Prove: Quadrilateral ABCD is a parallelogram
PLEASE HELP

A triangle is a plane figure which has three sides and angles. Thus the sum of internal angles of a triangle is [tex]180^{o}[/tex]. Thus the answers to the missing values are:

7. x =  [tex]108^{o}[/tex]

8. x = [tex]133^{o}[/tex]

9. x = [tex]124^{o}[/tex]

10. x = [tex]62^{o}[/tex]

11.  x = [tex]74^{o}[/tex]

12. x = [tex]77^{o}[/tex]

13. a = [tex]35^{o}[/tex]

14. b = [tex]74^{o}[/tex]

15. c = [tex]66^{o}[/tex]

The sum of the internal angles of a triangle is [tex]180^{o}[/tex]. Thus in a given question, the required value for each missing value is:

7. Let the unknown inter nal angle ne represented by r, so that;

70 + 38 + r = [tex]180^{o}[/tex]

r = [tex]180^{o}[/tex] - 108

r = 72

So that,

x + a = [tex]180^{o}[/tex] (sum of angles on a staight line)

72 + a = [tex]180^{o}[/tex]

a = [tex]180^{o}[/tex] - 72

  = [tex]108^{o}[/tex]

a = [tex]108^{o}[/tex]

8. x = 39 + 94 (Sum of two opposite interior angles is equal to an exterior angle)

   x   = [tex]133^{o}[/tex]

9. x = 43 + 81 (Sum of two opposite interior angles is equal to an exterior angle)

    x  = [tex]124^{o}[/tex]

10. x + 19 = 81 (Sum of two opposite interior angles is equal to an exterior angle)

    x = 81 - 19

      x = [tex]62^{o}[/tex]

11. 41 + x = 115 (Sum of two opposite interior angles is equal to an exterior angle)

    x = 115 - 41

      x = [tex]74^{o}[/tex]

12. x = 41 + 36 (Sum of two opposite interior angles is equal to an exterior angle)

    x = [tex]77^{o}[/tex]

13. 33 + 112 + a =  [tex]180^{o}[/tex] (sum of angles on a staight line)

     a = [tex]180^{o}[/tex] - 145

        = [tex]35^{o}[/tex]

14. b + 71 + a = [tex]180^{o}[/tex] (sum of angles on a staight line)

     b =  [tex]180^{o}[/tex] - 106

       b  = [tex]74^{o}[/tex]

15. c + 71 + 43 = [tex]180^{o}[/tex] (sum of angles on a staight line)

      c = [tex]180^{o}[/tex] - 114

        c = [tex]66^{o}[/tex]

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Answer:

[tex] \boxed{\sf{x = \frac{5 \pm \sqrt{97} }{12} }}[/tex]

Step-by-step explanation:

[tex]\sf{5x = 6 {x}^{2} - 3 }[/tex]

[tex]\sf{0 = 6 {x}^{2} - 3 - 5x }[/tex]

[tex]\sf{0 = 6 {x}^{2} - 5x - 3 }[/tex]

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

[tex]\sf{x = \frac{ - ( - 5) \pm \sqrt{ { - 5}^{2} - 4(6)( - 3)} }{2(6)} }[/tex]

[tex]\sf{x = \frac{5 \pm \sqrt{ 25 + 72} }{12} }[/tex]

[tex]\sf{x = \frac{5 \pm \sqrt{97} }{12} }[/tex]

Answer:

Step-by-step explanation:

Answer: [tex]3a+6+\frac{5}[a+2}[/tex]

Step-by-step explanation:

[tex]f(a+2)=3(a+2)+\frac{5}{a+2}=3a+6+\frac{5}[a+2}[/tex]

Answer:

[tex]y = \frac{1}{2} x + \frac{5}{2} [/tex]

Step-by-step explanation:

Since the line with equation y = 1 - 2x has slope -2, we need to find the equation of the line with slope 1/2.

[tex]3 = \frac{1}{2} (1) + b[/tex]

[tex]3 = \frac{1}{2} + b[/tex]

[tex]b = \frac{5}{2} [/tex]

[tex]y = \frac{1}{2}x + \frac{5}{2} [/tex]

Answer:

c

Step-by-step explanation:

[tex]x=5+i\sqrt{7} , y = 5-i\sqrt{7}\\ x^2-2xy+y^2=(x-y)^2\\ (x-y)^2=(2i\sqrt{7} )^2\\4.i^2.7\\-28[/tex]

Answer:

c

Step-by-step explanation:

given x = 5 + i[tex]\sqrt{7}[/tex] then y = 5 - i[tex]\sqrt{7}[/tex]

x² - 2xy + y² ← is a perfect square

= (x - y)² ← substitute values for x and y

= (5 + i[tex]\sqrt{7}[/tex] - (5 - i[tex]\sqrt{7}[/tex] )²

=  (5 + i[tex]\sqrt{7}[/tex] - 5 + i[tex]\sqrt{7}[/tex] )²

= (2i[tex]\sqrt{7}[/tex] )²

= 2² × i² × ([tex]\sqrt{7}[/tex] )²

= 4 × - 1 × 7

= - 28

The probability that an individual will score of 50 or less is 0.06.

Given mean of 60 and standard deviation of 8.

We have to find the probability that individual will score 50or less.

Probability is the chance of happening an event among all the events possible. The probability lies between 0 and 1. The formula to calculate probability is as under:

Probability = number of items/total items.

We have to first find the z value from 50 to 60 which can be found as under:

z value=(50-60)/60

=-0.167

P value from 50 to 60 is 0.44

probability that the individual will score 50 or less is 0.5-0.44

=0.06

Hence the probability that the individual will score 50 or less is 0.06.

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Answer:

The required line can be found by substituting the slope and the given point in the slope intercept form of a line and is given by y=mx+c, where m is the slope and c is the y intercept.

Step-by-step explanation:

The equation of a parallel line to a linear function that passes through a point can be explained using the examples below.

We have,

The parallel line to a linear function that passes through a point can be explained using the examples below.

Example:

Let's find a line parallel to the linear function y = 3x - 2 that passes through the point (2, 5).

Step 1: Given linear function and point

Linear function: y = 3x - 2

Point: (2, 5)

Step 2: Determine the slope of the given linear function

The slope (m) of the given function y = 3x - 2 is 3.

Step 3: Use the slope to find the equation of the parallel line

Since the parallel line has the same slope (3), its equation will be

y = 3x + b, where "b" is the y-intercept that we need to find.

Step 4: Substitute the coordinates of the given point into the equation of the parallel line

Using the coordinates (2, 5) of the given point, we can solve for "b":

5 = 3(2) + b

5 = 6 + b

b = 5 - 6

b = -1

So, the equation of the line parallel to y = 3x - 2 and passing through the point (2, 5) is:

y = 3x - 1.

Thus,

The equation of a parallel line to a linear function that passes through a point can be explained using the examples above.

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Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.

If we take a look at a rectangular bathtub, the volume of the bathtub can be expressed as:

Volume (V) = length × breadth × height

where;

the base = length × breadth = 16ft²

∴ the volume of the rectangular bathtub = 16h ---  (1)

Using differentiation to differentiate 16h with respect to t implicitly, then:

dV/ dT = 16 dH /dT

When the rate of rising of the volume is 0.5 ft³/min

Then:

0.5 = 16 dH /dT

dH /dT = 1 / 16 * 0.5

dH /dT = 0.3125.

Jon is filling the tub at a rate of 0.5 ft3/min is 0.3125 ft/min.

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Answer:

The actual length of the ship is 150 meters.

Step-by-step explanation:

The scale of the model is 1 cm:5 meters, which means that every 1 cm on the model represents 5 meters on the ship. Since the model ship is 30 cm long, that means it represents 150 meters on the real ship.

The probability that both are yellow is 3/10.

Using the probability method, we get

P(y1 and y2) =  P(y1) P(y2|y1)

= 3/5 x 2/4

= 6 / 20

= 3 / 10

The probability that both are yellow is 3/10.

Probability is sincerely how in all likelihood something is to manifest. each time we're uncertain approximately the final results of an occasion, we will speak about the possibilities of sure effects—how probably they're. The analysis of activities ruled by using possibility is known as statistics.

A series of actions where the outcomes are continually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a dice. occasion. It is a single final result of an experiment.

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Answer:

3*5*(x^3)*(y^2)

Step-by-step explanation:

Since we don't know what x and y are, we can leave them as they are. Now we just find the prime factorization of 15, which is 3*5.

The result to reject the null hypothesis can be interpreted as follows,

There is sufficient evidence to disprove the claim μ = 50.2

What is a null hypothesis?

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is H0.

To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts perform a hypothesis testing and employ the null hypothesis, often known as the conjecture. Any variation between the selected attributes that you observe in a collection of data is thought to be the result of chance, according to the null hypothesis.

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The statement which is true about the end behavior of the graphed function is third option that is as the x-values go to negative infinity, the function's values are equal to zero.

A coordinate plane is a two dimensional plane formed by the intersection of two number lines . One of these number lines is a horizontal number lines called the x-axis and the other number line is a vertical number line called the y-axis.

The exact answer is third option that is as the x-values go to negative infinity, the function's values are equal to zero.

Step by step explanation:

Minimum value (negative 1.25, negative 3.25)

Maximum value of (0.25, negative 1.75)

The x intercepts where the graph crosses the x axis.

Value of x when y=0 crosses x axis at (negative 2.25, 0)

The y intercept are where the graph crosses the y axis.

Value of y when x=0 crosses y axis at (0, negative 2)

The line exits the plane at (negative 2.75, 6) and (1.5, 6).

It can be seen from the coordinates that as the x-values go to negative infinity, the function's values are equal to zero, the coordinates of y approaches zero.

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Answer:

D

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Let N be the total number of spins.

Probability of A on Red and B on Red = 0.5 x 0 .6 = 0.3 (top branch of tree)

Therefore with N spins, the estimated number of times spinner A and spinner B land on red is 0.3N and we are given this as 84

So 0.3N = 84
N = 84/0/3 = 280

The probability of spinner A on blue and spinner B on blue is 0.5 x 0.4 = 0.2 (lowest branch of tree)

For 280 spins, the estimated number of times that both spinners land on blue is given by 0.2 x 280 = 56

Answer:

-3

Step-by-step explanation:

Define two points on the line:

Substitute the defined points into the slope formula and solve for m:

[tex]\begin{aligned} \textsf{slope}\:(m) & = \dfrac{y_2-y_1}{x_2-x_1}\\\\ \implies m & =\dfrac{-2-4}{2-0}\\\\ & =\dfrac{-6}{2}\\\\ & =-3\end{aligned}[/tex]

Therefore the slope of the given line is -3.

Answer:

JL = 14

Step-by-step explanation:

N represents the center of the rhombus

Then

N is the midpoint of the diagonal (line segment) JL

Then

JL = 2 × NL

    = 2 × 7

    = 14

Answer:

algebric expression

Answer:

Binomial

Step-by-step explanation:

Comment

Answer: Two terms make up the expression you are given (3x + 5) ).

When two terms are on either side of an isolated plus (or minus) sign, then the expression is called a Binomial.

Answer:

$1503.08 per month

Step-by-step explanation:

Answer:

35.3

Step-by-step explanation:

please mark brainliest

Answer:

35.3

Step-by-step explanation:

The correct answer is, b=4.

Given Information and To Find

It is given that in a right angled-triangle lmn,

∠m = 90°

∠l = x°

ln = 20 units

lm = 3b units

[tex]secx = \frac{5}{3}[/tex]

We have to find the value of b.

What is a right-angled triangle?

A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a right-angled triangle. Trigonometry's fundamental concept is the relationship between a right triangle's sides and other angles.

Applying Trigonometry

We know that in a right angled-triangle,

[tex]sec x=\frac{hypotenuse}{base}[/tex]

In this case, we have (refer to the diagram),

[tex]secx=\frac{ln}{lm}[/tex]

⇒ [tex]\frac{20}{3b} = \frac{5}{3}[/tex]

⇒ [tex]20(3) = 3b(5)[/tex]

⇒ [tex]15b = 60[/tex]

⇒ [tex]b=4[/tex]

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Using it's concept, the domain of the square root function shown in the graph is:

[tex]x \geq 0[/tex]

The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains the values of x.

Researching the problem on the internet, the graph is of the square root function, defined for [tex]x \geq 0[/tex], which is the domain of the function.

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The equation of the line with a slope of -3 and passing through the point (3, 16) is y = -3x + 25

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of a line is:

y = mx + b

Where m is the slope and b is the y intercept.

Given that the line has a slope of -3 and passes through (3, 16), hence:

y - 16 = -3(x - 3)

y = -3x + 25

The equation of the line with a slope of -3 and passing through the point (3, 16) is y = -3x + 25

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The calculated distance of this throw is given as 41.23 meters.

In order to solve for this, we have to make use of the formula for calculating distance.

This is given as:

[tex]\sqrt{(x^{2}-x^{1} ) } (y^{2} -y^{1} )[/tex]

This is substituted as

sqr(50-10)²+(5-15)²

= √40² +√ -10²

= √1700

= 41.23

b. The points were created to find the distance by making use of yards from the goals and the yards from the sidelines.

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Answer: 45 red marbles

Step-by-step explanation:

Using the ratios, we can create a fraction for the number of marbles.

3/5 of the bag would be red marbles, and 2/5 of the bag would be blue marbles.

(you get the 5 from adding 3+2 together)

If you take 3/5 of 75, you would get 45 red marbles.

The total volume of the purchased boxes is 14x^2+4x+1

Given the following parameters

Volume of a large box = 6x^2+2x+3 cubic units

Volume of medium = 2x^2-5 cubic units.

If a customer purchases two large boxes and one medium box, the total volume is expressed as:

Total volume = 2(6x^2+2x+3) +  2x^2-5

Expand

Total volume = 12x^2+4x+6+2x^2-5

Total volume = 14x^2+4x+1

Hence the total volume of the purchased boxes is 14x^2+4x+1

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Hello,

[tex] \sqrt{50} = \sqrt{2 \times 25} = \sqrt{2 \times 5 {}^{2} } = 5 \sqrt{2} [/tex]

The value of x from the given expression is 0.7558

The standard exponential equation is expressed as y = ab^x

Given the equation below

10^x +5 = 60

Subtract 5 from both sides

10^x = 60 - 5

10^x = 55

Take the log of both sides

log10^x = log55

x = log55/log10

x = 0.7558

Hence the value of x from the given expression is 0.7558

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Squares are the results of multiplying a value by itself. The correct option is B.

Squares are the results of multiplying a value by itself. Whereas the square root of a number is a value that when multiplied by itself yields the original value. As a result, both are vice versa approaches. For example, the square of 2 is 4 and the square root of 4 is 2.

The number 1764 in the form of prime factors can be written as,

1764 = 2×2×3×3×7×7×1

Therefore,

√1764 = 2×3×7 = 42

Hence, the correct option is B.

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Answer: d}2^2(3^2)(7^2)

Step-by-step explanation: I did the quiz