Determine the domain on which the following function is decreasing.

Step-by-step explanation:

Using Cosine rule, we have:

q² = r² + s² - 2(r)(s)(cosQ)

= 380² + 390² - 2(380)(390)(cos48°)

= 98169.688cm²

Hence q = 313cm. (nearest centimeter)

The required value of side q is 313 cm for the triangle ΔQRS.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

In triangle QRS side r = 380 cm, side s = 390 cm and angle Q = 48°.

To find the length of the side q,

Use cosine rule,

[tex]cos Q = \frac{(r^2 + s^2 - q^2)}{(2\times r \times s)}[/tex]

Substitute the values here,

[tex]cos 48 = \frac{(380)^2 + (390)^2- q^2}{2\times380 \times390} \\[/tex]

[tex]0.67 = \frac{144400 + 152100 - q^2}{296400}[/tex]

198,588 = 296500 - q²

q² = 97912

q = 312.90

q = 313 cm

The value of side q is 313 cm.

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Answer:

1

Step-by-step explanation:

A solution to a system of equations is the point where the 2 lines meet.

Answer:

d 91

Step-by-step explanation:

she is reaching it perfectly at this height in the problem, its super easy

Answer:

12 oz (1)  has the lowest

Step-by-step explanation:

ur wlcmeocxjvieirbvuubvuebwdfjvberlbf

a) 34y=15

=> y= 34-15

=> y = 19

b) -58y=20

=> y= -58-20

=> y = -78

c) -x=23

=> -1x=23

=> x= 23+1

=> x= 24

d) -51= -y

=> -51= -1y

=> y= -51+1

=> y= -50

Hope it helps!

Answer:

The answer is .875 cups of pudding for each person

Step-by-step explanation:

To solve this problem you will have to divide 3 1/2 among 4 people.

3 1/2 divided by 4 is equal to .875

Answer:

x > -2y + 8

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Set the two equations 13x+34 and 10x+10 together to add up to 90 on the right which should look like this 13x + 34 + 10x + 10 = 90.  Combine the two x-values to get 23x and the two other numbers to get 44.  Your equation should now be 23x + 44 = 90.  Subtract 44 on both sides to get this equation 23x = 46.  Divide 23 on both sides to get your x value which is 2.

Answer:

X is equal to 2

Step-by-step explanation:

90 = 13x + 34 + 10x + 10

Combine Like Terms:

90 = 23x + 44

Subtraction Property of Equality:

90 - 44 = 23x + 44 - 44 ---> 46 = 23x

Division Property of Equality:

46 ÷ 23 = 23x ÷ 23 ---> 2 = x

90 = 13x + 34 + 10x + 10

Fill In Variables:

90 = 13(2) + 34 + 10(2) + 10

90= 26 + 34 + 20 + 10

90 = 60 + 30

90 = 90

Answer:

65%

Step-by-step explanation:

Answer:

y = 0.5x + 9

Step-by-step explanation:

What we know:

An equation with the point (2,10) passing through it is perpendicular to the equation 2x+y=17.

The root of 2x+y=17 is (8.5, 0).

The two equations intersect at (3.2, 10.6)

Let's check if 3.2 and 10.6 work for 2x+y=17.

2(3.2) + 10.6 = 17

6.4 + 10.6 = 17, which is true.

Let's try y = 0.5x + 9, to see if we get the same output as the earlier equation.

y = 0.5(3.2) + 9

y = 1.6 + 9

y = 10.6, so 3.2 as x does work.

As a result, the perpendicular equation is y = 0.5x + 9.

Answer:

30 minutes after biker left

Step-by-step explanation:

Given that :

Speed of hiker = 3 mph

Speed of biker = (3 +6) = 9 mph

Present Distance of hiker when the biker set out ;

Present Distance of hiker = speed * time = (3 * 1) = 3 miles

Time taken to catchup equals :

Present distance + (distance when biker set out) = bikers distance

Let time taken = x

(3 + (3 * x)) = (9 *x)

(3 + 3x) = 9x

3 + 3x = 9x

3 = 9x - 3x

3 = 6x

x = 3/6

x = 1/2 hours

x = 30 minutes

30 minutes after biker left

Answer:

0.5 hrs or 30 mins

Step-by-step explanation:

=====================================================

Explanation:

Assume the polynomial we want to find is in the form Ax^2+Bx+C

The goal is to find the values of A, B, and C.

We start with 3x^2+4x-1, then we subtract off Ax^2+Bx+C. Set this equal to 1 and we get:

(3x^2+4x-1) - (Ax^2+Bx+C) = 1

3x^2+4x-1 -Ax^2-Bx-C = 0x^2 + 0x + 1

(3x^2-Ax^2) + (4x-Bx) + (-1-C) = 0x^2 + 0x + 1

(3-A)x^2 + (4-B)x + (-1-C) = 0x^2 + 0x + 1

From here we equate the coefficients of the x^2 terms together and we see that 3-A = 0 which leads to A = 3.

Do the same for the x terms to get 4-B = 0 leading to B = 4

Finally, we have -1-C = 1 lead to C = -2

The polynomial Ax^2+Bx+C becomes 3x^2+4x-2

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

Checking the answer:

(3x^2+4x-1) - (Ax^2+Bx+C)

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

3x^2+4x-1 - 3x^2-4x+2

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

0x^2 + 0x + 1

0 + 0 + 1

1

We get a difference of 1, so the answer is confirmed.

Answer:

The equation of line parallel to given line passing through (8,-7) is:

[tex]y = -\frac{5}{4}x+3[/tex]

Step-by-step explanation:

Given line is:

5x+4y=16

first of all, we have to convert the equation of given line in slope-intercept form

[tex]4y = -5x+16[/tex]

Dividing both sides by 4

[tex]\frac{4y}{4} = -\frac{5x}{4} + \frac{16}{4}\\y = -\frac{5}{4}x+4[/tex]

Slope intercept form is:

[tex]y=mx+b[/tex]

The slope of given line is:

[tex]m = -\frac{5}{4}[/tex]

Let m1 be the slope of line parallel to given line

"The slopes of two parallel lines are equal"

[tex]m = m_1\\m_1 = -\frac{5}{4}[/tex]

The equation of line parallel to given line will be:

[tex]y = m_1x+b[/tex]

Putting the value of slope

[tex]y = -\frac{5}{4}x+b[/tex]

Putting the point (8,-7) in the equation

[tex]-7 = -\frac{5}{4}(8)+b\\-7 = -(5)(2) + b\\-7 = -10+b\\b = -7 +10\\b = 3[/tex]

Putting the value of b

[tex]y = -\frac{5}{4}x+3[/tex]

Hence,

The equation of line parallel to given line passing through (8,-7) is:

[tex]y = -\frac{5}{4}x+3[/tex]

Answer:

6x^2 + 3x - 3

Step-by-step explanation:

Using the FOIL method, we would multiply 2x by 3x, then multiply 2x by 3, then multiply -1 by 3x, then multiply -1 by 3. This would bring the answer to 6x^2 + 6x -3x - 3. Combine the like terms 6x and -3x and you get 6x^2 + 3x - 3

Answer:

A. 5.444444444444   XD

Step-by-step explanation:

Answer:

I just thought about it in my head but possibly try A

Step-by-step explanation:

...

Answer:

The elements of the set C will be:

C = {-2, -1, 0, 1, 2, 3, 4, 5}

In other words,

[tex]-2\le \:x<6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-2\le \:x<6\:\\ \:\mathrm{Interval\:Notation:}&\:[-2,\:6)\end{bmatrix}[/tex]

The solution number line is also attached below.

Step-by-step explanation:

C = {x ∈ Z | such that -2 ≤ x < 6 }

It is clear that the x ∈ Z, meaning the x belongs to the set of integers Z.

It is given that -2 ≤ x < 6.

so x must be greater than or equal to -2 and less than 6.

Therefore, the elements of the set C will be:

C = {-2, -1, 0, 1, 2, 3, 4, 5}

In other words,

[tex]-2\le \:x<6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-2\le \:x<6\:\\ \:\mathrm{Interval\:Notation:}&\:[-2,\:6)\end{bmatrix}[/tex]

The solution number line is also attached below.

Step-by-step explanation:

The coordinates of Point S(1,2)

The coordinates of point T(7,5)

length of ST=√(7-1)²+(5-2)²

|ST|=√36+9

|ST|=√45=3√5

Answer:

a) S(1,2) T(7,5)

b)3√5 = 6.7 ( approximately)

Step-by-step explanation:

Look at the picture below.

Hope you find this helpful

Step-by-step explanation:

(T-S)(2000), when T(x) and S(x) are functions, is equivalent to T(2000)-S(2000), which is 17-7=10

We know that T(x) is equal to everything else, and everything else is S(x)+G(x), so T(x)-S(x) = G(x), or dollars spent on general science

It would be best to label the points if your turning it in. It can help people easily identify the points you've plotted.

From the looks of it, your equation is good.

The base is good and your math is right, but where did you get your height from?

If you count from point R up to line PQ you get 5 as the height.

I understand miscounting's a thing, no worries.

So if we input the correct height, we get A = 1/2 (3)(5)

1/2 * 15

7.5

The area of the polygon is 7.5 units.

I hope that helps and if you ever need any more help don't be afraid to reach out!

Answer:

10%

Step-by-step explanation:

The computation of the percentage of bulbs that switched on incandescent is as follows;

Let us assume the incandescent be I

And, the fluorescent be F

Now the equation is

0.4I + 0.9F = 0.8 (I+F)

0.41I + 0.9F = 0.8I + 0.8F

So here

0.4I = 0.1F

Now the percentage would be for incandescent in the case of switched on is

= 0.4I ÷  0.8(I+F) × 100

= 0.1F ÷ 1F

= 10%

Answer:

6 / 55 = x / 44

44*6/55= x

x = 4.8 miles

Step-by-step explanation:

Answer:

6x

Step-by-step explanation:

4 x - -5х + 3x- x+2х - 7х

Combine like terms so, so since all are the same you just do the operation they want u to do..

4x + 5x= 9x

9x + 3x = 12x

12x - x = 11x

11x + 2x= 13x

13x - 7x = 6x

Hint: 2 negatives make a postitive

Hint: in there is just an "x" there is always an invisible one in it... 1x

Hope this helped!

(-y −y) + (4x + 4x) + (-3 −3 + 2 + 2 + 2 + 2) + (-5x−5x)

-2y + 8x + 2 - 10x

-2y -2x +2

Subtract the amount he paid his mother back from the amount he borrowed from her:

20.50 - 20.50 = 0

He does not owe his mother any more.

Answer:

Step-by-step explanation:

m∠X + m∠Y + m∠Z = 180          {angle sum  property of triangle}

3x + 5 + 40 +4x - 5 = 180

3x + 4x  + 5 + 40 -5 = 180           {Combine like terms}

                   7x + 40 = 180        { subtract 40 from both sides}

                            7x = 180 - 40

                            7x = 140

                             x = 140/7

                            x = 20

m∠X = 3x + 5

         = 3*20 + 5

         = 60 + 5

m∠X = 65

m∠Z = 4x - 5

         = 4*20 - 5

        = 80 - 5

m∠Z = 75

Answer:

<OPQ = 23 degrees

Step-by-step explanation:

Given

Interior angles m∠PNO=(x+14) and m∠NOP=(x−1)

Exterior angle = m<OPQ = (5x-2)

The sum of interior angles is equal to the exterior angle, that is;

m∠PNO+m∠NOP = m<OPQ

x+14 + x-1 = 5x-2

2x + 13 = 5x-2

Collect like terms;

2x-5x = -2-13

-3x = -15

x = 15/3

x = 5

Get <OPQ

<OPQ = 5x - 2

<OPQ = 5(5)- 2

<OPQ = 25-2

<OPQ = 23 degrees

Answer:

See explanation

Step-by-step explanation:

The first option (4t - 8/5)... equals 16/3 t -23/5 (the fourth option in the first row)

The second option 7t - 22 (still in the first row) equals 3(3t-4)...(the third option in the second row)

The third option (still in the first row) 5(2t+1)... equals 3t + 33 (the final option in the second row)

The two options in the second row to the left equal each other

-11/4 t + 36 = (-9/2t + 3)+(7/4t + 33)

Answer:

x = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

5(x - 2) - 6 = 24

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that 24 does indeed equal 24.

∴ x = 8 is the solution to the equation.