simplify 2/3 (3x -2) – ¾ (2x -2)

13

5^2+12^=169

square root of 169=13

if the triangle wasnt a right angled triangle it would equal to 13 and would give u something else

Georgia will need [tex]\(\boxed{333}\)[/tex] square inches of cardboard to construct the square pyramid.

To calculate the amount of cardboard needed to construct the square pyramid, we need to find the surface area of each individual face and then add them together.

Given that the base of the pyramid is a square with side length [tex]\(b = 9\) inches[/tex] and the height of the triangular sides is [tex]\(a = 14\) inches[/tex], we can proceed as follows:

The surface area of the square base is [tex]\(b^2 = 9^2 = 81\)[/tex] square inches.

Each triangular face has a base equal to the side length of the square base, [tex]\(b = 9\) inches[/tex], and a height of [tex]\(a = 14\) inches[/tex]. Therefore, the surface area of each triangular face is [tex]\(\frac{1}{2} \times b \times a = \frac{1}{2} \times 9 \times 14 = 63\)[/tex] square inches.

Since there are four triangular faces in a square pyramid, the total surface area of the triangular faces is [tex]\(4 \times 63 = 252\)[/tex] square inches.

Adding the surface area of the square base and the total surface area of the triangular faces, we get [tex]\(81 + 252 = 333\)[/tex] square inches.

Therefore, Georgia will need [tex]\(\boxed{333}\)[/tex] square inches of cardboard to construct the square pyramid.

For more such questions on square pyramid: https://brainly.com/question/3688277

#SPJ11

The number of balloons needed to fill the room is given as follows:

5729 balloons.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions of the room are given as follows:

15 ft, 25 ft and 8 ft.

Hence the volume is given as follows:

V = 15 x 25 x 8

V = 3000 ft³

The volume of a sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:

V = 4πr³/3.

The balloon has a radius of 0.5 ft, hence it's volume is given as follows:

V = 4π x 0.5³/3

V = 0.5236 ft³.

Then the number of balloons is obtained as follows:

3000/0.5236 = 5729 balloons.

More can be learned about the volume of a rectangular prism at brainly.com/question/22070273

#SPJ1

The fountain will occupy a fraction of 50/173 of the Total area of the courtyard.

Let A be the area of the courtyard and F be the area of the fountain.

We know that the area of the stone-covered part of the courtyard is 246 square feet.

So, the area of the whole courtyard is A = 246 + F square feet.

The fraction of the area of the courtyard occupied by the fountain is given by:

F / A = F / (246 + F)

We can simplify this expression by multiplying the numerator and denominator by the reciprocal of the denominator:

F / A = F / (246 + F) * (1 / (246 + F))

F / A = F / (246 * (246 + F))

F / A = 1 / (246 / F + 1)

We don't know F yet, but we can use the fact that the fountain is rectangular to set up an equation relating the length and width of the fountain:

F = L * W

where L is the length of the fountain and W is the width of the fountain.

We also know that the perimeter of the fountain is 50 feet:

2L + 2W = 50

Simplifying this equation, we get:

L + W = 25

Solving for one variable in terms of the other, we get:

L = 25 - W

Substituting this expression for L into the equation for F, we get:

F = (25 - W) * W

Expanding this expression, we get:

F = 25W - W^2

We also know that the cost of the fountain is $600, which includes installation. So, we can set up another equation relating the cost of the fountain to its dimensions:

1.5LW = 600

Substituting 25 - W for L, we get:

1.5(25 - W)W = 600

Expanding and simplifying this equation, we get:

W^2 - 25W + 400 = 0

Solving this quadratic equation, we get:

W = 20 or W = 5

We reject the solution W = 5 because it implies a negative length for the fountain, which is not physically possible. Therefore, the width of the fountain is W = 20 feet and its length is L = 25 - W = 5 feet.

The area of the fountain is therefore:

F = L * W = 5 * 20 = 100 square feet

The fraction of the area of the courtyard occupied by the fountain is

F / A = 100 / (246 + 100) = 100 / 346 = 50 / 173

So, the fountain will occupy a fraction of 50/173 of the total area of the courtyard.

To know more about  Total area.

https://brainly.com/question/884576

#SPJ11

The numeric value of the derivative at x = 3 is given as follows:

C. 0.5.

The quotient function has the format given as follows:

(f/g)(x).

The derivative of the function is obtained applying the quotient rule, as follows:

(f/g)'(x) = [f'(x)g(x) - f(x)g'(x)]/[g(x)]².

Then at x = 3, the derivative is given as follows:

(f/g)'(3) = [f'(3)g(3) - f(3)g'(3)]/[g(3)]².

Replacing the values from the table, we have that:

(f/g)'(3) = [3 x 2 - 1 x 4]/2².

(f/g)'(3) = 2/4

(f/g)'(3) = 0.5.

Meaning that the correct option is given by option C.

More can be learned about the quotient rule at https://brainly.com/question/29232553
#SPJ1

The specific measurements or Dimensions of the cone and cylinder (such as the radius and height).

The volume of the component part consisting of a cone on top of a cylinder,  the volumes of the individual shapes and sum them together. the part consists of a cone and a cylinder/

1. Volume of the cone:

The volume of a cone can be calculated using the formula V_cone = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height of the cone.

2. Volume of the cylinder:

The volume of a cylinder can be calculated using the formula V_cylinder = π * r^2 * h, where r is the radius of the base and h is the height of the cylinder.

the given diagram and determine the necessary measurements. without the specific measurements or dimensions (such as the radius and height of the cone and cylinder), I am unable to calculate the volumes.

the specific measurements or dimensions of the cone and cylinder (such as the radius and height).

To know more about Dimensions .

https://brainly.com/question/28749362

#SPJ11

The total area of the figure is 50.13 square units.

We can decompose the figure into a rectangle of 12 by 3 units, and a semicircle whose radius is 3 units.

Remember that the area of a rectangle is equal to the product between its dimensions, then the area of the rectangle we will get.

A = 12*3 = 36 square units.

For a semicircle of radius R, the area is:

a = 0.5*3.14*R²

Here the radius is 3 units, then.

a =  0.5*3.14*3² = 14.13 square units.

Adding that we will get:

total area = 36 square units + 14.13 square units.

total area = 50.13 square units.

Learn moer about area at:

https://brainly.com/question/24487155

#SPJ1

Answer:

1/6

Step-by-step explanation:

1 x 1/6 = 1/6

Any number multiplied with one is that number itself.

1/6

Step-by-step explanation: Anything multiplied by 1 equals itself, therefore, the answer is 1/6. Hope this helps, and please give me Brainliest! :)

Five-number summary for data set A is: 21, 23.5, 27, 31.5, 34

Five-number summary for data set B is: 21, 22.5, 24.5, 28.5, 35

the five-number summary of a data set consists of:

The minimum or the lowest value

First quartile (Q1), that is the middle of the first part of the data set when ordered.

Median, that is the center of the data set.

Third quartile (Q3), that is the middle of the second part of the data set when ordered.

Maximum value or largest value.

The five-number summary is written from the least to the largest value.

Five-number summary for data set A:

Given, 24, 31, 30, 32, 23, 25, 34, 32, 25, 21, 22, 29;

Minimum: 21

First Quartile: 23.5

Median: 27

Third Quartile: 31.5

Maximum: 34

Five-number summary for data set B:

Given, 35, 33, 32, 21, 22, 23, 24, 25, 24, 22, 25, 25;

Minimum: 21

First Quartile: 22.5

Median: 24.5

Third Quartile: 28.5

Maximum: 35

Learn more about Five-number summary on:

https://brainly.com/question/24809873

#SPJ1

Answer:

       0      1      2      3      4      5      6      7

       |      |      |      |      |      |      |      |

     2/3   1     2.7    3.4         7      |

                         |_____________|

                               |

                             3 3/4

The quotient evaluated in 7 is equal to the quotient of the two functions evaluated in 7, thus:

(f/g)(7) = f(7)/g(7) = 3

Here we know the functions:

f(x) = 2x + 1

g(x) = x - 2

The quotient evaluated in 7 is equal to the quotient between the two functions evaluated in x = 7, then here we will get:

f(7) = 2*7 + 1 = 14 + 1 = 15

g(7) = 7 - 2 = 5

Then the quotient gives:

(f/g)(7) = f(7)/g(7) = 15/5 = 3

That is the value.

Learn more about functions at:

https://brainly.com/question/2328150

#SPJ1

Answer:

Step-by-step explanation:

You want to know the amounts invested in stocks, bonds, and CDs when the total investment is $145000, $10000 more is invested in bonds than CDs, earnings are $6977.50, and rates of return are 6.7% for stocks, 2.5% for bonds, and 5.75% for CDs.

We can write three equations in 3 unknowns for this problem. Let s, b, c represent amounts invested in stocks, bonds, and CDs, respectively. Then the problem statement tells us the relations are ...

These equations can be solved using any of several methods. The second equation offers a nice relation between b and c, so substitution for one or the other of those will reduce the equations to two equations in two unknowns.

We prefer a calculator solution using an augmented matrix of the coefficients. That is shown in the attachment. It tells us the investment amounts are ...

__

Additional comment

Using b = c +10000, the two remaining equations are ...

<95141404393>

Answer:100

Step-by-step explanation:

Step-by-step explanation:

The value of the digit 1 in the number 213,456 is 10,000.

Answer:

Step-by-step explanation:

You want to find the values of cos(x), tan(x), and sin(x) in right triangle DEF as shown in the figure.

The relationships between trig functions and sides of a right triangle are summarized in the mnemonic SOH CAH TOA. This tells you ...

  Cos = Adjacent/Hypotenuse

  cos(x) = f/e

  Tan = Opposite/Adjacent

  tan(x) = d/f

  Sin = Opposite/Hypotenuse

  sin(x) = d/e

<95141404393>

Answer:

i'm pretty sure it is "the graph forms a parabola"

Step-by-step explanation:

The probability of drawing a red or green M&M is 29/74.

The probability of drawing an M&M that is not blue or green is 36/74.

the probability of drawing an M&M that is not brown is 69/74.

The probability of drawing a red or green M&M is the sum of their probabilities, since they are mutually exclusive events (meaning that an M&M can't be both red and green at the same time):

P(red or green) = P(red) + P(green) = 8/74 + 21/74 = 29/74

The probability of drawing an M&M that is not blue or green is the complement of the probability of drawing a blue or green M&M:

P(not blue or green) = 1 - P(blue or green) = 1 - (P(blue) + P(green)) = 1 - (17/74 + 21/74) = 36/74

The probability of drawing an M&M that is not brown is the complement of the probability of drawing a brown M&M:

P(not brown) = 1 - P(brown) = 1 - 5/74 = 69/74

To determine which is more likely, drawing a red M&M or drawing an orange M&M, we need to compare their probabilities:

P(red) = 8/74

P(orange) = 12/74

Since 12/74 is greater than 8/74, it is more likely to draw an orange M&M than a red M&M.

The color with the highest chance of being drawn is the one with the highest probability, which is green with a probability of 21/74.

The probability of drawing any M&M is 1, since there is a 100% chance of drawing an M&M when you draw from the bag.

Probability is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

The value of the hypotenuse AB is 4.73 units.

Given is right triangle, we need to find the measure of side AB,

So, we know that the Sine of an angle is the ratio of the perpendicular side to the hypotenuse of the triangle,

So,

Sin A = BC / AB

Sin 25° = 2 / AB

AB = 2 / Sin 25°

AB = 4.73

Hence the value of the hypotenuse AB is 4.73 units.

Learn more about trigonometric ratios click;

https://brainly.com/question/25122825

#SPJ1

Answer:

To find the x-intercepts, we set y = 0 and solve for x:

f(x) = (x+9) (x+9) (x-8) = 0

The solutions are x = -9 (double root) and x = 8.

To find the y-intercept, we set x = 0:

f(0) = (0+9) (0+9) (0-8) = -583.

Therefore, the y-intercept is (0, -583).

the x coordinates are matched as follows

For y = √110/11  x = ± 1/√(11)

For y = 7/11  x = ± 6√(2) /11

For y = 5/11   x = ±4√(6) /11

For y = 9/11:   x = ±2√(10) /11

Using the equation of the unit circle

x² + y² = 1

For y = √110 / 11

x² + (√110/11)² = 1

x² + 110/121 = 1

x² = 1 - 110/121

x² = 11/121

x = ±√(11)/11

x = ± 1/√(11)

For y = 7/11

x² + (7/11)² = 1

x² + 49/121 = 1

x² = 1 - 49/121

x² = 72/121

x = ±√72/11

x = ± 6√(2) /11

For y = 5/11

x² + (5/11)² = 1

x² = 1 - 25/121

x² = 96/121

x = ±4√(6) /11

For y = 9/11

x² + (9/11)² = 1

x² = 1 - 81/121

x² = 40/121

x = ±√40/11

x = ±2√(10) /11

Learn more about unit circles at

https://brainly.com/question/29268357

#SPJ1

Answer: 5(x - 12) = 3x

Step-by-step explanation:

       We can cross-multiply to answer this question.

[tex]\frac{5}{x} =\frac{3}{x-12}[/tex]

5 * (x - 12) = 3 * x

5(x - 12) = 3x

Answer:

b) 5(x - 12) = 3x

Step-by-step explanation:

Given expression,

→ 5/x = 3/(x - 12)

Now we have to,

→ Find the equivalent expression.

Let's find the required answer,

→ 5/x = 3/(x - 12)

Cross multiplying both sides:

→ 5(x - 12) = 3(x)

→ 5(x - 12) = 3x

Applying Distributive property:

→ 5(x) - 5(12) = 3x

→ 5x - 60 = 3x

Solving for the value of x:

→ 5x - 3x = 60

→ 2x = 60

→ x = 60/2

→ [ x = 30 ]

Hence, the value of x is 30.

Her savings would be $12.72 ($760 - $744.80 - $2.48).

The difference in the final payment is therefore $221.50 - $150 = $71.50.

a. The printer's price after the trade discount is $760 ($860 - $100). If Janet takes the 2% cash discount, she'll pay $744.80 ($760 * 98%).

If she borrows this amount at 6% for 20 days (the difference between 30 days credit and 10 days cash discount), her interest cost will be $2.48 ($744.80 * 6% * 20/360).

Therefore, her savings would be $12.72 ($760 - $744.80 - $2.48).

b. For choice 1, Janet would pay $150 for 17 months and then the remainder ($4,020 * 75% - $150 * 17) in the 18th month.

For choice 2, the monthly payment is $221.50, calculated by using the formula for an installment loan.

The difference in the final payment is therefore $221.50 - $150 = $71.50.

Read more about monthly payments here:

https://brainly.com/question/28106777
#SPJ1

Answer:

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

Tangent is perpendicular to radius, hence ΔAOB is right triangle.

Given that OA = AB, and we know OA = OC as two radius. Therefore OAC is equilateral triangle, hence all its angles are same:

It means ΔOAB is a specific 30x60x90 right triangle.

The ratio of its sides is:

It gives us that:

Answer:

Squaring positive and negative numbers always yields a positive number; the product of two negative numbers is always a positve number.  Using √4 as an example, we know the positive answer is 2 since 2 * 2 = 4.  However, the negative answer is -2 since -2 * -2 = 4 also.

The greatest common factor of the given polynomial is 2, so we can factor it out to get: 2(x³ - 5)

We have to factories 2x³ - 10

So, 2x³ = 2 . x . x . x

10 = 2 . 5

Then, 2x³ - 10

= 2. x . x . x - 2.  5

= 2( x . x .x - 5)

= 2 (x³ - 5)

The greatest common factor of the given polynomial is 2, so we can factor it out to get: 2(x³ - 5)

Learn more about Greatest common factor here:

https://brainly.com/question/11221202

#SPJ1

Answer: $28.00 (C)

Step-by-step explanation:

The total is 28 (based on the equation).

No matter how many blueberries or raspberries Amit buys, the toal must equal 28 dollars.