MATHEMATICS HIGH SCHOOL

Mr. Atinga shared his cattle among his three children Lordia,Anita,and Richmond. He gave 3/5 of cattles to Anita and shared the remaining between Lordia and Richmond in the ratio 2:3 respectively. In all 80 cattle were shared between Lordia and Richmond. How many cattle were shared among the three children How many cattle did Anita receive than Richmond

Answers

Answer 1
Answer:

Answer:

a). The total number of cattle shared among the three children=200

b). Anita's share=120 cattle

    Lordia's share=32 cattle

    Richmond's share=48 cattle

Step-by-step explanation:

a)

Step 1

Determine fraction shared between Lordia and Richmond as follows;

Lordia:Richmond=2:3

Let the total cattle be x

Lordia's fraction=2/(2+3)=2/5 of x=(2/5)x

Lordia's fraction=(2/5)x

Richmond's fraction=3/(2+3)=3/5 of x=(3/5) x

but;

x=80 cattle

replacing;

Total number of cattle Lordia got=(2/5)×80=32 cattle

Total number of cattle Richmond got=(3/5)×80=48 cattle

Step 2

Express the total cattle Mr. Atinga had initially as follows;

Let the initial number of cattle be y

The fraction remainder given to Lordia and Richmond=Initial number-fraction of the totat given to Anita

where;

Initial number=y

fraction of the total given to Anita=3/5 y

replacing;

The fraction remainder given to Lordia and Richmond=y-3/5 y=2/5 y

but;

2/5 y=80

y=80×5/2=

y=200

The total number of cattle shared among the three children=200

b).

Anita's share=(3/5)×200=120 cattle

Lordia's share=(2/5)×80=32 cattle

Richmond's share=(3/5)×80=48 cattle

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Tom conducted a drawing competition at school. He bought 5 boxes of colored pencils and spent $5.25 on drawing paper. However, more contestants entered than he expected, and he had to buy 2 more boxes of colored pencils. The total cost of the paper and pencils was $82.95. Identify the equation and solution that would help to find the cost of each box of pencils.

Answers

82.92 - 5.25 = 77.67
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Thirty times the square of a non-zero number is equal to eight times the number. what is the number?

Answers

You said that        30 x²  =  8 x

I can divide
each side by 'x':     30 x = 8
 
Then divide
each side by 30:        x  =  8 / 30  =  4/15 .

Check to see if it works:

Does    30 (4/15)²  =  8 (4/15)  ?

Well, (4/15)² = 16/225

       30 · 16/225 = 480/225  =  32/15
and
         8 · 4/15  =  32/15                    yay !
Hello,

let x the unknowed number,

30*x²=8*x
==> 30x=8 (for x ≠0)
==>x=8/30
==>x=4/15

Confusion dans la traduction mentale désolé.

For which system of equations is (2, 2) a solution?a. –3x + 3y = 0 x + 6y = 10
b. –2x + 5y = –6 4x – 2y = 4
c. 5x – 2y = –6 3x – 4y = 2
d. 2x + 3y = 10 4x + 5y = 18

Answers

Plug the values (x,y)=(2,2) into the equations and check if they satsify them.

a.
-3x+3y=0 \nx+6y=10 \n \n\hbox{the first equation:} \n-3 * 2+3 * 2=0 \n-6+6=0 \n0=0 \ntrue \n \n\hbox{the second equation:} \n2+6 * 2=10 \n2+12=10 \n14=10 \nfalse \n \n\hbox{(2,2) satisfies only one of the equations} \n\hbox{so it's not a solution to the system of equations}

b.
-2x+5y=-6 \n4x-2y=4 \n \n\hbox{the first equation:} \n-2 * 2 + 5 * 2=-6 \n-4+10=-6 \n6=-6 \nfalse \n \n\hbox{the second equation:} \n4 * 2-2 * 2=4 \n8-4=4 \n4=4 \n true \n \n\hbox{(2,2) satisfies only one of the equations} \n\hbox{so it's not a solution to the system of equations}

c.
5x-2y=-6 \n3x-4y=2 \n \n\hbox{the first equation:} \n5 * 2 - 2 * 2=-6 \n10-4=-6 \n6=-6 \nfalse \n \n\hbox{the second equation:} \n3 * 2 - 4 * 2=2 \n6-8=2 \n-2=2 \nfalse \n \n\hbox{(2,2) satisfies none of the equations} \n\hbox{so it's not a solution to the system of equations}

d.
2x+3y=10 \n4x+5y=18 \n \n\hbox{the first equation:} \n2 * 2 + 3 * 2=10 \n4+6=10 \n10=10 \ntrue \n \n\hbox{the second equation:} \n4 * 2 + 5 * 2 =18 \n8+10=18 \n18=18 \n \n\hbox{(2,2) satisfies both of the equations} \n\hbox{so it is a solution to the system of equations}

The answer is D.

Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.

Answers

Answer:

153.1 square unit

Step-by-step explanation:

for rectangle

length = 16

breadth = 8

area of rectangle = l*b

=16*8

=128 square unit

semicircle

diameter =8

area of semicircle =πd^2/8

=3.14 * 8^2 /8

=3.14 *64/8

=200.96/8

=25.12 square unit

area of the givem figure = area of rectangle + area of semicircle

=128 + 25.12

=153.12

=153.1 square unit

Final answer:

To find the area of the figure made up of a rectangle and a semicircle, calculate the areas of both shapes and add them together. Use the formula for the area of a rectangle, and calculate the area of the semicircle by finding half the area of a full circle with the same radius. Finally, sum up the areas to find the total area of the figure.

Explanation:

To find the area of the figure, we need to find the areas of the rectangle and the semicircle, and then add them together. The area of the rectangle is found by multiplying its length by its width. The area of the semicircle is half the area of a full circle with the same radius. Finally, we add the two areas together to get the total area of the figure.

Let's assume the length of the rectangle is 10 units and the width is 5 units. The area of the rectangle is then 10 units * 5 units = 50 units^2. If the radius of the semicircle is 3 units, the area of the semicircle is half the area of a full circle with radius 3 units, which is 1/2 * 3.14 * 3^2 = 14.13 units^2 (rounded to the nearest tenths place).

Therefore, the total area of the figure is 50 units^2 + 14.13 units^2 = 64.13 units^2 (rounded to the nearest tenths place).

Learn more about Area of composite figures here:

brainly.com/question/16011845

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7. PQ contains points Rand S such that PR, RS and SQ are respectively three consecutive evenintegers. If PQ is 54, find the length of the middle segment, RS

Answers

The length of the middle segment RS is determined as 18.

How to calculate the middle segment?

Let's assume that the three consecutive even integers are x, x + 2, and x + 4

So, the length of PR (x) + the length of RS (x + 2) + the length of SQ (x + 4) equals the total length of PQ (54).

Mathematically, this can be represented as:

x + (x + 2) + (x + 4) = 54

Now, let's solve for x:

3x + 6 = 54

Subtract 6 from both sides:

73x = 48

Now, divide by 3:

x = 16

So, the first even integer (PR) is 16, the second even integer (RS) is 16 + 2 = 18, and the third even integer (SQ) is 16 + 4 = 20.

Thus, the length of the middle segment RS is 18.

Learn more about middle segment here: brainly.com/question/26166058

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Answer:

RS = 18

Step-by-step

PR = x

RS = x+2

SQ = x+4

x+(x+2)+(x+4)=54

3x+6=54

3x=48

x=16

PR = 16

RS = 18

SQ = 20

Naomi deposited money into a savings account that is compounded quarterly at an interest rate of 6%. she thinks this quarterly rate is the same as a monthly interest rate of 1.25%. Is Naomi right? If so, explain why and show how you got your answer. Is Naomi incorrect? if so, explain the mistake in her reasoning, give the correct monthly interest rate, and show how you got your answer.

Answers

answer is attached below
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