What is the slope of Y=5x+4

Answer:

When do you hit the water?

1.075 seconds after you jump.

What is your maximum height?

the maximum height is 12.5626 ft

Step-by-step explanation:

The equation:

h(t) = -16*t^2 + 6*t + 12

Is the height as a function of time.

We know that the initial height is the height when t = 0s

h(0s) = 12

and we know that the diving board is 12 foot tall.

Then the zero in h(t)

h(t) = 0

Represents the surface of the water.

When do you hit the water?

Here we just need to find the value of t such that:

h(t) = 0 = -16*t^2 + 6*t + 12

Using the Bhaskara's formula, we get:

[tex]t = \frac{-6 \pm \sqrt{6^2 - 4*(-16)*12} }{2*(-16)} = \frac{-6 \pm 28.4}{-32}[/tex]

Then we have two solutions, and we only care for the positive solution (because the negative time happens before the jump, so that solution can be discarded)

The positive solution is:

t = (-6 - 28.4)/-32 = 1.075

So you hit the water 1.075 seconds after you jump.

What is your maximum height?

The height equation is a quadratic equation with a negative leading coefficient, then the maximum of this parabola is at the vertex.

We know that the vertex of a general quadratic:

a*x^2 + b*x + c

is at

x = -b/2a

Then in the case of our equation:

h(t) = -16*t^2 + 6*t + 12

The vertex is at:

t = -6/(2*-16) = 6/32 = 0.1875

Evaluating the height equation in that time will give us the maximum height, which is:

h(0.1875) =  -16*(0.1875 )^2 + 6*(0.1875) + 12 = 12.5626

And the height is in feet, then the maximum height is 12.5626 ft

You hit the water 1.075 seconds after you jump.

The maximum height is 12.56.

Given that,

You are jumping off the 12-foot diving board at the municipal pool.

You bounce up at 6 feet per second and drop to the water your height h (in feet) above the water in terms of t seconds is given by,

[tex]\rm h(t)=-16t^2+6t+12[/tex]

We have to determine,

When do you hit the water?

What is your maximum height?

According to the question,

You bounce up at 6 feet per second and drop to the water your height h (in feet) above the water in terms of t seconds is given by,

[tex]\rm h(t)=-16t^2+6t+12[/tex]

1. The initial height is the height when t = 0 second,

[tex]\\\rm h(t)=-16t^2+6t+12\\\\\rm h(0)=-16(0)^2+6(0)+12\\\\ h(0) = 12[/tex]

And the diving board is 12 feet tall.

Then the zero in h(t)

h(t) = 0

When h(t) = 0 represent the surface of the water,

[tex]\rm h(t)=-16t^2+6t+12\\\\\rm -16t^2+6t+12 =0\\\\8t^2-3t-6=0\\\\x = \dfrac{-(-3)\pm \sqrt{(-3)^2-4\times8\times(-6)}}{2\times 8}}\\\\x = \dfrac{3\pm \sqrt{9+192}}{16}}\\\\x = \dfrac{3\pm \sqrt{201}}{16}}\\\\x = \dfrac{3\pm 14.77}{16}}\\\\ x = \dfrac{3+14.77}{16} \ and \ x = \dfrac{3-14.77}{16} \\\\x = \dfrac{17.77}{16} \ and \ x = \dfrac{-11.77}{16} \ \\\\ x = 1.075 \ and \ x = -0.855[/tex]

The value of x can not be negative then the value of x is 1.075.

Therefore, you hit the water 1.075 seconds after you jump.

2. The maximum height is reached by you, you first derivative the function h(t) with respect to t:

[tex]\rm \dfrac{dh(t)}{dt} = \dfrac{d(-16t^2+6t+12)}{dt}\\\\\rm \dfrac{dh(t)}{dt} = \dfrac{d(-16t^2)}{dt} +\dfrac{d(6t)}{dt}+\dfrac{d(12)}{dt}\\\\\rm \dfrac{dh(t)}{dt} = 2\times (-16t) + 6\times 1+0\\\\ \dfrac{dh(t)}{dt} = -32t+6\\\\[/tex]

To find the maximum height the value first derivative is equal to zero.

[tex]\rm \dfrac{dh(t)}{dt} = 0\\\\-32t+6=0\\\\-32t=-6\\\\t = \dfrac{6}{32}\\\\t = \dfrac{3}{16}\\[/tex]

Substitute the value of t in the equation to find the maximum height,

[tex]\rm h(\dfrac{3}{16})=-16(\dfrac{3}{16})^2+6(\dfrac{3}{16})+12\\\\ h(\dfrac{3}{16})=-(\dfrac{9}{16})+6(\dfrac{3}{16})+12\\\\ h(\dfrac{3}{16})=-\dfrac{-9}{16}+\dfrac{18}{16}+12\\\\ h(\dfrac{3}{16})= \dfrac{-9+18+192}{16} \\\\ h(\dfrac{3}{16}) = \dfrac{201}{16}\\\\h(\dfrac{3}{16}) = 12.56[/tex]

Hence, The maximum height is 12.56.

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Answer:

5*(s+12) = $105

Step-by-step explanation:

5 snacks + 5 tickets makes the total 105 so the equation

5*(s+12) = $105 is the answer to the question.

Answer:

Lateral Area: 120                                                                                    

Surface Area: 163.3

Answer:

Y=26.9x-1.3is the answer

Step-by-step explanation:

The best model represents y = 26.9x – 1.3

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

As, the data given about productivity is well defined by y = 26.9x – 1.3

As, we have 4 functions so by putting the values we get

x                  A                 B                C               D

2              66.66          49.3            52.5           50

4             94.57            71.44           106.3         104  

6             134.14           103.57         160.1          158

8             190.27          150.14          213.9         212

10           269.91           217.64         267.7         266

12           382.85          315.5           321.5          320.

So, the most accurate is (C)y = 26.9x – 1.3.

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Answer:

See explanation

Step-by-step explanation:

Given

[tex]3x = 6[/tex]

Solving (a): What the expression means

3 when multiplied by x, gives 6

Solving (b): Why 2 is the solution

We have:

[tex]3x = 6[/tex]

Divide both sides by 3

[tex]\frac{3x}{3} = \frac{6}{3}[/tex]

[tex]x = \frac{6}{3}[/tex]

[tex]x = 2[/tex]

Answer:8.5km

Step-by-step explanation:

Answer:

Kite because it has two pairs of opposite sides and opposite angles that are equal .

Answer:

Hello! answer: x = 68

Step-by-step explanation:

This is a complementary angle meaning it will add up to 90 degrees 90 - 22 = 68 therefore x = 68 HOPE THAT HELPS!

Answer:

2(-2,4) + 2(-1,8)=-8.4

Step-by-step explanation:

2x-2

2x4

2x-1

2x8

-8.4

Answer:

(3,9)

Step-by-step explanation:

9-6 = 3

Answer:

x=-3.5 , the points of the graph are 0,1 and 3,3

Step-by-step explanation:

Answer:

=> 2x²-7x+5

=> 2x²-2x-5x+5

=>2x(x-1)-5(x-1)

______________

Hope it helps

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Answer:

Step-by-step explanation:

Answer:

I think its A? Not sure though

Step-by-step explanation:

Answer:

[tex]x = \frac{22}{3}[/tex]

Step-by-step explanation:

Since both CB and ED intersect AD perpendicularly, we can say they are parallel and that ΔACB is similar to ΔAED from Thales intercept theorem. Now, we can set up a proportion from the definition of similar triangles:

[tex]\frac{AB}{AD} = \frac{BC}{DE}[/tex]

We can say that AD = AB + BD(segment addition postulate) and substitute to get AD = 11. Now we can plug in the numbers we have to the proportion:

[tex]\frac{6}{11} =\frac{4}{x}[/tex]

We can cross-multiply to get:

[tex]6x = 44[/tex]

and divide by 6 to get

[tex]x = \frac{22}{3}[/tex]

Step-by-step explanation:

a) for the first part, you take your compass and stretch it more than halfway on to line UV. Place the fixed point at V and draw a curve. make sure you keep your compass the same size, put the fixed part of your compass on point U and draw a curve again. both curves should go both upward and downward. Now, your curves should meet at two points. use your straight edge to draw the line that meets at both points. I have drawn an example of what it should approximately look like. for the second part you are simply using your straight edge to draw a line from T down to the median M you previously found. I have drawn a second picture to show you.

b) now to check if they are perpendicular, we must find the slope of each line. I will not be able to do this accurately since I didn't use an exact method to find M, so you must follow my steps.

Step 1: find the slope of UV. To do so, we must take two points from the line. I will take points U and V because they are easiest to see. To find the slope, we can use the equation:

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

where m is the slope.

so, let's define our points.

Point V is (4,4), let's call this point one.

Point U is (14,6), let's call this point two.

So,

x1= 4

y1= 4

and

x2= 14

y2= 6

now, we can plug these into our slope equation.

[tex]m = \frac{6 - 4}{14 - 4} = \frac{2}{10} = \frac{1}{5} [/tex]

You must then use the points T and M in order to solve the second slope. Where T is (2,12). I will keep M as (x1, y1) for now.

The equation should then look like:

[tex]m = \frac{2 - y1}{12 - x1} [/tex]

now, in order for it to be perpendicular to our original slope, it must be the opposite reciprocal, which is the number flipped and made negative. The opposite reciprocal of 1/5 will be -5.

It should NOT be, as we have been told. So, we can state:

"I know that TM is not perpendicular to UV because the UV has a slope of 1/5 and TM has a slope of x, which is NOT the opposite reciprocal on 1/5."

Hope this helps! :)

Answer:

x = 1.2

Step-by-step explanation:

12.50x = 15

12.50/12.50 x = 15/12.50

x = 1.2

(Sorry i dont understand what you mean by percent increase)

Answer:

[tex] {x}^{3} + {x}^{2} −24x+36[/tex]

Step-by-step explanation:

[tex](x + 6)(x - 2)(x - 3)[/tex]

[tex][x(x−2)+6(x−2)](x−3)[/tex]

[tex]( {x}^{2} −2x+6x−12)(x−3)[/tex]

[tex]( {x}^{2} +4x−12)(x−3)[/tex]

[tex] {x}^{3} + {x}^{2} −24x+36[/tex]

Step-by-step explanation:

1. C:arithmetic, 34, 39, 44

2. B: geometric, -64, 128, -256

3. C: geometric, 1, 1/3, 1/9

Answer:

B     5√34 / 34

Step-by-step explanation:

tan ∅ = opp/adj

In quad II

tan ∅ = 5 / (-3)

---------------------

hyp^2 = 5^2 + (-3)^2

hyp^2 =25 + 9 = 34

hyp = √34

---------------------------

sin ∅ = opp/hyp

sin ∅ = 5/√34

Rationalizing

sin  ∅ = 5√34 / 34

Consider this equation [tex]tan(\theta)=-5/3[/tex]. if theta is an angle in quadrant II the of  [tex]sin \theta = \dfrac{5\sqrt{34}}{{34} }[/tex].

Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.

In a right-angled triangle, two such angles are there which are not right-angled(not of 90 degrees).

The slanted side is called the hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.

Consider this equation

[tex]tan(\theta)=-5/3[/tex]

B     5√34 / 34

if theta is an angle in quadrant II what is the of sin(theta)

[tex]tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}[/tex]

In quadrant II

tan ∅ = 5 / (-3)

[tex]hyp^2 = 5^2 + (-3)^2\\hyp^2 =25 + 9 = 34\\hyp = \sqrt{34}[/tex]

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}[/tex]

[tex]sin \theta = \dfrac{5}{\sqrt{34} }[/tex]

Rationalizing

[tex]sin \theta = \dfrac{5\sqrt{34}}{{34} }[/tex]

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Answer:

15000000000000000000000000000000000000000000

Step-by-step explanation:

Answer:

150 centimeters

Step-by-step explanation:

just multiply!

hope this helps :)

Answer:

g = 4

Step-by-step explanation:

-7g - 2 = -30

Add 2 to both sides to get:

-7g -2+2 = -30+2

which is equal to:

-7g = -28

now divide both sides by -7 to get the value of g which is:

g = -28 / - 7

--> g = 4

Answer:

g = 4

Step-by-step explanation:

First you can add 2 to both sides to isolate the x term:

-7g -2 = -30

      +2   +2

-7g = -28

Now, you can divide by -7 both sides to find g,

-7g = -28

÷ -7     ÷ -7

g = 4

Answer:

2384

Step-by-step explanation:

40x50=2000

40x24/2=384

2000+384=2384

Answer:

2384

Step-by-step explanation:

1. Approach

To solve for the area of the given figure, divide the figure up into two parts. This will ensure that one can find the area of each individual part, and then add the two resulting areas up to find the total area of the figure. One can split this figure into a rectangle, and a triangle.

2.Find the area of the rectangle

The rectangle will have the following dimensions,

(40) x (50)

To find the area of a rectangle, one will use the following formula,

(length) * (width) = (area)

Therefore, the area is the following,

(40) * (50) = 2000

3.Area of the triangle

3a. Approach

To find the area of a triangle, one will use Heron's formula. Herons' formula states the following,

[tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where (s) is the semi-perimeter or half of the perimeter, and (a), (b), and (c) are the sides of the triangle. This requires that one knows all of the sides of the triangle.

3b. Find the unknown side and semi-perimeter

It is given that the triangle is right indicated by a box around one of the angles), thus one can use the Pythagorean theorem to find the length of the unknown side. The Pythagorean theorem states the following,

[tex]a^2+b^2=c^2[/tex]

Where (a) and (b) represent the legs, the sides adjacent (next to) the right angle. Moreover, (c) represents the hypotenuse or the side opposite the right angle. Substitute in the given values and solve for (b),

[tex](40)^2=(24)^2+(b)^2\\[/tex]

Simplify,

[tex]1600=576+b^2[/tex]

Inverse operations,

[tex]1024=b^2\\\sqrt{1024}=b\\32=b[/tex]

Add up all of the sides of the triangle and divide by (2) to fin the semi-perimeter,

[tex]\frac{a+b+c}{2}\\\\=\frac{20+24+32}{2}\\\\=48[/tex]

3c. Find the area of the triangle

Substitute into Heron's formula,

[tex]\sqrt{s(s-a)(s-b)(s-c)}\\\\=\sqrt{48(48-32)(48-40)(48-24)}\\\\=\sqrt{48(16)(8)(24)}\\\\=\sqrt{147456}\\\\=384[/tex]

Add the area of the rectangle and triangle together to find the answer,

384 + 2000

= 2384

Answer:

Step-by-step explanation:

Rectangle 4 sides, 4 right angles, and opposite Parallel sides

Rhombus 4 sides, all sides equal length, and 4 acute angles.

I am 100% positive this answer is correct plz mark as brainliest

Answer: Hope This Helps!

Step-by-step explanation:

Statistic Definition: A mathematical science concerned with data collection, presentation, analysis, and interpretation

Examples: "Statistics is the only mathematical field required for many social sciences." and "The statistics from the Census for apportionment are available."

Answer:

The experimental probability of flipping tails is 40%. Mentor: The experimental probabilities were 40% tails and 60% heads. This does not precisely match with the theoretical probability of 50% tails and 50% heads.

Step-by-step explanation:

Answer:

The diameter of the pizza = 14 in

Radius of the pizza = (14/2)in = 7in

Area of a whole pizza =

πr^2

=( 22/7 × 7^2)in^2

=( 22/7 × 49)in^2

154 in^2

Area of a half pie =( 1/2 × 154)in^2 = 77in^2

Area of one of 8 slices = (1/8 × 154)in^2 = 19.25in^2

Hope it helps