Please help me out!! :)

Please Help Me Out!! :)

Answers

Answer 1

Answer:

3.1 ft

Step-by-step explanation:

The segment from the centre of the circle to the chord is a perpendicular bisector.

Thus the third side of the right triangle is half of x

let the third side be a then x = 2a

Applying Pythagoras' identity to the right triangle with hypotenuse 2.1 then

a² + 1.4² = 2.1²

a² + 1.96 = 4.41 ( subtract 1.96 from both sides )

a² = 2.45 ( take the square root of both sides )

a = [tex]\sqrt{2.45}[/tex]

Hence x = 2 × [tex]\sqrt{2.45}[/tex] ≈ 3.1 ft


Related Questions

Determine the measure of angle FGC.

A. 22°

B. 70°

C. 11°

D. 120°

Answers

Answer:

it look like B but I'm not sure

Please help me out!!! :)

Answers

Answer:

x = 26°

Step-by-step explanation:

The measure of the secant- secant angle x is one- half the difference of the measures of the intercepted arcs , larger subtract smaller

x = [tex]\frac{1}{2}[/tex] (66° - 14°) = 0.5 × 52° = 26°

7. Find the percent of decrease from 290 to 100. Round to the nearest tenth of a
percent, if necessary.
A 65.5%
B 190%
C 290%
D 1.9%

Answers

Answer:

A 65.5%

Step-by-step explanation:

Percent decrease = (original - new)/ original * 100 percent

                              = (290-100)/290 * 100 %

                              = 190/290* 100%

                              =.655172414 * 100%

                               =65.5172414%

To the nearest tenth percent %

                                65.5%

Please help me out with this

Answers

Answer:

a. y = {x+1, x≤2; x+2, x>2}

Step-by-step explanation:

The open circle at (2, 4) means the function is not defined as y=x+2 at that point. Only one answer selection correctly uses the inequality symbol > for that part of the function definition.

___

Comment on the other answer choices.

One selection (b) uses the region definitions x < 2 and x ≥ 2. That would put the open circle at (2, 3) and the filled circle at (2, 4)—not a match with the graph. The other function definitions (c, and d) have the relation defined as two different values at x=2. Such a relation is not a function.

The sums that appear when two fair? four-sided dice? (tetrahedrons) with sides 1?, 2?, 3?, and 4 are tossed

Answers

Final answer:

When two four-sided dice are tossed, the combined outcome ranges from 2 to 8. The probability for each outcome can be calculated by counting the number of combinations that sum to that outcome and dividing by the total number of possible outcomes (16). For example, there's one way to get a sum of 2 (1+1), so the probability is 1/16.

Explanation:

The subject of this question is probability, particularly, the sums of outcomes when tossing two fair four-sided dice (or tetrahedrons). Each dice has sides 1, 2, 3, and 4. When these dice are tossed together, the combined outcome is anywhere between the minimum value 2 (1 from each dice) to the maximum value 8 (4 from each dice).

The probability of each combined outcome can be calculated based on the total possible different outcomes (4 outcomes from each die, 4 * 4 = 16 total possibilities). To determine the probability for each combined outcome, we'd need to count the number of ways to get that particular sum:

To get a sum of 2 or 8, there's only one possible way (1+1 or 4+4), so the probability is 1/16 To get a sum of 3 or 7, there are two combinations (1+2, 2+1 or 3+4, 4+3), so the probability is 2/16 = 1/8 Similarly for other sums, count the combinations and divide by 16

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A 15 ft ladder makes a 52° angle with the ground. How far will the top of the ladder be above the ground.

Answers

Answer:

11.820 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

Sin = Opposite/Hypotenuse

The length of the ladder is the hypotenuse of a right triangle with 52° as the base angle. The side opposite is the height up the building where the top of the ladder rests. So, you have the relation ...

sin(52°) = height/(15 ft)

Multiplying by the denominator gives you ...

height = (15 ft)·sin(52°) ≈ 11.820 ft

___

You may need to round this number appropriately.

The graph of a system of two linear equations has no solution. What is true about the lines? A. The lines are perpendicular. B. The lines have the same slope, but different intercepts. C. The lines have the same intercept, but different slopes. D. The lines are on top of each other.

Answers

Answer:

B. The lines have the same slope, but different intercepts.

Step-by-step explanation:

The solution of a system of linear equations doesn't exist if the lines do not intersect each other at any point. So if there is no solution that means the lines of both equations will not intersect.

Lets look at the options one by one.

For option A:

If the lines are perpendicular, they might intersect at any point so this is not the correct option.

For Option B:

If the lines have same slop and different intercepts that means the lines are parallel. We know that parallel lines never cross each other so option B is the correct answer.

For Option C:

The lines with same intercept and different might also intersect so option C is not correct.

For Option D:

The lines being on top of each other means that the lines intersect on all points. So option D is also not correct.

Name a line and plane shown in the diagram

Answers

Answer:

Line = To get a Unique line you need two distinct points.

In the given figure PQ is a line.

A plane is either a two dimensional or three dimensional surface such that if you take any two points on it ,the line joining these two points will completely lie on it.

You can name a plane by Single Alphabet or Set of Alphabet.

So,the plane can be Named as: P,Q,R , S→Single Alphabet or

P Q,PS,SR, R Q,→Using two Alphabet,

→ P QR, P Q S,......,P Q RS.

There are 11 paintings at an art show. Four of them are chosen randomly to display in the gallery window. The order in which they are chosen does not matter. How many ways are there to choose paintings? A. 7920 B. 330 C.44 D. 121

Answers

Answer:

B. 330

Step-by-step explanation:

The question indicates the order doesn't matter, so it's a combination and not a permutation.

The combinations are calculated using this formula:

[tex]C(n,r) = \frac{n!}{r! (n-r)!}[/tex]

In this case we have a population of 11 (n = 11) and a selection of 4 (r=4), so...

[tex]C(11,4) = \frac{11!}{4! (11-4)!} = 330[/tex]

So, there are 330 different combinations that can be made of 4 paintings out of a selection of 11.

Answer:

The correct answer is option B.  330

Step-by-step explanation:

It is given that,There are 11 paintings at an art show. Four of them are chosen randomly to display in the gallery window.

To find the possible ways

There are total 11 paintings.

We have to choose 4 of them

Possible number of ways = 11C₄

 = (11 * 10 * 9 )/(1 * 2* 3 * 4)

 = 330 ways

Therefore the  correct answer is option B.  330

Suppose the probability that the Seahawks will defeat the Raiders is 0.55. What is the complement and what does it mean?

20/9 ; the probability that the Seahawks will not defeat the Raiders.

20/9 ; the probability that the Seahawks will defeat the Raiders.

11/20 ; the probability that the Seahawks will defeat the Raiders.

0.45 ; the probability that the Seahawks will not defeat the Raiders.

Answers

Answer:

D: 0.45 ; the probability that the Seahawks will not defeat the Raiders.

Step-by-step explanation:

The complement of an event A is the set of all outcomes in the sample space that are not included in the outcomes of event A.

The Complement Rule states that the sum of the probabilities of an event and its complement must equal 1, or for the event [tex]A[/tex], and its complement event [tex]\overline{A}[/tex] always

[tex]Pr(A)+Pr(\overline{A})=1.[/tex]

If [tex]Pr(A)=0.55,[/tex] then

[tex]0.55+Pr(\overline{A})=1\\ \\Pr(\overline{A})=1-0.55=0.45.[/tex]

Event [tex]A[/tex] - the Seahawks will defeat the Raiders

Event [tex]\overline{A}[/tex] - the Seahawks will not defeat the Raiders

Hence, correct choice is D: 0.45 ; the probability that the Seahawks will not defeat the Raiders.

Final answer:

The complement of the probability of the Seahawks defeating the Raiders is 0.45, this represents the probability of the Seahawks not defeating the Raiders.

Explanation:

In probability theory, a complement refers to the opposite event of whatever has been defined. If the probability of a certain event, in this case the 'Seahawks defeating the Raiders', is given as 0.55, then the complement of that event, 'the Seahawks not defeating the Raiders', is calculated by subtracting the given probability from 1. Hence, the probability of the Seahawks not defeating the Raiders is 1 - 0.55, which equals 0.45.

Thus, the correct answer is '0.45; the probability that the Seahawks will not defeat the Raiders'.

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Can someone lend me a hand?

How many fourths are in 3/4

answers are in the picture below.

Answers

Answer:

3

Step-by-step explanation:

3/4 divided by 1/4=0.75/0.25=3

Answer:

3

Step-by-step explanation:

Think:  "3/4" reads "three fourths," and thus we have 3  fourths.

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

Which equation matches the graph?

Answers

Answer:  D) -2 |x| - 2

Step-by-step explanation:

A v-shaped graph is an absolute value graph.  

The general form of an absolute value equation is: y = a |x - h| + k

where (h, k) represents the vertex and "a" represents the vertical stretch (aka slope).  

The vertex of the given graph is (0, 2), however the graph is inverted (upside-down) which is a reflection across the x-axis.  Therefore,

a = -2(h, k) = (0, -2)                    --> y = -2 |x| - 2

A set of data items is normally distributed with a mean of 500. Find the data item in this distribution that corresponds to the given z-score. z = 2, if the standard deviation is 40.

Answers

The data item in this distribution that corresponds to the given z-score of 2 is 580.

Given:

Mean = 500

z score = 2

standard deviation = 40

To find the data item corresponding to a given z-score in a normally distributed data set, use the formula:

[tex]X = \mu + (z * \sigma)[/tex]

where X is the data item, μ is the mean, z is the z-score, and σ is the standard deviation.

Plugging the values into the formula, we have:

[tex]X = 500 + (2 * 40)[/tex]

[tex]X = 500 + 80[/tex]

[tex]X = 580[/tex]

Therefore, the data is 580.

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Final answer:

In a data set with a mean of 500 and standard deviation of 40, the data item that corresponds to the z-score of 2 is 580. This is computed by multiplying the standard deviation by the z-score and adding the product to the mean.

Explanation:

This question is dealing with z-scores and the standard normal distribution in statistics. The z-score is a measure of how many standard deviations an element is from the mean. In a standard normal distribution, the mean is 0 and the standard deviation is 1.

When you are given a z-score of 2 for a data set with a mean of 500 and a standard deviation of 40, it means the data item you're looking for is 2 standard deviations above the mean. You compute this by multiplying the z-score by the standard deviation and adding the product to the mean. So in this case, 500 + 2*40 = 580. Therefore, the data item in this distribution that corresponds to the z-score of 2 is 580.

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calculate cosine to two decimal places

Answers

Answer:

Final answer is approx -0.07.

Step-by-step explanation:

We have been given a picture of the triangle whose sides are 7, 8 and 11.

Apply cosine formula to find the value of [tex]\cos\left(\theta\right)[/tex].

[tex]a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos\left(a\right)[/tex]

[tex]11^2=7^2+8^2-2\cdot 7\cdot 8\cdot\cos\left(\theta\right)[/tex]

[tex]121=49+64-112\cdot\cos\left(\theta\right)[/tex]

[tex]121=113-112\cdot\cos\left(\theta\right)[/tex]

[tex]121-113=-112\cdot\cos\left(\theta\right)[/tex]

[tex]8=-112\cdot\cos\left(\theta\right)[/tex]

[tex]\frac{8}{-112}=\cos\left(\theta\right)[/tex]

[tex]-0.0714285714286=\cos\left(\theta\right)[/tex]

Hence final answer is approx -0.07.

The answer is C. -0.07.

△ TUV undergoes the dilation: (x, y) → → (2x, 2y). Then it is translated: (x, y) → → (x - 10, y - 8). If vertex T was at (8, 6), what are its coordinates after these two transformations?
(16, 12)
(-2, -2)
(6, 4)
(-4, -4)

Answers

Answer:

(6, 4)

Step-by-step explanation:

step 1

we have

The vertex T (8,6)

First transformation

The rule of the dilation is

(x, y) → → (2x, 2y)

so

(8, 6) → → (16, 12)

step 2

Second transformation

The rule of the translation is

(x, y) → → (x - 10, y - 8)

so

(16, 12) → → (16 - 10, 12 - 8) → → (6, 4)

The diagram shows a scale drawing of a lacrosse field. The diagram is 5 1/2 inches long and 3 inches wide. If 1 inch represents 20 yards, what is the area of the field?​

Answers

Answer:

  6600 yd²

Step-by-step explanation:

The area of the scale drawing is ...

  (5.5 in)(3 in) = 16.5 in²

Each square inch represents an area of the field that is ...

  (20 yd)×(20 yd) = 400 yd² . . . . per square inch of drawing

Then the scale drawing represents a field with an area of ...

  (16.5 in²)×(400 yd²/in²) = 6600 yd²

Conner's coin collection, which was worth $400 eight years ago, has been increasing in value by 12% per year since then. Use the formula A = P(1 + r)^t to find the current value of the collection.

Answers

Answer:

A = $784.00

Step-by-step explanation:

This is the answer

The current value of the coin is $990.38 if the Conner's coin collection, which was worth $400 eight years ago, has been increasing in value by 12% per year since then.

What is simple interest?

It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.

We have formula:

A = P(1 + r)^t

Here P = $400

r = 12% = 0.12

t = 8 years

A = 400(1+0.12)^8

A = 400(2.47596)

A = $990.38

Thus, the current value of the coin is $990.38 if the Conner's coin collection, which was worth $400 eight years ago, has been increasing in value by 12% per year since then.

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Help me with this please !

Answers

Answer:

True

Step-by-step explanation:

The formula for the circumference of a circle is:

C=2πr

So we can substitute in the numbers we have:

Radius=4, so:

C=8π (we multiplied the radius by 2)

So the statement is true.

Hope I... yeah you get it y now I've been answering your questions a lot.

I'm still gonna copyright it.

Copyright Potato 2019.

Answer:

True

Step-by-step explanation:

The circumference (C) of a circle is

C = 2πr ← r is the radius

For C = 8π, then

2πr = 8π ( divide both sides by 2π )

r = 8π ÷ 2π = 4

Hence the radius must be 4

Please please help me

Answers

Answer:

Your numbers are +7, -9, and 25

Step-by-step explanation:

Reverse the values of -7 and +9

Then you get +7 and -9

And also take radius squared which is 25

So, [tex](x--7)^{2} +(y-9)^{2}  = 25[/tex]

Find the distance between these points.

C(0, 4), T(-6, -3)

√(37)
√(85)
√(109)

Answers

Answer:

√85

Step-by-step explanation:

See image

Distance formula can be used to find the distance between two points.

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}  }[/tex]

Answer: Second option

[tex]d=\sqrt{85}[/tex]

Step-by-step explanation:

The formula to find the distance between two points is:

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

In this problem the points are C(0, 4), T(-6, -3)

This is

[tex]x_1=0\\\\x_2=-6\\\\y_1=4\\\\y_2=-3[/tex]

So the distance is:

[tex]d=\sqrt{((-6)-0)^2 + ((-3)-4)^2}[/tex]

[tex]d=\sqrt{(-6)^2 + (-7)^2}[/tex]

[tex]d=\sqrt{36 + 49}[/tex]

[tex]d=\sqrt{85}[/tex]

Please please help me out

Answers

Answer:

26.6 m

Step-by-step explanation:

Given the figures are similar

linear ratio = a : b

area ratio = a² : b²

here

area ratio = 16 : 25, then

linear ratio = 4 : 5 ( square root of both area ratio parts )

let the perimeter of the larger figure be x, then by proportion

[tex]\frac{4}{21.3}[/tex] = [tex]\frac{5}{x}[/tex] ( cross- multiply )

4x = 106.5 ( divide both sides by 4 )

x ≈ 26.6

Hence perimeter of larger figure is approximately 26.6 m

A 20m ladder and a 15m ladder were leaned against a building. The bottom of the longer ladder was 7m farther from the building than the bottom of the shorter ladder, but both ladders reached the same distance up the building. Find this distance.

6m

12m

10m

9m

Answers

Answer:

The correct answer is: d=9m

Step-by-step explanation:

Ok, the ladders leaned against a building make two right triangles with same the same height, which we will call h. For the 20m ladder, its leg is (7+d) and for the 15m ladder, its leg is d, and the two hypotenuses are 20 and 15 respectively.

Then, using the Pythagorean Theorem we have:  

20m ladder:

20^2 = h^2 + (d+7)^2    (Eq. 1)

400 = h^2 + d^2 + 2*7*d + 7^2  (expanding the theorem)

400 = (h^2 + d^2) + 14*d + 49   (Eq. 2)

15m ladder:

 15^2 = h^2 + (d)^2         (Eq. 3)

Since h^2 + (d)^2 is equal to 15^2, we can substitute (2) into (3):

400 = (15^2) + 14*d + 49

400 = 225 + 14*d + 49

14*d = 400 - 225 - 49  (clearing the variable d)

14*d = 126

d = 9 m

And since we now know that d is equal to 9m. For the longer ladder is (d+7)=(9+7)=16m.

And, then the shorter ladder is 9m from the building and the longer ladder is 16m from the building

A diameter of a circle has end points P(-10,-2) And Q(4,6)
A. Find the center of the circle
B. Find the radius.if your answer is not an integer express it in a radical form.
C.write and equation for the circle
GIVING BRAINLIEST

Answers

Answer:

Step-by-step explanation:

A]

The center is the average values of the 2 endpoints (which is also the diameter).

x:(-10 + 4)/2 = -6/2 = -3

y:(-2 + 6)/2 = 4/2 = 2

Center(-3,2)

B]

The radius is the distance from the center to one of the end points.

r^2 = (-3 - 4)^2 + (2 - 6)^2

r^2 = (-7)^2 + (-4)^2

r^2 = 49 + 16

r^2 = 65

r = sqrt(65)

C]

(x + 3)^2 + (y - 2)^2 = 65

Graph

The graph has been included so that you can see that the center I have calculated is between (-10,-2) and (4,6)

Further, it shows the the circle goes the two end points of the diameter.

The manager of a company that sells movie tickets online releases a report. The report states that the company's customers do not want the option of reserving a seat when they buy tickets. The report was based on a survey of 200 customers chosen at random from the company's database. Participants were asked the question, "Are you willing to spend the extra time and effort to reserve a seat when you buy tickets?"



Select ALL statements that correctly evaluate the report.




A. The question is biased toward a No response.

B. The question is biased toward a Yes response.

C. The sample is biased because it does not represent the population.

D. The sample is not biased.

E. The question is not biased.

Answers

The answer is a okay

Answer:

A and D

Step-by-step explanation:

The customers were chosen at random, so the sample is not biased.  However, the question is biased.  "Extra time and effort" is phrased to get a No response.

A and D.

F=7gh solve the formula for the variable h

Answers

Answer:

[tex]\large\boxed{h=\dfrac{F}{7g}}[/tex]

Step-by-step explanation:

[tex]F=7gh\to7gh=F\qquad\text{divide both sides by}\ 7g\neq0\\\\\dfrac{7gh}{7g}=\dfrac{F}{7g}\\\\h=\dfrac{F}{7g}[/tex]

The formula for the variable h is F/7g.

What is the variable?

A variable is an alphabet or term that represents an unknown number of unknown value or unknown quantity.

The given equation is;

F=7gh

The formula for the variable h is determined in the following steps given below.

[tex]\rm F=7gh\\\\ h =\dfrac{F}{7g}[/tex]

Hence, the formula for the variable h is F/7g.

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Describe the set of numbers using interval notation.
x > 8 or x ≤ 2

A. [2, 8)

B. (–∞, 2] ∩ (8, ∞)

C.(–∞, 2] ∪ (8, ∞)

D. (–∞, 2) ∪ (8, ∞)

Answers

Answer:

Option C.(–∞, 2] ∪ (8, ∞)

Step-by-step explanation:

we know that

The solution of the inequality [tex]x > 8[/tex] Is the interval (8,∞)

The solution of the inequality [tex]x\leq 2[/tex] Is the interval (-∞,2]

therefore

The solution of  [tex]x > 8[/tex] or [tex]x\leq 2[/tex] is equal to

(-∞,2] U (8,∞)

Final answer:

The correct interval notation for the inequality x > 8 or x ≤ 2 is (−∞, 2] ∪ (8, ∞), which represents all numbers less than or equal to 2 and all numbers greater than 8.

Explanation:

The question asks to describe the set of numbers using interval notation for the inequality x > 8 or x ≤ 2. Interval notation is a concise way of writing sets of numbers, using brackets to include endpoints and parentheses for exclusive limits. For an inequality like x > 8, we use the notation (8, ∞) to indicate all numbers greater than 8 but not including 8 itself. Likewise, for x ≤ 2, the interval notation is [−∞, 2] which includes all numbers less than or equal to 2. When we combine these with the union because of the 'or' condition, the correct interval notation is (−∞, 2] ∪ (8, ∞). Therefore, the correct answer is C. (8, ∞) indicates all the numbers larger than 8, and (−∞, 2] includes all the numbers up to and including 2.

A sailboat 18 m tall sails near a lighthouse. From the top of the lighthouse, the angle of depression to the top of the syllable is the degrees, to the bottom is 45°.

Answers

I believe it’s 245 I believe I did this before I don’t know

Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ±2/3x.

Answers

Check the picture below.

so the hyperbola looks more or less like so, is a hyperbola with a vertical traverse axis, with a = 4 and h = 0, k = 0.

[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \stackrel{\textit{the asymptotes are}}{\pm\cfrac{2}{3}x}\implies \pm\cfrac{2}{3}x=k\pm \cfrac{a}{b}(x- h)~~ \begin{cases} h=0\\ k=0\\ a=4 \end{cases} \\\\\\ +\cfrac{2}{3}x=0+\cfrac{4}{b}(x-0)\implies \cfrac{2x}{3}=\cfrac{4x}{b}\implies 2bx=12x \\\\\\ b=\cfrac{12x}{2x}\implies b=6 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y-0)^2}{4^2}-\cfrac{(x-0)^2}{6^2}=1\implies \cfrac{y^2}{16}-\cfrac{x^2}{36}=1[/tex]

Final answer:

The standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ±2/3x is \(\frac{y^2}{16} - \frac{9x^2}{64} = 1\).

Explanation:

Finding the Standard Form Equation of a Hyperbola

The student has asked for the standard form of a hyperbola given certain characteristics such as vertices and asymptotes.

The vertices at (0, ±4) indicate that this is a hyperbola centered at the origin with its major axis along the y-axis, while the asymptotes given by y = ±2/3x help determine the relationship between the semi-major axis a and semi-minor axis b.

General Structure of a Hyperbola

For a hyperbola centered at the origin with a vertical transverse axis, the standard form is:

[tex]\(rac{y^2}{a^2} - \frac{x^2}{b^2} = 1\)[/tex]

Given that the asymptotes have slopes of ±2/3, the relationship between a and b is b/a = 2/3. Since the vertices are at (0, ±4), a = 4. Solving for b gives us b = (2/3) × 4 = 8/3.

Standard Form Equation

The standard form equation of the hyperbola is therefore:

[tex]\(rac{y^2}{16} - \frac{x^2}{(8/3)^2} = 1\)Or simplified:\(rac{y^2}{16} - \frac{9x^2}{64} = 1\)[/tex]

Please please help me

Answers

Answer:

399.6 miles²

Step-by-step explanation:

The area (A) of the major sector is

A = area of circle × fraction of circle

   = πr² × [tex]\frac{255}{360}[/tex]

   = π × 13.4² × [tex]\frac{255}{360}[/tex]

   = [tex]\frac{13.4^2(255)\pi }{360}[/tex] ≈ 399.6 miles²

Explain how solve 4x + 3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

any help is appreciated!

Answers

Final answer:

The equation 4x + 3 = 7 is solved algebraically by subtracting 3 from both sides and then dividing by 4 to find x = 1. There is no need for logarithms or the change of base formula to solve this linear equation.

Explanation:

The equation 4x + 3 = 7 is a linear equation and can be solved using simple algebraic manipulations rather than the change of base formula for logarithms. However, to show how logarithms could hypothetically be used (even though it's over-complicating this particular problem), we can take the following steps:

Divide both sides by 4: x = 1.

Therefore, the solution to the equation is x = 1. There is no need to round to the nearest thousandth as the solution is a whole number. The change of base formula, logb y = (log y) / (log b), is not necessary for this equation.

The solution to the equation [tex]\(4x + 3 = 7\) is \(x = 1\),[/tex] obtained by isolating [tex]\(x\)[/tex]

Step-by-Step Solution:

1. Write down the equation:

[tex]\[ 4x + 3 = 7 \][/tex]

2. Isolate the term with the variable [tex]\(x\):[/tex]

  - To do this, we need to remove the constant term on the left side by subtracting 3 from both sides of the equation.

[tex]\[ 4x + 3 - 3 = 7 - 3 \][/tex]

  - Simplify both sides:

[tex]\[ 4x = 4 \][/tex]

3. Solve for [tex]\(x\):[/tex]

  - To isolate [tex]\(x\)[/tex], divide both sides of the equation by 4:

[tex]\[ \frac{4x}{4} = \frac{4}{4} \][/tex]

- Simplify both sides:

[tex]\[ x = 1 \][/tex]

Conclusion:

The solution to the equation [tex]\(4x + 3 = 7\)[/tex] is:

[tex]\[x = 1\][/tex]

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