Graphically, a point is a solution to a system of two inequalities if and only if the point
lies in the shaded region of the top inequality, but not in the shaded region of the bottom inequality.
lies in the shaded region of the bottom inequality, but not in the shaded region of the top inequality.
lies in the shaded regions of both the top and bottom inequalities.
does not lie in the shaded region of the top or bottom inequalities.

Answer:

its 1

Step-by-step explanation:

Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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Answer:

a) P(male=blue or female=blue) = 0.71

b) P(female=blue | male=blue) = 0.68

c) P(female=blue | male=brown) = 0.35

d) P(female=blue | male=green) = 0.31

e) We can conclude that the eye colors of male respondents and their partners are not independent.

Step-by-step explanation:

We are given following information about eye colors of 204 Scandinavian men and their female partners.

              Blue    Brown     Green    Total

Blue        78         23            13          114

Brown     19         23            12          54

Green     11           9             16          36

Total      108       55            41          204

a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?

Using the addition rule of probability,

∵ P(A or B) = P(A) + P(B) - P(A and B)

For the given case,

P(male=blue or female=blue) = P(male=blue) + P(female=blue) - P(male=blue and female=blue)

P(male=blue or female=blue) = 114/204 + 108/204 − 78/204

P(male=blue or female=blue) = 0.71

b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=blue) = 78/114

P(female=blue | male=blue) = 0.68

c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=brown) = 19/54

P(female=blue | male=brown) = 0.35

d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?

As per the rule of conditional probability,

P(female=blue | male=green) = 11/36

P(female=blue | male=green) = 0.31

e) Does it appear that the eye colors of male respondents and their partners are independent? Explain

If the following relation holds true then we can conclude that the eye colors of male respondents and their partners are independent.

∵ P(B | A) = P(B)

P(female=blue | male=brown) = P(female=blue)

or alternatively, you can also test

P(female=blue | male=green) = P(female=blue)

P(female=blue | male=blue) = P(female=blue)

But

P(female=blue | male=brown) ≠ P(female=blue)

19/54 ≠ 108/204

0.35 ≠ 0.53

Therefore, we can conclude that the eye colors of male respondents and their partners are not independent.

Answer:

30

Step-by-step explanation:

Answer:

3 times 10 + 5 times 1

Step-by-step explanation:

Answer:

\(x \leq -4\)

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

The relative maximum from the given graph is (2, 0). Therefore, options B, C, D and E are the correct answers

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

From the given graph,

The zeros of function are x=-3, x=2 and x=5.

So, the number of zeros are 3 and the degree of the polynomial is 3.

The relative maximum from the given graph is (2, 0).

The leading coefficient test tells us that the graph rises or falls depending on whether the leading terms are positive or negative.

Here, the leading coefficient is negative.

The edge multiplicity of a given end vertex in a multigraph is the number of multiple edges sharing that end vertex. The maximum edge multiplicity in such a graph is known as the graph multiplicity.

Here, the multiplicity is 2.

Therefore, options B, C, D and E are the correct answers

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The value of x in the given polygon is 31 degrees.

An exterior angle is an angle created by the expansion of the neighboring side and one of the sides of a closed shape construction, such as a polygon. Regardless of the number of sides in the polygons, the sum of the measures of the outside angles is equal to 360 degrees.

The sum of the exterior angle of any polygon is 360 degrees.

So,

360 = 57 + 41 + 82 +x + 62 + 87

360 = x + 329

x = 31

Hence, the value of x in the given polygon is 31.

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The blanks that are missing in the sequence are -3 and 11

from the question, we have the following parameters that can be used in our computation:

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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Answer:

y=4/3x-3

Step-by-step explanation:

In the triangles ABC and DCE the values for ∠1 and ∠2 is obtained as 35° each.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

The triangle ABC and DEC have a common vertex C.

From the diagram it can be seen that ∠ACD is given as 115°.

So, the value for ∠BCE will be equal to ∠ACD as they form vertically opposite angles pair.

This is represented as -

∠BCE = ∠ACD

∠BCE = 115°

Now, since ∠ACB and ∠ACD forms a linear pair so their sum will be 180°.

This is represented as -

∠ACB + ∠ACD = 180°

∠ACB + 115° = 180°

∠ACB = 180° - 115°

∠ACB = 65°

Now, in triangle ABC, the sum of all angles of the triangle will be equal to

180°.

∠BAC+ ∠ACB + ∠CBA = 180°

Substitute the values in the equation -

80°+ 65° + ∠1 = 180°

∠1 = 180° - 80°- 65°

∠1 = 180° - 145°

∠1 = 35°

Therefore, ∠1 measures 35°.

It can be seen that ∠2 and ∠1 form corresponding angles pair, so they must be equal.

This is represented as -

∠2 = ∠1

∠2 = 35°

Therefore, ∠2 measures 35°.

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Answer:

$47.70

Step-by-step explanation:

45 increase 6% =

45 × (1 + 6%) = 45 × (1 + 0.06) = 47.7

Solution:

A few tips...

Changing the sign of the given equation.

This could only mean that the arrow would go to 1.25 units forward. Then a second arrow will be drawn to go 0.75 units back.

The graph that matches with the above info is Option C.

Answer:

[C]

Step-by-step explanation:

Knowing that:

Alway start at 0.

Since 1.25 is the first number as well as it is positive..

Therefore, {Find a number lines that start at 0 going to the right of the number line}

Right of the number line ⇒ Positive

Left of the number line ⇒ negative

Hence, we can conclude that [B] and [D] and [A]  is wrong.

Because [B] is getting negative when 1.25 is positive

Because [D] Doesn't start at 0.

Because [A} Doesn't start a 0.

Now we have -0.75

which is 1.25 subtracted 0.75

1.25 - 0.75 = 0.5

Hence, base on [C] number line we can conclude that it correct.

~lenvy~

Answer:

  4 cm by 7 cm

Step-by-step explanation:

The relation between length and width can be used with the area formula to find the dimensions of the rectangle.

__

Let x represent the width of the rectangle. Then the length is (3x-5). The area is the product of length and width.

  A = LW

  28 = (3x -5)(x)

In standard form, this is ...

  3x² -5x -28 = 0

__

factor

To factor this equation, we are looking for factors of (3)(-28) = -84 that have a total of -5. The factor pairs of -84 are ...

  -84 = -84×1 = -42×2 = -28×3 = -21×4 = -14×6 = -12×7

Sums of these pairs are -83, -40, -25, -17, -8, -5.

The last pair, -12×7, gives us a clue as to how to factor the equation.

  3x² -5x -28 = (3x -12)(3x +7)/3 = (x -4)(3x +7)

Then the equation we want a solution for is ...

  (x -4)(3x +7) = 0

zero product rule

The only positive value of x that makes either factor zero is ...

  x = 4

And the other dimension is ...

  3x -5 = 3(4) -5 = 7

The rectangle is 5 cm wide and 7 cm long.

Answer: width of the garden is 42

Step-by-step explanation:

let's say "x" = the garden's length

and "y" = the garden's width

the length of the garden is 10 feet longer than its width

x-10=y

the garden's perimeter is 188 feet

we can set up a new equation like this:

2x+2y=188

now we have two equations and we can solve using the system of equations.

x-10=y

add 10 on both sides to isolate "x"

x=y+10

2x+2y=188

substitue x for y+10 in the second equation

2(y+10)+2y=188

expand

2y+20+2y=188

combine like terms

4y+20=188

subtract 20 from both sides

4y=168

divide by four on both sides

y=42

the width of the garden is 42 feet

Answer:

x^2 + 3x -1

Step-by-step explanation:

f(x) = 3x-2

g(x) = x^2+1

(f+g)(x) =  3x-2+x^2+1

Combine like terms

           = x^2 + 3x -1

Answer:

The answer is D

Step-by-step explanation:

Because the 2 represents 2,000 when you do 2,00o times the 20 in the answer, you get 40,000, and the 4 in the number 42,317 represents 40,000.

The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.

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To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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Therefore , as a result Two of a triangle's sides and the included  SAS angle are said to be congruent if they match the corresponding sides and angles of another triangle.

The Side-Angle-Side rule is applied to check the congruence of a set of triangles. The SAS rule states that a triangle is congruent if its two sides and included angles match those of another triangle.

Here,

if the first triangle's two sides and one of its included angles are equal to the second triangle's sides and one of its included angles.

Consequently, the SAS declares two triangles to be congruent. Two triangles are said to be congruent if their matching two sides and their included angles are found in a single triangle, according to the SAS theorem of congruence.

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\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{5}{2}}(x-\stackrel{x_1}{(-6)}) \implies y +2= \cfrac{5}{2} (x +6) \\\\\\ y + 2 = \cfrac{5}{2}x + 15\implies y = \cfrac{5}{2}x+13\)

In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:

In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).

The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22

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Answer:

4x + 10 is less than or equal to 18

Hope this helps :) Good Luck!

Answer:

g(x) = 5x² + 3

Step-by-step explanation:

8 units are added directly to each input so just subtract 5 from that to get + 3.

Answer:

3x^2 +3x +16

Step-by-step explanation:

do you need an explanation? if so I can put it in the comments

Answer:

4cm

Step-by-step explanation:

Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

A regular decagon is a polygon with ten sides of equal length and ten angles of equal measure.

To find the length of each of the other sides, we can use the fact that a regular decagon can be divided into ten congruent isosceles triangles.

The isosceles triangle can be split into two right triangles by drawing an altitude from the vertex opposite the base to the midpoint of the base.

Let's call the length of one of the equal sides of the isosceles triangle "s", and let's call the length of the altitude "h".

Then we can use the Pythagorean theorem to find the length of the other side:

s² = h² + (s/2)²

We can solve for "h" in terms of "s" as follows:

h² = s² - (s/2)²

h² = (4s²)/4 - s²/4

h² = (15s²)/16

h = (s√15)/4

Since the altitude divides the isosceles triangle into two congruent right triangles, each with a hypotenuse of "s",

We can use the Pythagorean theorem again to find the length of each of the other sides of the regular decagon:

s² = h² + (s/2)²

s² = [(s√15)/4]² + (s/2)²

s² = (15s²)/16 + (s²)/4

s² = (15s² + 4s²)/16

s^2 = (19s²)/16

s = √(19/16) s

s = (√19/4) cm

Therefore,

Each of the other sides of the regular decagon is (√19/4) cm long, or approximately 1.861 cm to three decimal places.

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The equation using the variable m to represent the cost of a Big Mac is

m + 1.07 = 15.07.

The cost of a Big mac is $14.

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

We have,

Let the cost of Big macs = m

cost of fries = $1.07

The total cost of Mig macs and fries = $15.07

This can be written as an equation:

m + 1.07 = 15.07

Subtract 1.07 on both sides.

m + 1.07 - 1.07 = 15.07 - 1.07

m = 14

The cost of a Big mac is $14.

Thus,

The equation using the variable m to represent the cost of a Big Mac is

m + 1.07 = 15.07.

The cost of a Big mac is $14.

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The 9 adult tickets and 93 children tickets were purchased.Let's assume the number of adult tickets purchased is "a" and the number of children tickets purchased is "c."

According to the given information, children tickets cost $9 and adult tickets cost $11. So, the total cost of children tickets is 9c, and the total cost of adult tickets is 11a.

The problem also states that the total cost of all the tickets is $936. Therefore, we can write the following equation:

9c + 11a = 936

Additionally, it is mentioned that the number of children tickets purchased was three more than ten times the number of adult tickets purchased:

c = 10a + 3

We can now solve this system of equations to find the values of "a" and "c." By substituting the value of "c" from the second equation into the first equation, we have:

9(10a + 3) + 11a = 936

90a + 27 + 11a = 936

101a = 936 - 27

101a = 909

a = 909 / 101

a = 9

Substituting this value back into the second equation, we find:

c = 10(9) + 3

c = 90 + 3

c = 93.

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