Consider the equation 6x +7=3x � 5. Which of the following possible first steps would prevent having to deal with fractions when solving the equation?

Answer:

Cost of each pencil = $12.5

Cost of each eraser = $7.5

Step-by-step explanation:

Given:

Number of eraser bought = 3

Number of pencil bought = 2

Total amount paid = $47.50

Cost of one pencil and one eraser = $20

Find:

Each cost

Computation:

Let;

Cost of each eraser = e

Cost of each pencil = p

So,

e + p = 20

e = 20 - p .................................... eq1

3e + 2p = 47.50

3(20 - p) + 2p = 47.50

60 - 3p + 2p = 47.50

-p = -12.5

Cost of each pencil = $12.5

e = 20 - p

e = 20 - 12.5

e = 7.5

Cost of each eraser = $7.5

Answer:

[tex]x=1[/tex]

[tex]y=2[/tex]

Step-by-step explanation:

[tex]y=x^2+3x-2[/tex] , [tex]y+3=5x[/tex]

Replace all occurrences of [tex]y[/tex] in [tex]y+3=5x[/tex] with [tex]x^2+3x-2.[/tex]

[tex](x^2+3x-2)+3=5x[/tex]

[tex]y=x^2+3x-2[/tex]

Add [tex]-2[/tex] and 3.

[tex]x^2+3x+1=5x[/tex]

[tex]y=x^2+3x-2[/tex]

Subtract 5x from both sides of the equation.

[tex]x^2+3x+1-5x=0[/tex]

[tex]y=x^2+3x-2[/tex]

Subtract 5x from 3x.

[tex]x^2-2x+1=0[/tex]

[tex]y=x^2+3x-2[/tex]

Rewrite 1 as [tex]1^2[/tex].

[tex]x^2-2x+1^2=0[/tex]

[tex]y=x^2+3x-2[/tex]

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

[tex]2x=2[/tex] · [tex]x[/tex] · [tex]1[/tex]

[tex]y=x^2+3x-2[/tex]

Rewrite the polynomial.

[tex]x^2-2[/tex] · [tex]x[/tex] · [tex]1[/tex] [tex]+[/tex] [tex]1^2=0[/tex]

[tex]y=x^2+3x-2[/tex]

Factor using the perfect square

trinomial rule [tex]a^2-2ab+b^2=(a-b)^2,[/tex]

where a = x and b = 1.

[tex](x-1)^2=0[/tex]

[tex]y=x^2+3x-2[/tex]

Set the [tex]x-1[/tex] equal to 0.

[tex]x-1=0[/tex]

[tex]y=x^2+3x-2[/tex]

Add 1 to both sides of the equation.

[tex]x=1[/tex]

[tex]y=x^2+3x-2[/tex]

Replace all occurrences of [tex]x[/tex] in

[tex]y=x^2+3x-2[/tex] with 1.

[tex]y=(1)^2+3(1)-2[/tex]

[tex]x=1[/tex]

[tex]y=2[/tex]

The profit percentage = 16.3%

Answer:

4

Step-by-step explanation:

7h-15h+40=-72

-8h=-32

h=4

Answer:

12 liters per min

Step-by-step explanation:

Math

27/4 = x

9/16      1

27/4=(9/16)x

Divide both sides by 9/16

12=x

option A.55°

Answer:

Solution given:

<x+<y=<z

exterior angle of a triangle is equal to the sum of two opposite interior angle

4n-18+n+8=133-6n

5n+6n=133+10

11n=143

n=143/11

n=13

exterior angle =133-6*13=55°

option A.55°

Answer:

(centre = (3, - 1 ) and radius = 7

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

x² + y² - 6x + 2y - 39 = 0 ( collect x/ y terms and add 39 to both sides )

x² - 6x + y² + 2y = 39

Using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 3)x + 9 + y² + 2(1)y + 1 = 39 + 9 + 1

(x - 3)² + (y + 1)² = 49 ← in standard form

with centre (3, - 1 ) and r = [tex]\sqrt{49}[/tex] = 7

Answer:

Find the area of the triangle from the coordinate plane.

Y

A

10-

5-1

с

B.

0

-20

-15

-10

-5Step-by-step explanation:

Answer:

A. It acts perpendicular to an object

Answer:

A - True

B - False

C - True

D - False

E - True

Step-by-step explanation:

Answer:

f(2) = - 5

Step-by-step explanation:

Using the recursive rule and f(1) = - 3 , then

f(2) = 2f(1) + 1 = 2 × - 3 + 1 = - 6 + 1 = - 5

Answer:

(2-a)^2

(2+a) (2-a)...

Answer:

Step-by-step explanation:

Use the identity:  a² - b² = (a+ b)(a - b)

4 - a² = 2² - a²        {Here a = 2 and b = a}

        = (2 +a) (2 - a)

Answer: B. Square

Step-by-step explanation:

The answer is B.), because if you have two pairs of parallel sides that means it looks like a square 1. || 2. _

                                                            _

- Chilio

Answer: the correct answer is A. Between 0 and 90

If an angle is between 0 and 90 it is acute

If an angle is EXACTLY 90 it is a right angle

If an angle is between 90 and 180 it is obtuse angle

If it's 360 then it is a full circle

Answer:

x = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{1}{x} + \frac{1}{3x} = 4[/tex] (Multiply everything by LCM)

[tex]3x*\frac{1}{x} + 3x*\frac{1}{3x}=3x*4[/tex] (Simplify the fractions)

[tex]3+1=12x\\4=12x\\x=4/12\\x=\frac{1}{3}[/tex]

SSS (side-side-side) requires that all three sides of the potentially congruent triangles be congruent.

Triangle WVU & Triangle UBW are our two triangles.

The middle line, UW and WU are congruent by the reflexive property, so that is not the information we need to prove SSS.

For SSS, we need to know that sides WV and UB are congruent.

Hope this helps!

Answer:

you need to solve for 'X'

mean 49 = 55 + 42 + 32 +48 + 55 + X

49 = (232+X) / 6

49 * 6 = 232 + X

294 = 232 + X

294 - 232 = X

62 = X

so therefore X is 62

Step-by-step explanation:

please give me a brainliest

Answer:

y = 25

Step-by-step explanation:

Given y = kx and k = 5 then

y = 5x ← equation of variation

When x = 5 , then

y = 5 × 5 = 25

Answer:

57°,123°,57°,123°

Step-by-step explanation:

as vertical angles are equal

so one angle=114/2=57°

other angle=180-57=123°

Answer:

pic pls

Step-by-step explanation:

Answer:

Let ten's place digit =x and unit place digit =y

Number=10x+y

x+y=5 ...(i)

10x+y−9=10y+x

9x−9y=9x−y=1 ...(ii)

from (i) and (ii) we get,

x=3,y=2

∴Number=10×3+2=32.

Step-by-step explanation:

Hope it helps!

4. MIke divided the group into 5 groups. If there were 28 people in each group how big was the original group?

a. What are they asking for?

how big was the original group?

b. identify all the necessary numbers.

28,5

c. write the equation or problem in numeric form.

x=28*5

d. solve the math.

x=140

e.write the answer

. the original group contains 140 people.

5. If he difference is 589 and the subtrahend is 339,what is the minuend?

a. What are they asking for?

what is the minuend?

b. identify all the necessary numbers.

589,339

c. write the equation or problem in numeric form.

x=589-339

d. solve the math.

x=250

e.write the answer.

minuend=250

6. If the quotient is 17 and the dividend 765, what is the divisor?

a. What are they asking for?

what is the divisor?

b. identify all the necessary numbers.

17,765

c. write the equation or problem in numeric form.

x=765/17

d. solve the math.

x=45

e.write the answer.

divisor is 45.

4. Solution

a. How big was the original group?

b. 28 and 5

c. x = 28×5

d. x = 140

e. There are 140 people in original group.

5. Solution

a. What is the minuend?

b. 589 and 339

c. x = 589-339

d. x = 250

e. The minuend is 250.

6. Solution

a. What is the divisor?

b. 17 and 765

c. x = 765/17

d. x = 45

e. Hence, 45 is the divisor.

EF is tangent to the circle we'll assume; otherwise there's no progress.

Call the center C. ECD is isosceles, formed from two radii and the chord.

Angle CED is complementary to DEF

CED = 90 - 65 = 25 degrees

CDE is congruent, isosceles triangle and all that: CDE=25

That leaves DCE=180-25-25=130 degrees

That's the measure of arc DE as well:

Answer: 130 degrees, choice A

Answer:

130

Step-by-step explanation:

Answer:

[tex] \frac{ - 81}{9} [/tex]

[tex] - 9[/tex]

Answer:

4.8 miles per hour.

Step-by-step explanation:

Average speed=Total distance/Time taken

=26.2miles/5.5hour

=4.8 miles per hour

Answer:

0.395

Step-by-step explanation:

We need to solve the given expression.

[tex]-\dfrac{3}{4}\times \dfrac{4}{5}-\dfrac{1}{2}\times\dfrac{1}{4}+\dfrac{4}{5}\times \dfrac{7}{5}[/tex]

We can also write it as :

[tex]-\dfrac{3}{4}\times \dfrac{4}{5}+\dfrac{4}{5}\times \dfrac{7}{5}-\dfrac{1}{2}\times\dfrac{1}{4}\\\\=\dfrac{4}{5}(\dfrac{-3}{4}+\dfrac{7}{5})-\dfrac{1}{2}\times\dfrac{1}{4}[/tex](Distributive property is used)

So,

[tex]=\dfrac{4}{5}\times \dfrac{13}{20}-\dfrac{1}{2}\times\dfrac{1}{4}\\\\=\dfrac{4}{5}\times \dfrac{13}{20}-\dfrac{1}{8}\\\\=\dfrac{13}{25}-\dfrac{1}{8}\\\\=0.395[/tex]

So, the value of the given expression is equal to 0.395.

Answer:

The balance after the 6 years of investment will be $ 15,442.08.

Step-by-step explanation:

Given that $ 13,700 was invested at a rate of 2% compounded quarterly during 6 years, to determine the final result of the investment, the following calculation must be performed:

13,700 x (1 + 0.02 / 4) ^ 4x6 = X

13,700 x (1 + 0.005) ^ 24 = X

13,700 x 1,005 ^ 24 = X

13,700 x 1.1271 = X

15,442.08 = X

Therefore, the balance after the 6 years of investment will be $ 15,442.08.