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2 years ago

After simplifying, which expressions are equivalent? Select three options.

Mathematics

2 answers:

Wewaii [24]2 years ago

6 0

Answer: Second option, third option and fifth option.

Step-by-step explanation:

In order to solve this exercise it is important to remember the multiplication of signs:

$(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-$

Knowing that, you can distribute the sign and add the like terms. Repeat this procedure in each expression given in the exercise.

Therefore, you get:

$a.\ (3.4a - 1.7b) + (2.5a - 3.9b)=3.4a - 1.7b + 2.5a - 3.9b=5.9a-5.6b\\\\b.\ (2.5a + 1.6b) + (3.4a + 4b)=2.5a + 1.6b + 3.4a + 4b=5.9a+5.6b\\\\c.\ (-3.9b + a) + (-1.7b + 4.9a)=-3.9b + a -1.7b + 4.9a=5.9a-5.6b\\\\d.\ -0.4b +(6b - 5.9a)=-0.4b +6b - 5.9a=6b-6.3a\\\\e.\ 5.9a - 5.6b$

You can identify that the expressions $(2.5a + 1.6b) + (3.4a + 4b)$ , $(-3.9b + a) + (-1.7b + 4.9a)$ and $5.9a - 5.6b$ are equivalent after simplifying.

Semmy [17]2 years ago

4 0

Answer:

b, c, e

Step-by-step explanation:

did it good luck

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A solid machine part is to be manufactured as shown in the figure. The part is made by cutting a small cone off the top of a lar

Alexxx [7]

Answer:

The answer is 390 × pi.

Step-by-step explanation:

Big cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 9^2 x 15

= 1272.3 cubic inches

Small cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 3^2 x 5

= 47.1 cubic inches

1272.3 - 47.1 = 1225.2 cubic inches

1272/3.14 ≈ 390

The answer is 390 × pi.

4 0

2 years ago

Show that the Fibonacci numbers satisfy the recurrence relation fn = 5fn−4 + 3fn−5 for n = 5, 6, 7, . . . , together with the in

Sonja [21]

Answer with step-by-step explanation:

We are given that the recurrence relation

$f_n=5f_{n-4}+3f_{n-5}$

for n=5,6,7,..

Initial condition

$f_0=0,f_1=1,f_2=1,f_3=2,f_4=3$

We have to show that Fibonacci numbers satisfies the recurrence relation.

The recurrence relation of Fibonacci numbers

$f_n=f_{n-1}+f_{n-2}$ , $f_0=0,f_1=1$

Apply this

$f_n=(f_{n-2}+f_{n-3})+f_{n-2}=2f_{n-2}+f_{n-3}$

$f_n=2(f_{n-3}+f_{n-4})+f_{n-3}=3f_{n-3}+2f_{n-4}$

$f_n=3(f_{n-4}+f_{n-5})+2f_{n-4}=5f_{n-4}+3f_{n-5}$

Substitute n=2

$f_2=f_1+f_0=1+0=1$

$f_3=f_2+f_1=1+1=2$

$f_4=f_3+f_2=2+1=3$

Hence, the Fibonacci numbers satisfied the given recurrence relation .

Now, we have to show that $f_{5n}$ is divisible by 5 for n=1,2,3,..

Now replace n by 5n

$f_{5n}=5f_{5n-4}+3f_{5n-5}$

Apply induction

Substitute n=1

$f_5=5f_1+3f_0=5+0=5$

It is true for n=1

Suppose it is true for n=k

$f_{5k}=5f_{5k-4}+3f_{5k-5}$ is divisible 5

Let $f_{5k}=5q$

Now, we shall prove that for n=k+1 is true

$f_{5k+5}=5f_{5k+5-4}+3f_{5k+5-5}=5f_{5k+1}+3f_{5k}=5f_{5k+1}+3(5q)$

$f_{5k+5}=5(f_{5k+1}+3q)$

It is multiple of 5 .Therefore, it is divisible by 5.

It is true for n=k+1

Hence, the $f_{5n}$ is divisible by 5 for n=1,2,3,..

8 0

2 years ago

A. One day Annie weighed 24 ounces more than Benjie, and Benjie weighed 3 1/4 pounds less than Carmen. How did Annie’s and Carme

Debora [2.8K]

<h2>Answer:</h2>

Let Annie's weight be = a

Let Benjie's weighs = b

Let Carmen's weight be = c

One day Annie weighed 24 ounces more than Benjie, equation forms:

$a=b+24$ ......(1)

Benjie weighed 3 1/4 pounds less than Carmen.

In ounces:

1 pound = 16 ounces

$\frac{13}{4}$ pounds = $\frac{13}{4}\times16=52$ ounces

$b=c-52$ or

$c=b+52$ ......(2)

Now adding (1) and (2), we get

a+b=b+24+c-52

=> $a=c-28$

This gives Annie weighs 28 ounces less than Carmen.

We cannot know anyone's actual weight, as we only know their relative weights.

3 0

2 years ago

Oliver and Paula both read the same book. Paula started reading after Oliver had already read 30 pages.

ahrayia [7]

Their lines intersect at this point, which mean that they did the same thing, so it can't be A or D, and we dont know the total number of pages so we can't for sure say it's B.

So it's C, because we can see that the point is on 10 for the x-axis, which represents # of nights, and 150 for the y-axis, which represents # of pages read.

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2 years ago

Read 2 more answers

Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates H(1,10) an

ss7ja [257]

The given information are the coordinates of points H, Z and B. So, the first step to do is to plot these points on a Cartesian plane as shown in the attached picture. We can deduce visually that horse Z is closer to the barns than horse H. But, to further justify the answer, we have to provide the magnitude of the distance of horses H and Z to barn B. In this approach, we use the distance formula:

d = √(x₂ - x₁)² + (y₂ - y₁)²

Use the coordinates of the two points to know their linear distances. These are represented by the red and green lines for each of the horses.

Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = √(⁻3 - 1)² + (⁻9-10)²
Distance between H and B = 19.4165

Since the scale is 1 unit = 100 meters, the actual distance between horse H and barn B is 19.416*100 = 1,941.65 meters

Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = √(⁻3 - 10)² + (⁻9-1)²
Distance between Z and B = 16.4012

Since the scale is 1 unit = 100 meters, the actual distance between horse Z and barn B is 16.4012*100 = 1,640.12 meters

Comparing the distances: 1,941.65 meters > 1,640.12 meters. Therefore, it justifies that horse Z is nearer to the barn.

4 0

2 years ago