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2 years ago

What is the value of x in the equation 3/4(14x+8)-(1/2x+2)=3/8(4-x)-1/4

Mathematics

1 answer:

Sedaia [141]2 years ago

4 0

Answer:

-37/68

Step-by-step explanation:

3/4(14x+8)-(1/2x+2)=3/8(4-x)-1/4

(21/2x+6)-(1/2+2)=(3/2x-3/8)-1/4

(21/2x-1/2x)+(6-2)=3/2x-3/8-1/4

10x+4=3/2x-5/8

37/8=-17/2x

37/8 (2)=-17/2x(2)

37/4=-17x

37/68=-x

-37/68=x

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Passing through (-2,1 ) and perpendicular to 4x + 7y + 3 = 0.

Lunna [17]

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

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

Let

$k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2$

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

We have the equation of a line in a general form (Ax + By + C = 0)

Convert it to the slope-intercept form:

$4x+7y+3=0$ subtract 7y from both sides

$4x+3=-7y$ divide both sides by (-7)

$-\dfrac{4}{7}x-\dfrac{3}{7}=y\to m_1=-\dfrac{4}{7}$

Therefore

$m_2=-\dfrac{1}{-\frac{4}{7}}=\dfrac{7}{4}$

We have the equation:

$y=\dfrac{7}{4}x+b$

Put the coordinates of the point (-2, 1) to the equation, and solve for b :

$1=\dfrac{7}{4}(-2)+b$

$1=-\dfrac{7}{2}+b$ multiply both sides by 2

$2=-7+2b$ add 7 to both sides

$9=2b$ divide both sides by 2

[te]x\dfrac{9}{2}=b\to b=\dfrac{9}{2}[/tex]

Finally:

$y=\dfrac{7}{4}x+\dfrac{9}{2}$ - slope-intercept form

Convert to the general form:

$y=\dfrac{7}{4}x+\dfrac{9}{2}$ multiply both sides by 4

$4y=7x+18$ subtract 4y from both sides

$0=7x-4y+18$

6 0

2 years ago

Joe ate twice as many pieces of Halloween candy as Ed. Together they ate 48 pieces. How many pieces of candy did ed eat ?

Lemur [1.5K]

48 in total theirs two people so that’s 12 each but joe had 2 twice as many as Ed. Which Ed ate 6

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2 years ago

What is the inverse function of f(x) = 19/x^3

erica [24]

Answer:

Step-by-step explanation:

1) Replace f(x) with y: y = 19/x^3

2) Interchange x and y: x = 19/y^3

3) Solve this result for y: xy^3 = 19, or y^3 = 19/x, or

y = ∛[19/x]

-1

4. Replace this y with the label f (x) = ∛[19/x]

8 0

3 years ago

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zheka24 [161]

Answer:

Step-by-step explanation:

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2 years ago

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A farm increases in value from $800,000 to $1,100,000 over a period of 6 years. Use the formula r=(F/P)^1/n−1 to find the annual

enot [183]

Answer:

Step-by-step explanation:

The formula representing the the annual inflation rate r is expressed as

r = (F/P)1/n−1

Where

n represents the the number of years during which the value increases from P to F

A farm increases in value from $800,000 to $1,100,000 over a period of 6 years. This means that

P = $800,000

F = $1,100,000

n = 6

Therefore,

r = (1100000/800000)1/6−1

r = 1.375/5 = 0.275

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2 years ago