4(x − 3) + 5x − x² for x = 2

Answer:

Statement 1 and 2

Step-by-step explanation:

If you take t^2 - 16t + 55 and find some of its graphical values, you will get:

Turning point: (8,-9)

Roots: (5,0) and (11,0)

When this graph is plotted and you imagine the x axis to be time (as stated in the question), each of the roots (x - intercept) must be when the swimmer goes under and when they come back up.

This means that the swimmer dived under the water at 5 seconds and came back up at 9, making the first 2 statements correct.

Now the fourth statement is ruled out.

The fifth statement is not plausible as the graph would have to have more than 2 roots for the swimmer to enter the water twice.

That leaves the third statement. If you imagine the depth of the swimmer to be the y axis of our imaginary graph, and we know that the y axis of the turning point is -9, that means that the swimmer's deepest dive was 9 feet under the water, ruling out the third statement too.

Hope this helps :D

Answer:

[tex]h(t)= (t-5)(t-11)[/tex]

The swimmer comes back up 11 seconds after the timer is started.

The swimmer dives into the water 5 seconds after the timer is started.

Step-by-step explanation:

Given function:

[tex]h(t)=t^2-16t+55[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],

find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]\implies ac=55[/tex]

[tex]\implies b=-16[/tex]

Two numbers that multiply to 55 and sum to -16 are: -11 and -5

Rewrite b as the sum of these two numbers:

[tex]\implies t^2-11t-5t+55[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies t(t-11)-5(t-11)[/tex]

Factor out the common term (t - 11):

[tex]\implies (t-5)(t-11)[/tex]

Therefore, the given formula in factored form is:

[tex]h(t)= (t-5)(t-11)[/tex]

The swimmer's depth is modeled as h(t).  Therefore, when h(t) = 0 the swimmer will be at the surface of the water.

[tex]\implies h(t)=0[/tex]

[tex]\implies (t-5)(t-11)=0[/tex]

[tex]\implies t-5=0\implies t=5[/tex]

[tex]\implies t-11=0 \implies t=11[/tex]

Therefore, the swimmer will be at the surface of the water at 5 s and 11 s.

The swimmer's maximum depth is the vertex of the function. The x-value of the vertex is the midpoint of the zeros.  Therefore, the x-value of the vertex is t = 8.

Substitute t = 8 into the function to find the maximum depth:

[tex]\implies h(8)=8^2-16(8)+55=-9[/tex]

So the swimmer's maximum depth is 9 ft.

True Statements

The swimmer comes back up 11 seconds after the timer is started.

The swimmer dives into the water 5 seconds after the timer is started.

A graph is a way to represent a lot of data in a visual format. The graph can be drawn as using the equation y=100x+24.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

Given a factory-made 424 items in 4 hours at a constant rate. Also, the table is given, therefore, the slope of the line can be written as,

m = (400-300)/(4-3) = 100

Therefore, the equation can be written as y=100x+C

now, substituting the point we will get,

424 = 100(4) + C

424 - 400 = C

C = 24

Therefore, the graph can be drawn as using the equation y=100x+24.

Learn more about Graph:

https://brainly.com/question/14375099

#SPJ1

Answer: 5%

Step-by-step explanation:

[tex]6615=6000(1+r)^{2} \\ \\ 1.1025=(1+r)^{2} \\ \\ 1.05=1+r \\ \\ r=0.05=\boxed{5\%}[/tex]

The length of the chord CE is 24.46 in

To find the length of the chord CE, we solve the question using pythagoras' theorem

A chord is a line segment touching two points in a circle.

Pythagoras' theorem states that in any right angled triangle with sides a, b and c where c is the hypotenuse side, we have that

c² = a² + b²

Now form the diagram the radius of the circle BE forms a right angled triangle with the perpendicular to the chord, BO and the midway between the chord, OE.

BO = BD - OD

= 20 in - 5 in

= 15 in

From pythagoras,

BE² = DE² + BO²

making DE subject of the formula, we have

DE = √(BE² - BO²)

DE = √((20 in)² - (15 in)²)

DE = √(400 in² - 225 in²)

DE = √(175 in²)

DE = 13.23 cm

Since the chord CE = 2DE,

So, CE = 2 × 13.23 in

= 26.46 in

So, the length of the chord CE is 24.46 in

Learn more about length of chord here:

https://brainly.com/question/12394106

#SPJ1

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

in our case

baseline × 5 / 2 = 20 in²

baseline × 5 = 40

baseline = 8 in

Answer:

x = -2

Step-by-step explanation:

[tex]2x(x-5)-x(3+2x) = 26\\2x^{2} -10x-3x-2x^{2} = 26\\-13x=26\\x=\frac{26}{-13} \\=-2[/tex]

Its basically the order of operations, from left to right , evaluate brackets (if possible), then multiplication or division, lastly followed by addition or subtraction.

2x2-10x-3x-2x2=26

Eliminam opusele

reducem termenii

-13x=26

imparte ambele parti

x=-2

Step-by-step explanation:

Answer:

35%

Step-by-step explanation:

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The percentage of people who supported the home team is 35%.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

20% = 20/100 = 1/5

25% = 25/100 = 1/4

We have,

Number of people who attended the basketball game = 1940

Number of people who supported the home team = 679

Number of people who supported the visiting team = 1261

The percentage of people who supported the home team.

= [ Number of people who supported the home team / Total number of people who attended the basketball game ] x 100

= [679 / 1940] x 100

= 67900 / 1940

= 35%

Thus,

The percentage of people who supported the home team is 35%.

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ2

Answer: 60 square units

Step-by-step explanation: i hope that helps buddy :)

Answer:

34/48

Step-by-step explanation:

So to answer this problem, we need to know two things:
1) The number of people who made a purchase
2) The number of people who came into the store

The problem gives us 1), which is 34.
The answer for 2) is 34+14, since that's the total number of people who came into the store. This means that the ratio is 34/48.

Answer:

=4x³-4x²+4x-3

Step-by-step explanation:

(f+g)(x)=4x³+2x²-6x²+4x-6+3

=4x³-4x²+4x-3

Answer: x = 0, 8

Step-by-step explanation:

x = 0

x - 8 = 0 ⇒ x = 8 (move 8 to the right)

x = 0, 8

Answer:

the green box is 0

Step-by-step explanation:

we are asked to find the x-intercept, which means y = 0

(x, y)

Another way to test this is plug it in 1 for x!  (1, y) where x = 1

[tex]y = \frac{2x^{2} -3x+1}{2x^{2} +8x+6} \\\\[/tex]

[tex]y = \frac{2(1)^{2} -3(1)+1}{2(1)^{2} +8(1)+6}[/tex]

[tex]y = \frac{2(1) -3(1)+1}{2(1) +8+6}[/tex]

[tex]y = \frac{2 - 3 + 1}{2 + 8 + 6}[/tex]

[tex]y = \frac{-1+1}{10 + 6}[/tex]

[tex]y = \frac{0}{16}[/tex]

y = 0

Answer:

-[tex]\frac{17}{3}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

jenny spin a fair-4 spinner

The probability that the spinner will land on a or b will be 0.50.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Jenny spins a fair 4-sided spinner.

Let the section be marked as a, b, c, and d.

Then the total number of the event will be given as,

Total events = 4

Then the probability that the spinner will land on a or b will be given as,

P = 1/4 + 1/4

P = (1 + 1)/4

P = 2/4

P = 1/2

P = 0.50

The probability that the spinner will land on a or b will be 0.50.

More about the probability link is given below.

https://brainly.com/question/795909

#SPJ5

Answer:

AB and DE are parallel because they have the same slope.

Step-by-step explanation:

Slope of the line AB :

[tex]=\frac{\text{rise} }{\text{run} } =\frac{CA}{-BC} =\frac{12}{-8} =-\frac{3}{2}[/tex]

Slope of the line DE :

[tex]=\frac{\text{rise} }{\text{run} } =\frac{CE}{-DC} =\frac{9}{-6} =-\frac{3}{2}[/tex]

Answer:

122x + 37

Step-by-step explanation:

hope this helps u

Answer:

[3×2⁵+13×2]+2³(-2²+3²)-3=

[3×32+26]+2³(-4+9)-3=

[96+26]+2³(5)-3=

122+40-3

162-3=

159...

note:-a×(-b)=+ab

Answer: 210

Step-by-step explanation:

      ! means, for example, 6! = 6 * 5* 4 * 3 * 2 * 1

Given:

[tex]\displaystyle \frac{10!}{6!(12-8)!}[/tex]

Subtract:

[tex]\displaystyle \frac{10!}{6!(4)!}[/tex]

Distribute:

[tex]\displaystyle \frac{10!}{6!*4!}[/tex]

Expand:

[tex]\displaystyle \frac{10 * 9 * 8 * 7 * 6 * 5* 4 * 3 * 2 * 1}{(6 * 5* 4 * 3 * 2 * 1)*(4 * 3 * 2 * 1)}[/tex]

Cancel out (6*5*4*3*2*1) in both the top and bottom as they equal 1:

[tex]\displaystyle \frac{10 * 9 * 8 * 7 }{4 * 3 * 2 * 1}[/tex]

Multiply:

[tex]\displaystyle \frac{5,040 }{24}[/tex]

Divide:

210

The approximate difference in years for Calvin and Makayla is that B. Makayla invests her money 2 years longer.

Given:

We use the compound interest formula,

[tex]A= P(1 + r/t)^t[/tex]

[tex]658.8/400= (1205/1200)^1^2^c[/tex]

c= 10 years approx.

For Makayla,

We use the same formula:

[tex]A= P(1 + r/t)^t\\[/tex]

[tex]613.4/300= (1206/1200)^1^2^m[/tex]

m= 12 years approx.

Hence, the difference in the years would be:

12-10

= 2 years.

Read more about compound interest here:

https://brainly.com/question/26646518

#SPJ4

Answer:

Makayla invests her money 2 years longer

Step-by-step explanation:

b on edge

Answer:

Yes, she should have only added the area of five of the six faces.

Step-by-step explanation:

The formula for determining the surface area of a cuboid or box is expressed as

Surface area = 2lw + 2lh + 2wh

Where l, w and h represents length, width and height of the box respectively.

2lw represents the area of the top and the bottom of the box. Since she doesn't want to cover the bottom, it becomes lw. Therefore,

Surface area = 15 + 6 + 6 + 10 + 10 = 47 in².

The cost would be

0.25 × 47 = $11.75

Therefore,

Yes, she should have only added the area of five of the six faces.

After 10 years, there will be 108 rabbits left in the park.

An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Here, the given equation;

       R = 120 (0.99)ⁿ

where, n is the number of years

n = 10 years (given)

R = 120 (0.99)¹⁰

R = 120 X 0.904

R = 108.52

Thus, After 10 years, there will be 108 rabbits left in the park.

Learn more about exponential equation from:

https://brainly.com/question/11672641

#SPJ1

Using it's concept, it is found that the correct option regarding whether the relation is a function is given by:

b. Yes, each year is paired with only one value for the birth rate.

It represents a function if each value of the input is mapped to only one value of the output.

In this problem, the inputs are the decades(1950 to 2000), and each has only one rate, hence it is a function and option b is correct.

More can be learned about functions at https://brainly.com/question/12463448

#SPJ1

Reason:

Rewrite the given equation into [tex](x-6)^2 + (y-(-5))^2 = 5^2[/tex]

I changed the y+5 into y-(-5), and also replaced 25 with [tex]5^2[/tex]

Then compare that to the circle template of [tex](x-h)^2 + (y-k)^2 = r^2[/tex]

We see that h = 6 and k = -5 to give a center of (h,k) = (6, -5)

Side note: the radius is r = 5 units

The area of a 2D form is the amount of space within its perimeter. The correct option is D.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The area of the L block will be the sum of the area of A and B. Therefore, the area can be written as,

Area of L block = Area of A + Area of B

                          = (7×2) units² + (1 × 5) units²

                          = 14units² + 5units²

                          = 19units²

Hence, the correct option is D.

Learn more about Area:

https://brainly.com/question/1631786

#SPJ1

The correct value of this equation is m = 24

This equation contains a fractional term. We note that the denominator of this equation is the term 4. Therefore, we will multiply the sides by 4:

13 = m/4 + 7

13 . 4 = 4(m/4) + 7 . 4

52 = m + 28

Now, let's isolate the variable "as negative" and after the equality - we'll be subtracting the terms:

52 = m + 28

-m = 28 - 58

-m = -24

m = 24

Therefore, the correct value of this equation will be m = 24

The value of n from the triangle = 2.5

Perimeter of a triangle= a +b+c

Where,

a= n

b= 5n - 6

C= 2n + 1

P= 15

Therefore n

15 = n + 2n + 1 + 5n - 6

15 = 8n-5

8n= 15+5

8n = 20

n= 20/8

n= 2.5

Therefore, the value of n = 2.5

Learn more about perimeter here:

https://brainly.com/question/19819849

#SPJ1

Answer:

6.4

Step-by-step explanation:

E bisects side MO, plot it in the center of M and O

MO is 8, split into two even parts, 4 and 4

TE is 5

set up Pythagorean theorem, 5^2 + 4^2 = x^2 to find MT

25+16=x^2

41=x^2

x=6.403

Answer:

B and C

Step-by-step explanation:

vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent = they are equally large.

the angles listed in B and C are mirrored across either an imaginary or a directly visible line. and that makes them vertical angles.

The area of the triangle will be 3240 square centimeters.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The diagram is given below.

The height of the triangle is 120 cm and the base of the triangle is 54 cm.

Then the area of the triangle will be

Area = 1 / 2 x 120 x 54

Area = 3240 square cm

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

Answer:

0.324

Step-by-step explanation:

Answer:

x ≈ 0.5

Step-by-step explanation:

using the tangent ratio in the right triangle

tan63° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{IJ}{JK}[/tex] = [tex]\frac{1}{x}[/tex] ( multiply both sides by x )

x × tan63° = 1 ( divide both sides by tan63° )

x = [tex]\frac{1}{tan63}[/tex] ≈ 0.5 ( to the nearest tenth )

Answer:

x = 0.5

Step-by-step explanation:

We can use tan Θ to find the value of x.

tan Θ = Opposite ÷ Adjacent

Let us solve it now

tan 63 = 1 ÷ x

1.9626 = 1 ÷ x

x = 1 ÷ 1.9626

x = 0.5095

x ≈ 0.5  ( nearest 10th )