The function y = f(x) is graphed below. What is the average rate of change of the
function f(x) on the interval -3 ≤ x ≤-1?

The limit in the given graph [tex]\lim_{x \to \ 2^{-} } f(x)[/tex] is 3 and [tex]\lim_{x \to \ 2^{+} } f(x)[/tex] is -2

Given graph of a function and we have to determine the limits when x tends to 2 minus and when x tends to 2 plus.

When we see the graph we can find that the graph is not of the linear function because it is not straight line.

From x=2 and onwards it gives values values of only -2 because it is parallel to x-axis at y=-2.From x=2 and leftwards it gives values values of only 3 because it is parallel to x-axis at y=3.

Hence the limit of the function whose graph is shown is 3 and -2.

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Answer:

h ≈ 259.81

Step-by-step explanation:

i used the hexagon calculator

Answer:

150 sqrt 3        = 259.8076  units^2

Step-by-step explanation:

Interior angles of hexagon = 120 degrees ....now look at the Right  1/2 of the hexagon...  see illustration....this is a trapezoid...

One base is 10 units

the other labelled 'base' is

 10 cos 60    +   10 cos 60   + 10    = 20 units

the height of this trapezoid is  10 sin 60 = 10 * sqrt(3)/2 = 5 sqrt(3)

   the area of this trapezoid is then   1/2 ( 10+ 20) * 5 sqrt (3)  = 75 sqrt 3

there are TWO of these trapezoids in the hexagon so total area is then

   2 * 75 sqrt 3

        150 sqrt 3

Mikaela's team's score is 8.33

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Viktoria's team's score = 7

According to question,

= 2+ 7*2 = 16

so, Mikaela team score= 16/3+3= 8.33      

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The diagram that shows all the lines of symmetry is diagram B.

We define a line of symmetry as a line such that if we perform a reflection over that line, the image coincides with the preimage (so the reflection does not change the figure).

With that in mind, any line that cuts the hexagon in exactly two halves is a line of symmetry.

So the image that shows all the lines of symmetry of the regular is B, where it shows all the lines that cut the hexagon in two equal halves.

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The surface area of the figure is approximately: 178 units².

The surface area of any figure is the area of all its faces.

Find the area of each face as shown below:

Area of base = w² = 6² = 36 units²

Area of the 4 rectangular faces = 4(6)(3) = 72 units²

Area of the 4 triangular faces = 4[1/2bh]

b = w = 6 units

h = √(y² + (w/2)²) = √(5² + (6/2)²) = 5.8 units

Area of the 4 triangular faces = 4[1/2(6)(5.8)] = 69.6 units²

Surface area = 36 + 72 + 69.6 ≈ 178 units²

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Work Shown:

x = number of quarters

3x = number of dimes

0.25x = value of just the quarters, in dollars

0.10(3x) = 0.30x = value of just the dimes, in dollars

0.25x+0.30x = 0.55x = total value in dollars

0.55x = 9.35

x = (9.35)/(0.55)

x = 17

Alison has 17 quarters and 3x = 3*17 = 51 dimes

17 quarters = 17*0.25 = $4.25

51 dimes = 51*0.10 = $5.10

17 quarters + 51 dimes = $4.25 + $5.10 = $9.35

The answers are confirmed.

Answer:

Rs 85

Step-by-step explanation:

Cost of 5kgs of rice = Rs 425

Cost of 1 kg of rice = 425/5

= Rs 85

So, the cost of a kg of rice is Rs 85

The steps that are used for creation of the graph of a polynomial function are listed below.

In Mathematics, the steps that are used for creation of the graph of a polynomial function are:

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Answer:

y=10

Step-by-step explanation:

Since this triangle has equal length sides, it is equilateral and also has equal measured angles. This means that each angle is 180/3=60 degrees.

To solve for y, we can do 5y+10=60. Simplifying, we get

5y=50

y=10.

Answer:

4

Step-by-step explanation:

So all the angles will have the same value. In a triangle all the angles will add up to 180, so each angle would have to be 60 degrees. So to know Y we need 6x+6=5y+10.  So subtract 10 from each side, then subtract 6x from each side to get 4=x

Using the same-side interior angles theorem, the values of x and y are:

x = 80

y = 130

The same-side interior angles theorem states that two interior angles on same side of a transversal are supplementary.

(x - 30) and (x + 50) are same-side interior angles, therefore:

(x - 30) + (x + 50) = 180

Solve for x

x - 30 + x + 50 = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 160/2

x = 80

(x - 30) + y = 180

Plug in the value of x

(80 - 30) + y = 180

50 + y = 180

y = 180 - 50

y = 130

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Answer:

X= 80

Y= 130

Step-by-step explanation:

do you trust me???

Answer:

6x-4

Step-by-step explanation:

3x•2= 6x

-2•2=-4

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Answer:  [tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]

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Given:  [tex]\textsf{(3x - 2)}^2[/tex]

Find: [tex]\textsf{Simplify the expression}[/tex]

Solution:  It looks like 2 is at the end of the parenthesis where the power would be instead of distributing the number.  If so the following steps would be followed.

Expand

Simplify

Therefore, after following the provided information we are able to determine that the expanded form would be 9x^2 - 12x + 4.

The expression that has a value of 16 when n = 5 is  [tex]\rm 7+ \dfrac{45}{n}[/tex] , Option C is the correct answer.

An expression is mathematical statement consisting of variables , constant and mathematical operators.

The expression given in the question is

[tex]\rm \dfrac{ 25}{n} + 7 \\\\30-3n\\\\7+\dfrac{45}{n}\\\\n^3 -114[/tex]

On solving it can be seen that

The value of 16 when n= 5 is given by

7 +45/5 = 7+9 = 16

Therefore Option C is the right answer.

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3(x-4) ≥ 5x +2

3*x - 3*4 ≥ 5x +2

3x - 12≥ 5x - 2

-12 + 2 ≥ 5x- 3x

-10 ≥ 2x

2x ≤ -10

x ≤ -5

The difference between Palomas and Antons' points on the English test is of 14 points.

When two numbers can be written in the form as p:q , they are said to be in Ratio.

It is given that

The ratio of Michaels point to Paloma point is 12 :11

The ratio of Michaels point to Anton's Point is 4:3

Let Paloma's point be x

then Michaels point will be 12x/11

and Anton's points will be

(12x/11 ) / Anton's points = 4 /3

Anton's points = 9x/11

It is given that the sum of the points of the three students is 224

so

x + (12x/11)+ (9x/11) = 224

32x /11 = 224

x = 77

Paloma's points = 77

Anton's Points = 9x/11 = 63

The difference between Palomas and Antons' points on the English test

=77 -63

= 14 points.

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If [tex]y' = e^y \sin(x)[/tex] and [tex]y(-\pi)=0[/tex], separate variables in the differential equation to get

[tex]e^{-y} \, dy = \sin(x) \, dx[/tex]

Integrate both sides:

[tex]\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C[/tex]

Use the initial condition to solve for [tex]C[/tex] :

[tex]-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2[/tex]

Then the particular solution to the initial value problem is

[tex]-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2[/tex]

(A)

Answer:

(1) 85×9=765 (2) 127×3=381

Step-by-step explanation:

I am not sure I can see the room limitations.

what I see is that the kitchen is one large rectangle from

(-8, 8) to (0, 0).

the rec room is Amado one large rectangle from

(5, 6) to (8, -7).

I am basing the rest in this.

for the area calculations, please consider that the area of a rectangle is length × width, and the area of a triangle is half of the rectangle it splits in half with its baseline (as diagonal).

A)

area 1 =

rectangle (-8, 8) to (-5, 3)

plus

half of the rectangle (-5, 8) to (-3, 3)

3×5 + 1/2 × 2×5 = 3×5 + 1×5 = 15 + 5 = 20 yd²

area 2 =

half of the rectangle (-5, 8) to (-3, 3)

plus

rectangle (-3, 8) to (0, 3)

1/2 × 2×5 + 3×5 = 20 yd²

area 3 = area 4 =

half of the rectangle (-8, 3) to (0, 0)

1/2 × 8×3 = 4×3 = 12 yd²

B)

the total area of the kitchen is the sum of all 4 areas

20 + 20 + 12 + 12 = 64 yd²

we can also calculate this in general, seeing that the general dimensions of the kitchen are 8×8 : from (-8, 8) to (0, 0).

8×8 = 64 yd²

After doing simplification, the result that we got is the quadratic formula

x = [-b ±√(b² - 4ac)] / 2a.

The given statement can be explained with the following equation:

[x + (b/2a)]² = (b² - 4ac) / 4a²

Now, we will take the root on both the sides:

x + (b/2a) = ±√[(b² - 4ac) / 4a²]

x = -(b/2a) ± √[(b² - 4ac) / 4a²]

x = [-b ±√(b² - 4ac)] / 2a

The final equation resembles the quadratic formula.

So, the result of applying the square root property to this equation is that we get the quadratic formula after simplification.

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Answer:

Step-by-step explanation:

1) y = [tex]\frac{1}{3}[/tex]

2) x = [tex]\frac{1}{3}[/tex]

3) y = -3

4) x = [tex]\frac{-1}{-12}[/tex]

Answer:

11,3,3,12

Step-by-step explanation:

1st y= 11 because -2/3(-6)=4 4+7=11

1st x= 3 because -2/3(3)=-2 and -2+7 is 5

2nd y=-3  because -2/3(15)=-10 -10 +7=-3

2nd x=-12 because -2/3(-12)=8 8+7=15

The value of x is 10√3 .

The missing figure is attached with the answer

A triangle is a polygon with three sides , three angles and three vertices.

A right angle is a triangle in which one of the sides of a triangle is equal to 90 degree.

As it is a right angled triangle therefore the trigonometric ratios are applicable

From the given figure sin 60 needs to be determine to find the value of x

sin x = Perpendicular / Hypotenuse

sin 60 = 5 / x

[tex]\rm \dfrac{\sqrt{3}}{2} = \dfrac{5}{x}[/tex]

x = 10√3

Therefore the value of x is 10√3

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Answer:

1/2, -1/8, 1/32

Step-by-step explanation:

[tex] - 2( - \frac{1}{4} ) = \frac{1}{2} [/tex]

[tex] \frac{1}{2} ( - \frac{1}{4} ) = - \frac{1}{8} [/tex]

[tex] - \frac{1}{8} ( - \frac{1}{4}) = \frac{1}{32} [/tex]

As per the question, the answer is ∠CAB is congruent to ∠BAD.

An isosceles triangle named BDC is positioned within a circle. The segments of the circle they pass through are congruent because the faces of the triangles BC and BD are congruent, or identical.

Due to the triangle's faces BC and BD being identical and congruent

BC=BD

Additionally, the segments of the circle it goes across are congruent.

In the case of ΔBAC & ΔBAD

AC=AD= the radius of the circle

AB=BA

Thus, BAC is consistent with BAD according to SSS guidelines.

As a result, the central angles of the sections are also congruent; hence, BAD and CAB are congruent.

As a result, ∠BAD is equivalent to ∠BAC OR ∠CAB.

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Answer:

B on edge

Step-by-step explanation:

CAD

Answer:

Subtraction will happen in this case.
14ft-5ft= 9ft
10 inches-8 inches= 2 inches
So, it grew 9ft. and 2 inches.

Any wave's speed is equal to its frequency times wavelength. Now, the question doesn't specifically state what kind of wave it is. Thus, there might be two distinct scenarios: If the wave is elastic (sound is an example), you can't calculate its speed unless you also know its frequency and wavelength. However, the speed in vacuum is constant (3*108 m/s) if the wave is electromagnetic (for instance, light). In order to maintain constant velocity, frequency must shift in response to variations in wavelength. The frequency of light rays is constant in all other optical media (apart from vacuum and air), although their velocity and wavelength change correspondingly. However, that is not the case here since if it must be an EM wave with a wavelength of 10 m, then it must be a radio wave that travels uniformly through all medium at a speed of 3*108 m/s.

Step-by-step explanation:

a) 14w + 21

- Factor out 7 from the expression

7 (2w + 3)

b) 27x + 18

- Factor out 9 from the expression

9 (3x + 2)

Hi!

___________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

#1 7(2w+3)

#2 9(3x+2)

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

We need to factor these two expressions.

[tex]\twoheadrightarrow\sf 14w+21[/tex] and [tex]\twoheadrightarrow\sf 27x+18[/tex]

For now let's focus on the first expression.

Note that both terms, 14w and 21, have something in common.

In fact, they have 7 in common. So we factor it out by dividing 14w and 21 by 7.

[tex]\twoheadrightarrow\sf14w\div7=2x\\\twoheadrightarrow\sf21\div7=3[/tex]

[tex]\bullet[/tex] Put the terms together, with a plus sign in between since they are positive

[tex]\twoheadrightarrow\sf 2w+3[/tex]

[tex]\bullet[/tex] Put parentheses around 2w+3

[tex]\twoheadrightarrow\sf (2w+3)[/tex]

[tex]\bullet[/tex] Put7 outside the parentheses

[tex]\twoheadrightarrow\sf7(2w+3)[/tex]

[tex]\bullet[/tex] Great job! We factored the expression

__________________________________________________________

This problem can be solved the same way!

This time, both terms have a 9 in common.

[tex]\twoheadrightarrow\sf 27x+18[/tex]

So we divide both terms by 9.

[tex]\twoheadrightarrow\sf 27x\div9=3x\\\twoheadrightarrow\sf18\div9=2[/tex]

[tex]\bullet[/tex] Put the terms together, with a plus sign in between since they're positive

[tex]\twoheadrightarrow\sf 3x+2[/tex]

[tex]\bullet[/tex] Next, put parentheses around 3x+2 and put 9 outside the parentheses

[tex]\twoheadrightarrow\sf 9(3x+2)[/tex]

[tex]\bullet[/tex] Great job! We factored both expressions

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

Answer:

[tex]0.07[/tex]

Step-by-step explanation:

FORMULA :

[tex]p\left( A|B\right) =\frac{p\left( A\cap B\right) }{p\left( B\right) }[/tex]

……………………………

then

[tex]p\left( \text{drive to school} |sophomore\right) =\frac{p\left( \text{drive to school} \cap \text{sophomore} \right) }{p\left( \text{sophomore} \right) }[/tex]

                                [tex]= \frac{2}{2+25+3}[/tex]

                                [tex]=\frac{2}{30}[/tex]

                                [tex]=\frac{1}{15}[/tex]

                                [tex]=0.066666666667[/tex]

Answer:

A resposta certa é:

[tex]6x \\x^3 - 5x^2 + 1 \\3 \\x^3 + 3x^2 + 7x \\-x^3 - 4x[/tex]

Step-by-step explanation:

1° equação:

Como há um x² positivo e um negativo, ambos irão se anular, sobrando apenas as incógnitas de potência 1 (ou, 6x)

2° equação:

Esta resulta em uma equação de 3° grau incompleta, já que há uma incógnita de potência 3, uma de potência 2, não há uma incógnita de potência 1 mas há as constantes, que as unindo forma a constante 1.

3° equação:

As incógnitas presentes há uma negativa e uma positiva de mesma potência, anulando-as e sobrando apenas a constante 3.

4° equação:

Considerando que há um 4x² e um -x² na equação, unindo-os forma o 3x², após isso é só repetir a equação.

5° equação:

Há -10x (-6x -4x = -10x) e 6x, resultando em um -4x, e então é só repetir a equação

Nota: I'm Brazilian, so I found it more practical to write the entire explanation in Portuguese, so if you can't understand, I ask you to use the translator, thanks for understanding :)

Answer:

79°

Step-by-step explanation:

An angle in standard position has it "initial" side glued on to the positive x-axis. The other ray that makes the angle swings around the origin, (0,0) like a hand of a analog clock (but moving backwards) straight up is 90°, straight to the left is 180° straight down is 270°. And all the way back to the start is 360°.

If the angle is 281° it can go 79° more degrees before getting back to the start.

360° - 281° = 79°