Aaaaa pls help ASAP on the second unanswered one
30 points!!

Step-by-step explanation:

a²+b²=c²

4²+b²=7²

b²=7²-4²

b²=49-16=33

Answer is

\( \sqrt{33} \)

Answer: ∠1 = 90°

Step-by-step explanation:

      There are a few steps we will take to solve this problem. In each step, I will write an equation to help us solve, then use inverse operations to solve.

      First, we will use the exterior angles theorem to find the measurement of ∠3 (this will help us solve for ∠2, then for ∠1).

89° = 51° + ∠3

∠3 = 38°

      Next, we will find the measurement of ∠2 since we know ∠2 plus ∠3 is 90 degrees, as shown by the perpendicular lines and the box.

90° = ∠3 + ∠2

90° = 38° + ∠2

∠2 = 52°

      Lastly, we will solve for ∠1. We know that there are 180 degrees in a triangle.

180° = 38° + ∠1 + ∠2

180° = 38° + ∠1 + 52°

180° = 90° + ∠1

∠1 = 90°

Answer:

90

Step-by-step explanation:

I started by finding angle 5

180 - 89 = 91  Supplemental angles

Then I found angle 3

The sum of the interior angles of a triangle is 180

180-89-91 = 38

Angle2 and 3 are complementary angles

90- 38 =52

the sum of the interior angles of a triangle is 180

Angle 1

180 - 52 - 38 = 90

Answer:

I will need a photo to answer this

Step-by-step explanation:

Kindly, please upload a photo, TQ!

The inequality x ≥ 10 represents the relationship where the blue team needs to advance the ball at least 10 yards to score any points.

The inequality that represents the relationship for the blue team needing to advance the ball at least 10 yards to score any points can be expressed as:x ≥ 10

In this inequality, x represents the number of yards the blue team needs to advance the ball. The "≥" symbol indicates "greater than or equal to," meaning that the blue team must advance the ball by at least 10 yards to score any points.

If the blue team advances the ball exactly 10 yards, the inequality is satisfied because it meets the minimum requirement. If the blue team advances the ball by more than 10 yards, the inequality is still satisfied.

However, if the blue team advances the ball by less than 10 yards, the inequality is not satisfied, and they will not score any points.

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Answer:

The first option.

Explanation:

Since these numbers are given in scientific notation, we must first look at the exponent to determine whether or not it's big or small. Negative exponents are less, so we start with that. Immediately, that eliminates the second and third options as -8 is less than -6 and 3. The last two numbers given in the first and last options, however, both have 3 as the exponent. Now, we look at the number given in front. 2.5 is less than 7, so we know that the first option is in order from least to greatest.

Answer:

7/2 pi

or approximately 10.99557429

Step-by-step explanation:

2 pi sqrt( a/b)

let a = 49 and b = 16

2 pi sqrt( 49/16)

We know that sqrt( a/b) = sqrt(a) /sqrt(b)

2 pi sqrt(49) / sqrt(16)

2pi ( 7) / (16)

2 pi ( 7/4)

7/2 pi

This is the exact answer

We can make an approximation for pi

Using the pi button on the calculator

10.99557429

The binomial distribution formula, we need to know the probability of a small business being owned by a woman and the total number of small businesses.

The questions using the binomial distribution formula, we need to know the probability of a small business being owned by a woman and the total number of small businesses.

Without this information, it is not possible to provide accurate calculations. The binomial distribution formula is used when we have a fixed number of independent trials (small businesses in this case) and each trial has two possible outcomes (owned by a woman or not).

We would need the probability of success (p) and the number of trials (n) to calculate the probabilities. Once we have these values, we can use the formula to find the desired probabilities, such as the expected number of small businesses owned by women, the standard deviation, and the probabilities for specific scenarios.

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

k is the smallest number such that 2(to the k)>n

Step-by-step explanation:

Frequency distribution is defined as the number of times the value occurs. It contains the class interval as well as the corresponding frequencies. A pivot table is used to represent the frequency distribution.

The "2 to the k" rule states that 2 to the power k should be less than equal n, where n is the number of the given data points. It should be the smallest number.

Thus the answer is : k is the smallest number such that 2(to the k)>n.

The values of \(x\) are \(1+\sqrt{89}\) and \(1-\sqrt{89}\).

To find the values of x:

Given equation: \((x+7)(x-9)=25\)

Then: \(x(x-9)+7(x-9)=25\)

Using the distributive property: \(a.(b+c)=a.b+a.c\)

\(x^{2} -9x+7x-63=25\)

Combine like terms:

\(x^{2} -2x-63=25\)

Subtract 25 from both sides and obtain:

\(x^{2} -2x-88=0\)

Using completing square form:

Add and subtract \((\frac{2}{2} )^{2} =1\) we have:

\(x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0\)

Add 89 to both sides we have:

\((x-1)^{2} =89\)

Taking square roots on both sides, obtain:

\(x-1=\) ± \(\sqrt{89}\)

Add 1 to both sides we have:

\(x=1\)±\(\sqrt{89}\)

Therefore, the values of \(x\) are \(1+\sqrt{89}\) and \(1-\sqrt{89}\).

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The complete question is given below:

Use completing the square to solve (x + 7)(x – 9) = 25 for x.

Answer:

7 - 2m can be translated to "7 minus two times m" or "the difference between 7 and twice m".

3(m + 2) = 15 can be translated to "three times the sum of m and 2 is equal to 15" or "the product of 3 and the sum of m and 2 is 15".

To solve the equation, we can start by distributing the 3 on the left side:

3(m + 2) = 15

3m + 6 = 15

Then, we can subtract 6 from both sides:

3m + 6 - 6 = 15 - 6

3m = 9

Finally, we can divide both sides by 3:

3m/3 = 9/3

m = 3

Therefore, the solution to the equation 3(m + 2) = 15 is m = 3.

5m - m(2 - m) can be translated to "5m minus the product of m and the difference between 2 and m" or "the difference between 5m and m times the quantity 2 minus m".

To simplify the expression, we can use the distributive property to expand the second term:

5m - m(2 - m) = 5m - 2m + m^2 = m^2 + 3m

Therefore, the simplified expression is m^2 + 3m.

Answer:

(5.5, -5.5)

Step-by-step explanation:

Find the average of the x coordinates:

(1 + 10) / 2

11/2

= 5.5

Find the average of the y coordinates:

(-8 + -3) / 2

-11/2

= -5.5

These two averages will be the x and y coordinates of the midpoint:

So, the midpoint is (5.5, -5.5)

The solution is Option C.

The equation of line is given by y = -2x + 58

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 2 , 54 )

Let the second point be Q ( 5 , 48 )

The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 54 - 48 ) / ( 2 - 5 )

On simplifying the equation , we get

Slope m = 6 / -3

Slope m = -2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 54 = -2 ( x - 2 )

On simplifying the equation , we get

y - 54 = 2x + 4

Adding 54 on both sides of the equation , we get

y = -2x + 58

Therefore , the graph is plotted through the points ( 0 , 58 ) , ( 1 , 56 )

Hence , the equation of line is y = -2x + 58

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The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

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Answer: 40cm

Step-by-step explanation:

3.07 x 4 = 12.28

6.93 x 4 = 27. 72

12.28 + 27.72 = 40cm

Answer:

40 cm

Step-by-step explanation:

A square-based pyramid is a three-dimensional geometric shape with a square base and four congruent triangular faces that meet at a single point called the "apex".

The edges of a square-based pyramid consist of 4 congruent slant edges and 4 congruent base edges. The slant edges form the sides of the triangular faces, and the base edges connect the vertices of the base.

Given the edges of the square base are 3.07 cm, and the slant edges are 6.93 cm, the total length of the wire is:

\(\begin{aligned}\sf Total\;length\;of\;wire&=\sf 3.07 \times 4+6.93 \times 4\\&=\sf 12.28+27.72\\&=\sf 40\; cm\end{aligned}\)

Therefore, the total length of the wire is 40 cm.

(a) Using combination, the number of ways to choose 10 players to take the field is 286. (b) Using permutation, the number of ways to assign the 10 positions is 1037836800.

The softball team has 13 people for a game.

a) Since the sequence doesn't matter, there are a total of 13 ways to select 10 players, which results in the following combination:

₁₃C₁₀ = 13! / ( 13 - 10 )! 10!

₁₃C₁₀ = ( 13 × 12 × 11 ) / ( 3 × 2 )

₁₃C₁₀ = 13 × 2 × 11

₁₃C₁₀ = 286

b) The permutation of 13 players for 10 slots yields a total of possible positions that can be assigned by choosing 10 players:

₁₃P₁₀ = 13! / ( 13! - 10! )

₁₃P₁₀ = 13! / 3!

₁₃P₁₀ = 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4

₁₃P₁₀  = 1037836800

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The triangle △ABD ≈ △BDC by using the SAS rule.

In triangle △ ABD and triangle △ BDC, we have that:

AB / BD = 25 cm / 30 cm

AB / BD = 5 / 6

BD / DC = 30 cm / 36 cm

BD / DC = 5 / 6

∠ABD = ∠ BDC ( as AB || DC and they form alternate interior angles)

So, AB / BD = BD / DC = 5 /6

So, we get that:

△ABD ≈ △BDC ( Similar by SAS rule )

Therefore, we get that, the triangle △ABD ≈ △BDC by using the SAS rule.

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Answer: x = -3

Step-by-step explanation:

i simply divided by -7, in order to get x by itself.

-7/-7x = 21/-7

that cancels out the -7 on the left side, and leaves us with -3 on the right side!

x = -3

Answer:

X=-3

Step-by-step explanation:

-7(-3)=21

the negatives when multipled become positive

21=21

so x=-3

Answer:

62.5 as a decimal would be 0.625

As a fraction it would be 625/1000.

Step-by-step explanation:

To write 0.625 as a fraction you have to write 0.625 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

0.625 = 0.625/1 = 6.25/10 = 62.5/100 = 625/1000  

And finally we have:

0.625 as a fraction equals 625/1000

Answer:

decimal

⇒\(\frac{62.5}{100}\)

⇒62.5÷100

⇒62.5

fraction

⇒\(\frac{62.5}{100}\)

Step-by-step explanation:

Step-by-step explanation:

worked is pictured and shown

Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9% compounded annually. Therefore,  the amount available for Peter's child education will be $147,330.55.

Given that Michael is saving $7,000 per year for his child's education which will occur in 13 years. If the interest rate is 9% compounded annually,

The problem of finding the amount of money Michael will have saved in 13 years is a compound interest problem.

In this case, the formula for calculating the future value of the annuity is: $FV = A[(1 + r)n - 1] / r

where: FV is the future value of the annuity, A is the annual payment,r is the annual interest rate, and n is the number of payments.

Using the above formula; the future value of Michael's savings is:

FV = 7000[(1 + 0.09)^13 - 1] / 0.09= 7000(1.09^13 - 1) / 0.09= 147,330.55

Therefore, the amount available for Peter's child education will be $147,330.55.

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The given autonomous first-order differential equation is dy/dx = (y - 1)^4. To analyze the critical points and phase portrait, we can rewrite the equation as (1/(y - 1)^4) dy = dx. By integrating both sides and solving for y, we find that the critical points occur at y = 1 and y = ∞. The phase portrait shows that the function approaches y = 1 as x approaches -∞ and diverges to ∞ as x approaches +∞.

To analyze the given differential equation, we start by rearranging it as (1/(y - 1)^4) dy = dx. Integrating both sides of the equation, we get ∫(1/(y - 1)^4) dy = ∫dx. This integration yields (-1/(3(y - 1)^3)) = x + C, where C is the constant of integration. Solving for y, we obtain (y - 1)^3 = -3/(x + C).

The critical points occur when (y - 1)^3 = 0, which happens when y = 1. Thus, y = 1 is a critical point of the differential equation. Additionally, as x approaches -∞, (y - 1)^3 becomes negative, which implies that y approaches 1 as x approaches -∞. On the other hand, as x approaches +∞, (y - 1)^3 becomes positive, indicating that y diverges to ∞ as x approaches +∞.

The phase portrait of the differential equation reveals the behavior of solutions over a range of x and y values. In this case, the phase portrait indicates that the function approaches the critical point y = 1 as x approaches -∞. As x moves towards +∞, the function diverges to ∞. Hence, the phase portrait exhibits an asymptotic behavior, converging to y = 1 from one direction and diverging towards ∞ from the other direction.

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The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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a) The vertical rise per step is of 18.1 feet.

b) The number of steps needed to climb from road level to the 2nd floor is of: 3 steps.

The rise is obtained applying the slope concept, as follows:

Rise = Total elevation x Tangent of Angle.

The parameters are given as follows:

Then the rise per step is calculated as follows:

Rise = 24 x tangent of 37 degrees = 18.1 feet.

The total vertical elevation needed to reach the second floor is given as follows:

24 + 24 = 48 feet.

Then the total number of steps needed to climb to the 2nd floor is found applying the proportion, as follows:

48/18.1 = 2.65 steps.

Rounding up, 3 steps are needed.

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Answer:

From this in-depth examination we aimed to draw out some of the key ... closely their business case and employ model makers to create a 3D prototype.

Step-by-step explanation:

Answer:

middle term = 7x

Step-by-step explanation:

in order to find the middle term, we will expand the bracket on the left hand side and compare the expressions on both sides.

(x + 2) (3x + 1) = 3x² + ___ + 2

let the unknown expression = y

(x + 2) (3x + 1) = 3x² + y + 2

Expanding the bracket on the left hand side by multiplication:

x + 2( 3x + 1) = (x × 3x) + (x × 1) + (2 × 3x) + ( 2 × 1)

= 3x² + x + 6x + 2

= 3x² + 7x + 2

Comparing with the expression on the right hand side:

3x² + 7x + 2 =  3x² + y + 2

∴ y = 7x

middle term = 7x