Find the value of x, y, and z in the figure below:
ہ
2y
IN
2x
90°
t

Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex](x-3)^2[/tex] is [tex]x^2 - 6x + 9[/tex]

Suppose a, b and c are three numbers. Then we have:

[tex]a(b + c) = a\times b + a\times c[/tex]

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

For the given case, the product needed can be calculated as:

[tex](x-3)^2 = (x-3) \times(x-3) = x(x-3) - 3(x-3) = x^2 - 3x - 3x + 9\\\\(x-3)^2 = x^2 - (3+3)x + 9 = x^2 - 6x + 9[/tex]

(coefficients of like terms were added)

Thus, the product result of given expression is

[tex]x^2 - 6x + 9[/tex]

Learn more about product of polynomials here:

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Answer:

x^2 - 6x + 9

Step-by-step explanation:

Hope this helps! :D

a) [tex]x^5-x^3[/tex]

[tex]x^3\left(x^2-1\right)[/tex] ........take out x³

[tex]x^3\left(x+1\right)\left(x-1\right)[/tex] ......separated (x²-1)

b) [tex]3x^2-75[/tex]

[tex]3\left(x^2-25\right)[/tex] ........took out 3.

[tex]3\left(x+5\right)\left(x-5\right)[/tex]  .......separated (x²-25)

c) [tex]3x^5y+4x^4y-5x^2y[/tex]

[tex]x^2y\left(3x^3+4x^2-5\right)[/tex] ............takeout x²y at the front.

d) [tex]81x^3-125[/tex]

[tex]81x^3-125[/tex] ......cannot be factorised much more further.

Solution:

Part - A:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x⁴ (GCF), which can factorize completely. This will subtract 4 from the exponents.

Part - B:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by 3 (GCF), which can factorize completely. This will divide 3 from the terms.

Part - C:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x²y (GCF), which can factorize completely.

Part - D:

Unfortunately, this expression can't factor with rational numbers. The expression results in 81x³ - 125.

Answer:

No, he incorrectly rounded 1.25 to 2

Step-by-step explanation:

hope this helps :)

Answer:

No, he incorrectly rounded 1.25 to 2

Step-by-step explanation:

To find out how many pages Yutto writes in 1 hour we divide

1.25/2=0.625

Now we multiply

0.625×6=3.75

3.75≠6

So now we know that Yutto was incorrect so we can eliminate the last two options. Now how did he get his original estimate? For option A,

1.25 is rounded to 2

2/2=1

1×6=6

So the answer is A

Answer:

24 units

Step-by-step explanation:

create a proportion:

15/20 = 6/XY

cross-multiply:

15·XY = 120

XY = 8

15/25 = 6/YZ

cross-multiply:

15·YZ = 150

YZ = 10

Perimeter:

6 + 8 + 10 = 24

Answer:

6/5

Step-by-step explanation:

rise/run

I hope this is right! :D

Answer:

The slope would be 6/5

Answer:

  12 cm by 14 cm

Step-by-step explanation:

The area is given by ...

  A = LW

The perimeter is given by ...

  P = 2(L +W)

Substituting the given values, we have ...

  168 = LW

  52 = 2(L +W)

The second equation can be used to find an expression for L:

  26 = L +W . . . . . divide by 2

  L = 26 -W . . . . . subtract W

Using this in the first equation, we have ...

  168 = (26 -W)(W)

  W² -26W +168 = 0

Factors of 168 are ...

  168 = (-1)(-168) = (-2)(-84) = (-3)(-56) = (-4)(-42) = (-6)(-28) = (-7)(-24)

     = (-8)(-21) = (-12)(-14)

Only the last factor pair (-12, -14) has a sum of -26, so the equation factors as ...

  (W -12)(W -14) = 0

Solutions are W=12, and W=14. The corresponding values of L are 14 and 12.

The quadrilateral has dimensions of 12 cm and 14 cm.

The word problem that must be solved with division and includes 2/7 as the dividend and 4 as the divisor is that John wants to buy a 4 yards cloth qnd there are pieces of 2/7 yards each. How many pieces will he buy?

In this case, it should be noted that division is used.to separate into different parts.

Therefore, John wants to buy a 4 yards cloth qnd there are pieces of 2/7 yards each.

The pieces to be bought will be:

= 4 ÷ 2/7

= 4 × 7/2

= 14

He'll buy 14 pieces.

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Answer:

84 cm

Step-by-step explanation:

the area of a parallelogram is the how tall is it times it by the how long the base

(H x B)

the answer is 84 cm

Answer:

(4, -3)

Step-by-step explanation:

Rewrite equations:

x−2y=10;6x+3y=15

Step: Solvex−2y=10for x:

x−2y=10

x−2y+2y=10+2y(Add 2y to both sides)

x=2y+10

Step: Substitute2y+10forxin6x+3y=15:

6x+3y=15

6(2y+10)+3y=15

15y+60=15(Simplify both sides of the equation)

15y+60+−60=15+−60(Add -60 to both sides)

15y=−45

15y

15

=

−45

15

(Divide both sides by 15)

y=−3

Step: Substitute−3foryinx=2y+10:

x=2y+10

x=(2)(−3)+10

x=4(Simplify both sides of the equation)

Therefore answer: is

x=4 and y=−3

Hope it helps!

Step-by-step explanation:

Use the Distributive Property:

[tex]-10(-7x^{2} +5x)[/tex]

[tex]70x^{2}-50x[/tex]

[tex]70x^{2}-50x[/tex] is your simplified expression.

By simplifying the given expression we will get that:

18*√8 = 36*√2

Here we start with:

18*√8

We can rewrite 18 as:

18 = √324

Replacing that in our expression we get:

√324*√8 = √(324*8) = √(2,592)

Now we need to rewrite 2,592 as the product of a square number and a non-square number (such that the non-square number is the smallest possible one).

If we divide 2,592 by 2, we get:

2592/2 = 1296

Then we can rewrite:

√2592 = √(2*1296) = √2*√1296 = √2*36

So this is the expression we wanted:

18*√8 = 36*√2

If you want to learn more about square roots, you can read:

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Answer:

[tex]36\sqrt{2}[/tex]

Step-by-step explanation:

The largest square factor under the radical is 4. This gives us the factorization [tex]\sqrt{8} =\sqrt{4} * \sqrt{2}[/tex].

Thus,

[tex]18\sqrt{8} = 18(\sqrt{4} * \sqrt{2})[/tex]

        [tex]= 18*2\sqrt{2}[/tex]

        [tex]= 36\sqrt{2}[/tex]

Hope this helps!

Using proportions, it is found that Jade's total yearly income was of $50,600.

A proportion is a fraction of a total amount.

In this problem, Jade's income is composed by:

Hence:

[tex]T = 18000 + 50(52) + 0.025(1200000) = 50600[/tex]

Jade's total yearly income was of $50,600.

More can be learned about proportions at https://brainly.com/question/24372153

Answer:

Triangle = 10

Circle = 5

Two halves of Square = 2

Fourth answer: 20

Step-by-step explanation:

Figuring out the triangle first is easiest because since 3 triangles make 30, then each triangle must be 10.

Now, we have our second equation become 10 + C + C = 20, and we get C=5 after solving for the value of the circle.

Our third equation will be 5 + S + S = 13, which becomes 5+2S=13, 2S=8, and then S=4, so the value of a square is 4

Our fourth equation will be 10 + 5*(1/2)(4) = ?, and we see that half of 4 is 2, so we have 10 + 5(2) = 10 + 10 = 20 as our answer.

The value of the given expression x + yz will be 20.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let 'x' represents an equilateral triangle, 'y' represent a circle, and 'z' represents the right triangle. Then the equations are given as,

x + x + x = 30

3x = 30

x = 10

x + y + y = 20

10 + 2y = 20

y = 5

y + 2z + 2z = 13

5 + 4z = 13

z = 2

Then the value of the expression is calculated as,

x + yz = 10 + 5 × 2

x + yz = 10 + 10

x + yz = 20

The value of the given expression x + yz will be 20.

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Answer:

7,500 was the attendance before the drop.

Step-by-step explanation:

3750 x 2

Answer:

88

Step-by-step explanation:

92 and angle 2 are corresponding and 180-92= 88

sin = 3/7

1 = sin²0 + cos²0

cos²0 = 1 - 9/49

cos²0 = 40/49

cos0 = √(40) / 7

since its in Quadrant 2 the sin is positive and cos is negative

cos0 = - √(40) / 7

Answer:

6 ducks and 13 horses

Step-by-step explanation:

x ducks

19-x horses

2x+4(19-x)=64

2x+76-4x=64

4x-2x=76-64

2x=12

x=6 ducks

19-x = horses

19-6=13 horses

6 ducks and 13 horses

Answer:

0

Step-by-step explanation:

its a straight line horizontally

Answer:

r = 2/3

Step-by-step explanation:

[tex]6^{3r} =36[/tex]

if:

[tex]36=6^{2}[/tex]

[tex]6^{3r} =6^{2}[/tex]

then:

[tex]3r=2[/tex]

[tex]r=2/3[/tex]

Hope this helps

Answer:

[tex]r=\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]6^{3r}=36\\\\log_6(6^{3r})=log_6(36)\\\\3r=2\\\\r=\frac{2}{3}[/tex]

Answer:

D. [tex]256\pi\ in^2[/tex]

Step-by-step explanation:

To do this, we need to plug in the given values into the equation:

[tex]SA=2\pi rh+2\pi r^2\\SA = 2\pi 8(8)+2\pi 8^2\\SA=2\pi 64+2\pi 64\\SA=128\pi + 128\pi\\SA=256\pi \ in^2[/tex]

Answer:

1. 4/5, 3/5, 4/3 || 2. x = 13.78

Step-by-step explanation:

1)

Sin = Opposite/Hypotenuse = 16/20 = 4/5

Cos = Adjacent/Hypotenuse = 12/20 = 3/5

Tan = Opposite/Adjacent = 16/12 = 4/3

So the answer is 4/5, 3/5, 4/3

2) The unknown side is the opposite, and 21 is the hypotenuse. Opposite/Hypotenuse is the sine function.

Sin(41) ≈ 0.656

0.656 = x/21

x = 13.776

The closest answer to this is 13.78

Answer:

[tex]x\leq 6[/tex]

Step-by-step explanation:

[tex]\frac{3x}{2} \leq 9[/tex]

multiply by 2 to cancel

[tex]3x\leq 18[/tex]

Divide by 3:

[tex]x\leq 6[/tex]

Hope this helps

Answer:

no

Step-by-step explanation:

Doesn't add to 12

[tex] - 5x + y = 12[/tex]

Add both sides 5x

[tex] - 5x + 5x + y = 5x + 12[/tex]

[tex]y = 5x + 12[/tex]

&

[tex]y = - x[/tex]

Thus :

[tex] - x = 5x + 12[/tex]

Add both sides x

[tex] - x + x = 5x + x + 12[/tex]

[tex]0 = 6x + 12[/tex]

Subtract both sides 12

[tex]0 - 12 = 6x + 12 - 12[/tex]

[tex] - 12 = 6x[/tex]

Switch sides

[tex]6x = - 12[/tex]

Divide both sides by 6

[tex] \frac{6x}{6} = \frac{ - 12}{6} \\ [/tex]

[tex]x = - 2[/tex]

We found the x-coordinate of the solution point ; to find the y-coordinate we just need to put the value of x in one 0f the given equations :

[tex]y = - ( - 2) [/tex]

[tex]y = 2[/tex]

Thus ( - 2 , 2 ) is the solution to this system of equations.

Answer:

I don't think so

Step-by-step explanation:

If I remember (based on memory) it's not equivalent

Reasoning: there's a different amount of Xs

Answer:

Please answer my question if you can, and gl understanding this! <3

Step-by-step explanation:

No, for if we subtract them, when we cancel out the 5x, 2, the integer, will not be equal to 2x, for not only is 2 already there, it is also being multipled by an integer. It possibly can equal though, if x was either 0, or positive 1, but if the x is not given, then no, they're not equivalent.

Answer:

d. $233.40

Step-by-step explanation:

you solve this by first multiplying Ryan's hourly rate($5.30) by how many hours he worked last week(32 hours)

5.30*32=169.6

then you take that number and subtract it from how much he earned($403) and the resulting number will be what he made in tips

403-169.9=233.40

Answer:

d. $233.40

Step-by-step explanation:

pay for 32 hours

= $5.30 × 32

= $169.60

tips = $403 - $169.60

= $233.40