The value of y varies directly with x. When y = 75, x = ½ . What is the value of y when x is 2 ¼ ? A. 168.75 C. 66.67 B. 16.67 D. 337.5

9514 1404 393

Answer:

Step-by-step explanation:

The intercepts are ...

  x-intercept = -4/-9 = 4/9

  y-intercept = -4/5

Knowing these intercepts means we can put the equation in intercept form.

  x/(4/9) -y/(4/5) = 1

The fractional intercepts make graphing somewhat difficult. However, we observe that the sum of the x- and y-coefficients is equal to the constant:

  -9 +5 = -4

This means the point (x, y) = (1, 1) is on the graph. Knowing a point, we can write several equations using that point.

We like a positive leading coefficient (as for standard or general form), so we can multiply the given equation by -1.

  9x -5y = 4 . . . . . standard form equation

Adding -4, so f(x,y) = 0, puts this in general form.

  9x -5y -4 = 0

We can eliminate the constant by translating a line from the origin to the point we know:

  9(x -1) -5(y -1) = 0

This can be rearranged to the traditional point-slope form ...

  y -1 = 9/5(x -1)

Yet another equation can be written that tells you the slope is the same everywhere:

  (y -1)/(x -1) = 9/5

These are only a few of the many possible forms of a linear equation.

Answer:

b:  irrational

Step-by-step explanation:

  (√5+2)

--------------  is given.

  (√5 - 2)

If we multiply numerator and denominator by (√5+2), we succeed in removing the square root symbol from the denominator:

(√5+2)(√5+2)

---------------------

(√5+2)(√5- 2)

and the denominator becomes 5 - 2, or 3.  The denominator is now rational, but the numerator still involves the square root symbol, so overall the given number is irrational.

Answer:

41,400 ft per second

Step-by-step explanation:

1 minute is 60 seconds.

x = ft per second

Ratio:

[tex]\frac{690}{1} =\frac{x}{60} \\\\x=41400[/tex]

Answer:

1.5

Step-by-step explanation:

To find out the gradient (or the slope), we can use the formula

Gradient = (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are any two points lying on the line.

Looking at the graph, we can take any two points and simply plug the coordinates in the equation. For instance, take (0,-2) and (2,1)

Therefore we get the gradient as (1- -2)/(2-0) = 3/2 or 1.5.

Feel free to ask any doubts you may have.

Hope this helps! :D

Answer:

A line is the locus of points that: are the same distance from two points. That's the equation for a line.

Step-by-step explanation:

hope its help

Answer:

A line is the locus of points that: are the same distance from two points.

Step-by-step explanation:

Answer:

8.07, excluding taxes.

Step-by-step explanation:

7x5.99 = 41.93

50-41.93 = 8.07

Answer:

i think its help..............

Answer:

[tex] \displaystyle \sin (x) - \frac{ { \sin}^{3} (x)}{3} + \rm C[/tex]

Step-by-step explanation:

we would like to integrate the following integration

[tex] \displaystyle \int \cos ^{3} (x) dx[/tex]

in order to do so rewrite

[tex] \displaystyle \int \cos ^{2} (x) \cos(x) dx[/tex]

we can also rewrite cos²(x) by using trigonometric indentity

[tex] \displaystyle \int( 1 - \sin ^{2} (x) )\cos(x) dx[/tex]

to apply u-substitution we'll choose

[tex] \rm \displaystyle u = \sin ^{} (x) \quad \text{and} \quad du = \cos(x) dx[/tex]

thus substitute:

[tex] \displaystyle \int( 1 - {u}^{2} )du[/tex]

apply substraction integration and:

[tex] \displaystyle \int 1du - \int {u}^{2} du[/tex]

use constant integration rule:

[tex] \displaystyle u - \int {u}^{2} du[/tex]

use exponent integration rule:

[tex] \displaystyle u - \frac{ {u}^{3} }{3} [/tex]

back-substitute:

[tex] \displaystyle \sin (x) - \frac{ { \sin}^{3} (x)}{3} [/tex]

finally we of course have to add constant of integration:

[tex] \displaystyle \sin (x) - \frac{ { \sin}^{3} (x)}{3} + \rm C[/tex]

Answer:

f(13)≈45.92

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

there are two numbers that fit in the x<=3 category, those being -3 and -5, so you add the two decimals for them (.17 and .13) to get .30 and move the decimal two times to the right to make it in percentage form.

The probability of P(x ≤ -3) is 0.30 or 30% if the probability table is provided.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have given a probability table in the picture.

P(x ≤ -3) = P(x = -5) + p(x = -3)

From the table:

P(x ≤ -3) = 0.17 + 0.13

P(x ≤ -3) = 0.30 or 30%

Thus, the probability of P(x ≤ -3) is 0.30 or 30% if the probability table is provided.

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Answer:

24 degrees

Step-by-step explanation:

Supplementary angles sum up to give 180°

E + H = 180°

156 + H = 180

H = 180 - 156

H = 24°

Answer:

The length of side x in a 30-60-90 triangle is 2√3.

Step-by-step explanation:

The numbers 30-60-90 are angles, so we need to find the side x of a right triangle with the following information:

θ: is one angle of the right triangle = 30°

α: is the other angle of the right triangle = 60°

a: is one side of the right triangle = √3

b: is the other side of the right triangle =?

x: is the hypotenuse of the right triangle =?

The length of the hypotenuse can be found by Pitagoras:

[tex] x^{2} = a^{2} + b^{2} [/tex]    (1)

So, we need to find the side "b". We can calculate it with the given angles.

From the side "a" we have:

[tex] cos(\alpha) = \frac{a}{x} [/tex]

[tex] cos(60) = \frac{\sqrt{3}}{x} [/tex]    (2)

From the side "b":

[tex] sin(\alpha) = \frac{b}{x} [/tex]

[tex] sin(60) = \frac{b}{x} [/tex]   (3)

Now, we can calculate "b" by dividing equation (3) by equation (2).

[tex] tan(60) = \frac{\frac{b}{x}}{\frac{\sqrt{3}}{x}} [/tex]

[tex] b = tan(60)*\sqrt{3} = 3 [/tex]

Finally, we can find the length of the hypotenuse with equation (1):

[tex] x = \sqrt{a^{2} + b^{2}} = \sqrt{(\sqrt{3})^{2} + (3)^{2}} = 2\sqrt{3} [/tex]

Therefore, the length of side x in a 30-60-90 triangle is 2√3.

I hope it helps you!

Given:

Height of a trapezoidal prism = 10 cm

Base lengths are 3 and 4 cm.

Base height = 2 cm

To find:

The volume of the trapezoidal prism.

Solution:

Base area of a trapezoidal prism

[tex]B=\dfrac{a+b}{2}\times h[/tex]

Where, a,b are base lengths and h is the base height.

Putting [tex]a=3,b=4,h=2[/tex], we get

[tex]B=\dfrac{3+4}{2}\times 2[/tex]

[tex]B=7[/tex]

The volume of a trapezoidal prism is:

[tex]V=Bh[/tex]

Where, B is the base area and h is the height of the prism.

Putting [tex]B=7,h=10[/tex], we get

[tex]V=7\times 10[/tex]

[tex]V=70[/tex]

Therefore, the volume of the trapezoidal prism is 70 cubic cm.

Answer:

The pyramid X has a square base with base length of 5 cm, base width of 6cm and makes a 90 degree angle with the pyramid height. A pyramid Y has a triangular base with 2 sides measuring 7.5 cm and 8 cm respectively.

Answer:

The volumes of X and Y are equivalent.

Step-by-step explanation:

Answer:

150 cm2

Step-by-step explanation:

one square would simply be base x height our base is 5 and height is 5 so i multiply that and get 25 since this is a cube all sides are equal so I will simply just multiply 25 by the number of sides since a cube has 6 sides our equation to get the answer would be 25 x 6 = 150 so 150 is our answer! Hope this is a good explanation! Have a good day!

Answer:

30000

Step-by-step explanation:

200x10x15=30000

Answer:

t=20

Step-by-step explanation:

Answer: c

Step-by-step explanation:

Answer:

When 2 lines are parallel, the sum of interior corresponding angles = 180

120 + b = 180

b = 180 - 120 = 60

a + 30 = 180

a = 180 - 30 = 150

Answer:

45.) 49.) V=LBH

Step-by-step explanation:

V= 15

5*3*1=15

V= 891

11*9*9

Answer:

x=19.88

Step-by-step explanation:

Okay, let's try and create a "table" of what we know, and what we are looking for.

4.5 litres of milk            cost                 89.5 rupees

1 litre                              costs                x rupees

Obviously, we are looking for x.

The method I'm about to tell you, might be familiar. Imagine that there was a giant X where the words cost and costs are above. There'd be a line connecting 4.5 litres of milk with the rupees we are looking for, and another line connecting 1 litre with the 89.5 rupees.

If we were to form an equation to solve for x, we'd put the connecting terms together, with an "=" between them, so we'd have this:

4.5*x=1*89.5

That's our equation, so let's solve for x.

x=89.5/4.5 => x=19.88 , let's say 20 rupees

Answer:

Step-by-step explanation:

hey watch it fatty

Answer:

5) 268.08cm

6)1150.35mi

7)33.51in

8)904.78yd

Step-by-step explanation:

5) V= 4/3πr^3

V=4/3π4^3

V=268.08257

6) r=1/2d

r=1/2(13)

r=6.5

V= 4/3πr^3

V= 4/3π 6.5^3

V=1150.3465

7) V= 4/3πr^3

V= 4/3π 2^3

V=33.510

8)V= 4/3πr^3

V= 4/3π 6^3

V=904.778

Answer:

D

Step-by-step explanation:

A = 4 π r^2

A/(4π) = r^2

r = sqrt(A/(4π))

Answer:

D

Step-by-step explanation:

Given

A = 4πr² ( divide both sides by 4π )

[tex]\frac{A}{4\pi }[/tex] = r² ( take the square root of both sides )

[tex]\sqrt{\frac{A}{4\pi } }[/tex] = r → D

Answer:

(2 , 72) and (5 , 180)

Step-by-step explanation:

Options A (2 , 72) and C (5 , 180) will be the correct options.

An equation is an expression that shows the relationship between two or more numbers and variables.

we are Given equation representing the relation between two variables 'x' and 'y' is,

y = 36x

Here, y = yards and x = inches

Now Satisfy this equation with each point given in the question;

Option A. (2, 72)

72 = 36 × 2

72 = 72

This is True

Option B. (4, 40)

40 = 36 × 4

40 = 144

This is False

Option C. (5, 180)

180 = 36 × 5

180 = 180

This is True

Option D. (40, 4)

4 = 36 × 40

4 = 1440

This is False

Option E. (72, 2)

2 = 36 × 72

2 = 2592

This is False

Option F. (180, 5)

5 = 36 × 180

5 = 6480

This is False

Therefore, Options (A) and (C) will be the correct options from all the other

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Answer:

10

Step-by-step explanation:

The highest exponent determines the degree of a polynomial.