Juan has a sandbox and wants to double the length, width and height. If the original box holds 1 cubic foot of sand, how many more feet of sand must be added to fill up the new box.

Answer:

yes

Step-by-step explanation:

All the real numbers x in the expression such that (3x - 27)³ + (27x - 3)³ = (3x + 27x - 30) is x = 1 .

In the question ,

it is given that the expression is

(3x - 27)³ + (27x - 3)³ = (3x + 27x - 30)

By using the identity a³ + b³ [tex]=[/tex] (a + b)(a² - ab + b² )

we get ,

[(3x - 27 + 27x - 3)] × [(3x - 27)² - (3x - 27)(27x - 3) + (27x - 3)² ] = 30x - 30

(30x - 30)×[(3(x - 9))² - (3(x - 9) × 3(9x - 1)) + (3(9x - 1))²] = 30x -30

using the identity (a-b)² [tex]=[/tex] a² -ab + b²

(30x - 30) × [9( x² - 18x + 81) - (9(9x² - 82x + 9)) + (9(81x² - 18x + 1)) = 30x-30

9(30x - 30)×[x² - 18x + 81 - 9x² + 82x - 9 + 81x² - 18x + 1] = 30x - 30

270×(x - 1)×[ 73x² + 46x + 73] = 30(x - 1)

taking (x-1) terms to LHS ,
we get

(270 - 30)×(x - 1)[ 73x² + 46x + 73 ] = 0

(240) (x - 1) [ 73x² + 46x + 73 ]  =  0     ....because 270-30 = 240

Dividing both sides by 240

we get ,

(x - 1) [73x² + 46x + 73] = 0

So , either x - 1 = 0    or      73x² + 46x + 73 = 0

on solving 73x² + 46x + 73 = 0

we get the discriminant of 73x² + 46x + 73  a negative number , so it cannot have real root .

hence x -1 = 0

x = 1

Therefore , the only real solution is x = 1 .

The given question is incomplete , the complete question is

Find all real numbers x in the expression such that (3x - 27)³ + (27x - 3)³ = (3x + 27x - 30)   ?

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Answer:Angles in a triangle may or may not be congruent.

The values of x and y are 90 and 47, respectively.

From the figure, we have:

This means that, angle x is a right-angle.

So, we have:

Triangle ABC is an isosceles triangle.

So, we have:

The measure of y is then calculated as:

--- sum of angles in a triangle

This gives

Subtract 137 from both sides

Hence, the values of x and y are 90 and 47, respectively.

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Step-by-step explanation:

The flowchart that is used to prove GR ║ F_K is presented as follows;

∠RND and ∠FDP are supplementary  ⇒    ∠RND + ∠FDP = 180°

Given                            [tex]{}[/tex]                                 Definition of supplementary

∠KDN  ≅ ∠FDP                 [tex]{}[/tex]                    ⇒    ∠KDN = ∠FDP

Vertical angles are congruent[tex]{}[/tex]                    Definition of congruent angles

∠RND and ∠KDN are same side interior angles [tex]{}[/tex] ⇒∠RND + ∠KDN = 180°    

Definition of same side interior angles[tex]{}[/tex]                    Substitution property

[tex]{}[/tex]                                           GR ║ F_K

The relationships between the angles formed by a transversal and two parallel lines are;

Definition of congruency;

Two lines, shape or figure are said to be congruent if they have the same size and shape.

Supplementary angles;

Supplementary angles are angles that have a sum of 180°

Substitution property of equality

The substitution property sates that if an expression a = b, then the expression b can replace a in any equation and the equation will remain valid.

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The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

In this question, we have been given there are 10 brown, 10 black, 10 green, and 10 gold marbles in bag.

The theoretical probability of pulling a brown marble from the bag would be,

P = 10/40

P = 0.25

P = 25%

A student pulled a marble, recorded the color, and placed the marble back in the bag.

The frequency of each color pulled during the experiment after 40 trials is:

Brown 13

Black 9

Green 7

Gold 11

So, the experimental probability of pulling a brown marble from the bag would be,

P = 13/40

P = 0.325

P = 32.5 %

Therefore, the theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

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Answer: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

Step-by-step explanation: :)

Answer A ; 4934 is the P-intercept. which indicates that 4934 people called Minnesota home in 2000.

Answer B ;  T-intercept is -4934/37, or approximately -133. This indicates that Minnesota had a population of 2000–133 in 1867.

Answer A : P=37t+4934 can be used to represent Minnesota's population in thousands over the t years after 2000.

P-intercept is the P value at time t=0.

P=37*0+4934\sP=0+4934\sP=4934

So, 4934 is the P-intercept. which indicates that 4934 people called Minnesota home in 2000.

Answer (B) : The term "t-intercept" refers to the value of the function t when P=0 0=37t+4934 -4934=37t divide by 37 -4934/37=t -133.351351351 = t

Hence T-intercept is -4934/37, or approximately -133. This indicates that Minnesota had a population of 2000–133 in 1867.

P=37t+4934 P-intercept means the value of P at t=0 P=37*0+4934 P=0+4934 P=4934

Given that Minnesota's population in thousands, t years since 2000, it can be expressed by the equation:

So, 4934 is the P-intercept. which indicates that 4934 people called Minnesota home in 2000.

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Answer:

$35

Step-by-step explanation:

All you have to do is subtract 10 from 45 because it was $10 off and the original price was $45.

The rate of change of the linear functions given in tabular form and equations are found as follows;

1. a. The rate of change of the function is 5

b. The rate of change of the function is 7

c. The rate of then function is 0.75

d. The function has a rate of change of -8

2. The rate of change of the function of -4, indicates that each unit increase in the input value results in 4 unit decrease in the output values

b. The number of days it took for the patients blood sample to have 360 antibodies is 13 days

c. The rate of change of the function is 20, which indicates that the antibody in the patients blood is increasing at a rate of 20 antibodies each day

The rate of change of a function is a measure of how much the output changes per unit change in the input.

1. The rate of change of the functions are as follows;

a. The first difference of the y-values is constant, therefore the function is a linear function

The formula for the rate of change of the linear function is presented as follows;

[tex]m = \dfrac{y_2-y_1}{x_2 - x_1}[/tex]

The rate of change of the function is therefore;

b. The first difference is constant and equal to 7, the rate of change of the straight line function is therefore;

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{49-42}{1-0} = 7[/tex]

c. The function is a linear function, as the first difference is constant and equal to 0.75

The rate of change of the function is therefore;

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{2.25-1.5}{-4-(-5))} = 0.75[/tex]

d. The first difference is constant and equal to -8

The rate of change of the straight line function is therefore;

[tex]\dfrac{\Delta y}{\Delta x} = \dfrac{5 - 13}{1 - 0} = -8[/tex]

2. a. The rate of change of the function, y = -4·x + 1 is found by taking the slope of the function

The function is the equation of a straight line, of the form, y = m·x + c with the slope, m = -4

The rate of change of the function is -4, such that for each unit increase in the input value, the output value decreases by 4 units

b. When the number of antibodies is 360, we have;

360 = 20·d + 100

20·d = 360 - 100 = 260

d = 260 ÷ 20 = 13

c. The rate of change of the function means that the number of antibodies the drug produces in the patients body each day is 20 antibodies.

3. The function that gives the amount of antibodies in the body is a = 20·d + 100

d = The number of days

a = The number of antibodies

a. The table is completed as follows;

Data for Medicine A

d    [tex]{}[/tex]                  a

0    [tex]{}[/tex]                  100

1    [tex]{}[/tex]                   120

2    [tex]{}[/tex]                  140

3    [tex]{}[/tex]                  160

4    [tex]{}[/tex]                  180

5    [tex]{}[/tex]                  200

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Answer: X

Step-by-step explanation:

you just start at 0 since that is the origin and go up 5

The solution set for the inequality is (-3, 3)

Here we have the absolute value inequality

|2x| - 6  < 0

To solve this, we need to isolate the variable, which in this case is x.

Adding 6 in both sides we get:

|2x| -6 + 6 < 0 + 6

|2x| < 6

This can be decomposed in the inequality:

-6 < 2x < 6

Now to competely solve the inequality, we will divide both sides by 2, so we get:

-6/2 < 2x/2 < 6/2

-3 < x < 3

So the solution set is (-3, 3)

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The missing value is 22

Direct proportion is the relation between two quantities or values where the ratio of the two will always equal a constant value. The symbol used for proportion is the symbol '∝'.

When two quantities are in direct proportion, if we increase one value, then the other will also increase, and if we decrease one value then the other value will also decrease.

Here we have  

x -    1     2    3     4      5

y -  -2    4    10    16     ?      

As we see the value of x is directly proportional to y  

For every 1 unit value of x, the y value is increasing 6 units

For more Understand observe the following

at x = 1  => y = -2

at x = 2 => y = -2 + 6 = 4  

at x = 3 => y = -2 + 2(6) = 10

Therefore,

The relation between x and y can derive as given below

=> y = - 2 + (x-1)6

=> y = - 2 + 6x -6  

=> y = 6x - 8  

at x = 5 => y = 30 - 8 =22

Therefore,

The missing value is 22

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Answer:

log4 (70)

Step-by-step explanation:

log4(7) + log4(10) = log4(7 * 10 ) = log4(70)

The answer is [14, 42].

The number 14 is even.

7 x 2 = 14

An even number, 42.

7 x 6 = 42

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Answer:

BC = 6

Step-by-step explanation:

since BD = CD then Δ BCD is isosceles.

the line a through D is a perpendicular bisector of BC, then

BX = CX = 3 , so

BC = BX + CX = 3 + 3 = 6

Answer:

[tex]-11[/tex]

Step-by-step explanation:

[tex]P(-1)[/tex] is the remainder when [tex]P(x)[/tex] is divided by [tex]x+1[/tex].

[tex]\frac{x^4 + 7x^3 - 6x-11}{x+1}=x^3 + 6x^2 - 6x-\frac{11}{x+1}[/tex].

The remainder is [tex]-11[/tex], so [tex]P(c)=-11[/tex].

It will take 7 days for Claire to sell as many candy bars as Ayden

Claire has sold 8 candy bars and sells 5 more each day

The first term = 8

Common difference = 5

nth term is = a+(n-1)d

= 8 +(n-1)5

= 8 + 5n - 5

= 3 +5n

Ayden has sold 20 candy bars and sells 3 more each day

The first term = 20

Common difference = 3

nth term = a+(n-1) d

= 20 +(n-1)3

= 20 + 3n -3

= 17 + 3n

Then,

3 + 5n = 17 + 3n

5n - 3n = 17 - 3

2n = 14

n = 14/2

n = 7

Hence, it will take 7 days for Claire to sell as many candy bars as Ayden

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The point (-6,6) is in the solution region of the inequality and is plotted in given below graph.

Given,

Equation -> y > x - 3 +8

                    y > x + 5

Lets take a point A(-6,6)

Putting the value in equation,

6 > -6 + 5

6 > -1

which is true.

Hence, A(-6,6) lies in the region of the inequality.

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Answer:

3

Step-by-step explanation:

The division of the given polynomial is [tex]13q - 9 + \frac{8}{q+7}[/tex].

What is the quotient of polynomials?

Any quotient of polynomials a(x)/b(x) can be expressed as q(x)+r(x)/b(x), where r(x) is a real number and b is a real number (x). For instance, x-2+3 can be used to represent (x2-3x+5)/(x-1) (x-1).

We have,

              [tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]

By dividing,

           [tex]\frac{(13q^{2} + 82q - 55)}{ (q + 7)} / \frac{(13q^{2} + 82q - 55)}{ (q + 7)}[/tex]

                  [tex]= 13q + \frac{-9q - 55)}{ (q + 7)}[/tex]

                   [tex]\frac{-9q - 55}{q+7} / \frac{-9q - 55}{q+7}[/tex]

                   [tex]= 13q - 9 + \frac{8}{q+7}[/tex]

Hence, the division of the given polynomial is  [tex]13q - 9 + \frac{8}{q+7}[/tex].

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The inequality that describes this situation is f ≥ 5

How to calculate the inequality ?

Use the steps below to solve an inequality:

Step 1: Subtract all fractions by multiplying each term by the sum of all fractions' least common denominators.

Step 2: Simplify the inequality by merging like terms on each side.

Step 3: Add or subtract amounts to get the unknown and the numbers on either side.

As per the question it tells the High- fiber should have at least 5g of fiber per serving

f = Number of grams of fiber per serving of high-fiber food

∴ f ≥ 5

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Answer:

$3

Step-by-step explanation:

Total of all = $19.50

3 Card holders total = $7.50

4 Baseball card total = ?

We know that 19.50 is the sum of the holders and cards together so we subtract $7.50 from $ 19.50.

$19.50-$7.50=$12 for ALL four baseball cards

We know that 4 baseball cards are $12, but if we DIVIDE 12 by four, we get the individual price per card.

12/4 = $3

Answer:

[tex]d=-8[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]258[/tex] and the second term is [tex]250[/tex], then each successive term in the sequence is [tex]8[/tex] less than the previous term. Therefore, the common difference is [tex]-8[/tex] ( [tex]d=-8[/tex] ).

The formula representing the arithmetic sequence is:

[tex]a_n=-8n+266[/tex]

Therefore:

Term 1: [tex]a_1=-8(1)+266=-8+266=258[/tex]

Term 2: [tex]a_2=-8(2)+266=-16+266=250[/tex]

Term 3: [tex]a_3=-8(3)+266=-24+266=242[/tex]

…

Term 9: [tex]a_9=-8(9)+266=-72+266=194[/tex]

The phrase that represents the algebraic expression n - 4 is option b four less than a number.

Given,

The algebraic expression; n - 4

We have to find the phrase that represents the given algebraic expression.

Algebraic expression;

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

An algebraic expression can be categorized into different categories depending on how many terms it contains: polynomial, quadrinomial, trinomial, monomial, and binomial.

So,

n - 4

That is,

4 is less than from a number

Therefore,

The phrase that represents the algebraic expression n - 4 is option b four less than a number.

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Answer:

the answer is b

Step-by-step explanation:

Answer:

224 in²

Step-by-step explanation:

The formula for the area of a triangle is 0.5bh, where b is the base and h is the height. Here the base is '4t' and the height is '7t'. Subbing in 4 for t, we get

Base = 4(4) = 16

Height = 7(4) = 28

Subbing this values into our formula for the area of a triangle, and we have:

Area = 0.5(16)(28) = 224 in²

To solve the given derivative we need to apply the chain rule.

Given that, [ln(g(x))]².

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

The chain rule is a formula that expresses the derivative of the composition of two differentiable functions [tex]f[/tex] and [tex]g[/tex] in terms of the derivatives of [tex]f[/tex] and [tex]g[/tex].

Find the derivative using the chain and power rules.

ln(g²x²)/x

Therefore, to solve the given derivative we need to apply the chain rule.

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The marble that is heavier based on the ratio is purple marble.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

This indicates that you're dividing information A by B. For instance, the ratio will be 5/10 if A is 5 and B is 10.

Red balloons float purple marbles at a ratio of 12: 4. This will be:

= 12/4

= 3

Red balloons float green marbles at a ratio of 15: 6. This will be:

= 15/6

= 2.5

In this case, the purple marble is heavier as 3 is more than 2.5.

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Hope this helps!! :]

Answer:

  (x, y) = {(-2, -3), (2, 5)}

Step-by-step explanation:

You want to solve the system of equations y=x²+2x-3 and y=2x+1.

The two expressions for y can be equated, and the resulting equation put in standard form.

  x² +2x -3 = 2x +1

  x² -4 = 0 . . . . . . . . . . subtract (2x+1)

  (x -2)(x +2) = 0 . . . . . factor

Values of x that make the factors zero are 2 and -2.

Corresponding values of y are ...

  y = 2x +1 = 2(2) +1 = 5

  y = 2(-2) +1 = -3

Solutions are ...