What is the solution of....

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:

$57

[tex]9w+6d[/tex]

Step-by-step explanation:

Given that:

Earnings per hour for washing cars = $9

Earnings per hour for walking dogs = $6

Number of hours for which car washing is done = [tex]w[/tex]

Number of hours taken for walking dogs = [tex]d[/tex]

Earnings for [tex]w[/tex] hours for washing cars = Per hour earnings multiplied by number of hours = $9[tex]w[/tex]

Earnings for [tex]d[/tex] hours for walking dogs = Per hour earnings multiplied by number of hours = $6[tex]d[/tex]

Total earnings by both = $([tex]9w+6d[/tex])

Now, given that

Number of hours spent washing cars = 5 hours

Number of hours spent walking dogs = 2 hours

Therefore, total earnings by both = 9 [tex]\times[/tex] 5 + 6 [tex]\times[/tex] 2 = $57

Answer:

16 cups is equal to 4 quarts

Step-by-step explanation:

Multiply the volume by 4

The required  4 quarts are equal to 16 cups. This means that if you have 4 quarts of liquid, you can pour it into 16 cups and it will completely fill them. Option D is correct.

1 quart is equivalent to 4 cups. This is a standard conversion ratio between quarts and cups. It means that if you have 1 quart of liquid and you want to know how many cups it is, you can simply multiply the number of quarts by 4.

So, to find out how many cups are in 4 quarts, we perform the following calculation:

4 quarts * 4 cups/quart = 16 cups

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★To Solve :

[tex]\rm\blue{13(y+7) = 3(y-1)}[/tex]

⠀⠀⠀⠀⠀

★SOLUTION :

[tex]\rm\red\leadsto{13(y+7) = 3(y-1)}[/tex]

[tex]\rm\red\leadsto{13\times{y}+13\times7= 3\times{y}-3\times1}[/tex]

[tex]\rm\red\leadsto{13y+91=3y-3}[/tex]

[tex]\rm\red\leadsto{13y-3y=-3-91}[/tex]

[tex]\rm\red\leadsto{10y=-94}[/tex]

[tex] \rm\red\leadsto{} y =\dfrac{ { \cancel{-94}}^{ \:-45 } }{ { \cancel{10}}^{ \: 5} } [/tex]

[tex]\rm\red\leadsto{y=}\dfrac{-47}{5}[/tex]

____________________

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:

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:

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

The answer is c. because all of the other answers arne tpossible due to where they graphed it

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!

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.

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:

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.

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:

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

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:

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.

(-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:

b)[tex]\frac{-13}{3}[/tex]

Step-by-step explanation:

[tex]\frac{xy + 5}{3}\\\\\frac{\frac{-2}{3}27 + 5}{3}\\\\\frac{-18 + 5}{3}\\\\\frac{-18 + 5}{3}\\\\\frac{-13}{3}[/tex]

Answer:

B

Step-by-step explanation:

Evaluate the numerator , that is

xy + 5 = ( - [tex]\frac{2}{3}[/tex] × 27 ) + 5 = - 18 + 5 = - 13 , then

[tex]\frac{-13}{3}[/tex]

= - [tex]\frac{13}{3}[/tex] → B

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:

12 oz (1)  has the lowest

Step-by-step explanation:

ur wlcmeocxjvieirbvuubvuebwdfjvberlbf

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

Answer:

6 / 55 = x / 44

44*6/55= x

x = 4.8 miles

Step-by-step explanation:

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:

Step-by-step explanation:

if there are  cups of sugar for 520 cookies

this means with one cup of sugar we can make 130 cookies

520/4=130

1300/130= 10 cups

for 1300 cookies we need 10 cups of sugar