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The answer is given below

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Applying the definition of the midpoint of a line and other properties, the proof that shows that AC ≅ CD is shown in the image attached below.

A line is divided into two equal parts by its midpoint. Thus, the midpoint of that line is that point where the line segment is bisected into two parts that are equal.

Given the image showing two lines that intersect each other at point C, the proof below shows that AC is congruent to CD:

1. C is the midpoint of line AE

C is the midpoint of line BD

AE is congruent to BD

(Reason: Given)

2. AC = CE; BC = CD

(Reason: Definition of midpoints)

3. AE = BD

(Reason: Definition of congruent segments)

4. AE = AC + CE;

BD = BC + CD

(Reason: Segment addition property)

5. AC + CE = BC + CD

(Reason: substitution property)

6. AC + AC = BC + BC

(Reason: substitution property)

7. 2AC = 2BC

(Reason: Simplify)

8. AC = CD

(Reason: division property)

9. AC ≅ CD

(Reason: definition of congruent segments).

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Step-by-step explanation:

it is just a matter of definition that can be easily looked up.

the domain is the interval or set of all valid x values.

while the range is the interval or set of all valid y (function result) values.

so, the domain here is every value of x used in this function.

e.g. does x = -6 have a functional (y) value in the curve ?

no, it does not.

x = - 4 ? no.

x = -2 ? no.

x = -1 ? ah, yes, this is just the left-most point of the curve.

and then all x values further to the right of -1 are covered. as the arrows indicate : into all eternity ("to infinity and beyond !")

so, the domain is [-1, +infinity).

and you need to use B.

please note, the round bracket indicates that that ends of the interval is not included or undefined (after all, infinity is not a number we can work with, it is basically undefined and only represents a principle).

for the range this is tricky, as the graph does not really show us the limit. it could be y = -1 or 0 down to y = -9 or -10.

Answer:

b

Step-by-step explanation:

because it is tht simpl

Answer: -12 and -9

Step-by-step explanation:

4p + 6 <3p

4p - 3p < -6

p < -6

So, -12 < -6 is CORRECT

     -9 < -6 is CORRECT

     -6 is not less than -6 SO THIS IS INCORRECT

     6 is not less than -6 so this is INCORRECT

Answer:

B) [tex](2,\infty)[/tex]

Step-by-step explanation:

Since we are given the graph of [tex]f'(x)[/tex], this gives us the value of the derivative, or the rate of change, of [tex]f(x)[/tex] given an x-value. For [tex]f(x)[/tex] to be increasing, then [tex]f'(x) > 0[/tex], which is a positive rate of change. As you may have noticed, when [tex]x > 2[/tex], the value of [tex]f'(x)[/tex] is positive. This means that f increases on the interval [tex](2,\infty)[/tex], or answer B.

Using combinations, we concluded that  the probability that fewer than 2 of the next 5 vehicles are from out of state is 0.907.

A checkpoint sees 75% of its traffic coming from within the state.

Therefore, there is a 0.75 percent chance that the car comes from the state.

1-0.75=0.25 represents the likelihood that the car is from outside the state.

Let x now act as the random variable. Consequently, n=9 and X=4

It is necessary to determine the likelihood that less than 2 of the following 5 automobiles are from another state.

We are to calculate the probability of x<2

p=0.25

q=0.75.

Using the formula,

P(x≤2) = ∑ ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

P(x≤2) = ∑ ⁵C₂ p² q³ + ⁵C₁ p¹ q⁴ +  ⁵C₀ p⁰ q⁵

P(x≤2) = ∑ [tex]\frac{5!}{2! 3!}[/tex] (0.25)² (0.75)³ + [tex]\frac{5!}{1! 4!}[/tex] (0.25)¹ (0.75)⁴ + [tex]\frac{5!}{0! 5!}[/tex] (0.75)⁵

P(x≤2) = 10 × 0.065 × 0.421875 + 5 × 0.25 × 0.3164 + 0.2373

P(x≤2) = 0.2742 + 0.3955 + 0.2373

P(x≤2) = 0.907

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The expression equivalent to [tex]2 log_4 x + 3 log_4 y - 5 log_4 z[/tex] is the first option that is [tex]log_4(\frac{x^2y^3}{z^5} )[/tex].

Logarithms

A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation.

For example, if  [tex]10^2 = 100[/tex] then [tex]log_{10} 100 = 2[/tex].

In a log function of the form [tex]log_ab=x[/tex] ,

a is the base of the log

b is the argument of the log and,

x is the real number

It is the most convenient way to express large numbers.

The properties of logarithms are,

1) [tex]xlog_ab =log_ab^x[/tex]

2) [tex]log_ab-log_ac=log_a(\frac{b}{c} )[/tex]

Hence,

According to 1) , we can write,

[tex]2 log_4 x =log_4x^2\\3 log_4 y = log_4y^3\\ 5 log_4 z = log_4z^5[/tex]

According to 1) and 2), we can write,

[tex]2 log_4 x + 3 log_4 y - 5 log_4 z= log_4(\frac{x^2y^3}{z^5} )[/tex]

Hence, the answer is the first option.

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The number of non-members is 12 and the number of members is 24.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the number of members, and the number of non-members.

3x + 5y = 132

x = 2y

After solving the above two linear equations:

6y + 5y  = 132

11y = 132

y = 132/11

y = 12 non-members

x = 24 members

Thus, the number of non-members is 12 and the number of members is 24.

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Answer:

h= 6

Step-by-step explanation:

To find out the value of h, start by forming an equation for the cost of renting a trampoline:

Cost of renting= $(75 +8t), where t is the rental duration.

When the cost is $125,

75 +8t= 125

Subtract 75 from both sides:

8t= 125 -75

8t= 50

Divide both sides by 8:

t= 50 ÷8

t= 6.25

Since she wants to spend less than $125, let's round the value down to the nearest hour.

∴ h= 6

Thus, she could rent it for 6 hours.

Let's check!

Total cost of renting for 6 hours

= 6(8) +75

= $123

Total cost of renting for 7 hours

= 7(8) +75

= $131

Hence, 6 hours is indeed the maximum number of hours she can rent the trampoline for, such that the total cost is less than $125.

Given data,

Use the law of cosines.

Thus, the value of b is

The cosines formula for angle A isThus, angle A will be

Therefore, angle A is 52.67 degrees.

Answer:

209 out of 230 completed   that is   209/230 x 100% = 90.869 %     the rest did NOT complete   100% - 90.8% = 9.13 %

Answer:

the answer is 93

Step-by-step explanation:

I'm very sure....

Answer: I really wish I could help you but I don't know the answer either

Step-by-step explanation:

JK

The amount that will be made by the local festival given the expression m=2p - 0.75p - 50 is 225.

From the information, at the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each.

The expression given was illustrated as:

m=2p - 0.75p - 50

Therefore since we are given the value of p as 220. This will be:

m=2p - 0.75p - 50

m = 2(220) - 0.75(220) - 50

m = 440 - 165 - 50

m = 440 - 215

m = 225

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At the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each. They also paid $50 to the festival's organizers for a vendor permit. Use the expression m=2p - 0.75p - 50 to answer the following questions.

Find the profit when the number of the ice cream pops represented by p is 220.

The constant of proportionality in the equation y=1.5x is 1.5 .

The Constant Of Proportionality(k) in the equation can be defined as the constant value of the ratio between the two proportional quantities .

In Direct proportionality y=kx , where k is the constant of proportionality

means that if x increases then y also increases at the same rate ,

and if x decreases then y also decreases at the same rate .

For Example : constant of proportionality in y=6x , will be 6 .

In the question ,

it is given that

Kevin earns $6 for 4 polished rocks ,

the equation to represent the situation is y=1.5x

So 1.5 is the constant of proportionality .

Therefore , the constant of proportionality in the equation y=1.5x is 1.5 .

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The amount that Sidney will have in her account in 1 year is $ 95,704.

Given that:-

Principal amount = $85,450

Interest Rate = 12 % per annum

i = prt

Where,

i represents interest,

p represents the principal,

r represents the interest rate, and

t represents the time (in years)

Hence, putting the values in the formula of simple interest, we get,

i = 85450*(12/100)*1 = $ 10,254

Hence, the amount that Sidney will have in her account in 1 year is

85450 + 10254 = $ 95,704

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The monthly payment when you want to buy a 28,000 car is $567.

It should be noted that when the 10% down payment is made, the amount left will be:

= $28000 - (10% × $28000)

= $28000 - $2800

= $25200

The interest will be:

= PRT / 100

P = $25200

R = 2%

T = 48 months = 4 years

Interest = (25200 × 2 × 4)/100

= $2016

Total amount to be paid:

= $25200 + $2016

= $27216

The monthly payment will be:

= Amount / 48 months

= $27216 / 48

= $567

The monthly payment is $567.

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Answer:

$546.72

Step-by-step explanation:

Hence the equation of the parabola is y = -x² + 4

In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical planar curve. The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.

The general equation of a parabola is given by y = ax² + bx+ c

The parabola passes through (-3,-5) , (-1,3) , and (0,4).

Now substituting the values in the parabola we get :

-5 =  a(-3)² + b(-3)+ c

or , -5 = 9a -3b + c

again:

3 = a(-1)² + b(-1)+ c

or, 3 = a -b + c

again

4 = a(0)² + b(0)+ c

or, c =4

Solving the equation we get :

9a - 3b = -9 and a-b = -1

a= -1 and b = 0

Hence the equation of the parabola is

y = -x² + 4

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The perimeter of a rectangle can be calculated using the following formula:

Where

"w" represents the width of the rectangle

"l" represents the length of the rectangle

If you know the perimeter and length of a rectangle, you can use the formula to determine the width. The first step is to write the formula for the width:

-Pass 2l to the left side of the expression by applying the opposite operation to both sides of it:

-Divide both sides by 2

Now that we have determined a formula for w, replace the value of the length and perimeter and calculate the width:

P=84in

l=28in

The width of the rectangular frame is 14 inches long

Answer:

alphabet

Step-by-step explanation:

Answer:

[tex]x = 3 - {e}^{12} [/tex]

Step-by-step explanation:

first let's isolate the logarythm:

[tex]ln(3 - x) = 12[/tex]

at this point we can apply the definition of logarythm to obtain

[tex]3 - x = {e}^{12} [/tex]

which, with some simple algebra returns

[tex]x = 3 - {e}^{12} [/tex]

Given:

The equations are given as,

Required:

Direct and inverse variation verification.

Explanation:

(a) The equations are given as follows:

On simplifying further,

The given equation is not a direct variation.

(b) The equation is given as,

The given equation represents inverse variation.

Answer:

Thus the required result is,

a) Not a direct variation

b) A direct variation( k = -2)

The option that is unique to only skeletal muscle is Option(B.) They can fatigue with too much movement or exercise.

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Answer: Choice A

15C12

=============================================

Reason:

Imagine there are 15 students and we wish to form a committee of three people, where order doesn't matter. The answer to this problem is 15C3 using the nCr formula. Here n = 15 and r = 3.

The 15C3 represents the number of ways to pick the three people on the committee, while 15C12 is the number of ways to not pick a person for the committee. We can think of it like two separate committees if you want.

So 15C3 = 15C12

The numbers after the "C" add to the value of n

The identity is [tex]_nC_r = _nC_{n-r}[/tex]

The r and n-r add to n.

The most appropriate choice for modulus of a number and ascending order will be given by-

|0.58|, 18, |-35| is in ascending order.

What is Modulus of a number and ascending order?

Modulus of a number returns the absolute value of the number.

Modulus of positive number is positive and modulus of negative number is also positive.

If the numbers in a series are arranged in increasing order of their value, then the series is arranged in ascending order

Here,

|-35| = 35

18 = 18

|0.58| = 0.58

As, 0.58, 18, 35 is in ascending order,

So, |0.58|, 18, |-35| is in ascending order

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Answer:

Step-by-step explanation:

Let n be the times that they knock on the door.

If five more than three times n and is equal to the difference between 21 and n;

Solve for n, using inverse operations to solve equations: