MATHEMATICS HIGH SCHOOL

a landscaper is designing a flower garden in the shape of a trapezoid. she want to make to shorter base 3 yards greater than the height and the longer base 7 yards greater than the base. she wants the area 295 square yards. the situation is modeled by the equation h^2+5h=295. use the quadratic formula to find the height that will give the desired area

Answers

Answer 1

Answer:

we know that

The formula to calculate the solutions of the quadratic equation of the form $ax^(2) +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^(2)-4ac}}{2a}$

in this problem we have

$h^(2) +5h=295$

equate to zero

$h^(2) +5h-295=0$

$a=1\ b=5\ c=-295$

substitute in the formula

$x=\frac{-5(+/-)\sqrt{5^(2)-4(1)(-295)}}{2*1}$

$x=(-5(+/-)√(25+1,180))/(2)$

$x=(-5(+/-)√(1,205))/(2)$

the positive solution is

$x=(-5+√(1,205))/(2)=14.86\ yd$

therefore

the answer is

The height is $14.86\ yd$

Answer 2

Answer: put you formula in this way: ax^2+bx+c=0 this is h^2+5h-295=0
Now solve with the second grade equation
a=1, b=5, c=-295
you will get h=14.86 and h=-19.86, you can not have negative numbers so the only answer is 14.86

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Answers

Answer:

2x+3=-13

x=5

Step-by-step explanation:

it says 2 times a number which would be the 2x, and it says the sum of that and 3 which would be 2x+3 and it says is 13. 2x+3=13

now solving it

2x+3=13

subtract 3 from both sides

2x=10

and divide 2 from both sides

x=5

Answer:

Equation: 2n+3 = -13 Number: -8

Step-by-step explanation:

Ok so, it states the sum of twice a number and 3 equals -13. The question states to consider the number as "n" so the equation is 2n + 3 = -13.

Subtract 3 on both sides. Now . you have 2n = -16.

Divide 2 on both sides.

n = -8

A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point. The motorboat has a speed of 22 mi/h relative to the water. In what direction should the boat be headed?

Answers

The direction should the boat be headed is 60 degrees north 30 degrees west and this can be determined by using the trigonometric functions.

Given :

A straight river flows east at a speed of 11 mi/h.
A boater starts at the south shore of the river and wants to arrive at a point on the north shore of the river directly opposite the starting point.
The motorboat has a speed of 22 mi/h relative to the water.

The following steps can be used in order to determine the direction should the boat be headed:

Step 1 - The trigonometric function can be used in order to determine the direction should the boat be headed.

Step 2 - The mathematicalexpression of the cosine function is given by:

$\rm cos\theta=(base)/(hypotenuse)$

where $\theta$ is the direction should the boat be headed.

Step 3 - Now, substitute the known values in the above formula.

$\rm cos\theta=(11)/(22)$

Step 4 - Simplify the above expression.

$\rm cos\theta=(1)/(2)$

$\theta = 60^\circ$

Step 5 - So, the angle from the west axis is given by:

$90-60=30^\circ$

The direction should the boat be headed is 60 degrees north 30 degrees west.

For more information, refer to the link given below:

brainly.com/question/11709244

Answer:

N 30 degree W

Step-by-step explanation:

We are given that

Speed of river flows=11 mi/h(East)

Speed of motorboat relative to water=22mi/h

We have to find the direction in which the boat should be headed.

Let direction of the boat = $\theta$

We know that

$Cos\theta=(Base)/(hypotenuse)$

Using the formula

$Cos\theta=(11)/(22)=(1)/(2)$

$Cos\theta=Cos60^(\circ)$

Because $Cos60^(\circ)=(1)/(2)$

$\theta=60^(\circ)$

Angle from the west axis= $90-60=30^(\circ)$ W

Hence, the direction of boat should be headed in N 30 degree W

If sin α = 12/13 , and cosα = 5/13 , then tanα =?It would be great if you could add a few words of explanation

Answers

$sin\alpha=(12)/(13)\n\ncos\alpha=(5)/(13)\n\ntan\alpha=(sin\alpha)/(cos\alpha)\n\ntan\alpha=(12)/(13):(5)/(13)=(12)/(13)\cdot(13)/(5)=(12)/(5)=2(2)/(5)=2.4$

If you draw a right angles triangle you can fill in the values. So since sinx= opposite/hypotenuse then the hypotenuse of the triangle is 13. And the side opposite the angle a is 12. Since cosx= adjacent/ hypotenuse, the adjacent side is 5.
Tanx=opposite/adjacent and therefore tana= 12/5

there are 750 spectators in the stadium,of which 420 are women and the rest are men what percent of the spectators are women? and what percent of the spectators are men?

Answers

The percentage of women spectators is 56%.

The percentage of men spectators is 44%.

What is a percentage?

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

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of spectators = 750

Number of women = 420

Number of men = 750 - 420 = 330

The percentage of women.

= 420/750 x 100

= 56%

The percentage of men.

= 330/750 x 100

= 44%

Thus,

56% of women are spectators.

44% of men are spectators.

Learn more about percentages here:

brainly.com/question/11403063

#SPJ2

$number \ of\ men=750-420=330\n\n(420)/(750)*100\%=(42000)/(750)\%=56\%\n\n100\%-56\%=44\%\n\nWomen\ are\ 56\%\ of\ spectators\ and\ men\ are\ 44\%.$

A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is 950 ft2. If the length of the pool is 8 feet longer than the width, find the dimensions of the pool.

Answers

Answer:

$x \approx 21.080\,ft$ , $y = 29.080\,ft$

Step-by-step explanation:

The total area of the pool and the walkway is:

$(x + 6\,ft)\cdot (y + 6\,ft) = 950\,ft^(2)$

$(x + 6\,ft)\cdot (x + 14\,ft) = 950\,ft^(2)$

$x^(2) + 20\cdot x + 84\,ft^(2) = 950\,ft^(2)$

$x^(2) + 20\cdot x - 866\,ft^(2) = 0$

The roots of the second-order polynomial is:

$x_(1) \approx 21.080\,ft$ and $x_(2) \approx -41.081\,ft$

The only possible root is:

$x \approx 21.080\,ft$

The other dimension of the pool is:

$y = x + 8\,ft$

$y = 21.080\,ft + 8\,ft$

$y = 29.080\,ft$

A bird flies due east for 600 meters at a constant speed of 10 m/s. What is the bird's acceleration? (a) with no change in velocity, there is no acceleration (b) 60 m/s (c) 6 m/s/s (d) 60 m/s/s (e) not enough information is given