The area of a rectangle is 4y + 10.

A. Represent the area of the rectangle in factored form.
B. Use the factored form to give one possible set of dimensions for this rectangle.

Answer:

The sum of the first seven terms of this geometric series is - 32,766

Step-by-step explanation:

Let's find out the result of the sum of a 7-term geometric series, which first term is -6, the last term is -24576, and the common ratio is 4

1st term = - 6

2nd term = - 6 * 4 = - 24

3rd term = - 24 * 4 = - 96

4th term = - 96 * 4 = - 384

5th term = - 384 * 4 = - 1,536

6th term = - 1,536 * 4 = - 6,144

7th term = - 6,144 * 4 = - 24,576

Sum = - 24,576 - 6,144 - 1,536 - 384 - 96 - 24 - 6

Sum = - 32,766

We can summarize these operations of the geometric series, this way:

Sₙ= a₁ * (1 − rⁿ)/1 − r, where:

n = Number of terms of the series

a₁ = First term of the series

r = Common ratio

Replacing with the real values, we have:

S₇= -6 * (1 −4⁷)/1 - 4

S₇= -6 * (1 − 16,384)/ -3

S₇= -6 * ( − 16,383)/ -3

S₇= 98,298/ -3

S₇= - 32,766

The sum of the first seven terms of this geometric series is - 32,766

Let X = the number of hours the server works.

The equation for the amount Nick spends is 15x + 47

The next job pays 14x + 54

Set the equations to equal and solve for x:

15x + 47 = 14x +54

Subtract 14x from both sides:

X + 47 = 54

Subtract 47 from both sides:

X = 7

Now replace x with 7 in the second equation:

14x + 54 = 14(7) + 54 = 98 +54 = 152

The job would pay $152 and be 7 hours long.

Answer:

y=-2/3x+20/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-6)/(4-1)

m=-2/3

y-y1=m(x-x1)

y-6=-2/3(x-1)

y=-2/3x+2/3+6

y=-2/3x+2/3+18/3

y=-2/3x+20/3

The equivalent expressions to [tex]5^2/5^8[/tex] are [tex]5^(^-^6^)[/tex] and [tex]\frac{1}{5^6}[/tex]

The expression[tex]5^2/5^8[/tex]can be simplified using the properties of exponents. When you have the same base raised to different exponents and they are being divided, you can subtract the exponents.

So, [tex]5^2/5^8 = 5^(^2^-^8^)[/tex] = 5^(-6).

Therefore, the equivalent expressions are [tex]5^(^-^6^)[/tex] and [tex]\frac{1}{5^6}[/tex]

In mathematics, equivalent expressions are algebraic expressions that have the same value for all possible values of the variables involved

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The expression 5^2/5^8 simplifies to 5^-6 due to the laws of exponents that allow subtracting of exponents when dividing like bases.

The expression 5^2/5^8 can be simplified by understanding the laws of exponents. When dividing like bases, you subtract the exponent in the denominator from the exponent in the numerator. By applying this law, the expression 5^2/5^8 simplifies to 5^(2-8) which equals 5^-6.

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Final answer:

To find the length of one leg of an isosceles right triangle with a hypotenuse of 10 inches, we use the Pythagorean theorem, which gives us a leg length of 5√2, or approximately 7.071 inches. The correct answer choice is StartFraction 10 Over StartRoot 2 EndRoot EndFraction.

Explanation:

The student is asking about the length of one leg of an isosceles right triangle where the hypotenuse measures 10 inches long. To find the length of one leg of this triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b).

Since the triangle is isosceles, the lengths of the legs are equal, so we have: a = b. The theorem can be expressed as a² + b² = c², which simplifies to 2a² = c² because a = b. We know the hypotenuse (c) is 10 inches, so the equation is 2a² = 10².

Let's find a:

2a² = 10²

2a² = 100

a² = 50

a = √50

a = √(25×2)

a = √25 × √2

a = 5√2

Therefore, the length of one leg of the triangle is 5√2, which is approximately 7.071 inches. So, the correct answer is StartFraction 10 Over StartRoot 2 EndRoot EndFraction.

Option A

Commutative property of addition  states that order of the addends does not affect the sum

Solution:

The commutative property of addition tells us that it does not matter which number we add first , We will still get the same answer if we add them backwards

This property is represented as:

For two numbers a, b:

a + b = b + a

In case of three numbers a, b, c:

a + b + c = c + b + a = b + a + c

So no matter how the addends are placed, the result of the operation (sum) remains the same

For example:

When we are adding 4 and 5

4 + 5 = 9 or 5 + 4 = 9 both the ways the result remains same

Thus Commutative Property of Addition states that changing the order of addends does not change the sum

Answer:

Commutative property of addition

Step-by-step explanation:

According to the commutative property of addition, changing the order of the numbers we are adding, does not change the sum.

Good luck, your day will be awesome!

The question is missing the table. So, it is attached below.

Answer:

The function is not linear. The student didn't evaluate the rate of change for the given points on the function.

Step-by-step explanation:

Given:

From the table, the set of points of the function are:

(-1, -5), (0, 0), (2,5), (3, 10), and (4, 15)

A function is said to be linear if the rate of change of the function is always a constant.

Rate of change for any two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, the rate of change for the points (-1, -5) and (0, 0) is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{0-(-5)}{0-(-1)}\\\\m=\frac{5}{1}=5[/tex]

Now, the rate of change for the points (0, 0) and (2, 5) is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{5-0}{2-0}\\\\m=\frac{5}{2}=2.5[/tex]

Hence, we can observe that, the rate of change is different for the given points. Hence, it is not a linear function.

Therefore, the student didn't evaluate the rate of change for the given points on the function.

A function is linear if the difference between y-values is constant when the difference between the corresponding x-values is constant. This is known as a constant rate of change and can be identified in a table of values for an x-y relationship. However, without the actual table's values, it's impossible to confirm its linearity.

In mathematics, a function is said to be linear if its graph forms a straight line. When analyzing a table of values, a function is linear if the difference between y-values is constant when the difference between the corresponding x-values is also constant. This is often called a constant rate of change.

For example, let's say we have an x-y table: for every 1 unit increase in x, if y increases by 2 units consistently, then the function represented by that table is linear. It directly satisfies the general definition of a linear function, y = mx + b, where 'm' is the slope (rate of change) and 'b' is the y-intercept.

However, without the actual values from the student's table, it's impossible to confirm whether the function is indeed linear. Always remember to check for a constant rate of change when reasoning about linearity.

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To calculate the probability of a student scoring 75% or above, count how many scores are 75 or higher, and then divide by the total number of scores. In this case, the probability is 6 out of 15, or 0.4.

The question asks about the probability that a student picked at random scored 75% or above based on a list of exam scores.

To find this probability, one must count the number of scores that are 75% or higher and divide by the total number of scores.

Out of the provided scores (61, 74, 60, 70, 83, 90, 90, 80, 100, 102, 28, 75, 98, 21, 49), we see that there are 6 scores that are 75 or above (83, 90, 90, 80, 100, 102, 98, 75).

Since there are 15 scores in total, the probability is calculated as -

= 6/15

= 0.4.

Answer:

12

Step-by-step explanation:

B is equal to -2, and D is equal to -6. A negative times a negative is a positive, and 2 x 6 = 12 (aka 6+6)

Answer:

A) -8

Step-by-step explanation:

-5+(-3)=-5-3=-8

Answer:

-85

Step-by-step explanation:

Answer:

-85

Step-by-step explanation:

Answer:

Step-by-step explanation:

The required simplified value of the a is given as a = 31.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
for the expression
12x² + ax + 20 = 0   (because this expression has factors)
The above expression has a factor (3x + 4)
3x + 4 = 0
x = -4 / 3
above the value of x is one of the zeroes for the given expression, so when we put it in the given expression the expression terminates to zero,
so,
f(-4/3) = 0
12(-4/3)² + (-4/3)a + 20 = 0
12×16/9 - 4a/3 + 20 = 0
-4a/3 = -20 - 64 / 3
-4a/3 = [-60 - 64] / 3
-4a = -124
a = 31

Thus, the required simplified value of the a is given as a = 31.

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If Sarah keeps all of the fish and they all live, then there are 24  fishes will Sarah have after 3 months

Multiplication is a method of finding the product of two or more numbers

Given,

Sarah bought 3 fish.

Every month the number of fish she has doubles.

After m months, she will have F fish, where F = 3 x 2m

If Sarah keeps all of the fish and they all live, We need to find number of fishes will Sarah have after 3 months

F = 3× 2m

M represents the number of months.

In start month 3 fishes

In first month the fishes are 6

In second month the fishes are 12.

In third month the fishes are 24.

Hence, If Sarah keeps all of the fish and they all live, then there are 24  fishes will Sarah have after 3 months

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Answer:

Account C will give George at least a 4% annual yield.

Step-by-step explanation:

This problem can be solved by using simple maths formula given below

Year rate = (1+i)^n-1

where i = compounding rate and n = interval period

Now checking annual rate for each option using above formula

Account A)

Yr = 3.8% ( n= 12 and i= 3.75/12)

Account B)

Yr = 3.9 % ( n= 4 and i= 3.85/4)

Account C)

Yr = 4 % ( n= 365 and i= 3.95/365)

Answer:

No, it's not a counterexample, because 48 is a multiple of 8

Step-by-step explanation:

I think like 4 x 3 + 8 x 2 = 28 is a counterexample, because 28 is not a multiple of 8.

Perl's conjecture that the sum of a multiple of 4 and a multiple of 8 must be a multiple of 8 is incorrect. In fact, the sum would definitely be a multiple of 4 but not necessarily a multiple of 8, since the sum of integers multiplied by 4 does not guarantee that it's a multiple of 8.

The subject of this question is Mathematics, specifically dealing with number theory and the properties of multiples and factorization. Perl's conjecture is that the sum of a multiple of 4 and a multiple of 8 must be a multiple of 8. We can examine this by understanding how multiples work.

A multiple of 4 can also be considered as 4n, where n is an integer. Similarly, a multiple of 8 is 8m, where m is integer. If we add both, we get 4n+8m. Now, as per distributive property of multiplication over addition, the expression becomes 4n+4(2m), which can be further simplified as 4(n+2m).

We can now see that the sum is actually 4 times the sum of some integer, so it must indeed be a multiple of 4. However, since it's not necessarily the case that 'n+2m' itself is a multiple of 2, we cannot say that the overall sum is guaranteed to be multiple of 8.

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Answer:

5.4

Step-by-step explanation:

1350/250=5.4

Final answer:

A truck with a maximum capacity of 1350 pounds can carry 5 full 250-pound loads of dirt, as partial loads cannot be accommodated.

Explanation:

How many 250-pound loads of dirt can a truck carry?

To determine how many 250-pound loads of dirt a truck can carry if its maximum capacity is 1350 pounds, you need to divide the truck's maximum capacity by the weight of one load of dirt:

1350 pounds ÷ 250 pounds per load = 5.4 loads

Since the truck cannot carry a fraction of a load, it can carry a maximum of 5 full 250-pound loads of dirt before it reaches its weight limit.

Step-by-step explanation:

the answer is B: y = 20x on edge.

The income for selling x purses is given by the linear equation:

y = $20*x

A general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

In this case, we know that each purse is sold by $20. So, if the company sells x purses, the income will be x times $20.

So the linear equation is:

y = $20*x

Then the correct option is B

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Answer:

x = 5

Step-by-step explanation:

Move the variable to the left side and change it's sign then move constant to the right side and change its sign you will get -3x+x = -8-2 collect like terms  then calculate the difference you will get -2x = -10 Divide both sides of the equations by -2 and you will get x =5

Answer:

The correct answer is D. π

Step-by-step explanation:

Let's recall that rational numbers are those that can be written as a ratio or fraction of two integers. Quite the opposite, irrational numbers can't be written as a ratio or fraction of two integers.

Upon saying that we have:

A. A fraction with numerator negative 15 and denominator 4 is a rational number because we can represent it: -15/4

B. A fraction with numerator negative 7 and denominator 9 is a rational number because we can represent it: -7/9

C. √4 is a rational number because we can represent it: 2 or 2/1

D. π is the most known irrational number because we can't represent it as a ratio or fraction: 3.14159265358979....and more can't be written as a ratio or fraction.

The correct answer is D. π

Answer:

15i+15

Step-by-step explanation:

(6+3i)(3+i)

18+9i+6i+3i^2

18+15i+3(-1)

18+15i-3

15i+15

After multiplyinh complex numbers (6+3i)(3+i), the final answer will be 15+15i.

To multiply complex numbers, we can use the distributive property.

First, distribute 6 to both terms of (3+i), giving us 18+6i.

Then, distribute 3i to both terms of (3+i), resulting in 9i+3i².

We can simplify 3i² by using the fact that i²=-1, so 3i²=-3.

Putting it all together, we have (6+3i)(3+i)

= 18+6i+9i-3

= 15+15i.

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Answer:

[tex]z^{5}[/tex] =  - 12 + 316 i

Step-by-step explanation:

Given that -

z = 3 + i

[tex]z^{2}[/tex] = [tex]( 3 + i )^{2}[/tex]

[tex]z^{2}[/tex] = 9 + [tex]i^{2}[/tex] + 6 i

[tex]z^{2}[/tex] = 9 - 1 + 6 i

[tex]z^{2}[/tex] = 8 + 6 i

[tex]z^{3}[/tex] = [tex]z^{2}[/tex] × z

[tex]z^{3}[/tex] = ( 8 + 6 i ) × ( 3 + i )

[tex]z^{3}[/tex] = 24 + 8 i + 18 i + 6 i²

[tex]z^{3}[/tex] = 24 + 26 i - 6

[tex]z^{3}[/tex] = 18 + 26 i

[tex]z^{5}[/tex] = [tex]z^{2}[/tex] × [tex]z^{3}[/tex]

[tex]z^{5}[/tex] = ( 8 + 6 i ) × ( 18 + 26 i )

[tex]z^{5}[/tex] = 144 + 208 i + 108 i + 156 i²

[tex]z^{5}[/tex] = 144 + 316 i -156

[tex]z^{5}[/tex] =  - 12 + 316 i

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1200 x 0.85 = 1020

The sale price is $1020

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Answer:

4/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-20-(-8))/(-12-(-3))

m=(-20+8)/(-12+3)

m=-12/-9

m=12/9

simplify

m=4/3

Answer:

(5,-1)

(10,2)

Step-by-step explanation:

The given equation is 3x - 5y = 20 ........ (1)

Now, putting x = 5, in equation (1) we get,

15 - 5y = 20

⇒ 5y = - 5

⇒ y = - 1

So, the ordered pair (5,-1) is a solution of the equation (1).

Now, putting y = 2, in equation (1) we get,

3x - 10 = 20

⇒ 3x = 30

⇒ x = 10

So, the ordered pair (10,2) is a solution of the equation (1). (Answer)

Answer:

Percent increase: 20%

Step-by-step explanation:

1. 4.2-3.5  x 100=20%

     3.5

2. Percent increase: 20%

The percentage increase in the price of a hamburger from $3.50 to $4.20 is a 20% increase. This is calculated by dividing the increase in price by the original price and then multiplying by 100.

To calculate the percentage increase in the price of a hamburger that went from $3.50 to $4.20, we first find the absolute increase by subtracting the original price from the new price.

The absolute increase is $4.20 - $3.50 = $0.70.

To find the percentage increase, we then divide the absolute increase by the original price, which gives us $0.70 / $3.50 = 0.2.

Finally, to express this as a percentage, we multiply by 100, resulting in a 20% increase in the price of the hamburger.

Answer:

-8

Step-by-step explanation:

(-8+6) * -4

-2 * -4= 8

Final answer:

The unknown number is -8, found by setting up the equation -4(x + 6) = 8 and solving for x.

Explanation:

To solve the problem stated, we need to set up an equation based on the provided information. The statement 'the sum of a number and six is multiplied by negative four' can be written as an algebraic expression: -4(x + 6), where 'x' is the unknown number we are trying to find.

We are told that this expression equals eight, so the equation we need to solve is -4(x + 6) = 8.

To solve for x, first we simplify the equation:

-4x - 24 = 8

Then we add 24 to both sides:

-4x = 8 + 24

-4x = 32

Now we divide both sides by -4 to solve for x:

x = 32 ÷ -4

x = -8

Therefore, the number we are looking for is -8.

Answer:

(x - 5)² + (y - 7)² = 169

Step-by-step explanation:

The standard form of the equation of a circle is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (5, 7), thus

(x - 5)² + (y - 7)² = r²

The distance from the centre to a point on the circle is the radius

Calculate the radius using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (5, 7) and (x₂, y₂ ) = (10, 19)

r = [tex]\sqrt{(10-5)^2+(19-7)^2}[/tex]

  = [tex]\sqrt{5^2+12^2}[/tex]

  = [tex]\sqrt{25+144}[/tex] = [tex]\sqrt{169}[/tex] = 13, hence

(x - 5)² + (y - 7)² = 169 ← equation of circle

Step-by-step explanation:

The answer will be 380 inches as of what I have done

To find the total number of people surveyed, you divide the number of people who chose chocolate (51) by the percentage that represents (0.68), resulting in 75 people surveyed.

The question posed involves determining the total number of people surveyed based on the percentage who favored chocolate ice cream. Since 68% of the people surveyed stated that chocolate was their favorite flavor, and it is known that 51 people chose chocolate, we can set up a proportion to find the total number of people surveyed. The proportion to find the total number of respondents (let's call it x) is as follows:

0.68 x = 51

To solve for x, you would divide both sides of the equation by 0.68, which gives you:

x = 51 / 0.68

x = 75 people

Therefore, the total number of people surveyed was 75.

Answer:

1][tex]measure\ angle\ DCA=measure\ angle\ CAB=18\ degree[/tex]

2][tex]measure\ angle\ A+measure\ angle\ B+measure\ angle\ C=180\ degree[/tex]

3][tex]18\ degree+3x+3x=180\ degree[/tex]

4][tex]x=27[/tex]

Step-by-step explanation:

Given:-measure angle DCA = 18 degree

line AB II line DC

Solution:-

1] measure angle DCA and measure angle CAB are interior  alternate angles and interior alternate angles are equal.

[tex]measure\ angle\ DCA=measure\ angle\ CAB=18\ degree[/tex]------------------ (Equation 1)

Therefore the equation for statement number 1 is [tex]measure\ angle\ DCA=measure\ angle\ CAB=18\ degree[/tex]

2]Sum of interior angles of triangle is equal to 180 degree.

In Triangle ABC,

measure angle A+measure angle B+measure angle C=180 degree

Therefore the equation for statement number 2 is measure angle A+measure angle B+measure angle C=180 degree

3] In Triangle ABC,

[tex]measure\ angle\ B=3x---------------(Given)[/tex]

[tex]measure\ angle\ C=3x---------------(Given)[/tex]

[tex]measure\ angle\ A=18\ degree---------------(from\ equation\ [tex]measure\ angle\ A+measure\ angle\ B+measure\ angle\ C=180\ degree[/tex]

Now substituting the value of angles we get,

[tex]18\ degree+3x+3x=180\ degree-------------(Equation\ 2)[/tex]

Therefore the equation for statement number [tex]3\ is\ 18\ degree+3x+3x=180\ degree[/tex]

4] After solving the equation 2 we get,

[tex]18+3x+3x=180[/tex]

[tex]6x=180-18[/tex]

[tex]6x=162[/tex]

[tex]x=27\ degree[/tex]

Therefore value of [tex]x=27\ degree[/tex]