How many solutions exist for the system of equations in the graph?

Answer:

y = -3 and y = -3

or y = -3 with a multiplicity of 2

Step-by-step explanation:

[tex](y+4)^2-2(y+4)+1[/tex]

If you want to factor this, heres what you do:

[tex](y+4)(y+4)-2(y+4)+1[/tex]

[tex]y^2+8y+16-2y-8+1[/tex]

[tex]y^2+6y+9[/tex]

Then factor:

[tex](y+3)(y+3)[/tex]

[tex](y+3)^2[/tex]

The value of y:

y + 3 = 0 and y + 3 = 0

y = -3 and y = -3

or y = -3 with a multiplicity of 2

The solution of the given function are; y = -3 and y = -3 or y = -3 with a multiplicity of 2.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The given function is;

[tex](y + 4)^2 -2(y + 4) + 1[/tex]

To solve;

[tex](y + 4)(y + 4) -2(y + 4) + 1\\\\y^{2} + 8y + 16 - 2y -8 + 1\\\\y^{2} + 6y + 9 \\[/tex]

Then the factor are;

(y + 3)(y + 3)

The value of y:

y + 3 = 0 and y + 3 = 0

y = -3 and y = -3

or y = -3 with a multiplicity of 2

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Answer:

First option

Explanation:

The inverse of a graph is its reflection on the line y = x.

This means that it is the graph that you get by reflecting the original graph on a line with the equation y = x.

In the picture below, we can see a function (red graph), its inverse (blue graph) and the line (green) that the two graphs are reflected on.

From the picture below, we can see that the shapes of the graph of a function and its inverse is similar and correspond to the shape given as the first option in the question. Therefore, the first option is the answer.

3) Alternate interior angles theorem

4) Definition of congruent angles

If m ∠ACD = 100°, then m ∠ACE = 80°, as ∠ACD and ∠ACE are supplementary angles.

Supplementary angles are the angles whose sum is equal to 180°. The angles formed when one straight line intersects the other, on the point of intersection on the same side of any line are always supplementary.

In the given question, AB and DE are two straight lines intersecting at point C. ∠ACD and ∠ACE lie on the same side of the line DE, thus they are supplementary angles.

Therefore, m ∠ACD + m ∠ACE = 180°.

But we know that m ∠ACD = 100°. So,

m ∠ACD + m ∠ACE = 180°,

or, 100° + m ∠ACE = 180°,

or, m ∠ACE = 180° - 100° = 80°.

Therefore, if m ∠ACD = 100°, then m ∠ACE = 80°, as ∠ACD and ∠ACE are supplementary angles.

For the complete question, check attachment 1.

For reference to the solution, check attachment 2.

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Answer: b=13, t=29

Step-by-step explanation:

Substituting the first equation into the second,

[tex]2b+2+b=41\\\\3b+2=41\\\\3b=39\\\\b=13\\\\\implies t=2(13)+2=29[/tex]

Based on the task given, Pamela's age and juri's age is 16 and 23 years respectively.

x + (x - 7) = 39

x + x - 7 = 39

2x = 39 + 7

2x = 46

x = 46/2

x = 23

Therefore,

Juri's age = x

= 23 years

Pamela's age = x - 7

23 - 7

= 16 years

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Based on the diagram, the true statement is "If a student is an honor student, then he/she may also be a band member."

It shows the intersection between two groups:

This intersection implies some band members are honor students and vice versa. However, not all band members are honor students and not all honor students are band members.

A correct conclusion is that an honor student may also belong to the band.

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Using translation concepts, the equation of the graph of f(x) is given as follows:

[tex]f(x) = \sqrt{x - 1}[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Function f(x) is a shift right of one unit of the square root function, hence x -> x - 1 and the equation is given by:

[tex]f(x) = \sqrt{x - 1}[/tex]

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Answer:

Domain: All Real Numbers

Step-by-step explanation:

Since this function is a linear function, it will use any x-value in order to continue with being a linear function. Therefore, if the line goes on for infinity, every x-value will be used for infinity. Therefore, the domain will be All Real Numbers since every number on the x-axis has a possibility of being used.

Answer:

50x+100=y
y=550

Step-by-step explanation:

Since the first caller can win $100, you add 100 onto the end. After you add 50 for every person who answered incorrectly. X being amount tried/answered incorrectly, and Y being the amount you can win at that given time

Answer:

A. a10=100+(10-1)50

Step-by-step explanation:

The conclusion is valid in this experiment because the sample is homogenous and an experimental study was performed.

It should be noted that an experimental study is one in which there is a dependent variable and there is a dependent variable. Also a control is used to establish the validity of the results.

In this case, the dependent variable is the level of softness after treatment while the independent variable is the type of water softener used.

The conclusion is valid in this instance because the sample is homogenous and an experimental study was performed.

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Answer:

C. 180°

Step-by-step explanation:

The degree measure of the arc of a full circle is 360°

A diameter divides a circle into two parts of equal size, so the degree measure of each part is half of the degree measure of a full circle.

360°/2 = 180°

Answer:

the slope of the coordinates will be 0-0/4-1 then you will get the coordinates of the graph

Answer:

0.016 decimeters

Step-by-step explanation:

16 x 10^-3 = 0.016dm

Answer:

0.016 hm

Step-by-step explanation:

i dont cap

Using it's concept, the domain and the range of the function are given as follows:

The function for this problem is:

[tex]y = \sqrt{4 - x}[/tex]

The square root is defined only for non-negative numbers, hence the domain is given as follows:

[tex]4 - x \geq 0 \rightarrow x \leq 4[/tex]

The outputs of the square root function are also non-negative numbers, hence the range is given as follows:

[tex]y \geq 0[/tex].

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Answer:

  2 units

Step-by-step explanation:

The given equation graphs as a parabola that opens to the right. It can be written in the form ...

  (4p)x = ay² +by +c

When the equation is written in the form ...

  (4p)x = ay² +by +c

The value of p is the focus-to-vertex distance. The length of the latus rectum (focal chord) is 4 times the value of p, so is the coefficient of x in the equation.

Rewriting the given equation to the form shown above, we have ...

  2x = y² +6y +13

That is, the value of 4p, the coefficient of x, is 2. The length of the focal chord is 2 units.

Using it's concept, it is found that the slope of the function is of -4.

The slope of a function is given by the change in the output of the function divided by the change in the input.

For this problem, in 9 months, his weight changed from 265 pounds to 229 pounds, hence it changed -36 pounds, which means that the slope is of:

m = -36/9 = -4.

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The objective function of a linear programming model should be to maximize or minimize the numerical value.

The objective function consists of linear functions which are subjected to constraints in the form of linear equations or in the form of inequalities.

The objective function is always stated as z = ax + by.

The numerical value may be the:

Thus, the objective function of a linear programming model, which is always linear, is to maximize or minimize a numerical value.

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Using a linear function, it is found that the product rs is rs = 81.

A linear function is modeled by:

y = mx + b

In which:

In this problem, when x changes by 68(from -64 to 68), y changes by -16(from 12 to -4), hence the slope is given by:

m = -16/64 = -0.25.

Hence:

y = -0.25x + b.

When x = 34, y = -4, hence this is used to find b.

-4 = -0.25(34) + b

b = 4.5.

Hence the function is:

y = -0.25x + 4.5.

f(r) = 0, hence:

-0.25x + 4.5 = 0

x = 4.5/0.25

x = 18

r = 18.

f (0) = s, hence s = 4.5.

Then the value of the product is:

rs = 18 x 4.5 = 81.

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The graph of f(x) = 0.5sin(4x)  is sketched below

From the question, we are to sketch the graph of the given trigonometric function.

The given trigonometric function is

f(x) = 0.5sin(4x)

The graph of f(x) = 0.5sin(4x)  is sketched below

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Answer:

30

Step-by-step explanation:

We can determine the number of different sets of reports by determining how many possible options are available per subject and then multiplying them.

There are 5 total options for geography, 3 for English, 1 for sciences, and 2 for maths. Multiplying these gets us 30.

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Calculate total choices for individual then multiply

Total choices

Option C

The best way to help them understand Seriation is; A: Read the story of the Three Billy Goats Gruff and discuss the little, medium and great big billy goat gruff brothers.

We are told that;

Seriation is a series or a growing pattern. This means arranged by an attribute such as height, length, or weight.

Now, we want to find the option that is the best way to help children understand Seriation. Looking at the options, the best option would be option A. This is because by reading the story of the three Billy Goats Gruff, we can be able to arrange them by little, medium and great big billy goat gruff brothers.

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If poaching reduces the population of an endangered animal by 6% and the criteria of population extinction is 20 with present population 1500 then it will take 3.62 years to reach to the mark of extinction.

Given Poaching reduces the population of endangered animals by 6% per year. The criteria of population extinction is 20. Present population being 1500.

Number of years taken by the population of endangered animals to reach to 20 mark can be calculated as under:

20=1500*[tex](1-0.06)^{n}[/tex]

20=1500*[tex]0.94^{n}[/tex]

20/1500=[tex]0.94^{n}[/tex]

0.133=[tex]0.94^{n}[/tex]

take log both sides

log(0.133)=log[tex]0.94^{n}[/tex]-------1

log(0.133)=nlog (0.94)

put the values log values:

log(0.133)=-0.8761

log(0.94)=-0.0268

Taking 1

-0.8761=n*(-0.0268)

n=0.8761/0.0268

n=3.269

Hence to reach level of 20 the population takes 3.2 years.

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Answer: its d

Step-by-step explanation:

above answer is wrong and D is right.

Answer:

a) If the question is 18 and 13, then 1. If 18 and 3, then 3.

b) 10

c) 5

d) 15

e) 11

f) 20

Have a nice day :)

The adjusted recipe for 6scones is shown as;

4.2 cup white sugar, cup butter,

7.2 teaspoons vanilla essence,

4.2 cups flour,

7.2 eggs,

37.2 teaspoons baking powder, cup of milk

Fractions are written as a ratio of two integers. Given the recipe for 18scones as

1 cup white sugar, cup butter,

2 teaspoons vanilla essence,

1 cups flour,

2 eggs,

12 teaspoons baking powder, cup of milk

For the given 60 scone;

4.2 cup white sugar, cup butter,

7.2 teaspoons vanilla essence,

4.2 cups flour,

7.2 eggs,

37.2 teaspoons baking powder, cup of milk

This given the adjusted recipe for 60 scones

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Answer:

Step-by-step explanation:

12x −3y=36  ⇔ 3y = 12x - 36

                          y = 4x - 12

y = 0 ⇔ 4x - 12 = 0 ⇔ 4x = 12 ⇔ x = 12/4 = 3

So (0 ; - 12) and (3 ; 0)

Answer:

x-intercept=3,  y-intercept=-12

Step-by-step explanation:

at x-intercept y=0 such that:

12x-3(0)=36

12x=36

[tex]x=\frac{36}{12} =3[/tex]

additionally, at y-intercept x=0 such that

12(0)-3y=36

-3y=36

[tex]y= \frac{36}{-3}=-12[/tex]

The complete equation is x^2 - 4x + (-2) = (-2)^2

The equation is given as:

x^2 - 4x + __ = (__)^2

_____________________________

Take the coefficient of x

k = -4

Divide by 2

k/2 = -4/2

k/2 = -2

Square both sides

(k/2)^2 = (-2)^2

_____________________________

Add the result of the above computation to both sides of x^2 - 4x + __ = (__)^2

So, we have:

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

Hence, the complete equation is x^2 - 4x + (-2) = (-2)^2

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Answer:

I think A

Step-by-step explanation: