Using that income equation, after how many years will the income be $300? Round your answer correct UP TO TWO (2) decimal digits.

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

x/3 - 3/4 = 5/12

Hence:

x/3 = 5/12 + 3/4

x/3 = 7/6

x = 7/2

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

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we conclude that the system of inequalities has more solutions than the system of equations.

We have the system of equations:

y = (-1/2)*x + 1

y = x - 5

And the system of inequalities:

y > (-1/2)*x + 1

y < x - 5

First, if you look at the first system you can see that we have two non-parallel lines, so that system has only one solution.

Now let's look at the system of inequalities, we can get solutions like:

x = 10

y = 1

1 > (-1/2)*10 + 1 = -4

1 < 10 - 5 = 5

So both inequalities are true, which means that the point (10, 1) is a solution.

And also is the point (11, 1), and (12, 1), and infinite other points.

Then we conclude that the system of inequalities has more solutions than the system of equations.

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The angles ∠1 ≅ ∠4 since the line BD bisects ∠ABC, AD║ BC, and AB ║ CD. This is obtained by using the angle bisector theorem, alternate interior angles, and the transitive property of congruence.

Transitive property:

If ∠a and ∠b are congruent and ∠b and ∠c are congruent, then ∠a and ∠c are also congruent.

I.e., If ∠a ≅ ∠b and ∠b ≅ ∠c, then ∠a ≅ ∠c.

The angles bisector theorem states that the ray or line which bisects the angle divides the angle into two equal parts.

I.e., If line BD bisects the angle ∠ABC, then ∠B = ∠B1 + ∠B2

(where ∠B1 = ∠B2)

The line BD bisects ∠ABC, AD║BC, and AB║CD

The line BD bisects ∠ABC. So,

∠B = ∠3 + ∠4

According to the angle bisector theorem, ∠3 ≅ ∠4.

Since AD║BC and AB║CD, the alternate angle are congruent.

I.e., ∠3 ≅ ∠1

Thus, by the transitive property of congruence,

∠1 ≅ ∠4

Hence proved.

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Answer:

A. x=5 is a solution, but x=3 is not

Step-by-step explanation:

When x=5, 11-5<7, 6<7, this is a solution

When x=3, 11-3<3l, 8<7, this is not a solution

The probability of catching a bass in the lake is given by:

Probability = probability 1 × probability 2

Since the forest ranger caught a fish from his prior fishing experience, we can infer that he has a probability of catching a bass in a lake:

Probability 1 = Number of fish caught/Number of tries

By using a special type of bait, he should calculate the probability of catching a fish as follows:

Probability 2 = Number of fish caught/Number of tries

Therefore, the probability of catching a bass in the lake is given by:

Probability = probability 1 × probability 2

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Equation of straight line in point - slope form :

[tex]\qquad❖ \: \sf \:y - y1 = m(x - x1)[/tex]

( m = slope = 4, point (5 , 17) )

[tex] \qquad◈ \: \: \sf \: y - 17 = 4(x - 5)[/tex]

[tex] \qquad◈ \: \: \sf \: y - 17= 4x - 20[/tex]

[tex] \qquad◈ \: \: \sf \: y = 4x - 20 + 17[/tex]

[tex] \qquad◈ \: \: \sf \: y = 4x - 3[/tex]

Now, it's the form of line in slope - intercept form, ( slope = coefficient of x = 4 and y - intercept = -3 )

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex] \qquad◈ \: \: \sf \: y \: \: int = - 3[/tex]

The curve passes through the point (3, 3), so [tex]y=3[/tex] when [tex]x=3[/tex]. Then

[tex]y = ax^2 + bx \implies 3 = 9a + 3b \implies 3a + b = 1[/tex]

The tangent line to the curve at (3, 3) has gradient [tex]\frac{dy}{dx}[/tex] at [tex]x=3[/tex]. Compute the derivative.

[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]

Then when [tex]x=3[/tex], the gradient is 4, so

[tex]2ax + b = 4 \implies 6a+b=4[/tex]

Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we find

[tex](6a+b) - (3a+b) = 4-1 \implies 3a = 3 \implies \boxed{a=1}[/tex]

and it follows that

[tex]3 + b = 1 \implies \boxed{b = -2}[/tex]

Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Part 1

Angles in a triangle add to 180 degrees, so

[tex]m\angle E=180^{\circ}-82^{\circ}-43^{\circ}=55^{\circ}[/tex]

Part 2

By the Law of Sines,

[tex]\frac{EF}{\sin 43^{\circ}}=\frac{15}{\sin 55^{\circ}}\\\\EF=\frac{15 \sin 43^{\circ}}{\sin 55^{\circ}}\\\\EF \approx 12.49[/tex]

Answer:

What is the measure of angle E?

m∠E =

✔ 55

°

What is the length of EF rounded to the nearest hundredth?

EF ≈

✔ 12.49

Step-by-step explanation:

Using the domain concept, the only value of x that is not on the domain of [tex]f(x) = \frac{1}{3x + 5}[/tex] is given as follows:

[tex]x = -\frac{5}{3}[/tex]

The domain of a function is the set that contains all possible input values for the function. For a rational function, for example, the zeros of the denominator are excluded from the domain. Another example is an even root, where the inside term has to be positive.

The rational function for this problem is given by the function f(x) presented below:

[tex]f(x) = \frac{1}{3x + 5}[/tex]

The denominator is 3x + 5, hence the restriction in the domain of f(x) is given as follows:

3x + 5 = 0

3x = -5

[tex]x = -\frac{5}{3}[/tex]

The solution to the equation above is the only value of x that is not part of the domain of f(x).

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The mean of the scores to the nearest 10th digit will be 74.9.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean.

Then the mean is given as,

Mean = (Total score) / (total student)

The total score will be

Total score = 65 x 8 + 70 x 7 + 75 x 3 + 80 x 8 + 85 x 3 + 90 x 2 + 95 x 2

Total score = 520 + 490 + 225 + 640 + 225 + 180 + 190

Total score = 2470

The total number of students will be

Total student = 8 + 7 + 3 + 8 + 3 + 2 + 2

Total student = 33

Then the mean will be

Mean = 2470 / 33

Mean = 74.85 ≈ 74.9

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Answer:

- 4/7 , -1/9, 7/4

Step-by-step explanation:

You know that 7/4 is the largest number because it is the only positive number.  To compare the two negative numbers you need common denominators.  The common denominator would be 133 (19 x 7).  Now make equivalent fractions.-4/7 = x/133  133 divided by 7 is 19.  Multiple the -4 by 19 to get -76/133.  Next, make an equivalent fraction for -1/19.  The new denominator will be 133.  If I divide 133 by 19, I will get 7, so I multiple -1x7 and get -7 and the new fraction -7/133.

I have two fractions to compare -7/133 and -76/133.  -76/133 if farthest from 0 so it has the least value.

Answer:

Step-by-step explanation:

A parallel line will have the same slope, m, as the reference line given by the form y=mx+b.  b is the y-intercept, the value of y when x=0.

The reference line of y = -(1/2)x + (3/7) has a slope of -(1/2).

The parallel line will have the same slope, so we can write:

y - -(1/2)x + b

We need a value of b that forces the line to go through point (-1,0).  Enter that point in the equation and solve for b:

y - -(1/2)x + b

0 - -(1/2)(-1) + b

b = -(1/2)

The equation of the line parallel to y = -(1/2)x + (3/7) and going through (-1,0) is

  y=-(1/2)x - (1/2)

Answer:

80

Step-by-step explanation:

To find the mean we add up all the numbers and then divide that number by the amount of numbers we added up.

So in this case we added up 65, 70, 75, 80, 85, 90 & 95. This gives us 560. Now we divide 560 by 7 as that is the amount of numbers we added up. This gives us 80 which means the answer is 80.

I hope this helped! :)

Answer: B

[tex]x + 2y \leq 4 \textrm{ and } 3x + y \leq 4[/tex]

Step-by-step explanation:

Insert the values of x and y for any point in the heavily shaded region and see if it satisfies both inequalities

We can see that the origin (0,0) is inside the shaded region so use these values because they are the easiest to compute

Plug in x = 0 and y = 0 into the first inequality
0 + 2.0 = 0 which is greater than 5.

So we can eliminate both A and D since they both contain incorrect inequalities

Now, test the second inequality with x = 0 and y = 0

For B we get

3.0 + 0 = 0 which is indeed less than 4

C is not applicable since 0 is not greater-than-equal to 4

Hence B is the correct solution

This can be verified using a graphing tool (see image)

Answer:

13%

15%

41%

31%

Step-by-step explanation:

To find the percentage one amount is out of another amount, divide the smaller amount by the bigger amount. You will end up with a decimal (0.xy where x is the 10% place and y is the 1% place).

For example: to find the percentage that 39 is out of 300 students, we divide 39 by 300. This gives us the decimal 0.13. Written as a percentage, that is 13%.

We can do this for all of them.

Here is the math for each one:

39 ÷ 300 = 0.13 → 13%

45 ÷ 300 = 0.15 → 15%

123 ÷ 300 = 0.41 → 41%

93 ÷ 300 = 0.31 → 31%

Once you have all these decimals, you might choose to check your work by adding them up. They should at up to 1.00, or 100%. In this case, they do, so we know these answers are correct.

I hope this helps. Please let me know if you have questions.

Answer:

Domain: ( Positive infinity, Negative Infinity)

Range: (-3, Positive Infinity )

Step-by-step explanation:

Answer:

Step-by-step explanation:

AC=DC. (Given in figure)

AB=BD. (Given in figure

BC=BC. (Common)

that means triangle BAC is congruent to triangle BDC by SSS criterion.

Answer:

Horizontal reflection

Step-by-step explanation:

a math chart that was labeled had these pattern examples with the the translation and transformation.

The probability solved by binomial distribution that all will survive is 0.8154.

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

Computation of probability of all survived people from heart attack;

A heart attack patient has a 0.04 percent chance of dying from the attack (i.e., 4 of 100 die of the attack).

What is the likelihood that each of the five patients who experience a heart attack will survive?

We'll refer to a victory in this scenario as a heart attack (p = 0.04). In other words, we are interested in the likelihood that none of our n=5 patients will die (0 successes).

Each attack has a chance of being fatal or not, with a probability of 4 percent for all patients, and each patient's result is independent.

Assume for the purposes of this example that the five individuals being examined are unrelated, of the same age, and free of any concomitant disorders.

By binomial distribution,

[tex]\begin{gathered}P(0 \text { successes })=\frac{5 !}{0 !(5-0) !} 0.04^{0}(1-0.04)^{5-0} \\P(0 \text { successes })=\frac{5 !}{5 !}(1)(0.96)^{5}=(1)(1)(0.8154)=0.8154\end{gathered}[/tex]

Therefore, with a 4 % chance that anyone will die, there is an 81.54% chance that every patient will survive the onslaught. The outcomes in this example could be 0, 1, 2, 3, 4 or 5 successes (fatalities).

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Answer:

I don't think the answer is in the options.

Sine rule:

30/sin(17) = x/sin(90)

x sin(90)

30 x sin(90) / sin(17) = x

x = 102.6091086

So, x = 102.6 to the nearest tenth.

Hope this helps!

The factored expression of the polynomial is (4 - x)(5 + x)

The polynomial expression is given as;

20 - x - x^2

Expand the expression

20 - 5x + 4x - x^2

Factorize the expression

5(4 - x) + x(4 - x)

Factor out 4 - x

(4 - x)(5 + x)

Hence, the factored expression of the polynomial is (4 - x)(5 + x)

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Answer:

blue dot have value of -6 in y inverse axis

Answer:

d. 64

Step-by-step explanation:

x^1/2 = 8

Square each side

(x^1/2 )^2=( 8)^2

x = 64

Answer:60g

Step-by-step explanation:

Hope this the answer

Probability that a card selected at random is purple = 7/25

Number of red cards, N(red) = 12

Number of blue cards, N(blue) = 17

Number of purple cards, N(purple) = 14

Number of yellow cards, N(yellow) = 7

Total number of cards, N(total) = 12 + 17 + 14 + 7

N(total) = 50

Probability that a card selected at random will be purple

P(purple) = N(purple) / N(total)

P(purple) = 14/50

Reduce to the lowest fraction

P(purple) = 7/25

Therefore, probability that a card selected at random is purple = 7/25

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Complete Question

There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat. If a card is selected at random, what is the probability that the card is purple