The 4th term of an arithmetic sequence is 12 and the 8th term is 36. Find the 17th term of the sequence.
How do you work it out?

Answer:

x = 16

Step-by-step explanation:

Given that the sum of the exterior angles is 360°

Sum the given exterior angles and equate to 360

47 + 93 + 46 + 3x + 62 + 4x = 360, that is

248 + 7x = 360 ( subtract 248 from both sides )

7x = 112 ( divide both sides by 7 )

x = 16

Option A

The vertex is (h, k) = (5, -25)

Solution:

Given function is:

[tex]f(x) = x^2-10x[/tex]

The vertex form is given as:

[tex]y = a(x-h)^2+k[/tex]

Rewrite the equation in vertex form

[tex]f(x) = x^2-10x[/tex]

Complete the square for  [tex]x^2-10x[/tex]

Use the form [tex]ax^2+bx+c[/tex] to find the values of  a, b, c

a = 1 , b = -10, c = 0

Consider the vertex form of a parabola

[tex]a(x+d)^2+e[/tex]

Substitute the values of a and b into the following formula to find "d" :

[tex]d = \frac{b}{2a}\\\\d = \frac{-10}{2 \times 1}\\\\d = -5[/tex]

Find the value of "e" using the formula,

[tex]e = c - \frac{b^2}{4a}\\\\e = 0 - \frac{(-10)^2}{4 \times 1}\\\\e = -25[/tex]

Substitute the value of a, d, e into vertex form

[tex]a(x+d)^2+e\\\\1(x-5)^2-25\\\\(x-5)^2-25[/tex]

Set y equal to above equation

[tex]y = (x-5)^2-25[/tex]

Compare the above equation with vertex form

[tex]y = a(x-h)^2+k[/tex]

[tex]y = (x-5)^2-25[/tex]

We find, h = 5 and k = -25

Thus the vertex is (h, k) = (5, -25)

Answer: the small cup cost the least per ounce

After calculating the cost per ounce for each cup size, we find that the small cup costs the least per ounce at $0.0989, making it the best value.

To determine which size cup offers the best value per ounce, we need to calculate the cost per ounce for each size. This can be done by dividing the cost of each cup by the number of ounces it holds.

For the small cup: $.89 / 9 ounces = $0.0989 per ounce

For the medium cup: $1.29 / 12 ounces = $0.1075 per ounce

For the large cup: $1.59 / 15 ounces = $0.106 per ounce

Now, comparing the cost per ounce for each cup size, we can see that the small cup offers the best value at $0.0989 per ounce.

Answer:x=40

Step-by-step explanation:

The measure of x in each figure, you need to solve the equation 4x + 20 = 180° by isolating the term with x and then solving for x. The solution is x = 40°, so the measure of x is 40 degrees.

The value of x. The given equation is 4x + 20 = 180°, representing a linear pair of angles.

Subtract 20 from both sides of the equation to isolate the term with x:

4x + 20 - 20 = 180 - 20

4x = 160°

Divide both sides of the equation by 4 to solve for x:

(4x)/4 = 160/4

x = 40°
Therefore, the solution to the equation is x = 40°.

Answer:

Step-by-step explanation:

12x-20=6(x-20)-9x

Opening bracket

12x - 20 = 6x - 120 - 9x

Collecting like terms

12x - 6x + 9x = -120 + 20

15x = -100

Dividing by 15

15x/15 = -100/15

x = -20/3

x = - 6 2/3

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

12x - 20 = 6( x - 20) - 9x

pay attention to the brackets as you simplify.

Let's work on it:

12x - 20 = 6x - 120 -9x

Collecting like terms to further simplify the equation.

12x - 6x + 9x = -120 + 20

15x = -100

Let's make x the subject formula by dividing through by 15

Therefore:

x = -100 / 15

Divide through by 5

x = -20 / 3

Since nothing can easily divide through, we turn it to a mixed fraction

x = - 6 2/3

( Minus six whole number, two divided by three)

Answer:

B. 3

Step-by-step explanation:

The shape of a box is a square. The volume for a square is lengthxwidthxheight.

For the first box it would be 2x3x6 or 36in.

For the second box, 3x4, which is 12.

Dividing 36 by 12, we get 3.

So 3x4x3 would result in 36in., the same as the first box.

The undefined terms needed to define parallel lines are "line" and "coplanar," as parallel lines lie in the same plane and never intersect.

To define parallel lines, the undefined terms needed are "line" and "coplanar."

Parallel lines are two lines that lie in the same plane and never intersect, which means they are coplanar and can be extended indefinitely.

So, the correct choice is: Coplanar, line.

Hey there!

I'm going to set up the equation slightly different.

[tex](3)(8)=t+5\\24=t+5\\t+15=24\\t+15-15=24-15\\t = 9 \checkmark[/tex]

Answer:

t = 9

Step-by-step explanation:

3x8 = t + 15

24 = t + 15

t = 24 - 15

t = 9

Answer:

all work is pictured and shown

Answer:

The solution is the point (2,-2)

Step-by-step explanation:

we have

[tex]-4x+8y=-24[/tex] -----> equation A

[tex]7x-5y=24[/tex] -----> equation B

step 1

Multiply by 7 equation A both sides

[tex]7(-4x+8y)=7(-24)[/tex]

[tex]-28x+56y=-168[/tex] -----> equation C

step 2

Multiply equation B by 4 both sides

[tex]4(7x-5y)=4(24)[/tex]

[tex]28x-20y=96[/tex] -----> equation D

step 3

Adds equation C and equation D

[tex]-28x+56y=-168\\28x-20y=96\\-----------\\56y-20y=-168+96\\36y=-72\\y=-2[/tex]

Find the value of x

substitute the value of y in any equation

equation A

[tex]-4x+8(-2)=-24\\4x=-16+24\\4x=8\\x=2[/tex]

therefore

The solution is the point (2,-2)

Answer:

0.9 / 90%

Step-by-step explanation:

54/60

=0.9

To calculate Kevin's score as a percent, we divide the number of correct answers by the total number of questions and multiply by 100. The answer, rounded to the nearest tenth of a percent, is 90.0%.

The subject of this question is Mathematics, particularly the area concerning percentage conversions. Kevin got 54 questions correct out of a total of 60 questions. To find Kevin's score as a percent, we first need to divide the number of questions he answered correctly (54) by the total number of questions (60). This gives us a decimal (0.9). To convert this decimal to a percent, we multiply by 100, which gives us 90%. This is Kevin's raw score. But the question wants the score rounded to the nearest tenth of a percent, so the final answer is 90.0%.

https://brainly.com/question/32297219

#SPJ2

Answer:

Bout which cars?

Step-by-step explanation:

Sorry, but I think you've missed out a part of the question

Answer:

1350

Step-by-step explanation:

I added tower A and B together (90+180) Which gives me 270. Then I did;

270 * 5= 1350 ft. Hope its correct!

Final answer:

Tower C is 5 times as tall as the combined height of Tower A (90 feet) and Tower B (180 feet), which together are 270 feet tall. Multiplying this by 5 gives us the height of Tower C, which is 1350 feet.

Explanation:

The question asks us to calculate the height of Tower C given the heights of Tower A and Tower B and the relationship between their heights. Tower A is 90 feet tall, and Tower B is 180 feet tall. According to the question, Tower C is 5 times as tall as both Towers A and B combined.

To find the combined height of Towers A and B, we simply add their heights:

Now, we need to calculate the height of Tower C:

Therefore, Tower C is 1350 feet tall.

Answer: i would help but i'm confused....what problem? can yhu attach it so i could help??! - Lexi@helps

Step-by-step explanation:

Option D

The total earnings of Yvette is $ 47, 400

Solution:

Given that, Yvette earns a $45,000 salary plus a 12% commission on any sales over $10,000

Last year Yvette made $30,000 in sales

Subtract 10,000 from her sales to get the amount she earns commission on:

30,000 - 10,000 = 20,000

Since Yvette gets 12% commission

So amount earned as commission would be 12% of $20,000

[tex]\text{Commission}=20000\times \frac{12}{100}\\\\\text{Commission}=20000\times 0.12\\\\\text{Commission}=2400\left\\\\[/tex]

Yvette also gets a salary of $45,000, so Yvette's total earnings would be $45,000 plus $2,400

[tex]Total\ Earnings = 45000 + 2400 = 47400[/tex]

Thus total earnings of Yvette is $ 47, 400

Answer:

D

Step-by-step explanation:

Answer: 54-7n

Step-by-step explanation:

When we talk about mathematical language, the difference between two numbers, quantities or terms is the substraction operation.

For example, the difference between a and b is:

a-b

On the other hand, if we read a numer c times a number n, this means both numbers are multiplied.

For example:

c times n is:

(c)(n)

So, according to the explained above, “the difference of fifty-four and seven times a number n” is:

54-7n

Answer:

Answer: 54-7n

Step-by-step explanation:

When we talk about mathematical language, the difference between two numbers, quantities or terms is the substraction operation.

For example, the difference between a and b is:

a-b

On the other hand, if we read a numer c times a number n, this means both numbers are multiplied.

For example:

c times n is:

(c)(n)

So, according to the explained above, “the difference of fifty-four and seven times a number n” is:

54-7n

and recall the you can divide everything by 100 like 74/n  n=100 so 74/100

see and pls give  me brainiest

Answer: 2x + 5y = -5

Step-by-step explanation:

Two lines are said to be parallel if they have the same slope.

The equation of the line given :

2x + 5y = 10

To find the slope , we will write it in the form y = mx + c , where m is the slope and c is the y - intercept.

2x + 5y = 10

5y = -2x + 10

y = -2/5x + 10/5

y = -2/5x + 2

This means that the slope is -2/5 ,the line that is parallel to this line will also have a slope of -2/5.

using the formula:

[tex]y-y_{1}[/tex] = m ([tex]x-x_{1}[/tex] ) to find the equation of the line , we have

y - 1 = -2/5(x -{-5})

y - 1 = -2/5 ( x + 5 )

5y - 5 = -2 ( x + 5 )

5y - 5 = -2x - 10

5y + 2x = -10 + 5

therefore :

2x + 5y = -5 is the equation of the line that is parallel to 2x + 5y = 10

Answer: 2x + 5y = -5

Step-by-step explanation:please see attachment for explanation

Answer:

geometric sequence

Step-by-step explanation:

If the sequence is geometric then there must be a common ratio r between consecutive terms, that is

320 ÷ 128 = 2.5

800 ÷ 320 = 2.5

2000 ÷ 800 = 2.5

Since there is a common ratio r = 2.5 between consecutive terms.

Then the sequence is geometric

Answer:

Therefore the first option gives the correct answer of a system of equations which has exactly one solution.

Step-by-step explanation:

i) the second option is 2x + 2y = 1  and -2x -2y = 1 . these two equation can be written as 2x + 2y = 1 and 2x + 2y = -1. Therefore we can see that that the expressions for used for the variables x and y are the same but the result is different. This is not possible and so there will be no solutions for these two equations

ii) the third option is 3x + y = -1 and 6x + 2y = -2. therefore these two equations can be written as  3x + y = -1 and 3x + y = -1 (dividing the second equation by 2) and thus we see that both the equations are exactly the same and hence these two equations will have an infinite number of solutions.

iii) the last option is 3x - 2y = 4 and -3x + 2y = 4. these two equations can be written as 3x -  2y = 4 and 3x - 2y = -4. Again we can see in this case that the two equations are exactly the same and therefore these two equations will have an infinite number of solutions.

iv) the remaining option is the first one 2x + y = 3 and 5x - y = 11.  If we add the first equation to the second one we 7x = 14 and therefore x = 2. If we substitute x = 2 in the first equation we get (2 × 2) + y = 3, therefore y = -1.

Therefore the first option gives the correct answer of a system of equations which has exactly one solution.

Answer:

14

Step-by-step explanation:

(2(19)-10)=2

(38-10)=2

(28)=2

÷2. ÷2

14

Answer:

Hence, the supplement of a 20˚ angle is a 160˚ angle. This can be proven again, since 20+160=180 , and supplementary angles have a sum of 180˚ .

Step-by-step explanation:

The answer is: ∠BOA

(Had the same question)

BTW, you forgot to add the picture.  That's why no one understands this, unless they had this question in their school work.

The best reflection of Jason's answer among the given options is option : [tex]\((5x + 1)(5x - 1)\).[/tex]

The correct option is (H).

To factor [tex]\(25x^2 - 1\)[/tex], Jason likely used the difference of squares formula. This formula states that for any expressions [tex]\(a\) and \(b\), \(a^2 - b^2\)[/tex] can be factored as [tex]\((a + b)(a - b)\).[/tex]

In our case, [tex]\(a = 5x\) and \(b = 1\)[/tex]. So, we apply the difference of squares formula:

[tex]\[25x^2 - 1 = (5x)^2 - 1^2\][/tex]

[tex]\[= (5x + 1)(5x - 1)\][/tex]

This factorization is a result of recognizing that [tex]\(25x^2 - 1\)[/tex] can be written as [tex]\((5x)^2 - 1^2\),[/tex] fitting the difference of squares pattern.

Now, let's compare Jason's answer to the options given:

- Option F: [tex]\((5x-1)(5x-1)\)[/tex] is not correct. This represents the square of [tex]\(5x - 1\),[/tex] not a difference of squares.

- Option G: [tex]\((5x+1)(5x+1)\)[/tex]is not correct. This also represents the square of [tex]\(5x + 1\),[/tex] not a difference of squares.

- Option H:[tex]\((5x+1)(5x-1)\)[/tex] is correct. This represents the correct factorization using the difference of squares formula.

- Option J: Prime. This is incorrect because [tex]\(25x^2 - 1\)[/tex] can indeed be factored as [tex]\((5x + 1)(5x - 1)\).[/tex]

Therefore, the best reflection of Jason's answer among the given options is option H: [tex]\((5x + 1)(5x - 1)\).[/tex]

complete question given below:

Jason was asked to factor 25x^2-1 on his algebra test. Which of the following could best reflect Jason's answer?

F. (5x-1)(5x-1)

G. (5x+1)(5x+1)

H .(5x+1)(5x-1)

J .Prime

Answer:

y = 5x - 3.

Step-by-step explanation:

The value of y will go down by 3 units so it is

y = 5x - 3.

The equation y = 9 + 3x represents a line with a y-intercept of 9 and a slope of 3. To translate the line down 3 units, subtract 3 from every y-coordinate.

The equation y = 9 + 3x represents a line with a y-intercept of 9 and a slope of 3. The y-intercept is the point where the line intersects the y-axis, and in this case, it is the point (0, 9). The slope of 3 means that for every increase of 1 on the horizontal axis, the line rises up 3 units on the vertical axis.

To translate the line down 3 units, we can subtract 3 from every y-coordinate. This means that the equation becomes y = 9 + 3x - 3, which simplifies to y = 6 + 3x.

Answer:

$50

Step-by-step explanation:

If the tip was $9, you can find the total price by dividing 9 by .18.  .18 is 18% but as a decimal (move to the left two decimal places).  9/.18 = 50.

You can also check the answer by finding the 18% tip of $50. 50*.18=9.

For this case we must solve the following equation:

[tex]12y + 6 = 6 (y + 1)[/tex]

We apply distributive property on the right side of the equation:

[tex]12y + 6 = 6y + 6[/tex]

We subtract 6y on both sides of the equation:

[tex]12y-6y + 6 = 6\\6y + 6 = 6[/tex]

We subtract 6 from both sides of the equation:

[tex]6y = 6-6\\6y = 0[/tex]

Dividing by 6 on both sides of the equation:

[tex]y = 0[/tex]

So, the result is [tex]y = 0[/tex]

Answer:

[tex]y = 0[/tex]

Answer:

[tex]x=\frac{5t^2-a}{6-5t}[/tex]

Step-by-step explanation:

Given equation is

[tex]6x+a=5t(x+t)[/tex]

We have to make [tex]x[/tex] the subject of formula. That means we have to isolate [tex]x[/tex].

[tex]6x+a=5t(x+t)[/tex]

Distribute [tex]5t[/tex]

[tex]6x+a=5tx+5t^2[/tex]

Subtract [tex]a[/tex] both side we get,

[tex]6x+a-a=5xt+5t^2-a[/tex]

[tex]6x=5xt+5t^2-a[/tex]

Subtract [tex]5xt[/tex] both side we get,

[tex]6x-5xt=5xt-5xt+5t^2-a\\6x-5xt=5t^2-a[/tex]

Now, take [tex]x[/tex] common from left side of equation

[tex]x(6-5t)=5t^2-a[/tex]

Divide [tex]6-5t[/tex] both side,

[tex]\frac{x(6-5t)}{6-5t}=\frac{5t^2-a}{6-5t}\\\\x=\frac{5t^2-a}{6-5t}[/tex]

80 USD × (1.0343 AUD / 1 USD)

Solution:

To convert 80 US dollars into Australian dollars.

1 US dollar = 1.0343 AU dollar

1 AU dollar = 0.9668 US dollar

To find 80 US dollars into Australian dollars multiply 80 US dollars by 1.0343

80 AU dollars = 80 × 1.0343/ 1 USD

The expression is 80 USD × (1.0343 AUD / 1 USD)

Hence, the expression which is used to convert 80 US dollars to Australian dollars is 80 USD × (1.0343 AUD / 1 USD).

Answer:

160,281

Step-by-step explanation:

Just add the assets together.

Answer:

$160,281

Step-by-step explanation:

Assets                             Value         Liabilities         Value  

Checking and Savings $2,378    Auto Loan       $4,502  

Automobile                 $8,765       Credit Cards   $435  

House Value                 $135,000   Mortgage        $51,208  

Furniture, etc.                 $13,900    Other Loans    $1,234  

Miniature Collection $238

Their total assets is obtained adding the values of each asset, as follows:

$2,378 + $8,765 + $135,000 + $13,900 + $238 = $160,281

Answer:

i think correct answer is a