Find the surface area of the composite solid.
PLZ HELP

Answer:

Answer/Step-by-step explanation:

Recall: the ratio of the areas of two similar figures = the square of the ratio of the corresponding sides of the similar figures.

This will give us the scale factor.

The scale factor indicates how many times larger the second triangle is than the area of the first.

Let's find how many times larger is the area of the second triangle is to the first:

1. ∆ G And ∆ F

\frac{Area_{F}}{Area_{G}} = \frac{side_{F}^2}{side_{G}^2}

Area

G

Area

F

=

side

G

2

side

F

2

\frac{Area_{F}}{Area_{G}} = \frac{6^2}{3^2}

Area

G

Area

F

=

3

2

6

2

= \frac{36}{9} = 4=

9

36

=4

∆F is 4 times larger than ∆G

2. ∆ G And ∆ B

\frac{Area_{B}}{Area_{G}} = \frac{side_{B}^2}{side_{G}^2}

Area

G

Area

B

=

side

G

2

side

B

2

\frac{Area_{B}}{Area_{G}} = \frac{2^2}{4^2}

Area

G

Area

B

=

4

2

2

2

= \frac{4}{16} = 0.25=

16

4

=0.25

∆B is 0.25 times ∆G

3. ∆ B And ∆ F

\frac{Area_{G}}{Area_{B}} = \frac{side_{F}^2}{side_{B}^2}

Area

B

Area

G

=

side

B

2

side

F

2

\frac{Area_{F}}{Area_{B}} = \frac{8^2}{2^2}

Area

B

Area

F

=

2

2

8

2

= \frac{64}{4} = 4=

4

64

=4

∆F is 16 times larger than ∆B

4. ∆ F And ∆ H

Answer:

Step-by-step explanation:

The given equation is not instandard form. First standard form is neccesary.

The result is 3x + 108 = 12y which is equal to 12y = 3x + 108

The slope is represented in this form as m (Y = mx + b)

(with b as the initial value)

Therefore, 3 is the slope.

To find its perpendicular slope.

To find it's perpendicular, know that it is the negative reciprocal.

FInally, the slope perpendicular to the line whose equation is 3x - 12y = -108 is \(\frac{1}{-3\\}\)

Answer:

Substitute the value of the variable into the equation and simplify.

48

Step-by-step explanation:

Answer:

42 or 48

Step-by-step expla

Answer:

-3

Step-by-step explanation:

Step 1: Solve (-2+(-1))^2/3 3

           1. -2+(-1) = -3

           2. (-3)^2 = 9

           3. 9/3 = 3

Step 2: Solve (-4)^2-17 -1

           1. 3/-1

Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!

2/9 is the probability of getting a green and purple in any order.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, A spinner has three sections colored green, purple, and pink. If the spinner is spun twice.

From the general formula of probability:

Probability = (desired outcomes)/(Total outcomes)

In our case,

The two possible outcomes of this event occurring are Green, Purple, and Purple, Green.

desired outcomes = 2

total outcomes = 3*3 = 9

Probability = 2/9

therefore, the probability of getting a green and purple in any order is 2/9.

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Answer:

Round 4264 to the nearest hundred so the answer is 4300.

Answer:

4300

Step-by-step explanation:

Answer: Another factor is 3x + 5.

Step-by-step explanation:

please view the attachment for the steps.

The other factor of the polynomial (6x² + x - 15) would be (3x + 5). Hence option 2 is true.

Given that the polynomial is,

6x² + x - 15

And, The polynomial has a factor of 2x - 3.

Now apply the factorization method to solve for the  factor,

6x² + x - 15

6x² + (10 - 9)x - 15

6x² + 10x - 9x - 15

2x (3x + 5) - 3 (3x + 5)

(2x - 3) (3x + 5)

Since The polynomial has a factor of 2x - 3.

Hence, the other factor would be (3x + 5). So option 2 is true.

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Answer:

0

Step-by-step explanation:

A six-sided die has the numbers 1, 2, 3, 4, 5, and 6, not 7. And even is 7 was on there the probability would be 1/6 whihc is approximently 0.167 which is about 0.2 so the probability is 0.

The probability of rolling a seven is 0.

The probability of an event occurring is defined by probability.

The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Given:

A single six-sided die is rolled.

So, the Sample space is= (1, 2, 3, 4, 5, 6}

As, there is no possibility of getting number 7 on the dice.

Hence, the probability of rolling a seven is 0.

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Answer:

13.8 minutes

Step-by-step explanation:

If 3 liters came out it would take 2 minutes

if 4.5 liters came out it would take 3 minutes

Therefor the time is the volume divided by the rate

20.7 / 1.5 = 13.8

13.8 minutes

Answer:

T = 50 + 30w

Step-by-step explanation:

Hope this helps :)

Answer:

T = 40 + 20w

Step-by-step explanation:

The initial amount is 50 and the rate per week is 30.

Step-by-step explanation:

1)1/2,1/5 and 0

2)In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

1/8

The probability of getting a head or a tail when flipping a coin is 1/2.  

Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.

The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.

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Answer:

4k + 13

Step-by-step explanation:

Base Expression: 8(2 - k) - 3(1 - 4k)

Step 1 - Distribution:

The values in the parenthesis must be simplified -

This is done simply by distributing the value in front of the parenthesis (8) into each of the values in the parenthesis (2 and -k).

The 8 is multiplied into the 2 giving us 16

The 8 is multiplied into the -k giving us -8k

Now we are left with 16 - 8k - 3(1 - 4k).

The same distribution must now be done on the other values in the parenthesis as well -

Again, the value in front of the parenthesis (-3) must be multiplied with the values inside the parenthesis (1 - 4k)

The -3 is multiplied into the 1 giving us -3

The -3 is multiplied into the -4k giving us 12k

Now our expression is 16 - 8k - 3 + 12k

For no reason other than simplicity, let's move the values around so they are easier to add and subtract:

16 - 8k - 3 + 12k  --->  16 - 3 + 12k - 8k

(no arithmatic is done here, but it is important to preserve the signs of all the values when moving them around)

From here we simply subtract the values to fully simplify the expression:

16 - 3 = 13

12k - 8k = 4k

4k + 13 is the final and most simplified expression of the original expression (without knowing the value for k)

P.S.: 13 + 4k is also technically correct, but, it's most often proper ettiquite (and often the simplest) to put more complex monomials (numbers) first in the expression.

Ex: 2x² + 6x + 8 rather than 8 + 2x² + 6x.

Hope this was comprehensive and helpful, good luck!

The final answer for df/dt is: df/dt = 4[(∛((t²+t+ln(11))/4))³ - (4/(3∛((t²+t+ln(11))/4) + 16))] + \(3e^(sin(t)t)(tcos(t) + 1)\)

To find df/dt using the chain rule, we need to compute the partial derivatives of f with respect to x, y, and z, as well as the derivatives of x(t), y(t), and z(t) with respect to t.

Starting with the partial derivatives of f:

∂f/∂x = 3x²y - (3/(3x + 4y))

∂f/∂y = x³ - (4/(3x + 4y))

\(∂f/∂z = 3te^zx\)

Next, we need to compute the derivatives of x(t), y(t), and z(t) with respect to t:

dx/dt = 0 (since x is not a function of t)

dy/dt = 4

dz/dt = cos(t)

Now we can use the chain rule to find df/dt:

df/dt = (∂f/∂x)(dx/dt) + (∂f/∂y)(dy/dt) + (∂f/∂z)(dz/dt)

Substituting in the partial derivatives and derivatives we calculated earlier, we get:

df/dt = (3x²y - (3/(3x + 4y)))(0) + (x³ - (4/(3x + 4y)))(4) +\((3te^zx)(cos(t))\)

Substituting the expressions for x, y, and z in terms of t, we get:

df/dt = (3(4t)²(x(t)) - (3/(3x(t) + 4(4t))))(0) + ((x(t))³ - (4/(3x(t) + 4(4t))))(4) + \((3te^(sin(t)t))(cos(t))\)

Finally, substituting the expression for f in terms of t, we get:

df/dt = (3(4t)²(x(t)) - (3/(3x(t) + 4(4t))))(0) + ((x(t))³ - (4/(3x(t) + 4(4t))))(4) + \((3e^(sin(t)t))(tcos(t) + 1)\)

where x(t) = ∛((t²+t+ln(11))/4)

Therefore, the final answer for df/dt is:

df/dt = 4[(∛((t²+t+ln(11))/4))³ - (4/(3∛((t²+t+ln(11))/4) + 16))] +\(3e^(sin(t)t)(tcos(t)\) + 1)

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Answer:

Area of trapezoid = 200 m²

Step-by-step explanation:

Parallel side1 a= 15m

Parallel side2 b= 25m

Perpendicular distance h = 10 m

We need to find area of the trapezoid.

The formula used to find area of the trapezoid is: \(Area \ of \ trapezoid=\frac{a+b}{2}h\)

Putting values and finding area of the trapezoid:

\(Area \ of \ trapezoid=\frac{a+b}{2}h\\Area \ of \ trapezoid=\frac{15+25}{2}\times 10\\Area \ of \ trapezoid=40\times5\\Area \ of \ trapezoid=200 \ m^2\)

So, area of trapezoid = 200 m²

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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Answer: 10 cm

Step-by-step explanation:

o=candle one. t=candle two. h=hours

5/6=5/6 cm per hour for o(candle one).

o=15-5h/6

t=25-5h/2

o=t

15-5h/6=25-5h/2

-5h/6=10-5h/2

(-5h/6=10-5h/2)*6

-5h=60-5h*6/2

-5h=60-30h/2

-5h=60-15h

10h=60

h=6

o=15-5h/6

o=15-5(6)/6

o=15-5

o=10 cm

Answer: 256

Step-by-step explanation:

that is just gonna be 16 x 16 which is 256

Answer:

16x2=32

Step-by-step explanation:

Multiple 16 twice, then you get 32!

Answer:

Right angle

Step-by-step explanation:

There are only three angles

Answer:

answer: 37

Step-by-step explanation:

Isosceles triangles are triangles with two sides of equal length so sense we know triangles add up to 180 we just have to do 180 - 106 = 74 so now we just divide by 2 so 74 ÷ 2 = 37 so our two angle our 37 degrees! Hope that helps you!

As a result, on a graph of dP/dt vs P, the curve would be concave down for P b/a and concave up for P > b/a. The curve would reach its maximum when P = b/a, with dP/dt equal to zero.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

The equation dP/dt = aP² - bP represents the rate of change of the population P over time t.

When dP/dt is positive, the population is increasing. When dP/dt is negative, the population is decreasing.

To find when dP/dt is positive and negative, we need to find the critical points where dP/dt = 0.

Solving the equation dP/dt = aP² - bP = 0, we get:

aP² - bP = 0

aP(P - b/a) = 0

This equation has two solutions: P = 0 and P = b/a.

For P < b/a, dP/dt is negative (the population is decreasing). For P > b/a, dP/dt is positive (the population is increasing).

So, on a graph of dP/dt against P, the curve would be concave down for P < b/a and concave up for P > b/a. At P = b/a, the curve would have a maximum and dP/dt = 0.

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Answer:I think CBD

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

-3x²-12x is your answer

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

If the temperature increases then it gets hotter so the outcome is that more people would go to a water park .

- the hotter it gets,the more people

Answer:

Step-by-step explanation:

1/2x - y = 8

1/2x = 8 + y

2(1/2x = 8 + y)

x = 16 + 2y

Answer: 120

Step-by-step explanation:

Since Angle formed at the center is equal to the angle measure of its opposite arc

⇒ ∠AOD = 104°

Also, The angle formed in the segment is half the angle formed at the center of the circle

⇒ ∠DOB = 2 × ∠BAD

⇒ ∠DOB = 2 × 68°

⇒ ∠DOB = 136°

Now, ∠AOB = 360 - ∠BOD + ∠AOD

⇒ ∠AOB = 360 - 136 - 104

⇒ ∠AOB = 120°

Now, Angle formed at the center is equal to the angle measure of its opposite arc

⇒ b = ∠AOB

⇒ b = 101°

Hence, the correct option is 120°

The combination of X and Y that yields the optimum solution for the given linear programming (LP) problem is option b. (5,6).

In linear programming, the objective is to maximize or minimize a linear function subject to a set of constraints. In this problem, we have two constraints: 30X + 10Y >= 300 and 21X + 7Y >= 147. The objective function is to maximize 15X + 12Y.

To find the optimum solution, we need to graph the feasible region defined by the constraints and identify the corner points. These corner points represent the potential solutions.

By solving the equations for the constraints, we find the following corner points: (0,30), (5,6), and (14,0). Plugging these points into the objective function, we obtain the following values:

- (0,30): 15(0) + 12(30) = 360

- (5,6): 15(5) + 12(6) = 135 + 72 = 207

- (14,0): 15(14) + 12(0) = 210

Among these corner points, the combination (5,6) yields the highest value of 207. Therefore, option b. (5,6) is the solution that maximizes the objective function and satisfies all the constraints.

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