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Talja [164]
3 years ago
13

What is the surface area of a square pyramid with a height of 12 mm and a base that measures 10mm on each side?

Mathematics
1 answer:
fiasKO [112]3 years ago
7 0

Answer:

The surface area is: 360 millimeters squared

Step-by-step explanation:

Base Surface Area =  10 squared

=  100 millimeters squared

Lateral Surface Area =  

2×10× √  

10/2 squared+ 12 squared

=  260 millimeters squared

Total Surface Area = 360 millimeters squared

Hope this helps!

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A line l2 is perpendicular to the line x + 2y – 5 = 0 without computing the gradient of this
Stells [14]

Answer:

y=2x-2

Step-by-step explanation:

first, let's put the line into y=mx+b form (slope-intercept form), where m is the slope (or gradient) and b is the y intercept

add 5 to both sides

x+2y=5

subtract x from both sides

2y=-x+5

divide by 2

y=-1/2x+5/2

perpendicular lines have slopes (gradients) that are negative (one is positive, another one is negative) and reciprocal (they are essentially the same number, just "flipped")

to find the slope of I2:

since -1/2 is negative, that means the slope of I2 will be 2 (2/1 is the reciprocal of 1/2 (positive version of -1/2))

so here's our equation so far:

y=2x+b

now we need to find b

because line will pass through (3,4), we can use it to solve for b

substitute 4 as y and 3 as x

4=2(3)+b

multiply

4=6+b

-2=b

therefore the equation is y=2x-2

hope this helps!!

3 0
3 years ago
Evaluate the series 72+12+2+
RUDIKE [14]
72+12=84
84+2=86
So add 72 plus 12 and you get Eighty-Four . Plus 2 equals 86
3 0
3 years ago
Find all solutions to the equation (x² + 5x + 6)(x² − 3x − 4) = 0.
Soloha48 [4]

Answer:

The solutions are:

x=-2,\:x=-3,\:x=-1,\:x=4

Step-by-step explanation:

To find the solutions to the equation \left(x^2+5x+6\right)\left(x^2-3x-4\right)=0 you need to:

  • Factor \left(x^2+5x+6\right)

Break the expression into groups

x^2+5x+6=\left(x^2+2x\right)+\left(3x+6\right)

Factor out x from (x^2+2x)

x^2+2x=x\left(x+2\right)

Factor out 3 from 3x+6

3x+6=3\left(x+2\right)

x^2+5x+6=x\left(x+2\right)+3\left(x+2\right)\\\\\mathrm{Factor\:out\:common\:term\:}x+2\\\\x^2+5x+6=\left(x+2\right)\left(x+3\right)

  • Factor \left(x^2-3x-4\right)

x^2-3x-4=\left(x^2+x\right)+\left(-4x-4\right)\\\\x^2-3x-4=x\left(x+1\right)-4\left(x+1\right)\\\\x^2-3x-4=\left(x+1\right)\left(x-4\right)

Therefore

\left(x^2+5x+6\right)\left(x^2-3x-4\right)=\left(x+2\right)\left(x+3\right)\left(x+1\right)\left(x-4\right)=0

Using the Zero Factor Theorem:

5 0
4 years ago
How do I solve for number 15
Mama L [17]
X=3 y=1
2x3 = 6 and 3x1 = 3. 6+3 = 9.
Hope this helped!
6 0
3 years ago
Given the functions f(x) = 3(0.56)^x and g(x) = 6(4)^x
rodikova [14]
A)  f(x) is decreasing because the base is less than 1.
      0.56 is close to 0.5, so its like saying that you are taking half each time, therefore the value is getting smaller.

g(x) is increasing because the base is greater than 1.
you are multiplying by 4 each time, making the value bigger.


B )  The y-intercept is where x=0.
      Anything to the '0' power is 1. Therefore the y-intercept is equal to the coefficient in front of each function.
    f(x) = 3 ,   g(x) = 6


C)  Just plug in x=4 to each function in a calculator.
 f(4) = 0.295
g(4) = 1536
7 0
4 years ago
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