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4 years ago

Solve the following equation, and check your solution. Be sure to show all work.

1 answer:

german4 years ago

4 0

24 - 3x = -27
Subtract 24 from both sides
-3x = -51
Divide -3 on both sides so that the only thing remaining on the left side is the variable x.
Final Answer: x= 17

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Here is a triangular pyramid and its net.

galben [10]

Answer:

a) Area of the base of the pyramid = $15.6\ mm^{2}$

b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. $\text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\$

${\Rightarrow \text{Area of pyramid's base = }\dfrac{1}{2} \times 6 \times 5.2\\\Rightarrow 15.6\ mm^{2}$

b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

$\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}$

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

$\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}$

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

$\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\ mm^{2}$

Hence,

a) Area of the base of the pyramid = $15.6\ mm^{2}$

b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

8 0

3 years ago

The area of circular garden is 530.66 feet2. What is the circumference of the garden? (Use 3.14 for .

iVinArrow [24]

$\bf \textit{area of a circle}\\\\
A=\pi r^2\quad 
\begin{cases}
r=radius\\
------\\
A=530.66
\end{cases}\implies 530.66=\pi r^2
\\\\\\
\cfrac{530.66}{\pi }=r^2\implies \sqrt{\cfrac{530.66}{\pi }}=r
\\\\\\
\textit{circumference of a circle}\\\\
C=2\pi r\qquad \implies C=2\pi \left( \sqrt{\cfrac{530.66}{\pi }} \right)$

3 0

3 years ago

In list T, consists of 30 positive decimals. None of which are integers. The sum of the 30 decimals is S. The estimated sum of t

Masteriza [31]

Answer: E - S = (-16 and 6)

Step-by-step explanation:1/3 of the 30 decimals in T have an even tenths digit, it follows that 1/3*(30)=10 decimals in T have an even tenths digit.

Hence: Te =list of 10 decimals

Se = sum of all 10 decimals in Te

Ee =estimated sum of all 10 decimals in Te after rounding up.

Remaining 20 decimals in T all have an odd tenths digits.

To =list of this 20 decimals

So = sum of all 20 decimals in To

Eo = estimated sum of 20 decimals in To

Hence,

E = Ee + Eo and S =Se +So, hence:

E-S, =(Ee+Eo) - (Se+So) =(Ee-Se) +(Eo-So)

Ee-Se >10 (0.1)=1

S=10(1.8)+20(1.9) =18+38=56

E=10(2)+20(1)=40

E-S =40-56=-16.

AlsoS=10(1.2)+20(1.1)=34

E=10(2)+20(1)=40

E-S=40-34=6

6 0

3 years ago

Find the length of h. Round your answer to the hundredths place if you get a decimal

Luda [366]

Answer:

sheeeeeeeeeeeeeesh

Step-by-step explanation:

7 0

3 years ago

3a^2 (ab^2+b^2)=<br> How much

kiruha [24]

Answer is 3a²b (a + b)

Step-by-step explanation:

Step 1: Find 3a² (ab²+b²)

⇒ 3a² (ab²+b²) = 3a³b + 3a²b² = 3a²b (a + b)

8 0

3 years ago