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For sin, cos, and tan, let's use an abbreviation.

SOH-CAH-TOA

[tex]sin=\frac{opposite}{hypotenuse}[/tex]

[tex]cos=\frac{adjacent}{hypotenuse}[/tex]

[tex]tan=\frac{opposite}{adjacent}[/tex]

But before that, we should solve for the missing side.

Since this triangle is a right triangle, we can use the Pythagorean Theorem.

[tex]a^2+b^2=c^2 \\ \\ 6^2+8^2=c^2 \\ \\ c^2=36+64 \\ \\ c^2=100 \\ \\ c=10[/tex]

So the hypotenuse is 10.

Let's plug in.

sin θ = 6/10 --> 3/5

cos θ = 8/10 --> 4/5

tan θ = 6/8 --> 3/4

Now for the cosectant, secant, and cotangent, we'll just use the definitions.

Cosectant is hypotenuse over opposite.

Secant is hypotenuse over adjacent.

Cotangent is adjacent over opposite.

So they are basically the inverses.

csc θ = 10/6 --> 5/3

sec θ = 10/8 --> 5/4

cot θ = 8/6 --> 4/3

X = -2500

This is because:

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

[tex]\sqrt {-4x} = 100[/tex]

Now, we square both sides of the equation:

[tex]-4x = 100 ^ 2\\-4x = 10000[/tex]

We divide between -4 on both sides of the equation:

[tex]x = \frac {10000} {- 4}\\x = -2500[/tex]

ANswer:

[tex]x = -2500[/tex]

Option A

Answer:

21.9%

Step-by-step explanation:

This involves binomial probability.

n = # of tries:  8

x = # of successes (heads):  3

Use your calculator's probability distribution function binompdf.

Type in binompdf(n, p, x), which in this case would be:

             bionompdf(8, 0.5, 3) = 0.219, or 21.9% (Answer C)

The probability of flipping a coin 8 times and getting heads 3 times is 21.9%. Therefore, option C is correct

To find the probability of flipping a coin 8 times and getting heads 3 times, we need to use the binomial probability formula. The formula is P(x) = (nCx) * p^x * (1-p)^(n-x), where n is the number of trials, x is the number of successful outcomes, p is the probability of success on a single trial, and nCx is the combination notation.

In this case, n = 8, x = 3, and p = 0.5 (since the probability of getting heads on a fair coin is 0.5). Plugging these values into the formula, we get:

P(3) = (8C3) * 0.5^3 * 0.5^(8-3)

= (8!/3!(8-3)!) * 0.5^3 * 0.5^5

= 56 * 0.5^3 * 0.5^5

= 56 * 0.125 * 0.03125

= 0.21875

= 21.9%

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Answer:

The Answer would be B.

Step-by-step explanation:

Rearrange

5+2*(3+2*x)-(x+3*(x+1))=0

Step 2:

 (5 +  2 • (2x + 3)) -  (4x + 3)  = 0

Step  3  :

 8  = 0

Step  4  :

Equations which are never true :

 8   =  0

This equation has no solution.

Answer:

The answer is B.

Answer:

Equation: a - 16 = 3

Answer: a = 19

Answer:

Step-by-step explanation

20=36

1=x

Then cross multiply

20x=36

x=1.8

If it takes her 1.8 minutes to complete 1 item then:

1=1.8

35=x

x=63

It takes her 63 minutes

Answer:

7)V=16257.74

8)V= 226.19

9)V=12.56

10)V=6283.18

11)r=6.631

12)h=69.05

13)V=35328.78

Step-by-step explanation:

Volume of cylinder is given by formula:

V=πr^2h

where r is radius and h is height of cylinder

7)

r=15

h=23

Putting values in formula:

V= π(15)^2(23)

 =5175π

  =16257.74

8)

diameter=6

r=d/2=3

height =?

Finding height by pythagoras theorem:

h^2= 10^2-6^2

     =100-36

     =64

h=8

Putting values in formula:

V=π(3)^2(8)

  = 72π

   = 226.19

9)

r= 2

h=1

Putting values in formula:

V=π(2)^2(1)

  =4π

  = 12.56

10)

diameter =20

r=d/2=10

h=20

Putting values in formula:

V=π(10)^2(20)

  =2000π

  =6283.18

Now finding the missing measures:

11)

Given V=210π

h = 15

r=?

Putting values in formula:

210π=π(r)^2(15)

r^2= 210π/15

    =14π

r= 6.631

12)

V=197.82

r=3

h=?

Putting values in formula:

197.82=π(3)^2(h)

h= 197.82/9π

 = 69.05

13)

r=21

h=25.5

Putting values in formula:

V= π(21)^2(25.5)

 =11245.5π

  =35328.78 !

The value of the calculated volume and height of the cylinders are

7) 16,259.9 mm³

8) 904.9 yd³

9) 12.6 ft³

10) 25136.0 ft³

11) 6.8 m

12) 7.0 m

13) 35333.4 in³

The volume of a cylinder is given by = πr²h

where

r is the radius

h is the vertical height

7) h = 23 mm, r = 15 mm

V = π(15)²(23)

=5175*π

= 16,259.9 mm³

8) r = 6 yd, slant height = 10 yd

Use Pythagorean theorem to find the height

10² = 6² + h²

h² = 100-36

= 64

h = √64 = 8 yd

V = π(6)²(8)

= 288*π

= 904.9 yd³

9) r = 2 ft, h = 1 ft

V = π(2)²(1)

= 4π

= 12.6 ft³

10) r = 20 ft, h = 20 ft

V = π(20)²(20)

= 8000*π

= 25136.0 ft³

11) V = 210 ft³, h = 15 ft

1 foot = 0.3048 m

15 ft = 0.3048*15

= 4.572 m

210π = πr²(4.572)

r² = 210/4.572

= 45.9317

r = √{45.9317}

= 6.8 m

12) V = 197.82 m³, r = 3 m

197.82 = π(3)²x

197.82 = 3.142*9*x

197.82 = 28.278x

x =197.82/28.278

= 7.0 m

13) r = 21 inches, h = 25.5 inches

V = π(21)²(25.5)

= 11245.5*π

= 35333.4 in³

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Answer:

(x -5) * (x -2) = x^2 -7 +10

Step-by-step explanation:

Answer:

There are 9 blueberry muffins.

Step-by-step explanation:

In order to find this amount, we need to multiply the fraction that represents blueberry muffins by the total number of muffins.

24 * 3/8 = 9

Answer:

9

Step-by-step explanation:

24/8=3

3x3=9, so there are 9 muffins

Total/denominator, then that number times the numerator.

Answer:

Option C. [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

and

The scale factor is equal to the ratio of its corresponding sides

Let

z-----> the scale factor

[tex]z=\frac{15}{18}[/tex]

simplify

[tex]z=\frac{5}{6}[/tex]

Answer:

a=1/16 ft2

Step-by-step explanation:

1/4x1/4=1/16

Answer:

1/16

Hope This Helps!  Have A Nice Day!!

Answer:

D, neither

Step-by-step explanation:

to determine whether a function is even, odd or neither, we need to know what it means

an even function is symmetric with respect to the y-axis

an odd function is symmetric with respect to the origin

to solve an equation to see if its even or odd, we would need to substitute x in the equation for -x.

in an even function when we substitute f(-x), it should be equal to to f(x)

in an odd function when we substitute f(-x), it should be equal to -f(x)

so lets test the function given to see if its even

f(x) = x³ + 4x

f(-x) = (-x)³ + 4(-x)

f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to the orignal function, we see that f(-x) = x³ - 4x is not even as we did not get the same output as the original function

now we should test to see if its odd. we have already seen what f(-x) is, now lets try -f(x) and compare it to f(-x) and f(x)

-f(x) = -(x³ + 4x) -->

-f(x) = -x³ - 4x ≠ f(-x) = x³ - 4x

f(-x) = x³ - 4x ≠ f(x) = x³ + 4x

comparing this to f(x) and f(-x), we see that it not odd as we did not get the same output

so the answer is D, neither even nor odd

Answer:0.81

Step-by-step explanation:

A: Given teenager owns a skateboard. P(A) = 0.48

B:  Given teenager owns roller blades. P(B) = ? - we dont know and dont need

AB: Given teenager owns a skateboard and roller blades. P(AB) = 0.39

P(B/A) = P(AB)/P(A) = 0.39/0.48 = 0.8125

Answer:

0.81

Step-by-step explanation:

Just divide them and write as a decimal.

Answer:

[tex]V=430.19\ cm^3[/tex]  or  [tex]V=136.93\pi\ cm^3[/tex]

Step-by-step explanation:

The surface area of a sphere is:

[tex]A_s=4\pi r^2[/tex]

Where r is the radius of the sphere

In this case we know that [tex]A_s = 275.561\ cm^2[/tex]

So

[tex]4\pi r^2=275.561[/tex]

We solve the equation for r

[tex]4\pi r^2=275.561\\r^2 = \frac{275.561}{4\pi}\\\\r=\sqrt{ \frac{275.561}{4\pi}}\\\\r=4.683\ cm[/tex]

Now we know the radius of the sphere.

The volume of a sphere is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

We substitute the value of the radius in the formula

[tex]V=\frac{4}{3}\pi (4.683)^3[/tex]

[tex]V=430.19\ cm^3[/tex]

Answer:

a) x ≥ -1 , x ≠ 6

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached images below, to find more information about the graph

The correct answer is option

a) x ≥ -1 , x ≠ 6

Answer:

a) [tex]x\geq -1,x\neq 6[/tex]

Step-by-step explanation:

We have been given a function [tex]f(x)=\frac{\sqrt{x+1}}{(x+4)(x-6)}[/tex]. We are asked to find the domain of our given function.

We can see that our given function is a rational function and numerator of our given function is a square root.

To find the domain of our given function, we will find the number that will make our denominator 0 and the domain of square root function will be the values of x that will make our numerator non-negative.

Undefined points for our given function:

[tex](x+4)(x-6)=0[/tex]

[tex]x+4=0\text{ or }x-6=0[/tex]

[tex]x=-4\text{ or }x=6[/tex]  

The domain of denominator is all values of x, where x is not equal to negative 4 and positive 6.

Non negative values for radical:

[tex]x+1\geq 0[/tex]

[tex]x+1-1\geq 0-1[/tex]

[tex]x\geq -1[/tex]

The domain of numerator is all value of x greater than or equal to negative

Upon combining real regions and undefined points for our given function, the domain of our given function will be all values of x greater than or equal to negative 1, where x is not defined for 6.

Therefore, domain of our given function is [tex]x\geq -1,x\neq 6[/tex].

Final answer:

The missing length of the hypotenuse (c) in the right triangle with legs a=6 and b=8 is found using the Pythagorean theorem. By squaring both a and b, adding those squares together, and then taking the square root, we determine that c equals 10 units.

Explanation:

To find the missing length of the hypotenuse (c) of the right triangle when given the lengths of the other two sides (a and b), we can use the Pythagorean theorem. The theorem states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In mathematical terms, this is represented as a² + b² = c².

Given that side a is 6 and side b is 8, we can substitute these values into the theorem's formula:

Therefore, the length of the hypotenuse (c) is 10 units.

Answer:

the answer is Z

Step-by-step explanation:

Answer:

[tex]\sin\left(-180^o+\theta\right)=-\sin\left(\theta\right)[/tex]

Step-by-step explanation:

We need to find the value of [tex]\sin(-180^o+ \theta)[/tex]

So let's apply formula

[tex]\sin\left(A+B\right)=\sin\left(A\right)\cos\left(B\right)+\sin\left(B\right)\cos\left(A\right)[/tex]

[tex]\sin\left(-180^o+\theta\right)=\sin\left(-180^o\right)\cos\left(\theta\right)+\sin\left(\theta\right)\cos\left(-180^o\right)[/tex]

[tex]\sin\left(-180^o+\theta\right)=0\cdot\cos\left(\theta\right)+\sin\left(\theta\right)\cdot\left(-1\right)[/tex]

[tex]\sin\left(-180^o+\theta\right)=0-\sin\left(\theta\right)[/tex]

[tex]\sin\left(-180^o+\theta\right)=-\sin\left(\theta\right)[/tex]

Answer: in explanation

Step-by-step explanation:  1.) Plug your input in for x and solve for your output, y. You are given the input (far left column). As for graphing, plot -5 on the y-axis (vertical one) and move down one, right one until you reach bottom. Then move up one, left one until you reach the top.

2.)Plug your input in for x and solve for your output, y. You are given the input (far left column). As for graphing, plot -1 on y-axis (vertical one) and move up two, right one and down two, right one until you reach either end of the graph.

Connect both with a solid line and put arrows on either end.

Answer:

[tex]\$3,200.57[/tex]  

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

[tex]A=P(e)^{rt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

[tex]t=7\ years\\ P=\$1,120\\ r=0.15[/tex]  

substitute in the formula above  

[tex]A=\$1,120(e)^{0.15*7}=\$3,200.57[/tex]  

Answer:3,200.57

Step-by-step explanation:

Answer:

D) 24 in3

Step-by-step explanation:

Volume of a box is length times width times height

2 in x 4 in x 3 in = 24

and its inches cubed because inches is multiplied 3 times

Answer:

Step-by-step explanation: it’s C

2x4x3

8x3

24 2in

Answer:

Step-by-step explanation:

let x be the number

2(x+8)=-4x+4

2x+16=-4x+4

6x=-12

x=-2

Answer:

x=-2

Step-by-step explanation:

2(x+8)=-4x+4

2x+16=-4x+4

6x=-12

x=-2

Answer:

V

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y) → (x, - y)

Under a reflection in the y- axis

a point (x, y) → (- x, y)

Hence

U(- 6.5, 1 ) → W(- 6.5, - 1) ← reflection in x- axis

W(- 6.5, 1) → V(6.5, -1) ← reflection in y- axis

Answer:

i think its v

Step-by-step explanation:

i hope this is right

Answer:

-3/5

Step-by-step explanation:

Answer:

[tex]-\frac{3}{5}[/tex]

Step-by-step explanation:

Remember that the tangent trigonometric ratio is the opposite side of right triangle divided by the adjacent side:

[tex]tan(\alpha )=\frac{opposite-side}{adjacent-side}[/tex]

[tex]tan(\alpha )=-\frac{4}{3}[/tex]

Comparing the equations we can infer that:

opposite side = 4

adjacent side = 3

Now we can use Pythagoras to find the hypotenuse of our right triangle:

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

[tex]hypotenuse^2=4^2+3^2[/tex]

[tex]hypotenuse^2=25[/tex]

[tex]hypotenuse=\sqrt{25}[/tex]

[tex]hypotenuse=5[/tex]

Remember that the cosine trigonometric ratio is the adjacent side divided by the hypotenuse; in other words:

[tex]cos(\alpha)=\frac{adjacent-side}{hypotenuse}[/tex]

We know that adjacent side = 3 and hypotenuse = 5.

Replacing values:

[tex]cos(\alpha )=\frac{3}{5}[/tex]

Now, remember that cosine means x and sine means y. In Quadrant 2 x is negative, which means that cosine is negative.

So, if [tex]tan(\alpha )=-\frac{4}{3}[/tex] in quadrant 2, then [tex]cos(\alpha )=-\frac{3}{5}[/tex]

Answer:

A.

[tex]2xy^2(10x+3)[/tex]

B.

[tex](x+5)^2[/tex]

C.

[tex](x-6)(x+6)[/tex]

Step-by-step explanation:

Part A. The expression [tex]2x^2y^2+6xy^2+18x^2y^2[/tex] consists of three terms: [tex]2x^2y^2,\ \ 6xy^2,\ \ 18x^2y^2[/tex] The first and the last terms are like terms, we can add them:

[tex]2x^2y^2+18x^2y^2=20x^2y^2[/tex]

Now,

[tex]20x^2y^2=2xy^2\cdot 10x\\ \\6xy^2=2xy^2\cdot 3[/tex]

So,

[tex]2x^2y^2+6xy^2+18x^2y^2=2xy^2(10x+3)[/tex]

Part B. The expression [tex]x^2+10x+25[/tex] is a square of [tex]x+5,[/tex] so

[tex]x^2+10x+25=(x+5)^2[/tex]

Part C. Use the difference of squares formula:

[tex]x^2-36=x^2-6^2=(x-6)(x+6)[/tex]

ANSWER

D. G(x)=(x+1)²

EXPLANATION

The equation of the red graph is

[tex]F(x) = {x}^{2} [/tex]

This function has its vertex at the origin.

The blue graph is obtained by shifting the red graph 1 unit to the left.

The vertex will now be at (-1,0)

The equation of the new function in the vertex form is

[tex]G(x)= {(x + 1)}^{2} [/tex]

The correct choice is D.

Answer: l = 4 cm, w = 7 cm

Step-by-step explanation:

i think that this is it

Answer:

it’s the third one

l = 4 w = 7

Step-by-step explanation:

to find the area you multiply length by width

4x7 = 28

answer

7x-12

explanation

13x -2(3x+6)

13x -6x-12

7x-12

Answer:

7x+12

Step-by-step explanation:

i just took a test and that was the answer  

good ?

Answer:

i think its the 2

Step-by-step explanation:

for sure❤

Answer:

Point (1 , 0.75) lies on the graph of the function ⇒ last answer

Step-by-step explanation:

* Lets revise the exponential function

- An exponential function with base b is defined by f (x) = ab^x  

 where a ≠0, b > 0 , b ≠1, and x is any real number.

- The base, b, is constant and the exponent, x, is a variable.

- The graph of it in the attached figure

- Features (for this graph):

• The domain is all Real numbers.

• The range is all positive real numbers (not zero).

• The y-intercept at (0 , 1.5). Remember any number to

  the power of zero is 1.  

• Because 0 < b < 1, the graph decreases (b = 1/2)

* Now lets check which point lies on the graph

- Substitute the value of x of the point, in the function

- If the answer is the same as y, then the point lies on the graph of

 the function

∵ y = 1.5(1/2)^x

∵ x = -3

∴ y = 1.5(1/2)^(-3) = 187.5 ≠ 1

∴ Point (-3 , 1) does not lie on the graph of the function

∵ x = 2

∴ y = 1.5(1/2)² = 3/8 ≠ 5

∴ Point (2 , 5) does not lie on the graph of the function

∵ x = -2

∴ y = 1.5(1/2)^-2 = 6 ≠ 3

∴ Point (-2 , 3) does not lie on the graph of the function

∵ x = 1

∴ y = 1.5(1/2)^1 = 0.75

∴ Point (1 , 0.75) lies on the graph of the function