A square pyramid has a base with a side length
of 8 feet and lateral faces with heights of 6 feet.
What is the lateral area of the pyramid?

Answer:

x+3y -10 =0

Step-by-step explanation:

In slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = -1/3x +10/3

We want it in the general form  ax+by +c =0  where a,b,c are integers and a>0

Multiply by 3 on each side

3*y = 3(-1/3x +10/3)

3y = -x +10

Add x to each side

x+3y = -x+10 +x

x+3y = 10

Subtract 10 from each side

x+3y -10 = 10-10

x+3y -10 =0

The slope of a line is [tex] - \frac{1}{3} [/tex] and the y-intercept is [tex] \frac{10}{3} [/tex]. What is the equation of the line written in general form?

○ 10x + 3y - 1 = 0

○ x + 3y + 10 = 0

○ x + 3y - 10 = 0

[tex] \quad \quad\quad\quad\boxed{\tt{y = mx + b}}[/tex]

[tex]\quad \quad\quad\quad\boxed{\tt{Slope (m) = \frac{1}{3} }}[/tex]

[tex]\quad \quad\quad\quad\boxed{\tt{y \: intercept(b) = \frac{10}{3} }}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{y = - \frac{ 1}{3}x + \frac{10}{3} }}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{ax + by + c = 0}}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{ (3)y = 3(- \frac{ 1}{3}x + \frac{10}{3} )}}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{ 3y = \cancel{ \color{red}3}(- \frac{ 1}{ \cancel{ \color{red}3}}x + \frac{10}{ \cancel{ \color{red}3}} )}}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{3y = - x + 10}}[/tex]

[tex] \quad\quad\quad\boxed{\tt{3y = - x + 10}} \: ➡ \: \boxed{\tt{x + 3y = 10}}[/tex]

[tex] \quad\quad\quad \boxed{\tt{x + 3y = 10}} \: ➡ \: \boxed{ \tt{x + 3y - 10 = 0}}[/tex]

[tex]\quad \quad\quad\quad \boxed{ \color{green}{ \tt{x + 3y - 10 = 0}}}[/tex]

_________

#LetsStudy

Answer:

Volumen A = 30000 cm³

Volumen B = 35000 cm³

Volumen C = 72000 cm³

Step-by-step explanation:

a) Volumen A

Largo = 50 cm, Ancho = 30 cm Alto = 20 cm

Volumen = Largo × Ancho × Alto

= 50 cm × 30 cm × 20 cm

= 30000 cm³

b) Volumen B

Largo = 35 cm, Ancho = 20 cm Alto = 50 cm

Volumen = Largo × Ancho × Alto

= 35 cm × 20 cm × 50 cm

= 35000 cm³

c) Volumen C

Largo = 40 cm, Ancho = 60 cm Alto = 30 cm

Volumen = Largo × Ancho × Alto

= 40 cm × 60 cm × 30 cm

= 72000 cm³

Answer:

the maximum amount that something can contain. hope this helps :)

Step-by-step explanation:

Answer:

neither

Step-by-step explanation:

Slope of the first line: (y2 -y1)/(x2-x1) = (3-(-5)/-1 = 8/-1 = -8

Slope of the second line: (2-3)/4-(-4) = -1/8

They are neither parallel nor perpendicular. In fact the two lines have different slope so they can’t be parallel. In addition the product of their slope is not -1, so they can’t be perpendicular,

[tex] - 11a(3a + 2) \\ = - 11a \times 3a \: \: \: \: \: \: \: \: \: \: \: \: \: - 11a \times 2a \\ = - 11 \times 3 \times a \times a \: \: \: \: \: \: \: \: \: \: \: \: \: - 11 \times 2 \times a \times a \\ =\boxed {- 33a {}^{2} - 22a {}^{2}}[/tex]

[tex]I \: hope \: it \: will \: help \: you[/tex]

Answer:

[tex](f-g)(x)=-4x^2+10x[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=-x^2+6x-1\text{ and } g(x)=3x^2-4x-1[/tex]

And we want to find:

[tex](f-g)(x)[/tex]

This is equivalent to:

[tex]=f(x)-g(x)[/tex]

Substitute:

[tex]=(-x^2+6x-1)-(3x^2-4x-1)[/tex]

Distribute:

[tex]=-x^2+6x-1+(-3x^2+4x+1)[/tex]

Rearrange:

[tex]=(-x^2-3x^2)+(6x+4x)+(-1+1)[/tex]

Combine like terms. Hence:

[tex](f-g)(x)=-4x^2+10x[/tex]

Answer:

2/25

Step-by-step explanation:

[tex]n^3 = \frac{8}{125}[/tex]

[tex]n^3 = (\frac{2}{5})^3[/tex]

[tex]n = \sqrt[3]{n^3} = \sqrt[3]{(\frac{2}{25})^3}[/tex]

[tex]n = \sqrt[3]{(\frac{2}{25})^3}[/tex]

[tex]n = \frac{2}{25}[/tex]

Answer:

4.383

Step-by-step explanation:

Pythagoras

a² + b² = c²

with c being the baseline of the rectangular triangle (the line opposite to the 90 degree angle).

so, in our example here c=6.5cm, a=QR, b=4.8cm

a² = c² - b² = 6.5² - 4.8² = 19.21

a = sqrt(19.21) = 4.383

Answer:

333831

Step-by-step explanation:

Answer:

10^7 is 10,000,000

3 x 10^3 is 3000

Therefore to find how many times 10^7 is as large as 3.10^3, divide 10,000,000 by 3000

& you’ll get 3333.3

Step-by-step explanation:

Answer:

a = 6

Step-by-step explanation:

Area = 36 [tex]in^{2}[/tex]

Only one number will make this missing length true.

Obviously it's a square so one number x one number will equal to 36 [tex]in^{2}[/tex]

6 x 6 = 36 [tex]in^{2}[/tex]

Answer:

The missing length of square is 6 in.

Step-by-step explanation:

Here we have given the area of square = 36 in ²

We need to find the missing length of square .

Using formula

Area of square = ( side ) ²

put the values

36 in² = ( side)²

Finding the square root of 36 in²

√36 in ² = side

6 in = side

Hence, the side of square is 6 in.

Answer:

Latoya will charge $10 more to tutor for 5.5 hours

Step-by-step explanation:

We shall look at the total charges of both tutors individually.

Oscar charges $25 for the first hour of tutoring and $15 for each additional hour of fraction of an hour counting as a whole hour.

This means that for the first hour, Oscar charges $25.

For every subsequent hour, regardless of whether the student was tutored for the full hour or only partial, Oscar still charges $15 for the particular hour. To clarify, here is an example.

If a student is tutored for 2 hours, the cost for Oscar's tutoring is $25 (first hour) + $15 (second hour) = $40. However, if the student is still tutored for 1.5 hours, the cost for Oscar's tutoring is still $25 (first hour) + $15 (second hour) = $40. This is because Oscar counts the partial minutes as a full hour in tutoring costs.

For 5.5 hours, the cost of Oscar's tutoring is

$25 (first hour) + $15*4 (2nd to 5th hours) + $15 (the last half an hour) = $100.

Now, we shall look at Latoya's tutoring cost.

f(x) =

30x,

[tex]0 \leqslant x \leqslant 3[/tex]

20x,

[tex]3 < x \leqslant 6[/tex]

10x,

[tex]x > 6[/tex]

The tutoring cost depends on x, the number of tutoring hours. In this case, x is 5.5. The cost for 5.5 hour depends on the formula 20x since 5.5 is more than 3 but less than 6.

Hence, the tutoring cost for Latoya is $20*5.5 = $110.

In this case, Latoya charges $110-$100=$10 more to tutor for 5.5 hours.

Step-by-step explanation:

hakdogg happyly ever after

Answer: C

Step-by-step-explanation: Given

- (12x + 8) ≤ - 2x + 11 ← distribute parenthesis on left side

- 3x - 2 ≤ - 2x + 11 ( add 3x to both sides )

- 2 ≤ x + 11 ( subtract 11 from both sides )

- 13 ≤ x , thus

x ≥ - 13

Since x can equal - 13 then a solid circle at - 13 represents the solution

Since x greater than - 13 then the arrow is facing to the right of - 13 on the number line.

Then the graph representing the solution is C

Answer:

Ascending order

Step-by-step explanation:

Ascending numbers are numbers that begin from smallest to biggest.

Step-by-step explanation:

The formula for the lateral area of a right cone is :

LA = rs

Where

r is the radius of the base and s is the slant height of the cone

Equivalent expression,

[tex]r=\dfrac{LA}{s}[/tex]

or

[tex]s=\dfrac{LA}{r}[/tex]

Hence, this is the required solution.

Answer:

The answers are C & E

Answer:

68°

Step-by-step explanation:

If a quadrilateral is inscribed in a cirle, the sum of its opposite angles is 180°. Angles B and D are opposite => B+D=180° => D=180°-B=180°-112°=68°

Answer:

68°

Step-by-step explanation:

Since angles B and D are opposite each other, they are supplementary.

Answer:

x ≈ 12.96

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + 11² = 17²

x² + 121 = 289 ( subtract 121 from both sides )

x² = 168 ( take the square root of both sides )

x = [tex]\sqrt{168}[/tex] ≈ 12.96 ( to the nearest hundredth )

Answer:

4.12m

Step-by-step explanation:

(distance of whole shadow - distance of Aisha from tree)

17.95-12.5=5.45m

17.95/5.45=3.29...(scale factor)

3.29...*1.25=4.12m(to the nearest hundredth)

Answer:

Y=40 X=75

Step-by-step explanation:

i think im not 100% on that, been a long time since i did stuff with triangles

Answer:

gdjksbdifkfnfuwiaksujdbf

Answer:

35.333333333...%

Step-by-step explanation:

954/2700 = 35.33333333333333...%

You could use a calculator to solve these types of problems, but I'm not saying you should use one for every single problem.

Anyway, hope this helps.

Answer:

$1.62

Step-by-step explanation:

Answer:

The triangles are congruent

Step-by-step explanation:

The Triangles are congruent because they have the same side lengths and and angle measures.

It's C.

The value is increasing threefold relative to the previous step.

all other function values increase by a fixed amount and are therefore linear

Answer:125

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

each term is 4 times the previous term

the common ration is 4

Answer:

r = 4

Step-by-step explanation:

The common ratio r of the geometric sequence is calculated as

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{4}{1}[/tex] = 4

Answer:

5/24.

Step-by-step explanation:

2/6 of 5/8 were beginners and girls

= 1/3 * 5/8

= 5/24.

Distance from A to B = B-A = 18-0 = 18

M is the midpoint which means it is equal distance between A and B

M = distance between A and B divided by 2:

M = 18/2 = 9

Answer: M = 9

Answer:

9

Step-by-step explanation:

If m is a midpoint of AB

then

M = 1/2AB

If AB = 18

Then M = 1/2 of 18

18/2 = 9

Hence M = 9