Determine which equation has the same solutions as the given equation. x2 − 10x − 11 = 0 A. (x − 5)2 = 36 B. (x − 10)2 = 21 C. (x − 10)2 = 36 D. (x − 5)2 = 21

Answer:

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

Step-by-step explanation:

Given

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

Required

Solve

[tex](1-cos^2 x ).(1+tan^2 x)[/tex]

In trigonometry;

[tex]1 - cos^2x = sin^2x[/tex]

So, make substitution

[tex](1-cos^2 x ).(1+tan^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(1+tan^2 x)[/tex]

Also; in trigonometry:

[tex]1 + tan^2x = sec^2x[/tex]

Make another substitution

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex]

Recall that [tex]secx = \frac{1}{cosx}[/tex]

So;

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(sec^2 x)[/tex] becomes

[tex](1-cos^2 x ).(1+tan^2 x) = (sin^2 x ).(\frac{1}{cos^2 x})[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = \frac{sin^2 x }{cos^2 x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = (\frac{sin x }{cosx})^2[/tex]

In trigonometry;

[tex]tan x = \frac{sin x}{cos x}[/tex]

[tex](1-cos^2 x ).(1+tan^2 x) = tan^2x[/tex]

The expression cannot be further simplified

Answer:25000 because 1 m is equal to 1000mm

PLEASE MARK ME AS BRAINLIEST

Answer:

d.mean =15, median =15.5, mode = 16

Step-by-step explanation:

hello,

to find the mean, you add all the numbers together and divide it by the total number of numbers. so that would be 150 (total sum) divided by 10 (number of numbers) to get 15.

to find the median, you would organize the numbers from least to greatest and find the middle number which is 15.5.

last but not least, to find the mode, just look for the number that appears most often. Therefore, the mode would be 16.

hope this helped!

Answer:

y = [tex]\frac{4\sqrt{3} }{3}[/tex]

Step-by-step explanation:

We are working with 30-60-90 triangles, and to solve for y we need to know the hypotenuse of the smaller triangle.

You can get that by finding the smaller value of the larger triangle.

[tex]\frac{8}{\sqrt{3} } =\frac{x}{1}[/tex]

x[tex]\sqrt{3}[/tex] = 8

x = [tex]\frac{8}{\sqrt{3} }[/tex]

x = [tex]\frac{8\sqrt{3} }{3}[/tex]

That is the hypotenuse of the smaller triangle. To find y...

[tex]\frac{(\frac{8\sqrt{3} }{3}) }{2} =\frac{y}{1}[/tex]

2y = [tex]\frac{8\sqrt{3} }{3}[/tex]

y = [tex]\frac{4\sqrt{3} }{3}[/tex]

Hope this helps!

Answer:

z=1

Step-by-step explanation:

3x7z+1

21z+3

divided by 3

7z

divide by 7

z=1

Answer:

Z<0

Step-by-step explanation:

21z+3<3

21z<3-3

21z<0

Z<0

Answer:

The correct option is;

Substitute x = 0 in the function  and solve for f(x)

Step-by-step explanation:

The zeros of a function are the values of x which produces the value of 0 when substituted in the function

It is the point where the curve or line of the function crosses the x-axis

A. Substituting x = 0 will only give the point where the curve or line of the function crosses the y-axis,

Therefore, substituting x = 0 in the function  can't be used to find the zero's of a function

B. Plotting a graph of the table of values of the function will indicate the zeros of the function or the point where the function crosses the x-axis

C. The zero product property when applied to the factors of the function equated to zero can be used to find the zeros of a function

d, The quadratic formula can be used to find the zeros of a function when the function is written in the form a·x² + b·x + c = 0

Answer: Substitute x = 0 in the function and solve for f(x).

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

Each can holds 2 liters of paint. There is 11 liters of paint. The question is asking you to figure out how many cans of paint you can fill with 11 liters of paint. We can divide 11 by 2 to get the answer. 11÷2=5.5. The reason this works is because we are dividing the total amount of paint by how much each can will hold. 5.5 can also be written as "five and a half". So, the 11 liters of paint will fill 5.5 cans. Hope this helps!

Answer:

y = (-2/125)(x - 50)² + 40

Step-by-step explanation:

The total length of the bridge is 100 meters.

Maximum height always occurs at midpoint of x.

So for x=50 meters , y = 40 meters.

As the vertex is given at the maximum height,  Vertex can be defined at the point (50,40)

We know that the general equation for vertical parabola is:

y = a(x - h)² + k

Where (h,k) = Vertex = (50,40)

Substitute in the equation:

y = a(x - 50)² + 40 ⇒ Equation (i)

We know 2 more points on the parabola. We know that when x=0 , y=0 and we also know that when x=100m, y=0 meters.

Substitute any point in the above equation

Substituting (100,0) in the equation

0 = a(100 - 50)² +40

Solve the equation for a:

a = - 2/125

Substitute a in Equation (i)

y = (-2/125)(x - 50)² + 40

Answer:

8

Step-by-step explanation:

because yes.

Answer:

93 hamburgers

Step-by-step explanation:

let cheeseburgers=c

let hamburgers=h

c=3h

c+h=372

Substitute c for 3h

3h+h=372

4h=372

h=93

c=h*3=93*3=279

279 cheeseburgers 93 hamburgers

Answer: C

Step-by-step explanation:

The formula for surface area of a cylinder is A=2πrh+2πr². Since we know the radius and height, we can directly plug it into this formula to find surface area.

A=2π(9)(12)+2π(9²)

A=2π(108)+2π(81)

A=216π+162π

A=378π

A=1186.92 units²

Answer:

Step-by-step explanation:Jo's Mobile Plan:

Fixed monthly charge = £16

Monthly 150 free minutes, post that 13p (or £0.13) per minute,

Monthly 150 free texts, post that 15p (or £0.15) per text

Jo's mobile phone usage details:

170 minutes of calls

182 texts

Total Charges for Jo = Fixed Monthly Charge + Charges for Calls + Charges for Texts

⇒ Total Charges for Jo = 16 + (170-150) × 0.13 + (182-150) × 0.15

⇒ Total Charges for Jo = 16 + (20) × 0.13 + (32) × 0.15

⇒ Total Charges for Jo = 16 + 2.6 + 4.8

⇒ Total Charges for Jo = 23.4

Hence, Jo should be charged £23.4 for the month.

Answer:

Step-by-step explanation:

Perimeter of the rectangle = 332m

Perimeter of a rectangle = 2(L+b)

Breadth = 75m

= 2 ( L + 75) = 332

2L + 150 = 332

2L = 332-150

L = 182/2

L= 91m

Answer:B.

Step-by-step explanation:

Answer:

Similar triangles are (roughly speaking) triangles that have the same angles and the same ratio of the length of their sides

We can use ratios to show that the triangles are not similar

14:20 as a fraction is 14/20 as a decimal is 0.7

12:16 as a fraction is 12/16 as a decimal is 0.75

The side lengths are not the same proportion as shown by the different decimal, so the triangles are not similar

10 L of a 25% acid solution contains 0.25 * (10 L) = 2.5 L of acid.

Adding x L of pure water dilutes the solution to a concentration of 10%, such that

(2.5 L)/(10 L + x L) = 0.10

Solve for x :

2.5 = 0.10 * (10 + x)

2.5 = 1 + 0.10x

1.5 = 0.10x

15 = x

so 15 L of pure water are needed.

Answer:

None. (or B)

Step-by-step explanation:

A)  AC≅ZY

B) AZ≅

C) ∠A ≅ ∠C

D) ∠B ≅ ∠X

Options C and D are not true and Options A is wrong and B is incomplete but using process of elimination, the answer is probably B.

The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Given that, Δ ABC has been translated right to create triangle Δ XYZ

We know that in translation transformation, in translation, only the position of the object changes, its size remains the same.

That means Δ ABC ≅ Δ XYZ Therefore, we get,

Congruent parts are;

Angles:-

∠ A ≅ ∠ X,

∠ B ≅ ∠ Y and

∠ C ≅ ∠ Z

Side:-

AB ≅ XY,

BC ≅ YZ and

AC ≅ XZ

Hence, The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

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Answer: B $2.22

Step-by-step explanation:

2 controllers will cost

= 2 x 18.50 = 37

6% tax = 37 x 0.06 = 2.22

Answer:

B

Step-by-step explanation:

i took the test

Answer:

Surface area of triangular prism is:

Surface area = 2376ft

Step-by-step explanation:

A triangular prism is the one which has 3 rectangular sides and 2 triangular sides. To find the surface area of a triangular prism, we have to find the surface area of 3 rectangular side and 2 triangular sides and add them up

Surface Area (rectangle) = Length · Width

Surface Area (triangle) = (1/2)(Base)(Height)

Rectangular side 1:

Length = 40 ft

Width = 24 ft

Surface Area = 40 · 24

Surface Area = 960ft

Rectangular side 2:

Length = 40 ft

Width = 15 ft

Surface Area = 40 · 15

Surface Area = 600ft

Rectangular side 3:

Length = 40 ft

Width = 15 ft

Surface Area = 40 · 15

Surface Area = 600ft

Triangular side 1:

Base = 24 ft

height = 9 ft

Surface Area = (1/2)(24)(9)

Surface Area = 108ft

Triangular side 2:

Base = 24 ft

height = 9 ft

Surface Area = (1/2)(24)(9)

Surface Area = 108ft

SURFACE AREA OF TRIANGULAR PRISM:

Add all surface areas found above

Surface area = 960 + 600 + 600 + 108 + 108

Surface area = 2376ft

Answer:

Answer:

(B) Surface area of triangular prism is:

Surface area = 2376ft

Step-by-step explanation:

A triangular prism is the one which has 3 rectangular sides and 2 triangular sides. To find the surface area of a triangular prism, we have to find the surface area of 3 rectangular side and 2 triangular sides and add them up

Surface Area (rectangle) = Length · Width

Surface Area (triangle) = (1/2)(Base)(Height)

Answer:

3f(x)  

3x^2  

12  

-x+6

0

Step-by-step explanation:

Fashoo

Answer:

x + y ≥ 3

x + y ≤ 3

Step-by-step explanation:

In the picture attached, the problem is shown.

The solution to the system:

x + y ≥ 3

x + y ≤ 3

is the line x + y = 3

In order to get a solution to a system of inequalities that is a line, we need the same equation on the left (here, x + y), the same constant on the right (here, 3), and the ≥ sign in one inequality and the sign ≤ in the other one.

Answer:

Answer:

3 < c < 13

Step-by-step explanation:

A triangle is known to have 3 sides: Side a, Side b and Side c.

For a triangle, one of the three sides is longer than the other two sides. (The only exception is when we are told specifically that a triangle is an equilateral triangle, where all the 3 sides are equal to each other).

To solve the above question, we would be using the Triangle Inequality Theorem.

The Triangle Inequality Theorem states that the summation or addition of the lengths of any two sides of a triangle is greater than the length of the third side.

Side a + Side b > Side c

Side a + Side c > Side b

Side b + Side c > Side a

For the above question, we have 2 possible side lengths for the third side of the triangle. We are given in the above question,

side (a) = 5

side (b) = 8

Let's represent the third side as c

To solve for the above question,we would be having the following Inequality.

= b - a < c < b + a

= 8 - 5 < c < 8 + 5

= 3 < c < 13

Answer: y = one sixteenth(x − 4)^2 + 2

Step-by-step explanation:

If the parabola is written as:

y = a*x^2 + b*x + c

then if the graph opens up, then a must be positive, so we can discard the third and fourth options, we remain with:

y = 1/6*(x - 4)^2 + 2 = 1/6x^2 - (8/6)*x + (16/6 + 2)

y =  1/6*(x + 4)^2 - 2  =  1/6x^2 + (8/6)*x + (16/6 - 2)

the vertex (4, 2)

then

x = -b/2a = 4.

this means that a and b must be of different sign, then the only correct option can be:

y = 1/6*(x - 4)^2 + 2 = 1/6x^2 - (8/6)*x + (16/6 + 2)

where:

x-vertex  = (8/6)/(2/6) = 4 as we wanted.

when we evaluate this function in x = 4 we get

y = 1/6*( 4 - 4)^2 + 2 = 2.

So the correct option must be: y = one sixteenth(x − 4)2 + 2

Answer: The correct answer is the first answer, a.  y = one sixteenth(x − 4)2 + 2

Answer: C

Step-by-step explanation:

In the quadrant IV, it is only a cos θ that is positive.

Given that tan θ = –8∕15

Where tan θ = opposite ÷ adjacent

Where opposite = 8 and adjacent = 15

We can find the hypothenus by using pythagorean theorem

Hypothenus = sqrt(15^2 + 8^2)

Hypothenus = sqrt(289)

Hypothenus = 17.

Sin θ = opposite ÷ hypothenus

Sin θ = 8/17

Since Sin θ is also negative in the fourth quadrant, therefore

Sin θ = - 8/17

Option C is correct.

Answer: its 3

Step-by-step explanation:

Answer:   2

Step-by-step explanation: Because their are 2 squares

Answer:

answer b

Step-by-step explanation:

Answer b is definitely the correct one.

The Empirical Rule states that 68% of normally distributed data lies within 1 standard deviation of the mean; 95% within 2 standard deviations, and 99.9% within 3.

The probability of an outcome that lies within 95% of the mean is a good indicator b is definitely the correct one.

We have given that,

a. There is a probability that the outcome is within 1 standard deviation of the mean.

b. There is a probability that the outcome is within 2 standard deviations of the mean.

c. Standard deviations are not reliable, so the probability cannot be determined.

d. There is a probability that the outcome is within 3 standard deviations of the mean.

The Empirical Rule states that 68% of normally distributed data lies within 1 standard deviation of the mean; 95% within 2 standard deviations, and 99.9% within 3.

The probability of an outcome that lies within 95% of the mean is a good indicator b is definitely the correct one.

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Answer:

c

Step-by-step explanation:

In the given line the relationship between angle w and z is Measure of angle w + measure of angle z = 180 degrees.

This is the type of angle that when measured, two of the angles would sum up to 180 degrees.

The supplementary angle is the sum of angle w + angle z = 180 degrees. Hence c is correct.

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Answer:

10 meters

Step-by-step explanation:because they are square and they would have to be 5 meters long and she dose not want any left over so...

Answer:

x=1 , y = -1

Step-by-step explanation:

-2.4x-3.6y = 1.2

2.4x+1.2y = 1.2

Add the equations together

-2.4x-3.6y = 1.2

2.4x+1.2y = 1.2

---------------------------

   -2.4 y = 2.4

Divide by -2.4

y = -1

Now find x

2.4x +1.2y = 1.2

2.4x +1.2(-1) = 1.2

2.4x -1.2 = 1.2

Add 1.2 to each side

2.4x -1.2+1.2 = 1.2+1.2

2.4x = 2.4

Divide by 2.4

x = 1

Answer:

x=1

Step-by-step explanation:

Answer:

132 dollars, I think

Step-by-step explanation:

15*2=30

66*2=132

Answer:

D

Step-by-step explanation:since 15 cases is $66 multiply 66 by 2 to get $132