Elena wants to prove that the measures of the 3 angles in a triangle always
sum to 180 degrees. She starts by using rigid motions to rotate triangle ABC
180° around 2 midpoints. Explain how Elena labeled her diagram and finish
her proof.
E
D
o
6
С
В
B

x = 3, y² = -5x -12, x² + y² =81. are all not functions. the others are functions.

Step-by-step explanation:

I just did it

A function assigns the values. The correct options are C and E.

A function assigns the value of each element of one set to the other specific element of another set.

An equation is said to be a function if for each different value of x(input) it should give a different output. Therefore, for different inputs of x, the value of the output y should be different and unique. Also, the values if the equation produces the same output for two values of x it also said to be a function.

A.)

x = 3, since for every value of x the value is 3, which is not possible. Hence, this is not a function.

B.)

x² + y² = 81

For the given equation if the value of x is given as 0, the value of y will be,

x² + y² = 81

0² + y² = 81

y² = 81

y = ±√81

y = -9, 9

Hence, this can not be a function.

C.) y = -x + 11

For the given equation if the value of x is kept anything the value of y will be different. Thus, this is a function.

D.)

y² = -5x - 12

For the given equation if the value of x is given as less than -2.4, there will be two values of y. Thus, the given equation is not a function.

E.)

y = 2x² - 6x + 4

The given function will return will the same value of y for 2 different values of x. Hence, this is a function.

F.)

y = -7

Since the given equation can only have the value of y as 7. Therefore, it is not a function.

Hence, the equations that are a function are y = -x + 11 and  y = 2x² - 6x + 4.

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Answer:

A.7,000

B20,000

c.300,000

Step-by-step explanation:

Answer:

x = 5

The two consecutive odd integers are: 5, 7

And...checking

sum = 12

Step-by-step explanation:

Answer:

use photmath or sum

Step-by-step explanation:

Answer:

a. given

b. addition property of equality

c. multiplication property of equality

Answer:

(1/2) qt/(3/4) hr = (1/2)*(4/3) qt/hr = (2/3) qt/hr

The rule for division of fractions is: invert the denominator and multiply.

Answer:

x = -4

Step-by-step explanation:

x-5 = -9

Add 5 to each side

x-5+5 = -9+5

x = -4

Answer:

A. x = -4

Step-by-step explanation:

x - 5 = -9 (plus 5 on each side to get rid on 5 on the left side) so -9 + 5

x = -4

Answer:

3/4 quarts of yellow paint is needed

Step-by-step explanation:

From the question, we are told that:

In order to make purple he must mix red and blue paint together at a ratio of 2 quarts red to 1 quart of blue.

3 quart of Purple paint mix requires 2quarts of red paint and 1 quart of blue paint.

We are also told that:

When George wants to make brown paint he must mix purple and yellow paint together in a 1:1 ratio.

This means 1 Purple paint to 1 Yellow paint

4/4 quarts of Yellow paint = 1 yellow paint

3/4 quarts of Yellow paint = 3/4 quarts of purple paint

the answer is A and D

when you differentiate the question you find that the maximum point is (0,0)i.e

[tex] \frac{dy}{dx} = - 8x[/tex]

when dy/dx is 0 values of x are 0,0

and the function shows that valies of x are real numbers.

The domain of the graph is (−∞,∞), {x|x∈R} and the maximum point (0,0) which is the correct answer would be options (A) and (D)

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

Given function as

f(x) = -4x²

The range is the set of values that correspond with the domain.

Range: (−∞,0], {y|y≤0}

Domain: (−∞,∞), {x|x∈R}

and the function shows that values of x are real numbers.

The maximum point is when differentiating the function, which is (0,0) i.e

dy/dx = -8x

Values of x are 0 when dy/dx is 0.

Hence, the domain of the graph is (−∞,∞), {x|x∈R} and the maximum point (0,0) which is the correct answer would be options (A) and (D)

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Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

if i am not wrong i think it is 1 bc u can only cut a verticle line in the middle, then i dont see any other ways.

Answer:

E.f(x)=log(x-1)

Step-by-step explanation:

f(x)=log(2-1)

=log1 (log1=0)

=0

Answer: 55

110 ÷ 2 = 55         110 in half is 55 because 10 in half is 5 and  100 in half is 50 so 55 +5 = 55

110÷2=55

Step-by-step explanation:

Answer:

50 students were in each bus.

Step-by-step explanation:

We first subtract the 4 students in cars from the total, then divide the remaining students, (450) into the 9 busses. 450 / 9 = 50. There are 50 in each bus.

Answer:

-3x – 4y = -4

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The pattern is +3 each time so -1 + 3 = 2

-10, -7 ,-4 , -1 ,2

Answer:

$25.5

Step-by-step explanation:

Answer:  (10) 3.2   (11) option 2   (12) option 4  

               (13) Distributive  (14) Associative

Step-by-step explanation:

10) "Absolute value" makes the number positive.

       - |-4| + |-7.2|

   =  -  4  +  7.2

   =       3.2

11) "Opposite" changes the sign.

    the opposite of   [tex]-\sqrt{\dfrac{2}{5}}[/tex]     is     [tex]+\sqrt{\dfrac{2}{5}}[/tex]

12) Reciprocal means "flip" the fraction

     the reciprocal of    [tex]-\sqrt{\dfrac{2}{5}}[/tex]     is    [tex]-\sqrt{\dfrac{5}{2}}[/tex]

13) a(b + c) = ab + ac    is the Distributive Property

     [tex]-\sqrt5(2+X)[/tex]

 =  [tex]-\sqrt5(2) -\sqrt5(X)[/tex]

 =  [tex]-2\sqrt5 -X\sqrt5[/tex]

14) a · (b · c) = (a · b) · c     is the Associative Property

    [tex]20(4\sqrt5)[/tex]

  = [tex](20\cdot 4)\sqrt5[/tex]

Answer:

H

Step-by-step explanation:

I searched it up :)

Answer:

H. {52, 72, 86, 105}

Step-by-step explanation:

Given 4 ordered pairs

The question asks for domain

The domain is the x-value of each ordered pair, and usually it is listed from least to greatest (increasing order)

Take out all of the x-values of the ordered pair 52,72,86,105

Notice that above is already in increasing order, so no further action is needed.

The domain for the situation is {52, 72, 86, 105}

Commutative property

commutative if changing the order of the operands does not change the result.

Answer:

8 quarters and 8 dimes

Step-by-step explanation:

Answer:

9 quarters 7 dimes they equal $2.95

Answer:

45 ft. 11.18 in.

Step-by-step explanation:

Answer:

45.93176 feet

Step-by-step explanation:

1 meter = 3.28084 feet

3.28084(14) = 45.93176 feet

Answer:

I think should add up to 360° because supplementary angles add up to 180°and in this case we have 2 angles

Answer:

180 degrees

Step-by-step explanation:

If two angles are supplementary when their measures add up to be 180

I attached an example of supplementary angles as well you can check

Answer:

36 identical bags with 2 antiseptic wipes, 1 adhesive bandage and 1 ointment in each bag.

Leftovers: 19 adhesive bandages.

Step-by-step explanation:

First of all, let us try to find out the maximum number of identical first aid bags that can be prepared from the given contents.

The maximum number of bags that can be prepared will be equal to the quantity of the content which is available in minimum amount.

And that is number of packets of ointments.

Therefore, greatest number of bags that can be prepared is 36.

Now, it can be seen that 72 antiseptic wipes are available.

72 is a multiple of 36.

Therefore, if we put 2 antiseptic wipes in each bag, no leftovers will be there for packet of ointments and antiseptic wipes.

Now, let us consider adhesive bandages.

Maximum of 1 adhesive bandages can be put in each bag because only 55 such bandages are available.

Therefore, the answer is:

36 identical bags with 2 antiseptic wipes, 1 adhesive bandage and 1 ointment in each bag.

Leftovers: 19 adhesive bandages.

Answer:

-7

Step-by-step explanation:

First, distribute. 30 = 14 - 12 - 4x

Then, simplify and get the regular numbers one the left side.

30 = 2 - 4x                             28 = -4x

Finally, divide both sides by -4 to get x by itself.

-7 = x

Answer:

$176.80

Step-by-step explanation:

$42.12 (what he had left) + 23.75 = 65.90

65.90 (Amount he had after he bought the painting) + 65.90 (The other half of his remaining money he spent on the painting) = 131.80

131.80 + 25 + 20 = 176.80

= $176.80

Problem 1

Answers:

Real = sqrt(49), 5/6, 12.5, 8/12, 225, sqrt(24)/16, sqrt(32)

Not real = sqrt(-20)  and  sqrt(-16)/9

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

Explanation:

Anything involving a square root of a negative number will result in a non-real answer. Anything else is real.

Traditionally y = sqrt(x) has a domain of nonnegative numbers. If x >= 0, then y is some real number. If x < 0, then we'll need to use the imaginary number i = sqrt(-1).

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

Problem 2

Answers:  

Rational = sqrt(49), 5/8, 12.5, 8/12, and 225

Irrational = sqrt(24)/16, sqrt(32)

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

Explanation:

Ignore the non-real numbers. Focus solely on the real values.

A rational number is where we can write it as a ratio of two integers. An example is 5/8 since 5 and 8 are integers. The denominator can never be zero.

Decimal values that terminate can be written as a fraction. For instance, 12.5 = 125/10.

Square roots of perfect squares are also rational. For example sqrt(49) = 7 = 7/1

Something like sqrt(32) is not rational because we can't write it in the form p/q with p,q being integers. We say it is irrational.

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

Problem 3

Answers:

Perfect Squares = 225

Non-perfect squares = everything else

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

Explanation:

A perfect square is of the form x^2, where x is a positive integer.

The only perfect square listed is 225 because 225 = 15^2. Here x = 15.

Note: a perfect square is an integer itself.

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

Problem 4

As discussed earlier, rational numbers are fractions of integers. So we have something of the form p/q where p,q are integers and q is nonzero. An example of a rational number is p/q = 7/8 with p = 7 and q = 8.

Irrational numbers are ones that cannot be written as p/q. A famous example of an irrational number is pi = 3.14, but we could do something like sqrt(17) for instance as well. The stuff under the square root must be a non-perfect square.

Perfect squares are integers in the form x^2, with x being an integer also. A visual way to think of perfect squares is to think of a square with side length x, so its area is x^2. If x = 9, then its area is x^2 = 9^2 = 81, so 81 is a perfect square. We only consider whole number side lengths.

well combine like terms

-3x = -21

divide both sides by -3

x = 7

Answer:

x = 7

Step-by-step explanation:

-6x + 3x = -21

Combine like terms

-3x = -21

Divide by -3

-3x/-3 = -21/-3

x = 7

The distance traveled after 4 hours is 260 miles.

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

Example:

2x + 4 - 9 = 9  is an equation.

We have,

Distance ∝ Time

Distance = K x Time

Now,

390 = 6K

K = 390/6

K = 65

Now,

Distance = 65 x 4

Distance = 260 miles

Thus,

After 4 hours the distance traveled is 260 miles.

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