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3 years ago

If x² - y² = 55, and x - y = 11, then y = a. 8 b. 5 c. 3 d. -8 e. -3

1 answer:

7 0

X^2-y^2=55
this means that
(x+y)(x-y)=55
we know that x-y=11 so we can write
(x+y)(11)=55
x+y=55/11 we divide by 11 and we obtain
x+y=5

x-y=11 this means
x=y+11 we replace in the other equation (x+y=5)

y+11+y=5
2y=5-11
2y=-6
y=-3
and you find out that also
x=8

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To solve y and x, I am adding a picture

Viktor [21]

Answer:

$x =\sqrt 5$

$y = \sqrt{5$

Step-by-step explanation:

Given

The attached triangle

Required

Solve for x

Considering angle 45 degrees, we have:

$\cos(45) = \frac{y}{\sqrt{10}}$ --- cosine formula i.e. adj/hyp

Solve for y

$y = \sqrt{10} * \cos(45)$

In radical form, we have:

$y = \sqrt{10} * \frac{1}{\sqrt 2}$

$y = \sqrt{10/2}$

$y = \sqrt{5$

To solve for x, we make use of Pythagoras theorem

$x^2 + y^2 = (\sqrt{10})^2$

$x^2 + y^2 =10$

Substitute for y

$x^2 + (\sqrt 5)^2 =10$

$x^2 + 5 =10$

Collect like terms

$x^2 =10-5$

$x^2= 5$

Solve for x

$x =\sqrt 5$

4 0

3 years ago

Find the length of B to the nearest tenth using the Pythagorean theorem.

bekas [8.4K]

Step-by-step explanation:

Here

BC=P=10

AC=B=b

AB=H=15

then using fourmula

h^2= p^2+ b^2

b^2= 15×15 - 10× 10

b^2= 125

b=11.2

4 0

3 years ago

Find an antiderivative F(x) with F′(x) = f(x) = 6 + 24x^3 + 18x^5 and F(1)=0.

7nadin3 [17]

Answer:

The antiderivative is $F(X) = 6x + 6x^4 + 3x^6 - 15$ .

Step-by-step explanation:

Antiderivative F(x)

This is the integral of $F^{\prime}(x)$

F′(x) = f(x) = 6 + 24x^3 + 18x^5

Then:

$F(x) = \int (6 + 24x^3 + 18x^5) dx$

$F(x) = 6x + \frac{24x^4}{4} + \frac{18x^6}{6} + K$

$F(x) = 6x + 6x^4 + 3x^6 + K$

F(1)=0

$F(X) = 0$ when $x = 1$ . We use this to find K.

$F(x) = 6x + 6x^4 + 3x^6 + K$

$0 = 6 + 6 + 3 + K$

$K = -15$

Thus

The antiderivative is $F(X) = 6x + 6x^4 + 3x^6 - 15$ .

7 0

3 years ago

37.1 pt= how Many gallons? Type a whole number or decimal. Round to the appropriate number of significant digits.

anzhelika [568]

Answer:

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Step-by-step explanwenfcbuwerhiducnuiadfvbhnwerbvijrifvuwefnovjndfihvnihmseubvniakjwrsdxuvgybqnaisefhcbatio347569874360532856923485723849527305873485693475gvtghb4rhnbthwesu8fhnviuryedbngjskuryufvsirhlbgfoiarlshfbvlkzrjnfer g bgergsjkrfvksnzekjvnzdijdfvn nzudflvhgiaejhgvaijrsnvipafrngfxpiuvjnzdfkv;lj zshdlvouhsrilgvjsrfnvfkjvbnfvkkjxfbnjxfbkjfxvbjlbfxkhjfbvhhxkjbcvkjnxfckvbjnzxfbvzhjkvcb ;xfhcjnvbjhkxfnv zxfjvhbdukjchvbfhdsbarbf vbousdjbgukyfbher,iyfhbvierygfhdyriudrkjdfijkcvx ncvxiu dbfedfiukjjakleriufhoriuthpiurhfbioerufuirtirhr8gujesriughirueghoisdrghiurjgoierdjgsoidrgj;sidfigjsdfiogjisdufgjidsfgjodfuhgjidfkgkohdflijvksdfbujlksdfjgndghiujnneuifjgknserujghdsfikugheridfjgnsiudfjgkdhrfgusfiusejrdfgiesrgjrshdfiughjdrhfogusdrghsdfjgfjgjseruhguaerkjsgesj.rhdfgiesbtldfhl.w,hetks;ifgkbjvidorstuljkfvnhse7izdyfhuxgcjudiflxhgnzdhoufhgfghskdhfgjkdsrfghjkfgsdjfghsjdfghsdfjghsdjghfjghfdjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjn:

3 0

2 years ago

Wendy wants to put a wallpaper border around her bedroom. The room has two walls that each measure 10 feet 5

cestrela7 [59]

Answer:

11 yards

Step-by-step explanation:

The room has two sides both measuring 10 feet 5 inches. This gives a total of 20 feet 10 inches. It also has the other two sides both measuring 6 feet 1 inch and that too gives a total of 12 feet 2 inches. Adding them all together results in 32 feet 12 inches. Better still, the perimeter of the room is derived as;

Perimeter = 2 (L + W)

Perimeter = 2 (10'5" + 6'1")

Perimeter = 2(16'6")

Perimeter = 32'12"

Having in mind our conversion rate of 12 inches equals 1 foot, the results can be properly expressed as 32 feet plus 1 foot which gives us 33 feet.

If the perimeter of Wendy's room is now given as 33 feet, the conversion rate between feet and yards can now be applied. Having been given that

3 feet = 1 yard

Then 1 yard = 3 feet/3, that is

y = 3/3

Hence,

y = 33/3

y = 11

The results show that Wendy would needs to buy a total of 11 yards of wallpaper border.

3 0

3 years ago