11
Simplify.
5-8 x 54
-​

Answer:

a. $18.36 for 3 pizzas  :  k  = 6.12

b. $4.17 for 3 pounds of bananas .   k  = 1.39

c. $16.48 for 4 pounds of potatoes .  k  = 4.12

d. 2 cups of flour to make 24 cookie .  k  = 12

Step-by-step explanation:

PROPORTIONALITY:

Two quantities x and y are said to proportional to each other

if for x ∝ y , x = y k.

Here, k is called the PROPORTIONALITY CONSTANT.

⇒  [tex]x\propto y \implies  k = \frac{x}{y}[/tex]

Now, for the given quantities:

a.  $18.36 for 3 pizzas [box]    

Here, [tex]k = \frac{18.36}{3}  = 6.12[/tex]

So, the proportionality constant is 6.12.

b. $4.17 for 3 pounds of bananas [box]

Here, [tex]k = \frac{4.17}{3}  = 1.39[/tex]

So, the proportionality constant is 1.39.

c. $16.48 for 4 pounds of potatoes [box]

Here, [tex]k = \frac{16.48}{4}  = 4.12[/tex]

So, the proportionality constant is 4.12.

d. 2 cups of flour to make 24 cookies

Here,  [tex]k = \frac{24}{2}  = 12[/tex]

So, the proportionality constant is 12

Answer:

Option A is correct.

Step-by-step explanation:

See the two graphs given in the diagram attached.

The first graph shows the function f(x) = x²

Hence, it passes through the points (1,1), (-1,1), (2,4) and (-2,4) points.

Now, from the plotted second graph we see the points (2,2), and (-2,2) are on the curve.

Hence, the y-value corresponding to the same x-value reduces by a factor [tex]\frac{1}{2}[/tex] in the second graph i.e. the graph of y = g(x) compared to the first graph.

So, we can conclude that the transformed graph has the equation [tex]g(x) = \frac{1}{2} x^{2}[/tex].

Hence, option A is correct. (Answer)

Answer:

The answer is g(x) = (1/2) x^2

Step-by-step explanation:

Answer:

y = 5

Step-by-step explanation:

Divide each side by 8 to get (y-9) = -4.

Add 9 to each side to isolate the variable y. This leaves you with y = 5

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}[/tex]

[tex]8(y-9)=-32\qquad\text{divide both sides by 8}\\\\\dfrac{8\!\!\!\!\diagup(y-9)}{8\!\!\!\!\diagup}=\dfrac{-32\!\!\!\!\!\diagup^4}{8\!\!\!\!\diagup_1}\\\\y-9=-4\qquad\text{add 9 to both sides}\\\\y-9+9=-4+9\\\\y=5[/tex]

[tex]\bold{METHOD\ 2:}[/tex]

[tex]8(y-9)=-32\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(8)(y)+(8)(-9)=-32\\\\8y-72=-32\qquad\text{add 72 to both sides}\\\\8y-72+72=-32+72\\\\8y=40\qquad\text{divide both sides by 8}\\\\\dfrac{8y}{8}=\dfrac{40}{8}\\\\y=5[/tex]

Nope!

They cannot be equal if they have the same numerator but different denominators. they need to be able to reduce into the same number

No, two fractions with the same numerator and different denominators can not be equal.

The numerator simply means the number that's on top of a fraction. The denominator simply means the number that's under the fraction.

Two fractions with the same numerator and different denominators can not be equal. An example is 1/4 and 1/6 aren't equal.

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Answer:

The Time taken by submarines to travel before the vessel is 11 hours

Step-by-step explanation:

Given as :

The average speed of aircraft carrier = 15 mph

The average speed of submarine = 15 mph

The distance between them = 300 mile

The time taken by aircraft = T hour

The time taken by submarine = T + 2  hour

Now, Speed = [tex]\dfrac{\textrm Distance}{\textrm Time}[/tex]

So, Distance =  Speed × Time

Now,

300 miles = 15 × T + 15 × ( T + 2)

Or, 300 = 15 T + 15 T + 30

or, 300 - 30 = 30 T

Or, 270 = 30 T

∴ T = [tex]\frac{270}{30}[/tex]

I,e T = 9 hours

So, T + 2 = 9 + 2 = 11 hours

Hence The Time taken by submarines to travel before the vessel is 11 hours Answer

Final answer:

To simplify the expression (6rs - 7bc )-( 9rs - 7bc), distribute the negative sign, combine like terms, and simplify to get -3rs.

Explanation:

To simplify the expression (6rs - 7bc )-( 9rs - 7bc), you can start by distributing the negative sign to the terms inside the second set of parentheses. This will change the signs of both terms inside it, making the expression become 6rs - 7bc - 9rs + 7bc. You can then combine like terms. Notice that -7bc and +7bc are like terms and cancel each other out, as do 6rs and -9rs. Simplifying these terms, you get -3rs.

Here is the step-by-step process:

Distribute the negative sign: 6rs - 7bc - 9rs + 7bc.

Combine like terms: (6rs - 9rs) + (-7bc + 7bc).

Simplify the expression: -3rs + 0.

Final answer: -3rs.

It's often helpful to eliminate terms wherever possible to simplify the algebra and then check the answer to ensure it is reasonable.

Answer:

9 Miles

Step-by-step explanation:

6+(6/2)=9

Hope this helps!

Answer: 9 miles

Step-by-step explanation:

6 = 10

x = 15

x= 15* 6/ 10

X= 90/10

x= 9

The area of the rectangle with dimensions (3x + 5) by (x - 2) is represented by the algebraic expression 3x² - x - 10.

The area of a rectangle is found by multiplying its length by its width. Given a rectangle with length (3x + 5) and width (x - 2), we can find its area by using the formula for the area of a rectangle, which is length × width.

Area = (3x + 5)(x - 2)
By expanding this, we use the distributive property:
Area = 3x(x) + 3x(-2) + 5(x) + 5(-2)
Area = 3x² - 6x + 5x - 10
By combining like terms, we get:
Area = 3x² - x - 10

Answer:

The correct answer is D. 15 squared centimeters.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Base one = 10 centimeters

Base two = 5 centimeters

Height = 2 centimeters

2. Let's find out the area of the trapezoid, using the following formula:

Area = 1/2 (Base one + Base two) * Height

Replacing with real values:

Area = 1/2 (10 + 5) * 2

Area = 1/2 (15 * 2) = 1/2 (30)

Area = 15 centimeters ²

The correct answer is D. 15 squared centimeters.

You can't factor anything out of this. At least I don't think

The expression 25x + 14 cannot be traditionally factored as it does not have any common factors, nor does it follow any special binomial patterns. It is already in its simplest form.

Explanation:

The expression 25x + 14 cannot be factored in the traditional sense because it does not have common factors nor does it fit the pattern of a special binomial such as a difference of squares or a perfect square trinomial. The expression is already in its simplest form unless we have additional restrictions or information about variable x. If we were to consider factorization in terms of factoring out a greatest common factor (GCF), since the coefficients 25 and 14 have no common factors other than 1, we cannot factor anything out. Sometimes, in different contexts, we can apply transformations, such as multiplying an equation by a constant to simplify fractions or rearranging terms for clarity, but these strategies do not apply to the expression 25x + 14 as given.

Answer:

560mph

Step-by-step explanation:

11,760÷21=560

label- 560mph

Answer:

560 MILES

Step-by-step explanation:

11760/21=560

Volume of sphere having radius of 3 inches is 113.04 cubic inches.

Solution:

Given that the radius of a sphere is 3 inches. Need to determine the volume of sphere

Formula for volume of sphere is as follows :

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

Where V is volume of sphere , π is constant value = 3.14 and r = radius of a sphere.

In our case, r = 3 inches

On substituting the value of π as 3.14 and value of r as 3 inches in the formula of volume of sphere, we get

[tex]V=\frac{4}{3} \times 3.14 \times 3^{3}=4 \times 3.14 \times 9=113.04 \text { cubic inches }[/tex]

Hence volume of sphere having radius of 3 inches is 113.04 cubic inches.

Answer:

The difference between the given two expression as - 19 w - 3 .

Step-by-step explanation:

Given algebraic expression as

- 14 w - 3  and  5 w

Now, Let the difference between the given two expression = x

or, x = ( - 14 w - 3 ) - 5 w

or , x = - 14 w - 5 w -3

or,  x = w ( - 14 - 5 ) - 3

Or, x = -19 × w - 3

∴  x = -19 w -3

So, The difference is - 19 w - 3

Hence The difference between the given two expression as - 19 w - 3 . Answer

Answer:

$8950.37

Step-by-step explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), in which P is the initial amount of money (the principal), r is the interest rate as a decimal fraction, n is the number of times per year that interest is compounded, and t is the number of years.

Here we have A = $11,000, n = 2, r = 0.07 and t = 3, and so:

$11,000 = P(1 + 0.07/2)^(2*3), or

$11,000 = P (1.035)^6

                                           $11,000        $11,000

Solving for P, we get P = ---------------- = ------------- = $8950.37

                                            1.035^6          1.229

Depositing $8950.37 with terms as follows will result in an accumulation of $11,000 after 3 years.

To determine how much money should be deposited today in an account that earns 7% compounded semiannually to accumulate to $11,000 in three years, one needs to apply the formula for compounded interest and solve for the principle amount.

The subject in question pertains to compounded interest under the domain of financial mathematics. In this context, the student wants to determine how much money needs to be deposited today to accumulate a given amount, in this case, $11,000, in an account that earns 7% compounded semiannually in three years. It's important to note that when interest is compounded, it's added to the principal, and future interest calculations are based on this adjusted amount.

Applying the formula for compounded interest: A = P(1 + r/n)^(nt)

Where:

our aim is to find P (the principal amount or the amount to be deposited today), which can be mathematically rearranged from the formula above as follows:

**P = A / [(1 + r/n)^(nt)]**

Substituting A = $11,000, r = 7% (or 0.07 in decimal form), n = 2 (since the interest is compounded semiannually), and t = 3, we calculate P (the amount to be deposited today).

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Answer: 1/6

Step-by-step explanation: To multiply fractions, first multiply across the numerators, then multiply across the denominators.

So here, we have 1 × 2 which is 2 and 4 × 3 which is 12. So now we have the fraction 2/12.

Notice however that 2/12 is not in lowest terms so we need to divide the numerator and the denominator by the greatest common factor of 2 and 12 which is 2.

So if we divide the numerator and the denominator by 2, we get 1/6.

Therefore, 1/4 × 2/3 = 1/6.

Answer:

1/6

Step-by-step explanation:

For fraction multiplication, multiply the numerators and then multiply the denominators to get

1 x 2           2

-------    = --------

4 x 3          12

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 2 and 12. GCF(2,12) = 2

2 divided by 2           1

------------------------   =  ----  

12 divided by 2         6

So...

1/4 x 2/3 = 1/6

The expression is ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )

Given that, we have to use the numbers 4.3 , - 1.07 and – 2.971 such that the value of the expression with the given numbers and the either addition or subtraction operation between them to be negative value.

So, now take the numbers.

If we add the negative numbers and subtract the positive number from it, we will always get a negative number  

So, expression will be ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )  

- 1.07 – 2.971 – 4.3  

- 8.341

Here the result is negative value.

Hence, the expression is ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )

Answer:  9

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

Explanation:

The intersection of the two sets is the list of all values that are in both sets at the same time.

Let's convert set A into roster notation. Roster notation means we just list out all the members (use ellipses if there are a lot of values you don't want to write out; luckily these sets are small). Plug n = 2 into x = 3n and you'll find that x = 6. Repeat for n = 3, and you get x = 9. Repeat for n = 4 and you get x = 12.

Set A looks like this: {6, 9, 12}

-------

Repeat the same basic steps for set B. We'll plug m = 1 into x = 4m-3 to get x = 1. Plug m = 2 into that same equation to get x = 5. Finally m = 3 leads to x = 9

Set B = {1, 5, 9}

-------

In summary,

A = {6, 9, 12}

B = {1, 5, 9}

We see that only 9 is in both sets at the same time.

Therefore, [tex]A \cap B = \left\{ 9 \right\}[/tex] which says "the intersection of set A and set B is the set { 9 } ".

The Venn Diagram shown below has the single element 9 in the overlapping region of the two circles. The other values are in their proper respective circles, but not inside the overlapping region. Set U is the universal set.

Answer:

275

Step-by-step explanation:

h hamburgers

c cheeseburgers

(h + c) -total

(c + h) = 614

64 more cheeseburgers sold then hamburgers:

64 more cheeseburgers sold then hamburgers

(c - h) = 64

(c + h) = 614

+(c - h) = 64

2c = 678

c = 678/2 = 339

c + h = 614

339 + h =614

h = 614 - 339 = 275

Answer:

[tex]\displaystyle -4 + c < -20[/tex]

Step-by-step explanation:

You could either do what I did in the above answer, or you could do this:

[tex]\displaystyle c - 4< -20[/tex]

It does not matter how you write it, as long as you understand the concept!

I am joyous to assist you anytime.

Answer:

x=11, now it's the right answer :/

Step-by-step explanation:

-3x+15=4-2x

-3x+11=-2x

11=x

Fixed

Answer:

5 numbers of stamp packs and 7 number of envelop packs that Alex has to buy.

Step-by-step explanation:

Alex wants to buy the same number of stamps and envelops.

Stamps are sold in packs of 14 and envelop are sold in the packs of 10.

Now, we have to find the least number of stamp packs and envelop packs that Alex should buy to get an equal number of stamps and envelops.

The least common multiple of 14 and 10 will give the result.

14 has multiples 14, 28, 42, 56, 70, .......

And 10 has multiples 10, 20, 30, 40, 50, 60, 70, ........

Therefore, 70 is the least common multiple.  

In that case 5 numbers of stamp packs and 7 number of envelop packs that Alex has to buy to get 70 stamps and 70 envelop. (Answer)

The least number of stamps and envelopes Alex can buy to have the same number is 70 of each, which he can get by purchasing five packs of each.

Alex wants to buy the same number of stamps and envelopes. To find the least number of each he could buy to have the same number, we need to find the least common multiple (LCM) of the two pack sizes, 14 (stamps) and 10 (envelopes).

The multiples of 14 are 14, 28, 42, 56, 70, etc., and the multiples of 10 are 10, 20, 30, 40, 50, 60, 70, etc. The first common multiple they share is 70.

Therefore, Alex can buy five packs of envelopes (5 x 10 = 50 envelopes) and five packs of stamps (5 x 14 = 70 stamps) to have the same number of each, which is 70.

Answer:

Step-by-step explanation:

[tex]9c-7=7c-11\qquad\text{add 7 to both sides}\\\\9c-7+7=7c-11+7\\\\9c=7c-4\qquad\text{subtract}\ 7c\ \text{from both sides}\\\\9c-7c=7c-7c-4\\\\2c=-4\qquad\text{divide both sides by 2}\\\\\dfrac{2c}{2}=\dfrac{-4}{2}\\\\c=-2[/tex]

Answer:

2

Step-by-step explanation:

Simplifying

9c + -7 = 7c + -11

Reorder the terms:

-7 + 9c = 7c + -11

Reorder the terms:

-7 + 9c = -11 + 7c

Solving

-7 + 9c = -11 + 7c

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-7c' to each side of the equation.

-7 + 9c + -7c = -11 + 7c + -7c

Combine like terms: 9c + -7c = 2c

-7 + 2c = -11 + 7c + -7c

Combine like terms: 7c + -7c = 0

-7 + 2c = -11 + 0

-7 + 2c = -11

Add '7' to each side of the equation.

-7 + 7 + 2c = -11 + 7

Combine like terms: -7 + 7 = 0

0 + 2c = -11 + 7

2c = -11 + 7

Combine like terms: -11 + 7 = -4

2c = -4

Divide each side by '2'.

c = -2

Simplifying

c = -2

For this case we have the following system of equations:

[tex]x-5y = 33\\5x-6y = 70[/tex]

We multiply the first equation by -5:

[tex]-5x + 25y = -165[/tex]

Thus, we have the equivalent system:

[tex]-5x + 25y = -165\\5x-6y = 70[/tex]

We add the equations:

[tex]-5x + 5x + 25y-6y = -165 + 70\\19y = -95\\y = - \frac {95} {19}\\y = -5[/tex]

We find the value of the variable "x":

[tex]x-5 (-5) = 33\\x + 25 = 33\\x = 33-25\\x = 8[/tex]

Thus, the solution of the system is:

[tex](x, y) :( 8, -5)[/tex]

Answer:

[tex](x, y) :( 8, -5)[/tex]

Answer:

1+3i

Step-by-step explanation:

(6+4i)-(5+i)

6+4i-5-i

1+4i-i

1+3i

Answer: 1+3i

Step-by-step explanation:

(6 + 4i) − (5 + i)

Before solving further, note that :

Minus × Minus = Plus

Plus × Minus = Minus

Plus × Plus = Plus

(6 + 4i) − (5 + i)

Open the bracket

= 6 + 4i - 5 - i

Collect like terms

= 6 - 5 + 4i - I

= 1 + 3i

Answer:

D. 158/6

Step-by-step explanation:

If you divide 158/6 you get 26.3333333333 which is a repeating decimal, and makes it a rational number.

Answer:

The value of y is 14

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have the points

[tex](-2, y)\ and\ (4, 6)[/tex]

[tex]m=-\frac{4}{3}[/tex]

substitute in the formula the given values

[tex]-\frac{4}{3}=\frac{6-y}{4+2}[/tex]

solve for y

[tex]-\frac{4}{3}=\frac{6-y}{6}[/tex]

Multiply by 6 both sides

[tex]-8=6-y[/tex]

[tex]y=6+8=14[/tex]

Answer:

Answer:

[tex]-\frac{1}{3} < x < 2[/tex] and -3 < x < 3

Step-by-step explanation:

The inequality equation is  

3x² - 5x - 2 < 0

⇒ 3x² - 6x + x - 2 < 0

⇒ (x - 2)(3x + 1) < 0

Therefore, either (x - 2) > 0 and (3x + 1) < 0

⇒ x > 2 and [tex]x < -\frac{1}{3}[/tex] which is not possible for any particular value of x.

or, (x - 2) < 0 and (3x + 1) > 0

⇒ x < 2 and [tex]x > -\frac{1}{3}[/tex] which is valid.

So, the solution is [tex]-\frac{1}{3} < x < 2[/tex] (Answer)

Now, another inequality is  

x² - 9 < 0

⇒ x² < 9

Therefore, -3 < x < 3 is the solution. (Answer)

Answer:

A subordinate clause—also called a dependent clause—will begin with a subordinate conjunction or a relative pronoun and will contain both a subject and a verb. This combination of words will not form a complete sentence. It will instead make a reader want additional information to finish the thought.