Does (9, 0) make the equation y = 8x + 9 true?

The height of the pole anchored to a cable is 6.17 meters.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, The anchor cable is forming an angle of 51° angle with the ground attached to a pole and the distance between them is 5 meters.

So, We need height or the opposite side length with an adjacent length of 5 meters.

We know, tan = opposite/adjacent.

tan51° = opposite/5.

opposite = tan51°×5.

opposite = 1.235×5.

opposite = 6.17 meters.

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The description of isometry and transformations is as follows,

isometry mean A distance-preserving transformation between metric spaces is known as isometry, congruence, or congruent transformation.

The transformation, or f, is a function that maps to itself: X  X. Following the transformation, the pre-image X transforms into the image X. Any or all of the operations like translation, rotation, reflection, and dilation can be used in this transformation. A function is translated by moving it in a particular direction, rotated by spinning it about a point, reflection by reflecting the function, and dilation by scaling it.

Isometry: If two distinct points, a and b, were to be mapped to the same point, then the coincidence axiom of the metric d would be violated. This proof is similar to the proof that an order embedding exists between partially ordered sets. Clearly, a topological embedding exists for each and every isometry between metric spaces.

A bijective isometry is a global isometry, isometric isomorphism, or congruence mapping. A global isometry, like any other bijection, has a function inverse. A global isometry is also the inverse of a global isometry.

Types of transformations;

Transformation of Reflection: The term "reflection" refers to the kind of transformation that takes place when every point in the shape is reflected over a line. The image is on the opposite side of the line from the pre-image but at the same distance from the line when the points are reflected over it. An image point (q,p) is reflected from each point (p,q).

Transformation of Rotation: Rotation is the transformation that rotates each point of the shape by a predetermined number of degrees around that point. When the number of degrees is positive, the shape rotates counterclockwise, and when the number of degrees is negative, the shape rotates clockwise.

Transformation of Translation:  Sliding occurs when a 2-d shape is translated. Let's look at how the vertices of the blue and red figures are positioned in relation to one another in order to describe their relative positions. By comparing its position to the positions of A, B, and C, we must determine their positions.

Hence the basic description of transformation is as follows.

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The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.

The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.

Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.

Given that ΔAED ≈ΔBEC & AC = BD.

as  ΔAED ≈ΔBEC, AD = BC     .................(1)

Now in  ΔABD and ΔBAC,

     AD = BC        

(corresponding sides of similar triangles) [from (1)]

     AB = AB        

(common side)

     AC = BD      

   (given)

∴     ΔABD ≈ΔBAC  (By SSS criteria)    

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The standard form of the function is f(x) = -x² +4x, The vertex form isf(x) = -(x-2)² + 4

What is a function?

A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

Given table is

x           f(x)

-1            -5

0             0

1               3

2              4

3               3

4                0

Find the difference to find the degree of the given function

f(x)                 -5           0           3            4         3          0

1st difference        5           3           1            -1          -3

2nd difference              -2          -2        -2          -2

The degree of the function is 2.

The general form of a second-degree function is

f(x) = ax²+bx+c

Putting x = 0 and f(0) =0 in f(x) = ax²+bx+c:

f(0) = a×0²+b×0+c

0 = c

Now putting x = 1 and f(1) =3 in f(x) = ax²+bx+c:

f(1) = a×1²+b×1+0    [since c=0]

3 = a + b ....(i)

Now putting x = 2 and f(2) =4 in f(x) = ax²+bx+c:

f(2) = a×2²+b×2+0    [since c=0]

4 = 4a + 2b ....(ii)

Solve equations (i) and (ii) by using the elimination method:

Multiply equation (i) by 2 and subtract it from (ii)

4a + 2b  = 4

2a  + 2b  = 6

(-)   (-)         (-)

__________

2a = -2

a = -1

Putting a = -1 in equation (i):

-1 + b = 3

b = 3+1

b = 4

The function is f(x) = -x² +4x

Rewrite the given function in vertex form:

f(x) = -(x² - 4x +4-4)

f(x) = -(x-2)² + 4

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Answer:

Step-by-step explanation:

Vertex (a max) is at (-3, 2).

Axis of symmetry is the vertical line x = -3.

y-intercept is (0, -1)

You can read this info directly from the illustration.

Answer:

use the formula (n-2)×180° where 'n' equals the number of sides the polygon has and this will be the total of all interior angles; if the polygon is 'regular' then you can find each angle measure by dividing total degrees by the number of sides

Step-by-step explanation:

Answer:

Conclusion: Straight line upwards from point (0,3) to (3, 5.25)

Step-by-step explanation:

Your part (a) answer is absolutely correct.

Equation is y = 3/4x + 3

For part (b), you are correct to say that the y-intercept of the graph is 3. The implication is that the initial height of the tree is 3 feet tall. (When the tree just starts to grow at time = 0 years)

Your part (c) answer is absolutely correct as well.

For the graph part,

x = years (independent variable)

y = height (dependent variable)

From the equation you have constructed in part (a), the y-intercept of the graph is 3. Hence, a point (0, 3) can be first plotted in the graph.

Secondly, for part (c), you have also obtained the answer (3, 5.25). Plot that point on the graph as well.

Next, we can see that the graph in (a) is a linear graph in the form y = mx + c, where m is the gradient and c is the y-intercept.

Hence, you can easily draw a straight line upwards from (0,3) to (3,5.25) . It is expected as the gradient of the graph is 3/4, which is a positive number.

If we assume that Cal lives between Beverly and Alex: so the distance between the two of them is 11-4 = 7 miles.

Number line is a line contain every real numbers which includes all rational and irrational number. Generally we use it for determining ranges of a set. Using number line we can understand range and domain of function easily. A number line is a picture representation of real numbers evenly laid out on a straight line.

The distance from zero of a positive number r is simply r. But if r is negative, then we make a positive number by multiplying by -1, in other words -r is the distance in that case.

There is a standard mathematical function that does this, called the modulus function.

And whether r is positive or negative we write it like this |r|

So for example |100|=100 and |-100|=100 as well.

Alex is 11 miles away, and Cal is 4 miles away, so the distance between the two of them is 11-4 = 7 miles.

If we assume that Cal lives on the opposite side of Beverly from Alex:

Alex is 11 miles away from Beverly, and Cal is 4 miles away from Beverly in the opposite direction from Alex, so the distance between Alex and Cal is 11 + 4 = 15 miles.

The easiest way to see this is by creating a number line.

(for the first possible solution) If you put Beverly as a point, let's call it 0, then we would put Alex at 11 and Cal at 4, and the distance between them is 7.

(for the second possible solution) If you put Beverly as a point, 0, then we would put Alex at 11 and Cal at -4, and the distance between them is 15.

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Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 6) and (x₂, y₂ ) = (- 1, 8) ← 2 ordered pairs from the table

m = [tex]\frac{8-6}{-1-1}[/tex] = [tex]\frac{2}{-2}[/tex] = - 1 , then

y = - x + c ← is the partial equation

To find c substitute any ordered pair from the table into the partial equation

Using (1, 6 ) , then

6 = - 1 + c ⇒ c = 6 + 1 = 7

y = - x + 7 → B

90% of all samples have a confidence interval that contains the right average travel time for all employed adults in California.

Increased Sample Size: This provides more information about the population and allows us to calculate an accurate estimate. Data collection is expensive and time-consuming.

Decrease in Confidence Level: Confidence interval having correct population interval is less confident. It has fewer possible values for true population parameters. Hence, it is less confident about the confidence interval has the correct population parameters.

Non-Response Bias

Nonresponse bias happens when there isn't enough data for everyone in the sample. People whose data is unavailable lead to bias and over- or underestimate the true population. The margin of error is not used because it merely takes potential variation into consideration.

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Answer:

C, D, E

Step-by-step explanation:

On solving the provided question we can say that - the probability of the event will be there are two red sides, thus multiplying 16.6667 by two results in 33.3333%.

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

Each side would be 50%, and if one side were divided among three people, it would equal 16.6667 per person.

Given that there are two red sides, you can multiply 16.6667 by 2 to get 33.3333%.

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On solving the provided question we cans ay that - the value of the following exponent is

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where

here,

= [tex]10^2 X 10^-3[/tex] X 32

= 100 X 1/1000 X 32

=1/10 X 32

=3.2

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Answer:

1,023-1,150= -127

Step-by-step explanation:

Answer:

-127

Step-by-step explanation:

Therefore , the solution of the given problem of interest rate comes out to be the amount after 5 years is A  ≈ 364.996.

With the help of an interest rate, you can determine how much borrowing will cost you and how much saving will yield. As a result, the interest rate is the cost of borrowing money and, if you're a borrower, it's expressed as a percentage of the total loan amount. An amount, expressed as a percentage of the loan amount, that a borrower is required to pay to a lender as interest during the term of a loan.

Here,

Given : Principal amount : $300

rate of interest :  4%

and time =5 years

Thus , to find the amount after 5 years as compounded

We use , the formula:

=> A = P

=> A  =

=> A =    

=> A  ≈ 364.996

Therefore , the solution of the given problem of percentage comes out to be the amount after 5 years is A  ≈ 364.996.

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The amount after 5 years with compound interest rate is option(A)  = $365. 00.

The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).

A savings account or certificate of deposit earnings at a bank or credit union may also be subject to an interest rate (CD). The interest received on these deposit accounts is measured in annual percentage yields (APY).

Given : Principal amount : $300

rate of interest :  4% (compounded yearly)

time =5 years

Thus , to find the amount after 5 years as compounded we use , the formula:

=> A = P(1 + r/100)^t.

=> A = $300 (1 +4/100)^5

=> A = $300 (104/100)^5

=> A = $300 (1.04)^5

=> A = $300 * 1.2167

=> A = $365.00

The amount after 5 years with compound interest rate is option(A)  = $365. 00.

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A solution set is the set of all variables or numbers that makes the equation true.

If solving a linear equation leads to a true statement is equal to 0 = 0 the equation is an identity. Its solution set is all real numbers.A solution set is the set of values that satisfy a given set of equations or inequalities. The feasible region of a constrained optimization problem is the solution set of the constraints.

There are three possibilities for the number of real solutions of a quadratic equation, and those are that a quadratic equation can have no real solutions, exactly one real solution, or exactly two real solutions.Zero is considered to be both a real and an imaginary number.

Now we can find solution set by solving the equation.

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Answer:

B.   100

Step-by-step explanation:

(m + n)^2

= m^2 + 2mn + n^2

Rearrange

(m^2 + n^2) + 2mn

Substitute

(68) + 2*16

= 68 + 32

= 100

Comparing the volume of the paints used and analyzing the proportions, The answer is Tina's shade is more blueish and Tyler's shade is more greenish.

A ratio is a way to compare two or more numbers or amounts. It tells you how much bigger or smaller one number is compared to the other. It is often written as two or more numbers separated by a colon, such as "3:5" or "2:4:6". For example, if a recipe calls for 2 cups of sugar to 4 cups of flour, the ratio would be 2:4. This means for every 2 cups of sugar, there are 4 cups of flour. It's a way to express a relationship between values or quantities and it helps to understand the proportion of one value to the other values.

Proportion is a relationship between two or more values or quantities that compares their sizes. It's a way of saying that two or more values are equal in some way. It can be written as an equation, such as "a/b = c/d", which means that the ratio of a to b is equal to the ratio of c to d. In other words, the proportion states that two or more ratios are equal to each other. For example, if a cake recipe calls for 2 cups of sugar to 4 cups of flour, the proportion would be 2/4 = 1/2. This means that for every 2 parts of sugar, there are 4 parts of flour, which can be written as a ratio 2:4 .

Tina's ratio of blue paint to green paint = 777:555

Tyler's favorite shade has a ratio =  555:777.

The ratio for Tina's shade is greater than 1 .

while the ratio for Tyler's shade is less than 1.

So Tina's shade is more blueish and Tyler's shade is more greenish.

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Answer:

x = 31

y = 59

Step-by-step explanation:

90 - 59 = x

x = 31

31 + y = 90

90 - 31 = y

y = 59

Have a nice day!

x² + 14x + 49, this is a perfect square trinomial, which is expressed as

(x + 7)².

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Given that,

x² + 14x + 49

(x)² + 2(7x) + 49

= (x)² + 2(x)(7) + 7²

This is similar to a² + 2ab + b² = (a + b)²

so, we can write:

= (x + 7)²

= (x +7) (x + 7)

so, this is a perfect square trinomial.

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Answer:

187.5

Step-by-step explanation:

Multiply 250 by 75%

Move the decimal over to the left two times= .75

250×.75=187.5

Answer: 201.062

Step-by-step explanation: [tex]A_{s} =4\pi r^2[/tex]

Answer:

B I am guessing, not that good at english, though

Answer:

B..........................................

Answer:

under the figure 16in

Answers

Step-by-step explanation:

You add all of them

Answer:

Step-by-step explanation:

Based on the fact that Ms. Michaels surveyed her class on whether they preferred free time at the beginning of class or at the end of class and found that students who prefer free time at the end of class are 12 over 19, the thing which the ratio 12 over 19 represents is C. 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

What is a Ratio?

This refers to the quantitative relation that is used to show the relation between two variables, which shows the number of times one is contained in the other.

Hence, it can be seen that based on the result of the survey by Ms. Michaels about the preference of the students about free time at the beginning of class or at the end of class, the meaning of the ratio is that 12 students prefer free time at the beginning of class, and 19 students prefer free time at the end of class.

Answer:

Step-by-step explanation:

the ratio 13 over 17 represents how many students preferred free time at the beginning of class to how many students preferred free time at the end of class.a little extra: more people want free time at the end of class than at the beginning

Answer:

$7500

Step-by-step explanation:

Let x = amount of monthly sales.

Choice A:

"monthly salary of $500 plus a bonus of 25% of his monthly sales"

monthly salary = 0.25x + 500

Choice B:

"$2,000 monthly salary with a 5% bonus on sales"

monthly salary = 0.05x + 2000

We set the total monthly salaries equal and solve for x.

0.25x + 500 = 0.05x + 2000

0.2x = 1500

x = 1500/0.2

x = 7500

Answer: $7500