What is the square of 16

Answer:

The factorization of [tex]729x^{15} +1000[/tex] is [tex](9x^{5} +10)(81x^{10} -90x^{5} +100)[/tex]

Step-by-step explanation:

This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form [tex](a^{3} +b^{3} )[/tex] or [tex](a^{3} -b^{3})[/tex]. It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of [tex]729x^{15} +1000[/tex] by using the sum and difference of cubes factorization.

1.) We calculate the cubic root of each term in the equation [tex]729x^{15} +1000[/tex], and the exponent of the letter x is divided by 3.

[tex]\sqrt[3]{729x^{15}} =9x^{5}[/tex]

[tex]1000=10^{3}[/tex] then [tex]\sqrt[3]{10^{3}} =10[/tex]

So, we got that

[tex]729x^{15} +1000=(9x^{5})^{3} + (10)^{3}[/tex] which has the form of [tex](a^{3} +b^{3} )[/tex] which means is a sum of cubes.

Sum of cubes

[tex](a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})[/tex]

with [tex]a= 9x^{5}[/tex] y [tex]b=10[/tex]

2.) Solving the sum of cubes.

[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )[/tex]

[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)[/tex]

.

Answer:

the number of sheet available is 75, 000

you take the total number of pages available = 8 x 75,000

= 600,000 pages

then each notebooks contains 200 pages

= 600,000 / 200

= 3000 notebooks can be made

Step-by-step explanation:

Answer:

3000 notebooks

Step-by-step explanation:

75,000*8=600000

600000/200=3000

Answer:

Step-by-step explanation:

For this, both sides added together will need to equal 180°.

So you need to set up an equation: p+28+3p=180

Now, solve for p

p+28+3p=180

    -28 .       -28

p+3p=152

combine p            (the single p counts as 1, so add it to 3p to get 4p)

4p=152

/4 .   /4

p= 38

You get p is equal to 38.

Answer:

The volume of oblique cylinders is the same volume as a right cylinder of the same radius and height. The height of cylinder must be the perpendicular height, but as long as the radius and height are the same the volume does not change, which is why the same formula can be used for both oblique and right cylinder.

For skewed and right prism, base length and height does not change, volume for both is calculated by area times height.

multiply the bracket by 2

-2x+18-x

Negative and Negative= positive

=-3x+18

Answer:A

Answer:

The answer is A

Step-by-step explanation:

The answer is:

The area that the want to cover with new grass will be:

[tex]Area_{grass}=8x^{2} -12x-22[/tex]

If we want to calculate what is the ara of the region of the backyard that they want to cover with new grass, we need to calculate the area of the backyard, calculate the area of the swimming pool and its patio, and the last step is to subtract the area of the swimming pool and its patio to the total area of the backyard.

So, to calculate the areas, we need to use the following formula:

[tex]Area=Length*Width[/tex]

Also, we need to remember how the distributive property works, since we are going to need it.

We have that:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

We are given the following information:

For the backyard we have:

[tex]Length=3x-2\\Width=3x+1[/tex]

For the swimming pool and its patio:

Since there it's not mentioned, let be the first expression the length, and the second one, the width.

[tex]Length=x+4\\Width=x+5[/tex]

Then, calculating we have:

Backyard:

[tex]Area_{backyard}=(3x-2)*(3x+1)=9x^{2}+3x-6x-2=9x^{2}-3x-2[/tex]

Swimming pool and patio:

[tex]Area_{swimmingpool}=(x+4)*(x+5)=x^{2}+5x+4x+20=x^{2}+9x+20[/tex]

Now, calculating the area that they want to cover with new grass, we have:

[tex]Area_{grass}=Area_{backyard}-Area_{swimmingPool}\\\\Area_{grass}=(9x^{2}-3x-2)-(x^{2}+9x+20)\\\\Area_{grass}=9x^{2} -x^{2} -3x-9x-2-20\\\\Area_{grass}=8x^{2} -12x-22[/tex]

Hence, we have that the area that the want to cover with new grass will be:

[tex]Area_{grass}=8x^{2} -12x-22[/tex]

Have a nice day!

Answer:

Sample Response: Gerard determined that the squares of the two smaller sides did not equal the square of the longest side. The side lengths did not create a true statement of the Pythagorean theorem.

Gerard most likely came to the conclusion that the sides of the triangle do not conform to the Pythagorean Theorem.

Therefore, Gerard most likely came to the conclusion that the sides of the triangle do not conform to the Pythagorean Theorem.

Learn more about the Pythagorean Theorem on:

https://brainly.com/question/654982

Answer:

147

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

here a = 3 and d = 9 - 3 = 15 - 9 = 6, hence

[tex]a_{25}[/tex] = 3 + (24 × 6) = 3 + 144 = 147

Answer:

It's a - (minus) sign.

Step-by-step explanation:

This is because √9 is 3, and therefore 6-3=3.

Hope I helped :)

The distance between two points on a number line is found using the absolute value of their difference. For instance, the distance between 2 and 14 is 12 units, and the distance between -10 and 8 is 18 units.

The concept of absolute value is crucial when determining the distance between two points on a number line. This distance is represented by the difference in their values, disregarding which one is larger or whether they are positive or negative.

The expression for the distance is |2 - 14|. Evaluating this, we find |2 - 14| = |-12| = 12. Therefore, the distance between the numbers 2 and 14 on the number line is 12 units.

The expression for the distance is |-10 - 8|. Evaluating this, we find |-10 - 8| = |-18| = 18. Therefore, the distance between the numbers -10 and 8 on the number line is 18 units.

Answer:

Area of Trapezoid is 88 Units^2

Step-by-step explanation:

Area of trapezoid = (a+b)/2 * h

where a and b are lengths of each base and h is the height of trapezoid.

In the question given:

a= 17 (because a is the upper base and value will be 17)

b= 27 (because b is the lower base and value will be 17+5+5 = 27)

h= 4

Area of trapezoid = (a+b)/2 * h

                             = (17 +27)/ 2 * 4

                             = 22 * 4

                             = 88 Units^2

Area of Trapezoid is 88 Units^2

Answer:

80 inches

Step-by-step explanation:

8*10=80

Answer:

80 in.

Step-by-step explanation:

So we know that 1/8 is 10 in.

So to get 8/8 (Original length), we need to multiply 10 by 8, because 8 is the denominator.

10 in * 8 = 80 in.

Hope I beat Jarid lol

The correct anwser would be 56

The volume of the prism filled with 30 cubes with side lengths of 1/2 unit is 3.75 cubic units.

To calculate the volume of a cube with a side length of 1/2 unit, we use the formula V = s³, where s is the side length of the cube.

For a side length of 1/2 unit, the volume of one cube is V = (1/2)³ cubic units.

Therefore, the volume of one such cube is 1/8 cubic units. If the prism is filled with 30 such cubes, we multiply the volume of one cube by the number of cubes:

Total Volume = Number of Cubes × Volume of One Cube = 30 × 1/8 cubic units = 30/8, which simplifies to 3.75 cubic units.

Answer:

The surface area of the rectangular pyramid is [tex]SA=109.50\ m^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the rectangular prism is equal to the area of the rectangular base plus the area of the four triangular faces

so

[tex]SA=(8)(5)+2[14.75]+2[\frac{1}{2}(8)(5)][/tex]

[tex]SA=40+29.50+40[/tex]

[tex]SA=109.50\ m^{2}[/tex]

Answer:

109.5

Step-by-step explanation:

Answer: B=27

Step-by-step explanation:

10.8 x 5=54/2= 27

Answer:

26in.^2 the first choice

Step-by-step explanation:

Just did the QC

Answer:

the probability is very high 86% > 14%

Step-by-step explanation:

55+20+11= 86%/100% 100-86=14% chance there will not be any rain or lightning

hope this helps!!

Answer: Equivalent

Step-by-step explanation:

[tex]y=-\dfrac{1}{3}x+\dfrac{2}{3}\\\\\text{Multiply by 3 to clear the denominator: }3y = -x + 2\\\text{Add x to both sides: }x+3y=2\\\text{Multiply both sides by 2: }2x+6y=4[/tex]

When given a system of equations, the definitions of the solution are:

In the given system, the equations are the same which means they have INFINITE solutions --> The system is Consistent & Dependent = Equivalent.

Answer:

[tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69

Step-by-step explanation:

To solve this we are using the standard exponential growth equation:

[tex]f(t)=A(1+r)^t[/tex]

where

[tex]f(t)[/tex] is the final population after [tex]t[/tex] years

[tex]A[/tex] is the initial population

[tex]r[/tex] is the growth rate in decimal form

[tex]t[/tex] is the time in years

We know from our problem that the initial population is 5000, the final population is 10000, and the time is 10 years, so [tex]A=5000[/tex], [tex]f(t)=10000[/tex], and [tex]t=10[/tex].

Let's replace the values and solve for [tex]r[/tex]:

[tex]f(t)=A(1+r)^t[/tex]

[tex]10000=5000(1+r)^{10}[/tex]

Divide both sides by 5000

[tex]\frac{10000}{5000} =(1+r)^{10}[/tex]

[tex]2=(1+r)^{10}[/tex]

Take root of 10 to both sides

[tex]\sqrt[10]{2} =\sqrt[10]{(1+r)^{10}}[/tex]

[tex]\sqrt[10]{2} =1+r[/tex]

Subtract 1 from both sides

[tex]\sqrt[10]{2}-1=r[/tex]

[tex]r=\sqrt[10]{2}-1[/tex]

[tex]r=1.0718-1[/tex]

[tex]r=0.0718[/tex]

We can conclude that the growth rate of our exponential equation is [tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69

Answer:

4/21

Step-by-step explanation:

In this case, carry out the indicated operations from left to right:

8      1

---- * --- = 4/21

7       6

Step-by-step explanation:

I think the answer is x=-4,x=+6

The values of the x are +6 and -4. The values of the x are obtained by the factorization method.

They are mathematical formulas containing variables raised by non-negative integers, coefficient, and constants involving only addition, subtraction, multiplication, and non-negative exponentiation of variables.

The given expression is;

x²-2x-24= 0

By factorization;

x²-6x+4x-24=0

After taking common terms, we get ;

x²-6x+4x-24=0

x(x-6)+4(x-6)=0

(x+4)(x-6)=0

The value of the x is found as;

x-4=0

x=-4

x-6=0

x=+6

Hence, the values of the x are +6 and -4.

To learn more about polynomials, refer:

https://brainly.com/question/27343162

#SPJ2

Pie. It’s pie 3.14.... the name of that sign is pie

Answer:

That symbol represents pi.

Step-by-step explanation:

Pi is used by mathematicians to represent the ratio of a circle's circumference to its diameter.  It is approximately equal to 3.14159. Hope this helps!

solution here,

slope(m)=(y2-y1)/(x2-x1)

=(5-1)/(1-0)

=4/1 =4

Answer:

The correct answer is D) 4

Step-by-step explanation:

I took the test and this was correct!

Theoretically, each letter should have the same probability of occurring since there are 15 of each. There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability [tex]\dfrac{15}{75}=\dfrac15[/tex] of being drawn.

This means one would expect a theoretical frequency of [tex]\dfrac{1250}5=250[/tex], i.e. any given letter should get drawn 250 times, which means the answer is D.

Answer:

252 D-O

Step-by-step explanation:

250 and theoretically 252

Answer:

The perimeter is 22.

Step-by-step explanation:

The perimeter formula (it sometimes varies) is 2(b+h)

b being base (in this example, 6)

h being height (in this example, 5)

So now, with substitution, we are left with:

2(6+5)

Which simplifies down to:

2(11)

22

Answer:

B

Step-by-step explanation:

Given

pitchers of grape juice=g=4

picthers of orange juice=o=6

Each pitcher contains 64 oz of juice

So in order to calculate, we will calculate the total number of pitchers and then multiply it by 64 to get total oz.

=(6+4)*64

=10*64

=640 oz

We can see that we added count of pitchers and then multiplied the sum by 64.

So option B is the correct answer ..  

I think either A or D makes more sense

Answer:

-2

Step-by-step explanation:

the coefficient is the number in front of the variable.

Answer:

[tex]\sqrt{5}\cdot\sqrt[3]{5} =\sqrt[6]{5^3} \cdot\sqrt[6]{5^2} =\sqrt[6]{5^5} =5^{(5/6)}[/tex]

Step-by-step explanation:

The rules of exponents apply, even when they are fractional exponents:

[tex]a^b\cdot a^c=a^{b+c}\\\\\sqrt[b]{x^a}=x^{(a/b)}[/tex]

Answer:

[tex] \frac{1}{2} \times 21.6 \times 5.9 = 63.72[/tex]

The area of this triangle is 63.72 square feet.

Answer:

90

Step-by-step explanation:

add them all up and divide by how many there are

The answer is 90.

Add all the numbers then average them out by how many numbers there are.

Answer:

[tex]\large\boxed{y=0.470793x+2.13908}[/tex]

Step-by-step explanation:

The slope intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

From your picture we have:

[tex]m=0.470793[/tex]

and

[tex]b=2.13908[/tex]

Substitute:

[tex]y=0.470793x+2.13908[/tex]