Which side lengths form a right triangle?

Answer:

The common difference is -5/4

T(n) = T(0)  - 5n/4,

where T(0) can be any number. d = -5/4

Assuming T(0) = 0, then first term

T(1) = 0 -5/4 = -5/4

Step-by-step explanation:

T(n) = T(0) + n*d

Let

S1 = T(x) + T(x+1) + T(x+2) + T(x+3) = 4*T(0) + (x + x+1 + x+2 + x+3)d = 240

S2 = T(x+4) + T(x+5) + T(x+6) + T(x+7) = 4*T(0) + (x+5 + x+6 + x+7 + x+8)d = 220

S2 - S1

= 4*T(0) + (x+5 + x+6 + x+7 + x+8)d - (4*T(0) + (x+1 + x+2 + x+3 + x+4)d)

= (5+6+7+8 - 1 -2-3-4)d

= 4(4)d

= 16d

Since S2=220,  S1 = 240

220-240 = 16d

d = -20/16 = -5/4

Since T(0) has not been defined, it could be any number.

Answer: If a scatterplot is included in the assignment

The dots plotted on the graph might closely follow the graph of exponential decline. There is a large number of texts per day by 19-20-21 year-olds, but the number seems to decline exponentially as age increases. With a little work, it may be possible to plot the curve and write an equation to model the decline.

Step-by-step explanation:  Look at some graphs of exponential decay. Also consider harmonic and hyperbolic decay. The trend in the data is evident. The main challenge is to look at the data and create an equation that models it.

Answer:

[tex]n^6[/tex].

Step-by-step explanation:

[tex]n^4 * \frac{n^7}{n^5}[/tex]

= [tex]n^4 * n^{7 - 5}[/tex]

= [tex]n^4 * n^2[/tex]

= [tex]n^{4 + 2}[/tex]

= [tex]n^6[/tex].

Hope this helps!

Answer:

Step-by-step explanation:

The given equation is expressed as

(x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12

Simplifying the right hand side of the equation, it becomes

[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)

x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)

(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)

4x/(x - 1)(x + 1)

Therefore,

4x/(x - 1)(x + 1) = 7/12

Cross multiplying, it becomes

4x × 12 = 7(x - 1)(x + 1)

48x = 7(x² + x - x - 1)

48x = 7x² - 7

7x² - 48x - 7 = 0

Applying the quadratic formula,

x = - b ± √(b² - 4ac)]/2a

from our equation,

b = - 48

a = 7

c = - 7

Therefore

x = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)

x = [48 ± √(2304 + 196]/14

x = (48 ± √2500)/14

x = (48 ± 50)/14

x = (48 + 50)/14 or x = (48 - 50)/14

x = 98/14 or x = - 2/14

x = 7 or x = - 1/7

Answer: The given equation is expressed as (x + 1)/(x - 1) - (x - 1)/(x + 1) = 7/12Simplifying the right hand side of the equation, it becomes[(x + 1)(x + 1) - (x - 1)(x - 1)]/(x - 1)(x + 1)x² + x + x + 1 - (x² - 2x + 1)/(x - 1)(x + 1)(x² + 2x + 1 - x² + 2x - 1)/(x - 1)(x + 1)4x/(x - 1)(x + 1)Therefore, 4x/(x - 1)(x + 1) = 7/12Cross multiplying, it becomes4x × 12 = 7(x - 1)(x + 1)48x = 7(x² + x - x - 1)48x = 7x² - 77x² - 48x - 7 = 0Applying the quadratic formula,x = - b ± √(b² - 4ac)]/2a from our equation, b = - 48a = 7c = - 7Thereforex = [- - 48 ± √(- 48² - 4(7 × - 7)]/2 × 7)x = [48 ± √(2304 + 196]/14x = (48 ± √2500)/14x = (48 ± 50)/14x = (48 + 50)/14 or x = (48 - 50)/14x = 98/14 or x = - 2/14x = 7 or x = - 1/7

Step-by-step explanation:

Answer:

90 ft²

Step-by-step explanation:

Given the sides of similar figures in the ratio a : b, then

ratio of areas = a² : b²

Here ratio of sides = 1 : 3 , thus

ratio of areas = 1² : 3² = 1 : 9

That is the surface area of the new solid is 9 times the first

SA = 9 × 10 = 90 ft²

The total surface area of the new solid in square feet is 90 square feet

Let the solid be a cube.

The surface area of a cube = 6L²

L is the length o the cube;

If the surface area of a solid is 10 square feet, then;

10 = 6L²

L² = 10/6

L = √10/6

If the dimensions of a similar solid are  three times as great as the first, then;

New length Ln = 3√10/6

Total surface area of the new solid = 6Ln²

Total surface area of the new solid = 6(3√10/6)²

Total surface area of the new solid = 6(9*10/6)

Total surface area of the new solid = 6(90/6)

Total surface area of the new solid = 90 square feet

This shows that the total surface area of the new solid in square feet is 90 square feet

Learn more here: https://brainly.com/question/23756628

Answer:

(-1, -2) last answer

Step-by-step explanation:

x = 1 is a vertical line

Answer:

(-1, -2)

Step-by-step explanation:

This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.

Answer:

288π

Step-by-step explanation:

V=4 /3πr^3 is the formula. We have the diameter, so the radius is half (6). We now have V=4 /3π(6)^3 = 4/3π216 = 288π.

Answer:

both the equation and it's inverse are functions

Answer:

Step-by-step explanation:

5x+30 is a corresponding angle with 4x-9 so set them equal to each other. 4x-9+2x+3 will equal 180

Answer:

no, the values would be above 180º

Step-by-step explanation:

if...

(4x - 9) + (2x + 3) + y = 180

(5x + 30) + y = 180

then...

(4x - 9) + (2x + 3) = 5x + 30

so...

6x - 6 = 5x + 30

x = 36

plug it in.

4(36) - 9 = 135

2(36) + 3 = 75

already you can see the sum of these two angles surpasses 180 which is not possible for a triangle.

Answer:

144 units²

Step-by-step explanation:

Surface area of a traingular prism is given as:

Area = 2(B.A) + P*L

Where,

B.A = base area of the triangular prism = ½*b*h

b = base of the triangular base = 4 units

h = height of the triangular base = 3 units

Base Area (B.A) = ½*4*3 = 2*3 = 6 units²

P = Perimeter of triangular face = sum of all sides the triangle = 3 + 4 + 5 = 12 units

L = length or height of prism = 11 units

Plug in all values into the formula for surface area of triangular prism = 2(B.A) + P*L

[tex] Area = 2(6) + 12*11 [/tex]

[tex] = 12 + 132 [/tex]

[tex] Surface Area = 144 [/tex]

Surface area of the triangular prism = 144 units²

Answer:

R = 21.8° to the nearest tenth

Step-by-step explanation:

To find Angle R we use tan

tan ∅ = opposite / adjacent

From the question

The opposite is 2

The adjacent is 5

So we have

tan R = 2/5

R = tan-¹ 2/5

Hope this helps you

Answer:

u = [tex]\sqrt{6}[/tex].

Step-by-step explanation:

This is a 45-45-90 triangle.

That means that there are two side lengths with lengths of x, and a hypotenuse with a length of xsqrt(2). We can then set up a proportion.

[tex]\frac{1}{\sqrt{3} } =\frac{\sqrt{2} }{u}[/tex]

1 * u = [tex]\sqrt{3} * \sqrt{2}[/tex]

u = [tex]\sqrt{6}[/tex].

Hope this helps!

Answer: x = -2 , y = 3

Step-by-step explanation:

4x-y=-11

2x+3y=5

Solve 4x-y=-11 for y

Add -4x to both sides

4x-y+-4x=-11+-4x

-y=-4x-11

Divide both sides by -1

-y/-1=-4x-11/-1

y=4x+11

Substitute 4x+11 for y in 2x +3y=5

2x+3y=5

2x+3(4x+11)=5

Simplify both sides of the equation

14x+33=5

Add -33 to both sides

14x+33+-33=5+-33

14x=-28

Divide both sides by 14

14x/14=-28/14

x=-2

Substitute -2 for x in y= 4x+11

y=4x+11

y=(4)(-2)+11

Simplify both sides of the equation

y=3

Answer:

Variance =10900.00

Standard deviation=104.50

Step by step Explanation:

Admissions Probability for 1100= 0.2

Admissions Probability for 1400=0.3

Admissions Probability for 1300 =0.5

To find the expected value, we will multiply each possibility by its probability and then add.

mean = 1100*0.2 + 1400*0.3 + 1300*0.5 = 1290

To find the variance, we will start by squaring each possibility and then multiplying it by its probability. We will then add these and subtract the mean squared.

E(X^2)=( 1100²*0.2)+ (1400²*0.3 )+ (1300²*0.5) = 1675000

Variance(X)=E(X²)- [E(X)]²

= 1675000 - (1290)²

=10900

Hence, the Variance(X)=10900

Then to calculate the standard variation , we will use the formular below,

standard variation (X)=√ var(X)= √10900

=104.5

Hence the standard variation=104.5

Answer:

a) A quadrilateral with 4 right angles

Answer:

I think the answer is b

I'm sorry if I'm not correct

Answer:

Step-by-step explanation:

Given

u = 14 , a = 8 , t = 4

Now, let's find the value of s

[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]

plug the values

[tex] = 14 \times 4 + \frac{1}{2} \times 8 \times {4}^{2} [/tex]

Reduce the numbers with G.C.F 2

[tex] = 14 \times 4 + 4 \times {4}^{2} [/tex]

Multiply the numbers

[tex] = 56 + 4 \times {4}^{2} [/tex]

Calculate the product

[tex] = 56 + {4}^{3} [/tex]

Evaluate the power

[tex] = 56 + 64[/tex]

Add the numbers

[tex] = 120[/tex]

Hope this helps..

best regards!!

Answer:

i believe a=105, b=29, and c=45

Answer: The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.

Step-by-step explanation:

There are three measures of the center: 1) Mean   2) Median  3) Mode

Mean : Average value of the data

Mode = The most repeated value.

Median is the middlemost value in a well-ordered data.

It measures the center of the data.

Hence, the completed statement would be:

The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.

Answer:

First ____ is median

Second ____ is center

Step-by-step explanation:

The median is the middle value of a set of numbers, and is found in the center.

Answer:

x = -5

Step-by-step explanation:

-7(x + 2) = 21​

Divide each side by -7

-7/-7(x + 2) = 21​/-7

x+2 = -3

Subtract 2 from each side

x+2-2 = -3-2

x = -5

Answer:

x = -5

Step-by-step explanation:

distribute: -7x-14 = 21

add 14 to both sides

divide by -7

x = -5

Answer:

Step-by-step explanation:

The area of a parallelogram is equal to the product of the length of its side and the height of the parallelogram perpendicular to that side.

H = 9 cm

S = 21 cm

A = S•H = 21 cm • 9 cm = 189 cm²

Answer:

y = -2/3x - 2

Step-by-step explanation:

Step 1: Find slope m of perpendicular line

Simply take the negative reciprocal of the given line

m = -2/3

y = -2/3x + b

Step 2: Find b

6 = -2/3(-12) + b

6 = 8 + b

b = -2

Step 3: Rewrite perpendicular equation

y = -2/3x - 2

Answer:

42

Step-by-step explanation:

P(left) = 0.10

Expected number of lefties among high school grads of 424

= 424 * 0.10

= 42 (to the nearest person)

Answer:

you do 20% of 424

1 0% of 424 =42.4

you could round it to 42

Answer:

Toa

48/55

Step-by-step explanation:

O/A

48/55

Answer:

19.5 km

Step-by-step explanation:

the actual distance between Harry and the Sea view:

if 24 km is 5 cm on map

24*4/5= 19.5 km

Answer:

Equation:-  [tex]x + y = 38.50[/tex]

Solution of x:-  [tex]x = 38.50 - y[/tex]

Step-by-step explanation:

Given

Total Purchase = $38.50

Required

Determine the equation for finding the cost of a bear

From the question; we understand that the cost of 1 bear is represented with x

Solving further; by representing the cost of 1 football uniform with y

So;

[tex]1\ bear + 1\ uniform = 38.50[/tex]

Substitute x for 1 bear and y for 1 uniform to give us an equation

[tex]x + y = 38.50[/tex]

Solving for x (Subtract y from both sides)

[tex]x +y - y = 38.50 - y[/tex]

[tex]x = 38.50 - y[/tex]

The equation can't be solved further

Answer:

50

Step-by-step explanation:

Answer:

2/13

Step-by-step explanation:

In a standard deck of cards, there are 52 cards total, 4 kings, and 4 queens.

Probability is calculated by (number of favorable outcomes)/(number of possible outcomes), so our probability would be 8/52, which can be simplified to 2/13.

Hope this helps!

Answer:

Step-by-step explanation:

eq. of line parallel to y=34x-9 is y=34 x+k

∵ it passes through (-8,-18)

∴-18=34×-8+k

k=-18+272

k=254

so reqd. eq. is y=34 x+272

Answer:

1: C) y = -x + 1

2: D) y = -3x + 8

Step-by-step explanation:

Well number 1,

c is the correct option because,

-2 -> 2

2+1 - 3

This rule applies for all the x values.

2,

X: -2, -1, 0, 1, 2

Y: 14, 11, 8, 5, 2

d is the correct option because -3*-2 is 6 + 8 = 14.

this rule applies for all x values.

Thus,

the answers are C and D.

Hope this helps :)