A round cake has a diameter of 30 cm. Angela places the cake on a circular cake board with a diameter 5 cm longer than that of the cake. What is the circumference of the cake board? Give your answer in terms of pi π

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

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

We have the points (-1, -10) and (1, 0). Substitute:

[tex]m=\dfrac{0-(-10)}{1-(-1)}=\dfrac{10}{1+1}=\dfrac{10}{2}=5[/tex]

Put the coordinates of the point (1, 0) to the equation of line:

[tex]0=5(1)+b[/tex]

[tex]0=5+b[/tex]      subtract 5 from both sides

[tex]-5=b\to b=-5[/tex]

For the line's equation, calculate the slope from the provided points to get 5, and use one point to find the y-intercept, which is -5. The line's equation is y = 5x - 5.

To find the equation of a line in slope-intercept form, which is y = mx + b.

We need to determine the slope (m) and the y-intercept (b).

Given two points on the line, (-1, -10) and (1, 0), we can calculate the slope using the formula

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}\\ m = \frac{0-(-10)}{1-(-1)}\\ m = 5[/tex]

Next, we use one of the points to find the y-intercept, b. If we use the point (1, 0), we can substitute the slope and the coordinates into the slope-intercept equation:

0 = (5)(1) + b, which simplifies to b = -5.

Thus, the equation of the line is y = 5x - 5.

I can't exactly SHOW you where to put the numbers, but I can teach you the process of how you'd do it.

First off, label your number line from 0-15, as it is the simplest. (You'd be counting by 1 per each line). Then, follow this process:

1) Look at the first digit of your value. Place your number according to your first digit. (So, you'd put 0.365 at the 0 line and 3.521 at the 3 line)

2) Look at the second digit of your value. Imagine that between the two main lines (0-1 and 3-4) that there is 10 smaller lines. Then, you can place your number according to your second digit. (So, you'd put 0.365 at the 0.3 line and 3.521 at the 3.5 line).

3) Look at the third digit of your value. Imagine that between the two smaller lines (0.3-0.4 and 3.5-3.6) that there is 10 smaller lines. Then, you can place your number according to your third digit. (So, you'd put 0.365 at the 0.36 line and 3.521 at the 3.52 line).

4) Look at the fourth digit of your value. Imagine that between the two even smaller lines (0.36-0.37 and 3.52-3.53) that there is 10 smaller lines. Then, you can place your number according to your fourth digit. (So you'd place 0.365 at the 0.365 line and 3.521 at the 3.521 line)

(x + y)^0 = 1

(x + y)^1 = x + y

(x + y)^2 = x^2 + 2x + y

(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3

(x + y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

.

.

.

1

1 + 1

1 + 2 + 1

1 + 3 + 3 + 1

1 4 6 4 1

.

.

.

I hope I helped you.

Odd exponents ensure at least one real root for polynomials, while even exponents may result in no real roots. Multiplying even functions together, or odd functions together, results in an even function. These properties have applications in areas like quantum mechanics.

Odd and even exponents greatly influence the behavior of polynomial functions. For polynomials with odd exponents, they will always have at least one real root. This is because polynomials of odd degree tend to positive infinity as x goes to positive infinity and negative infinity as x goes to negative infinity, therefore they must cross the x-axis at some point. A polynomial like x³ - x + 17 exemplifies this behavior.

On the other hand, polynomials with even exponents may not have any real roots, as they never need to cross the x-axis; for example, x² + 1 is always positive for any real value of x and thus has no real roots.

Even functions and odd functions also display characteristic properties when multiplied. An even function times an even function yields an even function (e.g., x² e⁻²), and an odd function times another odd function results in an even function (e.g., x sin x).

In contrast, an odd function times an even function gives an odd function. These properties are particularly useful in fields such as quantum mechanics where symmetry plays an important role in solving equations like Schrödinger's equation.

Answer:

A. 3 3/4

B. 4 5/9

C. 8 3/8

D. 12 3/11

E. 5 7/20

F. 2 145/174

Hope That Helps!

Answer:

the answer might be 336 sorry if i am not right

Step-by-step explanation:

Answer:

I think the answer is approximately 5 packs of pencils.Hooe this helps :)

Step-by-step explanation: what I did was I multiplied 3 and 28 then divide that number by 12 and rounded my answer up.

A. Negative Association

C. Strong Association

E. Linear

Answer:

1. Negative Correlation

3. Strong Correlation

5. Linear

Step-by-step explanation:

We have been given a scatter-plot. We are asked to choose the characteristics of the given scatter-plot.

Upon looking at our given scatter-plot, we can see that as the values of x are increasing values of y are decreasing.

We know that the relationship between two variables in which one variable increases as the other decreases is known as negative correlation. Therefore, the given scatter-plot represents negative correlation and 1st option is a correct choice.

We can also see that the slope of the line connecting all data points is approximately [tex]-1[/tex], which represents a strong negative correlation, therefore, 3rd option is correct as well.

If we draw a line on our given scatter-plot, it will connect all the data points. Therefore, the given scatter-plot has a linear correlation and 5th option is correct as well.

Answer:

[tex]1000 {e}^{.06 \times 5} = 1349.86[/tex]

The correct answer is B.

After 5 years with continuous compounding at 6%, $1,000 will grow to approximately $1,349.86.

To find the future value of an account with continuous compounding, we use the formula:

A = Pe^(rt)

where:

In your case:

P = $1,000, r = 6% (or 0.06 in decimal form), and t = 5 years.

So plug these values into the formula:

A = $1,000 * e^(0.06*5)

After you calculate this, you'll find that the value of A is approximately $1,349.86. Therefore, after 5 years, your balance would be $1,349.86 so the answer is (b).

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Answer:

is it 2/21 i hope im right cuz i just looked it up

Step-by-step explanation:

To find the sum, convert the fractions to have the same denominator. Add the whole numbers and the fractions separately. The sum of 12 1/4 and 5 5/6 reduced to lowest terms is 17 13/12.

To find the sum of 12 1/4 and 5 5/6, we need to convert the fractions to have the same denominator. The common denominator for 4 and 6 is 12. So, we can rewrite 12 1/4 as 12 3/12 and 5 5/6 as 5 10/12. Now we can add the whole numbers, 12 and 5, which gives us 17. Then, we add the fractions, 3/12 and 10/12, which equals 13/12. Therefore, the sum of 12 1/4 and 5 5/6 reduced to lowest terms is 17 13/12.

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I honestly don't know or I would have replied. Sorry :(

Answer:  y = -2

========================================

Explanation:

Find the slope of line m using the slope formula

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

slopeM = (2-8)/(-1-6)

slopeM = -6/(-7)

slopeM = 6/7

The slope of line m is 6/7. The perpendicular slope is -7/6. We flip the fraction (aka reciprocal) and flip the sign (from positive to negative). The phrase "flip the fraction and flip the sign" is a handy way to think of "negative reciprocal", at least in my opinion. Note how the two slopes 6/7 and -7/6 multiply to -1 to prove they are perpendicular slopes

We'll use the slope formula again to set up the slope for line n. We don't know y, but we can set the fraction equal to -7/6 and solve for it.

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

slopeN = (y-5)/(5-(-1))

slopeN = (y-5)/(6)

-7/6 = (y-5)/6

-7*6 = 6(y-5)

-42 = 6y-30

6y-30 = -42

6y = -42+30

6y = -12

y = -2

So in short, if y = -2, then line n goes through (-1,5) and (5,y) = (5,-2). The slope of line N is computed to be...

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

slopeN = (-2-5)/(5-(-1))

slopeN = (-2-5)/(5+1)

slopeN = -7/6

which is the proper slope value we want.

Answer: I believe that A is the correct answer.

Answer:

It's A

Step-by-step explanation:

I  just did this question

Answer:

Since both sides equal, there are infinitely many solutions

Step-by-step explanation:

Simplify brackets

2/3×3/1=1

Use this rule: a/b×c/d=ac/bd

Simplify 2×3 to 6

6/3×2=1

Simplify 3×2 to 6

6/6=1

cancel 6

1=1

Since both sides equal, there are infinitely many solutions

Answer:

SEE BELOW      PLEASE GIVE BRAINLIEST

Step-by-step explanation:

YEAR 1:  40000 X .03 = 1200       40,000 + 1200 = 41200

YEAR 2: 41,200 X .03 = 1236        41,200 + 1236 = 42436

YEAR 3: 42436 X .03 = 1273.08    42436 + 1273.08 = 43709.08

YEAR 4: 43709.08 x .03 = 1311.27    43709.08 + 1311.27 = 45020.35

YEAR 5: 45020.35 X .03 = 1350.61    45020.35 + 1350.61 = 46370.96

YEAR 6: 46370.96 X .03 = 1391.13         46370.96 + 1391.13 = 47762.09

YEAR 7: 47762.09 X .03 = 1432.86       47762.09 + 1432.86 = 49194.95

YEAR 8: 49194.95 X .03 = 1475.85        49194.95 + 1475.85 = 50670.80

YEAR 9: 50670.80 X .03 =  1520.12         50670.80 + 1520.12 = 52190.92

YEAR 10: 52190.92 X .03 = 1565.73         52190.92 + 1565.73 = 53756.65

YEAR 11: 53756.65 X .03 = 1612.70             53756.65 + 1612.70 = 55369.35

YEAR 12: 55369.35 X .03 = 1661.08           55369.35 + 1661.08 = 57030.43

YEAR 13: 57030.43 X .03 = 1710.91            57030.43 + 1710.91 = 58741.34

YEAR 14: 58741.34 X .03 = 1762.24            58741.34 + 1762.24 = 60503.58

YEAR 15: 60503.58 X .03 = 1815.11           60503.58 + 1815.11 = 62318.69

YEAR 16: 62318.69 X .03 = 1869.56         62318.69 + 1869.56 = $64,188.25 = $64188

$806275, hope this helps!

Typo free question:

Determine whether the binomial is a factor of F(x).

Answer:

Yes.

Step-by-step explanation:

Method one: evaluate F(5). If F(5) is zero then x-5 is a factor.

Method two: use long polynomial division to divide F(x) by (x-5). If the remainder is zero then (x-5) is a factor.

Answer:

I can be little confident because if it was just 0.7 then it would be I am not confident at all. This decimal is more than 0 so it would be a little and not a lot.

Step-by-step explanation:

Answer:

B) a = 32cx − b

Step-by-step explanation:

i just did it

Answer:

£ 75.60

Step-by-step explanation:

4 m ↔ £ 33.60

1 m ↔ £ 8.40

9 m ↔ £ 75.60

The cost of one meter of timber is £8.40, calculated by dividing £33.60 by 4. To find the cost of 9 meters, multiply £8.40 by 9, resulting in a total cost of £75.60.

To determine the cost of 9 meters of timber when we know that 4 meters cost £33.60, we can use a unit rate approach. First, we need to calculate the cost of one meter of timber by dividing the total cost by the number of meters. Then, we multiply the cost per meter by 9 to find the cost of 9 meters of timber.

Therefore, the cost of 9 meters of timber would be £75.60.

[tex]A=1+Prt\\\\Prt=A-1\\\\P=\dfrac{A-1}{rt}[/tex]

Answer:

$385.49

Step-by-step explanation:

285x1.35261=385.49385

round to the nearest cent and you get $385.49

To exchange 285 Euros for US dollars at an exchange rate of 1.35261, you would receive 385.80785 US dollars.

Current exchange rate = 1.35261 US dollars

To calculate how many dollars would be exchanged for 285 Euros at an exchange rate of 1.35261 US dollars per Euro:

Set up a simple multiplication problem: 285 Euros multiplied by 1.35261 US dollars per Euro.

Multiply the two numbers to get the total amount in US dollars.

So, 285 Euros x 1.35261 = 385.80785 US dollars would be exchanged for 285 Euros.

Answer,

(26/2) * 3

= 39

Explanation,

26 cookies is only 2/3 of 3/3. So, we divide 26 by 2 to see how many cookies are in 1/3. We then can find out that when you make 1/3 of the cookies there are 13. Since that is only 1/3 and we want to find out 3/3. We multiply 13 by 3 and get 39 which is all the cookies she planned to make.

Hope this helps :-)

Answer:

Measures of all angles is either 77.5° or 102.5°

Step-by-step explanation:

See the attached figure.

As shown:

line a parallel to line b with transversal m

So, all the angles are either congruent or supplementary.

Let the supplementary angles x and y and y > x

x + y = 180° ⇒ (1)

one angle is 25° bigger than another

y - x = 25° ⇒ (2)

solving (1) and (2)

∴ x = 77.5°  and y = 102.5°

[tex]\text{The quadratic formula:}\\\\ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\--------------------------------\\\text{We have}\ -5x^2-12x+8=0\\\\a=-5,\ b=-12,\ c=8\\\\\text{Substitute:}\\\\b^2-4ac=(-12)^2-4(-5)(8)=144+160=304\\\\\sqrt{b^2-4ac}=\sqrt{304}=\sqrt{16\cdot9}=\sqrt{16}\cdot\sqrt{19}=4\sqrt{19}\\\\x_1=\dfrac{-(-12)-4\sqrt{19}}{2(-5)}=\dfrac{12-4\sqrt{19}}{-10}=\boxed{-\dfrac{6-2\sqrt{19}}{5}}\\\\x_2=\dfrac{-(-12)+4\sqrt{19}}{2(-5)}=\dfrac{12+4\sqrt{19}}{-10}=\boxed{-\dfrac{6+2\sqrt{19}}{5}}[/tex]

Answer:

A'(3, - 1)

Step-by-step explanation:

Under a reflection in the y-axis

a point (x, y) → (- x, y), hence

A (- 3, - 1) → A'(3, - 1)

The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates.

Given here: The coordinate of a Triangle A as (-3,-1)

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Thus The vertex of the triangle (-3,-1) it changes to (3,-1)

The algebraic representation for the transformation is given by '

(x,y)⇒(-1×x,1×y)

     ⇒(-x, y)

Hence, The coordinate A(-3,-1) on reflection across y-axis transforms to (3,-1)

Learn more about cartesian coordinate system here:

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The mother can make 3 green curtains and 5 white curtains, using the greatest common divisor of 75 and 125 yards which is 25. Each curtain would thus be 25 yards.

This question can be solved using the concept of Greatest Common Divisor (GCD), which finds the largest possible length that can divide two given lengths without leaving any remainder. In this case, the lengths are 75 yards and 125 yards, which are the quantities of green and white fabric respectively. The GCD of 75 and 125 is 25.

Therefore, the largest number of curtains that can be made is based on this length, which means the mother can make 75/25=3 green curtains and 125/25=5 white curtains. Each curtain would be 25 yards.

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the solutions to a general quadratic equation is

X=-b±√b²-4ac/2a  ,, When ax²+bx+c=0

the discriminant is the expression under the radical b²−4ac

Part A:

discriminant is (-16)² - 4(9)(60) = -1904

there are two complex solutions  

Part B:  

4x² + 8x − 5 = 0

4x² + 10x -2x - 5=0

2x ( 2x + 5) - 1(2 x + 5) =0  

(2x + 5)(2x-1) = 0

      /                     \

    /                          \

2x+5 = 0                 2x-1 =0    

x = -5/2                     x = 1/2

If 24 ounce can of Fanta cost $1.75 then it cost 13.71 per ounce.

A division is a process of splitting a specific amount into equal parts.

Given that a 24 ounce can of Fanta cost $1.75.

We need to find the how many does it cost per ounce.

To find this we need to divide twenty four by one point seven five.

Cost per ounce is twenty four by one point seven five

Cost = 24/1.75

Cost per ounce=13.71

So a 24 ounce can of Fanta cost $1.75 can cost 13.71 per ounce.

Hence, if 24 ounce can of Fanta cost $1.75 then it cost 13.71 per ounce.

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Answer: 3/4

Step-by-step explanation:

Julie's salary started at $25,000. t is the number of years since her original $25,000 salary started. Each year she gets a 4% raise. The expression gives her salary at year t.

Answer:

b.

Step-by-step explanation:

Interpret the meaning of the expression.

A.  

Julia's initial salary is $4,000, and the growth rate is 25% per year.

B.  

Julia's initial salary is $25,000, and the growth rate is 4% per year.

C.  

Julia's initial salary is $4,000, and the growth rate is 2.5% per year.

D.  

Julia's initial salary is $25,000, and the growth rate is 40% per year.

Answer:

x=18

Step-by-step explanation:

We need to find the areas of the rectangles

1st rectangle

A= l*w

A = (2x+4)*9

   = 18x+36

2nd rectangle

A = l*w

   = 15*(3x-30)

    = 45x-450

Since the area of the rectangles are equal, we set these two equations equal

18x+36 = 45x-450

Subtract 18x from each side

18x-18x+36 = 45x-18x-450

36 = 27x-450

Add 450 to each side

36+450 =27x

486 = 27x

Divide by 27 on each side

486/27 = 27x/27

18=x

Answer:

X = -5

Step-by-step explanation:

3X=-15

Lets solve the equation for x.  We will isolate x by dividing each side by 3

3X/3 = -15/3

X = -5

Method 1:

Solve the equation

3x = -15     divide both sides by 3

3x : 3 = -15 : 3

x = -5

Method 2:

Put the value of x to the equation:

L = 3(-5) = -15

R = -15

L = R    CORRECT