x^2 - y^2 = 100
x + y = 5
The solution to the given system of equations is
(x, y). What is the value of x - y?

Answer:

A

Step-by-step explanation:

3x and x + 30 are vertically opposite angles and are congruent , then

3x = x + 30 ( subtract x from both sides )

2x = 30 ( divide both sides by 2 )

x = 15

Then

∠ A = 3x = 3(15) = 45°

See <A and x+30 are opposite angles .

We know that opposite angles are equal

so

Now

Option A is correct

Answer:

229 is the remainder.

Explanation:

In order to find the remainder, insert the value of x in the equation.

Given equation:

Given x value:

Find remainder:

[tex]\sf p(4) = 4^4 - 27[/tex]

[tex]\sf p(4) = 256 - 27[/tex]

[tex]\sf p(4) = 229[/tex]

Answer:

229

Step-by-step explanation:

Here we are given a polynomial p(x) and we need to find the remainder when it is divided by (x-4) . As we know that if a polynomial, say [tex]g(x)[/tex] is divided by [tex]x-a[/tex] then the remainder is [tex]g(a)[/tex] .

Firstly equate [tex] x -4[/tex] with 0 , we have;

[tex]\longrightarrow x -4=0\\[/tex]

[tex]\longrightarrow x =0+4\\ [/tex]

[tex]\longrightarrow x = 4 [/tex]

Now substitute [tex] x =4[/tex] in [tex]p(x)[/tex] ,

[tex]\longrightarrow p(x)= x^4-27\\[/tex]

[tex]\longrightarrow p(4)= (4)^4-27\\[/tex]

[tex]\longrightarrow p(4) = 256 - 27 \\[/tex]

[tex]\longrightarrow \underline{\underline{\boldsymbol{ p(4) = 229}}}[/tex]

Hence the remainder is 229 .

Answer:

y-2/3x-4

the answer is (0,3)

3x+4y-12

the answer is (0,3)

Answer:

8

I really hope this helped! :D

Step-by-step explanation:

X squared is equal to 64.

That also means X is the square root of 64.

8*8=64

8 Is the square root of 64, meaning it's also X.

Remember, when you square a number, you multiply it to itself.

8^2= 8*8

4^2=4*4

2^2= 2*2

So on, so forth.

Answer:

[tex] - 3 \times 5 \times - 9 \times - 2 \\ - 15 \times + 18 = 3[/tex]

Answer:

10

Step-by-step explanation:

(5+x=15)☞︎︎︎(Equation)

5-5+x=15-5

X=10

Problem 2

Why not? Well it's because the angles do not match up perfectly.

The triangle on the left is a 30-60-90 triangle; while the triangle on the right is a 40-50-90 triangle. The numbers mentioned are the angle values.

Only the "90"s match up, but everything else does not. We need to have three pairs of congruent angles to be able to use the angle angle (AA) similarity theorem.

Answer:

above is the solution to the question

Answer:

She sold $1800 worth.

Step-by-step explanation:

290-200=90

90 x 20 because 100÷5=20

90 x 20 = 1800

$1800

Answer:

55

Step-by-step explanation:

55+15=70 and u could also say 15 from 70 =55

Answer:

x = - 16

Step-by-step explanation:

Value of RHS is not given. If it's 0, then,

x + 4² = 0

x = 0 - 4²

x = 0 - 16

x = - 16

_______

Hope it helps ⚜

Answer:

x = -16

Step-by-step explanation:

=> x = ?

=> x + 4² = ?

=> x + 16 = ?

=> x = -16

Answer:

y=x+1.75

4x-2y = 4

The answer is (3. 75, 5.5)

Step-by-step explanation:

If you plot the two equations on Desmos' Graphing Calculator, you will see that the solution is intersected at (3.75, 5.5).

Explanation:

We can make use of the symmetry of the problem and properties of similar triangles.

Here's a "paragraph proof."

Draw line OP perpendicular to chord MN, such that P lies on line MB. Let the point of intersection of OP with chord MN be designated point Q. Line OP bisects angle MON, so has measure y/2.

Triangles OPM and MPQ are similar (by AA similarity; both right triangles contain angle OPM), so angle QMP ≅ angle MOP. As we observed above, angle MOP has measure y/2, so angle QMP has measure y/2.

Angle BMN is another name for angle QMP, so it has measure y/2.

__

Additional comments

By the HL congruence postulate, the perpendicular bisector of chord MN divides triangle MON into two congruent right triangles. (OM≅ON, MQ≅NQ). That means ∠MOQ≅∠NOQ, so OQ bisects angle MON, as we say above.

__

Another way to come to the desired conclusion is to recognize that for any point X on long arc MN, angle MXN will have measure y/2. (inscribed angle theorem) This remains true in the limit as X approaches M. As X approaches M, secant XM approaches tangent line MB. So, in the limit, angle BMN is y/2.

Answer:

I'd say On average, about 50% of students prefer elther extra cheese or pepperoni and On average, 1/4 of students prefer pineapple.

Also i tried my hardest to read the picture you took, so im assuming that the pineapple statement is 1/4 correct me if i'm wrong

Answer:4323.78cm^3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

when you look at it go to where x is -2 then go down to where the blue line goes on the point

Answer:

$820.00

Step-by-step explanation:

x = price yesterday (initital price)

If it is 67% off, then the price is 33% of the initial.

x(.33) = 270.60

divide .37 on both sides

x = 820.00

The price of the suit yesterday is $820.00.

Answer:

B

Step-by-step explanation:

3x + 7y = - 49 → (1)

10x - 7y = - 42 → (2)

adding (1) and (2) term by term will eliminate y

13x + 0 = - 91

13x = - 91 ( divide both sides by 13 )

x = - 7

substitute x = - 7 into either of the 2 equations and solve for y

substituting into (1)

3(- 7) + 7y = - 49

- 21 + 7y = - 49 ( add 21 to both sides )

7y = - 28 ( divide both sides by 7 )

y = - 4

solution is (- 7, - 4 ) → B

=[tex]9\sqrt{2}[/tex]

answer is tan 7 a 4 a tan4a

Answer:

subtract 9 from both sides

Step-by-step explanation:

m + 9 = 45 ( subtract 9 from both sides )

m = 36

Answer:

Subtract

Step-by-step explanation:

You should subtract since the equation says to add.

You basically do the opposite of what it says.

For example, if it was m - 9 = 45 you would add 9 on both sides, but in this case, you would subtract since its m + 9 = 45

m + 9 = 45

subtract nine by 9 and 45:

m = 36

36 + 9 = 45

[tex]\tt \dfrac{3}{8}\times 28.7=10.7625=10.76~kg[/tex]

Answer:

Step-by-step explanation:

As with other forms of direct and inverse variation, the "constant of variation" (k) is the constant multiplier in the equation. "Varies directly" means the independent variable is in the numerator. "Varies inversely" means the independent variable is in the denominator. The variation equation can be solved for missing values of constants or variables.

The equation for "varies directly with v and w, and inversely with z" means the equation is of the form ...

  y = k·v·w/z

Then the values of v or w are ...

  v = y·z/(k·w)

  w = y·z/(k·v)

__

  k = y·z/(v·w) = 5·24/(12·14) = 5/7; the equation is y = 5·v·w/(7·z)

  w = y·z/(k·v) = 18·8/(10·4) = 18/5; the equation is y = 10·v·w/z

  k = 3/2 (read from the equation); y = (3/2)v·w/z = 3·16·24/(2·6) = 96

  k = 8 (read from the equation); v = y·z/(k·w) = 20·2/(8·6) = 5/6

  y = k·v·w/z = 6·12·7/15 = 168/5; the equation is y = 6·v·w/z

Answer: 254.34 yd

Step-by-step explanation:

If the diameter is 18 yd then the radius:

radius = diameter/2

r = 18/2

r = 9 yd

So the area is:

[tex]A = \pi r^2\\= \pi (9)^2\\= (3.14)(81)\\ =254.34 \hspace2yd[/tex]

Therefore, the area of the circle is 254.34 yd

The possible outcomes of the fair coin and the dice is the sample space

The items are given as:

Coin = 1

Dice = 1

The sample space of both items are:

Coin = {H,T}
Dice = {1,2,3,4,5,6}

So, the list of possible outcomes is: {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

From the above list, there is only one outcome that has a head and a 3 out of 12 possible outcomes

So, the probability of getting a head and a 3 is:

p = 1/12

Hence, the probability of getting a head and a 3 is 1/12

Read more about probability at:

https://brainly.com/question/25870256

Answer:

What's the fraction

Step-by-step explanation:

I need to know the fraction in order to solve

Answer:

600

Step-by-step explanation: [tex]100\times2\times\frac{180}{60}[/tex]

Cross out the common factor

[tex]100\times2\times3[/tex]

Calculate the product or quotient

[tex]200\times3[/tex]
[tex]600\ YOUR\ ANSWER\ which\ can\ also\ be\ written\ as\ 6\times{10}^2\[/tex]

I hope this helps you

:)

If the initial population of the bacteria is 100, then the population of the bacteria after 180 hours will be 800.

Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

A colony of 100 bacteria doubles in size every 60 hours.

The exponential relation will be given below.

[tex]\rm P = 100 \times 2^{t/60}[/tex]

Where t is the number of hours

Then the population of the bacteria after 180 hours will be

[tex]\rm P = 100 \times 2^{t/60} \\\\P = 100 \times 2 ^{180/60}\\\\\rm P = 100 \times 2^{3}\\\\\rm P = 100 \times 8\\\\\rm P = 800[/tex]

More about the exponent link is given below.

https://brainly.com/question/5497425

The first step we take is to find the area of the square since the area of the square is equal to the area of the rectangle

       [tex]area-of-rectangle = area- of-square\\area-of-rectangle = 8*8 = 64in^2[/tex]

Another fact we know is that the length of the rectangle is four times the width.

      L = 4W

Now let's put the variables, found above, into the format to find the area of the rectangle

  [tex]area-of-rectangle = L * W, (L = 4W)\\area-of-rectangle = 4W * W\\\\64 = 4W^2\\16 = W^2\\\\W^2 = 16\\\\W = 4[/tex]

Since the Width is 4, L = 4 * W = 4 * 4 = 16 in.

So the length is 16 inches

Hope that helps!