The triangle below is equilateral. Find the length of side x in simplest radical form with a rational denominator.

Answer:

Slope-intercept form: y=3/4x+3

Slope:3/4

y-intercept: (0,3)

Slope of line perpendicular: -4/3

Slope of line parallel: 3/4

Hope this helps!!

y=3/4x+3

the slope for the line perpendicular is the inverse negative slope which would be -4/3x

put in the original slope for the slope and the y-i is (0,3)

any line with the same slope would be parallel (i.e 3/4)

Answer:

A) The verb "waddled" most accurately and vividly describes the action in this situation, as "waddle" is a verb used to describe a slow and awkward gait often associated with a heavily pregnant woman. This verb conveys the idea of the woman's awkward and unsteady movement, making it the most accurate and vivid description of her actions.

Prove of that if the lengths of two sides of a triangle are a and b, respectively, then the lengths of the corresponding altitudes to those sides are in the ratio b.

A triangle is a three by three-sided polygon having three angles and three sides. It is one of the most fundamental and basic shapes in geometry and is used in many other fields of physical science. Triangles are also utilized in architecture and other areas of design and come in a variety of shapes.

Let, a triangle Δ ABC be given, and let its sides be BC = a and AC = b

(figure is given below)

Let, AM and BN are altitudes of corresponding sides of traingle Δ ABC.

We know that the altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side.

Notice two right-triangles triangles Δ AMC and Δ BNC

We can conclude that the pairs of congruent angles are:

Δ AMC ≅ Δ BNC ≅ 90°

∠ACM ≅ ∠BCN          (common angle)

So, Δ AMC ≈ Δ BNC by the Angle-Angle Similarity Theorem

The triangles are similar and therefore their corresponding angles are congruent:

AM/BN = AC /BC = a/b

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The rate of change over the interval 15 ≤ x ≤ 18 is equal to 2/3 or 0.67.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function y(x) over the interval [15, 18]:

a = 15; g(a) = 3

b = 18; g(b) = 5

Substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (5 - 3)/(18 - 15)

Average rate of change = 2/3

Average rate of change = 2/3 or 0.67.

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Answer:

e and b!

Step-by-step explanation:

the difference is basically a "-minus"

- meaning it's getting smaller

meaning that it's subtracting from this number so basically 12 - 20% is basically what it means but if you take those altogether it takes out the b and e

basically in your head C&D will also be an answer

is definitely out of your track with the difference between those

could you please crouwn me brainliest?

Hello :3

Answer:

C. what is m<ACB

Explanation:

Because you found the angles of ABC and BAC which is 35 and 115, it would only be appropriate to find ACB as well! :)

Hope this helps! ;)

Answer:

155

Step-by-step explanation:

see attached.

Therefore , the solution of the given problem of relative frequency comes out to be  nonfiltered cigarettes have a higher relative frequency of cigarettes with higher tar grades.

A class interval's frequency is the amount of observations that take place during a specific predetermined interval. In other words, the frequency for such 5–9 age range is 20 if there are 20 children between the ages of 5 and 9 in the data from our study.

Here,

Tar(mg) Rel. freq.(Non-filtered) Rel. freq.(filtered)

4 to 9              0                            0.12

10 to 15               0                    0.08

16 to 21            0.04                       0.2

22 to 27           0.08                        0.6

28 to 33          0.52                           0

34 to 39            0.32                           0

40 to 45           0.04                            0

and

Yes, since nonfiltered cigarettes have a higher relative frequency of cigarettes with higher tar grades.

Therefore , the solution of the given problem of relative frequency comes out to be  nonfiltered cigarettes have a higher relative frequency of cigarettes with higher tar grades.

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The linear equation that represents the given literal problem is  3x+12= 28.50 (letter D) and Ava pays $5.5 (letter B)  for each pumpkin.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=9x+5. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=9 and b=5.

The exercise presents two questions, before solving them, you should convert the given text information into equations.

Data question

     1) Question 1

     Here you should write a linear equation that represents the given problem. Thus, you can write

    3x+12= 28.50

    Since 3x represents the payment of pumpkins and the value 12 is the difference between the total of Ava´s money and the total cost of pumpkins.  

    Therefore, the answer to question 1 is the letter D ( 3x+12= 28.50)

   2) Question 2

As you know the equation that represents the problem, for solving this question you need to find the value of x.

    3x+12= 28.50

     3x=28.5-12

    3x=16.5

      x=16.5/3

      x=5.5 (letter B)

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Erin uses sugar at a faster rate than Lucia. This can be seen by comparing the equation for Lucia's cups of tea (y = 10x) to Erin's cups of tea (6, 8, 10, 4).

An equation is a statement that expresses the equality of two values. It consists of an expression containing variables, constants, and operators, and is used to solve mathematical problems. Equations are used to describe the relationships between different variables and can be used to solve for the unknown value of one of those variables. As the number of cups increases, the amount of sugar used by Erin increases at a faster rate than the amount of sugar used by Lucia.

For example, for 6 cups of tea, Erin uses 8 pounds of sugar, while Lucia uses 10 pounds of sugar. For 12 cups of tea, Erin uses 10 pounds of sugar, while Lucia uses 20 pounds of sugar.

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Using time value of money tables the following are -

(a) The future value of $450 six years from now at 7 percent is $675.33.

(b) The future value of $900 saved each year for 10 years at 8 percent is $13037.91.

(c) The amount a person would have to deposit today (present value) at an interest rate of 6 percent to have $1,000 five years from now is $747.26.

(d) The amount a person would have to deposit today to be able to take out $600 a year for 10 years from an account earning 8 percent is $8691.93.

What in annuity?

An annuity is a contract that you have with an insurance provider that calls for regular payments to be made by the insurer to you, either now or in the future.

(a) The future value of $450 six years from now at 7 percent.

FV= PV × (1 + r)n

FV= $450 × (1 + 7%)6

FV= $450 × (1.07)6

FV= $450 × 1.50073

FV= $675.33

(b) The future value of $900 saved each year for 10 years at 8 percent.

This is annuity as $900 is saved each year

Formula :: FV = PMT * (((1 + r%)n - 1) / r%)

FV = $900 × (((1 + 8%)10 - 1) / 8%)

FV= $900 × 14.4865624

FV= $13037.91

(c) The amount a person would have to deposit today (present value) at a 6 percent interest rate to have $1,000 five years from now.

PV= FV / (1 + r)n

PV= $1000 / (1 + 6%)5

PV= $1000 / 1.3382255

PV=$747.26

(d) The amount a person would have to deposit today to be able to take out $600 a year for 10 years from an account earning 8 percent.

Annuity value = $600

FV= Annuity value × Annuity factor(10%,8 year)

= $600 × (((1 + 8%)10 - 1) / 8%)

= $600 × 14.4865624

= $8691.93

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The positive number we're looking for is 5/16.

What is the Equation?

An equation is a mathematical statement that asserts the equality of two expressions.

Let's call the positive number we're looking for x. Then, the problem can be expressed as two equations:

[tex]12x^2 = 4x + 5x^2 = (4/12)x + 5/12\\\x^2 = (1/3)x + 5/12\\\\x^2 - (1/3)x = 5/12\\(4/3)x = 5/12\\x = 5/12 * (3/4)\\x = 5/16[/tex]

Hence, the positive number we're looking for is 5/16.

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The positive number we're looking for is 5/16.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, the equation 6x + 5 = 20 consists of the two equations 6x + 5 and 20, which are separated by the 'equal' sign.

A mathematical statement that claims the equivalence of two expressions is known as an equation.

Let's call the positive number we're looking for x.

Then, the problem can be expressed as two equations:

12x² = 4x + 5x² = (4/12) x + (5/12)

x² = (1/3) x + (5/12)

x² - (1/3) x = (5/12)

(4/3) x = (5/12)

x = (5/12) × (3/4)

x = 5/16

Hence, the positive number we're looking for is 5/16.

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Answer:

Step-by-step explanation:

2:3 / 8/4

firt step you need factorize

2/3 /2

because 8/4 =2;

2/3:2/1

we have formula

2/3*1/2

answer is :2/6 => 2:2/6:2 => 1/3

The value of a must be equal to (k + 2), and then the equation is only true if k = 6, then a = 8.

We want the equation:

(k + 2)x + 3k = ax + 18

To be true for all values of x, then we must have the same thing in both sides of our equation.

Now we wod want the dependence on x to dissapear, then:

(k + 2)x = ax

(k + 2) = a

That must be value of a, and then the equation becomes:

k*x + 2x + 3k = (k+ 2)x + 18

3k = 18

This is only true if k = 6, then:

k + 2 = a

6 + 2 = a

a = 8

That must the value of a.

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The lowest score for the normally distribution with mean 72 and standard deviation 8 is equal to 82.

Mean of the normally distributed data 'μ' = 72

Standard deviation 'σ ' = 8

Lowest score with 10% ( 90percentile )

z = InvNorm(0.90)

 = 1.28

Let 'X' be the lowest score for the normal distribution

z = ( X - μ ) / σ

Substitute the values we get,

⇒ 1.28 = ( X - 72 ) / 8

⇒ X - 72 = 1.28 × 8

⇒ X = 10.24 + 72

⇒ X = 82.24

⇒ X = 82 ( round to an integer )

Therefore, the lowest score for normally distribution which will place manage on 90th percentile with given mean and standard deviation is equal to 82.

The above question is incomplete, the complete question is:

Scores on a management aptitude examination are normally distributed with a mean of 72 and a standard deviation of 8.we want to find the lowest score that will place a manager in the top 10% (90th percentile) of the distribution. Your answer is Please round to an integer number.

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Answer:

To convert the weight from pounds to tons, we can divide the weight by 2,000, since there are 2,000 pounds in a ton.

3.9 million pounds / 2,000 = 1,950 tons

So, a fully loaded and fueled spacecraft that weighs close to 3.9 million pounds can be said to weigh 1,950 tons.

The coordinates of point c on the coordinate plane are (4, 1)

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

B = (10, 7)

M = (7, 4)

The midpoint formula for two points (x1, y1) and (x2, y2) is:

(x1 + x2) / 2 = x_midpoint

(y1 + y2) / 2 = y_midpoint

So, for points B and C, we have:

x_midpoint = 7

y_midpoint = 4

Also, we have

x_B = 10

y_B = 7

The coordinates of C are calculated as

x_C = 2 * x_midpoint - x_B = 2 * 7 - 10 = 4

y_C = 2 * y_midpoint - y_B = 2 * 4 - 7 = 1

The coordinates of point C are (4, 1).

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Answer:x=8

Step-by-step explanation:

The interior angles of a triangle add up to 180 so

2x+39 + 2x+70 + x+31 = 180

2x + 2x +x=180-39-70-31

5x= 40

x=40/5

x=8

x+31 is in there because one of the int angles of the triangles is congruent with the angle of x+31

The equation of the surface of the sphere is

z = √(100 - (x - 4)² - (y + 3)²). The solution has been obtained by using equation of sphere.

What is a sphere?

A sphere has a round shape and symmetrical arrangement. This three-dimensional solid's surface points are evenly spaced apart from the centre. It has both a volume and a surface area, depending on the radius. It has no faces, corners, or edges.

We know that general form of an equation of sphere is

(x - a)² + (y - b)² + (z - c)² = r²

where a, b, c are the coordinates and r is the radius.

The equation of the sphere is

(x - 4)²+ (y + 3)² + z² = 10²

So, the equation of the bottom hemisphere of sphere is

z = √(100 - (x - 4)² - (y + 3)²)

Hence, the equation of the surface of the sphere is

z = √(100 - (x - 4)² - (y + 3)²).

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Answer:y = (5/4)x - 3/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the limit of f(x) as x approaches 6 is 2, then 3f(x) is 3 times 2 which is 6. If the limit of g(x) as x approaches 6 is 8, then 5g(x) is 5 times 8 which is 40. Subtract the two results:

6 - 40 = -34

Answer:

No solution.

Step-by-step explanation:

First, we can simplify both sides of the equation by squaring them. This gives:

(√x+12)² = (√x + 2)²

Expanding both sides, we get:

x + 24√x + 144 = x + 4√x + 4

Moving all the terms to one side, we get:

20√x + 140 = 0

Subtracting 140 from both sides, we get:

20√x = -140

Dividing both sides by 20, we get:

√x = -7

However, this is not a valid solution for x, since the square root of a number cannot be negative. Therefore, there is no solution for x that satisfies the given equation.

Using proportional relationships, it is found that:

1. A = 15.8, B = 5, C = 63.2.

2. A table with a rate of 0.82 represents the data.

3. Candidate B received 54 votes.

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, also called unit rate, as follows:

y = kx

here, we have,

For item 1, the constant is given as follows:

k = 31.6/4 = 7.9.

Hence the equation is:

y = 7.9x.

Then the value of A is found as follows:

A = 7.9(2)

= 15.8.

The value of B is found as follows:

7.9B = 39.5

B = 39.5/7.9

B = 5.

The value of C is:

C = 7.9(8) = 63.2.

For item 2, the rate is given as follows:

k = 35/42.5 = 0.82.

Hence a table with a rate of 0.82 represents the data.

For item 3, we have that the relation is:

B = kA.

Hence the constant is:

k = 18/15

k = 1.2.

Then the number of votes received by Candidate B is:

B = 1.2 x 45 = 54 votes.

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Answer:

3

Step-by-step explanation:

The degree of a polynomial in two or more variables is the highest of the sum of the degrees of each variable

Here there is only one term with variables x and y: xy²

Degree of x = 1, degree of y = 2

Sum of the individual degrees = 1 + 2 = 3

Answer:

y = 4/5 x + 5

Step-by-step explanation:

Slope

Change in y over the change in x

[tex]\frac{1-5}{-5-0}[/tex] = [tex]\frac{-4}{-5}[/tex] = [tex]\frac{4}{5}[/tex]

The slope is [tex]\frac{4}{5}[/tex]

The y-intercept is 5.  It comes from the point (0,5).

Given the problem: Linear equation that passes through the points of (0,5) and (-5,1).

First, whenever you are asked to find a linear equation that passes through two points, remember its going to be slope intercept equation, or y=mx+b. m is the slope, b is the y-intercept.

The y-intercept is where the line crosses the y-axis. The slope can be written as rise/run. Rise and run right is positive, drop and run left is negative.

So in this case, looking at the first point: (0,5), we can see that the y-intercept is 5. Now let's find the slope. We will start at (-5,1) and go to (0,5). Count how many units we rise/drop and how many units we run. Rise 4, run right 5. So the slope is 4/5. Now put all the information into y=mx+b.

Your answer is y=4/5x+5

the four key assumptions which are required for multiple linear regression analysis are.

A regression model known as multiple linear regression uses a straight line to calculate the association between two or more independent variables and a quantitative dependent variable.

1.

the four key assumptions which are required for multiple linear regression analysis are:

A non-linear data transformation or the inclusion of a quadratic factor may be able to solve the issue if the data are heteroscedastic.

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