What is the volume of the sphere below?
A. 817 units 3
B. 36 units 3
C. 27 units3
D. 12 units 3

Answer:

Question 1:

The smallest 5-digit no. is 10,000

The product of its prime factors is:

=> 10,000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

Question 2:

The prime factors of 1729 are:

=> 1729 = 7 × 13 × 19

The relation between their 2 consecutive prime factor is that when they both are subtracted, they give the result 6

Such as :

=> 13-7 = 6

=> 19-13 = 6

Hope this helps!

Don't hesitate asking anything regarding this question!

Answer:

1. The smallest 5-digit number is: 10000

10000= 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5

2. 1729= 7 × 13 × 19

7= 6+1

13= 6*2+1

19= 6*3+1

Answer:

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

Step-by-step explanation:

Given

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

Required

Solve

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

In trigonometry;

[tex]1 - cos^2x = sin^2x[/tex]

So, make substitution

[tex](1-cos^2 x ).(1+tan^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(1+tan^2 x)[/tex]

Also; in trigonometry:

[tex]1 + tan^2x = sec^2x[/tex]

Make another substitution

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex]

Recall that [tex]secx = \frac{1}{cosx}[/tex]

So;

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(\frac{1}{cos^2 x})[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = \frac{sin^2 x }{cos^2 x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = (\frac{sin x }{cosx})^2[/tex]

In trigonometry;

[tex]tan x = \frac{sin x}{cos x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

The expression cannot be further simplified

Answer:

Step-by-step explanation:

Perimeter of the rectangle = 332m

Perimeter of a rectangle = 2(L+b)

Breadth = 75m

= 2 ( L + 75) = 332

2L + 150 = 332

2L = 332-150

L = 182/2

L= 91m

Answer: its 3

Step-by-step explanation:

Answer:   2

Step-by-step explanation: Because their are 2 squares

Step-by-step explanation:

[70,30] = 210 miles per hour

d=76.157t is the expression for two vehicles, a car and a truck which were distance apart d (in miles) at the end of t hours.

Two vehicles, a car and a truck, leave an intersection at the same time. The car heads east at an average speed of 70 miles per hour, while the truck heads south at an average speed of 30 miles per hour. we need to find expression for their distance apart d at the end of t hours

Distance=Speed*Time

distance= speed * time.

*70t be the car traveling EAST at 60 miles per hour after t hours

*30t be the distance of the truck traveling SOUTH at 20 miles per hour after t hours.

*Use the Pythagorean Theorem to find the distance d.

The Pythagoras theorem states that sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

d^2=(70t)^2+(30t)^2

d^2=4900t^2+900t^2

d^2=5800t^2

d=76.157t

Therefore d=76.157t is the required expression for their distance apart d (in miles) at the end of t hours.

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Answer:

10 meters

Step-by-step explanation:because they are square and they would have to be 5 meters long and she dose not want any left over so...

Answer:

93 hamburgers

Step-by-step explanation:

let cheeseburgers=c

let hamburgers=h

c=3h

c+h=372

Substitute c for 3h

3h+h=372

4h=372

h=93

c=h*3=93*3=279

279 cheeseburgers 93 hamburgers

Answer:

c

Step-by-step explanation:

In the given line the relationship between angle w and z is Measure of angle w + measure of angle z = 180 degrees.

This is the type of angle that when measured, two of the angles would sum up to 180 degrees.

The supplementary angle is the sum of angle w + angle z = 180 degrees. Hence c is correct.

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Answer:

(-9/2 , -10)

Step-by-step explanation:

2x-3y=21

-6x+2y=7

Multiply the first equation by 3

3(2x-3y)=21*3

6x - 9y = 63

Add this to the second equation to eliminate x

6x - 9y = 63

-6x+2y=7

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

0x -7y = 70

Divide by -7

-7y/-7 = 70/-7

y = -10

Now find x

2x- 3y = 21

2x -3(-10) = 21

2x +30 =21

subtract 30 from each side

2x = 21-30

2x= -9

Divide by 2

x = -9/2

(-9/2 , -10)

Now lets solve it by elemination method !

[tex]:\implies\sf 2x-3y=21--------(1)\\ \\ \\ :\implies\sf -6x+2y=7-------(2)\\ \\ \\ \sf Eleminate\ (x) \\ \\ \\ \it Multiply\ first \ equation \ with \ 3\ \ \ and \ 2nd \ \ with \ 1 \\ \\ \\ :\implies\sf (2x-3y=21)\times 3 \\ \\ \\ :\implies\sf (-6x+2y=7)\times 1\\ \\ \\ :\implies\sf 6x-9y=63------(3) \\ \\ \\ :\implies\sf -6x+2y=7-----(4)\\ \\ \\ \it\ \ Add \ equation\ 3\ \ and \ 4\\ \\ \\ :\implies\sf 6x-9y=63+ (-6x+2y= 7)\\ \\ \\ :\implies\sf (6x-6x)+(-9y+2y) = 63+7\\ \\ \\ :\implies\sf 0-7y=70\\ \\ \\ :\implies\sf y= \cancel{\dfrac{70}{-7}}= - 10\\ \\ \\ :\implies\sf y= -10 [/tex]

★ Now find the value of x

let's substitute the value of y in equation 4

[tex]:\implies\sf -6x+2y=7\ \ \ \ \ \ (y= -10)\\ \\ \\ :\implies\sf -6x+2\times (-10)=7\\ \\ \\ :\implies\sf -6x-20= 7\\ \\ \\ :\implies\sf -6x = 7+20 \\ \\ \\ :\implies\sf x= \cancel{\dfrac{27}{-6}}= \dfrac{-9}{2}[/tex]

[tex]\underline{\textit{ \ \ So, \ the \ value \ of \ x\ and \ y }}[/tex]

[tex]\bigstar{\boxed{\sf x= \dfrac{-9}{2}}}[/tex]

[tex]\bigstar{\boxed{\sf\ y= (-10)}}[/tex]

Answer:

y = [tex]\frac{4\sqrt{3} }{3}[/tex]

Step-by-step explanation:

We are working with 30-60-90 triangles, and to solve for y we need to know the hypotenuse of the smaller triangle.

You can get that by finding the smaller value of the larger triangle.

[tex]\frac{8}{\sqrt{3} } =\frac{x}{1}[/tex]

x[tex]\sqrt{3}[/tex] = 8

x = [tex]\frac{8}{\sqrt{3} }[/tex]

x = [tex]\frac{8\sqrt{3} }{3}[/tex]

That is the hypotenuse of the smaller triangle. To find y...

[tex]\frac{(\frac{8\sqrt{3} }{3}) }{2} =\frac{y}{1}[/tex]

2y = [tex]\frac{8\sqrt{3} }{3}[/tex]

y = [tex]\frac{4\sqrt{3} }{3}[/tex]

Hope this helps!

10 L of a 25% acid solution contains 0.25 * (10 L) = 2.5 L of acid.

Adding x L of pure water dilutes the solution to a concentration of 10%, such that

(2.5 L)/(10 L + x L) = 0.10

Solve for x :

2.5 = 0.10 * (10 + x)

2.5 = 1 + 0.10x

1.5 = 0.10x

15 = x

so 15 L of pure water are needed.

Answer:  (b) x = -2/3

Step-by-step explanation:

The vertical asymptote is the restriction on x.

The denominator cannot be equal to zero so that it the restriction.

Set the denominator equal to zero and solve for x to find the asymptote.

3x + 2 = 0

3x       = -2

 x       = -2/3

Answer:

median, mode, range, mean

Step-by-step explanation

the median is found by putting the data in order and selecting the middle value

the mode is the value that occurs the most often

the range is the difference between the greatest and least value

and the mean is the sum of all the values divided by the number of values

Answer:

The  ✔ median   is calculated by putting the data in order and selecting the middle value.

The  ✔ mode   is the data value that occurs the most in a set of data.

The  ✔ range  is the difference between the maximum and minimum values of a data set.

The  ✔ mean  is the sum of the data divided by the number of data values.

Students were asked how many pairs of shoes they owned. Their responses were 8, 2, 1, 5, 7, 6, 2, 2, 8, and 3.

The mean of the data is 4.4.

The median of the data is  4 .

The mode of the data is  2 .

The range of the data is  7 .

Step-by-step explanation:

Just took the test from E D G E N U I T Y....

hope this helps :P

Answer:

y = (-2/125)(x - 50)² + 40

Step-by-step explanation:

The total length of the bridge is 100 meters.

Maximum height always occurs at midpoint of x.

So for x=50 meters , y = 40 meters.

As the vertex is given at the maximum height,  Vertex can be defined at the point (50,40)

We know that the general equation for vertical parabola is:

y = a(x - h)² + k

Where (h,k) = Vertex = (50,40)

Substitute in the equation:

y = a(x - 50)² + 40 ⇒ Equation (i)

We know 2 more points on the parabola. We know that when x=0 , y=0 and we also know that when x=100m, y=0 meters.

Substitute any point in the above equation

Substituting (100,0) in the equation

0 = a(100 - 50)² +40

Solve the equation for a:

a = - 2/125

Substitute a in Equation (i)

y = (-2/125)(x - 50)² + 40

Answer:

hi

Step-by-step explanation:

Answer:

The correct option is;

Substitute x = 0 in the function  and solve for f(x)

Step-by-step explanation:

The zeros of a function are the values of x which produces the value of 0 when substituted in the function

It is the point where the curve or line of the function crosses the x-axis

A. Substituting x = 0 will only give the point where the curve or line of the function crosses the y-axis,

Therefore, substituting x = 0 in the function  can't be used to find the zero's of a function

B. Plotting a graph of the table of values of the function will indicate the zeros of the function or the point where the function crosses the x-axis

C. The zero product property when applied to the factors of the function equated to zero can be used to find the zeros of a function

d, The quadratic formula can be used to find the zeros of a function when the function is written in the form a·x² + b·x + c = 0

Answer: Substitute x = 0 in the function and solve for f(x).

Step-by-step explanation:

Answer:

132 dollars, I think

Step-by-step explanation:

15*2=30

66*2=132

Answer:

D

Step-by-step explanation:since 15 cases is $66 multiply 66 by 2 to get $132

Answer:

There are 36 total possible outcomes.

Rolling a sum of 11 or higher, there are 3 possible rolls, to make a 3/36 = 1/12 probability.

Rolling a sum of 4 there are also 3 possibilities, so the chance would be the same.

Rolling a sum of 9, there are 4 possibilities, which is a better chance.

Rolling a sum less than 5, there is 6 possibilities, which is a better chance.

Rolling greater than 5 but less than 7 means rolling a sum of 6, there are 5 chances, which is a better chance.

Rolling greater than 9 but less than 11, means rolling a 10, there are 3 possibilities, which is the same.

Rolling greater than 2 and less than 4 means rolling a 3, there are 2 possibilities, which is less.

The answers would be:

Rolling a sum of 9,

Rolling a sum less than 5

Rolling greater than 5 but less than 7

Answer:

There are 36 total

Step-by-step explanation:

Answer:

Answer:

3 < c < 13

Step-by-step explanation:

A triangle is known to have 3 sides: Side a, Side b and Side c.

For a triangle, one of the three sides is longer than the other two sides. (The only exception is when we are told specifically that a triangle is an equilateral triangle, where all the 3 sides are equal to each other).

To solve the above question, we would be using the Triangle Inequality Theorem.

The Triangle Inequality Theorem states that the summation or addition of the lengths of any two sides of a triangle is greater than the length of the third side.

Side a + Side b > Side c

Side a + Side c > Side b

Side b + Side c > Side a

For the above question, we have 2 possible side lengths for the third side of the triangle. We are given in the above question,

side (a) = 5

side (b) = 8

Let's represent the third side as c

To solve for the above question,we would be having the following Inequality.

= b - a < c < b + a

= 8 - 5 < c < 8 + 5

= 3 < c < 13

Answer: B $2.22

Step-by-step explanation:

2 controllers will cost

= 2 x 18.50 = 37

6% tax = 37 x 0.06 = 2.22

Answer:

B

Step-by-step explanation:

i took the test

Answer:

None. (or B)

Step-by-step explanation:

A)  AC≅ZY

B) AZ≅

C) ∠A ≅ ∠C

D) ∠B ≅ ∠X

Options C and D are not true and Options A is wrong and B is incomplete but using process of elimination, the answer is probably B.

The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Given that, Δ ABC has been translated right to create triangle Δ XYZ

We know that in translation transformation, in translation, only the position of the object changes, its size remains the same.

That means Δ ABC ≅ Δ XYZ Therefore, we get,

Congruent parts are;

Angles:-

∠ A ≅ ∠ X,

∠ B ≅ ∠ Y and

∠ C ≅ ∠ Z

Side:-

AB ≅ XY,

BC ≅ YZ and

AC ≅ XZ

Hence, The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

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Answer:

Option B

Step-by-step explanation:

The absolute value of a number is how far a number is from zero. We can use ' | | ' to represent the absolute volume of a number.  The distance, or absolute value, of -8 is 8.

We can represent this by writing:

|-8| = 8

Option B should be the correct answer.

Answer:

B

Step-by-step explanation:

The absolute value of a number means the distance from 0.

For example, |-2| is 2 units from 0.

|-8| = 8

-8 is 8 units from 0.

Answer:B.

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Distribute

1/2 x + 3 = 18

Subtract 3 from each side

1/2x +3-3 = 18-3

1/2x = 15

Multiply each side by 2

1/2x*2 = 15*2

x = 30

Answer:

x + y ≥ 3

x + y ≤ 3

Step-by-step explanation:

In the picture attached, the problem is shown.

The solution to the system:

x + y ≥ 3

x + y ≤ 3

is the line x + y = 3

In order to get a solution to a system of inequalities that is a line, we need the same equation on the left (here, x + y), the same constant on the right (here, 3), and the ≥ sign in one inequality and the sign ≤ in the other one.

Answer:

3f(x)  

3x^2  

12  

-x+6

0

Step-by-step explanation:

Fashoo

Answer:

Similar triangles are (roughly speaking) triangles that have the same angles and the same ratio of the length of their sides

We can use ratios to show that the triangles are not similar

14:20 as a fraction is 14/20 as a decimal is 0.7

12:16 as a fraction is 12/16 as a decimal is 0.75

The side lengths are not the same proportion as shown by the different decimal, so the triangles are not similar

Answer:

x=1 , y = -1

Step-by-step explanation:

-2.4x-3.6y = 1.2

2.4x+1.2y = 1.2

Add the equations together

-2.4x-3.6y = 1.2

2.4x+1.2y = 1.2

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

   -2.4 y = 2.4

Divide by -2.4

y = -1

Now find x

2.4x +1.2y = 1.2

2.4x +1.2(-1) = 1.2

2.4x -1.2 = 1.2

Add 1.2 to each side

2.4x -1.2+1.2 = 1.2+1.2

2.4x = 2.4

Divide by 2.4

x = 1

Answer:

x=1

Step-by-step explanation:

Answer:

Choice D

Step-by-step explanation:

[tex]3\dfrac{1}{2}\cdot 5 \cdot \dfrac{1}{2}= 3.5\cdot 5\cdot 0.5=8.75 = 8\dfrac{3}{4}[/tex]

Hope this helps!

Cubic feet would be volume.

Volume = length x width x height

Volume = 3 1/2 x 5 x 1/2 = 8 3/4 cubic feet.

Answer:

A:

(4x+5)(3x+10)=

(12x^2) + (40x) + (15x) + (50)

12x^2 + 55x + 50

B: 2nd degree trinomial.

C:  it is demonstrated in part A because when we added it, the variable do not change and neither do the  exponents.  

Step-by-step explanation:

do not copy. used this on my test.