Let $ABC$ be a triangle. Points $A_1, B_1, C_1$ are, respectively, on sides $BC, AC, AB$ and:
$\frac{AC_1}{C_1B} = \frac{BA_1}{A_1C} = \frac{CB_1}{B_1A} \neq 1$
If $\frac{AB}{A_1B_1} = \frac{BC}{B_1C_1} = \frac{CA}{C_1A_1}$ prove that triangle $ABC$ is equilateral.Let ABC be a triangle. Points A1, B1, C1 are, respectively, on sides BC, AC, AB and:
AC1/C1B} = BA1/A1C = CB1/B1A which is not equal to 1
If AB/A1B1 = BC/B1C1} = CA/C1A1 prove that triangle ABC is equilateral.

Answer:

8a + 3a^2 + 8

Step-by-step explanation:

[tex] - \frac{x}{2} - 1 = (y - 3) {}^{2} [/tex]

[tex] - 0.5(x + 2) = (y - 3) {}^{2} [/tex]

A parabola with a vertex (-2,3)

If a sum of $500 were shared among a group of people in the following ratios,

a) 6:4 then, 6x = 300 and 4x = 200.

b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.

c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50

d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.

What is ratio?

a) 6:4

Let it be 6x , 4x

6x + 4x = 500

10x = 500

x = 50

Then, 6x = 300 and 4x = 200.

b) 1:4:5

Let be x, 4x, 5x

x + 4x + 5x = 500

10x = 500

x = 50.

Then x = 50 , 4x = 200 and 5x = 250.

c) 1 : 8 : 1

x + 8x + x =500

10x = 500

x = 50

Then, x =50 , 8x = 400 and x = 50

d) 10 : 5: 4: 1

10x + 5x + 4x + x = 500

20x = 500

x = 25

Then, 10x = 250 , 5x = 125, 4x = 100, x = 25.

Hence, If a sum of $500 were shared among a group of people in the following ratios,

a) 6:4 then, 6x = 300 and 4x = 200.

b) 1:4:5 then, x = 50 , 4x = 200 and 5x = 250.

c) 1 : 8 : 1 then, x =50 , 8x = 400 and x = 50

d) 10 : 5: 4: 1 then, 10x = 250 , 5x = 125, 4x = 100, x = 25.

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The ratio shows how many times one value is contained in another value.

The number of top dogs is 192.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

The ratio of top dogs to fat cats was 24 to 19.

if they were 152 fat cats.

This means,

Number of top dogs = 24x

Number of fat cats = 19x

Now,

Number of fat cats = 152

This means,

152 = 19x

x = 8

Now,

Number of top dogs = 24x

= 24x

= 24 x 8

= 192

Thus,

The number of top dogs is 192.

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The probability of the defective items is given as 0.015.

Given that,
A production line estimates that 1.50% of the items it produces is defective. In a package containing 200 items,

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
Number of the item = 200
1.5% of the item is defective, = 0.015 [200]
Probability of the defective item = 0.015[200] / 200 = 0.015

Thus, the probability of the defective items is given as 0.015.

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Answer:

sinA = 7/25

tanX = 35/12

Step-by-step explanation:

Trigonometric ratio for:

sinA = perpendicular/hypotenuse = 14/50 = 7/25

tanX = perpendicular/base = 35/12

Answer:

0,02

Step-by-step explanation:

i got it correct

Answer:

[tex]\frac{12}{35}[/tex]

Step-by-step explanation:

multiple the numerators together 2 x 6  = 12 and multiply the denominators togethers 5 7 = 35

The expected value of the game, given the amounts to be made when a number is rolled, is  $ 1.25

First, find the probability of rolling an 8 :
= Number of eights / Number of sides

= 1 / 8

= 0.125

The the probability of rolling an odd number :

= Odd numbers from 1 to 8 / Number of sides

= 4 / 8

= 0.5

The expected value of the game is:

= ( Probability of getting an 8 x Amount if you get 8 ) + (  Probability of getting an odd x Amount if you get an odd ) + (  Probability of not getting an 8 or odd x Loss )

=  ( 0.125 x 9 ) + ( 0.5 x 1 ) + ((1 - 0.125 - 0.5) x  -1)

= $ 1.25

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1.6 seconds. The ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.

To find the time it takes for the ball to hit the canopy, we need to solve the equation h(t) = 12 for t.

The given equation for h(t) is h(t) = -16t^2 + 52, so we can substitute this into the equation h(t) = 12 to get:

12 = -16t^2 + 52

To solve this equation, we can move all the terms to one side of the equation to get:

-16t^2 + 40 = 0

We can then divide both sides of the equation by -16 to get:

t^2 - 2.5 = 0

We can then use the quadratic formula to solve for t:

t = +/- sqrt(2.5)

t = +/- 1.58

Thus, the ball will hit the canopy after 1.58 seconds or -1.58 seconds. Since the time cannot be negative, the ball will hit the canopy after 1.58 seconds.

Rounding this answer to the nearest tenth gives us 1.6 seconds, so the correct answer is 1.6 seconds.

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The rate of change of the modelled equation is 3.5 and the initial value is 5.

Linear equation can be represented in different form such as slope intercept form, point slope form, general form and standard form.

Equation in slope intercept form is as follows:

y = mx + b

where

Therefore, Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modelled by the function y = 3.5x + 5 where y is the total miles jogged and x is the number of hours.

The equation is modelled in slope intercept form.

Therefore,

rate of change = 3.5

initial value  = 5

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Answer:

a

Step-by-step explanation:

just becsue

The set of scale factors that would produce a contraction under a dilation of the original image are:

B. -0.5

C. 0.5

A scale factor can be defined as the ratio of two corresponding length of sides or diameter in two similar geometric figures such as equilateral triangles, quadrilaterals, and other types of polygons.

In Mathematics, the following rules are applied to interpret and understand the dilation of a geometric figure:

For a contraction under a dilation of the original image, the scale factor (k) must either be negative or less than one (1). Therefore, the required values are -0.5 and 0.5 respectively.

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Answer:
S=64 x S = length

Value of composite function (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.

What is composite function?

Function composition is associate operation ∘ that takes 2 performs f and g, and produces a perform h = g ∘ f such h(x) = g. during this operation, the perform g is applied to the results of applying the perform f to x

Main body:

according to question;

f(x) = 2x³

g(x) = 3x³ -2

we need to find composite function:

f o g (x) = 2(3x³-2)

{to find composite function , we replace one function as value of x in another}

f o g(x) = 6x³ -4

           = 6x³ -4

f o g(1) = 6*1 -

          = 2

g o f(x) = 3(2x³)-2

g o f(x) = 6x³ -2

           = 6x -2

g o f(1) = 6*1 -2

           = 5

Hence value of (f∘g)(1) and (g∘f)(1) are 2 , 5 respectively.

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The rate of change of the function that is defined by the table:

X: 2 4 6 8 10

Y: 4 8 12 16 20

is r = 2

For a function with two known points (x₁, y₁) and (x₂, y₂), the rate of change between these two points is written as:

r = ( y₂ - y₁)/(x₂ - x₁)

Here we have the table that defines a function:

X: 2 4 6 8 10

Y: 4 8 12 16 20

Here we can use any pair of two points on the table, for example, if we use the first pair and last pair:

(2, 4) and (10, 20)

The rate is:

r = (20 - 4)/(10 - 2) = 16/8 = 2

If we use the first two pairs (2, 4) and (4, 8) we get:

r = (8 - 4)/(4 - 2) = 4/2 = 2

So the rate of change of the function is r = 2.

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A vertex with degree 2 in a graph has an edge that loops around itself. The graph is therefore a cycle graph.

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The probability that their mean pulse rate is less than 80 beats per minute is of:

0.7389 = 73.89%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 76, \sigma = 12.5, n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25[/tex]

The probability that their mean pulse rate is less than 80 beats per minute is the p-value of Z when X = 80, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (80 - 76)/6.25

Z = 0.64

Z = 0.64 has a p-value of 0.7389.

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The area of the figures is shown:

Rectangle A: 54 units²

Rectangle C: 21 units²

Triangle B: 3 units²

The measurement that expresses the size of a region on a plane or curved surface is called an area.

Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The area of rectangle A:

Area = l*b

Area = 9*6

Area = 54 units²

Area of rectangle C:

Area = l*b

Area = 3*7

Area = 21 units²

Area of triangle B:

Area = 1/2 * b * h

Area = 1/2 * 3 * 2

Area = 1 * 3

Area = 3 units²

Therefore, the area of the figures is shown:

Rectangle A: 54 units²

Rectangle C: 21 units²

Triangle B: 3 units²

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A trigonometric equation is an equation containing one or more trigonometric ratios of unknown angles. It is expressed as the ratio of the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation.

What are examples of trigonometric equations?

Trigonometric equations are equations containing trigonometric functions with one variable. For example, sin x + 2 = 1 is an example of a trigonometric equation. The equation can be as simple as this, or as complex as sin2 x – 2 cos x – 2 = 0.

What are the 4 types of trigonometry?

Side length ratios can be found with six trigonometric functions. The six functions are sine (sin), cosine (cos), tangent (tan), cosecant(cosec), secant (sec), and cotangent (cot).

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Answer(s):

[tex]\displaystyle y = 3sin\:(\frac{2}{3}x + \frac{\pi}{2}) + 2 \\ y = -3cos\:(\frac{2}{3}x \pm \pi) + 2 \\ y = 3cos\:\frac{2}{3}x + 2[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{3}{4}\pi} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{2}{3}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 3[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 2 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\pi} \hookrightarrow \frac{2}{\frac{2}{3}}\pi \\ Amplitude \hookrightarrow 3[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3sin\:\frac{2}{3}x + 2,[/tex]in which you need to replase “cosine” with “sine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{3}{4}\pi\:units[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{3}{4}\pi\:units,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{3}{4}\pi} = \frac{-\frac{\pi}{2}}{\frac{2}{3}}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\:(\frac{2}{3}x + \frac{\pi}{2}) + 2.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits [tex]\displaystyle [-4\frac{1}{2}\pi, -1],[/tex]from there to [tex]\displaystyle [-1\frac{1}{2}\pi, -1],[/tex]they are obviously [tex]\displaystyle 3\pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 3\pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 2,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

By using the concept of unitary method, it can be calculated that

a) For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required

b) For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here, unitary method will be used

The double number line has been shown below-

a) For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required

   For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required

   For 350 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 350[/tex] bags of mortar are required

   For 350 blocks of cement, [tex]\frac{35}{4}[/tex] bags of mortar are required

   For 350 blocks of cement, [tex]8\frac{3}{4}[/tex] bags of mortar are required

b)  For 100 blocks of cement, [tex]2\frac{1}{2}[/tex] bags of mortar are required

   For 1 block of cement, [tex]\frac{5}{2} \times \frac{1}{100}[/tex] bags of mortar are required

   For 50 blocks of cement, [tex]\frac{5}{2} \times \frac{1}{100} \times 50[/tex] bags of mortar are required

   For 50 blocks of cement, [tex]\frac{5}{4}[/tex] bags of mortar are required

   For 50 blocks of cement, [tex]1\frac{1}{4}[/tex] bags of mortar are required

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Answer:

  (a) (1, -3)

  (b) (2, -2)

Step-by-step explanation:

You want to identify two points on the line through (3, -1) that has a y-intercept of -4.

Graphing the line and points is suggested. The attached shows that graph, and identifies the two points on the line as ...

  (1, -3) and (2, -2)

__

Additional comment

The equation of the line is x-y=4, so you can tell if the points fall on the line by seeing if they have that difference.

The value of p pennies, n nickels and twice as many quarters as pennies is (51p + 5n) cents or  $(51p + 5n)/100.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).

Given that you have p number of coins of pennies, n number of coins of nickels and  twice as many quarters as pennies.

Thus the number of coins of quarters is 2p.

The value of penny, nickel, and quarter are

1 penny = 1 cent

1 nickel = 5 cents

1 quarter = 25 cents

The value of p number of pennies is p cents.

The value of n number of nickels is (n×5) =5n cents.

The value of 2p number of quarter is (2p × 25) = 50p cent.

The total value is p + 5n + 50p = (51p + 5n) cents

Divide 51p + 5n by 100 to convert it into dollar:

(51p + 5n) cents = $(51p + 5n)/100

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Answer:

9.22 minutes

Step-by-step explanation:

You could use the form y=mx + b to find this equation

y will represent the total liters

x will represent the total number of minutes

b will represent the initial number of liters in the beginning

1. Plug 194 in for y, plug 9 in for m, put 111 in place of b

The equation should look be:  [tex]194 = 9x + 111[/tex]

2. Solve the equation

3. Subtract 111 on both sides. The equation would now be:  [tex]83 = 9x[/tex]

4. Divide both sides by 9 (to get x by itself). [tex]\frac{83}{9} = 9.22222222[/tex]

5. Round to the nearest hundredth place to get 9. 22 minutes

Answer:

x>-3

Step-by-step explanation:

1

Add

3

to both sides

-3x-3<6

-3x-3+

2

Simplify

Add the numbers

Add the numbers

-3x<9

3

Divide both sides by the same factor, and flip the relation because the factor is negative

-3x<9

4

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

x>-3

For the given matrix the additive inverse property is shown.

What is additive inverse of matrix?

The matrix that is created by changing the sign of each matrix element is known as the additive inverse. -(-A)=A is the notation for the additive inverse of the matrix A.

Rows and columns serve as a measure of a matrix's dimensions. Given that it has three rows and three columns, for instance, the matrix below has a dimension of 3 x 3. Three by three can be read off as the matrix's dimension. We consequently obtain the additive inverse of the matrix

M = - M.

Consider the given matrix,

[tex]\left[\begin{array}{ccc}-6&15&-2\\9&0&-3\end{array}\right] + \left[\begin{array}{ccc}6&-15&2\\-9&0&3\end{array}\right] = \left[\begin{array}{ccc}0&0&0\\0&0&0\end{array}\right][/tex]

Here each element in first matrix is negative of the element of second matrix.

That is each element is inverse of the element in second matrix.

And the addition of elements is 0.

Hence, for the given matrix the additive inverse property is shown.

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Answer:

C is the answer

Step-by-step explanation:

Stem and leaf plots were also confusing to me at first, but once you understand they are actually easy!

Look at the first column where it says 2,3,4,5 and 6. Those are the tens place. The columns next to it with 2,3,8,9,etc are the ones place. For example, the first column has two, so we know that the number has a two in the tens place.

2_

Look at the numbers next to it, there's 2,3, and 8.

Since there's 3 numbers, that means that there are three numbers that have a two in the ones place. 2,3 and 8 are the numbers that go in the ones place.

So in the graph there is 22,23 and 28.

If you look at your choices, you can find all of them except 38, since on the row with the 3, next to it is the number 9 and not the number 8.

Answer: You Like Big Black Men and You love them dancing on you

Step-by-step explanation:

I have your search history ;)

The system of inequalities can LaShonda use to find the number of tickets she can buy will be;

⇒ x + y ≤ 25

⇒ 22.50x + 17.50y < 400

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

She wants to have at least 25 tickets. Each adult ticket costs $22.50 and each child ticket costs $17.50.

LaShonda wants to spend no more than $400.

Now,

Let the number of adult tickets = x

And, The number of child tickets = y

Here, She wants to have at least 25 tickets.

So, We get;

⇒ x + y ≤ 25

And, Each adult ticket costs $22.50 and each child ticket costs $17.50.

LaShonda wants to spend no more than $400.

So, We get;

⇒ 22.50x + 17.50y < 400

Thus, The system of inequalities can LaShonda use to find the number of tickets she can buy are;

⇒ x + y ≤ 25

⇒ 22.50x + 17.50y < 400

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Answer:

0.39, 0.388, 38.38%, 3/8

Step-by-step explanation: