Stephen wants to buy yellow tangs and clown fish for his saltwater aquarium. He wants to spend no more than $77 on fish. At the store, yellow tangs cost $15 each and clown fish cost $11 each. Write and graph a linear inequality to find the number of yellow tangs x and the number of clown fish y that Stephen could purchase. Name a solution of your inequality that is not reasonable for the situation. Explain

An expression is a sum of cubes if it can be written in form of a³ + b³, where a and b can be any constant/variables.

So, this means the given expression 125x³ + 144 can only be sum of cubes if the both the terms i.e. 125x³ and 144 are perfect cubes.

125x³ = (5x)³ . This means 125x³ is a perfect cube. However, 144 is not a perfect cube.

Hence we can conclude that the expression 125x³ + 144 is not a sum of cubes. So the answer to this question if FALSE

Answer;

(0,2)

Step-by-step explanation:

Answer:

90% of paperclips did not get used.

Step-by-step explanation:

Your office manager used 45 paperclips for handouts at his presentation from the 450 paperclips available in the stock room.

We have to calculate the percentage of the original number of paperclips did not get used.

number of paperclips did not get used = 450 - 45 = 405

the percentage of 405 out of 450 = [tex]\frac{405}{450}[/tex] × 100

                                                         =  0.9 × 100

                                                         = 90%

Therefore, 90% of paperclips did not get used.

Using the side lengths of △PQR and △STU, which angle has a sine ratio of 4/5?

Answer is A. ∠P

The angle that has the sine ratio, 4/5, is: A. Angle P.

Sine ratio is the ratio of the opposite side over the hypotenuse of the right triangle in respect to the given reference angle.

Given, sine ratio of 4/5, then it means:

Opposite side (side directly opposite to the reference angle) = 4

Hypotenuse (longest side) = 5.

Thus, in the image given, using P as the reference angle, the sine ratio of P is:

QR/PQ = 16/20 = 4/5

Therefore, the angle with the sine ratio of 4/5 is: A. P.

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For a triangle with an obtuse angle B and the longest side opposite it (side c), the correct statement is a^2 + c^2 > b^2.

The correct answer is option B.

In a triangle with sides a, b, and c, where angle B (opposite side b) is obtuse, and side c is the longest side (opposite the largest angle), we can apply the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles:

c^2 = a^2 + b^2 - 2ab * cos(B)

Given that angle B is obtuse, cos(B) will be negative. Therefore, the term -2ab * cos(B) will subtract from the sum of a^2 + b^2. The Law of Cosines now becomes:

c^2 = a^2 + b^2 + 2ab * cos(B)

Considering the given options:

A. a^2 + c^2 < b^2 - This is not necessarily true in this context.

B. a^2 + c^2 > b^2 - This is true based on the Law of Cosines.

C. b^2 + c^2 < a^2 - This is not necessarily true in this context.

D. a^2 + b^2 < c^2 - This is not necessarily true in this context.

Therefore, from the given options the correct one is option B.

The solutions are as follows:

11) 110 - alternate exterior angles

12) 84 - alternate interior angles

13) 80 - supplementary angles

14) 111 - alternate interior angles

15) 125 - alternate interior angles

16) 47 -  alternate exterior angles

17) 53- corresponding angles

18) 113-alternate interior angles

Here, we have,

from the given figure, we get,

11) the required angle is alternate exterior angle of 110,

so, the value is 110.

12) the required angle is alternate interior angle of  84

so, the value is 84

13) the required angle is supplementary angle of 100

so, the value is 80

14) the required angle is alternate interior angle of 111

so, the value is 111

15) the required angle is alternate interior angle of 125

so, the value is 125

16) the required angle is alternate exterior angle of 47,

so, the value is 47.

17) the required angle is corresponding angle of 53

so, the value is 53.

18) the required angle is alternate interior angle of  113

so, the value is 113.

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Algebraic equation is a mathematical way of expressing the way in which two expression are set equal to each other with given conditions. Using the algebraic equation we get that the age of the ms. Ford was exactly twice as old as ms. Lincoln. before 22 years ago.

Given-

The age of the Ms. Ford is 48.

The age of the Ms. Lincoln is 35.

Algebraic equation is a mathematical way of expressing the way in which two expression are set equal to each other with given conditions.

Let x years ago the age of the ms. Ford was exactly twice as old as ms. Lincoln.

Thus x years ago the age of the ms. Ford was [tex](45-x)[/tex]

x years ago the age of the ms. Lincoln was [tex](35-x)[/tex].

Make a equation using the given information. As the x years ago the age of the ms. Ford was exactly twice as old as ms. Lincoln. Therefore,

[tex](48-x)=2(35-x)[/tex]

[tex]48-x=70-2x[/tex]

[tex]2x-x=70-48[/tex]

[tex]x=22[/tex]

Hence, the age of the ms. Ford was exactly twice as old as ms. Lincoln. before 22 years ago.

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Answer: The answer is (B) This is the graph of a function, but it is not one-to-one.

Step-by-step explanation:  We are given a graph and four options out of which we are to select the statement that best describes the given graph.

Since the graph of a linear function is a straight line, so the first option is not correct.

The given graph is of a function because for a particular value of y, there is a fixed value of 'x'.

Also, since there are two different values of x having same value for y, so the function is not one-to-one. For example, If y = f(x) is the function, then f(1.5) = f(-1) = 3.

Therefore, the graph represents a function, but it is not one-to-one.

Thus, the correct option is (B).

Keywords:

Polynomial, variable, coefficients, constant term.

For this case, the first thing we must do is rewrite the polynomial in a standard way. For this, we reorder the polynomial coefficients.

The standard form of the polynomial is:

[tex]ax ^ 2 + bx + c[/tex]

Where,

a, b, c: are the coefficients of the polynomial.

x: is the variable

Rewriting the polynomial we have:

[tex]3x ^ 2-5x + 2[/tex]

Comparing with the standard form we have that the values of the coefficients are given by:

[tex]a = 3\\b = -5\\c = 2[/tex]

Answer:

The values for the coefficients and constant term are:

[tex]a = 3\\b = -5\\c = 2[/tex]

Answer:

a= 3 b= -5 c=2

Step-by-step explanation:

i just did it on edge

The last operation performed when evaluating (8-2x)^2+4 for x=3 is the addition operation.

Equations are known to make up of variables and constants. Given the expression;

(8-2x)^2+4

If x = 3, substitute into the expression to have:

(8-2x)^2+4

= (8-2(3))^2+4
=  (8 - 6)^2 + 4

Evaluate the expression in parenthesis

= 2^2 + 4
= 4 + 4

Add the resulting expression

(8-2x)^2+4  = 8

Hence the last operation performed when evaluating (8-2x)^2+4 for x=3 is addition operation

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Answer:

option A

[tex]0.55\ ft^{2}[/tex]

Step-by-step explanation:

Let

x-------> the area of the garage door on the blueprint

y------> the area of the actual garage door

z------> scale factor

we know that

The scale factor squared is equal to the area of the garage door on the blueprint divided by the area of the actual garage door

so

[tex]z^{2}=\frac{x}{y}[/tex]

In this problem we have

[tex]z=0.05, y=220\ ft^{2}[/tex]

substitute the values and solve for x

[tex]0.05^{2}=\frac{x}{220}[/tex]

[tex]x=220(0.05^{2})[/tex]

[tex]x=0.55\ ft^{2}[/tex]