If 225 is the dividend and 15 is the divisor, then what is the quotient?

Answer:

C.  1.11

Step-by-step explanation:

Ball: f(x) = 24 − 16x^2

Balloon: g(x) = 4x

4x = 24 - 16x^2

16x^2 + 4x - 24 = 0

4x^2 + x - 6 = 0

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] x = \dfrac{-1 \pm \sqrt{1^2 - 4(4)(-6)}}{2(4)} [/tex]

[tex] x = \dfrac{-1 \pm \sqrt{1 + 96}}{8} [/tex]

[tex] x = \dfrac{-1 \pm \sqrt{97}}{8} [/tex]

[tex] x = \dfrac{-1 + \sqrt{97}}{8} [/tex]   or   [tex] x = \dfrac{-1 - \sqrt{97}}{8} [/tex]

We discard the negative solution.

[tex] x = 1.11 [/tex]

Answer: C.  1.11

Answer:

lesser x = -12

greater x = 12

Step-by-step explanation:

3x^2 +4= 436

3x^2 = 432

x^2 = 144

lesser x = -12

greater x = 12

Answer:

The domain is x cannot equal 1 and range cannot equal 0. The first option you have is correct

Step-by-step explanation:

Answer:

3953

Step-by-step explanation:

67x59 = 3953

Answer:

-1/8

Step-by-step explanation:

lim x approaches -6     (sqrt( 10-x) -4) / (x+6)

Rationalize

   (sqrt( 10-x) -4)      (sqrt( 10-x) +4)

    ------------------- * -------------------

       (x+6)                 (sqrt( 10-x) +4)

We know ( a-b) (a+b) = a^2 -b^2

a= ( sqrt(10-x)   b = 4    

(10-x) -16

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

(x+6) (sqrt( 10-x) +4)    

-6-x

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

(x+6) (sqrt( 10-x) +4)

Factor out -1 from the numerator

-1( x+6)

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

(x+6) (sqrt( 10-x) +4)

Cancel x+6 from the numerator and denominator

-1

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

(sqrt( 10-x) +4)

Now take the limit

lim x approaches -6    -1/ (sqrt( 10-x) +4)

                                      -1/ (sqrt( 10- -6) +4)

                                      -1/ (sqrt(16) +4)

                                      -1 /( 4+4)

                                        -1/8

Answer:

[tex]\displaystyle \lim_{x \to -6}\frac{\sqrt{10-x}-4}{x+6} =-\frac{1}{8}[/tex]

Step-by-step explanation:

We want to evaluate the limit:

[tex]\displaystyle \lim_{x \to -6}\frac{\sqrt{10-x}-4}{x+6} \\[/tex]

When attempting to evaluate a limit, we should always try direct substitution. This yields:

[tex]\displaystyle \begin{aligned} &\Rightarrow \frac{\sqrt{10-(-6)}-4}{(-6)+6} \\ \\ &=\frac{\sqrt{16}-4}{-6+6}\\ \\ &=\frac{4-4}{-6+6}\\ \\ &=\underbrace{\frac{0}{0}}_{\text{Indeterminate}} \end{aligned}[/tex]

Since the result is an indeterminate form, we can try simplifying the limit.

Let's cancel the square root in the numerator. We can use the difference of two squares. Recall that:

[tex](a-b)(a+b)=a^2-b^2[/tex]

The expression in the numerator is:

[tex]\sqrt{10-x}-4[/tex]

Therefore, to cancel it out, we will multiply it by:

[tex]\sqrt{10-x}+4[/tex]

Multiply. This yields:

[tex]=\displaystyle \lim_{x \to -6}\frac{\sqrt{10-x}-4}{x+6}\cdot\frac{\sqrt{10-x}+4}{\sqrt{10-x}+4} \\[/tex]

Simplify:

[tex]\displaystyle \begin{aligned} &= \lim_{x \to -6}\frac{(\sqrt{10-x})^2-(4)^2}{(x+6)(\sqrt{10-x}+4)}\\ \\ &=\lim_{x\to-6}\frac{(10-x)-(16)}{(x+6)(\sqrt{10-x}+4)}\\ \\ &=\lim_{x \to \ -6}\frac{-x-6}{x+6(\sqrt{10-x}+4)}\end{aligned}[/tex]

Factor:

[tex]\displaystyle \lim_{x \to \ -6}\frac{-(x+6)}{(x+6)(\sqrt{10-x}+4)}[/tex]

Cancel:

[tex]\displaystyle \lim_{x \to \ -6}-\frac{1}{\sqrt{10-x}+4}[/tex]

Now, we can attempt direct substitution again. Thus:

[tex]\displaystyle \begin{aligned} &\Rightarrow -\frac{1}{(\sqrt{10-(-6)}+4)}\\ \\ &=-\frac{1}{\sqrt{16+4}}\\ \\ &=-\frac{1}{(4+4)} \\ \\ &=-\frac{1}{8}\end{aligned}[/tex]

Therefore:

[tex]\displaystyle \lim_{x \to -6}\frac{\sqrt{10-x}-4}{x+6} =-\frac{1}{8}[/tex]

Answer:

A: (x-3, y+4)

Step-by-step explanation:

A coordinate plane is basically just a number line with two axes.

If we move a numbet right 3, to return it back we’d need to bring it left 3.

If we move a number down 4, we need to bring it up 4 to bring it back to it’s original position.

So to get it back, we need to add the opposite.

(x + 3), 3’s opposite is -3

(y - 4), -4’s opposite is 4.

Hope this helped!

Answer:

15 minutes

Step-by-step explanation:

First, the motorcycle goes at a speed of 40 km/hr.

The question asks for how long it would take to travel 10 km.

Well, there are 60 minutes in an hour, since we will be translating into minutes.

Also, 10 km is 1/4 of 40 km, so it would make sense that the time length would be 1/4 of an hour as well.

1/4 of 60 minutes is 15 minutes.  So it takes 15 minutes for the motorcycle to travel 10 km.

Now, if all this wordy stuff is too much to comprehend, you can also solve using proportional relationships.

[tex]\frac{40km}{60min}=\frac{10km}{xmin}[/tex]

Now cross multiply:

[tex]40km*xmin=10km*60min\\40x=600[/tex]

Divide both sides by 40:

[tex]\frac{40x}{40}=\frac{600}{40}\\x=15[/tex]

Again, this shows that it wouls take 15 minutes for the motorcycle to travel 10 km.

Answer:

Step-by-step explanation:

Answer:

2.6305

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

152 - 20 + 80

▹ Step-by-Step Explanation

'Withdrawing' means taking out money which would be represented with a minus sign.

'Deposit' means you are adding money which would be represented with a plus sign.

Therefore, the answer is:

152 - 20 + 80

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

Step-by-step explanation:

First you have to change your fraction:

Change 7/4 into a mixed number

7/4 = 1  3/4

Then you 'guestamate' about 3/4 of the distance between 1 and 2 and mark your point. Like this:

Hope this helps

The number is expressed as the equation A = 7/4 or A = 1.75

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 7/4   be equation (1)

On simplifying the equation , we get

A = 1.75

Now , the number 1.75 lies on the positive side of the number line and is between 1 and 2

So , the number 1.75 lies between 1 < 1.75 < 2

Hence , the number is A = 1.75

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Step-by-step explanation:

x+y=9

x=9-y ----------(i)

Now in second eqn put the value of x

2x -3y=8

2(9-y) - 3y=8

18 - 2y - 3y=8

18-8=5y

10=5y

y=2

Then put the value of y in eqn (i)

x=9-y

x=9-2

x=7

I hope this will be helpful for you.

Answer:

Step-by-step explanation:

Given,

x + y = 9

2x - 3y = 8

Using substitution method:

In this method , a variable is expressed in terms of another variable from one equation and it is substituted in the remaining equation.

[tex] \mathsf{x + y = 9}[/tex]

Move y to right hand side and change it's sign

⇒[tex] \mathsf{x = 9 - y}[/tex]⇔equation ( i )

Now, put the value of X from equation ( i )

⇒[tex] \mathsf{ 2 (9 - y) - 3y = 8}[/tex]

Distribute 2 through the parentheses

⇒[tex] \mathsf{18 - 2y - 3y = 8}[/tex]

Collect like terms

⇒[tex] \mathsf{18 - 5y = 8}[/tex]

Move constant to right hand side and change it's sign

⇒[tex] \mathsf{ - 5y = 8 - 18}[/tex]

Calculate

⇒[tex] \mathsf{ - 5y = - 10}[/tex]

Divide both sides of the equation by -5

⇒[tex] \mathsf{ \frac{ - 5y}{ - 5} = \frac{ - 10}{ - 5} }[/tex]

Calculate

⇒[tex] \mathsf{y = 2}[/tex]

Now, Put the value of y in the equation ( i )

⇒[tex]x = 9 - 2[/tex]

Calculate the difference

⇒[tex] \mathsf{x = 7}[/tex]

Hence, x = 7 and y = 2

The possible solution of the system is the ordered pair ( x , y )

[tex] \mathsf{(x \: , y \: ) = (7 , \: 2)}[/tex]

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

Check if the given ordered pair is the solution of the system of equation

⇒[tex] \mathsf{7 + 2 = 9}[/tex]

⇒[tex] \sf{2 \times 7 - 3 \times 2 = 8}[/tex]

Simplify the equalities

⇒[tex] \sf{9 = 9}[/tex]

⇒[tex] \mathsf{8 = 8}[/tex]

Since all of the equalities are true , the ordered pair is the solution of the system.

[tex] \mathsf{ \underline{ \bold{(x \:, y \: ) = (7 \:, 2)}}}[/tex]

Hope I helped!

Best regards!!

Answer:

100. 120

101. 28

102. 1

103. 24

Step-by-step explanation:

Number of Permutation (P) can be obtained as follow:

nPr = n! / (n– r)!

Number of Combination (C) can be obtained as follow:

nCr = n! / (n– r)! r!

With the above ideas in mind, let us determine the answers to the questions given above.

100. Evaluation of ₅P₄

nPr = n! / (n– r)!

₅P₄ = 5! /(5 – 4)!

₅P₄ = 5! / 1!

₅P₄ = 5 × 4 × 3 × 2 × 1 / 1

₅P₄ = 120

101. Evaluation of ₈C₂

nCr = n! / (n– r)! r!

₈C₂ = 8! / (8 – 2)!2!

₈C₂ = 8! / 6!2!

₈C₂ = 8 × 7 × 6!/ 6! × 2 × 1

₈C₂ = 8 × 7 / 2 × 1

₈C₂ = 56/2

₈C₂ = 28

102. Evaluation of ₇C₀

nCr = n! / (n– r)! r!

₇C₀ = 7! / (7 – 0)!0!

₇C₀ = 7! / 7!0!

Note: 0! = 1

₇C₀ = 7! / 7!

₇C₀ = 1

103. Evaluation 4!

4! = 4 × 3 × 2 × 1

4! = 24

Answer:

C: (-5, 1)

Step-by-step explanation:

If you put the equation in a graphing calculator and examine all the points, C is the only one not on the line.

Answer:

20 questions

Step-by-step explanation:

Given

[tex]Correct \Marks= +5[/tex]

[tex]Incorrect\ Marks= -2[/tex]

[tex]Score\ Obtained = 30[/tex]

[tex]Number\ of\ correct\ answers = 10[/tex]

Required

Number of questions answered

First, we need to get the total correct marks obtained by Roy

This is calculated by multiplying the correct marks by number of correct answers

[tex]Total = +5 * 10[/tex]

[tex]Total = +50\ marks[/tex]

Subtract this from the total scores obtained; This gives the total incorrect answer obtained by Roy

[tex]Incorrect = Scores\ Obtained - Total[/tex]

[tex]Incorrect = 30 - (+50)[/tex]

Open bracket

[tex]Incorrect = 30 - 50[/tex]

[tex]Incorrect = -20[/tex]

Divide this by -2 to get the number of incorrect answers

[tex]Incorrect\ Answers = \frac{-20}{-2}[/tex]

[tex]Incorrect\ Answers = 10[/tex]

Add this to the number of correct answers to give the total number of question answered

[tex]Total = Correct\ Answers + Incorrect\ Answers[/tex]

[tex]Total = 10 + 10[/tex]

[tex]Total = 20[/tex]

Hence, Roy answered a total of 20 questions

Answer:

The difference between the 4th term of both series is 7

Step-by-step explanation:

The formula for the nth term of an APS is a + (n - 1)×d

The first term of one of the series = -1

The first term of the other of the series = -8

The fourth term of both series is thus;

4th term first series = -1 + (4 - 1)× d = -1 + 3·d

4th term second series =  -8 + (4 - 1)× d = -8 + 3·d

The difference between the 4th term of both series = -1 + 3·d - (-8 + 3·d)

-1 + 3·d - (-8 + 3·d) = -1 + 3·d  + 8 - 3·d = 8 - 1 = 7

The difference between the 4th term of both series = 7.

Step-by-step explanation:

....

.........

.

Answer:

Width   W = 7 m

Length  L =  9 m

Step-by-step explanation:

Area of a rectangle = L * W

Area = 63 m²

L = 3W - 12

Area = L * W

66 = (3W - 12) * W

63 = 3W² - 12W

3W² - 12W - 63 = 0     ( solve W by using quadratic equation)

       -(-12) ± √ -12² - 4 * 3 * (-63)

W = -------------------------------------------

                      2 * 3

W = 7 ;  W = - 3  

therefore use W = 7 m

solve for L:

L = 3W - 12

L = 3(7) - 12

L =  9 m

check:

Area = L * W

63 =  9 * 7

63 = 63  ----- OK

Answer:

Perimeter of the park = 300 yards

Step-by-step explanation:

Area of a rectangle= length * width

Area of the rectangular park = 5,400 yards squared

Let

Width= x

Length= 1.5 * x = 1.5 x

Area of a rectangle= length * width

5,400= 1.5x * x

5400= 1.5x^2

x^2= 5400 / 1.5

x^2 = 3600

Take the Square root of both sides

√x^2 = √3600

x=60

Therefore,

Width = x = 60 yards

Length = 1.5x

=1.5(60)

=90 yards

Perimeter of the rectangular park = 2(length + width)

=2(90+60)

=2(150)

= 300 yards

Answer:

how you convert feet to square feet

length X width = square feet

if the board is 3ft long and 1 foot wide

3ft X 1ft = 3square feet

so the length is 3 feet

Answer:

Step-by-step explanation:

the answer is 9

Answer:

5 + 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Given

[tex]\frac{\sqrt{3}+\sqrt{2} }{\sqrt{3}-\sqrt{2} }[/tex]

Multiply numerator/ denominator by the conjugate of the denominator

The conjugate of [tex]\sqrt{3}[/tex] - [tex]\sqrt{2}[/tex] is [tex]\sqrt{3}[/tex] + [tex]\sqrt{2}[/tex]

= [tex]\frac{(\sqrt{3}+\sqrt{2})(\sqrt{3}+\sqrt{2}) }{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2}) }[/tex] ← expand numerator/ denominator using FOIL

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

= [tex]\frac{5+2\sqrt{6} }{1}[/tex]

= 5 + 2[tex]\sqrt{6}[/tex] → with a = 5 and b = 2

Answer:

Los Amigos deberían comprar pizzas vendidas por la primera pizzería que cuestan S / 0.032 por cm² para obtener más ganancias.

Step-by-step explanation:

Los parámetros dados son;

El diámetro de las pizzas vendidas por la primera pizzería = 40 cm

El precio de las pizzas vendidas por la primera pizzería = S / 40

El diámetro de las pizzas vendidas por la segunda pizzería = 25 cm

El precio de las pizzas vendidas por la segunda pizzería = S / 25

El área de las pizzas vendidas por la pizzería = π × D² / 4

El área de las pizzas vendidas por la primera pizzería = π × 40² / 4≈1256.64 cm²

El costo por unidad de superficie de las pizzas vendidas por la primera pizzería = S / 40 / (1256.64 cm²) ≈ S /0.032/cm²

El área de las pizzas vendidas por la segunda pizzería = π × 25² / 4≈490.87 cm²

El costo por unidad de superficie de las pizzas vendidas por la primera pizzería = S / 25 / (490.87 cm²) ≈ S /0.051/cm²

Las pizzas vendidas por la primera pizzería que cuestan S /0.032/cm² s más baratas y producirán mejores ganancias que las pizzas vendidas por la segunda pizzería que cuestan S /0.051/cm²

Por lo tanto, los amigos deben comprar pizzas vendidas por la primera pizzería que cuestan S /0.032 / cm² para obtener más ganancias.

Answer:

1.AED

2.SAS

3.ACB

4.Aternate interior angles

Step-by-step explanation:

Answer:

edg just did it

Step-by-step explanation:

Answer:

5/8

Decimal Form: 0.625

​​

Step-by-step explanation:

Cancel 6.

−5×-5/8*1/5

cancel 5

-  -5/8

Move the negative sign to the left.

-  (-5/8)

remove parentheses

answer is 5/8

hope i helped

-lvr

Answer: 8.4 * 10^6

Step-by-step explanation:

Hope this helps^^

Answer:

10

Step-by-step explanation:

pi is 3.14...

pi - 1 is 2.14...

question becomes 1<2.14x and 2.14x < 10

1/2.14 < x, 0.46... < x

x < 10/2.14, x < 4.67...

combining

0.46< x < 4.67

x can be 1, 2, 3, 4

Answer:

Step-by-step explanation:

pi - 1 = 3.14 - 1 = 2.14

x has to be an integer, and the result must be greater than 1.

1 works.

1 < 2.14*1 < 10  2.14 is between 1 and 10.

2 works

1 < (2.14)*2 < 10

1 < 4.28 < 10

3 works

1 < 2.14 * 3 < 10

1 < 6.42 < 10

4 might work

1 < 2.14*4 < 10

1 < 8.56 < 10

and it does work.

5 can't work

1 < 5 * 2.14 < 10

1 < 10.7 < 10 is not true.

Answer: 1,2,3,4

Answer:

the price of the vanilla flavored coffee per pound is $8.50

the price of the espresso flavored coffee per pound is $9.00

Step-by-step explanation:

Let's give letters to the unknowns, so we can generate equations easily:

cost of espresso coffee beans per pound:  "E"

cost of vanilla flavored coffee beans per pound : "V"

Now, the first statement:

18 pounds of E plus 17 pounds of V cost $306.50, can be written as:

18 E + 17 V = 306.5

The second statement:

19 pounds of E plus 15 pounds of V cost $298.50, can be written as:

19 E + 15 V = 298.5

Now, in order to solve this system of linear equations we can use substitution for example:

E = (306.5 -17 V)/18

and use this expression to substitute for E in the second equation:

19  (306.5 - 17 V)/ 18 + 15 V = 298.5

multiplying by 18 on both sides to eliminate denominators, we get:

19 (306.5 - 17 V) + 270 V = 5373

5823.5 - 323 V +270 V = 5373

5823.5 - 53 V = 5373

5823.5 - 5373 = 53 V

450.5 = 53 V

V = 8.5

Therefore the price of the vanilla flavored coffee per pound is $8.50

Now we use this found value in the substitution equation:

E = (306.5 -17 V)/18

E = (306.5 - 17 (8.5))/18

E = 9

Therefore the price of the espresso flavored coffee per pound is $9.00

Answer:

0.123 GSD are expected to be received by each JPY.

Step-by-step explanation:

The exchange rate is the ratio of GSD per each JPY, that is:

[tex]x = \frac{12.33\,GSD}{100\,JPY}[/tex]

[tex]x = 0.123\,\frac{GSD}{JPY}[/tex]

Which means that 0.123 GSD are expected to be received by each JPY.

Answer:

12x+16-4y

Step-by-step explanation:

Answer:

lets start with x = 5x+7x=12x

now y = 2y-6y= -4y

now reg numbers = 8+8=16

now add all of them not litteraly add by add as in make them into a expression

so

12x-4y+16

Answer:

[tex] \frac{1}{3} - \frac{1}{2} + \frac{2}{5} [/tex]

[tex] = \frac{10 - 15 + 2 \times 6}{30} [/tex]

[tex] = \frac{10 - 15 + 12}{30} [/tex]

[tex] = \frac{ - 5 + 12}{30} [/tex]

[tex] = \frac{7}{30} [/tex]

Answer:

[tex] \frac{1}{3} - \frac{1}{2} + \frac{2}{5} [/tex]

[tex] = \frac{10 - 15 + 2×6}{30} [/tex]

[tex] = \frac{10 - 15 + 12}{30} [/tex]

[tex] \frac{-5 +12}{30} [/tex]

= 7 /30

Answer:

k=3 z=-6

Step-by-step explanation:

12k=36

k=36/12

k=3

-6z=36

z=36/-6

z=-6

12(3)-6(-6)=36