!!!!DONT SKIPP!!!!! ALGEBRA 12TH GRADE

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Answer:16

Step-by-step explanation:

Answer:

The height of the pyramid is 16 feet.

Step-by-step explanation:

A right pyramid with a square base has a base edge length of 24 feet.

The slant height is 20 feet.

We take the half of base here that is 12.

Let the height be h, applying Pythagoras theorem.

[tex]h^{2} =20^{2} -12^{2}[/tex]

Solving for h;

[tex]h^{2} =400-144[/tex]

=> [tex]h^{2} =400-144[/tex]

=> [tex]h^{2} =256[/tex]

=> [tex]h=\sqrt{256}[/tex]

h = 16

Therefore, The height of the pyramid is 16 feet.

Answer:

y = 1/2 x

Step-by-step explanation:

We have the slope of 1/2 and a point of (4,2)

We can use point slope form

y-y1 = m(x-x1)

y-2 = 1/2(x-4)

Distribute

y-2 = 1/2x -2

Add 2 to each side

y-2+2 = 1/2 x -2+2

y = 1/2 x

This is in slope intercept form

Answer:

speed in still water is 15 miles per hour; the speed of the current is 9 miles per hour

Step-by-step explanation:

This is a distance = rate times time problem.

We have to set up a table with the info we have and then take it from there.

                                                   d      =      r      x      t

downstream (w/ current)

upstream (against current)

We know the distance is 72 miles each way, so filling that in (I am also abbreviating downstream to d.s. and upstream to u.s.)

                  d      =      r      x      t

d.s             72

u.s             72

We also know that the trip with the current took 3 hours, and the trip back took 12.  Filling that in:

                d      =      r      x      t

d.s           72      =             x     3

u.s           72     =              x     12

Now we just need the rate values.  But we don't have anything solid to put in there.  We only know that WITH the current, the rate of the boat is faster; we also know that AGAINST the current, the rate of the boat is slower.  So the rate with the current is whatever the rate in still water is + the rate of the current or r + c.  The rate against the current is whatever the rate is in still water - the rate of the current or r - c.  Those values will fit into the rate column:

           d      =      r      x      t

d.s      72     =   (r + c)     x     3

u.s.     72     =   (r - c)      x     12

Since distance = rate * time, we set that equation up for each part of the trip.  For the first part:

72 = 3(r + c) and

72 = 3r + 3c

For the second part:

72 = 12(r - c) and

72 = 12r - 12c

Since the rate of the boat in still water is going to be the same whether you are being pushed along or being pushed against by the current, I solved the first equation for r:

72 = 3r + 3c and

3r = 72 - 3c so

r = 24 - c

and subbed that in for r in the second equation to solve for the rate of the current:

72 = 12(24 - c) - 12c and

72 = 288 - 12c - 12c

Combining like terms and we have

-216 = -24c so

c = 9

Now we can go back up the rate in terms of current, r = 24 - c, and plug in 9 for c to solve for r:

r = 24 - 9 so

r = 15

The boat's speed in still water is 15 miles per hour, and the speed of the current is 9 miles per hour.

The boat's speed in still water is 15 miles per hour, and the speed of the current is 9 miles per hour, determined by setting up equations based on rate, time, and distance for both downstream and upstream travel.

The question involves determining the speed of a boat in still water and the speed of the current given the times it takes to travel a certain distance downstream and upstream. To solve the problem, we use the concept of rate, time, and distance, where distance equals rate multiplied by time (D = RT). We know the distance (72 miles), the time downstream (3 hours), and the time upstream (12 hours).

Let's define the speed of the boat in still water as 'b' and the speed of the current as 'c'. When the boat travels downstream, it moves with the current, so its effective speed is 'b + c'. Upstream, it moves against the current, so its effective speed is 'b - c'. Using the distances and times given, we can set up two equations:

1) Downstream: 72 = (b + c) * 3

2) Upstream: 72 = (b - c) * 12

By solving these simultaneous equations, we find out:

Adding these two equations gives us 2b = 30, meaning b = 15 miles per hour. By substituting b in any of the above equations, we find c = 9 miles per hour.

Therefore, the boat's speed in still water is 15 miles per hour, and the speed of the current is 9 miles per hour.

Answer:

1) 51

2) 0.8

3) cosecant

Step-by-step explanation:

Question 1

The image for this scenario is attached below. Note that base of the television tower forms the side adjacent to the angle and the length of the tower forms the side opposite to the angle. The two angles marked in image are equal because of the property of Alternate Interior Angles.

So,

Adjacent side = 120 feet

Opposite side = 150 feet

Tangent of an angle is defined as:

[tex]tan(\theta)=\frac{Opposite}{Adjacent}[/tex]

Using the values, we get:

[tex]tan(\theta)=\frac{150}{120}\\\\ tan(\theta)=1.25\\\\ \theta = tan^{-1}(1.25)\\\\ \theta=51.34[/tex]

Rounded to the nearest degree, the angle of depression would be 51 degrees.

Question 2)

We have to find the cosine of angle Z. cos is defined as:

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

The side adjacent to angle Z is 24 and the hypotenuse is 30. So cos(Z) would be:

[tex]cos(Z)=\frac{24}{30}\\\\cos(Z)=0.8[/tex]

Therefore, value of cos(Z) for given triangle would be 0.8

Question 3

The opposite of sine ratio is known as cosecant which is abbreviated as csc

Since it is the opposite of sine ratio, it would be calculated as:

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

sine of angle is the ratio of opposite and hypotenuse, so csc would be ratio of hypotenuse to opposite side i.e.

[tex]csc(\theta)=\frac{hypotenuse}{opposite}[/tex]

Answer:

Step-by-step explanation:

QUESTION 1

Bottom leg of right triangle= 120 ft

Height= 150 ft

Angle of depression at the top of the tower = x

tan x= adjacent/opposite leg= 150/120= 1.25

tan x= 1.25

x ≈ 51.35°= 51°

QUESTION 2

Cos Z= adjacent side/hypotenuse

Cos Z= 24/30= 4/5

Z= 41.4°

QUESTION 3

Opposite of sine

The cosecant is the reciprocal of the sine

Cosecant Function:

 csc(θ) =  Hypotenuse/Opposite

Answer:

[tex]x=\frac{10\sqrt{6}}{7}\ in[/tex]

Step-by-step explanation:

step 1

In the right triangle DOC

Find the measure of side DO

Applying the Pythagoras Theorem

[tex]DC^{2}=DO^{2}+OC^{2}[/tex]

substitute the given values

[tex]7^{2}=DO^{2}+5^{2}[/tex]

[tex]DO^{2}=7^{2}-5^{2}[/tex]

[tex]DO^{2}=49-25[/tex]

[tex]DO^{2}=24[/tex]

[tex]DO=2\sqrt{6}\ in[/tex]

step 2

In the right triangle DOC

Find the sine of angle ∠ODC

sin(∠ODC)=OC/DC

substitute

[tex]sin(ODC)=5/7[/tex] -----> equation A

step 3

In the right triangle DOP

Find the sine of angle ∠ODP

sin(∠ODP)=OP/DO

substitute

[tex]sin(ODP)=x/2\sqrt{6}[/tex] -----> equation B

step 4

Find the value of x

In this problem

∠ODC=∠ODP

so

equate equation A and equation B

[tex]5/7=x/2\sqrt{6}[/tex]

[tex]x=\frac{10\sqrt{6}}{7}\ in[/tex]

Answer:

  B. {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}

Step-by-step explanation:

You are right, it is easy. Any relation with a repeated first value is not a function.

A has (-3, -1) and (-3, -3), so the value -3 is a repeated first value.

C has (2, 5) and (2, 3), so the value 2 is a repeated first value.

D has (5, 8), (5, 9), and (5, -3), so the value 5 is a repeated first value.

None of A, C, or D is a relation that is a function. The correct choice is B, which has first values 0, 1, 2, 3, 4 -- none of which is repeated.

_____

If you plot points with repeated first values, you find they lie on the same vertical line. If a vertical line passes through 2 or more points in the relation, that relation is not a function. We say, "it doesn't pass the vertical line test."

A relation must pass the vertical line test in order to be a function. This is true of graphs of any kind, not just graphs of discrete points.

Answer:

The correct answer option is B. {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}.

Step-by-step explanation:

We are to determine whether which of the given relations in the possible answer options is a function.

We know that the x values of a function cannot be repeated. It means that for each output, there must be exactly one input.

Therefore, we will look for the relation where no x value is repeated.

Function ---> {(1, 7), (2, 8), (4, 5), (0, 0), (3, 5)}

Answer:

Step 1: Finding r using the formula ln 2/h

[tex]1.\ r=\frac{ln\ 2}{h}\\ r=\frac{ln\ 2}{140}\\r=0.00495[/tex]

Step 2: Substitute the values in given formula

[tex]2.\ m_t=m_0e^{-rt}\\200=300e^{-0.00495t}[/tex]

Step 3: Divide both sides by 300

[tex]\frac{2}{3} =e^{-0.00495t}[/tex]

Step 4:  Take the natural logarithm on both sides

[tex]ln\ \frac{2}{3} =ln\ e^{0.00495t}[/tex]

Step 5: Simplify

[tex]-0.405 = -0.00495t[/tex]

Step 6: Divide both sides by 0.00495

[tex]\frac{-0.405}{-0.00495} =t[/tex]

Step 7: Simplify

[tex]t=81.8\ days[/tex]

Answer:

  $858

Step-by-step explanation:

You pay for 11 of the 12 months, so the average monthly payment is ...

  (11/12)×$936 = $858

Answer:

[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]

Step-by-step explanation:

The given ellipse has equation:

[tex]\frac{(y-2)^2}{64}+\frac{x^2}{9}=1[/tex].

The center of this ellipse is (h,k)=(0,2)

We use the equation: [tex]a^2-b^2=c^2[/tex] to determine the foci.

[tex]\implies 64-9=c^2[/tex]

[tex]\implies 55=c^2[/tex]

[tex]\implies c=\pm \sqrt{55}[/tex]

The directrices are given by [tex]y=k\pm\frac{a^2}{c}[/tex]

[tex]y=2\pm\frac{64}{\sqrt{55}}[/tex]

[tex]y=2\pm8.6[/tex]

[tex]y=2-8.6[/tex] and [tex]y=2+8.6[/tex]

The equation of the directrices are:

[tex]y=-6.6[/tex] and [tex]y=10.6[/tex]

The correct answer is D

Answer:

  21,550

Step-by-step explanation:

An increase of 5% means the population is multiplied by 100% +5% = 1.05. This occurs each year for 12 years, so the multiplier is ...

  1.05¹² ≈ 1.7958563

When the initial population is multiplied by this factor, it becomes ...

  12,000×1.7958563 ≈ 21,550

Answer: 21550

Step-by-step explanation:

Answer:

Step 4

Step-by-step explanation:

4^-4 is 1/256

-(1/4^-4) is -256

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x=-31+2y&\text{subtract}\ 2y\ \text{from both sides}\\5x+6y=23\end{array}\right\\\\\left\{\begin{array}{ccc}3x-2y=-31&\text{multiply both sides by 3}\\5x+6y=23\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}9x-6y=-93\\5x+6y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad14x=-70\qquad\text{divide both sides by 14}\\.\qquad x=-5\\\\\text{Put it to the second equation:}\\\\5(-5)+6y=23\\-25+6y=23\qquad\text{add 25 to both sides}\\6y=48\qquad\text{divide both sides by 6}\\y=8[/tex]

Answer:

B

Step-by-step explanation:

Answer:

8 + i

Step-by-step explanation:

What you need to simplify this is the following "definitions" of i to different powers.

[tex]i^1=i[/tex]

[tex]i^2=-1[/tex]

[tex]i^3=i^2*i=-1*i=-i[/tex]

[tex]i^4=1[/tex]

Now we can sub these in for the various powers of i in our expression:

[tex]6(1)+6(-i)-2(-1)+\sqrt{-1*49}[/tex]

Simplifying a bit:

[tex]6-6i+2+\sqrt{i^2*49}[/tex]

Since we know that the square root of i-squared is i, and that the square root of 49 is 7, we can get rid of the radial sign as follows:

6 - 6i + 2 + 7i

And the final answer, in a + bi form, is

8 + i

Answer:

  see the attachment

Step-by-step explanation:

f(x) is increasing for x > 0.

g(x) is increasing for x < 4.

Both functions are increasing on the open interval (0, 4). It will be graphed with a solid line between 0 and 4, and with open circles at 0 and 4. See the black line on the x-axis of the attachment for an example of such a graph.

Answer:

  see below

Step-by-step explanation:

Attached is the output of a computer program that picked two different numbers at random from the set 1-52, then converted those numbers to a suit and value.

Such a program could be written in a spreadsheet or any of a variety of computer languages.

Answer:

(3 x + 2) (4 x + 3)

Step-by-step explanation:

Factor the following:

12 x^2 + 17 x + 6

Factor the quadratic 12 x^2 + 17 x + 6. The coefficient of x^2 is 12 and the constant term is 6. The product of 12 and 6 is 72. The factors of 72 which sum to 17 are 8 and 9. So 12 x^2 + 17 x + 6 = 12 x^2 + 9 x + 8 x + 6 = 3 (3 x + 2) + 4 x (3 x + 2):

3 (3 x + 2) + 4 x (3 x + 2)

Factor 3 x + 2 from 3 (3 x + 2) + 4 x (3 x + 2):

Answer:  (3 x + 2) (4 x + 3)

The quadratic expression 12x^2 + 17x + 6 can be factored completely as (4x +3) * (3x +2).

To factor the quadratic expression 12x^2 + 17x + 6 completely, we need to find two binomial factors that multiply together to give the original quadratic expression.

The factored form will have the following structure: (ax + b)(cx + d), where a, b, c, and d are constants.

To factor 12x^2 + 17x + 6, we can look for two numbers whose product is equal to the product of the leading coefficient (12) and the constant term (6), which is

12 * 6 = 72.

we can split 72 into 8 * 9= 72

Next, we need to find two numbers whose sum is equal to the coefficient of the linear term (17x). In this case, we need two numbers that add up to 17.

so

8+9=17

Now we can write the expression:

12x^2 + 17x + 6

12x^2 + 8x + 9x + 6

Now take common:

4x (3x + 2 ) + 3 (3x +2)

Taking 3x + 2 common we get:

(4x +3) * (3x +2)

Therefore, the quadratic expression 12x^2 + 17x + 6 can be factored completely as (4x +3) * (3x +2).

To learn more about quadratic expression click:

https://brainly.com/question/10025464

#SPJ6

Answer:

(S+7)/4 = T

Step-by-step explanation:

S=4T-7

We want to solve to T

Add 7 to each side

S+7=4T-7+7

S+7 = 4T

Divide each side by 4

(S+7)/4 = 4T/4

(S+7)/4 = T

Answer:

Simplifying

0x =-2, 1

0 * x =-2.1

Apply rule () *a = 0

0=-2.1

Step-by-step explanation:

Therefore, the zeroes of the function [tex]\( f(x) = x^2 - x - 2 \)[/tex] are [tex]\( x = 2 \)[/tex] and [tex]\( x = -1 \).[/tex]

To find the zeroes of the quadratic function [tex]\( f(x) = x^2 - x - 2 \),[/tex] we need to solve for [tex]\( x \)[/tex] when [tex]\( f(x) = 0 \)[/tex]. This means we need to find the values of [tex]\( x \)[/tex]that make the function equal to zero.

We can solve this quadratic equation by factoring or using the quadratic formula. Let's use the quadratic formula:

For a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex], the solutions [tex]\( x \)[/tex] are given by:

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

For our equation [tex]\( f(x) = x^2 - x - 2 \)[/tex], we have [tex]\( a = 1 \), \( b = -1 \)[/tex], and [tex]\( c = -2 \)[/tex]. Substituting these values into the quadratic formula:

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

[tex]\[ x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2} \][/tex]

[tex]\[ x = \frac{{1 \pm \sqrt{9}}}{2} \][/tex]

[tex]\[ x = \frac{{1 \pm 3}}{2} \][/tex]

So, the solutions are:

[tex]\[ x_1 = \frac{{1 + 3}}{2} = 2 \][/tex]

[tex]\[ x_2 = \frac{{1 - 3}}{2} = -1 \][/tex]

Answer:

P (sum of two numbers is < 5) =2/9

Step-by-step explanation:

There are two numbers that can be picked such that the first number odd and less than 5:  1 and 3.

Then, the numbers that can be drawn with these numbers should be from: 1, 2, 3, 4, 5, 6, 7, 8 or 9.

The number of total possibilities = 18

Out of these, the following are the four possible options to have a sum which is less than 5 and 1:

1 and 1

1  and 2

1 and 3

3 and 1

So P (sum of two numbers is < 5) = [tex]\frac{4}{18}[/tex] = 2/9

Answer:

Step-by-step explanation:

2/9 is right because i just took it and got a 5/5

Answer:

B

Step-by-step explanation:

This was originally a third degree polynomial:

[tex]2x^3+4x^2-4x+6[/tex], to be exact.

When you divide by -3, you are basically trying to determine if x + 3 is a zero of that third degree polynomial.  The quotient is always one degree lesser than the polynomial you started with, and if there is no remainder, then x + 3 is a zero of the polynomial and you could go on to factor the second degree polynoial completely to get all 3 solutions.  To perform the synthetic division, you always first bring down the number in the first position, in our case a 2.  Then multiply that 2 by -3 to get -6.

-3|  2   4   -4   6

          -6

    2    -2

So far this is what we have done.  Now we multiply the -3 by the -2 and put that up under the -4 and add:

-3|  2   4   -4   6

          -6   6

    2    -2   2

Now we multiply the -3 by the 2 to get -6 and put that up under the 6 and add:

-3|   2   4   -4   6

           -6    6  -6

      2    -2   2   0

That last row gives us the depressed polynomial, which as stated earlier here, is one degree less than what you started with:

[tex]2x^2-2x+2[/tex]

Answer: OPTION B

Step-by-step explanation:

You need to follow these steps:

- Carry the number 2 down and multiply it by the the number -3.

- Place the product obtained above the horizontal line, below the number 4 and add them.

- Put the sum below the horizontal line.

- Multiply this sum by the number -3.

- Place the product obtained above the horizontal line, below the number -4 and add them.

- Put the sum below the horizontal line.

- Multiply this sum by the number -3.

- Place the product obtained above the horizontal line, below the number 6 and add them.

Then:

[tex]-3\ |\ 2\ \ \ \ \ 4\ \ -4\ \ \ \ \ \ 6\\\.\ \ \ \ \ |\ \ \ \ -6\ \ \ \ \ 6\ \ \ -6[/tex]

[tex]-----------------[/tex]

[tex].\ \ \ \ \ \ 2\ \ \ -2\ \ \ \ 2\ \ \ \ \ 0[/tex]

 Therefore, the quotient in polynomial form is:

[tex]2x^2-2x+2[/tex]

Answer:

If you want to round to the nearest hundredths, the answer is 1.73 seconds.

Step-by-step explanation:

So we want to solve h(t)=5 for t because this will give us the time,t, that the diver was 5 m above the water.

[tex]-4.9t^2+1.5t+17=5[/tex]

My goal here in solving this equation is to get it into [tex]at^2+bt+c=0[/tex] so I can use the quadratic formula to solve it.

The quadratic formula is [tex]t=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

So let's begin that process here:

[tex]-4.9t^2+1.5t+17=5[/tex]

Subtract 5 on both sides:

[tex]-4.9t^2+1.5t+12=0[/tex]

So let's compare the following equations:

[tex]-4.9t^2+1.5t+12=0[/tex]

[tex]at^2+bt+c=0[/tex].

[tex]a=-4.9[/tex]

[tex]b=1.5[/tex]

[tex]c=12[/tex]

Now we are ready to insert in the quadratic formula:

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

[tex]t=\frac{-1.5 \pm \sqrt{(1.5)^2-4(-4.9)(12)}}{2(-4.9)}[/tex]

I know this can look daunting when putting into a calculator.

But this is the process I used on those little calculators back in the day:

Put the thing inside the square root into your calculator first.  I'm talking about the [tex](1.5)^2-4(-4.9)(12)[/tex].

This gives you:  237.45

Let's show what we have so far now:

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

[tex]t=\frac{-1.5 \pm \sqrt{(1.5)^2-4(-4.9)(12)}}{2(-4.9)}[/tex]

[tex]t=\frac{-1.5 \pm \sqrt{237.45}}{2(-4.9)}[/tex]

I'm going to put the denominator, 2(-4.9), into my calculator now.

[tex]t=\frac{-1.5 \pm \sqrt{237.45}}{-9.8}[/tex]

So this gives us two numbers to compute:

[tex]t=\frac{-1.5 - \sqrt{237.45}}{-9.8} \text{ and } t=\frac{-1.5+\sqrt{237.45}}{-9.8}[/tex]

I'm actually going to type in -1.5-sqrt(237.45) into my calculator, as well as, -1.5+sqrt(237.45).

[tex]t=\frac{-16.90941271}{-9.8} \text{ and } t=\frac{13.90941271}{-9.8}[/tex]

We are going to use the positive number only for our solution.

So we have the answer is whatever that first fraction is approximately:

[tex]t=\frac{-16.90941271}{-9.8}=1.725450277[/tex].

The answer is approximately 1.73 seconds.

Final answer:

To determine when the diver was 5 m above the water, we need to solve the equation h(t) = 5. Using the given equation h(t) = -4.9t² + 1.5t + 17, we substitute 5 for h(t) and solve the resulting quadratic equation. The solution is t ≈ 1.82 seconds.

Explanation:

To determine when the diver was 5 m above the water, we need to solve the equation h(t) = 5. We can substitute 5 for h(t) in the given equation and solve for t:

5 = -4.9t² + 1.5t + 17

-4.9t² + 1.5t + 12 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac))/2a

Plugging in the values a = -4.9, b = 1.5, and c = 12, we get:

t = (-1.5 ± √(1.5^2 - 4(-4.9)(12)))/(2(-4.9))

Simplifying further, we find two solutions: t ≈ 1.82 seconds and t ≈ -0.44 seconds. Since time cannot be negative in this context, the diver was 5 m above the water at approximately 1.82 seconds.

Answer:

Step-by-step explanation:

1.6 pounds

Answer:

A.

Step-by-step explanation:

you add all prices together and then mulitplied by the 15%. that gives you 20.0655 so you subtract that from the total price so 133.77-20.0655 and get 113.7045 or 113.70 which is the final price you pay

Answer:

[tex](\frac{-\sqrt{2}}{2},\frac{\sqrt{2}}{2})[/tex]

Step-by-step explanation:

Unit circle has a radius of 1.

So x=cos(3pi/4)=-sqrt(2)/2 and y=sin(3pi/4)=sqrt(2)/2

So the ordered pair is (-sqrt(2)/2  , sqrt(2)/2)

The terminal point for the unit circle that is determine by the [tex]$\frac{3 \pi}{4} $[/tex]   radians is

[tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]

We know the coordinates of the terminal point will be :

[tex]$x= \cos \left( \frac{3 \pi}{4} \right)$[/tex]    and   [tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]

Therefore,

[tex]$x= \cos \left( \pi - \frac{ \pi}{4} \right)$[/tex]

[tex]$x= - \cos \frac{\pi}{4}$[/tex]

   [tex]$=-\frac{1}{\sqrt 2}$[/tex]

And

[tex]$y= \sin \left( \frac{3 \pi}{4} \right)$[/tex]

[tex]$y = \sin \left( \frac{\pi}{2} + \frac{\pi}{4} \right)$[/tex]

   [tex]$=\cos \frac{\pi}{4}$[/tex]

   [tex]$=\frac{1}{\sqrt 2}$[/tex]

Therefore the terminal points are : (x, y) = [tex]$\left( -\frac{1}{\sqrt 2}, \frac{1}{\sqrt 2} \right) . $[/tex]

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Answer:

  81.7 mpg

Step-by-step explanation:

"miles per gallon" means the number of miles is divided by the number of gallons.

  (425 mi)/(5.2 gal) = (425/5.2) mi/gal ≈ 81.7 mpg

Answer:

The first two graphs are the exact same but it is the first two.

Step-by-step explanation:

Answer:

In the beginning ,number of inventory in the warehouse =6,000

 Increment in each month in inventory in the warehouse=3000

So, writing the above situation in terms of linear equation

 if,y is the number of inventory after x months

 y=6000 +3000x

Correct graph is attached below

⇒Items in Inventory(Thousands) ----X axis

⇒Number of Months since Opening----Y axis

Answer:

B. assumption of conclusions without prior experimentation or observation.

Step-by-step explanation:

In scientific investigation is quite important to demonstrate with facts, with observations, with numbers.  All discoveries, new insights, new knowledge found in scientific investigation is based on a very careful finding of facts in a very systematic way of doing that to establish conclusions about the question to be answered and constantly looking for objective evidence.

For instance, one hundred years ago, some physicists found a crucial fact that support one of the predictions that Einstein posted regarding a phenomena described as curved space because of the effect that a massive object exerts around its surrounding space. In fact, that year of 1919, those physicists observed that light traveled around a massive start not in straight line but curving around start's space (a fact), of course, using telescopes, writing observations and quantifying them (a systematic way).

Einstein's theory (in this case, the famous General Relativity Theory) must be supported, at least in part, with the discovery of an important fact, and not because he assumed that it was 'true' without prior experimentation or observation but because some others experimental physicists took a 'secret' from Nature (objective evidence) and gave a crucial fact about what Einstein had predicted some years before.

But it is not a definitive fact, a definitive list, there will be some more facts to look for in order to support that theory (constantly looking) and, why not, some other scientist or scientists could find another one, make a new experiment, test another hypothesis or model that contradicts the whole theory or some part of it.

Answer:

See below.

Step-by-step explanation:

52 inches - 41 inches = 11 inches

She needs to be at least 11 inches taller to be at least 52 inches tall.

Statements that describe how much taller she must be:

(The correct answers are in bold and checked with the square root symbol, √.)

at least 11 inches √

no more than 11 inches

a maximum of 11 inches

a minimum of 11 inches √

fewer than 11 inches

at most 11 inches

Answer:

Step-by-step explanation:

at least 11 inches

a minimum of 11 inches