What number should be added to both sides of the equation to complete the square?

x^2-10x=12​

By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].

In the image attached we have a right triangle with two legs of same length. The hypotenuse of right triangles can be found by Pythagorean theorem, whose form is:

[tex]r = \sqrt{l^{2}+l^{2}}[/tex]

[tex]r = \sqrt{2}\cdot l[/tex], where l is the length of the legs.

By Pythagorean theorem we find that the length of the hypotenuse is [tex]r = \sqrt{2}\cdot l[/tex].

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a. The equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1

b. The equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx

To find the trigonometric expression for cos(4x)

cos(4x) = cos[2(2x)]

Now from trigonometric identities

cos2Ф = 2cos²Ф - 1

Let 2x = Ф.

So, cos(4x) = 2cos²2x - 1

Also, cos2x = 2cos²x - 1

So, substituting cos2x into cos4x, we have

cos(4x) = 2cos²2x - 1

cos(4x) = 2[2cos²x - 1]² - 1

cos(4x) = 2[4cos⁴x - 4cos²x + 1] - 1

cos(4x) = 8cos⁴x - 8cos²x + 2 - 1

cos(4x) = 8cos⁴x - 8cos²x + 1

So, the equivalent expression for cos(4x) in terms of just x is 8cos⁴x - 8cos²x + 1

To find the expression for sin(4x)

sin(4x) = sin2(2x)

From trigonometric identities sin2Ф = 2sinФcosФ

Let 2x = Ф

So, sin(4x) = sin2(2x)

= 2sin2xcos2x

Since

Substituting these into the equation, we have

sin(4x) =  2sin2xcos2x

sin(4x) = (2sinxcosx)(2cos²x - 1)

sin(4x) = 4sinxcos³x - 2sinxcosx

So, the equivalent expression for sin(4x) in terms of just x is 4sinxcos³x - 2sinxcosx

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The expression equivalent to -7(y - 2) is -7y + 14

Given the expression; -7(y - 2)

We expand the expression by multiplying each element inside the parentheses the element out i.e -7

-7(y - 2)

[ -7 × y and -7 × -2 ]

-7y + 14

Therefore, the expression equivalent to -7(y - 2) is -7y + 14.

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The surface area of the oblique prism is equal to 485 square units.

In this question we have an oblique prism with seven faces, consistiting in two regular hexagons and five parallelograms. The surface areas is the sum of these seven faces:

A = 2 · 50 + 5 · 11 · 7

A = 485

The surface area of the oblique prism is equal to 485 square units.

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Answer:

17√3

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.

17*√3 = 17√3

Answer: -8

Step-by-step explanation:

When x = 5, f(x) = -8.

The value of the function f(5) = -8.

We have,

The concept used to find the value of f(5) is function evaluation.

In this case, we are given a function represented by a table with x and f(x) values.

To evaluate the function at a specific value, such as f(5), we look for the corresponding x-value in the table and determine the corresponding f(x) value.

In this example, we found that when x = 5, f(x) is -8 by looking at the table provided.

To find the value of f(5), we need to look at the table and find the corresponding value of the function when x = 5.

From the given table, when x = 5, f(x) is -8.

Therefore,

The value of the function f(5) = -8.

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The factored form of the equation that has the zeros 4 and -7 is y = ( x - 4)( x + 7 ).

Roots are simply the points where the graph intercepts with the x-axis. ( y = 0 )
That is, y = 0 the roots

Given the roots of the equation;

Now, at x = 4,

x = 4

x - 4 = 0

y = ( x - 4)

Also, at x = -7,

x = -7

x - ( - 7 ) = 0

x + 7 = 0

y = ( x + 7 )

Hence; for the equation with the given roots; 4 and -7 will be;

y = ( x - 4)( x + 7 ).

The factored form of the equation that has the zeros 4 and -7 is y = ( x - 4)( x + 7 ).

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Answer: 98

Step-by-step explanation: 180 - 82 = 98

180 - 80 = 100, and 100 - 2 is 98.

Step-by-step explanation:

Set up a system of equations,

Consective numbers appear before and after so we need two number such that

[tex]x + 1 = y[/tex]

or

[tex]x - y = - 1[/tex]

Likewise, we also know that

[tex]4x + 3y = 157[/tex]

Let multiply the top equation by 3.

We get

[tex]3x - 3y = - 3[/tex]

Then we add the bottom equation to that

[tex]4x + 3y = 157[/tex]

[tex]7x = 154[/tex]

[tex]x = 22[/tex]

Then we plug in x for the original equation,

[tex]22 + 1 = 23[/tex]

So the two numbers are 22,23.

Answer:

Step-by-step explanation:

Let Kevin have x dollars. Then Latoya has x - 9 dollars and Milan has 4(x - 9) dollars.

x + (x-9) + 4(x-9) = 177

7x - 40 = 177

7x = 217

x = 31

Kevin has $31

Latoya has 31 - 9= $22

Milan has 4*24 = $96

A'(-6, -10), B'(-3, -13) and C'(-5, -1) are the vertices of the ΔA'B'C' given that the vertices of the ΔABC are A(-6, -7), B(-3, -10) and C(-5, 2) and translation rule (x, y) → (x, y-3) is applied. This can be obtained by putting coordinate values of vertices in the translation rule and then vertices of ΔA'B'C' are found.

Given that,

In ΔABC, the vertices are A(-6, -7), B(-3, -10) and C(-5, 2)

The translation rule that must be applied is ⇒ (x, y) → (x, y-3)

By applying the translation rule to each of the vertices of ΔABC we get,

That is,

These new coordinates are the vertices of  ΔA'B'C'.

Hence A'(-6, -10), B'(-3, -13) and C'(-5, -1) are the vertices of the ΔA'B'C'.

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The correct answer is  8.5 in.

we know that

The formula of area of triangle is equal to

             [tex]A = \frac{1}{2} (b) (h)[/tex]

We have

b = BC = 6 in

h = AD = x in

substitute

[tex]A = \frac{1}{2} (6) (x)[/tex]

[tex]A = 3x^{2} in^{2} ..................(1)[/tex]

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  

Let  a,b,c be the lengths of the sides of a triangle.  

The area is given by:-

[tex]A = \sqrt{p(p-a) (p-b) (p-c)}[/tex]                     where p is half the perimeter

[tex]p = \frac{a +b+ c}{2}[/tex]

a = 9 in , b= 9 in, c = 6 in

[tex]p = \frac{9 + 9 + 6}{2} = 12 in[/tex]

Find the area

[tex]A = \sqrt{12( 12 - 9) (12-9) (12 - 6)}[/tex]

[tex]A = \sqrt{12 (3)(3)(6)}[/tex]

[tex]A = \sqrt{648}[/tex]

[tex]A = 25.46 in^{2}[/tex]

Substitute the value of the area in the equation 1 and solve for x

[tex]A = 3x in^{2}[/tex]

25.46 = 3x

x = 25.46/3

x = 8.5 in

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The complete question is -

HELP PLEASE! Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.

A. 8 in.

B. 11.3 in.

C. 8.5 in.

D. 6.2 in.

Hello,

y = ax + b where a is the slope ! so here the slope is 6

Answer:

Step-by-step explanation:

$135 is less than or equal to 2 nights at the hotel (h)

135</=2h

Answer:

8/15 cm

Step-by-step explanation:

Volume = length x width x height

Volume = 4/5 cm x 1/5 cm x 10/3 cm

Volume = 4/25 cm x 10/3 cm

Volume = 40/75 cm = 8/15 cm

Brainliest, please :)

Answer:

[tex]\frac{8}{15}[/tex]

Step-by-step explanation:

Volume of prism = [tex]l[/tex] · [tex]w[/tex] · [tex]h[/tex]

which means

[tex]\frac{10}{3} *\frac{4}{5} *\frac{1}{5}[/tex]

which is [tex]\frac{8}{15}[/tex] by using cross simplify  

Hope this helps ;D

The tax due for the single taxpayer whose income is as described is; $14,459.5.

It follows from the task content that the tax due for a single taxpayer whose taxable income is; $65,725 is to be determined.

Since, the taxable income falls between the range; $40,526 to $86,375, 22% of the income is the tax due and hence, the tax due can be evaluated as follows;

= (22/100) × $65,725

= 14,459.5

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Answer:

patient A has the greater weight

Answer:

(0,0)

Step-by-step explanation:

The y-intercept (where the graph of the equation crosses the y-axis) occurs where x = 0. If you substitute 0 for x in the equation, y = 0. So the y-intercept is at (0,0).

Answer: See the attached image below for the filled in table.

=========================================================

Explanation:

The domain is the set of all allowed x inputs of a function.

The term "radicand" refers to the stuff under the square root.

We cannot have a negative number under the square root. Therefore, the radicand must be 0 or larger.

The first function must have [tex]4x+6 \ge 0[/tex] which becomes [tex]4x \ge -6[/tex] and leads to [tex]x \ge -\frac{6}{4}[/tex] aka [tex]x \ge -\frac{3}{2}[/tex]

So x = -3/2 is the smallest input allowed. Which is where the interval notation of [tex]\left[-\frac{3}{2}, \infty)[/tex] comes from. It's the interval spanning from -3/2 (inclusive) to infinity. This represents the set of all possible x inputs of the first function.

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Follow this same idea for problem 2. The steps would be something like this:

[tex]-20x - 6 \ge 0\\\\-20x \ge 6\\\\x \le \frac{6}{-20}\\\\x \le -\frac{3}{10}\\\\[/tex]

The inequality sign flips because we divided both sides by a negative number. That then leads to the interval notation of [tex](-\infty, -\frac{3}{10}\big][/tex]

The interval spans from negative infinity (exclusive) to -3/10 (inclusive).

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Problem 3 would have these steps

[tex]5x-16 \ge 0\\\\5x\ge 16\\\\x\ge \frac{16}{5}\\\\\big[\frac{16}{5}, \infty)\\\\[/tex]

No sign flip happens since we divided both sides by a positive number.

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Lastly, here are the steps for problem 4

[tex]20+6x \ge 0\\\\6x \ge -20\\\\x \ge -\frac{20}{6}\\\\x \ge -\frac{10}{3}\\\\\big[-\frac{10}{3}, \infty)[/tex]

Don't forget to use the square bracket to include the endpoints mentioned. We always use curved parenthesis for either infinity because we can't ever reach infinity. In a sense, we "approach" infinity.

Once again, all of this is summarized in the filled out table shown below (attached image). Feel free to ask any questions if they come to mind.

The period of simple harmonic motion is T = 4.19 seconds:

For given question,

A mass weighing 16 pounds is attached to a spring whose spring constant is 36 lb/ft.

So, we have mass (m) = 16 pounds

spring constant (k) = 36 lb/ft.

Let T be the period of simple harmonic motion.

Using the formula for the period of simple harmonic motion,

⇒ T = 2π√(m/k)

⇒ T = 2 × π × √(16/36)

⇒ T = 2 × π × √(0.444)

⇒ T = 2 × π × 0.666

⇒ T = 1.333 × π

⇒ T = 4.19 seconds

Therefore, the period of simple harmonic motion is T = 4.19 seconds

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0.129 is the change in the growth rate of company.

According to statement

we have to find and compare the growth rate of the company weekly.

we use the growth rate formula is

GROWTH RATE = present - past / present

Substitute the values in this formula

1st week = 220-190 / 220

1st week = 0.136

2nd week = 252-220 / 252

2nd week = 32 / 252

2nd week = 0.126

3rd week = 290-252 / 290

3rd week = 0.131

4th week = 337 - 290 / 337

4th week = 0.139

5th week = 380 - 337 / 380

5th week = 0.113

6th week = 440 - 380 / 440

6th week = 0.136

7th week = 505 - 440 / 505

7th week = 0.128

Now we find the average value of growth rate

Average = 0.136 + 0.126+0.131+0.139+0.113+0.136+0.128 /7

Average = 0.909/7

Average = 0.129

So, 0.129 is the change in the growth rate of company.

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The equations have the same solution are 2.3p – 6.5p + 0.01p =– 4  + 10.1 and -4.19p = 6.1

This are equations that has a leading degree of 1. GIven the expression as shown below

2.3p – 10.1 = 6.5p – 4 – 0.01p

Collect the like terms

2.3p – 6.5p + 0.01p =– 4  + 10.1

Simplify

-4.19p = 6.1

Hence the equations have the same solution are 2.3p – 6.5p + 0.01p =– 4  + 10.1 and -4.19p = 6.1

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Other than translation, the transformation that is used to create this frieze pattern is; B: Vertical Reflection

Now, we see all the Frieze Patterns on top are being transformed using Translation as it is the exact same pattern throughout the top.

Now, for the bottom we see that is is simply a reflection of the one on top and so it is a vertical reflection because it is reflected across the x-axis.

A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.

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The equation which could be used to find the length of the hypothenuse is; 5 squared + 8 squared = c squared.

It follows from the task content that the equation which could be used to find the length of the third side be determined.

Hence, since it follows from Pythagoras theorem that the square of the hypothenuse is equivalent to the sum of the squares of the two other sides of a right triangle.

Hence, the required equation is; 5 squared + 8 squared = c squared.

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Answer:

The answer is A
5 squared + 8 squared = c squared

Step-by-step explanation:

The volume of the cylinder is 301.593 cubic centimeter.

Volume exists as a scalar quantity representing the amount of three-dimensional space enclosed by a sealed surface. For example, the space that a substance or 3D shape inhabits or contains. The volume stands often quantified numerically utilizing the SI-derived unit, the cubic meter.

A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it has been regarded as a prism with a circle as its base.

The dimensions of the cylinder is given as - 8 cm and 12 cm .

The formula of the volume of the cylinder is given as -

V = π * (8) * (12)

Thus the volume is = 96π ≈ 301.593 cubic centimeter.

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Answer:

x = 0, y = 1

Step-by-step explanation:

2x + 6y = 6 → (1)

x - 3y = - 3 ( add 3y to both sides )

x = 3y - 3 → (2)

substitute x = 3y - 3 into (1)

2(3y - 3) + 6y = 6 ← distribute parenthesis and simplify left side

6y - 6 + 6y = 6

12y - 6 = 6 ( add 6 to both sides )

12y = 12 ( divide both sides by 12 )

y = 1

substitute y = 1 into (2)

x = 3(1) - 3 = 3 - 3 = 0

solution is x = 0 , y = 1

A confidence interval is an interval estimate of an individual y value, given values of the independent variables.

According to statement

we have to find a interval which give an estimate of an individual y value, given values of the independent variables.

Confidence interval tells that more than just the possible range around the estimate. It also tells about how stable the estimate is. A stable estimate is one that would be close to the same value if the survey were repeated.

So, A confidence interval is an interval estimate of an individual y value, given values of the independent variables.

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Answer:

a: (-1,0) , (3/5,0)

b:(-0.2,-3.2). It will be a minimum

c: To graph, you would first find the vertex using (-b/2a) and then plug that back into the equation to find the y coordinate of the vertex. Once you have the vertex plotted, you can then find the x-intercepts. This can be found by factoring the equation and finding the zeros. These 3 points you plot are enough to graph the line.

Step-by-step explanation:

For showing work on part a:

Turn 5x^2+2x-3 into

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

5x(x+1) -3(x+1)

Finally:

(5x-3)(x+1)

The zeros from that are -1 and 3/5

Answer:

76.25

Step-by-step explanation:

There will be total 14 hard centred and 14 soft centred choclates in the box.

The ratio is the division of the two numbers.

For example, a/b where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that in the question hard-centred and soft-centred chocolates in the ratio 5 : 2

Hard centred/ Soft centred = 5/2

And total

Hard centred + Soft centred = 49

Now let say hard centred is H and soft centred S

H/S = 5/2 and H + S = 49

Now H = (5/2)S put into second equation

(5/2)S + S = 49

S(7/2) = 49

S = 14 now put into second equation

H + 14 = 49 = 35 hence hard centred will be 35 and soft centred will be 14.

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