A group of students made trees out of paper for a scene in a school play. The trees are shaped like square pyramids. 70 cm70\text{ cm} 70 cm 140 cm140\text{ cm} 140 cm How much paper will it take to make each tree, including the bottom?

Answer:

Step-by-step explanation:

[tex] \frac{7x + 19}{(x + 1)(x + 5)} [/tex]

Multiply each term in the first parentheses by each term in second parentheses ( FOIL)

[tex] \frac{7x + 19}{x(x + 5) + 1(x + 5)} [/tex]

Calculate the product

[tex] \frac{7x + 19}{ {x}^{2} + 5x + x + 5} [/tex]

Collect like terms

[tex] \frac{7x + 9}{ {x}^{2} + 6x + 5 } [/tex]

Hope this helps...

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The value of (f - g)(x) is x² + 4x + 3 if f(x) =  2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) =  2x² - 5

g(x) = x² - 4x - 8

(f - g)(x) = f(x) - g(x)

= (2x² - 5) - (x² - 4x - 8)

= 2x² - 5 - x² + 4x + 8

= x² + 4x + 3

(f - g)(x) = x² + 4x + 3

Thus, the value of (f - g)(x) is x² + 4x + 3 if f(x) =  2x² - 5 and g(x) = x² - 4x - 8 option (B) is correct.

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Answer:

No

Step-by-step explanation:

The sum of two random sides of a triangle must be bigger than the third side and their differences must be smaller than the third side

For example

3 - 4 - 5 can be made into a triangle because 3 + 4 > 5 and 4 - 3 < 5

Answer:8/21

Step-by-step explanation:

cba to write it down

The probability of a student choosing running is 4/63.

Given that,

Total number of students = 63

Number of boys = 38

Number of girls = 63 - 38 = 25

Number of students who chose football = 20

Number of girls who chose football = 19

Number of students who chose tennis = 19

Number of girls who chose running = 5

To find the probability of a student choosing running,

We need to know the total number of students who chose running.

From the given information,

We know that the number of students who did not choose running is:

Number of students who chose football = 20

Number of students who chose tennis = 19

Number of girls who did not choose running = 25 - 5 = 20

Therefore, the total number of students who chose running is:

Total number of students - Number of students who did not choose running

= 63 - (20 + 19 + 20) = 4

So, the probability of a student choosing running is:

Number of students who chose running / Total number of students

= 4 / 63

Therefore, the probability that a student selected at random chose running is 4/63

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Answer:

2(a - 3). = 4

_______

3

Cross multiply.

2(a- 3) = 12

2a - 6 = 12

2a = 12 + 6

2a = 18

a = 18 ÷ 2

a = 9

Answer:

a = 9

Step-by-step explanation:

Given

[tex]\frac{2(a-3)}{3}[/tex] = 4 ( multiply both sides by 3 to clear the fraction

2(a - 3) = 12 ( divide both sides by 2 )

a - 3 = 6 ( add 3 to both sides )

a = 9

As a check substitute a = 9 into the left side of the equation and if equal to the right side then it is the solution.

[tex]\frac{2(9-3)}{3}[/tex] = [tex]\frac{2(6)}{3}[/tex] = [tex]\frac{12}{3}[/tex] = 4 = right side

Thus solution is a = 9

Answer:

10.375

Step-by-step explanation:

1.) Add up all the amount of pizzas |  12 + 9 + 11 +10+13+8+ 7,+ 13=83

2) Divide the total amount of pizzas by the amount of pizzas/amount of numbers of pizzas. | 83 divided by 8 =

10.375

Answer:

[tex]\boxed{\frac{25\pi }{36}}[/tex]

Step-by-step explanation:

Use the formula to convert from degrees to radians: [tex]x * \frac{\pi }{180}[/tex], where x is the value in degrees.

[tex]125 * \frac{\pi }{180}[/tex] = [tex]\frac{125\pi }{180}[/tex]

Then, simplify your fraction ⇒ [tex]\frac{125\pi }{180} = \boxed{\frac{25\pi}{36} }[/tex]

Answer: 283 cm2

Step-by-step explanation:

The formula for finding the surface area of a cone is:

A=[tex]\pi r(r+\sqrt{h2+r2})[/tex] Where r is the radius and h is the height.

Replacing: [tex]\pi 5(5+\sqrt{(12)2+(5)2}[/tex]

Solving: 282,7 ≈ 283cm2

Answer:

bee

Step-by-step explanation:

its be because its true

Answer:

p²q³ + pq and pq(pq² + 1)

Step-by-step explanation:

Given

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Required

Collect like terms

We start by rewriting the expression

3p²q² - 3p²q³ +4p²q³ -3p²q² + pq

Collect like terms

3p²q² -3p²q² - 3p²q³ +4p²q³ + pq

Group like terms

(3p²q² -3p²q²) - (3p²q³ - 4p²q³ ) + pq

Perform arithmetic operations on like terms

(0) - (-p²q³) + pq

- (-p²q³) + pq

Open bracket

p²q³ + pq

The answer can be further simplified

Factorize p²q³ + pq

pq(pq² + 1)

Hence, 3p²q² - 3p²q³ +4p²q³ -3p²q² + pq is equivalent to p²q³ + pq and pq(pq² + 1)

Answer:

11

Step-by-step explanation:

Given:

3/2y - 3 + 5/3z

When

y=6

z=3

3/2y - 3 + 5/3z

Substitute the value of y and z

3/2(6) - 3 + 5/3(3)

=18/2 - 3 + 15/3

=9-3+5

=6+5

=11

Answer:

[tex]y = \frac{5x}{2} - 5[/tex]

Step-by-step explanation:

Given the equation 5x - 2y = 10, to write the equation in slope-intercept form, we need to write it in the standard format y = mx+c where m is the slope/gradient and c is the intercept.

From the equation given  5x - 2y = 10, we will make y the subject of the formula as shown;

[tex]5x - 2y = 10\\\\subtract \ 5x \ from \ both \ sides\\\\5x - 2y - 5x = 10 - 5x\\\\-2y = 10-5x\\\\Dividing \ both \ sides\ by \ -2;\\\\\frac{-2y}{-2} = \frac{10-5x}{-2}\\ \\[/tex]

[tex]y = \frac{10}{-2} - \frac{5x}{-2} \\\\y = -5 + \frac{5x}{2}\\\\y = \frac{5x}{2} - 5[/tex]

Hence the equation that represents the first equation written in slope-intercept form is [tex]y = \frac{5x}{2} - 5[/tex]

Answer:

The number of boys, x = 12

Step-by-step explanation:

Given that the sum of the ages of the boys in a class = 84 years

The number of boys = x

A new boy aged 8 years 1 month is added and the average age increases by 1 month

We have

Average age = 84/x = y

Age of new boy = 8 years 1 month = [tex]8\frac{1}{12} \ year[/tex]

New average = y + 1/12 = [tex](8\frac{1}{12}+84) /(x + 1)[/tex] which gives;

84/x + 1/12 = [tex](8\frac{1}{12} + 84) /(x + 1)[/tex]

[tex]\dfrac{x +1008}{12 \cdot x} = \dfrac{1105}{12 \cdot x+ 12}[/tex]

(x + 1008)×(12·x + 12) = 1105× 12·x

12·x² -1152·x + 12096 = 0

x² -96·x + 1008 = 0

(x - 84)×(x - 12) = 0

Therefore, x = 12 or 84,

The number of boys are 12 or 84

For there to bee 84 boys, their average age would be one year each

Given that they are boys not babies, then there are only 12 boys.

Answer:

The height of the tower is:

24 meters

Step-by-step explanation:

1 meter = 100 centimeters

10 centimeters = 10/100 = 0.1 meters

8 centimeters = 8/100 = 0.08 meters

On a three rule:

0.1 meters is to 0.08 meters

30 meters is to A meters

A = 30*0.08/0.1

A = 24 meters

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Answer:

La magnitud del desplazamiento resultante es 2045.463 kilómetros. La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.

Step-by-step explanation:

En primer lugar, se construye el triángulo. La figura resultante se encuentra incluida como archivo adjunto. La magnitud del desplazamiento resultante se determina mediante la Ley del Coseno:

[tex]r = \sqrt{(800\,km)^{2}+(1400\,km)^{2}-2\cdot (800\,km)\cdot (1400\,km)\cdot \cos 135^{\circ}}[/tex]

[tex]r \approx 2045.463\,km[/tex]

La magnitud del desplazamiento resultante es 2045.463 kilómetros.

La dirección del desplazamiento resultante es hallada por medio de la Ley del Seno, sabiendo que el ángulo del desplazamiento resultante a la recta de 1400 kilómetros:

[tex]\frac{1400\,km}{\sin \alpha} = \frac{2045.463\,km}{\sin 135^{\circ}}[/tex]

Se despeja el ángulo correspondiente:

[tex]\alpha = \sin^{-1}\left(\frac{1400\,km}{2045.463\,km}\times \sin 135^{\circ} \right)[/tex]

[tex]\alpha \approx 28.945^{\circ}[/tex]

La dirección absoluta del desplazamiento resultante es:

[tex]\alpha' = 180^{\circ}-\alpha[/tex]

[tex]\alpha' = 180^{\circ}-28.945^{\circ}[/tex]

[tex]\alpha' = 151.055^{\circ}[/tex]

La dirección absoluta del desplazamiento resultante es 151.055º, el cual corresponde al sentido noroeste.

Answer:

T = - 3.2e + 80

Step-by-step explanation:

Given the following :

e = elevation in thousands of feets

T = temperature (°F)

e1 = 5 ; e2 = 10 (in thousands of feet)

T1 = 64° ; T2 = 48°

y = mx + c ; T = me + c

y = ; m = slope, c = intercept

64 = m5 + c - - - - (1)

48 = m10 + c - - - - (2)

From (1)

c = 64 - m5

Substitute c = 64 - m5 into (2)

48 = m10 + c - - - - (2)

48 = m10 + 64 - m5

48 - 64 = 10m - 5m

-16 = 5m

m = - 16 / 5

m = - 3.2

Substitute the value of m into c = 64 - m5

c = 64 - 5(-3.2)

c = 64 - (-16)

c = 64 + 16

c = 80

Inserting our c and m values into T = me + c

T = - 3.2e + 80

Where e is in thousands of feet

T is in °F

Answer:

C

Step-by-step explanation:

x+4> 8

Subtract 4 from each side

x+4-4>8-4

x > 4

Open circle at 4, line going to the right

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▹ Answer

[tex]Solved - x > 4\\Graphed - C[/tex]

▹ Step-by-Step Explanation

x + 4 > 8

x > 8 -4

x > 4

When graphing inequalities, you have less than, greater than, less than or equal to, and greater than or equal too. When graphing an inequality with less than or greater than, you use an open circle. When graphing an inequality with less than or equal too or greater than or equal too, you used a closed circle.

Since the numbers are positive, we are going to move up the number line therefore leaving us with the answer of C.

Hope this helps!

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Answer:

a. 4r² b. 2r c. 6 cm

Step-by-step explanation:

The surface area A of the cube is A = 24r². We know that the surface area, A of a cube also equals A = 6L² where L is the length of its side.

Now, equating both expressions, 6L² = 24r²

dividing both sides by 6, we have

6L²/6 = 24r²/6

L² = 4r². Since the area of one face is L², the polynomial that determines the area of one face is A' = 4r².

b.  Since L² = 4r² the rea of one face of the cube, taking square roots of both sides, we have

√L² = √4r²

L = 2r

So, the polynomial that represents the length of an edge of the cube is L = 2r

c. The length of an edge of the cube is L = 2r. When r = 3 cm.

L = 2r = 2 × 3 cm = 6 cm

So, the length of an edge of the cube is 6 cm.

Answer:

B.

Step-by-step explanation:

First, let's start from the parent function. The parent function is:

[tex]f(x)=\sqrt{x}[/tex]

The possible transformations are so:

[tex]f(x)=a\sqrt{bx-c} +d[/tex],

where a is the vertical stretch, b is the horizontal stretch, c is the horizontal shift and d is the vertical shift.

From the given equation, we can see that a=1 (so no change), b=3, c=-3 (negative 3), and d=3.

Thus, this is a horizontal stretch by a factor of 3, a shift of 3 to the left (because it's negative), and a vertical shift of 3 upwards (because it's positive).

Answer:

333 cars

Step-by-step explanation:

Assuming among 6 agents, the working efficiency is the same and constant. Fixing number of agents:

    6 agents can sell 333 cars in 3 months.

=> 6 agents can sell 333/3 cars in 3/3 month.

=> 6 agents can sell 111 cars in 1 month.

Fixing number of months:

=> 6/2 agents can sell 111/2 cars in 1 month.

=>  3 agents can sell 111/2 cars in 1 month.

Then considering that 3 agents worked in 6 months:

=> 3 agents can sell 6 x 111/2 cars in 6 x 1 months.

=> 3 agents can sell 333 cars in 6 months.

[tex](2+3)^{-1}\equiv5^{-1}\pmod7[/tex] is the number L such that

[tex]5L\equiv1\pmod7[/tex]

Consider the first 7 multiples of 5:

5, 10, 15, 20, 25, 30, 35

Taken mod 7, these are equivalent to

5, 3, 1, 6, 4, 2, 0

This tells us that 3 is the inverse of 5 mod 7, so L = 3.

Similarly, compute the inverses modulo 7 of 2 and 3:

[tex]2a\equiv1\pmod7\implies a\equiv4\pmod7[/tex]

since 2*4 = 8, whose residue is 1 mod 7;

[tex]3b\equiv1\pmod7\implies b\equiv5\pmod7[/tex]

which we got for free by finding the inverse of 5 earlier. So

[tex]2^{-1}+3^{-1}\equiv4+5\equiv9\equiv2\pmod7[/tex]

and so R = 2.

Then L - R = 1.

Answer:

0.15x + 0.20y = 1.80

Step-by-step explanation:

Here, we are interested in writing an equation for the total cost of the apples and bananas

before we write , kindly understand that 100p = £1

So the cost of apple which is 15p will be 15/100 =£ 0.15

The cost of bananas which is 20p will be 20/100 = £0.2

Thus, the total cost of the apples bought will be number of apples bought * price of apple bought = 0.15 * x = £0.15x

The cost of bananas = number of bananas bought * price of bananas = 0.2 * y = £0.2y

So the total cost of the apples and bananas will be;

0.15x + 0.20y = 1.80

Answer:

37.5 cm

Step-by-step explanation:

See attached for reference.

let the diagonal be x,

By Pythagorean formula:

x² = (22.5)² + (30)²

x = √[(22.5)² + (30)²]

x = 37.5 cm

Answer:

6

Step-by-step explanation:

I think the answer is 6

Answer:

the first one has one solution because eventually they will cross

Answer:

Option B.

Step-by-step explanation:

According to the question, the data provided is as follows

[tex]H_o : p_1 - p_2 = 0\ (p_1 = p_2)\\\\ H_\alpha : p_1 - p_2 < 0\ (p_1 < p_2)[/tex]

Based on the above information,

The type ii error is the error in which there is an acceptance of a non rejection with respect to the wrong null hypothesis. The type I error refers to the error in which there is a rejection of a correct null hypothesis and the type II refers that error in which it explains the failure of rejection with respect to null hypothesis that in real also it is wrong  

So , the type II error is option B as we dont create any difference also the proportion is very less

Answer:

prime

Step-by-step explanation:

x^2 - 2x + 3

What two numbers multiply to 3 and add to -2

There are none so this cannot be factored in the real numbers

Answer:

1. (2,1)

2. (6,-1)

3.(-2,3)

Answer:

1. (2,1)

2.  (6,-1)

3. (-2,3)

Step-by-step explanation:

Each of the answer is consistent system because the lines intersect at one point, which is one solution.

Answer:

1.

[tex](x , y) = (4 ,\: 0)[/tex]

2.

[tex](4,0) = (x,y)[/tex]

3.

[tex](x,y) = ( - 3,0)[/tex]

I hope it helps :)

Answer:  

Rectangular pyramid  8 edges

Rectangular prism    12 edges

Triangular Prism   9 edges

Triangular Pyramid  6 edges

Step-by-step explanation: Faces connected at edges

Rectangular pyramid    1 Base  and 4  slanted  triangular sides

Rectangular prism    2 top and bottom bases and 4 sides

Triangular Prism   2 top and bottom triangular bases 3 rectangular sides

Triangular Pyramid    1 triangular base, 3 slanted triangular sides

The matching is as follow:

Rectangular pyramid:  8 edges

Rectangular prism:  12 edges

Triangular Prism: 9 edges

Triangular Pyramid: 6 edges

A pyramid is a triangular-sided, single-polygonal base, three-dimensional polyhedron-shaped construction. A prism is a three-dimensional polyhedron with rectangular sides that are perpendicular to the base and two polygonal bases.

Rectangular pyramid have one Base and 4 slanted triangular sides

Rectangular prism have 2 top and bottom bases and 4 sides

Triangular Prism have 2 top and bottom triangular bases 3 rectangular sides.

Triangular Pyramid have 1 triangular base, 3 slanted triangular sides.

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Answer: The area of land =108 m²

Step-by-step explanation:

In the given piece of land is in the shape of a parallelogram.

Diagonals divide it into 2 equal parts.

So, area of parallelogram = 2 x (Area of triangle with sides 12m and 9 m and  15 m)

Heron's formula :

Area of triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\dfrac{a+b+c}{2}[/tex]

Let a= 12 , b= 9 and c = 15

[tex]s=\dfrac{12+9+15}{2}=18[/tex]

Area of triangle = [tex]\sqrt{18(18-12)(18-9)(18-15)}[/tex]

[tex]=\sqrt{18\times6\times9\times3}=\sqrt{2916}=54\ m^2[/tex]

Then, area of parallelogram= 2 x 54 = 108 m²

Hence, the area of land =108 m²