In the 30-60-90 triangle below, side s has a length of _
length of
_and side q has a?

Answer:

see explanation

Step-by-step explanation:

Using the cosine addition identity

cos(x + y) = cosxcosy - sinxsiny

and cos([tex]\frac{\pi }{2}[/tex]) = 0, sin([tex]\frac{\pi }{2}[/tex]) = 1

cos(x + [tex]\frac{\pi }{2}[/tex])

= cosxcos([tex]\frac{\pi }{2}[/tex]) - sinxsin([tex]\frac{\pi }{2}[/tex])

= cosx × 0 - sinx × 1

= 0 - sinx

= - sinx

The answer is:

The x-coordinate of the solution to the system of equations is:

[tex]x=-2[/tex]

We can solve the problem writing both equations as a system of equations.

So, we are given the equations:

[tex]\left \{ {{y=x+4} \atop {3y=-2x+2}} \right.[/tex]

Then, solving by reduction we have:

Multiplying the first equation by 2 in order to reduce the variable "x", we have:

[tex]\left \{ {{2y=2x+2*4} \atop {3y=-2x+2}} \right.[/tex]

[tex]5y=2x-2x+8+2\\\\5y=8+2\\\\y=\frac{10}{5}=2[/tex]

Now, substituting "y" into the first equation, to isolate "x" we have:

[tex]y=x+4\\\\2=x+4\\\\x=2-4=-2[/tex]

Hence we have that the x-coordinate of the solution to the system of equations is

[tex]x=-2[/tex]

Have a nice day!

Answer:

The x coordinate of the solution is -2

Step-by-step explanation:

* To find the x-coordinate of the solution to the system of the

  equations y = x + 4 and 3y = -2x + 2 solve the equations by the

  substitution method

- In the substitution method we substitute one of the two variables

 by the other to make an equation of one variable

∵ y = x + 4 ⇒ (1)

∵ 3y = -2x + 2 ⇒ (2)

- Substitute the value of y in equation (2) by the value of y in equation (1)

∵ The value y = 4 + x in the equation (1)

- Put this value of y in the equation (2)

∴ 3(x + 4) = -2x + 2 ⇒ open the bracket

∴ 3x + 12 = -2x + 2 ⇒ subtract 12 from both sides

∴ 3x = -2x - 10 ⇒ add 2x to both sides

∴ 5x = -10 ⇒ divide both sides by 5

∴ x = -2

* The x coordinate of the solution is -2

Answer:

D. 6^30

explanation:

(6^36)/(6^6)= 6^30

Divide the total amount of money by the number of boys:

1.92/3 = 0.64 cents

Each boy gets 0.64 cents.

Because you are told the two are similar, find the ratio of them.

Side AB = ft and side EF is 25 feet.

This means the larger rectangle is 5 times larger ( 25 /5 = 5).

Area is in square units, so square the ratio: 5^2 = 25

The area of the larger rectangle is 25 times the area of the smaller one.

Area = 35 x 25 = 875 ft^2

Answer:

A parallelogram is a quadrilateral with no axis of line symmetry.

Answer:

parallelogram

Step-by-step explanation:

a parallelogram does not have an axis of a line of symmetry

Answer:

56 eggs

Step-by-step explanation:

If [tex]\frac{2}{7}[/tex] of all eggs are green, [tex]\frac{1}{4}[/tex] of all are blue, then

[tex]1-\dfrac{2}{7}-\dfrac{1}{4}=\dfrac{28-2\cdot 4-7}{28}=\dfrac{13}{28}[/tex]

of all eggs are red.

We know that there are 26 red eggs

[tex]26\text{ eggs }-\dfrac{13}{28}\\ \\x\text{ eggs }- 1[=\dfrac{28}{28}][/tex]

Make a proportion

[tex]\dfrac{26}{x}=\dfrac{\frac{13}{28}}{1}\\ \\26\cdot 1=x\cdot \dfrac{13}{28}\ [\text{Cross multiply}]\\ \\13x=26\cdot 28\ [\text{Multiply by 28 to get rid of fraction}]\\ \\x=\dfrac{26\cdot 28}{13}\ [\text{Divide by 13 to get x}]\\ \\x=2\cdot 28\\ \\x=56[/tex]

Answer:

Step-by-step explanation:

Look at the picture.

Therefore we have:

[tex]\dfrac{4}{3}=\dfrac{x}{2.25}[/tex]            cross multiply

[tex]3x=(4)(2.25)[/tex]

[tex]3x=9[/tex]             divide both sides by 3

[tex]x=3[/tex]

Answer:

The hang time is 0.63 seconds

Step-by-step explanation:

We want to find out what the cricket's fall time is and we have the function that describes its height as a function of time.

The cricket is on the ground when its height is equal to zero. Therefore we must equal h to zero and solve the equation for t ..

[tex]h=-16t^2+10t\\\\-16t^2 +10t=0\\\\\\[/tex]

We take t as a common factor

[tex]-16t^2 +10t=0\\\\t(10-16t)=0[/tex]

Then the height is zero when t = 0 and when (10-16t) = 0

[tex]t=0[/tex]

[tex]10-16t= 0[/tex]

[tex]10 = 16t[/tex]

[tex]t=\frac{10}{16}\\\\t= 0.63\ sec[/tex]

At t = 0 seconds the cricket is still on the ground.

Then the cricket is in the air and after 0.63 seconds the cricket falls back to the ground

Complete the square:

[tex]-16t^2+10t=-16\left(t^2-\dfrac58t\right)=-16\left(t^2-\dfrac58t+\dfrac{25}{256}-\dfrac{25}{256}\right)=-16\left(t-\dfrac5{16}\right)^2+\dfrac{25}{16}[/tex]

That is, [tex]h(t)[/tex] has a maximum value of [tex]\dfrac{25}{16}\approx1.6[/tex] ft when [tex]t=\dfrac5{16}\approx0.3[/tex] s. It takes the cricket twice as much time to jump up to its maximum height and return to the ground, so that the hang time is about 0.6 s.

Answer:

B. 7/2, -8/3

Step-by-step explanation:

Move all the terms to the left side and set them equal to zero.  Then set each factor equal to zero.

Answer: 53 inches

Step-by-step explanation:

so to figure this out..

1. split the shape. there will be a 6 by 8 rectangle and a Height of 2 inches and the length of 5 inch triangle.

2.then find the area of 6 * 8 equals 48

3.Then find the area of the triangle. 5 * 2 equals 10. then  Divide 10 / 2 your answer will be 5

4.Then  add 48 and 5 together your answer will be 53

Answer:

48 miles

Step-by-step explanation:

1 Kilometer = 0.6 miles

80 kilometers = X miles

1 kilometer/0.6 miles = 80 kilometers/X miles

then cross multiply the ratio

X (1) = 80 (0.6)

X=48 miles

Answer:

48

Step-by-step explanation:

Step 1: In the equation 6x - 5y = 15 everytime you see the "x" plug in y+3. This will solve for y

6(y + 3) - 5y = 15

Step 2: Distribute the 6 to all the numbers in the parentheses

6y + 18 - 5y = 15

Step 3: Combine like terms (6y and -5y)

(6y - 5y) + 18 = 15

y + 18 = 15

Step 4: Isolate y by subtracting 18 to both sides

y + (18-18) = 15 -18

y = -3

Step 5: Plug y (-3) into the equation x= y + 3 to solve for x

x = -3 + 3

x = 0

For this system of equations y = -3 and x = 0

Hope this helped!

The solution to the system of equations 6x-5y=15 and x=y+3, using the substitution method, results in x = 0 and y = -3.

To solve the system of equations 6x-5y=15 and x=y+3, we can use the method of substitution since one equation is already solved for one of the variables. First, we replace x in the first equation with the expression from the second equation, (y + 3), resulting in a new equation 6(y + 3) - 5y = 15. Simplifying that gives 6y + 18 - 5y = 15, which simplifies to y = -3. Substituting y = -3 back into the second equation gives x = 0.

Answer:

3 hours

Step-by-step explanation:

We have the amount of miles that Tanika passed, 189 miles. We also have the speed at which Tanika was driving, 63 miles per hour. Basically, Tanika was passing 63 miles on every one hour of driving. In order to find out how much time was Tanika driving with that speed to pass those miles, we just simply need to divide the miles passed with the speed of driving:

189 / 63 = 3

So we have a result of 3, thus Tanika needed three hours with a speed of 63 miles per hour to pass 189 miles.

Question 1:

For this case we can raise a rule of three:

63 miles ---------------> 1 hour

189 miles -------------> x

Where "x" represents the number of hours it takes Tanika to travel 189 miles.

[tex]x = \frac {189 * 1} {63}\\x = 3[/tex]

So, Tanika takes 3 hours to travel 189 miles

Answer:

Three hours

Question 2:

For this case we must solve the following equations:

A) [tex]-2x <4[/tex]

Dividing between -2 on both sides of the inequality:

[tex]x <\frac {4} {- 2}\\x <-2[/tex]

B) [tex]5t + 7 <32[/tex]

We subtract 7 on both sides of the inequality:

[tex]5t <32-7\\5t <25[/tex]

Dividing between 5 on both sides of the inequality:

[tex]t <\frac {25} {5}\\t <5[/tex]

C) [tex]12s-17 \geq2s + 33[/tex]

We subtract 2s on both sides of the inequality:

[tex]12s-2s-17 \geq33\\10s-17 \geq33[/tex]

We are 17 on both sides of the inequality:

[tex]10s \geq33 + 17\\10s \geq50[/tex]

We divide between 10 on both sides of the inequality:

[tex]s \geq \frac {50} {10}\\s \geq5[/tex]

D) [tex]-8m> -24[/tex]

Dividing between -8 on both sides of the inequality:

[tex]m> \frac {-24} {- 8}\\m> 3[/tex]

E) [tex]8n + 7> 4n + 35[/tex]

Subtracting 4n on both sides of the inequality:

[tex]8n-4n> 35-7\\4n> 28[/tex]

Dividing between 4 on both sides of the inequality:

[tex]n> \frac {28} {4}\\n> 7[/tex]

Answer:

[tex]x <-2\\t <5\\s \geq5\\m> 3\\n> 7[/tex]

-is a positive parabola

-has two roots at x= 1 and x= 5

- has a y-intercept at y=5

- has a minimum at (3, -4)

- axis of symmetry is x=3

What they said ^^^^^^^^^^^^^^^

A variable in mathematical terms is said to be Independent, if it's value does not depend on other variable.

For, example

 y=x²

Here , you can take any one among, x and y as independent and other as Dependent to get value of other.

For, example

 x=2, gives y=4.

So,variable y is dependent on variable x.So, y is Dependent and x is Independent.

Now, Among the given options

 The Naturally Occuring product found on earth are Independent ,and Man made product which is a combination of Natural and Human beings are Dependent.

⇒Option A

Gasoline

⇒Option F

Oil

Gasoline, tires, and oil are the independent variables from the given options.

The independent variables are the ones that can be directly controlled or manipulated in an experiment or analysis.

The independent variables would typically be:

Gasoline: The amount of gasoline can be controlled by choosing how much to put in the vehicle.

Tires: The type and condition of tires can be chosen and changed.

Oil: The choice and frequency of oil changes can be controlled.

Hence, the independent variables are gasoline, tires and oil.

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Answer:

The correct graph is which x= -1 and y =1

Step-by-step explanation:

The question is on simultaneous equations

2x+y= -1.........................(a)

-x+3y = 4

Eliminate on side of the equation;

{2x+y= -1} 3

{-x+3y = 4} 1

open brackets

6x + 3y = -3

-x + 3y = 4......................eliminate y by subtraction

7x= -7.....................divide both sides by 7

x= -7/7 = -1......................use  this in (a) above

2x+y = -1

2(-1) + y = -1

-2 +y = -1

y= -1+2 = 1

hence x= -1 and y = 1

Answer:

1

Step-by-step explanation:

0 Triangles satisfy the given condition.

What is the triangle inequality?

Triangle inequality theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c.

In this question:

a,b and A are three sides of triangle.

a=14

b=2 and

A=66

In this triangle

Therefore, no such triangle with given dimension can exist.

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Answer:

Step-by-step explanation:

Weren't there possible answer choices?  Whenever there are, would you please share them.  Thank you.

n/4 - 13 could be written "13 less than one quarter of the number n."

Answer:

991 J

Step-by-step explanation:

At the bottom of the swing all of the potential energy has been converted to kinetic energy (assuming a lossless system).

Answer:

991 J

Step-by-step explanation:

At the highest point, an object has maximum potential energy and no kinetic energy. And at its lowest point, an object has maximum kinetic energy and no potential energy. All of the potential energy it had was converted into kinetic.

Answer:

[tex]490.9\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The total area is equal to

[tex]A=10(h)+2\pi r(h)+10(h)[/tex]

we have

[tex]h=9\ ft[/tex]

[tex]r=5.5\ ft[/tex]

[tex]\pi=3.14[/tex]

substitute

[tex]A=10(9)+2(3.14)(5.5)(9)+10(9)[/tex]

[tex]A=490.9\ ft^{2}[/tex]

Answer:

131.9468915

Step-by-step explanation:

Side length= 6*4*pi

Circles=2(9*pi)

Add them and you get that answer.

Easy! The formula to help with surface area is the first equation.

Answer:

C

Step-by-step explanation:

The statement deduced from the diagram is m∠1 + m∠2 = 180°

An angle is formed from the intersection of two or more lines. Angles less than 90 degrees are called acute angles, angles greater than 90° are called obtuse angles while angles with a measure of 90° are called right angles.

From the diagram:

m∠1 + m∠2 = 180° (sum of angles in a straight line)

The statement deduced from the diagram is m∠1 + m∠2 = 180°

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Answer:

x³ + 4 x² + x - 6

Step-by-step explanation:

( x - 1 ) ( x + 2 ) ( x + 3 )

( x - 1 ) ( x + 2 ) = x² + 2 x - 1 x - 2 = x² + x - 2

( x² + x - 2 ) ( x + 3 ) = x³ + 3 x² + x² + 3 x - 2 x - 6 = x³ + 4 x² + x - 6

The expression (x-1)(x+2)(x+3) can be written as x³ + 4x² + x—6 after multiplication of the expression.

It is defined as the combination of constants and variables with mathematical operators.

We have:

= (x-1)(x+2)(x+3)

After multiplying first and second terms:

[tex]\rm =\left(x^2+x-2\right)\left(x+3\right)[/tex]

Again multiplying:

[tex]\rm =x^3+4x^2+x-6[/tex]

Thus, the expression (x-1)(x+2)(x+3) can be written as x³ + 4x² + x—6 after multiplication of the expression.

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Answer:

2 13/20

Dude the blue trail is trying to trick you. scratch it out.

Step-by-step explanation:

Make the denominators the same

3 1/4 -->3 5/20

3/5   -->  12/20

covert this to an improper fraction-->3 5/20 --> 65/20

Subtract 65/20 - 12/20= 53/20

simplify 53/20 --> 2 13/20

Final answer:

To find the distance hiked before it started to rain, the length of the red trail (3 1/4 miles) is multiplied by 3/5, giving a distance of 1.95 miles.

Explanation:

The student has asked about the distance hiked on the red trail before it started to rain. To find the distance, we need to calculate 3/5 of the red trail length, which is 3 1/4 miles long. First, we must convert the mixed number to an improper fraction. 3 1/4 miles can be expressed as (3 × 4 + 1)/4 = 13/4 miles. Then we multiply 13/4 by 3/5 to find the distance hiked: (13/4) × (3/5) = (13 × 3) / (4 × 5) = 39/20. Converting this back to miles gives us 1.95 miles.

Answer:

x = +√96 = +√(16*6) = + 4√6

Step-by-step explanation:

Note that this is a large triangle with 2 smaller, similar triangles inside.  The base of the large triangle is 10, so the base of either of the smaller triangles is half that, or 5.  These are all right triangles.  We can now apply the Pythagorean Theorem to find x.

According to this Theorem, x² + 5² = 11², so that x² = 121 - 25 = 96.

Taking the positive square root to be the desired side length x,

x = +√96 = +√(16*6) = + 4√6

Answer:

The radius of the aquarium tank is [tex]8.25\ ft[/tex]

Step-by-step explanation:

we know that

Applying the Tangent Secant Theorem

[tex]DC^{2}=AC*8[/tex]

we have that

[tex]AC=(D+8)\ ft[/tex]

[tex]DC=14\ ft[/tex]

substitute

[tex]14^{2}=(D+8)*8[/tex]

[tex]196=8D+64[/tex]

Solve for D

[tex]8D=196-64[/tex]

[tex]8D=132[/tex]

[tex]D=16.5\ ft[/tex]

Find the radius

The radius is half the diameter

[tex]r=16.5/2=8.25\ ft[/tex]

Answer:

8.25

Step-by-step explanation:

DC = 14ft

AC = 8ft + the diametre

Lets use d for diametre

The equation we are using is the Segments of Secants and Tangents Theorem, which is [tex]DC^{2}[/tex] = 8ft (or the outside segment) * AC (the whole segment)

[tex]14^{2}[/tex] = 8 * (8 + d)

196 = 64 + 8d

Subtract 64 from 196 to get: 132 = 8d

Divide 8 from 132 to get: d = 16.5

Now the diametre is 16.5, but the radius is half the diametre, so now you have to do: 16.5 / 2

So the radius would end up being 8.25

Answer:

d^2 - 64

Step-by-step explanation:

This is the difference of squares. The middle 2 terms cancel out.

d^2 - 8d + 8d - 8*8

d^2 - 64

FOIL

FIRST

OUTSIDE

INSIDE

LAST

First:

(d-8)(d+8)

d * d

[tex]d^{2}[/tex]

Outside:

(d-8)(d+8)

d * 8

8d

Inside:

(d-8)(d+8)

-8 * d

-8d

Last:

(d-8)(d+8)

-8 * 8

-64

so...

d^2 + 8d + (-8d) + (-64)

d^2 - 64

Hope this helped!

Answer:

6√6 or 14.69694 (hope this helps)

Step-by-step explanation:

Product [tex]\sqrt{12}[/tex] times [tex]\sqrt{18}[/tex] is  6[tex]\sqrt{6}[/tex].

The square root of 12 can be written as

[tex]\sqrt{12} = \sqrt{2*2*3} = 2\sqrt{3}[/tex]

The square root of 18 can be written as

[tex]\sqrt{18} = \sqrt{2*3*3} = 3\sqrt{2}[/tex]

so, [tex]\sqrt{12} *\sqrt{18} = 2\sqrt{3} * 3\sqrt{2}[/tex]

=6[tex]\sqrt{3*2}[/tex]

=6[tex]\sqrt{6}[/tex]

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