Find the solutions of the given equation.
25x² +64 = 289
O A. x =
-√√3, √3
OB.
x =
-9,9
OC.
x = -3, 3
O D. x = -3√3, 3√/3

The Cartesian product that I read about is a mathematical concept that is used to combine two sets together in a specific way. The Cartesian coordinate system, on the other hand, is a way of representing points in a two-dimensional plane using a set of numerical coordinates.

The relationship between the two is that the Cartesian product is used to create the set of all possible coordinates that can be used in the Cartesian coordinate system. The Cartesian product of two sets, say set A and set B, is the set of all ordered pairs (a, b) where a belongs to set A and b belongs to set B.

When we graph a point in the Cartesian coordinate system, we are picking a specific point from the set of all possible points that can be created using the Cartesian product of the set of x-coordinates and the set of y-coordinates.

In other words, the Cartesian product is the foundation of the Cartesian coordinate system. It provides a set of all possible points that can be graphed using that system.

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Answer:

[tex]\frac{1}{36}[/tex]

Step-by-step explanation:

For negative exponents, you get the original number and make it into its reciprocal, and then whatever power it is to, is the power the bottom number is to, so you get:

[tex]6^{-2} = \frac{1}{6^{2} }[/tex]

Which simplifies to:

[tex]\frac{1}{36}[/tex]

So, [tex]6^{-2}[/tex] in fraction form, is [tex]\frac{1}{36}[/tex].

Hope this helped!
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Answer:

see the picture attached

Step-by-step explanation:

To graph this, we will count to a negative five on the graph. This means that we will move to the left five spaces and plot a point at (-5,0). Now, we will create a vertical line at -5 to encapsulate all of the values found at x = -5. This is essentially an infinite line, but the picture I included shows it on a 10 x 10 plane. Hope this helps!

Answer:

What is X= -5 graphed

Step-by-step explanation:

Graph x=-5 x = −5 x = - 5 Since x = −5 x = - 5 is a vertical line, there is no y-intercept and the slope is undefined.

The hypotenuse side of the right triangle is 7 units.

The value of x in the triangle is 5.92 units.

A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The side of a right triangle can be found using Pythagoras's theorem as follows:

using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

hypotenuse = 7

Let's find x.

7² - (√14)² = x²

49 - 14 = x²

x² = 35

square root both sides

x = √35

x = 5.9160797831

x = 5.92 units

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A graph will be drawn where a scale of 2 cm to 1 unit on x-axis and 2 cm to 2 units on the y-axis, draw on a graph sheet two perpendicular axes

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

Types of Graphs and Charts

Statistical Graphs (bar graph, pie graph, line graph, etc.)

Exponential Graphs.

Logarithmic Graphs.

Trigonometric Graphs.

Frequency Distribution Graph.

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Answer: The two problems aren't related

Step-by-step explanation:

The first problem has a 3 and a 9 but no 2, but the second problem does,  which shows that these two problems are not related. Also, if you simplify the first one, you will get 27 [tex]\sqrt[4]{3}[/tex], which is not related to the second problem

The smallest number of coins Freddie would need is 4 (one penny, one nickel, one dime, and one quarter).

What is algebra ?

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It includes the study of operations such as addition, subtraction, multiplication, division, and the extraction of roots, as well as the properties of operations such as commutativity, associativity, and distributivity.

In order to be able to pay any amount of money less than a dollar, Freddie would need to have at least one coin of each denomination: pennies, nickels, dimes, and quarters. The smallest number of coins he would need to achieve this is 4. With one penny, one nickel, one dime, and one quarter, he would be able to pay any amount of money less than a dollar by using combinations of these coins.

Therefore , The smallest number of coins Freddie would need is 4 (one penny, one nickel, one dime, and one quarter).

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Managers must make all the given vital decisions from the options, hence, d) All of the above is the correct answer.

Managers must make a number of important decisions about the use of control charts, some of which include:

These are all important decisions that managers need to make when using control charts to monitor and improve processes in an organization. The right decisions can help ensure that control charts are effective in detecting and addressing issues with processes, while the wrong decisions can lead to control charts being ineffective or even counterproductive.

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The complete question is -

Managers must make a number of important decisions about the use of control charts. what are they?

multiple select questions.

a) what size samples to take and how often samples should be taken.

b) how many control charts to use to monitor the process.

c) what type of control chart to use.

d) what tools to use to take measurements at what points in the process to use control charts.

e) All of the above.

In order to be in the 85th percentile Eli would need to score 26.62.

In statistics, a score below which a certain percentage of scores (k) in a frequency distribution falls is known as a k-th percentile, whereas a score at or below which a given percentage falls is known as a k-th centile.

Given that act math scores are approximately normally distributed,

mean (μ) = 21 and a standard deviation (σ) = 5.4

percentile P(X>x) = 85 =0.85

P(z<x) = 0.85

z = 1.04

y the formula

z = (x - μ)/ σ

⇒ 1.04 = (x - 21)/5.4

⇒ 1.04*5.4 = x - 21

⇒ 5.616 = x - 21

⇒ x = 5.616 + 21

⇒ x = 26.62

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Roxy can make her goal SMART by deciding an attainable amount of money, diving the total of money in paymets and using the money for emergencies only.

This is a technique to plan and achieve goals based on 5 characteristics:

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Answer:

Step-by-step explanation:

AB = √36 = 6 cm

Area of semicircle πr²/2 or 9π/2

Area of 4 semicircles = 18 π

Total area = 36 + 18 π ≈ 92.5 cm²

Answer:

500 > 40 + 5t

Step-by-step explanation:

At least 500

40 intro = initial, constant

t = time in seconds

5 words per second

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To find the amount of gold needed for gold plating a brick, total surface area of the brick would be needed to be calculated, assuming the brick is cuboid or cube shaped.

While dealing with cubes and cuboids, we should know how to find the surface areas and volumes of the two objects. When we either fill these or talk about all the three dimensions of an object, we talk about the volume of the said object. And, when we paint or talk about just the exterior or interior walls of an object, we talk about the surface area of the said object.

When all the six faces of a cube or a cuboid are used, we calculate surface area for all the faces and this is called the total surface area.

Let us look at the different formulas to calculate volume and total surface area of a cube and a cuboid,

Total surface area of a cube (side [tex]a[/tex]) =  6 × (area of each face)  

                                                          = 6 × [tex]a^{2}[/tex]  

Volume of a cube (side [tex]a[/tex]) = [tex]a^{3}[/tex]

Total surface area of a cuboid (length [tex]l[/tex], breadth [tex]b[/tex], height [tex]h[/tex]) = [tex]2 ( lb + lh + bh)\\[/tex]

Volume of a cuboid (length [tex]l[/tex], breadth [tex]b[/tex], height [tex]h[/tex]) = [tex]lbh[/tex]

For plating the brick with anything, gold for instance, total surface area of the brick would be calculated to determine the amount of gold needed as all the walls or faces of the brick would be plated but not the interior volume.

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Answer:

y = 0.5x + 4

Step-by-step explanation:

1. Move terms to one side of the equation

0.5y - 2= 0.25x +0

     +2               +2  

__________________

0.5y = 0.25x + 2

2. Divide the coefficient of y (0.5) to both sides of the equation

[tex]\frac{0.5y}{0.5} = \frac{0.25x}{0.5} + \frac{2}{0.5}[/tex]

3. Solve and simifpy

[tex]y = 0.5x +4[/tex]

The percentage for Utah is 9.0%.

The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.

All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.

A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.

Thus, The percentage for Utah is 9.0%.

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Answer:

Inconsistent as there are two same equations with different values.

So this doesn't make sense.

The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

If a road map has a scale of 3 inches to 100 miles.

Then the scale factor is given as,

Sclar factor = 100 / 3

Sclar factor = 33.33 miles per inch

Then the distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be given as,

Distance = 33.33 x 4.5

Distance = 150 miles

The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

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The measure of angle ∠LMN = 105°

What is a parallelogram?

A parallelogram is a quadrilateral, which is a four-sided polygon, with opposite sides that are parallel. Additionally, opposite angles in a parallelogram are congruent (equal in measure). So, if a figure has parallel opposite sides and congruent opposite angles, then it is called a parallelogram.

In the given figure, quadrilateral LMNO is a parallelogram in which ∠L = 25x° and ∠MNO = (22x + 9)°

We have get the measurement of ∠LMN

Since in a parallelogram opposite angles are equal.

Therefore 25x = 22x + 9

25x - 22x = 9

3x = 9

x = 3

From another property of a parallelogram, we know that consecutive angles are supplementary.

∠LMN + ∠ONM = 180°

∠LMN = 180 - ∠OLM = 180 - (25x) = 180 - (25×3)

∠LMN = 180 - 75 = 105°

Hence, the measure of angle ∠LMN = 105°

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The constant of proportionality for the proportional equation is 36.

Option A is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,
Box = b

Number of pencils in one box.

p = 36

Now,

The proportional equation for b and p.

p ∝ b

p = mb

where m is the constant of proportionality.

Now,

b = 1

p = 36

p = mb

36 = m x 1

m = 36

Thus,

The constant of proportionality is 36.

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If the sample standard deviation from the sample distribution is 0.0005 mm, the sample should have 16 axes.

Given,

μ = 40.125 mm, σ = 0.002mm σ(x) = 0.0005mm

The standard deviation of the sampling distribution of the sample mean is the population standard deviation divided by the square root of the sample.

    σ₁ = σ/√n

By multiplying both sides by √n

   √nσ(x) = σ

By dividing both the side by σ₂

    √n = σ / σ₁

By squaring both the sides

  n = σ²/σ²(x)

Now,

Calculate the value of n

n = 0.002² / 0.0005²

  = 16

Therefore,

If the sample's standard deviation of the sampling distribution is 0.0005mm, then the sample should be 16 axles.

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The area of shaded triangle is 20 square feet

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.

Area of triangle = 0.5*base*height

Area of whole triangle = 0.5*8*10 =  40 square feet

Area of unshaded triangle = 0.5*4*10 =  20 square feet

Area of shaded triangle

= Area of whole triangle  - Area of unshaded triangle

=  40 - 20

= 20 square feet

Thus, the area of shaded triangle is 20 square feet

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The point on the number line is between 6 and 7

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

Number = square root 38

The square root of 38 is approximately 6.16441400296898.

This number is between 6 and 7 on the number line, closer to 6.

Also, it should be noted that

It's not a rational number so it's not on the number line with integers, but it can be represented as a decimal or as an irrational number.

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The graph of the function h(x) = 7sin(x) is given by the image presented at the end of the answer.

The sine function is given as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

From this problem, the amplitude is given as follows:

A = 7.

Hence:

As there is no phase shift, the minimum and maximum values have the x-coordinate given as follows:

As the function has no phase shift, the period is given as follows:

2π.

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Answer: why is the question?

Step-by-step explanation: also the integer is the whole number whether if its negative or positive number e.g. -12 or 5

Integers = {...,−4, −3, −2, −1, 0, 1, 2, 3, 4, ... }

Negative Integers = { ..., −4, −3, −2, −1 }

Positive Integers = { 1, 2, 3, 4, ... }

Answer:

34

Step-by-step explanation:

They gave us -3+5i.

The conjugate of -3+5i is

-3 - 5i

You use the same numbers -3 and 5i, but with a minus sign instead of a plus.

Then multiply them together.

(-3 + 5i)(-3 - 5i)

-3•-3 + 15i - 15i - 25i^2

= 9 - 25i^2

Remember i^2 is -1.

= 9 - 25(-1)

= 9 + 25

= 34

Shortcut version:

When you multiply a complex number and its conjugate, square both numbers and add them together.

3^2 + 5^2

= 9 + 25

= 34

Answer:

Step-by-step explanation:

To prove that the diagonals of an isosceles trapezoid are congruent, we will first define the terms and draw a diagram of the isosceles trapezoid.An isosceles trapezoid is a quadrilateral with two congruent legs, a pair of parallel bases, and congruent base angles.Let's call the isosceles trapezoid ABCD and let the parallel sides be AB and CD, and the congruent legs be AD and BC. Let the diagonals be AC and BD.Since, AD and BC are congruent legs, therefore ∠BAD = ∠CAD by the definition of congruent legs.And since ABCD is a trapezoid, therefore, AB || CD and therefore, ∠BAD = ∠CBD, due to alternate angles are congruent.Therefore, ∠CAD = ∠CBD, by CPCTC (corresponding parts of congruent triangles are congruent)AC = BD , since both are congruent by ASA (angle-side-angle) congruence.Thus, the diagonals of an isosceles trapezoid are congruent.

Answer:

A, 6:00 P.M. EST

Step-by-step explanation:

The time difference between EST and PST is -3 hours

11 am - 9am = 2 hours

2 - (-3) = 2+3 = 5 hours

The flight time is 5 hours

Then:

The time difference between PST and EST is +3 hours

5 + 3 = 8

If the fly leaves Los Angeles at 10:00 AM PST

10 + 8 = 18

The plane will arrive at 6:00PM EST

Answer:

14.8%

Step-by-step explanation:

decrease = -100 * ((final - initial) / initial)

Answer:

14.8%

Step-by-step explanation:

Original fishing pole cost: $54

New fishing pole cost: $46

Using the percentage decrease formula:

[tex]\frac{Original Value - Final Value}{|Original Value|}[/tex]  ×100%

Substitute

[tex]\frac{54-46}{|46|}[/tex] ×100%

From this, you should get 14.814814814814814...

Round to nearest tenths.

Final answer: 14.8%

1. There is a correlation that exists between the average number of hours of internet browsing and the average score on the math test.

2. The function that best fits the data is: Y = f(X)

3. The slope and the intercept tells us that a student would be at their best in a test if they spent 0 hours browsing.

1. The correlation that exists in this data set tells us that as a person spends more time on the computer, they would spend less time on their test preparation. This would eventually affect their score.

When the student did not browse the internet, they had their highest score in math. As they started to spend more time on the internet, the score started to drop.

2. The function is given as

math test score Y = function of X: hours spent browsing the internet

this is written mathematically as:

Y = f(X)

3. The Y intercept is at the point where the student spent 0 hours browsing. this is the point where they did their best in this test. This tells us that if a student spent 0 hours on the internet, they would do their best in the test.

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