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3 years ago

What is one of the solutions to the following system of equations?

Mathematics

1 answer:

Inessa [10]3 years ago

6 0

Answer:

x = 2 and y = 7

Step-by-step explanation:

The given equations are :

$y^2+x^2=53\ ....(1)\\\\y-x=5\ ...(2)$

Squaring both sides of equation (2)

$(y-x)^2=5^2\\\\y^2+x^2-2xy=25\\\\53-2xy=25\ \text{from equation (1)}\\\\2xy=53-25\\\\2xy=28\\\\xy=14\ ...(3)$

Put the value of y from equation (2)

$x(5+x)=14\\\\5x+x^2-14=0\\\\x=2$

Put the value of x in equation (2)

y-x = 5

y = 5+x

= 5+2

= 7

Hence, the solution of the given equations are (2,7).

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How would I solve this

vova2212 [387]

$A=\frac{1}{2}\ln17 = 1.417$

Step-by-step explanation:

The area <em>A</em> under the curve can be written as

$\displaystyle A = \int_0^2\!\dfrac{4x\:dx}{1+4x^2}$

To evaluate the integral, let

$u = 1+4x^2 \Rightarrow du = 8xdx\:\text{or}\:\frac{1}{2}du = 4xdx$

so the integral becomes

$\displaystyle \int\!\dfrac{4x\:dx}{1+4x^2} = \dfrac{1}{2}\int\!\dfrac{du}{u} = \dfrac{1}{2}\ln |u|$

$\displaystyle \int\!\dfrac{4x\:dx}{1+4x^2} = \dfrac{1}{2}\ln |1+4x^2|$

Putting in the limits of integration, our area becomes

$\displaystyle A = \int_0^2\!\dfrac{4x\:dx}{1+4x^2} = \dfrac{1}{2}\left.\ln |1+4x^2|\right|_0^2$

$\;\;\;\;= \frac{1}{2}[\ln (1+16) - \ln (1)]$

$\;\;\;\;=\frac{1}{2}\ln17$

Note: $\ln 1 = 0$

3 0

3 years ago

Find UV (Pic Stated Below)

natta225 [31]

Answer:

UV=29

Step-by-step explanation:

In right triangles AQB and AVB,

∠AQB = ∠AVB ...(i) {Right angles}

∠QBA = ∠VBA ...(ii) {Given that they are equal}

We know that sum of all three angles in a triangle is equal to 180 degree. So wee can write sum equation for each triangle

∠AQB+∠QBA+∠BAQ=180 ...(iii)

∠AVB+∠VBA+∠BAV=180 ...(iv)

using (iii) and (iv)

∠AQB+∠QBA+∠BAQ=∠AVB+∠VBA+∠BAV

∠AVB+∠VBA+∠BAQ=∠AVB+∠VBA+∠BAV (using (i) and (ii))

∠BAQ=∠BAV...(v)

Now consider triangles AQB and AVB;

∠BAQ=∠BAV {from (v)}

∠QBA = ∠VBA {from (ii)}

AB=AB {common side}

So using ASA, triangles AQB and AVB are congruent.

We know that corresponding sides of congruent triangles are equal.

Hence

AQ=AV

5x+9=7x+1

9-1=7x-5x

8=2x

divide both sides by 2

4=x

Now plug value of x=4 into UV=7x+1

UV=7*4+1=28+1=29

<u>Hence UV=29 is final answer.</u>

7 0

3 years ago

What is 10 3/8 + 8 1/2.

motikmotik

Answer:

Step-by-step explanation:

8 0

3 years ago

Mariabella was 1/4 of the way through her book. Twenty pages later she was 1/3 of the way through her book. When she is 3/4 of t

Alex777 [14]

Answer: 60 pages left.

Step-by-step explanation:

Let the number of pages in the book be x.

As per given, we have

$\dfrac14x+20=\dfrac13x\\\\\Rightarrow\ \dfrac{1}{3}x-\dfrac14 x=20\\\\\Rightarrow\ \dfrac{4-3}{12}x=20\\\\\Rightarrow\ \dfrac1{12}x=20\\\\\Rightarrow x=20\times12\\\\\Rightarrow x=240$

$\dfrac34$ of total book = $\dfrac34\times 240=180$

Pages left = 240-180

= 60

Hence, 60 pages left.

3 0

3 years ago

A librarian arranged some books on the shelf using the Dewey decimal system. Choose the group of book numbers that

vovangra [49]

Answer:

The answer is C), 834, 834.19, 834.2, 834.29

Step-by-step explanation:

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3 years ago