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3 years ago

4x + 5x + 12 = 6(x-2) Math

Mathematics

1 answer:

Rashid [163]3 years ago

4 0

Hi there! :)

$\large\boxed{x = -8}$

4x + 5x + 12 = 6(x - 2)

Combine like terms and distribute the coefficient outside of the parenthesis:

9x + 12 = 6(x) + 6(-2)

9x + 12 = 6x - 12

Subtract 6x from both sides:

9x - 6x + 12 = 6x - 6x - 12

3x + 12 = -12

Subtract 12 from both sides:

3x + 12 - 12 = -12 - 12

3x = -24

Divide both sides by 3:

3x/3 = -24/3

x = -8.

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consider a wire 2 ft long cut into two pieces. one piece forms a circle with radius r and the other forms a square with side len

makkiz [27]

The formula for the radius r in terms of x . and for the maximum areas is x=2/ $\pi$ +4

Given that,

y forms a circle of radius r

y=2 $\pi$ r

r=y/2 $\pi$

(2-y)- forms Square Side x

(2-y) = 4x

x=(2-y)/4

Now Sum of Area's=Area of Square +Area of Circle

Sum = $\pi$ r² + x²

Substitute the r and x values in above equation,

A(y)= y²/4 $\pi$ +(y-2)²/ 16

To maximize Area A(y)

A'(y)= 0

2y/4 $\pi$ + 2(y-2)/16 =0

y/2 $\pi$ + (y-2)/8 =0

y = 2 $\pi$ / $\pi$ +4

Y max will be max, x to be maximum.

for maximum sum of areas,

x=2/ $\pi$ +4

Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/ $\pi$ +4

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4 0

2 years ago

If mRS=x then write an equation that could be used to solve for x and find the value of x

Fed [463]

Answer:

a) x = 30°

b) mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

Question:

The complete question as found on Chegg website:

In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs

intercepted have the following ratio of measurements:

mRS : mST :MTU : mUR=1:4:4:3

(a) If mRS = x, then write an equation that could be used to solve for x

and find the value of x.

(b) State the measure of each of the four arcs.

mRS =

mST =

MTU

MUR =

Step-by-step explanation:

Find attached the diagram related to the question

mRS : mST : mTU : mUR = 1:4:4:3

Since mRS = x

Writing the ratios of the measure of angle in terms of mRS:

mST = 4× mRS = 4×x = 4x

mTU = 4× mRS = 4×x = 4x

mUR= 3× mRS = 3×x = 3x

The sum of measure the 4 measures of arc = 360° (sum of angle in a circle)

mRS + mST + mTU + mUR = 360°

x + 4x + 4x + 3x = 360

12x = 360

x = 360/12

x = 30°

b) The measure of angle

mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

6 0

3 years ago

Which piece of additional information can be used to prove △CEA ~ △CDB?

Slav-nsk [51]

<u>Answer-</u>

<em>The correct answer is</em>

<em>∠BDC and ∠AED are right angles</em>

<u>Solution-</u>

In the ΔCEA and ΔCDB,

$m\angle BCD=m\angle ACE$

As this common to both of the triangle.

If ∠BDC and ∠AED are right angles, then $m\angle E=90=m\angle D$

Now as

∠BCD = ∠ACE and ∠BDC = ∠AED,

∠DBC and ∠EAC will be same. (as sum of 3 angles in a triangle is 180°)

Then, ΔCEA ≈ ΔCDB

Therefore, additional information can be used to prove ΔCEA ≈ ΔCDB is ∠BDC and ∠AED are right angles.

5 0

3 years ago

Read 2 more answers

Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12%

storchak [24]

Jane must therefore deposit her savings in the four rivers bank.

<h3>What is compound interest?</h3>

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the data provided in the question,

Rate, r = 12%

After five years, the total amount, if Jane had saved at Mystic Bank,if Jane had saved at Mystic Bank would be:

$A = P(1+\frac{r}{100} )^n$

For compounded quarterly,

n = 5 × 4

n = 20

A = 40000(1 + 12/(4 × 100))²⁰

A = 72244.44 (i)

If Jane placed her savings with the Four Rivers, then,

A = 40000(1 + 14/(2 × 100))¹⁰

A = 40000 × 1.9671

A = 78686.054 (ii)

Therefore, it is evident that case (ii) is higher than case (i). Jane must therefore deposit her savings in the four rivers bank.

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6 0

1 year ago

Find the values for a and b that would make the equality true.

zepelin [54]

Answer:

a = - 4, b = 5

Step-by-step explanation:

Expand the left side, then compare the coefficients of like terms.

- 3(2x² + ax + b)

= - 6x² - 3ax - 3b, compare to - 6x² + 12x - 15

Compare coefficients of x- terms

- 3a = 12 ( divide both sides by - 3 )

a = - 4

Compare constant terms

- 3b = - 15 ( divide both sides by - 3 )

b = 5

8 0

3 years ago