Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.) 9 + 4 + (-1) + ... + (-536)

Answers

Answer 1

SOLUTION

The terms below make an A.P. Now we are told to find the sum of the AP.

Sum of an AP is given by

[tex]S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack}[/tex]

Where S = sum of the AP, a = first term = 9, d = -5, n= ?

So we have to find n first before we can find the sum. The nth term which is the last term = -536. So we will use it to find the number of terms "n"

[tex]\begin{gathered} \text{From T}_{n\text{ }}=\text{ a +(n-1)d where T}_{n\text{ }}=\text{ -536} \\ -536\text{ = 9+(n-1)-5} \\ -536\text{ = 9-5n+5} \\ -536\text{ = 14-5n} \\ -5n\text{ = -536-14} \\ -5n\text{ = -550} \\ n\text{ = 110} \end{gathered}[/tex]

Now let's find the sum

[tex]\begin{gathered} S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack} \\ S\text{ = }\frac{110}{2}\lbrack2\times9\text{ + (110-1)-5\rbrack} \\ S\text{ = 55\lbrack{}18+(119)-5\rbrack} \\ S\text{ = 55\lbrack{}18 - 595\rbrack} \\ S\text{ = 55}\times-577 \\ S\text{ = -31735} \end{gathered}[/tex]

Therefore, the sum = -31735


Related Questions

In the following expression, place a decimal point in the divisor and the dividend that is 4368÷6208 to create a new problem with the same answer as in question 11 that is 7 meters / 7

Answers

[tex]\frac{4368}{6208}=\frac{273}{388}=0.7036[/tex][tex]\frac{4368.0}{620.8}=\frac{1395}{194}\approx7[/tex]

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

436.8m -------------------> 62.08s

xm -------------------------->1s

Using cross multiplication:

[tex]\begin{gathered} \frac{436.8}{x}=\frac{62.08}{1} \\ \text{solve for x:} \\ x=\frac{436.8}{62.08} \\ x=7.036082474m \\ \end{gathered}[/tex]

having trouble solving quadratic equations using factoring, examples are fine

Answers

Let's solve the quadratic equation using factorization:

x²-9x -22= 0

In order to solve using this method, we should beforehand factorize the polynomial:

The middle number is -9 and the last number is -22.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks? Let's think about two numbers that add up to -9 and multiply together to -22...

These numbers will be -11 and 2:

-11 +2= 9

-11*2= -22

So the factorization is:

(x+2)*(x-11) = 0

That means:

x + 2 =0

and

x - 11 = 0

Solving the equations:

x= -2

x= 11

S= {-2, 11}

Ken wants to install a row of cerámic tiles on a wall that is 21 3/8 inches wide. Each tile is 4 1/2 inches wide. How many whole tiles does he need?

Answers

We have the following:

[tex]a\frac{b}{c}=\frac{a\cdot c+b}{c}[/tex]

therefore:

[tex]\begin{gathered} 21\frac{3}{8}=\frac{21\cdot8+3}{8}=\frac{168+3}{8}=\frac{171}{8} \\ 4\frac{1}{2}=\frac{4\cdot2+1}{2}=\frac{8+1}{2}=\frac{9}{2} \end{gathered}[/tex]

now, we divde to know the amount:

[tex]\frac{\frac{171}{8}}{\frac{9}{2}}=\frac{171\cdot2}{8\cdot9}=\frac{342}{72}=4.75\cong4[/tex]

Therefore, the answer is 4 whole tiles

Divide 8 A) 3 B) 0) 7 16 D) 7. 32

Answers

Answer

3(1/2) or (7/2) or 3.5

Step-by-step Explanation

The question wants us to divide (7/8) by (1/4).

[tex]\frac{7}{8}\div\frac{1}{4}[/tex]

The first step to solving division when it comes to fractions is to change the division sign to multiplication sign, which changes the fraction after the division sign to its inverse.

That is, in changing ÷ into ×, (1/4) changes to (4/1)

So,

[tex]\begin{gathered} \frac{7}{8}\div\frac{1}{4} \\ =\frac{7}{8}\times\frac{4}{1} \\ =\frac{28}{8} \\ =\frac{7}{2} \\ =3\frac{1}{2} \end{gathered}[/tex]

Hope this Help!!!

8) What is the mass of the teddy bear if the toy car has a mass of 375 grams? 10 .S 0 4kg 3kg 1kg 2kg 000

Answers

The mass of the teddy is 1,225 grams

Here, we want to get the mass of the teddybear given the mass of the toy car

Since boith are on the scale, then it means they contribute to the mass on the scale

By reading the scale, we can see that the mass on the scale is 1.6 kg

As we know, 1000 g is 1 kg

It means 1.6 kg in g will be 1.6 * 1000 = 1,600 g

So, we can now subtract the mass of the toy car from this total to get the mass of the teddy

Mathematically, we have this as;

[tex]1600\text{ g - 375 g =1,225 g}[/tex]

HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST

Answers

[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.

1.1125 is located at point 6 on the number line.

14 / 8 is located at point 8 on the number line.

-0.875 is located at point 3 on the number line.

What are the locations of the numbers?

The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.

A mixed number is a number that has a whole number, a numerator and a denominator.  The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.

A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.

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[tex]-1\frac{3}{4}[/tex] is located at a point 1 on the number line.

1.1125 is located at point 6 on the number line.

14 / 8 is located at point 8 on the number line.

-0.875 is located at point 3 on the number line.

What are the locations of the numbers?

The numbers are made up of mixed fractions, improper fractions, decimals, positive numbers and negative numbers.

A mixed number is a number that has a whole number, a numerator and a denominator.  The numerator that has a smaller value than the denominator. and a proper fraction. . An example of a mixed number is 1 1/4. An improper fraction is a fraction in which the numerator is bigger than the denominator. An example of an improper fraction is 14/8.

A negative number is a number that is smaller in value than 0. Negative numbers would be to the left of zero on number line. An example of a negative number is -1.4. A positive number is a number that is greater in value than 0. Positive numbers are located to the right of 0 on the number line. An example of a positive number is 4.2.

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what does -1 3/4+4.7=

Answers

-1 3/4 + 4.7 = -1.75 + 4.7 = 2.95

3/4 = 0.75, so -1 3/4 is -1.75

-1.75 + 4.7 = 2.95

Answer: 2.95

please help me understand how to find the average rate of change of the function over the given interval and please show me work.

Answers

To answer this, you'll need to recall a formula for finding the rate of change of one variable with respect to another. Given f(x)=x^2 + x +1, the rate of change of the variable with respect to x is given by:

[tex]\begin{gathered} \frac{\differentialD yy}{\square}y}{dx}=n(ax^{n-1}),\text{ where n is the power of variable term, and a is the coefficient.}y}{\square}yy}{dx}=\text{nax}^{n-1} \\ So\text{ when f(x)=x\textasciicircum 2+x+1 is differentiated, we will arrive at } \\ \\ \frac{dy}{dx}=2x+1\text{ The average rate of change of the function within the range (-3,-2) means, we have to use x as -3 and also x as -2 into the derivative function } \\ x=-3 \\ \frac{\differentialD yy}{\square}y}{dx}=2(-3)+1=-6+1=-5y}{\square}y}{dx}=2(-3)+1=-6+1=-5 \\ \text{Also, } \\ x=-2 \\ \frac{\differentialD yy}{\square}y}{dx}=2x+1\text{ becomes}y}{\square}yy}{dx} \\ \\ \end{gathered}[/tex]

Which points are on the graph of y = cot x? (Select all that apply)A. (/3 , √3/2)B. (/2 , 0)C. (0 , )D. (/4 , 1)E. ( , 0)

Answers

Solution:

The graph function is given below as

[tex]y=cotx[/tex]

The graph is given below as

Therefore,

The points on the graph are

[tex]\begin{gathered} \Rightarrow(\frac{\pi}{4},1) \\ \Rightarrow(\frac{\pi}{2},0) \end{gathered}[/tex]

OPTION B AND option D are the right answers

what is 234,181 rounded to the nearest thousand

Answers

The figure 234,181 has the digit 4 in the thousands place.

Rounding to the nearest thouand would therefore be

234,000

This is because, the digit 1 that follows is not up to 5 and therefore is insignificant. So the digit 1 and the others after it are all rounded up to zeros.

In AOPQ, mZO = (6x – 14)°, mZP = (2x + 16)°, and mZQ = (2x + 8)°. Find mZQ.

Answers

[tex]\measuredangle Q=42[/tex]

Explanation

Step 1

the sum of the internal angles in a triangle equals 18o, so

[tex]\begin{gathered} (2x+16)+(6x-14)+(2x+8)=180 \\ 2x+16+6x-14+2x+8=180 \\ \text{add similar terms} \\ 10x+10=180 \\ \text{subtract 10 in both sides} \\ 10x+10-10=180-10 \\ 10x=170 \\ \text{divide both sides by 10} \\ \frac{10x}{10}=\frac{170}{10} \\ x=17 \end{gathered}[/tex]

Step 2

now, replace the value of x in angle Q to find it

[tex]\begin{gathered} \measuredangle Q=(2x+8) \\ \measuredangle Q=(2\cdot17+8) \\ \measuredangle Q=(34+8) \\ \measuredangle Q=42 \end{gathered}[/tex]

I hope this helps you

Does anyone know the answer to this?

Answers

The most appropriate choice for equation of line in slope intercept form will be given by

x + 2y = -16 is the required equation of line

What is equation of line in slope intercept form?

Equation of line in slope intercept form is given by y = mx + c

Where, m is the slope of the line and c is the y intercept of the line

The distance from the origin to the point where the line cuts the x axis is called x intercept

The distance from the origin to the point where the line cuts the y axis is called y intercept

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

[tex]m=tan\theta[/tex]

If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex])

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Here,

The line passes through (0, -8) and (-2, -7)

Slope =

[tex]\frac{-7 -(-8)}{-2-0}\\-\frac{1}{2}[/tex]

The line passes through (0, -8)

Equation of line

[tex]y - (-8) = -\frac{1}{2}(x - 0)\\\\y + 8 = -\frac{1}{2}x\\2y + 16 = -x\\x + 2y = -16[/tex]

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A rectangular pool is 7 meters wide and 12 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.

Answers

you would swim 15 meters

Answer: 15cm

Step-by-step explanation:

Your welcome

What is the prime factorization of 84.(A)2 x 3 x 7(B)2^2 X 3 X 7(C)2 X 21

Answers

Answer:

84=2^2 x 3 x 7

Explanation:

A prime number is any number that has only two factors: 1 and itself.

To find the prime factorization of 84, we are required to express it as a product of its prime factors.

[tex]\begin{gathered} 84=2\times42 \\ 84=2\times2\times21 \\ 84=2\times2\times3\times7 \\ =2^2\times3\times7 \end{gathered}[/tex]

Therefore, the prime factorization of 84 is:

84=2^2 x 3 x 7

Find the coordinates of each point under the given rotation about the origin (-5, 8); 180

Answers

As given by the question

There are given that the point, (-5, 8).

Now,

The given coordinate of point (-5, 8) which is lies on the second quadrant.

Then,

According to the question,

Rotate it through 180 degree about the origin

Then,

The given coordinate move from 2nd quadrant to 4th, where the value of x is positive and y is negative

Then,

The new coordinat will be, (5, -8).

Hence, the coordinate is (5, -8).

simplify -5m²n³ × 15m⁴ n⁶

Answers

To simplify the given expression we will use the following property of exponents:

[tex]a^n\times a^m=a^{n+m}.[/tex]

Using the above property we get:

[tex]-5m^2n^3\times15m^4n^6=(-5\times15)m^{2+4}n^{3+6}=-75m^6n^9.[/tex]

Answer:

[tex]-5m^2n^3\times15m^4n^6=-75m^6n^9.[/tex]

Which points are separated by a distance of 4 units?A. (3,6) (3,9)B. (2,7) (2,3)C. (1,5) (1,3)D. (4,2) (4,7)

Answers

let us take the point (2,7) and (2,3) the distance between these two is

[tex]\begin{gathered} d=\sqrt[]{(2-2)^2+(7-3)^2} \\ d=\sqrt[]{4^2} \\ d=4\text{ unit} \end{gathered}[/tex]

Hence these two points are separated by 4 units.

So option B is correct.

Figure R = figure R". Describe a sequence of three transformations you canperform on figure R to show this. Show your work.

Answers

1) Rotate the figure 90º clockwise.

To rotate a figure 90º clockwise you have to perform the following transformation:

(x,y)→(y,-x)

So for each point of the figure you have to swich places between x and y.

And you have to multiply the x coordinate by -1.

R has 6 points:

(-4,-5)

(-7,-5)

(-7,-4)

(-5,-4)

(-6,-3)

(-2,-2)

First step: swich places between the coordinates of each point:

(x,y) → (y,x)

(-4,-5)→(-5,-4)

(-7,-5)→(-5,-7)

(-7,-4)→(-4,-7)

(-5,-4)→(-4,-5)

(-6,-3)→(-3,-6)

(-2,-2)→(-2,-2)

Second step, multiply the y-coordinate of the new set by -1

(y,x)→ (y,-x)

(-5,-4)→ (-5,4)

(-5,-7)→ (-5,7)

(-4,-7)→ (-4,7)

(-4,-5)→ (-4,5)

(-3,-6)→ (-3,6)

(-2,-2)→ (-2,2)

After the rotation, the figure moved from the 3rth quadrant to the 2nd quadrant.

I need help with a word problem in algebra 2 please

Answers

We were given the following information:

Plan 1

Cost = $175

It has unlimited call & texts as well as 15gb

Plan 2

Cost = $50 per month

It has unlimited call & texts as well as 6gb

After 6gb, data is charged $5 per gb

From this we have the following equations:

[tex]undefined[/tex]

determine the area of the shaded regionA. 6 square unitsB. 19 square unitsC.20 square unitsD. 25 square units

Answers

area of the square:

[tex]\begin{gathered} a=l\times l \\ a=5\times5 \\ a=25 \end{gathered}[/tex]

area of the rectangle

[tex]\begin{gathered} a=b\times h \\ a=3\times2 \\ a=6 \end{gathered}[/tex]

area of the shaded region:

area of the square - area of the rectangle = area of the shaded region

[tex]25-6=19[/tex]

answer: B 19 saquare units

The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

Answers

50 X 5 X 3

answer divide

by 36

Question 3 (9 points)Find Pred then green)What is the probability that you select a red marble, then a green marbleP (red) -P (then Green) - (Total of marbles will be 1 less)P (red then green) = *Hint: Multiply

Answers

Solution

Step 1

Write out an expression for the probability

[tex]\text{The probaility of an event occurring= }\frac{\text{Number of required events}}{\text{Total number of events}}[/tex]

Step 2

Define terms

Total number of events = 8 marbles

Number of required events = red then marble

Number of red = 2 marbles2

Number of green = 2 marbles

Note: The question is without replacement.

Step 3

Get the required probabilities and the answer

[tex]\begin{gathered} Pr(\text{red marble) = }\frac{2}{8} \\ Pr(\text{green marble without replacement) =}\frac{2}{7} \end{gathered}[/tex]

Hence the Pr(of red then green) is given as

[tex]\begin{gathered} =Pr(\text{red) }\times Pr(green\text{ without replacement)} \\ =\frac{2}{8}\times\frac{2}{7}=\frac{1}{14} \end{gathered}[/tex]

Hence the probability of picking a red marble then a green marble = 1/14

p and q are roots of the equation 5x^2 - 7x +1. find to value of p^2 x q +q^2 x p and (p/q)+(q/p)

Answers

1) Let's find the roots of the equation: 5x² -7x +1

5x² -7x +1

2) Calling x_1 =p and x_2= q

Plugging them into the (p/q)+(q/p)​ expression, dividing the fractions. And then rationalizing it we'll have finally:

[tex]\frac{\frac{7+\sqrt[]{29}}{10}}{\frac{7-\sqrt[]{29}}{10}}+\frac{\frac{7-\sqrt[]{29}}{10}}{\frac{7+\sqrt[]{29}}{10}}=\frac{7+\sqrt[]{29}}{10}\cdot\frac{10}{7-\sqrt[]{29}}\text{ +}\frac{7-\sqrt[]{29}}{10}\cdot\frac{10}{7+\sqrt[]{29}}\text{ =}\frac{39}{5}[/tex]

if two angles measure 90 and are complementary and congruent, the measure of each angle is

Answers

Leonardo, the answer is

45 degrees.

Solve the inequality: y-5-20Which of the following is the graph of the solution?

Answers

Given the inequality:

[tex]y-5>-20[/tex]

Let's select the graph which represents the solution.

Let's solve the inequality.

Add 5 to both sides of the inequality:

[tex]\begin{gathered} y-5+5>-20+5 \\ \\ y>-15 \end{gathered}[/tex]

Since y is greater than -15, the graph of the inequality will be a number line which has an open dot at the point -15, then shaded to the right of the number line.

Therefore, the graph of the solution is:

ANSWER:

A

Darell made a scale drawing of a shopping center. The parking lot is 4 centimeters wide in the drawing. The actual parking lot is 40 meters wide. What scale did Darell use?

Answers

Answer:

1 cm to 10 m

Step-by-step explanation:

4 cm to 40 m = 1 cm to 10 m

Please help nobody knows the answer to my question. Round to 2 decimal places.

Answers

To answer this question we will use the z-score.

Recall that the z-score is given as follows:

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}, \\ \text{where x is the observed value, }\mu\text{ is the mean, and }\sigma\text{ is the standard deviation.} \end{gathered}[/tex]

The z-score of 54 is:

[tex]z=\frac{54-50}{5}=\frac{4}{5}=0.8.[/tex]

The z-score of 56 is:

[tex]z=\frac{56-50}{4}=\frac{6}{5}=1.2.[/tex]

Now, the probability of flipping 54, 55, or 56 heads is the same as the following probability:

[tex]P(0.8Now, recall, that:[tex]P(aNow, from the given table we get that:[tex]\begin{gathered} P(0.8)=0.7881, \\ P(1.2)=0.8849. \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} P(0.8Answer: 0.10.

The angle of elevation to the top of a Building in New York is found to be 7 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.

_________ feet

Answers

The height of the building is 649.44 feet

Given,

The angle of elevation of the building from ground = 7°

The distance from base of the building to the angle = 1 mile

We have to find the height of the building:

As this information are  noted, we will get a right angled  triangle(image attached).

So, by trigonometry:

Tanθ = opposite side / adjacent side

here,

θ = 7 degree

opposite side = x

adjacent side = 1 mile

Then,

Tanθ = opposite side / adjacent side

tan(7°) = x / 1

x = tan(7°) × 1

x = 0.123 × 1

x = 0.123 miles

1 mile = 5280 feet

Then,

0.123 miles = 0.123 × 5280 = 649.44 feet

That is,

The height of the building is 649.44 feet.

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composition of functions, interval notation

Answers

Given the functions:

[tex]\begin{gathered} g(x)=\frac{1}{\sqrt[]{x}} \\ m(x)=x^2-4 \end{gathered}[/tex]

I would like to find their domain as well and then complete the answers:

[tex]\begin{gathered} D_g=(0,\infty) \\ D_m=(-\infty,\infty) \end{gathered}[/tex]

For the first question: g(x) / m(x)

[tex]\begin{gathered} \frac{g(x)}{m(x)}=\frac{\frac{1}{\sqrt[]{x}}}{x^2-4}=\frac{1}{\sqrt[]{x}\cdot(x^2-4)}=\frac{1}{x-4\sqrt[]{x}} \\ x-4\sqrt[]{x}\ne0 \\ x\ne4\sqrt[]{x} \\ x^2\ne4x \\ x\ne4 \end{gathered}[/tex]

As we can see, the domain of this function cannot take negative values nor 4, 0. So, its domain is

[tex]D_{\frac{g}{m}}=(0,4)\cup(4,\infty)[/tex]

For the second domain g(m(x)), let's find out what is the function:

[tex]\begin{gathered} g(m(x))=\frac{1}{\sqrt[]{x^2-4}} \\ \sqrt[]{x^2-4}>0 \\ x^2>4 \\ x>2 \\ x<-2 \end{gathered}[/tex]

This means that x cannot be among the interval -2,2:

[tex]D_{g(m)}=(-\infty,-2)\cup(2,\infty)[/tex]

For the last domain m(g(x)) we perfome the same procedure:

[tex]m(g(x))=(\frac{1}{\sqrt[]{x}})^2-4=\frac{1}{x}-4[/tex]

For this domain it is obvious that x cannot take the zero value but anyone else.

[tex]D_{m(g)}=(-\infty,0)\cup(0,\infty)_{}[/tex]

720÷5 WORK OUT NEEDED

Answers

144

Explanation:[tex]720\text{ }\div\text{ 5}[/tex]

working the division:

The process:

7 ÷ 5 = 1 R 2

add the 2 to the next number: this gives 22

22 ÷ 5 = 4 R 2

add 2 to the next number: this gives 20

20 ÷ 5 = 4 R 0

The result of 720 ÷ 5 = 144

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