(-5a^2)^3•a^5find the product.

The polynomial function f(x) which produced the graph shown is f(x) = -6(x - 1/2)²(x + 1)²(x - 2).

In Mathematics and Geometry, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

By critically observing the graph of the polynomial function shown above, we can logically deduce that its x-intercepts include the following;

x = -1 ⇒ x + 1 = 0.

x = 2 ⇒ x - 2 = 0.

Also, the graph has a zero of multiplicity 2 at x = 1/2;

x = 1/2 ⇒ x - 1/2 = 0.

(x - 1/2)²

In this context, an equation that represent the polynomial function is given by:

f(x) = a(x - 1/2)²(x + 1)²(x - 2)

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 3), we have;

3 = a(0 - 1/2)²(0 + 1)²(0 - 2)

3 = a(1/4)(-2)

3 = -a/2

a = -6.

Therefore, the required polynomial function is given by:

f(x) = -6(x - 1/2)²(x + 1)²(x - 2)

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Answer:

D. I and II

Step-by-step explanation:

In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive. 

The solution is, sine is positive in,  D. I and II. Option (D) is correct because, In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles.

here, we have,

We are given to select the correct answer from the options provided.

The rule of signs for the trigonometric ratios in the four quadrants are as follows :

Quadrant I :    All the three ratios, tangent, sine and cosine are positive.

Quadrant II :   Only sine is positive, cosine and tangent are negative.

Quadrant III :  Only tangent is positive, sine and cosine are negative.

Quadrant IV :  Only cosine is positive, sine and tangent are negative.

so, we get,

In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.

Therefore, using the above rules, we can say that the options (B), (C) and (A) are incorrect.

so, we have,

Option (D) is correct because, In the first quadrant (I), all ratios are positive. In the second quadrant (II), sine (and cosec) are positive.

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Answer:

36 nickels and 20 quarters

Step-by-step explanation:

36x5= 180

25x20=500

500+180=680=6.80

Answer:I won’t give you a full answer but I can explain it.

Step-by-step explanation: Our “goal” is $6.80 we have to figure out how many nickels and quarters are in it. First off, which is bigger? A quarter. Count as far as you can until you can’t go over 6.80. Now add the remaining numbers (the nickels) and you will have your answer. Make sure when your adding to count each quarter and nickel!

The lateral surface area of a rectangular prism is 2(l + w)h sq units.

A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces).

The lateral surface area of a rectangular prism is given by

Where l, w, and h are the length, width, and height, respectively. To find the lateral surface area, we need the values of l, w, and h.

Without these values, it is not possible to determine the lateral surface area of the rectangular prism.

Therefore, the lateral surface area of a rectangular prism is 2(l + w)h sq units.

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Player B is the more consistent player, determined by the variability.

Range measures the difference between the highest and lowest numbers, whereas the IQR measures the difference between the first and third quartiles.

Range and IQR are both measures of variability that measure how spread out the data is.

Player B has a lower range and IQR than Player A, which indicates that Player B was more consistent.

Since Player B had a lower range and IQR than Player A, this indicates that Player B is the more consistent player.

This shows that Player B is more consistent because the data points are closer together.

This is because Player B had fewer outliers, which made the data points more consistent.

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Answer:you need to show the diagram in order for me to

Step-by-step explanation:

Answer:

15/-9

Step-by-step explanation:

Change in y divided by change in x.

(20-5)/(-3-6)

Image uploaded as a reference.

Hope this helps.

The additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria is

EJ ≅ GJ. Option A

We need to know the properties of a parallelogram, we have;

We know that FJ  ≅ JH, it's given by the marks, now if it were to happen that EJ ≅ GJ, that would mean that the diagonals on that quadrilateral are bisecting each other, and if that's so, then the quadrilateral it's indeed a parallelogram.

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The complete question:

What additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria?

A)

ej ≅ gj

B)

ej || gj

C)

fg || eh

D)

ef ≅ hg

Answer:

Rate of Change: 2

Step-by-step explanation:

Rate of change is the same as slope:

( y1 - y2 ) / ( x1 - x2 )

( 2 - 4 ) / ( 0 - 1 )

( -2 ) / ( -1 )

2

Hopefully this helps!

Brainliest please?

Answer:

#7

#8

The difference:

#9

#10

Max is right

Weight of Omar after 4 weeks is 9.4375 pounds.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Weight of Omar at the time of birth = 8 pound 3 ounces

Weight gained by Omar in 4 weeks = 5 × 4 = 20 ounces

New weight of Omar

= (8 lb 3 ounces) + 20 ounces

= 8 lb + 23 oz

As, we know 16 ounces = 1 pound

23 ounces = 1.4375 pound

Now, total weight of Omar after 4 weeks = 8 lb + 23 oz

                                                                  ≈ 8 lb + (1.4375) lb

                                                                   ≈ 9.4375 pounds

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*see attachment for the megaphone being referred to here

Answer:

9%

Step-by-step explanation:

==>Given:

Conical megaphone with the following dimensions:

Slant height (s) = 2.25 ft

Diameter (D) = 1.2 ft (radius r = 0.6 ft)

π = 3.1

Area covered by sticker on one side = area of square = 6 in × 6 in = 0.5 ft × 0.5 ft = 0.25 ft²

==>Required

% of the surface of area of the conical megaphone that is covered by the sticker = area covered by the sticker ÷ surface area of megaphone × 100

==>SOLUTION

Area covered by sticker on both sides = 0.25 ft² + 0.25 ft² = 0.5 ft²

Surface area of the megaphone = surface area of a cone = πrs + πr²

S.A of megaphone = (3.14 × 0.6 × 2.25) + (3.14 × 0.6²)

S.A = 4.239 + 1.1304

S.A = 5.3694 ft²

Therefore, % of the surface of area of the conical megaphone that is covered by the sticker = 0.5 ÷ 5.3694 × 100

= 9.31202741

= 9%

Answer:

Statistics show the megaphone was a success in South Carolina.

Step-by-step explanation:

Solution

Step 1:

Write the function:

Step 2:

Horizontally compressed is given below:

Final answer

The equation for the line through the point (-7,-4) and parallel to the line y = 8x - 4 in point-slope form is y = 8x + 52

The first equation is given as

y = 8x - 4

The slope of the above equation is

m = 8

Parallel lines have equal slope

So, the slope of the other line is

m = 8

The equation is then calculated as

y = m(x - x1) + y1

Where

m = 8

(x1, y1) = (-7, -4)

So, we have

y = 8(x + 7) - 4

Expand

y = 8x + 56 - 4

Evaluate the difference

y = 8x + 52

Hence, the equation for the line through the point (-7,-4) and parallel to the line y = 8x - 4 in point-slope form is y = 8x + 52

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Answer:

Step-by-step explanation:

when you combine the amount of almonds and raisins, you get 12 ounces. so out of those 12 ounces, 7 is going to be almonds. aka \(\frac{7}{12}\). now you just have to multiply that by 16 (since there are 16 ounces in a pound) and you'll get roughly 9.333

Answer:

4/11 divided by 5/8 is 0.58181818181

Step-by-step explanation:

Answer:

\( \frac{32}{55} \)

= 0.582

Step-by-step explanation:

\( \frac{4}{11} \div \frac{5}{8} = \frac{4}{11} \times \frac{8}{5} = \frac{32}{55}\)

2 pounds 6 ounces in ounces is equivalent to 38 ounces.

The given measurement is -

2 pounds 6 ounces

In 1 pound, there are 16 ounces.

So, we can write that -

2 pounds 6 ounces = 2 x 16 + 6

2 pounds 6 ounces = 38 ounces

So, 2 pounds 6 ounces in ounces is equivalent to 38 ounces.

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Answer:

The number of hours it takes the culture to reach 12,000 bacteria is 41 hours.

Step-by-step explanation:

To predict the number of hours it takes to culture a certain number of bacteria form a regression equation of number of hours (y) based on the number of bacteria (x) using the provided data.

The general form of the regression equation is:

\(y=a+bx\)

Compute the values of a and b as follows:

\(a=\frac{\sum Y\cdot \sum X^{2}-\sumX\sum XY}{n\cdot\sum X^{2}-(\sum X)^{2}}=\frac{15\cdot 32109075-12565\cdot39860}{5\cdot 32109075-(12565)^{2}}=-7.203\\\\b=\frac{n\cdot \sum XY-\sumX\sum Y}{n\cdot\sum X^{2}-(\sum X)^{2}}=\frac{5\cdot 39860-12565\cdot15}{5\cdot 32109075-(12565)^{2}}=0.004\)

*Use the Excel data sheet attached.  

The regression equation of number of hours based on the number of bacteria is:

\(y=-7.203+0.004x\)

Compute the number of hours it takes the culture to reach 12,000 bacteria as follows:

 \(y=-7.203+0.004x\)

   \(=-7.203+(0.004\times12000)\\=-7.203+48\\=40.797\\\approx 41\)

Thus, the number of hours it takes the culture to reach 12,000 bacteria is 41 hours.

Answer:

9/41

Step-by-step explanation:

Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side)  which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.

Answer:

x< -12

Step-by-step explanation:

-1/2x>6
x-2.   x-2

x>-12

Since we multiply by we negative we flip the sign

x< -12

Hopes this helps

Figure 1 Area = 4 x 15 = 60 cm²

Figure 2 Area = 3 x 18 = 54 cm²

Figure 3 Area = 6 x 11 = 66 cm²

Figure 4 Area = 12 x 5 = 60 cm²

Answer:

Therefore area of figure 1 and 4 are equal

The missing values are 60, 100 and 40 if the Median and Mode of the  wage distribution are known to be $33.5 and $34 respectively

Wages (in Rs)_freq____        CF

0-10________4___________4

10-20_______16________20

20-30_______x________20+x

30-40______y_________20+x+y

40-50______z________20+x+y+z

50-60______6_______26+x+y+z

60-70______4______30+x+y+z

Since total 230

So, 30+x+y+z=230

x+y+z=200

Mode =34

Median = 33.5

By solving the equations we get x=60, y=100 and z=40

Hence, the missing values are 60, 100 and 40

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Okay, here we have this:

Considering the provided graph, we are going to find the requested measure, so we obtain the following:

Let us remember that a rectangle besides having the properties of a parallelogram also stands out because it has congruent diagonals. So considering this we have:

BD=EC

EF=BF

EF=22

Finally we obtain that EF is equal to 22 units.

Answer: y+1 = 5(x-1)

Step-by-step explanation:

The linear functions in this problem are given as follows:

1. y = -x/2 - 4.

2. y = -3x + 7.

Considering the options in these problems, the linear functions are defined in slope-intercept format, given as follows:

y = mx + b.

The coefficients of the function are given as follows:

The slope-intercept definition of the two equations presented in this problem are given as follows:

When two linear functions are parallel, they have the same slope, hence the two functions will be given as follows:

For item 1, when x = 2, y = -5, hence the intercept b is calculated as follows:

-5 = -0.5(2) + b

b = -5 + 1

b = -4.

For item 2, when x = 1, y = 4, hence the intercept b is calculated as follows:

4 = -3(1) + b

b = 7.

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Answer:111

Step-by-step explanation:

1111

Answer:

y - 20 = 5( x - 70)

Step-by-step explanation:

There are many ways that you can write this.  I am use the point that is red on the graph.  It is point (70,20)  

The slope is 5.  I went up 50 from the red top and 10 to the right to get back on the line again.  50/10 = 5.