You have diving lessons every fifth day and swimming lessons every third day. Today have both lessons in how many days will you have both lessons on the same day again.

There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex]. Statement A best interprets the quotient.

A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.

The shaded part in step 1 is;

[tex]\rm 4 + \frac{1}{6} = 4 \frac{1}{6}[/tex]

Divide the shaded part with the unshaded part as ;

[tex]\rm \frac{4 \frac{1}{6} }{\frac{2}{3}}\\\\ \frac{25}{6} \times \frac{3}{2} \\\\\ \frac{25}{4} \\\\ 6 \frac{1}{4}[/tex]

There are [tex]\rm 6 \frac{1}{4}[/tex] two - third in [tex]\rm 4 \frac{1}{6}[/tex].

Hence, statement A best interprets the quotient.

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Answer: A

Step-by-step explanation:

Answer: B.

[tex]a_1=2\\a_n=a_n\times(-5)[/tex]

Step-by-step explanation:

The given geometric sequence : 2, -10, 50, -250

The first term of the sequence : [tex]a_1=2[/tex]

The common ratio between the terms :[tex]r=\dfrac{-10}{2}=-5[/tex]

We know that the recursive formula for geometric progression is given by :-

[tex]a_n=a_{n-1}r[/tex]

Then , the recursive formula for the given geometric progression will be :-

[tex]a_n=a_n\times(-5)[/tex]

The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles. Therefore, from the given diagram angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles. So, the correct options are: B), C), and E).

Given :

[tex]\angle 3 = 90^\circ[/tex]

The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles.

From the diagram given in the question it can be clearly observe that if [tex]\angle 3 = 90^\circ[/tex] than [tex]\rm \angle 4,\;\angle 5,\;and\;\angle 6[/tex] are also equal to [tex]90^\circ[/tex].

Than according to the definition of supplementary angles:

[tex]\angle 3 +\angle6 = 180^\circ[/tex]

[tex]\angle 3 +\angle4 = 180^\circ[/tex]

[tex]\angle 4 +\angle5 = 180^\circ[/tex]

[tex]\angle 5 +\angle6 = 180^\circ[/tex]

[tex]\angle 7 +\angle8 = 180^\circ[/tex]

Therefore, angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles.

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For a one-year investment, the equation is I = x imes 0.05 imes 1.

If Mary Ellen invests x dollars at an interest rate of 5%, we can write an equation that describes the total interest earned on that investment using the simple interest formula. The formula for calculating simple interest is Interest = Principal imes Rate imes Time. Assuming the investment is for 1 year, the equation for the total interest (I) Mary earns would be:

I = x imes 0.05 imes 1

This equation states that the interest Mary earns is equal to the amount of money she invested (x dollars) multiplied by the interest rate (5% or 0.05 as a decimal) and the time the money is invested (1 year).

If Mary Ellen invests $100, the total interest she would earn in one year at a 5% interest rate would be calculated as follows:

I = $100  imes 0.05 imes 1 = $5

Final answer:

Simplify the expression √(16 − x²) by substituting x with '4 sin x' to get 4|cos x|. Use trigonometric identities to arrive at the simplified expression.

Explanation:

The expression to simplify is: √(16 − x²) after substituting '4 sin x' for x.

Step-by-step solution:

Replace x with 4 sin x in the expression: √(16 − (4 sin x)²)

Simplify: √(16 − 16 sin² x)

Apply trigonometric identity: √(16 cos² x) = 4|cos x|

Answer:

[tex]y=3x+2[/tex]

Step-by-step explanation:

We are given equation as

[tex](y+4)=3(x+2)[/tex]

Since, we have to write equation in slope-intercept form

so, we can use slope-intercept formula

[tex]y=mx+b[/tex]

where m is a slope

b is y-intercept

so, we can write our equation in this form

[tex](y+4)=3(x+2)[/tex]

Distribute 3

[tex]y+4=3\times x+3\times 2[/tex]

[tex]y+4=3x+6[/tex]

Subtract both sides by 4

[tex]y+4-4=3x+6-4[/tex]

[tex]y+4-4=3x+6-4[/tex]

[tex]y=3x+2[/tex]

So, slope-intercept form of equation is

[tex]y=3x+2[/tex]

To achieve balance, the momentum on both sides must be equal so that it cancels out. Momentum is simply the product of mass and distance, therefore:

50 pounds * 6 ft = 100 pounds * X

X = 3 ft

Hence B must be placed 3 ft from the pivot.

Answer:

The solution of the given inequality  [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]

Step-by-step explanation:

Given inequality [tex]|x-4|<\:3\:[/tex]

We have to find the solution of the given inequality  [tex]|x-4|<\:3\:[/tex]

Using absolute rule, [tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex], we have,

[tex]-3<x-4<3[/tex]

Rewrite as [tex]x-4<-3\quad \mathrm{and}\quad \:x-4<3[/tex]

Consider , [tex]x-4>-3[/tex]

Adding 4 both side, we have,

[tex]x-4+4>-3+4[/tex]

Simplify, we have,

[tex]x>1[/tex]

Consider , [tex]x-4<3[/tex]

Adding 4 both side, we have,

[tex]x-4+4<3+4[/tex]

Simplify, we have,

[tex]x<7[/tex]

Combining, we have,

[tex]1<x<7[/tex]

Thus, The solution of the given inequality  [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]

The simplified expression is log (x⁴y²).

Inverse to exponentiation is the logarithm.

The given expression is 4log x + 2log y.

Simplify the expression as follows:

4log x + 2log y

= log x⁴ + log y²

= log (x⁴y²)

Hence, the simplified expression is log (x⁴y²).

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Answer:

30 millimeters

Step-by-step explanation: