is 12+12
then 12 puls 24 is 36
For this case we have to:
Let x be the variable that represents the amount of money Jamie has.
Let y the variable that represents the amount of money that Kristen has
We have to:
[tex]x = 2y\\x + y = 36[/tex]
We substitute the first equation in the second:
[tex]2y + y = 36\\3y = 36\\y = \frac {36} {3}\\y = 12[/tex]
Looking for the value of x:
[tex]x = 2y\\x = 2 (12)\\x = 24[/tex]
Answer:
So, Jaime has $ 24 and Kristen has $ 12.
A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is (x with a line over it), while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question.
Confidence Level. 90%. 95%. 99%
z*-score. 1.645. 1.96. 2.58
Answer:
the answer is the (1.645 over root of n) on e 2020
Step-by-step explanation:
Answer:The answer is D
Step-by-step explanation: Hope this helps
What is the slop of the line y = 3
3/1 is the slope of the line
Answer:
the slope of y = 3 is 0
Step-by-step explanation:
we can use the acronym VUX/HOY to remind us about the properties of a certain line
Vertical line
Undefined slope
X axis
VUX means that a line passing x = b will have an undefined slope and will be a vertical line
Horizontal line
0 slope
Y axis
HOY means that a line passing through y = b will have a slope of 0 and will be a vertical line
Simplify the expression. (0.4x10^-6)(0.7x10^-2)
Answer:
2.8 · 10^(-9)
Step-by-step explanation:
I'd suggest you do this problem through two separate multiplications:
First, 0.4·0.7 = 0.28, or 2.8 · 10^(-1)
Second, 10^(-6) · 10^(-2) = 10^(-8), and so the final result is
2.8 · 10^(-1) · 10(-8) = 2.8 · 10^(-9)
Please note: negative exponents (such as -9, above) should be enclosed in parentheses for added clarity.
Also this one as well :) I’m struggling pls help
Answer:
A,C,E
Step-by-step explanation:
x+4 6
------- ÷ ---------
3 x
Copy dot flip
x+4 x
------- * --------- (A)
3 6
Reversing the order
x x+4
------- * --------- (C)
6 3
x(x+4)
------------
18
x^2+4x
--------------(E)
18
The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is
16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed
with the radius and the height of the cone.
(a) Sketch the roof of the castle tower. Label the known lengths as described and label the
unknown length as x.
(b) What is the slant height of the roof?
HOPE THIS WILL HELP YOU
look at the picture and plzz help me and also pick from the boxed sentences
The answers are:
3. Addition property of equality
4. [tex]6x-7+7=12+7[/tex] - Simplification
7. [tex]x=\frac{19}{6}[/tex]
Why?To solve the problem, we need to start with the result of the second step:
[tex]6x-7=12[/tex]
So,
For the step 3:
Then, for the 3rd step, we have to apply the addition property of equality.
The addition property of equality states that if we add a term to one side of the equality, we need to add it to the other side of the equality, in order to not alterate the equality.
Then, applying the property, we have:
[tex]6x-7=12[/tex]
Adding 7 to both sides, we have:
[tex]6x-7+7=12+7[/tex]
For the step 4:
Now, for the 4th step, we have to simplify the expression:
[tex]6x-7+7=12+7[/tex]
Then, simplifying, we have:
[tex]6x=19[/tex]
For the step 7:
Simplificating, we divide each side of the equality by 6:
[tex]\frac{6x}{6}=\frac{19}{6} \\\\x=\frac{19}{6}[/tex]
Have a nice day!
!!!please help!!!
The diagram below shows the dimensions of Tessa’s garden.
A) What is the perimeter, in feet, of Tessa’s garden? Show or explain all your work.
B) What is the area, in square feet, of Tessa’s garden? Show it explain all your work.
C) Tessa decided that she liked the shape of her garden but wanted to have 2 times the area. She drew a design for a garden with every dimension multiplied by 2. Explain the error in Tessa’s design.
See photo
Perimeter = 525.66 ft
Area = 10913.27 ft2
Find the slope of each line
Answer:
10
Step-by-step explanation:
You have to go up 10 places to get from the first point to the second
You also have to go 1 place to the right
Since the slope is Y/X, the slope of this line is 10/1
a sociologist develops a test to measure attitudes towards public transportation and 27 randomly selected subjects are given the test.their mean score is 76.2 and their standard deviation is 21.4. construct the 95% confidence interval for the mean score of all such subjects
Answer:
The 95% confidence interval for the mean score is:
[tex]\mu[/tex] ∈ [tex](67.73,\ \ 84.67)[/tex]
Step-by-step explanation:
We want to estimate the population mean, that is, the average score of all the subjects.
An estimator for the population mean μ is [tex]{\displaystyle {\overline {x}}}[/tex]
Since the sample size is [tex]27 <30[/tex] then we use the statistic [tex]t_{\frac{\alpha}{2}}[/tex] with [tex]27-1 = 26[/tex] degrees of freedom
The confidence interval for the mean is:
[tex]({\displaystyle {\overline {x}}} + t_{\frac{\alpha}{2}}\frac{S}{\sqrt{n}},\ \ {\displaystyle {\overline {x}}} - t_{\frac{\alpha}{2}}\frac{S}{\sqrt{n}})[/tex]
Where
[tex]{\displaystyle {\overline {x}}}=76.2[/tex] is the average score of the sample
[tex]S=21.4[/tex] is the standard deviation of the sample
[tex]n= 27[/tex] is the sample size
[tex]t_{\frac{\alpha}{2}} = 2.056[/tex] for a confidence level of 95% and 26 degrees of freedom
Then confidence interval is
[tex](76.2 + 2.056\frac{21.4}{\sqrt{27}},\ \ {76.2 - 2.056\frac{21.4}{\sqrt{27}})[/tex]
[tex](76.2 + 8.467,\ \ 76.2 - 8.467)[/tex]
[tex]\mu[/tex] ∈ [tex](67.73,\ \ 84.67)[/tex]
The 95% confidence interval for the mean score of attitudes towards public transportation is (68.13, 84.27), calculated using the formula for a confidence interval.
Explanation:In this scenario, we would use the formula for a 95% confidence interval, which is the sample mean ± (1.96 * (standard deviation / √n)). In this case, n is 27 (the sample size), the sample mean is 76.2, and the standard deviation is 21.4.
Firstly, calculate the standard error by dividing the standard deviation by the square root of n:
SE = 21.4 / √27 ≈ 4.12
Then multiply the standard error by 1.96:
1.96 * SE ≈ 1.96 * 4.12 ≈ 8.07
Finally, add and subtract this value from the sample mean to get the confidence interval:
76.2 ± 8.07 gives an interval of (68.13, 84.27).
So, we can be 95% confident that the true population mean of attitudes towards public transportation lies between 68.13 and 84.27.
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Point B is the center of a circle, and AC is a diameter of the circle. Point D is a point on the circle different from A and C. If angle BDA = 20 degrees, then what is the measure of angle CBD?
Answer choices:
a) 70 degrees
b) 120 degrees
c) 140 degrees
d) 40 degrees
Answer:b
Step-by-step explanation:
in triangle ABC the measure of A is 33° and the measure of C is 90° . what is the measure of B
Answer:
57°
Step-by-step explanation:
ALL angles in a triangle add up to 180°
SO, if we know the sum of two angles which is 123° (why: 33+90=123), all we have to do is subtract this number from 180 to get the measure of the 3rd angle. Which in this case is 57°
The measure of angle B will be 57° for the given triangle.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right angle triangle, equilateral triangle, and much more.
The sum of all three interior angles of any triangle is 180°.
So,
A + B + C = 180°
Given,
A = 33° and C = 90°
33° + B + 90° = 180°
B = 180 - (90 + 33)
B = 180° - 123°
B = 57°
Hence, The measure of angle B will be 57° for the given triangle.
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What expression is equivalent to? Screenshots attached. Please help!
Answer:
the correct option is C i.e. [tex]8x^4yz^4\sqrt{2yz}[/tex]
Step-by-step explanation:
We need to solve the expression :
[tex]\sqrt{128x^8y^3z^9}[/tex]
Factors of 128 are: 2x2x2x2x2x2x2
and we know √ = 1/2
and √a.b = √a.√b
Solving:
[tex]=\sqrt{128x^8y^3z^9}\\\\=\sqrt{128} \sqrt{x^8} \sqrt{y^3} \sqrt{z^9}\\=\sqrt{2x2x2x2x2x2x2}\sqrt{x^8} \sqrt{y^2.y} \sqrt{z^8.z}\\=\sqrt{2^2x2^2x2^2x2}\sqrt{x^8} \sqrt{y^2.y} \sqrt{z^8.z}\\=(2^2)^{1/2} (2^2)^{1/2}(2^2)^{1/2} (2)^{1/2} (x^8)^{1/2} (y^2)^{1/2} (y)^{1/2} (z^8)^{1/2} z^{1/2}\\=2.2.2.(2)^{1/2}x^4y(y)^{1/2}z^4(z)^{1/2}\\=8x^4yz^4\sqrt{2yz}[/tex]
So, the correct option is C i.e. [tex]8x^4yz^4\sqrt{2yz}[/tex]