Draw the following triangle after a 90 degrees counterclockwise rotation about the origin.

Answer:

To make x the subject of the formula, we can isolate x by subtracting 1 from both sides of the equation:

x + 1 = 4y

x + 1 - 1 = 4y - 1

x = 4y - 1

So x is equal to 4y minus 1.

Answer:

[tex]x = 4y - 1[/tex]

Step-by-step explanation:

Currently x is on the left side of the equal sign and is being added to 1. x has to be isolated and be by itself on one side of the equal sign in order to be made the subject of the formula. Therefore the 1 needs to be moved to the other side of the equal sign:

             [tex]x = 4y - 1[/tex]

Answer:

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

Full surface area is the sum of areas of 4 triangles and the square base:

Find the height h of the pyramid, using slant height and the side of the base and Pythagorean:

Find the volume:

The points M(0, -1), and T(4, 6), on the diagonal [tex]\overline{MT}[/tex] of the rhombus MATH, indicates that the equation of the line containing the diagonal [tex]\overline{AH}[/tex], in slope and intercept form is; [tex]y = 3\frac{9}{14} - 4\cdot \frac{x}{7}[/tex]

A rhombus is a quadrilateral that has four congruent sides.

The specified shape of the quadrilateral MATH = A rhombus

The coordinates of the endpoints of the diagonal [tex]\overline{MT}[/tex] of the rhombus are;

The equation of the line that contains the diagonal [tex]\overline{AH}[/tex] of the rhombus can be found as follows;

The diagonals of a rhombus are perpendicular, therefore, the slope of the diagonal, [tex]\overline{AH}[/tex]is -1 divided by the slope of the diagonal [tex]\overline{MT}[/tex]

The slope of [tex]\overline{MT}[/tex] = (6 - (-1))/(4 - 0) = 7/4

The slope of [tex]\overline{AH}[/tex] = -1/(7/4) = -4/7

The diagonals of a rhombus bisect each other, therefore, the diagonals [tex]\overline{MT}[/tex] and [tex]\overline{AH}[/tex] intersect at the midpoint of point [tex]\overline{MT}[/tex]

Therefore, the midpoint of [tex]\overline{MT}[/tex] is a point on the diagonal line that contains the diagonal [tex]\overline{AH}[/tex]

The midpoint of [tex]\overline{MT}[/tex] = ((0 + 4)/2, (-1 + 6)/2) = (2, 2.5)

The equation of the line containing the diagonal [tex]\overline{AH}[/tex] is therefore;

y - 2.5 = (-4/7)·(x - 2)

y = -4·x/7 + 8/7 + 2.5 = -4·x/7 + 51/14

y = -4·x/7 + 51/14 = -4·x/7 + 3 9/14

y = [tex]3\frac{9}{14}[/tex] - 4·x/7

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Answer:

Angle P= Angle W=2(2x-6)

=4x-12

100%, If 12 of all  12 marbles are blue, its 100%

Answer:

x^2 + 3x + 2

Step-by-step explanation:

(x + 2) * (x + 1) =

= x * x + x * 1 + 2 * x + 2 * 1 =

= x^2 + x + 2x + 2 =

= x^2 + 3x + 2

A. There are 25^26 possible simple substitution ciphers.

(a) A simple substitution cipher is a substitution of one letter for another. In a simple substitution cipher, each letter in the alphabet can be mapped to one of the 25 other letters. Therefore, for each letter in the alphabet, there are 25 possible substitutions. The total number of possible simple substitution ciphers is the number of possible substitutions for each letter, raised to the power of the number of letters in the alphabet:

25^26 = 25 × 25 × 25 × ... × 25 (26 times)

So, there are 25^26 possible simple substitution ciphers.

(b) (i) If no letters are fixed, then each letter can be mapped to one of the 25 other letters. Therefore, the number of simple substitution ciphers that leave no letters fixed is:

25 × 24 × 23 × ... × 2 × 1 = 25!

(ii) If at least one letter is fixed, then for each letter in the alphabet, there are 24 possible substitutions. Therefore, the number of simple substitution ciphers that leave at least one letter fixed is:

25 × 24 × 23 × ... × 2 × 1 = 25!

(iii) If exactly one letter is fixed, then there are 26 possible letters that could be fixed. For each of these 26 possibilities, there are 24 possible substitutions for each of the remaining 25 letters. Therefore, the number of simple substitution ciphers that leave exactly one letter fixed is:

26 × 24^25 = 26 × 24 × 24 × ... × 24 (25 times) = 26 × 24!

(iv) If at least two letters are fixed, then the number of ways to choose the two fixed letters, multiplied by the number of ways to arrange the other 24 letters, gives the number of ciphers that have exactly two fixed letters. The number of ways to arrange 24 letters is 24!, and there are 26 choose 2 ways to choose two letters from 26:

26 choose 2 × 24! = 325 × 24!

However, this counts ciphers with exactly two fixed letters twice: once for each of the two fixed letters. So, to find the number of ciphers with at least two fixed letters, we need to subtract the number of ciphers with exactly two fixed letters and divide by 2:

(25! - 325 × 24!) / 2 = (25! - 325 × 24!) / 2.

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The average rate of change over the interval (-1, 2) of the function is 3.

A parabola is a curve drawn in a plane. Where any point is at an equal distance from a fixed point (the focus) and a fixed straight line (the directrix).

A graph of the parabola is given.

The vertex is (-1, -4).

And the y-intercept is -3.

So, the equation of the parabola is,

y = (x + 1)² - 4.

The average rate of change over the interval (-1, 2):

= f(-1) - f(2)/(-1 - 2)

= (-4 - 5)/-3

= 3

Hence, 3 is the average rate of change.

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The width of the rectangle is [tex]4x^8y^6[/tex]inches.

Option A is correct.

What is the area of the rectangle?

A rectangle is a four-sided polygon with two pairs of parallel sides, and all four angles are right angles (90 degrees). The area of a rectangle is the amount of two-dimensional space that it occupies and is given by the product of its length and width. In other words, the area A of a rectangle with length l and width w is given by the formula:

A = l x w

To find the width of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

In this case, we are given the area and the length of the rectangle, so we can rearrange the formula to solve for the width:

width = Area / length

Substituting the given values, we have:

width = [tex]\frac{(32x^{12}y^{9})}{(8x^4y^3)}[/tex]

Simplifying the expression, we get:

width = [tex]4x^{8}y^{6}[/tex]

Therefore, the width of the rectangle is[tex]4x^8y^6[/tex]inches.

Option A is correct.

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The total distance that Cami walked from home to school, then home, and then library, is 7. 46 miles

The distance walked by Cami, can be found to be :

= Distance from home to school + distance from school to home + distance from home to library

The distance in kilometers is:

= 5 + 5 + 2

= 12 kilometers

In miles, this is:

= 12 / 1. 60934 km per mile

= 7. 46 miles

In conclusion, the distance walked by Cami in miles, was 7. 46 miles.

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The Pythagorean inequality is given below.

Statement of Pythagoras theorem:

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

                                        [tex]AC^{2}=AB^{2} +BC^{2}[/tex]

Let ABC be a triangle with the longest side opposite B

We can also write as follows:

If [tex]AC^{2} > AB^{2} +BC^{2} \\[/tex], then B is an obtuse angle.

If [tex]AC^{2} < AB^{2} +BC^{2} \\[/tex], then B is an acute angle.

If [tex]AC^{2}=AB^{2} +BC^{2}[/tex], then B is a right angle.

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Answer:

  B.  24.28 square feet

Step-by-step explanation:

You want the area of a figure composed of a rectangle, triangle, and semicircle.

The formulas for the areas of the parts of the figure are ...

  A = LW . . . . rectangle of length L and width W

  A = 1/2bh . . . . triangle with base b and height h

  A = π/2r² . . . . . . semicircle of radius r

The area of the rectangle is ...

  A = (4 ft)(3 ft) = 12 ft²

The area of the triangle is ...

  A = 1/2(4 ft)(3 ft) = 6 ft²

The semicircle has a radius that is half the diameter. The diameter is shown as 4 ft so the radius is 2 ft. The area of the semicircle is ...

  A = π/2(2 ft)² = 4(3.14)/2 ft² = 6.28 ft²

The area of the composite figure is the sum of the areas of its parts:

  Area = 12 ft² +6 ft² +6.28 ft² = 24.28 ft²

The area of the composite figure is about 24.28 ft².

Answer:

The slope between the two points would be 5.

Answer: The slope would be 5

Step-by-step explanation:

Answer:

To solve this problem, we can use the formula for exponential growth:

V(t) = V0 * (1 + r)^t

where:

V(t) is the value of the equipment at time t

V0 is the initial value of the equipment ($15,000)

r is the annual growth rate (15.9% or 0.159)

t is the time in years

We want to find the time t when the value of the equipment will be less than $7500. So we can set up the following inequality:

V(t) < 7500

Substituting the formula for V(t), we get:

V0 * (1 + r)^t < 7500

Substituting the given values, we get:

15000 * (1 + 0.159)^t < 7500

Simplifying and solving for t,

we get:(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

So the company's new equipment will be worth less than $7500 after about 2.64 years.

Step-by-step explanation:

By using the substitution method, the value of x is equal to -1.94 and the value of y is 2.71.

In order to solve the given system of linear equations, we would apply the substitution method. From the information provided in the question above, we have the following system of linear equations:

y = 5x - 7      .......equation 1.

3y - 2x = -12          .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

-3(5x - 7) - 2x = -12

-15x + 21 - 2x = -12

-17x = -12 - 21

17x = -33

x = -33/17 or -1.94

For the value of y, we have:

y = 5(-33/17) - 7

y = -165/17 - 7

y = 2.71

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The point estimate of the population mean is 6

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

Measurements: 5, 10, 2, 7, and 6.

Sample size = 5

The point estimate of the population mean is the sample size of the mean

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

Sample mean  = Sum/Count

substitute the known values in the above equation, so, we have the following representation

Sample mean  = (5 + 10 + 2 + 7 + 6)/5

Evaluate

Sample mean = 6

Hence, the estimate is 6

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If John has 3 of 4 slices of pie, and Tom has 2 of 6 slices of pie, how many do they have all together?

I believe that is what type of story you needed, if wrong let me know.

Answer: Suppose Rita is trying to find the area of the carpet of 3/4 and 2/6 for a room of 4/4 sq to 6/6 sq with balcony of 1/4 and 4/6

Explanation: In the given rectangle fig. length is given 3/4 and breadth is given 2/6 for the whole rectangle is 4/4 to 6/6.

for each block length is given 1/4 and breadth is given 1/6. The darker shaded area represents the carpet of the above story.

The answer after multiplying it is 6/24 or 1/4.  

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Answer:

(a) Possible number(s) of positive real zeros:  3

(b) Possible number(s) of negative real zeros:  1

Step-by-step explanation:

Descartes' Rule of Signs tells us the maximum number of positive and negative roots.

Positive root case

[tex]f(x)=-3x^4+2x^3-x^2+9x+7[/tex]

As there are 3 sign changes, the maximum possible number of positive roots is 3.

Negative root case

[tex]\begin{aligned}f(x)&=-3(-x)^4+2(-x)^3-(-x)^2+9(-x)+7\\&=-3x^4-2x^3-x^2-9x+7 \end{aligned}[/tex]

As there is one sign change, the maximum possible number of negative roots is 1.

Answer:

Step-by-step explanation:

To solve for the value of "a", we can isolate "a" in one of the equations and then substitute the result into the other equation. Here's how we can do that:

Starting with the first equation:

5a - 26 = -10

5a = -10 + 26

5a = 16

a = 16 / 5

a = 3.2

Now that we know the value of "a", we can substitute it into the second equation:

6a + 46 = 36

6 * 3.2 + 46 = 36

19.2 + 46 = 36

65.2 = 36

This means that the system of equations has no solution, as the values of "a" and "b" can't both satisfy both equations at the same time.

Answer:

69

Step-by-step explanation:

if it bisects that mean both angles are equal which tells us we can just divide the whole angle by 2

angle BOA is 138

so when you divide 138 by 2 you get 69

hope it helped

please mark brainiest

Answer:

Step-by-step explanation:

All it's saying is that the 12% of the people are 35 and the 82% of people who did not submitted data is 175 people

The calculated test statistic (2.08) is greater than the critical value (1.96), we reject the null hypothesis and conclude that there is evidence to suggest that the contest has increased participation in the box tops for education program.

To determine if the contest has increased participation in the box tops for the education program, we need to conduct a hypothesis test.

We will use a significance level of 0.05, which means we are willing to accept a 5% chance of making a Type I error (rejecting the null hypothesis when it is actually true).

Null Hypothesis: The proportion of students submitting box tops for education is still 12% (or has decreased) after the contest.

Alternative Hypothesis: The proportion of students submitting box tops for education has increased after the contest.

To test this hypothesis, we will use a one-sample proportion test. We will use the sample proportion, p' = 35/210 = 0.1667, as an estimate of the population proportion, p. The test statistic is calculated as:

z = (p' - p) / √(p x (1-p)/n)

where n is the sample size.

Under the null hypothesis, the expected value of the test statistic is 0, and the standard deviation of the test statistic is sqrt(p*(1-p)/n).

Using p = 0.12 and n = 210, we have:

z = (0.1667 - 0.12) / √(0.12 x 0.88/210) ≈ 2.08

The critical value for a significance level of 0.05 and a two-tailed test is ±1.96.

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For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

What exactly is a linear inequality?

In mathematics, inequality denotes a mathematical statement with no equal sides. An inequality happens in mathematics when a connection results in a non-equal comparison of two expressions or two numbers. Any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), replace the equal sign "=" in the sentence. In mathematics, inequalities are classified into three types: polynomial inequalities, rational inequalities, and absolute value inequalities.

The characters "< and >" denote severe inequalities, whereas ‘≤’ and ‘≥’  denote slack inequalities. A linear inequality looks to be a linear equation, however the formula is different.

Now,

As stated in Commutative property the order in addition does not matter and in addition property the value added on both sides does not affect the result.

In step 3 we can write this as 5x-x-5<11x+x-21

which will not change result and

in step 7, 21 is added both sides which will not change result.

Hence,

           For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

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The probability that in a given week in September, it will rain on at most two days is 0.12.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The probability that it rains on any given day in September = 0.3.

P ( rains ) = 0.3

And,

The probability that it will not rain on any given day in September.

P (no rain) = 1 - 0.3

P(no rain) = 0.7

Now,

The probability is that in a given week in September, it will rain on at most two days.

= P (x ≤ 2)

= P(no rain) + P(rain) + P(rain)

= 0.7 + 0.3 + 0.3

= 0.12

Thus,

The probability that in a given week in September, it will rain on at most two days is 0.12.

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The volume of the cylinder is  

Using the volume of cone given by the formula

= π r² h/3

In the problem the volume is given by  222 and volume of cylinder is equal to

= π r² h

comparing the two volumes and taking proportions

volume of cone / volume of cylinder

π r² h/3 / π r² h = 222 / volume of cylinder

π r² h / 3 π r² h = 222 / volume of cylinder

1 / 3  = 222 / volume of cylinder

volume of cylinder = 3 * 222

volume of cylinder =  666

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The value of the camper after 5 years is given as follows:

$15,155.2.

An exponential function is defined as follows:

y = a(b)^x.

In which:

From the table, the rate of change is given as follows:

b = 29600/37000

b = 0.8.

Then the value of the camper after five years can be obtained applying the recursion, multiplying the value after 4 years by the rate of change of 0.8, as follows:

18944 x 0.8 = $15,155.2.

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WXYZ must be a square, all the sides must have a length of 5.

The vertices of the quadrilateral are:

W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3)

Distance can be calculated using the formula derived from Pythagoras theorem. In coordinate geometry, the distance formula is:

[tex]\sqrt{[(x_2 -x_1)^2 + (y_2 - y_1)^2]}[/tex]

We have to prove that WXYZ is a square.

Using the distance formula :

[tex]WX = \sqrt{(-1-3)^2+(1-4)^2}\\ \\WX = \sqrt{16 + 9}\\ \\WX = \sqrt{25}\\ \\WX = 5[/tex]

Since WXYZ must be a square, all the sides must have a length of 5.

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The given question is incomplete, complete question is:

Select the correct answer from each drop-down menu.

Given: W(-1, 1), X(3, 4), Y(6,0), and Z(2, -3) are the vertices of quadrilateral WXYZ.

Prove: WXYZ is a square.

Using the distance formula, I found that

…

A. all four sides have a length of 5

B. all four sides have different lengths

C. only 2 sides have the same length

D. all four sides have a length of 10

Answer:

12th term = -61

Step-by-step explanation:

Given sequence,

→ 5, -1, -7, ...

Now we have to,

→ Find the 12th term of the sequence.

The common difference is,

→ d = a2 - a1

→ d = -1 - 5

→ [ d = -6 ]

Formula we use,

→ an = a1 + (n - 1)d

Then value of 12th term will be,

→ an = a1 + (n - 1)d

→ a12 = 5 + (12 - 1) × (-6)

→ a12 = 5 + 11 × (-6)

→ a12 = 5 - 66

→ [ a12 = -61 ]

Therefore, the 12th term is -61.

Answer:

Answer is in the attached photo

Step-by-step explanation:

The solution is in the attached photo, do take note to find the value of y, we will have to make y the subject.

Translation the graph of the function  [tex]y=f(x)[/tex]a units to the right gives you the function [tex]y=f(x-a)[/tex]

If the graph of the function [tex]f(x)=3^{x}[/tex] is translated 6 units to the right, then the function becomes

[tex]g(x)=f(x-6)=3^{x-6}[/tex]

Answer: correct choice is A