The sum of 5 consecutive numbers is 135

1. Let m∠ABK=x°. Since line BK bisects ∠ABD, then

m∠ABK=m∠KBD=x°.

Also m∠ABD=m∠ABK+m∠KBD=2x°.

2. The diagonal BD of rhombus ABCD bisects ∠ABC, then

m∠ABD=m∠DBC=2x°.

This gives you that

m∠ABC=4x°.

3. Angles A and B are supplementary, so

m∠A+m∠B=180°,

m∠A=180°-4x°.

4. Consider triangle ABK. The sum of the measures of interior angles in triangle is always 180°, thus

m∠A+m∠ABK+m∠AKB=180°,

m∠AKB=180°-x°-(180°-4x°),

m∠AKB=3x°=3m∠ABK.

Answer:

Given information: ABCD is a rhombus, angle bisector of ∠ABD meets AD at point K.

[tex]\angle ABK\cong \angle DBK[/tex]         (Definition of angle bisector)

[tex]m\angle ABK=m\angle DBK[/tex]          (Definition of concurrency)

Let as assume the measure of angle ABK is x.

[tex]m\angle ABK=x[/tex]

[tex]m\angle ABD=m\angle ABK+m\angle DBK[/tex]

[tex]m\angle ABD=x+x[/tex]

[tex]m\angle ABD=2x[/tex]

All sides of a rhombus are same.

Since AB=AD, therefore ABD is an isosceles triangle and two angles of an isosceles triangle are congruent.

[tex]m\angle ADB=m\angle ABD[/tex]

[tex]m\angle ADB=2x[/tex]

According to exterior angle theorem, sum of two interior angles of a triangle is equal to third exterior angle.

Using exterior angle theorem, we get

[tex]m\angle AKB=m\angle ADB+m\angle DBK[/tex]

[tex]m\angle AKB=2x+x[/tex]

[tex]m\angle AKB=3x[/tex]

[tex]m\angle AKB=3(m\angle ABK)[/tex]

Hence proved.

Answer:NAME:     Nzube Erobu        DATE: 02/ 06 / 2020

Step-by-step explanation: With reference to the attached document, below:

1) False, the lines linking between TR and SV are diagonals

2) True,  ∠RVT = ∠ STV because they have the same right angled triangles.

3) True, because they separate triangles that have all angles in each triangle summing up to 180°  

4) (11 + 3)/2 = 14/2= 7

7) (15x - 5)° + (90 - 4x)° = 180°

(15x - 4x + 90 - 5)° = 180°

( x + 85)° = 180°

∴ x = 180° - 85° = 95°

8) (2x - 7)° + 117° = 180°

2x° +117° - 7° = 180°

2x° + 110° = 180°

2x = 180° - 110°

∴ x = 70°/2 = 35°

9) 4x - 1 + 6x + 11 = 60

4x + 6x + 11 -1 = 60

10x + 10 = 60

10x = 60 - 10 = 50

∴ x = 50/10 = 5

10) 18x + 19 - (10x + 3)  = 11

       18x - 10x + 19 - 3 = 11

8x + 16 = 11

8x = 11 - 16 = - 5

∴ x = - 5/8

11) 2x + 1 + 3x - 3 = 8

2x + 3x  - 3 + 1 = 8

5x - 2 = 8

5x = 8 + 2= 10

∴ x = 10/5 = 2

The expression for the total number of miles Maria drove in two weeks is 231 + k miles.

In order to find the total number of miles Maria drove in two weeks, we first need to find the sum of the miles she drove last week and the miles she drove this week.

Last week, Maria drove 231 miles.

This week, she drove k miles.

Therefore, the expression for the total number of miles she drove in two weeks is 231 + k miles.

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The equations that can be used to find students with tickets is given as m/2 + 4 = 20. The correct options are (B) and (D).

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

Suppose the number of students in homeroom be m.

Then, as per the question the equation can be written as,

m/2 + 4 = 20

It can also be written as,

4 = 20 - m/2

Hence, the required equation for the given case is m/2 + 4 = 20.

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The complete question with all the options is attached here.

Answer:

cosF = [tex]\frac{3}{5}[/tex] is the answer.

Step-by-step explanation:

In a right angle triangle cosine of any angle = [tex]\frac{Base}{Hypotenuse}[/tex]

In the given triangle base or adjacent side of the angle is = 6

Hypotenuse given as 10

So by putting the values of hypotenuse and base in the formula

∠F = [tex]\frac{6}{10}=\frac{3}{5}[/tex]

Therefore cosine of angle [tex]cosF=\frac{3}{5}[/tex] is the answer.

The number of students enrolled at the school is 540.

A survey asks 48 randomly chosen students if they plan to buy a school newspaper this week. Of the 48 surveyed, 32 plan to buy a school newspaper. If 360 students bought papers, predict the number of students enrolled at the school. To solve this, we use a proportion based on the survey results to predict the total enrollment. The proportion of students who plan to buy the newspaper based on the survey is 32 out of 48, which simplifies to 2 out of 3 when reduced. If 360 students actually bought the paper, and assuming the proportion holds for the entire school, we can set up the equation:

2/3 = 360 / total students

To find the total number of students, solve for 'total students':

total students = 360 × 3 / 2

total students = 540

Therefore, based on the survey results and the actual number of newspapers bought, we can predict there are 540 students enrolled at the school.

The inverse of the function f is denoted by f -1 (if your browser doesn't support superscripts, that is looks like f with an exponent of -1) and is pronounced "f inverse". Although the inverse of a function looks like you're raising the function to the -1 power, it isn't. The inverse of a function does not mean the reciprocal of a function.

A function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y.

A function f -1 is the inverse of f if

The domain of f is the range of f -1 and the range of f is the domain of f -1.

The inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if (4,6) is a point on the graph of the function, then (6,4) is a point on the graph of the inverse function.

Points on the identity function (y=x) will remain on the identity function when switched. All other points will have their coordinates switched and move locations.

The graph of a function and its inverse are mirror images of each other. They are reflected about the identity function y=x.

Try this:

2. 2.5/5=16/32; 2/4=16/34.

3. one - 6;6;6; two - 6;8;10; three - 5;10;12.

The value of 28-(8+4). (4-2) is 4

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

28-(8+4). (4-2)

=28-(32-16+16-8)

=28-24

=4

Therefore, the value of the algebra will be 4

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To simplify 28-(8+4)·(4-2), calculate the operations within the parentheses first, resulting in 28-12·2. Multiplying 12 by 2 gives 24, and subtracting this from 28 yields the simplified answer, which is 4.

The question requires us to simplify the expression 28-(8+4)·(4-2). We start by simplifying the operations inside the parentheses:

Next, we multiply the results from the parentheses:

Lastly, we subtract this value from 28:

Therefore, the simplified expression is 4.

Answer:

the answer is 4 and 2

Step-by-step explanation:

Final answer:

To convert 4,305.6 grams to kilograms, divide the gram value by 1000, resulting in 4.3056 kilograms, since there are 1000 grams in a kilogram.

Explanation:

The question asks to convert the weight of a rabbit from grams to kilograms. To perform this conversion, we need to know that 1 kilogram is equal to 1000 grams. Thus, we can convert the rabbit's weight by dividing the total grams by 1000 to get the weight in kilograms.

The rabbit weighed 4,305.6 grams. To convert this to kilograms, we divide by 1000:

Thus, the weight of the rabbit is 4.3056 kilograms.

Answer:

(2,4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

13/40 as a decimal  =  0.325

         0.325

40√ _ 130

          120

           _100

               80

                _200

                   200

13/40 as percent

13/40 x 100% = 0.325 x 100% = 32.5%

Final answer:

The number of adult tickets sold for the school play was 92, found by setting up an equation where the number of adult tickets plus twice the number of adult tickets equals the total of 276 tickets sold.

Explanation:

Calculating the Number of Adult Tickets Sold

The student is asked to find out how many adult tickets were sold for the school play, given that a total of 276 tickets were sold and the number of student tickets was two times the number of adult tickets sold. Let's denote the number of adult tickets as x and the number of student tickets as 2x. The total number of tickets is the sum of adult and student tickets which can be represented as:

x + 2x = 276

Combining like terms, we get:

3x = 276

To find the value of x, we divide both sides by 3:

x = 276 / 3

x = 92

Therefore, the number of adult tickets sold was 92.

Among the given options, the trail which is shorter than 7/12 is 3/8

From the question, we are to determine which trail is shorter than 7/12

To determine which of the given fractions is shorter than 7/12, we will express all the fractions in a common denominator

The given fraction are

3/8, 5/6, 3/4, 2/3

Using a common denominator of 48,

7/12 = 28/48

For the given options,

3/8 = 18/48

5/6 = 40/48

3/4 = 36/48

2/3 = 32/ 48

Now, we will compare their numerators. The fraction which has a numerator that is smaller than the numerator in 28/48 is the fraction smaller than 7/12.

Among the fraction, 18 is the smallest of the numerators and it is lesser than 28.

18/48 corresponds to 3/8

Hence, the trail which is shorter than 7/12 is 3/8

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Fraction of household owning pets = [tex] \frac{2}{5} [/tex]

[tex] Fraction \; of \; household \; owning \; cats \; \\\\=\; \frac{1}{3} \; of\; Fraction \; of\; household\; owning \; pets \\\\=\frac{1}{3} \times\frac{2}{5} \\ \\Multiply \; numerator\; with\; numerator\; and\; denominator\; with\; denominator\\\\= \frac{1 \times 2}{3 \times 5}= \frac{2}{15} [/tex]

Conclusion:

The fraction of the household own cats is two-fifteenth

Answer:

Let's approach this step by step.

First, reflect D across line l.

From there, reflect that image across line m.

Your final image should be the letter D.

Check out the image provided.

Hope this helped someone!

Step-by-step explanation:

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