Which choice is equivalent to the expression below?
√64
OA. -64
OB. 64i
OC. 8 + i
OD. -8
OE. 8i

Answer: -1/2

Step-by-step explanation:

Use double-angle identities:

cos(2θ)=cos^2θ−sin2^θ

cos(2θ)=1−2sin^2θ

cos(2θ)=2cos^2θ−1

sin(x)=1/2

cos(2x)=1−2sin^2x=1−2(1/4)=1/2

cos(4x)=2cos2^(2x)−1=2(1/4)−1=-1/2

Answer: cos4x=-1/2 if sinx=1/2.

Step-by-step explanation:

[tex]sinx=\frac{1}{2}\\ x=\frac{\pi }{6} .\\4x=4*\frac{\pi }{6}=\frac{2\pi }{3}.\\ cos4x=cos\frac{2\pi }{3}=-\frac{1}{2} .[/tex]

Answer:

Half of the perimeter is 300 feet.

If 100 feet are in the width, then 200 feet are in the length

Step-by-step explanation:

Perimeter is the sum of the lengths and the widths of the rectangle.

So P= l + l + w + w

perimeter is 600 and the width is 100.

so substituting in

600= 100 + 100 + l + l

600 = 200 + 2 l

solve for l

l = 200

hope this helps

Answer:

150 feet

Step-by-step explanation:

Length of playground = L + L + B + B

600 = 100 + 100 + 2L

600 = 200 + 2L

600 - 200 = 2L

300 = 2L

L = 300/2

L = 150

Therefore, the length of the playground is 150 feet.

A triangle is a three-edged polygon with three vertices. The length of the side MN is 3 cms.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The triangle formed by MN, MO, NO is an equilateral triangle, with the length of each side of the triangle equal to the radius of the triangle. Therefore, the length of MN will be,

MN = r

Now, the length of arc MN can be written as,

2 × π × r × (60° /360°) = π

r = 360 / (60 × 2)

r = 3

Hence, the length of the side MN is 3 cms.

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Answer:

10^6

Step-by-step explanation:

exponents show how many times a number multiplies by itself

in this case, 10 multiplies by itself 6 times, so the answer should be 10^6

so he paid Rs 170 for VAT

total amount paid = 170 x 10 = 1700

discount is 15%

so therefore

amount before discount = 1700/(1–0,15) = 2000

discount = 2000 x 15% = Rs 300

The 15% discount amount for the Nepali flag is 255 rupees.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

VAT = 10%

Discount = 15%

10% = 170 rupees

Multiply 15/10 on both sides.

15/10 x 10% = 15/10 x 170

15% = 255 rupees.

Thus,

The discount amount is 255 rupees.

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Answer:

1)The equation is 3^N, where N starts at 4 and goes down 1 each time

2) 1 would be the 5th term

Step-by-step explanation:

3^4=81

3^3=27

3^2=9

3^1=3

3^0=1

Answer:

Last option, y = -4/3x - 2/3

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

number that describes both the direction and the steepness of the line

slope = rise/run

           b represents the y-intercept  

point where crosses the y-axis

Given:

Let change 3x - 4y = 2 into y = mx + b form,

3x - 4y = 2

subtract 3x from both sides,

3x - 3x - 4y = 2 - 3x

- 4y = 2 - 3x

divided both sides by -4 to get y alone,

- 4y / -4 = 2 - 3x / - 4

  y = (3x / 4) - (2 / 4)

→ y = (3/4)x - (1/2)

Slope of perpendicular lines to another is the negative reciprocal

(ex. slope of 2 becomes -1/2)

So for y = (3/4)x - (1/2) the slope will be,

slope = -4/3

We need to find b (y-intercept),

we know it passes through point (1, - 2)

a point is (x, y) format

y = -(4/3)x + b

plug in the point (1, - 2),

-2 = -4/3(1) + b

-2 = -4/3 + b

add 4/3 to both sides to get b alone,

-2 + 4/3 = -4/3 + 4/3 + b

-2/3 = b

the perpendicular line equation is,

y = -4/3x - 2/3

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Answer:

Step-by-step explanation:

Most of the questions can be answered by comparing the given equation to vertex form.

The vertex form of the equation for a parabola is ...

  y = a(x -h)² +k

where 'a' is a vertical scale factor, and (h, k) is the vertex. The sign of 'a' determines whether the parabola opens upward or downward.

When we compare the given equation to the vertex form, we can easily see the values of 'a' and (h, k).

  y = -2(x -5)² +3 . . . . . . . given equation

  y = a(x -h)² +k . . . . . . . vertex form

The parameters are ...

  a = -2, (h, k) = (5, 3)

We notice ...

The axis of symmetry is the vertical line through the vertex. It has the equation ...

  x = h

  x = 5 . . . . equation of the axis of symmetry

The sign of 'a' is negative. This means that large x-values will result in large negative y-values. The parabola opens downward.

When the curve opens downward, it means the vertex is the highest point on the curve. The maximum is the y-value of the vertex: k. There is no minimum.

The maximum is y = 3.

The y-intercept is where the graph crosses the y-axis. It can be found by setting x=0, and computing the value of y:

  y = -2(0 -5)² +3

  y = -2(25) +3 = -50 +3

  y = -47 . . . . the y-intercept.

The ordered pair for the point there is (0, -47).

__

We show the graph so you can see how these features relate to the shape of the graph and points on it.

Answer:

LCM(24,30,40)=120.The Least common multiple for three numbers 24,30 and 40 is 120

Step-by-step explanation:

The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )²  is  [tex]\frac{1}{3^8}[/tex].

Hence, option B is the correct answer.

Given the expression;

( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )²

First, we use the properties of exponents.

( 2⁻²ˣ⁻³ × 3⁴ˣ⁻³ ) × ( 2⁻³ˣ² × 3²ˣ² )

( 2⁶ × 3⁻¹² ) × ( 2⁻⁶ × 3⁴ )

We take out the parentheses, such that;

2⁶ × 2⁻⁶ × 3⁻¹² × 3⁴

Note that: 2⁶ × 2⁻⁶ = 1, as [tex]2^6*2^{-6}=2^{6+(-6)}=2^0=1[/tex]

Hence, we have

1 × 3⁻¹² × 3⁴

3⁻¹²⁺4

3⁻⁸

Next, we express with positive exponent

[tex]\frac{1}{3^8}[/tex]

The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )²  is  [tex]\frac{1}{3^8}[/tex].

Hence, option B is the correct answer.

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Answer:

3x² + 6x + 4

Step-by-step explanation:

6x + 7 + x² + 2x² - 3

→ Collect like terms

x² + 2x² + 6x + 7 - 3

→ Simplify

3x² + 6x + 4

Answer:

3x^2+6x+4

Step-by-step explanation:

We can find the sum of the polynomials by combining like terms.

(6x+7+x²)+(2x²-3)

x^2+2x^2+6x+7-3

3x^2+6x+4

The required sample size is 694.

Given a student wants to make a guess within 0.03 of the true ratio with a 95% confidence level.

Margin of Error, E = 0.03

significance level α=0.05  {95% confidence}

A given estimate of the percentage of population p is p = 0.79.

The critical value for the significance level α = 0.05 is Zc = 1.96. This can be determined using either Excel or a normal probability table.

Use the following formula to calculate the minimum sample size required to estimate the percentage of population p within the required margin of error.

n≥p(1-p)(Zc÷E)²

n=0.796×(1-0.796)(1.96÷0.03)²

n=693.1016

Therefore, the  resample sizequired to meet the condition is n ≥ 693.1016 and must be an integer. From this, we conclude that the minimum sample size required is n = 694.

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The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6

The function is given as:

f(x) = x^2 + 6

Rewrite as:

y = x^2 + 6

Swap x and y

x = y^2 + 6

Subtract 6 from both sides

y^2 = x - 6

Take the square root

[tex]y = \sqrt{x - 6}[/tex]

Rewrite as:

[tex]f^{-1}(x) = \sqrt{x - 6}[/tex]

Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6

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Answer: a. -52 1/2

Step-by-step explanation:

    Given:

3/4(2/3 + 4/3) - 9 / 1/2 x 1/3

[tex]\displaystyle \frac{3}{4}(\frac{2}{3} +\frac{4}{3} )-\frac{9}{\frac{1}{2} *\frac{1}{3} }[/tex]

    Add and multiply:

[tex]\displaystyle \frac{3}{4}(\frac{6}{3} )-\frac{9}{\frac{1}{6} }[/tex]

    Simplify and divide:

[tex]\displaystyle \frac{3}{4}(2 )-54[/tex]

    Multiply:

[tex]\displaystyle 1.5-54[/tex]

    Subtract:

         a. -52 1/2

Answer:

Step-by-step explanation:

cos(20°) is the correct answer.

Congratulations! This is the unit circle. Literally everyone hates this. Everyone takes this in Trigonometry though, and it's required. I literally failed Trigonometry because of this and had to retake it when getting my degree in Mathematics.

So, what is the x-coordinate of this? Well, for any angle or (angle in triangle) [tex]\alpha[/tex], the coordinates are always ([tex]cos(\alpha), sin(\alpha)[/tex]).

In this case, angle [tex]\alpha[/tex] is 20°, and so the x-coordinate will be cos(20°) while the y-coordinate will be sin(20°).

Hope this helped!

Answer: cos 20

Step-by-step explanation:

Answer:

a.) The pizzas will cost the same at 4 toppings

Step-by-step explanation:

Medium Pizza:

$5.99 + $0.75x

Large Pizza:

$6.99 + $0.50x

Find x

$5.99 + $0.75x =  $6.99 + $0.50x

0.25x = 1

x = 4

Answer: 6

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{BD}{3}=\frac{27}{BD}\\\\(BD)^{2}=81\\\\BD=9\\\\\implies x=9-3=6[/tex]

Answer:

x = 6

Step-by-step explanation:

BD is the height of the triangle.

We can find the height of this triangle using one of the Euclidian Theorem:

h^2 = AD*DC rewrite the equation using the given information

(x + 3)^2 = 3*27 multiply

(x + 3)^2 = 81 find the root of both sides

x + 3 = 9 subtract 3 from both sides

x = 6

[tex]y=2(x+1)^2+6[/tex]

The vertex (−1,6)

Equation of axis of symmetry is x = -1

minimum at (-1,6)

[tex]y=\frac{-(x-1)}{2} ^2-4[/tex]

The vertex (1,-4)

Equation of axis of symmetry is x = 1

maximum at (1,-4)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

[tex]y=2(x+1)^2+6[/tex]

The vertex (−1,6)

Equation of axis of symmetry is x = -1

minimum at (-1,6)

[tex]y=\frac{-(x-1)}{2} ^2-4[/tex]

The vertex (1,-4)

Equation of axis of symmetry is x = 1

maximum at (1,-4)

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Using proportions, it is found that the expression that represents the final price is given as follows:

C(t) = 0.918t.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that:

Thus the expression for the final cost is:

C(t) = t x 0.85 x 1.08 = 0.918t.

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932°F to 36032°F

Celsius and Fahrenheit are both measures of temperature. However, Celsius is a metric measurement, and Fahrenheit is used in the USA primarily.

Conversion Formula

To convert the Celsius measurements to Fahrenheit we can use the formula:

So, in this formula, you can plug in whatever Celsius value you have in and solve for Fahrenheit. To convert from F to C you can use the second formula:

Solving for Fahrenheit

Now that we have the formula, we can plug in the 2 Celsius values to find the new range.

First, plug 500°C in

Next, multiply the terms within the parentheses

Finally, add the last terms

Then, plug in 20000°C

Next, multiply the terms within the parentheses

Lastly, add the terms together

This means that, in Fahrenheit, the temperature range of the welder's electrical arc is 932°F to 36032°F. This is a total range of 35100°F.

Answer:

-4 and -5

Step-by-step explanation:

is what i got from what i did

The parabola intersects x axis between -5 & -4 .

∴ The vertex of a parabola is located at (1.-7)

∵the parabola is symmetric  about the x = 1.

∴ The parabola intersects the axis between 6 & 7 .

            6 - 1 = 5               7 - 1 = 6

           1 - 5 = 4                 1 - 6 = 5

Therefore, the parabola intersects x axis between -5 & -4 .

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The rates of each cyclist are 17mi/h and 20mi/h

What is rate?

Rate is a ratio that compares two different quantities which have different units.

In this comparison, one unit is taken to be a standard unit in which the other is compared with.

Analysis:

Let the speeds of both cyclists be x,  x+3

distance travelled by x cyclist = 2x

distance travelled by (x+3) cyclist = 2(x+3)

Total distance = 2x + 2(x+3) = 74 miles

2x +2x +6 = 74

4x + 6 = 74

4x = 74 - 6

4x = 68

x = 68/4 = 17mi/h

The other cyclist speed is x +3 = 17 +3 = 20mi/h

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Answer:

-0.7

Step-by-step explanation:

Given x - y = 0.7

We will assign x and y random values that has a difference of 0.7

x = 1.3

y = 0.6

Using these 2 values,

y-x = 0.6-1.3

= -0.7

As you can see here , you will get a reversed value when you reverse the expression.

A total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.

We assume the number of covered pavilion tickets sold to be x and the number of lawn seat tickets sold to be y.

As a total of 1500 tickets were sold, we can form an equation:

x + y = 1500 ... (i),

as we had only those two types of tickets.

The cost of each covered pavilion ticket = $20.

Hence, the total revenue from covered pavilion tickets = $20x.

The cost of each lawn seat ticket = $10.

Hence, the total revenue from lawn seat tickets = $10y.

The total receipts were said to be $23,000.

Thus, we can represent this as an equation:

20x + 10y = 23000 ...(ii).

Combining (i) and (ii), we get a system of equations:

x + y = 1500 ... (i).

20x + 10y = 23000 ... (ii).

Dividing equation (ii) by 10, we get:

2x + y = 2300 ... (iii).

Subtracting (i) from (iii), we get:

2x + y = 2300.

 x + y = 1500.

(-)  (-)     (-)

____________

x = 800.

Substituting x = 800 in (i), we get:

x + y = 1500,

or, 800 + y = 1500,

or, y = 1500 - 800,

or, y = 700.

Thus, a total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.

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The recursive formula is mathematically given as

a_n=1266.77e^n

Generally, the equation for the decay is  mathematically given as

[tex]at=a_oe^{-\lambda t}[/tex]

Hence

a1=1400e^{-0.1 (1)}

In conclusion,

[tex]a_n=1400e^{-0.1 (n)}\\\\a_n=1266.77e^n[/tex]

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Answer:

x = 4

Step-by-step explanation:

The ages now are 5x and 7x.

The ages in 4 years are 5x + 4 and 7x + 4.

5x + 4 + 7x + 4 = 56

12x + 8 = 56

12x = 48

x = 4

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

• Given —

Age of Roony = 5x

Age of Herald = 7x

• After four years —

Age of Roony = (5x + 4)

Age of Herald = (7x + 4)

• Now, According to the question —

→ (5x + 4) + (7x + 4) = 56

→ 12x + 8 = 56

→ 12x = 56 - 8

→ 12x = 48

→ x = 4

Jane goes to the beach if and only if it is a sunny day.

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

Reason:

A regular conditional statement is in the form "If P, then Q" where P and Q are placeholders for other statements.

For example, we can replace "P" with "it rains" and replace "Q" with "the grass gets wet". This means "If P, then Q" becomes "If it rains, then the grass gets wet".

It's hopefully clear that the example above is a one way street. It points in only one direction. The act of raining leads directly to the grass being wet. However, we cannot go in reverse. If we see the grass is wet, it doesn't mean it rained. Perhaps someone turned on a hose or sprinkler system. P leads to Q, but Q does not lead to P.

In short, all of what is mentioned so far is considered a regular conditional statement. So far we haven't addressed bi-conditional statements.

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

Bi-conditional statements are conditionals that work in reverse.

An example would be "If a figure is a square, then it has 4 congruent sides and 4 right angles". That conditional statement works in reverse. Therefore "If a figure has 4 congruent sides and 4 right angles, then the figure is a square" is also true simply by what it means to be a square.

So the format "If P, then Q" can be reversed to "If Q, then P" to have an equivalently true statement. The common practice is to use "if and only if" to help shorten things.

We would have the template "P if and only if  Q" which is the same as "Q if and only if P". The order doesn't matter since we can reverse things just fine.

Often you'll find bi-conditional statements when it comes to definitions. The term "weekend" literally means the day is either Saturday or Sunday, which is why choice C is another bi-conditional. A very similar situation applies to choice D as well.

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

We've found that choices A, C and D are bi-conditional statements. They can be ruled out. We're left with choice B.

This is not a bi-conditional. Why not? It's assumed that Jane would go to the beach on a sunny day, but perhaps she enjoys the beach just fine on cloudy days. There's also the fact she could be doing other things on sunny days. The presence of the sun doesn't automatically mean the beach. If you said "It gets warm if and only if it's a sunny day", then I think this is more in line with a bi-conditional.

This is why choice B is the final answer.

Using translation concepts, the equation of the graph is:

y = |0.5x - 2.5| + 3.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The function is:

y = |0.5x - 2| + 3.

When it is shifted one unit to the right, we have that x -> x - 1, hence:

y = |0.5(x - 1) - 2| + 3

y = |0.5x - 2.5| + 3.

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