the measure of each side of an equilateral triangle whose are is [tex]\sqrt{3}[/tex] cm² is

Brainlist

Answer:

a=100, c=44

Step-by-step explanation:

# of adult tickets is represented by a

# of child tickets is represented by c

C+A=144

9a+6c=1164

system of equations is solved by solving 1 equation for 1 variable first.

c=144-a

plug in c in the second equation

9a+6(144-a)=1164

9a+864-6a=1164

combine like terms

3a=300

a=300/3

a=100

now we know a is 100 we can plug it into the original equation of c=a=144

c+100=144

c=144-100

c=44

The required answers for given similar triangles are DF= 3, EF= 2.25, and scale factor 4/3 respectively.

In geometry, two geometrical triangle are similar if they have the same shape, and corresponding sides are equate by some factor. More accurately, one can be obtained from the other by uniformly scaling.

For length of side DF, ratio of corresponding sides is equal.

⇒  [tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]

⇒  [tex]\frac{2}{1.5}=\frac{4}{DF}[/tex]

⇒  DF = 3

Similarly for EF,

 [tex]\frac{AB}{DE} =\frac{BC}{EF}[/tex]

⇒[tex]\frac{2}{1.5}=\frac{3}{EF}[/tex]

⇒ EF = 2.25

At last, by using same concept of similarity scale factor is

 [tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]

⇒ [tex]\frac{AB}{DE} =\frac{4}{3}[/tex]

This is our scale factor for both triangle.

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1.) Yes,it will fit because volume of the base ball is 13.36 cubic inch and the volume of box is 64 cubic inch which greater than the volume of baseball .

2) The ratio of the side length of box B to the side length of box

A is 1.472 inche : 6 inch.

What is cube ?

A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

What is circumference?

The circumference is the distance that surrounds a circle. We can measure the circumference of the earth by measuring the distance that we will have to walk all the way around the world.

To check whether the baseball is will till in the box we will check the maximum value of circumference.

⇒  [tex]2\pi r[/tex] = 9.25

⇒ [tex]r = \frac{9.25}{2\pi}[/tex]

⇒[tex]r = 1.472 in.[/tex]

Volume of the baseball [tex]= \frac{4}{3} \pi x^{3}[/tex]

                                      [tex]= \frac{4}{3}\times \pi\times (1.472)^3 in^3[/tex]

                                      [tex]= 13.36\ in^3 < 64 \ in^3\\[/tex]

So, it will fit inside the box.

2.)[tex]\sqrt[3]{216} = 6 \ (\therefore V = a^3)[/tex]

The length of each side of the box is 6 inches.

and the ratio of the side length of box B to the side length of box

A:

1.472 in : 6 inches

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The perimeter of rectangle ABDC is 61.24 units.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The rectangle ABDC is given in the question which has:

AB = 8 and AC = 24

Here AC is the diagonal of the rectangle which is the hypotenuse in a right triangle.

As per Pythagoras's theorem,

AC² = AB² + BC²

24² = 8² + BC²

576 = 64 + BC²

BC² = 512

BC = 22.62

The perimeter of rectangle ABDC = 2(AB + BC)

The perimeter of rectangle ABDC = 2(8 + 22.62)

The perimeter of rectangle ABDC = 2(30.62)

The perimeter of rectangle ABDC = 61.24 units

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The figure that is a dilation of figure E is the figure F

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The graph represents the given parameter

From the figure, we have the original shape to be figure E

The center point of figure E is the origin

This means that a line drawn from the origin that passes through point E must pass through the same point on the shape

From the figure, the line passes through the same point on figure E and F

Hence, figure F is a dilation of figure

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The dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

Rectangular Box with Square base

Volume v = a²b = 12

S = Surface area = 2a² + 4ab

v = a²b = 12

b = 12/a²

S = 2a² + 4ab = 2a² + 4a(12/a²) =2a² + 48/a

S'(a) = 4a -48/a² = 0

4a³ = 48

a = 12^ 1/3

b = 12/a² = 12/12^ 2/3 = 12^ 1/3

Therefore, the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

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Answer:

27/31

Step-by-step explanation:

Answer:

3×10^7

Step-by-step explanation:

Write 30 000 000 in standard form.

=3×10,000,000

=3×10^7

Step-by-step explanation:

this is

3.0 × 10⁷

as 30 000 000 has 7 zeroes (7 sequential and continuously increasing powers of 10 starting with 10¹).

and the first non-zero digit is 3.

Answer:

  (4)  5 m

Step-by-step explanation:

You want the length of side x of a right triangular prism with base edge lengths of 2.5 m and 2 m, and a volume of 12.5 m³.

The volume of the prism is given by the formula ...

  V = Bh

where B is the area of the base:

  B = 1/2bh . . . . where b and h are the leg dimensions of the right triangle

Using these formulas together, we have ...

  V = 1/2(2.5 m)(2 m)x

  12.5 m³ = 2.5x m²

Dividing by 2.5 m², we find x to be ...

  (12.5 m³)/(2.5 m²) = x = 5 m

The dimension labeled x has length 5 meters.

Part A: The formula 5d-13 indicates the distinction between the quantity of basic arrangements and deluxe arrangements sold.

Part B: The difference between the money the store made from basic arrangements and deluxe arrangements is $158.

An expression, also known as a mathematical expression, in mathematics is a finite combination of symbols that are well-formed in accordance with principles that depend on the context. Mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, grouping, and integers (constants) to help with logical grammar and operation ordering.

Part A: (8d-7)-(3d+6)

=8d-7-3d-6

=5d-13

Part B: For 7 days, d=7

              Cost        No. of sold

Basic       17          8(7)-7=49

Deluxe     25         3(7)+6=27

Therefore, Basic=17*49=$833

Deluxe=25*27=$675

Difference=833-675=158

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The height of the sand is changing when the height of the sand is 5 cm is 0.7848 in cm/sec

Volume is a measure of three-dimensional space that is occupied. It is frequently quantified numerically using SI-derived units (such as the cubic metre and litre) or various imperial units (such as the gallon, quart, cubic inch). The definition of length (cubed) is related to volume. The volume of a container is commonly understood to be its capacity; that is, the amount of fluid (gas or liquid) that the container can hold, rather than the amount of space it occupies.

Volume was measured in ancient times using similar-shaped natural containers, and later, standardized containers. Arithmetic formulas can easily calculate the volume of some simple three-dimensional shapes. Volumes of more complicated shapes can be calculated using integral calculus if a formula is provided.

The volume of the cylindrical is,

V = πr²h

V = volume

r = base radius

h = height

Calculate the difference between both sides of the equation in relation to time t. Because the radius r does not change over time, we can consider it a constant:

dv/dt = πr²(dh/dt)

Given,

dv/dt =555 cubic cm per second

r = 15

solve dh/dt:

555 = π(15)²(dh/dt)

dh/dt = 555(7/22)(1/225)

dh/dt =0.7848

The height of the sand is decreasing at a rate of 0.7848 in cm/sec

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The type of sampling is stratified random sampling

Given that,

The population is first divided into subgroups based on one or more important variables. this sampling is nothing but stratified random sampling

What Is Stratified Random Sampling?

A crucial element of the sampling method known as stratified random sampling is the division of a population into smaller subgroups known as strata. Strata are established in stratified random sampling, also known as stratification, based on the shared characteristics or attributes of the participants, such as wealth or level of education. Examining life expectancy and population demographics is just one of the many benefits and uses of stratified random sampling. Other names for stratified random sampling are proportional or quota random sampling..

Hence, this sampling is stratified random sampling

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Based on the calculations, the unknown number (x) is equal to 7.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the unknown number. Therefore, translating the word problem into an algebraic equation, we have the following;

Multiply a number (x) by 5 = 5x

The product is equal to the sum of 20 and 15 = 20 + 15 = 35.

Combining the above information, we have:

5x = 20 + 15

5x = 35

Dividing both sides by 5, we have:

x = 35/5

x = 7.

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Answer:

slope of the line = 1

Step-by-step explanation:

i hope i helped

Answer:

1. 384 cm square

2. m

3. -3 and 4

4.   1

Answer:

1) B

2) B

3) C

4) A

Step-by-step explanation:

     [tex]\sf \boxed{\text{Area of cube = $6a^2$}}[/tex]

Here, a is the side of the cube.

     Area of cube = 6 * 8 * 8

                            = 384 square cm  

Option B

2) y = mx + c.

Here, m is the slope or gradient and c is the y-intercept.

Option B

3) y = -3x + 4

Compare with y =mx + c,

         where m is the gradient and c is the y-intercept.

m = -3 and  = 4

Option C

4)

[tex]\sf Slope = \dfrac{y_2-y_1}{x_2-x_1}\\\\[/tex]

         [tex]\sf =\dfrac{-3-[-2]}{2-3}\\\\=\dfrac{-3+2}{-1}\\\\=\dfrac{-1}{-1}\\\\=1[/tex]

Option A

1.88 × 10² greater than 2.35 × 10⁻¹ by 800 times which is found by using division.

The two numbers given are:

1.88 times 10²

= 1.88 × 10²

And

2.35 times 10⁻¹

= 2.35 × 10⁻¹

We need to find that how much time is 1.88 × 10² greater than 2.35 × 10⁻¹.

We will use division for the same.

So, we get that:

= 1.88 × 10² / 2.35 × 10⁻¹

Using the rules of exponents and simplify the expression, we get that:

= 0.8 × 10 ²⁺¹

= 0.8 × 10³

= 0.8 × 1000

= 800

Therefore, we get that, 1.88 × 10² greater than 2.35 × 10⁻¹ by 800 times which is found by using division.

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Answer: By compare the graph of -6 ≤ x ≤-4 with the graph of x ≤-6 or x ≥-4 we can see that in first graph value is x belongs to [-6,-4] and in second graph we can see that x belongs to (-∞,-6] ∪ [-4,∞)

What does a coordinate mean in math?

a pair of values used to specify a point's position on a coordinate plane using the horizontal and vertical breakups from the two reference axes. typically represented by the pair of x-values and y-values (x,y).

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The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

Hence, The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

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To perform Rotation in coordinate plane the following information may help you.

What is Geometric Rotation ?

In geometry, rotation is a type of rigid motion or transformation that involves the movement of a shape about a point while preserving the shape, size, and distance between the points on the shape.The center of rotation is the location around which the shape is rotated.

To perform Rotation in coordinate plane

Last two questions sum up and I'm explaining like that,

      When a point is reflected in the x-axis then signs of it's ordinate (y-axis) change.

Mₓ (x, y) = (x, - y)

When a point is reflected in the y-axis then signs of it's abscissa (x-axis) change.

My (x, y) = (-x, y)

When a point is reflected in the origin , the signs of it's Abscissa and ordinate change.

M₀ (x, y) = (-x, -y)     (in origin the sign become opposite if there is '+' then it changes to '-' and vice versa)

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Answer:  The solution to this system is (1,3) as shown in the graph below.

Step-by-step explanation:

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NOTE: The red line is -x+y=2 and the blue line is y=3

Answer:

(x, y) = (1, 3)

Step-by-step explanation:

The property justified by step 4 is after substitution in the equation you get the desired result.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data in the question,

In step 3 substitution of value is taking place.

In step 4 when values are substituted the final result is obtained, so step 4 is the result step.

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Y=5p+3

Y equals the total amount of tape rolls

P is for the number of packages there are.

Hope this helped!

:)

Answer:

Y=5p+4

Y equals the total amount of tape rolls

P is for the amount of packages there are

Step-by-step explanation:

Answer:

infinite solution

Step-by-step explanation:

Since 0 = 0 for any value of y, the system of equations has infinite solutions.

The given function shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.

Given the parent function with base 10.

We want to find the given transformations.

The given parent function is y=log(x)

Firstly, we want to shift the given parent function 3 units left means we will add 3 in the parent function, we get

y=log(x+3)

Now, we want to do vertical compression by a factor of 2 means we will multiply the above function with 2, we get

y=2log(x+3)

Further, we want to reflected the above function across the y-axis means we will multiply the x with minus, we get

y=2log(-x+3)

Furthermore, we want to shift the above function down with 5 units means we will subtract 5 from the above function, we get

y=2log(-x+3)-5

Hence, the given parent function y=log(x) when shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.

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Answer: ∠B≈39.81°

Step-by-step explanation:

[tex]\displaystyle\\tg\angle B=\frac{AC}{BC} \\\\tg\angle B=\frac{5}{6} \\\\\angle B=arctg\frac{5}{6} \\\\\angle B\approx39.81^0[/tex]

The number of teams in the field hockey championship tournament is 16.

The total number of matches played in the field hockey championship are 120 matches.

Each pair of team played one match with each other.

So, let us say that there are N teams in the tournament.

So, we can chose any two teams for a match,

So, applying the permutation formula,

ⁿC₂ = 120

Solving further,

N!/2!(N-2)! = 120

N(N-1)/2 = 120

N(N-1) = 240

On observing closely and applying hit and trial method,

16(15) = 240

So, the values of N is 16.

Hence, 16 teams participated in the tournament.

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Step-by-step explanation:

well this is a rather odd equation but I'm assuming that

x+x+x+x+x = 5x

Answer:

The answer would be -4/5

Step-by-step explanation:

When you add a negative to a negative, you first take out the plus sign and rewrite it as: -2/5 - 2/5.

Now you just simply subtract 2/5 from -2/5 to get -4/5.

Hope this helps.

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When a bowling ball is propelled with a force of 22. 0 N and accelerates at a rate of 5. 5 [tex]ms^{-2}[/tex], its mass is 4. 0 kg.

Newton's Second Law of Motion states that force is the result of mass times acceleration.

[tex]F=m*a[/tex]

[tex]m = F / a[/tex]

A force of 22.0 Newtons (  [tex]kgms^{-2}[/tex] ) and an acceleration of 5.5 meters per second squared were used to drive the bowling ball.

F = 22.0 [tex]kgms^{-2}[/tex] and

a = 5.5 [tex]ms^{-2}[/tex]

Put the values in the formula as replacements.

M = 22 [tex]kgms^{-2}[/tex]/ 5.5 [tex]ms^{-2}[/tex]

Meters per second squared (m/s2) units cancel each other out.

M = 22 kg / 5.5

   = 4 kg

The bowling ball weighs 4 kilogram.

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1/36 is the probability that you score 4 points both times.It is the likelihood of scoring four points twice.

1/6 * 1/6 =1/36

The probability of an event occurring is measured by its probability. It determines the probability of an event. The probability calculation is P(E) = Number of Favourable Outcomes/Total Outcomes.A game is a formalized form of play that is frequently done for amusement or fun but can also serve as a teaching game tool.

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