Factor the polynomial expression 27x3−8 27 x 3 − 8 .

Answer:

Order of symmetry = 1

Step-by-step explanation:

First of all we will define rotational symmetry.

Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.

The order of rotational symmetry is how many times it matches the original shape during the rotation.

The given shape, when rotated will only have the shape like original shape after one complete rotation so the order of symmetry is one ..

Answer:

.75

Step-by-step explanation:

Answer:

she can make 50 different selections!

Step-by-step explanation:

To find the different selections that can be made, we use the formula:

nCr = n! / r! * (n - r)!. Where 'n' represents the number of items available and 'r' represents the nuber of items being chosen

In this case:

'n' equals 10 and 'r' equals 2. Therefore:

[tex]10C_{2} = \frac{10!}{2!(10-2)!} = \frac{10!}{2!8!} = \frac{90}{2} =50[/tex]

So she can make 50 different selections!

Answer: 45

Step-by-step explanation:

The combination of n things taking r at a time is given by :-

[tex]C(n;r)=\dfrac{n!}{(n-r)!}[/tex]

Given : Lucy Furr must supply 2 different bags of chips for a party.

She finds 10 varieties at her local grocer.

Then the number of different selections she can make is given by :-

[tex]C(10;2)=\dfrac{10!}{2!(10-2)!}\\\\=\dfrac{10\times9\times8!}{2\times8!}=\dfrac{90}{2}=45[/tex]

Hence, the number of different selections she can make= 45

Answer:

D. 35 degrees.

Step-by-step explanation:

125 = p + 90 (by the external Angle of a Triangle theorem).

p = 125 - 90

p = 35 degrees (answer).

Answer:

35 degrees

Step-by-step explanation:

Ok so that angle that has the 125 degree is adjacent to an angle inside the triangle. These adjacent angles are actually supplementary because they are formed by a straight-edge. So the angle inside adjacent to the 125 degree angle is 180-125=55 degrees.

Same logic applies to angle adjacent to the 90 degree angle. The angle adjacent to the 90 degree angle is also supplementary to the 90 degree angle. So 180-90=90 degrees for the other inside angle next to the 90 degree angle.

So the figure formed here is a triangle.  The angles in this triangle should add up to be 180 degrees.  So we have the equation 90+55+p=180.

Let's solve this by first simplifying the 90+55 part!

145+p=180

Subtract 145 on both sides:

p=180-145

Simplify.

p= 35 degrees

Answer:

5/9 from these categories can only be classified as rational and real.

Step-by-step explanation:

Natural numbers are counting numbers.  People don't ever say the number 5/9 when counting people. So 5/9 is not natural.

Whole numbers are counting numbers plus also including 0.  So we already said 5/9 is not natural and it is definitely not 0 so 5/9 is not whole.

Integers are whole numbers plus the opposite of the whole numbers.  5/9 is not whole and it is certainly not negative so we don't need to even consider if is the opposite of a whole number.

Rational numbers are numbers that can be expressed as a fraction where the top and bottom are integers. 5/9 is a rational number because 5 and 9 are whole numbers which are integers.

Irrational numbers are numbers that aren't rational. Our number 5/9 is rational so it isn't irrational.

Real numbers are any number that isn't imaginary. Doesn't include the imaginary unit. Our number doesn't include the imaginary unit so it is real.

Answer:

d. Rational Numbers

f. Real Numbers

Step-by-step explanation:

The number shown is 5/9

Let us see the options one by one

a. Natural numbers

Natural numbers consists of counting from 1 to infinity. The fractions are not included in the natural numbers hence it will not be the correct answer.

b. Whole numbers

Whole numbers is the set of natural numbers along with zero so it is also not the right answer.

c. Integers

Integers are combination of negative and positive whole numbers hence it is also not correct.

d. Rational numbers

Rational numbers are numbers which can be written in the form of p/q where p and belong to integers and q is not equal to zero. It is correct as the number is 5/9 where 5 is also an integer and 9 is also an integer. Also 9 ≠ 0 so 5/9 is a rational number.

e.  As the number is rational, it cannot be irrational

f. Real numbers

As real numbers is the set of all rational and irrational numbers, 5/9 will also be a part of the set .. Hence it is also correct ..

Answer:

Option A is correct.

Step-by-step explanation:

The formula used for finding the volume of right cone is:

Volume of Right cone = (1/3)π.r².h

We need to find altitude i.e h

Volume of cone=V = 8579 m^3

Radius=r = 16m

Altitude =h =?

Putting values,

8579 = (1/3) * 3.14 * (16)^2*h

8579 = 1/3 * 3.14 * 256 *h

8579 = 267.95 * h

=> h = 8579/267.95

h = 32.0 m

So, Altitude of right cone is 32.0 m

Option A is correct.

Answer:

4.04 m

Step-by-step explanation:

El arbol y el suelo forman un angulo de 90°. Son los catetos de un triangulo rectangulo.

Los rayos solares forman un angulo de 60° con el suelo y forman la hipotenusa del triangulo.

Se tiene un triangulo rectangulo de angulos de 30°-60°-90°.

En este genero de triangulo, el cateto mayor mide [tex] \sqrt{3} [/tex] veces el cateto menor.

cateto menor = [tex] \dfrac{7}{\sqrt{3}} [/tex]

[tex] = \dfrac{7\sqrt{3}}{3} [/tex]

[tex] = 4.04 ~m [/tex]

The length of the shadow of the tree would be -

s = {7/√3}.

Given is that at a certain time of day the sun's rays make an angle of 60° with the ground.

Assume that the length of the shadow is [x] meters. Using the trigonometric ratios, we can write -

tan (60) = (height of tree {h})/(length of shadow {s})

sin(60)/cos(60) = (height of tree)/(length of shadow)

(√3/2)/(1/2) = {7/s}

√3/2 x 2 = 7/s

√3 = 7/s

s = {7/√3}

Therefore, the length of the shadow of the tree would be -

s = {7/√3}.

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{The question in english is -

At a certain time of day the sun's rays make an angle of 60° with the ground. What shade will the 7 m tall tree cast?}

Answer:

The length of the third side could be all real numbers greater than 2 units and less than 16 units

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

so

Applying the triangle inequality theorem

Let

x ------> the length of the third side

we have

First case

1) 7+9 > x

16 > x

Rewrite

x< 16 units

Second case

2) 7+x > 9

x > 9-7

x > 2 units

therefore

The solution for the third side is the interval

(2,16)

All real numbers greater than 2 units and less than 16 units

Answer:

Step-by-step explanation:

[tex]\sqrt{\dfrac{896z^{15}}{225z^6}}=\dfrac{xz^4}{15}\sqrt{14z}\\\\\sqrt{\dfrac{896z^{15}}{225z^6}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\sqrt{\dfrac{(64)(14)z^{15-6}}{225}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\dfrac{\sqrt{64}\cdot\sqrt{14}\cdot\sqrt{z^9}}{\sqrt{225}}=\dfrac{8\cdot\sqrt{14}\cdot\sqrt{z^{8+1}}}{15}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{z^8z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]

[tex]=\dfrac{8\sqrt{14}\cdot\sqrt{z^8}\cdot\sqrt{z}}{15}=\dfrac{8\sqrt{14}\cdot\sqrt{z^{4\cdot2}}\cdot\sqrt{z}}{15}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{(z^4)^2}\cdot\sqrt{z}}{15}\qquad\text{use}\ (\sqrt{a})^2=a\\\\=\dfrac{8\sqrt{14}\cdot z^4\cdot\sqrt{z}}{15}=\dfrac{8z^4\sqrt{14}\cdot\sqrt{z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{8z^4\sqrt{14z}}{15}[/tex]

[tex]\dfrac{8z^4\sqrt{14z}}{15}=\dfrac{xz^4\sqrt{14z}}{15}\iff x=8[/tex]

[tex]|\Omega|=6^6\\|A|=6\cdot 5^5\\\\P(A)=\dfrac{6\cdot5^5}{6^6}=\dfrac{5^5}{6^5}=\dfrac{3125}{7776}\approx40.2\%[/tex]

The probability that a face with a 6 comes up exactly once will be 0.40.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

A number cube has 6 faces, numbered from 1 to 6.

If the cube is rolled six times.

Then the probability that a face with a 6 comes up exactly once will be

The total number of the event will be

Total event = 6⁶

Total event = 46656

Favorable event = 6 x 5⁵

Favorable event = 18750

Then the probability will be

P = 18750 / 46656

P = 3125 / 7776

P = 0.40

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Answer:

Natural numbers = {1,2,3,4,5…} Answer 1: A is the set of Natural numbers between 1 and 5 inclusive. Answer 2: A is the set of Natural numbers less than 6.

Step-by-step explanation:

Answer:

n = 1, 2, 3, 4

Step-by-step explanation:

Natural numbers are any integers (whole numbers) that are positive.

In this case, all natural number (n) is less than (<) 5

n < 5 is your equality, but in reality it looks like: 0 < n < 5

The numbers that can fit into your problem is n = 1 , 2, 3, 4

n = 1, 2, 3, 4 is your answer.

~

Answer:

D. 10i √(3)

Step-by-step explanation:

√(-300)

We know sqrt (ab) = sqrt(a) sqrt(b)

sqrt(-300) = sqrt(-3) sqrt(100)

                 = sqrt(-1) sqrt(3) sqrt(100)

The sqrt(-1) =the imaginary number 1 and sqrt(100) =10

                  = i * sqrt(3) * 10

                    =10i sqrt(3)

Answer:

Domain is all real numbers also known as [tex](-\infty,\infty)[/tex] in interval notation.

[tex]f(x)=\sqrt[3]{x-1}[/tex]?

Step-by-step explanation:

If your function is [tex]f(x)=\sqrt[3]{x-1}[/tex] then the domain is all real numbers because you can cube root any real number.

If x is a real number, then x-1 is a real number.

So if you cube root (x-1) for any x then you still get a real number back.

Now if it was a square root, that is when we can run into some problems.

Answer: -infinity and positive infinity

Step-by-step explanation: It's either a on your test or two zero's that look twisted :)

Answer:

Option B [tex]28.53\ units^{2}[/tex]

Step-by-step explanation:

The area of quadrilateral ABCD is equal to the area of triangle ABD plus the area of triangle ADC

we know that

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  

a,b,c be the lengths of the sides of a triangle.  

The area is given by:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]

where

p is half the perimeter

[tex]p=\frac{a+b+c}{2}[/tex]

step 1

Find the area of triangle ABD

we have

[tex]a=AB=2.89\ units[/tex]

[tex]b=BD=8.59\ units[/tex]

[tex]c=DA=8.6\ units[/tex]

Find the half perimeter p

[tex]p=\frac{2.89+8.59+8.6}{2}=10.04\ units[/tex]

Find the area

[tex]A=\sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex]

[tex]A=\sqrt{10.04(7.15)(1.45)(1.44)}[/tex]

[tex]A=\sqrt{149.89}[/tex]

[tex]A=12.24\ units^{2}[/tex]

step 2

Find the area of triangle ADC

we have

[tex]a=AC=4.3\ units[/tex]

[tex]b=AD=8.6\ units[/tex]

[tex]c=DC=7.58\ units[/tex]

Find the half perimeter p

[tex]p=\frac{4.3+8.6+7.58}{2}=10.24\ units[/tex]

Find the area

[tex]A=\sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex]

[tex]A=\sqrt{10.24(5.94)(1.64)(2.66)}[/tex]

[tex]A=\sqrt{265.35}[/tex]

[tex]A=16.29\ units^{2}[/tex]

step 3

Find the total area

[tex]A=12.24+16.29=28.53\ units^{2}[/tex]

Answer:

B.) 28.53 units²

Step-by-step explanation:

I got it correct on founders edtell

Answer:

11 meters

Step-by-step explanation:

Using the Pythagorean Theorem

a^2 + b^2 = c^2

a^2 + 60^2 = 61^2

a^2 + 3600 = 3721 (subtract 3600 from both sides)

a^2 = 121 (square root both sides so a^2 becomes a)

a = 11

Answer:

Step-by-step explanation:

This problem models a right rectangle, where the hypothenuse is the length of the string, and the legs are the height and the horizontal distance. So, to find the answer, we just have to use the pythagorean theorem

[tex]a^{2}=b^{2}+c^{2}[/tex]

Where

[tex]a=61;b=60;c=x[/tex]

Replacing and solving for [tex]x[/tex], which is the height

[tex]a^{2}=b^{2}+c^{2}\\61^{2}=60^{2}+x^{2} \\x^{2}=61^{2}-60^{2}\\x=\sqrt{3721-3600}=\sqrt{121}=11[/tex]

Therefore, assuming there is no slack in the string, the height of the kite from the ground is 11 meters.

Answer:

15x < 200; x < 13.33; the maximum price for a pair of shorts

Step-by-step explanation:

1. Set up the inequality

Let x = price of a pair of shorts. Then

 15x = price of shorts for the team

You have one condition:

15x < 200

2. Solve the inequality

[tex]\begin{array}{rcl}15x & < & 200\\\\x & < & \dfrac{200}{15}\\\\x & < & \mathbf{13.333}\\\end{array}[/tex]

3. Meaning of solution

The solution represents the maximum price the coach can pay for a pair of shorts.

If the coach pays $13.33 per pair, the total cost for the team will be $199.95, and the condition is satisfied.

Answer: The coach may spend up to $13.33 per pair of shorts.

Step-by-step explanation:

Hi, to answer this question we have to write an inequality with the information given:

So, we have to multiply the number of shorts by the price of each one, we will represent the price with the variable "x".(15x)

That cost must be equal or less to 200.

Mathematically speaking

15 x ≤ 200

Solving for x

x ≤200/15

x ≤ 13.33

This solution represents that the coach may spend up to $13.33 per pair of shorts.

Feel free to ask for more if needed or if you did not understand something.

Answer:

y = -8

Step-by-step explanation:

It is given that,

-x - y = 7  ---(1)

x - y = 9  ---(2)

To find the solution

Add eq (1) and eq(2) we get

-x - y = 7  ---(1)

x - y = 9  ---(2)

0 - 2y  = 16

y = 16/(-2) =  -8

Substitute the value of y in eq(1)

-x - y = 7  ---(1)

-x - -8 = 7

-x + 8 = 7

x = 8 - 7 = 1

Therefore x = 1 and y = -8

Answer:

Step-by-step explanation:

Rewrite -x-2y= -10 as  -2y= x - 10 and then as y = (-1/2)x + 5.

Then choose any 3 x values and find the corresponding y values using this formula.  For example:

 x     y = (-1/2)x + 5              (x, y)

-----   --------------------            ---------

 0                   5                    (0, 5)

-4       (-1/2)(-4) + 5 = 7         (-4, 7)

  6      (-1/2)(6) + 5 = 2          (6, 2)

Plot these three points and then draw a line through them.  

Answer:

0,5  2,6  4,7  

Step-by-step explanation:

You have to solve the equation by keeping y on its own. The equation is

y=-1/2x-5

Coordinates are:

0,5  2,6  4,7  

Answer:

3 5/6

Step-by-step explanation:

3 1/2 plus 2 2/3 equals 6 1/6. 10 minus 6 1/6 equals 3 5/6. So they still need to lose 3 5/6 pounds to reach their go of losing 10 pounds.

let's firstly convert the mixed fractions to improper fractions, and then subtract.

[tex]\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{goal}}{10}-\stackrel{\textit{first week}}{\cfrac{7}{2}}-\stackrel{\textit{second week}}{\cfrac{8}{3}}\implies \cfrac{10}{1}-\cfrac{7}{2}-\cfrac{8}{3}\implies \stackrel{\textit{using an LCD of 6}}{\cfrac{(6)10-(3)7-(2)8}{6}} \\\\\\ \cfrac{60-21-16}{6}\implies \cfrac{23}{6}\implies 3\frac{5}{6}[/tex]

Answer:

C

Step-by-step explanation:

O x² + 9x -3x – 27 = (x + 9)(x – 3)

x² + 6x - 27 = (x + 9)(x - 3)

Answer:

Area = [tex]3y^2 - 4y - 4[/tex] units square.

Perimeter = 8y units.

Step-by-step explanation:

Area of a rectangle = length * width.

Perimeter of a rectangle = 2*(length + width).

It is given that length = y−2 units and width = 3y+2 units. To find the area and the area of the rectangle in terms of y, simply put the length and the width in the above area and perimeter equations.

Area = length * width = (y-2)*(3y+2).

Expanding the expression gives:

Area = 3y^2 + 2y - 6y - 4 = (3y^2 -4y - 4) units square.

Similarly,

Perimeter = 2*(length + width) = 2*(y-2 + 3y+2) = 2*4y = 8y units.

Therefore, the expression for the area and the perimeter of the given rectangle is ([tex]3y^2 - 4y - 4[/tex]) units square and (8y) units respectively!!!

Answer:

4x^2/4x^2-x-3

Step-by-step explanation:

boomchakalaka

The quotient is 4x²/4x²-x-3.

In mathematics, a quotient is a quantity produced with the aid of the department of numbers.

The quotient is the solution acquired whilst we divide one range by using every other. for example, if we divide the quantity 4 by means of 2, we get the end result as 2, that's the quotient.

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Answer:

There were 12 + 28 = 40 pieces of fruit in the basket.

Step-by-step explanation:

Suppose there were x oranges and y grapefruit.

Then we have

1 /3 x =  4

x = 4*3 = 12.

1/4 y = 7

y = 7*4 = 28.

Answer:

0.00083

Step-by-step explanation:

200*300*30=1800000

1500/1800000=0.00083

The cost per cubic foot of the storage space is approximately $0.00083 per cubic foot. Hence the correct option is D.

To find the cost per cubic foot of the storage space, we need to calculate the total cubic footage of the space and then divide the monthly cost by that number. The storage space measures 200 ft x 300 ft x 30 ft, so the total volume is:

Total Volume = length times width times height

= 200 ft x 300 ft x 30 ft

= 1,800,000 cubic feet

Now, we calculate the cost per cubic foot:

Cost Per Cubic Foot = Total Monthly Cost / Total Volume

= $1500 / 1,800,000 cubic feet

= $0.00083 per cubic foot (rounded to five decimal places).

Answer:

f=-5

Step-by-step explanation:

1) Add 12 to both sides

2) You should get f=-5

Answer:

[tex]\huge \boxed{F=-5}\checkmark[/tex]

Step-by-step explanation:

First, switch sides.

[tex]\displaystyle F-7=-12[/tex]

Then, add by 7 from both sides of equation.

[tex]\displaystyle F-7+7=-12+7[/tex]

Simplify, to find the answer.

[tex]\displaystyle -12+7=-5[/tex]

[tex]\huge \boxed{F=-5}[/tex], which is our answer.

Answer:

x = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Given

9 - 3x = 7 ( subtract 9 from both sides )

- 3x = - 2 (divide both sides by - 3 )

x = [tex]\frac{-2}{-3}[/tex] = [tex]\frac{2}{3}[/tex]

[tex]\huge{\boxed{x=\frac{2}{3}}}[/tex]

Add [tex]3x[/tex] on both sides. [tex]9=7+3x[/tex]

Subtract 7 from both sides. [tex]2=3x[/tex]

Divide both sides by 3. [tex]\boxed{\frac{2}{3}}=x[/tex]

Answer:

B. Unimodal-Skewed

Step-by-step explanation:

A distribution is called unimodal if it has only one hump in the histogram.

A symmetric distribution is equally divided on both sides of the highest hump.

The given histogram has only one hump at 4 and as it is not symmetrically distributed, it is skewed.

So the correct answer is:

B. Unimodal-Skewed ..

Answer:

B. Unimodal Skewed

Step-by-step explanation:

The Histogram given in figure has one peak and it is skewed to the right So, it is Right Skewed Unimodal Histogram.

Moreover, Unimodal means the distribution has one peak, Skewed means this peak is present in either the left or right side of the center of the distribution.

Option A is incorrect because the given histogram is not symmetric, it is skewed distribution.

Option C can't be taken because uniform means the size of bars is approximately same for the given distribution.

Options D & E is not correct because the given distribution is not Bimodal it has only one peak.

Answer:

[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]

Explanation

The directrix y=7, is above the y-value of the focus. The parabola must will open downwards.

Such parabola has equation of the form,

[tex] {(x - h)}^{2} = - 4p(y - k)[/tex]

where (h,k) is the vertex.

The vertex is the midway from the focus to the directrix

The x-value of the vertex is x=-5 because it is on a vertical line that goes through (-5,-5).

The y-value of the vertex is

[tex]y = \frac{ 7 + - 5}{2} [/tex]

[tex]y = \frac{ 2}{2} = 1[/tex]

The equation of the parabola now becomes

[tex]{(x + 5)}^{2} = - 4p(y - 1)[/tex]

p is the distance from the focus to the vertex which is p=|7-1|=6

Substitute the value of p to get:

[tex]{(x + 5)}^{2} = - 4 \times 6(y - 1)[/tex]

[tex]{(x + 5)}^{2} = - 24(y - 1)[/tex]

We solve for y to get:

[tex]y = - \frac{1}{24} (x + 5) + 1[/tex]

Answer:

f(x) = −one twentyfourth (x + 5)2 + 1

Step-by-step explanation: