PLZ HELP!! What is the average rate of change of f(x) from -2 to 2?

Answer:

[tex] \frac{4}{5} \div \frac{2}{3} = n[/tex]

[tex] \frac{4}{5} = n \times \frac{2}{3} [/tex]

[tex] \frac{3}{2} \div \frac{4}{5} = n [/tex]

[tex] \frac{4}{5} = n \times \frac{2}{3} [/tex]

[tex] \frac{2}{3} \times n = \frac{4}{5} [/tex]

P: padre de Luis

h: hijo

P=32+h

P+h=78

Método: sustitución

*p + h = 78

(32 + h) + h = 78

32 + h + h = 78

2h + 32 = 78

2h = 78 - 32

2h = 46

[tex]h = \frac{46}{2} \\ \\ h = 23[/tex]

El hijo tiene 23 años

EL padre tiene 55 años

P = 32 + h

P = 32 + 23

P = 55

Answer:

x = 3

Step-by-step explanation:

You can multiply by 2x^2, then subtract x

2x = x +3 . . . . . multiply by 2x^2

x = 3 . . . . . . . . . subtract x

___

The attached graph shows the difference between the left side of the equation and the right side. When that difference is zero, the value of x is a solution. There is one solution at x=3. (x=0 is not in the domain of the relation. There is a vertical asymptote there.)

The correct answer is D, since if you simplify the equation 11 + 4 < -8 you get      x < -2. Since -2 is greater than x, the arrow would need to point to the left signifying that it is a lesser value.

Answer:

Step-by-step explanation:

D

area of rectangle=25*12=300

6 % of area=300*6 %=18

area of D=1/2 *6*6=18

so  D

The question about the shape representing 6% of a rectangle requires more information about the dimensions or sizes involved to be answered accurately in the context of Mathematics.

The question regarding which shape represents 6% of the rectangle pertains to understanding fractions or percentages of shapes and is related to the concepts of area and proportion within the field of Mathematics. To answer this, one would need more information about the dimensions of the rectangle or the sizes of the shapes involved.

The reference information provided seems unrelated to calculating percentages of a rectangle, and thus it is not possible to give a precise answer regarding the shape without additional context or clarification.

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318.83484250503 mm^2

The area of the regular 15-gon with a radius of 10mm is approximately 247.2mm².

Formula for a Regular Polygon Area:

The area (A) of a regular polygon can be calculated using the following formula:

A = 1/2 * n * s^2 * r

where:

n is the number of sides in the polygon (15 for this case)

s is the side length of the polygon

r is the radius of the polygon

Finding the Side Length (s):

We don't directly have the side length (s) of the regular 15-gon. However, we can relate it to the radius (r) using the following formula:

s = 2r * sin(π / n)

In this case:

r = 10mm

n = 15

Substituting these values:

s = 2 * 10mm * sin(π / 15)

s ≈ 8.24mm (round to 2 decimal places)

Calculating the Area (A):

Now that we have the side length (s) and the radius (r), we can calculate the area (A) of the regular 15-gon:

A = 1/2 * 15 * 8.24mm² * 10mm

A ≈ 247.2mm^2 (round to 1 decimal place)

Therefore, the area of the regular 15-gon with a radius of 10mm is approximately 247.2mm².

Answer:

c = [tex]\frac{27}{40}[/tex]

Step-by-step explanation:

To eliminate the fractions, multiply all terms by the lowest common multiple of 8 and 5

The lowest common multiple of 8 and 5 is 40

5 + 40c = 32 ( subtract 5 from both sides )

40c = 27 ( divide both sides by 40 )

c = [tex]\frac{27}{40}[/tex]

Final answer:

Explaining how to calculate density using the mass and volume of a rock.

Explanation:

Density can be calculated using the formula: Density = Mass/Volume. Given that the mass of the rock is 50 g and the volume is 10 mL, we can plug these values into the formula to find the density.

Mass = 50 g

Volume = 10 mL = 10 cm³

Density = Mass/Volume = 50 g / 10 cm³ = 5 g/cm³

Answer:

The values of x are x= 2i and x= -2i

Step-by-step explanation:

We need to solve the equation:

2x^2 + 8 =0

Taking 2 common

2(x^2 +4) =0

Dividing both sides by 2

x^2+4 =0

Adding -4 on both sides

x^2 +4 -4 = 0-4

x^2 = -4

Taking square root on both sides we get

√x^2 = √-4

we know √4 = 2 and √-1 = i so answer is:

x = ± 2i

The values of x are x= 2i and x= -2i

The graph is shown in figure attached.

To solve 2x² + 8 = 0 by graphing, one plots the corresponding quadratic function f(x) = 2x² - 8, which is a parabola that opens upwards. The equation has no real solutions as the function does not cross the x-axis, indicating that the original quadratic equation has no real roots.

To solve the quadratic equation 2x² + 8 = 0 by graphing the related function, we first need to rewrite the equation in the standard form of a quadratic function, which is f(x) = ax² + bx + c. In this case, the equation becomes f(x) = 2x² + 0x - 8.

The roots of the equation are the values of x where the function crosses the x-axis. To find these, we set the function equal to zero and solve for x. Subtracting 8 from both sides gives us 2x² = -8. Dividing by 2, we get x² = -4. Taking the square root of both sides, we see that x could be either positive or negative square root of -4, which does not have a real solution since you can't have a real number whose square is negative. Therefore, the graph of the function will not cross the x-axis and there are no real roots to this equation.

If we were to graph this function, we would plot the quadratic curve and notice that it is a parabola opening upwards because the coefficient of x² is positive. However, as we have established there are no real solutions, this would be confirmed by the fact that the vertex of the parabola is above the x-axis.

100,000

For each possible combination digit, there are 10 options: 0-9. Multiply ten by itself five times (for five digits) to find the number of combinations. This gives you 100,000 possible combinations.

D is the correct graph follows into whatever

Answer: OPTION C.

Step-by-step explanation:

Given a function f(x), the range of the inverse of f(x) will be the domain of the function f(x) and the range of the domain of f(x) will be the range of the inverse function.

For example, if the point (2,1) belongs to f(x), then the point (1,2) belongs to the inverse of f(x).

Observe that in the graph of the function f(x) the point (-3,1) belongs to the function, then the point (1,-3) must belong to the inverse function.

Therefore, you need to search the option that shown the graph wich contains the point (1,-3).

Observe that the Domain f(x) is (-∞,0) then the range of the inverse function must be (-∞,0).

This is the graph of the option C.

Answer:

Sorry, all I know is that after he got the 7 blocks of spruce he will have $3,600  left over. I don't know how many blocks he can buy with that.

Step-by-step explanation:

Answer:

Ted can buy 8 blocks of mahogany.

Step-by-step explanation:

Total amount Ted wishes to spend this month is $5000.

Mahogany costs $450 per block, and he has already bought 7 blocks of spruce at $200 each.

So, money spent on spruce = [tex]7\times200=1400[/tex] dollars

Money left after buying spruce = [tex]5000-1400=3600[/tex] dollars

Now as $450 will be spent on buying 1 block of mahogany.

So, $3600 will be spent on buying [tex]\frac{3600}{450}= 8[/tex] blocks of mahogany.

The answer is 8 blocks.

The water station would be located approximately 2.9 miles from the start.

A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

Let's call the distance from the start to the water station x. The distance from the water station to the finish line is 5 - x.

We know that the ratio of these two distances is 7:5, so we can write the following equation:

x / (5 - x) = 7/5

Expanding and solving for x, we get:

5x = 7(5) - 7x

12x = 35

x = 35/12 = 2.92 miles

So, the water station would be located approximately 2.92 miles from the start. Round to the nearest tenth of a mile, the answer is 2.9 miles.

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The water station will be placed approximately 2.9 miles from the start, rounding to the nearest tenth of a mile.

To find where to place the water station at a 7:5 ratio along a 5-mile race course, we must determine how many parts out of the total 12 parts (7+5) each section of the race is. Since the total race is 5 miles, we divide 5 miles by 12 parts, which gives us the length of one part. Multiplying that length by 7 will give us the distance from the start to the water station.

First, we find the length of one part:

Then, we find the distance to the water station:

The water station will be placed approximately 2.9 miles from the start, rounding to the nearest tenth of a mile.

Answer:

the answer is: 6z^3

Step-by-step explanation:

We need to solve this equation:

[tex]\sqrt{36z^6}[/tex]

We know that 6X6 = 36

and √ = 1/2

Solving:

[tex]=\sqrt{6*6*z*z*z*z*z*z}\\We\,\,know\,\,6X6=6^2\,\, and \,\,z*z=z^2\\=\sqrt{6^2*z^2*z^2*z^2} \\=(6^2)^{1/2}*(z^2)^{1/2}*(z^2)^{1/2}*(z^2)^{1/2}\\=6*z*z*z\\=6z^3[/tex]

So, the answer is: 6z^3

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} y=8\\ x=-2 \end{cases}\implies 8=k(-2)[/tex]

Answer:

50 degrees

Step-by-step explanation:

If angle A and angle B are complementary, that would mean that their sum is 90 degrees. A + B = 90 . We know that angle A is 40, so 40 + B = 90. It becomes a one step equation. Subtract both sides by 40. 90 - 40 = 50. Angle B is equal to 50 degrees.

Answer:

50 degrees

Step-by-step explanation:

we know that

If two angles are complementary, then their sum is equal to 90 degrees

so

A+B=90°

we have

A=40°

substitute and solve for B

40°+B=90°

B=90°-40°=50°

Answer:

[tex]p=-9[/tex]

Step-by-step explanation:

We want to solve the linear equation;

[tex]7p=-63[/tex]

We divide both sides of the given linear equation by 7 to obtain;

[tex]\frac{7p}{7}=\frac{-63}{7}[/tex]

This implies that;

[tex]p=\frac{-63}{7}[/tex]

[tex]p=\frac{-9\times7}{7}[/tex]

We now cancel out the common factors to get:

[tex]p=-9[/tex]

Answer:

[tex]\frac{95}{99}[/tex]

Step-by-step explanation:

The bar above 95 denotes that 95 is repeated, that is

0.959595,,,,

Create 2 equations with the repeating values after the decimal point, thus

let x = 0.9595.... → (1) ← multiply both sides by 100

100x = 95.9595.... → (2)

Subtract (1) from (2) eliminating the repeated value, so

99x = 95 ( divide both sides by 99 )

x = [tex]\frac{95}{99}[/tex]

Answer:

Width=5

Step-by-step explanation:

It would be 93,000 because it’s closed to 93,000 than 94,000

heya dear

93000.........

For this case we must find the solution of the following expression:

[tex](x + 7) (x + 7) = 0[/tex]

If we isolate a term and we equate to zero, we have:

[tex]x + 7 = 0[/tex]

Subtracting 7 on both sides of the equation we have:

[tex]x + 7-7 = 0-7\\x = -7[/tex]

Thus, the solution of the expression is given by:

[tex]x = -7[/tex]

ANswer:

[tex]x = -7[/tex]

Answer:

x = -7, multiplicity 2.

Writing it as a set it is {-7, -7}.

Step-by-step explanation:

(x + 7)(x + 7 )= 0

When 2 expressions are multiplied and the result is zero either of them can be zero, so

x + 7 = 0

x = -7.

In this case, since the 2 factors are the same, there are duplicate roots.

We write  this as  x = -7, multiplicity 2.

Answer:

1 = 60, 4 = 30, 5 = 30, 6 = 150, 7 = 110, 8 = 30, 9 = 60, 10 = 90.  2 = 47.5, 3 = 132.5

Step-by-step explanation:

Starting with angle 5:  knowing that arc BC = 30 and angle 5 is a central angle, it has an angle measure equal to the measure of the arc it intercepts.

Angle 6 is supplementary to angle 5, so 180 - 30 = 150.

Angle 9 = 60.  Ch is a diameter, so that means it splits the circle into 2 congruent halves, each measuring 180 degrees around the outside.  So if arcs AB and CB both measure 30, then arc AH measures 180 - 30 - 30 = 120.  By definition, the measure of angle 9 is half the measure of the arc it intercepts.

Angles 4 and 8 = 30 each.  Because you have AH parallel to CG, then CH is a transversal, creating a pair of alternate interior angles that are congruent.  Those angles are 4 and 8.  We find 8 to be an inscribed angle, cutting off arc ABC which measures 60 degrees.  An inscribed angle is half the measure of the arc it intercepts. Because angle 4 measures 30 degrees and is inscribed, the arc it cuts off, arc GH, measures twice the angle cutting it.  So arc GH measures 60.

Again, since CH is a diameter, then the semicircle CDEG measures 180.  Since we know from the description that arcs CD and DE are congruent, then arc CD + arc DE + arc EG (given as 50) + arc GH = 180.  Since arcs CD and DE are congruent, lets just call them "x" and we have two of them.  That gives us that 2x + 50 + 60 = 180.  x = 35.  Angle 1 is equal to half of the sum of its intercepted arcs ( 35 + 35 + 50) which is 60.

Angle COE intercepts arc CDE, and is central, so angle COE measures 70, and since angle 7 is supplemetray to angle COE, then angle 7 measures 180 - 70 = 110.

Angle 10 by definition is a right angle (refer to the theorem regarding a tangent line to a point on a circle).

Angle 2 is half of the sum of 35 (arc CD) and 60 (arc GH), so angle 2 measures 47.5 and that means that angle 3, supplementary to angle 2, measures 180 - 47.5 = 132.5.  I think those are all correct.  The only one I'm unsure of is angle 2.  

Answer:

Final answer is [tex](3x-y)(x+y)[/tex].

Step-by-step explanation:

Given expression is [tex]3x^2+2xy-y^2[/tex].

Now we need to factor the given expression [tex]3x^2+2xy-y^2[/tex] completely. Let's use factor by grouping method.

[tex]3x^2+2xy-y^2[/tex]

[tex]=3x^2+3xy-xy-y^2[/tex]

[tex]=3x(x+y)-y(x+y)[/tex]

[tex]=(3x-y)(x+y)[/tex]

Hence final answer is [tex](3x-y)(x+y)[/tex].

(3x−y)(x+y) is the answer but did you mean to put 3x^2 + 2xy - y^2 as your answer?

Answer:

Perimeter of polygon B = 80 units

Step-by-step explanation:

Since both polygons are similar, their corresponding sides and perimeters are proportional. Knowing this we can setup a proportion to find the perimeter of polygon B.

[tex]\frac{side-polygonA}{side-polygonB} =\frac{perimeter-polygonA}{perimeter-polygonB}[/tex]

Let [tex]x[/tex] be the perimeter of polygon B. We know from our problem that the side of polygon A is 24, the side of polygon B is 15, and the perimeter of polygon A is 128.

Let's replace those value sin our proportion and solve for [tex]x[/tex]:

[tex]\frac{side-polygonA}{side-polygonB} =\frac{perimeter-polygonA}{perimeter-polygonB}[/tex]

[tex]\frac{24}{15} =\frac{128}{x}[/tex]

[tex]x=\frac{128*15}{24}[/tex]

[tex]x=\frac{1920}{24}[/tex]

[tex]x=80[/tex]

We can conclude that the perimeter of polygon B is 80 units.

Answer:80 units

Step-by-step explanation:

I'm doing it right now. You got this have a great day!

When doing volume you do Length x Width x Height (9 x 2.5 x 10) the answer is 225 if I’m not mistaken

The volume of the cereal box is 225 in³

Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

Given that, a cereal box is 9 inches by 2.5 inches by 10 inches., we need to find its volume,

Volume of box = length x width x height

= 9 x 2.5 x 10

= 225

Hence, the volume of the cereal box is 225 in³

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Answer:

0.04

Step-by-step explanation:

Looking at the chart we can see that there are 0, 1, 2 and 3 defective parts in one column while the other column says the probability of each happening. Look at the probability of there being 2 defective parts and that will be your answer.

Answer:

0.04

Next answer is 0.15.

Step-by-step explanation:

Answer:

a) [tex]a_n = 50 (0.52) ^ {n-1}[/tex]

b) [tex]a_6 = 50 (0.52) ^ 5 = 1.90\ cm[/tex]

Step-by-step explanation:

If each curved path has 52% of the previous height this means that [tex]\frac{a_{n+1}}{a_n} = 0.52[/tex]

Then the radius of convergence is 0.52 and this is a geometric series.

The geometric series have the form:

[tex]a_n = a_1 (r) ^ {n-1}[/tex]

Where

[tex]a_1[/tex] is the first term of the series and r is the radius of convergence.

In this problem

[tex]a_1 = 0.5[/tex] meters = 50 cm

[tex]r = 0.52[/tex]

a) Then the rule for the sequence is:

[tex]a_n = 50 (0.52) ^ {n-1}[/tex]

b) we must calculate [tex]a_6[/tex]

[tex]a_6 = 50 (0.52) ^ 6-1\\\\a_6 = 50 (0.52) ^ 5 = 1.90\ cm[/tex]

Answer:

-4.5

Step-by-step explanation:

ANSWER

The midline y=3.6

EXPLANATION

The midline is the midpoint of the peak value and the least value.

The peak value is 5.20

The least value is 2

The midline is

[tex]y = \frac{5.20 + 2}{2} = \frac{7.2}{2} = 3.6[/tex]

Therefore the mid value is y=3.6

In this figure, ∠a and ∠b are supplementary. The answer is OPTION C.

A. Complementary angles are two angles whose sum is equal to 90 degrees. Since no information is given about the angles Za and Zb in the figure, we cannot determine if they are complementary. Therefore, this answer choice is not supported by the given information.

B. Equal angles have the same measure. Again, no information is given about the angles Za and Zb, so we cannot determine if they are equal. Thus, this answer choice is not supported by the given information.

C. Supplementary angles are two angles whose sum is equal to 180 degrees. Since the figure does not provide any specific angle measurements, we cannot directly determine if Za and Zb are supplementary. However, this answer choice is a possibility as supplementary angles are commonly encountered in geometry.

D. Vertical angles are a pair of non-adjacent angles formed by intersecting lines. Without any information about the lines or angles in the figure, we cannot determine if Za and Zb are vertical angles. Therefore, this answer choice is not supported by the given information.

In conclusion, the most accurate answer choice based on the given information is C. supplementary. However, without additional context or measurements, we cannot definitively determine the relationship between Za and Zb.

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According to the given figure, ∠a and ∠b are complementary angles.

The correct answer to the given question is option A.

These two could be any pair of angles and the relationship between them depends on their relative positions. If ∠a and ∠b are complementary, that means that the sum of their angle measures is 90 degrees.

This usually happens when two angles together form a right angle. On the other hand, if ∠a and ∠b are equal, that means that they have the same angle measure.

This usually happens when the angles are opposite each other in a shape with symmetry, such as an isosceles triangle or a rectangle. Should ∠a and ∠b be supplementary, it means that the sum of their angle measures is 180 degrees.

This usually happens when two angles form a straight line or the angles on a straight line sum to 180 degrees.

Finally, if ∠a and ∠b are vertical, that means they are opposite each other when two lines intersect.

Hence, ∠a and ∠b are complementary angles.

Therefore, the correct answer to the given question is option A.

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Answer:

4

Step-by-step explanation:

f⁻¹(x) = x²+3, but none of that matters, since f(f⁻¹(x)) = x