Solve the application using polynomials

The answers of all the blanks are as:

a) 3200ft².

b)  8 times.

c) 100ft.

What is the area of the rectangle?

When calculating a rectangle's area, we multiply the length by the width of the rectangle.

we have,

length = 40ft

width = 10ft

Leila's vegetable garden has an area of 400 ft.

a)

new length = 40 * 2 =80ft

new width = 10 * 4 = 40ft

Therefore,  this describes the size of Leila's new garden :

= 80 * 40 = 3200ft²

b)

3200 / 400 = 8

The expansion changes the area of the garden:

The area of the new garden will be 8 times the area of the current garden.

c)

Leila's friend Keiko wants to expand her rectangular garden by 20 times the area of her current garden:

400 * 20 = 8000ft²

Keiko's garden length would be  5 times the current length:

40 * 5 = 80ft

and the new width would be the current width :

new width of Keiko's garden = 8000 / 80 = 100ft.

Hence, the answers of all the blanks are as:

a) 3200ft².

b)  8 times.

c) 100ft.

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The solution for y in the inequality is (a) y ≥ 10

From the question, we have the following inequality expression that can be used in our computation:

42≤4.2y

Rewrite the expression properly

So, we have the following representation

42 ≤ 4.2y

Divide both sides of the inequality by 4.2

So, we have

42/4.2 ≤ 4.2y/4.2

Evaluate the quotients

So, we have the following representation

10 ≤ y

Rewrite the expression as

y ≥ 10

Hence, the solution is y ≥ 10

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Possible question

Solve for y. 42≤4.2y

y ≥ 10 y ≥ -10 y ≤ -10 y ≤ 10

Answer:

Step-by-step explanation:

5 is D

6 is also D

Answer: r = 12

Step-by-step explanation:

11 - 23 = 12

YOUR SO WELCOME!!! :D

The distance between us and a star with a parallax angle of 0.1 arcsecond is 3.26 light years.

The distance between us and a star with a parallax angle of 0.01 arcsecond is 326 light years.

The distance between us and a star with a parallax angle of 0.001 arcsecond is 3260 light years.

The distance between us and a star with a parallax angle of 0.0001 arcsecond is 32600 light years.

The distance at which an object has a parallax of 1 arcsecond is known as a parsec. 3.26 light years are about how far this is.

The length of one parsec is 3.26 light years.

One arcsecond is equal to one parsec, which is equal to 3.26 light years.

We determine the other provided arcseconds based on this comparison.

3.26 light years make up a parsec.

0.1 arcsecond = 10 parsec

= 10 * 3.26 light years

= 32.6 light years

0.01 arcsecond = 100 parsec

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Answer:

x = 5

TS = 17

QT = 17

Step-by-step explanation:

The tick marks show us that line segment QT is equal to TS.

QS = QT + TS  and QT and TS are the same length

34 = 2(3x + 2)  Distribute the 2

34 = 6x + 4  Subtract 4 from both sides

30 = 6x  Divide both sides by 6

5 = x

Substitute in 5 for x

3x + 2

3(5) + 2

15 + 2 = 17

TS is 17

QT is 17

Answer: -1001, -1002

Step-by-step explanation:

Answer:

$33.25

Step-by-step explanation:

Two packages cost $9.50

Divide $9.50 by two get the cost for one package

$4.75 per package

$4.75 * 7 to get the cost for 7 packages

$33.25

The total number of sandwiches they have in all on Sunday is 375 sandwiches.

The amount earned by the cafe if each sandwich cost $4.50 is $1,687.5

Total percentage of ham and turkey sandwiches = 35% + 25%

= 60%

So,

225 = 60% of x

225 = 0.60 × x

225 = 0.60x

divide both sides by 0.60

x = 225/0.60

x = 375

Hence,

Total number of sandwiches = 375

If the cafe sells all the sandwiches at $4.50 each

The total money earned by the cafe = cost of each sandwich × total number of sandwiches

= $4.50 × 375

= $1,687.5

Therefore, the total sandwiches sold in the cafe on Sunday is 375 sandwiches.

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According to the query that the function h is established, h(-3) = -1/2, h(2) = 4, and h(4) = -4/1 for all real integers.

An statement, rule, or law in mathematics that establishes the link between an independent variable and a predictor variables (the dependent variable). Equations may be found all around arithmetic, and they are essential for building physical connections in the sciences. A mappings between A and B will only be a function if every member in set A only has end and only 1 photo in set B. Where A & B even be two separate sets.

Have used the top form of h(x) for x = variables -3 and 4 (which deviate from 2):

[tex]\begin{aligned}& h(x)=-\frac{1}{2} x^2+4 \\& h(-3)=-\frac{1}{2}(-3)^2+4=-\frac{9}{2}+4=-\frac{9}{2}+\frac{4}{2}=-\frac{1}{2} \\& h(4)=-\frac{1}{2}(4)^2+4=-\frac{16}{2}+4=-\frac{16}{2}+\frac{4}{1}=-\frac{4}{1}\end{aligned}[/tex]

Alternatively, h(2) must be defined explicitly as stated in the function's second description (specific for when x equals 2). Thus, h(2) equals 4.

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Answer:

More than likely no full answer key however there might be answers for each individual question.

The probability of advancing five spaces is 3/13 and the odds against is 13 : 6

The board game

From the question, we have the odds to be

Odds in favour = 3/10

This can be rewritten as

Odds in favour = 3 : 10

For an odd represented as a : b, the probability is

Probability = a/a + b

Using the above as a guide, we have

Probability = 3/13

The box of candies

From the question, we have the probability to be

Probability = 6/19

For a probability represented as a/b, the odds against is

Odds = b - a : a

Using the above as a guide, we have

Odds = 19 - 6: 6

Evaluate

Odds = 13 : 6

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The time taken by the ball to hit the ground is 9 seconds in quadratic equation .

What does quartic equation mean?

A fourth-degree equation, also known as a quartic equation, is one that reduces a quartic polynomial to zero and has the formula: where a 0. A quartic function's derivative is a cubic function.

a) The maximum height of the ball can be obtained by differentiating the given quadratic function, h = -16t² + 136t + 72.

          Differentiating both sides.

    δh/δt = -32t + 136

    -32t + 136    = 0

or, t = 136/32 = 4.5.

To check whether the value of h is maximum/minimum at t = 4.5, we differentiate

               δh/δt = -32t + 136

                 δh/δt = -32

which is < 0, which that implies, h is maximum at t = 4.5.

        the maximum height, by putting in t = 4.5, in the equation, to get:

h = -16(4.5)² + 136(4.5) + 72,

or, h = -16(20.25) + 612 + 72,

or, h = -324 + 684 = 360

Therefore, The maximum height of the ball is 360 feet.

b) the quadratic function h = -16t² + 136t + 72, as the height of the ball at the ground is 0.

Therefore, it can be written as:

0 = -16t² + 136t + 72.

or, 16t² - 136t - 72 = 0.

Solving this using the quadratic equation, we get

           t = - ( -136)± √(-136)² - 4( 16 ) ( -72)/2 * 16

           t =  136 ± √18496 + 4608/32

            t = 136 ± √23104/32

             t = 136 ± 52/32

Therefore, either t = (136+152)/32 = 9,

or, t  (136 - 152)/32 = -0.5.

Since t represents time, we won't take the negative value, and hence t = 9.

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Answer:

show the choices please.

Step-by-step explanation:

Correct answer is:

27

Answer:

There would be 27 ounces of flour

Step-by-step explanation:

The ratio is 7:3 for sugar to flour.

I divided the 63 ounces of sugar by 7 to earn 9

Now, I multiplied 9 by 3 to get 27

Now thee ratio is 63:27

If you divide 7 and 3 you will get 2.3 repeating

If you divide 63 and 27 you will also get 2.3 repeating

Hope that makes sense! ;)

Answer  :      x= [tex]\sqrt{2wy}[/tex]/ y

Step-by-step explanation:

Answer 16

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf < p = 36\°}[/tex]

Step-by-step explanation:

Since, the line is tangent to the circle, it is making an angle of 90 degree with the radius.

So,

∠p + 54 + 90 = 180 (Interior angles of a triangle add up to 180°)

∠p + 144 = 180

Subtract 144 to both sides

∠p = 180 - 144

[tex]\rule[225]{225}{2}[/tex]

Answer:

36°

Step-by-step explanation:

Tangent lines form Right Angles (90°) with all radii of circles.

Triangle Angle Sum: the three angles in a triangle add to 180°

90 + 54 + p = 180

144 + p = 180

p = 36

Answer:

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{5x+2y=9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \atop {-0.5x-y=7.5\ \ \ \ \ \ \ \ |\cdot2}} \right. \\\\\\\left \{ {{5x+2y=9} \atop {-x-2y=15}} \right. \\+\\--------\\4x=24\ \ \Rightarrow\ x=24:4\Rightarrow\ x=6\\\\y=-0.5x-7.5=-0.5\cdot6-7.5=-3-7.5=-10.5\\\\\boxed{(x;y)=(6;-10.5)}[/tex]

Answer:

Step-by-step explanation:

4x-3y=11. 2 (2x-7y=22).=> 4x-14y=44. 4x-3y=11....................1. 4x-14y=44. 11y= -33. y= -3. then,putting it in 1. 4x-3 (-3)=11.

Answer:

8700kg

Step-by-step explanation:

b = mass of bricks

l = mass of lorry

b+l = total mass = 11600kg

b = 3l  ==>  l = b/3

substitute: b + b/3 = 11600

multiply every term by 3 to get rid of denominator: 3b + b = 34800

simplify and solve:  4b = 34800  ==>  b = 8700

check:  l = 8700/3 = 2900

2900 + 8700 = 11600?  YES

Answer: 80

Step-by-step explanation:

set the 4 numbers to be x,x+2,x+4,x+6

They add up to 332 so the equation would be

x+(x+2)+(x+4)+(x+6)=332

4x=320

x=80

the rest of the numbers are 82,84,86

smallest is 80

The solutions using completing the square of quadratic equations are;

1) B: 2

2) A: Divide both sides by this coefficient

3) B: 5

4) All are quadratic equations

5) C. Quadratic Equation

1) Completing the square is basically a method for solving quadratic equations. Now, quadratic equations are second degree polynomials and as such have 2 roots. Thus, the solutions are 2.

2) Usually when using the method of completing the square, we are also trying to get rid of the coefficient attached to x squared and as such if we notice x squared has a coefficient, we will divide both sides by this coefficient.

3) The general form of quadratic equation is;

y = ax² + bx + c

Thus, we have;

2x² + 5x - 7 = 0

Thus, b = 5

4) They are all quadratic equations.

5) The correct one here is Quadratic Equation

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Answer:

B and D

Step-by-step explanation: I got it right

The distance between the two points P(-5, 7) and Q(6, 7) is 11 units.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is,

D = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Two points are given P(-5, 7) and Q(6, 7).

∴ D = [tex]\sqrt{(6 + 5)^2 + (7 - 7)^2[/tex].

D = [tex]\sqrt{(11)^2[/tex].

D = 11 units.

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Answer: 4 feet of pipe

Step-by-step explanation:

1(f)+1(f)+(2(f)=4(f)

f=feet

Using tangent of the angle, the angle of elevation is 32.5 degrees

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

In this problem, we have to use the tangent of the angle since we know the opposite and adjacent sides

Tan θ = opposite / adjacent

tanθ = 222 / 348

tan θ = 0.6379

θ = tan⁻¹(0.6379)

θ = 32.5°

The angle of elevation is 32.5 degrees

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Answer:

fourteen-sixteenths or  seven eights = 7/8 or 14/16

Step-by-step explanation: