In spherical geometry, lines are called
OA. line segments
OB. radii
O c. diameters
O D. great circles

If [tex]A[/tex] is the set of positive divisors of [tex]m[/tex] and [tex]B[/tex] the set of positive divisors of [tex]n[/tex], then [tex]A\cup B[/tex] is the set of positive divisors of [tex]mn[/tex].

Use the inclusion/exclusion principle:

[tex]|A \cup B| = |A| + |B| - |A \cap B|[/tex]

where [tex]|\cdot|[/tex] denotes set cardinality (the number of elements the set contains). The set [tex]A\cap B[/tex] is the set of common divisors of [tex]m[/tex] and [tex]n[/tex]. Then

[tex]14 = 5 + 6 - |A\cap B| \implies |A\cap B| = 3[/tex]

so that [tex]m[/tex] and [tex]n[/tex] share 3 divisors [tex]d_1,d_2,d_3[/tex]; let [tex]k=d_1d_2d_3[/tex] be their product. They must be prime

This means we can write

[tex]m = p_1 p_2 k[/tex]

[tex]n = p_3 p_4 p_5 k[/tex]

[tex]\implies mn = p_1 p_2 p_3 p_4 p_5 k^2 = p_1 p_2 p_3 p_4 p_5 {d_1}^2 {d_2}^2 {d_3}^2[/tex]

so that [tex]mn[/tex] has up to 8 distinct prime factors.

Answer: 54

Step-by-step explanation:

By the inscribed angle theorem, angle ZXY measures half of 108 degrees, which is 54 degrees.

Using a system of equations, it is found that Charlie won $270.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Linda won $10 less than three times as much as Charlie, hence:

x = 3y - 10

Linda won $800, hence the amount won by Charlie is found as follows:

800 = 3y - 10

3y = 810

y = 810/3

y = 270

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Answer:

34079 millimeters

Step-by-step explanation:

__________________________________

I assume you mean millimeters, but

All together adds up to 79 millimeter

34000 + 40 + 5 = 34079 mm

__________________________________

Hope this helped

(Edit) Sorry I didn't see meters

If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate [tex]x^4[/tex].

We have

[tex]\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h[/tex]

Expand the numerator using the binomial theorem, then simplify and compute the limit.

[tex]\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}[/tex]

In general, the derivative of a power function [tex]f(x) = x^n[/tex] is [tex]\frac{df}{dx} = nx^{n-1}[/tex]. (This is the aptly-named "power rule" for differentiation.)

Answer:

72. 5

73. -5

74.r =2.40753645…,−2.90753645

75. v =1.53066238…,−0.13066238

Step-by-step explanation:

Answer:

6 pounds

Step-by-step explanation:

Let the can weigh x pounds

Let the milk weigh y when full, therefore half is [tex]\frac{y}{2}[/tex]

Now we for 2 simultaneous equations:

[tex]x + y =70[/tex] ....(i)

[tex]x+ \frac{y}{2}= 38[/tex] .... (ii)

we solve by eliminating the x in both equation throug subtraction

[tex]x - x + y- \frac{y}{2} =70-38\\y- \frac{y}{2} = 32\\\frac{y}{2} = 32\\y=2(32)\\y=64\\x+y=70\\x+64=70\\x=6[/tex]

The value of x when (f o g)(x) = -8 is 3

The composite function is given as:

(f o g)(x) = -8

The above is calculated as:

(f o g)(x) = f(g(x))

So, we have:

f(g(x)) = -8

From the table, we have:

f(-4) = -8

This means that:

g(x) = -4

From the ordered pair, we have:

g(x) = -4 when x = 3

Hence, the value of x is 3

Read more about composite functions at:

https://brainly.com/question/10687170

#SPJ1

The value of x when (f o g)(x) = -8 is 3

How to solve for x?

The composite function is given as:

(f o g)(x) = -8

The above is calculated as:

(f o g)(x) = f(g(x))

So, we have:

f(g(x)) = -8

From the table, we have:

f(-4) = -8

This means that:

g(x) = -4

From the ordered pair, we have:

g(x) = -4 when x = 3

Hence, the value of x is 3

Read more about composite functions at:

brainly.com/question/10687170

#SPJ1

Answer:

x = 10

Step-by-step explanation:

BF   is two times AX   so

2 ( 2x+10) = 5x+10

4x + 20 = 5x + 10

x = 10

Answer:

A

Step-by-step explanation:

calculate the ratios AB/DE BC/EF AND AC/DF。their ratios are 1/2

Answer:

Step-by-step explanation:

the first because the ratio is always from a small to a large triangle, and it is right, the second is wrong, the sides are not congruent, the third is also wrong, the last ratio is wrong

Answer:  [tex]\boldsymbol{\frac{5\text{x}-2}{\text{x}^2-\text{x}}}[/tex]  (choice D)

You have the correct answer.

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

Work Shown:

[tex]\frac{2}{\text{x}} + \frac{3}{\text{x}-1}\\\\\frac{2(\text{x}-1)}{\text{x}(\text{x}-1)} + \frac{3\text{x}}{\text{x}(\text{x}-1)}\\\\\frac{2\text{x}-2}{\text{x}^2-\text{x}} + \frac{3\text{x}}{\text{x}^2-\text{x}}\\\\\frac{2\text{x}-2+3\text{x}}{\text{x}^2-\text{x}}\\\\ \boldsymbol{\frac{5\text{x}-2}{\text{x}^2-\text{x}}}\\\\[/tex]

--------

Explanation:

The idea I used is that we cannot add the fractions unless the denominators are the same. The denominators x and (x-1) lead to the lowest common denominator, aka LCD, of [tex]\text{x}(\text{x}-1) = \text{x}^2 - \text{x}[/tex]. We multiply the denominators together to get the LCD.

The first original fraction [tex]\frac{2}{\text{x}}[/tex] is missing (x-1) in the denominator. This is why I multiplied top and bottom by (x-1) in the 2nd step. Similarly, the fraction [tex]\frac{3}{\text{x}-1}[/tex] is missing an x out front to get to x(x-1). This is why I multiplied top and bottom of that fraction by x.

After we get the denominators to be the same, we can then add the numerators like any other algebraic expression. The denominator stays the same the entire time.

It's similar to how [tex]\frac{2}{7} + \frac{3}{7} = \frac{2+3}{7} = \frac{5}{7}[/tex] has the numerators add like you'd expect while the denominator stays at 7 the entire time.

You can think of it like this: "2 sevenths + 3 sevenths = 5 sevenths" or "2s+3s = 5s" for short. The term "sevenths" is effectively a unit such as cm or meters. We must have common units if we want to add them.

Answer:

D. 30°

Step-by-step explanation:

QP and QR have the same length "8" , therefore, the triangle is an isosceles triangle. Opposite angles are congruent.

- ∠R = ∠P

- ∠R = 30°

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

Answer:

4√3.

Step-by-step explanation:

If the height is h then

tan 60 = h / (1/2*8)

tan 60 = h/4

h = 4 tan 60

   = 4 * √3.

Answer:

78 km!

Step-by-step explanation:

13 cm * 6 km per cm = 78 km in actual distance

Answer:

x = 9

Step-by-step explanation:

[tex]\sf \dfrac{(x +7)(x+8)}{(x -9(x + 6)} \ \div \ \dfrac{(x+8)(x - 2)}{(x+ 6)(x - 2)} =\dfrac{(x +7)(x+8)}{(x -9)*(x +6)}*\dfrac{(x + 6)(x - 2)}{(x +8 )(x - 2)}[/tex]

                                                   [tex]\sf =\dfrac{x +7}{x - 9}[/tex]

x - 9 = 0

   x = 9

If we plugin x = 9, then the denominator would become 0 and hence the expression will become undefined.

So, x = 9 is the restricted value of the expression.

The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a translation followed by a rotation.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a translation followed by a rotation.

Find out more on transformation at: https://brainly.com/question/4289712

#SPJ1

The probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.3 inches is 39.54%.

Given mean diameter of 207, variance=9, sample size of 72.

We have to calculate the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.3 inches.

The sample mean may be greater than or less than from population mean than 0.3 inches.

Either greater than 207+0.3=207.3 inches,

Smaller =207-0.3=206.7

Since the normal distribution is symmetric these probabilities are equal. So we find one of them and multiply by 2.

Probability of being less than 206.7

P value of z when X=206.7. So

Z=(X-μ)/s

=(206.7-207)/0.35

=-0.3/0.35

=-0.857

p value =0.1977

Probability of differing from population mean greater than 0.3 inches=2*0.1977

=0.3954

=39.54%

Hence the probability that the mean diameter of the sample shafts would differ from the population mean  by greater than 0.3 inches is 39.54%.

Learn more about probability at https://brainly.com/question/24756209

#SPJ4

Answer:

96 students

Step-by-step explanation:

I am not exactly sure if this question is talking about a 1:5 ratio, but that's what I am assuming. To get 96, you need to replace the 5 with 480 because the problem seems to mean 1 to every 5 people wear glasses. Next, you do 480/5 to get the number on the left side of the ratio. You get 96 when you do that. I am a little confused with the question because it isn't exactly formatted correctly, but this is what I am guessing. Hope this helps!

Answer:

6x+6x2+3

Step-by-step explanation:

6x2+5x+1+x+2

Combine 5x and x to get 6x.

6x2+6x+1+2

Add 1 and 2 to get 3.

6x2+6x+3

The simplified form of the expression (6x² + 5x + 1) + (x + 2) is 6x^2 + 6x + 3.

To solve the expression (6x² + 5x + 1) + (x + 2)

we need to combine like terms.

First, let's remove the parentheses:

6x² + 5x + 1 + x + 2

Next, we combine like terms:

6x² + (5x + x) + (1 + 2)

Simplifying further:

6x^2 + 6x + 3

Therefore, the simplified form of (6x² + 5x + 1) + (x + 2) is 6x² + 6x + 3.

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ6

To convert 2077₁₀ to base eight is 4035₈

Since 2077 is in base 10, to convert it to base 8, we successively divide it by 8 and keep the remainder. We divide until we have zero as the dividend then count the remainder from bottom to top.

So, to convert 2077 to base 8, we have

2077 ÷ 8 = 259 r 5

259 ÷ 8 = 32 r 3

32 ÷ 8 = 4 r 0

4 ÷ 8 = 0  r 4

So, counting the remainders from bottom to top, we have 4035₈

So, 2077₁₀ = 4035₈

So, to convert 2077₁₀ to base eight is 4035₈

Learn more about convert to base eight here:

https://brainly.com/question/13556214

#SPJ1

Answer:

The measure of angle DCB = 125

Step-by-step explanation:

This is because angle ACD and angle DCB are supplementary.

Supplementary angles are two angles with a sum of 180 degrees, and we know these angles are supplementary by the fact that angle ACB = 180 degrees.

Answer:

Option 1

Step-by-step explanation:

The equations in the options are in the slope-intercept form (y= mx +c, where m is the slope and c is the y-intercept).

In the graph, the line cuts through the y-axis at y= -2. Thus, c= -2 and the 2nd option can be eliminated.

The slope can be found using the formula below.

[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]

Let's choose 2 points on the line: (0, -2) and (-2, 4)

Slope

[tex]=\frac{4-(-2)}{-2-0}[/tex]

[tex]=\frac{4+2}{-2}[/tex]

[tex]=\frac{6}{-2}[/tex]

= -3

The equation of the line is thus y= -3x -2.

For more questions on equation of line, do check out the following!

Answer:

No solutions.

Step-by-step explanation:

Problem:

Solve y−4x=−3;y=4x+7

Steps:

I will solve your system by substitution.

y=4x+7;−4x+y=−3

Step: Solve y=4x+7 for y:

Step: Substitute 4x+7 for y in −4x+y=−3:

−4x+y=−3

−4x+4x+7=−3

7=−3(Simplify both sides of the equation)

7+−7=−3+−7(Add -7 to both sides)

0=−10

Answer:

No solutions.

Answer:

  No solutions

Step-by-step explanation:

It is easiest to determine whether the equations are consistent by putting both of them in the same form.

The equation on the left is in "standard form." The one on the right is in "slope-intercept form." We can rewrite either one of them to put it into the other form.

Rewriting the left equation to slope-intercept form, we have ...

  y = 4x -3 . . . . . . . add 4x to both sides

Comparing this to the right equation ...

  y = 4x +7

we see that the slopes are the same, and the intercepts are different. These equations describe parallel lines. Parallel lines can never meet, so cannot have any point in common. The equations are inconsistent and have no solution.

Rewriting the right equation to standard form, we have ...

  y -4x = 7 . . . . . . . subtract 4x from both sides

Comparing this to the left equation ...

  y -4x = -3

we see that the coefficients are the same, but the constants are different. There can be no values of x and y that will satisfy both equations. Any values that make the terms have one sum cannot also make them have a different sum.

There are no solutions.

Step-by-step explanation:

here a= 7 ,d=4

then S31= 31/2(7+7+30*4)= 31/2(14+120)= 31/2(134)= 31*67= 2077

hope it helps

The sum of the first 31 terms is 2077.

An arithmetic sequence is one in which each phrase grows by adding or subtracting some constant k. In contrast, in a geometric sequence, each term grows by dividing/multiplying some constant k.

We have,

Sequence:  {7, 11, 15, 19, 23 ...}

First term = 7

Common difference, d= 11- 7 = 4

Now, the sum of first 31 st term of sequence

= 31/2 [ 2(7) + (31-1)4]

= 31/2 [ 14 + 120]

= 31/2 x 134

= 31 x 67

= 2077

Learn more about Arithmetic Sequence here:

https://brainly.com/question/15412619

#SPJ2

Answer: 24 - 100, 12 - 5 - 22, -4, 37

Step-by-step explanation:

Simplificar:

-4 = -4

12 - 5 - 22 = -15

24 - 100 = -76

37 = 37

Ordenar de menor a mayor:

-76, -15, -4, 37

       \/

24 - 100, 12 - 5 - 22, -4, 37

Hello,

Answer:

S = { -0,42 ; 2,71 }

Step-by-step explanation:

7x² - 16x = 8 ⇔ 7x² - 16x - 8 = 0

a = 7 ; b = -16 ; c = -8

Δ = b² - 4ac = (-16)² - 4 × 7 × (-8) = 480 > 0

x₁ = (-b - √Δ)/2a = (16 - √480)/14 ≈ -0,42

x₂ =  (-b + √Δ)/2a = (16 + √480)/14 ≈ 2,71

Answer:

The two answers:

2.707778736

0.42206445

Step-by-step explanation:

Here is the equation:

[tex] {7x}^{2} - 16x = 8[/tex]

Take away the 8 from the right hand side, so that we are left with this quadratic equation:

[tex] {7x}^{2} - 16x - 8 = 0[/tex]

This equation is too complex to solve with the factorizing method, so let's use the quadratic formula, which is as follows:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

In this equation, a = 7, b = -16, and c = -8. So let's substitute in:

[tex]x = \frac{-( - 16) \pm \sqrt{ { - 16}^{2} - 4 \times 7 \times - 8}}{2 \times 7}[/tex]

[tex]x = \frac{ - ( - 16) \pm \sqrt{256 + 224} }{14}[/tex]

[tex]x = \frac{ 16 \pm \sqrt{480}}{14}[/tex]

And let's work out the two possible answers:.

2.707778736

0.42206445

The unit vectors are u = {1, 1}. Option C

Unit vectors can be defined as vector with magnitude of 1.

It is important to note that a unit vector is a vector quantity. Vector quantities are known to have magnitude and direction.

They are represented with the sign 'u'

Thus, the unit vectors are u = {1, 1}. Option C

Learn more about unit vectors here:

https://brainly.com/question/13696986

#SPJ1

Step-by-step explanation:

[tex] = \frac{ \frac{3}{x - 2} - 5 }{2 - \frac{4}{x - 2} } [/tex]

[tex] = \frac{ \frac{3 - 5.(x - 2)}{x - 2} }{ \frac{2.(x - 2) - 4}{x - 2} } [/tex]

[tex] = \frac{ \frac{3 - 5.(x - 2)}{ \cancel{x - 2}} }{ \frac{2.(x - 2) - 4}{ \cancel{x - 2} }} [/tex]

[tex] = \frac{3 - 5.(x - 2)}{2.(x - 2) - 4} [/tex]

[tex] = \frac{3 - 5x + 10}{2x - 4 - 4} [/tex]

[tex] = \frac{ - 5x + 13}{2x - 8} [/tex]

[tex] = \frac{13 - 5x}{2x - 8} [/tex]

The answer is D.

The equivalent value of the expression is A = ( 13 - 5x ) / ( 2x - 8 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.

Given data ,

Let the equation be represented as A

Now , the value of A is

[tex]A = \frac{\frac{3}{x-2}-5}{2\:-\:\frac{4}{x-2}}[/tex]

On simplifying , we get

[tex]A = =\frac{\frac{-5x+13}{x-2}}{2-\frac{4}{x-2}}[/tex]

On further simplification , we get

[tex]A = =\frac{\frac{-5x+13}{x-2}}{\frac{2x-8}{x-2}}[/tex]

Therefore , the value of A is A = ( 13 - 5x ) / ( 2x - 8 )

Hence , the equation is A = ( 13 - 5x ) / ( 2x - 8 )

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ5