Determine the length of side a in the triangle below. (Not drawn to scale.) the hypotenuse is 2.5 the leg is 2

Answer:

About 0.14 acres

Step-by-step explanation:

56 lb = 8 acres

1 lb = x

We can cross multiply:

(8 acres)(1 lb) = (56 lb)(x)

Solving for x:

x = 8 ÷ 56 ≈ 0.14 acres

Step-by-step explanation:

Amplitude is the distance between the center line of the function and the top or bottom of the function.

The amplitude is half the distance between the max and the min, so

Amplitude = 1/2(max - min)

Amplitude = 1/2(-2.2 -(-8.5))

So amplitude = 1/2(6.3)

= 3.15

Answer:

4x³+2x²+2x

Step-by-step explanation:

9x³-5x³+2x²-5x+7x+4-4

4x³+2x²+2x

The simplified expression for (9x³ + 2x² - 5x + 4)- (5x³ -7x + 4) is

2x( 2x² + x + 1).

We have the Expression,

(9x³ + 2x² - 5x + 4)- (5x³ -7x + 4)

Now, simplifying the expression we get

(9x³ + 2x² - 5x + 4)- (5x³ -7x + 4)

= 9x³- 5x³ +2x² -5x + 7x + 4 - 4

= 4x³ + 2x² + 2x

= 2x( 2x² + x + 1)

Thus, the simplified expression is 2x( 2x² + x + 1).

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Answer:

a) yes

b) yes

c) yes

d) no

e) no

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Answer and step by step esplanation:

The perpendicular line has the slope opposite and inverse, in our case [tex]-4 \rightarrow +\frac14[/tex]

Line passing through the point will have then equation - using the point-slope form [tex]y-y_0=m(x-x_0)[/tex]

[tex]y-5=\frac14 (x-(-5))\\y-5=\frac14(x+5)[/tex]

The parallel line will have the same slope as the given line, in our case -4. Again with the point-slope equation:

[tex]y-5=-4(x-(-5)\\y-5=-4(x+5)[/tex]

Answer:

Perpendicular: y = 1/4x + 5 3/4

Parallel: y = -4x - 7

Step-by-step explanation:

Hello!

A perpendicular line would have a negative reciprocal slope, meaning you flip the sign of the slope, and the numerator and denominator.

Given our equation: y = -4x + 2, we can find the perpendicular slope by finding the negative reciprocal:

So the perpendicular slope is 1/4.

We can now solve for the y-intercept by plugging in the x and y-value of the point into the equation y = 1/4x + b:

The y-intercept is 5 3/4, so the equation of the line would be y = 1/4x + 5 3/4.

_____________________

Parallel lines have the same slope. So we can use -4 as our slope, and plug in the points to find the y-intercept.

So the equation of the parallel line would be y = -4x - 7.

Check the picture below.

Make sure your calculator is in Degree mode.

The number of meters from that point on the ocean floor to the wreck is 319.83 meters.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

Tan 13.2° = 75 / x

x = 75/tan 13.2°
x = 75/0.2345                                      

x = 319.829 meters

x = 319.83 meters

Thus,

The distance from the point to the wreck is 319.83 meters.

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Step-by-step explanation:

Use these equations.

Equation of a Hyperbola, centered at orgin

[tex] \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

where a is the major axis

B is the minor axis.

Since a and X are first, the x axis is the major.

This also means the x axis contains the vertices and foci as well.

The equation of vertices when x is major axis is

[tex](x ±a)[/tex]

Since the vertices are (±1,0), and the orgin is (0,0). The length of a is 1.

So a=1.

The equation of foci is

[tex](x±c)[/tex]

Where c is formed by

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

We know that c is 2 since the distance from the foci and center is 2. A is 1, so let find b.

[tex] {2}^{2} = {1}^{2} + {b}^{2} [/tex]

[tex]4 = 1 + {b}^{2} [/tex]

[tex]3 = {b}^{2} [/tex]

[tex] \sqrt{3} = {b}[/tex]

So our equation is

[tex] \frac{ {x}^{2} }{1 {}^{2} } - \frac{ {y}^{2} }{ (\sqrt{3}) {}^{2} } = 1[/tex]

[tex] \frac{ {x}^{2} }{1} - \frac{ {y}^{2} }{3} = 1[/tex]

Answer:

y = 4.5x + 9, graphing done below.

Solving steps:

( -2 , 0 ), ( 0, 9)

slope:

[tex]\sf \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\sf \frac{9-0}{0+2}[/tex]

[tex]\sf 4.5[/tex]

equation:

y - 9 = 4.5 ( x - 0 )

y = 4.5x + 9

note: point -2 on x axis and 9 on y axis, and keep the ruler on those two points and draw a straight linear line, ta-daa you are done.

The exchange rate that She will receive is an algebraic expression

The exchange rate that Salma will receive in dollars per euro is [tex]\frac{12x - 9}{4x -6}[/tex]

The amount of dollars with Salma is given as:

[tex]Dollar = \frac{12x^2 + 15x - 18}{2x^2 + 14x + 20}[/tex]

The amount of Euro she can buy is:

[tex]Euro = \frac{2x^2 -x-3}{x^2 + 6x +5}[/tex]

Let the exchange rate be r.

So, we have:

[tex]Dollar * \frac 1r = Euro[/tex]

The equation becomes

[tex]\frac{12x^2 + 15x - 18}{2x^2 + 14x + 20}* \frac 1r = \frac{2x^2 -x-3}{x^2 + 6x +5}[/tex]

Factorize the expressions

[tex]\frac{3(x + 2)(4x - 3)}{2(x + 5)(x +2)}* \frac 1r = \frac{(x +1)(2x -3)}{(x + 5)*x + 1)}[/tex]

Cancel out the common factors

[tex]\frac{3(4x - 3)}{2}* \frac 1r = \frac{(2x -3)}{1}[/tex]

Make r the subject

[tex]\frac 1r = \frac{2(2x -3)}{3(4x - 3)}[/tex]

Expand

[tex]\frac 1r = \frac{4x -6}{12x - 9}[/tex]

Make r the subject

[tex]r = \frac{12x - 9}{4x -6}[/tex]

Hence, the exchange rate is [tex]\frac{12x - 9}{4x -6}[/tex]

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Answer:

1/4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

there are 4 cans of soup and 1 of them is tomato

you have a 1 out of 4 chance of picking tomato soup

Answer:

100cm = 1m

Thus, one more step should be added to your working to arrive at the final answer:

Perimeter

= 10m 160cm

= 11m 60cm

This is because 160cm= 100cm +60cm, which is also equivalent to 1m 60cm.

Alternative working:

Convert all the units to cm first.

[tex]\boxed{1 \: m= 100 \: cm}[/tex]

Length

= 5m 55cm

= 300cm +55cm

= 355cm

Breadth

= 2m 25cm

= 200cm +25cm

= 225cm

Perimeter

= 2(length +breadth)

= 2(355 cm +225 cm)

= 2(580 cm)

= 1160 cm

= 11m 60cm

From the second last step to the last step, you could divide 1160 by 100 to find how many meters are there. You would get a quotient of 11 and a remainder of 60. Since this 60 cannot be changed into meters as a whole number, we can leave it as 11m 60cm. Otherwise, it is also correct to leave it as 1160cm or 11.6m unless otherwise stated.

However, 10m 160cm is not preferred since the conversion of cm to m is done partially, as the 160 cm can still be further simplified.

Answer:

openup 1 em We want to find the points on the curve y=2x^3-3x^2-12x+20y where the tangent line is parallel to the xx-axis, which means that the slope=0

Answer:

Infinitely many

Step-by-step explanation:

There are many solutions because 0=0.

Answer:

x=-1

Step-by-step explanation:

2x-5=-5x+2

7x=-7

x=-1

Answer:

b.× = 14 16

Step-by-step explanation:

#stay safe

hope it helps

Answer:

D. 25.7 sq.ft

Step-by-step explanation:

Area of the Figure = Area of Rectangle - Area of Semi Circle

Area of Rectangle = LW = 8*4 = 32 sq.ft

Area of Semicircle = 0.5*π*r² = 0.5*3.14*2² = 6.28 sq.ft

Area of the Figure = 32-6.28 = 25.72 ≈25.7

EGA and AGB aka the fourth option

Step-by-step explanation:

EGA and AGB create a 180 degree angle together

Answer:

x= 8

Its 8 because when you add 65 and 76 you get 141 and 180 - 141 is 39. 6x8-9 is 39.

Answer:

x = 4

Step-by-step explanation:

If y = 36, that means the original y = 18 was multiplied by 2. So, we have to multiply x = 2 by 2 as well.

2 * 2  = 4, so x = 4

Answer:

False

Step-by-step explanation:

5:20 + 1:35 is 6:55, not 6:40/

Answer:

36,000-28,500

=7,500 decrease per year

Answer:

you have to add the circumference of the circle C≈131.95 to the two 100m  sides of the rectangle

Step-by-step explanation:

Answer:

$1107.55

Step-by-step explanation:

3,589.90 x .0590/12 = $17.653,589.90 + 17.65 =3,607.553,607.55 - 2,500 = $1,107.55

Answer:

[tex](x + 3)(x + 7) \\ (x)(x) + (x)(7) + (3)(x) + (3)(7) \\ = {x}^{2} + 7x + 3x + 21 \\ = {x}^{2} + 10x + 21[/tex]

Answer:

slope of perpendicular line= -⅕

slope of parallel line= 5

Step-by-step explanation:

y= 5x -4

The equation is in the slope-intercept form, thus the slope is the coefficient of x.

Slope of given equation= 5

The product of the slopes of perpendicular lines is -1.

Let the slope of the perpendicular line be m.

m(5)= -1

[tex]m = - \frac{1}{5} [/tex]

Thus, the slope of the perpendicular line is -⅕.

Parallel lines have the same gradient.

Slope of parallel line= 5

What is slope-intercept form?

Answer:

Consider the given vectors.

a=3i+2j−6k

b=4i−3j+k

Now,

a⋅b=(3i+2j−6k)(4i−3j+k)

a⋅b=12−6−6=0

Therefore,

Two vectors a and b are perpendicular.

Thus, the angle between the vectors a and b =90

∘

Hence, this is the answer.

Answer:

36

Step-by-step explanation:

2(4)^2 + 3(4) - 8

Use PEMDAS

2(16) + 3(4) - 8

32+12-8

=36