What is an angle that is adjacent to BEC?
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∠NSP ≅ ∠QSR, ∠MSP ≅ ∠PSR, ∠MSN ≅ ∠PSQ, ∠NSQ ≅ ∠MSP, ∠NSQ ≅ ∠PSR are the congruent angles.

∠NSP ≅ ∠QSR by the Congruent Complements Theorem. Because both are complementary to ∠PSQ.

∠MSP ≅ ∠PSR by the Right Angles Congruence Theorem. Because both ∠MSP = ∠PSR = 90°.

∠MSN ≅ ∠PSQ because they have the same measure. ∠MSN = ∠PSQ = 50°. Angles with same measure are congruent to each other.

∠NSQ ≅ ∠MSP by the Right Angles Congruence Theorem. Because ∠NSQ = ∠MSP = 90°.

∠NSQ ≅ ∠PSR by the Right Angles Congruence Theorem. Because ∠NSQ = ∠PSR = 90°.

Congruent Complements theorem states that if two angles are complementary (sum = 90°) to the same angle, then they are congruent.

Right Angles Theorem states that two right angles(90° angles) are congruent to each other.

Vertical Angles Congruence theorem states that two opposite angles formed between intersection of two lines are congruent. Here, ∠MSN is not congruent to ∠QSR because they are not vertical opposite angles.

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Cofunction equivalent to [tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex].

You use the formula for the sine of a sum:

[tex]$$\sin (a+b)=\sin a \cos b+\cos a \sin b$$[/tex]

Think of a pie divided into twelve slices. Three of them form one quarter, two more form one sixth of the pie. So, thinking of the "pie" as [tex]$\pi$[/tex]:

[tex]\frac{5 \pi}{12}=\frac{\pi}{4}+\frac{\pi}{6}[/tex]

With that in mind, put [tex]$a=\frac{\pi}{4}, b=\frac{\pi}{6}$[/tex] into the sine formula given above:

[tex]$$\sin \left(\frac{5 \pi}{12}\right)=\sin \left(\frac{\pi}{4}\right) \cos \left(\frac{\pi}{6}\right)+\cos \left(\frac{\pi}{4}\right) \sin \left(\frac{\pi}{6}\right)$$[/tex]

Plug in the familiar values [tex]$\sin \left(\frac{\pi}{4}\right)=\cos \left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}, \cos \left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}$[/tex], [tex]$\sin \left(\frac{\pi}{6}\right)=\frac{1}{2}$[/tex], and you get the answer given above. And, yes, putting that expression into a calculator gives [tex]$0.9659$[/tex] (four significant digits).

The cofunction of an angle θ is the trigonometric complement of an angle. It shows the relationship between trignometric functions:

List the cofunction formula for [tex]$\sin$[/tex]

[tex]$$\sin (\theta)=\cos (\pi / 2-\theta)$$[/tex]

Plug in [tex]$\theta=5 \pi / 12$[/tex] for our cofunction formula:

[tex]$$\sin (5 \pi / 12)=\cos (\pi / 2-5 \pi / 12)$$[/tex]

Determine common denominator in radians

We use a common denominator of [tex]$(12 \div 2)=6$[/tex]

[tex]$\sin (5 \pi / 12)=\cos (6 \pi / 12-(5 \pi / 12))$[/tex]

[tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex]

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On 4/5 gallon of gasoline, hybrid car will travel a distance of 48 miles.

Suppose, non hybrid car travel "x" distance in 1 gallon of gasoline

Then, hybrid will travel " 1 ⁹/₁₁ * x" distance in 1 gallon of gasoline

Given that, non hybrid car travel distance per gallon is; x = 33 miles per gallon

Then, hybrid car travel,  1 ⁹/₁₁ * x =  1 ⁹/₁₁ * x * 33 = 60 miles per gallon

On 1 gallon of gasoline hybrid car travel 60 miles

On 4/5 gallon of gasoline hybrid car will travel = 4/5 * 60 = 48 miles

On 4/5 gallon of gasoline, hybrid car will travel 48 miles of distance.

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Answer:

4x12 equals 48 therefore 48+5= 53......

Answer:

Please add the graph for these problems so I can solve your questions? Thank you!

Step-by-step explanation:

Explanation:

Place the decimal point between the first two digits to get 5.0

Then we must move the decimal point 4 spots to the right to get back to 50,000

So that's where the "4" comes in with the 10^4

This means 50,000 = 5 * 10^4 which is in scientific notation.

The answer in scientific notation is 5 times 10^4

The exponent of four tells you to multiply 10 by itself 4 times.

10 x 10 = 100 x 10 = 1000 x 10 = 10000

And 10000 times 5 is equal to 50,000.

Answer:

  19 seconds

Step-by-step explanation:

You want to know the time it takes for Juan, running 18 m/s, to overtake Mahdi, running 6 m/s, if Mahdi has a 228 meter head start.

The time to close the gap between the runners will be ...

  time = distance/speed

  time = (228 m)/(difference in speeds) = (228 m)/(18 m/s -6 m/s)

  time = (228 m)/(12 m/s) = (228/12) s = 19 s

It will take Juan 19 seconds to catch Mahdi.

__

Additional comment

The fastest human runner will not exceed 12.3 meters per second, especially over a 300+ meter distance.

The horizontal distance that the plane has flown can be represented as a function of t d(t) = 300t.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

An airplane is flying at a speed of 300 mi/h at an altitude of one mile.

As we know,

From the relation between time-distance-speed

distance = time×speed

Speed = 300 mi/h

let distance be d and time be t

d = 300t

We can write the above equation as:

The horizontal distance that the plane has flown:

d(t) = 300t

Thus, the horizontal distance that the plane has flown can be represented as a function of t d(t) = 300t.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

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Answer:

c) 144

Step-by-step explanation:

Since A is between Y and Z,

[tex]YZ = YA + AZ[/tex]

[tex]116 = 22 + 16x\\16x = 116 - 22\\16x = 144\\x = 9[/tex]

however, the question asks for [tex]the length of AZ[/tex], not the value of x.

Thus,

[tex]AZ = 16x[/tex]

[tex]AZ = 16\\[/tex] × [tex]9[/tex]

[tex]AZ = 144[/tex]

The domain is written in the form { x : x ≠ 7/3 }

Given data

Y= 1-7x / 8-|3x-15|

The domain refers to the values of x, from the equation we solve for the possible values that will not make the equation undefined.

For the equation to be undefined the denominator should be zero hence we solve for the value of x that will make the equation, to have a denominator equal to zero and the domain will be any other values of x except the value that gives the denominator equal to zero,

The denominator is 8-|3x-15|

solving for the value of x that gives the equation that makes the equation equal to zero

8-|3x-15| = 0

3x - 15 = -8

3x = -8 + 15

3x = 7

x = 7/3

The domain is written in the form { x : x ≠ 7/3 }

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2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)

Given two numbers

1)2.7×1012

2) 1.5×108

Two numbers can be equal or one is greater than the other or one is less than the other. there will be no other case rather than these three.

1)2.7×1012=2,732.4

2) 1.5×108=162

The value of the 1st number is 2,732.4 and the value of the 2nd number is 162

1st given number is greater than the 2nd number i.e. 2,732.4>162

Therefore,2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)

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In the garage 33.33 percentage of work were MOTS.

Percentage is defined as per-cent, that is out of hundred. The percentage is calculated by dividing the acquired value by the total value and multiplying the result by 100.

Now in the given problem,

Total number of vehicles on which Keith worked is 105.

The number of MOTS among the 105 is 35.

Now we have to calculate the percentage of the MOTS out of a total 105 vehicles.

Let us use the formula=(number of MOTS ÷ total vehicles)×100

Therefore required percentage=[tex]\frac{35}{105}\times 100\%[/tex]

or, percentage=33.333...%

Therefore we can conclude that the total percentage of MOTS were approximately 33.33%(rounded to 2 decimal places).

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If you meant to say [tex]|5x+1| < -2[/tex], then there are no solutions.

This is because the |5x+1| is never negative. This applies to the result of any absolute value function. Absolute value represents distance on a number line. Negative distance is not possible.

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If you meant to say [tex]|5x+1| \le 2[/tex], then the steps are shown below

[tex]|5x+1| \le 2\\\\-2 \le 5x+1 \le 2\\\\-2-1 \le 5x+1-1 \le 2-1\\\\-3 \le 5x \le 1\\\\-3/5 \le 5x/5 \le 1/5\\\\-3/5 \le x \le 1/5\\\\-0.6 \le x \le 0.2\\\\[/tex]

The interval notation would be [-3/5, 1/5] in fraction form

That is equivalent to [-0.6, 0.2] in decimal form.

Use square brackets to include each endpoint.

The domain is:

D: {-4, 5, 6, 8}

The range is:

R: {-4, 3, 5}

And yes, the relation is a function.

For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).

Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}

The domain is the set of the first values of each pair, so we have:

D: {-4, 5, 6, 8}

The range is the set of the second values of each pair:

R: {-4, 3, 5}

Now, is this a function?

Yes, it is a function, because each input is mapped into only one output.

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Answer:

8

Step-by-step explanation:

The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:

2,10,21,23,23,38,38

38 - 2 = 36

The range in this example is 36. Similar to the mean, range can be significantly affected by extremely large or small values. Using the same example as previously:

2,10,21,23,23,38,38,1027892

The range, in this case, would be 1,027,890 compared to 36 in the previous case. As such, it is important to extensively analyze data sets to ensure that outliers are accounted for.

Answer: Range is all the values of the y-axis therefore, the range of the graph is {0,4,6,8}

Answer:

y = -2x + 18

Step-by-step explanation:

Slope m = -2 with y = 8, x = 5

y = mx + b

8 = (-2)(5) + b

8 = -10 + b

b = 8 + 10 = 18

then y = -2x + 18

Slope of the point is 11/8.

here we use the slope equation so -1-10 would be -11, Then 1-9 is -8 and then -11 divided by -8 is a positive 11/8.

given;

x1=9

x2=1

y1=10

y2=-1

slope=y2-y1/x2-x1

        =-1-10/1-9

        = 11/8

therefore, the slope of the line that passes through the points ; 11/8.

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run"

there are 4 types of slope,

negative, positive, zero, and undefined. as x increases

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b)..

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Marty will have to pay $18,000 for his $15,000 car.

While taking out a loan, the amount taken has to be repaid along with an interest. Thus, the amount paid back by the borrower is always greater than the initial amount that the borrower gets from the lender as a loan.

Here, we are given that Marty has to pay $500 per month for 3 years to repay the loan for his $15,000 car.

Thus, for one month he pays = $500

and also we know that 1 year = 12 months

⇒ 3 years = 12(3) = 36 months

Therefore, for 36 months Marty will have to pay,

500 × 36 = 18,000

Thus, Marty will have to pay $18,000 for his $15,000 car.

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Answer: Answer  2, Triangle A is dilated from the origin by a scale of 1/2 to obtain triangle B

Step-by-step explanation:

Measure of linear pair A and B are 86 and 38 respectively.

Let the measure of  B = x

And measure of  A = 3x – 28

As  A and B are linear pair. Therefore their sum will be equal to 180

That is numerically,

      A + B = 180

Putting the required values of A and B we will get

     3x – 28 + x = 180

      4x  = 180-28

       4x = 152

        x = 38

Hence the measure of A = 3*38 – 28 = 86

And the measure of B = x = 38

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The statement correctly describes the perpendicular bisector construction below The construction of JK to bisect GH: Option D is the correct answer

The term perpendicular bisector refers to the line that divides another line into two equal parts, making an angle of 90 degrees. The term is made up of two words, perpendicular and bisector.

Perpendicular refers to angle 90 degrees, while the bisector refers to dividing into two equal parts.

In the picture, the main line is GH while JK is the line constructed to bisect the main line

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Answer:

y = 19.2

Step-by-step explanation:

We know there is relationship between y and x, so according to the formula [tex]y = kx[/tex]

k = 12/5

we get one function y = 2.4x

when x = 8, input it into the function,

y = 2.4×8 = 19.2

The midpoint of the line segment of the endpoints (6,-6) and (1,2) is given as:

(3½,-1)

What is the midpoint of a line segment in geometry?

The midpoint of a line segment is simply the centre point of a give segment that cuts or divides it into two congruent segments.

That is for example, if there are two points with coordinates (x1,y1) and (x2,y2), then their midpoint will be ; [(x1+x2)÷2,(y1+y2)÷2]

From the given question!

x1=6, x2=1 and y1=-6,y2=2

Thus, the midpoint is derived as;

[(6+1)÷2,(-6+2)÷2]

[(7)÷2,(-4)÷2]

(3½,-1).

The value of x in given diagram is x=3;

The entire area filled by a triangle's three sides on a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 b h, where b and h are the product of the triangle's base and height. All triangle shapes, including scalene, isosceles, and equilateral triangles, may be calculated using this formula. It is important to keep in mind that a triangle's base and height are perpendicular to one another.

Area of triangle SXY = 1/2 × SX × (x-2);

Area of triangle STR = 1/2 × ST × (x+3);

Area of trapezium XTRY = 1/2 × (x+3+x-2) × XT;

Area of triangle SXY = Area of triangle STR - Area of trapezium XTRY;

SX × (x-2) = ST × (x+3) - (2x + 1) × XT;

As; SX = TX = ST/2;

(x-2)/2 = (x+3) - (2x+1)/2;

x - 2 = 2x + 6 -2x -1

x = 3;

A triangle is a closed figure that has three vertices, three sides, and three angles.  It is one of the most fundamental geometric forms, and it is represented by the symbol△. Triangles in mathematics can be categorized according to their sides and angles into many categories.

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The length of the side of Amy’s printed picture is 6 inches.

A square is a two-dimensional closed shape with four equal sides.

Now, as per the given question;

The original length of the side of the square was 4 inches.

Thus, the area of the old photo was;

A = side²

A = 4²

A = 16 square inch.

Now, as the picture is increased by 225%.

Then, increase the area by 225%.

New area = 225% of old area

                = (16×225)/100

New area = 36

The length of the side of the new photograph is;

New area = length²

length = √New area

length = √36

length = 6 inches.

Therefore, the length of the side of Amy’s printed picture is 6 inches.

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Answer:

x=+2√7

Step-by-step explanation:

Step-by-step explanation:

[tex] 3\sqrt{8} + \sqrt{114} [/tex]