what is x3 - x2 - x + 1 = 0

Answer:

The probability of rolling a sum greater than 1 when rolling two fair numbered cube is 1 or 36/36.

Step-by-step explanation:

There is no 1 as a sum when rolling two fair numbered cubes, so all the sums will be greater than 1.

Answer:

D. 31°C

Step-by-step explanation:

I hope it helps you

Answer:

x=36° y=66°

Step-by-step explanation:

3x+6+x+30 = 180° (Supplementary angles)

4x+36 = 180

4x = 180 - 36

4x = 144

x = 36

y+3x+6 = 180° (Supplementary angles)

y+3*36+6 = 180 (plug in the value of x)

y+108+6 = 180

y= 180-108-6

y = 66

Answer:

★ For example, Graphing is one of the simplest ways to solve a system of linear equations, all you have to do is graph each equation as a line and find the points where the lines two intersect.

Step-by-step explanation:

Hope you have a great day :)

Answer:

5p + 4c = 20

Step-by-step explanation:

lets have p stand for the number of popcorn we buy and c stand for the number of candy we buy

you can only spend $20, so we know we need to set our equation equal to $20

now we take the price of of popcorn and multiply it p, the number of popcorn we buy. and we can do the same thing with candy.

so we end up with 5p + 4c = 20

The function A = 6xy subject to x + 2y = 24. The maximum value is 432 and it occurs when x = 12 and y = 6.

To maximize the value of the function A = 6xy subject to x + 2y = 24, follow these steps:

1. Express one variable in terms of the other using the constraint equation. We can solve for y in terms of x:

x + 2y = 24
2y = 24 - x
y = (24 - x) / 2

2. Substitute the expression for y into the function A:

A = 6x((24 - x) / 2)

3. Simplify the expression:

A = 3x(24 - x)

4. Find the critical points by taking the derivative of A with respect to x and setting it equal to 0:

dA/dx = 3(24 - 2x) = 0

5. Solve for x:

24 - 2x = 0
2x = 24
x = 12

6. Find the corresponding value of y using the expression for y:

y = (24 - 12) / 2
y = 6

The maximum value occurs when x = 12 and y = 6. Now, calculate the maximum value of the function A:

A = 6(12)(6)
A = 432

The maximum value is 432, and it occurs when x = 12 and y = 6.

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The  interval notation  of x^(2 )-2x-35>0  is (-∞,-5)∪(7,∞).

To solve the quadratic inequality x^(2)-2x-35>0, we first need to find the roots of the quadratic equation x^(2)-2x-35=0. We can do this by factoring the equation:

(x-7)(x+5)=0

The roots of the equation are x=7 and x=-5. Now, we can use these roots to determine the intervals where the inequality is true. We can do this by testing values in each interval:

- For x<-5, let's test x=-6: (-6)^(2)-2(-6)-35=1>0, so the inequality is true in this interval.
- For -57, let's test x=8: (8)^(2)-2(8)-35=29>0, so the inequality is true in this interval.

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A scientific calculator is typically used for pre-calculus.

This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.

It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.

Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.

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Answer:

6

Step-by-step explanation:

Answer:

Explanation

Step-by-step explanation:

First we convert the diameter to radius:

6/2=3

After that, we use the Circumference formula, 2\(\pi\)r to find how far it will reach:

\(C= 2\pi (3)\)

\(C=6\pi\) or, 18.84m

Hope this helped, have a good day!

The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:

log₂(x - 1) = x³ - 4x

Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.

For the point (2, 0):

log₂(2 - 1) = 2³ - 4(2)

log₂(1) = 8 - 8

0 = 0

The equation holds true for the point (2, 0), so (2, 0) is one solution.

For the point (1.1187, -3.075):

log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)

log₂(0.1187) = 1.4013 - 4.4748

-3.075 = -3.0735 (approx.)

The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.

Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

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Answer:

a). Regular Pentagon

b). 540°

c). 108°

d). 72°

Step-by-step explanation:

According To the Question

a). the name of the center polygon is Regular Pentagon

b). the sum of the interior angles of the Regular Pentagon is 540°

c). the measure of each interior angle of the Regular Pentagon is 108°

d). the measure of the Each exterior angle of the Regular pentagon is 72° & Sum of All Exterior Angle Of Regular Pentagon is 360°

Answer:

Anything with 2 Yellow and more than 3.5 Blue

Step-by-step explanation:

The answer is pretty obvious, but I will give a more mathimatical explanation that is easy to understand.  The ratio is saying that for every 2 units of yellow, there are 3.5 units of blue.  You can find ratios that are the same but use more/ less  amounts.  So if you use 4 units of yellow and 7 of blue it is the same ratio.  

If you multiply both parts of the ratio (or divide) by the same number you will always get the same ratio.  So if you want something more blue (or yellow) you just have to keep one the same while increasing the one you want to have more effect.  

Answer:

7182

Step-by-step explanation:

All you shoud do is to replace x by 9

● y = 10 * 9^3 -12*9

● y = 7182

Answer:

175×12+100×16=3700

this

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

The BOD5 for a sample of water from a stream with initial DO of 9.7 mg/L and final DO of 4.3 mg/L after incubation for 5 days at 20°C is 5.4 mg/L.

Biochemical Oxygen Demand (BOD5) is a parameter used to assess the amount of organic pollutants in water. It measures the oxygen required by aerobic bacteria to break down the organic matter present in the water sample.

BOD5 is measured by incubating the water sample in a BOD bottle under controlled conditions for five days, during which the DO (dissolved oxygen) is measured.

The formula to calculate BOD5 is:

BOD5 = DOi - DOf

Where,DOi = Initial DO (dissolved oxygen) of the sample before incubation

DOf = DO of the sample after 5 days of incubation at 20°C

Steps to calculate BOD5:

Subtract the DOf (final DO) from the DOi (initial DO) of the water sample to obtain the amount of oxygen consumed by the bacteria in five days.

This value is the BOD5 for that water sample.

BOD5 = DOi - DOf

BOD5 = 9.7 mg/L - 4.3 mg/L

BOD5 = 5.4 mg/L

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The approximate measure of angle z in triangle XYZ is 78.5°.

To determine the measure of angle z, we can use the properties of triangles. One way to find this angle is by using the slope formula to calculate the slopes of the lines formed by the given points. Then, we can use the inverse tangent function to find the angle.

First, let's calculate the slopes of the lines XY and YZ using the formula:

m = (y2 - y1) / (x2 - x1)

For line XY:

mXY = (1 - (-1)) / (-2 - (-1)) = 2 / (-1) = -2

For line YZ:

mYZ = (2 - 1) / (1 - (-2)) = 1 / 3

Next, we can calculate the angle using the inverse tangent function:

angle z = arctan(mYZ - mXY) = arctan(1/3 - (-2)) = arctan(1/3 + 2) = arctan(7/3)

Using a calculator, we find that arctan(7/3) is approximately 78.5°.

Therefore, the approximate measure of angle z in triangle XYZ is 78.5°.

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Answer:

3. < ACB=<DCE

Step-by-step explanation:

3. < ACB=<DCE, because both are vertical angles which are equal

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The value of x in the trapezium is 60 degrees.

A trapezium is a quadrilateral . The sum of angles in the trapezium is 360 degrees. The legs of the trapezium ABCD are congruent.

The length AB and CD are parallel to each other.

Let's find the angle x as follows:

Therefore, using trigonometric ratios,

cos x = adjacent / hypotenuse

Where

adjacent side = 3 m

hypotenuse side = 6 m

Hence,

cos x = 3 / 6

cos x = 1 / 2

x = cos ⁻¹ 0.5

x = 60 degrees

Therefore,

x = 60 degrees.

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A battery is a nice illustration. Atoms have had their electrons chemically removed in batteries. Because the positive ions and electrons are stored at the opposing ends of the battery, there is a potential difference between the two ends.

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Answer:

B and E

Step-by-step explanation:

im pretty sure what you have is correct

The correct histograms that are approximately symmetric and bell-shaped are - histograms B, C, and E because they are symmetric and bell-shaped.

A histogram is a convenient form or graphical representation of the frequency distribution of numerical data by means of rectangles. These histograms are found in different shapes and symmetries.

Bell-shaped curve:

Thus, the correct answer is - Histograms B, C, and E.

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Answer:

The time it takes Ms. Croft to reach the cruise ship by speedboat = 6.11 hours

The time it takes Ms. Croft to reach the cruise ship by helicopter = 6.25 hours

since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

Step-by-step explanation:

The given parameters are;

The elapsed time by which Ms. Croft missed the boat = 5 hours

The speed of the cruise ship = 528 mi/day

The speed of the speedboat = 100 miles in 2.5 hours

The speed of the helicopter = 90 mph

The time it would take Ms. Croft to arrive at the harbor = 3.5 hours

Therefore, we have;

The cruise ship's speed = 528 miles per 24 hours = 528/24 mph = 22 mph

The location of the cruise after the first 5 hours = 5 × 22 = 110 miles

The speed of the speedboat = 100 miles per 2.5 hours = 100/2.5 = 40 mph

By traveling with a speed boat

The time at which Ms. Croft will intercept the cruise ship is given by the following relation;

40 mph × t = 22 mph × t + 110 miles

Which gives;

40 mph × t - 22 mph × t = 110 miles

18 mph = 110 miles

t = 110 miles/(18 mph) = 55/9 hours ≈ 6.11 hours

By taking the helicopter, we have;

Upon arrival at the harbor, after 3.5 hours, we find

90 mph × t = 22 mph × t + 22 mph × 3.5 hours + 110 miles

90 mph × t - 22 mph × t = 22 mph × 3.5 hours + 110 miles

68 mph × t = 77 miles + 110 miles = 187 miles

t = 187 miles/(68 mph) = 11/4 hours = 2.75 hours

The total time it takes Ms. Croft to reach the cruise ship by taking the helicopter = 3.5 + 2.75 = 6.25 hours

Therefore, since it takes less time for Ms. Croft to reach the cruise ship by taking the speedboat, her best choice to retrieve the artifact is to take the speedboat.

The height at time t (in seconds) of a mass, oscillating at the end of a spring, is s(t) = 300 + 16 sin t cm. We have to find the velocity and acceleration at t = π/3 s.

Let's first find the velocity of the mass. The velocity of the mass is given by the derivative of the position of the mass with respect to time.t = π/3 s
s(t) = 300 + 16 sin t cm
Differentiating both sides of the above equation with respect to time
v(t) = s'(t) = 16 cos t cm/s

Now, let's substitute t = π/3 in the above equation,
v(π/3) = 16 cos (π/3) cm/s
v(π/3) = -8√3 cm/s

Now, let's find the acceleration of the mass. The acceleration of the mass is given by the derivative of the velocity of the mass with respect to time.t = π/3 s
v(t) = 16 cos t cm/s
Differentiating both sides of the above equation with respect to time
a(t) = v'(t) = -16 sin t cm/s²
Now, let's substitute t = π/3 in the above equation,
a(π/3) = -16 sin (π/3) cm/s²
a(π/3) = -8 cm/s²
Given, s(t) = 300 + 16 sin t cm, the height of the mass oscillating at the end of a spring. We need to find the velocity and acceleration of the mass at t = π/3 s.
Using the above concept, we can find the velocity and acceleration of the mass. Therefore, the velocity of the mass at t = π/3 s is v(π/3) = -8√3 cm/s, and the acceleration of the mass at t = π/3 s is a(π/3) = -8 cm/s².
At time t = π/3 s, the velocity of the mass is -8√3 cm/s, and the acceleration of the mass is -8 cm/s².

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The statement that cannot be true about the plane is (A) the plane is parallel to the base of the pyramid.

If the plane is parallel to the base of the pyramid, the intersection would be a cross-section of the pyramid that is also parallel to the base. This cross-section would not be a triangle, and therefore, it cannot be the intersection of the plane and the pyramid.

On the other hand, options (B), (C), and (D) are all possible.

(B) If the plane is perpendicular to the base of the pyramid, the intersection would be a triangle that is also perpendicular to the base.

(C) If the plane passes through two of the faces and the base of the pyramid, the intersection would be a triangle that shares two sides with the pyramid.

(D) If the plane passes through two of the edges of the pyramid, the intersection would be a triangle that shares two vertices with the pyramid.

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Answer:

8x³ - 2x² - 51x - 45

Step-by-step explanation:

Given

(x - 3)(2x + 3)(4x + 5) ← expand second/third factors using FOIL

= (x - 3)(8x² + 22x + 15) ← distribute

= x(8x² + 22x + 15) - 3(8x² + 22x + 15) ← distribute parenthesis

= 8x³ + 22x² + 15x - 24x² - 66x - 45 ← collect like terms

= 8x³ - 2x² - 51x - 45

Answer:

8x^3-2x^2-51x-45

Step-by-step explanation:

(x − 3)(2x + 3)(4x + 5)

(2x^2+3x-6x-9)*(4x+5)

(2x^2-3x-9)*(4x+5)

= 8x^3-2x^2-51x-45

5x

Step-by-step explanation:

6 will be y-(35_7890 go to y-4758_32458(+58855533

Answer:

$ 187

Step-by-step explanation:

Assuming the credit card is for Kohl's,

You make a 45 dollar payment: your debt goes down by 45

You make a 97 dollar purchase: your debt goes up by 97

135-45+97

Your current debt is 187 dollars. Not a nice way to live if you ask me!

The meaning of the inequality statement which has the greater than symbol ">" is best described as "20.2  miles is greater than 17.6 miles"

In any equality expression, there are mostly two sides, the left hand side and the right hand side, and the expression is read from left to right.

So, whenever we have an expression to interpret, we read from the left, then state the sign which can be less than sign "<" or greater than sign ">"

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Answer:

$5,177.80 would be the remaining amount of money left in the saving account after 6 years assuming there were no deposits or withdraws.

Step-by-step explanation:

Assuming that no money was added or withdrawn, after 6 years there would be $6166.50 in the savings account.

Compound interest is the interest that is added to the principal sum and the accumulated interest so far.

The amount after adding compound interest can be found using the following formula:

A = P(1 + r/(100*k))^nk

Where:

We can find the compounded amount as follows:

A = $5000(1 + 0.035/12)^(6*12)

= $5000*1.233301

≈ $6166.50.

Therefore, we have found that after 6 years there would be $6166.50 in the savings account. The correct answer is option D.

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