Find the angle A if angle B is 60 degrees and angle A and angle B are complementary

Call the number : a

We have : \(a^{2} - 15 = 2a\)
\(- > a^{2} - 2a = 15 - > a(a-2) = 15\)

Now, we list all the numbers that can be multiplied to get 15 :

1 x 15 (and reverse)
3 x 5 (and reverse)

-1 x (-15) (reverse)
-3 x (-5) (a l s o r e v e r s e)

We substitute in :

If a = 1 -> a(a-2) = 1 x (-1) = -1 (not equal 15)
If a = 3 -> a(a-2) = 3 x 1 = 3 (not equal 15)
If a = -1 -> a(a-2) = -1 x (-3) = -3 (also not equal 15)
And if a = -3 -> a(a-2) = -3 x (-5) = 15 (satisfied)

So, the number is -3

Recheck : -3(squared) - 15 = 9 - 15 = -6
Twice of -3 = -6

\(========================================\)

First of all, let the unknown number be z.

Then, "the square of z" means "z squared" which is the same as "z times z" or just z².

Now, "fifteen less than the square of z" means we subtract 15 from z²:

z²-15

Then, this equals twice the number, or 2 times z:

z²-15=2z

\(========================================\)

:-)

Answer:487.5

Step-by-step explanation:

if it is a 35% discount it means you are trying to find 65% of the number because 65+35=100%

to find 65%, you find 5% first, then multiply by 13 to get 65%.

to find 5%, you divide by 20.

750/20=37.5.

37.5*13=487.5

Answer:

333

Step-by-step explanation:

1/3x5= 1.66

Answer:

333

Step-by-step explanation:

i need points lol

Answer:

32

Step-by-step explanation:

Answer: The function of graph 2 has a higher rate of change than the function of graph 2

Step-by-step explanation:

Answer:

(x-y)^2

p^2+p^2

Step-by-step explanation:

^2 means square

Answer:

see explanation

Step-by-step explanation:

x² - y² ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - y²

= (x - y)(x + y)

------------------------------

(p + p)²

= (2p)²

= 2p × 2p

= 4p²

Downsizing refers to the process of reducing the size and workforce of a company to cut costs, increase efficiency, or adapt to changing market conditions. It involves eliminating positions, reducing staff numbers, or even closing down certain business units or branches.

Downsizing can occur for various reasons, such as financial difficulties, mergers and acquisitions, technological advancements, or strategic reorganization. Companies often assess their operational costs and decide to downsize to improve their financial performance.

During the downsizing process, companies may calculate the potential cost savings by considering factors such as salaries, benefits, severance packages, and operational expenses. For example, if a company decides to eliminate 100 positions with an average salary of $50,000 per year, it could result in annual savings of $5 million.

While downsizing can help companies achieve short-term cost reductions, it often has significant implications for the affected employees, including layoffs, reduced morale, and increased workload for remaining staff. It is crucial for organizations to handle the downsizing process with sensitivity and transparency, providing support to affected employees and communicating the rationale behind the decisions.

It is important to note that downsizing should not be seen as a long-term solution, but rather as a strategic measure to address specific challenges. Companies should also explore alternatives to downsizing, such as retraining and redeploying employees, implementing productivity improvements, or seeking new business opportunities, to ensure sustainable growth and success in the long run.

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Answer:

your answer would be 186

Step-by-step explanation:

310 / 5 = 62

62 x 3 = 186

Distance between two cars travelling in opposite directions with the equation 6x - 8 = 4x where x is the distance in miles is equal to 4 miles.

As given in the question,

Two cars travelling in opposite directions

x represents the distance in miles

Equation :

6x - 8 = 4x

⇒ 6x - 4x = 8

⇒ 2x = 8

⇒ x  = 4miles

Therefore, the distance between two cars travelling in opposite directions with the equation 6x - 8 = 4x where x is the distance in miles is equal to

4miles.

The complete question is:

The equation 6x - 8 = 4x represents two cars traveling in opposite directions, where x represents the distance in miles between the cars. what is the distance, in miles, between the cars?

A.  x = 0.8miles    B. x = 4miles      C. x = 8miles      D. x = 16miles

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Answer: C

Step-by-step explanation:

4/8 ×3/1

The exponential function that models the population growth over the 30-year period is \(P(t) = 227 * e^{(0.025t)}.\)

A number that increases or decreases over time at a constant percentage rate is described by an exponential function, which is a sort of mathematical function. Population expansion, compound interest, radioactive decay, and other natural processes that display exponential behaviour are frequently modelled using exponential functions. The base of the natural logarithm of exponential functions is frequently the mathematical constant e, which is roughly equal to 2.71828.

The population growth that corresponds to the exponential growth is given as:

\(P(t) = P_0 x e^{(rt)}\)

Now, for \(P_0 = 227\) (thousands), t = 30 we have:

\(309 = 227 * e^{(r x 30)}\\e^{(r x 30)} = 309/227\\r x 30 = ln(309/227)\\r = ln(309/227)/30\)

r ≈ 0.025

Substituting the value of r we have:

\(P(t) = 227 * e^{(0.025t)}\)

Hence, the exponential function that models the population growth over the 30-year period is \(P(t) = 227 x e^{(0.025t)}.\)

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The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.

Therefore, the p-value for study b exists 0.080.

The P value is the likelihood, for a particular statistical model, that the statistical summary would be either equal to or more extreme than the actual observed results if the null hypothesis were to hold.

In a two tailed test the probability of occurrence exists the total area beneath the critical range of values on both the sides of the curve (negative side and positive side)

Therefore, the probability values for a two tailed test as compared to a one tailed test exists given by the under given relation -

\($p-\text { value }=P\left(Z < -\frac{\alpha}{2}\right)+P\left(Z > \frac{\alpha}{2}\right)$$\)

simplifying the above equation, we get

\($P \frac{\alpha}{2}=0.040$\)

Substituting the given value in above equation, we get -

Probability values for a two tailed test

= 0.040 + 0.040

= 0.080

Therefore, the p-value for study b exists 0.080.

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Answer:

The walkway is approximately 34.64 feet long

Step-by-step explanation:

The length of the sides of the equilateral triangle shaped the city garden = 40 feet

The path of the walkway = From the midpoint of a side to the opposite vertex

Therefore, we have;

Let x, represent the length of the walkway

We have that the x, a side of the equilateral triangle, and half the side of the location of the gate, forms a right triangle, with a side of the equilateral triangle representing the hypotenuse side

Therefore, we have;

40² = x² + (40/2)²

40² = x² + 20²

x² = 40² - 20² = 1200

x = √1200 = 20·√3

The length of the walkway = x = 20·√3 ≈ 34.64 feet.

Answer:

\(\sqrt{246}\)

Step-by-step explanation:

The scale factor is \(\frac{4\sqrt{138} }{\sqrt{138}}\) = 4

If AB = 6\(\sqrt{3}\) then AC = 24\(\sqrt{3}\)   4 times longer.

Using a² + b² = c²    substitute a = 4\(\sqrt{138}\), b = 24\(\sqrt{3}\), and c = DC = x

         \((4\sqrt{138})^2 + (24\sqrt{3} )^2= x^2\)

            2208 + 1728 = x²

                3936 = x²

                 \(\sqrt{3936} = x\)

                 4\(\sqrt{246\)    this is the length of DC  

Now the length of EC is 4 times shorter, so EC = \(\sqrt{246}\)

Answer:

The 37th term of arithmetic sequence is 182.

Step-by-step explanation:

Here's the required formula to find the arithmetic sequence :

\(\longrightarrow\pmb{\sf{a_n = a_1 + (n - 1)d}}\)

Substituting all the given values in the formula to find the 37th term of arithmetic sequence :

\(\implies{\sf{a_n = a_1 + \Big(n - 1\Big)d}}\)

\(\implies{\sf{a_{37} = 2 + \Big(37 - 1\Big)5}}\)

\(\implies{\sf{a_{37} = 2 + \Big( \: 36 \: \Big)5}}\)

\(\implies{\sf{a_{37} = 2 + 36 \times 5}}\)

\(\implies{\sf{a_{37} = 2 + 180}}\)

\(\implies{\sf{a_{37} = 182}}\)

\({\star{\underline{\boxed{\sf{\red{a_{37} = 182}}}}}}\)

Hence, the 37th term of arithmetic sequence is 182.

\(\rule{300}{2.5}\)

The correct answer is: III only. Variance investigation is typically based on a cost-benefit analysis.

Statement I is incorrect because the relative size of a variance, in comparison to other variances, can be important in understanding its significance.

Statement II is incorrect because variance investigation does not focus solely on unfavorable variances. Both favorable and unfavorable variances are considered during the investigation.

Statement III is true. Variance investigation is typically based on a cost-benefit analysis, where the potential benefits of investigating and addressing variances are weighed against the associated costs.

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Answer........

Step-by-step explanation:

Answer:

21.6 minutes

Step-by-step explanation:

0.6 * 0.6 * 1

0.36 * 1

0.36 hours

0.36 * 60

21.6 minutes

The probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.

The probability that the digit 7 doesn't appear among 100 digits where each digit is one of (0-9) and all sequences are equally likely is given by the probability that all 100 digits are chosen from the set {0, 1, 2, 3, 4, 5, 6, 8, 9}. There are 10 choices for each digit, so there are 10^100 possible sequences of 100 digits. The number of sequences that don't contain the digit 7 is 9^100. Therefore, the probability that the digit 7 doesn't appear among 100 digits is: P(7 doesn't appear) = (9^100) / (10^100) = 9 / 10

Therefore, the probability that the digit 7 doesn't appear among 100 digits is 9/10, or 90%.

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Answer:

2 kg

Step-by-step explanation:

15/100 x = 0.3

x = 0.3 * 100/15

x = 2

(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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Answer:

(0,2)

Step-by-step explanation:

Multiply the x and y by 1/2

0*1/2=0

4*1/2=2

The image of (0,4) after a dilation is (0,2).

It is required to find the image .

Scale factor is the ratio of corresponding sides on two similar figures.

A scale factor is a number which multiplies (“scales”) a quantity. For example, the “C” in y =  C x is the scale factor for x.

Given:

scale factor =1/2 centered

Point=(0,4)

According to given question we have,

(x,y) -> (1/2x , 1/2y)

(0,6) -> (1/2 • 0, 1/2 • 4)

=(0,2)

Therefore, the image of (0,4) after a dilation is (0,2).

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The value of x in the triangle using the cosine rule is 22.1 degrees.

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

Cosine rule is used to show the relationship between the sides and angles of a triangle. It is given by:

c² = a² + b² - 2ab cos C

Where a, b, c are the sides and C is the angle opposite side c.

Using cosine rule:

8² = 14² + 19² - 2(14)(19) * cos(x)

cos(x) = 0.9267

x = 22.1°

The value of x in the triangle using the cosine rule is 22.1 degrees.

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Using the law of Cosines, the value of x to the nearest tenth is 77.8

From the question, we are to determine the value of x

Using the law of Cosines

c² = a² + b² - 2ab cos C

c is the unknown side length  

a and b are the given side lengths

and C is the included angle

From the given information,

a = 63

b = 62

C = 142°

Then,

x² = 63² + 61² -2×63×61 cos 142°

x² = 3969 + 3721 -7686(-0.788)

x² = 7690 + 6056.568

x² = 13746.569

x = √13746.569

x = 77.8

Hence, the value of x to the nearest tenth is 77.8

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Answer:

Refer to the step-by-step

Step-by-step explanation:

∠1 and ∠2 lie in the alternate interior of the parallel lines and are on opposite sides of the transversal. So, ∠1 and ∠2 are equal angles.

Answer:

262 good luck

Step-by-step explanation:

hope it's not wr6

Answer:

Brenda’s mom need to buy 16.5 litres.

Explanation:

The process of transferring the value of one form to another, such as inches to millimeters or liters to gallons, is known as conversion. In order to measure length, weight, capacity, temperature, and speed, units are used.

Step-by-step:

According, to the question, We divide by 1000 to convert from "milli-" to a conventional unit like meters or litres. One millilitre is one thousandth of a liter, while one liter is one thousand milliliters.

\(750 ml*32=16500 ml\\16500/1000=16.5 l\)

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Number of cards made from the sheet of paper is 243.

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

On the entire sheet of paper, 243 cards were created.

The sheet is described as being 324 cm 144 cm in size.

Measures 324 centimeters in length.

The sheet has a 144-cm width.

We need to determine how many cards with a 16 cm by 12 cm size can be produced from a single sheet of paper.

The paper's size is 324 144.

46656 sq. cm is the size of the paper's surface.

Now, one card is equal to 16 divided by 12.

Currently, the area of a single card is 192 square centimetres.

Hence, Number of cards made from the sheet of paper is 243.

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(a) To graph the constraints, we can rewrite them in slope-intercept form:

1) xx + 2yy ≤ 12

  2yy ≤ -xx + 12

  yy ≤ (-1/2)xx + 6

2) 3xx + 2yy ≤ 24

  2yy ≤ -3xx + 24

  yy ≤ (-3/2)xx + 12

The feasible region is the area that satisfies both inequalities. To graph it, we can plot the lines (-1/2)xx + 6 and (-3/2)xx + 12 and shade the region below both lines.

(b) To draw a line representing all combinations of x and y that make the objective function equal to a specific value, we can choose a value for the objective function and rearrange the equation to solve for y in terms of x. Then we can plot the line using the resulting equation.

(c) To find the optimal solution, we need to find the point(s) within the feasible region that maximize the objective function. If the optimal solution is at the intersection point of two constraints, we can solve the corresponding system of equations to find the coordinates of the intersection point.

(d) After finding the optimal solution(s), we can label them on the graph by plotting the point(s) where the objective function is maximized.

(e) To calculate the optimal value of the objective function, we substitute the coordinates of the optimal solution(s) into the objective function and evaluate it to obtain the maximum value.

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