Ryan bought a sofa on sale for $342. This price was 28% less than the original price.
What was the original price?

Rearrange:

6(-9w+7)-4w

Distribute:

-54w+42-4w

Combine the like terms:

-54w-4w

-58w

So, you get...

Answer:

x = -9

Step-by-step explanation:

Given:

BC = x + 19

ST = x + 29

Required:

Value of x

Solution:

Midsegment theorem states that the midsegment of a triangle = ½ of the length of its third side

Thus:

BC = ½(ST)

Substitute

x + 19 = ½(x + 29)

Multiply both sides by 2

2(x + 19) = x + 29

2x + 38 = x + 29

Collect like terms

2x - x = -38 + 29

x = -9

Answer:

Volume = 144 cm³

Step-by-step explanation:

Volume of the polyhedron = volume of triangular prism = ½*b*h*l

Where,

b = 4 cm

h = 6 cm

l = 12 cm

Substitute

Volume = ½*4*6*12

Volume = 144 cm³

Answer:

If you get the maximum grade in the last test, your average grade will still be below 0.9 = 90%, which means that it is not possible to average a 90%.

Step-by-step explanation:

Average grade:

The average grade is given by the sum of all averages, divided by the number of tests.

In this question:

99%, 67%, 83%, and 86%.

Next test counts twice, which means that in total, there are 6 tests.

Is it possible to average a 90%?

The maximum grade in a test is 100% = 1. I will calculate the average grade you get a 100% on the last test, which is worth 2. So

[tex]M = \frac{0.99+0.67+0.83+0.86+2*1}{6} = \frac{5.35}{6} = 0.892[/tex]

If you get the maximum grade in the last test, your average grade will still be below 0.9 = 90%, which means that it is not possible to average a 90%.

Answer:

4 3/4 is the mixed form

hope this helps!

Answer:

103453.17

Step-by-step explanation:

19% of 457,000 is 86,830 euros and use conversion rate to get a profit of 103453.17

Answer:

A

Step-by-step explanation:

Answer:

C on edge

hope this helps

Step-by-step explanation:

The answer was C for me on Edg.

Answer:

Step-by-step explanation:

hello :

z⁴=1+i      given : z² = t    t is the complex number  so :   z⁴= (z²)² =t²

solve for  t  this equation : t² = 1+i

if : t = x+iy     t² =(x+iy)² = x²+2xiy+(iy)² =x²-y²+2xyi ......     (  i² = -1)

t² = 1+i  means : x²-y²+2xyi = 1+i

you have this system :   x²-y² = 1.....(*)

                                      2xy  = 1.....(**)

slve for   x  and y    you ca add this equation :   ....(***)

( use : t² = 1+i

/t²/ = /1+i/   so :/t/² = /1+i/ .... (√(x²+y²))²=√(1²+1²) =√2  means x²+y² = √2)

the system is :   x²-y² = 1.....(*)

                         2xy  = 1.....(**)

                         x²+y² = √2 ....(***)

add (*) and (***) : 2x²= 1+√2

x² = (√2+1)/2

substrac  (*) and (***)  you have : y² = (√2-1)/2

use (**) the proudect  xy is positif (same sign)  so :

x=√( (√2+1)/2)  and  y = √( (√2-1)/2)   so :  t1 =√( (√2+1)/2)+i√( (√2-1)/2)  

x= -√( (√2+1)/2)  and  y = -√( (√2-1)/2) so :t2= -t1

same method for equation : z² =t1  ..(2 solution )  and z² = t2..(2 solution )

Answer:

sure what is it

Step-by-step explanation:

Well, it depends on the question!!

(comment it if you need me to answer it)

The solution of the inequality 2(x - 4) + 14 < x - 1 is:

x < -7

Here we have the following inequality:

2(x - 4) + 14 < x - 1

To solve it, we need to isolate the variable in one of the sides, so let's do that.

Expanding the right side we will get:

2x - 8 + 14 < x - 1

2x + 6 < x - 1

Now group like terms:

2x - x < - 1 -6

x < -7

That is the solution.

Learn more about inequalities at

https://brainly.com/question/24372553

#SPJ1

Step-by-step explanation:

this is the answer

hope it helped!!!

Answer:

k=29

Step-by-step explanation:

we know that

-------> by supplementary angles

Solve for k

Combine like terms in the left side

Substract  both sides

Divide by  both sides

therefore

the answer is the option

B

Answer:

315 ft²

Step-by-step explanation:

•Split the shape into a triangle and a square.

•A=bh so 15*15=225 (area of square)

•Since the height of the square is 15, subtract given height of 3 from 15 which is 12 and that is the base of triangle.

• To find the height, subtract 15 since the base is equal to the top side.

•A=1/2bh for triangles so 1/2(15)(12) is 90.

•Add 225 and 90 then boom. 315ft²

Step-by-step explanation:

8) Area of circle =

[tex]\pi {r}^{2} [/tex]

Radius = 1/2 of diameter (Diameter = 2x radius)

Radius = 1/2 × 10 in = 5 in.

Area of circle =

[tex]\pi {5}^{2} = 25\pi {in}^{2} [/tex]

11) Radius = 1/2 × 6m = 3m

Area of Circle =

[tex]\pi {3}^{2} = 9\pi {m}^{2} [/tex]

Note that I will leave both answers in terms of pi as I am not sure how you want to leave your answer as.

Answer:

area = πr×r

r = d/2

area = π (d/2)×(d/2)

so for problem 8,

area = pi×5×5 = 25π = 78.539 inches squared

continue the same logic for the next questions

Answer:

x=10

Step-by-step explanation:

50+x=6x

-x -x

50=5x

/5 /5

x=10

Answer:

Step 1: Find the prime factorization of the number inside the radical. Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind. Step 3: Move each group of numbers or variables from inside the radical to outside the radical.

Answer:

-4.25

Step-by-step explanation:

Y = -4

Z = ?

-4Z = 17

Z = -4.25

Answer:

How can I help you?

5−(x+y)35-(x+y)3

Simplify

Simplify the expression.

−3x−3y+5-3x-3y+5

Answer:

the difference of 5 and the cube of the sum of x and y

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

Explanation:

I'll represent the dice results as an ordered pair. Something like (6,2) means the first die is a 6 and the second is a 2. The sum being 6+2 = 8.

There are only two ways to get to a sum of 8, and those two ways are:

Here are other possibilities if we allow the sum to be larger than 8

You should find that there are a total of 10 ways to have two dice add to a value that is 8 or larger, given that at least one of the dice must be a 6.

This is out of 6*6 = 36 ways to roll two dice without such a restriction. The probability we're after is 10/36 = (2*5)/(2*18) = 5/18

Side note: 5/18 = 0.2778 = 27.78% approximately

Given,

Nepali speaker : 80% (Y)

Maithili speaker : 60% (X)

We know that,

Both language speaker = Y -X

Now,

Y- X

= 80- 60

= 20

Therefore, 20% people speak both languages

Answer:

answer is c

Step-by-step explanation:

Answer:

c. 586.2

Step-by-step explanation:

add all areas together:

127.2 for semi circle on right

22x18=396 for middle square

7*9=36 for 2 triangles on left

Answer:

Step-by-step explanation:

AB is a tangent to circle o

ABO is a right-angled

AO²=AB²+BO²

[tex]BO=\sqrt{AO^{2}-(AB)^{2})\\}\\\\\sqrt{(8.6)^{2}-(5)^{2} } \\\\=\sqrt{73.96-25} \\\\=\sqrt{48.9} \\\\=6.99\\\\Answer=7[/tex]

hope it helps....

have a great day :)

Answer:

1/12

Step-by-step explanation:

The probability of rolling an odd number = 3/6

The probability of rolling 2 after an odd number =

1/6

3/6 x 1/6 = 3/36

3/36 = 1/12 (after simplified)

Answer:

yeh you are correct so it will be b is equal to minus 42 minus 9.3 that will be equal to -51.3 so that is the value of b

Answer:

1,1, and 1000

Step-by-step explanation:

Answer:

(10 x 10) x 10 = 1000

Step-by-step explanation:

10 x 10 = 100

100 x 10 = 1000

Answer:

7z³

Step-by-step explanation:

7z³

[tex]\huge\boxed{Hi\:there!}[/tex]

To find the GCF of the polynomial, all we have to do is spot the common factor of all the terms of the polynomial.

21z⁵-42x⁴+14z³

The common term is

7z³

If we factor 7z³ out, we'll get

z³(3z²-6z+2)

[tex]\huge\boxed{\sf{Hope\:this\:helps!}}\\[/tex]

[tex]\huge\bold{Good\:luck!}[/tex]

[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]

Answer:

critical value = 5.29

Step-by-step explanation:

Given that they are divided into 4 groups and a sample of 5 test was selected

N = 5 * 4 = 20

k = 4

∝ = 0.01

Df for numerator ( SS group )= k - 1 = 3

Df for denominator ( SSE group )  = N - k = 20 - 4 = 16

DF ( degree of freedom )

Next we will use the F table to determine the critical value

Critical value =   [tex]F_{16,3,0.01}[/tex] = 5.29