Study the solutions of the three equations on the right. Then, complete the statements below. There are two real solutions if the radicand is There is one real solution if the radicand is There are no real solutions if the radicand is 1. y = negative 16 x squared + 32 x minus 10. x = StartFraction negative 32 plus-or-minus StartRoot 384 EndRoot Over negative 32 EndFraction. 2. y = 4 x squared + 12 x + 9. x = StartFraction negative 12 plus-or-minus StartRoot 0 EndRoot Over 8 EndFraction. 3. y = 3x squared minus 5 x + 4. x = StartFraction 5 plus-or-minus StartRoot negative 23 EndRoot Over 6 EndFraction.

Answer:

y=2x+1

Step-by-step explanation:

change -2x to 2x

6x -15y = 135

-15y = 135 -6x

y = (135-6x)/-15

y = 2/5x + 9

Answer:

121

we can factor it

121 = 11×11

121=(11)2

121=11

so options c is correct

Answer:

Stirring water increases the rate at

which a salt dissolves.

Step-by-step explanation:

The stirring allows fresh solvent molecules to continually be in contact with the solute.

Answer:

145

Step-by-step explanation:

110÷177.4=.62 cal per gram

.62×233.5=145 rounded

Answer:

10 + m  ≥ 30

You must spend AT MOST $20 or more

Step-by-step explanation:

Basically you have already spent 10 dollars and you have to pay MORE than or equal to 30. You cannot pay less than because you want the free songs. So the sign has to be  ≥ or the inequality will not be true.

10 + m  ≥ 30

10 - 10 + m  ≥ 30 - 10     ( subtract 10 from each side to isolate m)

m  ≥ 20     ( we are left with this )

The answer is :

m  ≥ 20

You must spend at most 20 dollars more to get the 3 free cd's. Your welcome :D

Answer:

Heres how to solve.

Step-by-step explanation:

3 cups of sugar for every 2 teaspoons of baking soda.

So 6 cups of sugar for 4 teaspoons of baking soda.

And 9 cups of sugar for 6 teaspoons of baking soda.

Basically you just multiply by 3, 3×3=9 and 2*3=6

The number of teaspoons of baking soda Trisha needed will be 6.

It is given that Trisha uses 3 cups of sugar for every 2 teaspoon of baking soda.

We have to find out that what will be the number of teaspoons of baking soda needed for 9 cups of sugar.

If a car goes 10 km in two hours , how far will it go in one hour ?

The car will go, 10 ÷ 2 = 5 km in an hour.

As Trisha uses 3 cups of sugar for every 2 teaspoons of baking soda.

For 1 cup of sugar Trisha will have to use 2/3 teaspoons of baking soda .

For 9 cup of sugar Trisha will use ;

= (2/3) × 9 = 18 ÷ 3

= 6

So, Trisha will have to use 6 teaspoons of baking soda for 9 cups of sugar.  

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Answer:

2x + 30 = -2x + 2

Step-by-step explanation:

left side has 2 x's so u get 2x and it also has 3 10's so 2x+30

do the same on the right

2 -xs so -2x and 2 ones

-2x+2

Answer:

the answer of the question is 7

Answer:

The answer is C

Step-by-step explanation:

(x, y) → (x + 8, y – 11)

Answer: The Answer is C (x, y) → (x + 8, y – 11)

Step-by-step explanation:

Right triangle LMN has vertices L(7, –3), M(7, –8), and

N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).

Hope this helps

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Enjoy your day!!!

Answer:

(140-15)÷15=W

Step-by-step explanation:

140-15=125

125 still needed.  divide that by the amount that will be saved each week which is 15 a week and you get 8.3.  If they want an actual answer you would say 9 weeks because if you only did 8 Anthony would be short $5 so hed have to wait an additional week to have enough to cover the purchase.  So thats why the answer would be 9

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Answer:

1079.9

Step-by-step explanation:

A = P(1 + [tex]\frac{r}{n}[/tex])^nt

A: ending amount

P: principal (850)

r: interest rate in decimal form (.06)

n: compounding periods, 12 months in a year.

t: time in years (4)

   = 850(1 + .06/12)^12(4)

    = 850(1.005)⁴⁸

    = 850(1.2704891)

    = 1079.9157

Answer:

1079.92

Step-by-step explanation:

Answer:  When you solve for w the equation is [tex]w= \frac{p-2l}{2}[/tex]

Step-by-step explanation:

p = 2L + 2w  subtract 2L from both sides

p -2L = 2L -2L + 2w     2L-2L = 0 om the right; they cancel

p - 2L = 2w     now get w alone

(p - 2L)/2  = 2w/2   divide both sides by 2  2w/2 = w  2/2=1  it "cancels"

[tex]\frac{p +2L}{2} = w[/tex]  rewrite Reverse sides to put w alone on the left side

[tex]w= \frac{p-2l}{2}[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

In the left problem, you use the fact that the sum of the segment lengths is equal to the overall length.

  AC +CB = AB

  (3x -4) +(x -2) = 62

  4x -6 = 62 . . . . . collect terms

  4x = 68 . . . . . . . add 6

  x = 17 . . . . . . . . . . divide by 4

__

In the right problem, you use the fact that the sum of the angles is equal to the overall angle. Here, that overall angle is a linear angle, so measures 180°.

  ∠DFG +∠GFE = ∠DFE

  (5y +3) +(2y -5) = 180

  7y = 182 . . . . . . . . . . . . . . collect terms, add 2

  y = 26 . . . . . . . . . . . . . . . .divide by 7

Answer:

a)C(x)=1500+35x

b)R(x)=60 x

c)P(x)=25x-1500

d)The number of lessons that must be held for the studio to break even ia 60

e)The studio will make 550 if 82 lessons are held

Step-by-step explanation:

Monthly cost that include rent, utilities, insurance, and advertising = $1500

The studio charges $60 for each private lesson but has a variable cost for each lesson of $35 to pay the instructor.

a)Write a linear cost function representing the cost to the studio C(x) to hold x private lessons  for a given month

Fixed monthly cost = $1500

Variable cost of trainer for each lesson = $35

Variable cost of trainer for x lessons = 35x

So, C(x)=1500+35x

b)Write a linear revenue function representing the cost to the revenue R(x) to hold x private lessons  for a given month

Charge for 1 lesson = 60

Charge for x lessons = 60 x

So, R(x)=60 x

c)Write a linear profit function representing the cost to the profit P(x) to hold x private lessons  for a given month

Profit = Revenue - Cost

P(x)=R(x)-C(x)

P(x)=60x-1500-35x

P(x)=25x-1500

d)Determine the number of lessons that must be held for the studio to break even

R(x)=C(x)

60x=1500+35x

25x=1500

x=60

So, the number of lessons that must be held for the studio to break even ia 60

e) If 82 lessons are held during a month how much money will the studio make or lose

P(x)=25x-1500

P(82)=25(82)-1500

P(82)=550

So, The studio will make 550 if 82 lessons are held

1)Profit function P(p)=25p-1500

2) For the break-even number of lessons to be held is 60 lessons.

3)Profit, when 82 sessions are held is $550.

The fixed monthly cost of the dance studio= $1500

The variable cost of the trainer for each lesson = $35

So, Variable cost of trainer for 'p' lessons = 35a

So, Total cost =1500+35p

Charge for 1 private lesson = 60

Charge for 'p' lessons = 60p

So, Revenue =60p

We know that, Profit = Revenue - Cost

So, Profit =60p-(1500+35p)

Profit=25p-1500

The break-even point is the point at which total cost and total revenue are equal.

For break-even

Cost = Revenue

1500+35p = 60p

p =60

So, for the break-even number of lessons to be held = 60 lessons

Profit when 82 sessions are held

Profit = 25p-1500

Profit = 25*82-1500

Profit = $550

Therefore, 1)Profit function P(p)=25p-1500

2) For the break-even number of lessons to be held is 60 lessons.

3)Profit, when 82 sessions are held is $550.

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Answer:

A

Step-by-step explanation:

Notice:  The literal factors are all the combinations of a and b where the sum of the exponents is 4:  a4,  a3b,  a2b2,  ab3,  b4.

The degree of each term is 4.

The first term is actually a4b0, which is a4 · 1.

Thus to "expand" (a + b)5, we would anticipate the following terms, in which the sum of all the exponents is 5:

(a + b)5 =  ? a5 +  ? a4b +  ? a3b2 +  ? a2b3 +  ? ab4 +  ? b5

The question is, What are the coefficients?

They are called the binomial coefficients.  In the expansion of

(a + b)4, the binomial coefficients are

1  4  6  4  1

The coefficients in the expansion are 1, 4, 6, 4, 1.

The sum of exponents of x and y is always n. The binomial coefficients which are equidistant from the beginning and from the ending are equal i.e. [tex]^nC_0[/tex]= [tex]^nC_n[/tex], [tex]^nC_1[/tex]= [tex]^nC_{n-1}[/tex], [tex]^nC_2[/tex]= [tex]^nC_{n-2}[/tex] ,….. etc.

The expansion of [tex](x+ y)^4[/tex]

= [tex]x^4[/tex] + 4x³y + 6x²y² + 4xy³ + [tex]y^4[/tex]

So, the highest degree is 4.

and, The literal factors are all the combinations are  [tex]x^4[/tex], 4x³y, 6x²y², 4xy³,[tex]y^4[/tex]

Hence, the coefficients in the expansion are 1, 4, 6, 4, 1.

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Answer: c

Step-by-step explanation:

Answer:

C. 75°

Step-by-step explanation:

Step 1:

70° + 35° + x = 180°    Sum of a Δ

Step 2:

105° + x = 180°       Combine Like Terms

Step 3:

x = 180° - 105°    Subtract

Answer:

x = 75°

Hope This Helps :)

Answer:

The scale factor is 2

Step-by-step explanation:

Answer:

y = 4

Step-by-step explanation:

You are solving for the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction.

Isolate the variable, y. First, subtract 6 from both sides of the equation:

7y + 6 (-6) = 34 (-6)

7y = 34 - 6

7y = 28

Next, divide 7 from both sides:

(7y)/7 = (28)/7

y = 28/7 = 4

y= 4 is one of the equivalent equations that can answer this question.

~

Answer:

$23

Step-by-step explanation:

move the decimal over left 1 time and double the amount

Answer:

$23.75

Step-by-step explanation:

As 20% equals to [tex]\frac{20}{100}[/tex], which is the same as 0.20, then all you have to do to get to the answer is to calculate:

0.2 * 118.75 = $23.75

Answer:

x=30

Step-by-step explanation:

they are conqruent,

the proportion is 2.5 as we can find that by 20/8

2.5 times 12 is 30

Answer: 20.25

Step-by-step explanation: Rebecca can expect to be making her regular 13.50 an hour, however once time and a half hits she’s looking at taking her 13.50 and dividing it by 2. So 13.50 divided by two is 6.75. You then take that 6.75 and add it on top of her regular 13.50 hourly. Putting you at 20.25 for time and a half.

The translation of the point (1, -4) when you move left 4 units and down 1 unit will be (0,-8).

Translation in mathematics is the movement of a shape in any direction—left, right, up, or down—without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

Given that you start at (1, -4). You move left 4 units and down 1 unit. The translated point will be calculated as,

(1, -4)  ⇒ ( 1 - 1 , -4 - 4)

( 1 , 4 ) ⇒ ( 0 , -8)

Therefore, the translation of the point (1, -4) when you move left 4 units and down 1 unit will be (0,-8).

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