Find two integers whose sum is -7 and whose product is 12. Explain how you found the numbers.

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]

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]

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:

30 millimeters

Step-by-step explanation:

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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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.

For more information, refer the link given below:

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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

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.