Triangle ABC is similar to triangle DEF. What is the value of x ?

log(6, 216) - log(6, 17)

To write log base 6 of 216 as a difference of logarithms, we can apply the Quotient Property of Logarithms. According to this property, the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator.

In this case, we have log base 6 of 216 divided by 17. By applying the Quotient Property, we can express this as the difference of two logarithms: log base 6 of 216 minus log base 6 of 17.

Now, let's simplify if possible. We can further evaluate the logarithms using the fact that log base a of b is equal to the exponent to which we must raise a to obtain b. In other words, log base a of b is the power to which we raise a to get b.

Therefore, log base 6 of 216 can be simplified as the exponent to which we raise 6 to obtain 216, which is 3. Similarly, log base 6 of 17 can be simplified as the exponent to which we raise 6 to obtain 17, which is less than 3.

Hence, the simplified expression becomes 3 - log base 6 of a number less than 6.

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Given information

Length AB = 6m

Breadth BC = 4m

The area of PQRS is  twice the area of ABCD

Firstly find the area of rectangle ABCD

Area of ABCD= Length × Breadth

Area of ABCD= 6 × 4

Area of ABCD = 24 m²

We know that the area of rectangle PQRS is twice the area of rectangle  ABCD so we simply double the area of rectangle ABCD

24m² × 2 = 48m²

We need to find 2 numbers which when multiplied give 48 however the 2 numbers that are chosen must be the same amount greater that the lengths of ABCD and divisible by 2 because the path is uniform.

8 × 6 = 48

8 - 6 = 2

6 - 2 = 2

Therefore the length of PQ is 8m and the length of QR is 6m

Answer:

Pretty sure it's 2:30 P.M.

Step-by-step explanation:

If her track practice started at 12:00 P.M., and and ran relays for one hour, it would already be 1:00 P.M.

Then she practiced the long jump for an hour and thirty minutes. Add another hour to that and it would be 2:00 P.M. Add thirty minutes, and it would be 2:30 P.M.

Hopefully that makes sense to you

Answer:

the answer is 1.258

Answer:

1.258

Step-by-step explanation:

Answer:

y=3/2x+3

Step-by-step explanation:

Answer:

y=3/2x+3

Step-by-step explanation:

Answer:

Step-by-step explanation:

5^1

Answer:

1) Distribute 1.2 to 6.3 and -7x

2)Combine 3.5 and 7.56

3)Subtract 11.06 from both sides

Step-by-step explanation:

3.5 + 1.2(6.3 - 7x) = 9.38

Distribute 1.2 to 6.3 and -7x

3.5 + 1.2* 6.3 - 1.2 * 7x = 9.38

        3.5 + 7.56 - 8.4x = 9.38

Combine 3.5 and 7.56

11.06 - 8.4x = 9.38

Subtract 11.06 from both sides

11.06 - 8.4x -11.06 = 9.38 - 11.06

                    -8.4x = -1.68

To find solution:

Divide both sides by (-8.4)

-8.4x/-8.4 = -1.68/-8.4

 x = 0.02

Answer:

B, D, and E

its right cus i took the test soo..

The change represents a growth and the percentage rate of increase is 3%.

Mathematically, an equation which can be used to model an exponential growth rate is given by this mathematical expression:

A(t) = P(1 + r)^{t}

Where:

Based on the exponential functions provided above, we can reasonably infer and logically deduce that the required exponential growth rate function is given by;

y = 65(1.03)^x

1 + r = 1.03

r = 1.03 - 1

Rate of change, r = 0.3 or 3%.

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(a) The differential equation that is satisfied by y is:

\(\frac{dy}{dt} = ky(1-y)\)

(b) To solve the differential equation, we separate the variables and integrate both sides:

\(\frac{dy}{y*(1-y)} = k*dt\)

Integrating both sides, we get:

\(\frac{lnly}{1-y} = k*t +c1\)

where C1 is an arbitrary constant of integration.

We can rewrite the equation in terms of y:

\(\frac{y}{1-y} = e^{(k*t+c1)}\)

Multiplying both sides by (1-y), we get:

\({y} = e^{(k*t+c1)} *(1-y)\)

\(y= \frac{C}{(1+(c-1)e^{-kt} }\)

where C = y(0) is the initial fraction of the population who have heard the rumor.

(c) In this case, the initial fraction of the population who have heard the rumor is y(0) = \(\frac{100}{1300}\) = 0.077. At noon, half the town has heard the rumor, so y(4) = 0.5.

Substituting these values into the equation from part (b), we get:

\(0.5= \frac{0.077}{1+(0.777-1) e^{-k4} }\)

Solving for k, we get:

\(k= ln(\frac{12.857}{4} )\)

Substituting this value of k into the equation from part (b), and setting y = 0.9 (since we want to find the time at which 90% of the population has heard the rumor), we get:

\(0.9= \frac{0.077}{1+(0.777-1) e^{-ln(12.857}*\frac{t}{4} }\))

Solving for t, we get:

t = 8.7 hours after the beginning (rounded to one decimal place)

A differential equation is a mathematical equation that relates a function to its derivatives. It is a powerful tool used in many fields of science and engineering to describe how physical systems change over time. The equation typically includes the independent variable (such as time) and one or more derivatives of the dependent variable (such as position, velocity, or temperature).

Differential equations can be classified based on their order, which refers to the highest derivative present in the equation, and their linearity, which determines whether the equation is a linear combination of the dependent variable and its derivatives. Solving a differential equation involves finding a function that satisfies the equation. This can be done analytically or numerically, depending on the complexity of the equation and the available tools.

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The value of x is 4.47 units

In the given figure, there are two right angle triangle, to find the value of x we have to solve each triangle using the Pythagorean theorem.

Consider the bottom triangle

Base of the triangle = 6 units

The hypotenuse of the triangle = 9 units

Apply the Pythagorean theorem

The third side of the triangle = \(\sqrt{9^2-6^2}\)

= \(\sqrt{81-36}\)

= \(\sqrt{45}\) units

Similarly consider the top triangle

The base of the triangle = 5 units

The hypotenuse of the triangle = \(\sqrt{45}\) units

The third side of the triangle = \(\sqrt{\sqrt{45}^2- 5^2}\)

= \(\sqrt{45-25}\)

= \(\sqrt{20}\)

= 4.47 units

Hence, the value of x is 4.47 units

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Answer:

(c) is correct.

Step-by-step explanation:

When two lines cross each other, the angles opposite to each other are called vertically opposite angles. They are always equal.

In this given figure,

Line TW and RU cross each other at Q, it means

\(\angle RQW=\angle TQU\) (vertically opposite angles)

Hence, the correct option is (c).

Matilda and Nancy are 60 miles apart and are both bicycling towards each other on the same road. This scenario implies that they are initially at a distance of 60 miles from each other.

As they cycle towards each other, the distance between them decreases over time. Suppose Matilda is at a point A and Nancy is at a point B on the road. Initially, the distance between A and B is 60 miles.

As they cycle towards each other, the distance between A and B decreases by a certain amount for each unit of time. Eventually, they will meet at a point C on the road where the distance between A and C is zero.

The exact time it takes for them to meet depends on their respective speeds and the rate at which they are closing the distance between them.

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Answer:

x=9

Step-by-step explanation:

to find ×=-intercept/zero substitute y=0 0=-3x+27

move the variable to find the left hand side and change its sign 3x=27

divide both sides of the equation by 3x=9

Answer:

( − ∞ , − 5 ) ∪ ( 5 , ∞ )

Step-by-step explanation:

have a good day uwu

Answer:

B

Step-by-step explanation:

B

Answer:

The answer is B.

Step-by-step explanation:

Plz mark as brainliest I only have one and need 4 more to reach the next rank. If you would, that would help me greatly.

\(9-\underline{9\div 9} + 9 - \underline{9 \div 9}\implies 9-\underline{1}+9-\underline{1}\implies 8+9-1\implies 17-1\implies 16\\\)

recall PEMDAS, MD are before AS, and both are performed from left to right.

Answer:

20

Step-by-step explanation:

first lets apply PEMDAS

\(9 - (9 \div 9) + 9 - (9 \div 9) \)

9 ÷ 9 = 1

1 × (-) = -1

9-(-1)= 10

( than do the same for other side )

and than you get

\(10 + 10\)

the answer is 20

Answer:

f = 3

g = -1

h = 6

r = 18

Step-by-step explanation:

Box 1

f(x) = \(2x^{4}\)-\(12x^{3}\)+\(16x^{2}\)+4x+15 with x = 3

f(3) = \(2(3^{4)}\) - \(12(3^{3} )\) + \(16(3^{2})\)+ 4(3) + 15

Reorder

Evaluate

Multiply

3f = 2 x 81 - 12 + 27 +16 x 9 + 12 +15

3f = 162 - 324 + 144 + 12 + 15

3f =  9

3  ÷  3

f = 3

Box 1

g(x) = \(3x^{3}\) - \(16x^{2}\) - 7x - 36 with x = 6

g(6) = \(3(6^{3} )\) - \(16(6^{2})\) - 7(6) - 36

g6 = 3 x 216 - 576 - 42 - 36

g6 = -6

6   ÷ 6

g = -1

Box 2

h(x) = \(5x^{3}\) - \(2x^{2}\) - 3 with x = -1

h(-1) = \(5(-1^{3} )\) - \(2(-1^{2})\) -3

h-1 = -5 + 2 -3

h-1 = -6

-1    ÷  - 1

h = -6

Box 2

r(x) = \(4x^{4}\) - \(9x^{2}\) + 5x - 2 with x = 2

r(2) = \(4(2^{4} )\) - \(9(2^{2} )\) + 5(2) - 2

r2 = 64 - 36 + 10 - 2

r2 = 36

2   ÷  2

r = 18

So, there are 20 different mix-and-match plates that can be created by combining one savory and one sweet dish from Alejandra's Tapas Bar's menu.

To determine the number of different mix-and-match plates that can be created from Alejandra's Tapas Bar's menu, we need to calculate the number of options for both the savory and sweet dishes and then multiply them together.
Let's assume that there are 5 savory dishes and 4 sweet dishes on the menu. To create a mix-and-match plate, we need to choose one savory and one sweet dish. The number of options for the savory dish is 5, and the number of options for the sweet dish is 4. Therefore, the total number of different mix-and-match plates that can be created is:
5 x 4 = 20
Customers can choose any combination they like and can enjoy a unique dining experience each time they visit the restaurant.

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Answer:

68

Step-by-step explanation:

let the angleAGF be y

then,

y+22=90

y=90-22

y=68

y=x(being vertically oppsite angle

Answer:

16 cm, 63 cm, 65 cm

Step-by-step explanation:

Because those side lengths are to big to make a right triangle

Answer:

18

Step-by-step explanation:

9 divided by 1/2

9 is a whole number

1 is the numerator and 2 is the denominator

To put it in fraction form multiple 9 x 2 over 1

Which equals 18/1

18 divided by 1 is 18

Answer:

18

Step-by-step explanation:

If you meant, what is the quotient of 9 ÷ 1/2 we get:

\(9/\frac{1}{2}=\\\\9*\frac{2}{1}=\\\\\frac{18}{1} =\\\\18\)

The erosion occurs at a rate of 2/1000 m/years. Over 1,000,000 years, the erosion will be 2,000 meters.

Rate is a ratio between one quantity to another quantity. Rate is also a measure of how fast a quantity changes when another quantity changes. For instance, velocity is a rate to measure the change of distance per amount of travelled time.

Suppose we have two quantities: x and y, with rate of change in y per change in x is denoted by dy/dx, then

y = dy/dx · x

In the given problem:

y = length of erosion

t = time

dy/dt = 2 meters / 1000year = 2/1000 meters/year

Then,

y = dy/dt · t

  = 2/1000 · 1,000,000 = 2,000 meters

Hence, over  1,000,000 years, the regional erosion = 2,000 meters

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Answer:

Options A and Option B

Step-by-step explanation:

All four sides AX, IX, IS and AS of the base are common in the four side walls of the prism.

In other words, edge AX is common in planes AXU and AXS,

Edge XI is common in planes XIB and AXS,

Edge SI is common in planes EBS and AXS,

Edge AS is common in planes CEA and AXS.

Therefore, plane AXS is intersecting planes AXU and EBS.

Options A and Option B are the correct options.

The correct answer is option D. We can be 95% confident that the sample proportion is captured by the confidence interval.

The margin of error of plus or minus three percentage points at a 95% confidence level means that the true proportion of people who jog regularly in the population is estimated to be between 15% and 21%. We can be 95% confident that the true proportion of people who jog regularly falls within this interval.

Therefore, option B is correct. Option A is incorrect because it implies that the margin of error always holds true for any sample size, which is not the case. Option C is incorrect because it presents a range of values for the population, not for the estimate. Option E is incorrect because it refers to the proportion of samples that would find the same sample proportion, not the range of values within which the true proportion lies.

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