The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet.

When the water was 4 feet from the end of the hose, what was its height above the ground?

3.2 feet
4.8 feet
5.6 feet
6.8 feet

Answer:

A

Step-by-step explanation:

First, let's label the variables:

[tex]\text{Let }x \text{ represent Kaylee's number of pens,}\\\text{Let }L \text{ represent Lou's number of pens,}\\\text{And let }I \text{ represent Ilene's number of pens.}[/tex]

The first and second sentence, Kaylee at the start has x pens. She gave half to Lou, who started out with two fewer than Kaylee.

In other words, the total Lou now has is:

[tex]L=(\frac{1}{2}x )+(x-2)[/tex]

The first term represents what Kaylee gave to Lou. The second term represents what Lou had originally (two fewer than Kaylee [x]).

Simplifying, we get:

[tex]L=\frac{3}{2}x-2[/tex]

Third sentence. Lou give half of his new total to Ilene, who started out with three fewer pens than Lou. Lou, remember, started with three fewer than Kaylee (x-2). In other words:

[tex]I=(\frac{1}{2}(\frac{3}{2}x-2) )+((x-2)-3)[/tex]

The left represents what is given to Ilene: one-third of Lou's new total. The right represents Ilene's original total: three fewer than Lou: or five fewer than Kaylee. Simplifying gives:

[tex]I=(\frac{3}{4} x-1)+(x-5)\\I=\frac{7}{4}x-6[/tex]

Finally, Ilene gives a third of this new amount to Kaylee, and Kaylee's final amount is 37. Thus:

[tex]37=x-\frac{1}{2}x+\frac{1}{3}(\frac{7}{4}x-6)[/tex]

The first term represents what Kaylee originally started with. The second term represents what she gave to Lou. And the third term represents what Ilene gave to Kaylee. Simplify:

[tex]37=\frac{1}{2}x+\frac{7}{12}x-2\\39=\frac{6}{12}x+\frac{7}{12}x \\39=\frac{13}{12}x\\ 468=13x\\x=36[/tex]

Answer:

it May be SAS postulate

from the above picture

2,3 = 1 quadrant

5,-6 = 4 quadrant

2,0 = on x axis

-5,2 = 2 quadrant

-2,-4 =3 quadrant

0,-2 = on y axis

Answer:

wa + 3p = q

3p = q - wa -- Subtract wa

p = (q - wa) / 3 -- Divide by 3

Answer:

[tex] \boxed{\sf p = \frac{1}{3} (p - wa)} [/tex]

Step-by-step explanation:

[tex] \sf Solve \: for \: p: \\ \sf \implies wa + 3p = q \\ \\ \sf Subtract \: wa \: from \: both \: sides: \\ \sf 3p = q - wa \\ \\ \sf Divide \: both \: sides \: by \: 3: \\ \sf \implies p = \frac{1}{3} (q- wa)[/tex]

Answer:

[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]

Step-by-step explanation:

If a complex number is z=a+ib, then the trigonometric form of complex number is

[tex]z=r(\cos \theta +i\sin \theta)[/tex]

where, [tex]r=\sqrt{a^2+b^2}[/tex] and [tex]\tan \theta=\dfrac{b}{a}[/tex], [tex]\theta[/tex] is called the argument of z, [tex]0\leq \theta\leq 2\pi[/tex].

The given complex number is -5i.

It can be rewritten as

[tex]z=0-5i[/tex]

Here, a=0 and b=-5. [tex]\theta[/tex] lies in 4th quadrant.

[tex]r=\sqrt{0^2+(-5)^2}=5[/tex]

[tex]\tan \theta=\dfrac{-5}{0}[/tex]

[tex]\tan \theta=\infty[/tex]

[tex]\theta=2\pi -\dfrac{\pi}{2}[/tex]    [tex][\because \text{In 4th quadrant }\theta=2\pi-\theta][/tex]

[tex]\theta=\dfrac{3\pi}{2}[/tex]

So, the trigonometric form is

[tex]z=5\left(\cos \left(\dfrac{3\pi}{2}\right)+i\sin \left(\dfrac{3\pi}{2}\right)\right)[/tex]

Answer:

in degrees the answer is 5 (cos 270 + i sin 270)

in radians the answer is 5 (cos (3pi/2) + i sin (3pi/2))

Step-by-step explanation:

Answer:

6√5

Step-by-step explanation:

We have to solve the expression [tex]\sqrt{180}[/tex]

Break 180 into its factors which are in the perfect square form.

Since, 180 = 9 × 4 × 5

                 = 3² × 2² × 5

Therefore, [tex]\sqrt{180}=\sqrt{3^{2}\times 2^{2}\times 5}[/tex]

                           = [tex]\sqrt{3^2}\times \sqrt{2^{2}}\times \sqrt{5}[/tex] [Since [tex]\sqrt{ab}=\sqrt{a}\times \sqrt{b}[/tex]]

                           = 3 × 2 × √5

                           = 6√5

Therefore, solution of the given square root will be 6√5.

Answer: Rs 1820

Step-by-step explanation:

This is profit, thus is it a percentage increase of 4%. Thus, she sold the saree for 104% of what she bought it for, Rs 1750.  Thus, simply do 1.04*1750 to get 1820.

Hope it helps <3

Answer:

v^10

Step-by-step explanation:

For this, we need to understand one important rule of exponents.  For powers of like bases, you add the exponents when they are being multiplied.  With this in mind let's continue.

In this problem, the base is v, each multiplied with different powers.  So:

v^4 * v^5 * v = v^(4+5+1) = v^10

So the solution will be v^10.

An additional example would be 2^2 * 2^3.

For this we know it would be 2^2 * 2^3 = 2^(2+3) = 2^5 = 32.

We can verify by simply doing 2 * 2 * 2 * 2 *  2 = 32.  Note both are 32, and this example shows the usefulness of exponent rules.

Hope this helps.  Cheers.

Answer:

v10

Step-by-step explanation:

v^4*v^5*v=v^10

add exponents when multiplying since we have exponents 4,5, and 1

4+5+1=10

Answer:

0.971

Step-by-step explanation:

Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.

From the expression given

(cos (arctan √3/7)), we need to get the expression in parenthesis first.

Let y = (cos (arctan √3/7))

If u = arctan √3/7

Then y = cos(u) .... 1

Let's get the value of u first

u = arctan √3/7

u = arctan(0.2474)

u = 13.896°

Substituting u = 13.896° into equation 1, we will have;

y = cos(u)

y = cos13.896°

y = 0.971.

Hence the expression (cos(arctan√3/7)) is equivalent to 0.971

Answer:

y = 0.971.

Step-by-step explanation:

Given the expression (cos (arctan √3/7)) which all lies in the first quadrant. Note that all the trigonometry identities (sin, cos and tan) are all positive in the first quadrant.

From the expression given

(cos (arctan √3/7)), we need to get the expression in parenthesis first.

Let y = (cos (arctan √3/7))

If u = arctan √3/7

Then y = cos(u) .... 1

Let's get the value of u first

u = arctan √3/7

u = arctan(0.2474)

u = 13.896°

Substituting u = 13.896° into equation 1, we will have;

y = cos(u)

y = cos13.896°

y = 0.971.

Answer:

24 cm

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

2304 pi = 4/3 pi r^3

Divide each side by pi

2304 = 4/3 r^3

Multiply each side 3/4

2304 * 3/4 = 4/3 r^3 * 3/4

1728 = r^3

Take the cube root of each side

1728 ^ 1/3 = r^3 ^ 1/3

12 = r

We want the diameter

d = 2*r

d = 2*12

d = 24

Answer:

24 centimeters

Step-by-step explanation:

A basketball is a sphere. The volume of a sphere can be found using the following formula:

V= 4/3 π r^3

We know that the volume is 2304 π cm^3, therefore we can substitute 2304π in for V.

2304π = 4/3 π r^3

We want to find out what r is. Therefore, we must get r by itself. First, divide both sides by pi.

2304π/π=4/3πr^3/π

2304π/π=4/3r^3

2304=4/3r^3

Next, divide both sides by 4/3, or multiply by the reciprocal of 4/3. The reciprocal of 4/3 is 3/4 (flip the numerator and denominator).

2304*3/4=4/3r^3*3/4

2304*3/4=r^3

1728=r^3

Now, take the cube root of both sides.

∛1728=∛r^3

∛1728=r

12=r

r= 12 cm

The radius is 12 centimeters, but the question asks us to find the diameter. The diameter is twice the radius.

d= 2r

d= 2* 12 cm

d= 24 cm

The diameter of the basketball is 24 centimeters.

Answer:

25 students

Step-by-step explanation:

What we need to do here is to do some tracing. We simply need to go to the point on the concert band where we have the value 35.

After sighting this value, we then make a tracing to the line of best fit. Then from this line of best fit, we trace the point on the matching band that correlated with the value 35.

If properly traced, we would arrive at a value of 25 on the marching band

Answer:

here is your answer

Answer:hey guys just saying its 1/52

Step-by-step explanation:

Answer:

TW = 3.18 yd (Approx)

Step-by-step explanation:

Given:

TV = 6 yd

∠TYW = 32°

∠TWV = 90°

Find:

TW

Computation:

Using trigonometry application.

TW / TV = Sin 32°

TW / 6 = 0.53

TW = 3.18 yd (Approx)

Answer:

(5, 7.5)

Step-by-step explanation:

Each day the movie is late adds $1.50 for late fees.Then, after 5 days of past due, the total late fee would be: 5 * $1.50 = $7.50

Then the coordinate pair representing this would be: (5, 7.5)

Answer:

24

Step-by-step explanation:

46 - 22 = 24

Answer:

The answer is d

Step-by-step explanation:

Answer:

[tex]d = \sqrt{85}[/tex] or d ≈ 9.22

Step-by-step explanation:

Distance formula:

[tex]d = \sqrt{(2 - (-4))^2 + (-3- 4)^2} \\d = \sqrt{36+ 49}\\d = \sqrt{85} \\[/tex]

Answer:

8

Step-by-step explanation:

2 x 2 x 2 = 8

you have 2 choices each time, with or without

Answer:

d is 5 units

Step-by-step explanation:

Answer:

Step-by-step explanation:

The quotient of two numbers is 305.4. Find the quotient if the divisor decreases 2 times and the divisor increases 3 times

x/y = 305.4

3x/(y/2) = 6x/y = 6*305.4 = 1832.4

Note that the question will be deleted soon because it is posted in a language other than English.

Обратите внимание, что вопрос будет удален в ближайшее время, потому что он размещен на языке, отличном от английского.

[tex] \Delta = \frac 1 2 a b \sin C[/tex]

[tex]\Delta=5, \quad a=5, \quad b=4[/tex]

[tex]\sin C = \dfrac{2 \Delta}{ab} = \dfrac{2 (5)}{5(4) } = \dfrac 1 2[/tex]

[tex]C=30^\circ \textrm{ or } C=150^\circ[/tex]

Answer: two possibilities, θ=30° or 150°

Answer:

Again the domain consists of the pre-images and the range the images.

When we are looking for the f(x) we just look at the number it is pointing to in the range (when we have a diagram), and when we are looking for x when f(x)=y we look at the number that has a line pointed to y.

So the f(4)=

f(x)=4 when x is 8

Answer:

[tex]\boxed{\sf 30 \ bean \ cans}[/tex]

Step-by-step explanation:

The ratio of bean cans to corn cans is 6 : 7

Given that Corn cans = 35

Let the bean can be x

So,

The proportion for it will be:

6 : 7 = x : 35

Product of Means = Product of Extremes

7 * x = 6 * 35

7x = 210

Dividing both sides by 7

x = 30

So, 30 bean cans have to be put on the table to hold the needed ratio

Answer:

A=24 CM²

Step-by-step explanation:

10 x 2 + x=28

20+x=28

x=8

a=b x h/2

a=6 x 8 / 2

a=24CM²

Answer:

152.87 degree/seconds

Step-by-step explanation:

1 rotation = Circumference of a circle = 2πr

r = 15 inches

1 rotation = 2 × 3.14 × 15

94.2 inches.

We are told in the question that it takes 30 seconds to roll 100 feet along the ground

Convert feet to inches

1 feet = 12 inches

100 feet =

100 × 12 = 1200 inches.

Hence, if

94.2 inches = 1 rotation

1200 inches = X

Cross multiply

94.2 × X = 1200 × 1

94.2X = 1200

X = 1200/94.2

X = 12.738853503 rotations

Formula for Angular velocity = Number of rotations × 2π/time in seconds

Time = 30 seconds

12.738853503 × 2 × 3.14/30

= 2.6666666667 rotations per second

Converting Angular velocity to degree per second

= 2.6666666667 × 180/ π

= 2.6666666667 × 180/3.14

= 152.86624204 degree/seconds

Approximately to 2 decimal places

= 152.87 degree/seconds

Answer:

The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60

Step-by-step explanation:

The given data are as follows

x,      p($)

10,    52.5

25,   41.25

40,   30

60,   15

We note that a plot of the given points give a straight line graph indicating a linear relationship

The rate of change of p($) with x is given by slope, m in the following relation;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Which gives;

[tex]Slope, \, m =\dfrac{41.25-52.5}{25-10} = \dfrac{30-41.25}{40-25} = \dfrac{15-30}{40-60} =-0.75[/tex]

Therefore, to write the equation in slope and intercept form, we have;

From the first point with coordinates (52.5, 10), we have

y - 52.5 = -0.75×(x - 10)

y = -0.75·x + 7.5 + 52.5 = -0.75·x + 60

The equation that represents the number of persons buying the phone and the price of the phone is y = -0.75·x + 60.

Answer:

Step-by-step explanation:

Answer:

Third term=4

Step-by-step explanation:

Given:

C(n)=4/9(-3)^n-1

Find the third term

Let n=3

Substitute n=3 into the equation

C(n)=4/9(-3)^n-1

C(3)=4/9(-3)^3-1

Step 1: evaluate the power 3-1

C(3) = 4/9(-3)^2

Step 2: evaluate (-3)^2

C(3) = 4/9(9)

It can be rewritten as

C(3) = 4/9*9

9 numerator will strike 9 denominator out leaving 4

C(3)=4

Therefore, the third term=4

C(3)=4

Answer:

(10, 17)

Step-by-step explanation:

It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.

Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)

From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.

y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.

The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.

x: 4+6 = 10

y: 8+9=17

The fruit market is at point (10,17)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates

[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]

[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]

Tia is at P(4, 8) and Lei is at Q(12, 20).

The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1

So,

[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]

Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.

Learn more about graph here:

brainly.com/question/16608196

#SPJ5

Answer:

3x-18x^2+1

Step-by-step explanation:

(6x+1)(1-3x)

6x-18x^2+1-3x

6x-3x-18x^2+1

3x-18x^2+1

Hope this helps :)

Answer:

[tex]-18x^2+3x+1[/tex]

Step-by-step explanation:

[tex]6x *1=6x\\6x*-3x=-18x^2\\1*1=1\\1*-3x=-3x\\[/tex]

Add all the like terms

[tex]-9x^2+3x+1[/tex]