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Answer:This is 69

Step by step explanation:67 +2 is 69

After a dilation with a scale factor of 2.5 and center of dilation (0, 0), the coordinates of the vertices of triangle A'B'C' are A' (-5, -2.5), B' (2.5, 5), and C' (5, -10).

Dilation simply refers to a type of transformation which changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

A scale factor can be defined as the ratio of two (2) corresponding length of sides or diameter in two similar geometric figures such as triangles.

For the given coordinates, the dilation with a scale factor of 2.5 and center of dilation (0, 0) should be calculated as follows:

Point A (-2, -1) → Point A' (-2 × 2.5, -1 × 2.5) = Point A' (-5, -2.5).

Point B (1, 2) → Point B' (1 × 2.5, 2 × 2.5) = Point B' (2.5, 5).

Point C (2, -4) → Point C' (2 × 2.5, -4 × 2.5) = Point C' (5, -10).

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Answer:

a

Step-by-step explanation:

Vertical angles are congruent, so:

[tex]7x+7=112 \\ \\ 7x=105 \\ \\ x=15[/tex]

Using linear pairs,

[tex]112+4y=180 \\ \\ 4y=68 \\ \\ y=17[/tex]

The average rate of change between the given points (3, 9) and (5, 15) is: 3.

To find the average rate of change between two points on a coordinate plane, the formula below is used:

Average rate of change = change of y over the change of x = (y2 - y1)/(x2 - x1).

Given the following points on a coordinate plane:

(3, 9)

(5, 15)

Let:

(3, 9) be represented as (x1, y1)

(5, 15) be represented as (x2, y2)

Substitute the values into the average rate of change formula:

Average rate of change = (15 - 9)/(5 - 3)

Average rate of change = 6/2

Average rate of change = 3

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If your train travels at 65 miles per hour for 3.5 hours, it go 227.5 miles.

What is Speed ?

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector, whereas speed is a scalar value.

Given:

Speed S = 65 miles per hour

Time T = 3.5 hours

We know that,

S= D/T  Where D is the distance traveled.

Therefore,

65 miles per hour = D/ 3.5 hours

D = 65 x 3.5 miles

=227.5 miles

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Answer:

Step-by-step explanation:

it's below

Answer:

(1, - 2 )

Step-by-step explanation:

7x - 3y = 13 → (1)

9x + 10y = - 11 → (2)

multiplying (1) by 10 and (2) by 3 and adding will eliminate y

70x - 30y = 130 → (3)

27x + 30y = - 33 → (4)

add (3) and (4) term by term to eliminate y

97x + 0 = 97

97x = 97 ( divide both sides by 97 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (2)

9(1) + 10y = - 11

9 + 10y = - 11 ( subtract 9 from both sides )

10y = - 20 ( divide both sides by 10 )

y = - 2

solution is (1, - 2 )

Answer: The first option (0,-3)

Answer:

(5,0)

Step-by-step explanation:

Let y=0. Then, x=5.

Lucy's gross pay per week is $393.75.

Lance's tax payment amount is $10983.

Lance's net pay is $41,317.

Lance's every paycheck of two will be around $2179 per month.

1) Lucy earns $15.75 per hour.

Last week she worked 25 hours.

Solution:

Lucy's gross pay per week is $15.75 * 25 hours.

Lucy's gross pay per week = 15.75 * 25  =  $393.75

2) Lance has a yearly salary of $52,300

He pays 21% as taxes.

Solution:

a) Lance tax pay amount = 21/100*52,300 = $10983

b) Lance's net pay =  $52,300 - $10983 =  $41,317

c) Per month salary = $52,300/12 =  $4358

Each paycheck will be 4358/2 = $2179

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Answer:

x = - 90

Step-by-step explanation:

1 = 0.4x - 0.8x - 35 ( add 35 to both sides )

36 = - 0.4x ( divide both sides by - 0.4 )

- 90 = x

The number of weeks needed to get $850 is 21 weeks.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.

Let the number of weeks be represented by w

Amount saved = $24

Amount needed = $850

Number of weeks = w.

This will be illustrated as:

24 + 40w = 850

Collect like terms

40w = 850 - 24

40w = 826

Divide

w = 826 / 40

w = 20.65 = 21 approximately

There'll be 21 weeks.

The complete question is written below.

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You have saved $24 towards the purchase of your own laptop. you get a job at the corner store cleaning after hours on sundays that pays $40 per week. the laptop you want costs $850 and includes everything you'll need to start college. How may weeks are needed?

Answer: 1122

Step-by-step explanation:

The degree measure of one angle of a 30 sided regular polygon is 168°​

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides or edges are made up of segments of straight lines that are joined end to end to create a closed shape.

The intersection of two lines is referred to as a vertex or corner, and an angle is created as a result. Regular polygons are those that have sides that are congruent.

We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is

(Side - 2) × 180°

(30 - 2) × 180°

= 5040°

Measure of each angle of 30-gon

= 5040°/30

= 168°​

Thus, the degree measure measure of One angle of a 30 sided regular polygon is 168°​

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Answer: 168

Step-by-step explanation: did the test

A property map is drawn at a scale of 1:1000, if the distance between two points on the map is 4.9cm. then the actual distance is = 4.9 * [tex]10^{3}[/tex]

A property map is drawn at a scale of 1:1000

The distance between two points on the map is 4.9cm

Based on the given conditions, formulate :

= 4.9 * 1000/1

= 4.9 * 1000

Calculate the product or quotient,

= 4900

This alternative forms is,

= 4.9 * [tex]10^{3}[/tex]

Therefore,

The actual distance is = 4.9 * [tex]10^{3}[/tex], if the distance between two points on the map is 4.9cm.

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Taking into account the definition of a system of linear equations, Kevin and Randy Muise have 19 quarters and 50 nickels.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. In this way, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that

You know that:

The system of equations to be solved is

q + n= 69

0.25q + 0.05n= 7.25

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "q" from the first equation:

q= 69-n

Replacing this expression in the second equation:

0.25(69 - n) + 0.05n= 7.25

Solving:

0.25×69 - 0.25n + 0.05n= 7.25

17.25 - 0.25n + 0.05n= 7.25

- 0.25n + 0.05n= 7.25 - 17.25

-0.2n= -10

n= (-10)÷ (-0.2)

n= 50

Remembering that q= 69 -n, you get:

q=69 - 50

q= 19

Finally, there are 19 quarters and 50 nickels.

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Answer:

x=40 degrees

Step-by-step explanation:

adjacent angles add up to 180 degrees

First angle=x

second angles=x+20

third angle =x+40

add all and equate to 180 degrees i.e.

x+x+20+x+40=180

3x=180-60

x=40 degrees

x+20=40+20=60 degrees

x+40=40+40=80 degrees

The range for both groups are the same, therefore: C. The variability in students’ heights of both groups is the same.

To find the mean of a data set, sum all data points given together and divide what you get by the number of data points that is given in the data set.

The range of a data gives us an idea of the spread of a data, which is a measure of variability. The larger the range, the more the variability that exist in the data set.

Given, Group A: 51, 53, 60, 64, 55, and Group B: 50, 55, 58, 63, 52, find the mean of each data set

Mean for Group A = (51 + 53 + 60 + 64 + 55)/5 = 283/5 = 56.6

Mean for Group B = (50 + 55 + 58 + 63 + 52)/5 = 278/5 = 55.6

Range for Group A = 64 - 51 = 13

Range for Group B = 63 - 50 = 13

This means that variability in students’ heights is the same for both group A and B.

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The 100 km difference between the two cities takes two trains to pass each other in 5 hours.

The relationship between speed, distance, and time is described using the formula of speed, distance and time.

That is speed = distance/time.

The velocity of an object in relation to another observer is referred to as the relative speed.

Given:

A train departs from city A and moves toward city B at a constant speed of 60 km/h and time taken is 8 hours.

At the same time, a second train departs city B and heads toward city A at a constant speed of 40 km/h.

The relative speed of first train with respect to the second train                                  = 60-40

= 20 km/h

It is given that the two cities A and B are located 100 kilometers apart from one another.

So, distance between both cities = 100 km

By using the speed formula,

Speed = Distance/Time

Time = Distance/Speed

Time = 100/20

∴ Time = 5 hours

Consequently, it takes 5 hours for the two trains to pass one another with 100 km distance between two cities.

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The set of constraints to model the problem include

The following is data given in the problem

The constraints to model the problem is as follows:

The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled.

Savanah will babysit at least 40 hours

The two constraints required is modelled using inequalities and represented as follows y < 5x and y ≥ 40 hours

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The value of k so that the equation has two equal roots is 4

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

kx^2 - 4x + 1

A quadratic equation is represented as

ax^2 + bx + c

This means that

a = k, b = -4 and c = 1

When the equation has equal roots, we have

b^2 = 4ac

So, we have

(-4)^2 = 4 * k * 1

Evaluate

k = 4

Hence, the value of k is 4

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cosine = adj/hypt.

inverse of cosine = arccosine

arccosine(6/22) = 74.34

Answer:

Step-by-step explanation:

3(x-2)+2x=1/2(10x-12)

3x - 6 + 2x = 5x - 6

5x - 6 = 5x -6

5x - 5x = 6 - 6

0 = 0

this equation is always true

Answer:

Infinitely many solutions

Step-by-step explanation:

[tex]\sf 3(x - 2) + 2x = \dfrac{1}{2}*(10x - 12)\\\\ 3x - 3*2 + 2x = \dfrac{1}{2}*10x - \dfrac{1}{2}*12 \ [\bf distributive \ property]\\\\ 3x - 6 + 2x = 5x - 6[/tex]

Combine like terms,

  3x + 2x - 6 = 5x - 6

         5x - 6  = 5x - 6

There are infinitely many solutions for this equation.

1) The value of x that would make m║n is; x = 13

2) The value of x that would make m║n is; x = 14

3)a) The angles are congruent by alternate interior angles postulate.

b) The angles are congruent by linear pairs postulate.

c) The angles are congruent by corresponding angles postulate.

When two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.

1) From definition of corresponding angles, line m is parallel to line n and as such, we can say that;

2x + 12 = 38

2x = 38 - 12

2x = 26

x = 13

2) From definition of corresponding angles, line m is parallel to line n and as such, we can say that;

3x + 41 = 8x - 29

8x - 3x = 41 + 29

5x = 70

x = 14

3) a) From definition of alternate interior angles, we can say that yes the angles are congruent by alternate interior angles postulate.

b) Linear pair of angles are formed when two lines intersect each other at a single point. Thus, the angles are supplementary and add up to 180° and they are congruent by linear pairs postulate.

c) The angles are congruent by corresponding angles postulate.

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Answer:

I djdhdhdh47747

Step-by-step explanation:

jrhrhdhrhdbdndbdbdjdjdjfjfjfjfjfjfjfjffuufufurtuhrbrbrnrntjrjfjfjdjfufufjfjfjfjffiitiririfiififig

Answer:

10m/7n

Step-by-step explanation:

distribute the

7n-7m=3m

7n=

Answer:

The expression is 1.07d.

Line A is perpendicular to D because a is parallel to c and c is perpendicular to d.

Parallel lines have the same slope since the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope. Since the given parallel line has equation y = 2x + 2, thus its slope is 2 and thus, the slope of the needed line is 2 too.

WE have been given that a ll b,b ll c,c is perpendicular to d.

Here the line a is parallel to b and b is parallel to c so a must be parallel to c.

As we know that c is perpendicular to d since, a is parallel to c.

Therefore, Line A is perpendicular to D because a is parallel to c and c is perpendicular to d.

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