The terminal side of an angle θ in standard position intersects the unit circle at (√30/7,-√19/7). What is cot(θ)?

The pairs of triangles can be proven similar through SSS similarity is given by Third pair.

We know that the SSS similarity criteria will have the ratio of three corresponding sides of both triangles congruent.

1. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

2. KL / EG = HL / DG = HK / DE

3/10 ≠ 6.5/13 ≠ 4/10

Thus, SSS similarity does not follow.

3. KL / EG = HL / DG = HK / DE

3/6 = 6.5/13 = 5/10

Thus, SSS similarity follow.

4. All three angles are congruent.

Thus, SSS similarity does not follow.

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Answer:

HCF = 12

Step-by-step explanation:

Expressing the numbers as products of their prime factors

84 = 2² × 3 × 7

120 = 2³ × 3 × 5

Identify the prime factors that both numbers have in common and multiply them.

Both have 2² and 3 in common, thus

HCF = 2² × 3 = 4 × 3 = 12

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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2 litres of water. A

Eric's drink 2 liters of water.

" Liter is a basic unit which is used to measure volume of any liquid."

According to question,

Capacity of one water bottle = 500mL

Capacity of 4 water bottles = \(500\) × \(4\)

                                              = 2000mL

1000mL = 1Liter

2000mL =2L

Hence we conclude that Option A is correct.

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Answer:

1 is 64

2 is 85

3 is 56 hope this helps  

Step-by-step explanation:

also how give brainly i want to give u brainly

Answer:

2.3 hours

Step-by-step explanation:

From 3:12 pm to 4:12 pm, one hour passes.

From 4:12 pm to 5:12 pm, another hour passes.

From 5:12 pm to 5:30 pm, there are 18 minutes that pass.

Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.

To convert this to a fraction, we can write:

2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours

So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.

Jasmine makes $2.08 more per hour cleaning a larger house compared to a smaller house.

Pricing strategies refer to the methods and techniques used by businesses or companies to set the prices of their products or services.

Let's first calculate the hourly rate Jasmine charges for cleaning a house with 2 bathrooms:

She charges $50 for a house with 3 bedrooms and 2 bathrooms, and it takes her 3 hours to clean it, so her hourly rate is:

⇒ $50 ÷ 3 hours = $16.67/hour

Now let's calculate the hourly rate she charges for cleaning a house with 3 or 4 bathrooms:

She charges $75 for a house with 3 to 4 bathrooms, and it takes her 4 hours to clean it, so her hourly rate is:

⇒ $75 ÷ 4 hours = $18.75/hour

Therefore, Jasmine makes $18.75/hour cleaning a larger house compared to $16.67/hour cleaning a smaller house.

To find out how much more Jasmine makes per hour cleaning a larger house compared to a smaller house, we can subtract the hourly rate for a smaller house from the hourly rate for a larger house:

⇒ $18.75/hour - $16.67/hour = $2.08/hour

So, Jasmine makes $2.08 more per hour cleaning a larger house compared to a smaller house.

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Tthe triangle that is a reflection of the green triangle is figure 1

From the question, we have the following parameters that can be used in our computation:

The figures

Where, we have:

This means that the triangle that is a reflection of the green triangle is figure 1

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Segments MS and QS are therefore congruent by the definition of bisector. Therefore, the correct answer option is: D. MS and QS.

In Mathematics and Geometry, a perpendicular bisector is a line, segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

This ultimately implies that, a perpendicular bisector bisects a line segment exactly into two (2) equal halves, in order to form a right angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment NS is a perpendicular bisector of isosceles triangle MNQ, we can logically deduce the following congruent relationships;

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Complete Question:

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅ ΔQNS

We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments _____ are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS

NS and RS

MS and RS

MS and QS

Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

Any whole number can be written as a fraction. All we do is place the number over 1.

For example, the whole number 7 is the same as the fraction 7/1.

If we wanted to multiply the whole number 7 with the fraction 2/3 then...

\(7 * \frac{2}{3}\\\\\frac{7}{1} * \frac{2}{3}\\\\\frac{7*2}{1*3}\\\\\frac{14}{3}\\\\\)

In the jump from the second step to the third step, we multiply straight across. The numerators multiply together. The denominators multiply together. The fraction 14/3 cannot be reduced because 14 and 3 don't have any factors in common other than 1.

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

In the equation, we will need to calculate the maximum amount of money Marian can spend on the house.

We can calculate the maximum amount of money Marian can spend on a house by multiplying her monthly income by the number of months she would want to save.

Marian earns $4,100.00 per month

Suppose Marian wants  to save for  x months,  then the maximum amount that she can spend on the house is:

4100  *   x    +  21390

The answer is:  4100x  +  21390

We need to know the number of months Marian wants to save to get the specific value.

Hope this helps!

Answer: They resold them for $30 more than the original price.

Answer: 37.5%

Step-by-step explanation:

$80 - $50 = $30,

$30/$80 = 0.375 > 37.5%

Answer:

70,000 = seventy thousand

Step-by-step explanation:

The place value of 7 in 8,72,164 is 70,000.

Every digit in a number has a place value in mathematics. The value a digit in a number represents based on where it is in the number is known as place value.

Given the number 8,72,164,

find the place value by table,

number  x  multiplier   =    value

8             x   1,00,000   =  8,00,000

7             x    10,000      =   70,000

2              x     1,000      =    2,000

1              x     1,00          =    1,00

6              x     10          =    60

4             x     1                 =    4

The place value of 7 is  70,000.

Hence the value of 7 is  70,000.

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Answer:

decimal - 0.875

percent - 87.50%

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

its a problem of fraction multiplication

This involves two steps

1. product of 15*-2 = -30

2. now we have to find 2/3 of -30

mathematically it can be written as

2/3 of -30

=> 2/3*-30 = 2*-10 = -20

Thus, answer is -20.

Answer:

2/3 of the product of 15 and -2 is -20

Step-by-step explanation:

2/3 of the product of 15 and - 2

Here, 15 × (-2) = -30

Now,

2/3 of -30

2/3 × (-30)

2 × (-10) = -20

Thus, 2/3 of the product of 15 and -2 is -20

-TheUnknownScientist

Answer:

\( \frac{11}{24} \: cups\)

Step-by-step explanation:

Please see the attached picture for the full solution.

Fraction of oil Ryan used to make 6 servings of Frech fries = 2 ¾ cups of oil

Fraction of oil Ryan would have used to make one serving =

= 6 ÷ 2 ¾

= 2 ¾ as an improper fraction = 11/4

= 11/4 ÷ 6

= 11/4 × 1/6 ( division of fractions is same as multiplication with their reciprocal )

= 11/24

Therefore , Ryan used 11/24 cup of oil for one serving of French fries .

Answer:

19 - 42x

Step-by-step explanation:

To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x

Answer:

x+600≥2400

Step-by-step explanation:

It has to be atleast 2400

(x² + 4)(x² - 4) = x⁴ - 16 and the product is placed in the grid.

Given expression is: (x² + 4)(x² - 4) To multiply two polynomials, we use the distributive property.

We will multiply x² with both x² and -4 and 4 with both x² and -4 as shown below.x² * x² + x² * (-4) + 4 * x² + 4 * (-4)x⁴ - 4x² + 4x² - 16.

The above expression can be simplified further by combining like terms. 4x² gets canceled on adding -4x² and 4x².

Simplified expression is: x⁴ - 16

Hence, (x² + 4)(x² - 4) = x⁴ - 16 and the product is placed in the grid below:   

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To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

The expected value of each warranty sold is $23.8.

Step-by-step explanation:

0.8% probability of the product failling.

If the product fails, the company will lose 400 - 27 = $373. So a net value of -373.

100 - 0.8 = 99.2% probability of the product not failling.

If the product does not fail, the company gains $27.

What is the company's expected value of each warranty sold?

We multiply each outcome by its probability.

0.008*(-373) + 0.992*27 = 23.8

The expected value of each warranty sold is $23.8.

It is given that the probability of 8th grade boy needs to be calculated.

The probability is given by:

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

The ROC of a given signal's Z-transform can be determined without actually computing the Z-transform by identifying the maximum and minimum magnitude of the signal and checking for any poles of the Z-transform within the resulting annular region.

Let's take a signal as an example, suppose x[n] = {1, -2, 3, -4, 5}. In order to determine the ROC of its Z-transform, we are firstly required to first look for any regions in the complex plane where the sum of the absolute values of the Z-transform is found finite. It can be done by looking for the maximum and minimum magnitude of x[n] and denote them as R1 and R2 respectively. Then, the ROC of the Z-transform will be the annular region between R1 and R2, excluding any poles of the Z-transform that lie within this annular region.

In this case, the maximum absolute value of x[n] is 5 and the minimum is found being 1. So, the ROC of the Z-transform will be the annular region between |z| = 1 and |z| = 5. We can denote this as 1 < |z| < 5. We also need to check if there are any poles of the Z-transform within this annular region. Since we haven't actually computed the Z-transform, we cannot determine the exact location of any poles.

However, we can check for any values of z that would make the Z-transform infinite. For example, if x[n] is a causal signal (i.e., x[n] = 0 for n < 0), then the ROC cannot include any values of z for which |z| < 1, since this would make the Z-transform infinite.

So, the ROC of the Z-transform for the given signal x[n] can be written as 1 < |z| < 5, assuming that x[n] is a causal signal.

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The complete question is :

Can you explain how to determine the ROCs (regions of convergence) for the Z-transform of a given signal without actually computing the Z-transform? Please provide an example signal with random data and demonstrate how to find its ROCs using this method.

Answer:

-4 and -2

Step-by-step explanation:

First find all the factors of 8, that would be 1 and 8, -1 and -8, 2 and 4, and -2 and -4.

Then, adding the groups of numbers you have should show you what would equal -6. So 1 + 8 = 9, -1 + (-8) = -9, same vice versa, 2 + 4 = 6, -2 + (-4) = -6. So -2 and -4 would be your two numbers.

Answer:

I think the image above will help you.

Answer:

Var = 6.31

Step-by-step explanation:

The Value at Risk (VAR)

\(P(X < x_o) = 0.01\)

By using normal distribution

Mean \(\mu\) = 10

Variance = 49

Standard deviation \(\sigma = \sqrt{49 } = 7\)

This implies that:

\(P\Big ( \dfrac{X - \mu}{\sigma } < \dfrac{x_o - \mu }{\sigma}\Big) = 0.01 \\ \\ P\Big ( Z < \dfrac{x_o - \mu }{\sigma}\Big) = 0.01 \\ \\ \dfrac{x_o - \mu }{\sigma} = invNorm(0.01) \\ \\ x_o = \mu + \sigma \times invNorm (0.01)\)

Using the z-table;

\(x_o = 10 + 7 \times (-2.33) \\ \\ x_o = -6.3100\)

Hence, there exist 1% chance that X < -6.31 or the loss from investment is > 6.31

From the calculated value above;

\(V = \mu -\sigma \times 2.33\); Since the result is negative, then it shows that the greater the value(i.e the positive or less negative it is ) the lower is the value of VAR. Thus, the least value of VAR is accepted by  the largest value of

\(min( \mu -\sigma \times2.33,0)\)