The equations X+5y = 10, 3x-y = 1, X-5y = 10, and 3x+y = 1 are shown on the graph below.

Which is the approximate solution for the system of equation x+5y=10 and 3x+y=1?

O (-.3, 2.1)
O (-0.3, -2.1)
O (0.9, -2.1)
O(0.9, 1.8)​

7) Required value of HG is 13 ft.

8) The measure of x in the triangle below is 13 ft.

What is value of cosine formula ?

let say there is AABC,and opposite side of ZA is a, opposite side of <B is b, opposite side of C is c.

then cos(A) = (b² × c² - a²)/(2bc)

given that AFGH . FH = 8ft , FG = 13ft ,and m angle F = 72 deg

by law of cosines to find the HG, since

we know the lengths of FH and FG and

the measure of angle F.

Let's say length of HG be "x".

Then by law of cosines:

x² = 8² + 13²- 2(8)(13) × cos(72°)

x²= 64 + 169 - 208cos(72°)

cos(72°) , which is approximately 0.309., we get:

x²= 233 - 208(0.309)

x² = 169.072

x² = 64+169-208cos(72°)

cos(72°), which is approximately 0.309., we get:

x² = 233-208(0.309)

x²= 169.072

Taking the square root of both sides, we get:

x = 13 (approx)

So the length of HG is approximately 13 feet.

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Answer: 445 triangles can be form with 15 dots of a circle (I hope good luck)

Step-by-step explanation:

Answer:

455

Step-by-step explanation:

There are 15 points on a circle.

We need three points to form a triangle

Therefore the number of triangles = 15 choose 3 ​= 15!/(3!x12!)​ = (15x14x13)/(3x2x1) = 5x7x13 = 455

Hence the number of triangles formed is 455

Check the picture below.

The given algebra tile shape can be divided into two rectangles and a square with the side length of 1 unit each.

Let the side length of the square be 'x'. The length of the horizontal rectangle is (2 + x) units, and the length of the vertical rectangle is (1 + x) units.

Now,

Perimeter of the given shape = Sum of the length of all the sides,

(2 + x) + (1 + x) + (2 + x) + (1 + x) + 4= 6 + 4x,

Area of the given shape = Area of the square + Area of the vertical rectangle + Area of the horizontal rectangle

x² + x(1 + x) + x(2 + x)= x² + 3x + x²= 2x² + 3x

Thus, the expressions for the perimeter and the area of the given algebra tile shape are

6 + 4x and 2x² + 3x,

respectively .Simplifying each expression by combining like terms,Perimeter of the given shape

= 6 + 4x= 2(3) + 2(2x)= 2(2x + 3)Area of the given shape = 2x² + 3x= x(2x + 3)Hence, the simplified expressions for the perimeter and the area of the given algebra tile shape are 2(2x + 3) and x(2x + 3), respectively.

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The relatively prime positive integers of m+n is 409.

Since ABCD is an isosceles trapezoid

An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure.

=>∠BAD = ∠ CDA Angles formed by the non parallel sides of an isosceles trapezoid are equal.

Given, AB = BC

Join AC

In ΔABC

∠BCA = ∠BAC Angle formed by the equal sides of and isosceles triangle

with its base are equal.

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length

AB = BC-CD Arcs formed by same side chords on the circle are equal.

Measure of complete angle is 360 degrees.

=2θ+2θ+2θ+2Φ+2Φ+2Φ

=6θ+6Φ=360

\($$& \widehat{A B}+\widehat{A F}=\widehat{B F}=120 \\\)

∠CDE=120

Join FB

In ΔFAB,

By Law of Cosine:

\($$\begin{aligned}& c^2=a^2+b^2-2 a b \cos C \\& \Rightarrow B F^2=3^2+5^2-2.3 \cdot 5 \cos 120 \\& \Rightarrow B F^2=3^2+5^2-30 \cos 120 \\& \Rightarrow B F^2=9+25-30 \cdot(-0.5) \\& =B F^2=34-30.5 \\& \Rightarrow B F^2=34+15 \\& \Rightarrow B F^2=49 \\& \Rightarrow B F=7\end{aligned}$$\)

Laws of Sine:

⇒\($ & \sin A / a=\sin B / b={Sin} C / c\)

⇒\(& \sin \Theta=5 \sqrt{3} / 14 \ \& \sin \Phi=3 \sqrt{3} / 14 \\\)

In ΔAFD,

⇒\(& \angle A F D=3 \Phi \ \& \angle A D F=\Theta \\\)

\(& \Rightarrow {Sin} \Theta / 5=\sin 3 \Phi / A D \\& \Rightarrow {Sin} \Theta=5 \sqrt{3 /} / 14 \\& \Rightarrow{Sin} 3 \Phi={Sin}(\Phi+2 \Phi) \\& \Rightarrow {Sin} 3 \Phi={Sin} \Phi . {Cos} 2 \Phi+{Cos} \Phi . {Sin} 2 \Phi\)

\(& \Rightarrow {Sin} 3 \Phi= {Sin} \Phi \cdot {Cos} 2 \Phi+{Cos} \Phi \cdot {Sin} 2 \Phi \\& \Rightarrow {Sin} 3 \Phi={Sin} \Phi \cdot\left(1-2 \sin ^2 \Phi+2 {Sin} \Phi \cdot \cos ^2 \Phi\right) \\& \left.\Rightarrow {Sin} 3 \Phi={Sin} \Phi \cdot\left(1-2 \sin ^2 \Phi\right)+2\left(1-\sin ^2 \Phi\right)\right) \\& \Rightarrow {Sin} 3 \Phi={Sin} \Phi \cdot\left(3-4 \sin ^2 \Phi\right) \\\)

\(& \Rightarrow {Sin} 3 \Phi=3 \sqrt{3} / 14 \cdot(3-27 / 49) \\& \Rightarrow {Sin} 3 \Phi=3 \sqrt{3} / 14 \cdot(120 / 49) \\& \Rightarrow {Sin} 3 \Phi=180 \sqrt{3} / 343\)

Now,

\($$&{Sin} \Theta / 5={Sin} 3 \Phi / A D \\& \Rightarrow A D=5 {Sin} 3 \Phi / {Sin} \Theta \\& \Rightarrow A D=180 \sqrt{3} / 343 / 5 \sqrt{3} / 14 \\& \Rightarrow A D=180 \sqrt{3} / 343 X 14 / 5 \sqrt{3} \\& \Rightarrow A D=360 / 49 \\& m+n=360+49 \\& \Rightarrow m+n=409\)

Therefore, the value of m + n is 409.

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Answer:

12 inches of wire.

Step-by-step explanation:

that is what I could think of good luck. if I'm wrong tell me I'll try again don't forget to tell me if I'm wrong.

Answer:

Step-by-step explanation:

Sum of interior angles of a triangle is 180degree.

2x + 105 + 31 = 180

2x = 44

x = 22

Answer:

The given Angles in triangle are 105° , 31° & 2x°

we have been asked to find the value of x .

We Know Sum of all three angles in a triangle is 180°

Now Let's put the given value we obtain

105° + 31° + 2x = 180°

136° + 2x = 180°

2x = 180° - 136°

2x = 44

x = 44/2

x = 22°

So, the value of x is 22°.

40 quarts of a 50% acid solution must be added to the 20 quarts of a 20% acid solution to obtain a 40% solution.

The problem provides a set of information that may be used to write a system of equations containing two unknowns. The equations must describe the total amount of the resulting solution and the total amount of acids in the solutions. The substitution method may then be employed to derive an equation containing only the unknown variable in question. By solving the final equation, the value needed may be found.

Let a be the amount of 50% acid solution and b represent the amount of a 40% acid solution.

The total amount of the final solution is given by:

b = a + 66

The total amount of acid in the final solution is given by:

0.50a + 0.20(20) = 0.40b

Employing the substitution method:

0.50a + 4 = 0.40(a + 20)      [Substitute b using the first equation]

0.50a + 4 = 0.40a +8

0.10a = 4        [Subtract 0.40a and 4 from both sides]

a =40     [Divide both sides by 0.10]

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Answer:

It will take 3.65 seconds at the rate it's being poured.

Step-by-step explanation:

The number of waffles can be made from 15 eggs are, 20 waffles.

the waffles can be calculates as follows

4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles

we need 6 eggs to make 8 waffles

So, the waffles can we make from 15 eggs = \(\frac{8}{6} X 15 = 20\) waffles

Hence, the number of waffles can be made from 15 eggs are 20 waffles.

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Answer:

first add 390 to 29 then, divided it to the sequence and there's your answer

Answer:

The numbers are 282,291,300,309,318,327,336,345,354,363,372,381,

Common rhg\(t(29) = 21 + (29 - 1)9\)

\( = 21 + (28)9\)

=21+252

=273

The numbers are 282,291,300,309,318,327,336,345,354,363,372,381

Answer:

dbc

Step-by-step explanation:

thats the only one that is obtuse

Answer:

So, the prime factorization of 828 can be written as 2^2 × 3^2 × 23 where 2, 3, and 23 are prime.

Step-by-step explanation:

828 / 2 = 414

414 / 3 = 138

138 / 2 = 69

69 / 23 = 3

3 / 3 = 1

Answer

put 1 on top and exo on bottom

Step-by-step explanation:

The complement rule states that the probability of an event occurring is equal to one minus the probability of the event not occurring. The probability of at least one individual having myopia is 1 - (1-p)^3.

To calculate the probability that at least one out of three randomly selected individuals suffers from myopia, we can use the complement rule. The complement rule states that the probability of an event occurring is equal to one minus the probability of the event not occurring.
So, let's first find the probability that none of the three individuals suffer from myopia. Assuming that the probability of an individual having myopia is p, the probability that one individual does not have myopia is (1-p). Therefore, the probability that all three individuals do not have myopia is (1-p)^3.
Now, we can use the complement rule to find the probability that at least one individual has myopia. The complement of none of the three individuals having myopia is at least one individual having myopia. So, the probability of at least one individual having myopia is 1 - (1-p)^3.
Therefore, the probability that at least one out of three randomly selected individuals suffers from myopia is 1 - (1-p)^3.
To determine the probability that at least one person out of three randomly selected individuals suffers from myopia, we can use the complementary probability method. First, we need to know the probability of an individual not having myopia (P(not myopia)). Assuming P(myopia) is the probability of having myopia, we can calculate P(not myopia) as 1 - P(myopia).
Next, we find the probability that all three individuals do not have myopia, which is the product of their individual probabilities: P(all not myopia) = P(not myopia) * P(not myopia) * P(not myopia).
Finally, we calculate the complementary probability, which is the probability that at least one person has myopia: P(at least one myopia) = 1 - P(all not myopia).
Remember to use the actual probability of myopia (P(myopia)) in the calculations to find the correct answer.

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Based on the SSS similarity theorem, the pair of triangles that can be proven to be similar is the pair shown in the image attached below.

The SSS similarity theorem states that two triangle area similar to each other if the ratio of the three corresponding sides of both triangles are equal.

Thus, in the image attached below, the ratio of the three corresponding sides of the pair of triangles are:

10/2.5 = 11/2.75 = 8/2 = 4

Therefore, the pair of triangles that we can prove to be similar using the SSS similarity theorem is the pair shown in the image attached below.

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The given statement exists true. A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization).

A matrix can be expressed as the union of two distinct matrices, Q and R, using the QR matrix decomposition. R is a square upper/right triangular matrix and Q is an orthogonal matrix. R is also invertible because it is square and doesn't have zeros in its diagonal entries.

A matrix is broken down into orthogonal (Q) and upper triangular (R) matrices in a process known as QR decomposition (factorization). Finding eigenvalues and solving linear least squares problems both use QR factorization.

A = QR. Be aware that the QR-factorization of a rectangular matrix A is sometimes understood with Q square and R rectangular rather than Q rectangular and R square, as with the MATLAB command qr.

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The area of the part of the plane 5x + 3y + z = 15 that lies in the first octant is 15x^3/6 + 45x^2y/2.

Area is a measure of the size of a surface or the amount of space it takes up. It can be measured in square units such as square feet, square meters, or acres. Area is used to describe the size of a two-dimensional object or shape, and is often used when discussing the size of a plot of land, a room, or other geographical area.

The first octant is defined as the area in the three-dimensional Cartesian coordinate system where all the coordinates are positive. In this case, the equation 5x + 3y + z = 15 can be rearranged to solve for z: z = 15 - 5x - 3y. This new equation can then be used to find the area of the plane that lies in the first octant by integrating the equation over the area of the octant.

To solve for the area, we must first find the boundaries of the octant. Since all coordinates must be positive, the boundaries of the octant are x = 0, y = 0, and z = 0. The area of the plane that lies in the first octant is then computed using the triple integral:

Area = ∫∫∫ 0 0 0 15-5x-3y dzdydx

= ∫∫ 0 0 (15x + 45y)dydx

= ∫ 0 (15x^2/2 + 45xy)dx

= 15x^3/6 + 45x^2y/2

Therefore, the area of the part of the plane 5x + 3y + z = 15 that lies in the first octant is 15x^3/6 + 45x^2y/2.

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The functions f(g(x)) and g(f(x)) are not inverse functions

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

f(x) = x³

g(x) = 1/3x

Calculate the composite function f(g(x)).

So, we have

f(g(x)) = (1/3x)³

This gives

f(g(x)) = 1/27x³

Calculate the composite function  g(f(x)).

So, we have

g(f(x)) = 1/3(x³)

This gives

g(f(x)) = 1/3x³

The functions f(g(x)) and g(f(x)) are not the same

Hence, they are not inverse functions

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The point which represents the number of dollars Carola makes per hour is (1, 8).

Two variables have a proportional relationship if all the ratios of the variables are equivalent.

The constant of proportionality is the ratio of the y value (total earnings) to the x value (hours worked). That is:

constant of proportionality (k) = y/x

Since Carola works for 6 hours and earns $48. Thus, the number of dollars Carola makes in 1 hour will be:

48/6 = $8

Therefore, the point which represents the number of dollars Carola makes per hour is (1, 8)

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Complete Question

Check attached image

Answer:

-1,7,15,23,31,39

Step-by-step explanation:

39-31=8

So keep adding 8 to the first number, in your case it is -1 so -1+8= 7. Then add 8 to the 7 to get 15, after that add 8 to the 15 to get 23. To make sure that your answer is right add 8 to 23, which will give you 31.

(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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Answer:

x = 3, 7

Step-by-step explanation:

Step 1: Write equation

x² - 10x + 21 = 0

Step 2: Factor

(x - 7)(x - 3) = 0

Step 3: Find roots

x - 7 = 0

x = 7

x - 3 =0

x = 3

Answer:

2

Step-by-step explanation:

Answer:

9×(10-5)-31)÷7

9×5-31÷7

45-31÷7

14÷7

2

Answer:

n = - 8

Step-by-step explanation:

0.4n = 4 + 0.9n ( subtract 0.9 from both sides )

- 0.5n = 4 ( divide both sides by - 0.5 )

n = - 8

Answer:

Step-by-step explanation:

Answer:

  (0, -2)

Step-by-step explanation:

The solution to a system of equations is the point on the graph where the lines intersect.

Here, both lines have a y-intercept of -2, so intersect there. The solution is ...

  (x, y) = (0, -2)

the equation of the plane that passes through the point (2, - 14) and is parallel to the vector (1, 1, 4) is given by:r.(1, 1, 4) = p.(1, 1, 4) => x + y + 4z = 2 + 14 + 4( - 2) => x + y + 4z = 6. Therefore, the equation of the required plane is x + y + 4z = 6.

Given equation of plane are:x - z = 2 ....(1)y + 4z = 2 ....(2)xy - 4z = 4 ....(3)We are supposed to find an equation of the plane that passes through the line of intersection of the planes (1) and (2) and is perpendicular to the plane (3).To find the line of intersection of the planes (1) and (2), we solve the two planes simultaneously. The solution is the line of intersection of the two planes.To find the solution, we first eliminate x by adding equations (1) and (2) to obtain:y + x + 4z = 4 ...(4)Similarly, we eliminate x from equations (1) and (3) to obtain:xy - z - 4z = 4 => y(z + 1) = z + 4 => y = \(\frac{(z + 4)}{(z + 1)}\) ...(5)Now, we eliminate y from equations (4) and (5) to get an expression for z. Substituting that value of z in any of the equations, we can obtain the corresponding values of x and y. Once we have two such points, we can write the equation of the line that passes through them. That will be the line of intersection of the planes (1) and (2).Solving equations (4) and (5), we get z = - 4 or z = 2. Putting z = - 4 in equation (5), we get y = - 2.5 and putting z = - 4 and y = - 2.5 in equation (4), we get x = 0.5. Therefore, the line of intersection of the planes (1) and (2) is (0.5, - 2.5, - 4).Similarly, putting z = 2 in equation (5), we get y = 2 and putting z = 2 and y = 2 in equation (4), we get x = - 2. Therefore, the line of intersection of the planes (1) and (2) is (- 2, 2, 2).We know that the equation of the plane that passes through a point A(x₁, y₁, z₁) and is perpendicular to a vector n = (a, b, c) is given by:a(x - x₁) + b(y - y₁) + c(z - z₁) = 0Therefore, the equation of the plane that passes through the line of intersection of the planes (1) and (2) and is perpendicular to the plane (3) is:x - 0.5y - 2z = 1 ...(6)To obtain the above equation, we first find a vector that is parallel to the line of intersection of the planes (1) and (2). For that, we take the cross-product of the normals to the planes (1) and (2) as follows:n₁ × n₂ = (1, 0, - 1) × (0, 4, 1) = (4, 1, 4)Now, we find a point on the line of intersection of the planes (1) and (2). One such point is (0.5, - 2.5, - 4).Therefore, the required plane is 4x + y + 4z = 14.Therefore, we found the required equation of the plane. The equation of the plane is x + y + 4z = 6.

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Answers:

(2, -3) and (3, -3)

==================================================

Work Shown:

Since f(x) = -3, we'll replace f(x) with -3 and solve for x

f(x) = x^2 - 5x + 3

-3 = x^2 - 5x + 3 .... f(x) replaced with -3

0 = x^2 - 5x + 3 + 3 ... adding 3 to both sides

0 = x^2 - 5x + 6

x^2 - 5x + 6 = 0

(x - 3)(x - 2) = 0 .... factor; you can also apply the quadratic formula

x-3=0 or x-2=0

x = 3 or x = 2

So that explains where that '2' comes from when they listed (2, ?)

-------------

To find what replaces the question mark, we will plug x = 2 into the function

f(x) = x^2 - 5x + 3

f(2) = 2^2 - 5(2) + 3

f(2) = 4 - 10 + 3

f(2) = -3

We could have skipped this portion and said that the solution is (2,-3) but plugging x = 2 into the function to get the output y = -3 helps confirm that x = 2 is one of the x solutions.

-------------

Let's do the same for x = 3

f(x) = x^2 - 5x + 3

f(3) = 3^2 - 5(3) + 3

f(3) = 9 - 15 + 3

f(3) = -3

We end up with the same output, so x = 3 is confirmed as well.

The graph below visually helps reinforce these confirmations. Each solution  is an intersection between the two curves.

Answer:

cool

Step-by-step explanation:

I'm not sure I'm just getting points

When it is required to minimize the effect of a few extreme scores, median is the measure of central tendency which is the most appropriate.

This is due to the fact that the median isn't influenced by extreme values, which means it is the middle value when the observations are ordered from least to greatest.There are several measures of central tendency, including the mode, median, and mean.

The most common measure is the mean, but it is greatly affected by the presence of a few very high or very low scores.To ensure that the mean isn't skewed too much by these scores, the median is a better choice. The median is the middle number in a data set when the observations are sorted from smallest to greatest.

In this way, if there are extremely high or low scores, they are not going to influence the median significantly as compared to the mean. Hence, we can say that the median is the most appropriate measure of central tendency when it is desired to minimize the effect of a few extreme scores.

The measure of central tendency that is most appropriate when it is desired to minimize the effect of a few extreme (very high or very low) scores is the median.

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