(-2)2+3 × (-5)
please helpe me answer this question

Answer:

I think either 1/10 or 2/5

Step-by-step explanation:

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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To calculate a fraction, it is almost the same as calculating a number normal to the power. The numerator and denominator of the fraction are multiplied as many times as possible indicated by its exponent, then:

    \(\boldsymbol{\sf{\left(\dfrac{1}{9}\right)^{2}=\dfrac{1\times1}{9\times9}=\cfrac{1}{81} }}\)

Therefore the fraction 1/81 is already in reduced form, so it is no longer possible to simplify it.

Answer:

\(y = \frac{3}{2}x + 5\)

y = (3/2)x + 5

Step-by-step explanation:

The format of an equation of a line is \(y = mx + b\). Y and X are the coodinates of a point along the line. b is the y intercept (where it crosses the Y axis). m is the slope. This format is called slope-intercept form.

First, you need to find the slope of the line. You can do this using the slope formula, which is \(m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\). \(y_{1}\) and \(x_{1}\) are the x and y values of a point along the line, and \(y_{2}\) and \(x_{2}\) are the x and y values of a different point along the line that has a greater x value. Lastly, \(m\) is the slope of the equation, same as slope-intercept form.

To find the slope, you have to plug in your points. (-4, -1) has a smaller X value so we'll replace the \(y_{1}\) and \(x_{1}\) with those coordinates. We'll replace \(y_{2}\) and \(x_{2}\) with the other point, (2, 8)'s coordinates.

Now, the equation is \(m = \frac{8-(-1)}{2-(-4)}\). TO solve, just simplify the right side. 8 minus negative one is 9 (since subtracting negative numbers is the same as adding. 2 minus negative 4 is 6. Now we're left with \(m = \frac{9}{6}\), and 9 over 6 simplifies to \(m = \frac{3}{2}\). So the slope is \(\frac{3}{2}\), or 1.5. This means the Y value goes up 1.5 for every 1 the x value goes up.

Now, you have to find the Y intercept. To do this, you can make a table and fill in missing values by adding the slope to the Y every time we increase the X:

x    |   y
-----------
-4   |   -1
-3   |  0.5
-2   |  2
-1    | 3.5
0    |  5

Since the X is 0, the line is crossing the Y axis at (0, 5). The y intercept is 5.

Now finally, you just have to plug in the slope and y intercept into slope-intercept form, which is \(y = mx + b\), as mentioned above. B is the y intercept, so we replace that with five, making \(y = mx + 5\). M is the slope, so you replace that with \(\frac{3}{2}\). This makes the equation \(y = \frac{3}{2}x + 5\). And that's your answer!

Hopefully this helps, good luck!

Answer:

The number of students that prefer to do homework from the group of all students

Step-by-step explanation:

The question says that the ratio between the student who prefer doing homework before school and the students who prefer doing homework after school is 7:15.

That means 7 students prefer doing homework before school and 15 students prefer doing after school.

In this scenario, the total number of students is 7 + 15 i.e. 22

So the percentage 7/22 is the number of students that prefer to do homework before school from the group of all students

Answer:

500 times

Step-by-step explanation:

Divide the thickness of a cat hair by the thickness of a human hair.

4.0 × 10^-1 / 8.0 × 10^-4 =

= 0.5 × 10^3

= 500

500 times

Answer:

did u ever get the answer? if so what is it??

Step-by-step explanation:

Answer:

X = 9287.5

Step-by-step explanation:

Solving steps

7.5+ 9287=x+7

Calculate

9294.5=x+7

Move the terms

-x=7-9294.5

Calculate

-x=-9287.5

Change the signs

Solution

X = 9287.5

Answer:

3/6 + 3/6 | 4/12 + 8/12 | 2.5/6 +3.5/6

Step-by-step explanation:

Answer: $227,226.51

Step-by-step explanation:

First, we need to convert the period to weeks.

9 1/2 years = 9.5 years

1 year = 52 weeks

9.5 years = 494 weeks

Next, we can use the formula for the future value of an annuity:

FV = (PMT x (((1 + r/n)^(n*t)) - 1)) / (r/n)

where:

PMT = payment amount per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

Plugging in the given values:

PMT = $300

r = 0.055 (5.5% expressed as a decimal)

n = 52 (compounded weekly)

t = 9.5 years = 494 weeks

FV = ($300 x (((1 + 0.055/52)^(52*494)) - 1)) / (0.055/52)

FV = $227,226.51

Therefore, the future value of the annuity is approximately $227,226.51.

Answer:

He solved 75% of the puzzles!

Step-by-step explanation:

Okay, let's look at our fraction 18 out of 24. We can see that they are both even numbers, so at worst, we can divide the entire fraction by two. However, they have a GCF of six, so we will use that.

18                               3

----  divided by 6  =  ----

24                              4

Now that we have the fraction 3/4, we can turn that into a percentage!

3/4 is 0.75. To get the percentage, we multiply that by 100--now we have 75%.

Around 0.000125 or 0.0125% of the time, the song will be played exactly six out of seven days.

Every day represents a trial in this binomial probability issue, and there are only two potential results:

either the music is played (a success), or it is not (failure). We're looking for the likelihood that exactly 6 out of 7 trials will be successful.

The likelihood of success (performing the song) is 1/6, while the likelihood of failure (not playing the song) is 1 - 1/6 = 5/6, on any given day.

We can use the binomial probability formula to find the probability of exactly 6 successes in 7 trials:

P(6 successes) = (7 choose 6) * (1/6)⁶ * (5/6)¹

where (7 choose 6) is the number of ways to choose 6 days out of 7 to play the song, and is calculated as:

(7 choose 6) = 7! / (6! * 1!) = 7

Plugging in the values, we get:

P(6 successes) = 7 * (1/6)⁶ * (5/6)¹

P(6 successes) ≈0.00012502

Therefore, the probability that the song will be played on exactly 6 days out of 7 is approximately 0.000125 or 0.0125%.

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Answer:

y = 5x.

Step-by-step explanation:

Every y value is the corresponding x value times 5. (For example, 3 x 5 = 15, 5 x 5 =25)

Hope this helps!

Answer:

75.4 inches

Step-by-step explanation:

circumference = 2πr = 24π ≅ 75.4 inches

It's really more of a tubcake than a cupcake.

Step-by-step explanation:

The radius of the orbit is r = 1150 km + 6400 km = 7550 km or

\(r = 7.55×10^6\:\text{m}\)

and it takes 140 minutes to complete 1 revolution. This is the same aa

\(140\:\text{min}×\dfrac{60\:\text{s}}{1\:\text{min}} = 8400\:\text{s}\)

The linear speed of the satellite then is simply equal to the orbital circumference divided by the orbital period T or

\(v = \dfrac{2\pi r}{T}\)

\(\:\;\:\:=\dfrac{2\pi(7.55×10^6\:\text{m})}{8.4×10^3\:\text{s}}\)

\(\:\:\:\:=5647.4\:\text{m/s}\)

In km/min, this is

\(v = \dfrac{2\pi(7550\:\text{km})}{140\:\text{min}} = 338.8\:\text{km/min}\)

The value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

It is given that the expression is,

x + 20 ≤ -10

Rearrange the expression as

x≤ -10-20

x≤ -30

Thus, the value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

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Answer:

x=-1/2

Step-by-step explanation:

2x+2=4x+3

-1=2x

x=-1/2

Answer:

9 pounds

Step-by-step explanation:

I converted it

The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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Answer:  \(\displaystyle \frac{1}{9(1-3x)^{3}}+C\)

Where C is a constant.

========================================================

Explanation:

Apply u-substitution

\(u = 1 - 3x\\\\\frac{du}{dx} = -3\\\\du = -3dx\\\\dx = -\frac{du}{3}\\\\\)

So,

\(\displaystyle \int \frac{dx}{(1-3x)^4} = \int \frac{dx}{(1-3x)^4}\\\\\\\displaystyle \int \frac{dx}{(1-3x)^4} = \int (1-3x)^{-4} \ dx\\\\\\\displaystyle \int \frac{dx}{(1-3x)^4} = \int (u)^{-4} \ \left(-\frac{du}{3}\right)\\\\\\\displaystyle \int \frac{dx}{(1-3x)^4} = -\frac{1}{3}\int (u)^{-4} \ du\\\\\\\)

which further leads to

\(\displaystyle \int \frac{dx}{(1-3x)^4} = -\frac{1}{3}\left[\frac{1}{1+(-4)}u^{-4+1}+C\right]\\\\\\\displaystyle \int \frac{dx}{(1-3x)^4} = -\frac{1}{3}\left[-\frac{1}{3}u^{-3}+C\right]\\\\\\\displaystyle \int \frac{dx}{(1-3x)^4} = -\frac{1}{3}\left[-\frac{1}{3}(1-3x)^{-3}+C\right]\\\\\\\displaystyle \int \frac{dx}{(1-3x)^4} = \frac{1}{9(1-3x)^{3}}+C\\\\\\\)

Don't forget about the +C at the end.

Answer:

21 students ride the bus

Answer:

A

Step-by-step explanation:

To support her discussion, it would be best for Alex to use Graph A for her presentation. Alex should use this graph for her presentation because the number of faulty products appears to decrease less on this graph.

In Mathematics and Geometry, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In order to determine an equation with a declining line, we would have to determine the slope of each line graphically and then taking note of the line with a negative rate of change (slope) because it indicates a decreasing function.

In this context, we can reasonably infer and logically deduce that Graph A is more suited for Alex's presentation because the number of faulty products appears to decrease less on it.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer: it would help if you added an image

Step-by-step explanation:

Answer:

Where is the cylinder?

Step-by-step explanation:

Answer:

0.0045248 ;

0.1312218 ;

0.0001809 ;

0.1659729

Step-by-step explanation:

Number of Kings in deck = 4

Total number of cards in deck = 52

Picking without replacement :

A = King on first draw :

P(A) = 4 / 52

A = King on 2nd draw :

P(B) = 3 / 51

A = King on 3rd draw :

P(C) = 2 / 50

1.) P(A n B) = P(A) * P(B)

P(A n B) = 4/52 * 3/51 = 12 / 2652 = 0.0045248

2.) P(A u B) = P(A) + P(B) - P(AnB)

P(AuB) = 4/52 + 3/51 - 0.0045248 = 0.1312218

3.) P(A ∩ B ∩ C) = P(A) * P(B) * P(C)

P(A ∩ B ∩ C) = 4/52 * 3/51 * 2/50 = 0.0001809

4.) P(A U B U C) =

P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) - P(AnBnC)

P(AnC) = P(A) * P(C) = 4/52 * 2/50 = 0.0030769

P(BnC) = P(B) * P(C) = 3/51 * 2/50 = 0.0023529

4/52 + 3/51 + 2/50 - 0.0045248 - 0.0030769 - 0.0023529 + 0.0001809 = 0.1659729

When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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