Simplify the expression by first substituting values from the table of exact values and then simplifying the resulting expression. Answer exactly.

(sin60∘+cos60∘)^2=

Answer30,082:

Step-by-step explanation:

The inequality relation  -q > -7  can be represented in the form of q as q < 7

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be A

The value of A is - q > - 7

Now , multiplying by (-1) on both sides of the equation , we get

( -1 ) ( -q ) > ( -1 ) ( - 7 )

The inequality relation will change the sign from > to < and ,

q < 7

So , the value of the inequality relation A is q < 7

Now , all the values in the number line which satisfy the inequality equation q < 7 are given in set A

The numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

Hence , The inequality relation  -q > -7  can be represented in the form of q as q < 7 and numbers in set A = { -8 , -7.1 , -7 , -6.9 , -6 , -2 , 0 , 2 , 6 , 6.9 }

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Answer:

The answer is

Step-by-step explanation:

From the above question the prism in the picture is a cube since all it's sides are equal

So the formula for finding the volume of a cube is

V = l³

where l is the length of one side

From the question l = 12″

Volume of the prism = 12³

= 1728″

Hope this helps you

Elise's number is 38.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

If you subtract 17 from my number and multiply the difference by negative 6​, the result is negative 126​.

let the number be x

So, the equation can be

-6(x- 17) = -126

Now, solving for x

Divide by -6

x-17= 21

Add 17 both side

x- 17+ 17 = 21 + 17

x= 38

Hence, Elise's number is 38.

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Answer:

y=3(x-2)^2-12

please let me know if its right.

The probability that the card is BLUE OR has an ODD number is 7/9

What is probability?

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

Given that, A deck of cards had RED cards numbered 1,2,3, BLUE cards numbered 1,2,3,4, and GREEN cards numbered 1,2.

The probability that the card is BLUE OR has an ODD number is

Favourable outcomes = 7

(RED - 1,3

BLUE - 1,2,3,4

GREEN - 1)

Total possible outcomes = 9

The required probability = favorable outcomes/total possible outcomes

= 7/9

Therefore, The probability that the card is BLUE OR has an ODD number is 7/9

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Answer:

12

Step-by-step explanation:

proportions

Answer:

Step-by-step explanation:

∠6 = 45     {Vertically opposite angles are equal}

∠6 + 5x + 35 = 180  {Co interior angles}

45 + 5x + 35 = 180  {add like terms}

80 + 5x = 180

5x = 180 - 80

5x = 100

x = 100/5

x = 20

5x + 35 =  5*20 + 35 = 100 + 35 = 135

∠8 = 5x + 35   { Corresponding angles}

3) ∠8 = 135

4) ∠ 3 = ∠6    {Alternate interior angles are equal}

∠3 = 45

5) ∠6 = 45

Answer:

10.5

Step-by-step explanation:

225÷21.50

=10.46511

=10.5(3sf)

The percentage is 50%

From the question we are told that  

The  mean is μ= 14 hours

The  standard deviation is σ=1 hour

Generally on the normal distribution curve the mean divides the curve into  two. with the half to the left of the mean (50% to the left )representing the percentage of the batteries that will last less than 14 hours and  the area under the curve to the right (50% to the right)representing the percentage of batteries that will last longer than mean (14 hours )

Hence the percentage of the cell phone batteries that will be expected to last longer than 14 hours is 50%

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Answer:

m∠B=63 degrees

AC≈23.6 units

AB≈26.4 units

Step-by-step explanation:

since the measures of ∠A and ∠C are given, we add 90 (∠C) to 27 (∠A) and x (∠B) which equals 180 by triangle angle sum theorem.

after isolating the variable, m∠B=63 degrees

we then use law of sin to find AC and AB

since \(\frac{sin(A)}{a}\) is already given, use that to find both AC and AB

the equation for AC would be: \(\frac{sin(27)}{12} =\frac{sin(63)}{AC}\)

the equation for AB would be: \(\frac{win(27)}{12} =\frac{sin(90)}{AB}\)

after isolating the variables, AC≈23.6 units and AB≈26.4 units

Answer:

670,000

Step-by-step explanation:

Answer:

670,000

Step-by-step explanation:

674,312 rounded to the nearest ten thousand is 670,000

Answer:

The square root of -1 is i

Step-by-step explanation:
"i" is the imaginary unit and represents the value of sqrt -1

Answer:

(Mostly) C. Or D

Step-by-step explanation:

Because you first have to factor out the equation by factoring the x . The this will leave you with the terms. Hopefully This Helps.

\(4 + 20 = 8d \\ \\ 8d = 24 \\ \\ d = \frac{24}{8} \\ \\ d = 3.\)

The value of d is 3 .

The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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The expression |-4| has a value of 4 when evaluated

From the question, we have the following parameters that can be used in our computation:

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

lower right

Step-by-step explanation:

The length of the third side is 14.4 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We find the third side of a triangle by using Pythagoras theorem.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

8²+12²=x²

64+144=x²

208=x²

Take square root on both sides

x=14.4

Hence, the length of the third side is 14.4 units.

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answer

symbolic materials ?

Answer:

14.28%

Step-by-step explanation:

Given that,

You can get a pair of shoes that normally cost $84 for only $72.

We need to find the discount percentage. So, it can be calculated as follows :

\(\%=\dfrac{84-72}{84}\times 100\\\\\%=14.28\%\)

So, the required percentage is 14.28%.

Answer:

44%

Step-by-step explanation:

40/90 when put into a decimal is 0.4 repeating. Rounding that, it is 0.44, or 44%

Answer:

D

Step-by-step explanation:

this answer is correct , i think if you think of it in logically

Step-by-step explanation:

It's easier to graph when both equations are in its slope-intercept form, y = mx + b.

-2x -10y = 10

-2x + 2x - 10y = 2x + 10

-10y = 2x + 10

-10y/-10 = (2x + 10)/-10

y = -1/5x -1  [slope: -1/5, y-intercept (0, -1)]

-3x -15y = 15

-3x + 3x - 15y = 15

-15y = 3x + 15

-15y/-15 = (3x + 15)/-15

y = -1/5x - 1  [slope: -1/5,  y-intercept (0, -1)]

To graph this system, plot the y-intercept, (0, -1) on the graph, then use the slope, m = -1/5 (down 1 unit, run 5 units to the right). Repeat the process until you have enough points to connect and create a line.  

Because the given systems of linear equations are equivalent, their lines coincide on top of each other. This means that they have infinitely many points of intersection. Hence, they have infinite solutions.

8x + 6y = 24

6y = -8x + 24

6y/6 = (-8x + 24)/6

y = -4/3x + 4 [slope: -4/3, y-intercept (0, 4)]

4x + 3y = 9

3y = -4x + 9

3y/3 = (-4x + 9)/3

y = -4/3x + 3 [slope: -4/3, y-intercept (0, 3)]

Use the same techniques as described in the first part. Plot the y-intercepts on the graph, then use the slope of each equation to plot other points.

These lines are parallel, which implies that they will never intersect each other. Hence, there's no solution to this system.  

Attached are the screenshots of the graphed systems of linear equations.

Answer:

The area of the garden is

797

f

t

2

.

Explanation:

First, let's find the area of the rectangle.

We know that the area of a rectangle is the length times width, or

20

⋅

32

in this example:

20

⋅

32

=

640

So the area of the rectangle is

640

f

t

2

.

You may not know the area of a semicircle, but that's fine

−

we know the area of a circle, or

π

r

2

.

Since the area of a semicircle is half the area of a circle, we just do the area of the circle divided by

2

:

So the area of a semicircle is

π

r

2

2

.

The question asks for

π

to just be

3.14

, so instead the equation is

A

=

3.14

r

2

2

The picture gives the diameter of the circle.

To find the radius, or

r

, we divide the diameter by

2

:

20

2

=

10

Now we can solve for the area of the semicircle:

3.14

(

10

)

2

2

3.14

(

100

)

2

314

2

157

f

t

2

Now that we now the areas of the rectangle and semicircle, we can add them up to find the area of the rose garden:

640

+

157

=

797

f

t

2

Answer:

  a. $16.90

  b. 23.5%

Step-by-step explanation:

a. After the two discounts, the original price is multiplied by ...

  (1 -10%)(1 -15%) = 0.90×0.85 = 0.765

Then the original price is found from ...

  $12.93 = 0.765 × original price

  original price = $12.93 / 0.765 ≈ $16.90

__

b. The effective discount from the original price is ...

  1 -0.765 = 0.235 = 23.5%