Combine like terms to find the perimeter of the figure.

The value of x and BD are 29 and 62

From the diagram shown, we can see that AC and BD are diagonals of the rectangle

It is important to note that the diagonals of a rectangle are equal

Then,

AC = BD

4x - 54 =  33 + x

collect like terms

4x - x = 33 + 54

Add/ subtract like terms

3x = 87

Make 'x' the subject

x = 87/ 3

x = 29

But BD = 33 + 1x = 33 + 1(29) = 33 + 29 = 62

Thus, the value of x and BD are 29 and 62

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It is square-shaped as it is 4-straight sides with equal length, and every interior angle is right angle.

A right angle is defined as an angle in geometry and trigonometry that is exactly 90 degrees, or pi /2 radians, or one-quarter turn. The adjacent angles are right angles if a ray is positioned so that its terminus is on a line and they are equal. An interior angle is a shape's internal angle. The closed shape with sides and vertices is a polygon. All of the inner angles of a regular polygon are equal to one another. For instance, a square has interior angles that are all exactly right angles, or 90 degrees. The right angle is created when two straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.

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We have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

We are given the expression:

cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A)

We need to prove the expression.

We know that:

Cos C + Cos D = 2 cos ( C + D / 2) cos ( C - D / 2)

Using this identity, we get that:

= cos 5 A + cos A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos ( 5A + A / 2) cos ( 5A - A / 2) + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= 2 cos 3 A cos 2 A + cos 2 A = cos 2 A (1 + 2 cos 3 A)

= cos 2 A ( 2 cos 3A + 1) = cos 2 A (1 + 2 cos 3 A)

= cos 2 A (1 + 2 cos 3 A) = cos 2 A (1 + 2 cos 3 A)

LHS = RHS

Hence proved.

Therefore, we have proved the trigonometric expression cos A + cos 2 A + cos 5 A = cos 2 A (1 + 2 cos 3 A) by using C/D formula.

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The difference of depths between them, and which trench is deeper is (a) 2 km, and the Mariana Trench is deeper

What is the difference of depths between them, and which trench is deeper?

The given parameters are:

Mariana Trench = 11 km

Japan Trench = 9 km

The Mariana Trench is deeper because 11 is greater than 9

The difference between the depth is

Difference = 11 km - 9 km

Difference = 2 km

Hence, the difference of depths between them, and which trench is deeper is (a) 2 km, and the Mariana Trench is deeper

Reason:

Both have the same slope of 3/2, aka "three-halves".

The slope is the rate of change. It tells us how fast or slow a plant is growing. The larger the number, the faster the growth.

Recall that y = mx+b has,

m = slope

b = y intercept

Therefore, the slope is thee number just to the left of x.

Step-by-step explanation:

Answer:

96.8 %

Step-by-step explanation:

not to bad

Answer: 1.03(1.35x)

Step-by-step explanation:

Answer:

2.395

Step-by-step explanation:

0.57+1.825 the answer is 2.395

Answer: To graph y = x is simple, it is a line that intercepts at 0, and goes up by 1/1, or 1 (rate of change)

Step-by-step explanation:

1. For C, it's simple, it is y = -x, since the negative reciprocal slope is usually perpendicular to the original number (if not able to convert to fractions, like 1, it's just the same whole number, but a negative).

2. For the "Rotate your slope triangle 90 degrees"; seems simple, which I think you should do a reciprocal of the number, and make it a negative, for ie. 3 is a slope, when changed, it becomes -1/3. so the new slope is a negative reciprocal.

Answer:

156

Step-by-step explanation:

568-412=156

Answer:

Step-by-step explanation: 568-412=156

Using linear equations, A rental car company charges prices based on the number of days you rent the car will charge  $185 if you rent the car for 7 days.

A linear equation is an algebraic equation of the form y=mx + b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let us consider the number of days = x

The equation when number of days(x) <= 4,

⇒ $50 + $25x1 = y1

If the car is rented for more than 4 days, (x>4)

⇒ $45 + $20x2 = y2

Now, we are to calculate the rent for 7 days,

which equals,

y2 = $45 + $20x2

for x2 = 7,

y2 = $45 + $20 × 7

⇒ 45 + 140

⇒ $185

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The equation of the absolute value function is y = -|x - 3| + 6

The given parameters are

Vertex = (3, 6)

Crosses the x-axis at (-3,0) and (9,0)

An absolute value equation is represented as

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

y = a|x - 3| + 6

At (-3, 0), we have

0 = a|-3 - 3| + 6

This gives

0 = a|-6| + 6

So, we have

0 = 6a + 6

Solve for a

a = -1

Substitute a = -1 in y = a|x - 3| + 6

y = -|x - 3| + 6

Hence, the equation of the absolute value function is y = -|x - 3| + 6

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Answer:

8+2g=11

1. subtract 8 from both sides

2g=3

2. Divide both sides by 2

ANSWER: g=1.5

If a chip is randomly drawn from the bag, the probability it is not a red one is P(not red)  = 12/19.

Probability of an event A is the number of event A divided by all possible outcomes. Mathematically,

P(A) = n(A)/n(S)

where:

n(A) = number of event A

n(S) = number of all possible outcomes or sample space.

Suppose there 3 possible outcomes, A, B, and C, then:

n(S) = n(A) + n(B) + n(C)

1 = P(A) + P(B) + P(C)

The probability the outcome is not event A is equal to the probability of (B or C), or in other words,

However,

    P(B or C) =  P(B) + P(C)

It means,

     P(not A)  = 1 - P(A)

In the given problem:

Number of chips:

Blue = 3

Red = 7

Yellow = 4

Green = 5

Total chips = 3 + 7 + 4 + 5 = 19

If a chip is randomly drawn, the probability it will be a red one is:

P(red) = 7/19

Hence

P(not red) = 1 - 7/19 = 12/19

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Answer:

6x-9=2

Step-by-step explanation:

Answer: it's 75

Step-by-step explanation:

acd= 165 bcd=90 165-90=75 therefore its a 75 degree angle

Here we have the quadratic function:

f(x) = 50 + 312*t - 16t²

The quadratic term:

- 16t²

Refers to the acceleration of the cannonball, in this case, caused by the gravitational force.

The linear term:

312*t

Refers to the vertical initial velocity of the cannonball (the velocity of the cannonball when t = 0)

The constant term:

50

Refers to the the initial height of the cannonball.

Now we want to graph between the boundaries "0 n", im not sure of what do you mean with that, so I will give the graph of the function in its whole domain, which can be seen below.

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The number of wins is 68 ad losses is 26.

Let the number of losses = l

Therefore, the number of wins will be: = (2 × l) + 16 = 2l + 16

Total games = 94

Therefore we will add the equation

l + 16 + 2l = 94

3l + 16 = 94

3l = 94 - 16

3l = 78

Divide

l = 78/3

l = 26

Losses = 26

Number if wins = 2l + 16 = 2(26) + 16 = 52 + 16 = 68

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Answer:

C ≈ 31.42 in

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( r is the radius ) , then

C = 2π × 5 = 10π ≈ 31.42 in ( to 2 dec. places )

Answer:

x=3 and N is the mid-point.

Okay, so if N is the mid-point.

E D=15

E N=4 x -1

N D=4+ 2 x

6 x -3=15

Now get the 6 x by itself, so move the 3 over

So it would be: 6 x =18

So that would be 6 divided by 6 is x and then 18 divided by 6 equals 3

So, X equals 3

The quadratic equation x² - 10x + 9 = 0. = 0 by completing the square, which of the following equations is a step in the process

(x – 10)2 = 34

(x – 10)2 = 16

(x – 5)2 = 34

(x – 5)2 = 16

Given that

To find

So, according to the question

We have

We have to solve that quadratic equation by completing square method.

So, we know that

In Completing square method, we have to convert this quadratic equation in square form.

So,

                  x² - 10x + 9 = 0.

Now, by multiplying both sides by the square of the x-coefficient, we get

                  x² - 10x + 9 + (-10/2)² = 0 + (-10/2)²

                       x² - 10x + 9 + (-5)² = 0 + (-5)²

Now, simplify it

                       x² - 10x + 9 + (-5)² = 0 + (-5)²

                          x² - 10x + 9 + 5² = 0 + 5²

                          x² - 2×5×x + 5² + 9 = 0 + 5²

∵ (a - b)² = a² - 2ab + b²

∴ (x - 5)² = x² - 10x + 5²

                                   (x - 5)² + 9 = 25   [since (x² - 10x + 5² = (x - 5)²]

                                        (x - 5)²  = 25 - 9

                                         (x - 5)² = 16

Answer:

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For the given function, we have that:

The domain of a function is the set that contains all possible input values for the function. In a graph, it is given by the values of x.

In this problem, the function is defined between x = -4 and x = 4, hence the domain is [-4,4].

The zeros are the values of x for which f(x) = 0, that is, when it crosses the x-axis.

Hence, for this problem, the zero is at (0,0).

The function is positive when it is above the x-axis, and negative when it is below, hence:

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The inequality to represent the number of students who can attend the field trip on the bus will be C. s≤48 s is less than or equal to 48.

From the information, Mrs. Milleman's math class is planning to going on a field trip. The school bus which is taking them can hold at most 48 people.

Therefore, the inequality to represent the number of students who can attend the field trip on the bus will be C. s≤48 s is less than or equal to 48.

In conclusion, the correct option is C.

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Expression to represent the number of tiles that must be added = 4(n + 2) - 4

Each time a new square floor design is created, there are 8 more new tiles added. To make Designs 2 and 3, respectively, 8 and 16 more tiles were placed on Design 1 and Design 2, respectively.

Possible expressions are:

4n + 4

2(n + 2) + 2n

(n + 2)² - n²

n + n + n + n + 4

4(n + 2) - 4

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Answer:

y = -5/4 x + 4

Step-by-step explanation:

Make sure the -5/4 is beside the x. It should not look like the x is on the bottom of -5/4 alongside of the 4.

Slope-intercept form of an equation is a shortcut, fill-in-the-blank form you can use to write the equation of a line.

Slope-intercept eq:

y = mx + b

You fill in slope where the m is. And you fill in the y-intercept for the b.

In your problem they gave you the slope: m = -5/4 and the y-intercept: b=4.

Fill the m and b in with the given numbers!

y = -5/4 x + 4

Answer:

3pi

Step-by-step explanation:

all of the other ones are out of range

The conversion factors are used to multiply to 18 cm/s to get meters per minute is 60s/1m.

The conversion procedure depends on the unique circumstances and the targeted goal. A rule, a contract, technical requirements, or other norms that have been made public may control this. The precision of the initial measurement must not be increased or decreased during some unit conversions from one system to another. Soft conversion is another name for this. It doesn't need altering the way the thing being measured is physically constructed.

A hard conversion or an adaptable conversion, on the other hand, could not be perfect equivalents. In the new system, it converts the measurement to practical and usable numbers and units. Sometimes it entails rearranging the item's parts significantly or changing its size.

18 cm/s means 18 cm in 1 second.

You must change 1 second into a minute and 18 cm into meters when converting 18 cm/s into meters per minute. 18 cm = 18/100 meters.

1 second = 1/60 minutes.

18/100 meters per 1/60 minutes

18/100÷1/60 = 18/100 ×60/1

= 18 ×(60/100) meters per minute

The factor is 60s/100cm, which is equivalent to 60s/1m

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The inverse of y = 7x² - 10 is √(x+10)÷7

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effects of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One is the result when a number is multiplied by its reciprocal, or inverse.

based on the available facts;

y = 7x^2 - 10

Switch y and x.

x = 7y^2 - 10

Solve for y.

Add 10 to both sides.

x + 10 = 7y^2

Divide both sides by 7.

(x + 10)/7 = y^2

√ both sides.

√(x + 10)/7 = y

Replace y with f^-1(x)

f^-1(x) = √(x + 10)/7y = 7x^2 - 10

Switch y and x.

x = 7y^2 - 10

Solve for y.

Add 10 to both sides.

x + 10 = 7y^2

Divide both sides by 7.

(x + 10)/7 = y^2

√ both sides.

√(x + 10)/7 = y

Replace y with f^-1(x)

f^-1(x) = √(x + 10)/7

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Examples of Algebra Word problems and their expressions are;

1) What is 9 increased by a number cubed?

9 + x³

2) What is the product of the sum of a number and five and the difference of a number and 5? (x + 5) * (x - 5)

Algebraic word problems are defined as questions that require translation of sentences into equations, and after that, we now solve those equations. They usually contain a single variable that depicts an unknown quantity in a real-life scenario.

Examples of Algebra Word problems and their expressions are;

1) What is 9 increased by a number cubed?

9 + x³

2) What is the product of the sum of a number and five and the difference of a number and 5? This is expressed as;

(x + 5) * (x - 5)

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