Giving 20 points for correct answer

Marty is 21 years old. Translated the problem statement into mathematical expressions and then used algebraic manipulation to solve for the unknown variable, which in this case is Marty's age (M).

Algebra is a branch of mathematics in which letters and symbols are used to represent numbers and quantities in equations and formulas. It is used to study mathematical relationships and properties, and to solve problems using mathematical models. Algebraic equations involve one or more variables (often represented by letters such as x, y, or z) that represent unknown values.

Let M be Marty's age.

According to the problem statement, Tonya is 9 years younger than twice Marty's age, so 2M - 9 = T (where T is Tonya's age).

Danielle is 2 years older than Tonya, so T + 2 = D (where D is Danielle's age).

We know that the sum of the three siblings' ages can be expressed as 3M + 8.

So, we can set up the following equation:

M + (2M - 9) + (2M - 9 + 2) = 3M + 8

Solving for M, we get:

M = 21

Therefore, Marty is 21 years old.

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Sin b=4/5 cos b=3/5 tan b=4/3 ctn b=3/4 sec b=5/3 csc b=5/4

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When  P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then the remainder is 4.

In the given question, when P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then we have to find the remainder.

The given equation is

P(x) = [tex]x^3-3x^2+4x+32[/tex]

We have to divide this equation by x+2.

To find the remainder we firstly equate x + 2 equal to zero to find the value of x.

x + 2 = 0

Subtract 2 on both side, we get

x = -2

Now we put x value in the given equation to find the remainder.

The equation

P(x) = [tex]x^3-3x^2+4x+32[/tex]

Put x = -2

P(x) = [tex](-2)^3-3(-2)^2+4(-2)+32[/tex]

Simplify

P(x) = -8 - 3×4 + (-8) + 32

P(x) = -8 - 12 - 8 + 32

P(x) = 4

Hence, when  P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then the remainder is 4.

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The complete question is:

When P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2. The remainder is?

Co-prime numbers are those numbers that have only one common factor, namely 1.

Coprimes are pair of numbers that have no common factor other than 1. There should be at least two numbers to form a set of coprimes. Such numbers have only 1 as their highest common factor, for example (4 and 7), (5, 7, 9) are co-prime numbers. It should be noted that concurrent primes need not always be primes. If the only common factor of two numbers a and b is 1, then a and b are coprimes. In this case, (a, b) is considered a prime pair. Minor primes are also referred to as relatively primes. To determine whether any two numbers are co-prime, we first find their greatest common factor (GCF). If their GCF is 1, we can say they are co-prime. Consider the two numbers 5 and 9. The factors of 5 are 1 and 5. The factors of 9 are 1, 3, and 9. The factor that is common to both 5 and 9 is 1. The GCF of (5, 9) = 1. Thus, (5 , 9) is a co-prime pair.

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If cos x = 3/5 then the value of b = 4

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

sin(tetha) = opp/hyp

cos ( tetha) = adj/hyp

tan ( tetha) = opp/ adj

In the triangle adj = 3b and hyp = 20

cos x = 3b/20

cos x = 3/5

therefore 3/5 = 3b/20

multiply both sides by 20

3/5×20 = 3b/20 × 20

3b = 12

divide both sides by 3

b= 12/3 = 4

therefore the value of b is 4

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Answer:A: b = 4

Step-by-step explanation:

Jayden makes 3 trays of dog treats for his puppy Spot

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem, we have to do the conversion of units with the given information:

Information about the problem:

By converting the unit from quart to ounce, we have:

1 quart * (32 ounce / 1 quart) = 32 ounce

Calculating the total of ingredients Jayden mixed we have:

Total ounces = Yogurt + peanut butter + honey

Total ounces = 32 ounces + 10 ounces + 6 ounces

Total ounces = 48 ounces

Calculating the number of tray that Jayden can make we have:

No. trays = Total ounces / tray capacity

No. trays = 48 ounces / 16 ounces/ tray

No. trays = 3 trays

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We'll cut straight to it: On average, hair grows at a rate of about half an inch per month, or six inches per year. Each hair on your head grows from an individual follicle.

We'll cut straight to it: On average, hair grows at a rate of about half an inch per month, or six inches per year. Each hair on your head grows from an individual follicle.

The average person's hair grows ½ an inch each month which sums up to 6 inches of growth per year.

For you I'd say maybe anywhere from 3 to 5 months it would be around the length you're looking for. It may take a year to get it to your shoulders.

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The general form of a perfect square trinomial is (x + y)², where x and y are the roots of the trinomial. It can also be written as x² + 2xy + y² or x² + (2xy)x + y².

The general form of a perfect square trinomial is (x + y)^2, where x and y are the roots of the trinomial. To check if a trinomial is a perfect square, we can try to factor it into the square of a binomial. We can also complete the square method, which involves adding and subtracting the square of half of the x-coefficient of the linear term and then grouping the resulting terms.

It is important to note that for a trinomial to be a perfect square trinomial, the constant term must be a square of an integer and the linear term must be an even number.

Perfect square trinomials are used in solving quadratic equations and understanding their solutions, they also have applications in algebra, geometry, and trigonometry. Factoring them is a fundamental skill in algebra and is used in solving different types of mathematical problems.

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The slope intercept form of the following equation 6x - 2y = 18 is y = 3x - 9

We knwo that the slope intercept form of equation of line is y = mx + b, where m is the slope and b is the y-intercept.

Consider given equation,

6x - 2y = 18

6x - 2y - 6x = 18 - 6x          .......(Subtract 6x from each side)

- 2y = 18 - 6x

- 2y × (-1) = (18 - 6x) × (-1)       ......(Multiply each side by -1)

2y = -18 + 6x

2y/2 = (-18 + 6x)/2                   ..........(Divide each side by 2)

y = -18/2 + 6x/2

y = -9 + 3x

y = 3x - 9              

This equation is in the form y = mx + b

Here, slope m = 3 and the y-intercept b = -9

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The complete question is:

What is the slope intercept form of the following equation 6x - 2y = 18?

The balance on the card, rounded to the nearest penny $15350.92..

The correct option is D.

Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to a period of time.

Formula of continuous compound interest rate;

P(t) = P₀[tex]e^{rt}[/tex]

where P₀ is the principal amount, r is the interest rate and t is the time period.

A customer uses a store credit card to purchase a boat for $10,500.

The store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years.

That means,

P₀ = $10500, r = 18.99 and t = 2.

So,

P(t) = P₀[tex]e^{rt}[/tex]

Substituting the values,

P(t) = (10500)

P(t) = (10500)(1.46199)

P(t) = 15350.917

P(t) = $15350.92

Therefore, the final amount is $15350.92.

The balance on the card, rounded to the nearest penny $15350.92.

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The length of the rectangle is 74 yard.

The perimeter of a rectangle is the sum of the lengths of all four sides of the rectangle. It is calculated by adding twice the length and twice the width. The formula to calculate the perimeter of a rectangle is

P = 2(L + W), where P is the perimeter, L is the length and W is the width of the rectangle. In simpler terms, it is the total distance around the rectangle.

The perimeter of rectangle is given by  2 ( l + b)

where l is length of rectangle and b is width of the rectangle

given that perimeter of rectangle is 274

so 2 (l+b)= 274

=>  l+b= 137   ---(i)

so l = 137 -b

=> l = 137 - 63

=> 74

so the lenth of rectangle is 74 yard.

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Cameron can download 4 movies with his $66. He can solve an equation of 14.50x + 22.50y = 66 and x + y = 4

14.50x + 22.50y = 66

14.50x = 66 - 22.50y

14.50x = 43.50

x = 3 (43.50/14.50)

x + y = 4

3 + y = 4

y = 1

Cameron wants to download some movies and an ebook with his $66. To figure out how many movies he can download, he needs to solve an equation. The equation is 14.50x + 22.50y = 66, where x is the number of movies and y is the number of ebooks. By solving for x, he can figure out how many movies he can get, which is 3 (43.50/14.50). To find the number of ebooks, he can solve for y in the equation x + y = 4, which is 1. Therefore, Cameron can download 4 movies with his $66.

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Answer:

As societies exchange ideas, globalization is unable to keep up with the speed at which culture has spread.

So, the gradient of y = -3x^1 is -3.

The gradient of a function y = f(x) with respect to x is the derivative of the function with respect to x, denoted by dy/dx or f'(x).

In the case of y = -3x^1, the gradient is -3.

It is a constant function, thus, the slope is always the same and equal to the coefficient of the x term, which in this case is -3.

The gradient of a function tells us the rate of change of the function with respect to x. In other words, it tells us how steep the function is at any given point. A positive gradient means that the function is increasing, while a negative gradient means that the function is decreasing.

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To prove the congruence between two triangles there are several postulates, that can be applied depending on the congruent parts of the triangles.

The postulates are:

SAS (Side-Angle-Side): This postulate states that if two triangles have two corresponding sides congruent and one corresponding angle congruent, we can conclude that those triangles are completely congruent.

ASA (Angle-Side-Angle): This postulate states that if two triangles have two corresponding angles congruent and one corresponding side congruent, then those triangles are congruent.

SSS (Side-Side-Side): This postulate states that if two triangles have all three corresponding sides congruent, then triangles are congruent.

AAS (Angle-Angle-Side): If two pairs of corresponding angles are congruent and one pair of corresponding sides is congruent, then both triangle are congruent each other.

HL (Hypothenuse-Leg): this postulate is applied when we have right angles. It states that two right triangles are congruent if they have one pair of corresponding leg congruent, and the hypothenuses are also congruent. We could conclude that those right triangles are congruent.

From these postulate, we can demonstrate the congruence between two triangles. Then, from that congruence, we deduct the congruence between each corresponding parts of those triangles. For example, if we demonstrate the congruence by AAS, we deduct that the third angle is also congruent, and the other two sides are also congruent.

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Answer: 7.9524 m^

Step-by-step explanation:

The square with the least area can only be formed when we take LCM of the dimensions of the rectangular tile I.e. 54 CM × 30 CM

LCM = 270

This means that a square of length 270 CM will be formed when we take least no. of tiles.

Also given in question, 6cm is left around the square that means 12cm is added on every side to make the floor with minimum area = 282 × 282 cm^2

minimum area = 79524 cm^

in m^2 = 79524/10000 = 7.9524 m^

The y-intercept of the line 4x + 2y ≥ 14 is y ≥ 7.

The y-intercept is the point where the graph intersects the y-axis. In other words, the y-intercept of a line is the value of y when x equals to zero.

In simpler term, the y-intercept of a function is the point(s) where the graph of the function crosses the y-axis.

Therefore, let's find the y-intercept of the inequality.

4x + 2y ≥ 14

let's substitute x as 0.

Therefore,

4x + 2y ≥ 14

4(0) + 2y ≥ 14

2y ≥ 14

divide both sides by 2

2y / 2 ≥ 14 / 2

Hence,

y ≥ 7

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Answer:

£56

Step-by-step explanation:

We know

The ratio Zoe and Hannah hare tip is

3:7

last week Zoe received £24

To find out how much did Hannah receive last week, we first take

24 / 3 = 8

Then we take

8 times 7 = £56

So, last wee Hannah receive £56

Answer:

28.6%

Step-by-step explanation:

10 minute difference, 10 is 28.6% of 35.

a. Even numbers are numbers that are divisible by 2

b. prime number is the number that has two factors by 1 and itself, all even numbers are divisible by 2 hence any other even number aside 2 will be divisible by 1, 2 and itself and this does not define a prime number any more

A prime number is a positive integer greater than 1 that is only divisible by 1 and itself. In other words, a prime number has exactly two positive integer divisors: 1 and itself.

For example, the first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and so on. The number 2 is the only even prime number, and all the other prime numbers are odd.

Prime numbers are important in mathematics because they play a crucial role in various fields such as number theory, cryptography, and coding theory. They are also used as basic building blocks for constructing larger composite numbers.

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Answer:

sea grass red algae green seaweed mangrove or -20 3/4, -15 1/2, -14 3/4, -1/4

Step-by-step explanation:

negatives switch around the rules of positive so the one with the number tat is bigger when not negative is the lowest when negative

The percentages for this problem are given as follows:

The percentages are obtained applying proportions, as a percentage is the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.

651 adults were surveyed, of which 21 + 90 + 118 = 229 were affiliated with neither party, hence the percentage is of:

229/651 x 100% = 35.2%.

104 + 87 + 90 = 281 said that the economy was about the same, hence the percentage is of:

281/651 = 43.2%.

90 people out of the 229 that were unaffiliated felt that the economy was the same, hence:

90/229 x 100% = 39.3%.

Of the 104 + 87 + 90 = 281 people that thought that the economy is about  the same, 90 were affiliated with neither part, hence:

90/281 = 32%.

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The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and y vary directly and y is 44 when x is 11.

Let, y ∝ x.

y = kx.

44 = 11k.

k = 44/11.

k = 4.

Now x = 9.

y = 4×9.

y = 36.

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The remote interior angles of ∠1 are 34° and the right angle. The amount of m∠2 is 56°.

∠1 is an exterior angle because it is located outside the triangle. It has 2 remote interior angles. Remote interior angles are the angles with no shared vertex with the exterior angle. In this case, the remote interior angle of ∠1 is angle 34° and the right angle.

m∠1 can be measured by adding the remote interior angles:

m∠1 = 34° + 90°

m∠1 = 124°

Since m∠1 share a vertex with m∠2, then the total of both angles should be equal to 180° (a straight line). Hence:

m∠1 + m∠2 = 180°

Using the value of m∠1 known above, we can find the value of m∠2:

m∠1 + m∠2 = 180°

124° + m∠2 = 180°

m∠2 = 56°

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A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.

MEAN =Sum of observations/Total number of observations.

MEDIAN= If n is odd, then the following formula is used: Value of (n+1/2th observation. If n is even, then the following formulae is used: {Value of (n/2) th observation + (n/2 +1)th observation/2}

MODE= Most number of times occurring value in the data

Note that your information wasn't properly written and a overview was given.

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Answer:

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

The inverse function, denoted as f^-1(x), can be found by swapping the x and y variables and solving for y.

So, x = 1/5^(1-y) + 2

To find the inverse, we need to solve for y:

y = 1 - log(5, x-2)

Note that the inverse only exists if the original function is a one-to-one function, meaning that it assigns a unique output to each input.

The domain of f is all x such that x > 2. And the range of f is all y such that y > 2. The domain of f^-1 is all x such that x > 2 and the range of f^-1 is all y such that y > 1.

----------------------------------------------------------

2.  1 - 5^x/5^(x-1)

The inverse function, denoted as f^-1(x), can be found by swapping the x and y variables and solving for y.

So, x = 1 - 5^y/5^(y-1)

To find the inverse, we need to solve for y:

y = log(5, 1/(x+1)) + 1

Note that the inverse only exists if the original function is a one-to-one function, meaning that it assigns a unique output to each input.

The domain of f is all x such that x < 1. And the range of f is all y such that 0 < y < 1. The domain of f^-1 is all x such that x < 1 and the range of f^-1 is all y such that y > 1.

--------------------------------------------------------------

3.  y = log1/5(x+1/2)-1

The inverse function, denoted as f^-1(x), can be found by swapping the x and y variables and solving for y.

So, x = log1/5(y+1) - 1/2

To find the inverse, we need to solve for y:

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

Note that the inverse only exists if the original function is a one-to-one function, meaning that it assigns a unique output to each input.

The domain of f is all x such that x exists. And the range of f is all y such that y > -1. The domain of f^-1 is all x such that x exists and the range of f^-1 is all y such that y > 0.

-----------------------------------------------------------------

In summary,

1.  f^-1(x) = 1 - log(5, x-2) Domain: x>2, Range: y>2.

2.  f^-1(x) = log(5, 1/(x+1)) + 1 Domain: x<1, Range: 0<y<1.

3.  f^-1(x) = 5^(x+1/2) - 1 Domain: x exists, Range: y>-1.

Answer:

The square root of 3 is an irrational number

Step-by-step explanation:

A rational number is defined as a number that can be expressed as the division of two integers, i.e. p/q. where q is not zero.

√3 = 1.7320508075688772...and keeps getting longer. √3 is an irrational number because the decimal point does not end or repeat.

Answer:

7.2 because 72 / 10 = 7.2

hope this helps!!!

An expression of the radius of the sphere in terms of h is; h = ⁴/₃r

We are given;

Height of cone = h

Radius of cone = 3r

Radius of sphere = r

Volume of cone = Volume of sphere

Now, formula for Volume of cone  = ¹/₃πr²h = ¹/₃π(3r)²h = 3πr²h

Volume of sphere = ⁴/₃πr³

Thus;

3πr²h = ⁴/₃πr³

Multiply both sides by 3/πr² to get;

9h = 12r

h = ⁴/₃r

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