What is the largest y-value that satisfies this system?
1/2(x-3)(x-2)=y
2(x-1/2)=y

According to the Pythagoras theorem, the value of the other leg is, 15.7 cm

Pythagoras theorem:

Pythagoras theorem defines that  the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Given,

One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm.

Here we need to find the measure of the other leg and round off it to nearest tenth.

Though the given question, we know that the value of

Hypotenuse = 16 cm

one leg = 3cm,

Then let us consider the length of the other leg as x.

So, according to the Pythagoras theorem,

It can be calculated as,

=> hypotenuse² = one leg² + other leg²

=> 16² = 3² + x²

=> 256 = 9 + x²

Here we need the value of x, so it can be rewritten as,

=> 247 = x²

=> x = √247

When we take square root for 247, then we get the value of x as,

=> x = 15.716

When we round off it to the nearest tenth then we get the value of another leg as 15.7 cm.

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Answer:

-1.49530965

Step-by-step explanation:

Answer: tyhe image / screenshot

Step-by-step explanation:

Answer:

The number is 27.

Step-by-step explanation:

Since the units digit has to be 5 more than the tens digit, there are only four possible two-digit numbers which satisfy this condition. They are 16, 27, 38, and 49.

Next, the digits can be added and multiplied by three to check that the answer is the same two-digit number.

3 (1 + 6) = 21 does not work because 16 isn't the same as 21.

3 (2 + 7) = 27 does work because 3 * 9 is 27.

3 (3 + 8) = 33

3 (4 + 9) = 39

If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°  then the height of the flagpole will be 24.8 m .

In the question ,

it is given that ,

the length of the shadow of the flag pole = 18m

the angle of "elevation" of the sun = 54°

let the height of the flagpole be = "x" ,

The flagpole and the shadow form a right triangle ,

So , tan(54°) = (height of flag pole)/(shadow of flagpole)

Substituting the values from above ,

we get ,

tan(54°) = x/18

on cross multiplication ,

x = 18 × tan(54°)

x = 18 × 1.3763

x = 24.7734

x ≈ 24.8

Therefore , If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°  then the height of the flagpole will be 24.8 m .

The given question is incomplete , the complete question is

A flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°. What is the height of the flagpole ?

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The radius of the circle to the nearest 10th is 2.0537.

Given:
In a circle, an angle measuring 9.3 radians intercepts an arc of length 19.1.

we know that,

radians = arc / radius

radius = arc/radians

= 19.1/9.3

= 191/10/93/10

= 191/93

≈ 2.0537

Therefore the radius of the circle to the nearest 10th is 2.0537.

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Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

here m = [tex]\frac{8}{9}[/tex] and c = - 4 , then

f(x) = [tex]\frac{8}{9}[/tex] x - 4 ← equation of line

Answer:

$11.89 is the answer

Step-by-step explanation:

because $3.25 + $8.64 is $11.89

Hope this helps

The population for 2015 is 1,640,000 ,so option A is correct.

Given:

The projected population in thousands for a city over the next several years can be estimated by the function P(x)=x³ + 2x² - 8x + 520.

where x is the number of years since 2005.

x = 2015 - 2005

x = 10

P(x) = x³ + 2x² - 8x + 520.

= [tex]10^{3} +2(10^{2} )-8*10+520[/tex]

= 1000 + 2*100 - 80 + 520

= 1520 + 200 - 80

= 1720 - 80

= 1640.

Given the projected population in thousands so = 1640 * 1000

= 1640000.

Therefore The population for 2015 is 1,640,000 ,so option A is correct.

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Answer:

The radius (in centimeters) is 18.9999, or roughly 19 centimeters.

Step-by-step explanation:

If you need a step-by-step explanation, please let me know and I will help you. Thanks!

Answer: [tex]-4(3-1)+2=-4(2)+2=-8+2=-6[/tex]

Answer:

This system has infinitely many solutions.

Step-by-step explanation:

The graphic in both functions is the same line, which means the system has many solutions

If you work $19.50 per hour and you work 40 hours a week, you need to multiply 19.50 by 40 to get your answer

19.50 x 40 = $ 780 a week.

I hope this helps!

Answer:

Step-by-step explanation:

so basically 2+2=3

The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%.

Compound interest is applicable when there will be a change in the principle amount after the given time period.

For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.

As per the given,

Principle amount P = $2800

Rate of interest = 6% = 0.06

Compound quarterly n = 4

Time period T = 5 yeras

a)

Total amount = P(1 + R/n)^(nT)

Total amount = 2800(1 + 0.06/4)^(4 x 5)

Total amount = 2800(1.015)^20

Total amount = $3771.19

b)

Let's say the equivalent annual interest rate is r.

n = 1

3771.19 = 2800(1 + r/1)^(1 x 5)

3771.19 = 2800(1 + r)^5

1.061 = 1 + r

r = 0.06136 = 6.136%

Hence"The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%".

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Answer:

14+(x*y)

Step-by-step explanation:

The best point estimate of the mean is 29 pounds.

Sample size n =65; sample means (X) =29; population std (s) =4.3

Since the sample size is more than 30 we can use the central limit theorem. Hence population means estimate is equal to the sample mean which is 29.

At 90% confidence z value = 1.645

Lower limit = X -z * s/[tex]n^{0.5}[/tex]= 29 -1.645 * 4.3/[tex]65^{0.5}[/tex] = 28.1

Upper limit = X -z * s/[tex]n^{0.5}[/tex] = 29 +1.645 * 4.3/[tex]65^{0.5}[/tex] = 29.9

At 95% confidence z = 1.96

Lower limit = X -z * s/[tex]n^{0.5}[/tex] = 29 -1.96 * 4.3/[tex]65^{0.5}[/tex] = 27.9

Upper limit = X -z * s/[tex]n^{0.5}[/tex] = 29 +1.96 * 4.3/[tex]65^{0.5}[/tex]= 30.1

95% confidence interval is larger. It has a wider range of values than 90% confidence. This is because we are covering more area on a normal curve with a higher confidence interval. So mean value is more likely to fall in the 95% range than the 90% range.

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The person that has a better performance is Puja Limbu.

From the information, Puja Limbu did 8 out of 10 math problem. This can be converted to percentage as:

= 8/10 × 100

= 80%

Raju Lama did 11 out of 15 similar math problem. This will be:

= 11/15 × 100

= 73%

Therefore, Puja has a better performance.

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Step-by-step explanation:

you have to transform the equations, so that in the end you have only x on one side, and everything else on the other.

and that is the solution.

remember, when doing such transformations, we have to do every change to both sides at the same time.

a)

x/5 = 3 | multiply both sides by 5

x = 3×5 = 15

b)

x/2 = 8.5 | multiply both sides by 2

x = 8.5×2 = 17

Answer:

a=15 b=17

Step-by-step explanation:

since we know x divided by something is 3 we do the inverse method so it's going to b 15. The same thing happened with b.

I hope this helps!!

Answer:

2m/4m = 9m/xm

2m(xm) = 4m(9m)

2xm = 36m

Answer:

[tex]-1\frac{5}{8}[/tex]

Step-by-step explanation:

-1 1/8 - 1/2 =- 1 1/8 -4/8

                 =  -9/8-4/8

                  =-13/8

                   =-1 5/8

Hopes this helps please mark brainliest

Answer:

Circle B and 3.14 cm

Step-by-step explanation:

Not 100% sure but good luck :)

The length 1 cm wider was the pair of compasses when Alex drew circle A than when he drew circle B.

A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.

Given:

Alex has drawn two circles, A and B.

Circle A has a diameter of 18 cm.

So, the radius is 18/2 = 9 cm.

And circle B has a diameter of 16 cm.

So, the radius is 16/2 = 8 cm.

To find how much wider was the pair of compasses when Alex drew circle A than when he drew circle B:

The difference in the radius,

= 9-8

= 1 cm

Therefore, when Alex drew circle A than when he drew circle B, the compass was wider 1 cm.

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There are 73 females currently involved in the competition.

The four basic arithmetic operations in Maths, for all real numbers, are: Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×') Division (Finding the quotient; '÷')

Given that, there is a table of male and female involved and not involved in a competition,

Female column total = 103

103-57 = 46

Female row total = 119

119-46 = 73

Hence, There are 73 females currently involved in the competition.

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(1 + 1/3)^2 - 2/9

= (3/3 + 1/3)^2 - 2/9

= (4/3)^2 - 2/9

= 16/9 - 2/9

= 14/9

Answer:

Your answer is correct.

Step-by-step explanation:

Answer:

p

Step-by-step explanation:

when p changes, it causes the equation to change

Answer:

not sure what the question is but if you look for the equation

it's
1/4 * x + 1
or in decimal
0.25x + 1

Answer:

1. 2 inches per hr

2. 24 hrs

Step-by-step explanation:

30/15=2/1

4ft=48in

48/2=24

hope it helps

Answer:

Step-by-step explanation:

ok  

The speed at which conical tank water will rise is 9/8[tex]\pi[/tex] m/min.

What is cone?

A cone could be a three-dimensional geometric type with a flat base and a sleek tapering apex or vertex.

Main body:

The quick way of solving this is simply to consider the horizontal cross sectional area of the tank at the 2m water depth. This is  2/3  of the way up a tank having radius increasing linearly with depth, and so the radius is  2/3  of the 2m at the top, i.e:  4/3  m. So the area is:

πr²=π(4/3)2=16/9π

Now water having this cross section filling at 2 m³  per minute would fill a cylinder having this volume and cross section each minute. A cylinder has volume equal to cross section times length, so the cylinder would have a height of:

2/(16/9π)=9/8π metres

Therefore the water at this depth is rising at a rate of  9/8π  meters per minute.

The longer way around is to calculate the water volume for a given depth and differentiate. We know that the volume of a cone is a third that of a cylinder with the same dimensions, ie:  1/3πr²h . So if our tank has radius R and height H, then the radius of the surface of the water at depth h is  (R/H)h , and so the water volume having this depth is:

v=1/3π(R/H)h)²h=[tex]\frac{\pi r^{2} }{3H^3} h^2[/tex]

We’re interested in rate of change with respect to time, so let’s try differentiating this formula with respect to time, remembering that  h  is changing with time and so we need to use the chain rule:

[tex]\frac{dv}{dt}[/tex]=[tex]\frac{\pi r^{2} }{3H^2} 3h^2[/tex][tex]\frac{dh}{dt}[/tex]=[tex]\frac{\pi r^{2} }{H^2} h^2[/tex][tex]\frac{dh}{dt}[/tex]

Notice that we can solve this for [tex]\frac{dh}{dt}[/tex] , which is the rate of water height change, i.e: the value that we want:

[tex]\frac{dh}{dt}[/tex]= [tex]\frac{H^2 }{\pi r^{2}} h^2[/tex][tex]\frac{dh}{dt}[/tex]

The rate of change of water volume  dv/dt  is just the rate that water flows in, so now all we need to do is slot the given numbers into the equation:

dh/dt=2(3²/π2²2²)=9/8π meters per minute

Hence the answer is 9/8[tex]\pi[/tex] m/min.

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