follow the steps to find the area of the Shaded region. use trigonometry to find the height of the triangle. ROUND TO THE FOURTH DECIMAL PLACE!

The equation of the line that passes through the points  (9,2) and (3,4) is x + 3y = 15  and the graph  is shown below .

In the question ,

it is given that

the required line passes through the points (9,2) and (3,4)

in order to find the equation of  line we first need to find slope .

so , the slope(m) will be

m = (4-2)/(3-9)

m = 2/(-6)

m = -1/3

The equation of the line passing through the point (3,4) having slope -1/3 is

y - 4 = (-1/3)(x - 3)

3(y - 4) = -1(x - 3)

3y - 12 = -x + 3

x + 3y = 12 + 3

x + 3y = 15

the graph of the line is drawn below .

Therefore ,The equation of the line that passes through the points  (9,2) and (3,4) is x + 3y = 15  .

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The distance of the intersection of 3 perpendicular bisectors of a triangle to  the 3 vertices are equal.

In other words, HF = HE = HG.

Therefore, we see that 3 isosceles triangles are identified : HFE, HFG, HGF.

We're given HF = 15, therefore HE = 15.

Since HJ is the perpendicular bisector of line EG, JE = JG.

Therefore, JE = 12.

Now, we use the Pythagorean theorem in the right triangle HJE :

[tex]HE^{2} = HJ^{2} + JE^{2} - > HJ = \sqrt{15^{2} - 12^{2} } =\sqrt{81} = 9.[/tex]

Answer:

The answer would be -4/5

Step-by-step explanation:

When you add a negative to a negative, you first take out the plus sign and rewrite it as: -2/5 - 2/5.

Now you just simply subtract 2/5 from -2/5 to get -4/5.

Hope this helps.

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Answer: a) = 4

b) = 30

Step-by-step explanation:

a) They are asking for the range of the marks so you do 10-6 as 10 is the highest mark and 6 is the lowest

b) You find this out by adding the frequency up 10+4+7+4+5 = 30

Answer:

infinite solution

Step-by-step explanation:

Since 0 = 0 for any value of y, the system of equations has infinite solutions.

The greatest percent error among the predictions is of:

2.23%.

The percent error of a measure is obtained by the division of the difference between the actual value and the estimated value by the actual value, and multiplied by 100%, hence the equation is:

Percent error = |Actual - Estimate|/Actual x 100%.

From the given dot plot, we have that the farthest measure from 22.4 seconds is of 22.9 seconds.

The difference between the actual time and the estimate time is of:

22.9 seconds - 22.4 seconds = 0.5 seconds.

Applying the presented division, the percent error is given as follows:

Percent error = 0.5/22.4 x 100% = 2.23%.

The dot plot is given by the image at the end of the answer.

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Answer:

85 ggoooofffffyyy

Step-by-step explanation:

Answer:

  no

Step-by-step explanation:

You want to know if side lengths 26 in, 36 in, 46 in form a right triangle.

The integer side lengths will form a right triangle if they are a Pythagorean triple, or a multiple of one.

We notice that these side lengths have a common difference of 10 in. That makes them an arithmetic sequence. The only Pythagorean triples that are an arithmetic sequence are {3, 4, 5} and its multiples. The shortest side is 3 times the common difference.

The lengths {26, 36, 46} cannot form a right triangle. The attachment shows the triangle is an obtuse triangle.

No, the triangle is not a right triangle.

__

Additional comment

The side lengths will form a right triangle if and only if they satisfy the relation a² +b² = c², where a, b are the two short sides.

  26² +36² = 1972 ≠ 2116 = 46²

By using addition and multiplication, the result obtained is

Kianna saves $3020 this year

What is addition and multiplication?

Suppose there are many numbers. To get the sum total of all the numbers, addition is used

Repeated addition is called multiplication

Addition and multiplication will be used here

Amount of money Kianna saves each month for the first 7 months = $215

Total amount of money Kianna saved in the first 7 months = $215 [tex]\times[/tex] 7

                                                                                                  = $1505

Amount of money she saves each month for the last 5 months = $305

Amount of money she saves in the last 5 months = $305 [tex]\times[/tex] 5 = $1515

Total amount of money Kianna saves this year = $(1505 + 1515)

                                                                              = $3020

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7. The composite functions are given as follows:

a. f(g(x)) = [tex]\frac{3x}{-x^2 + 3x - 1}[/tex].

b. g(f(x)) = [tex]\frac{3x(x - 1)}{9x^2 + x - 1}[/tex]

c. (f(g(3)) = -9.

8. The inverse function is given as follows:

[tex]f^{-1}(x) = \frac{4 + x}{3 - x}[/tex]

The composite functions are obtained using the inner function as the input to the outer function.

In this problem, the functions are defined as follows:

The composite of f and g is:

[tex]f(g(x)) = f\left(\frac{3x}{x^2 + 1}\right) = \frac{\frac{3x}{x^2+1}}{\frac{3x}{x^2+1} - 1} = \frac{\frac{3x}{x^2+1}}{\frac{-x^2 + 3x - 1}{x^2 + 1}} = \frac{3x}{-x^2 + 3x - 1}[/tex]

At x = 3, the numeric value of the composite function is given as follows:

f(g(3)) = 9/(-9 + 9 - 1) = -9.

The composite function of g and f is given as follows:

[tex]g(f(x)) = g\left(\frac{x}{x - 1}\right) = \frac{\frac{3x}{x - 1}}{\left(\frac{3x}{x - 1}\right)^2 + 1} = \frac{3x}{x - 1} \times \frac{(x - 1)^2}{9x^2 + x - 1} = \frac{3x(x - 1)}{9x^2 + x - 1}[/tex]

The function is given as follows:

y = (3x + 4)/(x - 1)

The find the inverse, the variables x and y are exchanged, and then y is isolated, as follows:

x = (3y + 4)(y - 1)

xy - x = 3y + 4

3y - xy = 4 + x

y(3 - x) = 4 + x

y = (4 + x)/(3 - x)

[tex]f^{-1}(x) = \frac{4 + x}{3 - x}[/tex]

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Answer:

V<4400

Step-by-step explanation:

Answer:

the answer is V<4,400

if you are using khan academy, do not add the comma for 4,400, otherwise it will not work.

khan academy answer: V<4400

Step-by-step explanation:

if the air leaked out, which is V, that means V would be less than 4,400 because 4,400 is what we have started with.

Therefore, the inequality would be V<4,400 or for khan academy, V=4400

The graph has no vertex

The transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

However, the graph has no maximum or minimum

This means that there is absence of a vertex in the graph

Here, we have:

This transformation can be represented as (x - 4, y - 2)

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Answer:

Step 6 is wrong

Answer:

The value of the equation will be 14

Answer:

The tablet costs more than the smartphone

Step-by-step explanation:

1 year tablet = $1.50

1 year smartphone = $0.02x12months = $0.24

The perimeter of the composite figure would be = 21 (to the nearest tenth).

Perimeter is defined as the quantity that is used to evaluate the total length of the sides of an object.

From the given diagram, the composite figure is made up of 6 sides. The addition of these sides is the figures perimeter.

The sides of the composite figure are:

a = 6; b = 12; c = 9; d = 9; e = -9; f = -6.

The perimeter = a + b + c + d + e + f.

= 6 + 12 + 9 +9+ (-9) + (-6)

= 27 - 6

= 21 ( to the nearest tenth)

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Answer:

5 and 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

(a)

y = 5x - 3 ← is in slope- intercept form

with gradient m = 5

(b)

3y - 12x + 7 = 0 ( add 12x to both sides )

3y + 7 = 12x ( subtract 7 from both sides )

3y = 12x - 7 ( divide through by 3 )

y = 4x - [tex]\frac{7}{3}[/tex] ← in slope- intercept form

with gradient m = 4

The factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).

Given expression:

= 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex]

divide by 18 .

= 4[tex]a^{9} b^{3}[/tex] - [tex]a^{7} b^{5}[/tex]

divide by [tex]a^{7}[/tex]

= 4[tex]a^{2}b^{3}[/tex] - [tex]b^{5}[/tex]

divide by [tex]b^{3}[/tex]

= 4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]

= 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).

Therefore the factor of the expression 72[tex]a^{9} b^{3}[/tex] - 18[tex]a^{7} b^{5}[/tex] is 18[tex]a^{7} b^{3}[/tex](4[tex]a^{2}[/tex] - [tex]b^{2}[/tex]).

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The area of the largest rectangle is 25 square units.

It is given that the radius of the semicircle is [tex]4[/tex].

It is required to inscribe a rectangle of maximum area.

Consider a rectangle of sides [tex]x[/tex], [tex]y[/tex] as shown in the given figure.

From the attached figure,[tex]AB=x[/tex], [tex]OB=r[/tex] and [tex]OB=\frac{y}{2}[/tex].

Now, in the triangle OAB, apply Pythagoras' theorem as,

[tex](OA)^{2}=(OB)^{2}+(AB)^2[/tex]

[tex]r^2=(\frac{y}{2} )^2+x^2\\\\[/tex]

[tex]16=\frac{y}{4}+x^2[/tex]

[tex]y^2=4(16-x^2)[/tex]

[tex]y=2\sqrt{16-x^2}[/tex]

So, the area of the rectangle will be,

Area,

[tex]A = 2x \times y[/tex]

= [tex]2x \times \sqrt{(16 - x^2)}[/tex]

Differentiate the area with respect to ,

[tex]A' = 2 \times \sqrt{(16 - x^2)} - 2x^2/(16 - x^2)[/tex]

Differentiate the area twice as,

When[tex]x = 0, y = 5[/tex] and when [tex]x = 5, y = 0[/tex], [tex]area = 0[/tex].

It implies that area is maximum when the value of x lies between 0 and 5.

This will occur where [tex]A'= 0[/tex].

⇒ [tex]2 \times \sqrt{(16 - x2) }- 2x^2/(16 - x^2) = 0[/tex]

⇒[tex]2 \times \sqrt{(16 - x^2)} = 2x^2/(16 - x^2)[/tex]

On simplification, we get,

⇒ [tex]2 \times (16 - x^2) = 2x^2[/tex]

⇒ [tex]16 - x^2 = x^2[/tex]

⇒ [tex]2x^2= 16[/tex]

⇒ [tex]x^2 = 16/2[/tex]

⇒ [tex]x = \sqrt{8}[/tex]

Now, [tex]y = \sqrt{(16 - x^2)}[/tex] becomes

⇒[tex]y = \sqrt{(16 - (\sqrt8)^2)}[/tex]

⇒ [tex]y = \sqrt{(16 - 8)}[/tex]

[tex]y =\sqrt{8}[/tex]

Maximum area = 2xy

[tex]=2(\sqrt{8)}(\sqrt{8})[/tex]

[tex]=16[/tex]

Therefore, the area of the largest rectangle is 16 square units.

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[tex]\fbox{90}[/tex]

In order to find 36 is 40% of what number, we will need to use the following formula:

[tex]number\times100/Percent[/tex]

[tex]\frac{36\times100}{40}[/tex]

[tex]36\times100=3,600[/tex]

[tex]3,600\div40[/tex]

[tex]=90[/tex]

The solution of the number in the expression ''40% of a number is 36'' is 90.

Given that,

To find the solution for 40% of that number is 36.

Used the concpet of percentage which stated that,

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.

Let us assume that the solution of the given condition is x.

So, it can be written as,

[tex]40\% \times x = 36[/tex]

[tex]\dfrac{40}{100} \times x = 36[/tex]

Multiply both sides by 100,

[tex]40x = 36 \times 100[/tex]

[tex]40x = 3600[/tex]

Divide both sides by 40,

[tex]x = \dfrac{3600}{40}[/tex]

[tex]x = 90[/tex]

So, the solution for the number is 90.

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The sides of the triangle are 150m, 200m and 250m.

What is distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Given: The sides of a triangle are in the ratio of 3:4:5. A man jogged around it 5 times and cover a distance of 3000m.

As man jogged around triangle  5 times and cover a distance of 3000m.

So, the distance for one round is 3000/5 = 600m.

The covered distance is nothing but the perimeter of the triangle.

So, the perimeter of the triangle is 600m.

Let, 3x, 4x, 5x are the sides of the triangle.

⇒ 3x + 4x + 5x = 600

                 12 x = 600

                      x = 50

Therefore,

3x = 3(50) = 150

4x = 4(50) = 200

5x = 5(50) = 250

Hence, the sides of the triangle are, 150m, 200m and 250m.

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Answer:

see explanation

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence, that is

8 - 13 = 3 - 8 = - 2 - 3 = - 7 - (- 2) = - 5

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 13 and d = - 5 , then

[tex]a_{n}[/tex] = 13 - 5(n - 1) = 13 - 5n + 5 = 18 - 5n

then

a₁₀₀ = 18 - 5(100) = 18 - 500 = - 482

Using simple mathematical operations, the missing values are as follows:

(B) Dijon Mustard: 18g

(C) Barbeque sauce: 70g

(D) Worcestershire sauce: 10.35g

(E) Kosher salt: 1.5g

(F) Ground black pepper: 2.3g

(G) Crushed red pepper: 1.15g

So, we can calculate missing values as follows:

(B) Dijon Mustard: 18g

(C) Barbeque sauce: 70g

(D) Worcestershire sauce: 10.35g

(E) Kosher salt: 1.5g

(F) Ground black pepper: 2.3g

(G) Crushed red pepper: 1.15g

Therefore, using simple mathematical operations, the missing values are as follows:

(B) Dijon Mustard: 18g

(C) Barbeque sauce: 70g

(D) Worcestershire sauce: 10.35g

(E) Kosher salt: 1.5g

(F) Ground black pepper: 2.3g

(G) Crushed red pepper: 1.15g

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Answer:  The correct answer is Option D: h=2A/(b1+b2)

Step-by-step explanation:

Solve for h:

a=(1/2h)(b1+b2)

Step 1: Flip the equation

1/2b^2h+1/2b1h=a

Step 2: Factor out variable h

h((b2+b1)/2)=a

Step 3: Divide both sides by (b^2+b1)/2

h((b2+b1/2))/(b2+b1/2)=(a/(b2+b1)/2)

h=2a/(b2+b1)  

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In given word problem ending time of the play is 10.50 AM.

What is word problem?

 A comprehensive list of math word problems focuses on addition, subtraction, multiplication, division and more specific operations. life scenario. This means that children must be familiar with vocabulary associated with familiar mathematical symbols in order to understand word problems.

Here starting time of play = 9:05 AM

It took 1 hour 45 minutes to end the play. Then ,

=> 9 hour  05 minutes

    1 hour   45 minutes +

=> 10 hour 50 minutes.

Hence ending time of the play is 10.50 AM.

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The value of y that makes the two matrices inverse of each other is 1/2

The inverse of a square matrix A, denoted by A⁻¹.

The formula is [tex]\frac{1}{|A|}.adj(A)[/tex]

The product of A and A⁻¹  should be the identity matrix. The identity matrix that results will be the same size as matrix A.

Inverse of given first matrix is

[tex]\left[\begin{array}{cc}6&14\\-2&-4\end{array}\right][/tex]

Determinant = |A|  = 6(-4) - (14)(-2)

= -24 + 28

= 4

Adjoint of matrix = [tex]\left[\begin{array}{cc}-4&-14\\2&6\end{array}\right][/tex]

Inverse of matrix = [tex]\frac{1}{|A|}.adj(A)[/tex]

Therefore , Inverse = [tex]\frac{1}{4}.\left[\begin{array}{cc}-4&-14\\2&6\end{array}\right][/tex]

= [tex]\left[\begin{array}{cc}-4/4&-14/4\\2/4&6/4\end{array}\right][/tex]

A⁻¹ = [tex]\left[\begin{array}{cc}-1&-7/2\\1/2&3/2\end{array}\right][/tex]

Is required inverse

If we compare the inverse with second matrix

y = 1 / 2

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Answer:

third option:      1/2

Step-by-step explanation:

The length of AC is 17.3 cm

acc to our question,

Hence,The length of AC is 17.3 cm

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Answer: z=-2

Step-by-step explanation:

3z+6z-30=-48

9z-30=-48

9z-30=-48+30

9z=-18

z=-2

Answer:

Step-by-step explanation:

16/(2+6)

16/8=2