(5√3-√27)^2
How do you prove this is an integer?

The volume of the right squared pyramid with the given base edges and slant height is 32768 cubic centimeters.

The volume of a square pyramid is expressed as;

V = (1/3)a²h

Where a is the base length and h is the height of the pyramid

Given that;

First, we determine the height of the pyramid using Pythagorean theorem.

c² = a² + b²

(40cm) = (32cm)² + h²

1600cm² = 1024cm² + h²

h² = 1600cm² - 1024cm²

h² = 576cm²

h = √576cm²

h = 24cm

Now, we calculate the volume of the right square pyramid;

V = (1/3)a²h

V = (1/3) × (64cm)² × 24cm

V = (1/3) × 409664cm² × 24cm

V = 32768cm³

Therefore, the volume of the right squared pyramid with the given base edges and slant height is 32768 cubic centimeters.

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Answer: 1/6

Step-by-step explanation: there is 6 faces on a standard die, one of them is 5.

Answer: the answer to your question is 42.2

Step-by-step explanation:25 x 25 + 34 X 34 = c^2

Answer:

20

Step-by-step explanation:

34 + 90 = 124

180-124 = 56 degrees

c = 56 degrees

to find x we need to use sin

sin = SOH (Sin = opposite/hypotenuse

sin 56 = x/25

sin 56 x 25 = x

x = 20.72593931

x = 20 (rounded to the nearest 10th)

hope this helped :)

The correct statement is that it is done by the converse of the triangle parts relationship theorem. The correct answer is option D.

The complete answer is given below and the figure is attached with the answer.

Consider the diagram and proof by contradiction.

Given: △ABC with ∠B ≅ ∠C

Prove: AB ≅ AC

It is given that ∠B ≅ ∠C. Assume AB and AC are not congruent. If AB > AC, then m∠C > m∠B by ________. If AC > AB, then m∠B > m∠C for the same reason. However, using the given statement and the definition of congruency, we know that m∠B = m∠C. Therefore, AB = AC and AB ≅ AC.

What is the missing reason in the proof?

the converse of the triangle parts relationship theorem

substitution

definition of congruency

the converse of the isosceles triangle theorem

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Isosceles triangle two sides of the triangle are equal and their opposite angles too.

Given

△ABC with ∠B ≅ ∠C

Prove that

AB ≅ AC

How to give a conclusion?

From the definition of the Isosceles triangle, it is proved that if ∠B ≅ ∠C Then AB ≅ AC. We know that if the length o the side increases then the opposite angle decreases. It is done by the converse of the triangle parts relationship theorem.

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Answer:

i might just be mind numb right now but you don't use pie on rectangles for area

Area = 6510

Step-by-step explanation:

A = L x W

A = 93 x 70

A = 6510

Answer:

f(x)=19

Step-by-step explanation:

2(3)²+1

2(9)+1

19

The value of function at x = 3 is,

⇒ f (3) = 19

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The function is,

⇒ f (x) = 2x² + 1

Now, Substitute x = 3 in above function,

⇒ f (x) = 2x² + 1

⇒ f (3) = 2 × 3² + 1

⇒ f (3) = 19

Thus, The value of function at x = 3 is,

⇒ f (3) = 19

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The growth of the plant is 25 inches last year.

Explanation:

Suppose the growth of the plant last year was y.

From the given situation, the normal growth was 10  inches more than twice the amount of last year.

So the equation will be

= 10 + 2y = 60

= 2y = 50

= y= 25 inches.

Therefore , the growth of the plant was 25 inches last year.

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The resultant speed of the plane is 100 mi/hr along the northeast direction.

Speed can be calculated as the ratio of distance traveled to the time taken

First, we need to find our coordinate axis, we will define the x-axis as the east and the y-axis as the north.

We are given that the plane travels at 150 mi/hr at 100° east of north, notice that if we measure from the positive x-axis, this is equivalent to an angle of -10°.

Then the x-component of the velocity ;

150mi/hr x cos(-10°) = 147.7 mi/hr

The y-component of the velocity;

150mi/hr x sin(-10°) = -26 mi/hr.

So, the vector is:

V = 147.7 mi/hr, -26 mi/hr

Now we know that the wind blowing at 50mi/hr at southwest, exactly southwest would be at an angle of 225°,

Thus, the components of the vector are:

x-component: 50mi/hr x cos(225°) = -35.4 mi/hr

y-component: 50mi/hr x sin(225°) = -35.4 mi/hr.

So, the vector is:

W = < -35.4 mi/hr, -35.4 mi/hr>

The sum of the vectors gives the total velocity of the plane in the wind is;

V + W = < 147.7 mi/hr -35.4 mi/hr , -26 mi/hr -35.4 mi/hr >

V + W = <112.3 mi/hr, -61.4 mi/hr>

The direction of a vector is;

θ = Atan(y/x)

Then, in this case the direction of the plane is:

θ = Atan(-61.4 mi/hr/112.3 mi/hr) = -28.7°

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Using it's concept, it is found that there is a 0.001 = 0.1% probability that he will forget to brush his teeth three days in a row.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, for each day, there is a 0.1 probability that he forgers to brush his teeth, and days are independent, hence for 3 consecutive days the probability is given by:

p = (0.1)³ = 0.001.

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Check the picture below, so the parabola looks more or less like so, with a "p" distance of 3 and the vertex at the origin, keeping in mind the vertex is half-way between the focus point and the directrix.

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=0\\ p=3 \end{cases}\implies 4(3)(x-0)~~ = ~~(y-0)^2\implies 12x=y^2\implies x=\cfrac{1}{12}y^2[/tex]

The solution of the equation when p = -1 is [tex]T=3x^{-2}[/tex]

The equation is given as:

[tex]T=3x^{2p}[/tex]

The value of p is -1.

So, we have:

[tex]T=3x^{2*-1}[/tex]

Evaluate the product

[tex]T=3x^{-2}[/tex]

Hence, the solution of the equation when p = -1 is [tex]T=3x^{-2}[/tex]

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If Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay. Then $728 she earns in a week in which she works 48 hours

Two or more expressions with an equal sign is called as Equation.

Given that Aleka earns her regular pay or $14 per hour for up to 40 hours of work per week.

14x40=560

For each hour over 40 hours of work per week, Aleka earns 14 times her regular pay.

Fourteen plus seven equal to twenty one

14+7=21

Twenty one times of eight is equal to one hundred sixty eight

21x8=168

Now let us add five hundred sixty and one hundred sixty eight

560+168=728

Hence she earns $728 in a week in which she works 48 hours.

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Answer:

200 dollars

Step-by-step explanation:

Let's say p equals the cost price of the article. Since the man made 25% profit, that means he got 100% of what he originally paid plus another 25% of what he originally paid. In other words, he sold the article for 125% of the original price. Converting that to a decimal we get:

250=p*1.25

Some simple division gets us a cost price of 200 dollars.

Based on the calculations, the solutions of this system of linear inequalities are equal to:

An inequality simply refers to a mathematical relation that's used to compare two (2) or more integers (variables) in an equation based on any of the following:

In order to determine the solutions of this system of linear inequalities, we would find the slope of each line.

For line A, we have:

Slope, m = (11 - 3)/(4 - 0) = 8/4

Slope, m = 2.

Mathematically, the standard equation of a line is given by y = mx + b.

y = 2x + 3

y ≤ 2x + 3.

For line B, the slope is equal to 4. Also, the y-intercept from the graph is equal to 5.

Therefore, the standard equation of a line is given by:

y = 4x + 5

y < 4x + 5

In conclusion, the solutions of this system of linear inequalities are equal to:

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1. Height of the equilateral triangle is: √3 units

2. Area of the equilateral triangle = √3 units²

3. Area = √3/4 x², when each side is x.

A triangle that has all its three sides equal in length, is referred to as an equilateral triangle.

1. Given the each side measures 2 units, and h is the height, applying the Pythagorean theorem, we would have:

h = √(2² - 1²)

h = √(4 - 1)

h = √3

2. Area of the equilateral triangle = 1/2bh = 1/2(2)(√3)

Area of the equilateral triangle = √3 units²

3. If x is the side length of the equilateral triangle, we would have:

height (h) = √[x² - (x/2)²] = √[x² - x²/4] = √(3x²/4) = √3/2x

Area = 1/2bh = 1/2(x)(√3/2x) = √3/4 x²

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The number of the years to take for the farmland's market value to reach $125,000 will be 19 years.

The missing function will be given below.

[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]

Let a is the base and x is the power of the exponent function and b is the y-intercept. The exponent is given as

y = aˣ

A patch of farmland is currently worth $78,125. The expected increase in its market value can be modeled by the function below.

[tex]\rm p(t) = 78,125\ e^{0.025t}[/tex]

Then the number of the years to take for the farmland's market value to reach $125,000 will be

[tex]\rm 78,125 \ e^{0.025t} = 125,000\\\\e^{0.025t} = 1.6[/tex]

Then take log on both sides, then we have

0.025t lne = ln 1.6

     0.025t = 0.47

               t = 18.8

               t = 19 years

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Answer:

No solution.

Step-by-step explanation:

[tex]\textbf{Given that,}\\\\~~~~~~~~3x = 3(x-1)\\\\\\\implies \dfrac{3x}3 = \dfrac{3(x-1)}{3}~~~~~~~~~~~~~~~~~;\textbf{Dividing both sides by 3}\\\\\\\implies x = x-1\\\\\\\implies x-x = x-1-x~~~~~~~~~~~~~;\textbf{Subtracting}~ x ~ \textbf{from both sides} \\\\\\\implies 0 = -1\\\\\\\textbf{Which is not true, so there are no solutions.}[/tex]

The probability that the selected element is a member of A n B is 2/9

The elements of the set are given as:

E = {1,2,3,4,5,6,7,8,9}

A = {1,3,4,8,9}

B = {2,4,9}

Using the above parameters, we have:

A only = {1, 3, 8}

B only = {2}

A and B = {4, 9}

None = {5,6,7}

The above dataset is the represented using the attached Venn diagram

In (a), we have:

A and B = {4, 9}

E = {1,2,3,4,5,6,7,8,9}

The probability is then calculated as:

P(A n B) = n(A n B)/n(E)

This gives

P(A n B) = 2/9

Hence, the probability is 2/9

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Answer:

positive

Step-by-step explanation:

(-a) (-a) (-a) (-a) = a

(-a)(-a) = a

a (-a) = -a

-a (-a) = a --> positive sign

If you multiply four negative numbers, what is the sign of the product?

You can test this with numbers, the easiest with -1:

(-1)(-1)(-1)(-1) = (1)(-1)(-1) = (-1)(-1) =  1

General:

(-a)(-b)(-c)(-d) = abcd

The sign of the product of four negative numbers is positive.

If you multiply five negative numbers, what is the sign of the product?

Testing with -1:

(-1)(-1)(-1)(-1)(-1) = (1)(-1)(-1)(-1) = (-1)(-1)(-1) = (1)(-1) -1

General:

(-a)(-b)(-c)(-d)(-e) = -abcde

The sign of the product of five negative numbers is negative.

General rule: The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative.

Answer:

x = 68

Explanation:

⇒ log₈(x - 4) = 2

apply log rules: logₐN = x then N = aˣ

⇒ (x - 4) = 8²

simplify

⇒ x - 4 = 64

add 4 on both sides

⇒ x = 64 + 4

add the integers

⇒ x = 68

Answer:

x = 68

Step-by-step explanation:

Given equation:

[tex] \rm log_{8}(x - 4) = 2[/tex]

To Find:

Value of x

Solution:

Rewrite the equation in exponential form which is equivalent to b^y = x.

[tex] \implies {8}^{2} = x - 4[/tex]

Now find the value of x.

[tex] \implies \:64 = x - 4[/tex]

Transpose 4 from RHS to LHS, make sure to change its sign from (-) to (+) .

[tex] \implies \: 64 + 4 = x[/tex]

Overturn the equation

[tex] \implies \: x = 68[/tex]

Thus, value of x is 68.

then for 5 tablespoons you use 12.5 ounces of milk

Answer: 5/6, 3/4, 4/12

Step-by-step explanation:

Convert them all into a common denominator, 12.

5/6=10/12, 3/4=9/12, and 4/12 stays the same. 10>9, and 9>4

Answer:

a) 150

b) 2650

Step-by-step explanation:

6% of 2500 is 150

150 + 2500 = 2650

Let's see

[tex]\\ \rm\Rrightarrow (x^{22}-3x^5+x^{-2}-7)5x^4[/tex]

Use distributive law

[tex]\\ \rm\Rrightarrow 5x^{22+4}-15x^{5+4}+5x^{-2+4}-35x^4[/tex]

[tex]\\ \rm\Rrightarrow 5x^{26}-15x^9+5x^2-35x^4[/tex]

Answer:

[tex]5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]

Step-by-explanation:

Given expression:

[tex](x^{22}-3x^5 + x^{-2} - 7) (5x^4)[/tex]

Use the Distributive Property Law  (b ± c)a = ab ± ac
to remove the parentheses:

[tex]\implies 5x^4 \cdot x^{22}-5x^4 \cdot 3x^5+5x^4 \cdot x^{-2}-5x^4 \cdot 7[/tex]

Simplify by multiplying the coefficients of each term:

[tex]\implies 5x^4 \cdot x^{22}-15x^4 \cdot x^5+5x^4 \cdot x^{-2}-35x^4[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]:

[tex]\implies 5x^{4+22}-15x^{4+5}+5x^{4-2}-35x^4[/tex]

[tex]\implies 5x^{26}-15x^{9}+5x^{2}-35x^4[/tex]

Answer:

[tex] \frac{32}{45} [/tex]

Step-by-step explanation:

if the multiplication of two numbers is 16)9, and one of the numbers is 5/2. then the other number can be found by dividing the number from the product to get the other number.

[tex] \frac{2}{3} (x - 4) = 2x \\ \frac{2}{3} x - \frac{8}{3} = 2x \\ \frac{2}{3} x - 2x = \frac{8}{3} \\ \frac{2}{3} x - \frac{6}{3} x = \frac{8}{3} \\ \frac{ - 4}{3} x = \frac{8}{3} \\ - 12x = 24 \\ x = \frac{24}{ - 12} \\ x = - 2[/tex]

Question 13

[tex]{12x+2}=\frac{18+34}{2}\\\\12x+2=26\\\\12x=24\\\\x=\boxed{2}[/tex]

Question 14

Base angles of an isosceles trapezoid are congruent, so:

[tex]73x+1=74\\73x=73\\x=\boxed{1}[/tex]