T/F: An altitude of a triangle is a line segment through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the opposite side of the triangle.

\(a) \frac{6}{3}+9=2+9=\boxed{11} \\ \\ b) 8(2)-3+1=\boxed{14} \\ \\ c) 2(5)(-3)=\boxed{-30} \\ \\ d) 2(3)^2-8=2(9)-8=18-8=\boxed{10}\)

The equation of the given curve is given by r2 cos(2θ) = 36.

To find the Cartesian equation of the curve, we need to convert the polar equation into its equivalent Cartesian form. This can be done by substituting x = r cos θ and y = r sin θ into the given equation, yielding:
x2cos(2θ) + y2cos(2θ) - 36 = 0
Using the identity cos(2θ) = cos2θ - sin2θ, the equation can be rewritten as:
x2(cos2θ - sin2θ) + y2(cos2θ - sin2θ) - 36 = 0
Simplifying, we get:
x2 - y2 - 36 = 0

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The measure of ∠V of the parallelogram is = 150.5°

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the measure of the angle ∠Y = 10x + 27

Let the measure of the angle ∠W = 2x + 29

Now , for a parallelogram the opposite sides are congruent and opposite angles are congruent

Substituting the values in the equation , we get

10x + 27 = 2x + 29

Subtracting 2x on both sides of the equation , we get

8x + 27 = 29

Subtracting 27 on both sides of the equation , we get

8x = 2

Divide by 8 on both sides of the equation , we get

x = 1/4

Let the measure of the angle ∠Y = 10 ( 1/4 ) + 27

Let the measure of the angle ∠Y = 2.5 + 27

Let the measure of the angle ∠Y = 29.5°

Now , same-side interior angles (consecutive angles) are supplementary

Substituting the values in the equation , we get

angle ∠Y + angle ∠V = 180°

29.5° + m∠V = 180°

Subtracting 29.5 on both sides of the equation , we get

m∠V = 150.5°

Hence , the measure of m∠V = 150.5°

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Answer:

x = 16 units

Step-by-step explanation:

∆ABC is a 45-45-90 triangle, and ∆BCD is a 30-60-90 triangle.

If side opposite of 90° [∆] = x, side opposite of 45° [∆] = x / √2 = x √ 2 / 2.

Given side AC is opposite of 90° [∆ABC] = 32 √ 2, side opposite of 45° [∆ABC] = 32 √ 2 / √ 2 = 32 which is AB or BC.

Since side BC is part of BCD.

Side opposite of 90° [∆BCD] = BC = 32.

Since x is opposite of 30° [∆BCD].

x = Side opposite of 90° [∆BCD] / 2 = 32 / 2 = 16.

At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

The speed of an object is the ratio of distance and time it takes for the object to travel that distance.

Mathematically,

S = D/T

where

S is velocity

D is the distance traveled or distance traveled

T is the time it takes to travel that distance

Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.

If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.

Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.

Mathematics,

a = v/t

When an object is in motion, its acceleration is never zero.

When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.

Given in the question:

First the plane was travelling at a constant rate of 250  miles per hour.

Initial height was 20000 feet

Now,

As the speed increases and travels at a constant rate of 400 miles per hour.

Now,

   (400 /250 ) × 20000

=  1.6 × 20000

= 32000 feet

Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.

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By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Step-by-step explanation:

given,

the complete angle is complementry angle which is 90°

let the first angle be x and second angle be 7x ( as second angle is 7 times more than first angle )

now,

→ x + 7x = 90

→ 8x = 90

→ x = 90/8 = 11.25

therefore

1st angle = x = 11.25°

2nd angle = 7x = 7 × 11.25 = 78.75°

hope this answer helps you dear take care and may u have a great day ahead!

If a 10-year-old can perform the same tasks as the average 15-year-old, then the child's "mental age" is 15, and their "IQ" is 150.

The concept of mental age, introduced by Alfred Binet, refers to an individual's level of cognitive functioning compared to others in their age group. It is a measure of intellectual development. In this case, the 10-year-old's mental age is considered to be 15 because they can perform tasks typically expected of a 15-year-old.

IQ (Intelligence Quotient) is a standardized measure of intelligence. It is calculated by dividing an individual's mental age by their chronological age and multiplying it by 100. In this scenario, if the 10-year-old's mental age is 15, their IQ would be 150 (15/10 * 100 = 150).

Therefore, the child's mental age is 15, and their IQ is 150.

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2x(6x2 + 4x − 3) × (2x − 3)(5x + 6)

= (2x)2(6x2 + 4x − 3)(5x + 6)

= 12x3(5x + 6) + 8x2(5x + 6) − 6x(5x + 6)

= 60x4 + 48x3 − 45x2 − 36x

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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250

250 is in-between 200 nd 300

Answer:

84 CDs last week and 26 CDs this week

Step-by-step explanation:

Answer:

<a=61 m<c and m<b=90

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

x=?

y=8

2x + 3y = 12

=>2x+(3 *8)= 12

=>2x+24 =12

=>2x=12-24

=>x=-12/2

=>x=-6

The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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Answer:

25

Step-by-step explanation:

5+9=14

5/14x70=25

Answer:

B: 10

Step-by-step explanation:

The angle measures are all multiplied by 2.

I believe the answer should the 10.

Looking at the two given triangles, the singular line in the bottom left triangles means that the angles are the same. As to the corner seen in cornerF and cornerC, and cornerD with cornerA. Knowing that all of the angles in the triangle are the same, means that the side lengths should all be generally on the same scale.

With triangle DEF, this triangle got scaled up by 2. This can be seen from line AB and line DE. AB was multiplied by two, in order to get line DE, which is 8. Apply the x2 rule to lines DF and EF, and the unknown "e" turns into 10. Unkown "d" turns into 12.

Answer:

option d

Step-by-step explanation:

(-4ab)^3 = (-4ab)(-4ab)(-4ab) = -64a^3b^3 (option d)

I hope this helped, please give brainliest if this is correct! Thank you!

Using the laws of logarithms, we can write:

ln[(x – 4)^38 (3x – 8)^34] = 38 ln(x – 4) + 34 ln(3x – 8)

This expression is now a sum of two logarithmic expressions which do not contain the logarithms of products, quotients, or powers.

To evaluate the derivative of ln[(x – 4)^38 (3x – 8)^34], we can use the chain rule and the fact that the derivative of ln(u) is du/u. Therefore:

d/dx ln[(x – 4)^38 (3x – 8)^34]

= d/dx [38 ln(x – 4) + 34 ln(3x – 8)]

= 38 d/dx ln(x – 4) + 34 d/dx ln(3x – 8)

= 38 * 1/(x - 4) + 34 * 3/(3x - 8)

= 38/(x - 4) + 102/(3x - 8)

= 100(3x - 32)/(x - 4)(3x - 8)

Therefore, the derivative of ln[(x – 4)^38 (3x – 8)^34] is 100(3x - 32)/(x - 4)(3x - 8).

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Answer:

(g · h)(t) = -6t - 6

Step-by-step explanation:

To find (g · h)(t), multiply g(t) by h(t).

g(t) = 3t + 3

h(t) = -2

(g · h)(t) = (-2)(3t + 3)

(g · h)(t) = -6t - 6

Step-by-step explanation:

4×100=400

400÷7=57.14......

hope it helps!

have a great day :)

The value of the three trigonometric ratios for angle L are 4/5, 3/5, and  4/3.

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Given

The opposite side of the triangle is 20, the adjacent side is 15, and the hypotenuse is 25.

The three trigonometric ratios are given by;

\(\rm Sin \theta=\dfrac{Opposite}{Hypotenuse}\\\\Sin\theta=\dfrac{20}{25}\\\\Sin\theta=\dfrac{4}{5}\\\\\rm Cos\theta=\dfrac{Adjacent}{Hypotenuse}\\\\ \rm \rm Cos\theta=\dfrac{15}{25}}\\\\ \rm Cos \theta =\dfrac{3}{5}\\\\\rm Tan\theta =\dfrac{Opposite }{Adjacent}\\\\\rm Tan \theta =\dfrac{20}{15}\\\\Tan \theta=\dfrac{4}{3}\)

Hence, the value of the three trigonometric ratios for angle L are 4/5, 3/5, and  4/3.

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The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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If the distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. the score separating the bottom 81% from the top 19% is 168.24.

 The value of p81, which is the score separating the bottom 81% from the top 19%, can be calculated as follows:

 The given, Mean = μ = 93.2

                    Standard deviation = σ = 87.4

      We are supposed to find the score separating the bottom 81% from the top 19% which is nothing but the 81st percentile.

       Let X be a random variable with a normal distribution, then the z-score of the 81st percentile is calculated as follows:

               z = InvNorm(0.81)

               z ≈ 0.8 (by standard normal distribution tables)

    The 81st percentile in terms of X is given by:

              p81 = μ + zσp81

                     = 93.2 + 0.8(87.4)p81

              p81 = 168.24

   Thus, the score separating the bottom 81% from the top 19% is 168.24.

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Answer: 2 2/3

Step by step explanation:

(4 - 1) + (3/6 - 5/6)

(3) + (-2/6)

-2/6 divided by 2/2 gets you -1/3

3 + -1/3 = 2 2/3..

i think i did that right. if i’m not listen to the other people haha

Answer:

1

Step-by-step explanation:

1 is the simplest probability

The 100W bulb will have a lower brightness than the 60W bulb because the resistance of the 100W bulb is less than that of the 60W bulb, so it will have the lowest voltage drop.

Since the power of a lamp of nominal voltage V can be defined as \(\bold{P = \frac{V {}^{2} }{R}}\), where R is the resistance to hot, this means that the resistance of the lamp is inversely proportional to its power, that is, the greater the power of the lamp, the lower its resistance.

Applying Kirchoff's second law to a series circuit with resistors R1 and R2 and power supply E we have:

\( \bold{E = I.R1 + I.R2}\)

Since the current I is the same for all elements connected in series. In this expression we see that the smallest resistance will have the smallest voltage drop.

Now, in our circuit with two bulbs in series, the 100W bulb will have less resistance than the 60W bulb, so it will have less voltage drop. As it has a lower voltage drop, the power developed in the 100W lamp will be less than that developed in the 60W lamp and the 100W lamp will have a weaker brightness than the 60W lamp.

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Answer:

≈ £ 4584.38

Step-by-step explanation:

Firstly, we need to find the number of litres that Mr. Leonard needs to fill up his tank:

We know that there is already 450 litres in the 1200 litre tank, so he must need 1200 - 450 = 750 litres.

I'm not quite sure what the variable p means, but I'm going to assume that p represents the number of litres and that 81.5 is the price per litre in pounds.

So:

Total price = 81.5p

Total price = 81.5(750)

Total price = £61125

We have to remember though that the question is asking for the discount and not the discounted price, so:

61125 × 7.5%

61125 × 0.075 = 4584.375

≈ £ 4584.38