A circle has a circumference of approximately 113.04 inches. What is the diameter and the radius of the circle.

Answer:

Step-by-step explanation:By AA similarity postulate

△ADB∼△ABC∼△BDC

therefore the sides of the triangles are proportional, in particular

ADAB=ABAC ACBC=BCDC

By algebra we have the following equations

AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC

this is the same as

AD⋅AC=AB2AC⋅DC=BC2

"Equals added to equals are equal" allows us to add the equations

AD⋅AC+AC⋅DC=AB2+BC2

By distributive property

AC(AD+DC)=AB2+BC2

but by construction AD+DC=AC.

Substituting we have

AC⋅AC=AB2+BC2

this is equivalent to

AB2+BC2=AC2

which is what we wanted to prove

The Pythagorean theorem uses similar triangles, This is equivalent to AB^2+BC^2=AC^2.

We have given that,

the converse of the Pythagorean theorem using similar triangles.

The converse of the Pythagorean theorem states that when the sum of the squares of the links of the legs of the triangle equals the shared length of the hypotenuse, the triangle is a right triangle.

[tex]hypotenuse ^2=side^2+side^2[/tex]

By AA similarity postulate

△ADB∼△ABC∼△BDC

Therefore the sides of the triangles are proportional, in particular

ADAB=ABAC  ACBC=BCDC

By algebra, we have the following equations

AD⋅AC=AB⋅ABAC⋅DC=BC⋅BC

This is the same as

AD⋅AC=AB^2AC⋅DC=BC^2

Equals added to equals are equal allows us to add the equations

AD⋅AC+AC⋅DC=AB^2+BC^2

By distributive property

AC(AD+DC)=AB^2+BC^2

but by construction AD+DC=AC.

Substituting we have

AC⋅AC=AB^2+BC^2

This is equivalent to

AB^2+BC^2=AC^2

Hence the proof.

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Answer:

d is the answer i believe

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

From the graph you can see that y changes from -2 to 2, so the range of the function is [tex][-2,2].[/tex]

Since the range of the functions [tex]y=\cos x[/tex] and [tex]y=\sin x[/tex] is [tex][-1,1][/tex] and the range of the functions [tex]y=k\cos x[/tex] and [tex]y=k\sin x[/tex] is [tex][-k,k],[/tex]  we can state that the correct option is  C: [tex]f(t)=-2\cos 3t.[/tex]

Check the value at t=0:

[tex]f(0)=-2\cos 3\cdot 0=-2\cos 0=-2.[/tex]

hope it helps you!!!!!!!!!!!!!!

Answer:

12.62

Step-by-step explanation:

you divide 3 by 8, then add the quotient of that to 3, then subtract that from 16

Answer:

Givens

First, we need to the number of pages dedicated to advertisements.

Let's transform the mixed number into a fraction

[tex]3\frac{3}{8}=\frac{27}{8}[/tex]

Now, let's multiply this fraction with the number of pages

[tex]\frac{27}{8} \times 16= 54[/tex]

That is, there are 54 pages dedicated to advertisements.

Pages without advertisements are 5/8, which is

[tex]\frac{5}{8} \times 16=5(2)=10[/tex]

The statement that best describes the domain and range of p(x) and q(x) is:

             p(x) and q(x) have the same domain and the same range.

We are given a function p(x) as:

[tex]p(x)=6-x[/tex]

AS the function is a polynomial function.

Hence it is defined everywhere for all the real values.

Hence, the domain of the function p(x) is: All  Real numbers.

and the range of the function p(x) is: All the real numbers.

and the function q(x) is given by:

[tex]q(x)=6x[/tex]

which is also a polynomial function.

Hence, it also has the same domain and range.

Domain and range are specific sets for each function. For given case, p(x) and q(x) have the same domain and range.

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

The domain and range of given functions are:

For any real number value of x, p(x) just takes 6-x(negates the input and add 6 to it), thus, its always defined, and thus, its domain is all real numbers.

Since p = 6-x is possible to go negatively infinite and positively infinite and always continuous, thus, its range is all real numbers(all numbers are possible as its output)

We can prove the above statement. Let some real number T is not in the range of p(x). But we have T = 6-x => x = 6-T which is a real number, thus, for input 6-T, there is output T. Thus, its a contradiction, and thus, all real numbers are in range of p(x).

Thus,

Its scaling all numbers. All numbers can be multiplied by 6 and produce a valid result. Thus, its domain is all real numbers.

Suppose that we've T as a real number. Then we can get this as output if we put input as x = T/6 (since then 6x = 6(T/6) = T)

Thus, all real numbers are in its output set, thus, its range is all real numbers.

The Range of q(x): [tex]x \in \mathbb R[/tex] and Domain of q(x): [tex]x \in \mathbb R[/tex]

Hence, for given case, p(x) and q(x) have the same domain and range.

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Answer:

its D

Step-by-step explanation:

The answer is:

C. 1.556.

[tex]csc(40\°)}=1.556[/tex]

To solve the problem using our calculator we need to set it to "Degree" mode in order to avoid miscalculations.

Also, we need to remember that the cosecant (csc) is the inverse function of the sine, so:

[tex]csc(40\°)=\frac{1}{sin(40\°)} =\frac{1}{0.6427}=1.556[/tex]

Hence, the answer is C. 1.556.

Have a nice day!

Answer:

  -8

Step-by-step explanation:

Let n represent the number. The stated relationship is ...

  5n -(-10) = -30

  5n = -40 . . . . . . . add -10

  n = -8

The number is -8.

Final answer:

To solve the equation given in the student's question, convert the operation of subtracting a negative number into addition, subtract 10 from both sides to isolate the term with x, and then divide by 5 to find that the number in question is -8.

Explanation:

The student's question is a linear algebra problem, which can be turned into a simple equation to find the unknown number.

According to the question, we multiply a number by five and then subtract a negative ten to get a difference of negative thirty.

Mathematically, this can be expressed as the equation 5x - (-10) = -30, and we can solve for x. First, we should simplify the equation by turning the subtraction of a negative number into an addition. This makes our equation 5x + 10 = -30.

To find the value of x, we then subtract 10 from both sides of the equation, which gives us 5x = -40.

Finally, we divide both sides by 5 to solve for x, leading us to an answer of x = -8.

Answer:

  30%

Step-by-step explanation:

24 of (40 +24 +16) = 3/10 of the turkey sandwiches were made with wheat bread. As a percentage, that is ...

  3/10 = 30/100 = 30%

Answer:

The minimum number of boxes needed is [tex]4[/tex] and the cost is [tex]\$10.40[/tex]

Step-by-step explanation:

step 1

Find the cost of one box

by proportion

[tex]\frac{5}{13}=\frac{1}{x}\\ \\x=13/5\\ \\x=\$2.60[/tex]

step 2

Find the number of boxes for 48 ounces of pasta

by proportion

[tex]\frac{1}{12}=\frac{x}{48}\\ \\x=48/12\\ \\x=4\ boxes[/tex]

step 3

Find the cost of 4 boxes

we know that

The cost of one box is [tex]\$2.60[/tex]

so

The cost of 4 boxes is

[tex]\$2.60(4)=\$10.40[/tex]

Final answer:

To determine the cost for 48 ounces of pasta, one must calculate the cost per box and multiply by the number of boxes required to reach 48 ounces. The cost for the needed 4 boxes is $10.40.

Explanation:

The cost of one box of pasta is calculated by dividing the total cost of the pasta by the number of boxes. Since the total cost of 5 boxes of pasta is $13, to find the cost per box, we divide $13 by 5, which is $2.60 per box. To find the cost of the minimum number of boxes needed to total 48 ounces of pasta, we then determine how many boxes are needed. Since each box contains 12 ounces of pasta, we need 48 ounces / 12 ounces per box = 4 boxes of pasta. Finally, we multiply the number of boxes by the cost per box, which is 4 boxes × $2.60 per box = $10.40.

Answer: last option.

Step-by-step explanation:

To apply the Distributive property, remember that:

[tex]c(a-b)=ca-cb[/tex]

Then, applying this, you get:

[tex]-4(x - 2) - 3x = 2(5x - 7) + 6\\\\(-4)(x)+(-4)(-2)-3x=(2)(5x)+(2)(-7)+6\\\\-4x+8-3x=10x-14+6[/tex]

Combine like terms means that you need to add the like terms.

Therefore, you get:

[tex]-7x+8=10x-8[/tex]

You can observe that the expression obtained matches with the expression provided in the last option.

Answer: Second Option

"the summation of 880 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is 1,173"

Step-by-step explanation:

We know that infinite geometrical series have the following form:

[tex]\sum_{i=1}^{\infty}a_1(r)^{n-1}[/tex]

Where [tex]a_1[/tex] is the first term of the sequence and "r" is common ratio

In this case

[tex]a_1 = 880\\\\r=\frac{1}{4}[/tex]

So the series is:

[tex]\sum_{i=1}^{\infty}880(\frac{1}{4})^{n-1}[/tex]

By definition if we have a geometric series of the form

[tex]\sum_{i=1}^{\infty}a_1(r)^{n-1}[/tex]

Then the series converges to  [tex]\frac{a_1}{1-r}[/tex]   if [tex]0<|r|<1[/tex]

In this case [tex]r = \frac{1}{4}[/tex] and [tex]a_1=880[/tex]  then the series converges to [tex]\frac{880}{1-\frac{1}{4}} = 1,173.3[/tex]

Finally the answer is the second option

Answer:

The number of people in the group must divide 40. 8 is the only selection that divides 40.

Considering the factors of 40 for even distribution of the slips of paper, 8 people can be fairly included in the group as 8 is a factor of 40. The correct answer is option b) 8.

To determine how many people could be in the group when forty slips of paper numbered 1 through 40 are distributed, and a random number generator selects a single number from this range, we need to consider the factors of 40. Each person must get at least one slip of paper, and the distribution needs to be equal to maintain fairness. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. However, the only possible numbers of people in the group, given by the options, are 6, 8, 12, and 15. Out of these, 8 is a factor of 40, meaning the slips of paper can be distributed evenly among 8 people.

Thus, the correct answer to the student's question is option b) 8.

Answer: Is it 169? i think that wright maybe.

Answer: 530.92916

Step-by-step explanation:

A=πr2=π·132≈530.92916

The formula of the surface area of a cube is 6 x s²

→ s = 9

→ s² = 9²

→ s² = 81

→ 6 x 81 = 486

So, the surface area of the cube is 486 units².

Answer:

The negative solution is between -3 and -2

The positive solution is between 11 and 13

Step-by-step explanation:

we have

[tex]0=x^{2} -10x-27[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2} -10x-27=0[/tex]  

so

[tex]a=1\\b=-10\\c=-27[/tex]

substitute in the formula

[tex]x=\frac{10(+/-)\sqrt{-10^{2}-4(1)(-27)}} {2(1)}[/tex]

[tex]x=\frac{10(+/-)\sqrt{208}} {2}[/tex]

[tex]x=\frac{10(+)\sqrt{208}} {2}=12.21[/tex]

[tex]x=\frac{10(-)\sqrt{208}} {2}=-2.21[/tex]

therefore

The negative solution is between -3 and -2

The positive solution is between 11 and 13

Answer:

Negative solution is between -3 and -2

Positive solution is between 12 and 13

Step-by-step explanation:

With

[tex]\vec r(t)=4t\,\vec\imath+6t\,\vec\jmath-t^2\,\vec k[/tex]

we have

[tex]\mathrm d\vec r=(4\,\vec\imath+6\,\vec\jmath-2t\,\vec k)\,\mathrm dt[/tex]

The vector field evaluated over this parameterization is

[tex]\vec f(x,y,z)=\vec f(x(t),y(t),z(t))=4t\,\vec\imath+t^2\,\vec\jmath+6t\,\vec k[/tex]

so the line integral is

[tex]\displaystyle\int_{-1}^1(4t\,\vec\imath+t^2\,\vec\jmath+6t\,\vec k)\cdot(4\,\vec\imath+6\,\vec\jmath-2t\,\vec k)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_{-1}^1(16t+6t^2-12t^2)\,\mathrm dt=-4[/tex]

To evaluate the line integral c f · dr, substitute the values of r(t) into f(x, y, z) to get a new vector function f(t). Find the derivative of r(t) using the chain rule. Take the dot product of f(t) and r'(t) and integrate the result with respect to t over the given bounds.

To evaluate the line integral c f · dr, we need to find the dot product of the vector function f and the derivative of r(t). Since c is given by r(t) and the bounds are -1 ≤ t ≤ 1, we can substitute the values of r(t) into f(x, y, z) and compute the dot product.

Compute the integral to find the final answer.

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Answer:

A. at (8,7) the maximum value is 98

Step-by-step explanation:

First draw the region, that is bounded by all inequalities. This is the triangle with vertices (6,1), (2,5) and (8,7).

Now you can see where the line f(x,y)=7x+6y intersect this region. The maximum value will be at endpoints of this region:

Thus, the maximum value of the function is 98 at the point (8,7).

For this case we must find the area of the figure composed of a triangle and a rectangle.

Triangle area:

[tex]A_ {t} = \frac {b * h} {2}[/tex]

Where b is the base and h is the height.

Area of the rectangle:

[tex]A_ {r} = a * b[/tex]

Where a and b are the sides.

The base of the triangle measures:

[tex]13-5 = 8[/tex]

We find the height by trigonometry:

[tex]tg (45) = \frac {h} {b}\\1 = \frac {h} {b}\\b = h[/tex]

So:

[tex]A_ {t} = \frac {8 * 8} {2}\\A_ {t} = 32 \ ft ^ 2[/tex]

On the other hand:

[tex]A_ {r} = 5 * 8\\A_ {r} = 40 \ ft ^ 2[/tex]

Thus, the total are the sum:

[tex](32 + 40) ft ^ 2 = 72 \ ft ^ 2[/tex]

Answer:

Option A

Option is A~ the answer is A

Answer:

2 2/3 cups of sugar

Step-by-step explanation:

If your ratio is 3 flour to 4 sugar, and you use 2 cups of flour, set up your proportion as follows:

[tex]\frac{3}{4}=\frac{2}{x}[/tex]

Cross multiply to get 3x = 8 and x = 8/3 which is 2 and 2/3 cups of sugar.

The cups of sugar used is 3/2 corresponding to 2 cups of flour.

If we are using the ratio of 3 flour to 4 sugar.

We have 2 cups of flour.

Let us consider the amount of sugar be 'y'.

By writing the proportion /as follows:

[tex]\frac{3}{4} = \;\frac{2}{y}[/tex]

4y =6

y =3/2

Thus, the amount of sugar used is 3/2.

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Answer:

25

Step-by-step explanation:

The radius of the circle, which is the perpendicular bisector of a 48-inch diameter kitchen breakfast bar template, is 30 inches. The correct option is C).

Let's break down the information given in the problem:

PQ is the perpendicular bisector of VW, and Q is the midpoint of VW. This means that PQ passes through the center of the circle.

The length of PQ (perpendicular bisector) is 18 inches.

VW is 48 inches in diameter, which means its radius is half of that, i.e., 48 inches / 2 = 24 inches.

Since PQ is the radius of the circle, and it is also the perpendicular bisector of VW, it divides VW into two equal parts, each measuring 24 inches (as VW has a diameter of 48 inches, and Q is the midpoint).

Now, we have a right-angled triangle, with PQ as the hypotenuse and two legs measuring 18 inches and 24 inches. We can use the Pythagorean theorem to find the length of PQ (the radius of the circle):

PQ² = 18² + 24²

PQ² = 324 + 576

PQ² = 900

PQ = √900

PQ = 30 inches

So, the radius of the circle is 30 inches.

The correct answer is option c) 30 inches.

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Answer:

[tex]7\sqrt[11]{x^{5}}[/tex]

Step-by-step explanation:

we know that

[tex]a^{\frac{n}{m}}=\sqrt[m]{a^{n}}[/tex]

In this problem we have

[tex]7x^{\frac{5}{11}}[/tex]

therefore

[tex]7x^{\frac{5}{11}}=7\sqrt[11]{x^{5}}[/tex]

Answer:

ABCD is an isosceles trapezoid.

Step-by-step explanation:

The line AB will be horizontal (parallel to the x axis), because the y values are both 3. It is 9--2 = 11 units long.

CD is also parallel to the  x axis because the y values of C and D are both 6. Itis 5 - 2 = 3 units long.

The x values of the four points are all different so ABCD is a trapezoid.

Let's check the lengths of the line segments AC and BD:

AC = √((5--2)^2 + (6-3)^2 = √58.

BD =  √((9-2)^2 + (3-6)^2 = √58.

They are equal in length so:

ABCD is an isosceles trapezoid.

I believe it is 60 but I’m not sure

[tex]\bf -\cfrac{5}{1-cos(-x)}\implies -\cfrac{5}{\underset{\textit{symmetry identity}}{1-cos(x)}}\impliedby \begin{array}{llll} \textit{let's multiply top/bottom}\\ \textit{by the conjugate 1+cos(x)} \end{array} \\\\\\ \cfrac{-5}{1-cos(x)}\cdot \cfrac{1+cos(x)}{1+cos(x)}\implies \cfrac{-5(1+cos(x))}{\underset{\textit{difference of squares}}{[1-cos(x)][1+cos(x)]}} \\\\\\[/tex]

[tex]\bf \cfrac{-5[1+cos(x)]}{1^2-cos^2(x)}\implies \cfrac{-5-5cos(x)}{\underset{\textit{pythagorean identity}}{1-cos^2(x)}}\implies \cfrac{-5-5cos(x)}{sin^2(x)} \\\\\\ \cfrac{-5}{sin^2(x)}-\cfrac{5cos(x)}{sin^2(x)}\implies -5\cdot \cfrac{1}{sin^2(x)}-5\cdot \cfrac{1}{sin(x)}\cdot \cfrac{cos(x)}{sin(x)} \\\\\\ -5\cdot csc^2(x)-5\cdot csc(x)\cdot cot(x)\implies \boxed{-5csc^2(x)-5csc(x)cot(x)}[/tex]

Given the speeds of the dog and cat, the dog will catch the cat in approximately 33.33 seconds by covering the 200-meter distance at a relative speed of 6 m/s.

Problem: A dog and a cat are 200 meters apart. The dog runs at 30 m/s, and the cat runs at 24 m/s. How soon will the dog catch the cat?

Calculate the relative speed at which the dog is gaining on the cat: 30 m/s - 24 m/s = 6 m/s.

Divide the initial distance (200 meters) by the relative speed (6 m/s) to find the time it takes for the dog to catch the cat: 200 m / 6 m/s = 33.33 seconds.

Answer:

40

Step-by-step explanation:

-5 x -8 = 40

40, because both numbers are negative, the answer is positive. So you would just multiply like normal.

Answer:

63.2702623...

Step-by-step explanation:

The ratio between FE and DE is the tangent of the angle EDF.[tex]tan 49 = \frac x {55}[/tex] or [tex]x= 55*tan 49[/tex]. With a calculator, you get 63.2702623... Cut where needed

55x tan49 =63.270

63.270.