Using the net below, find the surface area
of the pyramid.
9\cm
13 cm
m 3 cm
.
Surface Area =
[?] cm2

[tex]\dfrac 1{\sqrt 7- \sqrt 3}\\\\\\=\dfrac{\sqrt 7 + \sqrt 3}{\left ( \sqrt 7 -\sqrt 3\right) \left( \sqrt 7 + \sqrt 3\right)}\\\\\\=\dfrac{\sqrt 7 + \sqrt 3}{\left(\sqrt 7 \right)^2 - \left(\sqrt 3 \right)^2}\\ \\\\=\dfrac{\sqrt 7 + \sqrt 3}{7-3}\\\\\\=\dfrac 14\left(\sqrt 7 + \sqrt 3\right)[/tex]

Answer:

  about 626.1 ft

Step-by-step explanation:

The geometry of the problem can be modeled by a right triangle. The given angle is opposite the given side, and we are asked to find the hypotenuse. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

__

Solving for the hypotenuse, we get ...

  Hypotenuse = Opposite/Sin

  cable length = (balloon height)/sin(53°) = (500 ft)/0.79864

  cable length ≈ 626.1 ft

The direct variation of x to y implies that x and y increases at the same time, and the formula of x in terms of z is [tex]x = 4z^3[/tex]

The direct proportion of x to y is represented as:

[tex]x\ \alpha\ y^2[/tex]

As an equation, we have:

[tex]x\ =\ ky^2[/tex]

The direct proportion of y to z is represented as:

[tex]y\ \alpha\ z^3[/tex]

As an equation, we have:

[tex]y\ =\ kz^3[/tex]

Square both sides

[tex]y^2 = k^2z^3[/tex]

Substitute [tex]y^2 = k^2z^3[/tex] in [tex]x\ =\ ky^2[/tex]

[tex]x =k^3z^3[/tex]

When z = 2, x = 32.

So, we have:

[tex]32 =k^3 * 2^3[/tex]

Evaluate

[tex]32 =k^3 * 8[/tex]

Divide both sides by 8

[tex]k^3 =4[/tex]

Substitute [tex]k^3 =4[/tex] in [tex]x =k^3z^3[/tex]

[tex]x = 4z^3[/tex]

Hence, the formula of x in terms of z is [tex]x = 4z^3[/tex]

Read more about direct variation at:

https://brainly.com/question/6499629

[tex]\text{Given that,}\\\\\log_b x =2,~~ \log_b y=5,~~ \log_b z = 4\\\\\\\log_b(x\cdot y)\\\\=\log_b x + \log_b y~~~~~~~~~~~~~~~;[\log_b(MN) = \log_b M+ \log_b N ] \\\\=2+5\\\\=7\\\\\\\log_b\left( \dfrac{xy^2}{z^2}\right)\\\\=\log_b (xy^2) - \log_b z^2~~~~~~~~~~;\left[\log_b\left(\dfrac MN \right) = \log_b M - \log_b N \right] \\\\=\log_b x +\log_b y^2 - 2\log_b z\\\\=\log_b x + 2 \log_b y - 2 \log_b z\\\\=2+2 \cdot5 - 2 \cdot 4\\\\=2+10-8\\\\=10-6\\\\=4[/tex]

Answer:

the sum of 6 and a number g

Answer:

-3

Step-by-step explanation:

10x=-33+3 isolate the variable

10x=-30 divide by 10

X=-3

x=-3

Hope it helps.

Do comment if you have any query.

Answer:

O C. x = 3, y = -6

Step-by-step explanation:

Take Equation 1 and equate to x.

Now, substitute in Equation 2.

Answer:

C)  x = 3, y = -6

Step-by-step explanation:

[tex]\textsf{Equation 1}:x-2y=15[/tex]

[tex]\textsf{Equation 2}:2x+4y=-18[/tex]

Rewrite Equation 1 to make x the subject:

[tex]\implies x=15+2y[/tex]

Substitute into Equation 2 and solve for y:

[tex]\implies 2(15+2y)+4y=-18[/tex]

[tex]\implies 30+4y+4y=-18[/tex]

[tex]\implies 8y=-48[/tex]

[tex]\implies y=-6[/tex]

Substitute found value of y into Equation 1 and solve for x:

[tex]\implies x-2(-6)=15[/tex]

[tex]\implies x+12=15[/tex]

[tex]\implies x=3[/tex]

Therefore, the solution to the system of equations is:

x = 3, y = -6

Answer:

it would mean that the anwser is positive

Step-by-step explanation:

The weight of each of the two piles Tineka split the jellybeans in the sack to is 7/24 lb.

Division is when two numbers are grouped into equal parts using another number. The sign used to denote division is ÷.

In order to determine the weight of each pile, divide the weight of the sack by 2.

Weight of each sack = 7/12 ÷ 2

7/12 x 1/2 = 7/24

To learn more about division, please check: https://brainly.com/question/13281206

Answer:

g(x) = x² - 6

h(x) = x² + 3

   g(x) = h(x) + k

 x² - 6 = (x² + 3) + k

 x² - 6 = x² + 3 + k

- x²       - x²

     -6 = 3 + k

    - 3  - 3

     -9 = k

The value of k is -9.

Step-by-step explanation:

MathPapa.com

The pie chart of the number of text messages sent by the students represents the stem plot using a circle graph

The stem plot is given as:

0 | 37

1  | 0011223445 77 88 89

2 | 013557

From the above stem plot, we have the following frequency table

SMS        Frequency

0 - 9         2

10 - 19      16

20 - 29    6

Total       24

Next, we determine the relative frequency table

SMS        Frequency    Relative Frequency

0 - 9         2                           2/24 = 8.33%

10 - 19      16                          16/24 = 66.67%

20 - 29    6                            6/24 = 25.0%

Total       24                            100%

Next, we plot the pie chart

See attachment for the pie chart

Read more about stem plots at:

https://brainly.com/question/23616900

Answer:

3+3+6=12

Step-by-step explanation:

the sides are both3 and bottomed is 6

(1) A  quadratic equation that models the path of the golf ball, is 16.0850t² - 110.560t - 190 = 0.

(2) The angle the ball takes off is 64.4⁰.

The equation that models the motion of the gofl ball is calculated as follows;

Vf² = V₀² - 2gh

at maximum height, Vf = 0

V₀² = 2gh

V₀ = √2gh

V₀ = √(2 x 32.17 x 190)

V₀ = 110.56 ft/s

h = V₀t - ¹/₂gt²

-190 = 110.56t  - ¹/₂(32.17)t²

-190 = 110.56t - 16.0850t²

16.0850t² - 110.560t - 190 = 0

440 = Vxt

Vx = 440/t

The time of motion, t is determined as follows;

16.0850t² - 110.560t + 190 = 0

a = 16.0850, b = -110.560, c = 190, solve using formula method

t = 8.3 s

Vx = 440 /8.3

Vx = 53.01 ft/s

tan θ = (Vy) / (Vx)

tan θ = (110.56)/(53.01)

tan θ = 2.086

θ = tan⁻¹(2.086)

θ = 64.4⁰

Learn more about equation of motion here: https://brainly.com/question/25951773

Answer:

4800

Step-by-step explanation:

→ Find how 15yr periods there are in 45 years

45 ÷ 15 = 3

→ Substitute this value as x into the equation

75 × 4³ = 4800

Answer:

Acute

Step-by-step explanation:

Hope it helps you in your learning process.

Hello there.

What type of triangle is defined by the following set of side lengths

10, 9, 5

Answer:

Acute

Step-by-step explanation:

The triangle perimeter is the sum of the lengths of its three sides.

[tex]p=a+b+c=10+9+5=24[/tex]

The semiperimeter of the triangle is half its perimeter. The semiperimeter appears in formulas for triangles to be given a separate name. the triangle inequality, the longest side length of a triangle is less than the semi perimeter.

[tex]s=\frac{p}{2} =\frac{24}{2} =12[/tex]

using Heron's formula

Heron's formula gives the area of a triangle when the length of all three sides is known.

[tex]T=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]T=\sqrt{12(12-10)(12-9)(12-5)}[/tex]

[tex]T=\sqrt{504}=22.45[/tex]

There you go :) I even calculated it for you.

Hope this helps!

If you have any questions please ask.

Answer:

3.75.../ $1

Step-by-step explanation:

25 ounces ÷ 6.65

6.65 dollars ÷ 6.65

=

3.759398 ounces/1 dollar

Answer:
7

Step-by-step explanation:

because if you spinned it , it has a 1/5 chance, if we divide 35 by 5 we can see its 7 meaning she could exect a average of 7 spins.

Answer:

18.9

Step-by-step explanation:

Answer: 0.11

Step-by-step explanation:

I hope i helped TvT

Step-by-step explanation:

For Slant Height (l)

(l)^2=(3)^2+(4)^2

Using Pythagoras Theroem,

(l)^2=9+16

(l)^2=25

l=5cm

For lateral surface area (pi*r*l)

pi*4*5

20pi cm^2

The lateral area of the cone in terms of π, given that the cone has a radius of 4 cm is 20π cm²

First, we shall obtain the slant height of the cone. This is shown below:

L² = r² + h²

L² = 4² + 3²

L² = 16 + 9

L² = 25

Take the square root of both side

L = √25

= 5 cm

Finally, we shall obtain the lateral area of the cone. This is shown below:

LA = πrL

= π × 4 × 5

= 20π cm²

Thus, the lateral area of the cone is 20π cm²

Learn more about lateral area of cone:

https://brainly.com/question/27344591

#SPJ2

Answer:

12

Step-by-step explanation:

It is Given that two lines segment, AC and BD bisect each other at C.

The missing statement is ∠ACB ≅ ∠ECD

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given two lines segment, AC and BD bisect each other at C.

We have to prove that ΔACB ≅ ΔECD

In triangle ACB and ECD

AC=CE    (Given)

BC=CD   (Given)

so, as seen in options the angle ∠ACB ≅ ∠ECD due to vertically opposite angles

hence, the missing statement is ∠ACB ≅ ∠ECD

Learn more about triangles;

https://brainly.com/question/2773823

#SPJ1

Answer:

C.∠ACB ≅ ∠ECD

Step-by-step explanation:

Answer:

w = 10√2

y = 20

Step-by-step explanation:

Sum of interior angles of a triangle = 180°

Therefore, the triangle on the left (with side length 10) is a right triangle,
since 180° - 45°- 45° = 90°

As this triangle is also an isosceles triangle (since it has 2 equal angles), then it will have 2 sides of the same length.  
So the legs of the right triangle are both 10 units.

Using Pythagoras' Theorem to calculate the hypotenuse of this triangle:

⇒ 10² + 10² = c²

⇒ 200 = c²

⇒ c = √200

⇒ c = 10√2

The triangle with side w and base y is also isosceles triangle with base angles of 45°.

Therefore, the sides are equal in length.

So w = hypotenuse of the left triangle = 10√2

We know that the horizontal distance between the left base vertex and the top vertex of this triangle is 10, therefore y = 10 + 10 = 20

Check the picture below.

[tex]\textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=10 \end{cases}\implies \begin{array}{llll} SA=2\pi (3)(10+3) \\\\\\ SA=6\pi (13)\implies SA=78\pi \\\\\\ SA\approx 245.04 \end{array}[/tex]

Answer:

[tex]78\, \pi[/tex].

Step-by-step explanation:

A cylinder of height [tex]h[/tex] and radius [tex]r[/tex] could be unrolled into:

The radius of each circle is the same as the radius of the cylinder, [tex]r[/tex].

The height of the rectangle is the same as the height of the cylinder, [tex]h[/tex].

The width of this rectangle would be [tex](2\, \pi\, r)[/tex], same as the circumferences of the two circles. The reason is that when this rectangle is rolled to build the cylinder, the top and bottom edges of the rectangle would wrap around the circumference of the two circles.

The area of each circle would be [tex]\pi\, r^{2}[/tex]. Note that there are two such circles, one at the top of the cylinder and one at the bottom.

With a height of [tex]h[/tex] and a width of [tex](2\, \pi\, r)[/tex], the area of the rectangle on the side would be [tex](2\, \pi\, r)\, h[/tex]. Add these areas up to find the total surface area of this cylinder:

[tex]\begin{aligned}& \text{(Surface Area of the Cylinder)} \\ =\; & (\text{Surface area of circle on the top}) \\ & + (\text{Surface area of circle at the bottom}) \\ & + (\text{Surface area of rectangle on the side}) \\ =\; & \pi\, r^{2} + \pi\, r^{2} + (2\, \pi\, r)\, h \\ =\; & 2\, \pi\, r^{2} + (2\, \pi\, r)\, h \end{aligned}[/tex].

For the cylinder in this question, [tex]h = 10[/tex] whereas [tex]r = 3[/tex]. The surface area of this cylinder would be:

[tex]\begin{aligned}& 2\, \pi\, r^{2} + (2\, \pi\, r) \, h \\ =\; & 2 \,\pi \times 3^{2} + (2\, \pi\times 3) \times 10 \\ =\; & 78\, \pi\end{aligned}[/tex].

Answer:

18

Step-by-step explanation:

If you x 12x6 the area would get you 72 you already used 6 and 12 you just times 6x3 and that gets 18. If this didnt help im sorry!

The expression that represents the volume of the prism is x²(x-2).

Given side of the base =[tex]x[/tex]

So, the area of the base =[tex]x^{2}[/tex]

Given the height of the prism = [tex]x-2[/tex]

The volume of the prism with base area A and height h is Ah.

So, the volume of the given prism with the base area [tex]x^{2}[/tex] and height [tex](x-2)[/tex] will be:

V= [tex]x^{2} *(x-2)[/tex]

V= [tex]x^{2} (x-2)[/tex]

Hence, the expression that represents the volume of the prism is x²(x-2).

To get more about prisms visit:

https://brainly.com/question/23963432

Answer:

its C trust me

Step-by-step explanation:

Using the fraction model, Emma made a mistake by adding 5 and 3 to get 8/100, instead of 3/100 + 5/10 = 53/100.

Fractions can be referred to as a part of a whole number.

The following are the information given that was omitted:

1 grid having 10 equal columns. 5 are shaded.

This can be expressed as a fraction, as 5/10.

Another identical grid shows, 100 squares with 3 of them shaded, which can be represented in fraction, as 3/100.

The model for the addition problem would be solved as:

3/100 + 5/10 = 53/100

Therefore, using the fraction model, Emma made a mistake by adding 5 and 3 to get 8/100, instead of 3/100 + 5/10 = 53/100.

Learn more about fractions on:

https://brainly.com/question/26916131

Answer:

2/6th or 1/3rd of the pie

Step-by-step explanation:

Subtract 2/6 from 2/3:  convert 2/3 to 4/6.  Then 4/6 less 2/6 is 2/6.

Matt ate 2/6th, or 1/3rd, more pie than did his mother.