a sequence starts 2,-1,-4,-7 what is the 25th term

Answers

Answer 1

Answer:

-70

Step-by-step explanation:

They have a common difference of -3


Related Questions

The vector (a) is a multiple of the vector (2i +3j) and (b) is a multiple of (2i+5j) The sum (a+b) is a multiple of the vector (8i +15j). Given that /a+b/= 34 and the scaler multiple of (8i+15j) is positive, Find the magnitude of a and b.​

Answers

Answer:

[tex]\|a\| = 5\sqrt{13}[/tex].

[tex]\|b\| = 3\sqrt{29}[/tex].

Step-by-step explanation:

Let [tex]m[/tex],[tex]n[/tex], and [tex]k[/tex] be scalars such that:

[tex]\displaystyle a = m\, (2\, \vec{i} + 3\, \vec{j}) = m\, \begin{bmatrix}2 \\ 3\end{bmatrix}[/tex].

[tex]\displaystyle b = n\, (2\, \vec{i} + 5\, \vec{j}) = n\, \begin{bmatrix}2 \\ 5\end{bmatrix}[/tex].

[tex]\displaystyle (a + b) = k\, (8\, \vec{i} + 15\, \vec{j}) = k\, \begin{bmatrix}8 \\ 15\end{bmatrix}[/tex].

The question states that [tex]\| a + b \| = 34[/tex]. In other words:

[tex]k\, \sqrt{8^{2} + 15^{2}} = 34[/tex].

[tex]k^{2} \, (8^{2} + 15^{2}) = 34^{2}[/tex].

[tex]289\, k^{2} = 34^{2}[/tex].

Make use of the fact that [tex]289 = 17^{2}[/tex] whereas [tex]34 = 2 \times 17[/tex].

[tex]\begin{aligned}17^{2}\, k^{2} &= 34^{2}\\ &= (2 \times 17)^{2} \\ &= 2^{2} \times 17^{2} \end{aligned}[/tex].

[tex]k^{2} = 2^{2}[/tex].

The question also states that the scalar multiple here is positive. Hence, [tex]k = 2[/tex].

Therefore:

[tex]\begin{aligned} (a + b) &= k\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 2\, (8\, \vec{i} + 15\, \vec{j}) \\ &= 16\, \vec{i} + 30\, \vec{j}\\ &= \begin{bmatrix}16 \\ 30 \end{bmatrix}\end{aligned}[/tex].

[tex](a + b)[/tex] could also be expressed in terms of [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{aligned} a + b &= m\, (2\, \vec{i} + 3\, \vec{j}) + n\, (2\, \vec{i} + 5\, \vec{j}) \\ &= (2\, m + 2\, n) \, \vec{i} + (3\, m + 5\, n) \, \vec{j} \end{aligned}[/tex].

[tex]\begin{aligned} a + b &= m\, \begin{bmatrix}2\\ 3 \end{bmatrix} + n\, \begin{bmatrix} 2\\ 5 \end{bmatrix} \\ &= \begin{bmatrix}2\, m + 2\, n \\ 3\, m + 5\, n\end{bmatrix}\end{aligned}[/tex].

Equate the two expressions and solve for [tex]m[/tex] and [tex]n[/tex]:

[tex]\begin{cases}2\, m + 2\, n = 16 \\ 3\, m + 5\, n = 30\end{cases}[/tex].

[tex]\begin{cases}m = 5 \\ n = 3\end{cases}[/tex].

Hence:

[tex]\begin{aligned} \| a \| &= \| m\, (2\, \vec{i} + 3\, \vec{j})\| \\ &= m\, \| (2\, \vec{i} + 3\, \vec{j}) \| \\ &= 5\, \sqrt{2^{2} + 3^{2}} = 5 \sqrt{13}\end{aligned}[/tex].

[tex]\begin{aligned} \| b \| &= \| n\, (2\, \vec{i} + 5\, \vec{j})\| \\ &= n\, \| (2\, \vec{i} + 5\, \vec{j}) \| \\ &= 3\, \sqrt{2^{2} + 5^{2}} = 3 \sqrt{29}\end{aligned}[/tex].

Make a histogram, using a bin width of ten, to display the bowling scores for these 31 players: 87, 104, 79, 94, 117, 82, 72, 116, 105, 95, 88, 93, 109, 119, 75, 103, 112, 97, 73, 85, 91, 86, 102, 99, 106, 84, 98, 83, 81, 96, 92.

Answers

Step-by-step explanation:

Using R, I used the following code to create a histogram:

bowling.scores <- c(87, 104, 79, 94, 117, 82, 72, 116, 105, 95, 88, 93, 109, 119, 75,  

                   103, 112, 97, 73, 85, 91, 86, 102, 99, 106, 84, 98, 83, 81, 96, 92)

data.frame(bowling.scores)

ggplot(data.frame(bowling.scores), aes(x=bowling.scores)) +  

 xlim(c(70, 120)) +

 scale_y_continuous(breaks = seq(0, 10, by=1), "Frequency") +

 geom_histogram(breaks=seq(70, 120, by=10), color="black", fill="grey60") +

 labs(title="Histogram of Bowling Scores", x="Bowling Scores", y="Frequency")

What quantity of parsley would you need to make 5 times as much as the original recipe?

Answers

Original= x

5(x)=y
y= 5Xx

if a = 6 b=5, then find the value (a+b)​

Answers

Step-by-step explanation:

Put the numbers as the value is given

So,

(6+5)= 11 Answer

Answer:

11

Step-by-step explanation:

(a + b) where a = 6 and b = 5

Step 1. Substitute a for 6 and b for 5

(6 + 5)

Step 2. Add

11

GEOMETRY QUESTION- Find m < h

Answers

9514 1404 393

Answer:

  m∠H = 38°

Step-by-step explanation:

External angle GFD is the sum of internal angles G and H.

  14x +1 = 89° +(5x -7)

  9x = 81°

  x = 9°

Then the measure of angle H is ...

  angle H = 5(9°) -7° = 38°

Shaded areas ( What is the area of the shaded region? )

Answers

Answer:

119.43 cm²

Step-by-step explanation:

The shaded area (A) is calculated as

A = area of rectangle - area of circle

   = (11 × 12) - π × 2²

  = 132 - 4π

  ≈ 119.43 cm² ( to the nearest hundredth )

5. For an acute angle 0, cos(0) = sin(33) is true. What is the value of 0?

Answers

Answer:

Value is 57

Step-by-step explanation:

sin 33

= sin (90-57)

= cos 57

Answered by GAUTHMATH

Find the value of 65°11' - 58°32'​

Answers

Answer:

dddddd=666=7777

Step-by-step explanation:

what is 7/8 divided by 1/8

Answers

Answer:

7

Step-by-step explanation:

Concepts:

Division: a system of distributing a collection of things into equal partsFractions: #s that represent a part of a wholeDividing Fractions: dividing a fraction by another fraction = multiplying the fraction by the inverse (reciprocal) of the other oneInverse Operations: operations that are opposite of each other (e.g. inverse of addition is subtraction)

Solving:

1. First, let's set up the equation:

7/8 ÷ 1/8

2. We can get the reciprocal of 1/8 by doing the opposite of division; multiplication. 1/8 becomes 1 · 8, and that's equal to 8.

3. Now, since we know dividing a fraction by another one is exactly the same as multiplying the fraction by the reciprocal of the other, let's multiply 7/8 by the inverse of 1/8, which is 8.

7/8 · 8 = 56/8 = 7

Therefore, 7/8 divided by 1/8 is equal to 7.

The expression.1*e^0.0347t models.The balance in thousand of dollars where t represents time.In years after the account was opened. What does the 0.034 represent in this context? Write an expression for the number of years after which there will be 15,000 Dollars in the account?

Answers

Answer:

0.0347 = constant of proportionality

[tex]1 * e^{0.0347t} = 15000[/tex]

Step-by-step explanation:

Given

[tex]1*e^{0.0347t}[/tex]

Solving (a): what does 0.0347 represent?

An exponential model is represented as:

[tex]f(t) = a * e^{kt}[/tex]

Where:

[tex]k \to[/tex] constant of proportionality

So, by comparison:

[tex]k = 0.0347[/tex]

Hence:

[tex]0.0347 \to[/tex] constant of proportionality

Solving (b): Formula to calculate when balance equals 15000

To do this, we simply equate the formula to 15000.

So, we have:

[tex]1 * e^{0.0347t} = 15000[/tex]

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
An alphabetical list is generated of each member of the student body at a local middle school. The first name on the list is in the sample, along with every 5th name on the list after that. This is an example of a __________________.
A. systematic sample
B. stratified random sample
C. convenience sample
D. random sample

Answers

Answer:

Option A, systematic sample

how many metres of wire is needed to fence a circular pond of radius 7.7m if the fence is to have three strands of wire all the way around .Give your answer correct to one decimal place. (Take pi is 3.14)​

Answers

Find the circumference of the pond:

Circumference = 2 x pi x radius

Circumference = 2 x 3.14 x 7.7 = 48.356 m

You want to go around 3 times so multiply the circumference by 3:

48.356 x 3 = 145.068m

Rounded to 1 decimal = 145.1m

 A study found that healthy eating can help to cut the risk of heart disease. Therefore, a person can conclude that if they eat healthy they definitely will not have any heart issues.

True or false?

Answers

Answer:

False

Step-by-step explanation:

It only cuts the risk as stated and other factors such as lifestyle, age, bloodpressure and past medical background also have an impact so you can still have heart issues.

false , people can still develop heart issues

On Saturday, the fruit and juice bar was selling 22 glasses of fruit punch an hour. By 4 p.m., they had sold 132 glasses. If their goal was to sell more than 264 glasses of fruit punch, which inequality can be used to find h, the number of hours they must stay open to make their goal?
A. 132 + 22h > 264
B. 22h < 264 + 132
C. 132 + 22h < 264
D. 132 + 264 > 22h

Answers

Answer:

A. 132 + 22h > 264

Step-by-step explanation:

Hourly sales = 22 glasses of fruit punch

Sales by 4 p.m = 132 glasses

Goal = more than 264 glasses

h = number of hours they must stay open to make their goal

The inequality:

132 + 22h > 264

22h > 264 - 132

22h > 132

h > 132/22

h > 6 hours

This means, the number of hours they must stay open to make their goal of more than 264 glasses is more than 6 hours

find A={a,b,c} then find A*A.​

Answers

Assuming you want to do a cartesian product, then you basically form items (x,y)  such that x is in set A, and y is in set A

More generally, A * B will consist of items of the form (x,y) such that x is in A and y is in B. However, we have B = A.

So,

A * A = {

(a,a), (a,b), (a,c)

(b,a), (b,b), (b,c)

(c,a), (c,b), (c,c)

}

I broke things up into separate rows to show that we can form a 3x3 table. Each row is a different x value from the set {a,b,c}. Each column is a different y value from the set {a,b,c}

In my opinion, this helps organize things much better than rather have it all on one single line like this

A * A = { (a,a), (a,b), (a,c), (b,a), (b,b), (b,c), (c,a), (c,b), (c,c) }

which in all honesty looks like a bit of a cluttered mess.

Answer:

Step-by-step explanation:

A={a,b,c}

A×A={a×a,a×b,a×c,b×a,b×b,b×c,c×a,c×b,c×c}

An object that weighs exactly 1
pound is placed on a digital scale that measures weight in ounces.
If the scale is accurate and precise, what weight might be shown on the scale?

Answers

16 ounces= 1 pound.

An expression is shown below: \sqrt(50)+\sqrt(2) is it irrational or rational

Answers

Answer:

Irrational

Step-by-step explanation:

It's an irrational number since both of them are irrational

John earns $6 per hour for mowing the lawn. If t represents John's total earnings for h hours of mowing, which equations can be used to model the situation

Answers

Answer:

h=6

Step-by-step explanation:

The receipt shows the prices of goods that Mr. Baker bought at the store.
The state Mr. Baker lives in has a sales tax rate of 7% on all purchases.

How much money does Mr. Baker pay in sales tax and what is the total amount he must pay for his purchases?

Answers

Answer:

The answer is $82.46 sales tax

$1,260.46 Total

Step-by-step explanation:

Since the price before the Sales tax is $1,178.00 and if you add the 7% Sales tax the total is $1,260.46 and the price of the Sales tax is $82.46

$750x.07= $52.50
+
$329x.07=$23.03
+
$99x.07=$6.93
=
$82.46

1,178+82.46=
$1,260.46

Simplify and find the perimeter of the triangle

Answers

Answer:

2x - 19

Step-by-step explanation:

Perimeter = sum of sides

First let's simplify each side

We can simplify each side by using distributive property. Distributive property is where you multiply the number on the outside of the parenthesis by the numbers on the inside of the parenthesis.

2(x + 5)

Distribute by multiplying x and 5 by 2

2 * x = 2x and 2 * 5 = 10

2x + 10

1/2(4x + 8)

Distribute by multiplying 4x and 8 by 1/2

1/2 * 4x = 2x and 1/2 * 8 = 4

2x + 4

-3(2x + 11)

Distribute by multiplying 2x and 11 by -3

-3 * 2x = -6x

-3 * -33

-6x - 33

Finally add all the simplified expressions ( remember that they represent the side lengths of the triangle )

2x + 10 + 2x + 4 - 6x - 33

Combine like terms

2x + 2x - 6x = -2x

10 + 4 - 33 = -19

Perimeter: -2x - 19

Answer:

Perimeter = - 2x - 19

Step-by-step explanation:

[tex]Perimeter \: of \: a \: triangle \\ = Sum \: of \: the \: length \: of \: all \: sides \\ = [2(x+5)]+[-3(2x+11)]+[ \frac{1}{2} (4x+8)] \\ = [(2 \times x)+(2 \times 5)]+[(-3 \times 2x)+( - 3 \times 11)]+[ (\frac{1}{2} \times 4x) + ( \frac{1}{2} \times 8)] \\ = (2x + 10) + ( - 6x - 33) + (2x + 4) \\ = 2x + 10 - 6x - 33 + 2x + 4 \\ = 2x - 6x + 2x + 10 - 33 + 4 \\ = - 2x - 19[/tex]

So, the perimeter is - 2x - 19.

Dave solved a quadratic equation. His work is shown below, with Step 111 missing. What could Dave have written as the result from Step 111? \begin{aligned} \dfrac{1}{3}(x+4)^2&=48 \\\\ &&\text{Step }1 \\\\ x+4&=\pm 12&\text{Step }2 \\\\ x=-16&\text{ or }x=8&\text{Step }3 \end{aligned} 3 1 ​ (x+4) 2 x+4 x=−16 ​ =48 =±12 or x=8 ​ Step 1 Step 2 Step 3 ​ Dave solved a quadratic equation. His work is shown below, with Step 111 missing. What could Dave have written as the result from Step 111? \begin{aligned} \dfrac{1}{3}(x+4)^2&=48 \\\\ &&\text{Step }1 \\\\ x+4&=\pm 12&\text{Step }2 \\\\ x=-16&\text{ or }x=8&\text{Step }3 \end{aligned} 3 1 ​ (x+4) 2 x+4 x=−16 ​ =48 =±12 or x=8 ​ Step 1 Step 2 Step 3 ​

Answers

From the calculation above, Dave may have jumped the expression

[tex](x+4)^2= 144[/tex]

Given the expression solved by Dave from step 1 as;

[tex]\dfrac{1}{3}(x+4)^2&=48[/tex]

In order to determine what Dave would have written, we will solve the expression above as shown

[tex]\dfrac{1}{3}(x+4)^2&=48\\(x+4)^2 = 3*48\\(x+4)^2 = 144 ..............eqn \ 2\\[/tex]

Take the square root of both sides

[tex]\sqrt{(x+4)^2} =\pm\sqrt{144}\\x+4=\pm12[/tex]

Hence from the calculation above, Dave may have jumped the expression in equation 2 as shown below;

[tex](x+4)^2= 144[/tex]

Learn more on radical equations here: https://brainly.com/question/20931859

Answer:

previous answer is correct

Step-by-step explanation:

"A parabola has the equation = ^ + − . What are the coordinates of the vertex? (You must solve by factoring)!!!!!" I NEED THE ANSWER TO THIS FAST WITH STEPS I'm a grade 10 academic student by the way

Answers

Answer:

1

Step-by-step explanation:

1

Revolve into factor : 2x square + 5xy + 2y square​

Answers

Answer:

(2x + y) ( x + 2y)

Step-by-step explanation:

A 4-pack of plastic flower pots costs $4.08. What is the unit price?

Answers

Answer:

If 4 flower pots cost 4.08 dollars, then 1 flower pot costs 4.08/4 dollars.

4.08/4 = 1.02.

So the unit price is $1.02.

Let me know if this helps!

What is 4,327 rounded to the nearest thousand?

Answers

Answer: 4,000

Step-by-step explanation: To round 4,327 to the nearest thousand, we first find the digit in the rounding place, which in this case is the 4 in the thousands place. Next, we look at the digit to the right of the 4, which is 3.

According to the rules of rounding, since the digit to

the right of the rounding place is less than 5, we round down.

So the 4 in the rounding place stays the same

and all digits to the right of the 4 become 0.

So 4,327 rounded to the nearest thousand is 4,000.

solve using identities​

Answers

Answer:

Solution given

Cos[tex]\displaystyle \theta_{1}=\frac{13}{15}[/tex]

consider Pythagorean theorem

[tex]\bold{Sin²\theta+Cos²\theta=1}[/tex]

Subtracting [tex]Cos²\theta[/tex]both side

[tex]\displaystyle Sin²\theta=1-Cos²\theta[/tex]

doing square root on both side we get

[tex]Sin\theta=\sqrt{1-Cos²\theta}[/tex]

Similarly

[tex]Sin\theta_{1}=\sqrt{1-Cos²\theta_{1}}[/tex]

Substituting value of [tex]Cos\theta_{1}[/tex]

we get

[tex]Sin\theta_{1}=\sqrt{1-(\frac{-13}{15})²}[/tex]

Solving numerical

[tex]Sin\theta_{1}=\sqrt{1-(\frac{169}{225})}[/tex]

[tex]Sin\theta_{1}=\sqrt{\frac{56}{225}}[/tex]

[tex]Sin\theta_{1}=\frac{\sqrt{56}}{\sqrt{225}}[/tex]

[tex]Sin\theta_{1}=\frac{\sqrt{2*2*14}}{\sqrt{15*15}}[/tex]

[tex]Sin\theta_{1}=\frac{2\sqrt{14}}{15}[/tex]

Since

In III quadrant sin angle is negative

[tex]\bold{Sin\theta_{1}=-\frac{2\sqrt{14}}{15}}[/tex]

Answer:

- 2√14/15

Step-by-step explanation:

In the quadrant III both the sine and cosine get negative value.

Use the identity:

sin²θ + cos²θ = 1

And consider negative value as mentioned above:

sinθ = - √(1 - cos²θ) sinθ = - √(1 - (-13/15)²) sinθ = - √(1 - 169/225)sinθ = - √(56/225)sinθ = - 2√14/15

help please :) try to explain and answer math coordinates

Answers

The answer is (c-a , b)

The temperature of a 24-hour period ranged between -6°F and 35°F, inclusive. What was the range in Celsius degrees? (Use F = 9/5C + 32)

Answers

Your mum Your mum Your mum Your mum

find the transpose of matrics.
Q=[789]

Answers

Answer:

[7]

[8]

[9]

Step-by-step explanation:

according to your question

your answer is

[7]

[8]

[9]

you must be write this answer in one bracket

when graphing y=-2x+10, is it a line that shows only one solution to the equation, all solutions, or shows the y-intercept?

Answers

Answer:

there is always a y-intercept in all graphs.

Step-by-step explanation:

be it a line graph, quadratic graph or cubic graph. all graphs will definitely have a y-intercept. and in this case, since y=mx + c where c is the y-intercept. the y intercept of this graph is 10

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