MATHEMATICS MIDDLE SCHOOL

Enter values for a and b, so that the system of equation shown has one solution y=3x+4 and y=ax+b a=? b=?

Answers

Answer 1

Answer:

Answer:

a = 3 and b = 4

Step-by-step explanation:

Independent Equations

Lines intersect

One solution

In this case the two equations describe lines that intersect at one particular point. Clearly this point is on both lines, and therefore its coordinates (x, y) will satisfy the equation of either line. Thus the pair (x, y) is the one and only solution to the system of equations. One solution is called "consistent". This shows two distinct non-parallel lines that cross at exactly one point. This is called an "independent" system of equations, and the solution is always some x, y-point.

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A 30-30-120 isosceles triangle has two legs of length 4 units. If it is rotated around an axis that contains one leg, what is the volume of the solid of revolution?

Answers

Volume of the solid of revolution is 127.47 cubic units

What is Isosceles triangle?

An isosceles triangle is a triangle that has two sides of equal length.

What is Volume?

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

What is Solid of revolution?

A solid of revolution is a solid figure obtained by rotating a plane curve around some straight line that lies on the same plane

Angles of the given isosceles triangle = 30-30-120 triangle

Length of the leg = 4 units

Length of the Third side c = $\sqrt{a^(2)+b^(2)-2ab cos C }$

Where a and b are the length of the leg and C is the vertex angle

Then,

Length of the third side c= $\sqrt{4^(2)+4^(2)-2(4)(4)cos120 } =4√(3)$

It is rotated around an axis that contains one leg

Draw the figure,

From the figure we can say that we have to subtract the volume of the big cone from the volume of the small cone to find the required volume of the cone

Volume of big cone = $(1)/(3)\pi r^(2)\sqrt{l^(2).r^(2) }$

where, r is the radius and l is the slant length

r = $(4√(3) )/(2)=2√(3)$ unit

l= $4√(3)$ unit

Volume of the big cone = $(1)/(3)\pi (2√(3))^(2)\sqrt{(4√(3))^(2). (2√(3))^(2) }$ =301.59 cubic unit

Volume of small cone = $(1)/(3)\pi r^(2)\sqrt{l^(2).r^(2) }$

r = $(4√(3) )/(2)=2√(3)$ unit

l= 4 unit

Volume of the small cone = $(1)/(3)\pi (2√(3))^(2)\sqrt{(4^(2) . (2√(3))^(2) }$ =174.12 cubic unit

Volume of required region = Volume of big cone - Volume of small cone

=301.59 - 174.12

=127.47 cubic unit

Hence, volume of the solid of revolution is 127.47 cubic unit

Learn more about Isosceles triangle, Volume and Solid of revolution here

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i think i know how to solve it but i would take a couple of minutes

Is 7/8 or 11/10 closer to 1? How did you decide anybody help please?

Answers

Let

A-----> $(7)/(8)$

B-----> $(11)/(10)$

C-----> $1$

we know that

Point A-------> Multiply numerator and denominator by $10$

$(7*10)/(8*10) =(70)/(80)$

Point B-------> Multiply numerator and denominator by $8$

$(11*8)/(10*8) =(88)/(80)$

Point C-------> Multiply numerator and denominator by $80$

$(1*80)/(1*80) =(80)/(80)$

Find the distance Point A to Point C

$(80)/(80) -(70)/(80) =(10)/(80)$

Find the distance Point B to Point C

$(88)/(80) -(80)/(80) =(8)/(80)$

therefore

$(8)/(80) < (10)/(80)$

Point B is closer to Point C

$(11)/(10)$ is closer to $1$

the answer is

$(11)/(10)$ is closer to $1$

You can also figure it out by knowing that 7/8 is 1/8 away from 1 and 11/10 is 1/10 away from 1. since 1/10 is smaller than 1/8, you know that 11/10 is closer to 1 than 7/8.

Gavin's anemometer measures the wind speed at 44.14 kilometers per hour. 4 times faster than the wind speed 5 hours ago. What was the wind speed 5 hours ago?

Answers

The answer is 176.56! BTW how is that in the elementary category?

I think it is 55.175 but not quite sure

Glenn swam 2 laps every morning for 7 day. in addition to the laps he swam each morning, he swam 3 laps with his friends on Tuesday and Thursday. write the expression that show the number of laps he swam during the week. evaluate the expression to find the total number of laps he swam that week.

Answers

Answer:

Expression = 2 × 7 + 3 + 3

Evaluation of the expression = 20

Step-by-step explanation:

Number of laps Glenn swam every morning = 2

Number of days for which he swam these laps = 7 days

⇒ Number of laps swam in a week = 2 × 7

Number of laps swam with his friend on Tuesday = 3

Number of laps swam with his friend on Thursday = 3

So, Expression that show the number of laps he swam during the week = 2 × 7 + 3 + 3

By evaluating the above expression, the total number of laps he swam that week = 14 + 3 + 3 = 20 laps

The answer is 15 because its evaluates

heather allen works for the public works department as an electrical inspector. she earns $17.60 per hour for a 36 hour week. Her overtime rate is 1.5 times her regular hourly rate. this week she worked her regular 36 hours plus 8 hours of overtime. what is her total pay?

Answers

First, not accounting for overtime, Heather gets $17.60 * 36, or $633.6 dollars. Now, for overtime, her hourly rate is $17,60 * 1.5, or $26.4/hour, during overtime. Thus, adding the $26.40 * 8 (hours of additional overtime), gives $633.60 + $211.2 dollars, or $844.80 total dollars.

Her regular pay for a 36 hour week is $633.60. Her overtime rate is $26.40 per hour. If she worked 8 hours overtime, then you would multiply $26.40 by 8 and get $211.20. Add $633.60 and $211.20 to get her total pay, which is $844.80

a bag containes 8 white marbels and 48 green marbles. If a representative sample contains 2 white marblesthen how many green marbles would you expect it to contain?

Answers

Answer:

Step-by-step explanation:

8 white marbles and 48 marbles

each sample contains 2 white

so first

8 divide 2 = 4

then second

48 divide 4= 12

hope this helps

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