What is the distance between the following points?

Answer:

see explanation

Step-by-step explanation:

∠ CZD = 90° , then

∠ CZF = 90° - ∠ FZD = 90° - 40° = 50°

∠ FZD and ∠ AZG are vertically opposite angles and are congruent , so

∠ AZG = 40°

∠ CZF and ∠ GZE are vertically opposite angles and are congruent , so

∠ GZE = 50°

E

∠ AZB + ∠ BZC = 90° , that is

3x - 2 + 32 = 90

3x + 30 = 90 ( subtract 30 from both sides )

3x = 60 ( divide both sides by 3 )

x = 20

Answer:

  C.  ∆LMN ~ ∆OPQ, because of AA

Step-by-step explanation:

All of the triangle congruence postulates require at least one pair of corresponding sides be congruent (in addition to other requirements). Triangle similarity can be proved if there are two pairs of congruent corresponding angles.

__

No sides are given as congruent, so no congruences can be proved.

Two pairs of corresponding angles are said to be congruent, so we can say ...

  ∆LMN ~ ∆OPQ, because of AA

In the triangle represented in the diagram, The value of X is: 23°

A triangle can be defined as a plain shape that has three sides, three edges and three angles.

A triangle is majorly defined as a shape that possesses three angles and their interior angles sum up to 180°

In conclusion, in the triangle represented in the diagram, The value of X is: 23°

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Considering the sum of the internal angles of a triangle, it is value that the value of x is of x = 23º.

A triangle has three angles, and their sum is of 180º.

In this problem, the angles are:

x, 67º, 90º.

Hence:

x + 67º+ 90º = 180º.

x = 23º.

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Answer:

x= 131

y = 49

Step-by-step explanation:

X and 49 form a straight line so they add to 180

x+49 = 180

x = 180-49

x =131

49 and y are alternate interior angles and alternate interior angles have the same value

y = 49

Step-by-step explanation:

please mark me as brainlest

Answer:

See below.... several options

Step-by-step explanation:

Change is $3.56

  3 dollar bills    one 50 c piece     one nickel      one penny

  (though 50 cent  pieces are uncommon.....this may be 2 quarters)

[For a while , there was $ 2 bills

   so it could be   one 1 dollar bill and one $ 2 bill instead of three dollar bills]

Answer:

4/25

Step-by-step explanation:

total no of children-15

total no of mothers-50

probability that a mother has i child

1/50

=8/50

=4/25

Answer:

0.16

Step-by-step explanation:

A group of 50 mothers were asked how many children they have. the

table shows the results.

number of children     1      2      3     4     5    

number frequency      8     12    10     14    6

What is the experimental probability of a mother having 1

child?

Total number of mothers = 8 + 12 + 10 + 14 + 6 = 50

Number of mothers with 1 child = 8

p(1 child) = 8/50 = 0.16

Answer:

6¹¹

Step-by-step explanation:

Simplifying the numerator :

Solving the expression :

Answer:

Part A = 7

Part B = 1

I hope this is right, sorry if it isn't

Answer:

See below

Step-by-step explanation:

5 cups cheese    /  ( 2/3 cup cheese/plate ) =

 5 * 3/2  = 15/2   = 7 1/2     or   7 full plates

2/3 cup cheese / plate  * 9 plates  =

   2/3 * 9 = 6 cups cheese   total

       she has 5 cups to start.....she will need 1 cup more

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[1 - (-3)]^2 + [0 - 4]^2}\implies d=\sqrt{(1+3)^2 +(-4)^2} \\\\\\ d=\sqrt{32}\implies d\approx 5.66[/tex]

Answer:

4 different ways

Step-by-step explanation:

there are four different ways she can post it because there are four posters she want to hang on the wall.

Answer:

The period is 2π

Explanation:

The period is 2 times pi because 2 is the standalone-term multiplied by pi to get the period.

Answer:

Hi,

Step-by-step explanation:

The triangles CBA and DEA are equals ( 3 sides 2 to 2 equals), angles CAB and DAE are also equals:

6t-12=18-4t

10t=30

t=3(°)

angle CAB=6t-12=6*3-12=6(°)=angle(DAE)

angle BCA=(180-6)/2=87(°)=angle CBA=angle (ADE)=angle(DEA)

Answer:

12

Step-by-step explanation:

12/3=4

4*3=12

Hope this helps!

If not, I am sorry.

Answer:

12

Step-by-step explanation:

The quotient of a number and three is four. What is the number?

The word problem can be written as:

[tex]\sf{\dfrac{x}{3}=4}[/tex]

1. Multiply both sides by 3:

[tex]\sf{3\left(\dfrac{x}{3}\right)=4(3)}\\\\\implies x=12[/tex]

2. Check your work:

[tex]\sf{\dfrac{12}{3}=4}\\\\\implies 4=4 \ \checkmark[/tex]

Therefore, the number is 12.

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Answer:

D.

Step-by-step explanation:

You can see it in the graphs after you plot it.

The volume of each marble is 0.05 liter

The volume function is given as:

w = 32 - 0.05n

The variable n represents the number of marbles.

This means that 0.05n represents the volume of n marbles and 32 represents the total volume of the glass tank

To get the volume of each marble, we divide 0.05n by n

i.e.

Volume = 0.05n/n = 0.05

Hence, the volume of each marble is 0.05 liter

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Vertex is located over the center of the base of a regular pyramid.

Vertex angle is defined as the angle formed by two lines or rays that intersect at a point. These two rays make the sides of the angle.

Here,  Vertex is the point which is located over the center of the base of a regular pyramid.

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Answer:

should be the first one -inf < y < inf

Draw a graph of the temperatures; if the points form a straight line, then the temperatures vary directly , Option B is the correct answer.

When a quantity of one variable is increased and the value of the other also increases then they are said to be in direct variation.

For the data to be in direct variation

Draw a graph of the temperatures; if the points form a straight line, then the temperatures vary directly.

The points in any linear equation can only fluctuate directly, therefore all points will lie on the same line.

Option B is the correct answer.

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Answer:

ez b

Step-by-step explanation:

The approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour

The missing part of the question is represented by the following function:

[tex]T(h) = \frac{386 + 110h}{h}[/tex]

10:00 a.m is 3 hours after 7:00 am and 1:00 p.m is 6 hours after 7:00 am.

This means that:

h = 3 at 10:00 am

h = 6 at 1:00 pm

Next, we calculate T(3) and T(6)

[tex]T(3) = \frac{386 + 110*3}{3} =238.7[/tex]

[tex]T(6) = \frac{386 + 110*6}{6} =174.3[/tex]

The average rate of change is then calculated as:

[tex]T'(h) = \frac{T(3) - T(6)}{3 - 6}[/tex]

This gives

[tex]T'(h) = \frac{238.7 - 174.3}{-3}\\[/tex]

Evaluate

T'(h) = -21

This means that the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour

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Answer:

exact area = 81π in.²

approximate area = 254.34 in.²

Step-by-step explanation:

Exact:

area = πr²

r = radius = diameter/2 = 18 in./2 = 9 in.

area = πr²

area = π × (9 in.)²

area = 81π in.²

exact area = 81π in.²

Approximate:

π = 3.14 (approximately)

area = πr²

area = 81π in²

area = 81 × 3.14 in.²

approximate area = 254.34 in.²

Answer: pi/4 and -1

Step-by-step explanation:

Answer:

A triangle has side lengths 10 feet, V205 feet, and V105 feet

Step-by-step explanation:

Answer:

x is the midpoint of a segment in the diahram

Answer:

x is mid point

Step-by-step explanation:

I hope it's helpful for

Based on the sides of LMN and OPQ, the congruence postulate that applies is B. Congruent - SSS.

It is used when the two triangles given have three equal corresponding sides which also have equal angles.

All three sides of LMN and OPQ are equal sides and have equal angles and so the SSS rule applies.

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Answer:

The original price of the book was $12.50

Step-by-step explanation:

3x - 0.2(3x) + 10 = 40
30x - 2(3x) + 100 = 400
   30x - 6x + 100 = 400
           24x + 100 = 400
                     24x = 300
                         x = 12.50

Answer:

The correct answer is 13%.

Step-by-step explanation:

We can easily put in the equation:

95 - 82 = 13

Hope this helps:) Goodluck!

Answer:  Choice C

[tex]\frac{\sqrt[12]{55,296}}{2}[/tex]

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

Explanation:

Recall the process to rationalize the denominator is to multiply top and bottom by the denominator expression. This only works if we have a square root in the denominator.

For cube roots, we'll need to multiply two copies of the denominator to top and bottom. This will get us three copies of [tex]\sqrt[3]{2}[/tex] so that the cube root goes away.

Check out the steps below to see what I mean:

[tex]\frac{\sqrt[4]{6}}{\sqrt[3]{2}}\\\\\\\frac{\sqrt[4]{6}\sqrt[3]{2}\sqrt[3]{2}}{\sqrt[3]{2}\sqrt[3]{2}\sqrt[3]{2}}\\\\\\\frac{6^{1/4}*2^{1/3}*2^{1/3}}{\left(\sqrt[3]{2}\right)^3}\\\\\\\frac{6^{3/12}*2^{4/12}*2^{4/12}}{2}\\\\\\\frac{\left(6^3*2^4*2^4\right)^{1/12}}{2}\\\\\\\frac{\left(55,296\right)^{1/12}}{2}\\\\\\\frac{\sqrt[12]{55,296}}{2}\\\\\\[/tex]

In short,

[tex]\frac{\sqrt[4]{6}}{\sqrt[3]{2}}=\frac{\sqrt[12]{55,296}}{2}[/tex]

We have the 12th root of 55,296 all over top the integer 2. The "2" is not part of the 12th root. This shows why choice C is the final answer.

Answer:

C

Step-by-step explanation:

Answer: [tex]fx[/tex]

The slope is 0, and

the y-intercept is (0, 0)

[tex]\left[\begin{array}{ccc}x&y\\0&0\\1&0\end{array}\right][/tex]

In order to find the graph of "f(x)", we need to graph the line using the slope and y-intercept, or two points.

The solution to the questions are:

As a general rule, the sum of cubes x³ and y³ is:

x³ + y³= (x+y)(x² - xy + y²)

Replace x with a and y with b

a³ + b³= (a + b)(a² - ab + b²)

Hence, the expression that represents the factoring pattern is (a + b)(a² - ab + b²)

The equation is given as:

x³ + 2x² - 9x = 18

Subtract 18 from both sides

x³ + 2x² - 9x - 18 = 0

Factorize the expression

x²(x + 2) - 9(x + 2) = 0

Factor out x + 2

(x²- 9)(x + 2) = 0

Express x²- 9 as a difference of two squares

(x + 3)(x - 3)(x + 2) = 0

Split

(x + 3)  = 0 or (x - 3)  = 0 or (x + 2) = 0

Remove brackets

x + 3  = 0 or x - 3  = 0 or x + 2 = 0

Solve for x

x = -3, x = 3 and x = -2

Hence, the solutions of the equation x³ + 2x² - 9x = 18 are x = -3, x = 3 and x = -2

The polynomial equation is given as:

0 = x³ + 2x² - 5x - 6

Rewrite as:

x³ + 2x² - 5x - 6 = 0

Factorize the expression on the left-hand side

(x + 3)(x + 1)(x - 2) = 0

Split

x + 3 = 0 or x + 1 = 0 or x - 2 = 0

Solve for x

x = -3 or x = -1 or x = 2

Hence, the other roots are x = -3 and x = 2

The expression is given as:

(x² - 1) - (x³ - 2x + 1)

Expand

x² - 1 - x³ + 2x - 1

Collect like terms

- x³ + x² + 2x - 1 - 1

Evaluate the like terms

- x³ + x² + 2x - 2

Hence, the result of subtracting the expressions is - x³ + x² + 2x - 2

The polynomial is given as:

y = (x² - 1)(x + 2)(x + 4)

Express x² - 1 as a difference of two squares

y = (x - 1)(x + 1)(x + 2)(x + 4)

The power of each factor in the above expression is 1.

This means that the largest multiplicity is 1

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