In the diagram below, BC−→− bisects ∠FBE
If m∠DBC=(12x−3)°, m∠DBE=(5x+12)°, and m∠EBC=(3x+13)°, find m∠EBC

The reasons for the steps are given below.

The value of x is -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

-2(4x + 3) = 26

[ The distributive property of multiplication over addition ]

-2(4x) + -2(3) = 26

-8x - 6 = 26

[ Adding 6 on both sides ]

-8x - 6 + 6 = 26 + 6

-8x = 32

[ Divide -8 into both sides ]

-8x/-8 = 32/-8

x = -4

Thus,

The reasons for the steps are given above.

x = -4

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Answer:

Step-by-step explanation:

-2x² + 12x  + 32 = 0

discriminant = 12² - 4(-2)(32) = 400

positive discriminant means there are two distinct real roots

x = [-12 ± √(12² – 4(-2)·32)] / [2·(-2)]

 = [-12 ± √400] / (-4)

 = [-12 ± 20] /(-4)

 = 8, -2

Answer:

y = 3. last option is correct answer for 2nd question.

Step-by-step explanation:

f(x) just means y.

horizontal asymptote is y = 'something.'

the graph crosses y = 4, so y = 4 cannot be asymptote.

y = 3 is since the graph never quite touches it.

as for ∞, we see that as x approaches -∞, y almost reaches 3. but not quite. also, as x approaches +∞, y approaches +∞.

so the last option is the correct answer.

Answer:

  -1

Step-by-step explanation:

The line goes down 1 grid square for each grid square to the right. Each grid square represents 1 unit in both the x- and y-directions. That means the slope is ...

  m = rise/run = -1/1 = -1

The slope of the line is -1.

Answer:

2282 tablespoons

and 1 teaspoon

Step-by-step explanation:

The sine function for the graph is given as follows:

y = 1.5sin(2x) - 2.5.

The sine function is defined as follows:

y = Asin(Bx) + C.

In which the parameters are given as follows:

The function in this problem oscillates between -4 and -1, for a difference of 3, hence the amplitude is given as follows:

2A = 3

A = 1.5.

The function oscillates between 2.5 units below -A and 2.5 units below A, hence the vertical shift is given as follows:

C = -2.5.

The shortest distance between repetitions is of π, hence the period is of π and the coefficient B is given as follows:

2π/B = π

2/B = 1

B = 2.

Hence the function:

y = 1.5sin(2x) - 2.5.

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Answer: The sine function for the graph is given as follows:y = 1.5sin(2x) - 2.5.How to define the sine function?The sine function is defined as follows:y = Asin(Bx) + C.In which the parameters are given as follows:A: amplitude.B: the period is 2π/B.C: vertical shift.The function in this problem oscillates between -4 and -1, for a difference of 3, hence the amplitude is given as follows:2A = 3A = 1.5.The function oscillates between 2.5 units below -A and 2.5 units below A, hence the vertical shift is given as follows:C = -2.5.The shortest distance between repetitions is of π, hence the period is of π and the coefficient B is given as follows:2π/B = π2/B = 1B = 2.Hence the function:y = 1.5sin(2x) - 2.5.

Step-by-step explanation:

Answer:2^3

Step-by-step explanation:

The number of children ticket sold is 90 while the number of adult ticket sold is 200.

Math land theatre charges $5.00 for children's tickets and $9.00 for adult tickets. One night the theatre sold 290 tickets and took in $2250.

Therefore, let's find the number of each type of ticket sold as follows:

Hence,

Let

Therefore, using equation,

c + a = 290

5c + 9a = 2250

Multiply equation(i) by 5

5c + 5a = 1450

5c + 9a = 2250

subtract the equation

4a = 800

divide both sides by 4

a = 800 / 4

a = 200

Therefore, let's find c

c = 290 - 200

c = 90

Hence,

number of children's ticket = 90

number of adult tickets = 200

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According to the histogram, the percentage of participants aged 40 to 59, who attended the restaurant's food festival, is 35%.

A histogram approximately represents a distribution of grouped data with numerical values.

A histogram uses rectangular bars to show the frequency of data items in successive numerical intervals of equal sizes.

Age Group (year)  Number of People

0 to 19                            20

20 to 39                         40

40 to 59                         60

60 to 79                         50

Total                             170

Percentage of ages 40 to 59  =  60/170 x 100 = 35.29%

Thus, using the histogram, we can assure the restaurant manager that 35% of the festival participants are between 40 and 59 years old.

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Answer:

120 degress

Step-by-step explanation:

Answer:

x = 2     y = -12

Step-by-step explanation:

x+ y = -10

2 + y = -10

      y = -10 -2 = -12

The value of m that satisfies the equation -3 + m = 9 is m = 12.

To solve the equation -3 + m = 9, we can isolate the variable m by moving the constant term -3 to the other side of the equation.

-3 + m = 9

To move -3 to the other side, we can add 3 to both sides of the equation:

-3 + 3 + m = 9 + 3

Simplifying, we have:

m = 12

Therefore, the value of m that satisfies the equation -3 + m = 9 is m = 12.

None of the provided answer options (A, B, C, D) match the correct solution.

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Hello!

The distance, d, is less than 200 miles.

B. d > 200

The graph represents a functional relationship between two variables X and Y. We get y=3 for the value x=2

Domain is defined as the set of values of independent variables.

In the question, all x coordinates are domain.

In a function, for each domain we get a possible output from the dependent variables which is termed as range. In this graph, the y coordinates are range because y value is dependent on x value.

The graph shows five points are plotted on XY coordinate system that represents a relationship between independent variable X and dependent variable Y.

hence, this graph is plotted from a function.

from the graph we get the domain as {-4, -2, 0, 2, 4}

the ranges are = {-3, -2, -1, 1, 3}

we get, y=3 for the value of x= 2  

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Answer:d

Step-by-step explanation:

the equation straight line y = -1/5 x + 4. of the line drawn in the picture is attached below.

What is equation straight line?

There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1).

The given equation y = -1/5 x + 4.

Here m = -1/5

and c= 4

So the plot on the graph will be as fallow.

Hence the equation of the line drawn in the picture attached below

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The volume of cone is 175 m³

Firstly,

Volume of Pyramid.

The volume (V) of a pyramid is  

V = ⅓Ah

Data:

V = 175m³

Calculation:

175 = ⅓× A× h

Ah = 175*3

Ah = 525m³

Secondly,

The volume (V) of a cone is

V = ⅓Ah

Data:

Ah = 525 m³

Calculation:

V = ⅓ A× h

V = 175 m³

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Answer:

The average rate of change is 44.

Step by step:

FIRST STEP:

\(\frac{(294-118)}{(6-2)}\)

SECOND STEP:

\(\frac{176}{4}\) = 44

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Now, According to the question:

The order of calculate the confidence interval for the mean are as follows:

1. Select sample stat

2. select desired confidence

3. determine margin of error

4. specify upper and lower limits

Let's know:

What is Confidence Interval?

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

The common notation for the parameter in question is θ. Often, this parameter is the population mean μ , which is estimated through the sample mean bar x.

The level C of a confidence interval gives the probability that the interval produced by the method employed includes the true value of the parameter θ.

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Answer:

\(x=-\frac{11}{6}\)

Step-by-step explanation:

8x2=6x=5

16+6x=5

6x=5-16

6x=-11

\(x=-\frac{11}{6}\)

Answer:

See below.

Step-by-step explanation:

\(8x^2+6x=5\)

Reformat this so the equation equals zero:

\(8x^2+6x-5=0\)

\(a=8, b=6, c=-5\)

\(x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\)

\(x=\frac{-(6)\pm\sqrt{(6)^2-4(8)(-5)} }{2(8)}\)

\(x=\frac{-6\pm\sqrt{36+160} }{16}\)

\(x=\frac{-6\pm\sqrt{196} }{16}\)

\(x=\frac{-6\pm14 }{16}\)

\(x=\frac{-6+14}{16}=8/16=1/2\) or

\(x=\frac{-6-14}{16}=-20/16=-5/4\)

Answer:so what is the question

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

Option A is correct -- 19.9

from figure :

AB=\(5+\frac{9}{2}\)

    =9.5

From Pythagoras theorem:

\(x^{2} =(9.5)^2} +1\)

\(x^{2} =91.25\)

\(x=19.9\)

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This can be written as an equation:

\(a^{2} +b^{2}=c^{2}\)

where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

The Pythagorean theorem is a very useful tool for solving problems involving right triangles, such as finding the distance between two points or the height of a ladder. It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

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Answer:

f(x) = -3/2 x - 2

Step-by-step explanation:

The line rises to the left so the slope is negative, also:

the slope of the line is -3/2 and the y-intercept is at (0, -2)

Answer: b∈∅

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

12b + 9 = 12b + 11

Subtract 12b from each side

12b-12b + 9 = 12b-12b + 11

9 = 11

This is never true, so there are no solutions