What is the 6th term in the arithmetic sequence defined by the explicit formula

an=8n-3?

Answer:

12 x 2 = 24

24 x 3 = 72

72 x 4 = 288

288 x 5 = 1440

The result of each multiplication is being multiplied by the next consecutive number so the pattern is = x2,x3,x4,x5.

Step-by-step explanation:

Boom

To rewrite the inequality 5x - 5y ≥ 70 in slope-intercept form, we solve for y by subtracting 5x from both sides and then dividing by -5, resulting in y ≤ x - 14, with a slope of 1 and a y-intercept of -14.

The question is asking to rewrite the inequality 5x - 5y ≥ 70 in slope-intercept form. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To convert the given inequality into this form, we need to solve for y.

Steps to rewrite the inequality in slope-intercept form:

The inequality in slope-intercept form is y ≤ x - 14. The slope is 1 and the y-intercept is -14.

Answer:

10 possible outcomes

Step-by-step explanation:

- One coin has two sides (heads and tails)

- It is tossed 5 times

- 2 times 5 is 10

Answer:

Part to whole ratio

Step-by-step explanation:

The 1 represents the blueberry bagels. This is just a part of the entire variety that is offered, so this is a part.

The 4 represents all of the bagels. It is the whole amount, which makes this the whole.

This means it is a part to whole ratio.

The 575 written as a mixed number is A. 5 3/4 . Therefore , A. 5 3/4 is correct .

You have correctly outlined the steps to convert 575% to a mixed number. Let me summarize the process:

Convert the Percentage to a Decimal:

Divide the percentage by 100 to convert it to a decimal:

 [tex]\frac{575}{100}[/tex]%  = 5.75.

Separate the Whole Number and Decimal Part:

Separate the whole number part from the decimal part:

5.75=5+0.75.

Convert the Decimal to a Fraction:

Convert the decimal part to a fraction with a denominator of 100:

0.75× [tex]\frac{100}{100}[/tex]  = [tex]\frac{75}{100}[/tex] ​ .

Combine the Whole Number and Fraction:

Combine the whole number and the fraction into a mixed number:

5 + ​[tex]\frac{75}{100}[/tex] =5 [tex]\frac{3}{4}[/tex] .

Therefore, 575% written as a mixed number is 5 [tex]\frac{3}{4}[/tex]​ .

This means there are 5 whole units and [tex]\frac{3}{4}[/tex]of an additional unit in the given percentage.

It's a clear and accurate way to represent a percentage as a mixed number.

A.) 3 3/4

B.) 4 5/9

C.) 8. 375 - I couldn't solve this one

D.) 12 3/11

E.) 5 7/20

F.) 29

Answer:

.42

Step-by-step explanation:

Since we are rounding to the 2, we will look at the digit after it

4 < 5 so we leave the 2 alone

.424 is rounded to .42

Answer:

0.42 is your answer

Step-by-step explanation:

The underlined number is 2. Look at the place value to the right. It is a 4. Because 4 is less than 5, round down.

0.424 rounded to the nearest hundredth place is 0.42

~

Answer:

Figure (i) and (iv)

Step-by-step explanation:

We need to find two figures that are similar to the 5 by 10 figure.

that is we need to find the figure that is similar to 5 X 10 figure.

Observe that in a figure m X n, the letter m represent the number of rows and the letter n represents the number of columns.

Observe that in the given figure 5 by 10, the number of rows is 5 and number of columns is 10, that is, the number of columns is double of that the number of rows.

so we need to find two such figures whose number of columns is double of the number of rows.

from the given figures, we can see that in the figure (i) the number of rows is 2 and number of columns is 4, which is double of number of rows. so it is similar to 5 by 10 figure.

And the figure in (iv), the number of rows is 4 and number of columns is 8. so here since the number of columns is double the number of rows, so it is similar to the figure 5 by 10.

Thus the two figures that are similar to 5 by 10 figure are given in (i) and (iv).

The two figures that share a similarity with the 5 by 10 figure based on the doubling relationship between columns and rows are represented by options (i) and (iv).

In the provided 5 by 10 figure, it's evident that the number of columns is twice the number of rows.

Therefore, our goal is to identify two other figures with the same relationship.

Upon examination of the given options, we can see that in figure (i), there are 2 rows and 4 columns, which maintains the same doubling relationship between columns and rows as the 5 by 10 figure.

Thus, figure (i) is similar to the 5 by 10 figure.

Similarly, in figure (iv), there are 4 rows and 8 columns, and this also maintains the doubling relationship between columns and rows. Therefore, figure (iv) is another figure similar to the 5 by 10 figure.

In summary, the two figures that share a similarity with the 5 by 10 figure based on the doubling relationship between columns and rows are represented by options (i) and (iv).

Learn more about similar figures here:

https://brainly.com/question/20368229

#SPJ3

Answer:

1 3/40

Step-by-step explanation:

4/20 + 7/8

We can simplify 4/20 by dividing the top and bottom by 4

1/5 + 7/8

We need to get a common denominator of 50

1/5 * 8/8 = 8/40

7/8 * 5/5 = 35/40

8/40 + 35/40

43/40

Changing this to a mixed number

1 3/40

Answer:

1 3/40

Step-by-step explanation:

Answer:   b - 8  is what i believe the answer is make sure tho im only in 6 th grade Step-by-step explanation:

balance = $360

2% of balance = 0.02*360 = 7.20

Since $10 is larger than $7.20, this means the min monthly payment is $10

Answer: 10

10b+6=7b-6.

3b=-12

b=-4.

*Note that you can just divide by 12 on both sides to simplify the equation.

Answer:

x = 4

Step-by-step explanation:

distribute both parenthesis on the left side of the equation

6 + 3x - 2x - 1 = 9

x + 5 = 9 ( subtract 5 from both sides )

x = 4

Assuming that we are solving in terms of n.

Start by distributing:

2(n + 5)

(2*n) + (5*2)

2n + 10 = -2

Subtract 10 to start toward isolating your variable:

2n = -12

Divide by two to finish solving:

n = -6

Answer:

n=-6

Step-by-step explanation:

2(n+5)=-2

distribute the 2 to the numbers in the parentheses:

2n+10=-2

Get the n factor alone, subtract 10 from both sides:

2n=-12

Now you just want the n alone so you are going to use the inverse operation on 2n to both sides: 2n/2=-12/2

n=-6

If you need any other help i would be glad to assist.

Answer:

1:1

Step-by-step explanation:

If you're square is a true square, than the height and base will be the same. If one is larger than the other, it's a rectangle.

If you slice a square diagonally, you still have the original height of the square.

Final answer:

To find the ratio of the triangle's height to the square's side, set the area of the triangle (1/2 × base × height) to be twice that of the square (side²). Simplify by equating base to side as they are the same length and solve for the height. The resulting ratio of the height of the triangle to the side of the square is 4:1.

Explanation:

The question involves finding the ratio of the height of a triangle to the side of a square where the area of the triangle is twice that of the square, and they have one side in common. The area of a square is given by side² (s²), and the area of a triangle is given by 1/2 × base × height (1/2 × b × h). To solve this, we set the triangle's area to be twice the square's area: 1/2 × b × h = 2 × s². Since the base of the triangle (b) is equal to the side of the square (s), they can be represented by the same variable. Hence, the equation simplifies to 1/2 × s × h = 2 × s². Canceling s from both sides leaves us with h = 4 × s. Therefore, the ratio of the height of the triangle to the side of the square is 4:1.

Answer:

correct choice is C

Step-by-step explanation:

Triangle KLM has three known lengths of sides:

The greatest angle is opposite to the greatest side. The greatest side is LM, then the greatest angle is angle K. The smallest angle is opposite to the smallest side. The smallest side is MK, then the smallest angle is angle L.

Therefore, the list the angles of the triangle in order from smallest to largest is ∠L, ∠M, ∠K.

Based on the angle and side relationship of the triangle given, the angles of the triangle from smallest to the largest would be: C. ∠L, ∠M, ∠K

Thus, based on the angle and side relationship of the triangle given, the angles of the triangle from smallest to the largest would be: C. ∠L, ∠M, ∠K

Learn more about triangle angles and sides relationship on:

https://brainly.com/question/10695554

The student that solved at a rate of 28 per minutes was Logan

Answer:

Logan

Answer:

Logan solved problems at a rate of 28 problems per minute.

Step-by-step explanation:

To find the number of problems per minute that a person solved, you will divide the number of problems that they solved by the number of minutes that they took.

Murray:

58 problems in 2 minutes,

58 / 2 = 29

He solved problems at a rate of 29 problems per minute.

Kris:

78 problems in 3 minutes,

78 / 3 = 26

He solved problems at a rate of 26 problems per minute.

Logan:

84 problems in 3 minutes,

84 / 3 = 28

He solved problems at a rate of 28 problems per minute.

Since you found that Logan solved problems at a rate of 28 problems per minute, Logan is the student that solved problems at a rate of 28 per minute.

The equation representing the total cost after buying x slices of pizza

is [tex]\( C(x) = E + x \times P \)[/tex].

Let's denote the entrance fee as E (in dollars) and the cost of each slice of pizza as P (also in dollars). Given the problem, we can write the following equations based on the given information:

After having 1 slice of pizza, the total cost is $6:

[tex]\(E + 1 \times P = 6\)[/tex]

After having 2 more slices of pizza (total 3 slices), the total cost is $10:

[tex]\(E + 3 \times P = 10\)[/tex]

To find the equation that represents the total cost (y) after buying x slices of pizza (let's call it C(x), we need to generalize the pattern observed in the given equations.

Notice that the entrance fee remains constant regardless of the number of slices of pizza bought. So, we can write the equation as:

[tex]\[ E + x \times P = C(x) \][/tex]

Substituting the values given in the problem:

[tex]\[ C(x) = E + x \times P \][/tex]

So, the equation representing the total cost after buying x slices of pizza

is [tex]\( C(x) = E + x \times P \)[/tex]. This equation gives the total cost (y) as a function of the number of slices of pizza bought (x).

Step-by-step explanation:

We are given the co-ordinates,

x : -2, -1, 0, 1, 2

y : 8, 5, 2, -1, -4

According to the graph, we see that this function represents a straight line.

The general form of the straight line is y = mx + c, where m is the slope and c is the y-intercept.

So, taking any two points we will find the equation of the straight line.

Consider, (0,2) and (1, -1). Now, slope is given by,

m = [tex]\frac{-1-2}{1-0}[/tex]

i.e. m = -3

Now, we will find the y-intercept of this equation using (0,2) and m = -3,

i.e. y = -3x + c

i.e. 2 = c

Hence, the equation of the straight line is y = -3x + 2.

ΔABC and ΔFEG are congruent. Therefore we have the equation:

7x - 19 = 2x + 11      add 19 to both sides

7x = 2x + 30     subtract 2x from both sides

5x = 30     divide both sides by 5

x = 6

AB = 24

AC = 2x + 11 → AC = 2(6) + 11 = 12 + 11 = 23

BC = 6x - 8 → BC = 6(6) - 8 = 36 - 8 = 28

The perimeter of ΔABC = 24 + 23 + 28 = 75

Answer:

$4,461.60

Step-by-step explanation:

Answer:

The answer would be 484

Step-by-step explanation:

Step 1: Multiply the length, width, and height.

11x11x12=1452

Step 2: Divide by 3

1452/3=484

Answer:

Samuel uses 1 11/12 cups of flour.

Step-by-step explanation:

Okay, this is assuming he uses the rest of the flour she didn't use.

The first step would be to find the Greatest Common Factor(GCF) of the fractions

2 1/4 and 1/3 have different denominators, but they both can divide into 12.

1/4 * 3/3 = 3/12

1/3 * 4/4 = 4/12

Now we can also convert 2 3/12 into an improper fraction to make it easier

2* 12/12 = 24/12

24/12+ 3/12 = 27/12

Here's the part were we subtract the two numbers.

27/12- 4/12 = 23/12

The last step is to simplify the fraction

23/12 = 1 11/12 cups

Answer:

[tex]10\dfrac{2}{7}\ miles[/tex]

Step-by-step explanation:

If Kevin walked his dog 1 2/7 miles and Sam walked his dog 7 times as far, then Sam walked his dog

[tex]1\dfrac{2}{7}\cdot 7=\dfrac{1\cdot 7+2}{7}\cdot 7=\dfrac{9}{7}\cdot \dfrac{7}{1}=9\ miles.[/tex]

Together they walked

[tex]1\dfrac{2}{7}+9=10\dfrac{2}{7}\ miles.[/tex]

simplify to get 1/3 times 17/4 which simplifies to 17/12 or 1 and 5/12.

Answer:

17/12

Step-by-step explanation:

1/3 x 4 1/4 change to

1/3 x 17/4

multiply the top and then the bottom : 17/12

Answer:

BC = 6.7 cm (rounded to nearest tenth)

Explanation:

Given: ABC is a right triangle with right angle C as shown below.

Side AB=18 cm and m∠A=22°.

Using Sine ratio in triangle ABC to find BC.

Sine ratio is defined as the ratio of the opposite side of a right triangle to the hypotenuse.

i.e

[tex]\sin A = \frac{Opposite side}{Hypotenuse side}[/tex]

Let BC = x (opposite side) and AB = 18 cm(Hypotenuse side)

then;

 [tex]\sin 22^{\circ} = \frac{x}{18}[/tex]

[tex]0.37460659341 = \frac{x}{18}[/tex]

Multiply both sides by 18 we get;

[tex]x = 0.37460659341 \times 18 = 6.74291868[/tex]

therefore, value of BC (nearest tenth place) is, 6.7 cm

Answer: 6.7cm

Step-by-step explanation: I took the K12 test.

[tex]\text{l-length}\\\text{w-width}\\lw-area\\108\ m^2-area\\d-diagonal\\\\\text{The equation}\ \#1:\\\\lw=108\to l=\dfrac{108}{w}\\\\\text{The equation}\ \#2:\\\\\text{Use the Pythagorean theorem:}\\\\l^2+w^2=d^2\to l^2+w^2=15^2\to l^2+w^2=225\\\\\text{Subtitute from}\ \#1\ \text{to}\ \#2:[/tex]

[tex]\left(\dfrac{108}{w}\right)^2+w^2=225\\\\\dfrac{11,664}{w^2}+w^2=225\qquad\text{multiply both sides by }\ w^2\neq0\\\\11,664+w^4=225w^2\qquad\text{subtract}\ 225w^2\ \text{from both sides}\\\\w^4-225w^2+11,664=0\qquad\text{substitute}\ t=w^2 > 0\\\\t^2-225t+11,664=0\\\\\text{use the quadratic formula or solve by factoring}.\\\\t^2-144t-81t+11,664=0\\\\t(t-144)-81(t-144)=0\\\\(t-144)(t-81)=0\iff t-144=0\ or\ t-81=0\\\\\boxed{t=144}\ or\ \boxed{t=81}\to w^2=144\ or\ w^2=81\\\\w=\sqrt{144}\ or\ w=\sqrt{81}\\\\\boxed{w=12\ m}\ or\ \boxed{w=9\ m}[/tex]

[tex]\text{Put the values of}\ w\ \text{to the equation}\ \#1:\\\\l=\dfrac{108}{12}\to\boxed{l=9\ m}\ or\ l=\dfrac{108}{9}\to\boxed{l=12}\\\\\text{The formula of a perimeter of a rectangle:}\\\\P=2l+2w\\\\P=2(12)+2(9)=24+18=42\\\\Answer:\ \text{The perimeter of the rectangle is equal 42 m}.[/tex]

The perimeter of the rectangle is 42m.

To find the perimeter of the rectangle, we need to know the lengths of its sides. From the given information, we know that the area of the rectangle is 108m^2 and its diagonal is 15m. We can use this information to find the lengths of the sides.

Let the length of the rectangle be 'l' and the width be 'w'.
Given, lw = 108 and sqrt(l^2 + w^2) = 15.
Squaring both sides of the second equation, we get l^2 + w^2 = 225.
Since lw = 108, we can solve the quadratic equation l^2 - 108l + 225 = 0 to find l. In this particular case, the quadratic factors as (l - 9)(l - 12) = 0, so l = 9 or l = 12.
Substituting the values of l in the equation lw = 108, we find w = 12 or w = 9.
Since the perimeter is the sum of all the sides, the perimeter of the rectangle is (2l + 2w) = (2 * 9 + 2 * 12) = 42m.