2. Choose the correct answer.
Which theorem, term, or corollary is represented by the picture? The bold lines in the pictures represent the hypothesis of the theorem or corollary.

CPCTC

Corollary 1 to the Isosceles Triangle Theorem

Corollary 2 of the Isosceles Triangle Theorem

Isosceles Triangle Theorem

Converse to the Isosceles Triangle Theorem

Answer:

a) See attached (sorry if its a bit unneat, use 5 points for more accuracy while drawing. 3 points is generally accepted though.)

b) 80 mins

c) 4000 meters, 40 minutes

Step-by-step explanation:

First, lets define the literal meaning of the questions.

A) Graph the function (I will explain how to do below)

B) What is the absolute value of the distance of the x-intercepts?

C) What is the y value of the vertex (maximum/ minimum value). What is the x value of the vertex?

Lets solve these problems. To graph a quadratic equation by hand, first you must find the vertex. Formula for the x-value of the vertex:

[tex]\frac{-b}{2a}[/tex]

Because a quadratic equation is in the form:

[tex]ax^2 + bx + c = 0[/tex]

We can find the values of a and b.

Values of a and b in this equation:

a: -2.5

b: 200

Plug into the vertex formula (shown above), -b/2a

[tex]\frac{(-)(200)}{(2)(-2.5)}[/tex]

Simplify.

[tex]\frac{-200}{-5}[/tex]

Simplify.

-200/-5 = 40

Now we have 40, the x value of the vertex. Plug 40 back into the x values of the problem (t in this word problem) to find the y value of the vertex.

The equation:

[tex]h=-2.5t^2+200t[/tex]

Plug in 40 to the t values.

[tex]h = -2.5(40)^2 + 200(40)[/tex]

Simplify.

[tex]h = -4000 + 8000[/tex]

Add.

h = 4000

Now, we have the values of the vertex.

Values of vertex:

x: 40

y: 4000

This means that when the x-value is 40, the y-value is 4000. In this case, it means 40 minutes in, the altitude of the plane is 4000 meters.

On a graph, draw a point at x-value 40 and y-value 4000. This will be needed when we draw the graph.

We need at least 3 points to graph a quadratic equation (this applies to all parabolas.)

This part is a bit hard to explain, but you will get it with this example. Since we need 3 points, we need to solve for 2 more points like we just did. But what x-values do we use? For the vertex, we knew the x value was -b/2a!

Solve for x-values that have an equivalent absolute distance from the x value of the vertex.

For example, in this case, the x value of the vertex is 40.

If we were to pick the x value of 38 for the 2nd point, we would have to use the 42 for the 3rd point as they are both 2 away from 40.

|40-38| = 2

|40-42| = 2

I will use the x values of 38 and 42 to graph this. Lets do the same thing we did to find the y value of the vertex. Plug the x values into the equation individually.

Equation:

[tex]h=-2.5t^2+200t[/tex]

Plug in 38 to the x values (in this case its called t.)

[tex]h = -2.5(38)^2 + 200(38)[/tex]

Simplify.

h = -3610 + 7600

Add.

h = 3990

This means when the x value of the parabola is 38, the y value is 3990. In this case, it means after the plane has flown for 38 minutes, the altitude of the plane is 3990.

Now lets find what the y-value of the parabola would be when the x-value is 42 (when we've did this, we can graph it.)

But here is a little trick to speeden things up. If the absolute value of the difference of the x-value of the vertex (40 in this case) and the x value of the point we just found (38 in this case) is the same as the absolute value of the difference of the 3rd point we need to graph (42 in this case), which is always true if you followed the steps above, the y value is the same!

So, this means, when:

Point 2:

x: 38

y: 3990

Point 3:

x: 42

y: 3990

The y-value of the 3rd point we need to find is 3990.

Now we can graph it using our points.

Point 1 (Vertex):

x: 40

y: 4000

Point 2:

x: 38

y: 3990

Point 3:

x: 42

y: 3990

I'll just use paint to draw this, draw the points, label them, and connect the points with a parabola.

Now lets answer b using the definitions.

Because we need to find the x intercepts, lets use the quadratic formula.

[tex]\frac{ -b± \sqrt{b^2-4ac}}{2a}[/tex]

Ignore the A's, its a bug.

If you need to know how to use the quadratic equation, DM me. Otherwise, I will just write the x-intercepts.

x-intercepts:

0,80

Because it is asking for the distance between Toronto and Montreal in minutes, subtract 0 from 80.

80-0=80

B) 80 minutes

The maximum height of the aircraft is the y value of the vertex and the time that the aircraft reaches this height is the x-value of the intercept.

(Vertex):

x: 40

y: 4000

C) 4000 meters, 40 minutes

Answer:

a)  See attached.

b)  80 minutes

c)  Maximum height = 4000 m

    Time = 40 minutes

Step-by-step explanation:

Given function:

[tex]h=-2.5t^2+200t[/tex]

where:

The function is quadratic, which means the graph of the function is a parabola.  

Axis of Symmetry

A parabola has perfect symmetry.

For a quadratic in the form  [tex]ax^2+bx+c[/tex], its axis of symmetry is:

[tex]\boxed{x=-\dfrac{b}{2a}}[/tex]

Therefore, the axis of symmetry for the given function is:

[tex]x=-\dfrac{200}{2(-2.5)}=40[/tex]

Vertex

As the leading coefficient is negative, the parabola opens downwards.

Therefore, the vertex is the maximum point of the parabola.

The axis of symmetry is the x-value of the vertex.

Substitute t = 40 into the given function to find the y-value of the vertex:

[tex]\implies h(40)=-2.5(40)^2+200(40)[/tex]

[tex]\implies h(40)=4000[/tex]

Therefore, the vertex of the function is (40, 4000).

x-intercepts

To find the x-intercepts of the function, set the function to zero and solve for t:

[tex]\implies -2.5t^2+200t=0[/tex]

[tex]\implies -2.5t(t-80)=0[/tex]

Therefore:

[tex]\implies -2.5t=0 \implies t=0[/tex]

[tex]\implies t-80=0 \implies t=80[/tex]

Therefore, the x-intercepts are (0, 0) and (0, 80).

Graphing the function

Draw a coordinate plane where the axis scale is:

Plot:

Draw a curve, symmetric about the axis of symmetry, that passes through the vertex and the x-intercepts.

When the aircraft is in Toronto and Montreal, the height of the aircraft is zero.

The time at which the height of the aircraft is zero is t = 0 and t = 80 (from part a).  Therefore, the time it takes to fly from Toronto to Montreal is the difference between the two times:

[tex]\implies 80-0=80\; \sf minutes[/tex]

The maximum height of the aircraft is the y-value of the vertex of the parabola.

Therefore, as the vertex of the parabola is (40, 4000), the maximum height of the aircraft is 4000 m.  

The maximum height is reached 40 minutes after the aircraft leaves Toronto.

Answer:

Step-by-step explanation:

There is only one line of symmetry:

because the one that is vertical is not representing symmetry.

The Probability that at least one of the cards drawn is 3 is  0.3412 .

In the question ,

it is given that ,

number of cards  drawn from the deck [tex]=[/tex] 5 .

total cards in the deck is [tex]=[/tex] 52 .

number of "3" cards in the deck = 4

number of cards that are not "3" = 48 .

Number of ways to draw cards that are not 3 = ⁴⁸C₅

Total number of ways to draw 5 cards from the deck = ⁵²C₅

the probability that card dawn is not 3 = ⁴⁸C₅/⁵²C₅

as the value of ⁴⁸C₅ = 1712304 and ⁵²C₅  = 2598960  

= 1712304/2598960    

= 0.65885

So , the probability that at least one card is 3 = 1 - (probability that no card is 3)

= 1 - 0.65885

= 0.34115

≈ 0.3412

Therefore , The Probability that at least one of the cards drawn is 3 is  0.3412 .

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The 20th term of the given arithmetic progression is 119.

An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).

3,6,9,12,15,18, and 21 are A.P. examples.

So, the formula for the nth term:

a+(n-1)d, where d is the common difference

Now, take out the equation:

6th term = 35

a+(6-1)d= 35

a+5d=35 ....(1)

13th term = 77

a+12d= 77 .....(2)

Then, subtract equation (1) from equation (2):

a+12d-(a+5d)= 77-35

a+12d-a-5d= 42

7d=42

d=6

Calculate from equation (1):

a= 35-5d= 35-5(6)= 35-30 = 5

20th term= a+19d= 5+19(6)= 119

Therefore, the 20th term of the given arithmetic progression is 119.

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Annie paid a total of $2.6 for 1.2 pounds of strawberries

In this question, we have the following parameters:

Unit cost per pound = $2.13 per pound

Number of pounds = 1.2 pounds

The amount paid for the number of pounds is represented by the equation

Amount paid = Unit cost per pound x Number of pounds

Substitute the known values in the above equation So, we have the following equation

Amount paid = 2.13 * 1.2

Evaluate the products

Amount paid = 2.556

Approximate

Amount paid = 2.6

Hence, the amount is $2.6

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Answer:

2.56

Step-by-step explanation:

If you have 25 members, and wishes to pick a president, secretary, and treasurer, then we have 13,800 ways to choose the officers, if individual members may hold more than one office.

In the given question,

If you have 25 members, and wishes to pick a president, secretary, and treasurer, then we have to find how many ways can we choose the officers, if individual members may hold more than one office.

We have total 25 members.

Their have total 3 position president, secretary, and treasurer.

When the one position of president filled then their was left 24 member for the secretary position.

When the one position of secretary filled then their was left 23 member for the  treasurer position.

So the possible ways to fill the position is find by multiplying the 25,24 and 23. So

Possible ways=25*24*23

Possible ways=13,800

Hence, if you have 25 members, and wishes to pick a president, secretary, and treasurer, then we have 13,800 ways to choose the officers, if individual members may hold more than one office.

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To simulate the value of a card drawn at random, then option A. the simulation should model the real situation.

The likelihood that something will happen is what is commonly referred to as probability. When we don't know how something will turn out, we can talk about the possibility of a few outcomes or the probability of one. A probability distribution's effect on events is the subject of statistics. Probability theory is the name of the branch of mathematics that studies probability. The concept of probability, which has many different interpretations, is formalized by probability theory through a set of axioms. The term "simple probability" refers to the process of calculating a result or the probability that an event will ever occur. By dividing one possible event by all other possible outcomes, a basic probability can be calculated.

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The number is in between 8 and 9 on the right side of the line.

The number line is a line composed of numbers from negative infinity to positive infinity.

This means all kinds of numbers, except imaginary numbers, are included including integers (whole numbers), rational and irrational numbers.

Positive numbers lie on the right side while negative numbers lie on the left side.

In this case, the first thing to do is to convert the fraction part of 8 3/5 to estimate its location in the number line.

So, 3/5 is equal to 0.6.

Thus, 8 3/5 = 8.6.

The number is thus in between 8 and 9 on the right side of the line that is a little more than the half between these numbers. 

Hence the answer is the number is thus in between 8 and 9 on the right side of the line.

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The amount of cookies baked was 28 cookies

let the number of pumpkin cookies be x

half of them on a plate for your brother and you

= x - x/2 = x/2

Your dog Gobbles ate six

= x/2 - 6

Your brother ate half of what was left

= (x/2 - 6)) / 2

= x/4 - 3

you ate the last four means that what was left is equal to 4

x/4 - 3 = 4

x - 12 = 16

x = 16 + 12

x = 28

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Step-by-step explanation:

using Pythagoras theorem.

37,

x² = 6² + 8²

x = √6²+8² = 10ft

38.

13²=12²+x²

169 = 144 + x²

√169 - 144 = x = 5cm

hope it helps. :)

Answer:

x = 10 and x = 5

Step-by-step explanation:

using Pythagoras' identity

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

(36)

x² = 6² + 8² = 36 + 64 = 100 ( take square root of both sides )

x = [tex]\sqrt{100}[/tex] = 10

(38)

13² = x² + 12²

169 = x² + 144 ( subtract 144 from both sides )

25 = x² ( take square root of both sides )

[tex]\sqrt{25}[/tex] = 5 = x

x = 5

Step-by-step explanation:

cost at store A :

cost(b) = 10b + 75

cost at store B :

cosr(b) = 15b

b = the number of books bought.

to answer the question find for what b both functions deliver the same result :

10b + 75 = 15b

75 = 5b

b = 15

when buying the 15th book both costs are the same.

to keep the costs of store A truly less than the costs of store B the limit is therefore 14 books.

The value of f(16)=903.99, if f(x) is an exponential function where f(2)=3 and f(10.5)=96

The exponential function is a mathematical function that is represented by f(x)=exp or ex. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras. Although the exponential function was derived from the concept of exponentiation (repeated multiplication), modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers. Because of its prevalence in pure and applied mathematics, mathematician Walter Rudin called the exponential function the most important function in mathematics.

For exponential function,

f(x)= abˣ ; b>0, a, b ∈R

Given, f(2)=3

f(10.5)=96

Therefore, f(2)=ab²

3=ab²

a=3/b²

f(10.5)=a[tex]b^{10.5}[/tex]

96=a[tex]b^{10.5}[/tex]

a=96/[tex]b^{10.5}[/tex]

By equating a values then,

3/b²=96/[tex]b^{10.5}[/tex]

3[tex]b^{10.5}[/tex]=96b²

32=[tex]b^{10.5}[/tex]b⁻²

[tex]b^{8.5}[/tex]=32

b=[tex](32)^{1/8.5}[/tex]

Therefore, b=1.5034

a=3/b²

a=3/(1.5034)²

a=1.3273

f(16)=ab¹⁶

f(16)=(1.3273)(1.5034)¹⁶

f(16)=903.99

Therefore, the value of f(16)=903.99

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Jerry watched 1/10 part of the movie at night.

Given that,

Watched movie in morning = 1/2

Movie left to watch = 2/5

To find:

Movie she watch at night

Now,

Movie she watch at night= 1 - Watch movie in morning - Movie left to watch

                                         = 1 - 1/2 - 2/5

solving the right hand side by taking LCM , we get,

                            = 10 - 5 - 4/10

                            = 1/10

∴ Movie she watch at night is 1/10.

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The largest possible value of N is 42, which is equal to the sum of numbers of one group and product of numbers of other group.

We have provided the following informations,

total number = 10 and possible numbers are,

S = {1, 2,3,4,5,6,7,8,9,10}

Now, we have to split the 10 numbers into two groups. The conditions for group making are

maximum possible sum of numbers from S is 55.

because given numbers are in A.P and sum of A 10 terms is 55 in A.P.

but according to question, t the maximum possible value of N which follow the conditions is 42.

we can splits the set S elements in two groups such that one is P={6,7} and other one Q={ 1,2,3,4,5,8,9,10}

sum of numbers of Q is 42 and product of second group (P) = 42

No other value of N greater than 42 is possible for N .

Hence, 42 is largest possible value of N.

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Answer:

x = 4

Step-by-step explanation:

The solution of the system of equations is; (7, 45).

The solution in this situation means that after 7 days, Adela and Isaiah would each have 45 bracelets.

It follows from the task content that the solution to the system of equations is to be determined and interpreted accordingly.

Since the given equations are;

By elimination, we must subtract Isaiah's equation from Adela's so that we have;

(y - y) = (3x - 5x) + (24 - 10)

0 = -2x + 14

2x = 14; x = 7.

Consequently, y = 3 (7) + 24

y = 21 + 24; y = 45.

Consequently, the solution to the system of equations as given in the task content is; (7, 45).

This means that after 7 days, Adela and Isaiah would both have; 45 bracelets.

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The slope of the line perpendicular to the line whose equation is x+y = 3 is 1.

According to the question,

We have the following information:

The equation of the line:

x+y = 3

Now, we will convert this equation into the slope-intercept form:

y = -x+3

Now, slope of this line is -1.

Slope of the perpendicular line to this line = -1/m where m is the slope of the line

Slope of the perpendicular line to this line = -(-1)/1

Slope of the perpendicular line to this line = 1

Hence, the slope of the line perpendicular to the line whose equation is x+y = 3 is 1.

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The total percentage decrease in the investor's stock account is 5%.

Investment in stock A = 5200

Investment in stock B = 6450

Investment in stock A and B  worth

5200 × (1- 0.03) = 5044

6450× ( 1- 0.06) = 6063

Total investment in both stock A and B now

5044 + 6063= 11107

Total investment in both stock A and B last year

5200 + 6450 = 11,650

Hence,

Total percentage decrease = 1 - (11,107 /11,650)

Total percentage decrease  = 1 - 0.95

Total percentage  decrease = 5%

Therefore 5% is the percentage decrease.

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Answer: 11 cows and 19 chickens

Step-by-step explanation:

Answer:

if all this equals with zero the answer is x= - 5/7

Step-by-step explanation:

IF it is 5x+7=0 =} 5x= -7=} x= - 5/7

Answer:

18x +18

Step-by-step explanation:

We know the opposite sides of a rectangle are always equal, so all you need to do is double both sides and add them together.

(7x-1) + (7x-1) + (2x+10) + (2x+10) = 18x +18

The margin on the discounted bread is $2.33

Given,

In the question:

Your store cost on a loaf of bread is $0. 75,

and your retail price is $3. 85.

You are having a promotion which discounts the bread 20%.

To find the margin on the discounted bread.

Now, According to the question:

Given store cost on a loaf of bread is $0.75 and retail price is $3.85.

Discount is always given on retail price.

The amount of discount is 20%

Discount given on $3.85 = 20% of 3.85= .20(3.85)= 0.77.

Cost of bread after discount =3.85-0.77= 3.08

The discounted bread costs $3.08.

The difference in store cost and discounted cost = 3.08-0.75=$2.33

Hence, the margin on the discounted bread is $2.33

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Answer:

Step-by-step explanation:

Cost price is n.

Correct choice is C.

The least common denominator, LCD, for the given pair of fractions is x²- 25

From the question, we are to determine the least common denominators of the given fractions.

The given fractions are

3/x -5 and 3/x + 5

To determine the least common denominator of the fractions, we will determine the lowest common multiple of their denominators.

The denominators are x - 5 and x + 5

To do this, we will find the product of the expressions

(x -5)(x + 5)

Clear the parentheses by applying the distributive property

That is,

x(x + 5) -5(x + 5)

x² + 5x -5x - 25

x² - 25

Hence, the LCD is x² - 25

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The total number of changes in fishes is 63

The product is the multiplication of two or more integers together. Assume their are two integers and , then their product will be obtained when we multiply both the numbers together. 9× 7 = 63 . For example if there are 10mangoes in 5 basket, the total number of mangoes is 5×10= 50mangoes

3 fishes were added for 21 days in a pond. This means that the total number of fishes added = 21×3= 63 fishes

Therefore the total number of changes in the pond is 63 fishes.

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Answer: 1. 3

5. -3

Step-by-step explanation:

Applying the corresponding angles theorem, the measure of ∠HIJ = 33°.

If two triangles are similar to each other, their corresponding angles would be equal. Also, based on the corresponding angles theorem, corresponding angles are equal to each other.

Triangles IHJ and FGH are similar to each other, therefore, angles HFG and HIJ are corresponding angles.

Therefore:

The measure of angle HFG = the measure of angle HIJ

m∠HFG = 57 − 6x

m∠HIJ = −4x + 49

Thus:

57 − 6x = -4x + 49

Combine like terms

4x - 6x = -57 + 49

-2x = -8

Divide both sides by -2

-2x/-2 = -8/-2

x = 4

m∠HIJ = −4x + 49 = -4(4) + 49

m∠HIJ = 33°

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Complete Question:

In the diagram below of triangle FGH, I is the midpoint of FH and J is the midpoint of GH. If m∠HFG = 57 − 6x, and m∠HIJ = −4x + 49, what is the measure of ∠HIJ?

Answer:

soda: 97

Hot dogs: 56

Step-by-step explanation:

S-sodas

H- hot dogs

S+H=153

41+H=S

Substitute equation

(41+H)+H=153

41+2H=153

-41.        -41

2H=112

/2.   /2
H=56

S+56=153

 -56.  -56

S=97

Hopes this helps please mark brainliest

Answer:

Each piece will be 4.9 inches long

Step-by-step explanation:

All you have to do is divide 14.7 by three as the rope itself is cut into 3 equal parts

therefore: 14.7/ 3= 4.9

Answer:

-11r

Step-by-step explanation:

4r - 9r = -5r

-5r - 11r = -16r

-16r + 7r = -11r