What is the equation of circle C?

well, the midpoint of segment AB is the center of the circle, so

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 9 +1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies \stackrel{center}{(2~~,~~5)}[/tex]

now since we know AB is the diameter, so half that distance AB is its radius, so

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]

[tex]AB=\sqrt{(~~6 - (-2)~~)^2 + (~~9 - 1~~)^2} \implies AB=\sqrt{(6 +2)^2 + (9 -1)^2} \\\\\\ AB=\sqrt{( 8 )^2 + ( 8 )^2} \implies AB=\sqrt{ 64 + 64 } \implies AB=\sqrt{ 128 } \\\\\\ AB=8\sqrt{2}\hspace{5em}\stackrel{\textit{half that is the radius}}{\cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\implies \sqrt{32}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{\sqrt{32}}{r}} \\\\\\ (x-2)^2~~ + ~~(y-5)^2~~ = ~~(\sqrt{32})^2\implies {\large \begin{array}{llll} (x-2)^2~ + ~(y-5)^2~ = ~32 \end{array}}[/tex]

What is (9^6 x7^-9)^-4=

**Answer:**

[tex] \dfrac{7^{36}}{9^{24}} [/tex]

**Step-by-step explanation:**

(9^6 x7^-9)^-4=

[tex] = (9^6 \times 7^{-9})^{-4} [/tex]

[tex] = 9^{-24} \times 7^{36} [/tex]

[tex] = \dfrac{7^{36}}{9^{24}} [/tex]

On Wednesday, they pick a total of 89 kg of strawberries.

The mean mass of each strawberry is 22 g.

Work out the number of strawberries they picked.

Give your answer correct to the nearest 10

The **number **of **strawberry **they picked is about **4050.**

Multiplication is the opposite of **division**. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size **results **in 4 in each group. Creating equal groups or determining how many people are in each group after a fair **distribution **is the basic objective of **division**.

**89 kg = 89000 g **conversion

89000=22=4045.45** ≈4045**

{unit conversion}

**≈4050**

The number of **strawberry **{nearest lo} is about **4050**

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What percent of 933 is 391.83?

**Answer:**

42%

Tell me if you need expalining!

**Step-by-step explanation:**

44+400 divided by (4+62)-24

**Answer:**

185

**Step-by-step explanation:**

**Answer:**

18

**Step-by-step explanation:**

**250**

**244**

**18**

**10**

**are one of the answers**

**give this 5 stars if correct**

A full moon occurs every 30 days. If the last full moon occurred on a Friday, how many days will pass before a full moon occurs again on a Friday?

(I wrote the problem correctly, and its not 30)

**Answer:**

210 days

**Step-by-step explanation:**

7 x 30 = 210 days

**Answer:**

210

**Step-by-step explanation:**

A Friday occurs every 7 days.

A new moon occurs (approximately) every 30 days.

We need the smallest number that is a multiple of both 7 and 30.

We need the least common multiple (LCM) of 7 and 30.

This is the same as finding the least common denominator for two fractions that have denominators 7 and 30.

First, we find the prime factorizations of the two numbers.

7 = 7

30 = 2 × 3 × 5

The LCM is the product of common and not common factors with the larger exponent.

LCM = 2 × 3 × 5 × 7 = 210

Answer: 210

P.S. This is the correct answer for this problem, but the problem is stated incorrectly since a new moon occurs approximately every 29.5 days, so in reality, the true answer is not 210 days.

I NEED HELP WITH MY HOMEWORK

**Chester** made 9 sales and **Vickie** made 16 sales this week

Base **salary** of Vickie = $70

Vickie's commission per sale = $24

Base salary of Chester = $142

Chester's commission per sale = $9

Both people earned the same amount this week. Let x represent the number of **sales** made by Vickie, then sales made by Chester is x+7

Formulating the equation we get:

Base salary of Vickie + Vickie's commission per sale***Number** of sales = Base salary of Chester + Chester's commission per sale*Number of sales

= 70 + 24x = 142 + 9(x+7)

70+24x = 142+9x+63

70+24x = 205+9x

15x = 135

x = 9

Chester sales = 9

Vickies sales = 9+7 = 16

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Write an equation for the intervals of a parabola with x-intercepts at (2,0) and and (-5,0) that passes through the point (1, -18).

Help is always greatly appreciated.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= 3 {x}^{2} + 9x - 30[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The values of x where a parabola cuts the x - axis (y = 0) are the roots of the quadratic equation.

I.e -5 and 2 for the given problem.

and the equation can be represented as :

[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x - x1)(x- x2)[/tex]

where, x1 and x2 are the roots of the quadratic equation, a is a constant value (depicting strech in curve)

Now, plug in the values :

[tex]\qquad\displaystyle \tt \rightarrow \: y= a(x- 2)(x - ( - 5))[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x- 2)(x+ 5)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = a( {x}^{2} + 5x - 2x - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= a( {x}^{2} + 3x - 10)[/tex]

Now, we need to find the value of a, for that let's use the coordinates of a point lying on the curve (1 , -18)

[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a( {1}^{2} + 3(1) - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a(1 + 3 - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: - 18 = a( - 6)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: a = ( - 18) \div ( - 6)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: a = 3[/tex]

Now, we got all required values. let's plug the value of a in equation, and we will get the required equation of parabola.

[tex]\qquad\displaystyle \tt \rightarrow \: y= 3( {x}^{2} + 3x - 10)[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y= 3 {x}^{2} + 9x - 30[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

**Answer:**

[tex]\textsf{Factored form}: \quad f(x)=3(x-2)(x+5)[/tex]

[tex]\textsf{Standard form}: \quad f(x)=3x^2+9x-30[/tex]

**Step-by-step explanation:**

Factored form of a quadratic function

[tex]f(x)=a(x-p)(x-q)[/tex]

where:

p and q are the x-intercepts.a is some constant.Given **x-intercepts**:

Substitute the given **x-intercepts** into the **formula**:

[tex]\implies f(x)=a(x-2)(x+5)[/tex]

To find a, substitute the given **point **(1, -18) into the **equation **and **solve for a**:

[tex]\implies -18=a(1-2)(1+5)[/tex]

[tex]\implies -18=a(-1)(6)[/tex]

[tex]\implies -6a=-18[/tex]

[tex]\implies a=3[/tex]

Therefore, the **equation** of the function in f**actored form** is:

[tex]\boxed{ f(x)=3(x-2)(x+5)}[/tex]

**Expand **the brackets:

[tex]\implies f(x)=3(x^2+3x-10)[/tex]

[tex]\implies f(x)=3x^2+9x-30[/tex]

Therefore, the **equation **of the function in **standard form **is:

[tex]\boxed{f(x)=3x^2+9x-30}[/tex]

The point B divides AC in the ratio 2:3.

Work out vector OC in terms of a and b.

Simplify your answer.

It is said that the** ratio** of point B to point AC is 2: 3.

This implies;

BC/AB = 3/2

BC = 3(b - a)/2

Thus;

AB + BC Equals AC

AC equals b-a plus 3(b-a)/2.

b-a - 3b/2 - 3a/2 = AC

AC = 5b/2 - 5a/2

AC = ⁵/₂(b - a) (b - a)

Using the same **vector addition law**, we can state that;

OC = AC – AO

OC = ⁵/₂(b - a) - (-a) (-a)

Given that giving OA is the inverse of -a, I used -a for AO.

Thus;

OC = 5b/2 - 5a/2 + a

OC = (⁵/₂)b - (³/₂)a

OC = ¹/₂(5b - 3a) (5b - 3a)

What is **vector addition law**?

Objects with both direction and magnitude are referred to be **vectors**. When two **vectors** have the same magnitude and direction, they are deemed to be one and the same. A line and an arrow are used to symbolize these geometrical objects. This arrow points in the direction of the vector, and the line's length indicates the vector's magnitude. These arrows, therefore, have a starting point and an ending point. Physical quantities like velocity, displacement, and acceleration are represented by vectors.

Notation A **vector** is frequently written in bold letters, such as an or b.

As seen on the right side, a **vector** may alternatively be expressed as the letters for its head and tail with an arrow above it.

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Determine whether the two figures are similar.

The two **triangles** are **similar**.

**Similar triangles** are triangles that have the same shape, but their sizes may vary.

Two triangles are said to be** similar** if their corresponding angles are congruent and the corresponding sides are in proportion .

The side lengths of two **similar triangles** are proportional. That is, if ΔABC is similar to ΔDEF , then the following equation holds:

AB / DE = AC / DF = BC / EF

Hence,

6 / 3 = 10 / 5 = 8 / 4 = 2 / 1

This common ratio is called the scale factor .

The symbol ∼ is used to indicate similarity.

Therefore, the t**riangles** are similar.

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I have missing work may someone help me with my math

2)

[tex]w^2-3,\quad w=4[/tex]When we say that w = 4, it means that we can rewrite the expression and instead of "w", we will put "4", so

[tex]w^2-3\Rightarrow4^2-3[/tex]Now we have a numerical expression to solve, we can easily solve it!

[tex]\begin{gathered} 4^2-3 \\ \\ 4\cdot4-3 \\ \\ 16-3 \\ \\ 13 \end{gathered}[/tex]Therefore, the final answer is

[tex]4^2-3=13[/tex]5)

Here we will do the same thing, the "hard" part is solving the numeric expression, it will be a little bit harder than the 2).

[tex]3(6m-17),\quad m=5[/tex]Again, repeat the same process, rewrite the expression, and instead of "m" you put "5"

[tex]3(6m-17)\Rightarrow3(6\cdot5-17)[/tex]Again, another expression to simplify, remember that we always solve what is inside ( ) first, and we have a multiplication inside ( ) so we must solve it first

[tex]3(6\cdot5-17)=3(30-17)[/tex]Now we solve the multiplication inside ( ) we can do the subctration

[tex]3(30-17)=3\cdot(13)[/tex]The last step is just to solve another multiplication

[tex]3\cdot(13)=39[/tex]Now we simplified everything we can have the **final answer:**

6)

Here we have a division, but it's similar with 5) and 2), we have

[tex]\frac{2a}{3}+13,\quad a=15[/tex]No secrets, repeat the process, but here, "a" will turn into "15", then

[tex]\frac{2a}{3}+13\Rightarrow\frac{2\cdot15}{3}+13[/tex]We can do the multiplication at the numerator of the fraction

[tex]\frac{2\cdot15}{3}+13=\frac{30}{3}+13[/tex]Now we can simplify the fraction, 30 divided by 3 is 10, then

[tex]\frac{30}{3}+13=10+13[/tex]Now just do the sum and it's done!

[tex]10+13=23[/tex]Hence the final answer is

[tex]\frac{2\cdot15}{3}+13=23[/tex]ANSWERS:

1) 43

2) 13

3) 67

4) 12

5) 39

6) 23

Rodney is flying on an airplane to puerto rico. his suitcase and the contents inside must weigh less than 50lbs. his suitcase weighs 4 pounds and the contents he wants to pack weigh 49 pounds. if each of his shirts weighs 0.75 pounds, write an inequality to represent the number of shirts he needs to remove to meet the flight requirements.

The **inequality **that represents, the number of **shirts **he needs to remove to meet the **flight **requirements is 0.75p + 50ibs ≤ 49

If the **equation **or inequality contains variable **terms**, then there might be some values of those **variables **for which that equation or inequality might be true. Such values are called **solution **to that equation or **inequality**.

Let the weight of **Rodney **suitcase be p

First the contents **inside **must **weigh **less than 50lbs.

x < 50

The **suitcase **weighs 4 pounds and the **contents **he wants to pack weigh 49 pounds.

0.75p < 49

Therefore, 0.75p + 50ibs ≤ 49

The **inequality **that represents, the number of **shirts **he needs to remove to meet the **flight **requirements is 0.75p + 50ibs ≤ 49

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a playground is rectangular and the length is 7/8 miles. if the area is 8/20 what is the width?

**Answer:**

so the width is 16/35 miles

**Step-by-step explanation:**

Length - 7/8 miles

Area - 8/20 miles

we know from the equation that area = Length x width

we need to rearrange so the width = Area ÷Length

width = 8/20 ÷ 7/8

= 8/20 × 8/7

= 16/35

Which represents the inverse of the function f(x) = 4x?

Oh(x)=x+4

Oh(x)=x-4

Oh(x) = 3/4x

○ h(x) = 1/4x

**Answer:**

(d) h(x) = 1/4x

**Step-by-step explanation:**

You want to know the **inverse** of the **function f(x) = 4x**.

The inverse of y = f(x) will be the solution to x = f(y).

x = f(y)

x = 4y . . . . . . substitute the argument in the function definition

x/4 = y . . . . . divide by 4 to solve for y

The inverse function is ...

** h(x) = (1/4)x**

What is the remainder when f(x) = x3 + 5x2 –32x – 7 is divided by x – 4? Show your work.

The **remainder** of f(x) is **385.**

What are the 5 steps of **long division**?

The five steps of long division are given by:

Step 1: Divide

Step 2: Multiply

Step 3: Subtract

Step 4: Bring down

Step 5: Repeat

**Given,**

f(x) = x3 + 5x2 –32x – 7 is **divided** by x – 4

To find the **Remainder **

Now, The solution is:

[tex]x^{2} -9x+98[/tex]

[tex]x-4\sqrt{x^3+5x^2-32x-7}\\[/tex]

[tex]x^{3} - 4x^2[/tex]

- +

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

[tex]9x^{2} -32x[/tex]

[tex]9x^{2} +36x[/tex]

- -

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

98x -7

98x - 392

- +

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

Remainder 385

Hence, The **remainder** of f(x) is **385**.

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When driving up a certain hill, you rise 15 feet for every 1000 feet you drive forward. What is the slope of the rode?

**slope **of the **rode **is 0.015.

**What is slope of line ? **

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

The point with coordinate having same slope as with given coordinates can be plotted on the same line.

Here, it is given that :

When driving up a certain hill, we rise 15 feet for every 1000 feet that is :

for 15 **feet up **= 1000 **feet forward**

Now,

slope = upward distance / horizontal distance covered

slope = 15/1000

slope = 0.015

slope is a unitless quantity.

Therefore, **slope **of the **rode **is 0.015.

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Solve for x Correct Answers PLS show work

**Answer:**

x = 8

**Step-by-step explanation:**

The angles shown are vertical angles

Vertical angles are congruent (equal to each other)

This means that 8x + 36 = 5x + 60

Using this equation we can solve for x

8x + 36 = 5x + 60

==> subtract 36 from both sides

8x = 5x + 24

==> subtract 5x from both sides

3x = 24

==> divide both sides by 3

x = 8

**Answer:**

**8x + 36 = 5x + 60 **

**8x = 5x + 24**

**3x = 24**

**x = 8**

You have exactly 10 coins with a total

value is $1. Three of the coins are

quarters. What are the remaining coins?

The

**Answer:**

2 dimes and 5 pennies

**Step-by-step explanation:**

2 dimes (d) is 10 and 5 pennies (p) is 5

75+p+d=100

75+p=80

80+d=100

Answer: 3 quarters, 2 dimes, 1 nickel.

Step-by-step explanation: 3 quarters are worth 75 cents, 2 dimes are worth 20 cents, and 1 nickel is worth 5 cents! Hope this helps

Is the sequence {3, 6, 12, 6, 3, ...} a function? Explain.

The **sequence **{3, 6, 12, 6, 3, ...} is not a function

The **sequence **is given as

{3, 6, 12, 6, 3, ...}

In the above sequence, we can see that the sequence has **repeated numbers**

The **repeated numbers **are 3 and 6

These numbers are repeated twice

For a sequence of numbers to represent a **function**, the numbers in the **sequence **must be distinct

Hence, the **sequence ** is not a function

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-26, 174, 374, 574, …

Find the explicit and recursive formula.

The** explicit **formula and the** recursive **formula are aₙ₋₁ + 200 and the rest is mentioned below.

A formula can be either recursive or explicit. The main difference between **Recursive** and** Explicit** is that Recursive formula gives the value of a specific term based on the previous term while Explicit formula gives the value of a specific term based on the position.

Given : a₁ = -26, a₂ = 174, a₃ = 374, a₄= 574

The** common difference** that is d can be found out by

thus d = a₂ - a₁ = 174 -(- 26 ) = 174 + 26 = 200

And this is same for all the numbers of this particular sequence.

Thus aₙ = aₙ₋₁ + d

= aₙ₋₁ + 200

Recursive formula : aₙ₋₁ + d

That is the following **sequence **will have a common difference of 200 and the next 5th, 6th, 7th and nth term is going to be .

774 , 974 ... etc

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Tea that sells for $2.00 a pound is mixed with a different tea that sells for

$5.00 a pound to produce 40 pounds of a custom blended tea that will

sell for $4.25 a pound. How many pounds of the less expensive tea

should be used in the mixture?

(1) 10

(2) 15

(3) 25

(4) 30

Pls show work pls show work pls show work pls show work

**10 pounds** of less expensive tea should be used in the mixture.

Inferior tea price = $2.00

Superior tea price = $5.00

Blended tea price = $4.25

**Solution:**

Price of 40 pounds of a custom blended tea = $4.25 * 40 = $170

Let x be the inferior tea quantity and

(40 - x) be the superior tea quantity.

2x + 5(40 - x) = 4.25 * 40

2x + 200 -5x = 170

-3x = -30

** x = 10**

Therefore, **10 pounds** of **less expensive tea** should be used in the mixture.

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your company is producing special battery packs for the most popular toy during the holiday season. the life span of the battery pack is known to be normally distributed with a mean of 250 hours and a standard deviation of 20 hours. what is the probability that a randomly chosen battery pack lasts longer than 260 hours?

The probability that a randomly chosen battery pack lasts longer than 260 hours is **0.69**.

**What is a normal distribution?**

The **normal distribution** is a probability distribution that is symmetric about the **mean** and demonstrates that data that are closer to the mean are more likely to occur than data that are farther from the **mean**.

Since the life span of the battery pack is known to be **Normally distributed**, we would apply the formula for **normal distribution** which is expressed as

z = (x - µ)/σ

Where

x = life spans of battery packs.

µ = **mean** life span

σ = **standard deviation**

From the information given,

µ = 250 hours

σ = 20 hours

The probability that a battery pack lasts longer than 260 hours. It is expressed as

P(x > 260) = 1 - P(x ≤ 260)

For x = 260

z = (260 - 250)/20 = 0.5

Looking at the **normal distribution** table, the probability corresponding to the **z score** is 0.69

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The **probability** that a randomly chosen **battery pack** lasts longer than 260 hours is 0.69.

**What is a normal distribution?**

The **normal distribution** is a **probability** distribution that is symmetric about the **mean** and demonstrates that data that are closer to the **mean **are more likely to occur than data that are farther from the** mean**.

Since the life span of the battery pack is known to be **Normally distributed**, we would apply the formula for **normal distribution** which is expressed as

z = (x - µ)/σ

Where

x = life spans of battery packs.

µ = **mean** life span

σ = **standard deviation**

From the information given,

µ = 250 hours

σ = 20 hours

The **probability** that a battery pack lasts longer than 260 hours. It is expressed as

P(x > 260) = 1 - P(x ≤ 260)

For x = 260

z = (260 - 250)/20 = 0.5

Looking at the **normal distribution** table, the **probability** corresponding to the z score is 0.69

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Let g(x) = |2x - 10| find g(-3)

**Answer:**

g(-3) = 16

**Step-by-step explanation:**

**To find g(-3), we need to plus -3 into the given function. So, g(-3) = |2(-3) - 10|. Now we solve using PEMDAS. Two times -3 is -6, then we have g(-3) = |-6-10| which is essentially g(-3) = |-16|. Lastly, we take the absolute value of |-16| which is just 16, therefore g(-3) = 16.**

11-(15g-13)=-6

what does G stand for

**Answer:**

g = 2

**Step-by-step explanation:**

11- (15g - 13) = - 6 ( subtract 11 from both sides )

- (15g - 13) = - 17 ( multiply both sides by - 1 )

15g - 13 = 17 ( add 13 to both sides )

15g = 30 ( divide both sides by 15 )

g = 2

-15 = -3/4w solve for w and simplify your answer as much as possible

**Answer:**

w = 20

**Step-by-step explanation:**

a) Flip the equation.

-3/4 w = -15

b) Multiply both sides by 4/(-3).

(4/-3) * (-3/4 w) = (4/-3) * (-15)

**w = 20**

Solve the inequality. Graph the solution. |8x−8|≤24

The **solution **of the given inequality would be x = 4. the **graph **of the given **inequality **is attached below.

If the **equation **or inequality contains variable terms, then there might be some values of those **variables **for which that equation or inequality might be true. Such values are called **solution **to that equation or **inequality**. Set of such values is called solution set to the considered equation or inequality.

Given the **inequality **as |8x−8|≤24.

For solving the given **expression**,

|8x−8|≤24

We can **consider **the expression as;

8x−8 = 24

8x = 24 + 8

8x = 32

x = 32/8

x = 4

Hence, the **solution **of the given inequality would be x = 4.

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chegg a spherical ball is measured to have a radius of 5 mm, with a possible measurement error of 0.1 mm. use the differential to estimate the possible change in volume (in mm3) resulting from the error in measuring the radius.

The possible **change** in **volume** that results from the error in measuring the radius is 32. 06 millimeters

It is important to note that the formula for **volume** of a** sphere** is expressed by;

Volume = 4/3 πr³

Given that;

r is the radius of the sphereπ has the value 3.14Based on the information given, we have the measure of the radius to be 5 mm, with a possible measurement error of 0.1 mm

The original value of radius = 5mm

Radius after the measurement error = 5 + 0. 1 = 5. 01mm

Let's substitute the values into the formula

Volume = 4/ 3 (3.14)(5)³

We then expand the bracket

Volume = 4/ 3 (392.5)

Volume = 523. 3 cubic millimeters

For radius of the measurement error = 5.01mm

Volume = 4/ 3 (3.14)(5.1)³

Then, expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 cubic millimeters

Change in volume = 555. 4 - 523. 3 = 32. 06 cubic millimeters

Hence, the **change** in** volume** is given as 32. 06 cubic millimeters

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The angle a lies between 0° and 90° and is such that

2 tan²a + sec²a = 5-4 tana

Show that

3 tan²a +4 tana -4 = 0

and hence find the exact value of tan a

Good.

Now we know this property

Sec^2 A = 1 + tan^2 A

Now lets replace the sec square term with this in the given question

We get,

3tan^2(A) + 1 = 5 - 4tanA

Hence 3tan^2A + 4tanA - 4 =0

Hence proved

Lets take tanA as a value x.

Thus 3x2+4x-4=0

=> 3x2 + 6x - 2x - 4 =0

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

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

x=2/3 or x=-2

But tanA cant have a negative value as 0Thus tanA=x= 2/3

Now we know this property

Sec^2 A = 1 + tan^2 A

Now lets replace the sec square term with this in the given question

We get,

3tan^2(A) + 1 = 5 - 4tanA

Hence 3tan^2A + 4tanA - 4 =0

Hence proved

Lets take tanA as a value x.

Thus 3x2+4x-4=0

=> 3x2 + 6x - 2x - 4 =0

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

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

x=2/3 or x=-2

But tanA cant have a negative value as 0Thus tanA=x= 2/3

Quadrilateral EFGH is inscribed inside a circle as shown below. Write a proof showing that angles H and F are supplementary.

**Given**

**Find**

showing that angles H and F are supplementary.

**Explanation**

Let angle F , which is subtended by minor arc GHE.

so , angle F = half of angle GHE by subtended angle theorem.

similarly , angle H is the angle subtended by major arc GFE.

so , angle H = half of the angle subtended by major arc.

since , total angle around J is 360 degree.

as we know , the sum of angle subtended by minor arc and major arc is 360 degree.

so , angle F + angle H = 1/2(360) = 180 degree.

**Final Answer'**

Hence **, H and F are supplementary angles.**

A plane (at point P) sees a bridge (at point B) at an angle of depression on 28 degrees. The horizontal distance between the plane and the bridge is 3000 feet. Explain which trigonometric equation can be used to solve for the height of the plane (segment PA). What is the height of the plane? You must show all work and calculations to receive full credit. Round your answer to the nearest foot.

The **height** of the plane PA is given as; 1591 ft

How to use trigonometric ratios?

There are different **trigonometric ratios** such as;

cos θ = adjacent/hypotenuse

sin θ = opposite/hypotenuse

tan θ = opposite/adjacent

Now, looking at the given image showing plane and bridge indicated by lines, we can use one of the** trigonometric ratios** to get the height of the plane PA as;

PA/3000 = tan B

now angle B = 28 degrees from **alternate angles postulate**. Thus;

PA/3000 = tan 28

PA = 3000 * tan 28

PA = 3000 * 0.5317

PA = 1591 ft

Read more about **trigonometric ratios** at; https://brainly.com/question/13276558

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[tex]tan 28^o = \frac{PA}{3000}[/tex]

tan 28° · 3000= PA

(use a scientific calculator)

1595.128= PA

height = 1595

A ball is thrown in the air the function H = 30t￼-5t^2 can be used to find the height (h) of the ball in meters after t seconds￼￼. how long does it take the ball to reach a height of 45 meters?￼

The most appropriate choice for **Distance** will be given by:

The ball takes [tex]3s[/tex] to reach a **height** of [tex]45[/tex] [tex]m[/tex].

**What is Distance?**

The **length** of the** path** an object takes without taking into account the **direction of motion** of the object is known as** distance**.

If [tex]s[/tex] is the **speed **of the object and [tex]t[/tex] is the **time**, then

**Distance** = [tex]s \times t[/tex]

Here,

[tex]H(t) = 30t - 5t^2[/tex], [tex]t[/tex] is the time in seconds

For finding the time taken by the ball to reach a height of [tex]45[/tex][tex]m[/tex], we need to substitute [tex]H(t) = 45[/tex]

Now putting [tex]H(t) = 45[/tex]

[tex]45 = 30t - 5t^2\\5t^2 - 30t+45 = 0\\ 5(t^2 -6t + 9)=0\\t^2 -6t+9=0\\t^2-3t-3t+9=0\\t(t-3)-3(t-3)=0\\(t-3)(t-3)=0\\t-3 = 0\\t = 3s[/tex]

So the ball takes [tex]3s[/tex] to reach a height of [tex]45[/tex] [tex]m[/tex].

To learn more about **Distance**, refer to the link:

https://brainly.com/question/26046491

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