identify the correct trigonometry formula do you use to solve for the given angle

Answer:

[tex]2.5[/tex]

Step-by-step explanation:

The given radical expression is

[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })[/tex]

Observe that, the given expression can be written as difference of two squares.

That is; [tex](x+y)(x-y)=x^2-y^2[/tex]

We apply this property to obtain:

[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })=2^2-(\sqrt{-\frac{3}{2} })^2[/tex]

We now simplify to get:

[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })=4-\frac{3}{2}[/tex]

This simplifies to:

[tex](2+\sqrt{-\frac{3}{2} }) (2-\sqrt{-\frac{3}{2} })=\frac{5}{2}=2.5[/tex]

Answer:

The solutions of the equation is 0 , π , 2π

Step-by-step explanation:

* Lets revise some identities in the trigonometry

- tan²x + 1 = sec²x

- tan²x = sec²x - 1

* Now lets solve the equation

∵ tan²x sec²x + 2sec²x - tan²x = 2

* Lets replace tan²x by sec²x - 1

∴ (sec²x - 1) sec²x + 2sec²x - (sec²x - 1) = 2 ⇒ open the brackets

∴ sec^4 x - sec²x + 2sec²x - sec²x + 1 = 2 ⇒ add the like terms

∴ sec^4 x -2sec²x + 2sec²x + 1 = 2 ⇒ cancel -2sec²x with +2sec²x

∴ sec^4 x + 1 = 2 ⇒ subtract 1 from both sides

∴ sec^4 x = 1 ⇒ take root four to both sides

∴ sec x = ± 1 ⇒ x is on the axes

∵ sec x = 1/cos x

∵ sec x = 1 , then cos x = 1

∵ sec x = -1 , then cos x = -1

∵ 0 ≤ x ≤ 2π

∵ x = cos^-1 (1)

∴ x = 0 , 2π ⇒ x is on the positive part of x-axis

∵ x = cos^-1 (-1)

∴ x = π ⇒ x is on the negative part of x-axis

* The solutions of the equation is 0 , π , 2π

Answer:

a=0.343

Step-by-step explanation:

70/100=0.7

0.7x0.7x0.7=0.343

Answer:

Part A) The equation that represent the situation is [tex]\frac{n+54}{9}=21[/tex]

Part B) The value of n is [tex]n=135[/tex]

Part C) The equation is [tex]35+n=60[/tex] and the solution is [tex]n=25[/tex]

Step-by-step explanation:

Part A) A number is increased by 54. The sum is then divided by 9. The result is 21.  Write an equation to represent the description above. Use n for the number

Let

n-----> the number

we know that

The linear equation that represent this situation is equal to

[tex]\frac{n+54}{9}=21[/tex]

Part B) Find the value of n

we have

[tex]\frac{n+54}{9}=21[/tex]

solve for n

Multiply by 9 both sides

[tex]n+54=21*9[/tex]

[tex]n+54=189[/tex]

Subtract 54 both sides

[tex]n=189-54[/tex]

[tex]n=135[/tex]

Part C) Choose two numbers and use them to do the following:

Write an equation that shows your first number added to n equal to your second number. Solve your equation for n

I choose 35 and 60

[tex]35+n=60[/tex]

Solve for n

Subtract 35 both sides

[tex]n=60-35[/tex]

[tex]n=25[/tex]

The cross between Bbhh and bbHh yields genotypic frequencies

so that 1/4 of the offspring should be expected to be brown with long fur (genotype Bbhh)

Answer:

1/4

Step-by-step explanation:

Answer:

Scale factor: 4/7

perimeter ratio: 4:7

area: I don't know the height of the two

Step-by-step explanation:

Answer:

im not sure were you got this but are there any pictures?

Step-by-step explanation:

The figure ABCD represents a square

A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.

A square is a 4 sided polygon where all the sides are of equal length.

The area of the square is the square of any one of its side

Let a be the side of the square

Area of the square = a²

Given data ,

Let the figure be represented as ABCD

Now , the coordinates of ABCD are noted clockwise

And , the diagonals of the quadrilateral are AC and BD

Now , the diagonals AC and BD intersect at X

where the measure of angle ∠ABX = measure of ∠XBC

So , the diagonals are equal and the angles are equal

And , the figure represents a square

where the sides AB = BC = CD = AC

Hence , the figure is a square by SAS congruency

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Answer:

C [tex]\frac{2}{1}[/tex]

Step-by-step explanation:

Recall the mnemonics SOH-CAH-TOA

The tangent ratio is the ratio of the opposite side of the right triangle  to the adjacent side.

From the diagram, the side opposite to <B is 2 units and the adjacent side is 1 unit.

This implies that;

[tex]\tan \angle B=\frac{2}{1}[/tex]

The correct choice is C

Answer:

D

Step-by-step explanation:

The vertex is the turning point of the graph.

This is at (- 1, - 2)

The graph changes from decreasing to increasing at (- 1, - 2)

Hence is a minimum at (- 1, - 2)

The graph of the parabola is minimum at (-2, -1).

The path of an object that is thrown in the air and falls back to the earth.

A graph of the parabola is given.

a.   At ( -1, -2 ), the parabola is minimum.

b.   At ( -2, -1 ), point does not satisfy.

c.   At ( 2, 1 ), the point does not satisfy.

d.   At ( 1, 2 ), the point does not satisfy.

Thus, the graph of the parabola is minimum at (-2, -1).

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Answer:

3/5

Step-by-step explanation:

Bruh i gotchu Simple

Answer: Last option 155°

Step-by-step explanation:

We have the components of the vectors u and v.

Then, to find the angle between them, perform the following steps:

1) Calculate the scalar product u * v

If [tex]u = 2i + \sqrt{11}j[/tex]  and [tex]v = -3i-2j[/tex]

Then, the product scalar u * v is:

[tex]u * v = (2)(-3) + (\sqrt{11})(-2)[/tex]

[tex]u * v = -6-2\sqrt{11}[/tex]

[tex]u * v = -12.633[/tex]

2) Calculation of the magnitude of both vectors.

[tex]| u | = \sqrt{(2) ^ 2 + (\sqrt{11})^2}\\\\| u | = \sqrt{4+11}\\\\| u | = \sqrt{15}[/tex]

[tex]| v | = \sqrt{(- 3) ^ 2 + (- 2) ^ 2}\\\\| v | = \sqrt{9 +4}\\\\| v | = \sqrt{13}[/tex]

3) Now that you know the product point between the two vectors and the magnitude of each, then use the following formula to find an angle

[tex]u * v = | u || v |cos(\alpha)[/tex]

[tex]-12.633 = \sqrt{15}\sqrt{13}*cos(\alpha)\\\\cos(\alpha) = \frac{-12.633}{\sqrt{15}\sqrt{13}}\\\\arcos(\frac{-12.633}{\sqrt{15}\sqrt{13}}) = \alpha\\\\\alpha =155\°[/tex]

Answer:

65°, 70°, 80°, 155°, 170°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 ( pentagon )

sum = 180° × 3 = 540°

Sum the given angles and equate to 540

x + x - 5 + x + 10 + 2x + 15 + 2x + 30 = 540

7x + 50 = 540 ( subtract 50 from both sides )

7x = 490 ( divide both sides by 7 )

x = 70

Hence angles are

x = 70°

x - 5 = 70 - 5 = 65°

x + 10 = 7 0 + 10 = 80°

2x + 15 = (2 × 70) + 15 = 140 + 15 = 155°

2x + 30 = (2 × 70) + 30 = 140 + 30 = 170°

Answer:

3×3×3⁄3×3×3×2

Step-by-step explanation:

27 = 3×3×3

54 = 3×3×3×2

The prime factored form of 27⁄54 is thus;

3×3×3⁄3×3×3×2

Answer:

D= 3×3×3/2×3×3×3

Step-by-step explanation:

A prime factored form breaks the number into prime numbers that give the same value when multiplied

27= 3×3×3

54=2×3×3×3

To get the simplest form of a fraction you proceed with division.

=3×3×3 / 2×3×3×3.............................cancel 3 in the numerator and denominator

= 1/2

Answer:

D) The number line with a solid dot and the arrow going to the right of 3.

Step-by-step explanation:

x - 5 >/= -2

x >/= 3

x is greater than or equal to 3.

For this case we must find the solution of the following inequality:

[tex]x-5\geq-2[/tex]

So:

If we add 5 to both sides of the inequality we have:

[tex]x-5 + 5\geq - 2 + 5\\x\geq - 2 + 5\\x\geq 3[/tex]

Thus, the solution is given by all values of x greater than or equal to 3.

Answer:

Option D

Answer:

John will get more money after 5 years.

Step-by-step explanation:

To calculate compound interest we use the formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

A = Amount

P = Principal

r = Rate of interest ( in decimal )

n = number of compounding period (quarterly = 4) (monthly = 12)

t = time in years

John wants to deposit $1000 with an interest of 4% compounded quarterly for 5 years.

[tex]A=1,000(1+\frac{0.04}{4})^{(4)(5)}[/tex]

[tex]A=1,000(1.01)^{20}[/tex]

A = 1000 ( 1.22019 )

A = $1220.19

John will get $220.19 as interest after 5 years.

Cayden wants to deposit $1,000 with an interest of 3% compounded monthly for 5 years.

[tex]A=1,000(1+\frac{0.03}{12})^{(12)(5)}[/tex]

[tex]A=1,000(1.0025)^{60}[/tex]

A = 1,000 ( 1.161617 )

A = 1161.62

Cayden will get $161.62 as interest after 5 years.

Therefore, John will get more money after 5 years.

Answer:

i think that it is y=5n

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Use the formula for the surface area and plug in the given numbers. See work for more.

Answer: FR and NR

NO and NM

RC and RO

Step-by-step explanation: just did it on apex. good luck!

Answer:

The correct options are A, C and D.

Step-by-step explanation:

The given figure shows an unfolded paper. It is a square sheet.

Here the line of symmetry are diagonals FN, AK and midline CM, OI. All of these lines are intersecting at point R.

Diagonals of square bisect each other, therefore R is midpoint of FN.

[tex]FR\cong NR[/tex]

[tex]AO\cong ON[/tex]              (OI is line of symmetry)

[tex]PO\neq ON[/tex]

[tex]RC\cong RO[/tex]              (AK is line of symmetry)

[tex]NO\cong NM[/tex]              (FN is line of symmetry)

[tex]DV\cong HV[/tex]              (FN is line of symmetry)

[tex]DV\neq EW[/tex]

Therefore the correct options are A, C and D.

Jane had 10 Beanie Babies in the beginning.

The number of Beanie Babies Jane had in the beginning.

- She gave 8 to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.

- Her grandma bought her 5 more, so she then had [tex]\( x + 5 \)[/tex] Beanie Babies.

- Combining the Beanie Babies she had at the beginning, the ones she gave away, and the ones her grandma bought her, the total is 27.

- Solving the equation [tex]\( x - 8 + (x + 5) = 27 \)[/tex], we find [tex]\( x = 10 \)[/tex], the number of Beanie Babies Jane had in the beginning.

Jane had 20 Beanie Babies in the beginning.

To calculate:

1. Let's denote the number of Beanie Babies Jane had in the beginning as [tex]\( x \).[/tex]

2. She gave 8 of them to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.

3. Her grandma bought her 5 more Beanie Babies than she had in the beginning, so she now has [tex]\( x + 5 \)[/tex] Beanie Babies.

4. Given that she now has 27 Beanie Babies, we can set up the equation:

[tex]\[ x - 8 + (x + 5) = 27 \][/tex]

Now, let's solve for [tex]\( x \):[/tex]

[tex]\[ 2x - 3 = 27 \][/tex]

[tex]\[ 2x = 30 \][/tex]

[tex]\[ x = 15 \][/tex]

However, this is the number of Beanie Babies Jane had after her grandma bought her 5 more. To find out how many she had in the beginning, we need to subtract 5 from [tex]\( x \):[/tex]

[tex]\[ x = 15 - 5 = 10 \][/tex]

So, Jane had 10 Beanie Babies in the beginning.

- Let [tex]\( x \)[/tex] be the number of Beanie Babies Jane had in the beginning.

- She gave 8 to her friend, leaving her with [tex]\( x - 8 \)[/tex] Beanie Babies.

- Her grandma bought her 5 more, so she then had [tex]\( x + 5 \)[/tex] Beanie Babies.

- Combining the Beanie Babies she had at the beginning, the ones she gave away, and the ones her grandma bought her, the total is 27.

- Solving the equation [tex]\( x - 8 + (x + 5) = 27 \)[/tex], we find [tex]\( x = 10 \)[/tex], the number of Beanie Babies Jane had in the beginning.

Complete question

Jane had R Beanie Babies. She gave 8 of them to her friend. Later her grandma bought her 5 more Beanie Babies than she had in the beginning. How many Beanie Babies did Jane have in the beginning, if now she has 27 of them?

Answer:

[tex]\large\boxed{4\sqrt{-81}+\sqrt{-25}=41i}[/tex]

Step-by-step explanation:

[tex]i=\sqrt{-1}\\\\\sqrt{-81}=\sqrt{(81)(-1)}=\sqrt{81}\cdot\sqrt{-1}=9i\\\\\sqrt{-25}=\sqrt{(25)(-1)}=\sqrt{25}\cdot\sqrt{-1}=5i\\\\4\sqrt{-81}+\sqrt{-25}=4(9i)+5i=36i+5i=41i[/tex]

The same slope between line AD and line AB results from the property of similar triangles. This property states that corresponding sides are proportional, which also applies to the slopes of these sides. Hence, the slopes are equivalent.

The reason the slope of the line between point A and D is the same as the slope between points A and B derives from the concept of similar triangles in geometric math. In similar triangles, corresponding sides are proportional. This proportionality is carried over to the slopes of the lines that form these sides. Slope is defined by the change in y (vertical change) over the change in x (horizontal change). In similar triangles, these changes are proportional meaning the division, or the slope will be the same.

Consider this using Figure A1 Slope and the Algebra of straight lines where they indicate that the slope is the same all along a straight line. This also applies to the lines of similar triangles. Therefore, if triangles ADE and ABC are similar, then the slope of line AD will be the same as the slope of line AB because the ratios of their changes in y over changes in x are equal.

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The two lines with the equations are the same length.

Set the two equations to equal and solve:

3x +3 = 6x - 57

Add 57 to each side:

3x +60 = 6x

Subtract 3x from each side:

60 = 3x

Divide both sides by 3:

x = 20

Answer:

x= 20

Step-by-step explanation:

Answer:

B. 144^12

Step-by-step explanation:

[tex]{144}^{14} \div {144}^{2} \\ = {144}^{14 - 2} \\ = {144}^{12} [/tex]

The simplified exponent form of the given expression 144^14/144^2 would be 144^12.

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

The given expression can be solved by exponentially

[tex]\dfrac{144^{14}}{144^2}\\\\144^{14} \times144^{-2}}\\\\144^{14-2} \\\\144^{12}[/tex]

Therefore the simplified exponent form of the given expression would be 144^12.

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The slope of the graph is 3

The y-intercept is -4

The equation of the line is y=3x-4 it shouldn’t be y= then x=

Answer:

The slope  is 3

The y-intercept is -4

The equation of the line is y=3 x=-4

Step-by-step explanation:

:)

Answer:

3.70

Step-by-step explanation:

18.50 ÷ 5 = 3.70

fairly simple math but can be confusing depending upon how its asked, you just have to find the words that describe what you have to do and check your math to make sure

Answer:

3 ft

Step-by-step explanation:

It is because 3 times 18 is 54 and 3 is 15 less than 18

The width of a rectangle is 3 feet .

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.)

According to the question

Let length of rectangle = x

The width of a rectangle is fifteen feet less than its length.

i.e,

Width of a rectangle = x - 15

Now,

Area of the rectangle = 54 square feet .

Length * Width = 54

x (x - 15 ) = 54

[tex]x^{2}[/tex] - 15x - 54 = 0

[tex]x^{2}[/tex] - (18-3)x - 54 = 0

[tex]x^{2}[/tex] - 18x + 3x - 54 = 0

x(x-18) +3(x-18) = 0

(x-18) (x+3) = 0

x= 18 , -3

length of rectangle = 18 feet

Width of a rectangle = 18 - 15

                                  = 3 feet

Hence, The width of a rectangle is 3 feet .

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The property of the sample standard deviation that is not accurate is 'D. Resistant to extreme data values'. The sample standard deviation is indeed sensitive to extreme data values. The other properties listed are true about the sample standard deviation.

The property of the sample standard deviation (s) that is not accurate from the given options is 'D. Resistant to extreme data values'. The sample standard deviation is sensitive to extreme values, not resistant. In other words, if there are outliers or extreme values in the data, the sample standard deviation will tend to be larger, reflecting the increased variability.

Let's quickly review the other options for clarity. 'A. Sensitive to changes in the distribution' and 'B. Calculated based on the mean' are true properties of the sample standard deviation. The standard deviation, whether for a sample or a population, measures the spread or dispersion of the data points about the mean. Therefore, it changes with the distribution and is calculated based on the mean. 'C. Larger than the population standard deviation σ' is typically true, unless the sample perfectly represents the population.

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The sample standard deviation is C. larger than the population standard deviation o.

The sample standard deviation, denoted as s, is a measure of spread that quantifies how much the data values deviate from the mean. It is calculated based on the mean. However, it is not necessarily larger than the population standard deviation, o, as it depends on the specific data set.

The other options are not correct:

E. All of the above is not the correct answer, as the correct answer is C.

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Answer:

see explanation

Step-by-step explanation:

A recursive formula allows us to calculate any term in the sequence from the previous term.

These are the terms of a geometric sequence with r being the common ratio between consecutive terms.

r = 4 ÷ - 2 = - 8 ÷ 4 = 16 ÷ - 8 = - 2

Multiplying a particular term by - 2 gives the next term in the sequence.

Hence recursive formula is

[tex]a_{n+1}[/tex] = - 2 [tex]a_{n}[/tex] with a₁ = - 2

-2,4,-8,16,...

a₁ = -2

a₂ = -2a₁

a₃ = -2a₂

..................

=> aₙ₊₁ = -2•aₙ, with a₁ = -2

Answer:

See below

Step.-by-step explanation:

Choice A  has first term  -3 and common difference 5. The formula for the kth term is -3 + (k - 1)5. It is an arithmetic series.

The required expanded form for the Sum is:

         5

S5 =  ∑  [-3 + (k - )5)]

       k = 1

Answer:

Expanded form of the series is:

A. -3 + 2 + 7 + 12 + 17

Step-by-step explanation:

when k=1     -3+(k-1)5= -3

when k=2     -3+(k-1)5= -3+5=2

when k=3     -3+(k-1)5= -3+10=7

when k=4     -3+(k-1)5= -3+15=12

when k=5     -3+(k-1)5= -3+20=17

Hence, value of [tex]S_{5}= -3+2+7+12+17[/tex]

Hence, expanded form of the series is:

A. -3 + 2 + 7 + 12 + 17

The answer is 3 because you need to use the last equation which is x is greater than or equal to 3.it doesn't make sense to use any of the other two equations because it asked what is the value of g(3).hope this helps if it does please mark brainliest

The answer is 3 you’re welcome