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3 years ago

The perimeter of the rectangle is 32 m One side is 11m space, m long. What is the length of the missing side?

Mathematics

1 answer:

SVEN [57.7K]3 years ago

6 0

Hello!

The formula for the perimeter of a rectangle is: P = 2(l + w). In this formula, P is the perimeter, l is the length, and w is the width.

Suppose the length of the rectangle is 11 meters. We can substitute that value into our formula and solve for the missing side.

32 = 2(11 + w) (use the distributive property)

32 = 22 + 2w (subtract 22 from both sides)

10 = 2w (divide both sides by 2)

w = 5

Therefore, the length of the missing side is 5 meters.

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3.3^(2x+1)-103^x+1=0 need value of x

photoshop1234 [79]

Answer:

The value of $x$ is approximately -1.531.

Step-by-step explanation:

Let $3.3^{2\cdot x + 1}-103^{x+1} = 0$ , we proceed to solve this expression by algebraic means:

1) $3.3^{2\cdot x + 1}-103^{x+1} = 0$ Given

2) $3.3^{2\cdot x}\cdot 3.3 -103^{x}\cdot 103 = 0$ $a^{b}\cdot a^{c} = a^{b+c}$

3) $(3.3^{x})^{2}\cdot 3.3 -\left[\left( \sqrt{103} \right)^{2}\right]^{x}\cdot 103 = 0$ $(a^{b})^{c} = a^{b\cdot c}$

4) $(3.3^{x})^{2}\cdot 3.3 - \left[\left(\sqrt{103}\right)^{x}\right]^{2}\cdot 103 = 0$ $(a^{b})^{c} = a^{b\cdot c}$ /Commutative property

5) $\left[\left(\frac{3.3}{\sqrt{103}}\right)^{x}\right] ^{2}-\frac{103}{3.3} = 0$ Existence of multiplicative inverse/Definition of division/Modulative property/ $a^{b}\cdot a^{c} = a^{b+c}$

6) $\left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\frac{103}{3.3}$ Existence of additive inverse/Modulative property/ $(a^{b})^{c} = a^{b\cdot c}$

7) $\log \left(\frac{3.3}{\sqrt{103}} \right)^{2\cdot x}=\log \frac{103}{3.3}$ Definition of logarithm.

8) $2\cdot x\cdot \log \left(\frac{3.3}{\sqrt{103}} \right)= \log \frac{103}{3.3}$ $\log_{b} a^{c} = c\cdot \log_{b} a$

9) $2\cdot x \cdot [\log 3.3-\log \sqrt{103}] = \log 103 - \log 3.3$ $\log_{b} \frac{a}{d}$

10) $x\cdot (2\cdot \log 3.3-\log 103) = \log 103 - \log 3.3$ $\log_{b} a^{c} = c\cdot \log_{b} a$ /Associative property

11) $x = \frac{\log 103-\log 3.3}{2\cdot \log 3.3-\log 103}$ Existence of multiplicative inverse/Definition of division/Modulative property

12) $x \approx -1.531$ Result

The value of $x$ is approximately -1.531.

4 0

2 years ago

James and his 4 friends bought 2 pizzas.Each pizza was cut into 8 slices.If the boys share the pizza equally,how many pieces wil

Lelu [443]

Answer:3

Step-by-step explanation:

2x8=16

There are 5 people in total

16/5=3.2

Whole number so 3 slices

7 0

3 years ago

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tiny-mole [99]

$x = - 1 + \sqrt{10}$

Step-by-step explanation:

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2 years ago

Match the given equation with the verbal description of the surface:

san4es73 [151]

Match of the equation with the verbal description of the surface would be :

Equation 1 = C. plane

Equation 2 = F. Circular cylinder

Equation 3 = C. plane

Equation 4 = E. sphere

Equation 5 = A. cone

Equation 6 = E. Sphere

Equation 7 = F. Circular cylinder

Equation 8 = B. Eliptic or circular paraboloid

Equation 9 = A. cone

Hope this helps

5 0

3 years ago

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. $\text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\$