What is the lateral surface area of the triangular pyramid?

Answer:

The gradient of line perpendicular to AB is: m = [tex]\frac{1}{2}[/tex]

The equation of line passing through point A and perpendicular to AB is [tex]\mathbf{y=\frac{1}{2}x+6}[/tex]

Step-by-step explanation:

The line on the graph passes through the points A (0,6) and B (3,0)

b) Find the gradient of a line perpendicular to AB

First we will find gradient (slope) of AB

The formula used to find Slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

We have [tex]x_1=0, y_1=6, x_2=3, y_2=0[/tex]

Putting values and finding slope:

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{0-6}{3-0}\\Slope=\frac{-6}{3}\\Slope=-2[/tex]

So, we get slope: m = -2

Now, the gradient of line perpendicular to AB will be opposite to the slope of AB

The gradient of line perpendicular to AB is: m = [tex]\frac{1}{2}[/tex]

c) Find the equation of line passing through point A and perpendicular to AB

The equation of line can be found using slope m = [tex]\frac{1}{2}[/tex] and y-intercept b

We need to find y-intercept b:

Using slope m = [tex]\frac{1}{2}[/tex]  and point A (0,6)

y=mx+b

6= [tex]\frac{1}{2}[/tex] (0)+b

6=0+b

b=6

So, y-intercept is b =6

So, Equation of line with slope m = [tex]\frac{1}{2}[/tex]  and y-intercept b =6 is:

[tex]y=mx+b\\y=\frac{1}{2}x+6[/tex]

So, The equation of line passing through point A and perpendicular to AB is [tex]\mathbf{y=\frac{1}{2}x+6}[/tex]

Answer: 252

Step-by-step explanation:

Answer: n = 0

Step-by-step explanation: Let's solve for n, according to the linear equation given, this way:

10n + 0.3 = 0.1n + 0.3

10n - 0.1n = 0.3 - 0.3 (Like terms)

9.9n = 0

n = 0/9.9

n = 0

Answer:

x = 19.6

Step-by-step explanation:

By applying cosine rule in ΔBCD,

cos(30)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

              = [tex]\frac{BC}{BD}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{BC}{16}[/tex]

BC = [tex]8\sqrt{3}[/tex]

Now, by applying sine rule in ΔBAC,

sin(45)° = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{\sqrt{2}}=\frac{AB}{BC}[/tex]

[tex]\frac{1}{\sqrt{2}}=\frac{x}{8\sqrt{3}}[/tex]

x = [tex]8\sqrt{6}[/tex]

x = 19.59

x ≈ 19.6  

Answer:

c. 12

Step-by-step explanation:

if the pentagons are similar they have a common factor.

the factor between 16 cm and 8 cm is 2, so 6*2 is 12.

Answer:

C)3

Step-by-step explanation:

this is according to my test

Answer:

No correlation

Step-by-step explanation:

There's no discernible trend in the data.

Answer:

Step-by-step explanation:

First we start off by rounding that number to the nearest ten, not tenTH. This rounding would lead to 180$. Now comes the percent part. Here i use the percent equation, which is ____ is ____% of _____. our percent is 10%, and our whole goes at the end, 180$. The part( or the tax), becomes x, and now we translate. Is means = and of means times. so x=.10(180), and x will equal 18

so the tip will be around 18 dollars

hope it helped

Answer:

im not sure but i think 3

Step-by-step explanation:

Hey again!

The answer to your question is 98 feet squared

First, we find the new dimensions:

7 x 2 = 14

3.5 x 2 = 7

Area = length x width, so 14 x 7 = 98

Hope it helps!

Answer:

The average rate of change from 7 to 60 minutes is 0.36 miles per minute.

Step-by-step explanation:

at x₁ = 7, f(x₁) = 8

at x₂ = 60,  f(x₂) = 27

Using the formula to determine the average rate of change at which the total cost increases will be:

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]  

                     = [27 - 8] / [60-7]  

                     = 19 / 53

                     = 0.36

Therefore, the average rate of change from 7 to 60 minutes is 0.36 miles per minute.

Answer: I can only solve #3 The asnwer is -1.65x

Step-by-step explanation:

Multiplying a positive and a negative equals a negative

(+)x(-)=(-)

-X x 5.5 x 0.2 x 1.5.   <---- Calculate the product

and you will get -1.65x

Hey there!

The answer to your question is z > -4

We can solve this like it is an equation, with one exception. When you divide or multiply by a negative number, in an inequality, you have to flip the inequality sign.

-2z - 3 < 5           add 3 to both sides

     -2z < 8          divide both sides by -2, and flip the inequality sign

         z > -4      

Good luck! Hope it helps, and have a great day!

Answer:

The answer  is z > -4

but a line down were is the (>)

I ready!

holpe it help

Answer:

A) Plumber B charges 55 dollars per hour (105=50+55(1)) because for 1 hour the total is 105, meaning that 105 is y and 1 is x. 50+55=105

B) Plumber A charges more because he charges 100 dollars vs Plumber B's 50 dollars.

C) Plumber A:  250=100+30(5)       Plumber B:  325=50+55(5)

Plumber A charges less money for working 5 hours.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that,

Two plumbers charge an initial fee and an hourly rate.

The equation y=100+30x -----(I) models plumber A's fee, where y is the total charge, in dollars, and x is the number of hours worked.

Part A:

From the table, we have (1, 105) and (2, 160)

Now, m=(160-105)/(2-1)

= 55

Substitute m=55 and (x, y)=(1, 105) in y=mx+c, we get

105=55(1)+c

c=60

Substitute m=55 and c=60 in y=mx+c, we get

y=55x+60 -----(II)

By comparing (I) and (II), we can conclude that plumber B charges more hourly fee.

Part B: By comparing (I) and (II), we can conclude that plumber A charges more initial fee.

Part C: Substitute x=5 in y=100+30x, we get

y=$250

Substitute x=5 in y=55(5)+60, we get

y=$335

Plumber A charges less money for working 5 hours.

Therefore, plumber A charges more initial fee.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Answer:

10 cents

Step-by-step explanation:

Answer:

$0.25 for each egg

$2.5 for each pound of peanuts

$0.5 for each toilet paper roll

$0.35 for each apple

Step-by-step explanation:

3/12=.25

7.50/3=2.5

2/4=.5

3.5/10=.35

answer

Answer:

here you go

Step-by-step explanation:

-5x+2

Answer:

C=85+2x

Step-by-step explanation:

c=85+2(3)     --   $91

c=85+2(4)     --   $93

c=85+2(5)     --   $95

c=85+2(6)     --   $97

Step-by-step explanation:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

9514 1404 393

Answer:

Step-by-step explanation:

The equation of the given line is written in "slope-intercept form":

  y = mx + b . . . . . . where m is the slope

Matching this form to the equation you have, you see that ...

  m = 5 . . . the slope of your given line.

__

A parallel line will have the same slope: 5.

__

A perpendicular line will have a slope that is the opposite reciprocal of this. The reciprocal of 5 is 1/5. The opposite of that is -1/5.

A perpendicular line will have a slope of -1/5.

Answer:

the answer is 1 and 1 fourth

Answer:

x is in the top left of the triangle :)

Step-by-step explanation:

Answer:

its there....

Step-by-step explanation:

Answer:

104 = 10 × 10 × 10 × 10 = 10,000

Step-by-step explanation:

In words: 104 could be called "10 to the fourth power", "10 to the power 4" or "10 to the 4"

Answer:

a rational number

Step-by-step explanation:

1) First, find the sum of [tex]\frac{4}{7} +\frac{-1}{3}[/tex]:

[tex]\frac{4}{7} + \frac{-1}{3} \\= \frac{12}{21} - \frac{7}{21} \\= \frac{5}{21}[/tex]

2) Any number that can be written as a fraction is a rational number. Therefore, the sum, [tex]\frac{5}{21}[/tex], is rational.

Nolan has 20 pens and 3 pencils, while Fiona has 5 pens and 18 pencils.

Given that Nolan has 4 times as many pens as Fiona, and Fiona has 6 times as many pencils as Nolan, to determine, if Nolan has a total of 23 pens and pencils, and so does Fiona, the number of pens and pencils that either Nolan or Fiona has, the following calculation must be performed:

Therefore, Nolan has 20 pens and 3 pencils, while Fiona has 5 pens and 18 pencils.

Learn more about amount determination in https://brainly.com/question/14342345

Answer:

he donated 1/6 of the total land to charity

Step-by-step explanation:

1/2 went to daughter

1/3 went to daughter

combined, this equals 5/6 of the total land

this leaves 1/6 to be donated

Step-by-step explanation:

the given height is also the radius of the inscribed circle and the formula for the area is S=2r^2*sqrt(5*(5-2sqrt5))=490*tan18 which roughly rounds to 156.8