A common tangent is

segment CD
segment ST
segment RU

Answer:

4!=4 x 3 x 2 x 1=24

So the answer is 24.

Answer:

24 ways.

Step-by-step explanation:

If i have n different trophies to arrange on top shelf of a book case then the number of ways in which we can arrange the trophies will be

     = n!

When n = 4

Then number of ways in which we can arrange the books

= 4!

= 4 × 3 × 2 × 1

= 24

Therefore, answer is 24 ways.

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

sin of 52 is 0.98662759204

cos of 47 is 0.99233546915

Step-by-step explanation:

ANSWER

[tex]12y \sqrt{3} [/tex]

EXPLANATION

The given expression is

[tex]\sqrt{3y^2} + 4\sqrt{12y^2} - y\sqrt{75}[/tex]

We identity and remove the perfect squares to obtain

[tex]y\sqrt{3} + 16y\sqrt{3} - 5y\sqrt{3}[/tex]

We now observe that, the three terms are all similar.

We combine the similar terms to get:

[tex]y\sqrt{3} + 16y\sqrt{3} - 5y\sqrt{3} = 12y \sqrt{3} [/tex]

Answer:

4y square root of 3

Step-by-step explanation:

Answer:

No real solution

Step-by-step explanation:

There is no perfect squares in 50

ANSWER

[tex]x = \pm5\sqrt{2} [/tex]

EXPLANATION

The given equation is:

[tex]50 - {x}^{2} = 0[/tex]

Group the constant term to get:

[tex]- {x}^{2} = 0 - 50[/tex]

[tex] - {x}^{2}=- 50[/tex]

[tex]{x}^{2}=50[/tex]

Take square root to get:

[tex]x = \pm \sqrt{50} [/tex]

We simplify further to remove the perfect square.

[tex]x = \pm \sqrt{25 \times 2} [/tex]

[tex]x = \pm \sqrt{25} \times \sqrt{2} [/tex]

[tex]x = \pm5\sqrt{2} [/tex]

Answer:

The function that this scenario represents is:

[tex]P(x) = 5(4) ^ x[/tex]

Step-by-step explanation:

The initial number of foxes was 5. The following year they had

year 1: [tex]5 * (4) = 20[/tex] foxes

year 2: [tex]5 * 4 * (4) = 80[/tex] foxes

year 3: [tex]5 * 4 * 4 * (4) = 320[/tex] foxes

year x: [tex]5 * 4 ^ x[/tex] foxes

Then the equation that models the situation is an equation of exponential growth. Where P(x) is the population of foxes in year x.

So:

[tex]P(x) = 5(4) ^ x[/tex]

Answer:

78

Step-by-step explanation:

The tricky part of this is figuring out how to assign the unknowns.  We are told that we are working with two consecutive even integers.  Consecutive means "next to" or "in order" and sum means to add.  If we use 2 and 4 as examples of our 2 consecutive even integers and assign x to 2, then in order to get from 2 to 4 we have to add 2.  So the lesser of the 2 integers is x, and the next one in order will be x + 2.  (2 and 4 are just used as examples; they mean nothing to the solving of this particular problem.  You could pick any 2 even consecutive integers and find the same rule applies.  All we are doing here with the example numbers is finding a rule for our integers.)  Now we have the 2 expressions for the integers, we will add them together and set the sum equal to 158:

x + (x + 2) = 158

The parenthesis are unnecessary since we are adding, so when we combine like terms we get

2x + 2 = 158 and

2x = 156 and

x = 78

That means that the lesser of the 2 integers in 78, and the next one in order would be 80, and 78 + 80 = 158

Answer:

2A + (2A +2)  = 158

4A = 156

A= 39

2A = 78 and (2A + 2) = 80

Answer is A

Step-by-step explanation:

Answer:

30,000           5,000        400      10.    7

----------              ----

XXX                   V                CD.     X     VII

The question appears to be a misunderstanding as the number '35,417' is already represented as numerals, which are symbols used to denote numbers. Therefore, '35,417' is already in its correct numeral form.

The student is asking for the number '35,417' to be written in numerals but it is already written in numerals. Numerals are symbols used to represent numbers. For example, the numeral for the number one is 1, and the numeral for the number two is 2. Therefore, the numeral representation for '35,417' is simply 35,417.

The question appears to be a misunderstanding as the number '35,417' is already represented as numerals, which are symbols used to denote numbers. Therefore, '35,417' is already in its correct numeral form.

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Answer: 56

Step-by-step explanation:

4=(a+b-24)/2

32=a+b

32+24=56

Answer:

The perimeter of the triangle is 56 cm.

Step-by-step explanation:

Given:

The length of the hypotenuse is 24 cm

Radius of the circle r=4 cm

To Find:

The perimeter of the triangle=?

Solution:

Let us see the below diagram representing situation.  

Here, first we have drawn the radius of circle perpendicular to the sides of triangle,

We have Taken PB = 4 because, it is a side of square formed there, and we take OC as x.

Then, QC also becomes x as they are tangents from single point, so they are equal.

Now, AQ becomes 24 – x as AC is 24 according to given information.

So, perimeter = AB + BC + CA  

Perimeter = (24 – x + 4) + (4 + x) + (24 – x + x)

Perimeter = 28 – x + 4 + x + 24  

Perimeter = 28 + 28 = 56

Hence, the perimeter of the triangle is 56 cm.

Answer:

-7x+3y+3

Step-by-step explanation:

(4-5+4)=3

(-2x-5x)=-7x

(-4y+7y)=3y

For this case we must simplify the following expression:

[tex]4-5-2x-4y + 4-5x + 7y[/tex]

We must combine similar terms, taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the greater is placed:

[tex]4-5 + 4-2x-5x-4y + 7y =\\3-7x + 3y[/tex]

Answer:

[tex]3-7x + 3y[/tex]

Answer:

I think 478.4   ._.

Step-by-step explanation:

First, find out how many gallons of gasoline she can buy with $18.50 by dividing 18.50 by 1.25 to get 14.8 gallons. Then, since he already has 6 gallons in his tank, add 6 to 14.8 = 20.8. Finally multiply this by the ratio of gallons to miles (23) to get 478.4

Answer:

42.4

Step-by-step explanation:

1) use this formula of Area of the triangle:

[tex]A=\frac{1}{2} a*b*sin(a,b)[/tex]

2) using the formula described above:

A=0.5*14*11*0.55≈42.4 (mm²)

Answers:

#1: A

#2:C

#4:D

Answer:

  tan(∠B) = 2

Step-by-step explanation:

In a right triangle, the relationships of the tangents of the acute angles is ...

  tan(∠B) = cot(∠A) = 1/tan(∠A)

For tan(∠A) = 0.5, this means ...

  tan(∠B) = 1/0.5 = 2

Answer:the answer is C

Step-by-step explanation:

Call these numbers [tex]x,y[/tex]. Then [tex]x+y=7[/tex] or [tex]y=7-x[/tex].

We want to maximize their product,

[tex]f(x,y)=xy\implies f(x,7-x)=F(x)=7x-x^2[/tex]

We could consider the derivative, but I think that's overkill. Instead, let's complete the square:

[tex]7x-x^2=-\left(x^2-7x+\dfrac{49}4\right)+\dfrac{49}4=\dfrac{49}4-\left(x-\dfrac72\right)^2[/tex]

whose graph is a parabola opening downward with vertex at [tex]\left(\dfrac72,\dfrac{49}4\right)[/tex], so that the maximum product is [tex]\dfrac{49}4[/tex].

Now if [tex]x=\dfrac72[/tex], it follows that [tex]y=7-\dfrac72=\dfrac72[/tex].

The two numbers that have the maximum possible product and a sum of 7are 3.5 and 3.5

Let the two number be x and y

If the sum of the numbers is 7, then;

x + y = 7 ........................ 1

If their product is at maximum, then;

xy = P ............................. 2

From equation 1, y = 7 - x

Substitute into equation 2 to have:

x(7-x) = P
P = 7x - x²

If the function is at maximum, then;

dP/dx = 7 - 2x
0 = 7 - 2x
x = 7/2
x = 3.5

Recall that x + y = 7
x = 7 - y
x = 3.5

Hence the two numbers are 3.5 and 3.5

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Answer:

a) see your problem statement for the explanation

b) 2.54539334183

Step-by-step explanation:

(b) Many graphing calculators have a derivative function that lets you define the Newton's Method iterator as a function. That iterator is ...

  x' = x - f(x)/f'(x)

where x' is the next "guess" and f'(x) is the derivative of f(x). In the attached, we use g(x) instead of x' for the iterated value.

Here, our f(x) is ...

  f(x) = 3x^4 -8x^3 +6

An expression for f'(x) is

  f'(x) = 12x^3 -24x^2

but we don't need to know that when we use the calculator's derivative function.

When we start with x=2.545 from the point displayed on the graph, the iteration function g(x) in the attached immediately shows the next decimal digits to be 393. Thus, after 1 iteration starting with 4 significant digits, we have a result good to the desired 6 significant digits: 2.545393. (The interactive nature of this calculator means we can copy additional digits from the iterated value to g(x) until the iterated value changes no more. We have shown that the iterator output is equal to the iterator input, but we get the same output for only 7 significant digits of input.)

___

Alternate iterator function

If we were calculating the iterated value by hand, we might want to write the iterator as a rational function in Horner form.

  g(x) = x - (3x^4 -8x^3 +6)/(12x^3 -24x^2) = (9x^4 -16x^3 -6)/(12x^3 -24x^2)

  g(x) = ((9x -16)x^3 -6)/((12x -24)x^2) . . . . iterator suitable for hand calculation

The equation must have a root in the interval [2, 3] based on the Intermediate Value Theorem. Newton's method can be used to approximate the root to six decimal places.

To show that the given equation must have a root in the interval [2, 3], we use the Intermediate Value Theorem. The function f(x) = 3x4 − 8x3 + 6 is continuous on [2, 3], and f(2) < 0 while f(3) > 0. Therefore, by the Intermediate Value Theorem, there must be a number c in the interval (2, 3) such that f(c) = 0. This implies that the equation 3x4 − 8x3 + 6 = 0 has a root in the interval [2, 3].

To approximate the root of the equation using Newton's method, we start with an initial guess, let's say x0 = 2.5. We iterate using the formula xi+1 = xi - f(xi)/f'(xi) until we obtain the desired level of accuracy. By repeating this process, we can approximate the root of the equation correct to six decimal places.

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Answer:

YES

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Only perfect squares can be rational numbers. the square root of 80 is the only one that is not a perfect square.

D. Square Root of 80

Answer:

C. 7  1/2 pounds; 120 ounces

Step-by-step explanation:

I'll assume you wanted to write each loaf weighs 1 and 1/4 (1.25) pounds  and not 114 pounds... since that makes sense considering the choices for answer.

So, to get the total weight of the 6 loafs, we multiply by 6 the weight of one...

TP = 6 * 1.25 = 7.5 or 7 1/2 pounds

To get that in ounces, we just have to remember there are 16 ounces per pound... so

TO = 7.5 lbs * 16 ounces/lbs = 120 ounces

Answer:

y = 650·0.922^t

Step-by-step explanation:

At the end of each year, 92.2% of the amount at the beginning of the year remains. That is, the beginning amount is multiplied by 0.922. The exponent t in 0.922^t tells how many times (years) that multiplication has taken place. At the end of t years, the amount remaining in milligrams (y) is ...

y = 650·0.922^t

Answer:

90

Step-by-step explanation:

10x - x = 81

9x = 81

x = 9

larger number = 10 x 9 = 90

For this case we have that "x" is the variable that represents the smallest number to find. Let and the variable that represents the largest number, then:[tex]y = 10x\\y-x = 81[/tex]

Substituting the first equation in the second:

[tex]10x-x = 81\\9x = 81\\x = \frac {81} {9}\\x = 9[/tex]

So, the biggest number is:

[tex]y = 10 * 9 \\y = 90[/tex]

Answer:

10x

90

Answer:

distance

Step-by-step explanation:

Usually the absolute value of a complex number is called its magnitude. The squared magnitude is the algebraic quantity that's preferable to work with.

Let

[tex]z = a+bi[/tex]

[tex]|z|^2 = z^* z = zz^* = |a+bi|^2= (a+bi)(a-bi) = a^2 - i^2 b^2 = a^2+b^2[/tex]

[tex]|a+bi| = \sqrt{a^2+b^2}[/tex]

That's the distance from the origin to (a,b)

The absolute value of any complex number a + bi is the distance from (a, b) to (0, 0) in the complex plane.

This is a number which is in the form of a + bi in which a and b are expressed as real numbers.

|a + bi| = √a²+b² depicts the magnitude which therefore expresses the distance from the origin.

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Answer:

8 guppies

Step-by-step explanation:

Let:

x = number of goldfishes

y = number of guppies

We can come up with two equations:

x + y = 26

3x +4y = 86

We use the first equation to come up with a solution for one of the unknowns:

x = 26 - y

We can use this to substitute the x on the second equation:

[tex]3x + 4y = 86\\\\3(26-y) + 4y=86\\\\78 - 3y + 4y = 86\\\\78 + y = 86\\\\y = 86 - 78\\\\y = 8[/tex]

So she bought 8 guppies.

The total guppies Samantha buys are 8 and the total goldfish she buys are 18 and this can be determined by forming the linear equation.

Given :

Let the total number of goldfish be 'x' and the total number of guppies be 'y'. Then the linear equation that represents the total number of fish is given by:

x + y = 26  

x = 26 - y   ---- (1)

The linear equation that represents the total spent $86 is given by:

3x + 4y = 86    --- (2)

Now, substitute the value of 'x' in equation (2).

3(26 - y) + 4y = 86

Simplify the above equation.

78 - 3y + 4y = 86

y = 86 - 78

y = 8

Now, substitute the value of 'y' in equation (1).

x = 26 - 8

x = 18

So, Samantha buys 8 guppies.

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[tex]\bf \textit{Double Angle Identities} \\\\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ \boxed{1-2sin^2(\theta)}\\ 2cos^2(\theta)-1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ cos(2\theta )+sin^2(\theta )=0\implies \boxed{1-2sin^2(\theta)}+sin^2(\theta )=0 \\\\\\ 1-sin^2(\theta )=0\implies 1=sin^2(\theta )\implies \pm\sqrt{1}=sin(\theta ) \\\\\\ \pm 1=sin(\theta )\implies sin^{-1}(\pm 1) = \theta \implies \theta = \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}[/tex]

To solve the equation cos(2θ) + sin^2(θ) = 0 using a double- or half-angle formula, rewrite the equation and combine like terms to simplify.

To solve the equation cos(2θ) + sin^2(θ) = 0 using a double- or half-angle formula, we can rewrite the equation as:

2cos^2(θ) - 1 + sin^2(θ) = 0

Using the identity sin^2(θ) = 1 - cos^2(θ), we can substitute and simplify:

2cos^2(θ) - 1 + (1 - cos^2(θ)) = 0

Combining like terms, we have:

-cos^2(θ) + cos^2(θ) = 0

This simplifies to:

0 = 0

Since 0 = 0 is a true statement, the equation is satisfied for all values of θ within the interval [0, 2π).

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Answer:

  [4, ∞)

Step-by-step explanation:

The vertex of the upward-opening quadratic is (0, 4), so the function will take on values of 4 or more. The range is 4 to infinity, inclusive of 4.

Answer:

  a.  {(5, 0.6)}

Step-by-step explanation:

A graph is a useful tool. It can help you find that the set of points that satisfies both functions is ...

  {(5, 0.6)}

_____

Comment on the graph

Strictly speaking, the points connecting the dots of the second function are not part of the function. They are there simply to provide a visual aid in locating the points. As we see, the line goes through point (5, 0.6) exactly.

Answer:

The rectangle has the greater area

Is area is [tex]2\ cm^{2}[/tex] greater

Step-by-step explanation:

we know that

The area of rectangle is equal to

[tex]A=(6)*(4\frac{1}{2})=(6)*(\frac{9}{2})=27\ cm^{2}[/tex]

The area of the square is equal to

[tex]A=5^{2}=25\ cm^{2}[/tex]

therefore

The rectangle has the greater area

Find the difference

[tex]27\ cm^{2}-25\ cm^{2}=2\ cm^{2}[/tex]

Is area is [tex]2\ cm^{2}[/tex] greater

Step-by-step explanation:

[tex](4x - 2).6(2x + 7) \\ = (4x - 2)(12x + 42) \\ = 48 {x}^{2} + 168x - 24x - 84 \\ = 48 {x}^{2} + 144x - 84[/tex]

then

[tex]a = 48 \\ b = 144 \\ c = - 84[/tex]

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &radians\\ \cline{1-2} r=&10\\ \theta =&\frac{2\pi }{3} \end{cases}\implies s=10\left( \cfrac{2\pi }{3} \right)\implies s=\cfrac{20\pi }{3}\implies s\approx 20.94[/tex]

Answer:

C

Step-by-step explanation: