Please help answer this geometry

Please Help Answer This Geometry

Answers

Answer 1

Answer:

a. [tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]

b. [tex]100x+225y=100x+225[/tex] Which means it is an identity

Step-by-step explanation:

The Pythagorean Theorem states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.

If in a right triangle there are legs of length a, and b, and the measure of the hypotenuse is c, then The following relationship is fulfilled:

[tex]a^{2} +b^{2}=c^{2}[/tex]

a. Write an equation using the Pythagorean Theorem and the measurements provided in the diagram

From the exercise shown in the image, we can get the values of a, b, and c.

a = 8x+12y, b = 6x+9y, and c = 10x+15y

Write an equation using the Pythagorean Theorem

We obtain:

[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]

b. Transform each side of the equation to determine if it is an identity.

In mathematics, an identity is the realization that two objects that are mathematically written differently, are in fact the same object. In particular, an identity is an equality between two expressions, which is true whatever the values ​​of the different ones are.

So, we transform each side of the equation

[tex](8x+12y)^{2} +(6x+9y)^{2} = (10x+15y)^{2}[/tex]

[tex](8x)^{2} +(12y)^{2} +(6x)^{2} +(9y)^{2}= (10x)^{2}+(15y)^{2}\\64x+144y+36x+81y=100x+225y\\(64x+36x)+(144y+81y)=100x+225y\\100x+225y=100x+225[/tex] Which means it is an identity

.

Answer 2

Answer:

a). (10x + 15y)² = (8x + 12y)² + (6x + 9y)²

b). It's an identity

Step-by-step explanation:

a). Pythagoras theorem says

(Hypotenuse)² = Height² + Base²

Therefore, form the given picture

(10x + 15y)² = (8x + 12y)² + (6x + 9y)² will be the equation.

b). For an identity we have to prove Right hand side of the equation(R.H.S.) = Left hand side of the equation(L.H.S.)

Now we solve the L.H.S. of the equation

(10x + 15y)²

= 100x² + 225y² + 300xy  [ (a + b)² = a²+ b² + 2ab

Now we solve R.H.S. of the equation

(8x + 12y)² + (6x + 9y)²

= 64x²+ 144y² + 36x² + 81y² + 108y + 192xy + 108xy

= 100x² + 225y²+ 300xy

Therefore, L.H.S. = R.H.S.

The given equation is an identity.


Related Questions

A 4-PINT carton of ice cream costs $12.04. What is the price per QUART

Answers

1 quart = 2 pints.

This means a 4 pint container is 2 quarts.

To find the price for 1 quart divide the price by 2:

12.04 / 2 = $6.02 per quart.

Follow the process of completing the square to solve x2 - 10x + 8 = 0. How will the left side of the equation factor in step 5?

Answers

Answer:

[tex]x=5(+/-)\sqrt{17}[/tex]

Step-by-step explanation:

we have

[tex]x^{2}-10x+8=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}-10x=-8[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]x^{2}-10x+5^{2}=-8+5^{2}[/tex]

[tex]x^{2}-10x+25=-8+25[/tex]

[tex]x^{2}-10x+25=17[/tex]

Rewrite as perfect squares

[tex](x-5)^{2}=17[/tex]

Take square root both sides

[tex](x-5)=(+/-)\sqrt{17}[/tex]

Adds 5 both sides

[tex]x=5(+/-)\sqrt{17}[/tex]

6. Mr Wade works for 5 straight
hours when he opens his stand
After a 1 hour break he works
6 hours and 15 minutes before
Closing at 6:10p.m. What time
does Mr Wade open his stand

Answers

5:55am

Start by finding how long the stand was open. Add 5 hours + 1 hour + 6 hours 15 minutes to get 12 hours 15 minutes.

Now, just find the time that is 12 hours and 15 minutes before 6:10pm. Start by subtracting 12 hours, which just switches the time from a.m. to p.m. This brings you to 6:10am. Finally, subtract the 15 minutes to get 5:55am.

a small box has a length of (x) a width of (x+1) and a height of (x+2). what is the volume of the box

Answers

Answer:

Step-by-step explanation:

Final answer:

The volume of a box with dimensions length x, width (x+1), and height (x+2), is given by the formula x^3 + 3x^2 + 2x cubic units.

Explanation:

The volume of the box can be calculated by multiplying its length, width, and height together. Given that the length is x, width is (x+1), and height is (x+2), the volume would be x*(x+1)*(x+2).

To further expand this, apply the distributive law which first multiplies x*(x+1), resulting in x^2 + x. Then multiply this result by (x+2), giving the final volume V = x^3 + 3x^2 + 2x.

Therefore, the volume of the box given the stated dimensions is x^3 + 3x^2 + 2x cubic units.

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Please help, what is x?

Answers

Answer:

x = 18

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{x+x+3}{x+3}[/tex] = [tex]\frac{14+12}{14}[/tex]

[tex]\frac{2x+3}{x+3}[/tex] = [tex]\frac{26}{14}[/tex] ( cross- multiply )

14(2x+3) = 26(x + 3) ← distribute both sides

28x + 42 = 26x + 78 ( subtract 26x from both sides )

2x + 42 = 78 ( subtract 42 from both sides )

2x = 36 ( divide both sides by 2 )

x = 18

If angle abc is reflected across the y-axis, what are the coordinates of A”?

Answers

Answer:

The coordinates of A'' are (-2 , -5) ⇒ answer A

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) reflected across the x-axis

∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

∴ Its image is (-y , -x)

* Now lets solve the problem

- The vertices of triangle ABC are:

 A is (2 , -5) , B is (1 , -3) , C is (5 , -3)

∵ The triangle is reflected across the y-axis

∴ The x- coordinates of the three point are changed to opposite sign

∵ A is (2 , -5)

∴ its image A" is (-2 , -5)

* The coordinates of A'' are (-2 , -5)

Answer:

(-2, -5)

Step-by-step explanation:

HELPPP IDK WUT THE HECK THIS IS

Answers

ANSWER:

The 100 one is 10 and the 1,728 one is 12!

I think this is right and I hope I helped!

Tell me if it was right!

Helpppppppppp it’s due tomorrow!!!!!!!!

Answers

93.75h. Mr. Demir must work 93.75h at his part-time job to make sure that he and his wife have met their monthly budget.

This problem can be solved by simply  arithmetic, The montly budget is $5,500, Mrs. Demir takes home $4,000 each month.  Then what remains to achieve the budget is:

$5,500 - $4,000 = $1,500

Mr. Demir works part time and earns $16 per hour, In order to achieve the monthly budget, Mr. Demir need to take home $1,500. Then, to take home $1,500 Mr. Demir has to work:

1500/16 = 93.75

Mr. Demir has to work 93.75 hours per month in order to achieve the monthly budget

my bed is 3inches by 2 2/3 inches by 1/3. what is the volum of the bed

Answers

Answer:

2 2/3 inches cubed

Step-by-step explanation:

volume is length x width x height. 3 x 2 2/3 x 1/3 = 2 2/3.

Answer:

2 2/3 in cubed

Step-by-step explanation:

Which of the following is the product of the rational expressions shown below x+2/x-4•3x/x+4

Answers

Answer:

Final answer is [tex]\frac{3x^2+6x}{x^2-16}[/tex].

Step-by-step explanation:

Given rational expressions are [tex]\frac{x+2}{x-4}[/tex] and [tex]\frac{3x}{x+4}[/tex].

Now we need to find about what is the product of given rational expressions.

to multiply the rational expressions, we simply multiply numerator with numerator. Then multiply denominator with denominator.

[tex]\frac{x+2}{x-4}\cdot\frac{3x}{x+4}[/tex]

[tex]=\frac{\left(x+2\right)\cdot3x}{\left(x-4\right)\cdot\left(x+4\right)}[/tex]

[tex]=\frac{3x^2+6x}{x^2+4x-4x-16}[/tex]

[tex]=\frac{3x^2+6x}{x^2-16}[/tex]

Hence final answer is [tex]\frac{3x^2+6x}{x^2-16}[/tex].

Find the value of x so that the line passing through (x, 10) and (-4, 8) has a slope of 2/3

Answers

Answer:

x = -1

Step-by-step explanation:

We are given the following two points from which the line passes and has a slope of [tex]\frac{2}{3}[/tex].

We are to find the value of x.

Slope = [tex] \frac { y _ 2 - y _ 1 } { x _ 2 - x _ 1 } [/tex]

[tex]\frac{2}{3}[/tex] = [tex]\frac{10-8}{x-(-4)}[/tex]

[tex]\frac{2}{3}[/tex] = [tex]\frac{2}{x+4}[/tex]

By cross multiplication:

[tex]2(x+4)=3 \times 2[/tex]

[tex]2x+8=6[/tex]

[tex]2x=-2[/tex]

x = -1

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with ele axis and

[tex]m = \frac {y2-y1} {x2-x1}[/tex]

How we have:

[tex]\frac {2} {3} = \frac {8-10} {- 4-x}\\\frac {8-10} {- 4-x} = \frac {2} {3}\\\frac {-2} {- 4-x} = \frac {2} {3}[/tex]

We clear the value of "x"

[tex]2 (-4-x) = - 6\\-8-2x = -6\\-2x = -6 + 8\\-2x = 2\\x = \frac {2} {- 2}\\x = -1[/tex]

Answer:

[tex]x = -1[/tex]

somebody help fast??????

Answers

Answer:

Option 3 (angle WXY + angle YXZ = 180) is the answer.

For Spirit Day, each 8th-grade
homeroom designs a unique two-
color T-shirt. They get to choose from
the colors red (R), blue (B), green (G),
violet (V), and orange (O). Each T-shirt
is a solid color with a different color
used for the student's name. What is
the probability that a homeroom will
have a T-shirt with a combination of
blue and violet?

(A) P(B and V)=10%
(B) P(B and V)=20%
(C) P(B and V)=30%
(D) P(B and V)=40%

Answers

Answer: Option A

P(B and V)=10%

Step-by-step explanation:

To solve this poroblema we use the formula of combinations:

[tex]nCr =\frac{n!}{r!(n-r)!}[/tex]

Where n is the number of objects that can be chosen and you choose r from them.

There are 5 colors of shirts.

The number of shirts that can be made by combining 2 of the 5 possible colors is calculated as:

[tex]5C2[/tex]

[tex]5C2=\frac{5!}{2!(5-2)!}[/tex]

[tex]5C2=10[/tex]

The number of shirts that can be made by combining 2 of the 2 possible colors (B) and (V) is calculated as:

[tex]2C2 = 1[/tex]

Then the probability is:

[tex]P(B\ and\ V)=\frac{2C2}{5C2}\\\\P(B\ and\ V)=\frac{1}{10}\\\\P(B\ and\ V)=0.1=10\%[/tex]

Answer: the answer is D

Step-by-step explanation:

Cause you have to do 100% divided by 5 you will get 20%

So if you have two of the five colors you will have two multiple 20% times 2 and get 40%

A total of 430 dogs and people attend a fundraising dog walk. Altogether, 1210 legs participated in the walk. How many dogs were there? ​

Answers

1210÷4=302.5 and u can have a half of a dog so there would be 302

What percentage kf the rolls are greater than 3?​

Answers

Add the total number of rolls that were greater than 3.

This would be the number 4, 5 and 6.

8 + 11 + 10 = 29 rolls higher than 3.

Now divide the number of rolls higher than 3 by the total number of rolls which is given as 50:

29 / 50 = 0.58

Multiply by 100 to get the percent:

0.58 x 100 = 58% of the rolls were higher than 3.

Lydia bought a car for $20,000. It is expected to depreciate at a continuous rate. What will be the value of the car in 2 years? Use k = 0.105 and round to the nearest dollar.

Answers

Answer:

[tex]\$16,021[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-k)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

k is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$20,000\\k=0.105\\x=2\ years[/tex]

[tex]V=\$20,000(1-0.105)^{2}=\$16,020.50[/tex]  

round to the nearest dollar

[tex]\$16,020.50=\$16,021[/tex]  

the value of the car after 2 years will be approximately $16,212.

To find the value of the car after 2 years with continuous depreciation, we will use the formula for continuous exponential decay:

[tex]V(t) = V_0 \times e^{-kt}[/tex]

Where V(t) is the value after time t V_0 is the initial value, k is the decay constant and t is time

Plugging in the values:

[tex]V(2) = 20000 \times e^{-0.105 \times 2}[/tex]

Simplifying the exponent:

[tex]V(2) = 20000 \times e^{-0.21}[/tex]

[tex]V(2) = 20000 \times 0.8106 \approx 16212[/tex]

Thus, the value of the car after 2 years will be approximately $16,212.

A county government says that a safe level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.

a. Write and solve an absolute value inequality to represent this situation.
b. A lifeguard measures the chlorine level in the pool and finds it is 1.0 ppm. Should he add more chlorine? Explain.

Answers

Answer:

Part A : |x-2.5| ≤ 0.75  , x ∈ [1.75,3.5]

Part B : yes, the lifeguard should add more chlorine.

Step-by-step explanation:

Part A:

Let  C is the variation of the level of chlorine in a hot tub.

Level of chlorine in a hot tub is within 1.75 ppm of 3.25 ppm.

To find absolute value inequality, need to find the standard level of chlorine 1.75 + C or 3.25 - C

1.75 + C = 3.25 - C

2C = 5

C = 2.5

So, the standard level would be 2.5 ppm,

If x represents the present level of chlorine,

Then it would be lie within 1.75 ppm of 3.25 ppm.

1.75 ≤ x ≤ 3.25

Subtract 2.5 from all sides

1.75 - 2.5 ≤ x -2.5 ≤ 3.25 - 2.5

-0.75 ≤ (x-2.5) ≤ 0.75

which is equivalent to the following absolute value inequality.

|x-2.5| ≤ 0.75

And the solve of the inequality : x ∈ [1.75,3.5]

Part B:  If x = 1.0 ppm,

∴ |1.0-2.5| = 1.5 which is not less than equal to 0.75.

Another explanation:

the minimum safe level of chlorine in a hot tub is 1.75 ppm

Since 1 < 1.75

Therefore, lifeguard should add more chlorine.


Which statement describes the speed of the remote control car over time?​

Answers

Answer:

Step-by-step explanation:

D

what i 36 divide by 86.4

Answers

If your asking whats 86.4 divided by 36 its 2.4

Find the sum of all interior angles of the following regular 20 sided polygon

Answers

Answer:

3240°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 20, hence

sum = 180° × 18 = 3240°

I need answers for both please!!

Answers

1 = a

2 = h

have a good day

(20 points) Please answer and explain!

multiply and simplify -3x^2y^2 * y^4x3
a. -3x^5y^6
b. -3x^6y^2
c. 9x^5y^2
d. -3x ^5y^2

Answers

Answer:

[tex]\large\boxed{a.\ -3x^5y^6}[/tex]

Step-by-step explanation:

[tex]-3x^2y^2\cdot y^4x^3=(-3)(x^2x^3)(y^2y^4)\\\\\text{use}\ a^na^m=a^{n+m}\\\\=-3x^{2+3}y^{2+4}=-3x^5y^6[/tex]

what is the value of x to the nearest tenth?

Answers

tan 24 = x/12

0.4452 · 12 = X

5.34 = X

solve for K thanks!!!

Answers

4.5 + 1.5k = 18 - 3k

Bring -3k to the other side by adding 3k to both sides

4.5 + (1.5k + 3k) = 18 + (-3k + 3k)

4.5 + 4.5k = 18 + 0

4.5 + 4.5k = 18

Bring 4.5 to the other side by subtracting it to both sides

(4.5 - 4.5) + 4.5k = 18 - 4.5

0 + 4.5k = 13.5

4.5k = 13.5

Isolate k by dividing 4.5 to both sides

4.5k / 4.5 = 13.5 / 4.5

k = 3

Hope this helped!

~Just a girl in love with Shawn Mendes

Consider the function f (x) = x2.
What effect does subtracting 2 from the input have on the graph of the function?​

Answers

Answer: The graph is shifted 2 units to the right.

Step-by-step explanation:

Given a function f(x), we know that one transformation rule is:

If [tex]f(x-k)[/tex] then the function is shifted "k" units to the right.

 Therefore, for the function [tex]f(x)=x^{2}[/tex], when we subtract 2 from the input, then we get the function g(x) in the form:

 [tex]g(x)=(x-2)^{2}[/tex]

We can conclude that subtracting 2 from the input of the function [tex]f(x)=x^{2}[/tex], then the graph is shifted 2 units to the right.

The answer is right graph shifted 2 units to the right

Susie filled up her car with 12 gallons of gas.

Which number sentence could be used to figure out how many quarts of gas Susie put into her car?

(4 qt = 1 gal)

12 ÷ 4 = □

12 + 4 = □

12 × 4 = □

12 − 4 = □

Answers

12÷4

=3

because theres 12 gallons n theres four qts in each so you divide

The answer is the 12 multiplied by 4

A right rectangular pyramid is sliced parallel to the base as shown.

What is the area of the resulting two-dimensional cross-section?

A. 2
B. 3
C. 9
D. 12

Answers

Answer:

[tex]A=2\ m^{2}[/tex]

Step-by-step explanation:

we know that

The resulting two-dimensional cross-section is a rectangle 1 m x 2 m

so

the area of this rectangle is equal to

[tex]A=2*1=2\ m^{2}[/tex]

Which line is the line of best fit for this scatter plot?

Answers

The last one. It goes and touches the most points.

The 4th line is the line of best fit for this given scatter plot.

What is a scatter plot?

"A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed."

Here, 4 different lines are drawn for a given scatter plot.

We know, a line drawn on a scatter plot fits it the best is the line that is closer to most of the points.

Here, the 4th line is closer to most of the points on the scatter plot.

Therefore, 4th line is the best fit.

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adults have 32 teeth children have 62.5% as many teeth as adults. how many teeth do children have

Answers

The answer would be 20

You multiply 62.5% by 32

32*0.625=20

They are correct it is 20.

A cube has an edge length 12cm. If the edge length of the cube is doubled, what happens to the surface area?

Answers

Answer:

Surface area of original cube:

6(12²) = 6(144) = 864 cm²

Surface area of new cube:

6(24²) = 6(576) = 3,456 cm²

If the edge length of the cube is doubled, the surface area of the cube will be quadrupled.

Doubling the edge length of a cube from 12 cm to 24 cm increases the surface area by a factor of four, from 864 cm^2 to 3456 cm^2, because surface area is a two-dimensional measure and each dimension has been doubled.

If a cube has an edge length of 12 cm, its surface area is calculated by the formula 6s^2, where s is the length of a side. So the surface area of the original cube is 6  imes 122 cm^2 = 864 cm^2.

When the edge length of the cube is doubled to 24 cm, to find the new surface area, we also apply the formula 6s^2. Therefore, the new surface area is 6  imes 242 cm^2 = 3456 cm^2.

Comparing the new surface area to the original, we see that it has increased by a factor of 4, which is the square of the factor by which the edge length was multiplied (22 = 4). This occurs because surface area is a two-dimensional measure (involving length by width), so when each dimension is doubled, the overall area increases by a factor of four (2  imes 2).

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