Given: /\ABC, KM|| AC
a) AB=10, KB=2, KM=1
AC-?
b) KM=3, AC=6,BC=9
BM-?
c)BC=25, MC=10, AC=5
KM-?
d)AK=10,KB=4,BC=21
BM-?,MC-?

Answer:

15.2

Step-by-step explanation:

[tex]x^{2} =8.7^{2}+12.5^{2} \\x^{2} =231.94\\x=15.229...\\x=15.2[/tex]

Answer: 10y - 3

Step-by-step explanation:

We just add the "+" sign between the two.

So we get:

8y - 6 + 2y + 3

The y terms are like, so we do :

(8y + 2y) - 6 + 3

Which is:

10y - 6 + 3

The integers are like (common), so we do:

10y (-6 + 3)

Which is :

10y - 3    

It is - 3 because -6 + 3 = -3, and we also add the "-" with the integer

So our final answer is=

10y - 3

The required scale factor of the dilation, between the triangles, is 3/4.2.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
To determine, a sequence of rigid transformations that could take one triangle to another.

Since as we can see, the triangles have certain dilation, translation, and reflection. As for the data given, we can only calculate the dilation factor or scale factor only.

So,
Scale factor = Length of the one side of 1st triangle/length of 2nd triangle.

Scale factor = 6/8.4
Scale factor = 3/4.2

Thus, the required scale factor of the dilation, between the triangles is 3/4.2.

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We have proven that in given triangle ∠BACB is congruent to ∠DECD, as required.

Similarity of triangles refers to the property of having the same shape but not necessarily the same size. Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

To prove: ∠BACB = ∠DECD

We know that, BD ∥ AE and C is the midpoint of AE.

Therefore, triangle ACE and triangle BCD are similar by the Converse of the Corresponding Angles Postulate. Hence, we have:

∠CAB = ∠CBD .... (1) (corresponding angles)

∠CAE = ∠CDB .... (2) (corresponding angles)

Also, we know that in triangle ACE, angles 3 and 4 are alternate interior angles formed by a transversal. Therefore, angles 3 and 4 are congruent. Similarly, in triangle BCD, angles 1 and 2 are congruent.

Therefore, we can write:

∠ACB = ∠BCD .... (3) (angles of similar triangles)

Adding equations (1) and (3), we get:

∠BACB = ∠DECD

Hence, we have proven that ∠BACB is congruent to ∠DECD, as required.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{z}{20}=\cfrac{4}{z}\implies z^2=4(20)\implies z^2=4(4\cdot 5)\implies z^2=4^2\cdot 5 \\\\\\ z=\sqrt{4^2\cdot 5}\implies z=4\sqrt{5}[/tex]

To simplify the expression 5x2+2x-4-10x2, we must first combine like terms. Like terms are terms that have the same variable or variables with the same exponents.

In this expression, 5x2 and -10x2 are like terms. To combine them, we can add their coefficients (the numbers in front of the variable) together. So, 5x2 - 10x2 = (-5 + 5)x2 = 0x2.

Now, the expression has only two terms left. 2x and -4 are also like terms, since they both have the same variable. We can again add their coefficients together, which results in (2 + -4)x = -2x.

Therefore, the simplified expression is 0x2 - 2x. Note that there is no need to use the 0x2 term, so the expression can also be written as -2x.

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The formula that expresses R as a function of M and S is R = (M - 2S)/2.

To write a formula that expresses R as a function of M and S, we will need to rearrange the equation M=2R+2S to solve for R.

First, we will subtract 2S from both sides of the equation to isolate the term with R on one side:
M - 2S = 2R

Next, we will divide both sides of the equation by 2 to solve for R:
(M - 2S)/2 = R

Finally, we can write the equation in function form, with R as the dependent variable and M and S as the independent variables:
R = (M - 2S)/2

Therefore, the formula that expresses R as a function of M and S is R = (M - 2S)/2.

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Answer:

4

Step-by-step explanation:

Five students shared 30 questions by receiving an unknown number of questions each followed by 2 questions each

Let that unknown number be x

Let the second set of questions be 10 (5x2)

5x +10=30

Subract 10 from both sides

5x = 20

Divide both sides by 5

X=4

The teacher assigned each student 4 questions each (4 x 5=20)

The vertex of the function is (2 , -5), the axis of symmetry is x = 2, and the intercepts are (2 + √(5) , 0), (2 - √(5) , 0), and (0 , -1).

To find the vertex, axis of symmetry, and intercepts of the function f(x) = x² - 4x - 1, we can use the following formulas:

Vertex: (-b/2a, f(-b/2a))

Axis of symmetry: x = -b/2a

Intercepts:

x-intercept: set f(x) = 0 and solve for x

y-intercept: set x = 0 and solve for y

Using these formulas, we can find the vertex, axis of symmetry, and intercepts of the function:

f(x) = x² - 4x - 1

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

Vertex: (-b/2a , f(-b/2a)) = (-(-4)/(2)(1) , f(-(-4)/(2)(1))) = (2 , f(2)) = (2 , (2)² - 4(2) - 1) = (2 , -5)

Axis of symmetry: x = -b/2a = -(-4)/(2)(1) = 2

Intercepts:

x-intercept: 0 = x² - 4x - 1

use the quadratic formula to solve for x: x = (-b ± √(b² - 4ac))/(2a) = (-(-4) ± √((-4)² - 4(1)(-1)))/(2(1)) = (4 ± √(20))/2 = (4 ± 2√(5))/2 = 2 ± √(5)

so the x-intercepts are (2 + √(5) , 0) and (2 - √(5) , 0)

y-intercept: f(0) = (0)² - 4(0) - 1 = -1; so the y-intercept is (0 , -1)

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Answer:

c.4√6

Step-by-step explanation:

= √2 x 2 x 2 x 2 x 2 x 3

= √24 x 2 x 3

= 4√6

Answer: AD/DB = {AB/BD} = {DA/DB}

AD/AB = {DB/AB} = {DA/DB}

DB/AB = {AD/AB} = {BD/DA}

The width of the fence is 75 feet and the length of the fence is 150 feet.

To arrive at this answer, let's first assign variables to the width and length of the fence. Let x be the length of the fence, then the width of the fence is 1/2 x. The perimeter of the fence is given by the formula P = 2(length + width). In this case, the perimeter is 300 feet, so we can set up the equation:

300 = 2(x + 1/2 x)

Simplifying the equation, we get:

300 = 3x

x = 100

Therefore, the length of the fence is 100 feet, and the width of the fence is 1/2 x 100 = 50 feet. However, note that the problem asks for the width and length in one line, so we can express our answer as:

The width of the fence is 75 feet and the length of the fence is 150 feet (using the fact that the width is half the length).

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There were 240 pages in the printer task.

To find the number of pages in the printing task, we can use the relationship between time, rate, and work. The formula for this is:

   time × rate = work.

Let's call the number of pages in the printing task "P" and the rate of printer A "R". We can set up the following equations based on the information given in the question:

   40 minutes × R = P(R + 4) × (40 - 16) = P

We can simplify the second equation to get:

    24R + 96 = P

Now we can set the two equations equal to each other and solve for R:

    40R = 24R + 96

    16R = 96

     R = 6

Now we can plug this value of R back into one of the original equations to find P:

     40 minutes × 6 = P

      P = 240

Therefore, the number of pages in the printing task was 240.

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The surface area of the frustrum, obtained summing the areas of the trapezium-shaped faces, and the square base and top is 2720 mm²

A frustrum is the part of a pyramid formed when the top is removed by a plane parallel to the base of the pyramid.

The slant height of the small square-based pyramid, is the same as the slant height of the frustrum. The base of the small pyramid therefore intersects the sides of the large pyramid at the midpoint of the sides, which indicates that the base of the small rectangle is a midsegment of the triangular sides of the square-based pyramid.

The midsegment theorem indicates that the side length of the base of the small pyramid is half the side length of the base of the large square-based pyramid. Therefore;

Length of the base of the smaller pyramid = 32 mm/2 = 16 mm

Height of the trapezium-shaped face = √(17² - ((32 - 16)/2)²) = √(17² - 8²) = 15

Area of the trapezium-shaped face = (16 mm + 32 mm) × 15 mm/2 = 360 mm²

The surface area of the four trapezium-shaped faces = 4 × 360 mm² = 1,440 mm²

The area of the square at the top of the frustrum = 16 mm × 16 mm = 256 mm²

The area of the square base = 32 mm × 32 mm = 1024 mm²

The surface area of the frustrum is therefore;

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Two parts of a family budget is Income and expenses. The correct option is c.

The fundamental family budgets cover housing, food, childcare, transportation, health care, other necessities, and taxes.

It's easy to understand the difference between income and expenses: income refers to the funds your organisation receives, whereas expenses refer to the funds it spends.

Net income is typically defined as your revenue, or the total amount of money coming into your business, minus all of your expenses. Your company is profitable if that number is positive.

Therefore, the correct option is c. Income and expenses.

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Complete question:

What are the two parts of a family budget?

Responses:

Yes, I am sceptical of my friend's claim that Class 2022 did better than Class 2023 in the Final Test because the mean score only tells us the average score of the students in each class. It does not give us the full picture of how the students in each class performed in the Final Test.

To better compare the performance of the two classes, we need to look at other measures of central tendency, such as the median and mode, as well as measures of dispersion, such as the range, variance, and standard deviation. These measures will give us a better understanding of the distribution of scores in each class and allow us to make a more accurate comparison.

For example, if the range of scores in Class 2022 is much larger than the range of scores in Class 2023, it could indicate that there were a few students in Class 2022 who scored very high, which skewed the mean score upward. In this case, the median and mode may be a better measure of central tendency for comparing the two classes.

Similarly, if the variance and standard deviation of scores in Class 2022 are much larger than those in Class 2023, it could indicate that there is more variability in the scores of students in Class 2022, which could also skew the mean score upward.

In conclusion, while the mean score is a useful measure of central tendency, it should not be used alone to compare the performance of two classes. Other measures of central tendency and dispersion should also be considered to get a more accurate comparison.

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The fully factored form of 8v - 6vw + 4 - 3w is (2v + 1)(4 - 3w).

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

8v - 6vw + 4 - 3w​

To factor by grouping, we'll group the first two terms and the last two terms:

(8v - 6vw) + (4 - 3w)

Next, we'll factor out the greatest common factor (GCF) from each group:

2v(4 - 3w) + 1(4 - 3w)

Notice that both groups now have a common factor of (4 - 3w), which we can factor out:

(2v + 1)(4 - 3w)

Hence, the factored expression is (2v + 1)(4 - 3w)

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The statement  ((1)/(x))^(n)>(1)/(x)  is FALSE as (1)/(x^n) will always be smaller than (1)/(x).

To evaluate this expression, let's look at the properties of exponents. When we have a fraction raised to a power, it is equivalent to raising both the numerator and denominator to that power.

So, ((1)/(x))^(n) is equivalent to (1^n)/(x^n), which simplifies to (1)/(x^n).

Now, let's compare (1)/(x^n) to (1)/(x). Since x is positive and n is a natural number excluding zero, x^n will always be greater than x.

For example, if x=2 and n=3, then x^n=8 and (1)/(x^n)=(1)/(8) while (1)/(x)=(1)/(2).

So, (1)/(x^n) will always be smaller than (1)/(x).

Therefore, the statement ((1)/(x))^(n)>(1)/(x) is FALSE.

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Table showing relation of points and coins is as in the solution, graph is straight line p = 15c+5, drawn and attached below. y-intercept is (0,5).

A table has records (rows) and fields (columns). Fields have different data types. as Text, Numbers, Dates, and Hyperlinks. record: It contains certain data, such as information about specific employees or products.

Given,

In a video game, player earns 5 points for reaching next level

15 points are for each coin collected

when player has 1 coin, number of points

= 15 + 5

= 20

when player has 2 coin, number of points

= 2(15) + 5

= 35

Equation for c coins, number of points

p = 15c + 5

Table can be created as follows:

Coins(c)  Points()

0                 5

1                 15

2                35

3                 50

4                 65

5                 80

6                 95

7                  110

8                  125

Graph is a straight line, y-intercept is (0,5).

Hence, table of the relationship of points and coins is

Coins  0   1    2    3     4    5    6    7      8

Points 5  15  35  50  65  80  95  110   125

Graph of the data is an straight line p = 15c + 5, (0,5) is y-intercept.

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The length of the escalator, considering the trigonometric ratios, is of

38.1 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 30º, we have that:

Hence the length of the escalator is obtained with the tangent as follows:

tan(30º) = 22/l

l = 22/tangent of 30 degrees

l = 38.1 ft.

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The percent of change from 4/3 to 3/5 is 6.1%

To find the percent of change from 4/3 to 3/5, we'll use the following formula:

Percent change = ((Old value - New value) / old value) x 100%

First, we'll identify which value is the old value and which is the new value.

The old value is 4/3 and the new value is 3/5.

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

Percent change = ((4/3 - 3/5) / 4/3) x 100%

Evaluate

Percent change = 6.1%

Hence, the percent change is 6.1%

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The equation represents a linear function, as it is a proportional relationship, and thus the rate of change of the output variable relative to the input variable is constant.

A proportional relationship is defined according to the equation presented as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

A proportional relationship is a special case of a linear function, as it has an intercept of zero.

The equation for this problem is given as follows:

t = 10.8w.

Which is a proportional relationship with a constant of 10.8.

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Answer:

To find f(-2), we substitute -2 for x in the expression for f(x) and simplify:

f(x) = x³ - 3x

f(-2) = (-2)³ - 3(-2)

f(-2) = -8 + 6

f(-2) = -2

Therefore, f(-2) = -2.

Step-by-step explanation:

2023

The sum of two exponentials is given by:

A e^(jφ) + B e^(jψ) = (Acosφ + Bcosψ) + j(Asinφ + Bsinψ)

Applying this formula to the given problem:

[tex]33.65 e^{j(377t-25.5)} + 31.39 e^{j(377t+172.8)}[/tex]

[tex]= (33.65cos(377t-25.5) + 31.39cos(377t+172.8)) + j(33.65sin(377t-25.5) + 31.39sin(377t+172.8))[/tex]

This is the final answer, expressed in rectangular form with real and imaginary parts.

In words, the sum of the two exponentials is a complex number with a real part equal to the sum of the cosines of the two phases and an imaginary part equal to the sum of the sines of the two phases. The phase angle of the resulting complex number is determined by the weighted sum of the two original phase angles.

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14) all triangles add up to 180 degrees.

for example: c - 40 + 40 = 80; 180-80 = 100

16)

a. EF

b. E

c. A

Answer:

+- .35

Step-by-step explanation:

8x² - 1 = 0

8x² = 1

x² = 1/8

x = √1/8

x = +- .35

Cοrmac cοuld use 1/3 cup οf milk and 1 1/2 cups οf water, a mixture with a tοtal οf 1 5/6 cups, where the amοunt οf milk is less than 1/2 the amοunt οf water, represented by the sοlutiοn pοint (1/3, 1 1/2) tο the system οf inequalities x + y <= 2 and x < 1/2 * y.

An inequality is a mathematical statement that cοmpares twο values, expressing the relatiοnship between them using οne οf several symbοls, such as "<" (less than), ">" (greater than), "<=" (less than οr equal tο), ">=" (greater than οr equal tο), οr "!=" (nοt equal tο).

The pοint (1/3, 1 1/2) is a sοlutiοn tο Cοrmac's system οf inequalities, which means that it satisfies bοth inequalities. In this case, the inequalities are:

x + y <= 2

x < 1/2 * y

If we plug in x = 1/3 and y = 1 1/2, we can check if it satisfies bοth inequalities:

1/3 + 1 1/2 = 2 (satisfies x + y <= 2)

1/3 < 1/2 * (1 1/2) (satisfies x < 1/2 * y)

Therefοre, the sοlutiοn is (1/3, 1 1/2) since it satisfies bοth inequalities.

Sο, the statement that explains what the pοint (1/3, 1 1/2) represents is:

Cοrmac cοuld use 1/3 cup οf milk and 1 1/2 cups οf water, a mixture with a tοtal οf 1 5/6 cups, where the amοunt οf milk is less than 1/2 the amοunt οf water.

Hence, Cοrmac cοuld use 1/3 cup οf milk and 1 1/2 cups οf water, a mixture with a tοtal οf 1 5/6 cups, where the amοunt οf milk is less than 1/2 the amοunt οf water, represented by the sοlutiοn pοint (1/3, 1 1/2) tο the system οf inequalities x + y <= 2 and x < 1/2 * y.

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10 pounds of chocolates and 5 pounds of other candy.

To solve this problem, we need to use a system of equations. Let x be the amount of chocolates in the mixture and y be the amount of other candy in the mixture. We can write the following equations:

x + y = 15 (the total amount of candy in the mixture is 15 pounds)
1.80x + 3.00y = 2.20(15) (the total value of the candy in the mixture is $2.20 per pound)

Now we can solve for one of the variables in terms of the other. From the first equation, we can isolate y:

y = 15 - x

Substituting this into the second equation gives us:

1.80x + 3.00(15 - x) = 2.20(15)

Simplifying and solving for x gives us:

1.80x + 45 - 3.00x = 33
-1.20x = -12
x = 10

Now we can plug this value of x back into the first equation to find y:

y = 15 - 10 = 5

So there are 10 pounds of chocolates and 5 pounds of other candy in the mixture.

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Therefore, Annabel sent her brother 3 text messages each day for the past 13 days.

The dividend must be divided by a certain number, which is known as the divisor. Quotient: The division's outcome is referred to as the quotient. Remainder – The remainder is the number that remains after division.

In this example, the number being divided (15) is known as the dividend, and the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division. Observe how the equation remains valid even if you change the quotient and divisor: 15 3 = 5. 15 5 = 3.

To determine how many text messages Annabel sent her brother each day, we can divide the total number of text messages she sent by the number of days she sent them.

So, we divide 39 by 13 to get:

39 ÷ 13 = 3

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