HELP ASAP

A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27

Rewrite the formula in factored form and select each true statement below.

The swimmer is underwater for 12 seconds.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The swimmer dives into the water 12 seconds after the timer was started.

Answer:

3.5 gallons of punch

Step-by-step explanation:

There are 4 quarts in 1 gallon.

Set up equation to convert 14 quarts to gallons: 14÷4 = 3.5.

Elijah made 3.5 gallons of punch.

Answer:

Step-by-step explanation:

Explanation

On a 6 sided die, there are three even numbers (2,4,6)

That's 1/2 the number on the die.

So getting 6 even numbers is

P(6) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.00781

Where did that extra 1/2 come from? Well one of the numbers thrown was an odd number, and it has to be counted.

P(7) = the same answer.                            0.00781

Total                                                           0.0156

Answer:

25.5

Step-by-step explanation:

I did the same assignment

The value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We know that:

P + Q are complementary, which means that

P+Q = 90°

Then R is a right angle, i.e. it measures 90°.

sin(90-x) = cos (x)

cos(90-x) = sin (x)

Then sinQ = 4/5  

cos(90-Q) = cosP = 4/5

Now sin²(P) + cos²(P) = 1

sin²(P) = 1 - cos²(P)

sin²(P) = 1 -[4/5]² =9/25

sin(P) = 3/5

cos(Q) = sin(P) = 3/5

cos(P) + cos(Q) = 4/5 + 3/5 = 7/5

Thus, the value of the cos P + cos Q is 7/5 if sin Q = 4/5 after applying the identities of trigonometric.

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Answer:

Your first step would be to rewrite the equation, were x =8 so it would look like this

Step-by-step explanation:

23 + 8/8 = ?

than solve. 8/ 8 = 1 and 23+1 = 24

Answer:

[tex]\dfrac{1}{64}[/tex]

Step-by-step explanation:

Hemi-, demi- and semi- are prefixes which mean half.

When applied to musical notation, each time a prefix is added it means the note's value is halved.

Therefore, if a quaver is one-eighth of a semibreve, then a semiquaver is half of a quaver, which means it's one-sixteenth of a semibreve.

[tex]\large \begin{aligned}\sf quaver & = \sf\dfrac{1}{8}\:of\:a\:semibreve\\\\\implies \sf hemisemidemiquaver & = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times quaver\\\\& = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{8}\\\\& = \sf \dfrac{1}{64}\:of\:a\:semibreve\end{aligned}[/tex]

Therefore, a hemisemidemiquaver is one-sixty-fourth of a semibreve.

Answer:

[tex]d = \sqrt{109}[/tex]

Step-by-step explanation:

Use the distance formula.

[tex]\text{The distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) \text{ is given by the formula:}\\d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Your points are (-4, 11) and (6, 8).

[tex]d = \sqrt{(-4 - 6)^2 + (11 - 8)^2}\\\\d = \sqrt{(-10)^2 + (3)^2}\\\\d = \sqrt{100 + 9}\\\\d = \sqrt{109}[/tex]

Answer:

i believe the answer is false !

Step-by-step explanation:

Step-by-step explanation:

it is very simple :

the midpoint coordinates are created as the midpoint of the x coordinates, and the midpoint of the y coordinates.

the x coordinate of the midpoint is

(0 + 10)/2 = 10/2 = 5

the y coordinate of the midpoint is

(-2 + -6)/2 = -8/2 = -4

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.

Answer:

C. 91.46

Step-by-step explanation:

Use BODMAS!

Answer:

C. 91.46

Step-by-step explanation:

Using Pemdas to solve:

5.9 (9 - 5) + 4^3 + 3.86

First you have to solve in the parenthesis

5.9 (9 - 5) + 4^3 + 3.86

= 4

New equation:

5.9 x 4 + 4^3 + 3.86

Now solve the exponent:

5.9 x 4 + 4^3 + 3.86

= 64

New equation:

5.9 x 4 + 64 + 3.86

Now we have to do multiplication:

5.9 x 4 + 64 + 3.86

= 23.6

New equation:

23.6 + 64 + 3.86

Now all you have to do is add all that together and you have your answer:

23.6 + 64 + 3.86

= 91.46

Hope this helps.

Answer:

x=5 and y=7

Step-by-step explanation:

Just substitute in y=x+2 into the equation 5x-4y=-3 to get 5x-4(x+2)=-3 which simplifies to x=5. Substitute x into y=x+2 to find y=7

Monetary policy is the actions taken by the reserve banks to influence the real GDP and the inflation rate in the economy.

These are actions done by the central bank of a country and involves adjusting money supply so as to achieve economic growth.

This influences the real gross domestic product and inflation rate of the country .

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Answer: Monetary and Reserve Bank

Step-by-step explanation:

;)

Answer:

angle 700 < angle 1120 pounds

#a

[tex]\\ \rm\Rrightarrow f(-4)[/tex]

[tex]\\ \rm\Rrightarrow 3(-4)+2[/tex]

[tex]\\ \rm\Rrightarrow -12+2[/tex]

[tex]\\ \rm\Rrightarrow -10[/tex]

#b

#1

[tex]\\ \rm\Rrightarrow y=\dfrac{2x-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{2y-1}{3}[/tex]

Find y

[tex]\\ \rm\Rrightarrow y=\dfrac{3x+1}{2}[/tex]

Inverse is

[tex]\\ \rm\Rrightarrow g^{-1}(x)=\dfrac{3x+1}{2}[/tex]

#2

[tex]\\ \rm\Rrightarrow gof(x)[/tex]

[tex]\\ \rm\Rrightarrow g(f(x))[/tex]

[tex]\\ \rm\Rrightarrow g(3x+2)[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{2(3x+2)-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+4-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{6x+3}{3}[/tex]

If we factor out

[tex]\\ \rm\Rrightarrow \dfrac{2x+1}{1}[/tex]

[tex]\\ \rm\Rrightarrow 2x+1[/tex]

#c

[tex]\\ \rm\Rrightarrow f(x)=g(x)[/tex]

[tex]\\ \rm\Rrightarrow 3x+2=\dfrac{2x-1}{3}[/tex]

[tex]\\ \rm\Rrightarrow 3(3x+2)=2x-1[/tex]

[tex]\\ \rm\Rrightarrow 9x+6=2x-1[/tex]

[tex]\\ \rm\Rrightarrow 7x=-7[/tex]

[tex]\\ \rm\Rrightarrow x=-1[/tex]

Answer:

Given functions:

[tex]f(x)=3x+2[/tex]

[tex]g(x)=\left(\dfrac{2x-1}{3}\right)[/tex]

Part (a)

[tex]\begin{aligned}\implies f(-4) & = 3(-4)+2\\& = -12+2\\ & = -10\end{aligned}[/tex]

Part (b)(i)

[tex]\begin{aligned}g(x) & =\left(\dfrac{2x-1}{3}\right)\\\\\textsf{Swap }g(x) \textsf{ for }y : \\\implies y & = \left(\dfrac{2x-1}{3}\right)\\\\\textsf{Make } x \textsf{ the subject}: \\\implies 3y & = 2x-1\\3y+1 & = 2x\\x & = \dfrac{3y+1}{2}\\\\\textsf{Swap }x \textsf{ for }g^{-1}(x) \textsf{ and }y \textsf{ for }x:\\\implies g^{-1}(x) & = \dfrac{3x+1}{2}\end{aligned}[/tex]

Part (b)(ii)

[tex]\begin{aligned}gf(x) & = \dfrac{2[f(x)]-1}{3}\\\\& = \dfrac{2(3x+2)-1}{3}\\\\& = \dfrac{6x+4-1}{3}\\\\& = \dfrac{6x+3}{3}\\\\& = \dfrac{6x}{3}+\dfrac{3}{3}\\\\& = 2x+1\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}f(x) & = g(x)\\\\\implies 3x+2 & = \dfrac{2x-1}{3}\\\\3(3x+2) & = 2x-1\\\\9x+6 & = 2x-1\\\\7x & = -7\\\\\implies x & = -1\end{aligned}[/tex]

[tex]~~~~~~~\log_{10} N = 3.8609\\\\\\\implies N = 10^{3.8609} ~~~~~~~~~;[\log_b c =d \implies b^d = c]\\\\\\\implies N \approx 7259[/tex]

This is not an identity.

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} \neq \sec(x)[/tex]

Check x = π/4, for which we have cos(π/4) = sin(π/4) = 1/√2. Together with sin(2•π/4) = sin(π/2) = 1 and cos(2•π/4) = cos(π/2) = 0, the left side becomes 1, while sec(π/4) = 1/cos(π/4) = √2.

Keeping the left side unchanged, the correct identity would be

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = -2\cos(x) + 1 + \sec(x)[/tex]

To show this, recall

• sin(2x) = 2 sin(x) cos(x)

• cos(2x) = cos²(x) - sin²(x)

• cos²(x) + sin²(x) = 1

Then we have

[tex]\dfrac{2(\cos(x)\sin(x) - \sin(x)\cos(2x))}{\sin(2x)} = \dfrac{2\cos(x)\sin(x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = \dfrac{\sin(2x) - 2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)\cos(2x)}{\sin(2x)} \\\\ = 1 - \dfrac{2\sin(x)(\cos^2(x) - \sin^2(x))}{2 \sin(x)\cos(x)} \\\\ = 1 - \dfrac{\cos^2(x) - \sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{\sin^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \dfrac{1 - \cos^2(x)}{\cos(x)} \\\\ = 1 - \cos(x) + \sec(x) - \cos(x) \\\\ = -2\cos(x) + 1 + \sec(x)[/tex]

Answer:

-16.

Step-by-step explanation:

2/3 * (-3) * (4*5 + 6 - 2(-3)^2)

= -2(20 + 6 - 18)

= -2 * 8

= -16.

Answer:

Tabled Function

Step-by-step explanation:

To determine which function is increasing the fastest over the interval [-5, 3], we need to calculate and compare each function's average rate of change over the given interval.

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given interval:  -5 ≤ x ≤ 3

Therefore, a = -5  and  b = 3

[tex]f(3)=7[/tex]

[tex]f(-5)=-17[/tex]

[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-(-17)}{3+5}=3[/tex]

[tex]f(3)=(3)^2-2=7[/tex]

[tex]f(-5)=(-5)^2-2=23[/tex]

[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)}=\dfrac{7-23}{3-(-5)}=-2[/tex]

From inspection of the graph:

[tex]f(3)\approx8[/tex]

[tex]f(-5) \approx 0[/tex]

[tex]\implies \textsf{Average rate of change}=\dfrac{f(3)-f(-5)}{3-(-5)} \approx \dfrac{8-0}{3-(-5)}=1[/tex]

Therefore, the Tabled Function has the greatest average rate of change in the interval [-5, 3] and so it is increasing the fastest.

Answer:

y=586.4

Step-by-step explanation:

64^2= 64x64 = 4096

4096-7y+9=0

4105-7y=0    1. +7y on both sides

4105=7y       2. /7 on both sides

y=586.4

Answer:

3,-8

Step-by-step explanation:

x: from -3 to 0   is  +3    add +3 more     3

y: from -2 to -5 is   -3     add -3 more    -8

The value of x in all case is

1. The value of x is 2

2. The value of x is 1

3.The value of x is 57

4.The value of x is 93

If the sum of two angles is 180 degrees then they are said to be b angles, which form a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

1. As the given angle is 90 degree i.e., complementary angle.

So,

54+10x+16=90

20=10x

x=2

2. 65x-12=43x+10  (Vertically opposite angle)

 22x= 22

x=1

3. 72= x+15  (Vertically opposite angle)

x= 57

4.x+244+23=360  (Complete angle)

 x=93

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Answer: a1=6

               An = An-1 - 4

Step-by-step explanation:

N represent what number in the sequence you choose. So in the equation n-1 would be the umber in the equation subtracting 1 then subtracting the difference. The factor you are multiplying by in this sequence is -4. You find the difference by taking any number in the sequence and dividing it by the previous number in the sequence.

Answer: 18 kilograms

Step-by-step explanation:

If each pumpkin weighs 3 kilograms and the farmer has 6 pumpkins the equation would be 6x3=18 in order to find the mass of the farmer's pumpkins.

The quadrants is tan⁻¹x restricted is A. Quadrants I and IV

To answer the question, we need to know what tan⁻¹x is.

tan⁻¹x is the inverse trigonometric function of tanx, which is the value of the angle for tanx.

To find the quadrants in which tan⁻¹x is restricted, we know that tanx lies in the range

-∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°.

tan⁻¹x lies between quadrant I and IV

So, the quadrants is tan⁻¹x restricted is A. Quadrants I and IV

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Answer:

a) x = 1

Step-by-step explanation:

Given: 2x + 3 = 5

1. Subtract 3 from both sides:

2x + 3 - 3 = 5 - 3

⟹ 2x = 2

2. Divide both sides by 2:

2x ÷ 2 = 2 ÷ 2

⟹ x = 1

3. Check your work:

2(1) + 3 = 5

2 + 3 = 5

⟹ 5 = 5 ✔

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Step-by-step explanation:

the picture is not representing the real angle sizes. so, don't let yourself get confused by that.

the right neighbor angle of 90° at E is also 90°.

it has to be, because it is the supplementary angle to the left 90° (that means together they are 180°).

remember, all angles around a single point on one side of a line have to sum up to 180° (because the line can be seen as the diameter of a circle, with the point being the center of the circle, and so one side of the line is representing a half-circle and therefore 180°).

for the same reason angle 1 (the lower neighbor of the 90° angle at A) is also 90°.

for the same reason the lower neighbor angle of the 60° angle at E is 180 - 60 = 120°.

for the same reason the angle ABC is 180 - 40 = 140°.

for the angle BCD we need to remember :

the sum of interior angles of a polygon with n sides is

(n − 2) × 180°.

in our case ABCDE has 5 sides, so the sum of all interior angles is

(5 - 2) × 180 = 3×180 = 540°

we know 4 of the interior angles already, so

angle BCD = 540 - 90 - 90 - 120 - 140 = 100°

x is now the supplementary angle to the angle BCD.

so,

x = 180 - 100 = 80°

Answer:

141/1.95 km/hr, or 72.308 km/hr

Step-by-step explanation:

To find the average speed, we need to know the total distance traveled / time (hours).
The total distance is 72 km + 69 km =  141 km.
The total time is 48 minutes / 60 (because we want this in hours, not minutes) + 69/60 = 1.95 hours
141/1.95 =  72.3 km/hr

Answer:

=4x³-4x²+4x-3

Step-by-step explanation:

(f+g)(x)=4x³+2x²-6x²+4x-6+3

=4x³-4x²+4x-3