How do I write 58 2/3 as a decimal

Answer:

-2

Step-by-step explanation:

You have to simplify numerator and denominator through factoring. The you should get an expression involving only a + b which is given as -2

Take numerator
\(a^2-b^2-12b-36\)

Factor
\(-b^2-12b-36\)

\(= - (b^2 + 12b + 36)\\\\= -(b+6)^2\)

So numerator becomes
\(a^2-\left(b+6\right)^2\)

Apply difference of squares formula: \(\displaystyle x^2-y^2=\left(x+y\right)\left(x-y\right)\)

\(\mathrm{with\;} x^2 == > a^2, and y^2 == > (b + 6)^2\)

\(\implies a^2-\left(b+6\right)^2 \\== \left(a+\left(b+6\right)\right)\left(a-b-6\right)\)

Denominator
\(a^2-6a-b^2-6b\)

can be factored as follows

\(a^2-b^2 = (a + b) (a -b)\)
\(-6a-6b = -6\left(a+b\right)\)

So denominator becomes
\(\left(a+b\right)\left(a-b\right)+-6\left(a+b\right)\)

Factor out common term (a+b) to get
\(\left(a+b\right)\left(a-b-6\right)\)

So the original expression with Numerator and denominator

\(\displaystyle =\frac{\left(a+b+6\right)\left(a-b-6\right)}{\left(a+b\right)\left(a-b-6\right)}\)
Cancel the common factor (a-b-6) to get
\(\displaystyle \frac{a+b+6}{a+b}\)

Since a + b = -2, plug in this value of (a+b) in both numerator and denominator to get
\(\displaystyle \dfrac{-2 + 6}{-2}\)
\(\displaystyle = - 2\)

Answer: -2

Answer:-1

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

To find the slope, we have to choose to points

Substitute into the formula

The final answer is

Slope = 5

5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².

Firstly, we will calculate the area of the square of paper in which the holes are punched.

Side of square = 12 cm

Area of square = side²

= (12) ²

= 144 cm²

Now, we will calculate the area of the bigger punch holes

Radius of big punch hole = 3 cm

Area of 1 big punch = π (radius) ²

= 22/7 × (3)²

22 / 7 × 9

= 198 / 7 cm²

Area of 4 punches = 4 × 198/7

= 792/7 cm²

Now, we will calculate the area of smaller punch whose radius is 1cm

Area = 22/7 × 1²

= 22/7 cm²

Now, we will calculate the total area covered by circles

Total area covered by circles = area of small punch + area of 4 big punch

= 22/7 + 792/7

= 814 /7 cm²

Remaining area = area of square - area of circles

= 144 - 814/7

= (1008 - 814) / 7

= 194 / 7

= 27.714 cm²

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Answer:

x=2 and 2.6

Step-by-step explanation:

The required solutions for the given function |3 + 10x| = 23 are x = 2 and x = -2.6.

Absolute value is defined as the magnitude or size of a number, no negatives are allowed. The distance a number is from 0 on the number line is known as the absolute value of the number.  

The function is given in the question as:

|3 + 10x| = 23

To solve for x, we can begin by expressing the absolute value as a piecewise function:

|3 + 10x| = 23

(3 + 10x) = 23, if 3 + 10x ≥ 0

-(3 + 10x) = 23, if 3 + 10x < 0

If 3 + 10x ≥ 0, then 3 + 10x = 23, so x = (23 - 3) / 10 = 2.

If 3 + 10x < 0, then -(3 + 10x) = 23, so 3 + 10x = -23. This means that x = (-23 - 3) / 10 = -2.6.

Thus, the solutions for x are x = 2 and x = -2.6.

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yGiven a linear equation in two variables: y = -4x - 3.

We have to find five ordered pairs which satisfy the given linear equation.

When x = -2.

Thus, the first ordered pair is (-2,5)

At x = -1.

Thus, the second ordered pair is (-1,1).

At x = 0.

Thus, the third ordered pair is (0,-3).

At x = 1.

Thus, the fourth ordered pair is (1,-7).

At x = 2.

Thus, the fifth ordered pair is (2,-11).

Answer:

Hi mate

Step-by-step explanation:

Please broswer se search karo

Answer:

81 km²

Step-by-step explanation:

so the perimeter of the field is 288 : 8 = 36 km

the perimeter of square is 4 time side

4s = 36

s = 36 : 4 = 9 km

Area = side x side = s²

A = 9² = 81 km²

Let the figure number be x.

Then the equation will be:

3x

There will be 3x circles in the figure number x.

So, number of circles in 50th figure will be

= 3(50)

= 3 × 50

= 150 circles

The number of circles in the 50th figure is 150 circles.

A sequence in mathematics is a ordered set of objects or numbers which are related with something.

For example, 1, 3, 5, ..... is a sequence of odd numbers.

Here a pattern is shown in the form of the circles.

In the Figure 1, there are 3 circles.

In the figure 2, there are 6 circles.

In the figure 3, there are 9 circles.

It is clear that the pattern is in such a way that 3 circles are increasing to each succeeding figure.

So for the nth figure,

Number of circles will be 3n.

So for 50th figure, number of circles = 3 × 50 = 150 circles

Hence the number of circles in the 50th figure is 150.

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Answer:

3 bird HAHAHAH sana makatulong

Answer:

From point A to point B is x= -7 y= -4

From point B to point C is x= 6 y=-5

Step-by-step explanation:

I think it's kinda hard to see

Answer:

B  

y = 0.508 sine (0.212 x minus 1.529) + 0.512

Step-by-step explanation:

just took the test

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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Speed per hour = distance / time

Speed = 73 1/3 / 3/2

Speed = 220/3 / 3/2

Speed = 220/3 x 2/3

Speed = 440 /9

Speed = 48 8/9 miles per hour.

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Answer:2x34=344343

Step-by-step explanation:32323=23=232

The slope of a line perpendicular to the line whose equation is x - 2y = -8 is -2.

In Mathematics and Geometry, perpendicular lines are two (2) lines that intersect or meet each other at an angle of 90° (right angles).

From the information provided above, the slope for the equation of line m is given  by:

x - 2y = -8

2y = x + 8

y = x/2 + 4

slope (m) of line m = 1/2

In Mathematics and Geometry, a condition that is true for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

Slope, m₂ of perpendicular line = -2

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Answer:

cos(38°) = sin(52°)

sin(64°) = cos(26°)

cos(52°) = sin(38°)

sin(17°) = cos(73°)

Step-by-step explanation:

Answer:

1. cos 38 = sin 52

2. sin 64 = cos 26

3. cos 52 = sin 38

4. sin 17 = cos 73

Step-by-step explanation:

Use this website to help:

https://www.mathcelebrity.com/anglebasic.php?entry=17&pl=sin

I hope this helps you! :D

Plz mark me as brainliest!

Answer:

Z-score for 34-week baby = 0.643

Z-score for 41-week baby = 1.154

Baby weight of 41-week is more than the baby weight of 34-week in the gestation period.

Step-by-step explanation:

Given - Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2500 grams and a standard deviation of 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 3100 grams and a standard deviation of 390 grams. If a 34-week gestation period baby weighs 2950 grams and a 41-week gestation period baby weighs 3550 grams

To find - Find the corresponding z-scores. Which baby weighs more relative to the gestation period.

Proof -

Given that,

In between period of 32 to 35 weeks

Mean = 2500

Standard deviation = 700

In between after a period of 40 weeks

Mean = 3100

Standard deviation = 390

Now,

For a 34-week baby,

X = 2950

For a 41-week baby,

X = 3550

Now,

Z-score = (X - mean) / Standard deviation

Now,

For a 34-week baby,

Z - score = (2950 - 2500) / 700 = 0.643

For a 41-week baby,

Z-score = (3550 - 3100) / 390 = 1.154

∴ we get

Z-score for 34-week baby = 0.643

Z-score for 41-week baby = 1.154

As 1.154 > 0.643

So,

Baby weight of 41-week is more than baby weight of 34-week in the gestation period.

This type of data can be analyzed using a two-way analysis of variance (ANOVA) to determine the effect of both the day of the week (weekday or weekend) and the shift (morning or evening) on chair production. The manager can use this information to make predictions about future production based on the day of the week and shift.

The manager can start by creating a table to show the average number of chairs produced on each day of the week and shift. Then, a two-way ANOVA can be performed to determine if there is a significant difference in the mean number of chairs produced between weekdays and weekends, and between morning and evening shifts.

If the results of the ANOVA show that there is a significant effect of the day of the week and/or the shift on chair production, the manager can use this information to make more accurate predictions about future chair production. For example, if the results show that chair production is higher on weekdays compared to weekends, the manager can make predictions based on this information and allocate resources accordingly.

It is important to note that other factors such as the availability of materials, number of workers, and machine downtime can also impact chair production and should be considered when making predictions.

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A formula that gives the amount is

The half life of the element is calculated from the formula

N(t) = N'(1/2)^(t/t')

where

N(t) = quantity of the substance remaining

N' = initial quantity of the substance

t = time elapsed

t' = half life of the substance

Plugging the values from the problem

N(t) = ?

N' = 70 grams

t = t

t' = 2.6 years

N(t) = 70 (0.5)^t/2.6

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Answer:

Joey needs 9 boxes.

Step-by-step explanation:

You will use the fact that a dozen is 12 cookies. You're trying to find how many dozen are in 100.

Something like:

12b = 100

or if you're studying inequalities:

12b >= 100

Divide by 12 to solve. See image. Interpret the results. See image.

Answer:

<RST

Step-by-step explanation:

Make sure the vertex is in the middle

Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

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Answer:

Step-by-step explanation:

Given formula:

Need to find the value of t when G(t) = 150000

To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)

To simplify this expression, we can expand the square:

\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)

Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.

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The rate of return for the entire portfolio, given the amount allocated to each of the four securities is

The rate of return would be the expected return of the proportion of the amounts invested into the various investment vehicles and their rates of return.

The rate of return for the portfolio is therefore :

= ∑ ( proportion invested x rate of return )

= ( 25 % x 12 % ) + ( 10 % x 7 % ) + ( 35 % x 22 % ) + ( 30 % x  - 12 % )

= 7. 8 %

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Answer:

A

Step-by-step explanation:

Because the cost per pie is less.