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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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Applying the trapezoid midsegment theorem, the diameter of the bottom layer of the cake = KS = 26 inches.

The diameter of any circular shape is the length of the line segment that divides the shape into two equal halves and runs through its center.

The trapezoid midsegment theorem states that the length of the midsegment of a trapezoid that is parallel to its bases is equal to half of the sum of the bases.

Using the trapezoid midsegment theorem we have:

MQ = 1/2(NP + LR)

Substitute

MQ = 1/2(8 + 20)

MQ = 1/2(28)

MQ = 14 inches

Also, we would also have:

LR = 1/2(MQ + KS) [trapezoid midsegment theorem]

Substitute

20 = 1/2(14 + KS)

40 = 14 + KS

40 - 14 = KS

26 = KS

KS = 26

The diameter = KS = 26 inches.

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The diameter(KS) of the cake's bottom layer is calculated using the trapezoid midsegment theorem is 26 inches.

The diameter of a circle is equal to the length of the line segment running through its center and dividing it into two equal halves.

According to the trapezoid midsegment theorem the length of a trapezoid's midsegment that is parallel to its bases is equal to half of the sum of the bases.

MQ = 1/2(NP + LR)

MQ = 1/2(8 + 20)

MQ = 1/2(28)

MQ = 14 inches.

And,

LR = 1/2(MQ + KS).

20 = 1/2(14 + KS)

40 = 14 + KS

40 - 14 = KS

26 = KS

KS = 26

The diameter(KS) is 26 inches.

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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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Answer:

x = -5/2

Step-by-step explanation:

-15/2 = 3x

multiply both sides by 2:

2(-15/2) = 2(3x)

-15 = 6x

divide both sides by 6:

-15/6 = 6x/6

x = -15/6

this can be reduced to:

x = -5/2

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.

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:

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 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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Answer: Slope= -2.000

  x-intercept= -2

  y-intercept= -4.000

  Hope this helps !

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)

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.

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: -1 17/20

Step-by-step explanation: use order of operations to solve, parenthesis, multiplication, addition/subtraction

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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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%

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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Answer: 14/27

Step-by-step explanation:

Answer:29

Step-by-step explanation:

The value of x according to the complete task content as given is; 5.

It follows from the complete task content that a right angled triangle is given(in which case one of the angles is a right angle = 90°).

Hence, the required value of x can be determined from the; sum of interior angles of a triangle as follows;

90° + 54° + 7x + 1° = 180°

7x = 180° - 90° - 54° - 1°

Evaluate the right side of the equation;

7x = 35°

Divide both sides by; 7;

x = 35°/7

x = 5.

Ultimately, the value of x according to the task content is; 5.

Remark:

The completed task content is; The measures of the angles of a triangle are shown in the figure below. Solve for x. The figure is a right triangle with the other two interior angles 54° and (7x + 1)°.

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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)

Answer:

Step-by-step explanation:

Comment and Answer

√5^x

The square root is really 0.5 as a decimal or 1/2 as a fraction. Both are powers.

So the square root of 23 can be written as 23^.5

For your question, you divide the power (x) by 2 so it looks like this.

5^(x/2)

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

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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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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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.

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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Answer:

[tex]\dfrac{3}{2\cos\theta - r\sin\theta}[/tex]

Step-by-step explanation:

The polar coordinate system uses two parameters r and θ where r is the magnitude of the radius of the circle in polar form(also known as the radial coordinate) and θ  the angle which the which the radius makes relative to the x=axis

The following equations are used to convert from cartesian coordinate to polar coordinates

[tex]r = \sqrt{x^2 + y^2}\\\\\\x = r\cos\theta\\\\y= r\sin\theta\\\\[/tex]

Substituting for x and y in terms of r and θ into the equation 2x - 3y = 3 gives

[tex]2x - y = 3\\\\2r\cos\theta - r\sin\theta = 3\\\\r(2\cos\theta - r\sin\theta = 3\\\\r = \dfrac{3}{2\cos\theta - r\sin\theta}[/tex]

Let:

Oc = original cost = $17

Sp = Sale price

D = Discount percent = 12% = 12/100 = 0.12

The sale price will be:

The sale price is $14.96

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

In the pair of given angles, the value of 2x and x is 52° and 26°.

So, the value of 2x and x:

Now, solve for x and 2x as follows:

Therefore, in the pair of given angles, the value of 2x and x is 52° and 26°.

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