1.)Find the length of x and y in the 30 -60 -90 triangle.
2.) A triangle has side lengths 4ft 12ft and 13ft is the triangle acute obtuse or right
Show work please

Answer:

B. 1/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 4(2)ˣ

Step 2: Evaluate

The distance traveled by the car before it comes to a stop can be found by using the formula for distance traveled under constant acceleration:

\(d = v_0t + (1/2)at^2\)

where d is the distance traveled, v0 is the initial velocity, a is the acceleration, and t is the time.

We are given that \(v_0 = 20 m/s\) and \(a = -30/t + 20 m/s^2\). We need to find the time t when the car comes to a stop, which is when the final velocity is 0.

Using the formula for final velocity under constant acceleration:

\(v_f = v_0 + at\)

We can set vf = 0 and solve for t:

\(0 = 20 + (-30/t + 20)t \\0 = 20t - 30 + 20t \\30 = 40t \\t = 30/40 = 0.75 s\)

Now we can plug this value of t back into the formula for distance traveled to find the distance traveled before the car comes to a stop:

\(d = (20)(0.75) + (1/2)(-30/0.75 + 20)(0.75)^2\\ d = 15 + (1/2)(-40 + 20)(0.5625)\\ d = 15 + (1/2)(-20)(0.5625) \\d = 15 - 5.625\\ d = 9.375 m\)

Therefore, the distance traveled before the car comes to a stop is 9.375 m.

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Rodrigo traveled 0.5 feet further per second than Skyler if Skyler traveled 65 feet in 5 seconds and Rodrigo traveled 108 feet in 8 seconds.

As Skyler traveled 65 feet in 5 seconds; therefore the speed at which he traveled is calculated as follows;

Speed = distance traveled ÷ time taken = 65 ÷ 5

Speed = 13 feet per second

Similarly, as Rodrigo traveled 108 feet in 8 seconds, the speed at which he traveled is;

Speed = distance traveled ÷ time taken = 108 ÷ 8

Speed = 13.5 feet per second

Now to determine how much further Rodrigo traveled per second can be calculated by subtraction as follows;

13.5 feet per second - 13 feet per second = 0.5 feet per second

Therefore Rodrigo traveled 0.5 feet further per second than Skyler.

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Answer: The median changed the most.

Old median = 79.5

new median = 86.5

===============================================

Explanation:

To find the mean, we add up the values and divide by 12 since there are 12 numbers in this list.

mean = (add up the values)/(number of values)

mean = (58+61+71+77+91+100+105+102+95+82+66+57)/12

mean = 80.41667 approximately

--------

To get the median, we need to sort the numbers from smallest to largest

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

There are n = 12 items in this set.

Because n = 12 is an even number, the median is between slots n/2 = 12/2 = 6 and 7

The midpoint of those values is (77+82)/2 = 79.5 which is the median.

--------

The range is the difference between the min and max

range = max - min = 105 - 57 = 48

The IQR will involve splitting the sorted set into two halves

L = lower half = stuff below the median

L =  {57, 58, 61, 66, 71, 77}

U = upper half = stuff above the median

U = {82, 91, 95, 100, 102, 105}

The median of set L is (61+66)/2 = 63.5 which is the value of Q1.

The median of set U is (95+100)/2 = 97.5 which is the value of Q3

IQR = interquartile range

IQR = Q3 - Q1

IQR = 97.5 - 63.5

IQR = 34

--------

Here is a summary of what we calculated

If we were to replace the "71" with "93", and redo the calculations, then we'll get these results:

The range and IQR stay the same, but the mean and median values are different.

Let's see which of those two values changed the most.

The median has changed the most because the +7 is larger than +1.83333

Answer:

x = 12.

Step-by-step explanation:

There are 5 numbers so the total of the numbers

= mean * 5

= 25.

Now

4 + 3 + 3 + 3 + x = 25

So

13 + x = 25

x = 25 - 13 = 12.

The value of x is 12.

To find the value of x, we can set up an equation using the given information.

The mean (average) of the numbers 4, 3, 3, 3, and x is 5.

The sum of these numbers is (4 + 3 + 3 + 3 + x).

The mean is calculated by dividing the sum by the number of values, which in this case is 5.

So, we can write the equation as:

(4 + 3 + 3 + 3 + x) / 5 = 5

To solve for x, we can start by multiplying both sides of the equation by 5 to get rid of the fraction:

4 + 3 + 3 + 3 + x = 5 * 5

Simplifying the right side:

4 + 3 + 3 + 3 + x = 25

Now, we can combine the terms on the left side:

13 + x = 25

Next, we'll isolate x by subtracting 13 from both sides:

x = 25 - 13

Simplifying:

x = 12

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Answer:

∠ S = 80°

Step-by-step explanation:

Since the triangles are congruent then corresponding angles are congruent.

∠ T = ∠ B = 5x - 27

The sum of the angles in Δ STU = 180°

Sum the 3 angles and equate to 180

4x + 12 + 5x - 27 + 3x - 9 = 180 , that is

12x - 24 = 180 ( add 24 to both sides )

12x = 204 (divide both sides by 12 )

x = 17

Then

∠ S = 4x + 12 = 4(17) + 12 = 68 + 12 = 80°

Answer:

3 out of 4 I think

Step-by-step explanation:

because the total amount is 4 so there's a 3/4 chance youll get less than 4

Step-by-step explanation:

The equation of a parabola that relates it focus is

\( {x}^{2} = 4py\)

So here, we isolate x^2.

\(y = \frac{1}{32} {x}^{2} \)

\(32y = {x}^{2} \)

Next, we factor out 4.

\( {x}^{2} = 4(8)(y)\)

Our p=8 so this tells us the distance of the vertex to the focus.

Answer:

≈ 117.1537

Step-by-step explanation:

Pythagorean Theorem equation: c²=a²+b²

Here we need to solve for the hypotenuse (c)

c² = (90)² + (75)²

c² = 8100 + 5625

c² = 13725

√c = √13725

c ≈ 117.1537

Answer:117.1537

Step-by-step explanation:

Pythagorean Theorem equation: c²=a²+b²

need to solve for the hypotenuse (c)

c² = (90)² + (75)²

c² = 8100 + 5625

c² = 13725

√c = √13725

c ≈ 117.1537

The amount of money, to the nearest cent, in the account after 10 years is found as $742.87.

The formula for the continuous compound  is:

V = Pe^{rt}

In which:

V= 358*2.72*{0.073*10}

V = 358*2.07

V = 742.87

Thus, the amount of money, to the nearest cent, in the account after 10 years is found as $742.87.

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The number of periods is approximately 26.98.

To calculate the number of periods it takes to double your money at 5.25 percent interest, you can use the formula for compound interest:

Future value = Present value * (1 + interest rate) ^ number of periods

In this case, the future value is twice the present value, so the equation becomes:

2 = 1 * (1 + 0.0525) ^ number of periods

To solve for the number of periods, you can take the logarithm of both sides:

log(2) = log((1 + 0.0525) ^ number of periods)

Using the logarithmic properties, you can bring the exponent down:

log(2) = number of periods * log(1 + 0.0525)

Finally, you can solve for the number of periods:

number of periods = log(2) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 13.27.

To calculate the number of periods it takes to quadruple your money at 5.25 percent interest, you can follow the same steps as above, but change the future value to four times the present value:

4 = 1 * (1 + 0.0525) ^ number of periods

Solving for the number of periods using logarithms:

number of periods = log(4) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 26.98.

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Answer: 721 ft

Step-by-step explanation:

formula for area is a=l*w

Given: w=103, length=7

103*7=721

Answer: The answer 721. When you are finding an area of something you must multiply the length and the width so the information given.

103 x 7 = 721 feet long

Here is the real problem:

It's sloppy as long as you understand the concept : )

Answer:

Area = 1,344 cm²

Step-by-step explanation:

First, find the value of x and the numerical side length of all sides of the triangle before finding the area.

Thus:

Perimeter of a triangle = sum of all its side

Therefore,

(6x - 44) + (2x - 20) + (3x + 24) = 224

Solve for x

6x - 44 + 2x - 20 + 3x + 24 = 224

Add like terms

11x - 40 = 224

Add 40 to both sides

11x = 224 + 40

11x = 264

Divide both sides by 11

x = 24

Find the measurement of each side length by plugging in the value of x:

Hypotenuse = 6x - 44 = 6(24) - 44 = 100 cm

Height = 2x - 20 = 2(24) - 20 = 28 cm

Base = 3x + 24 = 3(24) + 24 = 96 cm

Find the area:

Area = ½×base×height

Plug in the values

= ½×96×28

Area = 1,344 cm²

x-coordinate of the vertex is time in seconds and y-coordinate of the vertex is the height of the football.

Coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given that Jevonte kicks a football. Its height in feet is given by h = -16t² +48t

where t represents the time in seconds after kick.

We have to find x-coordinate (or t-coordinate) of the vertex is time in seconds and y y-coordinate (or h-coordinate) of the vertex is the height of the football.

Hence, x-coordinate of the vertex is time in seconds and y-coordinate of the vertex is the height of the football.

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Answer:

1) 48

2)44

Step-by-step explanation:

Answer:  48 44 Are The Correct Answers

Step-by-step explanation:Hope This Helps

Answer:

Step-by-step explanation:

Given that the circumference  of the frame is 56in

we can proceed to obtain the radius of the frame

we know that

circumference= 2πr

56= 2*3.142*r

56= 6.284r

divide both sides by 6.284

r= 56/6.284

r=8.9

approximately radius is 9in

therefore the area of the mirror that is largest would be

Area=  πr^2

Area= 3.142*9^2

Area= 3.142*81

Area= 254.5 in^2

The largest area is 254.5 in^2

The area left for children for playing 114464 sq. m

As per the given data inside a park:

The length of the park is 400 m

The breadth of the park is 300 m

The formula for the area of the park = Length × Breadth

= (400 × 300) sq. m

= 120000 sq. m

The width of the walking track inside the park is 4 m

The length of the park without the walking track

= 400 − (4 + 4) m

= 400 − 8 m

= 392 m

The breadth of the park without the walking track

= 300 − (4 + 2) m

= 300 − 8 m

=292 m

Area of the park without the walking track:

= 392 × 292

= 114464 sq. m

Therefore the area left for children for playing other than the walking track is 114464 sq. m.

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Answer:

my answer is A

Step-by-step explanation:

if you work out the equation where you know that at the x intercept y=0 you will find A to be true

Answer:

Angle A: 90

Angle B: 48

Angle C: 42

Side length A (Hypotinuse): 23.9

SIde length B (Opposite): 17.8

Side length C (Adjacent): 16

Step-by-step explanation:

https://www.calculator.net/triangle-calculator.html?vc=42&vx=&vy=&va=90&vz=16&vb=&angleunits=d&x=0&y=0

Yes, the given function is a solution of the initial value problem. To verify this, we have to differentiate the given function and then set the initial value to check whether it satisfies the given initial value problem.

Differentiate the function y=xcosx

y' = cosx - xsinx

Compare the differentiated function with the given equation

y' = cosx - ytanx

cosx - xsinx = cosx - ytanx

Substitute the initial value

At x=π/4, y=π/4√2

cos(π/4) - (π/4√2)tan(π/4) = cos(π/4) - (π/4√2)tan(π/4

Verify whether or not the equation is satisfied.

The provided beginning value solves the problem. As a result, the supplied function provides an answer to the starting value question.

Complete Question:

Verify that the function is a solution of the initial value problem

y=xcosx;  y′=cosx−ytanx, y(π/4)=π/4√2.

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Answer:

not equivalent

Step-by-step explanation:

solve for x to see if they are equivalent

1/2x-8=9 and x-8=18

1/2x=17

x=34

x-8=18

x = 36

no they are not equivalent

The velocity of the satellite is \(\sf 3.6 \times10^3 \ m / s\).

Given data:

The velocity of the satellite is,

\(\sf Velocity =\sqrt{\dfrac{GM}{R} }\)

\(=\sqrt{\dfrac{6.7\times10^{-11}\times4.4\times10^{24}}{2.3\times10^7} }\)

\(\sf = 3.6 \times10^3 \ m / s\).

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The completed statements with regards to the compound interest of the amount in the account are;

If the account has a 5% interest rate and is compounded monthly, you have $101.655 million money after 2 years

If the account has a 5% interest rate compounded continuously, you would have $106.096 million money after 2 years

Compound interest is the interest calculated based on the initial amount and the accumulated interests accrued from the periods before the present.

The compound interest formula indicates that we get;

\(A = P\cdot (1 + \frac{r}{n}) ^{n\cdot t}\)

Where;

P = The principal amount invested = $92 million

r = The interest rate = 5% monthly

n = The number of times the interest is compounded per annum = 12

t = The number of years = 2 years

Therefore; \(A = 92\cdot (1 + \frac{0.05}{12}) ^{12\times 2}\approx 101.655\)

The amount in the account after 2 years is therefore about $101.655 million

The formula for the amount in the account if the principal is compounded continuously, we get;

A = \(P\cdot e^{(r\cdot t)}\)

Therefore, we get;

\(A = 96 \times e^{0.05 \times 2} \approx 106.096\)

The amount in the account after 2 years, compounded continuously therefore, is about $106.096 million

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The coordinates of point b' are (-4, 1) and the coordinates of point c' are (-6, 0).

To obtain the coordinates of points b' and c' after the same translation as point a', we need to apply the same translation vector to points b and c.

The translation vector can be found by calculating the differences between the x-coordinates and the y-coordinates of points a' and a.

Translation Vector = (x-coordinate of a' - x-coordinate of a, y-coordinate of a' - y-coordinate of a)

                   = (-2 - 3, -3 - (-4))

                   = (-5, 1)

Now, we can obtain the coordinates of points b' and c' by adding the translation vector to the respective coordinates of points b and c.

For point b':

Coordinates of b' = (x-coordinate of b + x-coordinate of translation vector, y-coordinate of b + y-coordinate of translation vector)

                 = (1 + (-5), 0 + 1)

                 = (-4, 1)

Therefore, the coordinates of point b' are (-4, 1).

For point c':

Coordinates of c' = (x-coordinate of c + x-coordinate of translation vector, y-coordinate of c + y-coordinate of translation vector)

                 = (-1 + (-5), -1 + 1)

                 = (-6, 0)

Therefore, the coordinates of point c' are (-6, 0).

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Answer:

\(I= \frac{1}{ {2}^{t} } \)

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer: x ≈ 2.9

Step-by-step explanation:

       Since this is a right triangle, we can use trigonometric functions to help us solve. We are given the opposite side and hypotenuse from our reference angle. This will use the sine function, sinθ = \(\frac{opposite}{hypotenuse }\).

sinθ = \(\frac{opposite}{hypotenuse }\)

sin(38°) = \(\frac{x+2}{8}\)

8sin(38°) = x + 2

8sin(38°) - 2 = x

x ≈ 2.9

Answer:

see explanation

Step-by-step explanation:

(a)

given m varies directly as n then the equation relating them is

m = kn ← k is the constant of variation

to find k use the condition m = 14 when n = 7

14 = 7k ( divide both sides by 7 )

2 = k

m = 2n ← equation of variation

(b)

when n = 16 , then

m = 2 × 16 = 32

(c)

when m = 30 , then

30 = 2n ( divide both sides by 2 )

15 = n