The proof that ΔACB ≅ ΔECD is shown.

Given: AE and DB bisect each other at C.
Prove: ΔACB ≅ ΔECD

Triangles A B C and C D E share common point C.

A flow chart has 5 boxes with arrows facing downward connecting the boxes. Each of the boxes are labeled. Box 1 contains line segment A E and line segment B E bisect each other at C and is labeled given. Box 2 contains line segment A C is-congruent-to line segment E C and is labeled definition of bisector. Box 3 contains question mark and is labeled vertical angles theorem. Box 4 contains line segment D C is-congruent-to line segment B C and is labeled definition of bisector. Box 5 contains triangle A C B is-congruent-to triangle E C D and is labeled SAS.

What is the missing statement in the proof?

∠BAC ≅ ∠DEC
∠ACD ≅ ∠ECB
∠ACB ≅ ∠ECD
∠BCA ≅ ∠DCA

Answer: The correct answer is c. $943.87.

Step-by-step explanation: To solve this problem, we need to first determine the length of time between October 1 and July 1 of the following year. This is a period of 9 months, or 3 quarters. We can then use this information to calculate the amount of interest earned over this time period.

The principal in Yujin Pon's account is $900, and the interest rate is 6.5% compounded quarterly. This means that for each quarter, the account will earn 6.5/4 = 1.625% in interest. Over the 3 quarters between October 1 and July 1 of the following year, the account will earn a total of 1.625% * 3 = 4.875% in interest.

To calculate the amount of interest earned, we can multiply the principal by the interest rate:

Interest = Principal * Interest Rate

= $900 * 0.04875

= $43.87

The total amount in the account on July 1 will be the original principal plus the amount of interest earned over the 3 quarters:

Total = Principal + Interest

= $900 + $43.87

= $943.87

Therefore, the correct answer is c. $943.87.

Answer:

0.402

Step-by-step explanation:

The probability of not rolling a one on any given roll is [tex]5/6[/tex].

Since the die is rolled 5 times, the probability is [tex](5/6)^5 \approx 0.402[/tex].

Answer:

Below

Step-by-step explanation:

To complete the square, the coefficient of x^2 must be 1  ( it is already)

   then take 1/2 of the x coefficient  .... 1/2.... square it and add it to both sides of the equation

   x^2 + x + 1/4   + 9   = 1/4

 then you can reduce this to

   ( x+ 1/2)^2  + 9 = 1/4   for further 'solving'

Then the orders can Cory eat the fruit is = 25

Given that,

If Cory has eat apples = 3$

If Cory has eat oranges = 2$

If Cory has eat bananas = 2$

Total eat fruits = 3 + 2 + 2

Total eat fruits = 7$

We have to express the amount of total fruits as an equation.

The amount of apples will be x,

The amount of oranges will be y,

The amount of bananas will be z

The amount of apples multiplied by 7 because they ate each day of the week.

7*(x) + y + z = now we have to replace the values ​​of x, y and z with the ones that gave us the problem

Then,

x = 3

y = 2

z = 2

So,

We can write,

7*(x) + y + z = 7 *(3) + 2 + 2

= 21 + 2 + 2

= 25

Therefore,

Then the orders can Cory eat the fruit is = 25

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Answer:

x= -2y/7

Step-by-step explanation:

y=-5x-2x-yif you switch sides you get

-5x-2x-y=y

add similar elements -5x-2x-y=-7x

-7x-y=y

move y to the right side

-7x=2y

decide both sides by -7

-7x/-7 = 2y/-7y

simplify

x = -2y/7

Answer:

-8x+25x+5-7=3x-9

or ,17x -2=-9+2

or, -14x=-7

or, x=-7/-14

x=1/2

Answer:

-8x +25x +5-7=3x-9

17x-2 = 3x-9

17x-3x=9+2

14x =11

x= 14/11

Your joints and bones would first have to work harder to support your heavier weight.

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Answer:

function

Step-by-step explanation:

I did this math before

Answer:

this relation is a function

Angle BAC is an inscribed angle, which means that its size is equal to the size of the arc it attempts to represent, arc BC, and that arc BC is the arc that it attempts to represent. Taking that portion of 360° will allow us to calculate the angle 45°.

A = π * 6 * 6 = 36π

The current value

Taking that portion of 360° will allow us to calculate the angle:

0.125 * 360 = 45°.

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The constant 5 represents the flat fee of $5, while the term 0.75x represents a cost of $0.75 per minute for use of the services for x minutes. Therefore, option D is the correct answer.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 5+0.75x.

In the given expression, 5 is constant term and 0.75x is another term.

In the term 0.75x, 0.75 is the coefficient of x

In the expression 5+0.75x, 5 is fixed price and 0.75 is price for second or minute or hour or year and x can be number seconds or minutes or hours or years.

Therefore, option D is the correct answer.

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The required trigonometric ratios of angle C in the given table are

(a) adjacent leg ÷ hypotenuse (cos C) = 0.95

(b) opposite leg ÷ hypotenuse (sin C) = 0.31

(c) opposite leg ÷ adjacent leg (tan C) = 0.33

The three important trigonometric ratios are:

sin θ = opposite leg ÷ hypotenuse

cos θ = adjacent leg ÷ hypotenuse

tan θ = opposite leg ÷ adjacent leg

In the given right-angle triangle, the ratios are given as

cos A = adjacent leg ÷ hypotenuse = 0.31

sin A = opposite leg ÷ hypotenuse = 0.95

tan A = opposite leg ÷ adjacent leg = 3.06

These ratios are w.r.t the angle A.

Since we know that, in the right angle triangle,

∠A + ∠B + ∠C = 180°

⇒ ∠A + 90° + ∠C = 180°

⇒ ∠A = 180° - 90° - ∠C

∴ ∠A = 90° - ∠C

So, the trigonometric ratios w.r.t the angle C are:

(a) cos A = cos (90° - ∠C) = sin C

But we have cos A = 0.31

∴ sin C = 0.31

(b) sin A = sin (90° - ∠C) = cos C

But we have sin A = 0.95

∴ cos C = 0.95

(c) Then, tan C = sin C/cos C

Here we got sin C = 0.31 and cos C = 0.95

So, tan C = 0.31/0.95 = 0.33

Thus, the table is as follows:

angle    adj ÷ hyp    opp ÷ hyp    opp ÷ adj

A              0.31              0.95               3.06

B              0.95             0.31                0.33

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After evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expresion 16/24.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

It's possible to multiply, divide, add, or subtract with this mathematical operation.

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression.

So, we have the expression:

16/24

We need to find the equivalent expression from the options as follows:

So, let's take option (E) as it seems the answer and evaluation is:

8/2 * 2/12 (Be LHS)

Now, multiply:

8/2 * 2/12 = 16/24

16/24 = 16/24

Therefore, after evaluation, we can conclude that the expression (E) 8/2 * 2/12 is equivalent to the given expression 16/24.

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Using a mean and standard deviation as inputs, the following formula can be used to get the percentile of a normal distribution:

Percentile Value is equal to z +.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation.

Standard deviation may be written as SD.

A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.

Though in algebra, it is simpler

According to our question-

a. 157 is less then 161

b. n>173, n be a real number.

Hence, Using a mean and standard deviation as inputs, the following formula can be used to get the percentile of a normal distribution: Percentile Value is equal to z +.

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Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

24 represents the cost per gallon of paint.

The process of finding the rate of change of the value dependent variable of the function changes with respect to that of the variable independent variable.

Given that, The expression 102+24x represents the total amount, in dollars, a painter spends at a store to purchase paintbrushes and x gallons of paint.

The equation is 102+24x

Here, the slope of the equation is 24, which tells the rate of change.

Hence, 24 is the cost per gallon of paint

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The solution to the products of exponents is as follows;

1) -24a³b⁷

2) 15a⁵b¹⁵

3) -10d⁴ + 17sd² - 6s²

4) 6x³ - 33x² + 45x - 6

5) 21x⁷y¹¹

6) 8y⁴ + 25y³ + 60y² + 10y + 7

7) 20s³ + 50s² + 32s + 6

The Product of Powers Property of exponents states that when we multiply two powers with the same base, we add the exponents.

1) (3a²b⁴) * (-8ab³)

= -24a³b⁷

2) (3a²b⁷) * (5a³b⁸)

= 15a⁵b¹⁵

3) (-2d² + s)(5d² - 6s)

Expanding the bracket to get;

(-10d⁴ + 5sd² + 12sd² - 6s²)

= -10d⁴ + 17sd² - 6s²

4) (3x - 6) * (2x² - 7x + 1)

= 6x³ - 33x² + 45x - 6

5) (7x²y³) * (3x⁵y⁸)

= 21x⁷y¹¹

6) (y² + 3y + 7) * (8y² + y + 1)

= 8y⁴ + 25y³ + 60y² + 10y + 7

7) (4s + 2) * (5s² + 10s + 3)

= 20s³ + 50s² + 32s + 6

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The function rule that could be represented by the graph is given as follows:

y = 2x³ + x - 3.

The first step in defining the function is looking at it's y-intercept, which is the value of y when the graph of the function crosses the y-axis.

This value is of -3, hence the function can be defined as follows:

f(x) = ax^n + x - 3.

Then we look at the behavior of the function. It has an inflection point, as it is concave down and then it becomes concave up, hence:

Thus:

f(x) = ax³ + x - 3.

Then we look at the x-intercept, meaning that when x = 1, y = 0, this the leading coefficient is obtained as follows:

0 = a + 1 - 3

a = 2.

Thus the function is defined as follows:

y = 2x³ + x - 3.

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Answer: g(f(-2))=-96

Step-by-step explanation:

[tex]Given: \ f(x)=e^{6x}\ \ \ \ g(x)=8ln(x)\ \ \ \ g(f(-2))=?\\\\f(-2)=e^{6*(-2)}\\\\f(-2)=e^{-12}\\\\Hence,\\\\g(f(-2))=8ln(e^{-12})\\\\g(f(-2))=8*(-12)\\\\g(f(-2))=-96[/tex]

Answer:

-96

Step-by-step explanation:

Given:

[tex]\begin{cases}f(x)=e^{6x}\\ g(x)=8 \ln (x) \end{cases}[/tex]

To find g[f(-2)], substitute x = -2 into the function f(x):

[tex]\implies f(-2)=e^{6 \times -2}=e^{-12}[/tex]

Then substitute the function f(-2) in place of the x in function g(x):

[tex]\implies g[f(-2)]=8 \ln \left(e^{-12}\right)[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\begin{aligned}\implies g[f(-2)]&=-12\cdot 8 \ln \left(e\right)\\&=-96 \ln \left(e\right)\end{aligned}[/tex]

Apply the log law:  ln(e) = 1

[tex]\begin{aligned}\implies g[f(-2)]&=-96 \ln \left(e\right)\\&=-96(1)\\&=-96\end{aligned}[/tex]

---------------------------------------------------------------------

As one calculation:

[tex]\begin{aligned}g[f(-2)]&=8 \ln \left(e^{6 \times -2}\right)\\& = 8 \ln \left(e^{-12}\right)\\& = -12 \cdot 8 \ln \left(e\right)\\& = -96(1)\\& = -96\end{aligned}[/tex]

The value of y is 10. The measure m∠ C and m∠ D are 40° and 76° respectively.

What is external angle?

The angle created when a transversal cuts one of two lines and is located outside of the line. It describes the angle between a side of a polygon and an expanded adjacent side.

The measure of an external angle of a triangle is equal to the sum of opposite interior angles.

∠DEF is an exterior angle. The opposite interior angles of ∠DEF are m∠ C and m∠ D

Therefore,

m∠ C + m∠ D = ∠DEF

4y° + (7y + 6)° = 116°

Add like terms

11y + 6 = 116

Subtract 6 from both sides:

11y = 110

Divide both sides by 11:

y = 10

Putting y = 10 in  m∠ C = 4y° and m∠ D =  (7y + 6)°

m∠ C = 40°

m∠ D = 76°

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Answer:

x =4 & y = -7

Step-by-step explanation:

this is the right answer

The probability that a  randomly selected bolt will have a diameter greater than 19.705 mm is 0.9812.

Given that:

mean = 19.0

standard deviation = 0.3

P(18.295 < x < 19.705)

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

= P[(18.295 - 19.0)/0.3) < (x-mean)/standard deviation < (19.705-19.0)/0.3)]

= P(-2.35 < z < 2.35)

= P(z<2.35)-P(z<-2.35)

= 0.9906 - 0.0094

= 0.9812

Probability = 0.9812

Hence we get the required probability.

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Answer:

Step-by-step explanation:

[tex]x^{2} +2x+16=0\\x^{2} +2x+1-1+16=0\\(x^{2} +2x+1)-1+16=0\\(x+1)^{2} +15=0\\(x+1)^{2}=-15[/tex]

The solution does not exist because all numbers squared are greater than zero.

The statement 2(1 / 2 x - 5), when x = 20 is justified by the property of substitution.

Substitution property in mathematics is a property that helps in substituting the value of a variable into an algebraic expression to solve a given problem.

Therefore, by substituting the value of x in the algebraic expression, the expression will be solved.

Hence,

2(1 / 2 x - 5) , when x = 20

Therefore,

2(1 / 2 (20) - 5)

2(10 - 5)

2(5) = 10

Hence, the property is substitution property.  

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Distributive property of real numbers illustrated by the equation. -2(x 4)=-2x-8

The equation -2(x 4)=-2x-8 is an example of the distributive property of real numbers. This property states that when a number is multiplied by a group of numbers that are being added together, the number can be distributed to each of the terms in the group. To rewrite this equation as -2x + (-2)(-4) = -2x - 8, the number -2 is allocated to each of the terms in the group (x and -4) in this equation.Simplifying further, we get -2x - 8 = -2x - 8.

-2(x 4) = -2x - 8

Distribute -2 to each term in the group

-2x + (-2)(-4) = -2x - 8

Simplify

-2x - 8 = -2x – 8

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Net payout will you be promised in a fair betting game in case your bet works out is $0 .

Given :

browns are expected to win with probability of 60% against their opponent, while steelers are also expected to win with probability of 40% against their opponent. the outcome of each game can be either a win or a loss (i.e., no ties). if you bet $10 on one of these two teams to win and another one to lose, no matter which one wins or loses, i.e., your bet is that only one team (browns or steelers) wins .

P ( browns ) = 60 / 100 = 0.60

P ( steelers ) = 40 / 100 = 0.40

Net payout = Number of wins * 10 - Number of loses * 10

= 1 * 10 - 1 * 10

= 10  - 10

= $0.

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Larry's tortilla chip has a surface area of 75 square inches.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

A triangle with base b and height h has a surface area of 1/2bh. You need to calculate the area of a triangle with a 15-inch base and a 10-inch height.

For b=15 and h=10,

Evaluate the expression

1/2bh for b=15 and h=10

1/2bh=1/2(15)(10)

=1/2(150)

=75inch

Larry's tortilla chip has a surface area of 75 square inches.

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Answer:

D. -6 < x ≤ -3

Step-by-step explanation:

21 ≤ -3(x − 4) < 30

21/3 ≤ -3(x − 4)/3 < 30/3

7 ≤ -(x − 4) < 10

7 ≤ -x - (-4) < 10

7 ≤ -x + 4 < 10

7 - 4 ≤ -x + 4 - 4 < 10 - 4

3 ≤ -x < 6

(3 ≤ -x < 6)/(-1)

-3 >= x > -6   ==> when dividing by a negative number, switch the inequality          

                           sign

-6 < x ≤ -3 ==> D

Answer:

7.7

Step-by-step explanation:

I got this by subtracting 13.3 - 5.6