MATHEMATICS MIDDLE SCHOOL

The product of 3/4 and 7/8 is less than 7/8

Answers

Answer 1

Answer:

Answer:

Yes, it is correct.

Step-by-step explanation:

When we multiply a positive real number by a positive real number less than 1,

Then the value of the original number is always decreased,

Here, $(7)/(8)> 0$

Also, $(3)/(4)<1$

Thus, by the above statement,

$(3)/(4)* (7)/(8) < (7)/(8)$

Verification :

$(7)/(8)=0.875$

Since, the product of $(3)/(4)$ and $(7)/(8)$ is,

$(3)/(4)* (7)/(8)$

$=(21)/(32)$

= 0.65625 < 0.875

$\implies (3)/(4)* (7)/(8) < (7)/(8)$

Answer 2

Answer: It would be less because any number, no matter big or small multiplied by a fraction is always less than that number.

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Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7, 2), and is parallel to the graph x + 3y = -5. Pls help ASAP btw, the answer isn’t -12/19 or 12/19

Answers

Answer:

$B - A = -6$

Step-by-step explanation:

Given

Point: (-7,2)

x + 3y = -5

Required

Find B- - A in Ax + By = 3

To start with; we need to calculate the slope of x + 3y = -5

$x + 3y = -5$

Subtract x from both sides

$x - x + 3y = -5 - x$

$3y = -5 - x$

Divide both sides by 3

$(3y)/(3) = -(5)/(3) - (x)/(3)$

$y = -(5)/(3) - (x)/(3)$

The slope of the line is the coefficient of x

Slope = $- (1)/(3)$

The question says line Ax + By = 3 is parallel to line x + 3y = -5; This means that they have the same slope of $- (1)/(3)$

Having calculated the slope, next is to calculate the equation of the line using the following formula;

$m = (y - y_1)/(x - x_1)$

Where m is the slope; m = $- (1)/(3)$ ; $(x_1, y_1) = (-7,2)$

Substitute these values in the formula above; the formula becomes

$-(1)/(3) = (y - 2)/(x - -7)$

$-(1)/(3) = (y - 2)/(x +7)$

Cross Multiply

$-1(x+7) = 3(y-2)$

Open brackets

$-x - 7 = 3y - 6$

Add x to both sides

$x - x - 7 = 3y - 6 + x$

$-7 = 3y - 6 +x$

Add 6 to both sides

$-7 + 6 = 3y -6 + 6 + x$

$-1 = 3y + x$

Multipby both sides by -3

$-3(-1) = -3(3y + x)$

$3 = -9y - 3x$

$-9y - 3x = 3$

$-3x - 9y = 3$

Comparing the above to Ax + By = 3

$Ax = -3x\nA = -3$

$By = -9y\nB = -9$

$B - A = -9 - (-3)$

$B - A = -9 + 3$

$B - A = -6$

What is the lcm of two numbers if one number is a multiple of the other give example

Answers

The LCM is multiple which is useful if fractions need to be expressed in the same name, and the further discussion can be defined as follows:

When the other number is multiple, LCM will have the larger number:

Example:

So, the 2 and 4 LCM.
The lcm is 4 since 2 and 4 are both 4 and 4.

Otherwise;

The number which multiplies the other one is the LCM of these two numbers.
The LCMs of 8 and 56 have such a factor of 56, as 8 are 56 and 56 can be seven times and 56 are an independent factor.

Learn more:

brainly.com/question/133207

the greater number will be the lcm if the other number is a multiple

For instance:

the lcm of 2 and 4

the lcm is 4 as 2 and 4 are both multiples of 4

A teacher purchased a total of 460 notebooks and pencils. Each notebook cost $1.75 and each pencil cost $0.05. If the teacher spent a total of $218.50, how many notebooks did the teacher purchase?

Answers

The number of notebooks the teacher purchased, is 115

What is the system of linear equations?

A system of linear equations is a collection of one or more linear equations involving the same variables.

Given that, a teacher purchased a total of 460 notebooks and pencils. Each notebook cost $1.75 and each pencil cost $0.05. If the teacher spent a total of $218.50, we need to find the number of notebooks the teacher purchased,

We will use the concept of system of linear equations to solve this,

Let the number of notebooks be n and that of pencils be p,

n + p = 460

p = 460-n....(i)

1.75n + 0.05p = 218.50...(ii)

Using equation (i) in eq(ii)

1.75n + 0.05(460-n) = 218.50

1.75n + 23-0.05n = 218.50

1.7n = 195.5

n = 115

Hence, the number of notebooks the teacher purchased, is 115

Learn more about system of linear equations, click;

brainly.com/question/19549073

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the teacher purchased 115 notebooks

A cylinder has a radius of 12m and a height of 8m. What is the approximate surface area of the cylinder? use 3.14 for Pi.

Answers

Surface Area = 2 × π × r × (r+h). So 2 × π × 12 × (12+8). Then 2 × π × 12 × 20. And then 480 π. And your answer is about 1507.

Simple, A=2πrh+2πr²=2*π*12*8+2*π*12²=1507.96447m². If you want to round your answer, it would be 1507.96m²

HOW MANY SQUARE NUMBERS IN A PACK OF 52 CARDS

Answers

in a pack of 52 cards, there are 3 square numbers - 1, 4, and 9.

1 × 1 = 1
2 × 2 = 4
3 × 3 = 9

(Use photo ) find the length of the hypotenuse in each right triangle. Please show work and round to the nearest tenth,if necessary.

Answers

9.) QP=5-1
QP=4units
QR=3+1
QR=4units

squareroot 4^(2)+4^(2)

and you should get 5.66 (cor. to 3 s.f.)

10.) LM=5units
MN=7units

squareroot 7^(2)+5^(2)
you should get 8.06 (cor. to 3 s.f.)

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