graph the equation y= 2/3x+5

The dilation scaling factor that would map ΔABC to ΔADE is \(k = \dfrac{5}{3}\)

A dilation transformation is one in which the size of the object enlarged or reduced by a scale factor.

Possible parts of the question obtained from a similar question, found online are;

Triangle ΔABC is similar to triangle ΔADE

ΔABC ~ ΔADE

The triangle ΔABC is inscribed in the triangle ΔADE, such that the vertex B is located on the side AD and the vertex C is located on the side AE

The similar relationship between the two triangles indicates that the ratio of the corresponding sides on each triangles have the same values, therefore;

\(\dfrac{AD}{AE}\) = The ratio of the corresponding sides on the triangle ΔABC

\(\dfrac{AD}{AE} = \dfrac{12+8}{18+12} = \dfrac{2}{3} = \dfrac{12}{18} = \dfrac{AB}{AC}\)

Therefore, the corresponding side to AD is AB, and the corresponding side to AE is AC

The scale factor, k, that maps ΔABC to ΔADE, produce the length of AD from AB, or AE from AC as follows;

AD = k × AB

20 = k × 12

Therefore; \(k = \dfrac{20}{12} = \dfrac{5}{3}\)

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Answer:

Let's first convert the time taken to cover the distance at 45 km/h into minutes:

3 hours and 20 minutes = 3 x 60 + 20 = 200 minutes

The distance covered by the bus at 45 km/h is:

distance = speed x time

distance = 45 km/h x 200 minutes

distance = 9000/60 km

distance = 150 km

Now, let's use the distance and the new speed of 36 km/h to calculate the time it would take to cover the same distance:

distance = speed x time

150 km = 36 km/h x time

time = distance / speed

time = 150 km / 36 km/h

time = 4.1667 hours or 4 hours and 10 minutes (rounded to the nearest minute)

Therefore, it would take approximately 4 hours and 10 minutes to cover the same distance at a speed of 36 km/h.

The given conditions to write an equation for the line passing through (−9,2) and parallel to the line whose equation is y = −3x+ 2.

There are many different methods to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically include one or more variables.

More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

\($$We have the equation of a parallel line and a point which it passes through. To write the equation of the line in point-slope form, we will use the following formula:y−y1=m(x−x1)We know that the slope of parallel lines are same and we are given the equation for parallel line, y=−3x+2$$\)

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If q² – 4pr > 0, the roots of the quadratic equation px² + qx + r = 0 will be: "negative, if p, q, and r are positive". Therefore, Suman answered correctly.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.

Generally speaking, the standard form of a quadratic function is given by ax² + bx + c = 0.

Assuming the roots of the quadratic function are a and b. Therefore, the sum of the roots of the quadratic function would be equal to -q/p;

a + b = -q/p

ab = r/p

This ultimately implies that, the nature of the roots would depend on the value of p, q and r, which make Zain's answer to be wrong.

Additionally, if p, q, and r are positive, a + b would be negative, and one or both roots must be negative, which make Vipul's to be wrong.

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Answer:

The first choice AB congruent to DE

Step-by-step explanation:

we already know that the other sides are congruent by looking at the dashes on the side, but there is no indicatation that that Side AB and side DE are congruent

Given :

A system of equations y = 5.69x + 25 and y = 9.49x + 6.

To Find :

The solution of the system of equation.

Solution :

Subtracting equation 2 by 1, we get :

y - y = ( 9.49x + 6 ) - ( 5.69x + 25 )

0 = 3.8x - 19

x = 5

Putting value of x in equation 1, we get :

y = (5.69×5) + 25

y = 53.45

Therefore, the solution of the system of equations is ( 5, 53.45 ).

Answer:B.Sample space

Step-by-step explanation:

Answer:

(2;-5) and (0;-4).

Step-by-step explanation:

if the given graph is the same as in the attached picture (y=-0.5x-4), then two points only belong to it.

The measure of the base of the triangle is 10 millimetres

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

Area of the triangle = 80 square millimetres

Height of the triangle = 16 millimetres

Using the above as a guide, we have the following:

The base of the triangle = 2 * Area/Height

Substitute the known values in the above equation, so, we have the following representation

The base of the triangle = 2 * 80/16

Evaluate

The base of the triangle = 10

Hence, the base is 10 millimetres

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Complete question

The area of the triangle is 80 square millimeters and the height of the triangle is 16 millimetres.

Calculate the length of the base

Answer:

$55.20 is Mrs. Barker hourly overtime rate.

Step-by-step explanation:

The term "time and a half" in your question means that Mrs. Baker's overtime rate is 1.5 times her usual hourly rate.

So, ----> $36.80 times 1.5 = $55.20

Answer:

35

Step-by-step explanation:

Law of cosines

c^2=a^2+b^2-2ab(cos(A))

14^2=11^2+8^2-2(11)(8)Cos(A)

A=93.5833

Law of Sines

Sin(A)/a=Sin(B)/a

Sin(93.5833)/11=Sin(B)/8

B=34.7719

The sum of 5x and x as given in the question is 6x

Given the following expression

5x + x

We are to take the sum and this is given as:

5x + x  = (x+x+x+x+x) + x

5x + x = 6x

Hence the sum of 5x and x as given in the question is 6x

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The probability of either A or B occurring is 0.5. The probability that neither A nor B will happen is also 0.5.

It is given that events A and B are mutually exclusive, meaning there is no intersection that is they are independent events. In simple terms, A and B are occurring at different times.

P(A or B) = P(A) + P(B) = 0.30 + 0.20 = 0.50

So the probability of either A or B occurring is 0.5.

Also, the total probability of the event is 1.

So to find the Probability of (neither A nor B):

P complement = 1 - P(A or B) = 1 - 0.50 = 0.50

So a,=0.5 and b,= 0.5

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Answer:

a_n = 5n, for n ≥ 1

Step-by-step explanation:

a_1 = 5

a_2 = 10 = 5 + 5 = a_1 + 5

a_3 = a_2 + 5

a_n = a_(n - 1) + 5

a_n = 5n

The dressmaker can cut 30 pieces of 12-inch long ribbon from 10 of these rolls of ribbon.

A dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 3 feet in length.

We are to determine how many 12-inch pieces the dressmaker can cut from 10 of these rolls of ribbon.

To do this, we need to find out the number of 12-inch pieces in 3 feet of ribbon and multiply that number by 10 (since we have 10 rolls of ribbon).

Let's begin by converting 3 feet into inches as follows;1 foot = 12 inches

Therefore,

3 feet = 3 × 12 inches

= 36 inches

From the above, we know that the dressmaker has 36 inches of ribbon to cut into 12-inch pieces.

Thus, the number of 12-inch pieces that can be cut from 36 inches of ribbon is given by dividing 36 by 12 as follows;

Number of 12-inch pieces = 36 ÷ 12

= 3 pieces

Therefore, from one roll of ribbon, the dressmaker can cut 3 pieces of 12-inch long ribbon

From 10 rolls of ribbon, the number of 12-inch pieces that can be cut is 10 × 3 = 30 pieces.

Hence, the dressmaker can cut 30 pieces of 12-inch long ribbon from 10 of these rolls of ribbon.

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Answer:

B

Step-by-step explanation:

We have to use the domain to see how much the line streches across the y axis

Answer:

c

Step-by-step explanation:

prime number is a natural number if it is greater than 1 and is not evenly divisible by any other numbers excepting 1 and itself.

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Answer:

1/2, 45, -2

Step-by-step explanation:

The approximate lateral area of the cylinder with a radius of 9 centimeters and height of 12 centimeters is 339 cm².

The lateral area of a cylinder is given by the formula

                                         A = 2πrh

where r is the radius and h is the height of the cylinder.

Plugging in the given values, we have

                              A = 2 × 3.14 × 9 × 12 = 678 cm²

However, the question asks for the answer rounded to the nearest whole number. Since 678 is closer to 680 than to 670, we round the value to 680 cm².

Therefore, the approximate lateral area of the cylinder is 680 cm².

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Given the provided coordinates of the points, The shape that is formed is a parallelogram because the slopes of the opposite sides are same.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

slope between (1,1) and (4,4),

m1 = 4-1/4-1 =3/3 =1

slope between (4,-2) and (7,1),

m2= 1+2/7-4 = 3/3 =1

m1=m2

similarly, slope between (1,1) and (4,-2),

m3= -2-1/4-1 = -3/3 =-1

slope between (7,1) and (4,4)

m4= 1-4/7-4 = -3/3 =-1

m3=m4

So, slopes of opposite sides are same that means they are parallel, The shape is parallelogram.

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It is false to say that the stack may be compared to a bank line, where the first person in line gets served.

A linear data structure resembles a stack and a queue in that it follows a specific sequence for the actions required to store data. First In First Out is the sequence (FIFO). A line of individuals waiting to get something in a sequential order that begins at the front of the line is what one may see as a queue. It is an ordered list where deletions are made from the front and insertions are made from the rear end, which is known as the list's end.

Any line of customers waiting to use a resource where the person in line who arrived first is serviced first is an excellent illustration of a queue. Stacks and queues differ from one another in terms of removal. In a stack, the most recent item added is removed; in a queue, the most recent item added is removed.

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Answer:

x < 2

Step-by-step explanation:

If 2x + 3 is less than 7, then 2x alone must be less than 4.

2x + 3 < 7

2x < 4

If 2x is less than 4, then x must be less than 2.

2x < 4

x < 2

Answer:

x<2

Step-by-step explanation:

2x+3<7

Subtract 3 from both sides:

2x<4

Divide both sides by 2:

x<2

Answer:

Step-by-step explanation:

2 cos(A+45)cos (B-45)

=2[cos A cos 45-sin A sin 45][cos B cos 45+sin B sin 45]

=2[cos A ×1/√2-sin A ×1/√2][cos B×1/√2+sin B×1/√2]

=2[1/√2(cos A-sin A)][1/√2(cos B-sin B]

=2×1/√2×1/√2 (cos A-sin A)(cos B+sin B)

=cosA cos B+cos A sin B-sin A cos B-sin A sin B

=cos A cos B-sin A sin B-(sin A cos B-cos A sin B)

=cos (A+B)-sin (A-B)

i think there should be A in place of B.

then

=cos (A+A)-sin (A-A)

=cos 2A-sin 0

=cos 2A

as sin 0=0

Answer:

6 kg/m

Step-by-step explanation:

mass m = 3x^2.

rho ρ= dm/dx =6x

ρ(1) =6 Kg/m

linear density is the derivative of mass (m)  with respect to position(x)

that is how fast is the mass changing at that position.

The probability that the number of answers represented by X = 2, which Cassey correctly guesses in the last 10 questions is the fraction 1/5 or 0.2.

Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.

The total possible event is the last 10 questions cassey will guess on

The required outcome is two correct guesses from the last 10 questions, given that;

X = the number of answers Casey correctly guesses in the last 10 questions

and X = 2

so;

probability of (X = 2) = 2/10

probability of (X = 2) = 1/5 {reducing fraction to its lowest term}

Therefore, the probability of X = 2 is the fraction 1/5 or 0.2 in decimal form.

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Answer:

3 and 7/8 gallons remaining

Step-by-step explanation:

You did not give the container options, but hopefully this will help

a) 7 examples are:

\(2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z\)

b) Fabric Larry will have left after using \(2\frac{2}{3}\) yard out of \(5\frac{5}{6}\) yard to make a bag for his computer is: \(3\frac{3}{6} yard\)

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

7 examples of mathematical expression are:

\(2x + 3y\\(4a - 5b) / 2c\\(5 + 8) * 3\\8^2 - 6\\√(64)\\(1/3) * π * r^2\\2(3x + 4y) - 5z\)

For the second part of the question:

Larry had 5 3/6 yards of fabric. He used 2 2/3 yards to make a bag for his computer. Write an expression that will show how much of the fabric Larry will have left.

The mathematical expression that represents the amount of fabric Larry has left is:

5 3/6 - 2 2/3 = 2 7/18

You can simplify this further:

2 7/18 = 2 1/6

The amount of fabric Larry will have left is 2 1/6 yards.

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Answer:14/29

Step-by-step explanation:

There are 14 even numbers and there are 29 numbers.

So it would equal 14/29