18. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the pair of triangles?

The instance has a mean of 1834 and a standard deviation of 231.2, respectively.

Given data;

A comparison of typical earnings for different professions can be found in the international average salary income database. The information is acquired from publications and reports that were obtained directly from governmental organizations, like the US Bureau of Labor Statistics or the ILO. Consider being informed that the standard deviation of the income of computer programmers in Canada is $458.60 and that a computer programmer in Canada making $2,063.30 has a z-score of 0.50 in comparison to other programmers in Canada. Consequently, the typical pay for computer programmers in Canada is. Assume you are also informed that the mean wage for computer programmers in Portugal is $1,387.40 and that a computer programmer in Portugal who earns $1,387.40 has a z-core of 2.00 in comparison to other computer programmers in Portugal is $925.

Since, the salaries are relative and we know that the z-score is given by;

z = X - μ / σ

0.50 = 2063.30 - μ / 458.60

μ = 2063.30 - 229.3

μ = 1834

As, the salaries are relevant so;

2 = 1387.40 - 925 / σ

σ = 462.4/2

σ = 231.2

Hence, the mean and standard deviation of the case is 1834 and 231.2 respectively.

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Answer:

-54

Step-by-step explanation:

8(-9)=-72

6(-3)=-18

-72+(-18)=-54

-Hope this helped

The angle between the two vectors < 8, 3 > and < 4, −3 > is 57.43°

Given: vectors < 8, 3 > and < 4, −3 >

To find the angle between two vectors, we can use the dot product method:

First, you will compute the dot product and magnitudes of both vectors. Thus,

Let a = < 8, 3 > and b = < 4, −3 >

a · b = <8, 3> ·<4, -3> = 8(4) + (3)(-3) =  32-9 = 23

|a| = √(8² + 3²) = √(64+9) = √73

|b| = √(4² + (-3)²) = √(16 + 9) = √25 = 5

By using the angle between two vectors formula using dot product,

θ = cos⁻¹ [ (a · b) / (|a| |b|) ]

θ = cos⁻¹ (23 / √73 · 5)

θ  = cos⁻¹ (23/42.72) = 57.43°

Therefore, the angle between the following two vectors is 57.43°

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Step-by-step explanation:

because

ST = QR = 16

that means that also the distance from the center point is the same.

in other words :

UC = VC

therefore,

2x = 5x - 9

0 = 3x - 9

9 = 3x

x = 3

The function, g(x), has a constant rate of change and will increase at a faster rate than the function f(x) for all the values of x.  

Given:

g(x) = 5/2 x -3 ..... (1)

f(x) = - 3.5 at x = 0

So, putting the value of x=0 in equation (1) for comparison. We get,

g(x) at x = 0

=> g(x) = 5/2 x (0) - 3

=> g(x) = -3

In this value of x function g(x) is faster than function f(x) having a value equal to -3.5.

Similarly, put x = 1 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (1) - 3

=> g(x) = (5-6)/2

=> g(x) = -1/2

In this value of x function g(x) is faster than function f(x) having a value equal to -1.

Similarly, put x = 2 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (2) - 3

=> g(x) = (5-3)

=> g(x) = 2

In this value of x function g(x) is faster than function f(x) having a value equal to 1.5.

Similarly, put x = 3 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (3) - 3

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

=> g(x) = 7.5 - 3

=> g(x) = 4.5

In this value of x function g(x) is faster than function f(x) having a value equal to 4.

Therefore, for all values of x function g(x) is faster than function f(x).

function f(x).

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Answer:

A)

[tex]\sf -2x+7=-x+9[/tex]

[tex]\sf -2x+7-7=-x+9-7[/tex]

[tex]\sf -2x=-x+2[/tex]

[tex]\sf -2x+x=-x+2+x[/tex]

[tex]\sf -x=2[/tex]

[tex]\sf \cfrac{-x}{-1}=\cfrac{2}{-1}[/tex]

[tex]\boxed{\sf x=-2}[/tex]

____________________

B)

[tex]\sf 4x +15=2x+6[/tex]

[tex]\sf 4x+15-15=2x+6-15[/tex]

[tex]\sf 4x=2x-9[/tex]

[tex]\sf 4x-2x=2x-9-2x[/tex]

[tex]\sf 2x=-9[/tex]

[tex]\sf \cfrac{2x}{2}=\cfrac{-9}{2}[/tex]

[tex]\boxed{\sf x=-\cfrac{9}{2}}[/tex]

____________________

C)

[tex]\sf 8x+26=5x+14[/tex]

[tex]\sf 8x+26-26=5x+14-26[/tex]

[tex]\sf 8x=5x-12[/tex]

[tex]\sf 8x-5x=5x-12-5x[/tex]

[tex]\sf 3x=-12[/tex]

[tex]\sf \cfrac{3x}{3}=\cfrac{-12}{3}[/tex]

[tex]\boxed{\sf x=-4}[/tex]

____________________

D)

[tex]\sf 7x+31=16x+17[/tex]

[tex]\sf 7x+31-31=16x+17-31[/tex]

[tex]\sf 7x=16x-14[/tex]

[tex]\sf 7x-16x=16x-14-16x[/tex]

[tex]\sf -9x=-14[/tex]

[tex]\sf \cfrac{-9x}{-9}=\cfrac{-14}{-9}[/tex]

[tex]\boxed{\sf x=\cfrac{14}{9}}[/tex]

The conversion of 41.98km to centimeters is gotten as; 4198000 cm

We are dealing with units conversion here and in this concept it involves converting from unit to the other using a standard conversion ratio.

Now, we are given the value as 41.98 km. However, we want to convert this value from kilometers to centimeters. The conversion ratio is;

1 kilometer = 100000 centimeters

Thus, using the conversion ratio above, we can say that;

41.98 km = (41.98 * 100000)/1

= 4198000 cm

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The greatest acceleration when the unbalanced force is applied will be experienced by the least weighted box ( i.e., the mass of 2 kg)

Acceleration: it is defined as rate of change of velocity with respect to time.

Unbalanced Force:  it means that the force applied in one direction is greatest than the force applied in the opposite direction.

Given that, F = 8n.

let us assume that the boxes are of 2kg, 4 kg, 6 kg and 8 kg.

According to the 2nd law of motion: the external unbalanced force is directly proportional to rate of change of momentum or Force is equal to the product of mass and acceleration.

                         F = m × a

                 ⇒     a = F/ m

where,  F is Force, m is mass and a is acceleration.

Now, acceleration of the box of 2kg = 8÷2 = 4 m/s²

         acceleration of the box of 4kg = 8÷ 4 = 2 m/m²

         acceleration of the box of 6 kg = 8÷ 6 = 1.34 m/s²

         acceleration of the box of 8kg = 8÷ 8 = 1 m/s²

∴ the box with mass of 2kg experience the greatest acceleration.

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The graph of the inequality 3x - 2y > 2 is attached below.

We are given an inequality. The inequality is given below.

3x - 2y > 2

First of all, we will simplify the inequality. We need to keep the variable "y" on one side of the inequality. The inequality is modified as given below.

3x - 2y > 2

3x > 2 + 2y

3x - 2 > 2y

2y < 3x - 2

y < (3x - 2)/2

Now, to draw the graph of the inequality. We will first find the equation of the straight line corresponding to the given inequality.

y = (3x - 2)/2

We will draw a dotted line according to the above equation. Now, we will shade the area that satisfies the inequality. Hence, the graph is obtained.

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The value of x is when the value of the function f(x) = 7 is x= -24 and x = 16

Function:

A correspondence from one value x of the first set A to another value y of the second set B. It relates inputs to output is known as the function of the relation.

Given,

Here we have the function f(x) = 0.5|x - 4| - 3.

Now, we have to find the value of x when the value of f(x) = 7.

In order to find the value of x as have to equate the give function with the value of f(x), that is 7,

So, when we apply these on the function then we get,

=> 7 = 0.5|x - 4|-3

Now, we have to move all the numbers instead of x, then we get,

=> 7 + 3 = 0.5|x - 4|

=> 10 = 0.5 |x - 4|

=> 10/0.5 = |x - 4|

=> 20 = |x - 4|

So in this place we can get the following forms,

=> x - 4 = 20 and

=> x - 4 = - 20

Because we get two values being an absolute value function.

Now, we have to add 4 on both sides

Then we get

=> x - 4 + 4 = 20 + 4 and

=> x - 4 + 4 = - 20 + 4

So, the value of x is

=> x = 24 and x = - 16

Therefore, for the given function the values of x are 24 and - 16.

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Answer:

7 :D

Step-by-step explanation:

Lets go step by step!

When we do something to one side, we must do it to the other!

2x - 5 < 9

2x - 5 + 5 < 9 + 5

2x < 14

2x/2 < 14/2

x < 7

Your answer is 7 :D

Have an amazing day!

Please rate and mark brainliest!

Answer:

x=7

Step-by-step explanation: Okay so,

2x−5=9

First, you take the 5 and add it to the 9:

2x=9+5=

2x=14

Then you divide 2x by 2 and what you do to one side you do to the other, so you also divide 14 by 2:

2x/2=14/2=

x=7

Hope this helps!

For the given triangles , developing proof is not possible due to following reasons:

First triangle : 21 + 25 < 48 not true.

Second triangle : Interior angle 130° > Exterior angle 125°

As given in the question,

For the given triangles developing proof is not possible due to following reasons:

First triangle:

Measure of three sides are given as 21, 25 , and 48.

As per the property to form a triangle : Sum of two sides is always greater than the third side.

Here, 21 + 25 < 48 .

Above mention property does not satisfied by given triangle.

Second triangle:

In a triangle, measure of exterior angle is always greater the opposite interior angles.

Here, measure of interior angle 130° > measure of exterior angle 125°

Does not satisfy the relation of exterior angles with interior angle.

Therefore, for the given triangles , developing proof is not possible due to following reasons:

First triangle : 21 + 25 < 48 not true.

Second triangle : Interior angle 130° > Exterior angle 125°.

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Answer:

  (a)  (-26, -34)

Step-by-step explanation:

You want the solution to the system of equations ...

apparently using inverse matrices.

The system can be represented by the matrix equation ...

  AX = B

where A is the 2×2 matrix of coefficients, X is the 2×1 variable vector, and B is the 2×1 matrix of constants.

The solution to this system is found by multiplying on the left by the inverse of A:

  A⁻¹·AX = A⁻¹·B

  X = A⁻¹·B

The attachment shows the result of making this calculation:

  [tex]\boxed{X=\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}-26\\-34\end{array}\right]}[/tex]

Let the number be x

10 - 2x = 14

2x = -4

x = -2

_ _ _                    _ _ _ _ _ _ _   _ _ _

|      |                     |      _ _ _    |    |      |

|      |                     |     |         |   |    |      |

|      |                     |     |         |    |   |      |  

|      |                     |    |          |    |   |      |      

|      | _ _ _ _ _ _  |    | _  _ _|    |  |      | _ _ _ _ _ _

| _ _ _ _ _ _ _ _|  | _ _ _ _ _ _|   | _ _ _ _ _ _ _ _|

The slope is 1/6x

You have to re-arranged the problem

x - 6y = 9 --> 6y = x - 9

6y = x - 9

__   ____    ---->  y = 1/6x - 3/2

6        6

The population of Shanghai is 5 times larger than population of Monterrey.

What is population?

Typically, the term "population" refers to the total number of people living in a particular area, be it a city or town, region, country, continent, or the entire world.

Main body:

The population of Monterrey, Mexico is  people = [tex]4*10^6[/tex]

The population of Shanghai, China is  people  = [tex]2*10^7[/tex]

To find how many times the population of Shanghai is lager than Monterrey.

In order to find how many times the population of Shanghai is lager than Monterrey we will find the ratio of populations of Shanghai and  Monterrey.

Thus we divide the population of Shanghai by the population of Monterrey to find how many time the population of Shanghai is larger.

Thus, we have:

[tex]\frac{2*10^7}{4*10^6}[/tex]

Simplifying by using properties of exponents.

⇒  [tex]\frac{2*10^7}{4*10^6}[/tex] , USING [tex]a^{x} -a^{y} =a^{(x-y)}[/tex]

⇒ [tex]\frac{2*10}{4}[/tex]

⇒ 20/4

⇒ 5

Therefore, we can say that the population of Shanghai is 5 times larger than population of Monterrey.

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Answer:

$24.27

Step-by-step explanation:

Original price: $

34.99

Discount percentage:

25

%

Results

Discount:

$8.75

Final Price:

$26.24

Details

Discount = Original Price x Discount %/100

Discount = 34.99 × 25/100

Discount = 34.99 x 0.25

You save = $8.75

Final Price = Original Price - Discount

Final Price = 34.99 - 8.7475

Final Price = $26.24

- 7.5% = $24.27

The cost of the sweater after a 25% of discount and 7.5% of sales tax will be 28.21.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A sweater priced at 34.99 is on sale for 25% off. Then the cost after the discount is calculated as,

⇒ (1 - 0.25) x 34.99

⇒ 26.24

If the sales tax is 7.5%. Then the cost after the sales tax is given as,

⇒ (1 + 0.075) x 26.2425

⇒ 28.21

The cost of the sweater after a 25% of discount and 7.5% of sales tax will be 28.21.

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A line passes through the points (0, 0) and (–17, –11). The equation in the slope-intercept form will be y=9/5x+0

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that, the line passes through the points (0, 0) and (–17, –11).

The slope of the line is,

m = (5+4)/(5-0)

m= 9/5

The equation of the line passes through the point as,

(y-y₁)=m(x-x₁)

(y-0)=9/5(x-0)

5(y-0)=9(x-0)

5y=9x+0

y=9/5x+0

Thus, a line passes through the points (0, 0) and (–17, –11). The equation in the slope-intercept form will be y=9/5x+0

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 4224 hours   integer represents the average temperature per hour change during the 8 hours.

What is the short definition of temperature?

the temperature dropped  = 528 degrees

total time = 8 hours

the average temperature per hour change during the 8 hours = 528  * 8

                                                                                 =        4224 hours

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The original price for the television is $883.51

A store will discount an item by a percent of the original price.

Given that, a store is having a sale on televisions, all televisions are on sale for 15% off, a customer buys a television for $750.99.

Let the original price be x

x*(100-15)% = 750.99

x = 750.99*100/85

x = 883.51

Hence, the original price for the television is $883.51

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Answer: We conclude that the mean commute time in the U.S. is less than half an hour. We are given a random sample of 500 people from the 2000 U.S. Census is selected who reported a non-zero commute time. In this sample, the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes.

So, Null Hypothesis,  :  30 minutes      {means that the mean commute time in the U.S. is more than or equal to half an hour}

Alternate Hypothesis,  :  < 30 minutes     {means that the mean commute time in the U.S. is less than half an hour}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

                          T.S. =    ~

where,  = sample mean commute time = 27.6 minutes

           s = sample standard deviation = 19.6 minutes

           n = sample of people from the 2000 U.S. Census = 500

So, the test statistics  =    ~

                                      =  -2.738

The value of t test statistic is -2.738.

Also, P-value of test statistics is given by the following formula;

          P-value = P(  < -1.645)

Since, we know that at large sample size, the t distribution follows like normal distribution, that means;

             P(  < -1.645)  =  P(Z < -1.645) = 1 - P(Z  1.645)

                                        =  1 - 0.95002 = 0.04998

Now, at 5% significance level the t table gives critical values of -1.645 at 499 degree of freedom for left-tailed test.

Since our test statistic is less than the critical value of t as -2.378 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean commute time in the U.S. is less than half an hour.

Step-by-step explanation:

Answer:

y = - [tex]\frac{3}{5}[/tex] x + 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{3}{5}[/tex] , then

y = - [tex]\frac{3}{5}[/tex] x + c ← is the partial equation

to find c substitute (5, 5 ) into the partial equation

5 = - 3 + c ⇒ c = 5 + 3 = 8

y = - [tex]\frac{3}{5}[/tex] x + 8 ← equation of line

Using the inequality concept, the expression which models the maximum

number of days in which she can rent the car is 56. 37x + 45 ≤ 440.

Maximum amount allowed to spend

= $440

Rental car company fixed charge per day to rent a car = $56.37

Hawa drives a car to 500 miles.

Rate per mile drive = $0.09

let x days be maximum number of days hawa afford rent with budget.

the inequality equation exists here is

(days × charge of rent per day) + (rate per mile x number of miles) ≤ 440

=> 56.37x + 0.09 × 500 ≤ 440

=> 56.37x + 45 ≤ 440

Therefore, the required inequality is 56.37x + 45 ≤ 440

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The area of the trapezoid formed is equal to 12 square meters.

The area of the trapezium is calculated by using the formula.

A =(a + b) × h / 2

In the given trapezium the length of the parallel sides are:

2 m and 4 meters.

The distance between the parallel sides is 4 m

Area of the trapezium = (2+4) × 4÷2 = 12 square meters

A trapezoid is a quadrilateral that has at least one pair of parallel sides.

A trapezoid is a convex quadrilateral by definition in Euclidean geometry. The parallel sides serve as the trapezoid's bases. The remaining two sides are referred to as the lateral sides or the legs if they are parallel; otherwise, the trapezoid appears to be a parallelogram, with two pairs of bases.

Therefore the area of the trapezium is 12 square meters .

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Answer: Carol's Thrift shop rate of change = $4.99/item

Wilma's Child Care rate of change is $7.50/hr

Step-by-step explanation:

Carol's Shop: equation of the line is in y=mx + b form, where m = slope = rate of change = $4.99/item

Wilma's slope = (y2 - y1) / (x2 - x1) = (15-0)/ (2-0) = $7.5/hr

Wilma's has the greater rate of change

Two positive integers have gcd (a, b) = 15 and lcm (a, b) = 90. Those two numbers are 15 and 90 or 30 and 45.

Suppose we have 2 positive integers, a and b, then:

gcd (a, b) = the greatest common divisor = common prime factors of a and b

lcm (a, b) = the least common multiple = multiplication of the greatest common prime factors of a and b

In the given problem:

gcd (a, b) = 15

prime factorization of 15:

15 = 3 x 5

Hence,

a = 3 x 5 x ....

b = 3 x 5 x ....

lcm (a, b) = 90

prime factorization of 90:

90 = 3 x 5 x 2 x 3

Therefore the possible pairs of a and b are:

Combination 1:

a = 3 x 5 = 15

b = 3 x 5 x 2 x 3 = 90

Combination 2:

a = 3 x 5 x 2 = 30

b = 3 x 5 x 3 = 35

We can conclude the two integers are 15 and 90 or 30 and 45.

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The relationship has a constant of proportionality of 38/39

From the question, the given parameters are

Variable 1 = 9/6

Variable 2 = 19/13

The above parameters can be represented as the following points

(x, y) = (9/6, 19/13)

The constant of proportionality of the points is then calculated as

k = y/x

Substitute the known values in the above equation

So, we have the following equation

k = (19/13)/(9/6)

Evaluate the quotient

So, we have

k = 38/39

Hence, the constant of proportionality is 38/39

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