What is the
intermediate step in the form
(x + a)² = b as a result of completing
the square for the following equation?
-3x² - 35x - 189 = 13x

sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.

Given,

sin(40 + 2°) cosec(30 + 5°) = 1

To prove the trigonometry function equal to 1.

Now, According to the question:

We know that

Sin 42° = 0.66913061

Cosec 35° = 1.7434468

sin(40 + 2°) cosec(30 + 5°) = 1

sin 42° × cosec 35° = 1

Plug the values of sin and cosec in above function:

0.66913061 × 1.7434468

= 1.16659

But we take the before decimal value i.e., 1

Hence,  sin(40 + 2°) cosec(30 + 5°) = 1 we proved that by the values.

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Answer:

1st one- 4

2nd one- 1

3rd one- 5

4th one-6

5th one-3

6th one-2

Answer: 14/27

Step-by-step explanation:

Answer:29

Step-by-step explanation:

The sum of the measures of an exterior angle of a polygon is 360°.

If the given angle divides 360 evenly, then it can be a measure of an exterior angle of a polygon. If otherwise, then it cannot be.

Out of the given angles, only 50 does not divide 360 evenly. Therefore, a regular polygon cannot have an exterior angle measuring 50°. (Option B)

this is the answer to your equation hope it helps thanks

Answer:

D. [tex]\dfrac{27}{4}\\\\[/tex]

Step-by-step explanation:

[tex]\mathrm{With\;x=\dfrac{1}{8}\;and\;y = \dfrac{3}{16}\;we\;get}\\\\[/tex]

[tex]2\left(\dfrac{1}{8}+4\right)-\left(\dfrac{3}{16}\cdot 8\right)\\\\[/tex]

[tex]\mathrm{Calculate\:within\:parentheses}\:\left(\dfrac{1}{8}+4\right) = \dfrac{1}{8}+\dfrac{32}{8}} = \dfrac{33}{8}\\\\[/tex]

[tex]2\left(\dfrac{1}{8}+4\right) = 2\cdot \dfrac{33}{8} = \dfrac{33}{4}[/tex]

[tex]y \cdot 8 = \dfrac{3}{16} \cdot 8} = \dfrac{3}{2}\\\\[/tex]

So

[tex]2(x + 4) - y\cdot 8 = \dfrac{33}{4} - \dfrac{3}{2}\\\\\\= \dfrac{33-6}{4}\\\\= \dfrac{27}{4}\\\\[/tex]

Answer: Slope= -2.000

  x-intercept= -2

  y-intercept= -4.000

  Hope this helps !

Answer:

75

Step-by-step explanation:

15 + 2 × 30

Answer:

1320 seats.

Step-by-step explanation:

The given scenario can be modeled as an arithmetic series.

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

The first term is the number of seats in the front row.

Given that the number of seats in a row increases by 2 with each successive row, the common difference is 2.

The nth term is 30 since there are 30 rows in the theater.

Therefore:

Substitute the values into the arithmetic series formula and solve:

[tex]\implies S_{30}=\dfrac{1}{2}(30)[2(15)+(30-1)2][/tex]

[tex]\implies S_{30}=15[30+(29)2][/tex]

[tex]\implies S_{30}=15[30+58][/tex]

[tex]\implies S_{30}=15[88][/tex]

[tex]\implies S_{30}=1320[/tex]

Therefore, the total seating capacity of the theater is 1320 seats.

The perimeter of the triangle ABC is 36 cm. Then the correct option is A.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees. If two triangles are similar, then the ratio of the corresponding sides will remain one.

Triangle ABC is congruent to triangle XYZ. In AABC, AB = 12 cm and AC = 14 cm. In AXYZ, YZ = 10 cm and XZ = 14 cm.

AB = XY = 12 cm

BC = YZ = 10 cm

AC = XZ = 14 cm

Then the perimeter of the triangle ABC is given as,

P = 12 + 10 + 14

P = 36 cm

The perimeter of the triangle ABC is 36 cm. Then the correct option is A.

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This postulate tells us that when we put two angles side by side with a ray touching the ray of the other angle, we are creating a new angle which is the addition of the two, and whose measure is the addition of the measures of the two angles we are contacting via a common ray.

The slope of the line with the given coordinates (2,8) and (4,7.5) is -0.25.

Slope is simply expressed as change in y over the change in x.

Rise over run.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1( 2,8) )

Point 2( 4,7.5 )

To find the slope, plug the given x and y values into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 7.5 - 8 )/( 4 - 2 )

Slope m = ( -0.5 )/( 2 )

Slope m = -0.5 / 2

Slope m = -0.25

Therefore, the slope of the line is -0.25.

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The recipe for the waffles presented using rational numbers are as follows;

1. The recipe for 2 waffles is as follows;

[tex] \displaystyle \frac{3}{5} [/tex] cups of flour

[tex] \displaystyle \frac{2}{15} [/tex] teaspoon of salt

[tex] \displaystyle \frac{4}{5} [/tex] teaspoons of baking powder

[tex] \displaystyle \frac{7}{20} [/tex] Cups of milk

[tex] \displaystyle \frac{1}{15} [/tex] Cup of butter

2. The recipe for 5 waffles is as follows;

[tex] \displaystyle 1\frac{1}{2} [/tex] cups of flour

[tex] \displaystyle \frac{1}{3} [/tex] teaspoon of salt

[tex] \displaystyle 2 [/tex] teaspoons of baking powder

[tex] \displaystyle \frac{7}{8} [/tex] Cups of milk

[tex] \displaystyle \frac{1}{6} [/tex] Cup of butter

3. The recipe for 300 waffles is as follows;

900 cups of flour

200 teaspoon of salt

1200 teaspoons of baking powder

525 Cups of milk

100 Cup of butter

4. The required number of waffle irons is 50

5. It would take approximately 6 servers

It would take 34 trips

A rational number is one that can be expressed as a fraction.

From the given table, we have;

The recipe for 10 waffles includes;

3 cups of flour

[tex] \displaystyle \frac{2}{3} [/tex] teaspoon of salt

4 teaspoons of baking powder

[tex] \displaystyle 1\frac{3}{4} [/tex] Cups of milk

[tex] \displaystyle \frac{1}{3} [/tex] Cup of butter

1. To make 2 waffles, we have;

[tex] \displaystyle 2 = \frac{10}{5} [/tex]

Dividing each of the quantities required to make 10 waffles by 5 gives;

[tex] \displaystyle \frac{3}{5} [/tex] cups of flour

[tex] \displaystyle \frac{2}{3 \times 5} = \frac{2}{15} [/tex] teaspoon of salt

[tex] \displaystyle \frac{4}{5} [/tex] teaspoons of baking powder

[tex] \displaystyle \frac{1\frac{3}{4}}{5} = \frac{7}{20} [/tex] Cups of milk

[tex] \displaystyle \frac{\frac{1}{3}}{5} = \frac{1}{15} [/tex] Cup of butter

2. If each person gets 1 waffle, we have;

Number of waffles = 1 + 4 = 5

[tex] \displaystyle 5 = \frac{10}{2} [/tex]

Dividing the recipe for 10 waffles by 2 gives;

[tex] \displaystyle \frac{3}{2} = 1\frac{1}{2} [/tex] cups of flour

[tex] \displaystyle \frac{2}{3 \times 2} = \frac{1}{3} [/tex] teaspoon of salt

[tex] \displaystyle \frac{4}{2} = 2 [/tex] teaspoons of baking powder

[tex] \displaystyle \frac{1\frac{3}{4}}{2} = \frac{7}{8} [/tex] Cups of milk

[tex] \displaystyle \frac{\frac{1}{3}}{2} = \frac{1}{6} [/tex] Cup of butter

3. When each of 300 people can have one, the number of waffles is 300, which gives;

30 × 10 = 300

Multiplying the quantity of each ingredients required to make 10 waffles by 300 gives;

300× 3 = 900 cups of flour

[tex] \displaystyle 300 \times \frac{2}{3} = 200 [/tex] teaspoon of salt

300 × 4 = 1200 teaspoons of baking powder

[tex] \displaystyle 300 \times 1\frac{3}{4} = 525 [/tex] Cups of milk

[tex] \displaystyle 300 \times \frac{1}{3} = 100 [/tex] Cup of butter

4. Time it takes to cook a waffle = 10 minutes

Number of waffles required = 300

Time allowed = 1 hour = 60 minutes

The number of waffle iron is therefore;

[tex] \displaystyle {n = \frac{300 \times 10}{60} = 50} [/tex]

The number of waffle irons required is 50 waffle irons

5. Number of waffles each server can deliver = 9 waffles

The time it takes each server per trip = 10 minutes

Number of waffles to be delivered = 300

Time in which to deliver the 300 waffles = 1 hour

The number of servers is therefore;

[tex] \displaystyle {n = \frac{300}{9 \times 6} = 5. \overline 5 \approx 6} [/tex]

The number of trips is therefore;

5 servers will deliver 5×9×6 = 270

The sixth server will deliver the remaining 300 - 270 = 30 waffles in 30 ÷ 9 = 3.3 ≈ 4

The number of trips all together is therefore; 5×6 + 4 = 34 trips

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Answer:

The missing angle in Triangle A is 66 degrees

The missing angle in Triangle B is 34 degrees

Because Triangle A has measures of 34 degrees, 80 degrees, and 66 degrees

and

Triangle B has measures of 80 degrees, 66 degrees, and 34 degrees, we can conclude that THEY ARE SIMILAR TRIANGLES

Explanation:

The sum of angles in a triangle is 180 degrees.

Given that triangle A has m<1 = 34 degrees, m<2 = 80 degrees. Let the missing angle be x, then

x + 34 + 80 = 180

x + 114 = 180

Subtract 114 from both sides

x = 180 - 114

= 66 degrees

Triangle B has m<1 = 80 degrees, m<2 = 66 degreess. Let the missing angle be y, then

y + 80 + 66 = 180

y + 146 = `180

Subtract 146 from both sides

y = 180 - 146

= 34 degrees

Triangles A and B are similar, since they have similar measure of angles.

Answer:

There are 25 5's in 125.

Step-by-step explanation:

5 can go in 125 25 times.

(unless you are talking about literally-- there is one 5 in 125)

The conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree, is 0.571.

The percentage of associate's degrees is 21%.

The percentage of degrees earned by people whose race is white is 58%.

The percentage of associate's degrees out of all degrees earned by people whose race is white is 12%.

Let the probability of earning an associate's degree be P(A).

P(A) = 0.21

Let the probability of earning a degree by the people whose race is white be P(B).

P(B) = 0.58

Let the probability of earning an associate's degree by the people whose race is white be P(C).

P(C) = 0.12

P(C) = P(A∩B)

We need to find the conditional probability that a degree is earned by a person whose race is white, given that it is an associate's degree.

P(B/A) = P(A∩B)/P(A)

P(B/A) = 0.12/0.21

P(B/A) = 0.571

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Answer:

20%

Explanation:

To know the percentage, we need to identify what percentage of $50 represents $10. So, we can calculate the percentage as:

Therefore, the answer is 20%

After evaluating the expression, the value of n is √(70/2C).

So, 2nCn = 70:

Now, solve for n as follows:

Therefore, after evaluating the expression, the value of n is √(70/2C).

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The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. When the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.

Given that,

The bottom of a 25 feet ladder is propped up against a wall, which is 7 feet away. A feet per second of the ladder's bottom begins to slide away from the wall.

We have to find when the ladder is 15 feet above the ground, how many feet per second is the top of the ladder falling down the wall.

Let us take x = height where the ladder hits the building

7 squared + x squared=25 squared

49+x squared=625

x squared=576

x=24 feet

Now,

If it slips 15 feet that 24-15=9 feet

Let x = distance from wall:

x² + 9² = 25²

x² + 81= 625

x² = 544

x = 23.3 feet

Therefore, when the ladder is 15 feet above the ground, 23.3 feet per second is the top of the ladder falling down the wall.

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Solution

We have the following info:

Grades Credits

B 2

B 5

B 5

C 2

And we know that A= 4, B= 3, C=2

So we can do this:

then the weighted average is 2.86

If the function f(3) has a value of 6, then the value of f⁻¹(6) is 3

From the question, the definition of the function is given as

f(x)

Such that

The value of f(3) is 6

This is represented as

f(3) = 6

Also, the function can be represented as

y = f(x)

In f(3) = 6, we have

x = 3 and y = 6

When the inverse function is calculated, we have

f⁻¹(y) = x

This means that

f⁻¹(6) = 3

Express as an inverse function

f⁻¹(6) = 3

Hence, the inverse function f⁻¹(6) has a value of 3

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The expression for a linear equation in thee slope-intercept form is ,

y = mx + b

the slope = m= (y2-y1)/ (x2-x1)

y-intercept is (0, b)

___________________

Rearreging tha expresion

y = 3x + 4

The rate is the slope (m) = 3

__________________________

Answer

the constant, in this case, is 3

From the translation described, If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at (-4, 8). See the justification for the same below.

A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect. Angles, polygons, polyhedra, and graphs are the most typical places to find vertices. Nodes are another name for graph vertices.

The explanation of the translation is given as follows:

According to the translation rule for translating a point h units left is given as:- (x, y) → (x-h, k)

The translation rule for translating point k units up is given as:

(x,y) → (x, y+k).

Since ∆ABC is translated 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at (1, 5).

Then,

The vertex A' =

A (-1, 2) → (-1 -3, 2+6)

= (-4, 8)

Therefore, the vertex A' is at (-4,8).

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From the translation described, the vertex A' is at the point (-4,8).

A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect.

Angles, polygons, and graphs are the most typical places to locate the vertices.

The explanation of the translation will be:

Based on the translation rule for translating a point h units left is follows as

(x, y) → (x-h, k)

The translation rule for point k units up is follows as:

(x,y) → (x, y+k).

Since ∆ABC is translated to the 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at; (1, 5).

The vertex A' ;

A (-1, 2)

(-1 -3, 2+6)

= (-4, 8)

Therefore, the vertex A' is at the point (-4,8).

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The midpoints of the first and last parts are 4/5m units apart

The length of the line segment is given as

Length = m units

From the question, the number of partitions is given as

Partition = 5

So, the length of each partition is

Each partition = Length/Partition

This gives

Each partition = m/5

The midpoint of a partition is

Partition midpoint = m/5 x 1/2

Evaluate

Partition midpoint = m/10

The distance between the midpoints of the first and last segments is then calculated as

Distance = Length - 2 x Partition midpoint

So, we have

Distance = m - 2 x m/10

Evaluate

Distance = m - m/5

This gives

Distance = 4/5m

Hence, the distance is 4/5m units

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We will have that the relationship is proportional because each time he bought more sets they had the same cost, and the total cost added to the sum of the independent cost. And we have the following relationship for the 2 sets and 4 sets:

2 sets:

So, each individual set is $12.5.

4 sets:

So, each individual set is $12.5.

So, each individual set for each relationship has the same cost, therefore the relationship is proportional.

On the first line the distributive property was used. This property says that the product of a constant with a sum of two numbers is equal to the sum of the products.

On the third line the "associative" property was used. This property says that if you have the sum of three numbers the order at which you sum them doesn't affect the results.

Answer:

-20

Step-by-step explanation:

1- each of the two numbers are inside parenthesis and are beside each other which means they should be multiplied like this: -5.6 * 3.4

2- because 5.6 is negative, the rule in multiplying different signs would result to a negative number

3- and when you accurately multiply them, the answer is 19.04, and the options here are estimated so you should estimate the 19.04 too

4- 1 after it is 9 and nine is a great number, 1 turns to 2 and 9 turns into 0, which equals to 20, and DO NOT forget to add the sign, which is negative as i said previously

The mean age of customers is 27.35 years.

It is well known that age has a normal distribution with a 5-year standard deviation. Additionally, 30% of the time, customers are under the age of 30.

Mathematically,

P (age ≤ 30) = 0.70

Let μ be the mean age of the customer.

P [z ≤ (30 - μ) / σ] = 0.70

The equivalent of "age" in a conventional normal distribution is the z-score or z. It is evident from the usual normal distribution table that when z=0.53, 0.70 probability is reached.

Thus,

z = (30 - μ) / σ

⇒ 0.53 = (30 - μ) / 5

⇒ μ = 27.35

As a result, the average consumer is 27.35 years old.

The probability at each z-score in a standard normal table is represented by the associated z-score. We will look for the number 0.70 in the table, then the row value of 0.5 and the associated column value of 0.03 will be examined. They add up to 0.53 when combined.

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The Probability that Robert randomly pulls out a black sock is 1/5  .

In the question ,

it is given that

Total number of socks in sock drawer = 30 socks

number of white socks in the drawer = 16 socks

number of black socks in the drawer = 6 socks

number of red socks in the drawer = 2 socks

number of yellow socks in the drawer = 6 socks

So , the probability that he randomly pulls out a black sock = (number of black socks in the drawer) / ( total number of socks in the drawer )

= 6 / 30

= 1/5

Therefore , The Probability that Robert randomly pulls out a black sock is 1/5  .

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