Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – 4. Her graph is shown below.

What are the solutions of –x2 + 4x = x – 4?

A. –5 and 0
B. –5 and –1
C. –1 and 4
D. 0 and 4

Answer:

∠2; vertical angle theorem; ∠3; transitive property of congruence

Step-by-step explanation:

∠2 and ∠1 are opposite angles that share only a vertex.  This is the definition of vertical angles, and by the vertical angle theorem they are congruent.

Substituting ∠2 for ∠1 in our "given" statement, we now know that ∠2≅∠4.

∠4 and ∠3 are opposite angles that share a vertex.  This makes them vertical angles, and the vertical angle theorem states that they are congruent.

The transitive property, algebraically, states "if a=b and b=c, then a=c."  Applied to this proof, it states "if ∠2≅∠4, and ∠4≅∠3, then ∠2≅∠3."

The required solution for the blacks,
Blank 1 = ∠2;
Blank 2 =  vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.

It is given that
∠1≅ ∠4 ​. By the vertical angle theorem, [blank] ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the [blank] , ∠4≅∠3 . So, ∠2≅[blank] by the [blank].
To determine the missing statement at the place of blanks in the statement.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Since
Black 1
∠2≅∠4
and  ∠1≅ ∠4

So ∠2 ≅ ∠1

Blank 2
∠2≅∠4 are equal by the vertical angle theorem.

Blank 3
∠4≅∠3
∠3 ≅∠1
So,
∠2 ≅ ∠1 ; ∠2≅∠3 and ∠4≅∠3  it is transitive property of congruence.

Thus, the required solution for the blacks,
Blank 1 = ∠2;
Blank 2 =  vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.

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Answer:

The answer to your question is:   x = 7; y = 6

Step-by-step explanation:

                                             2x+y=20             ( 1 )  Multiply by 5

                                             6x−5y=12            ( 2 )

                               5 (2x+y=20)    = 10x + 5y = 100

                                          10x + 5y = 100

                                            6x − 5y =   12             Eliminate y

                                          16 x        = 112

                                           x = 112 / 16

                                           x = 7

                                 2(7) + y = 20                 Substitution

                                 14 + y = 20

                                 y = 20 - 14

                                 y = 6

Answer:

26 cookies

Step-by-step explanation:

13 times 2

A non-transversal line in geometry is a line that does not intersect two or more lines at distinct points. Similarly, in geology, folds with a horizontal axial line, called non-plunging folds, can be analogous to non-transversal lines as they don't intersect with another structure at a distinct point.

In mathematics, specifcally in geometry, transversal is a line that passes through two lines in the same plane at two distinct points. If a line does not intersect two or more lines at distinct points, it can be considered as a non-transversal line.

According to the information provided, in the context of folds in geology, the axial line becomes a key concept. The axial line refers to an imaginary line drawn along the crest of a fold. If the axial line is horizontal, the fold is referred to as a non-plunging fold and it could be analogous to a non-transversal line in geometry, as it doesn't intersect with another structure at a distinct point.

However, if the axial line is tilted (plunging), it might be considered as a transversal in the sense that it 'intersects' the horizontal plane at a distinct angle. Similarly, if a line in geometry is tilted and intersects two or more lines at distinct points, it is a transversal line.

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To determine the exponential function, use the general form of an exponential function and substitute the given values. The equation is y = 1.4 * (1/2)^(x/4).

An exponential function represents exponential growth or decay. In this case, the given information states that the initial mass is 1.4g, and it is halving every 4 days. We can use the general form of an exponential function, y = ab^x, where a is the initial value, b is the growth/decay factor, and x is the time in days.

Since the mass is halving every 4 days, the decay factor is 1/2, since the mass is halving. The equation becomes y = 1.4 * (1/2)^(x/4).

This equation represents the exponential function that satisfies the given conditions.

Hence, the 8th term of the sequence is:

[tex]a_8=1[/tex]

We are defined the nth term in the sequence with the help of the relation or expression as:

[tex]a_n=25-3n-------(1)[/tex]

We are asked to find the 8th term of the sequence i.e. we are asked to find the value of [tex]a_n[/tex] when n=8.

so, we will put n=8 in the given expression (1).

[tex]a_8=25-3\times 8\\\\a_8=25-24\\\\a_8=1[/tex]

Hence, the 8th term of the sequence is:

[tex]a_8=1[/tex]

Answer:

Step-by-step explanation:

Givens

The second given statement expresses that this year there are 34 LESS floats. So, to know how many floats were there last year, we just need to sum

[tex]127+34=161[/tex]

Therefore, last year were 161 floats, that is, 34 more than this year.

Answer:

y = (x + 3)2 − 1

:)

Hello,

The correct answer is B) (-$8) × 12

Hope this helps!!!! :)

(Took the Math test)

**(Vanessa)**

Answer:A 3-cup bottle of dish soap costs $3.36. What is the price per fluid ounce.

Step-by-step explanation:

Answer:

a,b,c

Step-by-step explanation:

i guessed and then they told me the right answer .

Explanation:

Cost of 1 loaf of bread = $5

Cost of 1 roll = $1

The baker needs to sell both items and it should be worth $35.

To find the linear equation, Suppose, the baker sells “b” loaves of bread and “r” rolls.

Then the total cost of the sales has to be $35.

So, the linear equation will be:

5b + 1r = 35

For some reason I keep getting the result 50.

Answer:

Measure of arc AC = 100°

Step-by-step explanation:

For better understanding of the solution, see the attached figure :

Given : AB and CD are the diameters of the circle K and m∠BKD = 100°

To find : measure of arc AC

Solution :

The angle which is formed by the arc AC is m∠AKC so we need to find the measure of the angle ∠AKC

Now, m∠BKD = 100°

and m∠BKD = m∠AKC ( Vertically opposite angles are always equal)

⇒ m∠AKC = 100°

Hence, Measure of the arc AC = 100°

20/4 = 5

40/8 = 5

60/12 = 5

80/16 = 5

Answer is 5

Answer:

Option D 5

Step-by-step explanation:

Mike and Julie surveyed students to determine how many had a grade of A in math as given in the table.

We have to find the proportionality constant of the ratio of students surveyed to the number of A grades.

Since proportionality constant = [tex]\frac{\text{Students Surveyed}}{\text{number of A grades}}[/tex]

=[tex]\frac{20}{4}=5[/tex]

Similarly we can get the constant form other data which is equal to 5.

Therefore, Option D. 5 is the correct option.

Answer: The maximum value of the product x*y is 112.5

Step-by-step explanation:

We have that x + 2y = 30

so we can isolate one of the variables and get:

x = 30 - 2y

now, the product of x*y can be written as:

x*y = (30 - 2y)*y = 30y - 2y^2

now, we want to find the maximum of 30y - 2y^2

because the leading coeficient is negative (-2), we know that the hands of the quadratic function will go downwards, so the zero of the derivate of this quadratic equation will give us the value where the equation has a maximum:

f(y) = -2*y^2 + 30*y

f'(y) = -4*y + 30 = 0

y =  -30/4 = 7.5

So the maximum value is:

f(7.5) = -2*7.5^2 + 30*7.5 = 112.5

The playing surface where the college basketball semi-finals are played is called the court. It is rectangular in shape and has various markings such as the three-point line and free-throw line.

The playing surface where the college basketball semi-finals are played is called the court or the basketball court. The court is rectangular in shape with a length of 94 feet and a width of 50 feet. It is divided into two halves with a midcourt line and has markings such as the three-point line, free-throw line, and key.

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