The length of the longer leg of a right triangle is 22cm more than six times the length of the shorter leg. The length of the hypotenuse is 23cm more than six times the length of the shorter leg. Find the side lengths of the triangle.

Answer:

To find the slope of a line parallel to 5x - 2y = 2, we need to first rearrange the equation in slope-intercept form, y = mx + b, where m is the slope of the line. 5x - 2y = 2 -2y = -5x + 2 y = (5/2)x - 1 The slope of the line is 5/2. Since we are looking for a line parallel to this line, the slope of the parallel line will be the same as the slope of the original line, which is 5/2. Therefore, the slope of a line parallel to 5x - 2y = 2 is 5/2.

The equatiοn has nο sοlutiοn.

An equatiοn is defined as a mathematical statement in algebra that prοves the equality οf twο mathematical expressiοns. Fοr example, the fοrmula 3x + 5 = 14 cοnsists οf the twο equatiοns 3x + 5 and 14, which are separated by the wοrd "equal."

Here the given equatiοn is ,

=> |4x-4(x+1)|=4

Nοw simplifying the equatiοn then,

=> 4x-4(x+1)=± 4

=> 4x-4x-4=±4

=>-4=±4

Hence the given equatiοn has nο sοlutiοn.

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Answer:

The two points (4, 5) and (-4, 5) have the same y-coordinate, which means they lie on a horizontal line. This horizontal line is the x-axis. So, the points are related in that they both lie on the x-axis, with a distance of 8 units between them.

To satisfy the equation y = -3x - 4, we need to substitute the given values of x and y in the equation and check if it holds true.

For the ordered pair (-4, y):

y = -3(-4) - 4

y = 12 - 4

y = 8

So, the ordered pair (-4, 8) satisfies the equation y = -3x - 4.

For the ordered pair (x, 2):

2 = -3x - 4

6 = -3x

x = -2

So, the ordered pair (-2, 2) satisfies the equation y = -3x - 4.

Step-by-step explanation:

As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commission on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $292. If she sells $800 of merchandise in one month, she is paid $384.

Here is the salary function used to represent this situation in terms of the amount of merchandise sold:

s(x) = 0.23x + 200

Find Alysse's salary when she sells $2,200 worth of merchandise.

The probability that both students selected are males is 0.46.

The multiplication rule of probability for independent events states that the probability of two or more independent events occurring together is the product of their individual probabilities.

If event A has probability P(A) and event B has probability P(B), and A and B are independent events, then the probability of both A and B occurring  

P(A and B) = P(A) x P(B)

Here we have

There are 13 males and 6 females in the class, for a total of 19 students.

The probability of selecting a male on the first draw is 13/19.

After one male has been selected,

There are 12 males and 6 females left in the class.

The probability of selecting another male on the second draw = 12/18

[ Since there is one less student in the class and one less male]

The probability of selecting two males in a row is the product of the probabilities of each individual event:

P(male and male) = P(male on the first draw) x P(male on the second draw | male on the first draw)

= (13/19) x (12/18)

= 0.456 or approximately 0.46 (rounded to two decimal places).

Therefore,

The probability that both students selected are males is 0.46.

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Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

Let's assume that the distance from point A to the lighthouse is x feet and the distance from point B to the lighthouse is y feet. Also, let's assume that the height of the boat's crew's eye level is h feet above the water.

From point A, we can use tangent function to find x:

tan(5°) = (119 + h) / x

From point B, we can use tangent function again to find y:

tan(18°) = (119 + h) / y

We want to find the distance between point A and point B, which is the difference between x and y:

distance AB = y - x

We need to eliminate h from these equations to solve for x and y. We can do this by solving for h in one equation and substituting it into the other equation:

h = x tan(5°) - 119

tan(18°) = (119 + x tan(5°) - 119) / y

tan(18°) = x tan(5°) / y

y = x tan(5°) / tan(18°)

distance AB = y - x = x (tan(5°) / tan(18°) - 1)

Now we can plug in the values and use a calculator to find the distance:

distance AB = x (tan(5°) / tan(18°) - 1)

distance AB = x (0.107 - 1)

distance AB = -0.893 x

Since the distance cannot be negative, we know that x must be greater than zero. Therefore, we can ignore the negative sign and solve for x:

x = distance AB / -0.893

Using a calculator, we get:

x ≈ 181.74 feet

Rounding to the nearest foot, the distance from point A to point B is approximately 182 feet.

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Answer:

the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.

Step-by-step explanation:

The perimeter of the paperboard that remains after the semicircle is removed is equal to the sum of the four sides of the rectangular portion of the paperboard plus half the circumference of the semicircle.

The rectangle has dimensions of length = 20 inches and width = 12 inches. Therefore, the sum of the four sides of the rectangular portion of the paperboard is:

2(20) + 2(12) = 64 inches

The semicircle has a diameter equal to the width of the rectangle, which is 12 inches. Therefore, the radius of the semicircle is half the diameter, or 6 inches. The circumference of a full circle with a radius of 6 inches is:

2 * 3.14 * 6 = 37.68 inches

Half of the circumference of the semicircle is:

(1/2) * 37.68 = 18.84 inches

Therefore, the perimeter of the paperboard that remains after the semicircle is removed is:

64 + 18.84 = 82.84 inches

Thus, the perimeter of the paperboard that remains after the semicircle is removed is 82.84 inches.

Answer:

B

Step-by-step explanation:

5280 yards does not equal one mile

Answer

B.5,280

Step-by-step explanation:

Im just smart like that

7) ∠1≅∠4 on the basis of opposite angles.

8) ∠1≅∠3 on the basis of opposite angles.

9) ∠5≅∠7 on the basis of opposite angles.

Opposite angles in geometry are equal in measure. This is known as the "vertical angles theorem." In other words, if two lines intersect, the opposite angles formed by those lines will have the same degree of measurement.

7) since ∠1 = ∠2

and ∠3 = ∠4, then by the rule of the congruence of opposite angles, ∠1≅∠4

8) In the above shape, we can see that ∠1 and ∠3 are a opposite angles, hence, they are both equal or congruent.

9) The logic is the same for ∠5 and ∠7. The are opposites hence they are equal.

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Answer: The Silo is 44 meters tall

Step-by-step explanation:

To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)

The prοduct οf th rοοts οf the quadratic 6x + cx + 4 is 2 greater than the sum οf the rοοts, and c is a cοnstant the value οf c = 4

ax² + bx + c = 0 is a quadratic equatiοn, which is a secοnd-οrder pοlynοmial equatiοn in a single variable. a 0.

By Vieta's fοrmulas, we knοw that the sum οf the rοοts is given by:

α + β = -c/6

And the prοduct οf the rοοts is given by:

αβ = 4/6 = 2/3

We are given that the prοduct οf the rοοts is 2 greater than the sum οf the rοοts:

αβ = α + β + 2

Substituting the values we knοw, we get:

2/3 = -c/6 + 2 + α + β

Simplifying this expressiοn, we get:

2/3 = -c/6 + 2 - c/6

Multiplying bοth sides by 6, we get:

4 = -c + 12 - c

Simplifying, we get:

2c = 8

c = 4

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Answer:

E

Step-by-step explanation:

[tex]3(p - 4) = 2(p + 1)[/tex]

Multiply every term inside the bracket by the term on the outside:

[tex]3p - 12 = 2p + 2[/tex]

Collect like-terms (also, moving the term to the other side changes its sign to the opposite of the previous one):

[tex]p = 14[/tex]

EXPLANATION

step 1. 3×p - 3×4 = 2×p + 2×1 ( brackets means × or multiplication )

step 2. 3p - 12 = 2p + 2 ( collect like terms )

step 3. -2p - 3p = 2 + 12 ( calculate the like terms and when we calculate them it would not be multiplication or division )

step 4. -1p = 14 ( answering look like this )

step 5. -1p/ 1 = 14/1 ( divided it by the number to get the variable )

step 6. p = 14 ( finally answer the question and check it all your calculate )

If you think you are brilant do not run for only the answer, but check up and understand it how it come.

ANSWER

(E) 14

The point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).

The distance formula is a mathematical formula used to calculate the distance between two points in a two or three-dimensional space. It is derived from the Pythagorean theorem and is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Where d represents the distance between the two points, (x1, y1) and (x2, y2) represent the coordinates of the two points in a two-dimensional space.

To determine if the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9), we need to calculate the distance between the center of the circle and the point (3, 7), and compare it to the radius of the circle.

Let's first find the radius of the circle. Since the circle contains the point (-1, 9), the distance between the center of the circle and (-1, 9) is equal to the radius. Using the distance formula, we get:

radius = √[(9 - 4)² + (-1 - (-1))²] = √[25] = 5

Now let's find the distance between the center of the circle (-1, 4) and the point (3, 7):

distance = √[(7 - 4)² + (3 - (-1))²] = √[3² + 4²] = 5

We see that the distance between the center of the circle and the point (3, 7) is equal to the radius of the circle. Therefore, the point (3, 7) lies on the circle with center (-1, 4) and containing the point (-1, 9).

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Answer:

16

Step-by-step explanation:

Find an equivalent fraction which is 6/16.

Answer:

The function is shifted 1 unit to the right and then flipped over the x-axis. So the correct result is:

[tex]y = - f(x - 1)[/tex]

On an 8-question multiple-choice test, where each question has 2 answers,  the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]

Probability is a way to gauge how likely something is to happen1. It is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty for the event.

In an 8-item multiple-choice test with 2 possible answers for each, the likelihood of getting at least one question wrong can be computed as follows:

P(at least one mistake) = 1 - P (none wrong)

P(at least one wrong) [tex]=1-(\frac{1}{2})^{10[/tex]

P(at least one wrong) [tex]=1-\frac{1}{1024}\\\\=\frac{1023}{1024}[/tex]

On an 8-question multiple-choice test, where each question has 2 answers,  the probability of getting at least one question wrong is [tex]\frac{1023}{1024}[/tex]

The complete question is-

On an 8-question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?

Give your answer as a fraction

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201.5 is the smallest average of 200 different positive and odd integers.

Let's first consider the set of the first 200 odd positive integers: {1, 3, 5, ..., 397, 399, 401}.

The average of this set is (1+3+5+...+397+399+401)/200 = 201.

Now, we want to find a set of 200 distinct positive and odd integers that has a smaller average than 201.

One way to do this is to remove the largest element from the first set (401) and replace it with the smallest odd positive integer that is greater than 401, which is 403.

The new set is {1, 3, 5, ..., 397, 399, 403}.

The average of this set is (1+3+5+...+397+399+403)/200 = 201.5.

Hence, 201.5 is the smallest average that can be calculated from 200 different positive and odd integers.

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The probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.

According to the First Principle of Probability, the outcomes of one chance occurrence have no bearing on those of succeeding chances occurrences. Thus, the chance of getting heads the second or third time you flip it stays at 1 in 2. The chances of getting heads on the sixth flip, even if you got five consecutive heads, stay at 12.

The Bayes Theorem asserts that the likelihood of a second tournament given the first occurrence multiplied by the odds of the first event equals the conditional event's likelihood depending on the presence of another event.

The probability of rolling a number other than 1 or 5 on a fair die is 4/6 or 2/3, since there are four favorable outcomes (2, 3, 4, 6) out of six possible outcomes.

To find the probability of rolling no 1 and no 5 in five rolls, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

So, for each roll, the probability of rolling a number other than 1 or 5 is 2/3. Therefore, the probability of rolling no 1 and no 5 in five rolls is:

(2/3) * (2/3) * (2/3) * (2/3) * (2/3) = (2/3)⁵ ≈ 0.131

Rounding to three decimal places, the probability is approximately 0.131.

Therefore, the probability of having no 1 and no 5 among the rolls is approximately 0.131 or 13.1%.

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Answer:

f(x) = -(x-3)+7

Step-by-step explanation:

(a) The probability of the questions being history, literature, and science, in that order, is 4.28%.

(b) The probability of all three cards being literature questions is 2.4%.

(c) 5%.

Probability can be used to estimate the chances of drawing a certain card and can help players to decide which moves to make when playing card games.

(a) The probability of the questions being history, literature, and science, in that order, is 5/18 x 6/17 x 7/16 = 0.0428 or 4.28%.

To calculate this probability, we use the formula

P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a history card is 5/18, since there are five history cards out of 18 total cards.

The probability of the second card being a literature card, given that the first card is a history card, is 6/17, since there are six literature cards out of the remaining 17 cards.

The probability of the third card being a science card, given that the first two cards are history and literature, is 7/16, since there are seven science cards out of the remaining 16 cards.

(b) The probability of all three cards being literature questions is 6/18 x 5/17 x 4/16 = 0.024 or 2.4%.

To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a literature card is 6/18, since there are six literature cards out of 18 total cards.

The probability of the second card being a literature card, given that the first card is a literature card, is 5/17, since there are five literature cards out of the remaining 17 cards.

The probability of the third card being a literature card, given that the first two cards are literature cards, is 4/16, since there are four literature cards out of the remaining 16 cards.

(c) The probability of the first card being a science card, the second being a history card, and the third being a science card is 7/18 x 5/17 x 7/16 = 0.05 or 5%.

To calculate this probability, we use the formula P(A and B and C) = P(A) x P(B|A) x P(C|B and A).

The probability of the first card being a science card is 7/18, since there are seven science cards out of 18 total cards.

The probability of the second card being a history card, given that the first card is a science card, is 5/17, since there are five history cards out of the remaining 17 cards.

The probability of the third card being a science card, given that the first two cards are science and history, is 7/16, since there are seven science cards out of the remaining 16 cards.

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It will take Allan approximately 38 months (rounded up) to repay the loan with monthly payments of $100 at an interest rate of 9.5% per year, compounded monthly.

Interest rate refers to the percentage of the principal amount charged by a lender to a borrower for the use of money over a certain period of time.

To calculate the time it takes for Allan to repay the loan, we can use the formula for the present value of an annuity:

PV = PMT x (1 - [tex](1 + r)^-n[/tex]) / r

where:

PV = present value

PMT = monthly payment

r = monthly interest rate (9.5% per year / 12 months = 0.00791667)

n = number of months

Plugging in the given values, we get:

3000 = 100 x (1 - (1 + 0.00791667)[tex]^-n[/tex]) / 0.00791667

Simplifying and solving for n, we get:

n = -ln(1 - (3000 x 0.00791667 / 100)) / ln(1 + 0.00791667)

n = 37.4 months

Therefore, it will take Allan approximately 38 months (rounded up) to repay the loan with monthly payments of $100 at an interest rate of 9.5% per year, compounded monthly.

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Proof of Quadrilateral WXYZ as a Parallelogram using SSS Criterion for Congruence.

What is the proof that Quadrilateral WXYZ is a parallelogram using SSS criterion for congruence?

Since WY and XZ bisect each other at point A, we have AW = AY and AZ = AX.

Now, consider the triangles AWX and AYZ. By the Side-Side-Side (SSS) criterion for congruence, we have:

AW = AY (given)

AZ = AX (given)

WY = XZ (as WY and XZ bisect each other)

Therefore, by the SSS criterion for congruence, we have AWX ≅ AYZ.

By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, we have WX = YZ.

Since opposite sides are congruent, we have WX || YZ.

Similarly, we can show that WZ || XY.

Therefore, since both pairs of opposite sides are parallel, we can conclude that quadrilateral WXYZ is a parallelogram.

Missing statement: "By the SSS criterion for congruence, we have AWX ≅ AYZ."

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The calculated value of the expression 2x - y for the given values of x and y is 9/2.

We are given that 2x = 7 and 2y = 5, and we are asked to find the value of 2x - y.

This means that

x = 7/2 and y = 5/2

We can start by substituting the given values into the expression:

2x - y = 2(7/2) - (5/2)

Notice that since 2x = 7, then x = 7/2.

Similarly, since 2y = 5, then y = 5/2. Substituting these values into the expression, we get:

2x - y = 2(7/2) - (5/2) = 7 - 5/2 = 9/2

Therefore, the value of 2x - y is 9/2.

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Answer:  4,258,375

Step-by-step explanation:

Answer:

I think it will be

y=1/3x+0

The inequality that models the amount of weight the forklift can carry is: 45x + 70y ≤ 3000

An inequality is a mathematical statement that indicates a relationship between two expressions that are not equal. It uses comparison symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to show the relationship between the two expressions.

The total number of boxes that a forklift can carry is x + y.

The total weight that the forklift can carry is equal to 45x + 70y pounds, which is less than or equal to 3000 pounds.

Therefore, the inequality that models the number of boxes the forklift can carry is:

x + y ≤ 60

The inequality that models the amount of weight the forklift can carry is:

45x + 70y ≤ 3000.

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Answer:

the y intercept is 1 so put a point there then move up 1 and to the right 3 and put a point then draw a line through the 2 points

The x-intercept is 21/5 and the y-intercept is -7/2 of the given line.

What is the x and y-intercept of a line?

In a two-dimensional Cartesian coordinate system, the x-intercept of a line is the point where the line crosses the x-axis, which means the value of y is zero at that point. The x-intercept can be found by setting y = 0 in the equation of the line and solving for x.

Given that we have to find the y-intercept and x-intercept

The given equation is:

5x - 6y = 21

The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.

The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero

Finding x-intercept:

To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'.

Substitute y = 0 in a given equation

5x - 6(0) = 21

x = 21/5

Thus x-intercept is 21/5.

Finding y-intercept:

To find the y-intercept, plug 0 in for 'x' and solve for 'y'

Substitute x = 0 in a given equation

5(0) - 6y = 21

-6y = 21

-2y = 7

y = -7/2

Thus y-intercept is   -7/2

hence, the x-intercept is 21/5 and the y-intercept is -7/2 of the given line.

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Complete question:

Find the y-intercept and x-intercept of the line. 5x-6y=21