A triangle was dilated by a scale factor of 6. if sin a° = four fifths and segment de measures 30 units, how long is segment ef? triangle def in which angle f is a right angle, angle d measures a degrees, and angle e measures b degrees segment ef = 15.5 units segment ef = 24 units segment ef = 30 units segment ef = 37.5 units

The equation of the plane passing through (0, -3,1) that is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16x - 8y + 8z = 32

We know that the equation of plane passing through point (x₁, y₁, z₁) is given by,

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0

where, A, B, and C are direction ratios

In the question,  the plane passes through point (0, -3,1)

Let (x₁, y₁, z₁)  = (0, -3,1)

Using above formula the equation of the plane will be in the form,

A(x -0) + B(y - (-3))+C(z - 1) = 0            

Ax + B(y + 3)+C(z - 1) = 0                   ..........(1)

The required plane is orthogonal to the planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7.

So, their normal to the required plane would be perpendicular to the normal of both the planes.

The normal to the required plane is a cross-product of the normals of planes.

A cross-product of the normals of planes 3x + 2y - 4z = 0 and - X+ 2y + 4z = 7 is 16i - 8j + 8k

So, the direction ratios,

A = 16, B = -8, C = 8

So equation (1) becomes,

16x - 8(y + 3) + 8(z - 1) = 0  

16x - 8y - 24 + 8z - 8 = 0

16x - 8y + 8z - 32 = 0 is the required equation of the plane

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a)

g = m / 40

g = 140 /40

g = 3.5

b)

m = 40g

m / 40 = g

The length of an arc that has a measure of 190° is equal to 9 cm.

In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the length of an arc formed by a circle is given by:

Length of an arc = 2πr × θ/360

Length of an arc = C × θ/360

Where:

Substituting the given points into the length of an arc formula, we have the following;

Length of an arc = 36 × 90/360

Length of an arc = 36 × 1/4

Length of an arc = 9 cm.

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Answer:

Step-by-step explanation:

Step 1:

Make a proportion:

10/5 = 22/x

Step 2:

Cross multiply:

10x=22*5

10x=110

Step 3:

Divide by 10 to isolate x:

x=11

Answer:

The unit price for a coffee mug is $0.55.

Step-by-step explanation:

The unit price is simply just the price per unit.

We have a 4-pack of coffee mugs that costs $2.20.

He have 4 units and the price per 4 units.

Lets evaluate the price per 1 unit.

[tex]\frac{2.20}{4} =\frac{x}{1}[/tex]

Lets solve for [tex]x[/tex].

Divide [tex]x[/tex] by 1.

[tex]x=\frac{2.20}{4}[/tex]

Divide 2.20 by 4.

[tex]x=0.55[/tex]

The expression for the amount earned in one week per hour is 18 x $10

The expression for the amount earned in four weeks is 18 x $10 x 4

An expression is when numbers or letters are connected together by a mathematical operation without an equal to sign. An example of an expression is a + 3b.

The amount earned in one week = total number of hours worked in a week x amount earned per hour

18 x $10

The amount earned in four weeks = total number of hours worked in a week x amount earned per hour x 4

18 x $10 x 4

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We can conclude that (1-sinx)(1+cscx)=cscx-sinx is a true equation.

An equation is a mathematical expression containing symbols, constants, and/or numbers that combine to create an equation that states the equality of two mathematical expressions. Equations are used to describe relationships between different quantities and can be used to model real-world phenomena. Equations can also be used to solve problems and make predictions about a system.

To verify that this equation is true, we can use algebraic manipulation. First, we need to expand the left side of the equation. We can do this by multiplying (1-sinx) by (1+cscx). This gives us the equation (1-sinx)(1+cscx) = 1+cscx-sinx-sinxcscx.
Next, we need to simplify the right side of the equation. We can do this by combining the two terms with a minus sign. This gives us cscx-sinx.
Finally, we can compare the two equations. We see that both equations are equal, so the original equation is true.
Therefore, we can conclude that (1-sinx)(1+cscx)=cscx-sinx is a true equation.

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Ty works 22 hours in weekdays and 14 hours in weekends to earn at least $600 by working a total of 36 hours in a week.

In the question, we have to find how many hours he need work on the weekends.

Let he work x hours on weekdays.

Let he work y hours on weekends.

He works total 36 hours. So the required question is:

x + y = 36..................(1)

Ty earns $14 an hour working on weekdays. If he works x hours, then he earns total 14x.

Ty earns $21 an hour working on weekends. If he works y hours, then he earns total 21x.

He earns total $600.

So the required equation is:

14x + 21y = 600..................(2)

Multiply equation 1 by 21 and subtract by equation 2

21x + 21y - (14x + 21y) = 756 - 600

Simplify

7x = 156

Divide by 7 on both side, we get

x = 22.29

x = 22

Now put the value of x in equation 1, we get

22 + y = 36

Subtract 22 on both side, we get

y = 14

Hence, he works 22 hours in weekdays and 14 hours in weekends.

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If 6x/(x²-3x) is subtracted from the sum of 3/(5x-15) and (x+3)/(x-3) , then the result is (12 - 5x)/(x - 3) .

The sum of the algebraic expressions 3/(5x-15) and (x+3)/(x-3)  are written as ; ⇒ 3/(5x-15) + (x+3)/(x-3) ;

taking 5 common from the denominator of the first term ,

we get ;

⇒ 3/5(x-3) + (x+3)/(x-3) ;

taking LCM as 5(x-3) and simplifying further ,

we have ;

⇒ 3/5(x-3) + (x+3)/(x-3) ;

⇒ [3 + 5(x+3)]/5(x-3)  ;

⇒ (5x + 18)/5(x-3)  .......equation(1)

Now 6x/(x²-3x) is subtracted from the equation(1)

⇒ (5x + 18)/5(x-3) - 6x/(x²-3x)  ;

⇒ (5x + 18)/5(x-3) - 6x/x(x-3)  ;

⇒ (5x + 18)/5(x-3) - 6/(x-3)  ;

taking LCM as as 5(x-3) and simplifying further ,

we have ;

⇒ (5x + 18 - 30)/5(x-3)  ;

⇒ (5x -12)/5(x-3)  ;

Therefore , the  final result is (5x -12)/5(x-3) .

The given question is incomplete , the complete question is

If 6x/(x²-3x) is subtracted from the sum of 3/(5x-15) and (x+3)/(x-3) .  What is the result ?

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Answer: The answer is $13.19.

Step-by-step explanation:

1- Turn the percentage into a decimal by moving the percent sign twice to the left.

2- Multiply the bill by the decimal.

3-youll get 13.185 so you'll round up to 13.19.

hope this helps!!

The expression for the cost of gasoline and oil will be C. 3.35c + 2.65g

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

In this case, it should be noted that Joe bought g gallons of gasoline and c cans ofg oil. The prices were givn as well.

The expression for the cost of gasoline and oil will be:

= 3.35 × c + (2.65 × g)

= 3.35c + 2.65g

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The future value of the investment after 10 years is $14,158.54.

The future value refers to the value of an investment whose present value is compounded at an interest rate into the future.

We can compute the future value using an online finance calculator as below.

N (# of periods) = 10 years

I/Y (Interest per year) = 4%

PV (Present Value) = $9,565

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $14,158.54

Total Interest = $4,593.54

Thus, in 10 years, the initial investment of $9,565 at 4% a year will grow to $14,158.54.

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The transformation that does not preserve congruence is translation

The term called transformation is defined as the process of changing the position of an object on an xy-plane.

Here we have know that the  transformation is applied to a figure to create a new figure.

And here we also know that the only transformation that does not preserve congruence is a translation 7 units down

So the transformation of figure and the reflection preserve the congruence since it only create a mirror image of the figure.

And the term called dilation also preserve congruence since it only enlarges the given figure.

Here we want to know that concept of translation a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Based on this definition we have conclude that the solution is translation.

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Answer:

sorry I want to help you but I can't sorry

Step-by-step explanation:

i don't know how to solve this

The answer is The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.​

What is the one-to-one function?

The one-to-one function is a special function that maps every element of the range to exactly one element of its domain i.e, the outputs never repeat. As an example, the function g(x) = x - 4 is a one-to-one function since it produces a different answer for every input.

To be a function, it has to pass the vertical line test, which means a vertical line drawn anywhere in the graph should cut the graph only once, not more.

To be a one-to-one function, it has to pass the vertical line test as well as the horizontal line test, which means that a horizontal line drawn anywhere in the graph should cut the graph only once, not more.

Of course, it passes the vertical line test, so it's a function.

Does it pass the horizontal line test? NO! As shown in the attached picture, the blue line (horizontal line) cuts the graph at 3 places.

We, therefore eliminate choices A and B.

We can eliminate choice C because nowhere is it requires a function to pass through the origin for it to be one-to-one.

Hence, the answer is The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.​

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Answer:

D for Edge

Step-by-step explanation:

y

Pentagon, irregular polygon and convex polygon are the names that apply to the given form.

A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.

A pentagon is a polygon with five sides, and if these sides are uneven, it is an irregular pentagon, also known as an irregular polygon.

A convex polygon is one with all of its internal angles smaller than 180°.

As a result, the terms for the given form are pentagon, irregular polygon, and convex polygon.

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The question seems incomplete, the missing figure has been attached below

Answer:

36

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. A geometric sequence is a sequence of numbers in which any two consecutive terms have a constant ratio.

Given that 8, 2x, 2y is an arithmetic sequence, we know that:

2x - 8 = 2y - 2x

x = y

Given that 2x, 2y, 36 is a geometric sequence, we know that:

(2y)/(2x) = 36/2y

y^2 = 36x

Now, we can use the first equation to substitute for y in the second equation, and get:

x^2 = 36x

x^2 - 36x = 0

x(x-36) = 0

So x = 0 or x = 36

However, x cannot be equal to zero because in that case the second term of the arithmetic sequence will be zero, and it will not be a valid solution. Therefore, x = 36.

So, y = x = 36.

Therefore, the values of x and y are 36.

The angular speed is 8 rad/s and the angular position of point A  will be 8m/s².

The angular speed of the wheel at t=2s can be calculated using the equation ω=αt, where ω is the angular speed, α is the angular acceleration and t is the time. Substituting the given values, we get ω = 4 (2) = 8 rad/s.

The angular position of point A at t=2s can be calculated using the equation

θ = ωt + (1/2)αt².

Substituting the given values, we get

θ = 8 (2) + (1/2) (4) (2²) = 24 rad.

The total acceleration of point A at t=2s can be calculated using the equation a = rα, where a is the total acceleration, r is the radius of the wheel and α is the angular acceleration. Substituting the given values, we get a = 2 (4) = 8 m/s²

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Answer:

Step-by-step explanation: Hello! You know that there are 3 students who scored 55, 4 students who scored 60, 8 students who scored 65, 4 students who scored 70, 4 students who scored 75, 1 student who scored 80, 9 students who scored 85, and 5 students who scored 90.  To find the mean of a set of values, here is the formula:

a + b + c + d + e . . .

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

           2

Each variable should represent the score of a single student, so write each score for each individual student.

(55 + 55 + 55 + 60 + 60 + 60 + 60 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 65 + 70 + 70 + 70 + 70 + 75 + 75 + 75 + 75 + 80 + 85 + 85 + 85 + 85 + 85 + 85 + 85 + 85 + 85 + 90 + 90 + 90 + 90 + 90)/2

You could divide all of this by 2 or you could multiply the values and then add them:

((55 x 3) + (60 x 4) + (65 x 8) + (70 x 4) + (75 x 4) + 80 + (85 x 9) + (90 x 4))/2

Either way works, but the second way is probably faster.

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

How to find the answer:

55 x 3 = 165
60 x 4 = 240
65 x 8 = 520
70 x 4 = 280
80 = 80
85 x 9 = 765
90 x 4 = 360

Substitute this into the equation

(165 + 240 + 520 + 280 + 80 + 765 + 360)/2

(405 + 800 + 845 + 360)/2

(1205 + 1205)/2

2410/2

= 1205

The answer is 1205

This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.

An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.

The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation x2 - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.

The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation x2 - 6x + 5 = 0 being x = 1 and x = 5.

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The frequency table is given below.

The probability that a person chosen is a left-handed female is 31/140.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total number of employees = 140

Male:

Number of male = 65

Right-handed.

= Total number of right-handed - Female right handed

90 - 44 = 46

Left-handed.

= 65 - 46

= 19

Female:

Number of females.

= Total employees - Number of males

= 140 - 65

= 75

Right-handed.

= 75 - 31

= 44

Left-handed.

= 31

Now,

The frequency table.

                                            RH = 46

                                            LH = 19

           Male = 65    

140

          Female = 75  

                                             RH = 44

                                              LH = 31

Now,

The probability that a person is a left-handed female.

= Number of left-handed females / Total number of employees

31/140

Thus,

The frequency table is given above.

The probability that a person is a left-handed female is 31/140.

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Step-by-step explanation:

11.47 + 9.02

= 20.49 ...

[its takes so much time to solve and write here so plzzz =》]

Answer: 5R

Step-by-step explanation:

Half a dozen =6 pieces

R30/6=5R

How much is one dozen?

One dozen is equal to 12, so one half of a dozen is 6.

If 6 candles are priced at R30, we can divide R30 by 6 to get the cost of 1 candle.

30 ÷ 6 = 5.

Therefore, each candle costs R5.

The simplified algebraic expression for this problem is given as follows:

5x + 2y + 11.

The algebraic expression for this problem is defined as follows:

9x + 2y + 3 - 4x + 8.

To simplify the expression, we combine the like terms, which are the terms that have the same unknown variable, hence:

Hence the simplified algebraic expression for this problem is given as follows:

5x + 2y + 11.

Meaning that the third option is the correct option.

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Answer: To find the average of daily income of the week, we need to find the total income of the week and divide it by the number of days in the week.

We know that the average daily income of the week is Rs 1,300 and we know that he earned Rs 2,000 on Saturday. To find the total income for the week, we can add the Saturday income to the average daily income for the 6 days.

Therefore, the total income for the week = Rs 1,300 (average daily income) x 6 (days) + Rs 2,000 (Saturday income) = Rs 7,800 + Rs 2,000 = Rs 9,800

To find the average daily income for the week, we divide the total income by the number of days in the week (7)

Average daily income = Rs 9,800 / 7 = Rs 1,400

Therefore, the average daily income of the plumber for the week is Rs 1,400.

Step-by-step explanation:

Answer:

8 cups of flour

Step-by-step explanation:

If you want an equation it will be:

[tex]\frac{2}{8} * \frac{32}{1} = \frac{64}{8} = 8[/tex]

So Francessa used 8 cups of flour