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Class 10>>Maths>>Triangles>>Basic Proportionality Theorem (Thales Theorem)>>In the adjoining figure, DE || AB, AD =

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In the adjoining figure, DE || AB, AD = 7 cm, CD = 5 cm and BC = 18 cm. Find BE and CE.

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The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.

It is given that DE∣∣AB,AD=9cm, CD=5 cm and BC=13.5 cm.

Using the basic proportionality theorem, we have

CACD=ABDE=CBCE

⇒CACD=CBCE

⇒125=18CE

⇒18×5=12CE

⇒12CE=90

⇒CE=1290=7.5

Since CE=7.5 cm, therefore,

CB=CE+EB

⇒18=7.5+EB

⇒EB=17−7.5=9.5

Hence, BE=10.5 cm and 

9 dimes and 6 quarters

Answer:

To calculate the area of a sector, we can use the formula:

A = (θ/2) * r^2

where:

A is the area of the sector,

θ is the central angle of the sector in radians, and

r is the radius of the sector.

Given:

r = 2 (radius)

θ = 1.75 radians (central angle)

Plugging in the given values into the formula:

A = (1.75/2) * 2^2

A = 0.875 * 4

A = 3.5

So, the area of the se

These triangles can be proven congruent by using ASA RULE.

What is congruent triangles and its rules ?

When two triangles are congruent, their three sides and their three angles match precisely.

If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.

ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.

Main Body:

In ΔTUV and ΔTWV

VT =VT                 ----(1)

∠VTU=∠TVW      -----(2)

As TUVW is a parallelogram

so, ∠T = ∠U

hence, ∠TVU =∠VTW    ----(3)

taking equation 1, 2,3

therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.

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Answer umm i think oiuyg

Step-by-step explanation:

what is third law of motion/cihqepgpmy explain with example and what is different between pressure and area

Answer:

x^2 + 2

Step-by-step explanation:

The value of (2x2 + 4) ÷ 2 =

(2x2 + 4)/2 =

(2(x2 + 2))/2 =

x^2 + 2

Answer:

21 minutes

Step-by-step explanation:

hope it helps you

Answer:

  -4

Step-by-step explanation:

You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².

The product of the functions is the product of their values for each value of x.

  (f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)

  (f·g)(-1) = -4

The answer to the work shown is x = 8.

The law of indices are laws that has to be applied to expressions involving powers or fractions. These laws have individual application.

Considering the given question, we have;

16^(3x - 6) = 64^(x + 4)

It can be deduced that, the factors of;

16 = 4 x 4

   = 4^2

and

64 = 4 x 4 x 4

    = 4^3

So that;

4^2(3x - 6) = 4^3(x + 4)

Divide through by 4 to have;

2(3x - 6) = 3(x + 4)

6x - 12 = 3x + 12

collect like terms,

6x - 3x = 12 + 12

6x = 24

x = 24/6

  = 8

The answer to the work shown in the question is: x = 8

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Therefore, 70% of state capitals do not have interstate highways serving them.

Percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred". Percentages are usually denoted by the symbol %, which is placed after the numerical value. Percentages are used in many fields, including finance, science, and everyday life, to represent proportions, rates, and changes in quantities.

Here,

If all but 36 of the 120 state capitals have an interstate highway serving them, then the number of capitals that do not have interstates is 120 - 36 = 84.

To find the percentage of capitals that do not have interstates, we need to divide the number of capitals without interstates by the total number of capitals and then multiply by 100:

84 / 120 x 100% = 70%

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A fraction of the students who have brown hair is equal to 1/7.

You should shade only one (1) section on the pie chart to show the number of students with brown hair.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;

Number of brown hair = 1 brown hair.

Number of blonde hair = 4 blonde hair.

Number of black hair = 2 black hair.

Therefore, the total number of hairs is equal to 7 hairs.

For the fraction of students with brown hair, we have;

Fraction = 1/7.

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Answer:

I can help you, just tell me what it is.

Step-by-step explanation:

Step 1: Tell me the problem

Step 2: Wait for a response.

Answer:

yes it can help in some ways I think

The dimensions of the room are approximately 7 meters by 10.5 meters.

In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape. A rectangle has length and width as its dimensions that define the area of a rectangle.

Let's start by using algebra to represent the information given in the problem. Let x be the width of the rectangular room, then the length is 1.5 times the width or 1.5x.

The perimeter of a rectangle is the sum of the lengths of all its sides, which can be expressed as:

\(\text{Perimeter} = 2(\text{length} + \text{width})\)

Substituting the values we have for length and width, we get:

\(\rightarrow35 = 2(1.5\text{x} + \text{x})\)

Simplifying the equation, we get:

\(\rightarrow35 = 2(2.5\text{x})\)

\(\rightarrow35 = 5\text{x}\)

\(\rightarrow\text{x}=\dfrac{35}{5}\)

\(\rightarrow\bold{x\thickapprox7}\)

So the width of the room is 7 meters.

To find the length, we can substitute x into the expression we have for the length:

\(\rightarrow\text{Length} = 1.5\text{x}\)

\(\rightarrow\text{Length} = 1.5(7)\)

\(\rightarrow\bold{Length=10.5}\)

So the length of the room is 10.5 meters.

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Answer:

\(\displaystyle k = \frac{34}{3}\)

Step-by-step explanation:

We are given the polynomial:

\(\displaystyle P(x) = 3x^3 - kx^2 + 5x + k\)

And we want to determine the value of k such that (x - 2) is a factor of the polynomial.

Recall that the Factor Theorem states that a binomial (x - a) is a factor of a polynomial P(x) if and only if P(a) = 0.

Our binomial factor is (x - 2). Thus, a = 2.

Hence, by the Factor Theorem, P(2) must equal zero.

Find P(2):

\(\displaystyle \begin{aligned} P(2) &= 3(2)^3 - k(2)^2 + 5(2) + k \\ \\ &= 3(8) - 4k + 10 + k \\ \\ &= 34 - 3k \end{aligned}\)

This must equal zero. Hence:

\(\displaystyle \begin{aligned} 34 - 3k &= 0 \\ \\ -3k &= -34 \\ \\ k = \frac{34}{3} \end{aligned}\)

In conclusion, k = 34/3.

Answer:

11/2 times 1/3 is 11/6

Step-by-step explanation:

11/2 times 1/3,

We have to multiply the numerators and denominators,

\((11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6\)

hence we get 11/6

The range of the data is the difference between the highest and lowest values, which is 8 inches. Adding another plant with a height of 14 inches would not change the range, so the range would remain 8 inches.

Data is a collection of facts, figures, or information that can be processed and used to draw conclusions or make decisions. It can be stored in a variety of formats, including numerical, text, images, audio, and video. Data can be collected from a variety of sources, such as surveys, observations, experiments, or transactions. It can be used to inform decisions in areas such as business, health care, education, and research. Data can be analyzed to gain insight, develop strategies, identify trends, and make predictions. Data is a valuable resource and is increasingly important in today's digital age.

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1, 3n=8.

2, 1/4n=5.

3, n+4=9.

4, n-6=7.

5, n/3=8.

6, 5n=18.

7, n-7=16.

8, 5n=40.

9, n-8=15

10, 4x/3=28

Step-by-step explanation:

Answer:

(0,2)

Step-by-step explanation:

2:4 means one part is 2/(2+4)=1/3 of AB and the other part is 2/3 of AB

Add 1/3 of the distance from -2 to 4. (1/3)(4+2)=2. -2+2=0 The x coordinate is 0

Subtract 1/3 of the distance from 6 to -6, (1/3)6+6)=4 6-4=2 The y coordinate is 2

The point is (0,2)

We want to find the values of x and y. To do, we will use some trigonometric ratios to find their values.

Recall that given a triangle of this form

From this triangle we can define the following trigonometric ratios

Using the angle of 45° as a reference, we can write

Then, if we multiply both sides by x, we get

so, if we divide by cos(45) on both sides, we get

Using that

we have that

Now, we want to calculate the value of y. To do so, we can use the tangent as follows

then multiplying both sides by 3*sqrt(2) we get

Using the fact that

we get that

So, from this, we have that x=6 and y=3*sqrt(2)

13 diamonds, y = 3 chandeliers, x = 52 diamonds, x = 130 diamonds, y = 40 chandeliers. this is the complete table using equivalent ratios.

When we compare any two kinds of ratios, they are said to be equivalent. To determine whether these two or more ratios are equivalent, they can also be compared to one another. For instance, the ratios 1:2 and 2:4 can be called as equivalent.

Simply put, a ratio is a comparison of two numbers. When a ratio is equal, the proportionate relationship remains constant. By multiplying the first value by the same ratio, or unit of proportion, you can determine your own equivalent ratios.

It is possible to treat an equivalent ratio and a proportion interchangeably. An equivalent ratio is the result of simplifying the two ratios to the same fraction.

Let us take the value of x -----> the number of diamonds

Let us take the value of y ----> the number of chandeliers

we know that

The ratio present between the number of diamonds to that of the number of chandeliers is equal to

\(\frac{x}{y} = \frac{39}{3}\)

1) for y = 1,

x = 13 diamonds

2) for x = 39

y = 3 chandeliers

3) for y = 4

x = 52 diamonds

4) y = 10

x = 130 diamonds

5) x = 520

y = 40 chandeliers

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Answer: 52 and 130

Step-by-step explanation:

Answer:

Step-by-step explanation:

68=6x-4+2x

68=(6+2)x-4

68=8x-4

68+4=8x-4+4

72=8x

72%2F8=8x%2F8

9=cross%288%29x%2Fcross%288%29

9=x

The width:x=9km

Answer:

Step-by-step explanation:

Answer: serbia

Step-by-step explanation:

Answer: Given the following equations, determine the x value(s) that result in an equal output for both functions. f(x) = 3* g(x)=4x+1. C0 and 2.

Step-by-step explanation:

Given the following equations, determine the x value(s) that result in an equal output for both functions. f(x) = 3* g(x)=4x+1. C0 and 2.

The parts of the graph when labelled are :

There is the origin which is where the line starts from. The x-axis represents the independent variable, which is the variable that is being manipulated or changed in the experiment.

The y-axis represents the dependent variable, which is the variable that is being measured or observed. A trend line is a line drawn on the graph that shows the overall pattern or trend of the data. The x and y - intercepts are the points where the trend line crosses the x and y - axis.

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Answer:

x=5 :)

Step-by-step explanation:

Answer:

The required value of x for which the given equation is true is 5.

Step-by-step explanation:

The equation of the line in the slope-intercept form is: y = -2.00 x + 10.

The slope and provided point are both in the equation for the straight line.

The generic point (x, y) must satisfy the equation if we have a non-vertical land in a that passes through any point(x1, y1) has gradient m.

y-y₁ = m(x-x₁)

It is the necessary equation for a line in the form of a point-slope.

That gift card to the Coffee Café has been provided. = $10

Medium coffee = $2.00

customers

The quantity of coffees a consumer can purchase can be represented using a linear equation.

Slope formula

m = (8 - 10)/(1 - 0)

m = -2

Now consider the line's point-slope shape.

y-y₁ = m(x-x₁)

( y - 10) = -2.00 ( x - 0)

y = -2.00 x + 10

The slope: m = - 2.00

The equation of the line: y = -2.00 x + 10

The y-intercept is 10

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