A certain radioactive isotope has a half life of 6 hours. The starting amount is 100 grams. Write an exponential function to model this scenario. How much of the isotope remains after 12 hours?

Remember that i² = -1. Using FOIL...

(2i-6)(3i-9) = 6i²-36i+54

Now simplify by subbing in -1 for i².

6(-1)-36i+54 = 48-36i

answer: 48-36i

The correct answer is 12

Hope this helped!

Jane has 4 number of 20 phones and 11 number of 15 phone cards.

It is given that 15 phone cards worth either $20 or $15

lets Jane has x number of 20 phones  and y number of 15 phone cards

Then by the problem we have

x+y=15....(1)

20x+15y=245....(2)

Solve one of the equations either for the variable x or y. Now, substitute the solution from step 1 to the other equation.

So by using substitution method we have,

from equation 1 we get

y=15-x

use this value in equation 2

[tex]20x+15(15-x)=245\\\\20x+225-15x=245\\\\5x+225=245[/tex]

[tex]5x=20\\x=4\\y=15-4\\y=11[/tex]

Therefore we get x=4 and y=11

Therefore,Jane has 4 number of 20 phones and 11 number of 15 phone cards.

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Answer:

Therefore the price of an foundation drink is $ 3.20(approx).

Step-by-step explanation:

Let the price of one fountain drink be x and one beg of popcorn be y.

The Clayton family bought 4 fountain drinks and 3 begs of popcorn and paid $22.50. The Hanks family bought 5 fountain drinks and 2 begs of popcorn and paid $23.75.

According to the problem,

4x+3y=22.50..............(1)

5x+2y=23.75..............(2)

Equation (1)×5 - Equation (2)×4

20x+15y-(20x+8y)=112.5-91

⇔20x + 15y -20 x-8y=21.5

⇔7y=21.5

⇔y = 3.07

putting the value of y in equation (1)

4x+3×3.07 =22.50

⇔4x=22.50 -9.21

⇔x=3.20

Therefore the price of an foundation drink is $ 3.20(approx).

Answer:

The correct slope is 3/4

Step-by-step explanation:

If we take (0,1) and (4,4) as our points, we find (4-1)/(4-0)=3/4

Hope this helped!

Answer:

80 percent

Step-by-step explanation:

Answer:

80 percent

Step-by-step explanation:

Answer:

the answer is 192

Step-by-step explanation:

because 4^3 is 64

and if you multiply it by 3 it will give you 192

your welcome have a nice day!

Answer: 192

Step-by-step explanation:

3*4³

Since there is an exponent we have to do that first

4³

4*4*4=64

Plug 64 in 4³'s place

3*64

=192

Answer:

6

4 squared= 16

16÷8=2

2×3=6

Answer: the answer is 6

Step-by-step explanation:

Answer:

6360

Step-by-step explanation:

the steps is just 120 times 53 which equals 6360. area= length multiplied by width

The area of a football field that is 120 yards long and 53 yards wide is 98,304,000 square inches.

To calculate the total area of a football field that is 120 yards long and 53 yards wide, you can use the formula for the area of a rectangle, which is length× width.

Step 1: Identify the dimensions of the field. The football field is 120 yards long and 53 yards wide

Step 2: Convert the dimensions into a consistent unit of measure, such as feet. Since there are 3 feet in a yard, multiply each dimension by 3.

Length in feet: 120 yards× 3 feet/yard = 360 feet

Width in feet: 53 yards × 3 feet/yard = 159 feet

Step 3: Calculate the area in feet. Area = Length × Width.

Area = 360 feet × 159 feet = 57,240 square feet

Step 4: To get the area in square inches, recognize that there are 12 inches in a foot, so the area in square inch\

es is:

Area in square inches = 57,240 ft²× (12 inches/foot)² = 98,304,000 square inches.

This calculation shows that the total area of the football field is approximately 98,304,000 square inches.

Answer:

4

Step-by-step explanation:

Cuzzzzz I know this stuff realy well

To solve this, you need to isolate/get x by itself in the equation:

[tex]\frac{9}{4}x-\frac{5}{6}=-\frac{13}{12} x[/tex]      Subtract 9/4x on both sides

[tex]-\frac{5}{6} =-\frac{13}{12} x-\frac{9}{4} x[/tex]   To combine fractions, the denominator has to be the same. They both have a least common denominator (LCD) of 12, so multiply -9/4x by 3/3 to make the denominator 12

[tex]-\frac{5}{6} =-\frac{13}{12}x -(\frac{3}{3})\frac{9}{4}x[/tex]

[tex]-\frac{5}{6} =-\frac{13}{12}x-\frac{27}{12} x[/tex]

[tex]-\frac{5}{6} =-\frac{40}{12} x[/tex]     Multiply the reciprocal of -40/12 to get x by itself, which is -12/40 [basically flipping the fraction or switching the numerator and the denominator]

[tex](-\frac{12}{40})-\frac{5}{6} =(-\frac{12}{40})-\frac{40}{12} x[/tex]  [two negative signs cancel each other out and become positive]

[tex]\frac{60}{240} =x[/tex]      Simplify the fraction

[tex]\frac{1}{4} =x[/tex]

Answer: 66

Step-by-step explanation:see attachment.

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Answer:

66

Step-by-step explanation:

Answer:

next time please ask a real question

Thanks

Step-by-step explanation:

The question appears to explore historical texts or languages, likely suited for college-level English or History studies, focusing on linguistics, manuscript studies, or medieval literature.

Given the fragments provided, it's challenging to decipher a coherent question or subject matter directly. However, the content suggests a possible exploration of historical texts or languages, particularly those relevant to English or linguistics studies at the college level.

Understanding or translating ancient or cryptic texts can be a significant part of higher education in English, where students might delve into Old English literature, manuscripts, or historical documents.

The various fragments hint at texts that might be from different periods or contexts, suggesting a study that spans a range of historical documents, potentially requiring translation or interpretation skills. Such a task would be well-suited for college-level English or History students focusing on linguistics, manuscript studies, or medieval literature.

Answer:

B

Step-by-step explanation:

Given

2x + 10 = 6 ( divide all 3 terms by 2 )

x + 5 = 3 ← equivalent equation

The equation which is equivalent to 2x + 10 = 6 from the given options is x + 5 = 3.

Given the equation in the question:

2x + 10 = 6

Options:

A) 2x = 4

B) x + 5 = 3

C) x + 10 = 3

D) 2x + 6 = 10

To find the equation that is equivalent to 2x + 10 = 6, we check each of the options.

For A) 2x = 4

2x + 10 = 6

2x = 6 - 10

2x = -4

Option A is wrong.

For B) x + 5 = 3

2x + 10 = 6

Divide each term by 2:

2x/2 + 10/2 = 6/2

x + 5 = 3

Option B is correct.

For C) x + 10 = 3

2x + 10 = 6

Divide each term by 2:

2x/2 + 10/2 = 6/2

x + 5 = 3

Option C is wrong.

For D) 2x + 6 = 10

2x + 10 = 6

Subtract 6 and 10 from both sides:

2x + 10 - 10 - 6 = 6 - 6 - 10

2x - 6 = -10

Option D is wrong.

Therefore, x + 5 = 3 is equivalent  to the equation.

Option B) x + 5 = 3 is the correct answer.

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Answer:

16

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

15/3=5

5*8=40

Jimmy Dean would make 40 sausages in 8 hours, based on a calculation using his rate of sausage making determined from the 15 sausages he made in 3 hours.

If Jimmy Dean made 15 sausages in 3 hours, we can calculate the rate at which he makes sausages and then use this rate to find out how many he would make in 8 hours. First, find the sausage-making rate by dividing the total sausages made by the total hours worked:

Rate = Total Sausages / Total Hours = 15 sausages / 3 hours = 5 sausages per hour

Next, we multiply this rate by the number of hours we are interested in, which is 8 hours:

Sausages in 8 hours = Rate * 8 hours = 5 sausages/hour * 8 hours = 40 sausages

Therefore, at the same rate, Jimmy Dean would make 40 sausages in 8 hours.

Answer:

a = -7/23.

Step-by-step explanation:

For them to lie on the same line the slope of the line joining the first 2 points must equal the slope of the line joining the second and third points.

so (3 - -5) / (-a+2 - 3) =   (2 - 3) /[(2a + 3) - (-a + 2)]

8 / (-a - 1) = -1 /  (3a + 1)    Cross multiply:

-1(-a - 1) = 8(3a + 1)

a + 1 = 24a + 8

-7 = 23a

a = -7/23.

To find the value of a, we can set the slopes between pairs of points equal to each other and solve for a. The value of a is 14/13.

To determine the value of a such that the points (3, -5), (-a+2,3), and (2a+3, 2) lie on the same line, we can use the slope formula. The slope between two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1). We'll calculate the slopes for the two pairs of points and set them equal to each other to find a.

Let's start by finding the slope between the first two points: (-a+2, 3) and (3, -5).

The slope is: m1 = (3 - (-5)) / (-a+2 - 3), which simplifies to m1 = 8 / (-a-1).

Next, let's find the slope between the second and third points: (2a+3, 2) and (3, -5).

The slope is: m2 = (2 - (-5)) / (2a+3 - 3), which simplifies to m2 = 7 / (2a).

Setting the two slopes equal to each other, we have: m1 = m2. Plugging in the expressions for m1 and m2, we get: 8 / (-a-1) = 7 / (2a). To solve for a, we'll cross-multiply and simplify the equation.

After simplifying, we find that a = 14/13.

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Answer:201525

Step-by-step explanation:

In permutations, the order of items matters. The word 'TOY' can be arranged in 6 different ways, calculated using the formula: n!/(n-r)!.

The student is asking a mathematical question related to permutations. Permutations refer to the arrangements of items where the order is important. In this instance, the student is interested in arranging the letters in the word 'TOY'. To calculate the number of ways to arrange these letters, we use the formula: n!/(n-r)!. Here, 'n' is the total number of items and 'r' is the number of items to choose and arrange.

Since 'TOY' has three distinct letters, then 'n' would be 3 and 'r' would also be 3. Applied to the formula, this becomes 3!/(3-3)!. Once you calculate this, you get 6. Therefore, there are 6 possible arrangements of the word 'TOY'.

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Answer:

2-x=1

2-1=1

Step-by-step explanation:

1 + 1 - 1 x 1 / 1.

Uses all 4 basic symbols.

Step-by-step explanation:

The length of BC 7 8 9 6 would probaly wouldnt be parallel but most likely be perpendicular if not intersecting

The formula to find the volume of a cylinder is V = hπr², where h is the height of the cylinder and r is the radius of its base.

To find V, the volume of a cylinder in cubic inches, we can use the formula V = Ah, where A represents the cross-sectional area of the cylinder and h represents the height or depth of the cylinder. To find the cross-sectional area for a cylinder, the formula A = πr² can be used, where r is the radius of the cylinder's base. Substituting value of A in volume's formula will give V = hπr², which is commonly used formula to find the volume of a cylinder.

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To find the volume of a cylinder in cubic inches, use the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height of the cylinder.

The equation for finding the volume V of a cylinder in cubic inches can be derived from the basic principle that the volume of a shape is equal to the area of its base multiplied by its height. For a cylinder, the base is a circle, and the area of a circle is given by the formula πr², where r is the radius of the circle.

Therefore, the volume of the cylinder is the area of its base times its height, which can be written as V = πr²h, where h is the height of the cylinder. By using this formula, you can calculate the volume of a cylinder if you know the radius of its base and its height.

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The coordinates of where diagonals AC and BD intersect at O(2,7).

Step-by-step explanation:

We are given coordinates as A(-1,10) and C(5,4).And we know that the diagonals of parallelogram always bisect each other.

Let us consider O is the intersection point among the diagonals AC and BD. So, the point O bisects the line AC into two equal parts, and also it is the mid-point of AC.

We can find point O using the midpoint formula as,

O (x,y) = ([tex]\frac{(x1+x2)}{2}[/tex] , [tex]\frac{(y1+y2)}{2}[/tex])

         = ([tex]\frac{(-1+5)}{2}[/tex] , [tex]\frac{(10+4)}{2}[/tex])

      = ([tex]\frac{4}{2}[/tex], [tex]\frac{14}{2}[/tex])

     = (2,7)

So Diagonals AC and BD intersects at the point O (2,7).

Basically, we are trying to find the equation that goes through the two points shown in the table. The points are: (5,30) and (10,55). The equation of a line is y=my+b where m is the slope and b is the y intercept. To find slope look for the change in y over the change in x.

Slope = (55-30)/(10-5)=5

We can stop here because the only answer choice with a slope of five is choice A.

Answer: A

Answer:

530.66 cm^2

Step-by-step explanation:

[tex]area \: of \: circle = \pi{r}^{2} [/tex]

Using the above formula,

Area of plate= 3.14(13)^2 = 530.66 cm^2

(I replaced pi with 3.14 since the question said to use 3.14 for pi)

Answer:

the area of a circle

[tex] \pi{r}^{2} [/tex]π= 3.14

r=13

Final answer:

To determine the cost of streamers and party hats, a system of linear equations is created and solved. The streamers cost $2.50 each, and the party hats cost $1.50 each after solving the system by the elimination method.

Explanation:

To find the cost of streamers and party hats, we need to set up a system of linear equations based on the information provided. Let's denote the price of one roll of streamers as s and the price of one party hat as h.

From the first purchase:

3s + 15h = $30

From the second purchase:

2s + 4h = $11

Now, we'll solve the system using substitution or elimination method. For simplicity, we'll use the elimination method.

First, let's multiply the second equation by 3.75 to match the number of hats in the first equation:

7.5s + 15h = $41.25

Subtract the first equation from this new equation:

7.5s + 15h - (3s + 15h) = $41.25 - $30

4.5s = $11.25

s = $2.50

With the cost of a streamer found, substitute s = $2.50 into the second original equation:

2($2.50) + 4h = $11

$5 + 4h = $11

4h = $6  

h = $1.50

Therefore, the cost of one roll of streamers is $2.50 and the cost of one party hat is $1.50.

Final answer:To determine the cost of streamers and party hats, a system of linear equations is created and solved. The streamers cost $2.50 each, and the party hats cost $1.50 each after solving the system by the elimination method.Explanation:To find the cost of streamers and party hats, we need to set up a system of linear equations based on the information provided. Let's denote the price of one roll of streamers as s and the price of one party hat as h.From the first purchase:3s + 15h = $30From the second purchase: 2s + 4h = $11Now, we'll solve the system using substitution or elimination method. For simplicity, we'll use the elimination method.First, let's multiply the second equation by 3.75 to match the number of hats in the first equation:7.5s + 15h = $41.25Subtract the first equation from this new equation:7.5s + 15h - (3s + 15h) = $41.25 - $304.5s = $11.25s = $2.50With the cost of a streamer found, substitute s = $2.50 into the second original equation:2($2.50) + 4h = $11$5 + 4h = $114h = $6  h = $1.50Therefore, the cost of one roll of streamers is $2.50 and the cost of one party hat is $1.

Answer:

[tex]x^{4} -3x+2x^{3} y[/tex]

Step-by-step explanation:

use photo math and it will help with any math problem

do exponents first!

2x^5 = 32x

-6x^2 = -36x

4x^4y= 256xy

32x-36x+256xy/2x

Compare like terms, 32x-36x = -4x^2

-4x^2+256xy/2x

do, -4x^2=-16

-16+256xy/2x

Thats all, hope this is helpful!!!!!!!(:

Answer:

The co-ordinates of A' is

A)  [tex](-2,\frac{14}{3})[/tex]

Step-by-step explanation:

Given point:

(-3,7)

The point is dilated with a scale factor  [tex]r=\frac{2}{3}[/tex]  with the center of dilation at the origin.

To find the co-ordinates of the dilated point A'.

Solution:

Any  point dilated with the center of dilation at the origin with a scalar factor [tex]k[/tex] is given by:

[tex]D(x,y)\rightarrow D(kx,ky)[/tex]

Thus, the point (3,-7) dilated with a scale factor  [tex]r=\frac{2}{3}[/tex]  with the center of dilation at the origin  is given as :

[tex]A(-3,7)\rightarrow A'(\frac{2}{3}\cdot -3,\frac{2}{3}\cdot 7)[/tex]

[tex]A(-3,7)\rightarrow A'(-2,\frac{14}{3})[/tex]

Thus, the co-ordinates of A' is [tex](-2,\frac{14}{3})[/tex].

-p - 4p > -10

-5p > -10

p < 2

Hope this helps! ;)

Answer:

The correct answer is: [tex]4\frac{3}{5}[/tex]

Step-by-step explanation:

According to the rule of BODMAS, division is done before addition.

So, in a + b ÷ c, we will first calculate,  b ÷ c

Given b =  [tex]2\frac{2}{5}[/tex] = [tex]\frac{12}{5}[/tex] , c = [tex]\frac{3}{4}[/tex] .

So, [tex]\frac{b}{c}[/tex] = [tex]\frac{12}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex]

So, [tex]\frac{b}{c} = \frac{12}{5} \times\frac{4}{3}[/tex] , as the numerator and denominator gets reversed as division is changed to multiplication.

So, [tex]\frac{b}{c} = \frac{16}{5}[/tex] .

Next the value of a to  [tex]\frac{b}{c}[/tex]  , where, [tex]a = 1\frac{2}{5} = \frac{7}{5}[/tex], we get,

[tex]\frac{7}{5} +\frac{16}{5} = \frac{23}{5} = 4\frac{3}{5}[/tex].

Answer:

The vertex is (-4, -52), and it represents the minimum for the function.

Step-by-step explanation:

Cost of item of $ 310 including the sales tax is $358.05.

Convert the percentage rate of sales tax to a decimal by dividing the percentage by 100.

A 15.50% sales tax rate becomes 0.155 when converted to a decimal.

After performing the multiplication, you will get the amount of sales tax that needs to be added to the item's price. So, $310  x 0.155 = $48.05.

Therefore, the total cost of the item after sales tax would be the original price plus the amount of sales tax, which is $310 + $48.05 = $358.05.