The winning car in a race beat the second car by 19/100 of a second. The third car was 4/10 of a second behind the second car. By how much did the first car beat the third car?

Answer:  [tex]\frac{-3\sqrt{13}+4\sqrt{3}}{20}[/tex]

This is the single fraction of -3*sqrt(13)+4*sqrt(3) up top all over 20.

sqrt = square root

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Explanation:

Angle theta is between pi and 3pi/2. This places the angle in quadrant Q3 where both cosine and sine are negative

Use the pythagorean trig identity to get the following:

[tex]\sin^2 \theta + \cos^2 \theta = 1\\\\\sin^2 \theta + \left(-\frac{\sqrt{3}}{4}\right)^2 = 1\\\\\sin^2 \theta + \frac{3}{16} = 1\\\\\sin^2 \theta = 1 - \frac{3}{16}\\\\\sin^2 \theta = \frac{16}{16} - \frac{3}{16}\\\\\sin^2 \theta = \frac{16-3}{16}\\\\\sin^2 \theta = \frac{13}{16}\\\\\sin \theta = -\sqrt{\frac{13}{16}} \ \text{ ... sine is negative in Q3}\\\\\sin \theta = -\frac{\sqrt{13}}{\sqrt{16}}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\[/tex]

Angle beta is in Q1 where sine and cosine are positive.

Draw a right triangle with legs 3 and 4. The hypotenuse is 5 through the pythagorean theorem. In other words, we have a 3-4-5 right triangle.

Since [tex]\tan \beta = \frac{3}{4}[/tex], this means [tex]\sin \beta = \frac{3}{5} \ \text{ and } \ \cos \beta = \frac{4}{5}[/tex]

Use these ideas:

In this case we have: opposite = 3, adjacent = 4, hypotenuse = 5.

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To recap:

[tex]\cos \theta = -\frac{\sqrt{3}}{4}\\\\\sin \theta = -\frac{\sqrt{13}}{4}\\\\\cos \beta = \frac{3}{5}\\\\\sin \beta = \frac{4}{5}\\\\[/tex]

They lead to this

[tex]\sin\left(\theta + \beta\right) = \sin \theta * \cos \beta - \cos \theta * \sin \beta\\\\\sin\left(\theta + \beta\right) = -\frac{\sqrt{13}}{4} * \frac{3}{5} - \left(-\frac{\sqrt{3}}{4}\right) * \frac{4}{5}\\\\\sin\left(\theta + \beta\right) = -\frac{3\sqrt{13}}{20}+\frac{4\sqrt{3}}{20}\\\\\sin\left(\theta + \beta\right) = \frac{-3\sqrt{13}+4\sqrt{3}}{20}\\\\[/tex]

Answer:

B is answer

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A and B are linear because both the x-and-y variables are to the power of one

C is linear because, for each increase in 'x' the 'y' value increases by a constant 2

D is not linear because the y-values increase by 4 then 3; not constant

Answer:[tex]\frac{1}{64}[/tex]

Step-by-step explanation:4^-3=1/(4^3)=1/64

The height of the all after 2 secs is 86 feet

Given the height in feet above the ground was given by the following function h(t) = -16t^2 + 75t

where:

t is the number of seconds since the ball was punted.

If the value of t = 2s, hence;

h(t) = -16t^2 + 75t

h(2) = -16(2)^2 + 75(2)

h(2) = -64 + 150
h(2) = 86

Hence the height of the all after 2 secs is 86 feet

Learn more about linear equation here: https://brainly.com/question/14323743

Answer:

-10 vertically and -1 horizontally

Explanation:

shifts -1 horizontally, -10 vertically

note: vertically is up ↑ and bottom ↓ , horizontal is right → and left ←

Answer:

Step-by-step explanation:

Answer:

33. 72 cm²

Step-by-step explanation:

A= 1/2 x h x (b1+b2)

 = 1/2 x 6 x (10+14)

 = 1/2 x 6 x 24

 = 6 x 12

A= 72 cm²

(btw thats the only one i know how to do, so sorry!)

Answer:

301.6 (I rounded)

Step-by-step explanation:

Please mark brainlest

5.009, 5.09, 5.3, 5.3071.

Answer:

M= sq root of 2 and N= sq root of 5 would be irrational

Step-by-step explanation:

These two answer choices are irrational because they cannot be shown or expressed as a fraction.

Answer:

[tex]a_{n}=2+3(n-1)[/tex]

Step-by-step explanation:

Step 1. To find the equation that describes the pattern, we use the arithmetic sequence formula:

[tex]a_{n}=a_{1}+d(n-1)[/tex]

Where a_n is the n'th terms and d is the common ratio between the numbers.

Step 2. The sequence we have is:

2 5 8 11

The first term is:

[tex]a_{1}=2[/tex]

And the common ratio or the difference between consecutive numbers is:

3 2+3=8 5+3=8  8+3=11

This will be the value of d:

d=3

Step 3. Substituting a_1 and d into the formula:

[tex]a_{n} =a_{1}+d(n-1)\\a_{n}=2+3(n-1)[/tex]

This is the equation that represents the number pattern, it represents that we add three each time to the previous number in the sequence.

Hence, the correct answer is [tex]a_{n}=2+3(n-1)[/tex]



Answer:

135 in

Step-by-step explanation:

convert inches to feet

11*12=132

135>132

135 inches are longer

In 1 hour, both the pumps can drain 1 : 3 = 1/3 of the pool

And in an hour, the older pump can drain 1 : 7 = 1/7 of the pool

So in 1 hour, the newer pump will drain 1/3 - 1/7 = 4/21 of the pool

It will take the newer pump 1 : 4/21 = 21/4 hours to drain the pool on its own.

Answer:

See below.

Step-by-step explanation:

f(X) =x5+3x4+5x3+15x2+4x+12

=x5+12+15+30+4x+12

=(x5+4x)+(12+15+30+12)

=9x+69

Answer:

[tex]\dfrac{12}{35}[/tex]

Step-by-step explanation:

2/5 ths of 6/7 ths:

[tex]\implies \dfrac67 \times \dfrac25=\dfrac{6\times 2}{7\times5}=\dfrac{12}{35}[/tex]

Answer:

38

Step-by-step explanation:

5+5=10+14+14=38

Answer:

44,5%

Step-by-step explanation:

20x100= 2000

45 x X= 45x

2000÷45= 44,444...

Rounded 44,5

Answer:

5, 25

Step-by-step explanation:

When you multiply any two whole numbers with each other and get 125 as the answer, you can say that both the numbers will be the factors of 125. 1× 125 = 125 and 5 × 25 = 125; thus, the factors of 125 are 1, 5, 25, and 125.

Answer: a. pi=3.1, sqrt of 3=1.7, 2*sqrt of 3=3.5, sqrt of 5=2.2

b. sqrt of 3, sqrt of 5, pi, 2*sqrt of 3

Step-by-step explanation: Hi there.

1. Calculate the value of each (value shown above; sqrt= square root)

2. Order them from smallest to biggest.

You multiply the two items together.

For instance, if there were 10 students and each painted 3 pictures, then we'd have 10*3 = 30 pictures total. In this case, the "10" is replaced with a more general term "s" as a placeholder.

Answer:

A = 2500 + 2500 · 0.06 · 4 = 3100

Step-by-step explanation:

Answer:

[tex]A=\pi\times r^2[/tex]

Step-by-step explanation:

In order to find the area of a circle we multiply π by the radius, and to find the radius of a circle we have to look at the line that stops directly in the middle of the circle.

[tex]\pi\times r[/tex]

Once we then have the radius, we simply multiply the radius, (with an exponent of 2) by π and then we will have our answer. Of course, round if needed.

[tex]A=\pi\times r^2[/tex]

Hope this helps.

Answer:

[tex]-5xy -13xy=-18xy[/tex]

[tex]m^8n^1 * m^3n^5=m^{11} n^6[/tex]

Step-by-step explanation:

[tex]-5xy -13xy=-18xy[/tex]

[tex]m^8n^1 * m^3n^5[/tex]

[tex]m^{8+3} =m^{11}[/tex]

[tex]n^{1+5} =n^6[/tex]

[tex]m^{11} n^6[/tex]

Hope this helps!

Solution:

Note that:

Simplify the equation to find out how much cookies did each friend get.

One friend got 2/9 of tray of cookies.

Answer: Substitute: 4×7 Calculate the product or quotient: 28 the answer is 28

Answer:

200/3n

Step-by-step explanation:

It is a strangely worded question but you are dividing the paper in 3's n times so 3n will be part of the answer and you are dividing 200. So, the answer is 200/3n.

Perimeter of a rectangle is double of sum of its length  and width. The perimeter P of the considered rectangle is: Option B: [tex]P = 2x + 2y - 8[/tex]

Its the sum of length of the sides used to made the given figure.

For a rectangle, as its two sides are equal to its length and two other sides are equal to its width, thus, its perimeter is:

[tex]P = 2 \times length + 2 \times width = 2(length + width)[/tex]

For the given case, it is already given that:

The length of the considered rectangle  = x + 5 units

The width of the considered rectangle  =  y - 1 units.

Thus, we get this rectangle's perimeter as:

[tex]P = 2( x + 5 + y - 1) = 2(x + y + 4) = 2x + 2y - 8\\\\P = 2x + 2y - 8 \: \rm units[/tex]

Thus,  The perimeter P of the considered rectangle is: Option B: [tex]P = 2x + 2y - 8[/tex]

Learn more about perimeter here:

https://brainly.com/question/11702831

The equation which results from applying the secant and tangent segment theorem to the figure is

[tex]10(a+10)=(12)^2[/tex]

The secant-tangent theorem tells the relation of the line segment made by a tangent and the secant lines with the connected circle.

According to this theorem, if the tangent and secant segments are drawn from an exterior point, then the square of this tangent segment is equal to the product of the secant segment and the line segment from that exterior point.

In the figure attached below for the circle O, the length of the DB is,

[tex]DB=10[/tex]

Here, the line segment AB is a unit. Thus, the length of line segment AD is,

[tex]AD=a+10[/tex]

The length of the tangent DE is 12 units. Thus, by the above theorem,

[tex](DE)^2=AB\times BD\\(12)^2=(a+10)\times10\\[/tex]

Hence, the equation which results from applying the secant and tangent segment theorem to the figure is

[tex]10(a+10)=(12)^2[/tex]

Learn more about the secant-tangent segment theorem here;

https://brainly.com/question/10732273

Answer:

h = 2 cm

402 over 3.14 x (8) to the power of two. SImplifies to about the answer of 2