x^2+4xy+4y^2-8x-16y-20​

Answer:

5 : -1.5

10: -4

y =  1 -.5x

noticed the pattern of subtracting .5 .... then plugged in x = 4

and saw that -2 had to be combined with "1" to end up with a "-1"

Step-by-step explanation:

Answer:

28g.

Step-by-step explanation:

35% of 80g

= 0.35*80

= 28.

The 80g solution contains 28g of salt and 52g of water.

To calculate the amount of salt you would get by evaporating all the water from a 35% salt solution weighing 80g.

To find out how much salt is in the 80g of the 35% salt solution, we'll first need to determine the amount of salt and water present in the solution.

Let's assume:

- Mass of salt (NaCl) in the solution = m salt

- Mass of water (H₂O) in the solution = m water

The concentration of the salt solution is given as 35%, which means 35g of salt is present in every 100g of the solution.

1. First, we'll find the mass of salt (m salt) in the 80g solution:

  m salt = 35% of 80g

  m salt = 0.35 * 80g

  m salt = 28g

2. Next, we'll find the mass of water (m water) in the 80g solution:

  m water = Total mass of the solution - Mass of salt

  m water = 80g - 28g

  m water = 52g

Now, if we evaporate all the water from the solution, the salt will be left behind. So, the mass of the salt remaining after evaporation will be 28g (m salt).

Therefore, by evaporating all the water from the 80g of the 35% salt solution, you will get 28g of salt.

To summarize, we found that the 80g solution contains 28g of salt and 52g of water. By evaporating all the water, we are left with 28g of salt, as per our calculations.

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Answer:

a. 2,727

b. (85.6%, 87.6%)

Step-by-step explanation:

The percentage of the adults aged 57 through 85 that used at least one prescription medication = 86.6%

a. The expected number of the 3,149 subjects aged 57 through 85 that used at least one prescription medication = 3,149 × 86.6/100 = 2,727.034 ≈ 2,727 (subjects)

b. The 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is given as follows;

[tex]CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p} \cdot (1-\hat{p})}{n}}[/tex]

Where;

[tex]\hat p[/tex] = 86.6/100= 0.866

n = 3,149

z = The z-value at 90% confidence level = 1.645

Therefore, we get the following confidence interval of the percentage of adults (rounded to one decimal place as required);

[tex]\left (0.866 - 1.645\times \sqrt{\dfrac{0.866 \times (1-0.866)}{3,149}}\right) \times 100 \% \approx 85.6 \%[/tex]

[tex]\left( 0.866 + 1.645\times \sqrt{\dfrac{0.866 \times (1-0.866)}{3,149}} \right) \times 100 \% \approx 87.6 \%[/tex]

The 90% confidence interval, of the percentage C.I. ≈ (85.6%, 87.6%).

Answer:

4       :  5

Step-by-step explanation:

boys : girls

12          15

Divide each by 3

12/3 :  15/3

4       :  5

Answer: 4:5

Step-by-step explanation:

To simplify the ratio 12:15, divide both numbers by the GCF of the 2 numbers (3). This gives you the simplified ratio, 4:5.

Answer:

20% of 10% of 1000 = 20

Step-by-step explanation:

Now we have to,

→ find the 20% of 10% of 1000.

Let's find 10% of 1000,

→ (10/100) × 1000

→ 0.1 × 1000

→ 100

Then 20% of 10% of 1000 is,

→ (20/100) × 100

→ 0.2 × 100

→ 20

Hence, the answer is 20.

Answer:

5.7

Step-by-step explanation:

First find the coordinates of the points

A ( 2,2)

B ( -2,-2)

The distance is

d = sqrt(  (x2-x1)^2 + (y2-y1)^2)

  = sqrt(  (-2-2)^2 + (-2-2)^2 )

   = sqrt( (-4)^2 + (-4) ^2)

   = sqrt( 16+16)

  = sqrt( 32)

  =5.656854249

To the nearest tenth

5.7

Answer:

5.65

Step-by-step explanation:

(2,2) (-2,-2)

√(x2 - x1)² + (y2 - y1)²

√(-2 - 2)² + (-2 - 2)²

√(-4)² + (-4)²

√(16) + (16)

√32

= 5.65

Answer:

70 degrees

Step-by-step explanation:

there are multiple ways, as all the trigonometric functions are related.

let's try it this way :

consider the missing side to be the radius of a circle.

then 41 would be the cos value of the angle (multiplied by that radius, of course).

so, let's calculate the missing side per Pythagoras

c² = a² + b² = 113² + 41² = 12769 + 1681 = 14450

c = 120.21

and now

41 = cos(?) × 120.21

cos(?) = 41/120.21 = 0.341...

? = 70.0576... ≈ 70 degrees

Answer:

70°

Step-by-step explanation:

tangent θ = (opposite side / adjacent side)

tangent θ = (113 / 41)

θ = arctan (113 / 41)

θ = 70.0576°

*Note: "arctan" is the same as "inverse tangent"

**Note: "soh-cah-toa" (and "cho-sha-cao" for sec, csc, & cot) is an easy mnemonic device to remember the trig functions (sin, cos, & tan) and their relations to the sides of a given angle.

Answer:

Let the inverse of f(x) be h(x):

[tex]{ \tt{h(x) = \frac{1}{4x} }}[/tex]

Answer:

6 ft

Step-by-step explanation:

Draw a plane, showing the three (non-linear) points that define it.[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

See this attachment

Answer:

Acute and scalene

Step-by-step explanation:

All the three interior angles of triangle are less than 90 then it is an acute triangle.

All the sides have different length then it is Scalene triangle. In Scalene triangle, all the sides have different length and so all the angles are of different

Explanation:

You have the right idea. The triangle is acute since all three angles are less than 90 degrees. The triangle is also scalene because all three sides are different lengths.

For a triangle to be equilateral, the three sides must be the same length. So we can rule out choice A.

We can rule out choice B since none of the angles are larger than 90 degrees. This contradicts choice E.

We can rule out choice C because we don't have exactly two sides the same length. This contradicts choice D.

We can rule out choice F because we don't have a 90 degree angle. This contradicts choice E.

Answer:

here

Step-by-step explanation:

Answer:

x = 6 x 7 = 42

Step-by-step explanation:

hope this helps

Answer:

[tex] \frac{x}{6} = 7 \\ x = 6 \times 7 \\ x = 42[/tex]

Answer:

Total time taken by train = 8 hour 32 minutes

Step-by-step explanation:

Given:

Time train leave Zurich = 22:40 min

Time train arrives in Vienna = 07:32

Find:

Total time taken by train

Computation:

Total time taken by train = [23:60 - 22:40] + 7:32

Total time taken by train = 1:20 + 7:32

Total time taken by train = 8:52

Total time taken by train = 8 hour 32 minutes

Correct question is;

The function f(x) = 6x + 8 represents the distance run by a cheetah in miles. The function g(x) = x − 2 represents the time the cheetah ran in hours. Solve (f/g)(3), and interpret the answer.

Answer:

26 is the cheetahs rate in miles per hour.

Step-by-step explanation:

We are given;

f(x) = 6x + 8

g(x) = x − 2

Thus;

f/g = f(x)/g(x)

> (6x + 8)/(x − 2)

Since we are looking for (f/g)(3), then we have;

> (6(3) + 8)/((3) − 2) = 26

Since f(x) is distance and g(x) is time, then, we know that distance/time = speed. Thus, the interpretation is 26 mph which is the speed of the cheetah.

Answer:

26; the cheetah's rate in miles per hour

Step-by-step explanation:

I just took the test

Answer:

uh the 2nd one

Step-by-step explanation:

cause im smart

Recall that the tangent function is defined by

tan(x) = sin(x)/cos(x)

Also recall the double angle identity for sine,

sin(2x) = 2 sin(x) cos(x)

Then the equation is the same as

3 sin(x)/cos(x) = 4 sin(x) cos(x)

Move everything to one side to prepare to factorize:

3 sin(x)/cos(x) - 4 sin(x) cos(x) = 0

sin(x)/cos(x) (3 - 4 cos²(x)) = 0

As long as cos(x) ≠ 0, we can omit the term in the denominator, so we're left with

sin(x) (3 - 4 cos²(x)) = 0

and so

sin(x) = 0   or   3 - 4 cos²(x) = 0

sin(x) = 0   or   cos²(x) = 3/4

sin(x) = 0   or   cos(x) = ±√3/2

On the interval [0, 2π),

• sin(x) = 0 for x = 0 and x = π

• cos(x) = √3/2 for x = π/6 and x = 11π/6

• cos(x) = -√3/2 for x = 5π/6 and x = 7π/6

(None of these x make cos(x) = 0, so we don't have to omit any extraneous solutions.)

Answer:

15

Step-by-step explanation:

32-19 = 13 that have both

70-57= 13 that have both again from that sample

total number of people that have both : 13 + 13 = 26

11 kids don't have either one, so :

26-11 = 15

Answer:

5x-6

Step-by-step explanation:

f(x) = 2x + 3

g(x) = 3x - 9

f(x) + g(x) = 2x + 3  + 3x-9

               = 5x-6

Answer:

i dont see anything

Step-by-step explanation:

Answer:

Step-by-step explanation:

For this, we kind of have to test points to solve it. First, we can test theh interval x<= -2. Plug in  -2 and we get a negative value which works. Next, let's try -2<x<0. Plug in -1 and get a positive value which doesn't work.

Next try 0<=x<=7. Plug in any number like 4 and get a negative value which works.

Finally, try x>7. Plug in 8 for example and you would get a positive value. So the solution is

x <= -2 OR 0 <= x <= 7

Answer:

x = 9b/C

Step-by-step explanation:

Cx – 4b = 5b

Add 4b to each side

Cx – 4b+4b = 5b+4b

Cx = 9b

Divide by C

Cx/C = 9b/C

x = 9b/C

x=9b

Step-by-step explanation:

because if you subtract 9-4 it would equal 5 and then you would just add the b to the equation.hope this is helps

Answer:

2x+8w

I hope this will help you

Answer:

70 x 47x = 3290

.

. . . . . . . . . . ........

Answer: 6x^3-35x^2+47x-12

Step-by-step explanation:

(2x-3)(x-4)(3x-1)

=(2x^2-11x+12)(3x-1)

=6x^3-35x^2+47x-12

Answer:450

Step-by-step explanation:

The correct answer is option (F) 450 cm

For a circle with radius 'r' and the central angle 'θ' (in radians), an arc length 's' is,

s = r × θ

C = 2 × π × r

We have been given that the length of xy (the minor arc) is 15 cm and angle = 12°.

⇒ θ = 0.209 radians

Let r be the radius of the circle.

xy = 15

⇒ r × θ = 15

⇒ r × 0.209 = 15

⇒ r = 71.77 cm

The circumference of the circle is,

C = 2 × π × r

⇒ C = 2 × π × 71.77

⇒ C = 450.95

⇒ C ≈ 450 cm

Therefore, the circumference of the circle is option (F) 450 cm

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