In the figure, ∠ABD = 50° and ∠BCD = 60°.
Calculate ∠ADC and ∠ADO.​

The solution to the given inequality will be x ≤ -2 and x > -5

Inequality are expressions not separated by an equal sign

Given the expression below

2≤-4-3x<11

Split

2≤-4-3x and -4-3x<11

Solve both inequalities

-4-3x≥2

-3x ≥ 6

x ≤ -2

Similarly

-4-3x<11

-3x < 15

x > -5

The solution to the given inequality will be x ≤ -2 and x > -5

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Answer:

7.25

Step-by-step explanation:

Simplify

36x = 261

Divide both sides by 36

x = 261/36

Simplify

x = 7.25

Hope this helps!

Answer:

7.25 or 7[tex]\frac{1\\}{4}[/tex]

Step-by-step explanation:

261 ÷ 6 ÷ 6 = 7.25

The equation represents the intersections. The correct option is A:

If we have two functions:

y = f(x) and y = g(x), the equation:

f(x) = g(x) gives the value of x such that the two functions have the same output. So, that equation gives the intersection points between the two graphs.

By looking at the graph, we can see that we have two intersections, one at:

(2, 0) and other at (0, 4).

This means that:

So the correct option is the first one.

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Using it's concept, the mean amount of precipitation (in inches) on March 9 for the areas listed the table was of:

C. 1.56.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

The observations given in the problem are:

0.45, 0.63, 1.34, 3.53, 2.57, 0.84.

Hence the mean is:

M = (0.45 + 0.63 + 1.34 + 3.53 + 2.57 + 0.84)/6 = 1.56.

Which means that option C is correct.

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Answer:

17.25

Step-by-step explanation:

Answer:

2300

Step-by-step explanation:

53%=1219

100=X

X=[(1219)(100)]/53=2300

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

53% = 1219

100% = 2300

The total number of seats in the theater is 2300

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of seats filled by all the students = 1219

1219 is 53% of the total seats in the theater.

This means,

53% = 1219

Now,

Total number of seats in the theater = 100%

53% = 1219

Multiply 100/53 on both sides.

100/53 x 53% = 100/53 x 1219

100% = 2300

Thus,

The total number of seats in the theater is 2300

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The value of the variable x equation 0.2x+0.2+0.5x=-0.3x+1.2 is x=1.

Given a linear equation 0.2x+0.2+0.5x=-0.3x+1.2

Equation is a combination between two or more variables which is usually expressed in equal to form. Equation of two variable looks like ax +by=c. It is solved to find the quantity of x.

Given equation is as under:

0.2x+0.2+0.5x=-0.3x+1.2

It is a linear equation and will have only 1 solution. Linear equation is a equation which is having a straight line graph.

Adding the coefficients of variable

0.7x+0.2=-0.3x+1.2

Take -0.3 to other side

0.7x+0.3x=1.2-0.2

Adding the coefficients of variables

x=1

Hence the value of x in the equation 0.2x+0.2+0.5x=-0.3x+1.2 is x=1.

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The subtraction property of inequality can be used to proof that x = 7 from  x + 8 = 15

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

Given that x + 8 = 15

Hence:

x + 8 - 8 = 15 - 8 (subtraction property of inequality)

x = 7

The subtraction property of inequality can be used to proof that x = 7 from  x + 8 = 15

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Answer:

i 4 boys

ii 3 boys

III 5 boys

A quadratic equation in the form of ax²+bx+c. The zeroes of the polynomial are -2.4 and -7.5.

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c. The Root of the quadratic equation are given as,

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

The zeroes of the polynomial are:

f(x)=x² + 9.9x + 18

0 = x² + 9.9x + 18

[tex]x= \dfrac{-9.9\pm \sqrt{(9.9)^2-4(1)(18)}}{2(1)}\\\\[/tex]

x = -2.4, -7.5

Hence, the zeroes of the polynomial are -2.4 and -7.5.

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The point estimation based on the given interval limits is 0.706.

The use of sample data to compute a single value that will serve as a "best guess" or "best estimate" of an unknown population characteristic is referred to as point estimation.

The point estimation based on the given interval limits is,

Point Estimate = (0.688+0.724)/2 = 0.706

Hence, The point estimation based on the given interval limits is 0.706.

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Answer: B

Step-by-step explanation:

When drawing the stretch-out arc for the pattern of a cone fitting, the radius should be equal to the true length of the side.

The 3 tactics typically used in developing patterns are parallel-line, radial-line, and triangular improvement.

To make such objects, a drafter has to first draw them as a pattern or pattern improvement. A pattern improvement additionally known as a stretch out or simply an improvement is a format of an object made on a single flat aircraft.

In radial traces, we develop styles for shapes that have a taper, all element lines (bends) should radiate returned to a not unusual factor, a radius point. We want matters for this procedure to paintings: A radius factor is in the center (right cone). A radius point is inside an inexpensive distance.

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The Linear inequality that is graphed with y > –x – 2 to create the given solution set is; y < x + 1

From the attached graph of inequalities, we see that one of the lines has its' y - intercept as -2 with a slope of -1. Thus, the equation in slope intercept form is; y = -x - 2.

The shaded region will have the inequality; y > -x - 2.

The other line has its' y - intercept as 1 and a slope of 1.

Thus, the equation of line is; y = x + 1.

The shaded part is above the line and as such the inequality region is represented by the inequality y < x + 1.

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Answer:

D

Step-by-step explanation:

The recursive formula of the arithmetic sequence 13, 6, -1, -8,... is a(n) = 20 - 7n.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have an arithmetic sequence:

13, 6, -1, -8,...

The first term:

a = 13

The common difference:

d = 6 - 13 = -7

The recursive formula of the arithmetic sequence:

a(n) = a + (n - 1)d

a(n) = 13 + (n - 1)(-7)

a(n) = 20 - 7n

Thus, the recursive formula of the arithmetic sequence 13, 6, -1, -8,... is a(n) = 20 - 7n.

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The vertex form of the Quadratic equation is y =  [tex](x-3)^{2}[/tex] +5. The vertex is (3, 5), which is a maximum point.

A quadratic equation is an algebraic equation with the power of its variable 2.

it can be written in standard form which is called vertex form or in the general form.

Analysis:

y = [tex]x^{2}[/tex] -6x +14

y = [tex]x^{2}[/tex] -6x +9 +5

Simplifying this perfect square expression y = [tex]x^{2}[/tex] -6x +9

y  = [tex]x^{2}[/tex] -3x -3x +9

y = x(x-3) -3(x-3) + 5

y = (x-3)(x-3) +5

y = [tex](x-3)^{2}[/tex] + 5

In conclusion, the Vertex form of the equation is y = [tex](x-3)^{2}[/tex] + 5

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Step-by-step explanation:

the y intercept is found by equating X to 0

hence, y = 3

answer is: (0,3)

The graph that represents the exponential function [tex]y = 8\left(\frac{1}{3}\right)^x[/tex] is given at the end of the answer.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, the function is:

[tex]y = 8\left(\frac{1}{3}\right)^x[/tex]

It has an initial value of 8 and rate of change of 1/3, as shown in the graph given at the end of the answer.

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If triangle RST and RZX are similar then the perimeter of triangle RZX is 150 units.

Given triangle RZX and RST are similar and RZ=28, RY=40,ZY=16 and SW=24.

In the similar triangles the ratio of sides are in proportion to the sides of other triangle.

The ratio of ZY to SW is 16:24 meaning it is 2:3. So all the sides of RST are 1.5 times as long as RZX.

RZ=28 so RS=28*1.5=42

RX=40 so RT=40*1.5=60

ZX=ZY+XY and since they are the of the same length , ZX=32 (ZY given)

Then ST=48

Perimeter of a triangle is the sum of sides of the triangle.

Perimeter of RST=RS+ST+RT

=42+60+48

=150

Hence the perimeter of triangle RST is 150 units.

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Question is incorrect as it should be as under:

Given the following information, calculate the perimeter of triangle RST. Assume triangle RZX is similar to RST. RZ=28, RY=40, ZY=16 and SW=24.

Figure should also be given.

The probability that more than 210 people will pass in front of his store is 0.2272.

In the question, we are given that a coffee shop owner wants to examine the number of customers who pass in front of his store in the morning from 7:00 A.M to 7:30 A.M.

We are asked to find the probability that more than 210 people will pass in front of his store if the mean number of customers during this time is 210.

This experiment follows a Poisson Distribution with a mean (λ) = 200, and the random variable X = 210.

To find the probability that more than 210 people will pass in front of his store, we will find P(X > 200).

P(X > 200) = 1 - P(X ≤ 210).

Now, P(X ≤ 210) can be calculated using the function poissoncdf(200,210) on the calculator.

As to find the probability of a Poisson Distribution P(X ≤ x), for a mean = λ, we use the calculator function poissoncdf(λ,x).

The value of poissoncdf(200,210) = 0.77271.

Thus, the value of P(X > 210) = 1 - 0.77271 = 0.22729.

Thus, the probability that more than 210 people will pass in front of his store is 0.2272.

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By critically observing the two triangles, we can deduce that they: B. might not be congruent.

In Geometry, two triangles are said to be similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

By critically observing the two triangles, we can logically deduce that the three angles of both triangles are congruent in accordance with AAA similarity postulate:

However, AAA isn't a congruence postulate and as such all similar triangles might not be congruent.

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Answer:

40

Step-by-step explanation:

The dependent variable in the given research description is sleep quality.

Given variables :1) participants, 2) sleep quality, 3) organic cotton shirts and organic linen shirts, 4) different clothing materials.

We have to identify the dependent variable among all the variables.

Dependent variable is a variable whose quantity depends on other variables.

Independent variable is a variable whose value does not depend on other variables.

In the given research there are four variables:

1) participants,

2) sleep quality,

3) organic cotton shirts and organic linen shirts,

4) different clothing materials.

Among all these sleep quality is a dependent variable because it depends on the quality of clothes whether they or organic shirts or organic linen shirts.

It may be possible that some people get quality sleep in organic cotton shirts and some may get in organic linen shirts.

Hence the dependent variable is sleep quality.

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Answer:

Step-by-step explanation:

    Cost =  fixed rate + number of guests* cost per meal.

Let  x be the number of guests.

a)  Pin hall:

       Fixed rate = $ 500

      Cost per meal = $15

      Cost = 500 + 15*x

    [tex]\sf \boxed{\bf C = 500 + 15x}[/tex]

Bloom place:

       Fixed rate = $350

   Cost per meal = $18

         [tex]\sf \boxed{\bf C = 350 +18x}[/tex]

b) Given the charges are same at both halls.

  350 + 18x = 500 + 15x

             18x = 500 + 15x - 350

              18x = 150 + 15x

        18x -15x = 150

                3x  = 150

                  x = 150 ÷ 3

                  x = 50

When the number of guests is 50, the cost is same at both the halls

Hello!

Forming the equations :

y = mx + b

m = rate per hour

b = fixed charge

[tex]\fbox {y = 15x + 500}[/tex]

[tex]\fbox {y = 18x + 350}[/tex]

Solving for number of guests at which cost is the same :

15x + 500 = 18x + 350

3x = 150

x = 25 guests

Applying the midsegment theorem, the perimeter of triangle JKL is: D. 19.

The perimeter of triangle JKL = JK + JL + KL

Find the lengths of JK, JL, and KL using the triangle midsegment theorem.

JK = 2(3.5) = 7 units

JL = 2(4) = 8 units

KL = 2(2) = 4 units.

Perimeter of triangle JKL = 7 + 8 + 4

Perimeter of triangle JKL = 19 units.

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Answer:  D. 19

Step-by-step explanation:  Answer is correct on Edge. Trust Me! :)

MO, MN, and ON are the midsegments of △JKL.

Triangle M N O is inside triangle J K L. Points M, N, and O are the midpoints of sides J K, J L, and K L.

Q: What is the perimeter of △JKL?  

A:  D. 19

The measure of angle x that is formed around a point is: 145°.

The measure of the angle around a point equals 360 degrees.

The the angles formed by the fork in the road equals 360 degrees.

Therefore, we would have the following equation:

x + 165 + 50 = 360

x + 215 = 360

Subtract both sides by 215

x = 360 - 215

x = 145°

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The statement which best describes the similarity of the two triangles is; Choice D; There is not enough information to determine whether the triangles are similar.

The two triangles given in the task content are expected to be assessed to determine if they are similar.

From the concept of congruence in triangles, two triangles are congruent only if all 3 angle measures in one are similar to that in the other, or if the ratio of all corresponding pairs of sides are equal.

Hence, since neither of the conditions is satisfied by the information given, it follows that Choice D is correct.

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Step-by-step explanation:

simple answer mate..

under root 2 is right because angle are same.. option d

Answer:

√2

Step-by-step explanation:

Angle ( θ ) = 45

Hypotenuse side = 2

Opposite side = x

Formula : -

sin θ = Opposite side / Hypotenuse side

Note :

The value of sin 45 = 1/√2

sin 45 = x/2

1/√2 = x/2

Cross multiply,

x*√2 = 2*1

x√2 = 2

2 can be simplified as √2 * √2

x√2 = √2*√2

Divide √2 on both sides,

x = √2