One leg of a right triangle has a length of 5m. The other sides have lengths that are consecutive integers. Find these lengths.

Answers

Answer 1

The lengths of the other two sides of the right triangle are 12 and 13

Pythagorean theorem

From the question, we are to determine the lengths of the other sides of the triangle

From the given information,

The other sides have lengths that are consecutive integers

Thus,

If the length of the other side is x

Then,

The hypotenuse will be x + 1

By the Pythagorean theorem, we can write that

(x+1)² = x² + 5²

(x+1)(x+1) = x² + 25

x² + x + x + 1 = x² + 25

x² - x² + x + x = 25 - 1

2x = 24

x = 24/2

x = 12

∴ The other leg of the right triangle is 12

Hypotenuse = x + 1 = 12 + 1 = 13

Hence, the lengths of the other two sides are 12 and 13

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Related Questions

In 2015, around ____ percent of the world’s population had an internet connections.

Answers

Around 43% of the worlds population had an internet connection

Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.

Answers

Answer: [tex]\triangle RQP \sim \triangle VPW[/tex]

Step-by-step explanation:

By the corresponding angles theorem, [tex]\angle RPQ \cong \angle VWP[/tex] and [tex]\angle RQP \cong \angle VPW[/tex].

Therefore, [tex]\triangle RQP \sim \triangle VPW[/tex] by AA.

The solution to the system of equations shown is (2, 0).

3x − 2y = 6
x + 4y = 2

When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14
.

Which system of equations will also have a solution of (2, 0)?

Answers

Answer:

7x = 14

x + 4y = 2

Step-by-step explanation:

3x − 2y = 6

x + 4y = 2

6x - 4y = 12

x + 4y = 2

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

7x = 14 Replace the first equation with this one.

"The average speed of a vehicle and the distance it covers in a period " Is this a direct proportion​

Answers

Answer:

Yes

Step-by-step explanation:

As the Average speed increases, the amount of distance covered will increase. As the average speed decreases, the amount of distance traveled will decrease as well over a certain period.

Help please having trouble solving these two problems

Answers

Answer:

First function:

Zeros = 6 and -6. Y-intercept = (0,72). X-intercepts = (6,0) and (-6,0).

Second function:

Zeros = 3 and -3. Y-intercept = (0, -27). X-intercepts: (3, 0) and (-3, 0).

Step-by-step explanation:

The zeros are x-intercept numbers.

The y-intercept can be found when the function is in standard form. Plug in 0 for x, then solve.

Hope this helps!

Answer:

1. x₁ = 6, x₂ = -6

2. x₁ = 3, x₂ = -3

Step-by-step explanation:

Given functions:

[tex]1)\ f(x) = -2(x-6)(x+6)[/tex]

[tex]2)\ f(x)=(x-3)(3x+9)[/tex]

..................................................................................................................................................

Zero Product Property: If m • n = 0, then m = 0 or n = 0.

Standard Form of a Quadratic: ax² + bx + c = 0.

..................................................................................................................................................

1. f(x) = -2(x - 6)(x + 6)

Step 1: Set the function to zero.

[tex]\implies 0 = -2(x-6)(x+6)[/tex]

Step 2: Divide both sides of equation by [tex]-2[/tex].

[tex]\implies \dfrac{0}{-2} = \dfrac{-2(x-6)(x+6)}{-2}[/tex]

[tex]\implies 0=(x-6)(x+6)[/tex]

Step 3: Apply the Zero Product Property.

[tex]x_1 \implies x-6=0[/tex]

[tex]x_2 \implies x+6=0[/tex]

Step 4: Solve for x in both equations.

[tex]x-6+6=0+6 \implies \boxed{x_1 = 6}[/tex]

[tex]x+6-6=0-6 \implies \boxed{x_1 = -6}[/tex]

The zeros (x-intercepts) of this function are: [tex]x_1=6,\ x_2=-6[/tex].

.................................................................................................................................................

2. f(x) = (x - 3)(3x + 9)

Step 1: Set the function to zero.

[tex]\implies 0 = (x - 3)(3x + 9)[/tex]

Step 2: Apply the Zero Product Property.

[tex]x_1 \implies x-3=0[/tex]

[tex]x_2 \implies 3x + 9=0[/tex]

Step 3: Solve for x in both equations.

[tex]x-3+3=0+3 \implies \boxed{x_1 = 3}[/tex]

[tex]3x=-9 \implies \dfrac{3x}{3}=\dfrac{-9}{3} \implies \boxed{x_1 = -3}[/tex]

The zeros (x-intercepts) of this function are: [tex]x_1=3,\ x_2=-3[/tex].

..................................................................................................................................................

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Pedro owns a shrimp truck near the beach. he sells garlic shrimp for $8 a plate and spicy shrimp for $6 a plate. each day pedro stocks enough shrimp to sell at most 120 plates total, but he would like to earn at least $800. which combination of garlic shrimp plates and spicy shrimp plates can pedro sell to meet his goal?

Answers

Pedro can sell enough by combining the sales of 40 plates of garlic shrimp and 80 dishes of spicy shrimp to reach his objective.

As a result

Near the shore, Pedro runs a shrimp delivery business.

He offers spicy shrimp for $6 a plate and garlic shrimp for $8 per plate.

Pedro wants to make at least $800 per day but only stocks enough shrimp to sell a maximum of 120 plates.

We need to ascertain,

Which dish combining hot shrimp and garlicky shrimp can Pedro sell to reach his objective?

In response to the query,

Let's sell the x dishes of garlic shrimp.

And plates of hot shrimp were sold.

Pedro has 120 dishes' worth of shrimp in stock each day.

Then,

Shrimp sold daily total is equal to the sum of plates of garlic shrimp and spicy shrimp.

                           X + Y = 120

Furthermore, He offers $6spicy and $8garlic shrimp, per plate.

To make at least $800 is what he wants to do.

Then,

the sum of the price of the spicy shrimp per plate and the price of the garlic shrimp per plate,

                             8X + 6Y = 800

When the two equations are solved,

                              X + Y = 120

                           8X + 6Y = 800

From equation 1,

                             Y = 120 - X

In equation 2, replace x with its value.

8X + 6Y = 800

8(120 - Y) + 6Y = 800

960 - 8Y + 6Y = 800

- 2Y = - 160

Y = 160/2

Y = 80

                         

In equation 1, replace y with its value.

X + Y = 120

X + 80 = 120

X = 120 - 80

X = 40

                     

In order to achieve his objective, Pedro sold a combination of 40 plates of garlic shrimp and 80 dishes of spicy shrimp.

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Answer:

Step-by-step explanation:

Make equations

8x+6y≥800

x+y≤120

Graph the system of equations and see which answer falls in the shaded area

Answer: 90 Garlic, 25 Spicy

Given: quadrilateral MNOL with MN ≅ LO and ML ≅ NO

Prove: MNOL is a parallelogram.

Quadrilateral L M N O is shown. Sides M N and L O are congruent. Sides L M and O N are congruent.

Complete the paragraph proof.
We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △
. By CPCTC, ∠LMO ≅ ∠ and ∠NMO ≅ ∠LOM. Both pairs of angles are also , based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.

Answers

The answers to the quadrilateral are ONM, NOM, and alternate interior angles.

How to explain the quadrilateral?

Based on the SSS postulate, the two triangles △MLO and △ONM are congruent since three sides of △MLO are respectively equal to the three sides of △ONM.

Based on CPCTC, all of the corresponding angles of △MLO and △ONM are congruent as well since the two triangles are congruent, that is,  

∠LMO≅∠NOM and ∠NMO≅∠LOM.

Since the pair ∠LMO and ∠NOM as well as ∠NMO and ∠LOM are angles on the inner side of two lines but on opposite sides of the transversal MO, these pairs of angles are also alternate interior angles.

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Answer:    ONM

                 NOM

                alternate interior angles

Step-by-step explanation:  Complete the paragraph proof.

We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △

✔ ONM

. By CPCTC, ∠LMO ≅ ∠

✔ NOM

and ∠NMO ≅ ∠LOM. Both pairs of angles are also

✔ alternate interior angles

, based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.

Please explain the answer before, and also help with number line!

Answers

The solution to the given inequality is x < -6

For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.

Number line and inequality

Given the inequality expression as shown

6x + 6 < -30

Subtract 6 from both sides

6x < -30 - 6

6x < -36

Divide through by 6

x < -36/6

x < -6

For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.

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What is the
y-intercept
of this line?

Answers

Answer: (0, 3)

Step-by-step explanation:

     The y-intercept of the line is where the line intercepts the y-axis. In other words, the coordinate value of the line when x is 0.

Answer: (3, 0)

Step-by-step explanation:

y-intercept = y=a number and x=0

So, y=3, x=0.

(3, 0)

PLS HELPPP!!!! Look at pic

Answers

The correct option regarding whether the equation x² = y² is a function is:

No, since if you solve the equation for x, then [tex]x = \pm y[/tex]

What is needed for a relation to represent a function?

In a function, each value of x can be associated with only one value of y.

In this problem, the equation is:

[tex]x^2 = y^2[/tex]

Then:

[tex]x = \pm \sqrt{y^2}[/tex]

[tex]x = \pm \sqrt{y}[/tex]

x is associated with two values, [tex]-\sqrt{y}[/tex] and [tex]\sqrt{y}[/tex], hence it is not a function.

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There are 752 cal in 8 ounces of a certain ice cream how many calories are there in 2 pounds

Answers

So, 8 ounces is equivalent to .5 pounds. Therefore, 32 ounces is equivalent to 2 pounds. Or, there are 4 8ounce measurements to get to 2 pounds.

752 calories * 4 = 3008 calories in 2 pounds of ice cream.

Irene knows her blood type is A, but William does not know his blood type. However, William knows that his mother and father both had blood type B. Irene and William's first child is a boy with type O blood. Based on this information, William's blood type could be

Answers

Based on this information, William's blood type could be either B or O.

What is Segregation of alleles?

Allele pairs (several features of the same gene) are segregated during meiosis so that they can be transferred selectively to different gametes.During meiosis, maternal and paternal alleles separate.

What is genotype vs phenotype ?

Genotype: An organism's genetic makeup. Phenotype. physical characteristic that arises within an organism as a result of its genotype. Probability law.Genotype - the set of alleles that make up an organism.

How does genotype influence phenotype ?

The alleles you have for a specific gene or collection of genes are referred to as your genotype. The physical attribute itself, or phenotype, can be affected by both genotype and environmental variables.

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PLEASE HELP I GIVE 95 POINTS

Answers

D,
3^x is positive, and the y-in. is 1.
3^0 = 1
Process of elimination.

how do you graph y=12/x

Answers

Answer: [tex]\frac{12}{x}[/tex] is an asymptote

Step-by-step explanation:

Apply a table, and plug in values of x into the equation.  For example f(2)=[tex]\frac{12}{2} =6[/tex]. That's one of the points on the graph that we just found (2,6)

A map's numerical coordinates are in kilometres. Town A is at (16.3, 2.9) and town B is at
(4.5, 6.3). A road is to be constructed on a direct line between the two towns. Each town is
responsible for the construction up to the mid-point at a cost of $150 000 for each kilometre.
Determine the cost for each town.

Answers

Answer:

$92,250 per town

Step-by-step explanation:

See attached image.

The two towns may be connected with a straight line, the road, that can be made into the hypotenuse of a right triangle.  The twio sides are calculated from the coordinates and shown in the image.  Then use the phythagorean theorem to calculate the hypotenuse.  The towns are 12.3 km apart.  The total road cost would be:

 ($150,000/km)(12.3 km) = $1,845,000, or $92,250 per town.

Help please im bad at math!

Answers

Hello, the solution is in this photo.

The correct answer is 300

Answer:

300cm^2

Step-by-step explanation:

Replace pie by 3. 3(10)^2 which equals to 300cm^2. 10 is radius.

Convert 10000 seconds in to the number of equivalent hours minutes and seconds

Answers

Answer:

2 hours 46 minutes and 40 seconds

Step-by-step explanation:

First we divide by 60 to find how many minutes are in 10000 seconds :

10000÷60 = 166 minutes with remainder 40 seconds

If 166 minutes and 40 seconds is 100000 seconds then we change 166 minutes into hours and minutes :

We do this by dividing 166 by 60 :

166 ÷ 60 :

2 hours Remainder 46 minutes

So our final answer is :

2 hours 46 minutes and 40 seconds

Hope this helped and have a good day

Complete the sentence using the following formula. Enter your answer using digits.
area
The length of a rectangle can be found using the following formula: length width
The length of a rectangle that has a width of 2.5 cm and an area of 20.5 cm² is __ cm.

Answers

Answer: 8.2 cm

Step-by-step explanation:

Area of a rectangle = l x w

[tex]A= 25 cm^{2}[/tex]

[tex]l= ?[/tex]

[tex]w= 2.5 cm[/tex]

[tex]25cm^{2} = l(2.5cm)[/tex]

Rearrange the equation to get Length by itself

[tex]\frac{25cm^{2} }{2.5cm}= l[/tex]

[tex]8.2 cm=l[/tex]

How do you find
arcsin (-1)

Answers

By the definition of inverse functions, we will get:

[tex]arcsin(-1) = -pi/2[/tex]

How to find the arcsin of -1?

The function arcsin(x) is the inverse of the sine function, such that, if:

[tex]sin(x) = y\\\\arcsin(y) = x[/tex]

Now, we know that:

[tex]sin( -pi/2) = -1[/tex]

Where pi = 3.14

Then, using the above rule:

[tex]arcsin(-1) = -pi/2[/tex]

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20 POINTS
good morning, can you please help me

Answers

The area of the paper that remains is 391.04 cm²

Calculating area

From the question, we are to calculate the area of the remaining part of the paper

Area of the paper that remains = Area of rectangle - 2×Area of semicircle

Area of the paper that remains = (l×w) - 2(πr²/2)

Area of the paper that remains = (l×w) - (πr²)

Where l is the length of the paper

w is the width if the paper

and r is the radius of the semicircle

From the given information,

l = 37 cm

w = 16 cm

r = w/2 = 16/2 = 8 cm

Putting the parameters into the equation,

Area of the paper that remains = (37×16) - (3.14(8)²)

Area of the paper that remains = 592 - (3.14×64)

Area of the paper that remains = 592 - 200.96

Area of the paper that remains = 391.04 cm²

Hence, the area of the paper that remains is 391.04 cm²

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Write the expanded expression in expanded form using the definition of an exponent.
2wz^2?

Answers

The expanded form of the given expression is 2 × w × z × z

Writing an expression

From the question, we are to determine the expanded form of the given expression

The given expression is

2wz²

To write an expression in an expanded form, we will write the expression as a repeated multiplication in the simplest way possible.

To do this, we will first expand the index in the given expression.

The index in the given expression is z²

Thus, we get

z² = z × z

Now, we will include the remaining individual terms in the expression and write them as product.

That is,

2wz² = 2 × w × z × z

Hence, the expanded form of the given expression is 2 × w × z × z

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I need to find the equation of the line

Answers

Answer:

y = 3x + 3

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, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

Answer:

y = 3x + 3

Step-by-step explanation:

See attached image.

Can someone help with this problem please.
A sheet of paper, 12 inches by 18 inches, is folded so that 2 opposite corners touch, as shown in the figures below. What is the area, in square inches, of the shaded triangle formed as the result of the overlap. (Please look at the picture!)

Answers

The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²

Calculation of the equilateral triangle

After folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.

An equilateral triangle is a type of triangle where by all the three sides are equal.

To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.

Using the formula for the area of an equilateral triangle,

A = √¾ a²

a= 12 inches

A = √¾ ×12²

A = 62.35 inches ²

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Answer:

Its 78!!!!

Solution:

1/2(12 * 18 - 5 * 12) = 78

A scale drawing of a house addition shows a scale factor of 1 in. = 3.3 ft. Josh decides to make the house addition smaller, and he changes the scale of the drawing to 1 in. = 1.1 ft.

What is the change in the scale factor from the old scale to the new scale?

Answers

The change in the scale factor from the old scale to the new scale is 3.

What is the change in the scale factor?

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension.

The change in the scale factor = larger scale / smaller scale

3.3 / 1.1 = 3

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which of the following points could be added to the graph f(x)=-|x+3| to keep the graph a function?
a.(0.3) b.(-3,-6)
c. both a and b d. none of the above

Answers

None of the points could be added to the graph f(x)=-|x+3| to keep the graph a function

How to determine the point?

The equation of the function is given as:

f(x) = - |x + 3|

The points are given as:

(0, 3) and (-3, -6)

When x = 0, we have:

f(0) = - |0 + 3|

f(0) = -3 --- different y value from (0, 3)

When x = -3, we have:

f(-3) = - |-3 + 3|

f(-3) = 0 --- different y value from (-3, -6)

This means that the x values point to different y values (this does not represent a function)

Hence, none of the points could be added to the graph f(x)=-|x+3| to keep the graph a function

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The following two-way table describes student's
after school activities. find the probability that a
randomly selected student either does sports or
works.
grade
sports
music/drama
work
20
7
sophomore
3
junior
20
13
2
25
5
senior
5
p(sports u work) = [?]
round to the nearest hundredth.
lol

Answers

P ( work/ senior ) = 0.14

The attached table

required

P ( work/ senior )

This is calculated using:

P ( work/ senior ) = n ( work/ senior )/ n ( senior ).

n ( work/ senior ) = 5

n ( senior ) = 25 + 5 + = 35

So:

P ( work/ senior ) = 5/35

P ( work/ senior ) = 0.14

Add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).

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A right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid m. what is the shape of the cross section?

Answers

The cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.

If the peak of the rectangular pyramid is directly above the center of the base, it creates a perpendicular to the base, indicating the height of the pyramid. This type of rectangular pyramid is known as the right rectangular pyramid.

A rectangle is a quadrilateral, that is a closed figure with 4 line segments, with all four interior angles at 90°.

When we slice a right rectangular pyramid vertically down at the red line by a plane, not passing through the vertex, of the pyramid will be a dilated image of its base.

A dilated image is an enlarged or diminished image of the preimage, similar with all angles.

Thus, the cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.

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For complete question, refer to the attachment.

Answer:trapozoid

Step-by-step explanation:


Question 1
Which equation represents the relationship shown in the table
at the right?

Answers

Answer:

Option (4)

Step-by-step explanation:

When x = 0, y = -3.

Eliminate Option 1.

Also, the slope is

[tex]\frac{-1-(-3)}{1-0}=2[/tex]

So, the equation is y = 2x - 3.

if the length of a rectangle is decreased by 2cm and the width is increased by 6 cm the result will be a square the area of this square will be 64 cm^2 greater than the area of a rectangle find the area

Answers

The area of the rectangle is 105 square cm

How to determine the rectangle area?

Represent the dimensions of the rectangle with x and y

So, the length of the square would be:

Length = x - 2

Width = y + 6

The areas are then calculated as:

Rectangle = xy

Square = (x -2)(y + 6)

The relationship between the areas is:

(x -2)(y + 6) = 64 + xy

Expand

xy + 6x - 2y - 12 = 64 + xy

This gives

6x - 2y - 12 = 64

Add 12 to both sides

6x - 2y= 76

Divide through by 2

3x - y = 38

By trial by error, we have:

x = 15 and y = 7

The rectangle area is then calculated as:

Rectangle = xy

This gives

Rectangle = 15 * 7

Evaluate

Rectangle = 105

Hence, the area of the rectangle is 105 square cm

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Again pls help out!

Answers

Answer:

okay so I think its, horizontal shift right 2 and a vertical shift down 1

Step-by-step explanation:

so x says + 2 so right 2 and y says -y so down 1..?

I'm kinda rusty tho so yeah

Other Questions
5.MATHEMATICS Year'A square is folded into half to form a rectangle as shown below. The perimeter of the rectangle is 36 cm.Calculate the area of the square. Find the Diameter of the Circle with the following equation. Round to the nearest tenth.(x - 2)2 + (y + 6)2 = 35 On december 5, z-mart purchased $1,800 worth of merchandise. on december 7, z-mart returned $800 worth of merchandise. on december 8, it paid the balance in full after taking a 2% discount. the amount of the payment was multiple choice $1,000 $1,600 What is the domain of the function shown on the graph? The _____ is commonly used to examine whether exactly two groups are significantly different from each other on some score or measure. Solve for X. Please solve this. should the united states have dropped atomic bombs on japan? why or why not? Read this excerpt from "A Retrieved Reformation." On the Monday night after Jimmy wrote this letter, Ben Price jogged unobtrusively into Elmore in a livery buggy. He lounged about town in his quiet way until he found out what he wanted to know. From the drug-store across the street from Spencer's shoe-store he got a good look at Ralph D. Spencer. "Going to marry the banker's daughter are you, Jimmy?" said Ben to himself, softly. "Well, I don't know!" What can the reader predict based on the foreshadowing in the passage above? Ben Price will ruin Jimmys plan to marry Annabel. Jimmy will discover Ben Price has tracked him down. Ben Price will allow Jimmy to go free. Jimmy will use the bankers daughter to rob the bank. "Do what you do best" is most consistent with which target marketing strategy?O ConcentratedO DifferentiatedO UndifferentiatedO AggregatedO Sales-oriented The surface area of a rectangular prism that has height of 4 inches, width of 9 inches and length of 3 inches The graph shows the speed of a cart over a period of several minutes. At approximately what time did the speed of the cart begin to decrease? 22. Robert Hooke, a French scientist, published Micrographia in which he described manyof his microscopic observations.a. True b. False George is driving at an average speed of 707070 miles per hour. At this rate, how long, in minutes, will it take him to complete a 400400400-mile road trip Suppose that when the price of peanut butter falls from $5 to $4 per jar, the quantity of jelly purchased rises from 10 million jars to 15 million jars. Write an essay on "The use of modern technology in education" in about 200 words. Revenues, gains, and investments by owners are all increases in net assets. what are the distinctions among them? The practice of sending suspected terrorists to foreign prisons that permit torture in the interrogation of suspects is called ______ A charge for the use of money, usually figured as a percentage of the principal is called? Employees who come forth with incriminating information are protected in the Sarbanes Oxley (SOX) by which provision One cupcake weighs 3 1/2 ounces how many cupcakes are there in 28 ounce package