A circle centered at $A$ with a radius of $1$ and a circle centered at $B$ with a radius of $4$ are externally tangent. A third circle is tangent to the first two and to one of their common external tangents as shown. What is the radius of the third circle

Answer:

-2/3x + y = -7

Step-by-step explanation:

So, y = 2/3x - 7 is the slope-intercept equation. Now, we need to turn it into the standard equation of a slope.

Standard equation --> Ax + By = C

y = 2/3x - 7

-2/3x     -2/3x

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

-2/3x + y = -7 --> this is your equation in standard slope form.

Answer:

-2/3x + y = -7  is.

Part A:  the perimeter of the enlarged garden is 15.36 meters.

A) The new length of the garden will be:

5.4 meters x 1.2 = 6.48 meters

The new width of the garden will be:

1.5 meters x 1.2 = 1.8 meters

The perimeter of the enlarged garden will be:

2(6.48 meters) + 2(1.8 meters) = 15.36 meters

Part B:

The original area of the garden is:

5.4 meters x 1.5 meters = 8.1 square meters

The new area of the garden will be:

6.48 meters x 1.8 meters = 11.664 square meters

The increase in area will be:

11.664 square meters - 8.1 square meters = 3.564 square meters

the area of the garden will increase by 3.564 square meters.

what is area?

In mathematics, the area is a measurement of the size of a two-dimensional region or surface, typically expressed in square units. It is the amount of space inside a closed shape or a surface, and is calculated by multiplying the length and width or height of the shape or surface.

The units used to express area can vary depending on the context and the system of measurement being used. For example, in the metric system, the most commonly used units for area are square meters (m²) and square centimeters (cm²), while in the imperial system, the most commonly used units are square feet (ft²) and square inches (in²).

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Answer:

\( d = sin(39) \times 30\)

The derivatives of the given functions with respect to x are as follows:

i) For y = \(ln(x^4 + 3x^2 + 6)\), the derivative is dy/dx = \((4x^3 + 6x)/(x^4 + 3x^2 + 6)\).

This is obtained using the chain rule and the derivative of ln(u) = (1/u)(du/dx).

ii) For y =\(2x - 12x^2 - x +\)4, the derivative is dy/dx = 2 - 24x - 1. This is obtained by taking the derivative of each term separately, as the derivative of a constant is zero and the derivative of \(x^n is nx^(n-1)\).

iii) For y = \(4(x^2 - 4x + 6)^3\), the derivative is dy/dx = 1\(2(x^2 - 4x + 6)^2(2x - 4)\). This is obtained using the chain rule and the power rule, where the derivative of \((u^n) = n(u^{n-1})(du/dx)\).

In summary, the derivative of \(ln(x^4 + 3x^2 + 6)\) with respect to x is \((4x^3 + 6x)/(x^4 + 3x^2 + 6)\). The derivative of \(2x - 12x^2 - x + 4\) with respect to x is 2 - 24x - 1. The derivative of\(4(x^2 - 4x + 6)^3\) with respect to x is \(12(x^2 - 4x + 6)^2(2x - 4)\).

i) The derivative of \(ln(x^4 + 3x^2 + 6\)) is obtained by applying the chain rule. The derivative of ln(u) is (1/u)(du/dx), where \(u = x^4 + 3x^2 + 6\). By finding the derivative of u with respect to x and substituting it into the chain rule formula, we get\((4x^3 + 6x)/(x^4 + 3x^2 + 6)\).

ii) The derivative of \(2x - 12x^2 - x + 4\) is obtained by taking the derivative of each term separately. The derivative of 2x is 2, the derivative of \(-12x^2 is -24x\) (using the power rule), and the derivative of -x is -1. The derivative of a constant term is zero. Combining these derivatives, we get dy/dx = 2 - 24x - 1.

iii) The derivative of \(4(x^2 - 4x + 6)^3\) is obtained using the chain rule and the power rule. We first apply the power rule by multiplying the exponent (3) by the expression inside the parentheses, resulting in \((x^2 - 4x + 6)^2\). Then, using the chain rule, we multiply by the derivative of the expression inside the parentheses, which is 2x - 4. Combining these results, we get dy/dx = \(12(x^2 - 4x + 6)^2(2x - 4).\)

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The median is greater than the mean. From the shape of the distribution, the data set has more values on the left, so we can say it is skewed to the left. In every distribution that is skewed to the left, the median is always greater than the mean.

In the given chart we can deduce the following;

These numbers can be listed as follows;

5, 6, 7, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12

The median of these numbers is calculated as;

\(median = \frac{9+ 10}{2} = 9.5\)

The mean of these numbers is calculated as;

\(mean = \frac{5+6+7+8+9+9+9+10+10+10+10+11+11+12}{14} = 9.07\)

Thus, the median is greater than the mean.

Also, from the shape of the distribution, the data set has more values on the left, so we can say it is skewed to the left. In every distribution that is skewed to the left, the median is always greater than the mean. But if the distribution is skewed to the right, the mean is always greater than the median.

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If event a and event b cannot occur at the same time, then events a and b are said to be a. mutually exclusive.

Probability and Statistics are two basic concepts in the branch of Mathematics. Probability is all about the likelihood of an event, whereas statistics is more about how we handle various data using different techniques.

By using probability and statistics, you can process complex data in a way that is very easy to understand.

Probability is one of the topics that often comes up when discussing statistics. The reason is, this one theory is commonly used when trying to predict something.

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The best answer that describes the meaning of the multiplicities next to the number 1 in the preceding diagram is: the number 1 represents the solution that repeats thrice.

A multiplicity is a mathematical concept used to describe the number of times a value appears as a root of a polynomial equation. The number of times a specific value appears as a root of a polynomial is referred to as the multiplicity of that value.

In the given diagram, the number 1 represents the solution of the equation x = 1. The multiplicities of the number 1 are represented by the number 3.

Therefore, the number 1 has a multiplicity of 3. This means that the solution of the equation x = 1 repeats thrice. This can be better understood by looking at the graph of the equation.

The graph of the equation x = 1 is a vertical line that intersects the x-axis at 1.

Since the equation has a multiplicity of 3, the vertical line intersects the x-axis three times.

This means that the point (1, 0) occurs three times on the graph. This is shown in the diagram as three dots along the x-axis.

Therefore, the meaning of the multiplicities next to the number 1 in the preceding diagram is that the number 1 represents the solution that repeats thrice.

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Answer:

1.b

2.a

3.c

4.a

5.a

6.c

7.b

8.a

9.c

Step-by-step explanation:

please mark as brainliest!!!!

hope this helps

Answer:

a = 3

Step-by-step explanation:

2 + \(\frac{2a}{3}\) = 4

\(\frac{2a}{3}\)  = 4 - 2

\(\frac{2a}{3}\)  = 2

2a = 2 x 3

2a = 6

a = 3

The equation that represents h(x) is h(x) = (f(x))(g(x)).

To determine which equation represents h(x), we need to analyze the given table and understand the relationship between the functions f(x), g(x), and h(x).

Since h(x) represents the output values obtained by multiplying f(x) and g(x), we should look for values in the table where h(x) is the product of the corresponding values of f(x) and g(x).

Let's examine the table and compare the values:

x | f(x) | g(x) | h(x)

1 | 3 | 4 | 12

2 | 5 | 2 | 10

3 | 2 | 6 | 12

From the table, we can see that the values in the h(x) column are the products of the corresponding values in the f(x) and g(x) columns. Therefore, the equation that represents h(x) is h(x) = (f(x))(g(x)).

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Answer:

It's B.

Step-by-step explanation:

Edge 2020.

Step-by-step explanation:

REFER TO THE ATTACHMENT!!

HOPE IT WILL HELP YOU

Answer:

my answer is 11.4

Step-by-step explanation:

solve for the first triangle which has both sides then solve the other

Answer: 1:35

Step-by-step explanation:

Just go and hour back from 2:30 and add 5 minutes

Answer:

1:35

i subtracted at a 1 back from 2:30 -5 minutes which would be 1:35 sorry if i confused you

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\( { - a}^{3} . {b}^{3} = ( { - a \times b})^{3} = ( { - ab})^{3} \\ \)

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The number of pet owners who owned a cat but not a dog is 57.

Here, we are given that a survey was conducted of 126 pet owners.

Let A = people who own a dog

A = 27

B = people who own a cat

B = 78

Thus, the people who own both a cat and a dog will be depicted as-

A ∩ B which is given to be 21

Now, here-

B = people who own only a cat + people who own both a cat and a dog

Thus, we get the following equation-

78 = people who own only a cat + 21

people who own only a cat + 21 = 78

people who own only a cat = 78 - 21

= 57

Thus, the number of pet owners who owned a cat but not a dog is 57.

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The derivative of f(x) = cos(x² - x) is \(3(2x - 1)cos(x^{2} - x)sin(x^{2} - x).\)

To find the derivative of the function f(x) = cos(x² - x), we can use the chain rule.

The chain rule states that if we have a composite function, such as cos(g(x)), the derivative of this composite function is given by the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is cos(u), where u = x² - x, and the inner function is u = x² - x.

The derivative of the outer function cos(u) is -sin(u).

To find the derivative of the inner function u = x² - x, we apply the power rule and the constant rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1), and the constant rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

Applying the power rule and the constant rule, we find that the derivative of u = x² - x is du/dx = 2x - 1.

Now, using the chain rule, the derivative of f(x) = cos(x² - x) is given by:

df/dx = \(-sin(x^{2} - x) * (2x - 1)\)

Simplifying, we have:

df/dx = -\(2xsin(xx^{2} - x) + sin(x^{2} - x)\)

Therefore, the correct answer is option a. 3(2x-1)cos(x²-x)sin(x²-x).

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Answer:

Sample response:

Both inequalities use the division property to isolate the variable, y. When you divide by a negative number, like –7, you must reverse the direction of the inequality sign. When you divide by a positive number, like 7, the inequality sign stays the same. The solution to the first inequality is y > -23, and the solution to the second inequality is y <>

Answer:

47

Step-by-step explanation:

Hey There!

So remember all of the angles in a triangle will add up to equal 180

So to find the missing angle we subtract the given angles (65 and 68) from 180

180-65-68-47

so we can conclude that the measure of the missing angle is 47

Answer:

Step-by-step explanation:

Step one:

for Tyson

P=$2500

rate= 5.75%= 0.0575

time t= 6years

The compound interest formula is

A=P(1+r)^t

A=2500(1+0.0575)^6

A=2500(1.0575)^6

A=2500*1.3985

A=3496.25

Tyoson Earned $3496.25

Step two:

for Ariana

P=$2500

rate= 5.75%= 0.0575

time t= 6years

the simple interest formula is

A=P(1+rt)

A=2500(1+0.0575*6)

A=2500(1+0.345)

A=2500(1.0345)

A=3362.5

Ariana earned  $3362.5

The difference in their earnings is

=3496.25-3362.5

=$133.75

Answer:

D

Step-by-step explanation:

38+(-18) can be changed to 38-18 and the answer will still be the same

The absolute maximum and absolute minimum values of f on the given interval f(t) = 2 cos (t) + sin (2t), [0, π/2] is 3√3/2 and 0 respectively.

Given :Y = 2cost + sin2t

differentiate wrt t

dy/dt = -2sint +2cos2t = 0

sint = cos2t = 1 - 2sin²t

2sin²t + sint -1 = 0

2sin²t + 2sint - sint - 1 = 0

2sint (sint +1 ) -(sint+1) = 0

sint = 1/2 and -1

but  t € [ 0, π/2 ] so, sint = 1/2 = sinπ/6

t = π/6

again, differentiate wrt t

d²y/dt² = -2cost -4sin2t

put t = π/6

d²y/dt² = -2× √3/2 - 4×√3/2 < 0

hence, d²y/dt² < 0

So, at t = π/6 function gain, Maxima

now,

f(0) = 2cos(0) +sin2(0) = 2

f(π/6) = 2cos(π/6) + sin2(π/6) = 3√3/2

f(π/2) = 2cos(0) + sin2(π/2) = 0

hence , absolute maximum = 3√3/2

and absolute minimum = 0

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Step-by-step explanation:

because because if we solve for m in the first equation then the answer is -8 and from second equation the answer is also - 8 that's why the answer is yes

Answer:

\(\Large \boxed{\sf Yes}\)

Step-by-step explanation:

First equation:

\(m+3=-5\)

Subtract 3 from both sides

\(m+3-3=-5-3\)

\(m=-8\)

Second equation:

\(m-4=-12\)

Add 4 to both sides

\(m-4+4=-12+4\)

\(m=-8\)

m = -8  for both equations, therefore both equations are equivalent

The volume of the cylnder is  9,728.5 ft³

For a cylinder of radius R and height H, the volume is given by:

V = pi*R^2*H

Where pi = 3.14

Here we know that the height is.

H = (20 + 1/2) ft = 20.5 ft

And the diameter is (1 + 1/5) times the height, then:

D = (1 + 1/5)*(20 + 1/2) ft = (1.2)*(20.5)ft = 24.6ft

And the radius is half of that, so:

R = 12.3ft

Then the volume is:

V = 3.14*(12.3ft)^2*20.5ft = 9,728.5 ft³

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The answer is $6.93. Hope it helped.

Answer:

z=25

Step-by-step explanation:

(3+5)^2+[8-11]+z=4(z-2)

(8)^2 +3+z=4z-8

square 8

add 8 to both sides

mines z from both sides

64+3+8=3z

75=3z

25=z

\(a_{n+1}=a_n+n\)

The formatting was a bit confusing, so please do let me know if this isn't the correct equation for the sequence.

The first term is given, which is

\(a_1=-9\)

Now, use the equation for the next terms:

\(a_{1+1}=a_2=-9+1=-8\)

\(a_{2+1}=a_3=-8+2=-6\)

\(a_{3+1}=a_4=-6+3=-3\)

Thus, the first 4 terms are -9, -8, -6, and -3. Let me know if you need any clarifications, thanks!

To solve the expression (42 + 20) ÷ 4 - 2 · (9 ÷ 3) - 2 · [18 + 3 · (13 - 9) - 5], we follow the hierarchy of operations known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

By applying this hierarchy, we can simplify the expression step by step to find the result.

Following the hierarchy of operations, we start by simplifying expressions within parentheses and brackets.

First, within the brackets, we evaluate the expression (13 - 9) which equals 4. Therefore, [18 + 3 · (13 - 9) - 5] becomes [18 + 3 · 4 - 5].

Next, we evaluate the multiplication within the brackets: 3 · 4 equals 12. Thus, [18 + 3 · 4 - 5] simplifies to [18 + 12 - 5].

Moving outside the brackets, we proceed with addition and subtraction: 18 + 12 equals 30, and 30 - 5 equals 25. Therefore, [18 + 12 - 5] becomes 25.

After simplifying the brackets, we can now evaluate the remaining expression: (42 + 20) ÷ 4 - 2 · (9 ÷ 3) - 2 · 25.

Within the parentheses, we perform addition: 42 + 20 equals 62. Thus, the expression becomes 62 ÷ 4 - 2 · (9 ÷ 3) - 2 · 25.

We continue by evaluating the division: 62 ÷ 4 equals 15.5. The expression now becomes 15.5 - 2 · (9 ÷ 3) - 2 · 25.

Next, we perform the division within the parentheses: 9 ÷ 3 equals 3. The expression becomes 15.5 - 2 · 3 - 2 · 25.

Finally, we evaluate the remaining multiplications: 2 · 3 equals 6, and 2 · 25 equals 50. The expression becomes 15.5 - 6 - 50.

Continuing with the subtraction, we have 15.5 - 6 equals 9.5. Therefore, the final result of the expression (42 + 20) ÷ 4 - 2 · (9 ÷ 3) - 2 · [18 + 3 · (13 - 9) - 5] is 9.5.

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The question is to solve the differential equation x'=2(100-x)

or, dx/dt=200- 2x

or, ∫dx/(200-2x) = ∫dt.  Now, put 200-2x=z. Or, -2dx=dz.

substituting the variables, we get

-(1/2)∫dz/z= dt

or, -(1/2) ㏑z= t + ㏑c

or, ln z= -(2t+ 2*㏑c)

or, z= (1/c²)*exp(-2t) substituting the value of x in z and 1/c²=c1

x= (200- c1* exp(-2t))/2  putting c1/2=c2

or, x= 100- (c2*exp(-2t)).

x(0) =80 or, 100-80= c2 or, c2=20

so, x= 100- (20*exp(-2t))

now x(t)=40, or, 40=100- (20*exp(-2t))

or, 60/20= exp(-2t)

or, ㏑3=-2t

or, t= -0.54

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Once we have established that all three angles are congruent and all three sides are proportional, we can conclude that the two triangles are similar.

To prove that the two triangles are similar, we need to show that all three angles are congruent, and all three sides are proportional.

We know that angle N is congruent to angle Q, but we need to find additional information to prove that the triangles are similar. One possible piece of information could be the length of one side or the ratio of two sides.

If we know the ratio of the lengths of two corresponding sides in the two triangles, we can use that information to show that all three sides are proportional.

Alternatively, if we know the length of one side in both triangles, we can use the angle-angle similarity theorem to show that all three angles are congruent.

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