Given the graph of a quadratic function, use the intercepts and another point on the graph to write the equation of the function in standard form.

Answer:

A) s=32t

B) 224 ft/s

Step-by-step explanation:

A)

In the form (time, speed), the question gives us the following data: (1,32) and (5,160). Since we are told that the relationship between​ time, t, and​ speed, s, is linear, we know the equation will fit the formula y=mx+c, where m is slope c is the y-intercept and y and x are the co-ordinate values. Plug in (1,32) and (5,160) to find the formula:

y=mx+c

s=mt+c

32=1m+c

c=32-m

160=5m+C

160=5m+32-m

128=4m

m=32

c=32-m

=32-32=0

So our equation is s=32t

B)

s=32t

s=32(7)=224 ft/s

Answer:

hope help you stay happy and safe

Answer:

7x=5x/67

Step-by-step explanation:

Answer:

Obtuse

Step-by-step explanation:

[tex]10^{2} > 3^{2} + 9^{2}[/tex]

Answer:

The greatest common factor is 7

[tex]35 + 14 = 49[/tex]

Step-by-step explanation:

Given

[tex]35 + 14 =[/tex]

Required

Apply distributive property

Express 35 as 7 * 5 and 14 as 7 * 2

[tex]35 + 14 = 7 * 5 + 7 * 2[/tex]

Apply distributive property

[tex]35 + 14 = 7 ( 5 + 2)[/tex]

The greatest common factor is 7

Solving further to get the solution

[tex]35 + 14 = 7 * 7[/tex]

[tex]35 + 14 = 49[/tex]

Answer:

7(5+2)

hope this helps <3

Answer:

I don't know the answer please

Answer:x=-5.22311 and x=1.72311

Step-by-step explanation:

2x^2-3x+10x-15=3

Then put into quadratic formula and use calculator

Answer:

it's 189 the area

Step-by-step explanation:

area =189

Answer:

15.95 feets

Step-by-step explanation:

Given that:

Angle of elevation = 62°

Using trigonometric relation :

Tanθ = opposite / Adjacent

From the drawing attached :

Opposite = 30 feets

Distance between girl and lighthouse = d

Tan 62 = 30 / d

1.8807264 * d = 30

d = 30 / 1.8807264

d = 15.951283

d = 15.95 feets

Answer:

P

K

P

K

P

K

Step-by-step explanation:

If it's not moving, it's potential energy

If it's moving, it's kinetic energy

Answer:

The water droplet will hit the ground 1.58 seconds after it started falling.

Step-by-step explanation:

The function:

y = -16*t^2 + 40

represents the height of a water droplet t seconds after falling from an icicle.

We want to find the value of t such that the water droplet hits the ground, and this will happen when y = 0.

Then we only need to solve the equation:

0 = y =  -16*t^2 + 40

0 =  -16*t^2 + 40

16*t^2 = 40

t^2 = 40/16

t = √(40/16) = 1.58

The water droplet will hit the ground 1.58 seconds after it started falling.

Answer:

B 54.5°

Step-by-step explanation:

Since we have a triangle,

CAB + ABC + BCA = 180 (sum of angles in a triangle)

Since CAB = 80° and ABC = 45.5°, substituting these into the equation, we have

80° + 45.5° + BCA = 180°

simplifying, we have

125.5° + BCA = 180°

collecting like terms, we have

BCA = 180° - 125.5°

BCA = 54.5°

So, the answer is B

Answer:

Volume = 42 units^2

x = 5 units

Total Surface Area = 96 units

Step-by-step explanation:

Volume

V = bh, where b = 1/2 * 3 * 4 and h = 7,

= 6 * 7 = 42 units^2

x

You can solve for this variable by using the pythagorean theorem;

a^2 + b^2 = c^2, where a = 3 and b = 4,

9 + 16 = x^2

= 25 = x^2

= x = 5 units

Total Surface Area

You can solve this by multiplying the perimeter of the base (3 + 4 + 5) by the height and adding that to two times the area of the base:

7 * (3 + 4 + 5) + 2(1/2*3*4)

= 7*12 + 12

= 96 units

Answer: lol your using canvas

1. 63

2. D

3. B

4. A

Sorry for the bland explinations havin a bad day.

Step-by-step explanation:

1. The way we solve this is by adding the degrees 72 and 45. then we subtract it by 180. this is because in all triangles the angles always add up to 180 degrees.

2. Like question one what set of angles measures to 180 degrees.

3. The sides of a triangle should define the angle measurements. you can also see if its a triangle if the numbers are continues like 3,4,5 or in this case 4,5,6

4. like in questions 1 and 2 the angles of a triangle has to equal 180 degrees so 60 times 3 is 180 so each angle would have to be 60 degrees.

Answer:

b^8

Step-by-step explanation:

Answer:

b^8, with m = 8

Step-by-step explanation:

Apply the algebraic rule: (x^a)/(x^b) = x^(a-b)

Note: This rule is true because we can cancel all b factors that occur in both numerator and denominator.

From this rule, we know that (b^10)/(b^2) = b^(10-2)

b^(10-2) can be written b^8

Step-by-step explanation:

f(x) = -3x²

f(4) = -3(4²)

= -48

Answer:

50

Step-by-step explanation:

180-30=150/3=50

3x + 30 = 180

     -30     -30     subtract 30 on both sides, solve for 180 - 30 which is 150.

___________

3x = 150

__    ___       divide 3 on both sides, solve for 150 ÷ 3 which is 50.

3       3

x = 50, final answer

hope this helps! :)

Answer:

The answer is 20

Step-by-step explanation:

The wave starts at the origin and doesn't complete the cycle until unit 20.

Answer:

[tex]\displaystyle 20[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = cos\:(\frac{\pi}{10}x - \frac{\pi}{2})} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{5} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{\pi}{10}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{20} \hookrightarrow \frac{2}{\frac{\pi}{10}}\pi \\ Amplitude \hookrightarrow 1[/tex]

OR

[tex]\displaystyle \boxed{y = sin\:\frac{\pi}{10}x} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{20} \hookrightarrow \frac{2}{\frac{\pi}{10}}\pi \\ Amplitude \hookrightarrow 1[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = cos\:\frac{\pi}{10}x,[/tex] in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle 5\:units[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle 5\:units,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{5} = \frac{\frac{\pi}{2}}{\frac{\pi}{10}}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = cos\:(\frac{\pi}{10}x - \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-15, 1],[/tex]from there to [tex]\displaystyle [5, 1],[/tex]they are obviously [tex]\displaystyle 20\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 20.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Considering the definition of an inequality, the number must be less than 12.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that the difference of a number and 4 is no more than 8.

Being "x" the number you want to know, and considering that the difference is the difference between two numbers or expressions, the inequality that expresses the previous relationship is

x - 4 < 8

Solving:

x < 8 +4

x < 12

Finally, the number must be less than 12.

Learn more about inequality:

https://brainly.com/question/17578702

https://brainly.com/question/25275758

https://brainly.com/question/14361489

https://brainly.com/question/1462764

Answer:

Step-by-step explanation:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. y=6 is a straight line perpendicular to the y-axis at point (0,6) , which means that the range is a set of one value {6} .

Answer:21 1/8 is the answer

Step-by-step explanation:

Answer: B: 15 Dollars

Answer: C: 0

Answer:y=-x

Step-by-step explanation:

Answer:

smallest -3,-2,2,9 biggest

Answer:

-3, -2, 2, 9

Step-by-step explanation:

-3 is the smallest (it is below 0), -2 is second because it is closer to 0 than -3 but still below it, 2 follows, and then 9