Question 2 of 10
The expression √3x is equivalent to the expression x√3.

The number that we need to add to "complete the square" when solving x² – 14x – 40 = 0 using the method of completing the square is 49.

To solve a quadratic equation using the method of completing the square, we need to add the square of half of the coefficient of the x term to both sides of the equation.

This will convert the left side of the equation into a perfect square trinomial.

Then, we can take the square root of both sides and isolate the variable x.

To solve the quadratic equation x² – 14x – 40 = 0 using the method of completing the square, we need to add the square of half of the coefficient of x to both sides.

The coefficient of x is -14, so half of it is -7.
The square of -7 is 49.

Therefore, we need to add 49 to both sides of the equation to "complete the square".

Now, we have: x² – 14x + 49 = 40 + 49

Simplifying this gives: (x - 7)² = 89

Taking the square root of both sides gives: [tex]x - 7 = \pm\sqrt{89}[/tex]

Adding 7 to both sides gives:[tex]x = 7 \pm\sqrt{89}[/tex]

Therefore, the number that we need to add to "complete the square" when solving x² – 14x – 40 = 0 using the method of completing the square is 49.

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Answer:

Step-by-step explanation:

I can't really explain, but Here comes the hoping:

Equation 1:

Equation 2:

Equation 3:

Equation 4:

Equation 5:

Answer:

Length = 15.14, width = 7.14 and height = 2.43  inches.

( correct to the nearest hundredth).

Step-by-step explanation:

Let the lengths of the squares cut out be x inches.

Then the width of the box will be 12 - 2x and the length will be

20 - 2x inches.

The height of the box is x inches.

Volume V = x(20-2x)(12-2x)

To find the value of x when V is a maximum we find the derivative and equate it to zero.

V = x( 240 - 64x + 4x^2)

V = 4x^3 - 64x^2 + 240x

dV/dx = 12x^2 - 128x + 240 = 0

4(3x^2 - 32x + 60) = 0

This won't factor so we use the formula:

x = [-(-32) +/- √((-32)^2 - 4*3*60)] / 6

= 8.24, 2.43.

So one of these gives a maximum Volume.

The second derivative

d^2V/dx^2 = 24x - 128

When x = 8.24,  this = 69.6 (positive) so this gives a minimum.

x = 2.43 gives a negative  value ( -49.7)  so this is the maximum

So the dimensions are:-

length = 20 - 2(2.43) = 15.14

width = 12 - 2(2.43) = 7.14

height = 2.43.

Answer:

The third measurement is 62°

Step-by-step explanation:

Hey there! Please take a look at the explanation for clear understanding to the answer and also let me know in comment if you have any doubts!

The theorem regarding it states that, sum of all 3 interior angles must equal to 180°.

That means, we will have this equation:

[tex]\displaystyle \large{28^{\circ} + 90^{\circ} + x=180^{\circ}}[/tex] because we know two interior angles and one missing angle - sum of them equals to 180 degrees.

Then we solve for x-term to find the third measurement!

[tex]\displaystyle \large{118^{\circ}+x=180^{\circ}}[/tex]

Subtract both sides by 118 degrees.

[tex]\displaystyle \large{118^{\circ}-118^{\circ}+x=180^{\circ}-118^{\circ}}\\\\\displaystyle \large{x=62^{\circ}}[/tex]

Henceforth, the third measurement is 62°

Answer:

-102.1

Step-by-step explanation:

When adding negative numbers, act as if you are subtracting that same number, but in its positive form.

So in reality, you could rewrite the equation as: (-7.8) - 12 - 82.3 = -102.1

Answer:

X Intercepts: (3,0) , (-1,0)

Y Intercepts: None

Hope this helps.

The surface area of the triangular prism is 330 centimetres cube.

surface area of a triangular prism = (a + b + c) l + 2(base area)

where

Hence,

surface area = (5 + 12 + 13)9 + 5 × 12

surface area = 30(9) + 60

surface area = 270 + 60

surface area = 330 cm³

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Answer:

Question 6a: [tex]p \leq 16[/tex]

Question 6b: option d

Step-by-step explanation:

Question 6a: [tex]6p \leq 96\\6p/6 \leq 96/6\\p \leq 16[/tex]

Question 6b:

- closed dot since its equal to 16

- p is less than 16 (arrow pointing left)

Answer:

Just add me and let's our journey begins :3

Step-by-step explanation:

Just add me and let's our journey begins :3

Answer:

D

Step-by-step explanation:

cotangent = cos / sin        

                 = 4/3

using pythagorean theorem   4^2 + 3^3 = h^2      <=====  h = 5

      then cos = 4/5    sin = 3/5    

               then,  since    csc = 1/sin = 5/3

Answer:

8.2 * 10^-3 is the greatest and 5.2 * 10^-6 is the smallest.

Step-by-step explanation:

Answer:

Domain=[67,78]

Step-by-step explanation:

To find domain:

  ⇒ must define what is a domain

       ⇒ Domain is the set of input values or the values of the x-axis of

           graph that is covered by the function

Based on the definition:

    ⇒ 67 ≤ x ≤ 78 is the domain of the function

Answer: 67 ≤ x ≤ 78 where x is a whole number

Hope that helps!

Answer:

Y less than or equal to zero

Step-by-step explanation:

The graph shows that its moving downwards, therefore the Y value is decreasing..

Answer:

1 hot dog = $1.50 each

1 hamburger = $1.75 each

Step-by-step explanation:

Answer:

The prices must be $1.50 and $1.75

Step-by-step explanation:

For instance, seven hot dogs and two hamburgers cost $14: 7D+2B=14

We also know that two hot dogs and seven hamburgers cost $15.25: 2D+7B=15.25

Now, if we combine these two equations, we have a system where EVERYTHING has to be true at the same time 

7D+2B=14

2D+7B=15.25

From here there are a couple trick you should know to solve a system of equation, especially substitution and elimination. I see a coefficient of 2, so I'd rather use substitution by dividing the entire first equation in half:

3.5D+B=7

Now I'll solve for B

B=7-3.5D

Now that I've solved for a variable, I can substitute the solution into the other equation

2D+7(    B   )=15.25

becomes

2D+7(7-3.5D)=15.25

Now I can distribute and solve for D:

2D+49-24.5D=15.25

22.5D=33.75

D=1.5

Now we can replace D from either (or both) of our original equations and see what B has to be

7(1.5)+2B=14

10.5+2B=14

2B=3.5

B=1.75

2(1.5)+7B=15.25

3+7B=15.25

7B=12.25

B=1.75

The prices must be $1.50 and $1.75. The most important part of all this is setting up the equations, the rest is just being careful with your calculations.

Answer:

(-1;4)

Step-by-step explanation:

as the triangles are congruent

The coordinate of point F is (1-, 4). Therefore, option A is the correct answer.

A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.

From the given graph, the coordinate points are A(-5, 0), B(-5, -5) and C(2, -5).

Here, ΔABC and ΔDEF are congruent triangles.

So, the coordinate of point F are (1-, 4)

Therefore, option A is the correct answer.

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[tex]\dfrac{x^2y}{2} = \dfrac{(-1)^2 \cdot 5 }{2} = \dfrac{1 \cdot 5}2 = \dfrac 52[/tex]

Answer:

4/5

Step-by-step explanation:

Answer:

=4/5 or 0.8 as decimal

Step-by-step explanation:

8/10

Factor the number: 8=2· 4

2x4

Factor the number: 10 = 2· 5

2x4/2×5

Cancel the common factor: 2

=4/5

or (decimal 0.8)

Answer:

9/12 or 75%.

Step-by-step explanation:

Let's first add the choices all up.

5+4+3= 12.

We have 12 movie choices in total.

Now, we know that we have 3 drama movie choices...so the chance we will choose drama is 3/12, but we are not finding that.  We want the chance she will NOT choose drama, so that would be 9/12.

*Since the chance she will choose drama is 3/12, the chance she will not choose is 9/12. 9+3 is 12, the total amout.*

Answer:

<A = 60°

Step-by-step explanation:

The triangle is 180° Angle A and B add up to 118°

4y° + (3y + 13)° = 118°

7y + 13 = 118°

7y = 105

y = 15

Since you solve for y, plug your y into the angles to solve.

<A = 4y

<A = 4 * 15

<A = 60°

The missing parts of the given table are

∠1 ≅ ∠4                  → Alternate interior angles Theorem

DB ≅ DB                 → Reflexive property

ΔDAB ≅ ΔBCD       → SAS (Side Angle Side)

From the question, we are to complete the table to prove that ABCD is a parallelogram

The missing parts in the table can be completed as shown below

∠1 ≅ ∠4                  → Alternate interior angles Theorem

DB ≅ DB                 → Reflexive property

ΔDAB ≅ ΔBCD       → SAS (Side Angle Side)

Hence, the missing parts of the given table are

∠1 ≅ ∠4                  → Alternate interior angles Theorem

DB ≅ DB                 → Reflexive property

ΔDAB ≅ ΔBCD       → SAS (Side Angle Side)

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.

Answer:

I believe it would be 15, apologies if its incorrect.

Step-by-step explanation:

Answer:

If they are 28 Oz and a deviation of 2 it will be 26 so 26 times 800 will be 4800. so technically 1 bag is 26oz so the answer is 1 bag.

Answer:2/7

Step-by-step explanation:

TThe solution is in the image

Answer: 473 square meters

Step-by-step explanation:

Answer: 1980 calories

Step-by-step explanation:

290grams of carbs=1160g

60 grams of fat=540

70 grams of protein=280 calories

290 x 4=1160

60 x 9=540

70 x 4=280

1160+540+280=1980 calories

carbs provide 4 calories per gram

fat provides 9 calories per gram

protein provides 4 calories per gram

Answer:

x=63/8

Step-by-step explanation:

9/8=x/7

or, 9*7=x*8

or, 63=8x

x=63/8

Answer:

Step-by-step explanation:

Remark

9.3 x and 60 degrees are all related to the Tangent of L or Tan(L) as you would find it on your calculator.

Givens

Formula

Tan(60) = opposite / Adjacent                Substitute Values

Solution

Tan(60) = 9.3 /  x                                      Multiply both sides by x

x*Tan(60) = x * 9.3 /x              

x* Tan(60) = 9.3                                         Divide both sides by Tan(60)

x * Tan(60) / Tan(60) = 9.3/Tan(60)

x = 9.3 / 1.7321

x = 5.369

Answer

x = 5.4                              

Answer:

168 [tex]cm^{3}[/tex]

Step-by-step explanation:

Start by finding the whole prism's volume. 9 x 3 x 8 = 216 Then find the volume of the missing part. 8 x 6 x 1 = 48. Subtract the missing volume from the whole volume. 216 - 48 = 168