The sum of 4 consecutive odd numbers is 40. What is the 2nd number in this sequence?

Answers

Answer 1

Try this option (it is not the only way):
1. if to use for consecutive odd numbers: n; n+2; n+4 and n+6), then it is possible to write their sum in equation: n+n+2+n+4+n+6=40.
2. if to solve this equation: n=7 it means that 7 - the 1st number of the given sequence.
Using n=7 the 2d number of this sequence is n+2=9.

answer: 9.

Related Questions

116=0.0625. Which calculation is NOT a way to find 1516?

Answers

we have that
1/16=0.0625

we know that
Multiply (0.0625) by 15 is a way to find (15/16)--------> 0.0625*15=0.9375
so
any operation that results in any other value is not a way to find (15/16)

Answer: 16 divided by 15

Step-by-step explanation:

I got it right.

Please explain how you worked the problem to find x!

1/x +1/(x+4) =1/5

Answers

[tex]\frac{1}{x} +\frac{1}{x+4}[/tex] (by taking the common factor for the two elements of the equation
[tex]\frac{1]{x} *\frac{x+4}{x+4} +\frac{1}{x+4}*\frac{x}{x}=\frac{x+4}{x*(x+4)}+\frac{x}{x*(x+4)}[/tex] now we can add both of the equation as the denominators have the same value.
[tex]\frac{x+4+x}{x*(x+4)}=\frac{2x+4}{x^{2}+4x} = \frac{1}{5}[/tex] by multiplying both sides by [tex]5*(x^{2}+4x)[/tex]
[tex] 5*(2x+4)=x^{2} +4x[/tex]
[tex] 10x+20=x^{2}+4x[/tex] by subtracting both sides by (10x+20)
[tex] x^{2} -6x -20 = 0[/tex] (by using the quadratic formula)
we will find two answers for this equation
x={[tex]\frac{-6- \sqrt{116}}{-2}[/tex] and [tex] \frac{-6+\sqrt{116}}{-2}[/tex]

The sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?

Answers

let one of the number be x

one number = x
the other number = 3x

Given that the sum of these two number is 44.
x + 3x = 44
4x = 44
x = 44 ÷ 4
x = 11

x = 11
3x = 11 x 3 = 33

The two numbers are 11 and 33

Set up 2 variables:
x = larger number
y = smaller number

Set up equations:
[tex]x + y = 44[/tex]
[tex]3y = x[/tex]

Solve by substituting. I will use the x already given to us (in second equation) to substitute in 1st equation (x = 3y):
[tex]3y + y = 44[/tex]
[tex]4y = 44[/tex]
[tex]y = 11[/tex]

Plug it back into 2nd equation to solve for x:
[tex]3y = x[/tex]
[tex]3(11) = x = 33[/tex]

So, our two values are: x = 33 and y = 11.

We can check, x + y = 33 + 11 does equal 44 and 33 times is 3 times larger than 11. So, the initial criteria work out and we are right.

Charlie reads quickly. He reads 1 and 3 seventh pages every 2 third minutes. Charlie reads at a constant rate. How many pages does charlie read per minute?

Answers

The unit rate would be 1 3/7 ÷ 2/3 10/7 ÷ 2/3 10/7 · 3/2 separate by division, rearrange and multiply 15/7

Charlies reads 15/7, or 2 1/7, page per minute.

Hope this helps a bit.

1) Which two lines are parallel?

I. 5y = -3x-5
II. 5y = -1 - 3x
III. 3y - 2x = -1

a. I. and II.
b. I. and III.
c. II. and III.
d. No two of the lines are parallel.

2) Which do lines are parallel?

I. 3y = -2x - 3
II. 3y = 1 - 2x
III. 4y - 3x = -1

a. I. and II.
c. II. and III.
b. I. and III.
d. No two of the lines are parallel.

Answers

1)a

2)a
hope this helps

martin paid $120 towards his $2400 credit card bill. what percentage did he pay

Answers

5%
120/2400*100/1 =120/24 =5%

What is the factored form of x2 - 4x - 5 ?

Answers

(X-5)(x+1)

Two factors of five that subtract to four

if tyrone works 40 hours per week and has no other sources of income what is his total monthly cash inflow

Answers

[tex]18 \times 40 = 720[/tex]

[tex]720 \times 4 = 2880[/tex]

[tex]2880 - 1800 = 1080[/tex]

~~

Answer : B

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

Find the values of a b and c for which the quadratic equation ax^2+bx+c=0 has the solutions -3 and 1

Answers

It may be easier to start from

.. a(x +3)(x -1) = 0
.. a(x^2 +2x -3) = 0

The quadratic
.. ax^2 +bx +c = 0 will have solutions -3 and 1 for ...

.. a ≠ 0
.. b = 2a
.. c = -3a

What is the constant term in the expression 4x3y + 8x2 + 6x + 5?

Answers

Answer:

Step-by-step explanation:

The constant term is the one with no variables in it: +5.

Answer:

i took the test and its 5.

If the sum of four consecutive odd integers is 208, what is the smallest of the four integers?

Answers

The least of these numbers is 20.

A cylinder has a radius of 4x+2 and a height of 5x+4. Which polynomial in standard form best describes the total volume of the cylinder. Use the formula V=pir^2h for the volume of a cylinder.

Answers

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=4x+2\\ h=5x+4 \end{cases}\implies V=\pi (4x+2)^2(5x+4) \\\\\\ V=\pi [(4x+2)(4x+2)](5x+4)\\\\\\ V=\pi \stackrel{FOIL}{(16x^2+16x+4)}(5x+4) \\\\\\ V=\pi[ (80x^3+80x^2+20x)+(64x^2+64x+16)] \\\\\\ V=80\pi x^3+144\pi x^2+84\pi x+16\pi [/tex]

A candy maker buys a bar of chocolate weighing 162 ounces. About how many pounds does the bar weigh?

Answers

For this case, the first thing you should keep in mind is the following conversion:
1 pound = 16 ounces
Applying the comversion we have:
(162) * (1/16) = 10,125 pounds
Therefore, the weight of the chocolate bar in pounds is 10,125
Answer:
the bar does weigh 10,125 pounds

Answer and how you get then answer

Answers

Percent Change = ((new value)/(old value) -1) * 100%
= (480/540 -1)*100%
≈ -11.11%

The number of calories in a child's meal was reduced about 11%.

is possible to have a shape with different dimensions while having the same volume?

Answers

Yes, they could be different and still have the same volume

yes,

a cuboid with dimensions 2, 4, 8 has volume = 64 unit^3

a cube with side 4 has volume = 64 unit^3

so, they have different shapes but same volume

Let u = (1,0,2) , v = (0,-1,2) and w = (2,1,0). Compute

(i) the area of the parallelogram bounded by u and v (5)

(ii) the equation of the plane parallel to v and w pass through the tip of u

Answers

Answers:

(i) 3
(ii) [tex]-2x + 4y + 2z = 2[/tex]

Explanation:

(i) The area of the parallelogram bounded by vectors u and v is given by:

[tex]\text{Area} = \left \| u \times v \right \|[/tex]

Note that if [tex]u = (u_1, u_2, u_3) = (1, 0, 2), v = (v_1, v_2, v_3) = (0, -1, 2) [/tex],

[tex]u \times v \\ = \left(u_2v_3-u_3v_2, u_3v_1-u_1v_3, u_1v_2-u_2v_1\right) \\ = \left((0)(2)-(2)(-1), (2)(0)-(1)(2), (1)(-1)-(0)(0)\right) \\ \boxed{u \times v = \left(2, -2, -1 \right)}[/tex]

Thus, the area of the parallelogram formed by vectors u and v is calculated as

[tex]\text{Area} = \left \| u \times v \right \| \\ = \left \| \left(2, -2, -1 \right) \right \| \\ = \sqrt{(2)^2 + (-2)^2 + (1)^2} \\ \boxed{\text{Area} = 3}[/tex]

Hence, the area of the parallelogram is 3.

(ii) To obtain the equation of the plane, we must get its normal vector and a point in the plane.

As calculated in (i), the normal vector to the plane is [tex]v \times w[/tex] because the plane is parallel to vectors v and w. Note that if [tex]v = (v_1, v_2, v_3) = (0, -1, 2), w = (w_1, w_2, w_3) = (2, 1, 0)[/tex],

[tex]v \times w \\ = \left(v_2w_3-v_3w_2, v_3w_1-v_1w_3, v_1w_2-v_2w_1\right) \\ = \left((-2)(0)-(2)(1), (2)(2)-(0)(0), (0)(1)-(-1)(2)\right) \\ \boxed{v \times w = \left(-2, 4, 2 \right)}[/tex]

Thus, a normal vector to the plane is [tex]\left(-2, 4, 2 \right)[/tex].

To get a point in the plane, note that vector u can be represented by any pairs of points. So, we can take (0, 0, 0) to be the starting point of vector u. Since [tex]u = (1, 0, 2)[/tex], the tip of vector u is [tex](0 + 1, 0, 0 + 2) = (1, 0, 2)[/tex]. Because the plane passes thru the tip of vector u, a point in the plane has coordinates [tex] (1, 0, 2)[/tex].

So for any point [tex](x, y, z)[/tex] in the plane, the equation is given by

[tex]n \cdot (x - 1, y - 0, z - 2) = 0[/tex]

Where n is the normal vector to the plane.

Since [tex]n = \left(-2, 4, 2 \right)[/tex], the equation becomes

[tex]\left(-2, 4, 2 \right) \cdot (x - 1, y - 0, z - 2) = 0 \\ \left(-2, 4, 2 \right) \cdot (x - 1, y, z - 2) = 0 \\ -2(x - 1) + 4y + 2(z - 2) = 0 \\ -2x + 2 + 4y + 2z - 4 = 0 \\ -2x + 4y + 2z - 2 = 0 \\ \boxed{-2x + 4y + 2z = 2 }[/tex]

Which of the following is a monomial?
A. 2xyz2
B. 2x + yz
C. 2 + xyz
D. 2x − yz

Answers

A monomial has one term, even if it has multiple variables.
So your answer would be A. 2xyz2. Hope it helps! :)

Analyze the following budget, with an income of $750, to determine how much can be spent on food for the month. Month________ Budgeted Amount Food $___ Personal Items $20 Cell Phone $75 Entertainment $85 Car Expenses – Gas, Insurance $260 College Savings $250 a. No more than $70 can be spent on food. b. No more than $75 can be spent on food. c. No more than $80 can be spent on food. d. No more than $60 can be spent on food.

Answers

The answer is D
Hope it helps

A monthly of $60 can be spent for food after all the expenses and savings

are sorted.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The numerical form of the given information can be formed as,

$(750 - 20 - 75 - 85 - 260 - 25).

= $60.

So, With an income of $750 and all the expenses including saving for for college worth of $250 the amount that can be spent on food is $60.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ2

A triangle has sides with lengths of 6 millimeters, 8 millimeters, and 10 millimeters. Is it a right triangle?

Answers

If it is a right triangle, then a^2 + b^2 = c^2
6^2 + 8^2 = 100^2
36 + 64 = 100
100 = 100

Yes, the triangle is a right triangle.

Hope this helps =)

The sides 6 mm, 8 mm and 10 mm forms a right angles triangle.

We have,

The sides of the triangle are of lengths 6 mm, 8 mm and 10 mm.

The longest side length is 10 mm.

Now, the sum of squares of the smaller sides is given as:

6² + 8² = 36 + 64 = 100 = 10²

As, the sum of squares of the smaller sides is equal to the square of the longer side.

So, by the Pythagorean Theorem, the sides form a right triangle.

Learn more about Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ2

$8000 invested at an APR of 6% for 10 years.
If interest is compounded annually, what is the amount of money after 10 years?

Answers

The formula in finding the maturity value is the following:

A = P (1 + r) ^t

Where A = Maturity value

P = principal amount

r = Annual percentage rate

t = time in years

Substituting the given amount to the formula:

A = $8,000 (1 + 6%) ^10

= $8,000 (1.7908)

= $14,326.40

Therefore, the amount of $8,000 after 10 years compounded annually at 6% is $14,326.40

how many time does 2 go into 19

Answers

Hello There @Diamondinthesky123 (Cute Username)

When you state the question, "How many times does 2 go into 19", I assume your talking about Long Division. (Not so long in this case)

In this case, we would divide 19 by 2, resulting in 9 with a remainder of 1.
Thats It! :)

I hope I helped, Have a great Day!

Thank you,
Darian D.

Final answer:

In basic division, 2 goes into 19 a total of 9 times with 1 leftover. This demonstrates division and the concept of remainders in mathematics.

Explanation:

The student is asking about basic division in mathematics, specifically how many times 2 goes into 19. To find this, we divide 19 by 2.

Doing the division, we get:

19 divided by 2 equals 9 with a remainder of 1.

Therefore, 2 goes into 19 9 times with 1 left over.

It's worth noting that there's also a mathematics technique called estimation that might be considered here. If we estimate to the nearest whole number, 2 would go into 19 approximately 9 times since 2 times 9 is 18, which is very close to 19.

2x+5y=-6 , wht is the x intercept, what is the y intercept

Answers

Final answer:

The x-intercept is (-3,0) and the y-intercept is (0,-6/5).

Explanation:

The x-intercept is the point where the line crosses the x-axis. To find the x-intercept, we set y=0 and solve for x. In the equation 2x+5y=-6, we substitute 0 for y and solve for x:

2x + 5(0) = -6

2x = -6

x = -3

So, the x-intercept is the point (-3,0).

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we set x=0 and solve for y. In the equation 2x+5y=-6, we substitute 0 for x and solve for y:

2(0) + 5y = -6

5y = -6

y = -6/5

So, the y-intercept is the point (0,-6/5).

Assume that the weights of all packages of a certain brand of cookies are normally distributed with a mean of 32 ounces and a standard deviation of 0.3 ounce. find the probability that the mean weight, x¯, of a random sample of 20 packages of this brand of cookies will be between 31.8 and 31.9 ounces.

Answers

That probability is about 6.7%.

5 plus 500% of 10 is the same as 110% of what number?

Answers

5+10×500%=5+50=55
55÷110%=50
so 5 plus 500% of 10 is the same as 110% of 50

Use the data to create a scatter plot. Year 0 1 2 3 4 Population 3 4 6 11 15 Use the point tool to plot the points from the table in the coordinate grid to create a scatter plot.

Answers

In order to create the scatter plot in your point tool, mark the points one by one on the coordinate grid. The first point will be (0,3). This means for location 0 on x-axis the value on y axis is 3. First point goes there. The second point is (1, 4). Move one unit on the x-axis and 4 units on y-axis. Second point goes there. Do this process for all the points to complete the scatter plot. I used Microsoft excel to create the scatter plot. Your plot will be similar to the plot shown below.

Enter the values in the first two columns of MS excel. Then go on the insert tab and click insert scatter plot. A scatter plot will be made as shown below in the attached picture.

The same plot can be made by hand by simply inserting the correct points on the graph. From the scatter plot we can observe that a positive correlation occurs in the given variables. A straight line can be used to approximate the trend of the data.

Answer:

Refer the attached figure.

Step-by-step explanation:

Given : Data of population

To find : Use the data to create a scatter plot?

Solution :

Data :

Year(x) Population(y)

0 3

1 4

2 6

3 11

4 15

A Scatter Plot has points that show the relationship between two sets of data.

With the help of scatter plot graph,

We plot the points of the data.

Refer the attached figure below.

Melissa had a balance of $104 in her checking account at the beginning of the month. She made one additional deposi of $216 and wrote checks $78 , $119 , and $105. What was the balance in her checking account at end of the month

Answers

Do you deposit or cash the checks?

Answer:

She only had $18 left

Step-by-step explanation:

solve the proportion
[tex] \frac{3}{4} = \frac{x}{6} [/tex]

Answers

To solve a problem like this, you can use a method called cross-multiplying. This is when you multiply the denominator of the first fraction by the numerator of the other and then multiply the two remaining numbers.

[tex] \frac{3}{4} = \frac{x}{6} [/tex] Multiply 3 by 6 and multiply 4 by x.
4x = 18 Divide by 4.
x = [tex] \frac{18}{4} [/tex] Simplify!
x = [tex] \frac{9}{2} [/tex]

You can check this by comparing the fractions with [tex] \frac{9}{2} [/tex] in the place of x.

[tex] \frac{3}{4} = \frac{ \frac{9}{2} }{6} [/tex] Divide [tex] \frac{9}{2} [/tex] by 6 ( [tex] \frac{9}{2} [/tex] times [tex] \frac{1}{6} [/tex]).
[tex] \frac{3}{4} = \frac{9}{12} [/tex] Simplify!
[tex] \frac{3}{4} = \frac{3}{4} [/tex]

The fractions are equal, so x = [tex] \frac{9}{2} [/tex] .

Which terms accurately classify this triangle? Choose exactly two answers that are correct. A. right B. acute C. isosceles D. scalene

Answers

The answer is (C isosceles) hope it helps and have a great day!

what term has to be added to x^2-3x to be a trinomial 3/2 9/4 6 9

Answers

Your question is probably what should be added to the given expression to make it a perfect square.

The given expression is:

[tex] x^{2} -3x[/tex]

The formula of [tex] (a-b)^{2} [/tex] is [tex] a^{2} -2ab+ b^{2} [/tex]

Re-writing the given expression:

[tex] x^{2} - 2(x)( \frac{3}{2}) [/tex]

So, we have the square of first term and twice the product of first and second term. What is missing is the square of second term.

So, the complete expression for perfect square will be:

[tex] x^{2} -2(x)( \frac{3}{2})+ ( \frac{3}{2} )^{2} \\ \\ x^{2} -2(x)( \frac{3}{2})+ \frac{9}{4} [/tex]

Therefore, 9/4 should be added to the given expression to make it a perfect square.

Answer: The correct option is (B) [tex]\dfrac{9}{4}.[/tex]

Step-by-step explanation: We are given to find the term that has to be added to [tex]x^2-3x[/tex] to be a perfect trinomial.

Let, c denote the term to be added.

Then,

[tex]x^2-3x+c\\\\=x^2-2\times x\times \dfrac{3}{2}+c\\\\\\=x^2-2\times x\times \dfrac{3}{2}+\dfrac{9}{4}+c-\dfrac{9}{4}\\\\\\=\left(x-\dfrac{3}{2}\right)+c-\dfrac{9}{4}.[/tex]

Therefore, the given expression will be a perfect trinomial if

[tex]c-\dfrac{9}{4}=0\\\\\\\Rightarrow c=\dfrac{9}{4}.[/tex]

Thus, the required term to be added is [tex]\dfrac{9}{4}.[/tex]

Option (B) is CORRECT,

15% of the toddlers in a preschool class drink water with their lunch. How many toddlers
are in the class if 3 toddlers drink water with their lunch?
(a) Draw a model for the situation (if you prefer to use a 100-grid model or ratio table
model, that’s fine too!) and label the “part,” “whole,” and “percent.”

Answers

15/100 = 3/x

15x = 300
x = 300/15
x = 20 kids

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