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GenaCL600 [577]

3 years ago

11

Please help, it's very urgent

1 answer:

Vinil7 [7]3 years ago

4 0

Step-by-step explanation:

Divide by any number except 0 means the same as multiply by its inverse.

The inverse of $a$ is $\dfrac{1}{a}$

Therefore

$n\div(-1)=n\div\left(\dfrac{-1}{1}\right)=n\times\left(\dfrac{1}{-1}\right)=n\times(-1)=(-1)\times n=-1\times n$

Used the commutative property of multiplication: a × b = b × a

$\huge\boxed{-1\times n=n\div(-1)}$

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Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of

Tom [10]

Question:

Abel planned for a garden to be 42 m long but found that it needs to be 24 m long to fit in his backyard. He found the change of scale below.

$\frac{42m}{7}/{\frac{24m}{7} = \frac{6}{4}$

Which is Abel’s error?

Abel should have written the ratio as $24 metres/7 metres$

Abel should have written the ratio as $24 metres/42 metres$

Abel should have divided both numbers by 6.

Abel should have divided both numbers by 4.

Answer:

Abel should have divided both numbers by 6.

Step-by-step explanation:

Given

Measured Length of backyard = 42m

Actual Length of backyard = 24m

Measured Ratio: $\frac{42m}{7}/{\frac{24m}{7} = \frac{6}{4}$

Required

Error in calculation of measured ratio

From Abel's calculation:

It can be observed that He divided both numbers by 7

Though 42/7 = 6 but that's not so for 24/7

24/7≠4;

Instead 24/7 = 3.43 (Approximated)

To get the actual ration, he has to divide both numbers by the highest common factor

The common factors of 42 and 24 include 2,3,6 of which the highest is 6

Hence; HCF of 42 and 24 = 6

So, we can conclude that the error in his calculation is having not dividing both numbers by 6

7 0

4 years ago

Read 2 more answers

Multiply and find the total<br><br> Algebra

fomenos

Answer:

n - 1

Step-by-step explanation:

(n-1)(n-5) / 2(n+3) ×2(n+3) / (n-5)

Kindly check attached picture for simplification

6 0

3 years ago

A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

ASHA 777 [7]

Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

7 0

3 years ago

In a right triangle ΔABC, the length of leg AC = 5 ft and the hypotenuse AB = 13 ft. Find: Chapter Reference b The length of the

Butoxors [25]

Answer:

The length of the angle bisector of angle ∠A is 6.01.

Step-by-step explanation:

It is given that length of leg AC = 5 ft and the hypotenuse AB = 13 ft.

Using pythagoras theorem

$(AB)^2=(BC)^2+(AC)^2$

$(13)^2=(BC)^2+(5)^2$

$169=(BC)^2+25$

$BC=12$

$\sin A=\frac{\text{perpendicular}}{\text{hypotenuse}}$

$\sin A=\frac{BC}{AB}$

$A=\sin ^{-1}\frac{12}{13}$

$A=67.38$

Bisector divides the angle in two equal parts, therefore,

$A'=\frac{67.38}{2} =33.69$

In triangle ACD.

$\cos A'=\frac{\text{Base}}{\text{Hypotenuse}}$

$\cos A'=\frac{AC}{AD}$

$\cos (33.69^{\circ})=\frac{5}{AD}$

$0.832=\frac{5}{AD}$

$AD=\frac{5}{0.832} =6.009\approx 6.01$

Therefore the length of the angle bisector of angle ∠A is 6.01.

4 0

3 years ago

What is the answer to my question? Help please, urgent.

svetlana [45]

Answer:

k

Step-by-step explanation:

8 0

3 years ago