Help me? Product of a sum and a difference
Formula; (a + b)(a - b) = a^2 - b^2

Find the product of the following

1. (2x - 5)(2x + 5)

2. (5b - 6y)(5b + 6y)

3. (4k + 7)(4k - 7)

4. (y - 5)(y + 5)

5. (3x - 2)(3x + 2)

6. (13x + 2x^3)(13x - 2x^3)

7. (2a + 1)(2a - 1)

8. (9y^2 + 8)(9y^2 - 8)

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Answer:

  6.  4

  7.  36

Step-by-step explanation:

The given conditions in each case allow you to conclude that the triangles are congruent. Corresponding parts of congruent triangles are congruent.

__

6. YX = YZ = 4

7. Angle XWY is congruent to angle ZWY, so is 18. Angle XWZ is the sum of those two angles, so ...

  ∠XWZ = ∠XWY +∠ZWY = 18 + 18

  ∠XWZ = 36

Step-by-step explanation:

The equation with the highest leading coefficient (the number before the x^2 term) will have the narrowest graph. Here, we have to choose between -1, 1/6, 2, and 1/8. The highest number out of all of those numbers is 2, so y = 2x^2 will have the narrowest graph.

Answer:

66 1/6ft

Step-by-step explanation:

I have calculated by saying perimeter =2(length+width). I think that's the answer hope it helps.

Answer: 46 1/4

Step-by-step explanation:

Perimeter = (L+W) x 2

So basically ... (10 1/4 + 12 5/6) x 2

Which would be ...  23 1/12 x 2

Which gives you the answer of 46 and 1/4

Answer:

x=10

Step-by-step explanation:

Because of the two parallel lines, the ratio between the sides must be the same.  Since the bottom is 12 to 18 (a ration of two to three) we know that x and x+5 would have the same ratio.  Logically, x would have to equal 10 so that x+5 would equal 15 and a ratio of two to three would exist there too.  If you go to solve a problem and the answer isn’t obvious, jut set up a ratio.

12/18=x/(x+5)

then cross multiply and solve

12(x+5)=18x

12x+60=18x

60=18x-12x

60=6x

10=x

Answer:

x=10

Step-by-step explanation:

You can set it up as a proportion, since the lines are parallel, the sections are proportionate to each other.

[tex]\frac{x}{12} = \frac{x+5}{18} \\18x=12(x+5)\\18x=12x+60\\6x=60\\x=10[/tex]

Answer: D 1,500

Step-by-step explanation:

Because there is 2,000 milliliters in 2 liters, so if we do 2,000 - 500 we get 1,500 left

Answer:

Both A and D

Step-by-step explanation:

Because 500 milliters is half of one liter which makes the total 1.5 liters or 1500 mililliters

Answer:

13

Step-by-step explanation:

43 - 30 = 13

q = 13

Answer:

q=13

Step-by-step explanation:

first, subtract 30 from both sides of the equation

30-30+q=43-30

you should be left with q=13

that's your answer

Answer:

B

Step-by-step explanation:

The circumference is just diameter x π (3.14 in this case) so 42 x 3.14 = 131.88

Answer:

B

Step-by-step explanation:

the circumference of a circle is

2×pi×r

with r being the radius (half the diameter).

2r is then the diameter.

so, in our case the circumference is

42×pi = 42 × 3.14 = 131.88 mm

Answer:

The answer is -5.

Step-by-step explanation:

The absolute value of -9 is 9.

Then it would be like 4= x + 9.

If you solve it, you get -5.

Answer:

Step-by-step explanation:

we will find the area of the inner circle and then the area of the outer circle and see what the ratio is between those 2

area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]  (where r is the radius, NOT the diameter, easy to confuse)

the radius of the inner circle is 2.5. which  is half of the diameter of 5

inner circle = [tex]\pi[/tex]*(2.5)^2

inner circle =  19.6349...

outer circle = [tex]\pi[/tex]*(10^2)

outer circle = 314.1592...

the ratio is    19.6349... /  314.1592...  = 0.0625

0.0625 = 6.25%

= 6% ( rounded to nearest whole number )

Answer:

$506.25

Explanation:

assuming it is simple interest,

$1500 × 6.75% = $101.25 (interest earned each year)

$101.25 × 5 = $506.25 (interest earned in 5 years)

i hope this helps, feel free to comment if you need to clarify anything!

Answer:

50 cents

Step-by-step explanation:

half of 5.00$ is 2.50$

Answer:

628

Step-by-step explanation:

1) Find the circumference of the wheel (the distance it travels in 1 revolution)

[tex]C=\pi d[/tex] where d is the diameter

Plug in 2 ft as the diameter

[tex]C=(3.14) (2)\\C=6.28[/tex]

Therefore, the circumference of the wheel is 6.28 ft.

2) Multiply the circumference by 100

6.28 × 100

= 628 ft

Therefore, Joe would travel 628 feet if his wheel turns exactly 100 complete revolutions in one direction.

I hope this helps!

Answer:

Step-by-step explanation:

5 + 6 = 11 x 2 - 1 = 21 therefore its 21

Answer:

eight chairs.

Step-by-step explanation:

five quarts= 40/8 quarts

one chair= 5/8 quarts

40/8-5/8x=0

(-40/8)/(-5/8)=x

eight chairs

Answer: the chances are 5 out of 15 so in 30 draws she would draw 10 green hope it helps

Answer:

Step-by-step explanation:

(4 , 1) ; x₁ = 4   and y₁ = 1

(4 , -5) ; x₂ = 4  and y₂ = -5

The slope of the the line is undefined as the line is parallel to y-axis

Answer:

75

90

15, i think ??

165

hope this helps !!!! :D

Step-by-step explanation:

Solution:

Here,

In triangle LKM,

6x+5x+x=180

12x=180

x=180/12

x=15

Now,

1.75

2.90

3.15

4.165

Answer:

Negations.

Step-by-step explanation:

The first statement is:

p ∧ q

(p and q)

This statement is only true when:

p = true

and

q = true.

And is false in all the other cases.

The other statement is:

¬q ∨ ¬p

(not q or not p)

This statement is only true if at least one of the elements is true, this happens if:

q =false (then ¬q = true)

or

p = false (then ¬p = true)

Then the first statement needs p and q to be true.

The second statement needs at least one of these to be false.

This means that when the first statement is true, the second statement is false.

When the first statement is false, the second one is true.

Then the statements are negations.

The mass of Sand that Carla needs to purchase for the sand tank is gotten to be; 25811 g

Formula for density is;

Density = mass/volume

From the box we are given, it's volume is;

Volume = 30 * 30 * 76

Volume = 68400 cm³

Now, from conversion;

1 cm³ = 1g. Thus;

68400 cm³ = 68400 g

Volume = Mass/density

Volume = 68400/2.65

Volume = 25811 g

Read more about mass required at; https://brainly.com/question/1762479

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Answer:

  x = ∛4 ≈ 1.587 m

  y = (∛4)/2 ≈ 0.794 m

Step-by-step explanation:

Short answer:

An open-top box will use minimum material when it has the shape of half a cube. That is, the x-dimensions will be ...

  x = ∛(2·2 m³) = ∛4 m

The y-dimensions will be half that:

  y = x/2 = (∛4)/2 m

__

Long answer:

The volume is ...

  V = x^2·y

so the y-dimension is ...

  y = V/x^2

The area of the sides and bottom will be ...

  A = 4xy + x^2

  A = 4x(2/x^2) +x^2 = 8/x +x^2

The area is minimized when the derivative of this is zero.

  A' = 0 = -8/x^2 +2x

  x^3 = 4 . . . . . . . divide by 2 and rearrange

  x = ∛4 . . . . . . . . cube root

  y = 2/x^2 = 2∛4/4

  y = (∛4)/2

___

Additional comment

If you follow the numbers through, you see that the value under the cube-root radical is twice the volume. This is the result we used in the "short answer."

Answer:

500 dino nuggies.

Step-by-step explanation:

Hope this helps

Answer:

500 dino nuggies!!!

Step-by-step explanation:

Answer:

Box dimensions:

L = 3 ft

D = 6 ft

H = 1 ft

Volume  V = 18 ft³

Step-by-step explanation:

a) Each side of the future box is

L = 5 - 2*x     D = 8 - 2*x  

height of the box is   x

Then the volume of the box as function of x is:

V(x) =  ( 5 - 2*x ) * ( 8  - 2*x ) * x

V(x) = ( 40 - 10*x - 16*x + 4*x² ) * x

V(x) = 40*x - 26*x² + 4*x³

Tacking derivatives on both sides of the equation:

V´(x) = 40 - 52*x + 12x²     or     V´(x) = 20 - 26*x + 6*x²

If V´(x) = 0

6*x² - 26*x + 20  = 0

Solving for x

x₁,₂  = (-b ± √ b² - 4*a*c  ] /2*a

x₁,₂  = ( 26  ±  √ 676  - 480  ) / 12

x₁,₂  =  (26 ± 14 )/ 12

x₁  = 1

x₂ = 3,33        ( we dismiss this solution since is not feasible according to cardboard dimensions )

Then the sides of the box are:

L = 5 -2*x      L  =  5 - 2*1     L = 3 ft

D = 8 - 2*x    D  = 8 - 2*1     D = 6 ft

H = x = 1 ft

And the volume is    V = 6*3*1 = 18 ft³

Answer:

The problem is telling you to find g ( f ( x ) )

Since we know that f(x) is square root of x, we can put the function this way.

g(√x)

Then, we use  √x as our x in our g(x) function.

You plug in  √x for x and you solve.

(√x ) ^2 is just x.

Finally the answer is

x-3

hope this helps :)

Step-by-step explanation:

Answer:

178.3

Step-by-step explanation:

Hello There!

We can find the value of y using trigonometry

These are the trigonometric ratios

Remember SOHCAHTOA

Sine = Opposite over Hypotenuse

Cosine = Adjacent over Hypotenuse

Tangent = Opposite over Adjacent

For the angle that has a measure of 27 degrees

we are given its adjacent angle and we need to find its opposite angle (y)

Adjacent and Opposite sides corresponds with the trigonometric ratio Tangent so we are going to use the trigonometric ratio tan to solve for y

Now we set up an equation (remember tangent = opposite over adjacent)

[tex]tan(27)=\frac{y}{350}[/tex]

Now that we have created an equation we want to solve for y

What we want to do is isolate the variable using inverse operations

So basically we want to get rid of the 350

The opposite of division is multiplication so we multiply each side by 350 to get rid of it

[tex]tan(27)*350=350tan(27)\\\frac{y}{350} *350=y\\y=350tan(27)\\350tan(27)=178.3339073\\[/tex]

so we can conclude that y = 178.3339073

finally we want to round to the nearest tenth and we get that the answer is 178.3

Answer:

0.4% or in decimal form 0.004

Step-by-step explanation:

took the test and got it right!

Answer:

Step-by-step explanation:

Integer roots:

a = 6 n + 1, b = 7, c = -3 n^2 - n, n element Z

a = 6 n + 5, b = 7, c = -3 n^2 - 5 n - 2, n element Z

Derivative:

d/da(1/7 (a^2 + 12 c) b - 1) = (2 a b)/7

Indefinite integral:

integral(-1 + 1/7 b (a^2 + 12 c)) da = (a^3 b)/21 + (12 a b c)/7 - a + constant

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