can 18 in, 6 in, 13 in form a triangle

Answer:

c.    x = -2  or x = -3

Step-by-step explanation:

The vertical asymptotes occur where the denominator = 0.  That happens when the f(x) is undefined.  So,

x^2 + 5x + 6 = 0

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

x = -2  or x = -3

Answer:

24 cubes

Step-by-step explanation:

You can figure this a couple of ways.

I usually find it easiest to figure in terms of the number of cubes each dimension represents. The vertical dimension (3/2 cm) is the length of 3 cubes; the front-back dimension (2 cm) is the length of 4 cubes, and the width (1 cm) is the length of 2 cubes.

The total number of cubes required is the product of the dimensions in cube-lengths: 3×4×2 = 24 cubes.

I think itś 11 on both sides bc positive and negative 11 would cancel out and then 5-11 would -6. if you look at the bottom question there is a negative 6 there too. if im wrong its mb.

Answer:

Step-by-step explanation:

\(-\frac{3}{4} n+11-11=5-11 ~subtract~11~from~both~sides\\-\frac{3}{4} n=-6\\multiply~both~sides~by ~-\frac{4}{3} \\(-\frac{3}{4} n)(-\frac{4}{3} )=(-6)(-\frac{4}{3} )\\n=8\)

Answer:

\(D.\ 720\ degrees\)

Step-by-step explanation:

\(We\ are\ given:\\The\ following\ polygon\ has\ 6\ sides\ and\ is\ a\ hexagon.\\We\ know\ that,\\The\ Interior\ Angle\ Sum\ of\ a\ polygon\ with\ sides\ n\ is\ given\ by\ the\ formula:\\Interior\ Angle\ Sum=180(n-2)\\Here,\\As\ the\ number\ of\ sides\ are\ 6,n=6\\Hence,\\The\ Interior\ Angle\ Sum\ of\ a\ hexagon=180(6-2)=180*4=720\)

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:

When rolling di.e #2, since we must roll a different odd number, the probability of doing so is 2/6 = 1/3. Thus, the probability is 1/2 x 1/3 = 1/6.

Answer:

$269.49

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 349.99 × 23/100

Discount = 349.99 x 0.23

You save = $80.50

Final Price = Original Price - Discount

Final Price = 349.99 - 80.4977

Final Price = $269.49

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer: tens

Step-by-step explanation:

Answer:

Instead of adding the exponents of 2 to get four you should just leave the exponent as two in the final answer.

The volume of the bottle is 56.52 cubic inches, and the density is 22.12 g/in³.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 ).

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that:

Diameter = 3 in

Radius r = diameter/2 = 3/2 = 1.5 in

Height h = 8 in

Mass m = 1250 g

Find the volume:

V = π × r² × h

V = 3.14 × (1.5 in )² × 8in

V = 56.52 in³

Find the density:

p = m / v

p = 1250g / 56.52 in³

p = 22.12 g/in³

Therefore, the density is 22.12 g/in³.

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Answer:

33.33

Step-by-step explanation:

Answer:

about 33.33

Step-by-step explanation:

Answer: 6/(6+2x) ; (-infinity, -3) U (-3, infinity)

Step-by-step explanation:

(a) This can be read as f(x) composed of g(x). Plug in the expression given for g(x) for every x value in f(x):

(6/x)/(6/x+2)

I gave the terms in the denominator the same denominator to combine the bottom two terms into one term. 6/x + 2 is equal to 6/x + 2x/x -->

(6 +2x)/x

Do the classic keep, change, flip. \(\frac{6}{x} * \frac{x}{6+2x}\)

This simplifies to: \(\frac{6}{6+2x}\)

(b) Domain is all real numbers except for what makes the denominator equal to 0.     6 + 2x = 0 when x = -3. Therefore it is all real numbers except -3.

Answer:

The length of line segment is 3 -(-3) = 6 units

Step-by-step explanation:

Answer: this might help I’m not sure

Step-by-step explanation:

Answer:

5m+3m=8m

simplified

Step-by-step explanation:

combine all m's together 5m's +3m's =8m's

(☆▽☆)

The domain of the function above is [-2, 3].

The range of the function above is [-2.5, 2].

The intervals over which the function is increasing is [-2, 1.5] U [-2.5, 2].

The intervals over which the function is decreasing is [1.5, -2.5].

In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph of this rational expression (function)   shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain = [-2, 3] or -2 ≤ x ≤ 3.

Range = [-2.5, 2] or -2.5 ≤ y ≤ 2.

Additionally, the intervals over which the function is increases over the interval [-2, 1.5] and [-2.5, 2], while it decreases over the interval [1.5, -2.5].

In conclusion, the given function is not constant over any interval.

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Answer:

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

Answer:

The answer is 254.34 square inches

Step-by-step explanation:

Now,

Radius = Diameter ÷ 2

r = 18/2 = 9 inches

So,

A = π r²

A = 3.14 × 9² inches

A = 3.14 × 81 inches

A = 254.34 square inches

Thus, The area of the circle is 254.34 square inches

-TheUnknownScientist 72

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

Answer:

C, 4.

Step-by-step explanation:

Im not sure how to explain it, i just know that it's C! :))

Using the equations, the total pay adding pay at each job is obtained to be $1590.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's start by finding the total pay earned at Amazon in a week -

Hourly wage = $16

Weekly hours worked = 25

The equation will be -

Regular weekly pay = Hourly wage × Weekly hours worked

Regular weekly pay = $16 × 25

Regular weekly pay = $400

Hiring bonus = $1000

The equation will be -

Total pay earned in a week = Regular weekly pay + Hiring bonus

Total pay earned in a week = $400 + $1000

Total pay earned in a week = $1400

Now, let's find the total pay earned at UPS in a week.

Hourly wage = $18

Weekly hours worked = 30

The equation will be -

Regular weekly pay = Hourly wage × Weekly hours worked

Regular weekly pay = $18 × 30

Regular weekly pay = $540

Sunday bonus = $50

The equation will be -

Total pay earned in a week = Regular weekly pay + Sunday bonus

Total pay earned in a week = $540 + $50

Total pay earned in a week = $590

We want to find the point at which the total pay earned at each job is the same, so we can set the two expressions for total pay equal to each other and solve for the unknown variable (the number of weeks worked) -

$1400 = $590n, where n is the number of weeks worked

Solving for n, we get -

n = $1400/$590 ≈ 2.37

So, the total pay earned will be the same for both jobs after working for about 2.37 weeks (or about 17 days).

At that point, the total pay earned at either job will be -

Total pay = Regular weekly pay + Hiring bonus + Sunday bonus

Total pay = $540 + $50 + $1000

Total pay = $1590

Therefore, the total pay value is $1590.

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Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

Answer:

\(\huge\boxed{-\frac{7}{8}a - \frac{1}{6}}\)

Step-by-step explanation:

This question utilizes combining like terms and common denominators. First you have to convert both terms including "a" to have a denominator of 8. You would do this by multiplying both the numerator, and the denominator by the same value. This value in the case of \(-\frac{1}{4} a\) would be 2, and in the case of \(\frac{2}{3}\) the value would be 2. This would result in the equation: \(-\frac{5}{8}a+\frac{4}{6}-\frac{2}{8}a-\frac{5}{6}\). Then simply combine like terms to get your final answer.

Answer:

2062 4/11

Step-by-step explanation:

Okay so assuming 2003 4/11 is a mixed number, we just add:

2003 4/11 + 59 = 2062 4/11

Hope this helps:)

Answer:

9

Step-by-step explanation:

9^4=3^8

27^2=3^6

when we divide the powers of the same base ,we take the common base and subtract their exponent.

3^8-^6

=3^2

=9

Answer: supplement <17

Step-by-step explanation:

1. 17 is greater

2. supplement is smaller

The probability that the submitted responses to the questions were correct will be 2/11.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.

Statistics is the study of events that follow a probability distribution.

Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective.

So, the probability formula is as follows:

Probability = Favourable events/Total events

Now, insert values as follows:

Probability = Favourable events/Total events

Probability = 1+1/5+6

Probability = 2/11

Therefore,  the probability that the submitted responses to the questions were correct will be 2/11.

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Answer:

cos B = 9/41

tan B = 40/9

sin B = 40/41

Step-by-step explanation:

There is no picture, so I am making a few assumptions.

I am assuming that angle C is the right angle and is opposite 41.

I am also assuming that angle B is formed by the sides that measure 9 and 41. The hypotenuse is 41.

For angle B, the adjacent leg is 9, and the opposite leg is 40.

cos B = adj/hyp = 9/41

tan B = opp/adj = 40/9

sin B = opp/hyp = 40/41

The Isosceles triangle JKL has two equal sides

The x-coordinate of point L is 2 or 8

The coordinates of the triangle are given as:

J = (5,-2)

K = (2,2)

L = (x, 2)

Start by calculating the distance between the vertices using the following distance formula

\(d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}\)

So, we have:

\(JK = \sqrt{(5 -2)^2 + (-2 -2)^2} = 5\)

\(KL = \sqrt{(2 -x)^2 + (2 -2)^2} = 2 -x\)

\(JL = \sqrt{(5 -x)^2 + (-2 -2)^2} = \sqrt{(5 -x)^2 + 16}\)

The triangle is an isosceles triangle.

So, we have:

JK = JL

The equation becomes

\(\sqrt{(5 - x)^2 + 16} = 5\)

Take the square of both sides

\((5 - x)^2 + 16 = 25\)

Subtract 16 from both sides

\((5 - x)^2 = 9\)

Take the square root of both sides

\(5 - x = \pm3\)

Solve for x

\(x = 5 \pm 3\)

x = 2, or 8

Hence, the x-coordinate of point L is 2 or 8

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