plssssssssssssssssssssss help

We can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

If there are integers s and t such that as + bt = 15, then we can conclude that gcd(a, b) divides 15. This is known as Bézout's identity, which states that for any two integers a and b, there exist integers s and t such that as + bt = gcd(a, b).

To see why this is true, consider the set of all linear combinations of a and b, that is, the set {ax + by : x, y are integers}. This set contains all multiples of gcd(a, b) since gcd(a, b) divides both a and b.

Therefore, gcd(a, b) is the smallest positive integer that can be expressed as a linear combination of a and b.

Now, if as + bt = 15, then 15 is a linear combination of a and b, which means that gcd(a, b) divides 15.

Conversely, if gcd(a, b) divides 15, then we can find integers s and t such that as + bt = gcd(a, b), and we can scale this equation to obtain as' + bt' = 15, where s' = (15/gcd(a, b))s and t' = (15/gcd(a, b))t.

Therefore, we can conclude that gcd(a, b) divides 15 if and only if there exist integers s and t such that as + bt = 15.

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Answer:

Negative

Step-by-step explanation:

Positive discriminant: graph cuts x axis twice

Zero discriminant: graph touches x axis once

Negative discriminant: graph does not cut or touch x axis

Answer:

18

Step-by-step explanation:

x= Chargers

x+14= Vikings

x + x + 14 = 50 Combine the x's to be 2X

2x + 14 = 50 Subtract 14 from both sides

2x -14 = -14

2x = 36 Divide 2 into to 2x and 36

2x /2 = 36 /2

x= 18

Answer:

  -56

Step-by-step explanation:

It is often easiest to find terms of a sequence by simply writing each one based on the previous one. Here, the common ratio of -2 tells you that each term is -2 times the previous term.

The first four terms are ...

  7, -14, 28, -56

The fourth term is -56.

Answer:

Inertia is a tendency to do nothing or to remain unchanged.

It is a property of matter by which it continues in its existing state of rest or uniform motion in a straight line unless that state is changed by an external force.

Answer:

Inertia is the resistance to a change in motion.

Therefore, an object at rest remains at rest and an object in motion remains in motion with the same velocity unless acted upon by an unbalanced/external force.

The four step to graphing the linear inequalities are: Always begin by separating the variable y from the inequality's left side, Replace the inequality symbol with the equality symbol, In XY plane, graph the boundary line from step 2, The final step is to shade a portion or one side of the border line.

In the given question we have to explain the 4 steps in graphing linear inequalities.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In XY plane, graph the boundary line from step 2.

Step 4: The final step is to shade a portion or one side of the border line.

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Answer:

ok, so, since the angles in a traingle all sum up to 180°, that would make:

36°+61°+(4x-17)°=180°

We simplify it:

95°+(4x-17)°=180°

Then, we subtract 95° on both sides:

95°+(4x-17)°=180°

-95°               -95°

Then we get:

4x-17°=85

We add 17° on both sides

4x-17°=85

   +17°  +17°

And we get:

4x=102°

Divide 4 on both sides...

4x=102°

➗4 ➗4

Therefor:

X=25.5

Hope this helps, but tell me if i'm wrong, and have a good day!

Answer: 1/2 or 5/10

Step-by-step explanation:

Because the fractions have the same denominator, you can just subtract the top numbers from the fractions to 5/10. 5/10 is equivalent to 1/2.

ASA (Angle-Side-Angle) and we observed  and  proved that △GHL ≅ △KHJ.

we are asked to find the congruence theorem, which will prove that △GHL ≅ △KHJ.

we can see that side length GH of △GHL is equal to side length KH of △KHJ.

We are also given that m<HGL = m<HKJ.

We can see that  <GHL is vertical opposite angle of  <KHJ as they are formed by the intersection of line segments GK and JL. Therefore ,m<GHL congruence m<KHJ , by vertical angles theorem.

We can see that both triangles have two congruent angles and one congruent included side, therefore, △GHL ≅ △KHJ by ASA congruence and option B is the correct choice.

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Answer:

Step-by-step explanation:

The given statement mathematical and statistical tools give us many ways to rate the overall performance of a system and its components is True.

Mathematical and statistical tools provide various methods to assess and evaluate the performance of a system and its individual components. These tools enable quantitative analysis , modeling , prediction , and inference , allowing us to measure and interpret the effectiveness , efficiency, reliability, and other relevant characteristics of systems and their components.

Examples of such tools include statistical analysis, regression analysis, hypothesis testing, optimization techniques, control charts, simulation, and more.

Therefore, the given statement is true.

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Complete question is below

Mathematical and statistical tools give us many ways to rate the overall performance of a system and its components.

true or false

Answer:   -___-

Step-by-step explanation:

The statement "Two events are mutually exclusive events if they cannot occur at the same time (i.e., they have no outcomes in common)" is true.

Two events are mutually exclusive events if they cannot occur at the same time (i.e., they have no outcomes in common) which means that the occurrence of one event automatically eliminates the possibility of the other event happening.

                 For example, when flipping a coin, the outcome of getting heads and the outcome of getting tails are mutually exclusive because only one of them can happen at a time. Mutually exclusive events are important in probability theory, especially in determining the probability of compound events.

                            If two events are mutually exclusive, the probability of either one of them occurring is the sum of the probabilities of each individual event.

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In Microsoft PowerPoint 2016, under the Slide Master tab, you will find six command groups. The names of these command groups are:

1. Edit Master: This command group allows you to modify the overall design and layout of the slide master, including background styles, fonts, and placeholders.

2. Background: This command group provides options to customize the background of the slide master, such as applying a solid color, gradient, texture, or picture.

3. Layout: The Layout command group allows you to manage the layout of slides within the slide master. You can add or modify placeholders for text, images, charts, and other content elements.

4. Colors: This command group enables you to choose and apply different color schemes to the slide master, affecting the colors used throughout the presentation.

5. Fonts: The Fonts command group allows you to select and apply specific font styles to the slide master, which will influence the text appearance in your presentation.

6. Arrange: This command group provides options for arranging and aligning objects within the slide master, such as bringing objects to the front or back, aligning them, and distributing them evenly.

These command groups offer a range of customization options to help you design and modify the slide master in PowerPoint 2016.

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When diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

Step 1: Create an equation that connects a sphere's volume to radius as the first step.

V = 4/3*π*r³

Step 2: Calculate each side's derivative in respect to time (Let the time be "t").

(d/dt)V = (d/dt)(4/3*π*r³)

dV/dt = 4πr²*dr/dt

Step 3: The problem description informs us that the diameter is 600 m, hence r must be 30 mm.

Additionally, it is stated that now the radius of a sphere is expanding at a rate of 2 mm/s; as a result, dr/dt must equal 2 mm/s.

We are interested in dV/dt, or the rate of change of the sphere's volume.

dV/dt = 4π(30mm)²*(2mm/s)

dV/dt = 22,620 mm³/s

So, when diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

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Answer:

2:5:4

Step-by-step explanation:

24:60:48

This can be simplified by dividing each of them by 2- 12:30:24 and then dividing by 3 - 4:10:8

It can now be divided by 2 - 2 : 5 : 4 in its simplest form

The equation of a parabola with a given focus and directrix is:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

In this equation, (a, b) represents the coordinates of the focus, and c represents the y-coordinate of the directrix. This equation describes a parabola where all points on the parabola are equidistant from the focus and the directrix.

To write the equation of a parabola with a given focus and directrix, we can use the geometric definition of a parabola. A parabola is the set of all points that are equidistant from the focus and the directrix.

Let's assume the focus is denoted as F(a, b) and the directrix is a horizontal line given by y = c. The vertex of the parabola is at the midpoint between the focus and the directrix, which is V(a, (b + c) / 2).

The distance from any point (x, y) on the parabola to the focus F(a, b) is given by the distance formula:

sqrt((x - a)^2 + (y - b)^2)

The distance from the point (x, y) on the parabola to the directrix y = c is given by |y - c|.

According to the definition of a parabola, these two distances are equal. Thus, we can set up the equation:

sqrt((x - a)^2 + (y - b)^2) = |y - c|

Squaring both sides of the equation eliminates the square root:

(x - a)^2 + (y - b)^2 = (y - c)^2

Expanding and rearranging the terms:

x^2 - 2ax + a^2 + y^2 - 2by + b^2 = y^2 - 2cy + c^2

Simplifying and canceling out the y^2 terms:

x^2 - 2ax + a^2 + b^2 - 2by = c^2 - 2cy

Rearranging the terms to obtain the standard form of the equation:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Thus, the equation of the parabola with focus F(a, b) and directrix y = c is given by:

x^2 - 2ax + 2by + (a^2 + b^2 - c^2) = 0

Complete Question - Write the equation of a parabola with focus F(a, b) and directrix given by y = c.

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Answer:

1:27

Step-by-step explanation:

I will use solve in terms of pi

Know that Original volume * scale factor cubed = new volume.

The scale factor is 3 and 3^3 is 27,

Therefore the ratio is 1:27

Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. The correct option is D.

Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. They have scaled versions of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:

\(L = k \times M\)

where 'k' will be called a scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple linear things twice grow by the square of the scale factor. Thus, we need to multiply or divide by k²

to get each other corresponding quantities from their similar figures' quantities.

So the area of the first figure = k² × the area of the second figure

Similarly, increasing product-derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or

The volume of the first figure = k³ × volume of the second figure.

It is because we will need to multiply 3 linear quantities to get volume, which results in k getting multiplied 3 times, thus, cubed.

Given that the diameter of sphere A is 2 units, it is dilated by a scale factor of 3 to create sphere B. Therefore, the diameter of sphere B is,

Diameter of sphere B = 3 × Diameter of sphere A

                                    = 3 × 2 units

                                    = 6 units

Now, the ratio of diameters of the sphere and the volume of the sphere can be written as,

\((\dfrac{\text{Diameter of sphere A}}{\text{Diameter of sphere B}})^3 = \dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}} \\\\\\(\dfrac{2}{6})^3 = \dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}}\\\\\\\dfrac{\text{Volume of sphere A}}{\text{Volume of sphere B}} = \dfrac{1}{27}\)

Hence, the correct option is D.

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Answer:

10 falls between 4 and 2 but is closer to 2.

92 falls between 10 and 8 but is closer to 10

Answer:

No, she will have 140 cards in 4 months

Step-by-step explanation:

the equations is:

f(x) = 100 + 10x

now x = 4

f(4) = 100 + 10(4)

f(4) = 100 + 40

f(4) = 140

140 does not = 60

Answer:

No, in 4 months she will have 140 cards.

Step-by-step explanation:

If Victoria has 100 cards now, and adds 10 cards every month, she will have added 40 cards in 4 months.

10 x 4 = 40

40 + 100  = 140

Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

Answer:

$82.50

Step-by-step explanation:

Given that the unit rate is $13.75 per hour,

1 hour -----> $13.75

6 hours -----> $13.75 x 6 = $82.50

The value of 'a' in the given expression is 11/2.

The square root formula can be used to calculate the square root of any number. The square root of any number is the value that, when multiplied by itself, yields the original number. Each number has two square roots, one positive and the other negative. For example, the number four has two square roots, -2 and 2.

Given \($32 \sqrt{2}=2^a$\)

We can write 32 as:

32 = 2 × 2 × 2 × 2 × 2

32 = \(2^{5}\)

We can write \($\sqrt{2}=2^{1 / 2}$\).

Now,

\($$\begin{array}{r}32 \sqrt{2}=2^a \\2^5 \cdot 2^{1 / 2}=2^a \\2^{5+1 / 2}=2^a \\2^{1 / 2}=2^a \\\end{array}$$\)

Therefore, the value of a = 11/2.

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To verify the parallelogram law for vectors u and v in R^n, we will follow these steps:
1. Write the given equation: ||u+v||^2 + ||u-v||^2 = 2||u||^2 + 2||v||^2
2. Use the definition of the norm in terms of the inner product: ||u+v||^2 =  and ||u-v||^2 =
3. Use properties of inner product.

Now, let's apply these steps:
Step 1: We have the equation ||u+v||^2 + ||u-v||^2 = 2||u||^2 + 2||v||^2.
Step 2: Replace the norms with their corresponding inner products:
+  = 2 + 2
Step 3: Apply properties of inner products and expand the terms:
(u⋅u + 2u⋅v + v⋅v) + (u⋅u - 2u⋅v + v⋅v) = 2(u⋅u) + 2(v⋅v)
Now, observe that the terms "2u⋅v" and "-2u⋅v" cancel each other out: 2(u⋅u) + 2(v⋅v) = 2(u⋅u) + 2(v⋅v)
As the equation holds true, we have successfully verified the parallelogram law for vectors u and v in R^n using the definition of the norm in terms of the inner product and properties of inner product.

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In mathematics, the place value chart is a tool that helps students understand the value of digits in a number. It is a visual representation of how digits are grouped and arranged to represent numbers. The place value chart is arranged in columns, with each column representing a different place value.

The place value chart starts with the ones place, also called units place. This is the rightmost column and it represents the ones digit in a number. The next column is the tens place, which represents the tens digit in a number. The hundredth place represents the hundreds digit and so on. Each column is ten times larger than the previous one.

A place value chart can be used to understand the value of a digit in a number.

Place value chart also helps to understand decimal numbers, which are numbers that have a decimal point. The decimal point separates the whole numbers from the fractional numbers. Each place to the right of the decimal point represents a smaller value.

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Answer:

I believe it should be 216.54

Step-by-step explanation:

Multiply $200.5 by .08 (the tax) and then add the answer from the multiplication to the $200.5.

A percentage is a way to describe a part of a whole. The cost of a bicycle with tax included is $216.54.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given Megan bought a bicycle that cost $200.50 at a sporting goods store. The sales tax on the bicycle was 8%. Therefore, the total cost will be,

Total cost = $200.50 + 8%

                = $200.50 + (0.08 × $200.50)

                = $216.54

Hence, the cost of a bicycle with tax included is $216.54.

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Answer:

For some reason i couldn't add an answer, but it 8.80 because 9 was rounded to 10 and changed the 7 to 8.

Step-by-step explanation:

First solve for y in \(2x - 3y \le 12\) to get \(y \ge \frac{2}{3}x-4\). The inequality sign flips because we divided both sides by a negative value.

To graph \(y \ge \frac{2}{3}x-4\) we need to graph the boundary line y = (2/3)x - 4. This line has a y intercept of (0,-4) and another point on the line is (6,0).

Draw a solid line through (0,-4) and (6,0). The boundary line is solid because of the "or equal to" part of the inequality sign. The last part is to shade above the boundary line because of the "greater than" sign in \(y \ge \frac{2}{3}x-4\).

---------------

As for graphing y < -3, we draw a horizontal dashed line through -3 on the y axis. The line is dashed because there is no "or equal to" here. We do not include boundary points as part of the solution set. Shade below this dashed line due to the "less than" sign.

---------------

After doing both of these things on the same xy grid, you'll get something that looks like choice C. I'm assuming choice C has a dashed line for the red region.

The graph is image 2. (last option)

We first draw the lines 2x - 3y = 12 and y=-3. Image 1.

For 2x - 3y ≤ 12

or, 2x - 12 ≤ 3y

or, 3y ≥ 2x - 12

or, y ≥ (2x - 12)/3

we shade upwards.

For y < - 3 we shade below.

So the graph is image 2.

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The area of the parallelogram is \(\sqrt{132}\).

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. Sum of all the interior angles equals 360 degrees.

Given that,

vertices k(1, 1, 3), l(1, 3, 5), m(6, 9, 5), and n(6, 7, 3)

Area of Parallelogram = |KL × KN|

KL = (1, 1, 3) - (1, 3, 5) = (0, 2, 2)

KN = (1, 2, 3) - (3, 7, 3) = (2, 5, 0)

Area of the parallelogram = cross product of two vectors, represented by the adjacent sides.

Area of Parallelogram = |(0, 2, 2) × (2, 5, 0)|

                                    = |i(2 × 0 - 5 × 2) - j(0 × 0 - 2 × 2) + k(0 × 5 - 2 × 2)|

                                    = |i(-10) - j(-4) + k(-4)|

                                    = |-10i + 4j - 4k|

                                    = \(\sqrt{(-10)^{2}+(4)^{2}+(-4)^{2} }\)

                                    = \(\sqrt{100+16+16}\)

                                    = \(\sqrt{132}\)

Hence, The area of the parallelogram is \(\sqrt{132}\).

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