What is the length of the hypotenuse ?

A geometric sequence goes from one term to the next by always multiplying or dividing by the constant value except 0. The constant number multiplied (or divided) at each stage of a geometric sequence is called the common ratio (r).

We have:

[tex]a_1=\dfrac{1}{2}\\\\a_2=2\\\\a_3=8\\\\a_4=32\\\vdots[/tex]

Find the common ratio:

[tex]\boxed{r=\dfrac{a_n}{a_{n-1}}}\Rightarrow r=\dfrac{2}{\frac{1}{2}}=\dfrac{8}{2}=\dfrac{32}{8}=...\\\\\boxed{r=4}[/tex]

[tex]\boxed{a_n=a_1\cdot r^{n-1}}[/tex]

Substitute:

[tex]a_1=\dfrac{1}{2},\ r=4,\ n=8\\\\a_8=\dfrac{1}{2}\cdot4^{8-1}=\dfrac{1}{2}\cdot4^7=\dfrac{1}{2}\cdot16384\\\\\huge\boxed{a_8=8192}[/tex]

[tex]a_4=32,\ r=4\\\\a_5=a_4\cdot r\Rightarrow a_5=32\cdot4=128\\\\a_6=a_5\cdot r\Rightarrow a_6=128\cdot4=512\\\\a_7=a_6\cdot r\Rightarrow a_7=512\cdot4=2048\\\\a_8=a_7\cdot r\Rightarrow a_8=2048\cdot4=8192[/tex]

Answer: 30 cm

Step-by-step explanation:

The volume of the composite solid is 17000 cm³. To find h, we must first subtract the volume of the half cylinder from the composite volume.

From the figure, AE = MK, and so the radius of the half cylinder is 10cm. The volume of the half cylinder is thus [tex]\frac{1}{2}[/tex] the volume of a cylinder. The volume of a cylinder is πr²h. So a half cylinder is 1/2 πr²h. This gives us a volume of  [tex]\frac{1}{2} (\frac{22}{7})(10 cm)^2(28 cm) = 4400 cm^3[/tex].

Thus, the volume of the right prism is 17000cm³ - 4400cm³ = 12600cm³. Consider the cross-section ABKJ. If we multiply this by AE, we'll have the volume of the right prism.

The ABKJ is a trapezoid so it's area is [tex]\frac{1}{2}(AJ + BK) \cdot AB[/tex]. Thus the volume of the right prism is [tex]\frac{1}{2}(AJ + BK) \cdot AB \cdot AE[/tex]. This gives us [tex]\frac{1}{2}(28 + 14) \cdot h \cdot 20 = 12600[/tex], and thus h = 30 cm.

Answer:

38,710.

Step-by-step explanation:

This is an arithmetic series  with common difference  8 , first term a = 7 and last term L = 783.

The number of terms n = (783 - 7) / 8 + 1 = 98

Sum of 98 terms = (n/2)[a + L)

= (98/2)(7 + 783)

= 49 * 790

= 38,710.

1. x < 20

x - 7 < 13

x < 20

2. x > -7

-3(x + 4) < 9

-3x - 12 < 9

-3x < 21

x > -7

Hope this helps!

The probability that he rolls a 4 and flips a head is 1/12

Probability determines odds that a random event would happen. The odds of the random event happening lie between 0 and 1.

The probability that he rolls a 4 and flips a head = (number of sides that is a 4 / total number of sides) x (number of sides that is a head / total number of sides)

(1/6) x (1/2) = 1/12

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Answer: 1/12

Step-by-step explanation:

just say the answer

m∠X + m∠Y < 90° is true.

XYZ is a triangle.

We have to find the option that is true about △XYZ.

By angle sum property of a triangle,

The sum of all the interior angles of a triangle is always equal to 180°.

So, ∠X + ∠Y + ∠Z = 180°

Given, m∠Z > m∠X + m∠Y.

This implies that ∠Z is greater than the sum of the angles ∠X and ∠Y.

so, ∠X + ∠Y must be less than 90°.

Hence, we can say that ∠X + ∠Y < 90°

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Answer: Option 4 or D. m∠x + m∠y∠90°

Step-by-step explanation: Trust Me! It is correct on Edge!

Q: In triangle xyz, m∠z > m∠x m∠y. which must be true about △xyz?

A: D. m∠x + m∠y∠90°

The amount remaining out the money earned is $37.5

Given the following parameters

Amount earned by kevin = $80

If he spent $68/5 on shopping, $51/2 on food, and $22/5 for taxi, the total money spent is given as;

Total money spent = 51/2 + 68/5 + 22/5

Total money spent = 51/2 + 90/5

Total money spent = 25.5 + 18

Total money spent = 43.5

Amount remaining = 80. - 43.5

Amount remaining = 37.5

Hence the amount remaining out the money earned is $37.5

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The expected value of y when x-value is 45 is 35.06

Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called a linear equation in two variables. For example, y = 2x+3 and 2y = 4x + 9 are two-variable linear equations.

In the given question value of x is given and value of y is asked.

The given equation : y = -2.61x+152.51 Such questions can be solved by substituting the given value of variable in the equation which will help us find the unknown.

Substituting x = 45 in the given equation , we get

y = -2.61 x 45 + 152.51

y =  -117.45 + 152.51

y = 35.06

Thus the expected value of y when x-value is 45 is 35.06

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The triangle congruence postulate is illustrated below

It should be noted that two triangles are congruent if they have the same shape and size.

AAS: The angle-angle-side theorem illustrates that two triangles are congruent if the two angles and a side note between the two angles are identical to that of another triangle.

SSS: This illustrates that the three sides of a triangle are congruent to the corresponding three sides of the other triangle.

ASA: This illustrates that the triangles are congruent when the two angles and the side are the same as the corresponding angles and sides of the other triangle.

SAS: When two sides and the included angle of a triangle are congruent to the corresponding sides and the included angle if a second triangle then it follows the side-angle-side theorem.

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By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to  57.

For a quadratic equation of the form a · x² + b · x + c = 0, the discriminant is equal to d = b² - 4 · a · c. In this problem we must transform the polynomial into the canonical form and calculate the discriminant:

2 · x² - 9 · x + 2 = - 1

2 · x² - 9 · x + 3 = 0

d = (-9)² - 4 · (2) · (3)

d = 81 - 24

d = 57

By applying the concept of discriminant, the discriminant of the quadratic equation 2 · x² - 9 · x + 2 = - 1 is equal to  57.

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The domain and the range of f(x) = -25x + 50 are the set of all real numbers

The function is given as:

f(x) = -25x + 50

The above function is a linear function.

All linear functions have their domain and range to be the set of all real numbers

Hence, the domain and the range of f(x) = -25x + 50 are the set of all real numbers

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False, An exponential growth function represents a quantity that has a constant doubling time.

What does an exponential growth function represent?

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Answer:

3 2/3

Step-by-step explanation:

To do this question, you would need to multiply 7 1/3 with 1/2. The answer is 3 2/3.

Answer:

3 2/3 albums

Step-by-step explanation:

Let's say that the stamp album has 12 stamps (12 is just an arbitrary number used to make calculation easier). If Linda collects half of the album, it means she has 6 stamps. If that is the case, Becky has 6 * 7 1/3 stamps. Since 7 1/3 is equivalent to 22/3, we can determine that Becky has collected 44 stamps (6*22/3). There are 12 stamps in one album, which means there are 44 stamps in 3 2/3 (11/3) albums:

[tex]\frac{12}{1}=\frac{44}{y} \\12y=44\\y=11/3[/tex]

Since the ratio of stamps to albums is constant, the calculation above demonstrates that the number of albums it takes to have 44 stamps is 3 2/3. Please note that the numbers I used are arbitrary. If you substitute 12 for a variable x, you will get the same result.

Answer:

The second choice.

Step-by-step explanation:

The length of AC must be equal to 5, since it is horizontally five units. We can rule out the first option.

Length BC cannot be the square root of 16, since that would be exactly 4 units. BC is slanted and does not represent a completely vertical line, so it is not a whole number. We can rule out the fourth option.

Length AB cannot be a whole number, being a slanted line that crosses a total of more than four units. Option three can be ruled out.

Therefore, we are left with the second option.

Answer:

AC = 5, BC = √17, AB = √32

Explanation:

Given points: A(-3, -2), B(1, 2), C(2, -2)

Use distance between two points formula:

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

AC length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-(-3))^2 + (-2-(-2))^2} = \sqrt{25+ 0} = 5[/tex]

BC length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(2-1)^2 + (-2-2)^2} = \sqrt{1 + 16} = \sqrt{17}[/tex]

AB length:

[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(-3-1)^2 + (-2-2)^2} = \sqrt{16 + 16} = \sqrt{32}[/tex]

Based on the matrices given, the true statement on matrices AB = BA is A. A⁻¹ = ¹/₃B.

If:

AB = BA = [3    0]

                 [0    3]

Then:

AB = BA = 3 [1    0]

                    [0    1]

This can be further written as:

AB = BA = 3I₂

And again as:
A (¹/₃ B) = I

This then allows us to either write this as:

A⁻¹ = ¹/₃ B

Or:

B⁻¹ = ¹/₃ A

In conclusion, option A is correct.

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Based on the CPCTC theorem, the complete statement is: RQ ≅ RT.

According to the CPCTC theorem, if two triangles are said to be congruent, then all the corresponding parts of both triangles are congruent.

Given that ΔPQR ≅ ΔSTR, RQ corresponds to RT. Therefore, both sides are congruent to each other.

Thus, the complete statement is: RQ ≅ RT.

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The inequalities represented by the graph are; y > -1 and y <= -x.

The graph as shown in the task content includes the horizontal line; y = -1 and the line; y = -x.

However, the area shaded in the graph coincides with the upper area of y = -1 with broken lines as boundary and the lower area of line; y = -x with a solid boundary line.

Ultimately, the graph represents the inequalities y > -1 and y <= -x.

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Answer:The inequalities represented by the graph are; y > -1 and y <= -x.

What are the inequalities described by the graph?

The graph as shown in the task content includes the horizontal line; y = -1 and the line; y = -x.

However, the area shaded in the graph coincides with the upper area of y = -1 with broken lines as boundary and the lower area of line; y = -x with a solid boundary line.

Ultimately, the graph represents the inequalities y > -1 and y <= -x.

Step-by-step explanation:

The expression is -1/6 x (-1/5) = 1/30.

An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given:

negative 1 over 6 multiplied by negative 1 over 5.

As per the data,

if -1/6 is multiplied with -1/5 then the resultant value will be

=-1/6 * -1/5

= 1/5*6

=1/30

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Considering the expression of a line, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.

A linear equation o line can be expressed in the form y = mx + b.

where

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

In this case, the function f(x) is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9. This is:

So, the slope m can be calculated as:

[tex]m=\frac{-5.9-11.5}{0.4-0.1}[/tex]

Solving:

m= -58

Considering point 1 and the slope m, you obtain:

11.5= -58×0.1 +b

11.5= -5.8 + b

11.5 + 5.8= b

17.3= b

Finally, the equation for the function that is represented through the points f(0.1) = 11.5, and f(0.4) = -5.9 is y= -58x +17.3.

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Answer:

Answer:

1/6

Step-by-step explanation:

Solution:

The given equation is:y=x/6 -5

arranging the equation :x/6-y=5

Given,

Coefficient of x=1/6

coefficient of y=-1

So,

Slope(m)=-(Coefficient of x/coefficient of y))

= -(1/6 / -1) {minus divided by - becomes plus }

1 by 6 whole divide by 1

= 1/6 ans✓

Answer:

12

Step-by-step explanation:

Diagonals of a rhombus bisect each other at right angles, so in triangle JNK, we have JK=20 and JN=16.

Using the Pythagorean theorem, it follows that KN = 12.

Answer: [tex]y=x+2[/tex]

Step-by-step explanation:

The slope is

[tex]\frac{0-2}{-2-0}=1[/tex]

since the y-intercept is 2, the equation is [tex]y=x+2[/tex]

The area of the rectangle URST is 135 mm². so the option C is correct.

Congruent rectangles have the same lengths of sides, same measures of angles and same areas and same perimeters

The Rectangle ABCD is congruent to rectangle URST

Given; Rectangle ABCD ≅ rectangle URST

AB = UR , BC = RS , CD = ST , AD = UT

AB = 9 millimeters

UR = 9 millimeters

We know that, The area of any rectangle = l × w,

In rectangle URST

∵ UR = 9 millimeters

∵ RS = 15 millimeters

- Assume that UR = l and RS = w

The area of rectangle URST = UR × RS

The area of rectangle URST = 9 × 15 = 135 millimeters²

Hence, The area of rectangle URST is 135 mm²

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Answer:

2,000

Step-by-step explanation:

⇒ 200/8 = 25

⇒ 25 * 80 = 2,000

Answer:

2000.

Step-by-step explanation:

8 * x = 200

x = 200/8

80x = 80 * 200/8

       = 10 *200

       = 2000.

Answer:

xyucyxxhc9gohjpbkvicucucuc7vucuc7cucuc7cuvuv8v8

Step-by-step explanation:

q+++

The pattern {1, 3, 5, ...} is an arithmetic sequence with the following rule:

[tex]a_n = 1 + 2(n - 1)[/tex].

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The nth term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

The pattern {1, 3, 5, ...} has first term and common difference given, respectively, by:

[tex]a_1 = 1, d = 2[/tex]

Hence the rule for the pattern is given by:

[tex]a_n = 1 + 2(n - 1)[/tex].

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The probability of selecting a black sock is 1/4.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.  It is more likely that an event will occur if its probability is higher.

Number of white socks=20

Number of black socks=10

Number of red socks=6

Number of purple socks=4

Total number of socks=20+10+6+4

                                     =40

Probability of getting a black sock=Number of black socks/Total number                                                                                                        of socks

                                                         =10/40

                                                         =1/4

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The graph doesn't show a function as C. No; the graph fails the vertical line test.

It should be noted that a graph is the diagrammatic representation of data.

In this case, the graph doesn't show a function as the graph fails the vertical line test.

The vertical line test is a visual way that's uses to determine if the curve is a graph of the function.

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Answer: Option (1)

Step-by-step explanation:

The slope of the line is

[tex]\frac{9-6}{4-(-4)}=\frac{3}{8}[/tex]

This eliminates all the options except for (1).