If x varies inversely as y and x = 18 when y = 2.4, what is the value of x when y = -6 ?​

Answer:

Step-by-step explanation:

I am using trig identities and the formula for the difference of the cos of 2 angles to solve this. I'll do the steps one at a time. It's super tricky. First I'm just going to work on simplifying the sec² part and then I'll introduce the sin²(x) - sin⁴(x) when I need it. Beginning with the identity for the difference of the cos of 2 angles, knowing that sec²(x) = [tex]\frac{1}{cos^2(x)}[/tex]:

[tex]sec^2(\frac{\pi}{2}-x)=\frac{1}{cos^2(\frac{\pi}{2}-x )}[/tex] and expand that using the formula for the difference:

[tex]\frac{1}{cos(\frac{\pi}{2}-x)cos(\frac{\pi}{2}-x) }=[/tex] [tex]\frac{1}{(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x))(cos\frac{\pi}{2}cos(x)+sin\frac{\pi}{2}sin(x)) }[/tex] and all of that simplifies down to

[tex]\frac{1}{(0cos(x)+1sin(x))(0cos(x)+1sin(x))}[/tex] which simplifies further to

[tex]\frac{1}{(sin(x))(sin(x))}=\frac{1}{sin^2(x)}[/tex] Now we'll bring in the other term. This is what we have now:

[tex]\frac{1}{sin^2(x)}(\frac{sin^2(x)-sin^4(x)}{1})[/tex] and distribute in to get:

[tex]\frac{sin^2(x)}{sin^2(x)}-\frac{sin^4(x)}{sin^2(x)}[/tex] which simplifies to

[tex]1-sin^2(x)[/tex] and that, finally, simplifies down to a simple

[tex]cos^2(x)[/tex]

Answer:

m = 11

Step-by-step explanation:

11 - 5 = 6

Answer:

120 muffins

Step-by-step explanation:

If The Bake Shop makes 24 muffins in one hour and we need to find out how many muffins will the bake make in five hours, we need to multiply 24 times 5 which would equal 120 muffins in five hours.

Hope this is helpful

Answer:

74 deg

Step-by-step explanation:

Ok, so this is a bunch of steps.

Answer:

D = 3 √5 units

Step-by-step explanation:

Here, we want to find the distance between these two points

to get this, we use the distance formula as follows

D = √(x2-x1)^2 + (y2-y1)^2

so we have for (3,-6) and (9,-3)

D = √(3-9)^2 + (-6 + 3)^2

D = √(36 + 9)

D = √(45)

D = 3√5 units

Answer:6x + 3x^2 +4

depending on what your on

Step-by-step explanation:

Answer:

9x^3 + 6x ^2 + 12x + 8

Step-by-step explanation:

Do each individually.

First (3x^2)(3x) = 9x^3

Then (3x^2)(2) = 6x^2

Then (3x)(4) = 12x

Then (4)(2) = 8

Finally add everything together, since everything has a different exponent, then just combine like I have above.

Answer:

the answer is 42/100

42 blocks are shaded out of 100

9514 1404 393

Answer:

  31°

Step-by-step explanation:

The measure of inscribed angle A is half the measure of intercepted arc BC.

  ∠CAB = 62°/2 = 31°

Answer:

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

Step-by-step explanation:

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

Answer:

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

Step-by-step explanation:

Given

y = [tex]\sqrt{ax+b}[/tex] ( square both sides )

y² = ax + b ( subtract b from both sides )

y² - b = ax ( isolate x by dividing both sides by a )

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

Answer:

5r³ - 34r² + 44r - 16

Step-by-step explanation:

[tex] \small \sf \: (5r − 4)(r² − 6r + 4)[/tex]

use the distributive property

5r × (r² − 6r + 4) - 4× (r² − 6r + 4)

5r³ - 30r² + 20r - 4r² + 24r - 16

combine like terms

5r³ - 30r² - 4r² + 20r + 24r - 16

5r³ - 34r² + 44r - 16

The product of the expressions is 5r^3 - 34r^2 + 44r - 16

The product of two expression is done by multiplying the expressions

The product expression is given as:

[tex](5r - 4)(r^2 - 6r + 4)[/tex]

Expand the expression

[tex]5r^3 - 30r^2 + 20r - 4r^2 + 24r - 16[/tex]

Collect like terms

[tex]5r^3 - 30r^2 - 4r^2 + 20r + 24r - 16[/tex]

Evaluate the like terms

[tex]5r^3 - 34r^2 + 44r - 16[/tex]

Hence, the product of the expressions is 5r^3 - 34r^2 + 44r - 16

Read more about product at:

https://brainly.com/question/4344214

Answer:

28 km per hour

Step-by-step explanation:

First determine the amount of time that the trip took

17:55 - 17:40 = :15 or 15 minutes

We need the time in hours

15 minutes * 1 hour/ 60 minutes = 15/60 hours = 1/4 hours

To determine speed, take distance and divide by time

7 km ÷( 1/4 hours)

Copy dot flip

7 * 4/1

28 km per hour

Answer:

527 grams

Step-by-step explanation:

Use the density formula, d = m/v

Plug in the density and volume, then solve for m (mass):

d = m/v

0.85 = m/620

527 = m

So, the mass is 527 grams

Answer:

The inverse is x-3

Step-by-step explanation:

y = x+3

To find the inverse, exchange x and y

x = y+3

Solve for y

x-3 = y+3-3

x-3 =y

The inverse is x-3

Answer:

x - 3

Step-by-step explanation:

f(x) = x + 3

y = x + 3

x = y - 3

Inverse is h(x) = x - 3

Answer:

6,068

Step-by-step explanation:

the length of the segment AB is 7.7*sin(52°) = 6,068

Answer:

6,068

Step-by-step explanation:

the length of the segment AB is 7.7*sin(52°) = 6,068

Step-by-step explanation:

Answer:

BELOW

Step-by-step explanation:

1) C= PD so

a) 12.56

b) 18.84

c) 37.68

2) C=2PR so

a) 2*3.14*2= 12.56

b) 2*3.14*14= 87.92

c) 2*3.14*12= 75.36

3)  C=2PR so

a) 56.52

b) 69.08

c) 43.96

4)

a) 31.4

b) 56.52

c) 40.82

Answer:

See Explanation

Step-by-step explanation:

a) Additive inverse of −2

b) Additive identity of −5

c) additive inverse of 3

d). multiplicative identity of 19

e) multiplicative inverse of 7

d)  | 11-5|×|1-5|

Answer:

0

Step-by-step explanation:

think of the decimal as one

Answer:

Step-by-step explanation:

Zero (0) is in the tenths place here.

Answer:

the answer is 1/45

Step-by-step explanation:

just use the proportion method

Answer:

B. a = 3

Step-by-step explanation:

4a + 3(a + 1) = 24

4a + 3a + 3 = 24

7a + 3 = 24

7a + 3 - 3 = 24 - 3

7a = 21

7a ÷ 7 = 21 ÷ 7

a = 3

Answer:

B

Step-by-step explanation:

Given

4a + 3(a + 1) = 24 ← distribute parenthesis and simplify left side

4a + 3a + 3 = 24

7a + 3 = 21 ( subtract 3 from both sides )

7a = 21 ( divide both sides by 7 )

a = 3 → B

Answer:

The vertex of the graph is at (6,0) and the Axis of symmetry is at x= 6

Step-by-step explanation:

Answer:

4, 5, and 7

Step-by-step explanation:

Length of two sides are 4 and 7 feet.

Thier sum = 4 + 7 = 11 feet.

We know that, sum of two sides is always larger than the third side.

So, 4, 5, and 7, can not be the third side here.

Answer: 13

Step-by-step explanation: a= 4,

B= 7 a+b= 7+4=11 A+b>C 11>13 does not work so that’s could NOT be the length. there fore the answer is 13

Step-by-step explanation:

the correct answer is

a. { ½(c-a), ½(d-b) }

________________

General formula

So

Here

for (a,b) and (c,d)

Midpoint

Option A

Answer:

[tex]x=-4+\sqrt{7}[/tex]

[tex]x= -4-\sqrt{7}[/tex]

Step-by-step explanation:

Quadratic

Answer:

infinitely many

Step-by-step explanation:

All triangles that you can construct will be "similar", in that they have the same angles, but different sizes. The angles have to add up to 180, and they do in the measurements that you're given.

Answer:

pie

Step-by-step explanation:

Answer:

2166.53

Step-by-step explanation:

a = 10,000(1.04)⁵

a = 12,166.53

12,166.53 - 10,000 = 2166.53

Answer:

$4.7 (approx)

Step-by-step explanation:

Simple interest = (principle * time * rate) / 100

Answer:

5,000

Step-by-step explanation:

Step-by-step explanation:

6x-3x=14-5

3x=9

x=9/3

x=3

Step-by-step explanation:

6x + 5 = 3x + 14

6x - 3x = 14 - 5

3x = 9

x = 9/3

x = 3