Henry bought 9 3/4 pounds of oranges at the market. If the oranges cost $1.20 per pound, how many did Henry pay for the oranges.

Answer:

Given:- [tex]y=-5x^3+10x+20[/tex]

A parabola attain maximum height at the vertex: formula to find x-coordinate of vertex is, [tex]x=-\frac{b}{2a}[/tex]

plug in a=-5 and b=10

so, [tex]x=-\frac{10}{2(-5)} =-\frac{10}{-10} =1[/tex]

Now plug in x=1 to get maximum height,

[tex]y=-5(-1)^2+10(1)+20[/tex]

[tex]=-5+10+20[/tex]

[tex]=+25[/tex]

so, maximum heigh reached by the rocket was 25 yards

Rocket will hit the ground when y=0

[tex]0=-5x^2+10x+20[/tex]

[tex]0=-5(x^2-2x-4)[/tex]

[tex]\frac{0}{-5} =\frac{-5}{-5} (x^2-2x-4)[/tex]

So, [tex]x^2-2x-4=0[/tex]

quadratic formula is,

[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

plug in a=1, b=-2,and c=-4

[tex]x=-\frac{(-2)=-\sqrt{(-2)^2-4(1)(-4)} }{2(1)}[/tex]

[tex]=\frac{2=-\sqrt{4+16} }{2}[/tex]

[tex]=\frac{2+-\sqrt{20} }{2}[/tex]

[tex]=\frac{2+-2\sqrt{5} }{2}[/tex]

[tex]=1+-\sqrt{5}[/tex]

[tex]=1-\sqrt{5} ,1+\sqrt{5}[/tex]

[tex]=1-5.236,1+2.236[/tex]

[tex]=-1.236,3.236[/tex]

So, it takes 3.2 seconds to hit the ground.

OAmalOHopeO

Answer:

Step-by-step explanation:

[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]

Answer:

11/43

Step-by-step explanation:

A local community college has 860 students

Out of this 860 students, 220students ride bikes

Therefore the fraction of bike riders to the number of students can be calculated as follows

= 220/860

= 11/43

Answer:

5x10^-2 option B

Step-by-step explanation:

Answer:

5x10^-2

the second one.

Answer:

the fourth option (A and B are the same distance from the origin)

Step-by-step explanation:

since B is the result of a rotation of A around the origin, they are both on the same circle (center point is the origin). so, they have both the same distance (the radius of the circle) from the center of the circle, which is the origin.

the third option is tempting, as the rotation was 90 degrees, but it was clockwise !

Answer:

h=17.3 A=173

Step-by-step explanation:

Calculator

Answer:

height = 17.3 mm

area = 173 mm²

Step-by-step explanation:

all three sides are of the same length (20 mm).

so, the height actually splits the baseline in half

(2 × 10 mm) while hitting it at a 90 degree angle.

so, we use Pythagoras, where the full side opposite of this 90 degree angle is c (Hypotenuse), the height of the main triangle is one side, and half of the baseline is the other side.

c² = a² + b²

20² = 10² + height²

400 = 100 + height²

300 = height²

height = 17.3 mm

the area of the main triangle is baseline (20) times height divided by 2.

so,

At = 20×17.3/2 = 10×17.3 = 173 mm²

Answer:

Step-by-step explanation:

I hope these are people in vehicles travelling toward each other.

80 mh * t + 40 mph * t = 420 miles

The two vehicles are going to travel a total of 420 miles. B will cover a lot more ground than A, but together they will make 420 miles

80t + 40t = 420

120t = 420

t = 420/120

t = 3.5

So after driving 3.5 hours, the two cars will meet.

Answer:

32 newspapers

Step-by-step explanation:

6.4 / 0.2 = 32

Answer:

32 papers

Step-by-step explanation:

Take the total amount and divide by .20

6.40 / .20

Multiply the top and bottom by 10

64/2

32

Area = Side^2

Area =( 4x + 2 )^2

Area = (4x)^2 + 2(4x)(2) + (2)^2

Area = 16x^2 + 16x + 4

Thus the correct answer is option B .

Answer:

θ = 51.7

SOH-CAH-TOA

CAH: COS = ADJ/HYP   cos(θ) = 19.4/29.3

θ = 48.5

93.2 + 48.5 + x = 180

x = 38.3

90 + 38.3 + θ = 180

θ = 51.7

Step-by-step explanation:

Answer:

56.57

Step-by-step explanation:

See attached photo for steps

EDIT: I forgot to add 3.14, I am so sorry

Answer:

56.52

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

ans is 10

because 2×5 is 10

Answer:

2x5= 10

Step-by-step explanation:

5, 10,15,20

five 2 times is 10

Step-by-step explanation:

Asymptote: y = 2 y-intercept: (0,8)

Step-by-step explanation:

The given function is

f(x) = 6(0.5)^{x} + 2f(x)=6(0.5)

x

+2

This function is of the form:

f(x) = a {b}^{x} + cf(x)=ab

x

+c

where y=c is the horizontal asymptote.

By comparing , we have c=2 hence the horizontal asymptote is

y = 2y=2

To find the y-intercept, we put x=0 into the function to get:

f(0) = 6(0.5)^{0} + 2 = 6 + 2 = 8f(0)=6(0.5)

0

+2=6+2=8

Therefore the y-intercept is (0,8).

Answer:

x>20

Step-by-step explanation:

You want to try and get the x alone so

5x + 20 > 120

     -20     -20  Subtract 20 from each side

5x        > 100

5x/5    > 100/5 Divide 5 from each side

       x  > 20

Answer:

2a+b=0

ac-b=16

a+b/a=-4

8a+5b=-4

-4a-b =4

3c/-5=6

Complete question is;

RS is the perpendicular bisector of PQ . Point T is the midpoint of PQ. Point U lies on RS. If the length of UP is 7 units, the length of UQ is ______ units.

Triangle is attached

Answer:

UQ = 7 Units

Step-by-step explanation:

From the image attached, we can see that;

T is the midpoint of PQ

Thus;

PT = TQ

Since RS is perpendicular to PQ, then we can say that;

∠PTU = ∠QTU

Now, from SAS congruence theorem, we can say that;

△PTU = △QTU

Thus, from corresponding sides of both triangles, we can say that;

UP = UQ

Thus,

UQ = 7 Units

Answer:

7 units

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

Answer:

D. exponential; y = 98 • 0.79x

Step-by-step explanation:

Answer:

Option D is correct.

Exponential model are the data best represented.

Equation:  

Step-by-step explanation:

An exponential function is in the form of   .....[1] where a is the initial value and b≠0 , b > 1.

Consider any two points from the table;

(0, 98) and ( 1, 77)

Then substitute these in [1];

For (0, 98)

x = 0 and y = 98 substitute in [1] we get;

98 = a

Similarly, For (1, 77)

we have;

77 = ab

Substitute the value of a =98 we get;

Divide both sides by 98 we get;

⇒ b = 0.79

We get an equation;  

Therefore, the data represent here is, Exponential function.

also, an equation to model the data is;  

...............................................................................................................................................

All the functions grow with x except B that decreases when x grows. That i your function. Also check that when you divide the population of two consecutive years, the ratio remains 0.79 approx

The solution is D

...............................................................................................................................................

Exponential would be the correct answer I believe...

...............................................................................................................................................

For a better understanding of the explanation provided here please find the attachment.

The solution will employ the use of the trial and error method and basic math.

As can be see from the given data, the deer population keeps on falling from the year zero. Thus, we can safely conclude that the quadratic and the linear models will not represent the situation at all.

We are left with the exponential model and since we have  in it we can see that the deer population will fall as the years pass.

We have checked it in the table that has been provided and we have concluded that the data is best represented by the exponential model because when the exponential formula is applied it is almost equal to the actual number of deers.

Please check the attached table for a better understanding.

Answer:3165

Step-by-step explanation:

Answer:

Approximately 9.2

Step-by-step explanation:

For right triangle, if you know 2 sides, you can find the third using pythagorean theorem, a^2 + b^2 = c^2. 'a' and 'b' are the lengths of the legs, while 'c' is the hypotenuse. You can plug in what you know into this formula:

9^2 + 2^2 = c^2

81+4 = c^2

c = √85, or approximately 9.2

==========================================================

Explanation:

HL stands for Hypotenuse Leg. This rule works only for right triangles.

So we must have two hypotenuses that are congruent, and we must have two legs that are congruent

The diagram shows that AB = DE are the congruent hypotenuses. So we have "H" taken care of. We just need the "L" portion.

We can see that only choice D works, which is AC = EC. If we knew that AC and EC were the congruent legs, then we have enough info to use HL.

Answer:

3596

Step-by-step explanation:

Use long multiplication to evaluate.

Answer:

3596

Step-by-step explanation:

(58*10) = 580

580*6 = 3480

58 * 2 = 116

3480 + 116 = 3596

Nate had $3000 at the beginning.

The percentage is defined as a ratio expressed as a fraction of 100.

Let the original amount of money is P

Nate spent 12 % of his paycheck on car repairs

⇒ 12% of P = 12P/100

And he spent 25 % of the remainder on food.

⇒  0.25(88/100)P

He gave $ 1,320 of the remaining money to his parents

⇒ 1320  

If the usual price of the computer was $ 825 and the discount was 20 %

⇒ 825 - 0.20(825) = 660

P = 12P/100 + 0.25(88/100)P + 1320 + 660

P - 34P/100 = 1980

100P - 66P = 198000

P = 3000

Hence, Nate had $3000 at the beginning.

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ2

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Short answer: to solve this problem, follow directions.

Let c and p represent numbers of cakes and pies produced daily. Then the constraints are ...

  2c +3p ≤ 108 . . . . . . . . available hours of preparation time

  1c +0.5p ≤ 20 . . . . . . . available hours of decoration time

  p ≥ 0, c ≥ 0 . . . . . . . . . negative numbers of cakes or pies cannot be produced

__

It works well to let a graphing calculator do this.

The feasible region is the doubly-shaded area with vertices ...

  (0, 0), (0, 36), (3, 34), (20, 0)

__

Profit is $25 per cake and $12 per pie, so is ...

  p = 25c +12p

__

The attached table shows the profit for the various mixes of cakes and pies in the feasible region. The most profit is had by production of cakes only.

The maximum profit is $500 per day for production of 20 cakes.

_____

Additional comment

We have used x for cakes and y for pies in the attachment, because those are variables that the Desmos calculator prefers.

As is sometimes the case, the production point giving maximum profit leaves one of the resources (preparation time) only partially utilized.

Answer:

17

Step-by-step explanation:

2f + 4f + 2 - 3 when f = 3

1) first we multiply 3 wherever f is

2 x 3 + 4 x 3 + 2 - 3 (solve)

6 + 12 + 2 - 3

18 + 2 - 3

20 - 3

17

Answer:

6+12+2-3=17

Step-by-step explanation:

Answer:

here's the answer to your question about

Answer:

Chukwu's share is of $57.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

Chukwu's share is x.

Abdul's share is y.

Kunle's share is z.

Chukwu, Abdul and kunle are to share $142

This means that [tex]x + y + z = 142[/tex]

Abdul gets $11.00 less than Chukwu

This means that:

[tex]y = x - 11[/tex]

$7.00 more than Kunle.

This means that:

[tex]y = z + 7[/tex]

So

[tex]z = y - 7[/tex]

[tex]z = x - 11 - 7[/tex]

[tex]z = x - 18[/tex]

How much is Chukwu's share?

We want to find x, so:

[tex]x + y + z = 142[/tex]

[tex]x + x - 11 + x - 18 = 142[/tex]

[tex]3x - 29 = 142[/tex]

[tex]3x = 171[/tex]

[tex]x = \frac{171}{3}[/tex]

[tex]x = 57[/tex]

Chukwu's share is of $57.

Answer:

y = 1/2x + 5/2

Step-by-step explanation:

y = 1/2x + b

5 = 1/2(5) + b

5 = 5/2 + b

5/2 = b