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with answer

Step-by-step explanation:

A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point.

Answer: 9/16 as a decimal is 0.5625

9-16-as-a-decimal-is-0.5625

Let's look into the two methods to write 9/16 as a decimal.

Explanation:

Method 1: Writing 9/16 as a decimal using the division method

To convert any fraction to decimal form, we just need to divide its numerator by denominator.

Here, the fraction is 9/16 which means we need to perform 9 ÷ 16

This gives the answer as 0.5625. So, 9/16 as a decimal is 0.5625

Method 2: Writing 9/16 as a decimal by converting the denominator to powers of 10

Step 1: Find a number such that we can multiply by the denominator of the fraction to make it 10 or 100 or 1000 and so on.

Step 2: Multiply both numerator and denominator by that number to convert it into it's an equivalent fraction.

Step 3: Then write down just the numerator, putting the decimal point in the correct place, that is, one space from the right-hand side for every zero in the denominator.

9/16 = (9 × 625) / (16 × 625) = 5625/10000 = 0.5625

Irrespective of the methods used, the answer to 9/16 as a decimal will always remain the same.

You can also verify your answer using Cuemath's Fraction to Decimal Calculator.

Thus, 9/16 as a decimal is 0.5625

The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²

What is rectangle short answer?

the points (-1 , 2) and (3 , 2 ) form one the of the rectangle w =     [tex]\sqrt{( 3 + 1 )^{2} + ( 2 - 2 )^{2} }[/tex]

= [tex]\sqrt{4^{2} + 0 }[/tex]

= √ 16

= 4

The length can be obtained by finding distance between the points (-1,2) and ( -1, - 5)  = [tex]\sqrt{( -1 -2 )^{2} + ( -5 + 1)^{2} }[/tex]

                 = [tex]\sqrt{(-3)^{2} + ( -6)^{2} }[/tex]

                 = √9 + 36

                  = √45 = 3√5

The perimeter of the rectangle is: P = 2( w + L) = 2( 4 + 3√5) ⇒ 8 + 6√5 unit

The area of the rectangle is A = L w, A = 4 * 3√5 = 12√5 Unit²

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Answer:

23

110

Step-by-step explanation:

We have a + 1/a = 5

(a + 1/a)² = a² + (1/a²) + 2.a.1/a =  a² + (1/a²)  + 2

But (a + 1/a)² = 5² = 25

So a² + (1/a²) = 25 - 2 = 23

(a + 1/a)³ = a³ + 3a²(1/a) + 3a(1/a)² + (1/a)2

= a³ + 1/a³ + 3a + 3/a

= a³ + 1/a³ + 3(a + 1/a)

= a³ + 1/a³ + 3(5)

=  a³ + 1/a³ + 15

But (a + 1/a)³ = 5³ = 125

So

a³ + 1/a³ + 15 = 125

a³ + 1/a³  = 110

Answer:

23 and 110

Step-by-step explanation:

using the expansion

(a + b)² = a² + 2ab + b² , then

a + [tex]\frac{1}{a}[/tex] = 5 ( square both sides )

(a + [tex]\frac{1}{a}[/tex] )² = 5²

a² + 2(a × [tex]\frac{1}{a}[/tex] ) + [tex]\frac{1}{a^2}[/tex] = 25

a² + 2(1) + [tex]\frac{1}{a^2}[/tex] = 25

a² + 2 + [tex]\frac{1}{a^2}[/tex] = 25 ( subtract 2 from both sides )

a² + [tex]\frac{1}{a^2}[/tex] = 23

---------------------------------------------------------------------

using the expansion

(a + b)³ = a³ + b³ + 3ab(a + b) , then

a + [tex]\frac{1}{a}[/tex] = 5 ( cube both sides )

(a + [tex]\frac{1}{a}[/tex] )³ = 5³

a³ + [tex]\frac{1}{a^3}[/tex] + 3(a × [tex]\frac{1}{a}[/tex] )(a + [tex]\frac{1}{a}[/tex] ) = 125

a³ + [tex]\frac{1}{a^3}[/tex] + 3(1)(5) = 125

a³ + [tex]\frac{1}{a^3}[/tex] + (3 × 5) = 125

a³ + [tex]\frac{1}{a^3}[/tex] + 15 = 125 ( subtract 15 from both sides )

a³ + [tex]\frac{1}{a^3}[/tex] = 110

The equation x/-2 = -9 has only one solution and is x = 18.

We are given an equation x/-2 = -9 for which we need to check whether it has a solution, no solution or infinite solutions.

For this we first solve this equation.

x/-2 = -9

⇒ x = -9 x -2

⇒ x = 18

So this equation has only one solution and it is unique.

Hence we cannot find two values of to support this conclusion, since x = 18 is the only value which satisfy this equation.

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Answer:

y + 3 = (1/9) (x - 4)

Step-by-step explanation:

y2-y1 / x2-x1

-4 -(-3) / -5 - 4

Double negative switches the # to a positive

-4+3 / 5 - 4

= -1 / -9

Two negatives equal a positive

m=1/9

y-y1=m(x-x1)

y-(-3)=(1/9)(x-4)

Double negative=positive #

y+3=(1/9)(x-4)

Distribute (1/9) to the x and -4

y+3= (1/9)x - (4/9)

Subtract 3 from both sides

y = -3.4

The value of r is calculated as (m/-6) + 3 for the line with undefined slope passing through (3,2) and (r,-4).

We must determine the value of r that gives the line passing through (3,2) and (r,-4) an undefined slope.

Let,

x₁ = 3

y₁ = 2

x₂ =r

y₂ = -4

slope = m

Using the slope equation we get,

m = (y₂ - y₁)/(x₂ - x₁ )

m = (-4-2)/(r-3)

m/-6 = r - 3

r = (m/-6) + 3

Therefore, the value of r is calculated as (m/-6) + 3 for the line passing through (3,2) and (r,-4) with undefined slope.

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Answer: [tex]x=20, m\angle 1=109^{\circ}, m\angle 2=71^{\circ}[/tex]

Step-by-step explanation:

Angles that form a linear pair add to 180 degrees, so:

[tex]5x+9+3x+11=180\\\\8x+20=180\\\\8x=160\\\\x=20\\\\\implies m\angle 1=5(20)+9=109^{\circ}\\\\\implies m\angle 2=180^{\circ}-109^{\circ}=71^{\circ}[/tex]

The final point where -(-7)−(−7) number after simplification lie is 14

In the above question it is given,

-(-7)−(−7)

We need to find the position of this number on the number line.

A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can be infinitely expanded in any direction.

To do that, we will first simplify the given numbers by using the sign rules of the real numbers

According to the sign rule of real numbers,

(i) (-) x (-) = +

(ii) (-) x (+) = -

(iii) (-) +(-) = -

(iv) (+) + (+) = +

Now using the above sign rules, we will simplify the given number

-(-7)−(−7)

-(-7)+ [-(−7)]

7 + 7

Now, on the number line, we'll move 7 steps in the positive direction of 0, we'll be on 7. Again from 7 we'll take next 7 steps in the same direction and we'll reach the point 14.

Hence, 14 is the final point where -(-7)−(−7) number after simplification lie.

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Notice that:

Which means that, for large values of x:

Since the function:

is a 4th degree monomial, with positive coefficient, then it keeps growing as x grows. Then, we know that:

Which means that the end behavior is such that f(x) approaches infinity as x approaches infinity.

On the other hand, for large negative values of x, the function is also positive. Then:

The length and breadth should be 2 feet each and height should be 3 feet to minimize the cost of the materials.

Let consider the length of the box =x

considering a square bottom ,

length = breadth = x

and let the height  =h

The surface area of the box is

SA = x² + 4xh      ( box is open from top )

cost of 1sq feet material for bottom =$3    

cost of 1sq feet material for sides =$1    

The cost functions can be written as

C =  3x² + 1(4xh)

C =   3x² + 4xh

Also the volume equation is

x²h = 12

h = 12/x²

substituting the value of h into the cost function.

C =  3x² + 4x (12/x²)

C =  3x² + 48/x

C = (3x³ + 48)/ x

Take the derivative of C and set it equal to zero. So we get

6x³ - 48 = 0

x³ = 48/6 = 8

x = 2

∴ h = 12/x²

h = 12/4

h = 3

This is the value of x and h that minimizes the cost.

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Answer:

I think it's B

Step-by-step explanation:

It's the only one with 3 x's to represent the part where it's cut into four pieces the x represents the 3 numbers and then the 4x means how the x = the number that the 3 represent plus the 4 feet longer

Using substitution method, For the given equations, the value of x is 1/2 or x = -3

A fundamental operation in computer algebra is substitution. In computer algebra systems, it is frequently abbreviated as "subs" or "subst."

When a variable (or set of letters) in an algebraic statement is substituted, its numerical value is used instead. The expression's total value can then be calculated.

Given,

y= 9 - x

y= 2x² + 4x + 6

Substituting the value of y from 1 equation to other.

⇒ 9 - x = 2x² + 4x + 6

Now factorizing the equation,

⇒ 2x² + 5x - 3 = 0

⇒ 2x² + 6x - 1x - 3

⇒ 2x(x + 3) -1 (x + 3)

⇒ (2x - 1) (x + 3)

x = 1/2 or x = -3

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If a value that is is greater than 100% of the original value will always be larger than original value.

If a value is less than 1% of the original value will always be less than the original value.

Given,

A value that is greater than 100% of the original value.

And it is 1% less than the original value.

We have to compare these values with the original value;

That is,

A value that is greater than 100% of the original value,

eg;

130% of 20 = 20 × 130/100 = 26

26 is greater than 20.

That is,

If a value that is is greater than 100% of the original value will always be larger than original value.

Next,

It is 1% less than the original value.

eg;

1% of 20 = 1/100 × 20 = 0.2

0.2 is less than 20

That is,

If a value is less than 1% of the original value will always be less than the original value.

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Answer:

To decrease it by 13% we will multiple (100-13 = 87) .

Step-by-step explanation:

Multiply the decimal form of the number (in this case 13) to the number.

For example: 13% of 50

13% can also be said as 0.13 in decimal form.

50*0.13=6.5

13% of 50 is 6.5.

Answer:

450

Step-by-step explanation:

Based on the given conditions, formulate:

Calculate the sum or difference:

Convert decimal to fraction:

Divide a fraction by multiplying its reciprocal:

Cross out the common factor:

Calculate the product or quotient:

Answer:

Let:

A = students who passed the test = 14

B = students who completed the assignment = 13

N = Total students = 22

(A⁺ ∩ B⁺) = 6

P(A ∪ B) = 1 - 6/22 = 8/11

P(A ∩ B) = P(A) + P(B) - P(A ∪ B) = 14/22 + 13/22 - 8/11 = 1/2

P(A|B) = P(A ∩ B)/P(B) = (1/2)/(13/22) = 11/13 ≈ 0.85 ≈ 85%

Answer:

value of -4x=16.

value of -4x=10.

Answer in the attachment

Answer:

the little peice (x) is 37 cm

the second piece(x +26) = 37 + 26 = 63 cm

Step-by-step explanation:

think the little or second piece is x

and another piece is (x + 26)

according to question,

x + x+26 = 100

2x + 26 = 100

2x = 100 - 26

2x = 74

x = 74 ÷ 2

x= 37

The area of a regular polygon is 84.87 in²

A polygon with congruent sides and equal angles is referred to as a regular polygon. Equilateral triangles, squares, regular pentagons, and more are examples of regular polygons.

In this case Formula of the area of the equilateral triangle is (  [tex]\sqrt{3\\}[/tex]×a²)/4

where a is the length of the side of triangle.

Here the length of the side of the polygon(triangle) is 14in.

So the area of the equilateral triangle is (√3xa²)/4.

And a=14 in the above equation.

So the area of the regular polygon is: (√3x14x14)/4 =84.87 in²

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(f + d)/c.

First get rid of -d on the left side by adding d to both sides

cx - d = f  -->   cx = f + d

Then remove c from the left side by dividing both sides by c.

cx = f + d  -->  x = (f + d)/c

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Answer:

The answer is 3 or 3/1

Step-by-step explanation:

The equation you use is m=y2-y1/x2-x1

Answer:

Slope = 3

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Define two points on the line from the given table:

Substitute the defined points into the formula:

[tex]\implies \textsf{Slope}=\dfrac{13-7}{4-2}=\dfrac{6}{2}=3[/tex]

Note:

Therefore, the question may require you to enter 6/2 into the answer boxes.  However, the slope of the line is 3.

The scalar factor is of 6.

What is the scalar factor?

A scale factor is the ratio between corresponding measurements of an object and a representation of that object. in simple words how big or small is one object compared to another.

We are given two triangle and the measurements of the corresponding sides of the triangle.

side of one triangle is 4 and side of another triangle is 24.

To find the scalar factor we divide the two

We get the answers as 6

Hence the scalar factor is of 6

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The expected number of unaffected kittens should be 84

Find the below calculation of chi square:

Category   Affected Unaffected Total

Observed values   44                 84                 128

Expected Ratio         1                  3                   4

Expected Values, E  32             96

Deviation, D              12              -12

Deviation Squared     14            144

D^2/E                           4.5      1.5                  6

X^2                               6  

Degrees of freedom                       -                  1

Unaffected number of kittens:

Observed values for Affected=44

Total=128

25% of the 128 are affected.

The unaffected proportion is,

Total-Observed values for Affected kittens

=128-44

=84

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Answer:

2√2 x ³y

Step-by-step explanation:

1) Write the number in exponential form with the base of 2

2) Rewrite the exponent as a sum where one of the addends is a multiple of the index

3) Use a m+n m n = a xa to expand the expression

4) Any expression raised to the power of 1 equals itself

5) The root of a product is equal to the product of the roots of each factor

6)Reduce the index of the radical and exponent with 2

Then you get your answer!! Hope this helps

Answer: Hello Love I believe the answer is the LAST one

Step-by-step explanation:

The radius of the hole to the nearest hundredth of a foot is 2.88 feet.

What is radius?

The volume of the cylinder, V = 4200 cubic feet

Height, H = 2.1 miles = 11088 feet

The volume of the cylinder is given by the formula, V =πr²H

Putting values in the formula to find out radius,

4200=πr²(11088)

r²=[(11088)π]/4200

r²=8.2938

r=2.879~2.88 feet

The radius of the hole to the nearest hundredth of a foot is 2.88 feet.

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Answer:

319

Step-by-step explanation:

hope this helps

There are two questions to be solved, therefore, I'll solve the buckets one first and then I'll solve the other one. To solve both we need to apply LCM (least common multiple).

There are three buckets with differente capacities, one with 15 litres, one with 18 litres and one with 24 litres. Since they can fill a drum in an exact number of times, this means that the capacity of the drum is a multiple of the capacity of each bucket, therefore we should break each number into their multiples and find the common ones as shown below.

We now need to multiply all the common multiples:

For the second problem we have three items a book, a pen and a box. They cost respectively 36, 45 and 54. We need to then find the smallest sum of money that could buy a exact number o each item. We need to apply LCM once again as shown below:

We now need to multiply all the common multiples: