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3 years ago

Abc is equilateral with AB=3x-2,BC=2x+4, and CA= x+10

1 answer:

7 0

AB = BC, so 3x-2 = 2x+4. Also, BC = CA, so 2x+4=x+10.

Solve this system of linear equations:

3x-2 = 2x+4
2x+4=x+10 => x=6

Check: Does AB=BC? Does AB=BC?

Does 3(6)-2 = 2(6)+4? Does 16=16? YES.
Does BC = CA? Does 2(6)+4 = 6+10? YES

x = 6 (answer)

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If each quadrilateral below is a parallelogram,find the missing measures.

zhenek [66]

Answer:

Part 1) $MN=31\ units$

Part 2) $KN=45\ units$

Part 3) m∠K=61°

Part 4) m∠L=119°

Part 5) m∠M=61°

Step-by-step explanation:

we know that

In a parallelogram opposite angles and opposite sides are congruent and consecutive angles are supplementary

Part 1) Find the side MN

we know that

MN≅KL ----> by opposite sides

we have

$KL=31\ units$

therefore

$MN=31\ units$

Part 2) Find the side KN

we know that

KN≅LM ----> by opposite sides

we have

$LM=45\ units$

therefore

$KN=45\ units$

Part 3) Find the measure of angle K

we know that

m∠K+m∠N=180° ----> by consecutive interior angles

we have

m∠N=119°

substitute

m∠K+119°=180°

m∠K=180°-119°

m∠K=61°

Part 4) Find the measure of angle L

we know that

m∠L≅m∠N ----> by opposite angles

we have

m∠N=119°

therefore

m∠L=119°

Part 5) Find the measure of angle M

we know that

m∠M≅m∠K ----> by opposite angles

we have

m∠K=61°

therefore

m∠M=61°

7 0

3 years ago

find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximu

topjm [15]

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

$\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}$

Now, differentiate P with respect to x, and we get,

$\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}$

Solving the above equation to zero, we get,

$\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}$

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

$\begin{aligned}y&=108-36\\y&=72\end{aligned}$

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

brainly.com/question/1635103

#SPJ4

4 0

1 year ago

Solve 8=3r-1 step by step

tatuchka [14]

1+8=3r
9=3r
Both divided by 3
3=r

7 0

3 years ago

Read 2 more answers

The graphs of three functions are shown.

satela [25.4K]

Answer:

The square root and quadratic function share a y-intercept.
The range of the square root and absolute value function are the same.

Step-by-step explanation:

Y-intercepts are the same when the curves meet the y-axis at the same point. That is true of the root and quadratic functions.

X-intercepts are the same when the curves meet the x-axis at the same point. None of these functions share an x-intercept.

The ranges of the functions are the same when they have the same vertical extent. The range of the quadratic is different from the range of the other two functions.

The absolute value and root functions have the same minimum (lower end of their range). That is the same as the maximum of the quadratic function.

The statements that match the graphs are ...

The square root and quadratic function share a y-intercept.
The range of the square root and absolute value function are the same.

7 0

3 years ago

Read 2 more answers

Plsss guyss help with this

Fofino [41]

Answer:

360 cm^2.

Step-by-step explanation:

Area of the base = 10*10 = 100 cm^2.

We find the slant height of the sides using Pythagoras:

h = sqrt ( 12^2 + 5^2)

h = sqrt 169

h = 13.

Area of the triangular sides = 4 * 1/2 * 10* 13

= 260 cm^2

So the total surface area = 100 + 260

= 360 cm^2.

6 0

3 years ago