Meghan swam 84 kilometers in 3 days.

How many kilometers did Meghan swin per day?

Answer:

  x = -3, 0, or 7

Step-by-step explanation:

After removing common factors, the remaining quadratic can be factored by comparison to the factored form of a quadratic.

__

Write the equation in standard form.

  4x³ -16x² -84x = 0

Factor out the common factor from all terms.

  = 4x(x² -4x -21) = 0

Compare to the factored form of a quadratic:

  (x +a)(x +b) = x² +(a+b)x +ab

This tells you the constants 'a' and 'b' in the factors can be found by considering ...

  (a+b) = -4 . . . . the coefficient of the x term of the quadratic

  ab = -21 . . . . . the constant term of the quadratic

It is often helpful to list factor pairs of the constant:

  -21 = (-21)(1) = (-7)(3) . . . . integer pairs that have a negative sum

The sums of these pairs are -20 and -4. We are interested in the latter. We can choose ...

  a = -7, b = 3

Put it all together.

  4x³ -16x² -84 = (4x)(x -7)(x +3) = 0 . . . . . factored form of the equation

Apply the zero product rule. This rule tells you the product of factors will be zero when one or more of the factors is zero:

  4x = 0   ⇒   x = 0

  x -7 = 0   ⇒   x = 7

  x +3 = 0   ⇒   x = -3

Solutions to the equation are x ∈ {-3, 0, 7}.

_____

Additional comment

What we did in Step 3 is sometimes referred to as the X-method of factoring a quadratic. The constant (ab product) is put at the top of the X, and the sum (a+b) is put at the bottom. The sides of the X are filled in with values that match the product and sum: -7 and 3. The method is modified slightly if the coefficient of x² is not 1.

A graphing calculator often provides a quick and easy method of finding the real zeros of a polynomial.

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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The 7x side is half the length of the 28 side.

           7x = 14

             x = 2

We know, the probability of an event = Favorable outcomes / Total outcomes.

In a case of two dices,

Total outcomes = 6 × 6 = 36

A.T. Q favorable outcome is a sum of 6,

Ways of obtaining a sum of 6

(1,5), (5,1), (2,4),(4,2) and (3,3). Total 5 ways in which 6 can be obtained using two dices.

Therefore, required probability (P),

P = 5/ 36

Answer:

9

Step-by-step explanation:

{(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

When one magnitude depends on another, the relationship between them is known as a mathematical function. So long as they are uniquely and solely connected.

Every mathematical function is the relationship between an element of group A and an element of group B. Consequently, the following algebraic expression can be used to represent this function:

Therefore, the {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range that defines the correct relation. The correct option is D.

The complete question is given below,

Which relation describes a function? What makes it a function?

A) {(-2,3),(-2,5),(-6,7)} Each member of the range is unique.

B) {(2,3),(3,3),(3,4)} Each member of the domain and range is positive.

C) {(2,3),(3,3),(3,4)} Each member of the domain and range is a real number.

D) {(-2,3),(-3,3),(-4,3)} Each member of the domain is assigned exactly one member of the range.

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Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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The product and the quotient of the functions are as follows:

(rs)(4) =8

(r / s)(3) = 2

A function relates input and output. It relates an independent variable with a dependent variable.

Therefore, let's solve the function as follows:

r(x) = 2√x

s(x) = √x

Therefore, let's find

(rs)(4) = r(4) × s(4) = 2√4 × √4 = 4 × 2 = 8

Let's find

(r / s)(3) = r(3) / s(3) = 2√3 / √3 = 2

Therefore,

(rs)(4) =8

(r / s)(3) = 2

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The area of each composite figure is 828.96 cm².

A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.

Given:

Surface area = SA of Cone + SA of Hemisphere

Cone:

radius = 8 cm

slant height = 17 cm

So, SA of Cone = πrl

                          = 3.14 x 8 x 17

                          = 427.04 cm²

Hemisphere:

radius = 8 cm

So, SA of Hemisphere = 2πr²

                                     = 2 x 3.14 x 8 x 8

                                     = 401.92 cm²

Thus, the SA of figure = 427.04 + 401.92 = 828.96 cm²

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We will investigate the application of taxes on receipts.

We are given that a sales tax rate ( r ) is applied on all the customer receipt purchase. The sales tax applied on the bill is:

The value of the receipt-purchase ( p ) is given as follows:

We will first determine the sales tax amount ( s ) applied on the purchase receipt ( p ) by considering the applicable tax rate ( r ) as follows:

We will use the above relation to determine the sales tax ( s ) amount:

The sales tax amount ( s ) is the extra amount that a customer has to pay over the value of the purchased items.

The total amount that a customer pays at any retail or receipt has the following costs:

We will use the above relation to determine the total cost as follows:

Therefore, the answer is:

Answer:

-57.6=x

Step-by-step explanation:

-22.3= x/3-3.1
-19.2=x/3
-57.6=x

The true statement is that the sample mean is not biased

From the question, we have the following parameters that can be used in our computation:

Sample selection of 2

The sample is selected such that all 4 samples are equally likely

This means that

P(Each selection) = 1/4

An unbiased sample is such that reflects all members of the population and in this case, this sample reflects the population

Hence, the sample is unbiased

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\(y^3 - 6y^2 = 0\\y^2(y-6)=0\\y^2=0 \vee y-6=0\\y=0 \vee y=6\)

Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?

f(x) has a point of inflection at x = 0 and x = 1/2.To find the values of x where the graph of the function\(f(x) = x^4 - x^3\) has a point of inflection, we need to find where the second derivative of the function changes sign from positive to negative or vice versa.

The first derivative of the function is:

\(f'(x) = 4x^3 - 3x^2\)

The second derivative of the function is:

\(f''(x) = 12x^2 - 6x\)

Setting f''(x) equal to zero and solving for x gives:

\(12x^2 - 6x = 0\)

6x(2x - 1) = 0

This equation has two solutions:

x = 0, or x = 1/2

To determine whether these values of x correspond to points of inflection, we need to look at the sign of the second derivative on either side of each value.

When x < 0, f''(x) is positive because both \(12x^2\) and -6x are positive. When 0 < x < 1/2, f''(x) is negative because \(12x^2\)is positive but -6x is negative. When x > 1/2, f''(x) is positive again because both \(12x^2\) and -6x are negative.

Therefore, f(x) has a point of inflection at x = 0 and x = 1/2.

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Answers in bold:

expression one: 6 + x + 9 = x + 15

Expression two: x + 2 + 8x = 9x + 2

Expression three: 4x + 3y + 23y = 4x + 26y

expression four: 4 (15a) = 60a

expresion five: x²+2x+3x²+10x​ = 4x² + 12x = 4x(x + 3)

Answer:

Step-by-step explanation:

The total cost of Tandoori Seasoning is incorrect.

Vijay made an error when multiplying 3.5 ounces by $3.60 .

Cost of both spice blends is actually $23.6.

it is defined as the deviation of an entitiy from its corrected value while calculating.

Now it is given that,

Tandoori Seasoning = 3.5 ounces for $3.60 an ounce

Garam Masala =  4 ounces for $2.75 an ounce

Hence, total cost of  Tandoori Seasoning =  3.5*$3.60

⇒ total cost of Tandoori Seasoning = $12.6

and total cost of Garam Masala =  4*$2.75

⇒ total cost of Garam Masala = $11

Therefore, total cost for the spices =cost of Tandoori Seasoning + cost of Garam Masala

⇒  total cost for the spices = $12.6 + $11

⇒  total cost for the spices =  $23.6

Hence, we conclude that,

The total cost of Tandoori Seasoning is incorrect.

Vijay made an error when multiplying 3.5 ounces by $3.60 .

Cost of both spice blends is actually $23.6.

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Answer:*

Step-by-step explanation:

To calculate the interest for 1/2 a month over a period of 8 years, we first need to calculate the total number of months in 8 years:

Total number of months = 8 years x 12 months/year = 96 months

Next, we can calculate the interest for half a month:

Interest = Principal x Rate x Time

Where:

- Principal = $90,900.00

- Rate = 8.25% (annual interest rate)

- Time = 0.5/12 years (half a month, expressed in years)

Rate needs to be converted to a monthly rate, so we divide it by 12:

Rate = 8.25% / 12 = 0.6875% (monthly interest rate)

Time needs to be expressed in years, so we divide it by 12:

Time = 0.5/12 years

Now we can calculate the interest:

Interest = $90,900.00 x 0.006875 x 0.0416667

Interest = $25.08 (rounded to the nearest cent)

Therefore, the interest for 1/2 a month on a principal of $90,900.00 with an annual interest rate of 8.25% over a period of 8 years is $25.08.

Answer:

The interest for 1/2 month is $312.47, and the total interest for 8 years is $30, 032.64

Step-by-step explanation:

Make a plan:

Draw the conclusion:

Hope this helps!

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Analyze the different intervals at which the function takes the values provided by the graph. Pay special attention on the circles, whether they are filled up or not.

From the graph, notice that the function takes the value of 3 when x is equal to -4, -2 or any number between them. Therefore, the condition is:

If x is greater (but not equal) than -2 and lower or equal to 3, the function takes the value of 5. Therefore:

Finally, the function takes the value of -3 whenever x is greater (but not equal) to 3 and less than or equal to 5. Then:

Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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Step-by-step explanation:

1. 44

2. 26 95

3. 294

4. 126

5. 36.04

6. 52.02

Answer:

4

Step-by-step explanation:

(3+5+6+2+4) / 5 = ?

(20) / 5 = 4

Answer: $13, don't just copy that answer actually try to understand it. ⬇️

Step-by-step explanation: Think of it as a number line.

$12-$12.10-$12.20-$12.30-$12.40-$12.50-$12.60-$12.70-$12.80-$12.90$13

the $12.50 is directly in the middle of $12 and $13. Lets say it $12.51 now its not directly in the middle, but more over to the $13, so then we would go up to 13$ which is the nearest dollar. If it were $12.49 then it would be closer to the $12, so we would go down to $12.

I hope this helps!

Answer:

--

Step-by-step explanation:

Show all the options please

Not able to see all options