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1 year ago

B.

Mathematics

1 answer:

yarga [219]1 year ago

7 0

6) The number of sweets that tolu had is; 8 sweets

7) The number of sweets that Ogechi had is; 10 sweets

8) The number of sweets that Tamuno had is; 12 sweets

9) The number of sweets that Tamuno must give Tolu for them to have equal number is; 2 sweets

10) If Tolu gave four sweets to Tamuno, then Tamuno would have 4 times more sweets than Tolu

<h3>How to solve Algebra Word Problems?</h3>

Let the number of sweets that tolu had be x

Let the number of sweets that Ogechi had be y

Let the number of sweets that Tamuno had be z.

Thus;

x + y = 18 -----(1)

y + z = 22 -----(2)

x + y + z = 30 ------(3)

Substitute 22 for (y + z) in eq 3 to get;

x + 22 = 30

x = 30 - 22

x = 8

Substitute 18 for (x + y) in eq 3 to get;

18 + z = 30

z = 30 - 18

z = 12

y + z = 22

y + 12 = 22

y = 10

Read more about Algebra Word Problems at; brainly.com/question/21405634

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Find the constant of proportional (r) in the equation y = rx

RUDIKE [14]

Answer:

Constant of proportionality,

Step-by-step explanation:

Constant of proportionality states that the constant value of the ratio of two proportional quantities x and y,

it is written in the form of y = kx, where k is the constant of proportionality.

Given the equation: .....[1]

where r is the constant of proportionality.

From the table we consider

x = 14 and y = 1.4

Substitute these given values in [1] to solve for r;

Divide both sides by 14 we get;

therefore, the Constant of proportionality,

4 0

3 years ago

the length of a rectangle is 5 less than twice the width.if the perimeter of the rectangle is 146,find the area of the rectangle

raketka [301]

Answer:

The area of the rectangle is 1222 units²

Step-by-step explanation:

The formula of the perimeter of a rectangle is P = 2(L + W), where L is its length and W is its width

The formula of the area of a rectangle is A = L × W

∵ The length of a rectangle is 5 less than twice the width

- Assume that the width of the rectangle is x units and multiply

x by 2 and subtract 5 from the product to find its length

∴ W = x

∴ L = 2x - 5

- Use the formula of the perimeter above to find its perimeter

∵ P = 2(2x - 5 + x)

∴ P = 2(3x - 5)

- Multiply the bracket by 2

∴ P = 6x - 10

∵ The perimeter of the rectangle is 146 units

∴ P = 146

- Equate the two expression of P

∴ 6x - 10 = 146

- Add 10 to both sides

∴ 6x = 156

- Divide both sides by 6

∴ x = 26

Substitute the value of x in W and L expressions

∴ W = 26 units

∴ L = 2(26) - 5 = 52 - 5

∴ L = 47 units

Now use the formula of the area to find the area of the rectangle

∵ A = 47 × 26

∴ A = 1222 units²

∴ The area of the rectangle is 1222 units²

7 0

3 years ago

A recursive arithmetic sequence is defined ad f(1)=6, f(n+1)=f(n)+5 for n>1. The first four terms of the sequence are shown i

Dennis_Churaev [7]

Write the first few terms of the sequence.
f₁ = 6
f₂ = f₁ + 5 = 11
f₃ = f₂ + 5 = 16
f₄ = f₃ + 5 = 21
and so on

The sequence is
6, 11, 16, 21, ...,
This is an arithmetic sequence with a common difference of 5.

In function notation, the sequence is
$f_{n+1} = 6 + 5n, \\ \, n=0,1,2, \, ...,$

This represents the equation of a straight line with n as the independent variable and f as the dependent variable.
The slope is 5.
A graph of the line is shown below.

Answer:
The sequence is $f_{n+1} = 6 + 5n, \,\, n=0,1,2, \, ...,$
The slope is 5.

7 0

3 years ago

Read 2 more answers

Question: What is the measure of angle 2?

ad-work [718]

Answer:

56 degrees

Step-by-step explanation:

We know that the angle TWR must be 90 degrees because TWK is 90 degrees and the two angles msut add up to 180. Since we know that TWR=90 degrees and since LWR=34 degrees we do 90-34 so angle 2=56 degrees.

8 0

3 years ago

Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance be

Oksana_A [137]

<h2>Hello!</h2>

The answers are:

$FirstCarSpeed=41mph\\SecondCarSpeed=55mph$

To calculate the speed of the cars, we need to write two equations, one for each car, in order to create a relation between the two speeds and be able to calculate one in function of the other.

So,

Tet be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

$x_{FirstCar}=x_o+v*t$

For the second car:

We know that the speed of the second car is the speed of the first car plus 14 mph, so:

$x_{SecondCar}=x_o+(v+14mph)*t$

Now, from the statement that both cars met after 2 hours and 45 minutes, and the distance between to cover (between A and B) is 264 miles, so, we can calculate the relative speed between them:

If the cars are moving towards each other the relative speed will be:

$RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph$

Then, since we know that they covered a combined distance equal to 264 miles in 2 hours + 45 minutes, we have:

$2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours$

Writing the equation:

$264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph$

So, the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

$SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph$

We have that the speed of the second car is equal to 55 mph.

Hence, the answers are:

$FirstCarSpeed=41mph\\SecondCarSpeed=55mph$

Have a nice day!

7 0

3 years ago