Use Descartes Rules of signs to complete the chart with possibilities for the nature of the roots of the following equations:A) x^3 - x^2 + 4x - 6 = 0B) x^5 - x^3 + x + 1 = 0

The probability that a randomly selected student will be taller than 71 inches tall is 0.010.

We use z score formula to calculate :

z = (x-μ)/σ

where,

z = standard score

x = observed value

μ = mean of students height

σ = standard deviation of students height

x  = 63 inches

μ = 70 inches

σ = 3 inches

For x shorter than 63 inches we calculate

Z = (x - μ)/σ

then put the given values in above equation.

= (63 - 70)/3

= -2.33333

Probability value is :

P(x<63) = 0.0098153

Approximately to the nearest thousandth = 0.010

The probability that a randomly selected student will be taller than 71 inches tall is 0.010.

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given details

STEP 2: Write the formula for finding sum of arithmetic series

STEP 3: Find the sum of the series

By substitution,

Hence, the sum is 416

Given the table showing the number of days since wound began to heal and area of wound in square millimeters

To determine the statement that are correct from the option provided

From the table shown it can be seen that as the day increases by 1, the area of wound in square millimeters decreases by a common ratio of

Suppose that an expression to represent the area of wound is

The modelled expression from the table is

Let us use the modelled expression to verify each of the given conditions

The modelled expression can be simplified as shown below:

Then, we have the modelled expression becomes

From the two modelled expression we can see that

Then we can conclude that the two conditions that are true from the options are

If the value of c = n, the value of a is 31.25, and

If the value of c = n, the value of b is 0.8

Segment C prime D prime has endpoints located at C′(0, 0) and D′(4, 0). It was dilated at a scale factor of one half from centre (4, 0). the pre-image

B- segment CD is located at C(2, 0) and D(6, 0) and is twice the length of segment C prime D prime period

According to the question,

Segment C prime D prime has endpoints located at C' (0, 0) and D' (2, 0).

The coordinates are given as:

C' (0, 0) and D' (4, 0).

Since,

Centre of dilation = D = (4,0)

Here, CD seems to be the dilated image of CD by something like a factor of two. It follows that M must have been at (0,0).

It's one-half units left from the centre of dilated.

Then, C` = 1/2 x 4  = 2

Since the dilation is (4, 0),

C = (2+4, 0) = (6,0)

Hence,

segment CD is located at C(2, 0) and D(6, 0) and is twice the length of segment C prime D prime period

Segment simplifies  data collection and integrates new tools, allowing you to spend more time using data and less time collecting it. A segment allows you to track events that occur when a user interacts with user interfaces. "Interfaces" is the segment's umbrella term for all the digital real estate you own: your website, mobile apps and processes running on a server or OTT device.

When you capture interaction data in a segment, you can send it (often in real time) to your marketing, product and analytics tools and data warehouses. In most cases, you don't even need to touch the tracking code to connect to the new tools.

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The value of k when one angle measures 140°, and another angle measures (5k + 85)° and if the angles are vertical angles is 11.

Vertical angles are angles opposite each other where two lines cross.

Note: Vertical angles are equal.

To calculate the value of k, we use the principle of vertical angle

From the question,

Solve for k

Divide both side by the coefficient of k (5)

Hence, the value of k is 11.

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The quadratic is decreasing in the interval in which the y values decrease with the increase in x values.

In the interval, (-∞, 0), the y values decrease with increase in x values.

Hence, the quadratic is decreasing in the interval (-∞, 0),

There are two known angles in such a manner:

We know that the sum of internal angles of a triangle is equal to 180 degrees. This means that we can find the missing angle by adding all the internal angles and making it equal to 180

The missing angle is 45 degrees.

Let x be the number of cups of lemonade sold, and y the number of cups of orange drinks sold, then we can set the following equation:

Now, recall that the standard form of a linear equation is:

Where, A≥0, B and C are integers.

Simplifying the first equation, we get:

Answer:

Answer:

x < 2 or x > -11

Step-by-step explanation:

b. 1. add 12 to both sides to get -1/3x > 33

2. multiply by -3/1 to both sides to get x > -11

a. 1) subtract 10 to both sides

2) divide by -6 to both sides

To answer this question we will set and solve a system of equations.

Let k be the number of orders that Kala served on Monday, a be the number of orders that Abdul served, and j be the number of orders that Joe served.

Since they served a total of 71 orders, Kala served 5 fewer orders than Abdul, and Joe served 2 times as many orders as Abdul, then we can set the following system of equations:

Substituting the second and third equation in the first one we get:

Adding like terms we get:

Adding 5 to the above equation we get:

Dividing the above equation by 4 we get:

Finally, substituting a=19 in the second and third equation we get:

Answer:

Number of orders Kala served: 14.

Number of orders Abdul served: 38.

Number of orders Joe served: 19.

Given:

Given that a right triangles.

Required:

To find the value of variables in each triangle.

Explanation:

In right triangles,

(C)

Here,

The price of the bookcase in the funiture store is:

$206.72

Given that the markup is 36% of $152

This is:

0.36 * 152 = $54.72

Therefore, the price of the bookcase in the funiture store is:

$152 + $54.72

= $206.72

Answer:

Step-by-step explanation:

What we know:

m = 4, b = -5

y = mx + b where m is the gradient/slope and b is the y-intercept

Substitute m and b values:

y = 4x + -5 which is the same as y = 4x - 5

Substitute all x values to find y coordinate:

When x = -7, y = (4 x -7) - 5 = -33

When x = -6, y = (4 x -6) - 5 = -29

When x = -5, y = …

Continue for all x values

step 1

Find out the slope of the given line

we have

-(4/3)x+2y=4/3

isolate the variable y

2y=(4/3)x+(4/3)

Divide both sides by 2

y=(4/6)x+(4/6)

simplify

y=(2/3)x+(2/3)

the slope is m=2/3

Remember that

If two lines are perpendicular, then their slopes are negative reciprocal

that means

the slope of the perpendicular line to the given line is

m=-3/2

step 2

Find out the equation in slope-intercept form of the perpendicular line

y=mx+b

we have

m=-3/2

point ( 1,0)

substitute and solve for b

0=-(3/2)(1)+b

0=-(3/2)+b

b=3/2

therefore

the equation is

SOLUTION

(a) Complementary angles are angles that add up to 90 degrees. So the angle that will complement 50 degrees will add to it to get 90. Let the angle be x, we have

Hence the measure of the compelement is 40 degrees

(b) Supplementary angles are angles that add up to 180 degrees. So the angle that will supplement 135 degree will add to it to make it 180 degrees. Let this angle be y, so we have

Hence measure of the supplement is 45 degrees

The solution set of the inequality 2 · x² + 5 · x - 3 > 0 is (- ∞, - 3) ∪ (1 / 2, + ∞).

Herein we find a quadratic inequality, whose solution set can be found by factoring the expression and determine the interval where the expression is greater than zero. Initially, we use the quadratic formula to determine the roots of the quadratic function:

2 · x² + 5 · x - 3 = 0

x₁₂ = [- 5 ± √[5² - 4 · 2 · (- 3)]] / (2 · 2)

x₁₂ = (- 5 ± 7) / 4

x₁ = 1 / 2, x₂ = - 3

Then, the factored form of the inequality is:

(x - 1 / 2) · (x + 3) > 0

In accordance with the law of signs, we must look for that intervals such that: (i) (x - 1 / 2) > 0, (ii) (x + 3) > 0, (ii) (x - 1 / 2) < 0, (x + 3) < 0. Then, the solution set of the quadratic inequality is:

Inequality form - x > 1 / 2 ∨ x < - 3

Interval form - (- ∞, - 3) ∪ (1 / 2, + ∞)

The solution set of the inequality is (- ∞, - 3) ∪ (1 / 2, + ∞).

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Hello there. To find this minimum weight resistance, we need to convert the percentage value to decimals and multiply it by the weight of the person.

8% converted to decimals is equal to 0.08.

Now, multiply it by the weight of the 230 pound man

0.08 * 230 = 18.4 pounds

This is the minimum weight resistance this U gym offers to the customers.

The budget is 20000 times greater.

Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.

The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.

Here we are discussing the four basic rules of arithmetic operations for all real numbers.

Company A = $2 × [tex]10^{4}[/tex]e

Company B = $ 5 × [tex]10^{8}[/tex]

The difference = $2 × [tex]10^{4}[/tex]

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Question:

Solution:

A quadratic Equation in Standard Form is given by the following formula:

now, the given equation is

this is equivalent to:

According to the Quadratic Equation in Standard Form, we can conclude that

and

The domain of the function which is the entire x values during the strike is

SOLUTION

Let us make a diagram to interpret the question

from the diagram above, we can make the right-angle triangle as follows

So we can use SOHCAHTOA to solve this. The opposite side to the angle 52 degrees is 45.5 ft, this is gotten by adding the height of the cliff to Maria's height from her feet to her eyes.

The adjacent side is d, that is the distance from the seal to the cliff, so we have

Hence the answer is 36 foot to the nearest foot

We need to find the equation of the line which:

• crosses the y-axis at -5

• crosses the x-axis at 2

The y-axis cutting point is (0,-5)

The x-axis cutting point is (2,0)

The equation of line is:

Where m is the slope and b is the y-axis cutting point

m is given by:

Where

y_2 = 0

y_1 = -5

x_2 = 2

x_1 = 0

So, slope is:

We got m, we also know b.

The y cutting point is -5, so b = -5

The equation is:

The graph would look like:

More clear version:

Given:

A line passes through the point,

The slope of the line is m = -1.

The objective is to find the equation of the line in point-slope and slope-intercept form.

Explanation:

To find equation in point-slope form:

The general formula of point-slope form is,

On plugging the given values in equation (1),

To find the equation in slope-intercept form,

The general formula of slope-intercept form is,

On further solving the equation (2),

Hence,

The equation of the line in point-slope form is y+6 = -x+5.

The equation of the line in slope-intercept form is y = -x-1.

Answer

The rate of change of both functions is 2.

Explanation

To know the statement that best compares the rate of change of the two functions, we need to first calculate the rate of change for each function.

Rate of change of function A

Using x₁ = 7, y₁ = 14, x₂ = 8 and y₂ = 16

Rate of change = Δy/Δx

Δy = (y₂ - y₁) = 16 - 14 = 2

Δx = (x₂ - x₁) = 8 - 7 = 1

⇒ Rate of change = 2/1 = 2

Rate of change of function B

From the graph

Using coordinate x₁ = 2, y₁ = 4, x₂ = 3 and y₂ = 6

Rate of change = Δy/Δx

Δy = (y₂ - y₁) = 6 - 4 = 2

Δx = (x₂ - x₁) = 3 - 2 = 1

⇒ Rate of change = 2/1 = 2

Since the rate of both functions are the same (2), then the statement that best compares the rate of change of the two functions in the options given is "The rate of change of both functions is 2"

Given:

Length(l) of the garden is 3.1 meters

Width(w) of the rectangular garden is 5.6 meters

Area of the garden is 17.36 square meters.

Recall that the numbers in a die are 1,2,3,4,5,6.

Hence the number of possible outcomes is 6.

We need a number less than 3. Let A be this event.

The favorable outcome is 2.

Since there are 1,2 less than 3 in a die.

Substitute n(A)=2 and n(S)=6, we get

Hence the required probability is 0.333.

The given equation is-

If we multiply the equation by 6, we would have the same value for the variable x since we are multiplying the same number on each side. So, the second choice is an equivalent equation to the given one.

Let's multiply by 6.

So, the third expression is also an equivalent expression.

Then, let's subtract 4 on each side.

The last choice is also an equivalent expression.

Let's begin by listing out the information given to us:

Line AB is parallel to Line CD; this implies that the angle formed by the two lines are right angles (90 degrees)

E is the intersecting point of both lines AB & CD (figure attached)

Let us put this into its mathematical form:

Given

The displacement (in meters) of a particle moving in a straight line is given by s = t^2 - 9t + 15,