How many solutions does this equation have?
5g + 4(-59 - 5) = -159 - 20

The Quantities of height, length and width are: 9,32, 18.32, 12.32 cubits.

Suppose the height is x.

The width 3 cubits more than the height.

Therefore, width = 3+x

The length being 6 cubits more than the width.

thus, length = 6+3+x

An oracle ordered a prince to build a sacred building whose space would be 400 cubic cubits.

Volume = 400 cubic cubits.

if x is the height, then 3(x+3) (x+9) =400

Find the value of x.

\(3(x+3)(x+9)=400\\3(x^{2} +12x+27)=400\\3x^{2} +12x^{} +27-400 =0\\3x^{2}+12x-373 =0\)

\(x = \frac{-12±\sqrt{12^{2}-4.3(-373) } }{2.3} \\x = \frac{-12±\sqrt{^{}1155 } }{6} \\x= \frac{-6+\sqrt{^{}1155 } }{3}=\frac{-6+33.98}{3} =9.32\\x= \frac{-6-\sqrt{^{}1155 } }{3}=-13.32\)

Consider the positive value now.

therefore, height = x =9.32

Length = 9+x = 9+9.32 = 18.32 cubits

Width = 3+x = 3+9.32 = 12.32 cubits

The height, length and width are: 9,32, 18.32, 12.32 cubits.

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Answer:

dy = 6x(x²+9)²dx

dy =  291.6

Step-by-step explanation:

We need to use both the power rule and the chain rule to differentiate this function

The power rule states that \(x^{n} = nx^{n-1}\)

The chain rule states that f(g(x)) = f'(g(x)) * g'(x)

For this equation, f(x) = x³ and g(x) = x²+9

Using these two formulas results in the equation:

dy = 6x(x²+9)²dx

Substituting our given values in results in the following answer:

(6(3) * (3²+9)² )(0.05) = 291.6

The value of AB is,

⇒ AB = 5.9

(rounded to nearest tenth)

We have to given that,

A right triangle ABC is shown.

Now, By trigonometry formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

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Answer:

4 times

Step-by-step explanation:

The total model is 3 miles, divided by 3/4 equals the multiplication problem 3/1 times 3/4 but use the reciprocal of 3/4 which is 4/3 so it would be 3/1 times 4/3 which is 12/3 which is equivalent to 4. :)

There are 4 times did Eber stop.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Eber ran 3 miles.

And, He stopped to take a break every 3/4 mile.

Now,

Let number of times stop = x

So, We can formulate;

⇒ 3/4x = 3

⇒ x = 3 × 4 / 3

⇒ x = 12/3

⇒ x = 4

Thus, There are 4 times did Eber stop.

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The simplified expression is \(-4x^2 + 3x + 1\), which is a quadratic polynomial. Option D.

To simplify the expression \((8x^2 + 3x) - (12x^2 - 1)\), we can distribute the negative sign to each term within the parentheses:

\(8x^2 + 3x - 12x^2 + 1\)

Next, we can combine like terms by adding or subtracting coefficients of similar powers of x:

\((8x^2 - 12x^2) + 3x + 1\)

Simplifying further, we have:

\(-4x^2 + 3x + 1\)

The resulting polynomial \(-4x^2 + 3x + 1\) is a quadratic polynomial since it has a highest power of x^2 (the exponent of x is 2), which is\(-4x^2.\)Quadratic polynomials are polynomials of degree 2 and can be represented by a parabola when graphed.

In summary, the simplified expression \((8x^2 + 3x) - (12x^2 - 1)\) simplifies to \(-4x^2 + 3x + 1\) , which is a quadratic polynomial. So Option D is correct

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Note the complete question is

Elise's number is 38.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

If you subtract 17 from my number and multiply the difference by negative 6​, the result is negative 126​.

let the number be x

So, the equation can be

-6(x- 17) = -126

Now, solving for x

Divide by -6

x-17= 21

Add 17 both side

x- 17+ 17 = 21 + 17

x= 38

Hence, Elise's number is 38.

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The rectangle

The equation of the perimeter of a rectangle is

We know the value of the perimeter and have a unknow for l(lenght) and w(width) so, we can replace and we will have an equation with the variable x(length)

replacing

simplify parenthesis

add x's

and solve for x dividing the equation on 3

the value of x or the length is 180 ft

Answer:

21

Step-by-step explanation:

Answer:

24,48,72

Step-by-step explanation:

multiples of 6- 6,12,18,24,30,36,42,48,54,60,66,72

multiples of 8- 8,16,24,32,40,48,56,64,74,80

Answer:

7/6 or 1 1/6

Step-by-step explanation:

2/3 = 4/6

1/2 = 3/6

3/6 + 4/6 = 7/6 = 1 1/6

Answer:

\(\displaystyle \frac{dy}{dx} = 20x^3\)

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)

Derivative Property [Addition/Subtraction]:                                                         \(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)  

Basic Power Rule:

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle y = 5x^4 + 4\)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

the correct answer is 15.2

The answer will be 7.45628

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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The simplified sum is 191/30.In mixed number form, this is 6 and 11/30.3 2/3 + 2 7/10 equals 6 and 11/30.

To add the mixed numbers 3 2/3 and 2 7/10, we can follow these steps:First, convert both mixed numbers into improper fractions.

3 2/3 = (3 * 3 + 2)/3 = 11/3

2 7/10 = (2 * 10 + 7)/10 = 27/10

Now, we have 11/3 + 27/10.

To find a common denominator, we multiply the denominators: 3 * 10 = 30.Rewriting the fractions with the common denominator, we have 110/30 + 81/30.

Adding the numerators, we get 110 + 81 = 191.

The sum is 191/30.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 1.

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Answer:

When takiing the 2a to the other side she forgot to change sign:

8(−a+4)=−6a−8+8a

−8a+32=2a−8

−10a=−40

a = 4

The answer is C

The mistake that Lily made if this equation has no solution is (B. She applied the distributive property incorrectly).

Lily applied the distributive property incorrectly when trying to simplify the left-hand side of the equation. The correct steps should involve distributing the 8 to both terms inside the parentheses, but it seems like Lily only distributed the 8 to the first term and missed the second term. This resulted in an incorrect simplified equation and subsequent steps.

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Both men are committing fallacies in their reasoning. The occurrence of a hurricane on that land cannot be predicted with certainty, and making decisions based on fallacious reasoning can lead to poor outcomes.

A fallacy refers to the statement in an argument that makes an error in logic. Fallacies are very dangerous because they lead to incorrect thinking about certain topics and may lead to an incorrect conclusion about that topic most of the time.

The fallacy in Poindexter's uncle's reasoning is known as the fallacy of induction. This fallacy occurs when someone assumes that because a certain event has happened in the past, it is likely to happen again in the future. While it is true that the land has been hit by hurricanes 160 times in the past, it doesn't necessarily mean that it will happen again in the near future.

On the other hand, Poindexter's nephew is committing the fallacy of the Gambler's Fallacy. This fallacy occurs when someone assumes that because something hasn't happened in a while, it is more likely to happen soon. In this case, the nephew assumes that a hurricane must be due soon simply because it hasn't happened in the past 13 years. However, the occurrence of a hurricane is not influenced by the time that has passed since the last one. Each hurricane is a unique event that is not influenced by previous occurrences.

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Answer:

76

Step-by-step explanation:

Angle bisectors split angles into two. So, angle BAD must be twice of BAC.

Substituting, we get 38*2=76

Answer:

yes

Step-by-step explanation:

The required present value needed now to get $700 after 4 years at 11% compounded monthly is $451.73.

To find the present value of $600 after 4 years at 7% compounded monthly, we can use the formula for compound interest:

Compound Interest =P(1+r/n)^rt

Substituting the given values, we get:

Compound Interest =600 (1+7/n)^4

Simplifying this equation, we get

P = 600 / 1.487

P = 451.73

Therefore, the present value needed now to get $600 after 4 years at 7% compounded monthly is $451.73.

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Using translation concepts, it is found that:

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

\((-5,-4) \rightarrow (-5 - 3, -4 + 2) = (-8, -2)\)

\((1,7) \rightarrow (1 - 3, 7 + 2) = (-2, 9)\)

Thus:

B' is: (-8, -2).

C' is: (-2, 9).

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Answer:

T=98W-115W+1840

Step-by-step explanation:

$98 per credit at Westside (W)

$115 per credit at Pinewood (P)

Expression 1 : 98W+115P=T

Expression 2 : W+P=16

Combined: if W=16-P

Total=98W+115(16-W)

T=98W-115W+1840

Answer:

C: 85 + 30x ≥ 500

Step-by-step explanation:

None

The value of the expression 16/2 + 6 (7 + 4 x 5) will be 848.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of the expression 16/2 + 6 (7 + 4 x 5) will be:

= 16/2 + 6 (7 + 4 x 5)

= 8 + 6(7 + 20)

= 8 + 6(140)

= 8 + 840

= 848

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Answer:(2,4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

The 10,100 cards will be necessary to build a 100-story card tower.

To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:

Triangular number = (n * (n + 1)) / 2

In this case, n represents the number of stories in the tower (100). Plug in the value for n:

Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050

Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:

Total cards = 5,050 * 2
Total cards = 10,100

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Answer: 500.7

500.75 = 500.7

Step-by-step explanation:

The estimated value is 500

Estimating in math is a way of approximately calculating an answer (getting a 'rough answer') or to check its accuracy (the 'right answer').

Given that, 9965 divided by 19.9 estimate

Let 9965 ≈ 9970

19.9 ≈ 20

9970 ÷ 20

9970 / 20

= 498.5

≈ 500

Hence, the estimated value is 500.

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The quadratic equation whose roots are -6 and -1 with leading coefficient 1 is \(x^{2} +7x+6=0\).

Given that a Quadratic equation whose roots are -6 and -1 with leading coefficient is 1 and asked to find the equation of quadratic equation.

Quadratic equation:

The polynomial equations of degree two in one variable of form f(x) = a\(x^{2}\) + bx + c = 0 and with a, b, c, ∈ R and a ≠0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" is for the absolute term of f(x).

For a quadratic equation if (a,b) are roots then,

(x-a)(x-b) is the quadratic equation having roots "a" and "b"

The equation with roots -6 and -1 is
⇒(x+6)(x+1)

⇒\(x^{2}\)+7x+6

Threfore,The quadratic equation whose roots are -6 and -1 with leading coefficient 1 is \(x^{2} +7x+6=0\).

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