Determine which consecutive integers the real zeros of f(x) = x^3 - 2 are located

the answer is A) between 1&2

I believe your answer should be 3.

Really?

5 down to 4 down to 3.

I think 3 is the best answer.

Answer:

(x - 2)² + (y +8)² = 49

Step-by-step explanation:

Points to remember

Equation of a circle passing through the point (x₁, y₁) and radius r is given by

(x - x₁)² + (y - y₁)² = r ²

To find the radius

It is given that, center of circle = (-5, -8) and passes through the point (2 -8)

By using distance formula,

r = √[(2 --5)² + (-8 --8)²]

 = √7²

r = 7

To find the equation of the circle

Here (x₁, y₁) = (2, -8)

Equation of circle is,

(x - x₁)² + (y - y₁)² = r ²

(x - 2)² + (y - (-8))² = 7²

(x - 2)² + (y +8)² = 49

Answer:

The equation of circle is [tex](x+5)^2+(y+8)^2=49[/tex].

Step-by-step explanation:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]              .... (1)

where, (h,k) is the center of the circle and r is the radius.

It is given that the center of the circle is (-5,-8). it means h=-5 and k=-8.

The circle passes through the point (2,-8). So, the radius of the circle is the distance between point (-5,-8) and (2,-8).

[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]r=\sqrt{(2-(-5))^2+(-8-(-8))^2}[/tex]

[tex]r=\sqrt{7^2+0}[/tex]

[tex]r=7[/tex]

Substitute h=-5, k=8 and r=7 in equation (1), to find the equation of circle.

[tex](x-(-5))^2+(y-(08))^2=(7)^2[/tex]

[tex](x+5)^2+(y+8)^2=49[/tex]

Therefore the equation of circle is [tex](x+5)^2+(y+8)^2=49[/tex].

Answer:

A

Step-by-step explanation:

10-6 X 10-1 = 10-7

5.7*46.2=263.34

263.34=2.6334 x 10^2

10^2 x 10^-7 = 10^-5

so

=2.6334 x 10-5

The standard form of the product of the mathematical expression (46.2×10⁻¹)(5.7×10⁻⁶) is 2.6334×10⁻⁵ option (A) is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have a mathematical expression:

= (46.2×10⁻¹)(5.7×10⁻⁶)

= 46.2×5.7×10⁻⁷

= 263.34×10⁻⁷

= 2.6334×10⁻⁵

Thus, the standard form of the product of the mathematical expression (46.2×10⁻¹)(5.7×10⁻⁶) is 2.6334×10⁻⁵ option (A) is correct.

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For this case we have the following functions:

[tex]f (x) = x + 7\\g (x) = x-4[/tex]

We must find the product of the functions:

[tex]f (x) * g (x) = (x + 7) (x-4)[/tex]

We apply distributive property:

[tex]f (x) * g (x) = x ^ 2-4x + 7x-28\\f (x) * g (x) = x ^ 2 + 3x-28[/tex]

Finally, the product of the functions is:

[tex]x ^ 2 + 3x-28[/tex]

Answer:

[tex]x ^ 2 + 3x-28[/tex]

Step-by-step explanation:

log₅ 9 = x

5^(log₅ 9) = 5^x

9 = 5^x

1.

[tex]3x-6=36\\3x=42\\x=14[/tex]

2.

[tex]8y-5=99\\8y=104\\y=13[/tex]

bearing in mind a leap year has 366 days, with February 29th.

[tex]\bf \begin{array}{ccll} ounces&days\\ \cline{1-2} 16&1\\ x&366 \end{array}\implies \cfrac{16}{x}=\cfrac{1}{366}\implies 5856=x[/tex]

that many ounces, how many gallons(US) is that?

well, there are 128 oz in 1 gallon(US), so in 5856 oz there are 5856 ÷ 128 = 45.75 gallons(US).

58.56 gallons of milk,a person will drink in a leap year.

What is leap year?

A Leap Year has 366 days (the extra day is the 29th of February).

How to know if it is a Leap Year:

Leap Years are any year that can be exactly divided by 4 (such as 2016, 2020, 2024, etc)

except if it can be exactly divided by 400, then it is (such as 2000, 2400)

How many galllons will a person drink in a leap year?

We have given,

Average person drinks 16 ounces of milk in 1 day.

We have to find milk consume by average person in 366 days in gallons.

We know, 1 ounce (oz)=0.01 gallons

So, 16 ounce = 16×0.01 gallons

=0.16 gallons

We can say milk consume in one day = 0.16 gallons

Therefore,milk consume in 366 days(in gallons)=366×milk consume in 1 day.

=366×0.16

=58.56 gallons.

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Answer:

  13/20 = 0.65 mile

Step-by-step explanation:

Finding the difference of two fractions is usually done by first expressing each of them using a common denominator. Here, both 4 and 10 are factors of 20, so 20 is a suitable common denominator.

  9/10 - 1/4 = 18/20 - 5/20 = (18 -5)/20 = 13/20

This can be expressed as a decimal:

  13/20 = (13·5)/(20·5) = 65/100 = 0.65

9/10 of a mile is 13/20 of a mile larger than 1/4 of a mile. In decimal, that is 0.65 miles larger.

Answer:

Step-by-step explanation:

The answer is b. left skewed

Left-skewed describes the shape of the temperature data.

A distribution exists skewed if one of its tails is longer than the other. The first distribution shown includes a positive skew. This suggests that it has a long tail in the positive direction. The distribution below it has a negative skew since it includes a long tail in the negative direction.

In this distribution, the majority of the data is to the right of the graph.  The "tail" of the distribution is to the left.  This defines a left-skewed distribution.

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Answer:

1800

Step-by-step explanation:

The original population occurs when time (i.e x) is zero.

hence we substitute x = 0 into the function

Original population, f(0),

= 1800 [tex](0.7)^{0}[/tex] .......... recall anything raised to power of zero is 1

= 1800 (1)

= 1800

The original population of the penguins on island be, 1800.

The correct option is (c)

A function is defined as a relation between a set of inputs having one output each. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given: f(x)=18000[tex](0.7)^{x}[/tex]

The original population will occurs when time is zero.

So, put x = 0 into the function f(x),

we have,

f(0)= 1800[tex](0.7)^{0}[/tex]

f(0)= 1800*1

f(0)=1800

Hence, the original population of the penguins on island is 1800.

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Step-by-step answer:

There are two squares, the inner one of which is a garden, surrounded by a path 1 foot wide.

The outer square represents the periphery of the path, as shown in the attached image.

One bag of gravel covers 8 square-feet.  Need the number of bags required to cover the path.

Solution:

We first need to find the total area of the path by subtracting the area of garden from the overall area, namely the outer square.

Area of path = 12^2 - 10^2 = 144-100 = 44 sq. ft.

Number of bags required

= area (sq.ft) / area each bag covers

= 44 sq.ft / 8 (sq.ft / bag)

= 5.5 bags

Answer: 6 bags need to be purchased.

Answer:

Part 1) The radius of the circle is [tex]r=17\ units[/tex]

Part 2) The point (-15,14) and the point (-15,-16) lies on the circle

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

To find the radius of the circle calculate the distance between the center of the circle and the point (8,7)

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

[tex](-7,-1)\\(8,7)[/tex]  

substitute

[tex]r=\sqrt{(7+1)^{2}+(8+7)^{2}}[/tex]

[tex]r=\sqrt{(8)^{2}+(15)^{2}}[/tex]

[tex]r=\sqrt{289}[/tex]

[tex]r=17\ units[/tex]

step 2

Find the equation of the circle

The equation of the circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center

r is the radius

substitute

[tex](x+7)^{2}+(y+1)^{2}=17^{2}[/tex]

[tex](x+7)^{2}+(y+1)^{2}=289[/tex]

step 3

Find the y-coordinate of the point (-15.y)

substitute the x-coordinate in the equation of the circle and solve for y

[tex](-15+7)^{2}+(y+1)^{2}=289[/tex]

[tex](-8)^{2}+(y+1)^{2}=289[/tex]

[tex]64+(y+1)^{2}=289[/tex]

[tex](y+1)^{2}=289-64[/tex]

[tex](y+1)^{2}=225[/tex]

square root both sides

[tex](y+1)=(+/-)15[/tex]

[tex]y=-1(+/-)15[/tex]

[tex]y1=-1(+)15=14[/tex]

[tex]y2=-1(-)15=-16[/tex]

therefore

The point (-15,14) and the point (-15,-16) lies on the circle

see the attached figure to better understand the problem

Answer:

plato users the answer is 17 units and (-15,14)

Step-by-step explanation:

Answer:

if the distance in the map is 3.5 inches the actual distance is 87.5 miles

Answer:

Parallel

Step-by-step explanation:

Note for any function h(x) = mx + b

m = slope of the function

in this case, both functions have the same slope of [tex]\frac{3}{5}[/tex]

Hence the functions must parallel

Answer:

It's 90 degrees.

Step-by-step explanation:

You have to use your instincts here, the angle is not acute, so it can't be 60. The angle is not obtuse either, so it can't be 120 or 180, leaving 90. Also the degree of the arc of a circle is usually 2x the measure of the corresponding angle.

Answer:

90 degrees

Step-by-step explanation:

I say the third circle from the top down. The central angle is the measure of minor arc AB.

The central angle here is 60 degrees, shown by the third circle down from the top. This is the right answer.

The circle that shows chord AB to measure 60 degrees is Option(C).

A chord of a circle divides the circle into two regions, which are called the segments of the circle. The minor chord is the shorter arc connecting two endpoints on a circle . The measure of a minor chord is always less than 180° .

In the four Options given alongside diagram, Option(C) represents a minor chord with its central angle subtended by the minor segment as 60°.

Thus AB is the minor sector of the circle and the angle measures 60° with that chord itself. The other three options do not define the minor chord or segment AB therefore not measuring its central angle.

Therefore, the circle that shows chord AB to measure 60 degrees is Option(C).

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Answer:

  hyperbola

Step-by-step explanation:

If the sum is constant, the figure is an ellipse.

If the difference is constant, you get a hyperbola.

If one length is constant, you get a circle.

If the length to a point is the same as the length to a line, you get a parabola.

Answer:

There are four type of conic generated when a double napped cone is cut by a plane

1.Circle

2.Parabola

3.Ellipse

4.Hyperbola

Among these four, Hyperbola is the conic , ,all points in a plane where the difference between the lengths of segments x and y remains constant.

A point on Semi major Axis=(a,0),lying on the Hyperbola.

A point on Semi Minor axis =(0,b),not lying on the Hyperbola.

Take a point D lying on the hyperbola,and two points M and N not lying on the hyperbola.

DM-DN=2a(Length of major axis)

Answer:

The probability that the students chosen are not both girls is 62/95 ⇒ (c)

Step-by-step explanation:

* Lets explain how to find the probability of an event  

- The probability of an Event = Number of favorable outcomes ÷ Total

  number of possible outcomes

- P(A) = n(E) ÷ n(S) , where

# P(A) means finding the probability of an event A  

# n(E) means the number of favorable outcomes of an event

# n(S) means set of all possible outcomes of an event

- Probability of event not happened = 1 - P(A)

- P(A and B) = P(A) . P(B)

* Lets solve the problem

- There is a group of students

- There are 8 boys and 12 girls in the group

∴ There are 8 + 12 = 20 students in the group

- The students are sent to represent the school in a parade

- Two students are chosen at random

∴ P(S) = 20

- The students that chosen are not both girls

∴ The probability of not girls = 1 - P(girls)

∵ The were 20 students in the group

∵ The number of girls in the group was 12

∴ The probability of chosen a first girl = 12/20

∵ One girl was chosen, then the number of girls for the second

   choice is less by 1 and the total also less by 1

∴ The were 19 students in the group

∵ The number of girls in the group was 11

∴ The probability of chosen a second girl = 11/19

- The probability of both girls is P(1st girle) . P(2nd girl)

∴ The probability of both girls = (12/20) × (11/19) = 33/95

- To find the probability of both not girls is 1 - P(both girls)

∴ P(not both girls) = 1 - (33/95) = 62/95

* The probability that the students chosen are not both girls is 62/95

Answer:

  x² +81 = x² +20x +100

Step-by-step explanation:

Square both sides of the original equation:

  (√(x² +81))² = (x +10)²

  x² +81 = x² +20x +100

Answer:

[tex]x =18.0[/tex]

Step-by-step explanation:

To solve this problem use the Law of cosine.

The law of cosine says that:

[tex]c^2 = a^2 + b^2 -2abcos(C)[/tex]

In this case we have that:

[tex]c = x\\\\a=30\\\\b=16\\\\C=30\°[/tex]

Therefore

[tex]x^2 = 30^2 + 16^2 -2(30)(16)cos(30\°)[/tex]

[tex]x = \sqrt{30^2 + 16^2 -2(30)(16)cos(30\°)}[/tex]

[tex]x = \sqrt{1156 -831.38}[/tex]

[tex]x = \sqrt{324.62}[/tex]

[tex]x =18.0[/tex]

Answer: A. The molten mixture of rock-forming substances, gases, and water from the mantle

Magma is a mass of molten rock that is found in the deepest layers of the Earth at high temperature and pressure, and that can flow out through a volcano.

The composition of this mass is a mixture of liquids, volatile and solids that when they reach the surface in an eruption becomes lava, which when cooled crystallizes and gives rise to the formation of igneous rocks.

Final answer:

Explanation on solving the equation p = 55 - 0.5w to find Rocco's weight after w weeks.

Explanation:

Solving the Equation:

Since Rocco lost half a pound per week, the equation would be: p = 55 - 0.5w, where p is Rocco's weight in pounds and w is the number of weeks.

Substitute the value for the first week: p = 55 - 0.5(1) = 55 - 0.5 = 54.5 pounds.

Therefore, Rocco's weight after w weeks would be p = 55 - 0.5w.

Answer:

The equation of the scenario is

✔ p = 55 – 0.5w

.

The values of p must be

✔ any real number 45 to 55

Step-by-step explanation:

Answer:

  Cassie is traveling 63.6 mph

Step-by-step explanation:

If the three numbers, left to right, are A, B, C, then the tire radius in millimeters is ...

  A×B/100 + 12.7×C

For the factory tires, the tire radius is ...

  240·75/100 + 12.7·16 = 180 +203.2 = 383.2 . . . . millimeters

For the replacement tires, the tire radius is ...

  290·70/100 +203.2 = 406.2 . . . . millimeters

The speedometer is calibrated based on the number of revolutions the tire makes in a given time period. If the truck goes farther for each revolution, its speed is higher by the same proportion.

If the speedometer on the truck with these replacement tires reads 60 mph, the actual speed is ...

  (406.2/383.2)×60 mph = 63.6 mph

_____

Comment on the problem statement

Caroline's truck has the replacement tires. If Cassie's speedometer reads 60 mph, we have no reason to assume Cassie is traveling at any speed other than 60 mph.

Answer:

1, 3, 6, 7, 9...

1, 4, 8, 7, 11...

Step-by-step explanation:

(1, 3, 6, 7, 9...)

This one is the sequence because it follows a specific pattern, which is 2n-1, or (2 x figure number) - 1. 1x2-1=1. 2x2-1=3. 3x2-1=7. And so on.

(1, 4, 8, 7, 11...)

This one, no matter how you look at it, has no pattern. Its not a proper sequence of numbers.

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Number of sides of die = 6

Number of sides with even numbers = 3

P( rolling an even number 1 time) = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

P(rolling even number 3 times) = [tex]\frac{1}{2}[/tex] x [tex]\frac{1}{2}[/tex]  x [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{8}[/tex]

Answer:

  d.  12 units, 14 units, 10 units

Step-by-step explanation:

The side lengths differ by 2 units from one to the next larger one:

  (2t+2) - (2t) = 2

  (2t+4) - (2t+2) = 2

So, you're looking for answer numbers that can make a sequence with differences of 2, and that add to 36. Only the last choice matches that description.

_____

You can solve this "directly" by adding up the side lengths and setting that result to the perimeter length.

  (2t+2) + (2t+4) + (2t) = 36

  6t +6 = 36 . . . . . collect terms

  6t = 30 . . . . . . . . subtract 6

   t = 30/6 = 5 . . . . divide by 6

The shortest side is 2t, so is 2·5 = 10 units. Only the last answer choice matches this.

  Side lengths are 12 units, 14 units, 10 units.

Answer:

  80 cars will maximize revenue

Step-by-step explanation:

The revenue per square meter for parked cars is ...

  $2.00/5 = $0.40

The revenue per square meter for buses is ...

  $6.00/32 = $0.1875

Thus the available space should be used to park the maximum number of cars.

80 cars should be in the lot to maximize income.

To maximize income, the parking lot should have 69 cars and 11 buses parked, resulting in a total income of $282.

To maximize income, we need to maximize the revenue generated from parking fees. Let's denote the number of cars as x and the number of buses as y.

Given:

- Area of parking lot: 805 square meters

- Space required for a car: 5 square meters

- Space required for a bus: 32 square meters

- Maximum number of vehicles: 80

We have the following constraints:

1. [tex]\( 5x + 32y \leq 805 \)[/tex]  (total area constraint)

2. [tex]\( x + y \leq 80 \)[/tex] (maximum number of vehicles constraint)

The objective function to maximize income is:

Income [tex]\( I = 2x + 6y \)[/tex]

To solve this problem, we'll analyze the feasible region defined by these constraints and find the combination of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that maximizes income.

By solving these constraints, we find that the maximum income occurs at the vertex where [tex]\( x = 69 \) and \( y = 11 \)[/tex].

Therefore, to maximize income, there should be 69 cars and 11 buses parked in the lot.

Answer:

Step-by-step explanation:

[tex]3.75\times 10^8=3.75\times 100,000,000=375,000,000.[/tex]

The decimal point is moved 8 places to the right. The number is "very large" in relation to most folks' personal experience with counting things, but is "very small" in relation to quantities and sizes in the known universe.

Answer:

This will convert to a very large number.

This is the same as the product of 3.75 and 100,000,000.

Step-by-step explanation:

scientific notation.

[tex]3.75 \cdot 10^8[/tex]

To get the standard form we multiply the decimal number by 10^8

When we multiply by 10^8, move the decimal 8 places the right

This will convert to a very large number

[tex]10^8 = 100,000,000[/tex]

[tex]3.75 \cdot 100000000[/tex]

This is the same as the product of 3.75 and 100,000,000.

Answer:

  Your choice is correct.

Step-by-step explanation:

magnitude = √(6² +5²) = √61 ≈ 7.81

direction = arctan(5/6) ≈ 39.81°

The polar coordinates are (7.81, 39.81°).

Answer:

  A.  T = 20°C - (2.8°C/h × 4h)

Step-by-step explanation:

The rate of change of temperature (-2.8°C/h) is multiplied by time (4h) to get the change in temperature (-11.2°C). That change is added to the initial temperature (20°C) to find the temperature after 4 hours.

Only equation A properly expresses this calculation.

In choice B, the rate of change is (wrongly) shown as +2.8°C/h. In the other choices, the combinations of units are nonsense. (What is a °C·h?)