Area of Rectangle: A = length*width
One side of a rectangle is twelve kilometers longer than three times another side of the rectangle. Find the
sides if we also know that the area of the rectangle is 135 km².
shorter side:
longer side:

Using scientific notation, the length of the hydrogen atom is given as follows:

[tex]1.9 \times 10^{-10}[/tex]

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

The diameter of a proton is given by:

[tex]1.9 \times 10^{-15}[/tex].

The hydrogen atom has an overall length of 100,000 times the diameter of the proton, hence the length is given by:

[tex]L = 100000 \times 1.9 \times 10^{-15} = 10^5 \times 1.9 \times 10^{-15} = 1.9 \times 10^{5 - 15} = 1.9 \times 10^{-10}[/tex]

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Aimee is shipping a care package to her friend in college, the max volume of the box is mathematically given as

V=1539.6007

Generally, the equation for the height is mathematically given as

V=(20-2x)(40-2x)x

Where x is the height

V=4x^3-120x^2+800x

differentiate v and solve

dv/dx=3x^2-60+200

3x^2-60+200=0

Therefore

x=[tex]\frac{60\pm \sqrt{60^2-4x3x200}}{2*3}[/tex]

x=[tex]\frac{60-34.64}{6}[/tex]

x=4.2265

In conclusion, the second differentiation of v and solve we have

d^2v/dx^2=24-240

Hence

d^2v/dx^2< 0

V=(20-2x(40-2x)x

subsitute x

V=(20-2(4.2265))(40-2(4.2265))(4.2265)

V=1539.6007

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The sum of the next 5 consecutive positive integers is w + 25

Let the first five numbers be A - E

So, we have:

A + B + C + D + E = W

The next five numbers would be

A + 5, B + 5...... E + 5

So, we have:

Sum = A + 5 + B + 5 + C + 5 + D + 5 + E + 5

Evaluate the like terms

Sum = A + B + C + D + E + 25

Substitute A + B + C + D + E = W

Sum = W + 25

Hence, the sum of the next 5 consecutive positive integers is w + 25

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The solution of the first graph is 1, 2 while the second graph is a straight line.

We have y > 2x

y< x

First you have to replace the inequality by a mathematical operator

y - 2x = 0

y - 3 = 0

equation 1 is of the form

y = mx

The slope here is 2,

to make a graph we need to have x = 1 then the line would pass through

(1,2).

The second equation is simply a second line that would pass through the x axis.

The correct graph is below:

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The asymptote of the function given in the task content is the line; x = 25.

It follows from the task content that the function given is a rational function and hence, the asymptote of the function is the X-value which renders the function undefined in which case, the denominator is equal to 0.

x - 25 = 0.

x = 25.

The end behaviour of the functions graph is that it approaches the line x = 25 but never touches the line.

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You will need 252 mL of pure water to obtain 0.25 mL of the desired 25% solution.

If we add X amount of water to the solution, the total amount of solution is 375+X.

And that must be 25%.

The amount of solute in the current amount of solution is

0.6(375)=225.

That amount won't change by adding water.

So we set up the equation so that the amount of solute divided by the new total amount of solution equals 25%.

225/(375+X)=0.25

cross multiply and solve

225/0.25=(375+X)

900-375=X

X=525

The pure water will you need to add to obtain the desired solution is 525.

Then we check 225/(375+525)=0.25.

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Answer:

96 sq. inch

Step-by-step explanation:

rectangle has 24 inches × 8 inches dimensions

Hence, Area of Rectangle,

A1=24×8

=192 sq. inch

We, know triangle with base 24 inches and height 8 inches has area exactly half of the rectangle's.

ie. A2=½(24×8)

=96 sq. inch

This was for unshaded region. Then remaining half area is for shaded region.

A1-A2=A

ie. 192-96=96 sq. inch

The area of the shaded region is 96 square inches.

To find the area of the shaded region, we need to subtract the area of the triangle from the area of the rectangle.

The area of a rectangle is calculated by multiplying its length by its width. In this case, the rectangle has a length of 24 inches and a width of 8 inches, so its area is 24 inches * 8 inches = 192 square inches.

The area of a triangle is calculated by multiplying its base by its height and dividing the result by 2. In this case, the triangle has a base of 24 inches and a height of 8 inches, so its area is (24 inches * 8 inches) / 2 = 96 square inches.

Now, to find the area of the shaded region, we subtract the area of the triangle from the area of the rectangle:

Shaded Area = Area of Rectangle - Area of Triangle

= 192 square inches - 96 square inches

= 96 square inches

Therefore, the area of the shaded region is 96 square inches.

..

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The coordinates of B' are 3 and -12. so option D is correct (3, -12)

The point P(x, y) may undergo translation to form P' by using a defined translation rule :

If given the rule T(a, b) synch that P undergoes translation on T; then we will have P'(x+a; y+b)

Therefore,

The point B has its coordinates as B(1, - 5)

Translation rule, T(2, - 7) then the coordination of B after undergoing transformation according to T2;

B(1, - 5) - - - > T(2, - 7) - - - - > B'(1+2 ; - 5+-7)

= B'(3, -12)

Hence, the coordinates of B' are 3 and -12. so option D is correct.

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Answer:

(D)   (3, –12)  

Step-by-step explanation:

If a translation of T2, –7(x, y) is applied to ΔABC, what are the coordinates of B'? The answer is (3, –12).

The value of y in the code segment is 444

The code segment is given as:

y = int(3 * '4')

Evaluate the expression in the bracket

y =int('444')

Remove the bracket

y = 444

Hence, the value of y in the code segment is 444

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The solution to the given expression is 2

Given the equation 48 ÷ ((2 + 6) × 2) − 1

Using PEMDAS

48 ÷ ((8) × 2) − 1

48÷(16) - 1

3 - 1

2

Hence the solution to the given expression is 2

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For the coordinate (5,6), the 90 degree rotation will be equivalent to (-6, 5)

Rotation is a technique used to change the position of an object on an xy-plane.

If the coordinate point (x, y) is rotated 90degrees, the rule will be:

(x, y) -> (-y, x)

For the coordinate (5,6), the 90 degree rotation will be equivalent to (-6, 5)

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The value of the expression is 188

Given the expression

= [tex]\frac{7 + (2 + 6)^2}{4 * \frac{1}{2}^4}[/tex]

Expand the bracket

= [tex]\frac{7 + 4 + 36}{ 4 * 1/16}[/tex]

We have

= [tex]\frac{47}{1/4}[/tex]

The denominator becomes the multiplier, we have

= 47 × 4

= 188

Thus, the value of the expression is 188

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Number of physics textbooks sold was 261 & number of maths textbooks sold was 199.

Let, the number of physics textbooks sold = x

According to the question,

The number of math textbooks sold was 62 less than the number of physics textbooks sold.

So, Number of maths textbooks sold = x-62

The textbook store sold a combined total of 460 physics and math textbooks in a week.

So, the equation becomes,

(x-62)+x = 460

⇒ x-62+x = 460

⇒ 2x-62 = 460

⇒ 2x = 460+62

⇒ 2x = 522

⇒ x = 522/2

⇒ x = 261

So, 261 physics textbooks were sold

(261-62) = 199 maths textbooks were sold.

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The exact time is 93 days

The interest is  $20.38

The maturity value is  $1020.38

The interest is a function of the time, amount borrowed and the interest rate.

Interest = amount borrowed x time x interest rate

Time = June 9 - March 8 = 93 days

1000 x 0.08 x (93/365) = $20.38

Maturity value = 1000 + 20.38 = $1020.38

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Answer:

K=4a-1

Step-by-step explanation:

K = 4a- 1 (shifting -4a to right side from left)

Assuming he has the money to make the down payment, my classmate will borrow 90% of the home price.

A down payment is the upfront payment or an initial portion of the total purchase price of expensive property.

It is required that the buyer of a mortgaged property deposits this initial portion before taking the mortgage for the balance.

Mortgage period = 30 years

Interest rate = 3.5% fixed

Down payment = 10%

Balance (Mortgage) = 90% (1 - 10%)

Thus, assuming he has the money to make the down payment, my classmate will borrow 90% of the home price.

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The end behaviour of the function is When x ---> ∞ , f(x) ---> -∞  , when x ---> -∞ f(x) ----> ∞  , Option D is the correct answer.

A function is a mathematical statement that related the independent and the dependent variable.

The function given is

f(x) = [tex]\rm -2 \sqrt[3]{x}[/tex]

To understand the end behaviour the graph is plotted

When x ---> ∞ , f(x) ---> -∞

when x ---> -∞ f(x) ----> ∞

Therefore Option D is the correct answer.

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In accordance with propositional logic, quantifier theory and definitions of simple and composite propositions, the negation of a implication has the following equivalence:

[tex]\neg (\exists \,x\, (P(x) \implies Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x))[/tex] (Correct choice: iii)

Herein we have a composite proposition, that is, the union of monary and binary operators and simple propositions. According to propositional logic and quantifier theory, the negation of an implication is equivalent to:

[tex]\neg (\exists \,x\, (P(x) \implies Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x))[/tex]

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Answer:

The G.C.F of (8,24) is 8

Step-by-step explanation:

look at the attachment above ☝️

The equation of the line in slope-intercept form that passes through the point (-6, -5) with a slope of 6 is y = 6x + 31. The correct answer is option (D).

Given that the line passes through the point (-6, -5) with a slope of 6, we can plug these values into the equation to find the y-intercept (b).

Using the point-slope form of the equation:

y - y₁ = m(x - x₁)

Substitute (-6, -5) and the given slope (m = 6):

y - (-5) = 6(x - (-6))

y + 5 = 6(x + 6)

Now, let's simplify the equation:

y + 5 = 6x + 36

To get the equation in slope-intercept form (y = mx + b), isolate y:

y = 6x + 36 - 5

y = 6x + 31

Thus, the correct answer is option (D).

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Answer:

The first one: 12/13  > 36/30

Step-by-step explanation:

The first one would be correct as 12/13 is less than 36/30.

To explain why 13/17 is actually less than 24/28, see below:

So when comparing fractions, we must follow steps.

Step One: convert mixed numbers to a fraction, if there are any

There are not mixed numbers to compare, so we can move to the next step.

Step Two: find the least common denominator of the two fractions

Least common denominator = 476

Check out our least common denominator calculator for help on finding this.

Step Three: rewrite each fraction to an equivalent fraction using the denominator 476

To do this, start by dividing 476 by the denominator of the first fraction. Next, multiply the result by the numerator to find the new numerator. To rewrite, put the new numerator over 476. Repeat this for the second fraction

364/476                              408/476

Step Four: compare the numerators

At this point, to compare the fractions, we can simply compare the numerators to see which is larger

364<408

Step Five: rewrite each fraction as the original fraction

13/17<24/28

Therefore, the first statement (12/13 > 36/30) is true.

Answer:

  12/13 < 36/30

Step-by-step explanation:

There are many ways to compare numbers. One way is to compare them to some value that lies between. Another is to consider their difference from a value that does not lie between.

In the first fraction, 12 < 13, so the value of the fraction is less than 1:

  12/13 < 1

In the second fraction, 36 > 30, so the value of the fraction is greater than 1:

  1 < 36/30

Then the order of the fractions is ...

  12/13 < 1 < 36/30

  12/13 < 36/30 . . . . . the given order is True

We notice the difference between numerator and denominator is 4 in each case, so we can write each fraction as a difference from 1:

  (13/17) vs (24/28)

  = (1 - 4/17) vs (1 -4/28) . . . . . fractions rewritten

  = -4/17 vs -4/28 . . . . . . . . . subtract 1 from both

The first fraction, 4/17, has a smaller-value denominator, so its magnitude is larger than that of the fraction 4/28. In other words, the ordering of these fractions is ...

  -4/17 < -4/28

  1 -4/17 < 1 -4/28 . . . . . . add 1 to both sides

  13/17 < 24/28 . . . . . the given order is False

__

Additional comment

One sort of "no brainer" way to compare the fractions is to multiply them by the product of their denominators. This looks like "cross multiplication" where each numerator is multiplied by the opposite denominator. As long as you keep the numerators in the same relative places, the comparison symbol will be the correct one for the fractions.

  12/13 vs 36/30   ⇒   (12·30) vs (13·36)   ⇒   360 < 468

The left fraction is smaller than the right fraction.

Similarly, ...

  13/17 vs 24/28   ⇒   (13·28) vs (17·24)   ⇒   364 < 408

The left fraction is smaller than the right fraction.

__

Here, we have used the fractions "as is." In each case, the fraction on the right could be reduced, possibly making the comparison easier.

The triangle KLM is rotated about origin by 90 degrees to form the triangle K'L'M'.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Rotation does not change the size and shape of the geometry.

The triangle KLM is rotated about origin by 90 degrees to create the triangle K'L'M'.

The diagram is given below.

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Answer:

4x+6

Step-by-step explanation:

x/x^2+3x+2 + 3/x+1

x/(x+1)(x+2) + 3/x+1

make the denominator the same

x/(x+1)(x+2) + 3 (x+2)/(x+1)(x+2)

x/(x+1)(x+2) + 3x+6/(x+1)(x+2)

4x+6/(x+1)(x+2)

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The requried, numerator of the simplified sum is 4x + 6. The option is correct.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property

The given expression is x/(x²+3x+2) + 3/(x+1). To make the denominators the same, we need to factor the denominator of the first fraction:

x/(x+1)(x+2) + 3/(x+1)

Now we can add the two fractions by finding a common denominator, which is (x+1)(x+2):

x/(x+1)(x+2) + 3(x+2)/(x+1)(x+2)

Simplifying the numerators, we get:

x + 3x + 6 / (x+1)(x+2)

Combining like terms in the numerator, we get:

4x + 6 / (x+1)(x+2)

Therefore, the simplified expression is (4x+6)/(x+1)(x+2).

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The equivalent expressions are (b) (7 * 7)^x , (c) 7^x * 7^x and (e) 7^(2x)

The expression is given as:

49^x

Express 49 as 7 * 7

(7 * 7)^x ---- option (b)

Express 7 * 7 as an exponent

7^(2x) ---- option (e)

Express 2x as x + x

7^(x +x)

Expand

7^x * 7^x --- option (c)

Hence, the equivalent expressions are (b), (c) and (e)

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Answer:

$26.08.

Step-by-step explanation:

[tex]1. \ \frac{16.95}{0.65} =\frac{x}{1};[/tex]

2) x=16.95/0.65≈$26.076923076923076923

The units digit of the given exponential expression will be 6

From the question, we are to determine the units digit of the given exponential expression

The given exponential expression is

4⁸⁰⁰

We know that

4¹ = 4

4² = 16

4³ = 64

4⁴ = 256

4⁵ = 1024

4⁶ = 4096

From above, we can observe that the units digit of the odd exponents is 4 while the units digit of the even exponents is 6.

The exponent of the given expression is 800. 800 is an even number.

Hence, the units digit of the given exponential expression will be 6

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Using it's concept, an even function is given by:

B. [tex]F(x) = 2\cos{\frac{1}{2}x}[/tex]

Even functions are functions for which the following statement is true for all values of x.

f(x) = f(-x).

The cosine function, without a phase shift, is an example of an even function, hence option B is correct.

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Answer:

2nd Option

Step-by-step explanation:

Hello!

First, let's solve the inequality for x.

Since the symbol is less than or equal to, it will be a closed circle on Point -8 going in the left direction (all values less than -8).

The answer is the Second Number Line.