The yearbook club had a meeting. The meeting had 30 people, which is five-sixths of the club. How many people are in the club?

Answer/Step-by-step explanation:

149.99+(149.99*0.07)=160.4893. Round to $160.49

Answer:

1

Step-by-step explanation:

Answer is 1 for Apex Precal

Final answer:

The values of k that ensure the points (-5, 5) and (k, 0) are [tex]\(\sqrt{29}\)[/tex]units apart are -3 and -7, derived using the Pythagorean theorem and algebraic manipulation.

Explanation:

To find all values of k so that the points (-5, 5) and (k, 0) are \(\sqrt{29}\) units apart, we use the distance formula derived from Pythagoras’ theorem, which is[tex]d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]. Here, [tex]\(x_1 = -5\), \(y_1 = 5\), \(x_2 = k\), and \(y_2 = 0\). Substituting the given values, we get:[/tex]

[tex]\(\sqrt{29} = \sqrt{(k + 5)^2 + (0 - 5)^2}\)[/tex]

Squaring both sides to eliminate the square root gives:

[tex]29 = (k + 5)^2 + 25[/tex]

Subtracting 25 from both sides, we get:

[tex]4 = (k + 5)^2[/tex]

Therefore, \(k + 5 = \pm2\), which simplifies to:

[tex]\(k + 5 = 2\) giving \(k = -3\)[/tex]

[tex]\(k + 5 = -2\) giving \(k = -7\)[/tex]

The values of k are -3 and -7, so the correct option is c. -3, -7.

The correct answer is option (c) -3, -7.

How is it so?

To find the values of k such that the given points (-5, 5) and (k, 0) are [tex]\(\sqrt{29}\)[/tex] units apart, use the distance formula between two points in a plane:

[tex]\[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Given that the distance between the points is [tex]\(\sqrt{29}\)[/tex], we have:

[tex]\[ \sqrt{(k - (-5))^2 + (0 - 5)^2} = \sqrt{29} \][/tex]

[tex]\[ \sqrt{(k + 5)^2 + 5^2} = \sqrt{29}[/tex]]

[tex]\[ \sqrt{k^2 + 10k + 25 + 25} = \sqrt{29} \][/tex]

[tex]\[ \sqrt{k^2 + 10k + 50} = \sqrt{29} \][/tex]

Squaring both sides to eliminate the square root:

[tex]\[ k^2 + 10k + 50 = 29 \][/tex]

[tex]\[ k^2 + 10k + 21 = 0 \][/tex]

Solve this quadratic equation

[tex]\[ k = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

Where a = 1, b = 10, and c = 21.

[tex]\[ k = \frac{-10 \pm \sqrt{10^2 - 4 \cdot 1 \cdot 21}}{2 \cdot 1} \][/tex]

[tex]\[ k = \frac{-10 \pm \sqrt{100 - 84}}{2} \][/tex]

[tex]\[ k = \frac{-10 \pm \sqrt{16}}{2} \][/tex]

[tex]\[ k = \frac{-10 \pm 4}{2} \][/tex]

[tex]\[ k = \frac{-10 + 4}{2} \] or \( k = \frac{-10 - 4}{2} \)[/tex]

[tex]\[ k = \frac{-6}{2} \] or \( k = \frac{-14}{2} \)[/tex]

[tex]\[ k = -3 \] \:or \( k = -7 \)[/tex]

So, the correct answer is option (c) -3, -7.

Answer:

a) (3x+4)(9x^2-12x+16)

Step-by-step explanation:

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

Dimensions of the photo is given by

[tex]20\ in.\ by\ 24\ in.[/tex]

According to question, the photo is reduced so that the longer dimension is 15 inch.

So, Let the width of the reduced photo be x.

So, it becomes,

[tex]\frac{20}{x}=\frac{24}{15}\\\\x=\frac{15\times 20}{24}\\\\x=12.5\ in.[/tex]

So, the width of the reduced photo is 12.5 inch.

Hence, Option 'B' is correct.

The solution to the system of equations are ±2i and ±i

Given the quartic equation

x^4 + 3x^2 + 2 = 0

Let u = x^2 to have:

(x^2)^2 + 3x^2 + 2 = 0

u^2 + 3u + 2 = 0

Factorize

u^2 + u +2u + 2 = 0

u(u + 1) + 2(u + 1) = 0

(u + 2)(u + 1) = 0

u = -2 or -1

If u = x^2

-2 = x^2

x = √-2

x = 2i

Similarly

If u = x^2

-1 = x^2

x = √-1

x = i

Hence the solution to the system of equations are ±2i and ±i

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Final answer:

To solve the equation x^4 + 3x^2 + 2 = 0 using u substitution, substitute x^2 for u and solve the quadratic equation. The resulting solutions in the complex number system are x = i, -i, √2i, and -√2i. There are no real solutions for this equation.

Explanation:

The solutions of the equation x4 + 3x2 + 2 = 0 can be found using u substitution. First, let's substitute u for x2, which transforms the original equation into the form u2 + 3u + 2 = 0. This is a quadratic equation, and we can solve it using the quadratic formula or by factoring. Factoring (u + 1)(u + 2) = 0, we get the solutions for u as u = -1 and u = -2. Since u is a substitute for x2, we then solve for x.

For u = -1, the equation x2 = -1 has no real solutions because the square of a real number cannot be negative. However, in the complex number system, the solutions are x = i and x = -i, where i is the square root of -1.

For u = -2, the equation x2 = -2 also has no real solutions, but the complex solutions are x = √2i and x = -√2i.

Therefore, the full set of solutions for the original equation are x = i, -i, √2i, and -√2i.

Final answer:

To convert 7 square yards to square meters, you multiply by the conversion factor, resulting in approximately 5.85 square meters. Hence, the correct answer is C. 5.85 square meters.

Explanation:

7 square yards is equal to how many square meters? To convert square yards to square meters, you can use the conversion factor 1 square yard = 0.83612736 square meters. Therefore, to convert 7 square yards to square meters:

7 sq yards * 0.83612736 sq meters/sq yard = 5.85289152 sq meters

When rounding to two decimal places, this is approximately 5.85 square meters. So, the correct answer would be C. 5.85 square meters.

The distance from Honolulu to Turtle Bay is approximately 37 miles. To calculate this distance, you can use a map or a GPS tool. The most direct route between the two locations is along the Kamehameha Highway.

The distance from Honolulu to Turtle Bay is approximately 37 miles. To calculate this distance, you can use a map or a GPS tool. The most direct route between the two locations is along the Kamehameha Highway.

It's important to note that the actual distance traveled may vary depending on the specific route taken and any detours or alternate paths chosen.

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Answer:

[tex]2\sqrt{5}[/tex]

C is the correct option.

Step-by-step explanation:

The given expression is [tex]\sqrt{180}-\sqrt{125}+\sqrt{5}[/tex]

In order to simplify the expression, we find the factors.

180 =6 ×6×5

125 = 5 ×5×5

Hence, we can rewrite the expression as

[tex]\sqrt{6\times6\times5}-\sqrt{5\times5\times5}+\sqrt{5}[/tex]

We can further write this expression as

[tex]\sqrt{6^2\times5}-\sqrt{5^2\times5}+\sqrt{5}[/tex]

Now, we can use the rule [tex]\sqrt{x^2}=x[/tex]

[tex]6\sqrt{5}-5\sqrt{5}+\sqrt{5}[/tex]

Finally, we can combine these like terms

[tex]2\sqrt{5}[/tex]

Hence, C is the correct option.

Answer:

B. 4

Step-by-step explanation:

This table that shows the input and output values for an exponential function f(x) is,

x                -3          -2       -1      0      1      2       3

f(x)          1/256      1/64    1/16   1/4    1     4       16

Taking [tex]x=2[/tex] and [tex]x=3[/tex] as input (because they are 1 apart), the ratio of output is,

[tex]=\dfrac{f(3)}{f(2)}[/tex]

[tex]=\dfrac{16}{4}[/tex]

[tex]=4[/tex]

Answer:

The correct answer is B. 4

Step-by-step explanation:

Answer:

A) -5

Step-by-step explanation:

If triangle EFG is congruent to triangle STU, the following statements are true:

* Angle E = angle S.

* Angle F = angle T.

* Side EF = side ST.

* Side FG = side TU.

* Side EG = side SU.

If triangle EFG is congruent to triangle STU, then we can conclude that the following pairs of angles are congruent:

* Angle E is congruent to angle S.

* Angle F is congruent to angle T.

This is because congruent triangles have corresponding angles that are congruent.

We can also conclude that the following pairs of sides are congruent:

* Side EF is congruent to side ST.

* Side FG is congruent to side TU.

* Side EG is congruent to side SU.

This is because congruent triangles have corresponding sides that are congruent.

Therefore, the following statements are true:

* Angle E = angle S.

* Angle F = angle T.

* Side EF = side ST.

* Side FG = side TU.

* Side EG = side SU.

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A polygon can grow from one-dimensional objects, which are lines. Zero-dimensional objects, which are points or vertices, also play a role as they define the positions where lines meet, but a polygon cannot directly grow from three-dimensional objects because polygons are two-dimensional shapes.

A polygon can grow from one-dimensional objects, specifically from lines. In geometric terms, a polygon is a two-dimensional shape that is formed by connecting straight line segments. Each line segment connects to two others to form the polygon's perimeter. Moreover, the line segments join at their endpoints, known as vertices, which are zero-dimensional objects that contain only a single coordinate pair.

The formation of a polygon from lines is analogous to constructing a shape on a piece of paper by drawing lines that connect to form a closed loop. In this process, the lines are the sides of the polygon, and the points where the lines meet are the vertices. It is not possible for a polygon to directly grow from three-dimensional objects, as polygons are inherently two-dimensional.

For example, to represent a soccer ball in a simplified manner such as in geographic information systems (GIS), we can use polygons in the shape of pentagons and hexagons. The soccer ball itself is a three-dimensional object but the representation involving pentagons and hexagons is a two-dimensional schematic, emphasizing the importance of polygons in various mapping and modeling applications.

To solve for 'x' in the parallelogram area equation, we multiplied the given base (5 units) by the height (x + 6 units) and set it equal to the given area (20 square units). After simplifying, we found that x must be -2 to satisfy the equation 5x + 30 = 20.

The question presented is a typical algebra problem where we need to find the value of 'x' in the context of the area of a parallelogram. The base of the parallelogram is given as 5 units and its height is given as (x + 6) units, with the total area given as 20 square units. Since the formula for the area of a parallelogram is base × height, we can set up the equation 5 × (x + 6) = 20 to find the value of x.

Now, we will solve for x:

Hence, the correct answer is b. x=-2.