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3 years ago

Write an equation of the line parallel to 3x + 5 = 2y that has a y-intercept of -1

Mathematics

1 answer:

denpristay [2]3 years ago

8 0

Answer:

3x - 2 = 2y

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 5 = 2y into this form by dividing all terms by 2

$\frac{3}{2}$ x + $\frac{5}{2}$ = y ← in slope- intercept form

with slope m = $\frac{3}{2}$

Parallel lines have equal slopes and c = - 1, thus

y = $\frac{3}{2}$ x - 1 ← in slope- intercept form

Multiply through by 2

2y = 3x - 2 ← equation of line

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If log(x + y) = log 3 + ½log x + ½log y, prove that x² + y² = 7xy

Free_Kalibri [48]

Answer:

See Explanation

Step-by-step explanation:

$log(x + y) = log3 + \frac{1}{2} logx+ \frac{1}{2} logy \\ \\ log(x + y) = log3 + logx ^{\frac{1}{2}} + logy ^{\frac{1}{2}}\\ \\ log(x + y) = log3 + log(xy) ^{\frac{1}{2}} \\ \\ log(x + y) = log[3(xy) ^{\frac{1}{2}}] \\ \\ x + y = 3(xy) ^{\frac{1}{2}} \\ \\ squaring \: both \: sides \\ {(x + y)}^{2} = \bigg(3(xy) ^{\frac{1}{2}} \bigg)^{2} \\ \\ {x}^{2} + {y}^{2} + 2xy = 9xy \\ \\ {x}^{2} + {y}^{2} = 9xy - 2xy \\ \\ \purple{ \bold{{x}^{2} + {y}^{2} = 7xy}} \\ thus \: proved$

7 0

3 years ago

Read 2 more answers

Manny can assemble a computer by himself in 50 minutes. Lucy does the same job in 45 minutes. How long will it take to assemble

jonny [76]

Manny can assemble a computer in 50 minutes. That means, in a minute Manny does $\frac{1}{50}$ job.

Lucy can assemble a computer in 45 minutes. That means, in a minute Lucy does $\frac{1}{45}$ job.

If they are working together, in a minute they will do:
$\dfrac{1}{50} + \dfrac{1}{45}$
$= \dfrac{9}{450} + \dfrac{10}{450} \text{(equalize the denominator)}$
$=\dfrac{19}{450}$
In a minute they will do $\frac{19}{450}$ job

To finish the job they will do it in $\frac{450}{19}$ minutes or about 24 minutes.

5 0

3 years ago

10.<br> JKLM is a rhombus KLN is a triangle. Find MKN.

rjkz [21]

Answer:

65°

Step-by-step explanation:

JM = JK (all sides of a rhombus are equal)

Angle JKM = 25° (isosceles triangle)

Angle JKL = 50° (consecutive angles of rhombus)

Angle MKL = 25° (angle subtraction)

Angle MLK = 130° (opposite angles of a rhombus)

Angle KLN = 50° (angles on a straight line)

Angle LKN = 40° (angle sum of triangle)

Angle MKN = 65° (angle addition)

7 0

2 years ago

1) There are 80 grams of salt in a 32% solution. Find the weight of the solution

alukav5142 [94]

Answer:

Weight of the solution = 250 grams

Step-by-step explanation:

1) Consider the weight of solution as x grams.

32 % solution = 80 grams salt

32% of x = 80

(32/100)*x = 80

Solving for x:

x = (80*100) / 32

x = 250 grams

7 0

3 years ago

5. One ship sailed from Hawaii on a course represented by the equation 3 215 2 y x . Another ship left Tahiti on a course repres

Alex777 [14]

100000 I really don’t know to be honest

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3 years ago