The sum of the squares of the odd integers between 0 and 100.

Using summation notation

To find the slope, we must have two points

   --> Two points: (-3,1) and (-1, -5)

The slope's formula is -->  [tex]\frac{y2-y1}{x2-x1}[/tex]

So the slope = [tex]\frac{-5-1}{-1--3} =\frac{-6}{2} =-3[/tex]

The line graphed below has a slope of -3

Hope that helped!

Step-by-step explanation:

- The distance traveled to get to the top of the hill will be equal to the distance traveled to get to the bottom of the hill. Distance down the hill = Distance up the hill = 187.5 meters.

- Only the speed of going up the hill and down the hill will be different.

Answer:

C: f(x) = 0.5(x-4)^2-5

Step-by-step explanation:

I graphed each function on Desmos, and matched it up with option C:

Answer:

the answer is C

Step-by-step explanation:

c: f(x)=0.5(x-4)^2-5

Based on the amounts that Jack invested into the different investment vehicles, the amount Jack earns a year would be $1,132.87.

The amount invested is:

= 2 / 3 x 15,000

= $10,000

Amount after a year:

= Amount x e ^ (rate x time)

= 10,000 x e ⁰.⁰⁸ ˣ ¹

= $10,832.87

Amount invested:

= 1/3 x 15,000

= $5,000

Amount after a year:

= 5,000 x (1 + 6%)

= $5,300

= (10,832.87 + 5,300) - 15,000

= $1,132.87

#SPJ1

Find out more on continious compounding at https://brainly.com/question/3932907.

The time taken by Nadia for her entire journey is 5 hours

Speed is the rate at which an object is moving, and it is defined as the distance traveled per unit of time. The formula for speed is:

           Speed = Distance/Time

Where distance is the distance traveled by an object and time is the time taken to travel that distance.

From the fomrula, we can write as

          Distance = Speed × Time

Here we have

Nadia walks at an average speed of (x + 2) km/h for (x – 3) hours and cycles at an average speed of (3x + 5) km/h for x hours.

As we know, Distance = Speed x Time  

Distance walked = (x + 2)(x - 3)

Distance cycled = (3x + 5)(x)

The total distance covered is given as 74 km,

=> (x + 2)(x - 3) + (3x + 5)(x) = 74

=> x² - 3x + 2x - 6 + 3x² + 5x = 74

=> 4x² + 4x - 80 = 0

Hence, the final equation is 4x² + 4x - 80 = 0

(ii) The quadratic equation, can be solved as follows

=> x² + x - 20 = 0  

=> x² + 5x - 4x - 20 = 0

=> x(x + 5) -4(x + 5) = 0

=> (x + 5) (x - 4) = 0

=> x = - 5 and x = 4

Here we cant take time as negative so take x = 4 hours

(iii) To find the time taken for her entire journey, we need to add up the time taken for walking and cycling:

Total time = (x - 3) + x

Total time = 2x - 3

Substituting the value of x  

Total time = 2(4) - 3 = 8 - 3 = 5

Therefore,

The time taken by Nadia for her entire journey is 5 hours

Learn more about Speed and distance at

https://brainly.com/question/17277454

#SPJ1

Answer:

Use the formula of Range Large-Small Data

I think it will help you.

Answer:

First option

Step-by-step explanation:

The expression can be simplified to:

[tex]\frac{8g^{15} }{64h^6}[/tex] = [tex]\frac{g^{15} }{8h^{6} }[/tex]

You can't simplify this further since the indices if you think about it is g 15 times or h 6 times so you can't simply them further.

Answer:

159°

Step-by-step explanation:

Angle 21° and <4 are supplementary angles!

21 + x = 180

x = 159°

Hope this helps!

The measure of angle ∠4 is 159.

The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.

Corresponding angles are always equal.

We can also have alternate angles which are always equal.

We can also have alternate interior and exterior angles which are equal.

The angles on the same side make upto 180 degrees

We have,

From the figure,

The angle opposite to 21° and ∠4  sum is 180.

This means,

Angles on the same side.

Now,

Opposite angles are equal.

So,

21 + ∠4 = 180

∠4 = 180 - 21

∠4 = 159

Thus,

The measure of angle ∠4 is 159.

Learn more about corresponding angles here:

https://brainly.com/question/1597341

#SPJ7

k²= 6²+5²

k²= 36+25

k²= 61

k= V61

k=7.81

Answer:

  u = v = 14

Step-by-step explanation:

The ratios of side lengths in a 45-45-90 triangle are ...

  1 : 1 : √2

Here, the long side is 14√2, so is 14 times this basic ratio.

  1 : 1 : √2 = u : v : 14√2 = 14 : 14 : 14√2

This means ...

  u = v = 14

Answer:

Below in bold.

Step-by-step explanation:

The ratio of the sides in a 45-45-90 are 1:1:√2.

so V / 14√2 = 1 / √2

V = 14√2 / √2 = 14.

and U = V = 14 also.

Answer:

The formula for the area of a circle:

[tex]A = \pi r^{2}[/tex]

You have said:

[tex]r = 14m[/tex]

So substitute the values of pi and r into the formula:

[tex]A = \pi r^{2} \\A = (3.14)(14m)^{2} \\A = (3.14)(196m^{2} )\\A = 615.44m^{2}[/tex]

Length of AB is not given so insufficient info provided

Let's see how to solve then

Scale factor is 3/2 means 3/2 is multiplied with AB to form A'B'

If length of AB is n the. then length of A'B' is 3n/2

Answer:

4A - 8 = 3A + 4

Step-by-step explanation:

Answer:

31/5

Step-by-step explanation:

3x+9=-2x+40

when you solve the equation, you get 31/5!

Please mark as brainliest if you can. Hope this helps!

Answer:

y = 0 , y = - [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

- 32y² - 24y = 0 ← factor out - 8y from each term

- 8y(4y + 3) = 0 equate each factor to zero and solve for y

- 8y = 0 ⇒ y = 0

4y + 3 = 0 ⇒ 4y = - 3 ⇒ y = - [tex]\frac{3}{4}[/tex]

Answer:

The square below represents one whole.

What percent is represented by the shaded area?

The square below represents one whole.

What percent is represented by the shaded area?The square below represents one whole.

What percent is represented by the shaded area?The square below represents one whole.

What percent is represented by the shaded area?The square below represents one whole.

What percent is represented by the shaded area?vvvvStep-by-step explanation:

Answer:

Step-by-step explanation:

Each number has initially 10 options.

If one option used for the first number then the second number has one less, 9 options. Similarly, the third number has one less number of options than the second number, 8 options.

Total number of combinations is

Answer:

6/12 of a mile

Step-by-step explanation:

7/12-1/12=16/12

Answer:

119 cm^2

Step-by-step explanation:

To find the area of the white border, simply find the area of the outside rectangle and subtract the middle(dark) rectangle's area from that value.

White rectangle: 15x9 = 135

Dark rectangle: 8x2 = 16

135 - 16 = 119 cm^2
The unit is squared when finding the area of a two dimensional figure.

Answer:

g(x) = 4x + 5

Step-by-step explanation:

f(x) + g(x) = 10x + 7 , then

6x + 2 + g(x) = 10x + 7 ← subtract 6x + 2 from both sides

g(x) = 10x + 7 - 6x - 2 ← collect like terms

g(x) = 4x + 5

Let's find

Option D

Answer: Choice E

[tex]x \ne -4, -1[/tex]

This is the same as saying [tex]x \ne -4 \text{ and } x \ne -1[/tex]

======================================================

Reason:

If we plugged x = -4 into the function, then the x+4 in the denominator turns to 0.

x+4 = -4+4 = 0

Dividing by zero is not allowed. It leads to a division by zero error. Therefore, we need to exclude -4 from the domain. Similar reasoning will exclude -1 as well because it makes the x+1 in the denominator to be zero.

Any other x value is valid.

Side note: The (x+1) terms cancel, which may appear that x = -1 is valid. However, your calculator will likely not perform such a simplification. It will simply try to directly compute the result using PEMDAS. That means x = -1 is likely to produce a division by zero error.

Answer:

The type of function is cexponential and Alinear

Answer: your obviously going to need to use the method a2+b2=c2

Try to calculate the radius if not given to you.

Step-by-step explanation:

In order to use the Pythagorean Theorem, you must know the lengths of at least 2 sides (any 2 sides, but it has to be 2.) of the triangle and know that the measure of one of the angles is 90 degrees.

Step-by-step explanation:

Tn = a + (n-1)d

where a is the first term, d is the common difference and n is the nth term

For the 6th term: T6 = a + (6-1)d

= a + 5d

For the 8th term: T8 = a + (8-1)d

= a + 7d

From the question (a + 5d)/(a + 7d) = 7/9

From the Equation above, we can say that;

a + 5d = 7......1

a + 7d = 9.....2

Solving equations 1 & 2 simultaneously, we have that a = 2 and d = 1

Sn = n/2[2a + (n-1)d]

where Sn is the sum of nth terms, n is the nth term, a is the first term and d is the common difference.

By substituting the values gotten into this equation. You would be able to find the ration between the sum of the first 10 terms to the sum of the first 20 terms

Answer:

see analysis for detailed explanation

Answer: 31/83  (decimal form 0.373494)

Step-by-step explanation:

[tex]\sf f(x) = 3 \ * \ 2^x[/tex]

insert x = -2

[tex]\sf f(-2) = 3 \ * \ 2^{-2}[/tex]

[tex]\sf f(-2) = 3 \ * \ \dfrac{1}{4}[/tex]

[tex]\sf f(-2) = \dfrac{3}{4}[/tex]

option D. 3/4 will be the correct answer.

[tex]\\ \rm\Rrightarrow f(x)=3.2^x[/tex]

[tex]\\ \rm\Rrightarrow f(-2)[/tex]

[tex]\\ \rm\Rrightarrow 3.2^{-2}[/tex]

[tex]\\ \rm\Rrightarrow 3(1/4)[/tex]

[tex]\\ \rm\Rrightarrow 3/4[/tex]

Answer:

2.5, 3, 6, 9, 2.8, 6, 1.5

Is this what you're asking for?

Step-by-step explanation:

The equation that relates the number of campers this year to the number of campers last year is c = 440 / 1.10

The number of campers last year is 400.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentages are used to measure frequency.

The number of campers last year = number of campers this year / (1 + percentage increase)

440 / 1.1 = 400

To learn more about percentages, please check: https://brainly.com/question/25764815

Answer:

[tex] - 12[/tex]

Step-by-step explanation:

[tex]x1 = x \: \: y1 = 3 \\ x2 = 4 \: \: y2 = 3 \\ distance \: betwen \: two \: points = \sqrt{(x2 - x1) {}^{2} +( y2 - y1) {}^{2} } \\ 16= \sqrt{(4 - x) {}^{2} + (3 - 3) {}^{2} } \\ 16 = \sqrt{(4 - x) {}^{2} + 0} \\ 16 = \sqrt{(4 - x) {}^{2} } \\ 16 = 4 - x \\ 16 - 4 = - x \\ 12 = - x \\ x = - 12[/tex]

Answer:

y = 5x + 3

Step-by-step explanation:

If the slope is 5 and the y-intercept is 3, we can substitute the value of the variables into the formula.

y = mx + b

y = (5)x + 3

y = 5x + 3

I hope this helps!