a triangle ABC angle ABC =90 has length of the side AB= 72 cm and the length of BC = 54cm what is the length of the perpendicular line from side AC to point B?​

The opposite rational number of -3/2 is -2/3.

p/q where q is not equal to 0 is the form of a rational number, which is a sort of real number in mathematics. A rational number is any fraction with a non-zero denominator. 1/2, 1/5, 3/4, and other like numbers are a few examples of rational numbers. A rational number is one that can be stated mathematically as the quotient or fraction pq of two numbers, p and q, with p being the numerator and q being the denominator. Every integer, such as 5 = 51, is a rational number, as is the number 37.

Given,

Rational number:

-3/2

Reciprocating,

-2/3

The opposite rational number of -3/2 is -2/3.

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The quartiles of the distribution are given as follows:

The sample size of the distribution is of:

n = 40.

The first quartile is the value that is greater than 25% of the distribution, hence it is the value at the position which is 25% of the sample size, hence:

The second quartile is the value that is greater than 50% of the  distribution, hence it is the value at the position which is 50% of the sample size, hence:

The third quartile is the value that is greater than 75% of the  distribution, hence it is the value at the position which is 75% of the sample size, hence:

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The equation that represents the relationship on the graph attached below is: y = 4/5x + 3.

Given a linear graph like the one attached below, showing the relationship between x and y, the equation that represents the relationship between x and y in the given graph can be expressed as: y = mx + b, where m is the slope (m) and b is the y-intercept (b) of the graph.

In the given image, the line intercepts the y-axis at 3, therefore the y-intercept of the graph is b = 3.

The slope of the graph (m) = change in y / change in x = (11 - 7)/(10 - 5)

m = 4/5

To write the equation of the relationship, substitute m = 4/5 and b = 3 into y = mx + b:

y = 4/5x + 3

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The representation of the given equation 'v' as subject of the formula v = 6 ( T - 5 ).

Given,

T = v / 6 + 5

substract 5 on both the sides, we get

⇒ T - 5 = v / 6 + 5 - 5

⇒ v / 6 = T - 5

Now represent 'v' as a subject of the formula we get,

v = 6 ( T - 5)

Hence, v = 6 (T - 5 ) is the representation of the given equation 'v' as subject of the formula.

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Answer:

- 2 - 16i

Step-by-step explanation:

(5 - 6i) + (- 7- 10i ) ← remove parenthesis

= 5 - 6i - 7 - 10i ← collect like terms

= (5 - 7) + (- 6i - 10i)

= - 2 + (- 16i)

= - 2 - 16i

The correct estimate is 2000. Thus, Lenore’s estimate is not reasonable

Estimation is a method used for calculating the approximate value of a quantity (just to get a 'rough answer')

In estimation 1, 2,3, and 4 are rounded down while 5, 6, 7, 8 and 9 are rounded up.

Given:  51 x 37

In order round each factor to the nearest ten to estimate the reduction

51 will be rounded down to 50 (because of the 1 after the 5 in 51)

37 will be rounded up to 40 (because of the 7 after the 3 in 37)

Thus, the estimate will be:

50 x 40 = 2000

Therefore, Lenore’s estimate is not reasonable because she rounded down 37 to 30

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Answer:

97 yards

Step-by-step explanation:

conversion factor 36 in = 1 yard

(3492/1 in)(1yd/36in)

3492/36 yd = 97 yards

Answer:

97 yards

Step-by-step explanation:

First, convert inches to feet:

3492in / 12in = 291 ft

(12 inches in one foot)

Then, convert feet to yards:

291ft / 3ft = 97 yds

(3 feet in one yard)

The line x1 = b/2a serves as the axis of symmetry for the graph of a quadratic equation with the form y1 = ax1²+bx1+c.

A parabola is the name for a quadratic function's graph.

Finding the vertex for the given equation is the first step in drawing a parabola graph. To accomplish this, use the formulas x=-b/2a and y=f(-b/2a). When the quadratic equation is stated in the vertex form, f(x) = a(x-h)2 + k, where (h, k) is the parabola's apex, the graph is plotted.

Let y equal the phrases on both sides of the equal sign as the first step.

Step 2: Graph the two newly formed functions.

Step 3: Estimate the location(s) where the function graphs intersect.

Hence a quadratic equation with the form y1 = ax1²+bx1+c is graphed, and the line x1 = b/2a acts as the axis of symmetry.

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Answer:

See below

Step-by-step explanation:

From the graph , function 1 has a max value of   1 at  4,1

From the equation for function 2, its max occurs at x = - b/2a = - (2/(2*-1) = 1

   plugging in this value shows max value of   - 14     (1,-14)  

69200000 in scientific notation is  6.92 × 10⁷.

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

Scientific Notation is a special way of writing numbers:

For example 800 is written as 8 × 10² in Scientific Notation.

Therefore, let's write the scientific notation of the number 69200000.

Hence,

69, 200, 000 = 6.92 × 10⁷

The logic is that we will count backwards until we meet the last number. Since we counted towards the left side, the exponent will be positive.

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Answer:

no

Step-by-step explanation:

For a relation to be a function each input must have only one output.

If you look at the points (-4,-1) and (-4,-3) you can see that The input (-4) has more than one output (-1 and -3), so it is not a function.

Answer:

A(1,2) -> A'(3,6)

B(3,1) -> B'(9,3)

Step-by-step explanation:

A(1,2) ×3 -> A'(3,6)

B(3,1) ×3 -> B'(9,3)

Answer:

a)  A = (1, 2),   A' = (3, 6)

b)  B' = (9, 3)

Step-by-step explanation:

From inspection of the given diagram:

   A = (1, 2)

   A' = (3, 6)

As the triangle has been enlarged by a scale factor of 3 and centre (0, 0), to find the coordinates of B' simply mulitply the coordinates of B by the scale factor:

   As B = (3, 1)

   ⇒ B' = (3 × 3, 1 × 3) = (9, 3)

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=[tex]\frac{550}{c}[/tex]

csin8°=550

c=550/sin8°

c= 3,952

The required value of x is  135° in the given polygon. which is the correct answer would be an option (A).

A polygon is given in the figure

According to the given question, the required solution would be as:

Number of sides = 8

The required value of x is the equal to measure of one Interior angle in the given polygon.

Interior angles of a polygon = (sides - 2) × 180°

In this case, the number of sides is 8

Sum of Interior angles = (8 - 2) × 180

Sum of Interior angles = (6) × 180

Sum of Interior angles = 1080°

the measure of one Interior angle = 180°/8

the measure of one Interior angle = 135°

Thus, the required value of x is  135°.

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Answer:

56 cm²

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{3.5 cm}\underline{Area of a rectangle}\\\\$A=w\;l$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]

The given composite figure is made of two rectangles joined together.

Area of rectangle 1

[tex]\begin{aligned}\implies A&=4 \cdot 8\\&=32\; \sf cm^2\end{aligned}[/tex]

Area of rectangle 2

[tex]\begin{aligned}\implies A&=(8-5)(12-4)\\&=3 \cdot 8\\&=24\; \sf cm^2\end{aligned}[/tex]

Therefore:

[tex]\implies \textsf{Total area}=32+24=56\; \sf cm^2[/tex]

Answer:

56 cm²

Step-by-step explanation:

We are interested in finding the area of the given shape which is made up of two rectangles .

(for figure refer to the attachment)

Step 1 : Find the area of two rectangles

[tex]\longrightarrow Area_{AGHE}= length \times breadth \\[/tex]

[tex]\longrightarrow Area_{AGHE}= 5cm (4cm)\\[/tex]

[tex]\longrightarrow Area_{AGHE}= 20cm^2 [/tex]

Again ,

[tex]\longrightarrow Area_{GBCD}= 3cm(12cm)\\[/tex]

[tex]\longrightarrow Area_{GBCD}=36cm^2[/tex]

Step 2: Add up the areas

[tex]\longrightarrow Area = 20cm^2+36cm^2\\[/tex]

[tex]\longrightarrow \underline{\underline{Area = 56cm^2}}[/tex]

Answer:

Step-by-step explanation:

A. 60 + 30 = 90

B. 690000

C. 90 x 2000 = 180000

The dimension outside the frame is 11 inches long and 9 inches wide.

In the given question we have to find the outside dimensions of the frame.

In the given question, a picture 10 inches long by 8 inches wide has a frame whose area is one half the area of the picture.

The dimension of a picture is 10 inches long by 8 inches wide.

The area of the frame is one half i.e(1/2=0.5)to the area of the picture.

So the length of the frame is

=10+0.5+0.5

=11 inches

The width of the frame is

=8+0.5+0.5

=9 inches

Hence, the dimension outside the frame is 11 inches long and 9 inches wide.

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Answer:

68 and 40

Step-by-step explanation:

x - y = 28

x * y = 2720

x = 28 + y

(28+y)y = 2720

28y+y^2 = 2720

y^2 + 28y - 2720 = 0

discriminant = 28^2 - 4(-2720) = 784 + 10 880 = 11 644

we are searching only the positive value

y = (-28 + 108)/2 = 80/2 = 40

x = 28 + 40 = 68

Answer:

51 x 51 = 2601

Step-by-step explanation:

Answer:

2601

Step-by-step explanation:

hope it helps

Answer:

[tex]r=12, y=12x[/tex]

Step-by-step explanation:

[tex]\frac{y}{x}=\frac{48}{4}=12 \\ \\ \therefore r=12 \implies y=12x[/tex]

1.2.1 There are 18 houses in the neighborhood.

1.2.2 The building located next to the park is the hospital.

1.2.3 The business which appears more than all the other businesses in the neighborhood is the Cafe.

1.2.4. The bar scale measures 25 centimeters.

1.2.5 Based on the above measurement, the scale of this street map has a scale factor of 0.005468, compared to the original distance of the neighborhood.

1.2.6 There are 3 more houses in the street at the top than the street at the bottom.

The scale factor is the ratio between two scales of an object.

The scale factor shows how larger or smaller the new scale is compared to the old scale (original measurement).

The formula for the scale factor is as follows:

Scale factor = Dimension of the new scale ÷ Dimensions of the original scale.

1 yard = 91.44 centimeters

50 yards = 4,572 centimeters (91.44 x 50)

The original (larger) dimension of the neighborhood = 50 yards or 4,572 centimeters

Scale (smaller) dimension of the map = 25 centimeters

Scale factor = Smaller dimension/Larger dimensions

= 25/4,572

= 0.005468

The number of houses at the top street = 8

The number of houses at the center street = 5

The number of houses at the bottom street = 5

The total number of houses in the neighborhood = 18

The difference between the top street houses and the bottom street houses = 3 (8 - 5)

The number of cafes = 2

The number of parks = 1

The number of other businesses = 1 each

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Answer:

B and F

Step-by-step explanation:

B: f(x) = 2 lx+1l +3 vertex: (-1,3)

F: f(x) = lx+1l +3 vertex: (-1,3)

Answer:

mixed number: 12 2/5

improper fraction: 62/5

Step-by-step explanation:

Answer:

[tex]\frac{4\pi }{5}[/tex]

Step-by-step explanation:

the 2 angles lie on the x- axis and sum to π , then the curved arrow angle is

π - [tex]\frac{\pi }{5}[/tex] = [tex]\frac{5\pi }{5}[/tex] - [tex]\frac{\pi }{5}[/tex] = [tex]\frac{4\pi }{5}[/tex]

According to the given confidence interval, the number of samples for this research is 1134.

Confidence interval

Confidence interval means the percentage of probability, or certainty, that the confidence interval would contain the true population parameter when you draw a random sample many times.

Given,

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.18.

Here we need to find the number of samples.

Here we know that the Confidence level=0.99,

So, the value of

=> 1−α=0.99,

Noe, the estimate of population proportion = 0.18,

So, the value of pˆ=0.19,

And the Allowable error = 0.03

Which is E=0.03

Now, the determined value of α is calculated as,

=> α = 1 − 0.99 = 0.18

Thus, the value of z will produce 99%confidence is,

=> zα / 2 = z 0.01/2

=> z0.005 = 2.575

=> (2.575)√(.18)(1-0.18)/√0.03

Therefore, the resulting value is 1134

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The graph of the function f(x) is negative and decreasing from point a to point b.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

From the given graph of f(x) it is decreasing as it is going downwards in the interval from a to b where x is increasing and the graph is negative also in the interval a to b as it is in the negative y-axis.

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The percentage of the purchase price is 180%

In this question, the figures are given as

Amount bought = $55

Amount sold = $99

These figures can be represented as

Cost price = 55

Selling price = 99

The sales price as a percentage of the purchase price is then calculated as

Percentage = Selling price/Cost price

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

Percentage = 99/55

Evaluate

Percentage = 1.8

Express as percentage

Percentage = 180%

Hence, the percentage is 180%

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The probabilities are given as follows:

a) Ann gets Introduction to Counting & Probability: 1/4 = 0.25 = 25%.

b) Ann gets Introduction to Counting & Probability and Beth does not get Introduction to Geometry: 1/6 = 0.167 = 16.7%.

c) Counting & Probability and Beth does not get Introduction to Geometry and Caleb gets Introduction to Algebra: 1/24 = 0.0417 = 4.17%.

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

In this problem, the total number of outcomes is the arrangements of 4 elements, hence:

Total = 4! = 24.

For item a, we want Ann to get one book, and the remaining 3 books are arranged, hence the probability is of:

p = 3!/4! = 1/4 = 0.25 = 25%.

For item b, we want for Ann to get one book, Beth can get 2 of them, and the remaining 2 are arranged, hence the probability is of:

p = 2 x 2!/4! = 4/24 = 1/6 = 0.167 = 16.7%.

For item c, we have a fixed book for each student, hence the probability is of:

p = 1/24 = 0.0417 = 4.17%.

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The values of the expression are;

1. bd/a + c = 6

2.  ac/b - (a + d) = 14

3. d³/a² - (c + b) = 63/4

4. pr/n + m = - 48

5.  p²/m - (np + r) = 10

6. p³/r² - (m + np) = 16

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are,

a = - 2, b = 3, c = - 12 and d = - 4

m = - 32, n = 2, p = - 8 and r = 4

Now,

Find the values of the expressions as;

1. bd/a + c

Substitute all the values, we get;

bd/a + c = (3 x - 4)/(-2) + (-12)

             = - 12/- 2 - 12

             = 6 - 12

             = - 6

2. ac/b - (a + d)

Substitute all the values, we get;

⇒ ac/b - (a + d) = - 2 x - 12 /3 - (- 2 - 4)

                    = 8 + 6

                    = 14

3. d³/a² - (c + b)

Substitute all the values, we get;

d³/a² - (c + b) = 3³/(-2)² - (-12 + 3)

                    = 27/4 + 9

                    = 63/4

4. pr/n + m = - 8 x 4 /2 + (-32)

                 = - 16 - 32

                 = - 48

5. p²/m - (np + r) = (-8)²/- 32 - (2 x - 8 + 4)

                         = - 64/32 - (- 16 + 4)

                          = - 2 + 12

                          = 10

6. p³/r² - (m + np) = (-8)³/4² - (- 32 + 2 x - 8)

                           = - 32 - (- 32 - 16)

                           = - 32 + 48

                           = 16

Thus, The values of the expression are;

1. bd/a + c = 6

2.  ac/b - (a + d) = 14

3. d³/a² - (c + b) = 63/4

4. pr/n + m = - 48

5.  p²/m - (np + r) = 10

6. p³/r² - (m + np) = 16

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