The quadratic function

R(p)= -5.2p^2 + 65p - 75

gives the amount of revenue R(p) in dollars generated by a product priced at p dollars.

Question: What is the maximum revenue that can be generated?

For this case we must solve the following equation:

[tex]\frac {x} {4} + 2 = -12[/tex]

Subtracting 2 from both sides of the equation we have:

[tex]\frac {x} {4} = - 12-2[/tex]

Equal signs are added and the same sign is placed.

[tex]\frac {x} {4} = - 14[/tex]

Multiplying by 4 on both sides of the equation we have:

[tex]x = -14 * 4\\x = -56[/tex]

Thus, the solution of the equation is [tex]x = -56[/tex]

Answer:

[tex]x = -56[/tex]

Answer:

Andre has the correct answer. When simplified his answer is equivalent to the original equation.

Answer:

2pg1

Step-by-step explanation:

Hehe

Answer:

[tex]1\dfrac{1}{4}a^6b^3[/tex]

Step-by-step explanation:

A square of a monomial is [tex]1\dfrac{9}{16}a^{12}b^6[/tex] that is [tex]\dfrac{25}{16}a^{12}b^{6}[/tex]

Use properties of exponents:

[tex](a^m)^n=a^{mn}\\ \\\dfrac{a^m}{b^m}=\left(\dfrac{a}{b}\right)^m\\ \\a^mb^m=(ab)^m[/tex]

Note that

[tex]\dfrac{25}{16}=\dfrac{5^2}{4^2}=\left(\dfrac{5}{4}\right)^2\\ \\a^{12}=a^{6\cdot 2}=(a^6)^2\\ \\b^6=b^{3\cdot 2}=(b^3)^2[/tex]

Then

[tex]\dfrac{25}{16}a^{12}b^{6}=\left(\dfrac{5}{4}\right)^2\cdot (a^6)^2\cdot (b^{3})^2=\left(\dfrac{5}{4}a^6b^3\right)^2[/tex]

So, the monomial is

[tex]\dfrac{5}{4}a^6b^3=1\dfrac{1}{4}a^6b^3[/tex]

Answer:

Temperature of the ice for ice-skating = -5 °C

Step-by-step explanation:

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

Temperature of the ice for an ice hockey match = - 7 °C

Temperature for ice- skating is 2 degrees warmer.

2. What is the temperature of the ice for ice-skating?

For the correct calculation, we use this formula:

Temperature for ice-skating = Temperature of the ice for a hockey match + 2

Temperature for ice-skating = -7 + 2

Temperature of the ice for ice-skating = -5 °C

We add 2 to the temperature of the ice for a hockey match because the temperature for ice-skating is described as warmer. If it were described as colder, we should subtract.

Answer:

-5c

Step-by-step explanation:

because basically  you subtract because it is below normal

Answer:whole wheat

Step-by-step explanation:

Its whole wheat because when you divide the cost by the weight whole wheat is the best deal

So this is the answer...

Hope this can help :)

Answer:

Speed of Carol is 78 mph and that of Steve is 84 mph.

Step-by-step explanation:

Let the speed of Carol is x mph and that of Steve is (x + 6) mph.

If they move towards each other with that speed, then the resultant speed will be (x + x + 6) = (2x + 6) mph

With this resultant speed, they cover 405 miles in 2.5 hours.

So, [tex]2x + 6 = \frac{405}{2.5} = 162[/tex]

⇒ 2x = 156

⇒ x = 78 mph

So, speed of Carol is 78 mph and that of Steve is (78 + 6) = 84 mph. (Answer)

Answer:

x = 20

Step-by-step explanation:

-7 (2) = -14 so...

10 (2) = 20

Answer:

Step-by-step explanation:

20y - 60 = 5x

add 60 to both sides:

20y = 5x + 60

divide through by 20:

y = (1/4)x + 3

slope = 1/4

y-intercept = (0, 3)

Answer:

5

Step-by-step explanation:

(-3)(2)-7(-3)-10

-6+21-10

15-10

5

Answer:

Step-by-step explanation:

-8(k - 4)         use the distributive property: a(b + c) = ab + ac

= (-8)(k) + (-8)(-4) = -8k + 32

Answer:

-8k+32

Step-by-step explanation:

-8(k-4)=-8k+32

Step-by-step explanation:

When a factor appears in both the numerator and denominator, that is a hole in the function.

Therefore, the domain of h(x) is (-∞, 4) (4, ∞).

Which means the range of h(x) is (-∞, 5) (5, ∞).

Graph: desmos.com/calculator/j58gdgugxy

See the explanation

Since you haven't provided any options I'll face this problem in a general way. Linear functions are given of the form:

[tex]y=mx+b[/tex]

This is called the slope-intercept form of the equation of a line. When modeling a linear function we need to take into account that we will have a constant rate of change and that when plotting our model this will follow a line. In order to model a problem as a linear function we need to follow some tips:

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The quantity that is best modeled by a linear function must fit into y = mx + c

A model is a representation of reality. There are many different types of models such as;

A linear function is a function of the sort y =mx + c. The quantity is not shown in the question hence the question is incomplete.

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Answer:

D) 0.0004

Step-by-step explanation:

(0.02)^2=0.02*0.02=0.0004

The factorization of the expression 2b + 8 is 2 ( b + 4 ).

Given data:

The expression is represented as 2b + 8.

To factor out the coefficient of the variable in the expression 2b + 8, determine the greatest common factor (GCF) of the terms.

The GCF of 2b and 8 is 2.

So, divide each term by 2 to factor out the coefficient:

2b + 8 = 2(b) + 2(4)

Now, rewrite the expression factored out:

2b + 8 = 2(b + 4)

Hence, the expression 2b + 8 factored is 2(b + 4).

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Answer:

The average speed of the first plane is 315 mph and that of the second plane is 105 mph.

Step-by-step explanation:

Let us assume that the first plane has speed x mph and that of the second plane is y mph.

So, as per given condition x = 3y ......... (1)

Now, given that after traveling in the same direction for 7.5 hours, they are 1575 miles apart.

So, we write the equation as  

7.5x - 7.5y = 1575

⇒ x - y = 210 ........ (2)

Now, solving equation (1) and (2) we get, 3y - y = 210

⇒ 2y = 210

⇒ y = 105 mph

So, from equation (1) we get, x = 3y = 315 mph.

So, the average speed of the first plane is 315 mph and that of the second plane is 105 mph. (Answer)

Final answer:

To translate the given statement into an inequality, it converts to 3x - 4 ≥ 2x + 8. Through simplification, we find that x must be at least 12. This showcases the application of basic algebra rules and solving inequalities.

Explanation:

The question asks to translate 'The sum of three times a number and -4 is at least twice the number plus 8' into an inequality. This can be put into mathematical terms as 3x - 4 ≥ 2x + 8, where 'x' represents the unknown number. To solve, we follow several steps:

Subtract 2x from both sides, resulting in x - 4 ≥ 8.

Add 4 to both sides to isolate the variable, giving x ≥ 12.

This inequality tells us that for the original statement to hold true, the number (x) must be 12 or greater. The process involves understanding operations with numbers, such as adding, subtracting, and applying the rules of inequality to solve for 'x'.

Answer: 15

Step-by-step explanation:

Recall : if sin α = cos β , then α + β are complementary , that is

α + β = 90

Since  sin (2x+7) = cos(4x-7) , then (2x+7) and (4x-7)  are complementary , that is:

2x + 7 + 4x - 7 = 90

6x = 90

x = 90/6

x = 15

The missing value x is constituting the angles of both sin and cos trigonometric ratios.

By using complementary property, the value of x for given condition is evaluated as 15.

The missing value x is constituting the angles of both sin and cos trigonometric ratios.

Its known by trigonometry that  when [tex]sin(\alpha) = cos(\beta)[/tex], then [tex]\alpha + \beta = 90^{\circ}[/tex]

Thus, we have:

[tex]2x + 7 + 4x - 7 = 90\\\\6x = 90\\\\x = \dfrac{90}{6}\\\\x = 15[/tex]

Thus, value of x for given condition is 15.

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Answer:

-1/2 = n

Step-by-step explanation:

2/3(1+n) = -1/2n

2/3 + 2/3n = -1/2n

2/3 + 2/3n - 2/3n = -1/2n

2/3 = -1/2n -2/3n

2/3 = -.5n -.66n

2/3 = -1.16n

2/3/-1.16 = n

.66 - 1.16 =n

-0.5=n

- 1/2 = n

Answer:

-4 = x

Explanation:

-11x +3x =-8x

24=-8x-8

+8= +8

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

32=-8x

--- -----

-8. -8

x= -4

To solve for x in the equation 24 =-11x-8+ 3x, combine like terms and isolate the variable by performing algebraic operations.

To solve for x in the equation 24 =-11x-8+ 3x, we can combine like terms:

Therefore, the solution for x is -4.

The number is -9

Step-by-step explanation:

Let x be the number then according to given statement

[tex]4x+10 = x-17[/tex]

Subtracting 10 from both sides

[tex]4x+10-10 = x-17-10\\4x = x-27[/tex]

Subtracting x from both sides

[tex]4x-x = x-x-27\\3x = -27[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3} = \frac{-27}{3}\\ x = -9[/tex]

Verification:

[tex]4(-9)+10 = -9-17\\-36+10=-26\\-26=-26[/tex]

The number is -9

Keywords: Linear equation, variables

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[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{4(3x^2y^4)^3}{(2x^3y^5)^4}\implies \cfrac{4(3^3x^{2\cdot 3}y^{4\cdot 3})}{(2^4x^{3\cdot 4}y^{5\cdot 4})}\implies \cfrac{4(27)x^6y^{12}}{16x^{12}y^{20}}\implies \cfrac{108x^6y^{12}}{16x^{12}y^{20}} \\\\\\ \cfrac{108}{16x^{12}x^{-6}y^{20}y^{-12}}\implies \cfrac{108}{16x^{12-6}y^{20-12}}\implies \cfrac{27}{4x^6 y^8}[/tex]

Step-by-step explanation:

speed= distance/time

time is meant to be in seconds

1mins = 60 secs

75mins =75 x 60 = 4500

distance is meant to be in metres

1metre= 0.001km

100 km = 100 x 1000= 100000

speed =distance/time

speed = 100000/4500

speed=22.22m/s

Answer:

[tex]\large\boxed{80\dfrac{km}{h}}[/tex]

Step-by-step explanation:

[tex]speed=\dfrac{distance}{times}\\\\\text{We have:}\\\\distance=100km,\ time=75min\\\\1h=60min\to1min=\dfrac{1}{60}h\\\\time=\dfrac{75}{60}h=\dfrac{5}{4}h=1.25h\\\\\text{Substitute:}\\\\speed=\dfrac{100km}{1.25h}=80\dfrac{km}{h}[/tex]

Answer:

y=-3x-3

Step-by-step explanation:

The equation of the line written in the form y=mx+b that passes through G and has y-intercept of -3 is y=-3x-3

The slope-intercept form is y = m x + b, where

m is the slope

b is the y-intercept

Given that the line passes through G and has y-intercept of -3

Now Substitute it in the form of the equation

∴ y = mx - 3

From the given graph we can see that the slope is -3.

Then substitute it in the equation

y = -3x - 3

The new equation is y=-3x-3

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Answer: 12

Step-by-step explanation: To solve this equation, since x is being divided by 2, in order to get x by itself, we need to multiply by 2 on both sides of the equation.

On the left side of the equation, the 2's cancel and we have x and on the right side of the equation, 6 × 2 gives us 12 so we have x = 12 which is the solution for our equation.

To check our solution, we plug 12 in for x in the original equation.

Image provided.

Answer:

The length of the diagonal measures 54.2 meters

Step-by-step explanation:

Pythagorean theorem,

a² + b² = c²

a = 21

b = 50

c = diagonal

21² + 50² = c²

441 + 2500 = c²

2941 = c²

√2941 = c

54.23098... = c

54.2 = c

The length of the diagonal measures 54.2 meters.

We have given that,

A rectangular swimming pool is 21 meters

wide and 50 meters long.

We have to determine the length of the diagonal.

a² + b² = c²

a and b are sides of the triangle and c is the hypotenuse

a = 21,

b = 50

c = diagonal

21² + 50² = c²

441 + 2500 = c²

2941 = c²

Taking square root on both side

√2941 = c

54.23098 = c

54.2 = c

Therefore the length of the diagonal measures 54.2 meters.

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There were 9 cats on the shelter on thursday

Solution:

Let "a" denote number of cats

Let "b" denote number of dogs

Cost per day for each cat = $ 4.50

Cost per day for each dog = $ 8.50

Given that Violet found a record showing that there were a total of 30 cats and dogs on Thursday

Thus, number of cats + number of dogs = 30

a + b = 30  ------ eqn 1

Also given that Violet noticed that the shelter spent $219.00 caring for cats and dogs on Thursday

Number of cats x cost per day for each cat + Number of dogs x cost per day for each dogs = $ 219

[tex]a \times 4.50 + b \times 8.50 = 219[/tex]

4.5a + 8.50b = 219  ----- eqn 2

Multiply first equation by 4.5

4.5a + 4.5b = 135  ---- eqn 3

Subtract eqn 2 from eqn 3

4.5a + 4.5b = 135

(-)4.5a + 8.50b = 219

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

-4b = -84

b = 21

Substitute this y value into the first equation

a + b = 30

a + 21 = 30

a = 9

Thus "a" denotes number of cats, so number of cats on thursday = 9

Answer:

6

Step-by-step explanation:

it's asking how much makes 10% of 60 and to find it we use this formula :

60 ÷ 100 × 10 = 6

Answer:

6 milkshakes

Step-by-step explanation:

All you need to do is multiply:

60 (0.10) = 6