A circle with radius r is inscribed into a right triangle. Find the perimeter of the triangle if the length of the hypotenuse is 24 cm and r=4 cm;

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:

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:

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

[tex]y \geqslant \frac{1}{4} x - 1[/tex]

EXPLANATION

The graph has a solid boundary line.

The region above the boundary line is shaded

Therefore the inequality sign involved is '≥'

The boundary line has equation

[tex]y = \frac{1}{4} x - 1[/tex]

We can now conclude that, the inequality graphed above is

[tex]y \geqslant \frac{1}{4} x - 1[/tex]

Answer:

The answer is

Step-by-step explanation:

The inequality in the  graphed above is y≥1/4x-1

Answer:

  d. Distributive property

Step-by-step explanation:

The Distributive property of multiplication over addition is what allows you to multiply each of the terms in parentheses by the factor outside parentheses. It tells you ...

  a(b +c) = ab + ac

It works both ways, also allowing you to remove a common factor to outside parentheses.

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]

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:

-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:

sin of 52 is 0.98662759204

cos of 47 is 0.99233546915

Step-by-step explanation:

Answer:

6x is indeed the Greatest Common Factor.

Step-by-step explanation:

6x[3 - y² + 2y⁶]

Answer:

D)

y > x + 4

y ≥ -3x - 2

Step-by-step explanation:

Blue line's boundary is above the line and dotted (>) so the equation: y > x + 4

Red line's boundary is above the line and solid (≥) so the equation: y ≥ -3x - 2

Answer

D)

y > x + 4

y ≥ -3x - 2

Answer:

D

Step-by-step explanation:

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

Hello There!

Martha’s first step would represent “Associative Property Of Addition”

This basically means that you can add or multiply these numbers regardless of how they are grouped in a sequence.

Check the picture below.

make sure your calculator is in Degree mode.

Answers:

#1: A

#2:C

#4:D

Answer:the answer is C

Step-by-step explanation:

Answer:

in the US, yes

in some other English-speaking countries, no

Step-by-step explanation:

"Standard form" depends on where you live. In the UK, the "standard form" of a quadratic equation is what is called "vertex form" in the US. That form is ...

3(x +1/3)^2 +29/3 = 0

In the US, the equation you show is in standard form.

Answer:

A

Step-by-step explanation:

The average rate of change is the change in attendance over change in time.

Δy / Δx

(333.7 - 298.3) / (5 - 2)

11.8

So the average rate of change is an increase of 11.8 thousand people per year.

The average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7

It is defined as the change in values of a dependent variable with respect to the independent variables.

We have to find the average rate of change from Year 2 to Year 5:

At year 2 the attendance = 298.3

At year 5 the attendance = 333.7

Average rate of change = (333.7-298.3)/(5-2)

= 11.8

Thus, the average rate of change from Year 2 to Year 5 is 11.8 if at year 2 the attendance is 298.3 and at year 5 the attendance is 333.7

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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:

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:

  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.

[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:

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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Answer:

  b ≈ 3.1

Step-by-step explanation:

The law of sines tells you ...

  b/sin(B) = c/sin(C)

Here, you have to find angle C based on the sum of the angles of a triangle being 180°.

 C = 180° - A - B = 180° - 69° - 32° = 79°

Multiplying the above law of sines equation by sin(B), you have ...

  b = c·sin(B)/sinc(C) = 5.7·sin(32°)/sin(79°) ≈ 3.07707

  b ≈ 3.1 . . . . . rounded to tenths

Answer:

[tex]\displaystyle 3,1 ≈ b[/tex]

Step-by-step explanation:

First, find [tex]\displaystyle m∠C,[/tex]accourding to the Triangle-Sum Theorem:

[tex]\displaystyle 180° = 32° + 69° + m∠C \hookrightarrow 180° = 101° + m∠C; 79 = m∠C[/tex]

Now that we have all three angles, we can solve for edge b

[the second edge], using the Law of Sines:

[tex]\displaystyle \frac{c}{sin∠C} = \frac{b}{sin∠B} = \frac{a}{sin∠A} \\ \\ \frac{5,7}{sin\:79°} = \frac{b}{sin\:32°} \hookrightarrow 3,0770743283... = \frac{5,7sin\:32°}{sin\:79°} \\ \\ 3,1 ≈ b[/tex]

I am joyous to assist you at any time.

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:

$33.00

Step-by-step explanation:

You find out how much the sale price is by subtracting 25% of 40 from 40:

40 - [(.25)(40)] and that equals 30.  So the sale price is $30.  Now if the tax is 10% (.1 in decimal form), we find the total cost by adding .1(30) to 30:

30 + [(.1)(30)] which is $33

B is correct. I’ve noticed that you’ve posted a lot of questions like this, so here’s how I remember it. Soh-Cah-Toa

Soh stands for Sin=Opposite (the side opposite to the angle) over hypotenuse (the side opposite to the right angle)

Cah stands for Cos=Adjecent (the side next to the angle that is not the hypotenuse) over the hypotenuse

Toa stands for Tan=opposite over adjacent

Good luck! Hope I helped you understand.

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

[tex]16\pi \: sq.in[/tex]

EXPLANATION

The area of a sector is calculated using the formula,

[tex]Area = \frac{arc \: measure}{360 \degree} \times \pi {r}^{2} [/tex]

The arc measure is given as 45°

The radius of the circle is 8 inches.

We substitute to obtain,

[tex]Area = \frac{45 \degree}{360 \degree} \times \pi \times {8}^{2} [/tex]

[tex]Area = \frac{1}{4} \times 64\pi = 16\pi[/tex]

The answer is:

The correct option is the second option:

[tex]SectorArea=8\pi in^{2}[/tex]

To answer the question, we need to calculate the total area of the circle (which corresponds to 360°) and then, calculate the equivalent area to the sector of the arc that measures 45°

Calculating the total area, we have:

[tex]TotalArea=\pi radius^{2} \\\\TotalArea=\pi 8^{2} =64\pi in^{2}[/tex]

Now, we need to consider that the calculated area (total area) correspondes to all 360° that conforms the interior angle of a circle, now, if we want to calculate the area that represents a sector of the arc that measures 45°, we have to use the following formula:

[tex]SectorArea=\frac{360\°}{45\° }*TotalArea\\\\SectorArea=\frac{45\°}{360\° }*64\pi in^{2}=\frac{1}{8} *64\pi in^{2}\\\\SectorArea=8\pi in^{2}[/tex]

Hence, we have that the correct option is the second option:

[tex]SectorArea=8\pi in^{2}[/tex]

Have a nice day!