Triangle FGH is an isosceles right triangle with a hypotenuse that measures 16 units. An altitude, GJ, is drawn from the right angle to the hypotenuse.

What is the length of GJ?

A. 2 units
B. 4 units
C. 6 units
D. 8 units

Answers

Answer 1
It's D) 8 units HOPE IT HELPS
Answer 2

The value of the length GJ for the given triangle will be 8 units thus option (D) is correct.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

As per the given isosceles triangle which has two equal sides so suppose the length of those sides is x unit.

By Pythagoras' theorem,

⇒ x² + x² = 16²

⇒ 2x²  = 256

⇒ x² = 128

The area of a triangle is given as,

⇒ (1/2) × x × x

⇒ (1/2) x²

⇒(1/2) × 128

⇒ 64 units²

The area of the triangle will also be given as,

A = (1/2) × 16 × (GJ)

Compare both areas as

64 = (1/2) × 16 × GJ

GJ = 8 units

Hence"For the provided triangle, the length GJ value will be 8 units".

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Related Questions

Which point is on the interior of ∠BAC?

point D

point B

point C

point A

Answers

the answer is point D, the main points of the triangle is BAC but the interior point is D.


Final answer:

When talking about ∠BAC, points B and C are on the rays, and A is the vertex. Thus, only point D could be on the interior of the angle, assuming it falls within the area enclosed by these lines.

Explanation:

In geometric terms, an angle is made up of two rays that share a common endpoint, known as the vertex. The interior of an angle is the area enclosed by the rays. When we talk about ∠BAC, points 'B' and 'C' are on the rays while 'A' is the vertex. Therefore, only point D could potentially be on the interior of ∠BAC, assuming it lies within the space enclosed by the lines extending from point 'A' to points 'B' and 'C'. Without further context or a diagram to confirm D's position, this is the best conjecture we can make based on the given information.

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The sum of 5 consecutive integers is 310 What is the third number in this sequence?

Answers

310/5 = 62

60 +61 +62 +63 +64 = 310

 3rd number is 62

Which equation can be used to find the answer? an aquarium worker removed 78 fish from a tank. there were still 186 fish left in the tank. how many fish were in the tank before any were removed?
a. f ÷ 2 =78 f = 156 156 fish
b. f ÷ 2 =186 f = 372 372 fish
c. f – 78 = 186 f = 264 264 fish
d. f + 78 = 186 f = 108 108 fish?

Answers

The answer is B. Hope I helped!

Answer:

f/2=186 fish

186 x 2 = 372

372 fish left in the tank

Step-by-step explanation:

What's the unit rate for 4 shirts for $32:00

Answers

The unit rate for 4 shirts is $8 per shirt.
32/4 = 8
$32 ÷ 4 shirts = $8
The unit rate (price per t-shirt) is $8

Please help, will give brainliest.

If the area of a parallelogram is to remain constant, what change must take place in the base if the altitude is multiplied by three? (1a)____ by(1b) _____. If the altitude is divided by two? (2a)____ by(2b) _____.

1a) A. divide. B. Multiply. C. Addition.
1b) A.6 B.3
2a) A. Divide. B. Multiply
2b) A. 2 B. 6

Please help, will give brainliest.

Answers

Divide by 3, and multiply by 2.

Answer:

The answers are:

1a --> divide

1b --> 3

2a --> multiply

2b --> 2

By the way, I turned in my assignment and these are the answers on the answer key, so they are correct for sure!   :)

Use the graph of the function y = (x + 3)(x − 2) to find the solutions of the quadratic equation 0 = (x + 3)(x − 2).

Answers

we have the equation: (x+3)(x-2) = 0

For a product to be zero, one of the two operands needs to be a zero.
This means that either x+3 = zero or x-2 = zero

For: x+3 = zero ...................> x = -3
For: x-2 = zero ..................> x = 2

So, the two points on the graph that has a y = 0 are (-3 , 0) and (2 , 0)

Answer:

-3 and 2 are the answer

Hope this helps!

The value that results from plugging in an x term.

Answers

 The answer to your question is x=-b+√b2-4ac2a x=2

If the ratio of soccer balls to footballs is 7:6 and the ratio of footballs to basketballs is 2:1, what is the ratio of soccer balls to basketballs?

Answers

let soccer balls be s, football be f and basketball be b.

s:f is 7:6
f:b is 2:1
f:b can also then be written as 6:3 (multiply by 3)
therefore s:f:b is 7:6:3

therefore ratio of s:b is 7:3

How to tell if a function is continuous or discontinuous?

Answers

A functions is discontinuous if it has stuff like holes, jumps, or vertical asymptotic. In addition, it's continuous if it stays in a line the whole time (it doesn't have to be straight or anything!)

Final answer:

A function is continuous at a point if it is defined at that point, the limit exists as it approaches the point, and the limit is equal to the function's value at that point. If these conditions are not met, the function is discontinuous. The first derivative must also be continuous unless given specific exceptions.

Explanation:

To determine if a function is continuous or discontinuous, you can apply several tests. A function y(x) is said to be continuous at a point if it meets three conditions:

The function must be defined at that point.The limit of the function as it approaches that point exists.The limit of the function as it approaches the point is equal to the function's value at that point.

If any of these conditions fail, the function is discontinuous at that point. For example, a function with a hole, jump, or asymptote at a point would be discontinuous there. Also, if the first derivative of y(x) is not continuous, unless the potential function V(x) is infinite, this indicates a discontinuity. In continuous probability functions, such as probability density functions, discontinuities are not present, and the function's graph does not have breaks or holes. Instead, the entire graph is a single unbroken curve.

What are the possible solutions to 33⋅3333⋅33, if 11⋅11=411⋅11=4 and 22⋅22=1622⋅22=16?

Answers

Since 11*11 = 4, therefore in this case 11 = 2. Since 22*22 = 16, therefore in this case 22 = 4. So we can see that the common ratio is 2. Based from this, we can say that 33 = 6.

So that:

33*33 = 36

What is 8 21/40 I don't understand how to do it

Answers

Hey, there !

If you want to know it as a "improper fraction" , you can

Multiply the denominator from the front number
Whatever the denominator and front number is , you add it to the numerator

So, for this problem we first have the multiply the front number from the denominator

Like: 8 (40)
That gives us the answer of: 320

Now we have to add 320 to 21

Like: 320 + 21

That gives us the answer of:341

We keep our denominator (which is "40" )

Your improper fraction would be:

341 / 40

Good luck on your assignment and enjoy your day!

~MeIsKaitlyn:)
8 21/40

You can either solve this by dividing 21/40 and then adding 8 to it.
21/40 = 0.525
0.525 + 8 = 8.525

Another way is to change it into an improper fraction. This is done by multiplying the denominator (40) by the whole number (8) then adding that to the numerator (21). That number then becomes the numerator, but make to keep the denominator the same (40).
40 × 8 = 320
320 + 21 = 341
8 21/40 = 341/40
Then input 341/40 into a calculator or do long/short division.
341/40 = 8.525

Either way, the answer will be 8.525.

what is y=2-3x in standard form?

Answers

standard form is (y=x+n) *n=number* y=-3x+2
Final answer:

The given equation of the line is in slope-intercept form. To convert it to standard form, simply rearrange so that all terms are on one side of the equation resulting in 3x + y = 2.

Explanation:

The equation you're given is y=2-3x which is in the slope-intercept form i.e., y = mx + b, where m is the slope and b is the y-intercept. To convert this equation to a standard form, the general approach is to eliminate fractions and have the 'y' and 'x' terms on the same side of the equation.

Starting from y = 2 - 3x, add 3x to both sides of the equation to get it in the standard form. So, it becomes 3x + y = 2, which is the standard form of the given equation.

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In the figure below, if segment B E is the perpendicular bisector of segment A D, what is the value of x?

Answers

Because AE and ED are equal, ABE and EBD are equal. And because BEA and BED are right angles, they are congruent too.

These triangles are congruent because of AAS.

So,

2x + 4 = x + 7
x = 3

Hope this helps!

There is a 12% sales tax. The pre-tax cost of a mobile phone is $280. What is the tax payable on this mobile phone?

Answers

Hello there! I can help you with this question! So, the cost of the phone before tax is $280. To find the tax, we must multiply 280 by 12% (0.12). When you do 280 * 0.12, your product should be 33.6. The tax payable on this mobile phone is $33.60.

The tax payable on this mobile phone is $33.60.

Using this formula

Tax payable=Sales tax × Pre tax cost

Where:

Sales tax =12%

Pre tax cost=$280

Let plug in the formula

Tax payable=12%×$280

Tax payable=$33.60

Inconclusion  the tax payable on this mobile phone is $33.60.

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The first three terms of a geometric sequence are as follows. −4 , 20 , −100 find the next two terms of this sequence. give exact values (not decimal approximations).

Answers

You multiply by -5 to find any next term. so next two are 500 then -2500

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 5θ

Answers

Looking at the graph, we'll notice that there is a local maximum at x=0 and it looks similar on both sides of the y axis, therefore making it symmetric around the y axis given the options

Answer:

The graph is symmetric about the x-axis.

Step-by-step explanation:

1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point  (r, -θ ) or (-r, π - θ ) also lies on the graph.

2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,  π - θ ) or (-r, -θ ) also lies on the graph.

3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.

The given polar equation is

[tex]r=2\cos (5\theta)[/tex]

Check the equation by (r, -θ).

[tex]r=2\cos (-5\theta)=2\cos (5\theta)=r[/tex]

Therefore, the graph is symmetric about the x-axis.

Check the equation by (-r, -θ).

[tex]-r=2\cos (-5\theta)=2\cos (5\theta)=r\neq -r[/tex]

Therefore, the graph is not symmetric about the y-axis.

Check the equation by (-r, θ).

[tex]-r=2\cos (5\theta)=2\cos (5\theta)=r\neq -r[/tex]

Therefore, the graph is not symmetric about the origin.

A stack of four hundred twenty cards is placed next to a ruler, and the height of stack is measured to be 7/8 inches. How thick is one card?

Answers

7/8 divided by 420 = 7/8 x 1/420 by inverting & multiplying 
= 7/3360 by multiplying tops together & bottoms together 
= 1/480 inch reducing fraction by dividing top & bottom by 7 

(and yes, I know that top is called numerator & bottom is called denominator, otherwise known as upstairs & downstairs) 

Could also work by cross-cancelling earlier, dividing 7 by 7 = 1 and dividing 420 by 7 = 60 
leaving 1 x1 on the top & 8 x 60 on the bottom. Will get same result as before, 1/480 inch.

A statement Sn about the positive integers is given. Write statements Sk and Sk+1, simplifying Sk+1 completely. Show your work. Sn: 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3

Answers

Alright, for the sum part, it really seems like it's x*(x+1) +(x+1)*(x+2)repeating forever. Therefore, it is  ∑ (1 at the bottom, n at the top) k*(k+1)=[n(n + 1)(n + 2)]/3

Answer with explanation:

[tex]S_{n}= 1 \times 2 + 2 \times 3 + 3 \times 4 + . . . + n\times(n + 1) = \frac{n(n + 1)(n + 2)}{3}\\\\S_{k}= 1 \times 2 + 2 \times 3 + 3 \times 4 + . . . + k\times(k + 1) = \frac{k \times(k + 1)(k + 2)}{3}\\\\S_{k+1}= 1 \times 2 + 2 \times 3 + 3 \times 4 + . . . + k\times(k + 1)+(k+1) \times (k+2)=\frac{(k+1) \times(k +1+ 1)(k +1+ 2)}{3}\\\\=\frac{(k+1) \times(k +2)\times(k +3)}{3}[/tex]

Find the distance between the points t(13, 1.6)t(13, 1.6) and v(5.4, 3.7)v(5.4, 3.7).

Answers

7.88 units is the distance between points T(13, 1.6) and V(5.4, 3.7).

To find the distance between the points T(13, 1.6) and V(5.4, 3.7), we can use the distance formula:

Distance formula:

For two points [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex], the distance between them is [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.[/tex]

Let's plug in the coordinates of points T and V:

Distance = [tex]\sqrt{(5.4 - 13)^2 + (3.7 - 1.6)^2}[/tex]

= [tex]\sqrt{(-7.6)^2 + (2.1)^2}[/tex]

= √(57.76 + 4.41)

= √62.17

= 7.88.

So, the distance between points T(13, 1.6) and V(5.4, 3.7) is approximately 7.88 units.

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Which graph below shows a system of equations with infinitely many solutions?

A)coordinate plane with two parallel lines
B)coordinate plane with two intersecting lines
C)coordinate plane with two coinciding lines
D)coordinate plane with two intersecting lines

Answers

That would be a coordinate plane with two coinciding lines. Coinciding lines are two lines laying one on top of the other. Same line, infinite solutions.

Answer: C)coordinate plane with two coinciding lines  has infinitely many solution.

Step-by-step explanation:

Since, By option A) If there is a coordinate plane with two parallel lines.

Then, It has no solution ( because, we get the solution at the the intersection point of the two lines but parallel lines do not intersect each other).So, it does not have infinite many solution.

By Option B) If there are two intersecting lines then we can get only one solution. So, it does not have infinite many solution.

By Option C) If there are two coinciding lines then we can get infinite number of intersection points therefore the system must have infinite number of solution.

Note: here, Option D) is same as Option B)

Therefore Only option C) is correct.


a square reflecting pool has an area of 183.84 square meters. What is the approximate perimeter of the reflecting pool?

Answers

Final answer:

The perimeter of a square reflecting pool with an area of 183.84 square meters is approximately 54.24 meters.

Explanation:

The area of a square is calculated by squaring the length of one of its sides. So, to find the side length of the square reflecting pool, we need to take the square root of the area. The square root of 183.84 is approximately 13.56 meters.

Now considering that a square has four equal sides, the perimeter is calculated by multiplying the side length by 4. So, the perimeter of the pool is 13.56 multiplied by 4, which gives us approximately 54.24 meters. Therefore, the approximate perimeter of the reflecting pool is 54.24 meters.

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The Environmental Protection Agency (EPA) estimates that the average passenger vehicle emits about 5 1/2 (5.5) metric tons of CO2 each year. How much is this in pounds?

(A) about 12000 pounds

(B) about 120 pounds

(C) about 5500 pounds

Answers

5.5 metric ton is about 12000 pounds

So answer is A.

Answer:

its A about 12,000 pounds.

Step-by-step explanation:

At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?

Answers

The slope of the line will be ZERO.
From the question given above, we are told that when the freezer is working perfectly that the temperature will remain constant over time. This means that if the graph of temperature and time is drawn, the slope of the graph will be constant from one point of the graph to the other, which means that the values will cancel each other out and will be zero.

Erudite1 is right it will be zero

Last year, a baseball team paid $20 per bat and $12 per glove, spending a total of $1040. This year, the prices went up to $25 per bat and $16 per glove. The team spent $1350 to purchase the same amount of eqipment as last year. How many bats and gloves did the team purchase each year?

Answers

Hey there!

You can solve this question using a system of equations. Let x be the number of bats and y be the number of gloves. The first equation will contain 20x and 12y and the second equation will contain 25x and 16y. The equations will be set to the total amount of money they were given per year:

20x + 12y = 1040
25x + 16y = 1350

To solve the system, make one of the terms the same but have the opposite signs using multiplication. This will cancel one of them out. It can be any term you see is easiest. Just make sure that one of the terms is set to 0 by the end of this step. 

–1.25(20x + 12y = 1040)
25x + 16y = 1350

In this case, you can multiply the first equation by –1.25 to make 20x into –25x. This will cancel out the x term. Make sure you multiply the entire first equation. 

–25x + (–15y) = –1300
25x + 16y = 1350

Now, just add the two equations together. 

0x + 1y = 50
y = 50

Now that you know what y is equal to, plug it into your first equation (the original) to find x. This pair will be your answer. 

20x + 12y = 1040
20x + 12(50) = 1040
20x + 600 = 1040
20x = 440
x = 22

So, the pair is (22, 50). This means that the team bought 22 bats and 50 gloves. 

Hope this helped you out! :-)
Final answer:

The baseball team purchased 22 bats and 50 gloves last year.

Explanation:

To solve this problem, let's use a system of equations. Let x represent the number of bats and y represent the number of gloves purchased last year. We can set up the following equations:

20x + 12y = 1040 (equation 1) 25x + 16y = 1350 (equation 2)

We can solve this system of equations by using either the substitution method or the elimination method. Let's use the elimination method:

Multiply equation 1 by 5 and equation 2 by 4 in order to create equal coefficients for x:100x + 60y = 5200 100x + 64y = 5400 Subtract the equations to eliminate x:(100x + 64y) - (100x + 60y) = 5400 - 5200 4y = 200 y = 50

Now we can substitute the value of y back into equation 1 to solve for x:

20x + 12(50) = 1040 20x + 600 = 1040 20x = 440 x = 22

Therefore, the team purchased 22 bats and 50 gloves last year.

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You are planning a party to the local pizza arcade for your child's birthday. The cost of a birthday party is $8.95 per person, and you plan to have 12 people at the party.

Answers

Because it's $8.95 per person, you would make it 12 * 8.95

The total cost would be $107.40

After you complete your survey of students reported heights at your school, you discover that your sample is biased. Exactly 10% of the students in your sample tended to over report their height more than the average student in the general population at the school. What conclusion can you reach about the mean of the average difference in your sample?

a.It is greater than the mean of the average difference of the population

b.It is less than the mean of the average difference of the population

c.It is exactly 10% greater than the mean of the average difference of the population

d.It is exactly 10% less than the mean of the average difference of the population

Answers

your answer would be A. hope this helped! :D

Answer:

a. It is greater than the mean of the average difference of the population

Step-by-step explanation:

Given is - Exactly 10% of the students in your sample tended to over report their height more than the average student in the general population at the school.

It is very certain that the sample is biased towards the higher spectrum.

We can say that the real value of the mean is lower than the original value of our sample population.

So, option A is correct.

if p is the midpoint of xy, xp=8x-2 and py=12x-30, find the value of x

Answers

check the picture below.

surely, you'd know how much that is.
Final answer:

To find the value of x, we can use the midpoint formula which is 16/9.

Explanation:

To find the value of x, we can use the midpoint formula. According to the formula, the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the same applies to the y-coordinate.

Given that XP = 8x - 2 and PY = 12x - 30, we can set up the equation:

(8x - 2 + 12x - 30) / 2 = x

Simplifying the equation, we get:

(20x - 32) / 2 = x

Multiplying both sides of the equation by 2 to eliminate the fraction, we get:

20x - 32 = 2x

20x - 2x = 32

18x = 32

x = 32/18

x = 16/9

There were 25 questions on the test you got a 74 percent what is the number of question you got correct

Answers

To find a percent on something u take the amount u got correct divided by what the total questions are, so what I would do is start with 22/25 and go up or down from that. 
22/25=.88
20/25=.80
19/25=.76
18/25=.72
So the correct answer would be 18 and a half questions right.

74% = 0.74

 multiply 25 by 0.74

25*0.74 = 18.5

 so you got 18 1/2 questions correct

Given that (1,5) is on the graph of f(x), find the corresponding point for the function f(x-1)

Answers

The point (1,5) on the graph of f(x) means x = 1 and y = 5

So we plug x = 1 into f(x) to get f(1) = 5

If we replace x with x-1, then we have x = 1 turn into x-1 = 1. Solve for x to get x = 2

So this means that the point (2,5) is on the graph of f(x-1). Every point on f(x-1) will be the result of shifting a corresponding point on f(x) 1 unit to the right.

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

Final Answer: (2,5)

The pair of points is on the graph of an inverse variation. Find the missing value. (2.4, 3) and (5, y) 1.44 6.25 0.69 1

Answers

In verse variation would be 3  = k / 2.4   so k  = 7.2

So we have  y = 7.2 / 5  = 1.44

Answer is 1.44.

Answer:

Hence, the value of y is:

1.44

Step-by-step explanation:

It is given that:

The pair of points is on the graph of an inverse variation.

(2.4, 3) and (5, y)

We have to find the missing value y in the point.

As we know that in the inverse variation the value of y is the inverse value of x by some k.

i.e. in first point (2.4,3) let 'k' be a number such that:

[tex]3=\dfrac{k}{2.4}\\\\k=7.2[/tex]

Hence, the inverse is k=7.2

Now in the second point (5,y) we find the value of y as:

[tex]y=\dfrac{7.2}{5}\\\\y=1.44[/tex]

Hence, the value of y is:

1.44

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