Expanding each integer in the expression 21 × 12, the result is [(2 × 101) + (1 × 100)] × [(1 × 101) + (2 × 100)]. Replace the 10s with x’s and then multiply this expression using FOIL. Compare it with the normal integer multiplication method used above: How are they similar? Show your work.

Answer:

7 km

Step-by-step explanation:

let the speed of boat in still water is x km/hr. 

given speed of stream is 3 km/hr. 

then speed of boat upstream = ( x - 3) km/hr

speed of boat downstream = (x + 3 ) km/hr 

Distance travelled upstream = 4 km

time taken to travel upstream = distance travelled upstream / speed of boat 

upstream

= 4 / (x - 3 ) .............(1) 

Distance travelled downstream = 10 km

time taken to travel downstream = distance travelled downstream / speed of boat 

downstream

= 10 / (x + 3) ............(2)

given that boat takes same time to travel upstream and downstream.i.e; (1) & (2) are equal

i.e. 4/(x-3) = 10/ (x + 3 ) 

4 * (x +3 ) = 10 * (x- 3)

4x + 12 = 10x - 30

12 + 30 = 10x -4x 

42 = 6x 

x = 42 / 6 = 7. 

i.e speed of boat in still water is 7 km/hr.

Answer:

Step-by-step explanation:

sup

Answer:

Yes, your total savings on gas is proportional to the number of beverages you purchase.

Step-by-step explanation:

What is a proportional relationship?

A proportional relationship, also known as direct relation, between two variables exists when the ratio between every pair of data is constant.

In this case the variables are:

number of beverage purchased

savings

Thus, as per every beverage purchase you save $ 0.20 the ratio of total savings to the number of beverage purchases is:

savings / beverages purchase = $ 0.20 / beverage

That means that you can determine the savings by multipliying the number of beverages times $ 0.20.

For proportional relationships it is easy to build a table that shows the behavior of the variables. This shows you that:

Number of beverages   savings    ratio

        1                              $ 0.20      $0.20 / 1 beverage = 0.20

        2                             $ 0.40      $0.40 / 2 beverages = 0.20

        3                             $ 0.60       $0.60 / 3 beverages = 0.20

        4                             $ 0.80       $0.80 / 4 beverages = 0.20

Answer:

x=24

Step-by-step explanation:

Step 1: Add 3 to both sides: 1/2x-3+3=9+3

Simplify that: 1/2x=12

Step 2: Multiply both sides by 2: 1/2x*2=2*12

Simplify: x=24

Hope this helped! :)

I assume you're asked to solve

4 cos²(x) - 7 cos(x) + 3 = 0

Factor the left side:

(4 cos(x) - 3) (cos(x) - 1) = 0

Then either

4 cos(x) - 3 = 0   or   cos(x) - 1 = 0

cos(x) = 3/4   or   cos(x) = 1

From the first case, we get

x = cos⁻¹(3/4) + 2nπ  or   x = -cos⁻¹(3/4) + 2nπ

and from the second,

x = nπ

where n is any integer.

A quadratic equation is an equation that can be placed in the form a·x² + b·x + c = 0

The option that gives the true statement about the quadratic equation is option C.

C. There are two complex solutions

Reason:

The given quadratic equation can be presented as follows;

y = -2·x² + 9·x - 12

The factored form of the quadratic equation is presented as follows;

The radical of the given quadratic equation is therefore;

[tex]\sqrt{9^2 - 4 \times (-2) \times (-12)} = \sqrt{81 - 96} = \sqrt{-15}[/tex], which gives the following solutions;

[tex]x = \dfrac{(-9\pm\sqrt{-15} )}{2 \times (-2)} = \dfrac{-9 \pm \sqrt{-15} }{-4}[/tex]

[tex]x = \dfrac{-9 +\sqrt{-15} }{-4} \ or \ x = \dfrac{-9 -\sqrt{-15} }{-4}[/tex]

Therefore there are two complex solutions;

Learn more about quadratic equations here:

https://brainly.com/question/12402430

Answer:

the answer is c

Step-by-step explanation:

There are two complex solutions.

Answer:

hey im not actually here to help you, i just need points. thanks for the points

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Answer:

The answer is 66 feet.

Hope it helps!!

Answer:

Unit rate

Step-by-step explanation:

Answer:

Unit rate

Step-by-step explanation:

Unit rate -- A rate in which the second quantity in the comparison is one unit.

Answer:

7/9

Step-by-step explanation:

To add fractions, you have to have like denominators. First find the LCM (Least Common Multiple) of both denominators. That is 9. The second fraction already has a denominator of 9, so leave it as is. The first fraction doesn't so what will happen is you will be converting it into a fraction with a denominator of 9. Multiply the denominator by 3 to get 9. Then multiply the top by 3 because whatever you do to the bottom you do the top. You will then get 3/9. 3/9+4/9 is equal to 7/9 because you just add the numerators, but keep the denominators the same.

Answer:

3x^2+17x+20

Step-by-step explanation:

Answer: x = y

y = -4

y = 3x + 2

x = 8

Simplify: (-3a2b5)2

Find (x - 4)2`Find the product: (3x + 5)(4x - 1)

Use FOIL:

F: 3x*4x=12x^2

O: 3x*-1 = -3x

I: 5*4x = 20x

L: 5*-1 = -5

Combine these products to get:

12x^2+17x-5

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

Which of the following is the equation of a vertical line?

x = y

y = -4

y = 3x + 2

x = 8

Answer x=8 ; The graph is the set of points where x=8.

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

Simplify: (-3a2b5)2

=(-3a^2b^5)(-3a2b^5)

=9a^4b^10

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

Find (x - 4)^2

=(x-4)(x-4)

Use FOIL to get:

x^2-4x-4x+16

=x^2-8x+16

Step-by-step explanation:All work needed to arrive at a correct answer. If it is not a question that requires work, you will need to provide a complete explanation of how you determined the correct answer. (Explanations for those problems not requiring work must demonstrate your understanding of the concept.)

Answer:

Y=1/2x+2

Step-by-step explanation:

The slope is always rise/run and the Y intercept is 2.

Answer:

o

Step-by-step explanation:

o

Answer:

Kaylee earned $24.8 per minute.

Step-by-step explanation:

Basically, just divide the total wage, by hours earned.

in the blanks I assume you just put 24.8 dolars per 1 hour and then the final 446.40 for 18 hours at the end of the number line :)

If possible may I have brainlist? Thanks g

Answer:

Option C

Step-by-step explanation:

x - 3 = 0

Add 3 to both sides;

x = 3

x + 2 = 0

Subtract 2 from both sides;

x = -2

x - 2 = 0

Add 2 to both sides;

x = 2

Answer:

243

Step-by-step explanation:

Answer:

A) 4k + 3p < 36

B) 3 kitten magazines and 4 puppy magazines

4 kitten magazines and 6 puppy magazines

C) If bill bought 3 kitten magazines, then he buys less than 8 puppy magazines.

Step-by-step explanation:

Let:

The number of kitten magazines = k

The number of puppy magazines = p

A) Write an inequality that describes the situation

We are told:

Bill spent less than $36 on Kitten and puppy magazines kitten magazines cost $4 each and puppy magazines cost $3 each

Hence:

$4 × k + $3 × p < 36

4k + 3p < 36

B) List two possible combinations of puppy and kitten magazines

4k + 3p < 36

Bill can buy:

3 kitten magazines and 4 puppy magazines

4 kitten magazines and 6 puppy magazines

C) If bill bought 3 kitten magazines, how many puppy magazines can he buy?

Using the inequality above:

4k + 3p < 36

4k + 3p < 36

4 × 3 + 3p < 36

12 + 3p < 36

3p < 36 - 12

3p < 24

p < 24/3

p < 8

If bill bought 3 kitten magazines, then he buys less than 8 puppy magazines.

Answer:

the pattern is going by 3s and u would multiply 3 by each number

It would be 288 ft.

Answer:

4/5

Step-by-step explanation:

Rise = 4

Run = 5

~theLocoCoco

Answer:

4/5

Step-by-step explanation:

Answer:

-8=6-7x (subtract 6 from both sides)

-14=-7x (divide each side by -7)

x=2

the answer is C

Answer:

c: 2

Step-by-step explanation:

-8 = 6 -7x, isolate the -7 by moving the 6 to the left side of the equation so it becomes -8-6 = -7x --> -14 = -7x and then divide by both sides by -7 and then you get x =2, you can plug in the number back into the equation to make sure

All we need to do is solve for y.

[tex]y - 3 = 4(x + 2)\\\\y - 3 = 4x + 8\\\\y = 4x + 11[/tex]

The answer is A. y = 4x + 11.

Answer:

lool what's the question

Step-by-step explanation:

how is life treating you?

Answer:

6x - 2y

Step-by-step explanation:

3x - 4y + 3x + 2y

combine like terms

6x -2y

hope this helps!!!

Answer:

The inequality which correctly compares Three-fourths, One-seventh, and Five-sixths is : One-seventh < Three-fourths < Five-sixths.

The first option is correct.

Step-by-step explanation:

To determine which inequality correctly compares Three-fourths, One-seventh, and Five-sixths, we will arrange them in ascending order.

To do this, first, we will determine the LCM of the fractions denominators..

Three-fourths, One-seventh, and Five-sixths

[tex]\frac{3}{4}, \frac{1}{7}, and \frac{5}{6}[/tex]

The denominators are 4, 7 and 6.

LCM of 4,7 and 6 is 84

Then, we will write the fractions in a form whereby they all have the same denominators.

[tex]\frac{3}{4}, \frac{1}{7}, and \frac{5}{6}[/tex]  can be written as

[tex]\frac{63}{84}, \frac{12}{84}, and \frac{70}{84}[/tex]

The resulting order of the numerators gives the order of the fractions.

Now, we will arrange [tex]\frac{63}{84}, \frac{12}{84}, and \frac{70}{84}[/tex] in ascending order. This becomes

[tex]\frac{12}{84}, \frac{63}{84},and \frac{70}{84}[/tex].

∴ The ascending order of the fractions is [tex]\frac{1}{7}, \frac{3}{4},and \frac{5}{6}[/tex].

That is, One-seventh, Three-fourths, and Five-sixths.

Hence, we can write that

One-seventh < Three-fourths < Five-sixths.

This is the inequality which correctly compares Three-fourths, One-seventh, and Five-sixths

Answer:

d

Step-by-step explanation: