The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70​

Answer:

Proof in the explanation.

Step-by-step explanation:

I expanded both sides as a first step. (You may use foil here if you wish and if you use that term.)

This means we want to show the following:

[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]

[tex]=12\cos^2(\theta)-9-4\cos^2(\theta)\tan^2(\theta)+3\tan^2(\theta)[/tex].

After this I played with only the left hand side to get it to match the right hand side.

One of the first things I notice we had sine squared's on left side and no sine squared's on the other. I wanted this out. I see there were cosine squared's on the right. Thus, I began with Pythagorean Theorem here.

[tex]3-9\tan^2(\theta)-4\sin^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]

[tex]3-9\tan^2(\theta)-4(1-\cos^2(\theta))+12\sin^2(\theta)\tan^2(\theta)[tex]

Distribute:

[tex]3-9\tan^2(\theta)-4+4\cos^2(\theta)+12\sin^2(\theta)\tan^2(\theta)[/tex]

Combine like terms and reorder left side to organize it based on right side:

[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

After doing this, I since that on the left we had products of sine squared and tangent squared but on the right we had products of cosine squared and tangent squared. This problem could easily be fixed with Pythagorean Theorem again.

[tex]4\cos^2(\theta)-1+12\sin^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+12(1-\cos^2(\theta))\tan^2(\theta)-9\tan^2(\theta)[/tex]

Distribute:

[tex]4\cos^2(\theta)-1+12\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

Combined like terms while keeping the same organization as the right:

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

We do not have the same amount of the mentioned products in the previous step on both sides. So I rewrote this term as a sum. I did this as follows:

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-12\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

Here, I decide to use the following identity [tex]\cos\theta)\tan(\theta)=\sin(\theta)[/tex]. The reason for this is because I certainly didn't need those extra products of cosine squared and tangent squared as I didn't have them on the right side.

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\cos^2(\theta)\tan^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]

We are again back at having sine squared's on this side and only cosine squared's on the other. We will use Pythagorean Theorem again here.

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8\sin^2(\theta)-9\tan^2(\theta)[/tex]

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8(1-\cos^2(\theta))-9\tan^2(\theta)[/tex]

Distribute:

[tex]4\cos^2(\theta)-1+3\tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)-8+8\cos^2(\theta)-9\tan^2(\theta)[/tex]

Combine like terms:

[tex]12\cos^2(\theta)-9+3tan^2(\theta)-4\cos^2(\theta)\tan^2(\theta)[/tex]

Reorder again to fit right side:

[tex]12\cos^2(\theta)-9+4\cos^2(\theta)\tan(\theta)+3\tan^2(\theta)[/tex]

This does match the other side.

The proof is done.

Note: Reordering was done by commutative property.

Answer:

umm it's a piecewise function and I think the graph is correct I don't really understand what you mean by what is the "graph" of the following function since the graph is already there...

Step-by-step explanation:

Answer:

The first table

x 3 4 6 1 7 8 1 2

y 5 9 3 2 7 6 4 5

Answer:

6x-21

Step-by-step explanation:

Area of a rectangle is length times width.

3*(2x-7)-

6x-21

Answer:

6x - 21

Step-by-step explanation:

Since area = L x W (Length x Width)

--> 3(2x - 7)

6x - 21

Step-by-step explanation: The first rectangle to the right is 24 because 10+14 equals 24. The rectangle to the left is 19 because 10+9 equals 19. Finally the rectangle on the bottom is 23 because 14+9 is 23

Answer:

-1

Step-by-step explanation:

3/2 * (-22/33)

Simplify by dividing the second fraction by 11

3/2 * (-2/3)

Rewriting

3/3 * (-2/2)

-1/1

Answer:

-1

Step-by-step explanation:

(a/b)(c/d) = (a*c)(

(3/2)(-22/33)

(3*-22)/(2*33) = -66/66 = -1

Answer:

488

Step-by-step explanation:

Answer:

To calculate the vertex you can use the vertex form ( i searched about the vertex and found it) but i don't know how to use it so i used another method.

The vertex is where the function inverts (y values) so it is going to be or a maximum or a minimum of the function. To calculate the min/max you derivate the function and then equal it to zero.

1) y  = -3x^2 -12x -10

the derivative of y is y' = -6x -12 = -6(x+2)

y'=0 <=>  -6(x+2) = 0 <=> x+2=0 <=> x=-2

y(-2) = -3(-2)^2 -12*(-2) -10 = 2

So the vertex is the point (-2,2) .

Because the slope of the equation is negative that means that the vertex is going to be the maximum , so the maximum is (-2,2) .

To find another 4 points you just have to pick values of x and replace them in the equation y  = -3x^2 -12x -10  to find y.

2) y = -2x^2 -12x -16

Do the same thing we did in point 1

y'= -4x-12 = -4(x+3)

y'=0 <=>  -4(x+3) = 0 <=> x+3=0 <=> x=-3

y(-3) = -2(-3)^2 -12*(-3) -16 = 2

So the vertex is the point (-3,2) .

Answer:

135

Step-by-step explanation:

The equation is 135+90+x=360. x=360-(225)=135

Answer:

See attached

Step-by-step explanation:

13450 = 13000 + 400 + 50

Answer: The required ratio is PT:TR  = 1:2.

Step-by-step explanation:

Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².

To find : PT:TR

.i.e. Ratio of PT to TR.

Here, PT:TR[tex]=\dfrac{PT}{TR}[/tex]

[tex]=\dfrac{4\ cm}{8\ cm}[/tex]

Divide numerator and denominator by 4 , we get

[tex]\dfrac{1}{2}[/tex]

Therefore, the required ratio is PT:TR  = 1:2.

You can use any calculator in Maths.

Answer:

AE = 18 units

Step-by-step explanation:

Δ AEB and Δ DEC are similar , then corresponding sides are in proportion, that is

[tex]\frac{AE}{DE}[/tex] = [tex]\frac{AB}{DC}[/tex] , substitute values

[tex]\frac{2x+4}{x+8}[/tex] = [tex]\frac{12}{10}[/tex] ( cross- multiply )

10(2x + 4) = 12(x + 8) ← distribute parenthesis on both sides

20x + 40 = 12x + 96 ( subtract 12x from both sides )

8x + 40 = 96 ( subtract 40 from both sides )

8x = 56 ( divide both sides by 8 )

x = 7

Then

AE = 2x + 4 = 2(7) + 4 = 14 + 4 = 18 units

Answer:

The answer to your question is 7 lbs.

Step-by-step explanation:

Data

angle = 70°

force = 20 lb

horizontal component

Process

To solve this problem just imagine a right triangle, where the force is the hypotenuse and the horizontal component is the adjacent side.

1.- Look for a trigonometric function that relates the adjacent side and the hypotenuse.

                  cos Ф = adjacent side / hypotenuse

- Solve for the adjacent side

                  adjacent side = hypotenuse x cosФ

- Substitution

                  adjacent side = 20 x cos 70

- Simplification

                  adjacent side = 20 x 0.342

- Result

                  adjacent side = 6.84 ≈ 7 lb  

Here,

x+50°+70°= 180° [°.°Angle sum of triangle]

↪x= 180°-120°

↪x=60°

.°. x = 60°

Now,

Let z be the unknown angle of the second triangle

z+60°+50°=180° [°.° Angle sum of triangle ]

↪z=180°-110°

↪z=70°

. ° . z=70°

Then,

z+x+y= 180°

↪70°+60°+y=180°

↪y=180°-130°

↪y=50°

.°.y = 50°

Answer:

x = 60°, y = 50°

Step-by-step explanation

We know: the angles measures in a triangle add up to 180°.

(look at the picture)

z + 50 + 60 = 180

z + 110 = 180    subtract 110 from both sides

z = 70°

x + 50 + 70 = 180

x + 120 = 180         subtract 120 from both sides

x = 60°

Angles x, y, and z are on one side of a straight line. Therefore they add to 180°.

x + y + z = 180

60 + y + 70 = 180

y + 130 = 180         subtract 130 from both sides

y = 50°

Answer: The number would be 18

Step-by-step explanation:

18/2=9 9-3=6 6*3=18

The equation be (x/2) - 3 = x/3 then, the number of x = 18.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Let x be the number

From the given information, we get

(x/2) - 3 = x/3

The set all the fractions on one side and constants on another side

(x/2) - (x/3) = 3

Multiply by LCM

3x - 18 = 2x

Add 18 to both sides

3x - 18 + 18 = 2x + 18

simplify

3x = 2x + 18

Subtract 2x from both sides

3x - 2x = 2x + 18 - 2x

x =18.

Therefore, the number is x = 18.

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Intersection point of graph of function is known as solution of the function.

Graph is attached below, in which solution is shown.

1. Here, given that  [tex]3x^2-3x+2=2[/tex]

It can be written as,   [tex]y=3x^2-3x+2\\\\y=2[/tex]

Intersection point of graph of above two equation will be the solution of given function,

Solutions are (1, 2) and (0, 2)

2. Given that , [tex]3x^2-3x-1=x+1[/tex]

It can be written as

                [tex]y=3x^2-3x-1\\\\y=x+1[/tex]

Intersection of graph of above two equation will be the solution of given equation.

Solutions are  (1.721, 2.721) and (- 0.387, 0.613)

Both graph attached below,

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Answer:

76 degrees

Step-by-step explanation:

Let the angles be x, y and z

As per given:

Considering the first 2 equations in the third one:

So the third angle is:

Answer:

Step-by-step explanation:

Answer:

k) the product of ant 2 odd numbers is odd

I don't know.

Let's check um out.

For each choice, I'll try to find an example to show that it's false.

F. The sum of any 2 even numbers is odd.  

    2+2=4. 4 is even. This one is false.

G. The sum of any 2 odd numbers is ood.

    3+3=6.  6 is even.  This one is false.

H. The quotient of any 2 even numbers is odd.

    8÷4=2. 2 is even. 10÷4=2.5.  2.5 is neither odd nor even. This one is false.

J. The quotient of any 2 even numbers is even.

   10÷2=5.  5 is odd.  This one is false.

K. The product of any 2 odd numbers is odd.

    I can't find an example where this is false.

    So I'm gonna say that this is the true one.

Answer:  D. (-2, -1)

Step-by-step explanation:

Here we do two reflections to the point (-1, 2).

First, we do a reflection over the line x = y.  Remember that a reflection over a line keeps constant the distance between our point and the given line, so we have that for a pint (x, y), the reflection over the line y = x is:

Ry=x (x, y) = (y, x)

so for our point, we have:

Ry=x (-1, 2) = (2, -1)

Now we do a reflection over the y-axis, again, a reflection over a line keeps constant the distance between our point and the given line, so if we have a point (x,y) and we do a reflection over the y-axis, our new point will be:

Ry-axis (x,y) = (-x, y)

Then in our case:

Ry-axis (2, -1) = (-2, -1)

The correct option is D.

Answer:

  70, 140, 280, 350

Step-by-step explanation:

Obviously, it must have the factors 2, 5, 7 as a minimum, so the smallest value is 2×5×7 = 70.

Any of these primes can be added to the product. In increasing order, the smallest additional factors will be 2, 4, 5, 7, 8, 10, ...

So, the four smallest numbers with prime factors of 2, 5, and 7 are ...

  70 = 2·5·7

  140 = 2²·5·7

  280 = 2³·5·7

  350 = 2·5²·7

Answer:

D

Step-by-step explanation:

Doubling the height will guarantee that the volume gets twice since V=(1/3)*B*h

If Bob wants to create a pyramid of volume 28 then he needs to double the height of the pyramid.

Design or construction with a base that is a polygon and sides that are three or more triangles that come together at the top.

A pyramid is a 3D shape where 3 triangle comes and meet in such a way that the base side creates a triangle.

The volume of a pyramid is given by

Volume = (1/3)base²×height.

Let say

Base width is = w

Height is = h

Volume V = w²h/3

Given

14 = w²h/3

For volume to be 28

28 = w²(2h)/3

So it is clear that he needs to double the height.

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Answer:

42 + 2/3

Step-by-step explanation:

First, to calculate the sum of an infinite geometric series, our formula is

a₁/(1-r), with a₁ being the first term of the series and r being the common ratio. Therefore, we want to find both a₁ and r.

To find r, we can first determine that 2 * r = a₄ and a₄ * r = a₅, as the ratio separates one number from the next in a geometric series. Therefore, we have

2 * r * r = a₅

2 * r² = 1/8

divide both sides by 2 to isolate the r²

r² = 1/16

square root both sides to isolate r

r =± 1/4. Note the ± because r²=1/16 regardless of whether r = 1/4 or -1/4. However, because all terms are positive, r must be positive as well, or a₄, for example, would be 2 * (-1/4) = -0.5

Therefore, r = 1/4 .

To find the first term, we know that a₁ * r = a₂, and a₂ * r = a₃. Therefore, a₁ * r² = a₃ = 2

a₁ * 1/16 = 2

divide both sides by 1/16 to isolate a₁

a₁ = 2 * 1/ (1/16)

= 2 * 16

= 32

Plugging a₁ and r into our infinite geometric series formula, we have

a₁/(1-r)

= 32  / (1-1/4)

= 32/ (3/4)

= 32/ 0.75

= 42 + 2/3

Answer:$60,000

Step-by-step explanation:

If he bought it for $50,000 and then spent $5,000 on repairs then he spent a total of $55,000. For a profit of $5,000 he would need to sell it for $60,000 Because

60,000 - 55,000 = 5,000

Answer: 1/4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

=(-5)+(-10)+(-9)/2*(-3)

=-5-10-9/-6

=-24/-6

=4 ans.....

Answer:

D

Step-by-step explanation:

add everything up devide by 3

Answer:

C. 1/2 liter

Step-by-step explanation:

First, find the total amount of water by multiplying the amounts of water by the number of bottles, then adding all 3 values together:

1/4(1) = 1/4 liter

1/2(4) = 2 liters

3/4(1) = 3/4 liter

1/4 + 2 + 3/4 = 3 liters

There are 6 bottles in total, if we count the number of dots.

To find how much water would be in each bottle if the water was equally divided, divide the total amount of water by the number of bottles:

3 / 6 = 1/2

= 1/2 liter

Complete question :

A pool holds 1440 cubic feet of water, the city charges $1.75 per cubic meter of water used.

How much will it cost to fill the pool?

Answer:

$71.36

Step-by-step explanation:

Amount charged per cubic meter = $1. 75

Total volume of pool = 1440 ft^3

Using the conversion unit chart :

1 cubic meter = 35.3147 cubic foot

Then we can express the capacity of water held by the pool in cubic metre.

If 1 cubic meter = 35.3147 cubic foot

Then ;

y cubic meter = 1440 cubic foot

y = 1440/35.3147

y = 40.776220 cubic meter

Thus;

Cost of filling the pool will be;

$1.75 × 40.776220

= $71.358386

= $71.36

Answer:

5.2 inches

Step-by-step explanation:

Let a be the side of the square poster.

The area of it is:

● A = a^2

● 27 = a^2

● a = √27

● a = √(9×3)

● a = 3√3

● a = 5.19

Round it to the nearest tenth

● a = 5.2 inches

The length of one side of the poster is approximately 5 inches rounded to nearest tenth.

We round numbers because they are easy to deal with and they also retain their value to that place they have been rounded.

According to the given question the area of a square poster is 27inch².

We have to determine the length of one side of the poster.

We know area of a square is (side)².

∴ (side)² = 27.

side = [tex]\sqrt{27}[/tex].

We know [tex]\sqrt{25}[/tex] is 5 and [tex]\sqrt{36}[/tex] is 6 so [tex]\sqrt{27}[/tex] will lie between 5 and 8 and much closer to 5.

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