What is the area of this triangle ?

Answer:

n = p+3q

Step-by-step explanation:

2^p x 8^q = 2^n

Exponent rules

Rewriting 8 as 2^3

2^p x 2^3^q = 2^n

Using the rule a^b^c = a^(b*c)

2^p x 2^3q = 2^n

Using the rule a^b * a^c = a^(b+c)

2 ^(p+3q) = 2^n

Since the bases are the same, the exponents are the same

p+3q = n

Answer:

\( \sf \: p + 3q = n\)

Step-by-step explanation:

\(2^p*8^q=2^n\)

First, write 8^q as a power of 2.

\(2^p*8^q=2^n\\2^p*2^3^q=2^n\)

As all the bases are same, exponents are also equal.

Now add the powers.

∴ p + 3q = n

The tangent plane approximation at h(4.001,0.997) is 72.026, where h(x, y) = x³ + 2xy.

Plane is h(x, y) = x³ + 2xy.

Substitute the value of x and y in the plane

h(4, 1) = (4)³ + 2(4)(1)

h(4, 1) = 64 + 8

h(4, 1) = 72

Partial Differentiation with respect to x

hₓ = ∂h/∂x

hₓ = 3x² + 2y

at (4, 1)

hₓ = 3(4)² + 2(1)

hₓ = 3(16) + 2

hₓ = 48 + 2

hₓ = 50

Partial Differentiation with respect to x

\(h_{y}\) = ∂h/∂y

\(h_{y}\) = 2x

at (4, 1)

\(h_{y}\) = 2(4)

\(h_{y}\) = 8

tangent plane is

z = h(4, 1) + hₓ(x - x₀) + \(h_{y}\)(y - y₀)

z = 72 + 50(x - 4) + 8(y - 1)

z = 72 + 50x - 200 + 8y - 8

z = 50x + 8y - 136

at (x, y) = (4.001, 0.997)

z = 50(4.001) + 8(0.997) - 136

z = 200.05 + 7.976 - 136

z = 72.026

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Answer:

11 - 125 and 55

12 - supplementary

Step-by-step explanation:

5x+20+3x-8=180

step 1 combine like terms

8x+12=180

step 2 subtract 12 from each side

8x=168

step 3 divide each side by 8

x=21

then you just plug in 21 to each equation to find that angle 1 = 125 and angle 2=55

Problem 11

Answers:

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

Explanation:

The two angles shown here form a linear pair. They supplementary so they add to 180.

(5x+20)+(3x-8) = 180

(5x+3x) + (20-8) = 180

8x+12 = 180

8x = 180-12

8x = 168

x = 168/8

x = 21

We then find the angles to be

5x+20 = 5*21+20 = 125

3x-8 = 3*21-8 = 55

Note how 125+55 = 180 to help confirm the answers

===================================================

Problem 12

Answer: B) Vertical angles

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

Explanation:

Vertical angles are angles that form after intersecting two lines, and the angles are opposite one another. So one example of a vertical angle pairing would be angles 1 and 3. The other vertical angle pair of this diagram are angles 2 and 4. Vertical angles are always congruent to one another.

In this diagram, angles 1 and 4 are adjacent since they are next to each other. In other words, they share a common line (think of apartment neighbors sharing a common wall). Since they are adjacent angles, there is no way they are vertical angles.

Angles 1 and 4 are also supplementary since they form a straight line. They are a linear pair for very similar reasons. This allows us to rule out choices A, C and D.

Side note: the term "linear pair" means that the angles are adjacent and supplementary.

Answer:

area: 14

Step-by-step explanation:

Answer: x=3.88

Step-by-step explanation: hope it helps

Answer:

\(x=3.88\)

Step-by-step explanation:

Move all the terms to the right side to isolate x:

\(-1.5(x+5.24)=-13.68\\(x+5.24)=9.12\\x=3.88\)

The function iteratively calculates the next number in the heavy sequence until it reaches 1 or detects a repeating pattern. If the next number becomes equal to the current number, it means the sequence does not converge to 1 and the number is not heavy in the given base. Otherwise, if the sequence reaches 1, the number is heavy.

Here's a Python implementation of the heavy function that checks if a number y is heavy in base N:

python

Copy code

def heavy(y, N):

   while y != 1:

       next_num = sum(int(digit)**2 for digit in str(y))

       if next_num == y:

           return False

       y = next_num

   return True

You can use this function to check if a number is heavy in a specific base. For example:

python

Copy code

print(heavy(4, 10))        # False

print(heavy(2211, 10))     # True

print(heavy(23, 2))        # True

print(heavy(10111, 2))     # True

print(heavy(12312, 4000))  # False

The function iteratively calculates the next number in the heavy sequence until it reaches 1 or detects a repeating pattern. If the next number becomes equal to the current number, it means the sequence does not converge to 1 and the number is not heavy in the given base. Otherwise, if the sequence reaches 1, the number is heavy.

Note: This implementation assumes that the input number y and base N are within the specified value ranges of non-negative y and 2 <= N <= 4000.

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Answer:

A-- 98.9 degrees in the morning

B-- 0.3 degrees above average

Step-by-step explanation:

Answer:

98.9 degrees F, .3 degrees

Step-by-step explanation:

Brainliest Please!!!

Answer:

y=-4x+2

Step-by-step explanation:

B is the y-intercept and M is the sope, or x, knowing this now we slove:

(-4, 2)

m    b

y=mx+b

y=-4x+2

Have a beautiful day! v(⌒o⌒)v♪

For more help take a look at the picture below.

Let x be women and y men.

x + y = 65 equation 1.

y = x - 7 equation 2.

Now we need to solve the equation system, as follows:

- on eq. 2 y is already solved, so we can replace y on eq. 1:

x + x - 7 = 65

2x - 7 = 65

2x = 65 + 7

2x = 72

x = 72/2

x = 36 women

Finally, we replace x on eq 2:

y = 36 - 7

y = 29 men

Answer:

B

Step-by-step explanation:

3(x +1) =3x +3

Plug it in

3(5+1)=3(5)+3

3(6)=15+3

18=18

Using the angle addition postulate, we found that the measure of the angle, ∠LMN is 135°.

What is the angle addition postulate?

The measure of the angle created by the non-common sides of two adjacent angles is equal to the total of the measures of the two adjacent angles. The angle addition postulate in geometry asserts that if we position two or more angles side by side, with a shared vertex and an arm between each pair of angles, the sum of those angles will be equal to the sum of the resulting angle. Adjacent angles are those two angles that are connected by a common ray. Any pair of neighbouring angles in mathematics can be applied to this postulate.

The figure is given below.

We can solve this using the angle addition postulate.

Given,

m∠FMN = 99°

m∠LMF = 36°

We are asked to find the measure of angle ∠LMN.

According to the angle addition postulate,

m∠FMN + m∠LMF =  m∠LMN

99 + 36 = m∠LMN

m∠LMN = 135°

Therefore using the angle addition postulate, we found that the measure of the angle, ∠LMN is 135°.

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Answer:

They celebrated it on March 14 at 1:59 because...

The first few digits of pi are --- 3.14159

The date of March 14 is 3/14. Then you add the 1:59 it makes the first few digits of pi.

Step-by-step explanation:

The tradition to celebrate Pi Day on 14th March started in the late 80's, when the physicist Larry Shaw organized the first Pi Day celebration at the San Francisco Exploratorium. Since then, Pi Day has become a popular way for mathematicians, educators, and students to celebrate and share their interests in mathematics. Many schools, universities, and math clubs around the world host events, such as pi recitation contests, pi-themed games, and pie-eating contests, to celebrate this day.

Eating pie is also a way to join the celebration, as the word "pi" sounds like "pie". People often eat different types of pie on Pi Day, such as pizza pie, sweet pies, and savory pies to celebrate the mathematical constant pi and its connection to the word “pie”.

The series for the following evaluations and first five terms of the series are to be determined as given below:1. `e³ = -Σ((-1)ⁿ⁺¹ / (n-1)!)`

First five terms of the series:`e³ = -1 + 3 - (9/2) + (9/2) - (27/8) + ...`2. `e⁻⁴=0(1/n!)`

First five terms of the series:`e⁻⁴=0(1/n!) = 0 + 0 + 0 + 0 + 0 + ...`3. `2√e= - Σ((-1)ⁿ / (n-1)!)`

First five terms of the series:`2√e= -1 + 1/2 - 1/8 + 1/48 - 1/384 + ...`

The terms of the above series can be found by plugging in n=1, 2, 3, 4 and 5. The series is usually defined using the sigma notation which is expanded above using the ellipses symbol.

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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(a) The height after t years is given by the function h(t) = (0.55t^2 + 6t + 19) cm.

(b) The shrubs are sold after 8 years of growth and shaping, so we can substitute t = 8 into the function h(t) to find their height, which is approximately 83 cm.

(a) To find the height after t years, we need to integrate the given growth rate function dh/dt = 1.1t + 6 with respect to t. By integrating, we obtain the height function h(t) = 0.55t^2 + 6t + 19.

(b) The shrubs are sold after 8 years, so we substitute t = 8 into the height function h(t) to find their height. Evaluating h(8), we get h(8) = 0.55(8)^2 + 6(8) + 19 = 83 cm.

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The X and Y angles created by lines intersection in the pictures are 18° and 54°.

Based on the picture, angle ∠MON is a right angle hence it has an 90° angle. We then know that the ∠MOA is 72°. Because angle ∠MOA lies within the angle ∠MON, hence we can write the following formula:

∠MON = ∠MOA +∠AON = 90°

∠MON = 72° + ∠AON = 90°

∠AON = 18° ... (i)

If we focus on the line CD being intersected by the line AB, hence we can conclude that the angles form by this intersection will follow these rules:

∠AOD = ∠BOC

∠AOC = ∠BOD

∠AOD + AOC = 180°

∠BOC + ∠BOD = 180°

Based on the picture, we know that:

∠BOC = x

∠AOC = ∠MOA + ∠MOC

∠AOC = 72° + y ...(ii)

∠AOD = ∠AON + ∠NOD

∠AOD = 18° +2x

∠BOC = 3x ... (iii)

Because we already know that ∠BOC = AOD, hence we could rewrite the formula into:

∠BOC = ∠AOD

3x = 18° + 2x

x = 18° ... (iv)

To find the value of y, we need to focus on angle ∠AOC. Based on the previous calculations and formulas, we  know that:

∠AOC + ∠BOC = 180° ... (v)

Input equations (ii) and (iv) into (v)

∠AOC + ∠BOC = 180°

(72° + y) + 3x = 180°

72° + y + 3(18°) = 180°

126° + y = 180°

y = 54° ... (vi)

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The transmitted intensity i1 is approximately 19.32 watts per square meter.

An indicator of a physical phenomenon's strength or power, such as light, sound, or radiation, is its intensity. It is often expressed in terms of the quantity of energy being transmitted or received per unit area or volume. For instance, the intensity of light is expressed in watts per square metre, while the strength of sound is expressed in watts per square metre per hertz. Distance, direction, and the qualities of the medium through which the phenomenon is transmitted can all have an impact on intensity.

To find the transmitted intensity (i1), we need to use the formula:

\(i1 = i0 * cos(θ0 - θta)\)

where i0 is the initial intensity, \(θ0\)is the initial angle, and \(θta\) is the transmitted angle.

Step 1: Calculate the difference between the angles:
\(Δθ = θ0 - θta\) = 25.0 degrees - 40.0 degrees = -15.0 degrees

Step 2: Convert the angle difference to radians:
\(Δθ\)(in radians) = -15.0 degrees *\((\pi /180)\) ≈ -0.2618 radians

Step 3: Calculate the cosine of the angle difference:
\(cos(Δθ) ≈ cos(-0.2618)\)≈ 0.9659

Step 4: Calculate the transmitted intensity (i1):
i1 = i0 * \(cos(Δθ)\) = 20.0\(W/m^2\) * 0.9659 ≈ 19.32 \(W/m^2\)

So, the transmitted intensity i1 is approximately 19.32 watts per square meter.

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Answer:Answer:

d=√

−2x2+y

900f4i2n2x

or d=−√

−2x2+y

900f4i2n

Step-by-step explanation:

Let's solve for d.

y=2x2+9xfindf(10)findf(10)

Step 1: Flip the equation.

900d2f4i2n2x+2x2=y

Step 2: Add -2x^2 to both sides.

900d2f4i2n2x+2x2+−2x2=y+−2x2

900d2f4i2n2x=−2x2+y

Step 3: Divide both sides by 900f^4i^2n^2x.

900d2f4i2n2x

900f4i2n2x

=

−2x2+y

900f4i2n2x

d2=

−2x2+y

900f4i2n2x

Step 4: Take square root.

d=√

−2x2+y

900f4i2n2x

or d=−√

−2x2+y

900f4i2n2x

2x

Answer:

d=√

−2x2+y

900f4i2n2x

or d=−√

−2x2+y

900f4i2n

The value of f(10) for function f(x) = 2x² + 9x is 290.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given function is,

f(x) = 2x² + 9x     (1)

To find the value of f(10),

Substitute x = 10,

f(10) = 2(10)² + 9(10)

f(10) = 2 x 100 + 90

f(10) = 200 + 90

f(10) = 290

The required value of f (10) is 290.

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Answer:

14.135

Step-by-step explanation:

6 divided by 2 (half) = 3, π·32≈28.27433 dived by 2 (half) equals 14.135

Answer:

14.13 units ^2

Step-by-step explanation:

A= 3.14 (3)^2 (area of a circle)

A= 28.26 / 2 (divide to find half of the circle)

A=14.13 units ^2

Answer:4x+32+5x-15

Step-by-step explanation: that’s the simplified equation, you would just have to distribute the 4 to its own equation and the 5 into its own equation.. but i think the second part of ur question is missing..

Answer:

C. 9x+17

Step-by-step explanation:

The probability that they have an average weight of greater than 10 pounds and less than 15 pounds is 0.84134

In this question we have been given there are 250 dogs at a dog show who weigh an average of 15 pounds, with a standard deviation of 6 pounds. of 10 dogs are chosen at random.

We need to find the probability that they have an average weight of greater than 10 pounds and less than 15 pounds.

Given, μ = 12, σ = 8, n = 4

P(X > 8)

= P(z > (8 - 12 / 8/√4))

= P(z > -1)

= 1 - P(z ≤ -1)

= 1 - [1 - P(z ≤ 1)]

=  P(z ≤ 1)

= 0.84134

Therefore, the required probability is 0.84134

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Answer: 9.375 or rounded is 9.38

Step-by-step explanation:

Answer:

x=120

Step-by-step explanation:

so if you look at a angle ruler you will see it's 120 so now if you look one up and put it to 120 it would match i wouldn't know how accurate it is but from what i know its 120

Answer:

Each girl earned 2 points

Each boy earned 5 points

Step-by-step explanation:

Let x represent the number of points one girl earned

Let y represent the number of points one boy earned

4x + 2y = 28

4x - 2y = 12

8y = 40

y = 5 points

4x + (2)(5) = 28

4x + 20 = 28

4x = 8

x = 2 points

Each girl earned 2 points

Each boy earned 5 points

Answer:

B

Step-by-step explanation:

AB=6 therefore Pto Q should be 6

6^2=36

8^2=64

add them together

=100

square root 100=10

divide by 2=5

Answer:

C. 9

Step-by-step explanation:

15/100*60

3/20*60

180/20

9

Answer:

The answer is 9

Step-by-step explanation:

15% * 60

"OF" mean multiplication so we multiple

¹⁵/100 * 60

we cancel "Zero cancel Zero"

we left with

¹⁵/10 * 6

but we can make the fraction to be uniform

so we say ¹⁵/10 * ⁶/1

we multiply

15 * 6=90

10 * 1=10

⁹⁰/10

we divide

10 into 90 is 9

10 into is 1

so we say ⁹/1 is the same as 9.

Hence our answer is 9

The ball is approximately 4 units away from its initial position at t = 1.

To find the position of the ball at t = 1, we need to integrate the velocity function. The velocity function v(t) is obtained by integrating the acceleration function a(t):

v(t) = ∫ a(t) dt = ∫ (8j − 16k) dt

Integrating the j-component of the acceleration gives the j-component of the velocity:

v_j(t) = ∫ 8 dt = 8t + C₁,

where C₁ is the constant of integration.

Integrating the k-component of the acceleration gives the k-component of the velocity:

v_k(t) = ∫ (-16) dt = -16t + C₂,

where C₂ is another constant of integration.

Given the initial velocity v(0) = 3i + 8k, we can determine the values of C₁ and C₂:

v(0) = 3i + 8k = 8(0) + C₁ j + C₂ k

Comparing the coefficients, we have C₁ = 0 and C₂ = 8.

Thus, the velocity function v(t) becomes:

v(t) = (8t)j + (8 - 16t)k = 8tj + 8k - 16tk.

To find the position function r(t), we integrate the velocity function:

r(t) = ∫ v(t) dt = ∫ (8tj + 8k - 16tk) dt

Integrating the j-component of the velocity gives the j-component of the position:

r_j(t) = ∫ (8t) dt = 4t^2 + C₃,

where C₃ is the constant of integration.

Integrating the k-component of the velocity gives the k-component of the position:

r_k(t) = ∫ (8 - 16t) dt = 8t - 8t^2 + C₄,

where C₄ is another constant of integration.

Using the initial position r(0) = 0, we find C₃ = C₄ = 0.

Therefore, the position function r(t) becomes:

r(t) = (4t^2)i + (8t - 8t^2)k.

To find the distance traveled at t = 1, we substitute t = 1 into the position function:

r(1) = (4(1)^2)i + (8(1) - 8(1)^2)k

= 4i + 0k

= 4i.

The distance traveled is the magnitude of the position vector:

| r(1) | = | 4i | = 4.

Hence, the ball is approximately 4 units away from its initial position at t = 1.

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