Identify the segments that are parallel, if any, if ∠ADH≅∠ECK.A. AD¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯B. AC¯¯¯¯¯¯¯¯ || CD¯¯¯¯¯¯¯¯C. AE¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯D. none of these

An envelope is rectangular in shape.

Given the width = 15cm, and diagonal = 17cm

Let h represent the tall length of the envelope

Applying Pythagoras theorem, we have

The envelope is 8cm tall

The resultant matrix for the given expressions are as follows -

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

Matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. A matrix has [n] rows and [m] columns. The order of a matrix is given by - [m] x [n].

Given are the three different matrices as -

A = [tex]\left[\begin{array}{ccc}9&-6\\7&5\\\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}4&3\\-7&-6\\\end{array}\right][/tex]

C = [tex]\left[\begin{array}{ccc}0.5&3.6\\2.4&-3.2\\\end{array}\right][/tex]

We can solve the given expressions as follows.

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

Therefore, the resultant matrix for the given expressions are as follows -

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

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Given the inequality:

We need to solve the inequality to get a range of values for x.

This we can do by finding the square of both sides:

On checking the options given, we will pick the numbers that are strictly less than 25.

Therefore, the correct options are:

OPTION A

OPTION B

OPTION C

OPTION F

GIven the table above :

We have that

x y

2 8

4 4

6 0

8 4

The table represents a Non - Linear Function

Reason: It is because there is no constant ratio or proportion between x and y.

The y-intercept of y = 250 + 15x is (0,250)

A line's y-intercept is the distance in y coordinates from the line's intersection with the y-axis at its origin. A location on the graph where x is 0 is known as the y-intercept. The y-intercept of a line that is perpendicular to the x-axis is undefined.

This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

Here to determine the y-intercept put x=0,

Given, y = 250 + 15x

Replacing x by 0 in the above equation we get,

y = 250 + 15×0

y=250 +0

y=250

Therefore, the y-intercept of y = 250 + 15x is (0,250)

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Given:

To find:

The value of n.

Explanation:

The nth term formula for the arithmetic sequence is,

Substituting the given values we get,

Thus, -24 is the 4th term of the sequence.

Final answer:

The term -24 is the 4th term of the sequence.

Comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :

Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.

Contrast is range is different:

Range = { 3, 5, 7, 9} for domain {1,2,3,4}

Range = set of all real numbers for domain all real numbers.

As given in the question,

Given function for the graphs are:

y =2x+1

Different domains

Domain ={1,2,3,4}

Domain =All real numbers

Compare with y=mx +c

Slope m =2

For y-intercept put x=0

y=2(0) +1

 =1

For x-intercept put y=0

0 =2x+1

⇒x=-1/2

Contrast:

For domain ={1,2,3,4}

Range is :

y = 2(1)+1

  =3

y=2(2)+1

 =5

y=2(3) +1

 =7

y=2(4)+1

 =9

Range ={ 3, 5, 7,9}

For domain= all real numbers

Range = set of all real numbers

Therefore, comparison of both the graphs y=2x+1 with domain {1,2,3,4} and set of all real numbers is :

Slope =2 , y-intercept =1 and x-intercept = -1/2 is same.

Contrast is range is different:

Range = { 3, 5, 7, 9} for domain {1,2,3,4}

Range = set of all real numbers for domain all real numbers.

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The value of the composite function is determined as: (g o f)(5) = 6.

To determine the value of a composite function, first evaluate the inner function by plugging in the value of x given, then use the output of the inner function as an input to evaluate the outer function.

Given the following:

f(x) = x² - 6x + 2

g(x) = -2x

Therefore:

(g o f)(5) = g(f(5))

Find f(5):

f(5) = (5)² - 6(5) + 2

f(5) = 25 - 30 + 2

f(5) = -3

Find g(f(5)) by substituting x = -3 into g(x) = -2x:

g(f(5)) = -2(-3)

g(f(5)) = 6

Therefore, (g o f)(5) = 6.

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The statement that reflects the running rates is Pepe ran 9/8  mile in 1/2 hour and Paul ran 19/24 mile in 1/3 of an hour.

Speed is the total distance run per time. It can be determined by dividing the total distance travelled by the total time.

Speed = distance / time

Speed if Paul ran 1/5 mile in 4/15 hour

Speed = 1/5 ÷ 4/15

1/5 x 15/4 = 3/4 miles per hour

Speed if Pepe ran 8/10 mile in 1/4 of an hour

Speed = 8/10 ÷ 1/4

8/10 x 4 = 16/5 = 3 1/5 mile per hour

Difference in speeds =

[tex]3\frac{1}{5}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]3\frac{4 - 15}{20}[/tex] = [tex]2\frac{9}{20}[/tex]

Speed if Paul ran 4/15 mile in 1/5 hour

Speed = 4/15 ÷ 1/5

4/15 x 5 = 4/3 = 1 1/3 miles per hour

Speed if Pepe ran 1/4 mile in of 8/10 an hour

Speed = 1/4 ÷ 8/10

1/4 x 10/8 = 5 / 16

Difference in speeds = [tex]1\frac{1}{3} - \frac{5}{16}[/tex] = [tex]1\frac{1}{48}[/tex]

Speed if Paul ran 1/3 mile in 19/24 hour

Speed = 1/3 ÷ 19 / 24

1/3 x 24/19 = 8/19 miles per hour

Speed if Pepe ran 1/2 mile in of 9/8 an hour

Speed = 1/2  ÷ 9/8

1/2 x 8/9 = 4/9 mile per hour

Difference = 4/9 - 8/19 = 4/171

Speed if Pepe ran 9/8  mile in 1/2 hour

Speed = 9/8 ÷ 1/2

9/8 x 2 = 2 1/4  miles per hour

Speed if Paul ran 19 / 24 mile in of 1/3 an hour

Speed =  19 / 24  ÷ 1/3

19 / 24 x 3 = 2 3/8 miles per hour

Difference =

[tex]2\frac{3}{8} - 2\frac{1}{4}[/tex]

[tex]\frac{3 - 2}{8}[/tex] =  [tex]\frac{1}{8}[/tex] miles per hour

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The slope of the given equation is 0.075 and  y-intercept is 0.125

What is slope of line ?

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

The point with coordinate having same slope as with given coordinates can be plotted on the same line.

First writing the given equation in standard slope intercept form :

y = mx + c.........(1)

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• c is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function

8y = 0.2(3x - 5)

8y = 0.6x - 1

y = 0.6/8x - 1/8

y = 0.075x - 0.125

Now, comparing it with equation (1) we get :

m = 0.075 and c = - 0.125

hence the slope of the given equation is 0.075 and  y-intercept is 0.125

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∠A + ∠B + ∠C = 180°

reason : Sum of all angle of triangle is 180°

72° + 86° + ∠C = 180°

158° + ∠C = 180°

∠C = 180° - 158°

∠C = 22°

hence the value of ∠3 is 22°

Now ,

∠3 =∠4

reason : Being vertically opposite angle

4 = 22°

hence the value of ∠4 is 22°

Again ,

∠C + ∠D + ∠E = 180°

reason : Sum of all angle of triangle is 180°

22° + ∠D + 70° = 180°

92° + ∠D = 180°

∠D = 180° - 92°

∠D = 88°

hence the value of ∠5 is 88°..

[tex]...[/tex]

hope it helps ....☘✨

Problem

Solution

Let x = age, W= weight the two variables of interest

We have the following probabilities given:

P(x<37) =0.142

P(W< 2500) = 0.051

P(x <37 AND W<2500)= 0.031

And we want the following probability and we can use the total probability rule:

P(x < 37 OR W< 2500) = P(x<37) +P(W< 2500) -P(x<37 AND W<2500)

If we replace we got:

P(x < 37 OR W< 2500)= 0.142+ 0.051- 0.031= 0.162

The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .

The equation of parabola with vertex (h,k) is denoted by the equation

y = a(x-h)² + k

In the question ,

it is given that

the vertex of the Parabola is (3,-2) and the point is (2,3)

So, the equation of the parabola with vertex (3,-2) will be

y = a(x-3)² - 2

Since the point (2,3) lies on the parabola ,

So, 3 = a(2-3)² - 2

3 + 2 = a*(-1)²

5 = a

Substituting a in the equation  y = a(x-3)² - 2 ,

we get

y = 5(x-3)² - 2

Therefore , The equation of Parabola in the vertex form with vertex (3,-2) and point(2,3) is y = 5(x-3)² - 2 .

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So 4/5 times 5/8 is 1/2.

Answer: A) 4 B) 30 C) 6

Step-by-step explanation:

For question A, you subtract the highest number and the lowest number (10-6)

For question B, you add all the frequency numbers together

For question C, you use your answer on B and divide it by 5

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

triangle diagram

Step 02:

angles:

we must analyze the diagram to find the solution

angle 1:

angle 1 = 180° - 155° = 25°

angle 2:

angle 2 = angle 1 = 25°

angle 3:

angle 3 = 180° - 25° - 25° = 130°

angle 4:

angle 4 = 155°

angle 5:

angle 5 = 180° - 25° = 155°

That is the full solution.

0.12

Probability is the likelihood or chance that an event will occur. It ca be expressed as:

where:

n(E) is the expected event

n(S) is the total sample space

If Mrs. Maria's Market buys 75% of eggs from farm A and the rest from farm B, the percentage amount of egg bought from B will be 25% (100-75)

n(S) = 25%

If 3% of the eggs from B are green, hence n(E) = 3%

Determine the required probability

Pr(egg is from farm B) = n(E)/n(S)

Pr(egg is from farm B) = 3/25 = 0.12

Hence the probability that the egg is from farm B is 0.12

To find z, consider the right-angled triangle at the botton in the diagram showm

Let the common base of both triangles be m

To find y:

To find x:

SOL

Step 1 :

In this question, we are meant to find the value of

the hypotenuse in the right angle below:

Before, we proceed, we still need to remind ourselves of Pythagoras' theorem,

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

Step 2 :

From the above theorem, we can see that that the two adjacent sides are :

14 inches and 48 inches.

From the principle of Pythagoras' Theorem,

CONCLUSION :

The value of the hypotenuse in the Right angle, c = 50 inches.

Given:

To find:

We need to solve this sum and find the final answer

Step-by-step solution:

To solve this problem, we need to know the square root of 100 and 64.

√100 = 10

√64 = 8

Final answer:

Thus 2 (Option A) is the correct answer.

Input data

75% = 0.75

format

y = kx

Procedure

The k factor would be equal to 0.25

The answer would be

Sue's total pay for the year given the salary, bonus and share of profit is  £38,110.

Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.

Salary for the year = monthly salary x number of months in a year

£1410 x 12 = £16,920

The next step is to determine the profit last year

Profit = total revenue - total cost

£549,000 - £473,500 = £75,500

Now determine the share of profit that Sue would earn.

Share of profit = 26% x  £75,500

0.26 x  £75,500 = £19,630

Now determine the total bonus she would earn : 4 x £390 = £1560

Total salary = £1560 +  £19,630 +  £16,920 = £38,110

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The point that best represents 1/3 is point M .

The number line ranges from 0 to 0.5 with 10 divi

Answer:

-2 and -10

Explanation:

There are two numbers at a distance of 4 units from -6, the number that is 4 units to the right and the number that is 4 units to the left.

So, the number that is 4 units to the right is equal to

-6 + 4 = -2

And the number that is 4 units to the left is equal to

-6 - 4 = -10

Therefore, the numbers are -2 and -10 and they are represented as

we have that

Divide $90 by the number of shares

so

90/9=$10

the answer is $10

To prove that p || r, we will complete the data in the given table

Explanation:

If she spent $28 of the $50 she withdrew, she now has:

$22

The fraction is:

Answer:

Anna has 11/25 of her money left.

1) Let's sketch this out to better grasp it

2) We can see that there are two legs and two angles (one of them is missing) so let's solve it using the Law of Sines: