For equation y = - 4x + 5, a) complete the table of values. Table of Values X. Y 0 1 2B) plot the points found in the above table using •C) Graph the line represented by the given equation using

Answer:

We conclude that \(\sqrt{5}, \sqrt{5},\sqrt{10}\) is an isosceles right triangle.

Step-by-step explanation:

Given the sides of a triangle

\(\sqrt{5}, \sqrt{5},\sqrt{10}\)

Given that the two sides are equal. Thus, it must be an isosceles triangle.

Let us check whether it is an isosceles right triangle or not.

We know that for a right-angled triangle with sides a, b and the hypotenuse c is defined as:

\(c=\sqrt{a^2+b^2}\)

Given

\(a=\sqrt{5}\)

\(b=\sqrt{5}\)

now substituting \(a=\sqrt{5}\) and \(b=\sqrt{5}\) in the equation

\(c=\sqrt{a^2+b^2}\)

\(c=\sqrt{\left(\sqrt{5}\right)^2+\left(\sqrt{5}\right)^2}\)

\(c=\sqrt{10}\)

Thus,

\(a=\sqrt{5}\)

\(b=\sqrt{5}\)

\(c=\sqrt{10}\)

Which satisfies the given side lengths \(\sqrt{5}, \sqrt{5},\sqrt{10}\)

Therefore, we conclude that \(\sqrt{5}, \sqrt{5},\sqrt{10}\) is an isosceles right triangle.

The coordinate of point D and point E will be (x, y) and (-x, y), respectively.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line in the m:n ratio, finding the mid-point of the line, etc.

Let the coordinate of the point D be (x, y).

Point E has a similar y-coordinate as point D. Then the ordinate of the points will be the same.

And the x-direction of point E is something contrary to the x-direction of point D. Then the coordinate of point E will be (-x, y).

The coordinate of point D and point E will be (x, y) and (-x, y), respectively.

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Answer: A on Edge

Step-by-step explanation:

Hi there!

\(\boxed{-\frac{4x}{3}sin(2-3x) + \frac{4}{9}cos(2-3x) + C}\)

To find the indefinite integral, we must integrate by parts.

Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":

u = 4x

du = 4

dv = cos(2 - 3x)

v = 1/3sin(2 - 3x)

Write into the format:

∫udv = uv - ∫vdu

Thus, utilize the solved for expressions above:

4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx

Simplify:

-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx

Integrate the integral:

∫4/3(sin(2 - 3x)dx

u = 2 - 3x

du = -3dx ⇒ -1/3du = dx

-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C

Combine:

\(-\frac{4x}{3}sin(2-3x) + \frac{4}{9}cos(2-3x) + C\)

Answer:

this is your answer look it once

Answer:

  B.  A point

Step-by-step explanation:

You want a description of the intersection between a plane and a cone given that the plane is parallel to the base and passes through the vertex of the cone.

The vertex of a cone is a single point. If a plane passes through that, but does not intersect the base of the cone, it will not intersect anywhere else.

The intersection is one point.

__

Additional comment

Figure f in the attachment illustrates this case.

Answer:

Step-by-step explanation:

ANSWER

Length = 12 ft;

Width = 6 ft

EXPLANATION

We have that the ratio of the length and width is 6 : 3.

The area of the rectangle is 72 square feet.

The area of a rectangle is given as:

A = L * W

where L = length

W = width

From the ratio, we have that:

L : W = 6 : 3

That is:

Therefore, the area of the rectangle is:

Therefore, the length is:

L = 2 * W

L = 2 * 6

L = 12 ft

Therefore, the dimensions of the rectangle is length of 12 ft and width of 6 ft.

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x).

\(lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5\)

from the graphs n f (x) and g( x) are 1 and 5 .

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The measure of the angles are 60 degrees each

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

AOB = 138 degrees

Also, we have:

The line OX bisects the angle AOB

Using the above as a guide, we have the following:

AOX = AOB/2 = 138/2 = 69

Also, we have

XOB = AOB/2 = 138/2 = 69

Hence, the angles are 69 degrees each

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The acceleration of the car is 8 m/s^2.

The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.

Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.

(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m

(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2

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It is just a way of describing a set.

You put the set in braces (sometimes called curly brackets), {}, which is a typical way to show that you are talking about sets.

Here are a few examples:

{x| x > 0} This is read: The set of all x such that x is greater than 0.

Reading it character by character:

{ — shows you that we are talking about a set, and it sort of opens up, or starts the set

x — tells you that we are talking about a set of elements x

| (and a : is also used sometimes) — such that (this is just notation). This says that you are about to be given to rule to see what “rule” or characteristic the x’s will have.

x > 0 — This just says what characteristics x must have to be in this set. So 7, 1/2, .3 and pi are all in this set, while -1, 0, -radical(2) are not.

So this example is just how you would use set builder notation to talk about the set “the positive real numbers”

So why use it? Because it can describe more complicated sets much more succinctly.

2. {3n + 1 | n is an element of the natural numbers} (and this could be written more succinctly if I used certain symbols) would be the set {4, 7, 10, 13, …}

3. {n^2 + n + 1 | n is an element of the natural numbers} would be the set {3, 7, 13, 21, …} and notice here, if you didn’t see the set builder notation, you might have trouble knowing what the next term in the set was.

Answer:-2

Step-by-step explanation:

Ok so I’m assuming the x stands for the multiplication sign

7/2-4.5*3+8

Use pemdas

Multiplication first

7/2-4.5*3+8

-4.5*3

7/2-13.5+8

Then addition

-13.5+8

Lastly subtraction

7/2-5

-2

Answer:

50%

Step-by-step explanation:

because 15 is half of 30

From the graph, the coordinates of the points of the equation y=(x-1)(x-3): (1,0) (4,0), P(0,3) and turning point (2.5,2)

You should know that these are possible reading from the graph

The scale of the graph is [laced at 1 com to 1 unit on both axes

From the graph, the coordinates of A are (1, 0) This is where x=1 and y=0

The coordinates of B = (4, 0) This is where x=4 and y=0

b)  The coordinates of point P are (0,3) This is where x=0 and y= 3

c) The coordinates of the turning point are (2.5, 2) This is the minimum value of the curve

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There are 152 red pens and 190 blue pens in Max's drawer, given that there are a total of 342 pens altogether.

Let's solve the problem step by step:

Identify the given information:

The ratio of red pens to blue pens is 4 to 5.

There are a total of 342 pens in the drawer.

Set up the ratio equation:

Let's assume the number of red pens is 4x, and the number of blue pens is 5x.

Here, 'x' is a scaling factor that allows us to find the actual number of pens.

We can write the equation as: 4x + 5x = 342.

Simplify and solve the equation:

Combining like terms, we have 9x = 342.

Divide both sides of the equation by 9 to solve for 'x':

x = 342 / 9 = 38.

Calculate the number of red pens and blue pens:

Now that we have the value of 'x', we can find the number of red and blue pens:

Number of red pens: 4x = 4 × 38 = 152.

Number of blue pens: 5x = 5 × 38 = 190.

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Answer:

See Explanation

Step-by-step explanation:

Given

\(Weight = 41.3kg\)

Required

Determine the weights that approximates to 41.3kg

The options are not given but the question is still solvable

In approximation:

0 - 4 approximates to 0

This implies that:

41.30 to 41.34 approximates to 41.3

Also:

5 - 9 approximates to 1

This implies that:

41.25 to 41.29 approximates to 41.3

Bring the range together, we have:

\(Range = 41.25\ to\ 41.34\)

Select any three numbers within this range, and you have your answer

Examples are: 41.25, 41.28, 41.34\

The complete expression is 8/6 < 9/6

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

_ / 6 < 9/6

Express properly

So, we have the following representation

_ / 6 < 9/6

Represent the blank with x

x / 6 < 9/6

Multiply both sides of the expression by 6

So, we have the following representation

x < 9

This means that x is any value less than 9

An instance is 8

Hence, the solution to the expression is 8/6 < 9/6

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A 45°-45°-90° triangle is a special right triangle where the two legs are congruent and the hypotenuse is √2 times the length of the legs.

Let's say that the length of one leg is "x". Because the two legs are congruent, the length of the other leg is also "x".

Using the Pythagorean theorem, we can find the length of the hypotenuse:

c² = a² + b²

c² = x² + x²

c² = 2x²

c = √(2x²) = x√2

Therefore, the length of the hypotenuse is x√2.

To find the missing sides of the triangle, we need to know one side length. If we are given the length of the hypotenuse or one of the legs, we can easily find the other sides.

For example, if we are given the length of one leg as 5 cm, we can find the lengths of the other sides as follows:

Legs = 5 cm

Hypotenuse = legs * √2 = 5 cm * √2 ≈ 7.071 cm

Therefore, the missing sides of the 45°-45°-90° triangle with one leg equal to 5 cm are approximately 5 cm and 7.071 cm.

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Answer:

Step-by-step explanation:

8.008.009

Answer:

0.783, just look at the pattern.

If you're comparing, this is the answer:

<

A zero of a polynomial f(x) is a value of x such that f(x)=0.

When a polynomial is written as the product of binomial factors, we can easily find its zeroes by looking at the values of x which make each binomial equal to 0. In this case:

Notice that this polynomial is composed by two different binomial factors:

If any of those factors are equal to 0, the whole polynomial will be equal to 0 since the product of 0 times any algebraic expression is always equal to 0.

Then. the zeroes of the function are the values of x such that:

Solving each equation for x, we can see that the zeroes of the polynomial are x=5 and x=-1.

On the other hand, the multiplicity of those zeroes is equal to the exponent of the corresponding binomial. The exponent of (x-5) is 5, then the multiplicity of the x=5 zero is 5.

Similarly, the multiplicity of the x=-1 zero is 7.

Therefore, the zeroes of the polynomial f(x)=(x-5)^5*(x+1)^7 and their multiplicities are:

The group of rotations and symmetries of a geometric configuration is the group of isometries.

According to the above paragraph, "the group of rotations and symmetries of the configuration" refers to the group of isometries of a geometric configuration that preserve the configuration itself, without involving any translations. This group consists of rotations about a fixed point and symmetries about a straight line that pass through that point.

This group is formed by combining isometries of the configuration through the operation of composition, and it satisfies certain properties, such as closure, associativity, identity, and inverses. It is a useful tool for studying the symmetries and transformations of the configuration, and it is used in fields such as crystallography and quantum mechanics.

In summary, the group of rotations and symmetries of a geometric configuration is the group of isometries that preserve the configuration and can be composed with each other to obtain new isometries.

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Answer:

9/41

Step-by-step explanation:

Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side)  which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.

Answer:

B

Step-by-step explanation:

Answer:

68.42%

Step-by-step explanation:

We need to find the percent of Cr in \(Cr_2O_3\).

Mass of Cr = 52 amu

Mass of O = 16 amu

Firstly, we will find the molar mass of \(Cr_2O_3\) as follows :

M = 2(52) + 3(16)

M = 152 amu

Percent of Cr in  \(Cr_2O_3\) will be :

\(Cr=\dfrac{2\times 52}{152}\times 100\\\\=68.42\%\)

Hence, the required percentage is 68.42%.

Answer:

Second test=88

Third test=89    Hope this helps please mark brainliest it helps a lot! Thanks!

Step-by-step explanation:

According to the question, here we got to know that John scored 72 points in the first test

In the second he scored higher than the 1st test

In the third he scored 1 mark more than the second test

His average in the three tests was 83

So,

Let's the marks scored in the 2nd test be x

Hence, in the third test he got x + 1

Average is 83

\( \frak{Average = \frac{{1}^{st} \: test + {2}^{nd} \: test + {3}^{rd} \: test }{3} } \\ \\ \dashrightarrow \frak{83 = \frac{72 + x + x + 1}{3}} \\ \\ \dashrightarrow \frak{83 = \frac{73 + 2x}{3}} \\ \\ \dashrightarrow \frak{249 = 73 + 2x } \\ \\ \dashrightarrow \frak{249 - 73 = 2x} \\ \\ \dashrightarrow \frak{249 = 73 + 2x } \\ \\ \dashrightarrow \frak{x = \frac{176}{2} } \\ \\ \dashrightarrow \frak{249 = 73 + 2x } \\ \\ \dashrightarrow \frak{249 - 73 = 2x} \\ \\ \dashrightarrow \frak{249 = 73 + 2x } \\ \\ \star \qquad \boxed{ \green{\frak{x = 88}}} \\ \\ \sf{ \underline{{2}^{nd} \: test }} : \\ \\ \boxed{ \red{88}} \\ \\ \sf{ \underline{{3}^{rd} \: test }} : \\ \\ \rightarrow x + 1 \\ \\ \rightarrow 88 + 1 \\ \\ \boxed{ \red{ 89 }}\)

First, let's define rational and irrational numbers.

Rational numbers. Are those numbers that can be expressed as the ratio of 2 integers.

Irrational numbers. These numbers are the opposite of rational numbers, they can't be expressed at the ratio of 2 integers abd their decimal numbers are infinite.

Now, addressing the question, to order rational and irrational numbers we must take a close look th the decimal numbers given for the rational number.

For example, say that we are comparing 9.43 and \(\sqrt{89} \\\). Let's convert the numbers to their decimal form to easily compare them.

9.43 is already a decimal.

\(\sqrt{89} =9.433981132\).

Based of the obtained values, the greatest number of these 2 is, clearly, \(\sqrt{89} \\\). In case we are comparing these same 2 numbers, and we are only given the decimal form of \(\sqrt{89} \\\) as 9.43, we can still affirm that \(\sqrt{89} \\\) is the greatest number, because it's irrational, it has more decimal numbers that are greater than those on 9.43, which only has 2.

The way to compare and order rational and irrational numbers is to convert all the numbers to their decimal form and see who has the greater value. It's important to always keep in mind that irrational numbers have infinite decimal figures. If we have the exact same decimal figures for an irrational and a rational number, the irrational number will always be greater since it has infinite decimal places.

9514 1404 393

Answer:

Step-by-step explanation:

Corresponding sides have the same ratio in similar figures.

1. x/20 = 6/15

  x = 20(6/15) = 8 . . . . multiply by 20

__

2. x/20 = 14/8

  x = 20(14/8) = 35 . . . . multiply by 20