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Express the statement as an inequality part 8a^2

Answer:

Step-by-step explanation:

x + 5 = 3x - 7

-2x = -12

x = 6

x + 5 = 6 + 5 = 11

3(6) - 7 = 18 - 7 = 11

Because the sine of angle ACB = 3/5, then the sine of angle ANM will be equal to 3/5 too.

A triangle is a shape with 3 sides. There are 3 types of triangle which are:

From the diagram, we can see that we have a small triangle inside a big triangle. From the principle of triangle, the angle C is equal to angle N.

Let us say angle C is 30° then the angle N will also be equal to 30*. Therefore the angle ACB = angle ANM = 3/5

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The horizontal asymptote   of  the given function is 0

Given the function y = 19800/x

Vertical asymptote occurs at when f(x) = 0 where;

f(x) is the denominator of the given function.

From the expression given: f(x) = x

Since f(x) => 0, hence x = 0

To get the horizontal asymptote, we will look at the degree of the numerator and denominator.

If the degree of numerator is less than the denominator,

the horizontal asymptote will be zero. From the function, we can see that the degree of the numerator is zero (being a constant) and that of the denominator is 1.

Since 0<1, hence the horizontal asymptote is 0

x = 0, y = 0

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After answering the presented question, we may conclude that  the solution of the expressions are as follows.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

the solution of the expressions are as follows -

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Answer:

need better photos

Step-by-step explanation:

Answer: Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

Step-by-step explanation:

Line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points.

The value of tanQ is 4/3

What is trigonometric ratio?

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

The values of the functions are expressed as follows;

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

The opposite in the triangle is 12 and the adjascent is 9 while th hypotenuse is 15.

therefore , since tan(tetha) = opp/adj

then, tanQ = 12/9

simplifying the value to the nearest term,

tanQ = 4/3

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1. The rule states that the product of the lengths of the two segments of one chord equals the product of the lengths of the two segments of the other chord (i.e., (a1 x a2) = (b1 x b2), where a1 and a2 are segments of chord A, and b1 and b2 are segments of chord B).

2. The rule states that the product of the length of the external segment of one secant and the length of the entire secant equals the product of the length of the external segment of the other secant and the length of the entire secant (i.e., (e1 (e1 + i1)) = (e2 (e2 + i2)), where e1 and e2 are the external segments and i1 and i2 are the internal segments).

3.  The rule states that the square of the length of the tangent segment equals the product of the length of the external segment of the secant and the length of the entire secant (i.e., t^2 = e * (e + i), where t is the length of the tangent segment, e is the external segment, and i is the internal segment).

The three rules of segments are:

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Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

A path that encircles a region is referred to as a perimeter. Adding the lengths of every one of the sides together is the simplest formula for calculating the perimeter. The word circumference, that only encompasses a circle's perimeter, is used to describe the distance around a circle.

Given that:

Perimeter = sum of all sides

Perimeter = AB + BC + CA

Estimate each distance using the distance formula:

d = √(x2 - x1)² + (y2 - y1)²

AB = √(1 - 5)² + (5 - 3)²

AB = √(-4)² + (-2)²

AB = √(16 + 4)

AB = √20

BC = √(3 - 1)² + (0 - 5)²

BC = √(2)² + (-5)²

BC = √(4 + 25)

BC = √29

CA = √(5 - 3)² + (3 - 0)²

CA = √(2)² + (3)²

CA =  √(4 + 9)

CA = √13

Perimeter = AB + BC + CA

Perimeter = √20 + √29 + √13

Perimeter = 4.47 + 5.38 + 3.60

Perimeter = 13.45 units.

Thus, the perimeter of the shown triangle using the distance formula is found as  13.45 units.

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The angle of depression that the paper airplane is flying down at 55. 78 degrees

Note that the different trigonometric identities in mathematics are;

These identities also have their ratios are;

sin θ = opposite/hypotenuse

cos θ = adjacent//hypotenuse

tan θ = opposite/adjacent

From the information given, we have;

Using the cosine identity

Adjacent = 9 feet

Hypotenuse = 16 feet

Substitute the values

cos θ = 9/ 16

divide the values

cos θ = 0. 5625

θ = 55. 78 degrees

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Answer:

55.8° (nearest tenth)

Step-by-step explanation:

The angle of depression is the angle between the horizontal line of sight at the top of the treehouse and line of sight to the sandbox (the flight path of the paper airplane). (See attached diagram).

To find the angle of depression, we can use the cosine trigonometric ratio. The cosine of an angle is equal to the ratio of the length of the side adjacent the angle to the length of the hypotenuse.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

In this case, the length of the side adjacent the angle of depression is equal to the distance between the base of the tree and the sandbox, so A = 9 ft. The hypotenuse is the distance the airplane flies through the air, so H = 16 ft.

Substitute these values into the cosine ratio and solve for θ:

[tex]\cos (\theta)=\dfrac{9}{16}[/tex]

[tex]\theta=\cos^{-1}\left(\dfrac{9}{16}\right)[/tex]

[tex]\theta=55.7711336...^{\circ}[/tex]

[tex]\theta=55.8^{\circ}\; \sf (nearest \; tenth)[/tex]

Therefore, the angle of depression that the paper airplane is flying down at is 55.8° (nearest tenth).

Answer:

5.1

Step-by-step explanation:

x = x+10

6. 42

cross multiply

42x= 6x + 60

42x-6x =60

36x=60

x=1.7

3x= 3×1.7

=5.1

Since p and q are real numbers, the value of q is 21.

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 8x - 5 = 0

x² - 8x = 5

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 8x + (-8/2)² = 5 + (-8/2)²

x² - 8x + 16 = 5 + 16

x² - 8x + 16 = 21

By simplifying, we have;

(x - 4)² = 21

p = 4 and q = 21

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The total number of employees in the organization will be 140.

Given that:

There are 40 employees who have a technical degree

There are 100 employees who have a non-technical degree

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The total number of employees are calculated as,

Total = Employees who have a technical and non-technical degree

Total = 40 + 100

Total = 140

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Therefore , the solution of the given problem of expression comes out to be 6.5 is the abbreviated numerical expression.

Shifting numbers, which can be expanding, variable diminishing, or blocking, should be used instead of random estimations. Only through exchanging goods like tools, expertise, or answers to problems could they assist one another. The explanation on the reality equation may include the justifications, elements, or mathematical claims for tactics like increased argumentation, falsification, and blending.

Here,

The mathematical expression is expressed as follows:

=> 42 / 7 + (3 / 6)

We can use the division operations to make the expression simpler:

=> 7 /42 = 6

=> 6 / 3 = 0.5.

The statement is thus more easily expressed as follows

=> 6 + 0.5

When we add the two numbers, we get:

=> 6.5

Therefore, 6.5 is the abbreviated numerical expression.

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The median is the best measure of center, and it equals 8.

A measure of center is important to understand the central tendency of data.

In this case, the best measure of center for the given data is the median.

The median is preferred over the mean because it is not influenced by extreme values.

By looking at the line graph, it is clear that there are more data points around 8 than any other value.

Therefore, the median would be closest to 8, making it the best measure of center. The median can be calculated by ordering the data from smallest to largest and selecting the middle value.

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Answer:

See the below process

Step-by-step explanation:

let the Unknown value be x.

Now

[tex] \frac{17}{24} + x = \frac{ - 5}{12} [/tex]

[tex]x = \frac{ - 5}{12} - \frac{17}{24}[/tex]

Taking LCM

[tex]x = \frac{ - 10 - 17}{24} [/tex]

[tex]x = \frac{ - 27}{24} \\ = \frac{8}{9} [/tex]

we should add 8/9 to 17/24 to get -5/12

I hope it helped you

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The measure of arc BC is 40⁰.

The measure of angle BPE is 50⁰.

The measure of angle BAD is 55⁰.

The measure of angle AOP is 110⁰.

The measure of angle AFB is 70⁰.

The value of arc DE is 110⁰.

The measure of each angle is calculated as follows;

if arc BA = arc CD, then value of arc BC is calculated as follows;

BA + CD + BC = 180 (sum of angles of a semi circle)

arc CD = 70 (intersecting chord theorem)

70 + 70 + BC = 180

140 + BC = 180

BC = 180 - 140

BC = 40

Arc AE = 70⁰, since angle EOF = 70 (vertical opposite angles)

Arc AB = 180 - (AE + BC)

arc AB = 180 - (70 + 40)

arc AB = 70⁰

The value of angle P is calculated as follows;

arc EB = 70 + 70 = 140⁰

m∠BPE = ¹/₂ (140 - 40)

m∠BPE = 50⁰

m∠BAD = ¹/₂ (BC + CD) (intersecting chord theorem)

m∠BAD = ¹/₂ (40 + 70)

m∠BAD = 55⁰

m∠AOP =  (AB + BC) (intersecting chord theorem)

m∠AOP = (70 + 40)

m∠AOP = 110⁰

m∠AFB = (AB) (intersecting chord theorem)

m∠AFB = 70⁰

The value of arc DE is calculated as follows;

DE = 360 - (180 + CD) (sum of angles of a circle)

DE = 360 - (180 + 70)

DE = 360 - 250

DE = 110⁰

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The value of x unknown for the given shape with given measurements 131°, 122°, 125°, 148°, 107°, 126° is equal to 141°.

The attached figure is seven sided polygon.

Seven sided polygon is called Heptagon.

Sum of all the interior angles of seven sided polygon = 900 degrees

Measurements are,

131°, 122°, 125°, 148°, 107°, 126°

Measurement of seventh angle is unknown.

let the measure of seventh angle be x°

⇒ x° + 131° + 122° + 125° + 148° + 107° + 126° = 900°

⇒ x° + 759° = 900°

⇒ x° = 900° - 759°

⇒ x° = 141°

Therefore, the value of x for the given shape with measurements is equal to 141°.

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The above question is incomplete , the complete question is:

what is the value of x if a shape has sides measuring 131, 122, 125, 148, 107, 126.

Attached figure.

Answer:

t = r + cm

Step-by-step explanation:

t = total amount of money spent on rental car

r equals the original payment amount (like how much it cost to even attain tthe car)

c = the number of dollars for every mile

m = amount of miles

You would multiply c and m since every mile the dollars goes up by itself

You need to add the original payment, r, to find the correct total

If there is no original payment then the formula could also just be :

t = cm

total = miles x money per 1 mile

I could provide better explanation if I had the chart you mentioned but hope this helps!

The sketch of the graph of y = 1/f(x) is added as an attachment

To find the function equation, we need to determine the factors of the equation based on the zeros of the function.

Since the zeros of the function are at x = -5, -1, and 4, the factors of the equation will be:

(x + 5), (x + 1), and (x - 4)

Multiplying these factors together gives us:

f(x) = a(x + 5)(x + 1)(x - 4)

To find the value of the constant term a, we can use the fact that the graph passes through the point (0, -4):

-4 = a(0 + 5)(0 + 1)(0 - 4)

-4 = -20a

So, we have

a = 1/5

Therefore, the function equation is:

f(x) = 1/5(x + 5)(x + 1)(x - 4)

For the graph of y = 1/f(x), we have

y = 5/[(x + 5)(x + 1)(x - 4)]

See attachment for the graph

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Answer: 285 mg is more than 34.4 mg

Step-by-step explanation:

To compare the two quantities, we can simply look at the whole numbers before the decimal point.

285 is a larger whole number than 34, so we can say that 285 mg is more than 34.4 mg.

The decimals after the whole numbers are used to represent the fractions of the numbers.

The probability that the pink can was chosen because the cookie was a sugar cookie is about 0.282, or about 28.2%.

Probability is simply how likely something is to happen. When we are uncertain about the outcome of an event, we can talk about the probability of certain outcomes - how likely they are. The analysis of events driven by probabilities is called statistics.  

We can use Bayes' theorem to calculate the probability that the pink can was chosen because the cookie was a sugar cookie. Let P(P) be the probability that the pink jar was chosen, P(S) be the probability that the chosen cookie  was a sugar cookie, and P(S|P) be the probability that a sugar cookie was chosen given that the pink one was chosen. Then we have:

P(P|S) = P(S|P) * P(P) / P(S)

We can calculate all these probabilities as follows:

P(S|P) = 9 / (15 9 13) = 9/37

This is the probability of choosing a sugar cookie, given that the pink can was chosen.  

P(P) = 1/4

This is the probability of choosing the pink can.

To calculate P(S), we need to consider all possible options for choosing a sugar cookie. We can choose a sugar loaf from a blue, green  or  pink jar. So:

P(S) = P(S|B) * P(B) P(S|G) * P(G) P(S|P) * P(P)

where P(S|B) is the probability of choosing a sugar cookie from the blue jar, P(G) is the probability of choosing the green jar, and so on. We can calculate all these probabilities as follows:

P(S|B) = 12 / (7 12) = 12/19

P(S|G) = 8 / (6 8 5) = 8/19

P(S|P) = 9 / (15 9 13) = 9/37

P(B) = 1/2

P(G) = 1/4

P(P) = 1/4

So,

P(S) = (12/19) * (1/2) (8/19) * (1/4) (9/37) * (1/4) = 271/444

We can now calculate P(P|S) using Bayes' theorem:

P(P|S) = (9/37) * (1/4) / (271/444) ≈ 0.282

Therefore, the probability that the pink can was chosen because the cookie was a sugar cookie is about 0.282, or about 28.2%.

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Answer: D-perimeter

Step-by-step explanation: The sum of the lengths of all the sides of a closed figure is called its perimeter.

Answer:

Perimeter

Step-by-step explanation:

The sum of the lengths of all the sides of a closed figure is called its perimeter.

The equation of the ellipse is ((x+2)² / 36) + ((y-4)² / 35.12) = 1

To find the center of the ellipse, we can find the midpoint between the two vertices:

Midpoint = ((-8 + 4)/2, (4 + 4)/2) = (-2, 4)

So the center of the ellipse is (-2, 4).

To find the semi-major axis (a), we can find the distance from the center to one of the vertices:

Distance = √[(-8 - (-2))² + (4 - 4)²] = √36 = 6

So the semi-major axis is 6.

To find the distance between the foci (2c), we can find the distance between the two foci:

Distance = √[(-3 - (-1))² + (4 - 4)²] = 2

So 2c = 2 and c = 1.

Now we can use the relationship between a, b, and c in an ellipse:

c² = a²- b²

(1)² = (6)² - b²

b² = 35

b ≈ 5.92

So the semi-minor axis is approximately 5.92.

Therefore, the equation of the ellipse is ((x+2)² / 36) + ((y-4)² / 35.12) = 1

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Correct question is "vertices at (-8, 4) and (4, 4), foci at (-3, 4) and (-1, 4), find the equation of the ellipse."

The reasonable constraint so the function is at least 600 would be A. 0 ≤ x ≤ 20.

Given the function y = -2x² + 40x + 600, we want to find the constraint for x so that the function's value is at least 600.

Since the parabola opens downward (as a is negative), the function will be at least 600 for all values of x within the interval where the parabola is above y = 600. The vertex of the parabola is at its maximum value, so we should look for the interval around the vertex (10, 800).

Looking at the given constraints, the option "0 ≤ x ≤ 20" is a reasonable constraint that ensures the function is at least 600. The parabola starts at a value of 600 at x = 0, reaches its maximum value at the vertex, and then returns to a value of 600 at x = 20.

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Each cube has a volume of 1 cm³, and the rectangular prism contains 320 cubes, so the volume of the rectangular prism is 320 cm³.

Volume is a physical quantity that measures the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters (m³) or cubic centimeters (cm³).

Here,

Length side = 4 cubes

= 5 cm

Width side = 2 cubes

= 2 cm

Height side = 2 cubes

= 2 cm

The length of the rectangular prism is 4 cubes which are equal to 5 cm each, so the length is 4 x 5 cm = 20 cm. The width of the rectangular prism is 2 cubes which are equal to 2 cm each, so the width is 2 x 2 cm = 4 cm. The height of the rectangular prism is 2 cubes which are equal to 2 cm each, so the height is 2 x 2 cm = 4 cm.

To find the volume of the rectangular prism, we multiply the length by the width by the height:

Volume = length x width x height

Volume = 20 cm x 4 cm x 4 cm

Volume = 320 cubic cm

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Complete question:

Each cube in this rectangular prism is 1 cm³. What is the volume of the rectangular prism?

The tools you can use to measure the object is Ruler

First you need to Indicate the starting and ending points of the curved line on the string. To determine the distance between the two markings on the string, lay the string flat on a ruler, or a stretched-out measuring tape if the line is curved, and measure the length in between.

Commonly found in bars and restaurants, disposable straws intended for one-time use have a common size of 8.5 inches in length and width. The typical size of a drinking straw is  one that is having a width of 24 inches. At times, you may need a lengthier or broader straw to suit yourself.

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Row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

row 1 of the given matrix are: 2, 0, and 3, multiplying row 1 with 1/4 gives;

1/4 × 2 = 1/2

1/4 × 0 = 0

1/4 × 3 = 3/4

Therefore, row 1 in the matrix multiplied by 1/4 will produce: 1/2, 0, and 3/4 respectively.

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The system of equations defined is:

x = 2y

x*0.05 + y*0.10 = 1.40

First we need to define the variables:

x = number of nickels

y = number of dimes.

Now we can find the equations, we know that he has twice as many nickels as dimes, then:

x = 2y

We also know that Tristan has $1.40 then we can write:

x*0.05 + y*0.10 = 1.40

So the system of equations is:

x = 2y

x*0.05 + y*0.10 = 1.40

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