Find the Area. The figure is not drawn to scale.

Answer:

x = 2

Step-by-step explanation:

Given 2 secants drawn from an external point to the circle, then

EC × ED = EB × EA, that is

(x + 4)(x + 4 + 1) = (x + 1)(x + 1 + 11)

(x + 4)(x + 5) = (x + 1)(x + 12) ← expand factors on both sides

x² + 9x + 20 = x² + 13x + 12 ← subtract x² + 13x from both sides

- 4x + 20 = 12 ( subtract 20 from both sides )

- 4x = - 8 ( divide both sides by - 4 )

x = 2

For this case we have a function of the form [tex]y = f (x)[/tex]

Where:

[tex]f (x) = 5x[/tex]

We must find the value of the function when [tex]x = 2,[/tex] that is, [tex]f (2).[/tex] Then, replacing the value of x in the function:

[tex]f (2) = 5 (2)\\f (2) = 10[/tex]

Thus, when [tex]x = 2[/tex] the function has a value of 10.

Answer:

[tex]f (2) = 10[/tex]

Answer: [tex]f(2)=10[/tex]

Step-by-step explanation:

You have the following linear function:

[tex]f(x)=5x[/tex]

To evaluate this function for the given value, you need to substitute the value of the variable "x" ([tex]x=2[/tex]), which is the input value, into the linear function to obtain the output value. Then:

For [tex]x=2[/tex]

[tex]f(2)=5(2)[/tex]

Make the multiplication.

Therefore, the result is:

[tex]f(2)=10[/tex]

Answer:

10.5

Step-by-step explanation:

6x +3 = 66

Subtract 3 from each side

6x+3-3 = 66-3

6x = 63

Divide each side by 6

6x/6 = 63/6

x = 10.5

the answer is X= 10.5

Answer:

[tex]x_{1}=\frac{1+\sqrt{33} }{4}\\x_{2}=\frac{1-\sqrt{33} }{4}[/tex]

Step-by-step explanation:

Using quadratic formula

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

we will have two solutions.

2x^2 - x - 4 = 0

So, a=2   b=-1  c=-4, we have:

[tex]x_{1}=\frac{+1+\sqrt{-1^{2}-4*2*-4} }{2*2}\\\\x_{2}=\frac{+1-\sqrt{-1^{2}-4*2*-4} }{2*2}[/tex]

Finally, we have two solutions:

[tex]x_{1}=\frac{1+\sqrt{33} }{4}\\\\x_{2}=\frac{1-\sqrt{33} }{4}[/tex]

Answer:

[tex](\pm \sqrt{2}, 0)[/tex]

Step-by-step explanation:

The x intercepts are basically the points at which y = 0.

-x^2 + 2 = 0

-x^2 = -2

x^2 = 2

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

For this case we have by definition, that to find the x-intercept points, we must make the variable y = 0 and clear the value of "x". So:

[tex]y = -x ^ 2 + 2\\0 = -x ^ 2 + 2\\x ^ 2 = 2\\x = \sqrt {2}[/tex]

So, the x-intercepts are:

[tex](x_ {1}, y_ {1}) = (\sqrt {2}, 0)\\(x_ {2}, y_ {2}) = (- \sqrt {2}, 0)[/tex]

ANswer:

[tex](x_ {1}, y_ {1}) = (\sqrt {2}, 0)\\(x_ {2}, y_ {2}) = (- \sqrt {2}, 0)[/tex]

Answer: The formula for the volume of a cylinder is v = πr2h. The volume for a cone whose radius is R and whose height is H is V = 1/3πR2H.

Answer:

Step-by-step explanation:

16 units

Answer: There would be 190 catfish in all 200 samples in the population.

Step-by-step explanation:

Since we have given that

Number of fish = 6

Mean number of catfish = 5.7

If the number of fish = 200

So, we need to find the proportion to find the number of catfish in the population.

Let the number of catfish in the population be 'x'.

According to question, it becomes,

[tex]\dfrac{6}{5.7}=\dfrac{200}{x}\\\\6x=5.7\times 200\\\\6x=1140\\\\x=\dfrac{1140}{6}\\\\x=190[/tex]

Hence, there would be 190 catfish in all 200 samples in the population.

Answer:

A

Step-by-step explanation:

edge 2021

The given triangle has a right angle.

We use the mnemonics SOH-CAH-TOA.

1i) [tex]\sin C =\frac{Opposite}{Hypotenuse}[/tex],[tex]\implies \sin C =\frac{30}{34}[/tex],[tex]\implies \sin C =\frac{15}{17}[/tex]

ii) [tex]\cos C =\frac{Adjacent}{Hypotenuse}[/tex],[tex]\implies \cos C =\frac{16}{34}[/tex],[tex]\implies \cos C =\frac{8}{17}[/tex]

[tex]\tan C =\frac{Opposite}{Adjacent}[/tex],[tex]\implies \tan C =\frac{30}{16}[/tex],[tex]\implies \tan C =\frac{15}{8}[/tex]

2. We want to find the hypotenuse.

We know an angle to be 23 degrees.

We were also given the side opposite to this angle to be 1200km.

Therefore we use the sine ratio.

Answer:

1) sin C = 30 / 34

cos C = 16/34

tan C = 30/16

2) The value of x = 1304.34

Step-by-step explanation:

1.

In a right angled triangle, we have perpendicular, hypotenuse and base.

The hypotenuse is the longest side and opposite to the right angle. the side having 90 degree angle is perpendicular.

Applying formulas we can find the values:

the formulas are : cos (Ф) = Base / hypotenuse

sin (Ф) = Perpendicular / hypotenuse

tan (Ф) = Perpendicular / Base

Putting values in the formula from figure:

sin C = Perpendicular / Hypotenuse

sin C = 30 / 34

cos C = Base / Hypotenuse

cos C = 16/34

tan C = Perpendicular / Base

tan C = 30/16

2.

We need to find the hypotenuse of the given triangle, we are given base = 1200 m and the angle is 23°

We know, cos Ф = Base / Hypotenuse.

Solving this, We can find the value of x.

cos (23) = 1200 / x

x cos (23) = 1200

x (0.920) = 1200

x = 1200 / 0.920

x = 1304.34

The value of x = 1304.34

Answer:

Bass = 5x = 312

Pike = 3x = 188

Step-by-step explanation:

8x = 500

x = 62.5 (But since there can't be 1/2 fish, it should be rounded)

Bass = 5x = 312

Pike = 3x = 188

Answer:

300 bass and 200 pike

Step-by-step explanation:

2 x square - 18 x + 36

2 x square - 6 x -12 x + 36

2 x (x - 3 )- 12 (x - 3 )

x - 3 2 x =12

x = 3 x =6

Answer:

A) x=3 or x=6

Step-by-step explanation:

Factor out the GCF : 2(x^2-9x+18)

Then, set to zero.

2(x^2-9x+18)=0

2(x-3)(x-6)=0

x=3 or x=6

ANSWER

[tex]{(x - 4)}^{2} + {y}^{2} = 12[/tex]

EXPLANATION

The equation of a circle given the center (h,k) and radius r is given by:

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

The circle has center (4,0) and radius

[tex]r = 2 \sqrt{3} [/tex]

We substitute the center and radius to get,

[tex]{(x - 4)}^{2} + {(y - 0)}^{2} = {(2 \sqrt{3)} }^{2} [/tex]

[tex]{(x - 4)}^{2} + {(y - 0)}^{2} = 12[/tex]

[tex]{(x - 4)}^{2} + {y}^{2} = 12[/tex]

Without the specific details of the spinner's sections, it is impossible to determine the exact odds of landing on yellow. Generally, the odds are calculated as the number of yellow sections divided by the total number of sections minus the yellow sections, such as 1:7 for a spinner with one yellow and seven other sections.

The question seems to be about calculating probabilities in different scenarios involving a spinner or balls with various colors. However, the exact description of the spinner is not provided. To calculate the odds of spinning yellow, we need the total number of sections on the spinner and the number of those sections that are yellow. Without this information, we can't provide a specific numerical answer. If we knew the spinner had a certain number of equal-sized sections, the odds of spinning yellow would be the number of yellow sections divided by the total number of sections minus the yellow sections.

If we assume there is one yellow section on the spinner, and there are a total of eight sections, then the odds of spinning yellow would be calculated as 1/(8-1), which simplifies to 1/7. Therefore, the odds of spinning yellow would be 1:7.

The odds of landing on yellow on the spinner in the image are 50%. This is because there are two equally sized sections of the spinner colored yellow, and two sections of other colors.

The probability of landing on any particular section is equal to the size of that section divided by the total size of the spinner. In this case, each of the yellow sections takes up half of the spinner, so the probability of landing on yellow is 1/2, or 50%.

It is important to note that this assumes that the spinner is spun fairly, and that each section has an equal chance of landing at the bottom. If there is any bias or if the sections are not of equal size, then the actual odds of landing on yellow will be different.

Answer: y2/10

Step-by-step explanation:

The equivalent expression for [tex]\( y^{1/5} \)[/tex] using radicals is [tex]\( \sqrt[5]{y} \).[/tex]

Sure, I can help with that! To express [tex]\( y^{1/5} \)[/tex] using radicals, we need to rewrite the exponent [tex]\( \frac{1}{5} \)[/tex] as a radical.

The expression [tex]\( y^{1/5} \)[/tex] can be written as [tex]\( \sqrt[5]{y} \)[/tex].

Here's the step-by-step calculation:

1. Start with the expression [tex]\( y^{1/5} \).[/tex]

2. Rewrite the exponent [tex]\( \frac{1}{5} \)[/tex] as a radical, giving [tex]\( \sqrt[5]{y} \)[/tex].

To understand why [tex]\( y^{1/5} \)[/tex] can be expressed as [tex]\( \sqrt[5]{y} \)[/tex], let's break it down:

The exponent [tex]\( \frac{1}{5} \)[/tex] means taking the fifth root of [tex]\( y \)[/tex]. The radical symbol [tex]\( \sqrt[5]{\;} \)[/tex] represents the fifth root. So,[tex]\( y^{1/5} \)[/tex] is equivalent to [tex]\( \sqrt[5]{y} \).[/tex]

In other words, raising [tex]\( y \)[/tex] to the power of [tex]\( \frac{1}{5} \)[/tex] is the same as finding the number which, when multiplied by itself five times, equals [tex]\( y \)[/tex]. This is precisely what the fifth root accomplishes.

Therefore, the equivalent expression for [tex]\( y^{1/5} \)[/tex] using radicals is [tex]\( \sqrt[5]{y} \).[/tex]

Complete question:

Using radicals write an equivalent expression for the expression y1/5

Answer:

The volume of the mailbox is [tex]936\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the prism (mailbox) is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of the prism

h is the height of the prism

we have

[tex]B=52\ in^{2}[/tex]

[tex]h=18\ in[/tex]

substitute

[tex]V=52(18)=936\ in^{3}[/tex]

Answer:

∠B = 65°; ∠C = 115°

Step-by-step explanation:

The first thing you to do is set ∠B and ∠D equal to each other.

[tex]3n+20=6n-25[/tex]

The reason you do this is because the oppisite angles are equal to each other in a parallelogram.

Next, you want to start simplifying the equation (I personally like to start with the variables).

[tex]....3n+20=6n-25\\-3n.....-3n[/tex]

Then, you simplify again (you can combined these if you want but for example I am breaking it down more.

[tex]....20=3n-25\\+25.......+25\\....45=3n[/tex]

Then you dived by 3, and you get 15=n. Now (and people often forget this step) you have to plug it back in to solve for the equartion. ∠B=3(15)+20, ∠B=65. Now you have to subtract 65 from 180 because ∠B and ∠C are completmtry. 180-65=115=∠C

the answer is b=3a+2 so B

The answer is B hope this helped!

Answer:

[tex]\sec \theta=-\sqrt{5}[/tex]

Step-by-step explanation:

The hypotenuse is [tex]h^2=6^2+3^2[/tex]

[tex]h^2=36+9[/tex]

[tex]h^2=45[/tex]

[tex]h=\sqrt{45}[/tex]

[tex]h=3\sqrt{5}[/tex]

The terminal side of [tex]\theta[/tex] is in the second quadrant.

In this quadrant; the secant ratio is negative.

[tex]\sec \theta=-\frac{hypotenuse}{adjacent}[/tex]

[tex]\sec \theta=-\frac{3\sqrt{5}}{3}[/tex]

[tex]\sec \theta=-\sqrt{5}[/tex]

The value of sec theta is [tex]\sec(\theta) = -\sqrt5[/tex]

From the diagram, we start by calculating the length of the hypotenuse (h).

So, we have:

[tex]h = \sqrt{6^2 + 3^2[/tex]

Evaluate

[tex]h = \sqrt{45[/tex]

Simplify

[tex]h = 3\sqrt{5[/tex]

The value of the secant in the second quadrant is calculated as:

[tex]\sec(\theta) = -\frac{Hypotenuse}{Adjacent}[/tex]

So, we have:

[tex]\sec(\theta) = -\frac{3\sqrt5}{3}[/tex]

Evaluate

[tex]\sec(\theta) = -\sqrt5[/tex]

Hence, the value of sec theta is [tex]\sec(\theta) = -\sqrt5[/tex]

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Answer:

ok thanks :)

Step-by-step explanation:

Answer:

Sounds epic

Step-by-step explanation:

Your answer for this question will be B.4

Answer:

Choice B; 4

Step-by-step explanation:

The solution to a system of equations is a pair of points (x, y) such that both equations pass through the given point. The number of solutions will thus be the number of such points where both functions pass through or intersect. The solutions to a system of equations can be determined analytically or graphically.

In this case, the graphical approach is much easier to use. We simply graph the two equations on the same graph and determine the number of points where they intersect.

From the attachment below, we see that the functions intersect at 4 distinct points. Hence there are 4 solutions to the system of equations given.

Answer:

1. 12(2x+3y)

2. 20x+4x+30y+6y

3. 6(4x+6y)

Step-by-step explanation:

The three equivalent expression of 24x + 36y are,

1). 12(2x + 3y).

2). 6(4x + 6y)

3). 4(6x + 3y).

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given expression:

24x + 36y.

To find the equivalent expressions:

First, we will find the common factor and simplify the expression.

That means,

the common factors of 24 and 36 are 2, 3, 4, 6, 12.

We can make three expressions,

24x + 36y = 12(2x + 3y).

24x + 36y = 6(4x + 6y).

And 24x + 36y = 4(6x + 3y).

Therefore, three equivalent expressions are 12(2x + 3y), 6(4x + 6y) and 4(6x + 3y).

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Answer:

I would say it's b because that makes the most sense tbh

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Below is the sequence of steps which are required to follow in order to have the expression in its simplified form.

Step 1

[tex](875x^{5}y^{9})^{\frac{1}{3}}[/tex]

Step 2

[tex](125.7)^\frac{1}{3}.x^{\frac{3}{5}}.y^{\frac{9}{3}}[/tex]

Step 3

[tex](125)^{1/3}.(7)^{1/3}.x(^{\frac{3}{3}+\frac{2}{3}}).y^{3}}[/tex]

Step 4

[tex](5^{3} )^{\frac{1}{3}}.7^\frac{1}{3}.x^{(1+\frac{2}{3})}.y^{3}[/tex]

Step 5

[tex]5^{1}.7^\frac{1}{3}.x^{1}.x^\frac{2}{3}.y^3[/tex]

Step 6

5xy³([tex]7^{\frac{1}{3} }[/tex][tex]x^{\frac{2}{3} }[/tex])

Step 7

5xy³([tex]7x^{2}[/tex])[tex]\frac{1}{3}[/tex]

Step 8

5xy³[tex]\sqrt[3]{7x^{2}}[/tex]

Answer:

C= 2*pi*r

Step-by-step explanation:

Answer:

x = √(13² - 12²) = √(169 - 144) = √25 = 5

C. 30 divided by 7 is roughly 4.3 which’s is between 4 and 5

[tex]m < \frac{ - 185}{k} [/tex]

HOPE THIS WILL HELP YOU

For this case we must find the value of the variable "m" of the following expression:

[tex]-mk-110> 75[/tex]

We follow the steps below:

We add 110 to both sides of the inequality:

[tex]-mk> 75 + 110\\-mk> 185[/tex]

We divide between k on both sides of the inequality:

[tex]\frac {-mk} {k}> \frac {185} {k}\\-m> \frac {185} {k}[/tex]

We multiply by "-" on both sides of the inequality, remembering that the sense of inequality changes:

[tex]m <- \frac {185} {k}[/tex]

ANswer:

[tex]m <- \frac {185} {k}[/tex]

Answer:

25

Step-by-step explanation:

12/x = 48/100

48/100 = 0.48

12 = 0.48x

12/0.48 = 25

Answer:

b

Step-by-step explanation:

13

Answer:

[tex]h(x)=5^x[/tex]

Step-by-step explanation:

All the graphs are growing bigger and bigger as x-values grows bigger.

This implies that the graphs represent exponential growth.

Hence their equation is in the form;

[tex]y=a^x[/tex]

The bigger the value of 'a' the faster the graph grows

We can see that h, grew faster than all the other graphs, hence 'a' should be the largest value, which is 5.

Therefore the function is :

[tex]h(x)=5^x[/tex]

Answer:

Correct choice is function  [tex]h(x)=5^x[/tex]

Step-by-step explanation:

We have been given a graph of three functions f, g and h.

Now we need to find the best matching equation for the function h(x).

From graph we can see that all of the curves are increasing must faster as the move from left side to right side. That indicates they are exponential functions.

We know that if base is larger then graph will move upward much faster.

largest base from available bases is 5.

So the correct function is [tex]h(x)=5^x[/tex]

Answer:

Step-by-step explanation:

Think about it for a second.

Take log 3 (-9). 3 to what power is -9.

Let's try:

3 ^ 2 = 9. So it's not negative 9.

Maybe 3 ^ -2 = 1/9. Still not -9.

Let's try 3 ^ 1/3 = 1.4422. Still not remotely close.

So we can make a conclusion that a positive number to any real exponent can't give us a negative number.

A logarithmic equation exists as an equation that involves the logarithm of an expression including a variable. To translate exponential equations, first, see whether you can write both sides of the equation as powers of the identical number.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.

As the base of a power function, 0, 1, and every negative integer provide a possible issue. Furthermore, if those values cannot be relied upon to be the base of a power function, they cannot be relied upon to be the base of a logarithm either. For this reason, we restrict the base of the logarithm to only positive numbers other than 1.

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