For question 14, use Descartes' rule of signs to describe possible combinations of roots for the polynomial. 1h(x)=2x^3 +5x^2 - 31x - 15

Answer:

see below

Step-by-step explanation:

7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".

Answer:

  $28

Step-by-step explanation:

Each round trip will be double the price of a one-way trip, so will be ...

  2 × $3.50 = $7.00

Diego and his 3 friends will require a total of 4 round-trip tickets for a cost of ...

  4 × $7.00 = $28.00

The number of Cheetos you can buy in the supermarket is 7.

You have $16 and a coupon for a five dollar discount at a local

supermarket . One bag of hot Cheetos cost 3 dollars. Therefore, the

number  of bag of Cheetos you can buy can be calculated as follows:

Therefore, altogether he has 16 + 5(coupon discount)  = 21 dollars to spend

in the super market.

Therefore,

number of Cheetos worth 3 dollars one can buy = 21 / 3

number of Cheetos worth 3 dollars one can buy = 7

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Answer:

y = (-1/6)x+2

Step-by-step explanation:

The general form is y=mx + b where m is the slope and b is the y intercept.

Notice that the graph is sloping down - - - as x increases, y decreases, so make sure that that m (slope) ends up being negative.

We can see the y intercept is 2.

So y=mx+2

Now let's calc the slope.

We have a couple of choices. We can use the slope formula OR we can substitute. I'm going to do both.

Slope formula = (y2-y1)/(x2-x1). Pick any 2 points. (-6,3) and (6,1) are plotted with dots on your graph.

slope = (3-1)/(-6-6)

= 2/-12 = -1/6

so y = (-1/6)x+2

Here's another way to solve: use any point and solve for m.

y=mx+2

We'll use the point (6,1)

1 = m*6+2

1-2 = 6m

-1 = 6m

-1/6 = m

Same slope!

No matter how you solve, the equation is y = (-1/6)x+2.

Answer:

P(0) = 4C0 * 0.75⁰ * 0.25⁴ = 0.00390625 . = 0.004

P(1) = 4C1 * 0.75¹ * 0.25³ = 0.046875 . . . = 0.047

P(2) = 4C2 * 0.75² * 0.25² = 0.2109375 . . = 0.211

P(3) = 4C3 * 0.75³ * 0.25¹ = 0.421875 . . . = 0.422

P(4) = 4C4 * 0.75⁴ * 0.25⁰ = 0.31640625 . = 0.316

Check:

P(0) + P(1) + P(2) + P(3) + P(4) = 1 . . . ok

Step-by-step explanation:

Answer:

4.8%

Step-by-step explanation:

Given that :

Stock beta (B) = 1.5

Expected return = 16.35% = 0.1635

Maeket rate of return (Rm) = 12.5% = 0.125

Risk-free rate of return (Rf) =?

Using the relation :

Expected rate of return = risk free rate + Beta(market rate - Risk-free rate)

Expected rate of return = Rf + B(Rm - Rf)

Plugging our values :

0.1635 = Rf + 1.5(0.125 - Rf)

Open the bracket

0.1635 = Rf + 0.1875 - 1.5Rf

Collect like terms

0.1635 - 0.1875 = Rf - 1.5Rf

−0.024 = - 0.5Rf

Divide both sides by - 0.5

0.024 / 0.5 = Rf

Rf = 0.048

Rf = 0.048 * 100% = 4.8%

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

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Answer:

I'm sorry, I think you mistyped, but the answer for this is 53.130997227947970715758049612623

Have a nice day! :)

-Vana

TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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The value of x with the given condition is 10

From the question, we have the following parameters that can be used in our computation:

D(7,2), E(1, 9), F(4,8), and G(x, 1),

Also, we have

DE || FG

This means that the lines DE and FG are parallel lines and they have equal slope

The slope is then calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

So, we have

(9 - 2)/(1 - 7) = (1 - 8)/(x - 4)

Evaluate the difference

-7/6 = -7/(x - 4)

So. we have

x - 4 = 6

Evaluate

x = 10

Hence. the value of x is 10

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Answer:

42/11

Step-by-step explanation:

11/7 = 6/v

cross multiply:

11v = 6x7 = 42.

v = 42/11 ≈ 3.81

The smallest integer that Pearl wrote down is -12.Let's assume the smallest integer that Pearl wrote down is represented by the variable "x."

According to the given information, the sum of the seven consecutive integers is equal to $\frac{21}{4}$ times the largest integer.

The sum of consecutive integers can be expressed as the sum of an arithmetic series. The sum of an arithmetic series can be calculated using the formula:

Sum = (n/2)(first term + last term)

In this case, the first term is x and the last term is x + 6 (since there are seven consecutive integers). Therefore, the sum of the integers can be written as:

Sum = (7/2)(x + (x + 6))

Simplifying the equation:

(7/2)(2x + 6) = (21/4)(x + 6)

Multiplying both sides by 4 to eliminate the fractions:

14x + 42 = 21x + 126

Subtracting 14x from both sides:

42 = 7x + 126

Subtracting 126 from both sides:

-84 = 7x

Dividing both sides by 7:

-12 = x.

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The total area of the garden is 52 ft².

First we need to calculate the area of the current garden and the area of the rectangular piece that will be added, and then add them together.

The current garden has an area of 20 square feet.

To find the area of the rectangular piece that will be added, we can use the formula for the area of a rectangle:

Area = length x width

The length of the rectangle is the distance between the points (-18, 13) and (-14, 13), which is 4 units. The width of the rectangle is the distance between the points (-18, 13) and (-18, 5), which is 8 units.

Therefore, the area of the rectangular piece that will be added is:

Area = 4 x 8 = 32 square feet

The total area of the garden is the sum of the areas of the current garden and the rectangular piece that will be added:

Total area = 20 + 32 = 52 square feet

Therefore, the total area of the garden is 52 ft².

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Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

The measure of angle DEF is 37 degrees.

What is chord in circle

In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. More specifically, a chord of a circle is a line segment whose endpoints lie on the circle.

Every circle has infinitely many chords, but some of the most commonly discussed chords are the diameter (a chord that passes through the center of the circle), and the secant (a chord that intersects the circle at two distinct points).

Chords play an important role in geometry, as they can be used to determine various properties of circles, such as their radius, diameter, and area.

Since G is the center of the circle, the angle DGE is a central angle of the circle.

Therefore, the angle DGE is equal to twice the inscribed angle DEF that subtends the same arc DE.

Let x be the measure of angle DEF. Then, we have:

2x = 74

x = 37

Hence, the measure of angle DEF is 37 degrees.

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For this problem we want to find the equation of a line perpendicular to the line y=-2x-8 and passing through the point (4,4). We can see that the slope for the line given is m1=-2 and since we want a perpendicular line we need to satisfy the following:

And solving for m2 we got:

And then with the point given we can find the intercept:

And the equation for the line would be:

We are given:

f(x) = 3x + 8

g(x) = -x³

__________________________________________________________

The Concept:

We have to find the values of f(g(3)), which means that we have to apply the function g() on 3 and apply the function f() on the value we get.

Finding f(g(3)):

Finding g(3):

g(x) = -x³

g(3) = -(3)³

g(3) = -27

Finding f(g(3)):

f(x) = 3x + 8

f(g(3)) = 3(g(3)) + 8

f(g(3)) = 3(-27) + 8

f(g(3)) = -81 + 8

f(g(3)) = -73

Hence, f(g(3)) = -73

Answer:

Step-by-step explanation:

\((-\frac{1}{3} \sqrt{\frac{7}{2} } )^2+(\frac{1}{3} \sqrt{\frac{13}{2} } )^2\\=\frac{1}{9} (\frac{7}{2} +\frac{13}{2} )\\=\frac{1}{9} (\frac{7+13}{2} )\\=\frac{1}{9} \times10\\=\frac{10}{9} \neq 1\)

not a unit vector.

b.

\((\frac{1}{\sqrt{3} } )^2+(-\sqrt{\frac{2}{3} } )^2\\=\frac{1}{3} +\frac{2}{3} \\=\frac{1+2}{3} \\=\frac{3}{3} \\=1\)

it is a unit vector.

c.

\((\frac{1}{2} \sqrt{\frac{5}{3} } )^2+(-\frac{1}{2} \sqrt{\frac{7}{3} } )^2\\=\frac{1}{4} (\frac{5}{3} +\frac{7}{3} )\\=\frac{1}{4} (\frac{5+7}{3} )\\=\frac{1}{4} (\frac{12}{3} )\\=\frac{1}{4} (4)\\=1\)

it is a unit vector.

d.

\((\frac{3}{\sqrt{7} } )^2+(-\frac{2}{\sqrt{7} } )^2\\=\frac{9}{7} +\frac{4}{7} \\=\frac{9+4}{7} \\=\frac{13}{7} \neq 1\)

it is not a unit vector.

Answer: 32

Step-by-step explanation:

a=4×8=32

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

Step-by-step explanation:

I think it's the loan balances decreases $500 per month because every month it starts decreasing down by 500

Answer:

Answer is B

Step-by-step explanation:

The amount that would be in the account when Alana is 21  is $2890

We have to know the formula for simple interest.

This is expressed as;

S.I = PRT/100

Given that the parameters of the formula are enumerated as;

From the information given, substitute the values, we have;

SI = 1000 × 9 × 21/100

Multiply the values,

Then, divide by the denominator, we have;

SI = $1890

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Answer:

The answer is B. 105 miles

Step-by-step explanation:

I just used a calculator and put in 30 times a random number until I got 63. So, 30 times 2.1 is 63. Then, I multiplied 50 times 2.1 to get 105 as the answer.

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Speed is measured as the ratio between distance and time.

The distance traveled for 50 minutes with a speed of 63 miles in 30 minutes is 105 miles.

Speed is measured as the ratio between distance and time.

Its SI unit is m/s.

We have,

Car speed = 63 miles in 30 minutes.

We need to find the distance traveled in 50 minutes with a speed of 63 miles per 30 minutes.

Speed is given by:

Speed = Distance / Time

Distance = Speed x Time

Distance = 63 miles / 30 minutes x 50 minutes

Distance = (63 x 50) / 30

Distance = 21 x 5 = 105 miles.

Thus the distance traveled for 50 minutes with a speed of 63 miles in 30 minutes is 105 miles.

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When a distribution has three or more peaks then it is said to be a multimodal distribution .

In histograms, there are often three types of distributions which are classified according to the number of peaks that they have . A unimodal distribution would be a histogram that has a single peak in its distribution .

Then there are binomial distributions which boast of having two peaks , Then finally, there is the multimodal distribution which is for all distributions with either three peaks, or more than that .

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The equation of line in standard form is  y = -146x + 69.

A line equation is an algebraic way of representing a set of points that together form a line in a coordinate system. The various points that together form a line of axes can be represented as a set of (x,y) variables and form an algebraic equation, also called the line equation. You can use the straight line equation to determine if a given point lies on a straight line.

Each row of equations is a linear equation of degree 1. Read the entire article to learn about the different forms of linear equations and how to determine them. A line segment can be defined as a connection between two points. Any two points in a 2D geometry can be connected by a line segment or a simple straight line. The equation of a straight line can be obtained in three ways:

slope intercept method

point slope method

Standard method

Given two points lying on a given line, we usually follow the point-gradient method.

The equation for a straight line is y−y1=m(x−x1)

where y1 is the Y-axis coordinate, m is the tilt, x1 Coordinates on the x-axis.  m = y2-y1/x2-x1

eqn = y +4 = (-36/1/4)(x-1/2)

y +4 = -146x + 73

y = -146x + 69

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The numbers are 1 and 8.

We have,

Let's assume the lesser number as "x" and the greater number as "8x".

According to the given information, when the lesser number is subtracted from the greater, the result is 2 more than 5 times the lesser number:

8x - x = 5x + 2

Simplifying the expression:

7x = 5x + 2

Subtracting 5x from both sides:

2x = 2

Dividing both sides by 2:

x = 1

So, the lesser number is 1 and the greater number is 8 times that, which is 8.

Therefore,

The numbers are 1 and 8.

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The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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