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What is the solution set of the inequality?

A^2 -b^2 / a +b

Apply the difference of two squares formula to the top :

A^2 - b^2 = (a+b)(a-b)

now you have :

(A+b)(a-b) / a+b = 12

the two (a+ b)’s cancel each other out so you are left with a-b = 12

answer: a-b = 12

[tex]\dfrac{x^2 +7x +14 }{x+4} = x+3+ \dfrac{2}{x+4}[/tex]

Answer:

[tex]\{58198.2573,58239.7427\}[/tex]

Step-by-step explanation:

We assume that the following conditions are true before constructing the confidence interval:

Assumption #1: Random Sampling.

Assumption #2: Independence.

Assumption #3: Large Sample.

Assumption #4: The 10% Condition (sample size is no bigger than 10% of population

Assumption #5: The Success / Failure Condition.

Assumption #6: Homogeneity of Variances.

A 95% confidence level correlates to a critical value of [tex]z^*=1.96[/tex], hence:

[tex]\displaystyle CI=\bar{x}\pm z^*\biggr(\frac{s}{\sqrt{n}}\biggr)\\\\CI=58219\pm 1.96\biggr(\frac{56}{\sqrt{28}}\biggr)\\\\CI=58219\pm20.7427\\\\CI=\{58198.2573,58239.7427\}[/tex]

Therefore, we are 95% confident that the true mean of the average yearly income for a married couple living in city C is between $58,198.2573 and $58,239.7427

Answer:

all x intercepts [-4, 0] [4, 0]

Step-by-step explanation:

x-intercept, i.e. y=0

f(x) = x^3 - 4x^2 - 16x + 64 = 0

(x^3 + 4^3) - 4x^2 - 16x = 0         [FYI, x^3 + y^3 = (x + y)(x^2 - xy + y^2)]

(x + 4)(x^2 - 4x + 16) - 4x^2 - 16x = 0

(x + 4)(x^2 - 4x + 16) - 4x(x + 4) = 0

(x + 4)(x^2 - 4x + 16 - 4x) = 0

(x + 4)(x^2 - 8x + 16) = 0

(x + 4)(x - 4)^2 = 0

x = -4 or 4

all x intercepts [-4, 0] [4, 0]

Step-by-step explanation:

one thing immediately catches the eye : the factors of the terms in the function follow the powers of 4 :

4⁰, 4¹, 4², 4³

and they are going against the powers of x :

x³ has the factor 4⁰

x² has the factor 4¹

x has the factor 4²

x⁰ has the factor 4³

with that we see that one 0 solution (an x- intercept) is x = 4.

f(4) = 4³ - 4×4² - 4²×4 + 4³ = 4³ - 4³ - 4³ + 4³ = 0

so, the functional expression is

(x-4)(x² + ...)

the other 2 zero solutions are covered by the quadratic term.

to get the quadratic term we divide f(x) by (x-4).

x³ - 4x² - 16x + 64 ÷ x - 4 = x² - 16

- x³ - 4x²

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

0 0 - 16x + 64

- - 16x + 64

----------------------‐--------

0 0

so,

f(x) = (x - 4)(x² - 16)

and as we know

(a² - b²) = (a + b)(a - b)

we get

f(x) = (x - 4)(x + 4)(x - 4) = (x - 4)²(x + 4)

so, x = 4 counts as 2 zero solutions, it is a point, where the curve makes a turn and only touches the x-axis, but does not fully intercept it (in the sense to continue on the other side of the x-axis).

and x = -4 is the third zero solution.

so, the x-intercepts are at x = -4, +4

Answer:

See below

Step-by-step explanation:

Use the formulae directly

For a cone, with base radius = r and height = h, here are the related formula

[tex]\textrm{Slant height l} = \sqrt{r^2 + h^2}[/tex]  (1)

[tex]\textrm{Lateral surface area} = \pi r l[/tex]

[tex]\textrm {Base area} = \pi r^2[/tex]

[tex]\textrm { Total Surface Area SA} = \textrm{Base Area + Lateral Area} = \pi r^2 + \pi rl = \pi r(r + l)[/tex] (2)

[tex]\textrm{Volume V = } (1/3) \pi r^2h[/tex] (3)

Therefore directly plugging in the numbers in the above equations:

Note:

l = slant height in cm
SA = total surface area in sqcm
V = Volume in cubic cm

Figure(a)

r = 4, h = 8

[tex]\textrm{l} = \sqrt{4^2 + 8^2} =\sqrt{80} = 8.944 \\\textrm{SA} = 4\pi(4 + 8.944) = 4\pi(12.944) = 162.66\\\textrm{V} = (1/3)\pi(4^2)(8) = 134.04[/tex]

Figure(b)

r = 7, h =15

[tex]\textrm{l} = \sqrt{7^2 + 15^2} =\sqrt{274} = 16.55[/tex]

[tex]\textrm{SA} = 7\pi(7 + 16.55) = 517.89[/tex]

Figure (c)

r = 5, l = 8

[tex]h = \sqrt{l^2 - r^2} = \sqrt{8^2 - 5^2} = \sqrt{39} = 6.245\\SA = \textrm{SA} = 5\pi(5 + 8) = 204.2\\V = (1/3)\pi(5^2)(6.245) = 163.5[/tex]

Answer:

+64

Step-by-step explanation:

the opposite of a positive number is it's negative version while the opposite of a negative number is it's positive version.

so from the question above, the opposite of -64 is+64

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

[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

What is the opposite number from -64?

[tex]\blue{\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]

If a number's negative, its opposite is a positive; if a number's positive, its opposite is a negative.

Since -64 is  negative, its opposite is

[tex]\bigstar\sf{64}[/tex]

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

Answer:

A) [tex]\frac{x}{11} < -21[/tex]

Step-by-step explanation:

Let "a number" be denoted by the variable, x. Set the equation:

"A number divided by 11": x/11

"is less than": <

"-21": -21

Put all the parts together:

"A number divided by 11 is less than -21": x/11 < -21

A) [tex]\frac{x}{11} < -21[/tex] is your answer.

~

Answer:

Step-by-step explanation:

3.46410161514

Answer: The answer is 3.46410161514

A coordinate system is a method of determining the position of points or other geometric components on a manifold. The points which vary are on a graph where y varies directly with x are (-1, 1), (0, 0), and (-5, 5).

A coordinate system is a method of determining the position of points or other geometric components on a manifold, such as Euclidean space, by using one or more integers, or coordinates.

Given that y varies directly with x, therefore, we can write,

y∝x

y = kx

Also, y=3 and x=-3, therefore, the value of k can be written as,

3=k(-3)

k=-1

Now, the points which vary are on a graph where y varies directly with x are (-1, 1), (0, 0), and (-5, 5).

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The 73 customers who spend money in this store if  margin of error of at most 0.075 with 80% confidence.

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            n is the number of samples.

We have p = 0.50 MOE = 0.075

Z = 1.282 at 80% confidence from the Z table.

[tex]\rm 0.075 = (1.282)\sqrt{\dfrac{0.50(1-0.50)}{n}}[/tex]

After solving, we get:

n = (0.5)(0.5)/(0.0585)²

n = 73

Thus, the 73 customers who spend money in this store if  margin of error of at most 0.075 with 80% confidence.

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Answer:

.................... .

============================================================

Explanation:

Let's go through each answer choice one by one to see if it's true or false.

Answer: [tex]y=\frac{7}{2} x+10[/tex]

Step-by-step explanation:

y=mx+b

b=the y intercept

m=slope

In this graph, the y intercept is 10 so we can substitute b for that.

You find the slope with 2 points on the line.

(2,17) (6,31)

[tex]\frac{31-17}{6-2}[/tex]=[tex]\frac{14}{4}[/tex] which is simplified to [tex]\frac{7}{2}[/tex]

You can substitute m for [tex]\frac{7}{2}[/tex] now and your equation is [tex]y=\frac{7}{2} x+10[/tex]

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{1}{2}\theta r^2~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=12\\ \theta =\frac{3\pi }{4} \end{cases}\implies \begin{array}{llll} A=\cfrac{1}{2}\left( \cfrac{3\pi }{4} \right)(12)^2\implies A=\cfrac{432\pi }{8} \\\\\\ A=54\pi \implies \stackrel{using~\pi =3.14}{A=169.56} \end{array}[/tex]

Answer:

6 goats and 6 ducks

Step-by-step explanation:

Answer:

28 meters cubed

Step-by-step explanation:

V = 1/3 BH

V = 1/3 (4)(21)

V = 28

Hope this helped :))

have a great day :D <3

Answer:

nope

Step-by-step explanation:

Answer:  123.3364311 degrees approximately

Round that value however your teacher instructs.

==========================================================

Explanation:

Use the law of cosines to find side b

[tex]b^2 = a^2 + c^2 - 2*a*c*\cos(B)\\\\b^2 = 43^2 + 19^2 - 2*43*19*\cos(35)\\\\b^2 \approx 871.5055596\\\\b \approx \sqrt{871.5055596}\\\\b \approx 29.521273\\\\[/tex]

Now use the law of sines to find angle A.

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\\\\frac{\sin(A)}{43} \approx \frac{\sin(35)}{29.521273}\\\\\sin(A)\approx 43*\frac{\sin(35)}{29.521273}\\\\\sin(A) \approx 0.8354581\\\\A \approx \sin^{-1}(0.8354581) \text{ or } A \approx 180-\sin^{-1}(0.8354581)\\\\A \approx 56.6635689^{\circ} \text{ or } A \approx 123.3364311^{\circ}\\\\[/tex]

Due to the side angle side (SAS) congruence theorem, we know that only one triangle is possible (notice angle B is between sides 'a' and c). This means only one of those values for angle A is possible.

The question is: Which one?

Well if you were to use the converse of the pythagorean theorem, then you'll find that the triangle is obtuse.

For any obtuse triangle, the longest side is always opposite the obtuse angle (aka the angle over 90 degrees). The side a = 43 is the longest side of this particular triangle.

This means angle A must be obtuse and the only possibility is that angle A = 123.3364311 degrees approximately.

Rs. 5000

Step-by-step explanation:

To Find MP = ?

SP = rs 3000

Discount = 40%

=> MP-MP×40/100=3000

=> 100MP-40MP/100= 3000

=> 60MP/100 = 3000

MP = 3000 × 100 / 60

MP = 500 × 10

MP = Rs. 5000

Answer:

633.94 squared inches

Step-by-step explanation:

15.75 x 15.75 = 248.0625

12.25 x 15.75 x 1/2 = 96.46875

since there are 4 triangles and they are equivalent...

96.46875 x 4 = 385.875

Surface area is...

385.875 + 248.0625 = 633.9375

changing my answer hh

Answer:

200 miles

Explanation:

Here map to actual to scale: 1 inch = 50 miles

To find actual distance, simply multiply map distance by scale factor

Actual Distance : 4 × 50 = 200 miles

Não, não podemos fazer um triângulo com os comprimentos dos lados de 2 cm, 3 cm e 10 cm. Isso ocorre porque a soma de 2+3 < 10. (in english: No, we cannot make a triangle with the side lengths of measurement 2 cm, 3 cm, and 10 cm. This is because sum of 2+3 < 10).

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]

Now, for this case, the sides given are:

But we see that:

a+ b = 5 cm which is < c which is of 10 cm.

Thus, these lengths don't satisfy the triangle inequality theorem, and therefore, cannot be sides of any triangle.

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Answer:

box plot

Step-by-step explanation:

Step-by-step explanation:

Cost prevents one of the biggest barriers to restaurants offering healthier menu options. Fast-food chains like McDonald's have made their fortune by offering food with a long shelf life, which tends to be less healthy. As pointed out in The New Yorker, even if every restaurant in America decided to drop the fries and embrace kale and watermelon radish salads, the U.S. lacks the agricultural infrastructure to support that kind of dietary shift. Big farm crops like soybeans (for frying oil), corn (for high fructose corn syrup), and grain (livestock feed) receive millions of tax breaks and other government subsidies, making it hard for smaller farms to compete.

Answer:

B) Quadratic Function

Step-by-step explanation:

[tex]f(x)=2x(x+3)=2x^2+6x[/tex], which is a second-degree polynomial, so it is a quadratic function.