In a right angled triangle ABC with hypotenuse c and sides a and b. Find the unknown leangth

b = 5dm, a=5√7dm, c = ?​

We have to fill in the table that we have in the question with the following values as the solution

a. log6⁰, log 2 . 1, log 8/3

b. log 1 .4 , 1 , log 4. 6

c. log 9/2, log 3. 5 , log 5⁷

To do this, you have to decide on that particular number that you want to find the logarithm on. Next you have to find the base of that number.

The logarithm of the number is the power that it would have to be raised for us to obtain a different number.

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Answer:

There are 17 natural numbers divisible.

There are 17 natural numbers between 150 and 300 that are divisible by 9.

To find the number of natural numbers between 150 and 300 that are divisible by 9, we need to find the count of multiples of 9 within this range.

The first multiple of 9 greater than or equal to 150 is 153 (9 x 17), and the last multiple of 9 less than or equal to 300 is 297 (9 x 33).

Now, we can calculate the number of multiples of 9 between 153 and 297 (inclusive):

Number of multiples of 9 = (Last multiple - First multiple) / 9 + 1

Number of multiples of 9 = (297 - 153) / 9 + 1

Number of multiples of 9 = 144 / 9 + 1

Number of multiples of 9 = 16 + 1

Number of multiples of 9 = 17

So, there are 17 natural numbers between 150 and 300 that are divisible by 9.

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The end behavior of the given polynomial is that as x → -∞ or  x → ∞, then, f(x) → 5

We are given the polynomial;

f(x) = 5x/(x - 25)

Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get;

f(x) = 5/(1 - (25/x))

Thus, applying limits we have;'

lim x → ±∞ [5/(1 - (25/x))]

From algebraic limit laws we know that;

If f(x) = k, then;

lim x → +∞ [f(x)] = k

Also, lim x → -∞ [f(x)] = k

Thus, applying limits at infinity to our polynomial gives;

lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5

This is because lim x → ∞ for 1/x is 0.

Thus, f(x) has horizontal asymptotes at y = 5

Thus, we conclude that the end behavior is that as x → -∞ or  x → ∞, then, f(x) → 5

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The limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.

According to the given question.

We have to find the limit of [tex]\lim_{x \to \infty} 5x - lnx[/tex]

As we know that L'hospital rule is a theorem which provides a technique to evaluate limits of indeterminate forms.

And the formual for L'hospital rule is

[tex]\lim_{x \to \ c} \frac{f_{x} }{g_{x} } = \lim_{x \to \ c} \frac{f^{'}( x)}{g^{'} (x)}[/tex]

[tex]\lim_{x \to \infty} 5x - lnx[/tex]  can be written as

[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]

If we put the value of limit in lnx/x we get an indeterminate form ∞/∞.

Therefore, [tex]\lim_{x \to \infty} \frac{lnx}{x} = \frac{\frac{1}{x} }{1}[/tex]

[tex]\implies \lim_{x \to \infty} \frac{1}{x} = 0[/tex]   (as x tends to infinity 1/x tends to 0)

So,

[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]

[tex]= \lim_{x \to \infty}x(5 -0)[/tex]

[tex]= \lim_{n \to \infty} 5x \\= \infty[/tex](as x tends to ∞ 5x also tends to infinity)

Therefore, the limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.

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Answer:

Hope you like my answer

Answer:

radius = 10 feet

Step-by-step explanation:

C represents the circumference.

C = 2πr  ,where r is the radius.

We are given C = 62.8 ft

Equating the two expressions of C :

2πr = 62.8

Then

2 × 3.14 × r = 62.8

Then

6.28 × r = 62.8

Then

[tex]r = \frac{62.8}{6.28} = 10[/tex]

Answer:

student 2 is correct

Step-by-step explanation:

there are 10 [tex]\frac{1}{10}[/tex] ' s in 1 , so

37 × 10 = 370 ← number of tenths in 37

0.6 = [tex]\frac{6}{10}[/tex] , that is 6 tenths

then

37.6 = 370 + 6 = 376 ← number of tenths

Equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18

The correct option is C.

One or two variables make up a linear equation. Neither the numerator nor the denominator of a fraction can be a variable in a linear equation raised to a power higher than 1. The lines that connect all the points on a coordinate grid when you identify the values that make a linear equation true are congruent.

Let x stand for the number of pencils Stella purchased, and y for the number of pens Stella purchased.

Since Stella purchased a total of 18 things, the quantity of pencils and pens purchased must equal 18 or one of the following:

x + y = 18

We also know she spent $21, that a pencil costs $1, and that a pen costs $1.50. Therefore,

1x + 1.5y = 21

Thus, the set of equations that may be utilized to determine the quantity of pencils (x) and pens (y) that she purchased is as follows:

X+1.5Y = 21, and X+Y = 18

equations can be used to find the number of pencils (x) and pens (y) she bought are X+1.5Y = 21, and X+Y = 18

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Answer:

[tex]x =\frac{5}{3} \pm \frac{\sqrt{10}}{3} \\\\x=2.72076\\x=0.612574\\[/tex]

Step-by-step explanation:

The quadratic equation is:

[tex]3x^2 - 10x + 5 = 0[/tex]

The roots (solutions) of a quadratic equation of the form
[tex]a^2 + bx + c = 0\\[/tex]

are

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

in this case we have a = 3, b = -10, and c = 5

So, substituting for a, b and c we get

[tex]x = \frac{ -(-10) \pm \sqrt{(-10)^2 - 4(3)(5)}}{ 2(3) }[/tex]

[tex]x = \frac{ 10 \pm \sqrt{100 - 60}}{ 6 }\\[/tex]

[tex]x = \frac{ 10 \pm \sqrt{40}}{ 6 }[/tex]

Simplifying we get

[tex]x = \frac{ 10 \pm 2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 10 }{ 6 } \pm \frac{2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 5}{ 3 } \pm \frac{ \sqrt{10}\, }{ 3 }\\\\\frac{ 5}{ 3 } + \frac{ \sqrt{10}\, }{ 3 } = 2.72076\\\\\\[/tex]  (First root/solution)

[tex]\frac{ 5}{ 3 } - \frac{ \sqrt{10}\, }{ 3 } = 0.612574[/tex]  (Second root/solution)

The overall algebraic  expression will be:   [tex]\frac{5(x+11)}{3(x+8)}[/tex]

Definition of algebraic expression -

An expression obtained by a finite number of the fundamental operations of algebra upon symbols representing numbers.

Five times the sum of a number and eleven, divided by three times the sum of the number and eight.

Let the number be x.

Five times the sum of a number and eleven means 5 multiplied to the sum of x and 11. In expression this will be written as:

5(x + 11)

Three times the sum of the number and eight means 3 multiplied to the sum of x and 8. In expression this will be written as:

3(x + 8)

So, the overall algebraic expression will be:    [tex]\frac{5(x+11)}{3(x+8)}[/tex]

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Answer:

30°

30 is the value of x that’s makes AB//CD.

Step-by-step explanation:

the angles of measures 2x + 40 and 3x + 10 are two Alternate interior angles

If these two angle were congruent then the lines AB and CD

would be parallel .

2x + 40 = 3x + 10

⇔ 40 - 10 = 3x - 2x

⇔ 30 = x

⇔ x = 30

Recall that for [tex]|x|<1[/tex], we have the convergent geometric series

[tex]\displaystyle \sum_{n=0}^\infty x^n = \frac1{1-x}[/tex]

Now, for [tex]\left|\frac x5\right| < 1[/tex], we have

[tex]\dfrac1{5 - x} = \dfrac15 \cdot \dfrac1{1 - \frac x5} = \dfrac15 \displaystyle \sum_{n=0}^\infty \left(\frac x5\right)^n = \sum_{n=0}^\infty \frac{x^n}{5^{n+1}}[/tex]

Integrating both sides gives

[tex]\displaystyle \int \frac{dx}{5-x} = C + \int \sum_{n=0}^\infty \frac{x^n}{5^{n+1}} \, dx[/tex]

[tex]\displaystyle -\ln(5-x) = C + \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]

If we let [tex]x=0[/tex], the sum on the right side drops out and we're left with [tex]C=-\ln(5)[/tex].

It follows that

[tex]\displaystyle \ln(5-x) = \ln(5) - \sum_{n=0}^\infty \frac{x^{n+1}}{5^{n+1}(n+1)}[/tex]

or

[tex]\displaystyle \ln(5-x) = \boxed{\ln(5) - \sum_{n=1}^\infty \frac{x^n}{5^n n}}[/tex]

Orders of top-three finishers that are possible is given as follows:

[tex]n P_{r}=\frac{14 !}{11 !}=2184[/tex]

In a broad sense, a permutation of a set is the rearrangement of its elements inside an already ordered set, or the arrangement of its members into a sequence or linear order. The act or process of altering an ordered set's linear order is referred to as "permutation."

The number of possible permutations of x elements from a set of n elements is given by:

[tex]n P_{r}=\frac{n !}{(n-r) !}[/tex]

The order in which the cars finish is important, hence the permutation formula is used instead of the combination formula.

In this problem, 3 cars are taken from a set of 14, hence the number of different orders is given as follows:

Using the permutation formula, it is found that the number of different orders of top-three finishers that are possible is given as follows:

[tex]n P_{r}=\frac{14 !}{11 !}=2184[/tex]

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I understand that the question you are looking for is:

How many different orders of top-three finishers are possible? drag the tiles to the correct locations on the equation. not all tiles will be used.

Answer:

1. Given.

2. Reflexive Property of Congruence.

3. Alternate Interior Angles Theorem.

4. SAS

5. <4 ~= <2

6. Converse of Alternate Interior Angles Theorem.

Based on the given task content; the product of StartFraction 4 n Over 4 n minus 4 EndFraction times StartFraction n minus 1 Over n + 1 EndFractiontartFraction 2 Over x EndFraction is (4n² - 8n) / (4n²x - 5nx - x)

Product of numbers refers to the multiplication of two or more values to arrive at a single result.

4n / (4n - 1) × (n - 1) / (n + 1) 2/x

= 4n / (4n - 1) × 2(n - 1) / x(n + 1)

= 4n / (4n - 1) × (2n - 2) / (nx + x)

= 4n(2n - 2) / (4n - 1) (nx + x)

= 4n² - 8n / (4n²x - 4nx - nx - x)

= (4n² - 8n) / (4n²x - 5nx - x)

Therefore, the product of 4n / (4n - 1) × (n - 1) / (n + 1) 2/x is (4n² - 8n) / (4n²x - 5nx - x)

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Answer:

Step-by-step explanation:

1. $135

2. a. no

    b. $340

3. a. 33

   b. $135*33= $4455+340= $4795

4. a. $7630 = 135v + 340

     b. 135v + 340 = 7630

          135v = 7290

              v = 54 vacuums        

The value of w is 12.5 when x = 5 , y= 5  and z = 10.

What is Equation of variation?

Equation of variation w = [tex]\frac{kxy^{2} }{z}[/tex]

Constant of variation  k = [tex]\frac{wz}{xy^{2} }[/tex]

Find k when w = 1/2, x = 2 and z = 36

k = [tex]\frac{wz}{xy^{2} }[/tex]

[tex]k = \frac{\frac{1}{2} * 36 }{2 * 3^{2} }[/tex]

[tex]k = \frac{18}{2 * 9}[/tex]

[tex]k = \frac{18}{18}[/tex]

k= 1

find the value of w when x = 5 , y = 5 and z = 10

[tex]w = \frac{kxy^{2} }{z} \\w= \frac{1 * 5 * 5^{2} }{10}[/tex]

[tex]w = \frac{5^{3} }{10}[/tex]

w = 125 /10

w = 25 /2

w = 12 . 5

Therefore, the value of w is 12.5 when x = 5 , y= 5  and z = 10

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The "given series" should be for [tex]\cos(x)[/tex], not [tex]x[/tex], so that

[tex]\cos(x) = 1 - \dfrac{x^2}2 + \dfrac{x^4}{24} - \dfrac{x^6}{720} + \cdots[/tex]

In the limit (which should say [tex]x\to\infty[/tex], not [tex]n[/tex]), we have

[tex]\displaystyle \lim_{x\to\infty} \frac{\frac{x^2}{1+\cos(x)}}{x^4} = \lim_{x\to\infty} \frac{1}{x^2\left(2 - \frac{x^2}2 + \frac{x^4}{24} - \cdots\right)} = \boxed{0}[/tex]

The angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

In this question,

A normal vector to the plane is any vector that starts at a point in the plane and has a direction that is orthogonal (perpendicular) to the surface of the xy plane .

The magnitude of the xy plane, hypotenuse = 25 units

The x component of the xy plane, base = 12 units

Let θ be an angle, then the angle it makes with the positive x axis is

[tex]\theta = cos^{-1}(\frac{base}{hypotenuse} )[/tex]

⇒ [tex]\theta = cos^{-1}(\frac{12}{25} )[/tex]

⇒ [tex]\theta = cos^{-1}(0.48)[/tex]

⇒ [tex]\theta = 61.3145[/tex]

Hence we can conclude that the angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

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Answer:

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

Step-by-step explanation:

So when it says simplify the right side, all it's doing is distributing the square root across division.

So when we distribute the square root we get the fraction

[tex]\frac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}[/tex]

And it's important to know that you cannot distribute the square root across addition/subtraction, but you can with multiplication.

There's a radical identity that states: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex] and this works both ways, so we can use this to combine like radicals or separate them into multiple. In this case we can separate the square root of 4a^2 into two radicals

[tex]\frac{\sqrt{b^2-4ac}}{\sqrt{4} * \sqrt{a^2}}[/tex]

And from here it's pretty easy to see that the square root of 4 is 2, and the square root of a^2 is a, since the square exponent and square root just cancel out.

So we get the following expression on the right side

[tex]\frac{\sqrt{b^2-4ac}}{2a}[/tex]

The surface area of the triangular prism is of 162 cm².

The surface area of a prism is given by the sum of all the areas of the prism.

This prism is composed by:

For a rectangle, the area is the multiplication of the dimensions, hence:

A1 = 10 x 15 = 150 cm².

For a right triangle, the area is half the multiplication of the sides, hence:

A2 = 0.5 x 6 x 4 = 12 cm².

Hence the surface area is:

A = A1 + A2 = 150 cm² + 12 cm² = 162 cm².

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Just me:

? I will just explain what I understand

Answer:

(Think hard) If you cut a snake in half you get 1/2 but if you cut it into 4's 1/5

I tried.

Inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.

To find the domain:

Therefore, inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.

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The correct question is given below:

If f (x) = start root 4 x 9 enroot 2, which inequality can be used to find the domain of f(x)?

(A) startroot 4 x endroot greater-than-or-equal-to 0                                        

(B) 4x+9 greater-than-or-equal-to 0

(C) 4 x greater-than-or-equal-to 0

(D) startroot 4 x 9 endroot 2 greater-than-or-equal-to 0

Answer:

(B)- 4X+9 greater than or equal to 0

Step-by-step explanation:

The constant of proportionality is 25 and the distance at 10 seconds is 250 m.

To find the constant of proportionality, find the slope of the graph.

Now, input in slope intercept form of equation to find distance at 10 seconds.

Answer:

Rotate 180 degrees with the center the origin (0,0)

Step-by-step explanation:

Try drawing a small square in the first quadrant, then reflect it like the direction. If you use tracing paper and and copy the figure, you will see that if you rotate the figure at the origin, it will land on the same spot as the translations.

Answer:

Power Bars are cheaper!

Step-by-step explanation:

FG: $18/12 Bars = $1.50 per bar

PB: $21.75/15 Bars = $1.45 per bar

Answer:

Super Power bars

Step-by-step explanation:

In order to find the best price, we want to calculate the unit rate, or the price for each bar. Let's start with the Fee Great energy bars. Since they are $18 for 12 bars, we divide 18 by 12 to figure out how much each bar costs. We get 1.5, or $1.50 per bar. Next lets claculate the unit rate for the Super Power bars. Since its $21.75 for 15 bars, we divide 21.75 by 15. We get 1.45, or $1.45 per bar. Since the price for one bar is cheaper for the Super Power bars as $1.45 is less than $1.50, the Super Power bars are the best price for each bar.

the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.

It is important to note that according to Euler’s formula for any convex polyhedron, the number of Faces (F) and vertices (V) added together is exactly two more than the number of edges (E).

It is mathematically written as;

Face + vertices = 2 + edges

F + V = 2 + E

From the figure given, we can see that it is a kite

Number of vertices = 4

Number of faces = 4

2 + edges = faces + vertices

2 + edges = 4 + 4

2 + edges = 8

Edges = 8 - 2

Edges = 6

Thus, the number of faces, edges and vertices the shape below has is 4, 4 and 6 respectively.

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Answer:

D

Step-by-step explanation:

An angle of depression is measured from the horizontal downwards.

this is angle D in the diagram

Answer + Step-by-step explanation:

10 × 5 × 2

= 10 × (5 × 2)   (associative property)

= 10 × (10)

= 10 × 10

= 100