Hello! Can I get some help with calculus please? #14 and #18. Don't forget to show your work. I appreciate the help! ​

Answer:

Step-by-step explanation:

We have alternative external corners.

The lines m and n are parallel. That is why the alternative external angles are congruent (they have the same measure).

In the triangle RTS we have angles:

[tex]4x^o,\ 54^o,\ 2x^o[/tex]

We know: The sum of the angles of the triangle is equal to 180 °.

Therefore we have the equation:

[tex]4x+54+2x=180[/tex]            subtract 54 from both sides

[tex]6x=126[/tex]           divide both sides by 6

[tex]x=21[/tex]

Answer:

  buying in packets of 100

Step-by-step explanation:

Adding the given numbers results in a total that is twice the total number of cards the girls have. That total is 1256, so the total of the girls card collections is 628 cards.

  Mai has 628 -371 = 257 cards, so will need ceiling(257/9) = 29 pages

  Ellen has 628 -481 = 147 cards, so will need ceiling(147/9) = 17 pages

  Lora has 628 -404 = 224 cards, so will need ceiling(224/9) = 25 pages

Together, the girls need 29 +17 +25 = 71 pages.

If they were to buy packets of 10, they would need 8 packets, or 80 pages at 0.20 per page, for a cost of $16.00.

If they were to buy packets of 100, they would need 1 packet, or 100 pages at 0.15 per page, for a cost of $15.00.

Buying their pages in packets of 100 will cost the girls less.

First, we figure out how many cards each girl has, then determine how many pages they need in total. Comparing the costs, it is clear that it would cost less for the girls to buy the packets of 100 pages.

To answer this question, the first step is to find out how many cards each girl has. From the question, we understand that Ellen and Lora together have 371 cards and Lora and Mai together have 481 cards. The sum of Ellen's and Mai's cards totals to 404. By using these equations, we can determine that Lora has 227 cards, Ellen has 144 cards, and Mai has 254 cards.

Next, we need to find out how many pages each girl needs. Since each page has 9 pockets, Lora needs 26 pages (227 divided by 9, rounded up), Ellen requires 16 pages and Mai requires 29 pages. Altogether, they need 71 pages.

Now, let's get to the cost. At .20 cents per page, packets of 10 would cost $2, and they need 8 packets, which totals to $16. Alternatively, a packet of 100 costs .15 cents per page, which equals to $15.

Therefore, buying pages in packets of 100 will save the girls money as compared to buying in smaller packs of 10.

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Answer: [tex](x+10)^2+(y+6)^2=121[/tex]

Step-by-step explanation:

The equation of a circle in the general form is:

 [tex]ax^{2}+by^2+cx+dy+e=0[/tex]

The equaton of  a circle in standard form is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where the center is at (h, k) and r is the radius

To write the equation of a circle from general form to standard form, you must complete the squaare, as you can see below:

1- Given the equation in general form:

[tex]x^{2}+y^2+20x+12y+15=0[/tex]

2- Complete the square:

-Group the like terms and move the constant to the other side.

- Complete the square on the left side of the equation.

- Add the same value to the other side.

Then you obtain:

[tex](x^{2}+20x)+(y^2+12y)=-15\\(x^2+20x+(\frac{20}{2})^2)+(y^2+12y+(\frac{12}{2})^2)=-15+(\frac{20}{2})^2+(\frac{12}{2})^2\\\\(x+10)^2+(y+6)^2=-15+100+36\\(x+10)^2+(y+6)^2=121[/tex]

Answer:

Step-by-step explanation:

f and g will be inverses if f(g(x)) = x.

A — f(g(x)) = 5(0.2x -2) +10 = x -10 +10 = x . . . . . inverses

B — f(g(x)) = (±√x+3)^2 +3 = x ±6√x +9 +3 ≠ x . . . . . not inverses

  (even if it is g(x) = ±√(x+3), the functions are still not inverses)

C — 1/2(2x -7) +7 = x -7/2 +7 = x +7/2 ≠ x . . . . . not inverses

D — 1/4(4x +4) -1 = x +1 -1 = x . . . . . inverses

Answer:

158

Step-by-step explanation:

Hey there!

503 - 345 = 158

Therefore, the answer is 158

Hope this helps you!

God bless ❤️

xXxGolferGirlxXx

Answer:

28.8 ft

Step-by-step explanation:

SOH CAH TOA reminds you that ...

Tan = Opposite/Adjacent

The height to the top of the antenna is opposite the angle of elevation, and the distance to the building is adjacent. So, we have ...

tan(58°) = (160 ft +antenna height)/(118 ft)

(118 ft)·tan(58°) = 160 ft + antenna height . . . . . . . multiply by 118 ft

188.8 ft - 160 ft = antenna height = 28.8 ft . . . . . . subtract 160 ft, evaluate

The height of the antenna is 28.8 ft above the top of the building. (The total height of building + antenna is 188.8 ft.)

The problem can be solved using trigonometry. The tangent of the angle of elevation equals the total height (building plus antenna) divided by the distance from the point to the base of the building. Subtract the building's height from the total height to get the antenna's height.

To find the height of the antenna, we need to solve a right triangle problem using trigonometry. We know that the building is 160 Ft tall, and the angle of elevation to the top of the antenna is 58 degrees from a point 118 Ft from the base of the building. This forms a right triangle, with the building's height as one side, the horizontal distance of 118 Ft as another, and the antenna height as the hypotenuse. We can use the tangent of the angle to calculate the height of the antenna:

tangent(58) = opposite/adjacent

Here, 'opposite' represents the antenna's total height above the ground and 'adjacent' the distance from the point to the base of the building. So:

tangent(58) = total height / 118

To find the total height, we rearrange the formula:

total height = tangent(58) * 118

But remember the total height includes the building's height, so we subtract that to get the antenna's height:

antenna's height = total height - height of the building

Which, after substituting the known values, gives us the antenna's height.

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Answer:  overspending $50 per month

Step-by-step explanation:

Income (Money In):           Expenses (Money out):

              $800                   Rent = $400

                                          Food = $200

                                          Gas   = $100

                                  Insurance = $ 50

                                      Phone = $100  

TOTAL = $800             TOTAL = $850

Jessie has more money out than money in so she is overspending

by $850 - $800 =  $ 50

Answer:4

Step-by-step explanation:4/5 / 1/10= 4/5*10/1=20/5=4

4/5 divided by1/10 equals 4/5 times 10/1 which is 40/5=8

Answer:

ΔXOY ≅ ΔZOW ⇒ proved down

Step-by-step explanation:

* Lets study some facts on the circle

- If two chords equidistant from the center of the circles,

 then they are equal in length

* the meaning of equidistant is the perpendicular distances

 from the center of the circle to the chords are equal in length

* Lets check this fact in our problem

∵ XY and WZ are two chords in circle O

∵ OT ⊥ XY

- OT is the perpendicular distance from the center to the chord XY

∵ OU ⊥ WZ

- OU is the perpendicular distance from the center to the chord WZ

∵ OT ≅ OU

- The two chords equidistant from the center of the circle

∴ The two chords are equal in length

∴ XY ≅ WZ

* Now in the two triangles XOY and ZOW , to prove that

 they are congruent we must find one of these cases:

1- SSS ⇒ the 3 sides of the 1st triangle equal the corresponding

               sides in the 2nd triangle

2- SAS ⇒ the two sides and the including angle between them

                in the 1st triangle equal to the corresponding sides and

                including angle in the 2nd triangle

3- AAS ⇒ the two angles and one side in the 1st triangle equal the

                corresponding angles and side in the 2nd triangle

* Lets check we will use which case

- In the two triangles XOY and ZOW

∵ XY = ZW ⇒ proved

∵ OX = OZ ⇒ radii

∵ OY = OW ⇒ radii

* This is the first case SSS

∴ ΔXOY ≅ ΔZOW

the next number can be 34 as the sequence goes in difference of 1,2,3,4,5,6,5,2,1,1so I think it will continue with sequence 1

The value of the next number is 34

A sequence is defined as an arrangement of numbers in a particular order. On the other hand, a series is defined as the sum of the elements of a sequence.

There are two types of sequence, the arithmetic sequence and geometry sequence.

Example of arithmetic sequence is 2,4,6 ,8, 10... and we get the next number by adding 2. Also

Example of geometry sequence is 2,4,8,16,32... we get the next number by multiplying 2.

From the sequence above the next number will be 34 because the last three number has a common difference of 1.

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Answer:

[tex]f^{-1}(x)=(+/-)\sqrt{4-x}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=4-x^{2}[/tex]

Let

y=f(x)

[tex]y=4-x^{2}[/tex]

Exchange the variables x for y and y for x

[tex]x=4-y^{2}[/tex]

Isolate the variable y

[tex]y^{2}=4-x[/tex]

square root both sides

[tex]y=(+/-)\sqrt{4-x}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=(+/-)\sqrt{4-x}[/tex] -----> inverse function

Answer:

f⁻¹(x) = ±√x-4

Step-by-step explanation:

We have given  a function.

f(x) = 4-x²

We have to find the inverse of given function.

Putting y = f(x) in given equation, we have

y  = 4-x²

Adding -4 to both sides of equation, we have

y-4 = 4-x²-4

y-4 = -x²

x² = 4-y

Taking square root to both sides of above equation, we have

x = ±√4-y

Putting x = f⁻¹(y) , we have

f⁻¹(y) = ±√4-y

Replacing y by x, we have

f⁻¹(x) = ±√x-4 which is the answer.

let's firstly convert the mixed fractions to improper fractions and then add them up.

[tex]\bf \stackrel{mixed}{9\frac{3}{4}}\implies \cfrac{9\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{39}{4}}~\hfill \stackrel{mixed}{1\frac{1}{8}}\implies \cfrac{1\cdot 8+1}{8}\implies \stackrel{improper}{\cfrac{9}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{39}{4}+\cfrac{9}{8}\implies \stackrel{\textit{using and LCD of 8}}{\cfrac{(2)39~~+~~(1)9}{8}}\implies \cfrac{78+9}{8}\implies \cfrac{87}{8}\implies 10\frac{7}{8}[/tex]

Answer:

  D. A table of values represents points that lie on the graph of a linear function.

Step-by-step explanation:

A table of values can represent any relation, not necessarily a linear function. Statement D is not always true.

Statement D, 'A table of values represents points that lie on the graph of a linear function,' is not always true. A table of values could represent various types of functions or data sets. All other statements are correct for a linear function.

Let's analyze each of the given statements to identify which one is not always true:

Therefore, the correct answer is D. A table of values represents points that lie on the graph of a linear function.

Answer:  [tex]sin\ 2x=-\dfrac{240}{289}\qquad cos\ 2x=\dfrac{161}{289}\qquad tan\ 2x=-\dfrac{240}{161}[/tex]

Step-by-step explanation:

[tex]cos\ x=\dfrac{15}{17}\quad and\quad csc\ x<0\implies sin\ x=-\dfrac{8}{17}\ and\ tan\ 2x=-\dfrac{8}{15}\\\\sin\ 2x=2(sin\ x\cdot cos\ x)\\\\.\qquad =2\bigg(\dfrac{-8}{17}\cdot \dfrac{15}{17}\bigg)\\\\\\.\qquad =2\bigg(\dfrac{-120}{289}\bigg)\\\\\\.\qquad=\large\boxed{-\dfrac{240}{289}}[/tex]

[tex]cos\ 2x=cos^2\ x-sin^2\ x\\\\.\qquad=\bigg(\dfrac{15}{17}\bigg)^2-\bigg(\dfrac{-8}{17}\bigg)^2\\\\\\.\qquad=\dfrac{225}{289}-\dfrac{64}{289}\\\\\\.\qquad=\large\boxed{\dfrac{161}{289}}[/tex]

[tex]tan\ 2x=\dfrac{sin\ 2x}{cos\ 2x}\\\\\\.\qquad=\large\boxed{-\dfrac{240}{161}}[/tex]

The trigonometry values are:[tex]\mathbf{sin(2x) = -\frac{240}{289}}[/tex], [tex]\mathbf{cos(2x) =\frac{161}{289}}[/tex] and [tex]\mathbf{tan(2x)= -\frac{240}{161}}\\[/tex]

The given parameter is:

[tex]\mathbf{cos(x) = \frac{15}{17}}[/tex]

If csc(x) is less than 0, then sin(x) is less than 0.

Using the following trigonometry ratio,

[tex]\mathbf{sin^2(x) +cos^2(x) = 1}[/tex]

Substitute [tex]\mathbf{cos(x) = \frac{15}{17}}[/tex]

[tex]\mathbf{sin^2(x) +(\frac{15}{17})^2 = 1}[/tex]

Expand

[tex]\mathbf{sin^2(x) +\frac{225}{289} = 1}[/tex]

Collect like terms

[tex]\mathbf{sin^2(x) = 1 -\frac{225}{289}}[/tex]

Take LCM

[tex]\mathbf{sin^2(x) = \frac{289-225}{289}}[/tex]

[tex]\mathbf{sin^2(x) = \frac{64}{289}}[/tex]

Take square roots

[tex]\mathbf{sin(x) = \pm\frac{8}{17}}[/tex]

Recall that, the sine of the angles is negative.

So, we have:

[tex]\mathbf{sin(x) = -\frac{8}{17}}[/tex]

sin(2x) is then calculated as:

[tex]\mathbf{sin(2x) = 2sin(x)cos(x)}[/tex]

This gives

[tex]\mathbf{sin(2x) = 2 \times \frac{-8}{17} \times \frac{15}{17}}[/tex]

[tex]\mathbf{sin(2x) = -\frac{240}{289}}[/tex]

cos(2x) is then calculated as:

[tex]\mathbf{cos(2x) =cos^2(x) - sin^2(x)}[/tex]

This gives

[tex]\mathbf{cos(2x) =(\frac{15}{17})^2 - \frac{64}{289}}[/tex]

[tex]\mathbf{cos(2x) =\frac{225}{289} - \frac{64}{289}}[/tex]

Take LCM

[tex]\mathbf{cos(2x) =\frac{225 - 64}{289}}[/tex]

[tex]\mathbf{cos(2x) =\frac{161}{289}}[/tex]

Lastly, tan(2x) is calculated using:

[tex]\mathbf{tan(2x)= \frac{sin(2x)}{cos(2x)}}[/tex]

So, we have:

[tex]\mathbf{tan(2x)= \frac{-240/289}{161/289}}[/tex]

[tex]\mathbf{tan(2x)= -\frac{240}{161}}\\[/tex]

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The answer is c)

Here’s why:

Answer: D. [tex] 7t^2+3+6[/tex]

Step-by-step explanation:

Given: The function 'a' represents the cost of manufacturing product A, in hundreds of dollars, and the function 'b' represents the cost of manufacturing product B, in hundreds of dollars.

[tex]a(t)=5t+2\\\\b(t)=7t^2-2t+4[/tex]

The expression that describes the total cost of manufacturing both products will be ,

[tex] a(t) + b(t)=5t+2+7t^2-2t+4[/tex]

Combining like terms, we  get

[tex] a(t) + b(t)=7t^2+5t-2t+4+2\\\\\Rightarrow\ a(t) + b(t)=7t^2+3+6[/tex]

Answer:

5 seconds

Step-by-step explanation:

The relationship between "d" and "the ground" is not described. If we assume that "d" is distance above the ground, then the rock will hit the ground when d=0. This gives rise to the quadratic equation ...

-t^2 +4t +5 = 0

-(t -5)(t +1) = 0

t = 5 or t = -1 are solutions. Only the positive solution is useful.

The rock will hit the ground after 5 seconds.

Negative exponents work like this: you have to consider the multiplicative inverse of the positive exponent.

So you have

[tex] y={-3} = \dfrac{1}{y^3},\quad x^{-5} = \dfrac{1}{x^5}[/tex]

The third expression already contains positive exponents only, you don't have to do anything.

Answer: Darren’s range is 20 points.

Step-by-step explanation: A range is the difference between the highest score and the lowest score. With the lowest score being 280 and the highest score being 300, the difference is 20 points for the range.

Answer:

  B

Step-by-step explanation:

The question asks why you can use the argument that two angles are congruent. Hence, you want to have a statement that involves two angles in the two triangles. Only statement B is such a statement.

_____

Multiple choice questions often answer themselves, if you understand what you're reading.

Answer:

73.19

Step-by-step explanation:

4 * (1/2)* (6.5) * (5.63)

Answer:

Part a) [tex]\$17,622.72[/tex]

Part b) [tex]\$20,442.36[/tex]

Part c) [tex]\$23,713.13[/tex]

Part d) [tex]\$27,507.23[/tex]

Step-by-step explanation:

we know that  

The compound interest formula is equal to

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

Part a) How much would you have at the end of 1 year?

in this problem we have

[tex]t=1\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*1}=\$17,622.72[/tex]

Part b) How much would you have at the end of 2 year?

in this problem we have

[tex]t=2\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*2}=\$20,442.36[/tex]

Part c) How much would you have at the end of 3 year?

in this problem we have

[tex]t=3\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*3}=\$23,713.13[/tex]

Part d) How much would you have at the end of 4 year?

in this problem we have

[tex]t=4\ years\\ P=\$15,192\\ r=0.16\\n=1[/tex]

substitute in the formula above

[tex]A=15,192(1+\frac{0.16}{1})^{1*4}=\$27,507.23[/tex]

Answer:

  18 minutes 34.8 seconds

Step-by-step explanation:

We assume the minutes of commercials are proportional to the minutes of television, so we have ...

  (6 minutes of commercials)/(6 + 25 minutes of television) = x/(96 minutes of television)

Multiplying by 96, we get ...

  x = 96·6/31 = 576/31 = 18 18/31 . . . . minutes of commercials

That's about 18 minutes, 34.8 seconds of commercials in 1 hour 36 minutes of television.

Answer:

1/2 inch

Step-by-step explanation:

The area of a rectangle is the product of its length and width. So, the length and width of the photo will give a product of 24 when they are multiplied together.

One set of factors of 24 is 4 and 6, each of which is 1 unit less than the 5 and 7 dimensions of the paper on which the photo is printed. Hence a 1/2-inch border all around will result in a printed photo that is 4x6 on a 5x7 piece of paper.

___

If you want to write and solve equations, you can let b represent the border width. Then the photo area is ...

(5 -2b)(7 -2b) = 24

35 -24b +4b^2 = 24

4b^2 -24b +11 = 0

(2b -1)(2b -11) = 0

Solutions to this quadratic are b = 1/2, b = 11/2. The only viable solution is b = 1/2.

The border is 1/2 inch wide.

Answer:

y-5=3x+2

Step-by-step explanation:

1) to make up the equation through the given two points:

[tex]\frac{x+8}{-6+8}= \frac{y+1}{5+1}; \ => \ y=3x+24[/tex]

2) to change that equation according to the condition:

y-5=3x+24-5; ⇔ y-5=3x+19.

P.S. the way suggested above is not the shortest one.

put it on negative three

Answer:

Draw an open circle at -4 and shade in the line to the left of -4.

Step-by-step explanation:

x < -4 means that the number is to the left of -4 on the number line.

To graph the inequality, draw an open circle at -4 to show that the number cannot be -4.

However, the number can be anywhere to the left of -4, so you shade in that part of the line.

Answer:

C) 7 ft 4 in

Step-by-step explanation:

Shadows are assumed to be proportional to the height of the object casting them. Hence the brother's shadow will satisfy ...

shadow/(6 ft) = (5.5 ft)/(4.5 ft) = 11/9 . . . . . reduce the fraction

shadow = (6 ft) · (11/9) . . . . . . . . . . . . . . . . . multiply by 6 ft

shadow = 7 1/3 ft = 7 ft 4 in

Answer:

The vale of 6 is 'Thousands'

Answer:

Place value of 6 is thousand and tens.

Step-by-step explanation:

6560   is the number where 6 has 2 place value

(1) at thousands

(2) at tens .

6,560 = 6000+500+60

          = 6x1000 +5x100+6x10

              Here we can see that 6 is at two places

              thousand and tens

Answer:

B.) (x+3, y-7)

Step-by-step explanation:

x-coordinates increase farther to the right of the y-axis. Increasing the x-coordinate of a point by 3 will move the point 3 units to the right.

y-coordinates increase farther above the x-axis. Decreasing the y-coordinate of a point by 7 will move the point 7 units down.

To translate a point (x, y) 3 units right and 7 units down, the new coordinates need to be ....

(x +3, y-7) . . . . . . . . matches selection B

We know that, usually,

[tex] c^2 = a^2+b^2 [/tex]

In this case, we also know that

[tex] c^2 = 2ab [/tex]

We deduce that

[tex] a^2+b^2 = 2ab [/tex]

If we subtract 2ab from both sides, we get

[tex] a^2-2ab+b^2 = 0 \iff (a-b)^2 = 0 \iff a=b [/tex]

So, the triangle is an isosceles right triangle, and so the angles are 90-45-45

Answer: 14 gallons

Step-by-step explanation:

Let's call the total gallons Abdul's tank can hold x.

Then, based on the information given in the problem, you can write the following expression:

[tex]\frac{1}{5}x+7=\frac{7}{10}x[/tex]

Therefore, when you solve for x, you obtain the following result:

[tex]\frac{1}{5}x+7=\frac{7}{10}x\\\\\frac{1}{5}x-\frac{7}{10}x=-7\\\\-\frac{1}{2}x=-7\\\\-x=(-7)(2)\\x=14[/tex]

Abdul's tank can hold 14 gallons of gas. This is determined by establishing that 7 gallons brought the tank level from 1/5 to 7/10 full and calculating that 7 gallons is equivalent to half the tank's total capacity.

When solving for how many gallons Abdul's tank can hold, we need to create an equation based on what we know from the problem.

Originally, the gas tank is 1/5 full. After adding 7 gallons of gas, it is 7/10 full. The difference between 7/10 and 1/5 (which is the same as 2/10) gives us the amount of gas that was added to reach 7/10 full from 1/5 full. Therefore, 7/10 - 2/10 equals 5/10 or 1/2. This means the 7 gallons added filled up half of the tank's capacity.

If 7 gallons represent 1/2 of the tank's capacity, then the full capacity (C) can be found by doubling the 7 gallons:

Therefore, Abdul's tank can hold 14 gallons.