Graph the hyperbola with equation (x+1)^2/9-(y-4)^2/25= 1

Answers

Answer 1

Answer:

Step-by-step explanation:

Hope it helps <3

Graph The Hyperbola With Equation (x+1)^2/9-(y-4)^2/25= 1

Related Questions

Paul developed a roll of film containing 36 pictures. If he made 2 prints each of half of the pictures and 1 print of each of the rest, how many prints did he make in all?

Answers

Answer:

54

Step-by-step explanation:

Total pictures in the roll = 36

half of the roll = 1/2 of the total pictures in the roll = 1/2 * 36 = 18

Given Paul made 2 prints of each of the half pictures

no. of prints made of half of the pictures = 18*2 = 36

No. of prints left after the half of the roll is printed for two prints= 36-18 = 18

No. of prints made of rest of the pictures 1

Therefore , no of prints made of rest half of pictures = 18*1 = 18

Total prints made = 36 + 18 = 54.

Thus, Paul made 54 prints in all.

Which of the following is an equivalent form of the compound inequality -44 > -2x - 82-8?
0-2x - 8 >-44 and -2x - 82-8
O-2x > -44 and -8-8
0-2x - 8<-44 and -2x -85-8
0-2x -8<-44 and -2x - 82-8


I NEED HELP ASAP

Answers

Answer:

  (d)  -2x -8 < -44  and -2x -8 ≥ -8

Step-by-step explanation:

A compound inequality is a mathematical sentence that combines two simple inequalities. A solution will satisfy both inequalities. That is, it represents an "and" (intersection) condition for the solution sets.

Equivalent pair

An inequality of the form ...

  a > b ≥ c

can be written as a pair of inequalities by considering what is on either side of each of the relation symbols:

left symbol: a > bright symbol: b ≥ c

Application

Given: -44 > -2x -8 ≥ -8

We can decompose the given inequality into the system ...

-44 > -2x -8 . . . . . . . . left symbol-2x -8 ≥ -8 . . . . . . . . . right symbol

When we compare these to the offered answer choices, we see that we need to rewrite the first inequality so the constant is on the right:

  -2x -8 < -44

Then the equivalent form of the given inequality is ...

  -2x -8 < -44  and  -2x -8 ≥ -8

__

Additional comment

The transitive property of inequality means that ...

  a > b ≥ c

implies that a > c.

You will notice that our given inequality, written in this way, becomes ...

  -44 > -8 . . . . . . not true

This means the inequality has no solution. (The solution set is the empty set.)

If a rabbit can move 1 5/19 miles every hour, then how many hours would it take a rabbit to go 72 miles?

Answers

Answer:

57 hours

Step-by-step explanation:

72 ÷ (1 + (5 ÷ 19))-57

57 hours Just divide them bois

A company makes concrete bricks shaped like rectangular prisms. Each brick is 10 inches long, 6 inches wide, and 4 inches tall. If they used 13,200in3 of concrete, how many bricks did they make?

Answers

Answer:

The company used 55 concrete bricks.

Step-by-step explanation:

We should first find the volume of one of the rectangular bricks.

10×6×4=240in³.

Now, let's divide 13,200in³ by 240in³.

13,200÷240=55

Hence, the company used 55 concrete bricks.

Hope this helps! (It's probably too complicated, I'm very sorry ;-;)

It’s the company used 55










Thanks :)

Please Help Me What are the roots of the equation? x2+2x−24=0 Enter your answers in the boxes.

Answers

Answer:

x   = 4 , − 6

Step-by-step explanation:

Answer:

x=4,-6

Step-by-step explanation:

Add 24 to both sides.

x2+2x=24

Plug in 4

4^2+2(4)=24

Solve

16+8=24

24=24

Add 24 to both sides.

x^2+2x=24

Plug in -6

-6^2+2(-6)=24

Solve

36-12=24

24=24

A factory can work its employees no more than 5 days a week, and no less than 2 days per
week. Create an inequality to represent the range of days an employee can work. Solve the
inequality to determine the range in hours. Show all of your work and explain each of your
steps. Explain your answer.

Answers

Answer:

2≥d≤5

Step-by-step explanation:

Let d be days worked weekly.

You can't work more than 5, so 5 is the most you can work so d is less than or equal to 5

AND

You can't work less than 2 days, so 2 is the least you can work so d is greater than or equal to 2

Ms. White measured the number of the ounces of juice left behind by 3 students after breakfast. She plotted the data on the line plot shown below

Answers

Answer: The answer is 7 3/4 :)) <3 have a good day.

The amount of juice left by the three students is (31/4) ounces.

What is dot plot?

A dot plot, also called a dot chart, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete bins.

Given is that Ms. White measured the number of the ounces of juice left behind by 3 students after breakfast.

The total juice left by 3 students is equivalent to -

{x] = 2 x {2[tex]\frac{1}{4}[/tex]} + 3[tex]\frac{1}{4}[/tex]

{x} = 2 x 9/4 + 13/4

{x} = 18/4 + 13/4

{x} = 31/4

Therefore, the amount of juice left by the three students is (31/4) ounces.

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Given the function f(x) = | -2x + 4 |. Complete the table.
-the table is in the picture provided help me complete it please (algebra 1)

Answers

Answer:

See below.

Step-by-step explanation:

To complete the table, start by copying the given function.

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

Now let's start with the first line of the table: x = 6.

You are finding the value of function f when x = 6.

Replace x with 6 and evaluate the expression.

f(6) = |-2(6) + 4|

f(6) = |-12 + 4|

f(6) = |-8|

f(6) = 8

Second line of table:

x = -1

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

f(-1) = |-2(-1) + 4|

f(-1) = |2 + 4|

f(-1) = |6|

f(-1) = 6

For the third and fourth lines, you are given a y value, or the value of function f, and you are looking for x. Now you use the given value to set the function equal to, and you solve for x.

Line 3: f(x) = 4

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

|-2x + 4| = 4

-2x + 4 = 4   or   -2x + 4 = -4

-2x = 0   or   -2x = -8

x = 0    or   x = 4

Line 4: f(x) = 14

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

|-2x + 4| = 14

-2x + 4 = 14   or   -2x + 4 = -14

-2x = 10   or   -2x = -18

x = -5    or   x = 9

The table looks like this:

x          f(x)

6         8

-1         6

0,4      4

-5, 9     14

[tex] \end{center} [/tex]

For the given function f(x) = | -2x + 4 |, the data is shown in the table below.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that the function is,  f(x) = | -2x + 4

Let's begin with the table's first line: x = 6, When x equals 6, you are determining the value of function f. Evaluate the equation after substituting 6 for x.

f(6) = |-2(6) + 4|

f(6) = |-12 + 4|

f(6) = |-8|

f(6) = 8

For the Second line of the table,

x = -1

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

f(-1) = |-2(-1) + 4|

f(-1) = |2 + 4|

f(-1) = |6|

f(-1) = 6

The third line of the table,

f(x) = 4

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

|-2x + 4| = 4

-2x + 4 = 4   or   -2x + 4 = -4

-2x = 0   or   -2x = -8

x = 0    or   x = 4

Line 4: f(x) = 14

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

|-2x + 4| = 14

-2x + 4 = 14   or   -2x + 4 = -14

-2x = 10   or   -2x = -18

x = -5    or   x = 9

Thus, for the given function f(x) = | -2x + 4 |, the data is shown in the table below.

Learn more about the function here,

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Which of the following is a numerical expression that involves addition? x + 8 7 – x 2 + 5 6x

Answers

Answer:

x+8

Step-by-step explanation:

This is because in this answer, there are two terms with an addition sign in between them.

In an arithmetic sequence a7 −2a4 = 1, a3 = 0. Find the common difference.

Answers

0.5

a7=0+4d
a4=0+d
(0+4d)-2d=1
2d=1
d=0.5

This is correct cause I did this question too

Answer:

1/2

Step-by-step explanation:

Given AP, where:

a7- 2a4= 1a3= 0

d=?

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

a7= a1+ 6d  a4= a1 +3da7- 2a4= a1+6d- 2a1 - 6d= - a1= 1 ⇒ a1= -1a3= a1+2d= - 1 +2d= 0 ⇒ 2d=1 ⇒ d= 1/2

what is 17/32 rounded to the nearest half)need help now) ?

Answers

Answer:

1/2.

Step-by-step explanation:

16/32 = 1/2 so the answer is 1/2.

Answer:

you cant bring that fraction any lower so 17/32 is 17/32

or if you need it in a decimal 0.53

Step-by-step explanation:

Expression
3x2
5a²b4
2x2 + 3x - 8
Type of Polynomial


Coefficient


Constant

Answers

Answer with explanation:

An algebraic expression having one term is known as a monomial.An algebraic expression having two terms is known as binomial.An algebraic expression having three terms is known as trinomial.Numerical coefficient - Number written before variable in each term.Constant - term with no variable ( only number).

Let's check the given expressions :

[tex]3x^2[/tex]

Type - Monomial ( having one term)

Coefficient of [tex]x^2[/tex]= 3

Constant =0

[tex]5a^2b^4[/tex]

Type - Monomial ( having one term)

Coefficient of [tex]a^2b^4[/tex]= 5

Constant =0

[tex]2x^2 + 3x - 8[/tex]

Type - trinomial ( having 3 terms)

Coefficient of [tex]x^2[/tex] = 2

Coefficient of [tex]x=3[/tex]

Constant = -8

Box 2:
length width • height = (4x-1). xox?
volume = 4x - x4
Degree of length:
- Degree of width:
Degree of height:
Degree of volume:

Answers

Answer:

1

1

3

5

Step-by-step explanation:

Answer:

1 1 3 5

Step-by-step explanation:

Find the remainder when f(x) = x3 − 14x2 + 7x − 10 is divided by x − 3. 184 164 −88 −122

Answers

Answer:

122

Step-by-step explanation:

For this case we must build a quotient that, when multiplied by the divisor, eliminates the terms of the divide until it reaches the remainder.

It must be fulfilled that:

Dividend = Quotient * Divisor + Remainder

we have that the remainder is 122.

have a good day

Answer:

The answer would be D) -122

Which value is equivalent to 7 multiplied by 3 multiplied by 2 whole over 7 multiplied by 5, the whole raised to the power of 2 multiplied by 7 to the power of 0 over 5 to the power of negative 3, whole to the power of 3 multiplied by 5 to the power of negative 9? 6 over 25 36 over 25 12 over 5 252 over 5

Answers

Answer:

i think it might be A

Step-by-step explanation:

Answer:

Its B trust and can you give me the brainlist

Step-by-step explanation:

Using the following parent function, please explain how each variable transforms the parent
function. Make sure to discuss all transformations using complete sentences.
f(x)= a(b(g(x)+c))+d

Answers

Answer:

a is a dilation in the y axis by a factor of a, b is dilation in the x axis by a factor of 1/b, + c is a translation c units to the left and d is a translation d units up.

Step-by-step explanation:


Which function is the result of vertically stretching ƒ(x) = x2 by a factor of 2 and translating it 4 units upward?
Question 20 options:

A)

y = –4x2 + 2

B)

y = 4x2 + 2

C)

y = 2x2 + 4

D)

y = 2x2 – 4

Answers

Answer:

The correct answer is the letter C.

Step-by-step explanation:

In order to stretch a function we need to multiply it by the factor we want to stretch, if we want to shrink the function we will have to divide it by the factor. On the other hand in order to translate it we need to sum the factor we want the function to shift. In this case we want to stretch the function by 2, therefore the new function must be 2*f(x), but we also want it to shift by 4 units so it has to be 2*f(x) + 4. Applying the given expression:

[tex]g(x) = 2*f(x) + 4\\g(x) = 2*x^2 + 4[/tex]

The correct answer is the letter C.

Answer:

C

Step-by-step explanation:

y= 2x^2 + 4

am I correct? if not what's the right answer?​

Answers

Answer:

2x+y -3 =0

Step-by-step explanation:

0 = Ax + By + C is the general form of a line

2x+4y +2 = 3y +5

Subtract 3y from each side

2x+4y-3y +2 =3y+5-2y

2x+y +2 = 5

Subtract 5 from each side

2x+y +2-5 = 5-5

2x+y -3 =0

If two similar cones have volumes of 320 cm³ and 1,080 cm³, find the scale factor.
A. 1/3
B. 2/3
C. 3/4
D. 7/8​

Answers

Answer:

B. 2/3

Step-by-step explanation:

The scale factor is B.2/3

How many numbers less than 1000 are there that use only the digits of 2088?

Answers

Answer:

  17 numbers with any number of digits

  12 numbers using as many digits as possible

Step-by-step explanation:

It depends on how many digits you are required to use. If you're not required to use more than one digit, then the possible numbers are ...

  0, 2, 8, 20, 28, 80, 82, 88,

  208, 280, 288, 802, 808, 820, 828, 880, 882

for a total of 17 numbers.

__

If you must use the maximum possible number of digits, then the 1-digit numbers and the 2-digit numbers containing 0 must be taken off the list, leaving ...

  028, 082, 088, (and all the above 3-digit numbers)

for a total of 12 numbers.

Which phrase best describes mortgage collateral?
A.money used as a down payment for the loan
B.assets obtained after securing the loan
C.the purchased property that secures the loan
D.closing costs covered by the buyer​

Answers

Answer:

C. the purchased property that secures the loan

Step-by-step explanation:

Mortgage collateral describe the use of a property e.g house to secure a loan. This collateral is always requested when a large amount of money is involved. The house could be sold if the borrower renege (fail to meet up with) on the due date as regards the agreement after collecting the loan.

Therefore, a mortgage collateral could be referred to as the purchased property that has been used to secure a loan by a borrower.

Therefore the purchased property that secures the loan is the correct answer.

What is Collateral ?

Collateral refers to an asset that a borrower offers as a guarantee for a loan, such as a mortgage.

When you obtain the loan, the lender puts a lien on the collateral. The lien stipulates that the lender can seize the collateral if you don’t repay the loan under the terms of the contract.

Once you repay the loan, the lender removes the lien and no longer has a claim to the collateral.

In the case of a mortgage, the collateral is the real property.

When determining whether to approve your loan, the lender will  ensure that the property ,the collateral ,is actually worth what you propose to pay for it with the loan.

If it isn’t, the lender can deny the mortgage because the asset isn’t worth the risk.

Therefore the purchased property that secures the loan is the correct answer.

To know more about Collateral

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The number of hot peppers in a salad is based on the number of servings, as shown in the table below. Salad Servings Hot peppers 2 4 4 8 8 ? 12 24 How many hot peppers are in an 8-serving salad?

Answers

the answer is 16

because 4,8,12,16,20,24

its closest to 24

Answer:

16

Step-by-step explanation:

Select the expression that is equivalent to 3(2x + 5) − 4x. A. 2x + 15 B. x + 8 C. x + 15 D. 2x + 5

Answers

Answer:

A. 2x + 15

Step-by-step explanation:

3(2x + 5) - 4x =

= 6x + 15 - 4x

= 2x + 15

Answer: A. 2x + 15

Answer:

2x +15

Step-by-step explanation:

3(2x + 5) − 4x

Distribute

6x + 15 -4x

Combine like terms

2x +15

Find the volume of a pyramid with a square base, where the side length of the base is
12.8 in and the height of the pyramid is 20.4 in. Round your answer to the nearest.
tenth of a cubic inch.

Answers

Answer:

Volume = 1114.1 [tex]in^3[/tex]

Step-by-step explanation:

Recall that the formula for the volume of a pyramid is given by:

[tex]Volume=\frac{1}{3} \,B\,*\,H[/tex]

where B is the area of the pyramid's base (in our case a square of side 12,8 in), and H the pyramid's height (in our case 20.4 in).

Then the square base of the pyramid has an area given by: [tex](12.8\,\,in)^2=163.84\,\,in^2[/tex]

Finally,we can now write the volume of the pyramid as:

[tex]Volume=\frac{1}{3} \,B\,*\,H\\Volume=\frac{1}{3} \,(163.84)\,*\,20.4\,\,in^3\\Volume=1114.112\,\,in^3[/tex]

Rounding the answer to a tenth of a cubic inch, we get:

Volume = 1114.1 [tex]in^3[/tex]

Find the area of the shaded polygons:

Answers

Answer:

6.5 square units

Step-by-step explanation:

There are MANY ways to do this problem, most of them involving breaking it into 3 or four shapes.  But this one is easier if you do most of it by taking out the squares and half squares.  

Squares - 3

Half squares - 4 (totals 2 squares)

Triangle - 1 - 1/2bh = 1/2x1x3 = 1.5

TOTAL = 3+2+1.5=6.5

Answer:

6 sq. un

Step-by-step explanation:

Tasha used the pattern in the table to find the value of 4 Superscript negative 4. Powers of 4 Value 4 squared 16 4 Superscript 1 4 4 Superscript 0 1 4 Superscript negative 1 One-fourth 4 Superscript negative 2 StartFraction 1 Over 16 EndFraction She used these steps. Step 1 Find a pattern in the table. The pattern is to divide the previous value by 4 when the exponent decreases by 1. Step 2 Find the value of 4 Superscript negative 3. 4 Superscript negative 3 = StartFraction 1 Over 16 EndFraction divided by 4 = StartFraction 1 Over 16 EndFraction times one-fourth = StartFraction 1 Over 64 EndFraction Step 3 Find the value of 4 Superscript negative 4. 4 Superscript negative 4 = StartFraction 1 Over 64 EndFraction divided by 4 = StartFraction 1 Over 64 EndFraction times one-fourth = StartFraction 1 Over 256 EndFraction Step 4 Rewrite the value for 4 Superscript negative 4. StartFraction 1 Over 256 EndFraction = negative StartFraction 1 Over 4 Superscript negative 4 EndFraction In which step did Tasha make the first error? Step 1 Step 2 Step 3 Step 4

Answers

Answer:

Step 4

Step-by-step explanation:

The table is given below

[tex]\left|\begin{array}{c|c}$Powers of 4 &$Value\\---&---\\4^2&16\\4^1&4\\4^0&1\\4^{-1}&\dfrac14\\4^{-2}&\dfrac{1}{16}\end{array}\right|[/tex]

Tasha wants to find the value of [tex]4^{-4}[/tex].

Her steps are:

Step 1: Find a pattern in the table.

The pattern is to divide the previous value by 4 when the exponent decreases by 1.

Step 2: Find the value of [tex]4^{-3}[/tex].

[tex]4^{-3}=\dfrac{1}{16} \div 4= \dfrac{1}{16} \times \dfrac{1}{4}= \dfrac{1}{64}[/tex]

Step 3: Find the value of  [tex]4^{-4}[/tex].

 [tex]4^{-4}= \dfrac{1}{64} \div 4 = \dfrac{1}{64} \times \dfrac{1}{4}= \dfrac{1}{256}[/tex]  

Step 4: Rewrite the value for  [tex]4^{-4}[/tex].

[tex]\dfrac{1}{256} = -\dfrac{1}{4^{-4}}[/tex]

Tasha made her first error in Step 4. The correct step is:

[tex]\dfrac{1}{256} = \dfrac{1}{4^{4}}[/tex]

Answer:

Step-by-step explanation:

First error step 4

PLLZZZZZZZ HELP I WILLL GIVE BRAINLIEST TO THE FIRST ONE TO ANSWER

Answers

Answer:

positive

Step-by-step explanation:

What is 131x682 can anyone tell me the step of doing it I don’t know how to

Answers

Answer:

91232

Step-by-step explanation:

Please help :) is the relationship linear, if so model the data with and equation.

Answers

Answer:

pretty sure it's A

Step-by-step explanation:

The problems don't add up so I'd say it's linear (you probably shouldn't take my advice I'm as bad at math as you are-)

Answer:

C. y + 4 = -1/2 (x - 1)

Step-by-step explanation:

The x values go up by 6 units each step, 1, 7, 13, 19.

Start with 1 and add 6 to get 7, then add 6 to get 13, then add 6 to get 19.

For each corresponding step in x, y becomes 3 less.

Start with -4, then subtract 3 to get -7, subtract 3 to get -10, subtract 3 to get -13.

For every change of 6 in x, you get a change of -3 in y. This means a linear relationship.

To find the equation, we can use any two of the given points and the point-slope equation of a line.

y - y1 = m(x - x1)

m = slope = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line, and m = slope.

Let's use the points (x1, y1) = (1, -4) and (x2, y2) = (7, -7)

y - y1 = (y2 - y1)/(x2 - x1) * (x - x1)

y - (-4) = (-7 - (-4))/(7 - 1) * (x - 1)

y + 4 = (-7 + 4)/(6) * (x - 1)

y + 4 = (-3/6)(x - 1)

y + 4 = -1/2 (x - 1)

On a coordinate plane, a quadrilateral has points W prime (negative 4, 1), X prime (negative 2, 2), Y prime (0, negative 3), and Z prime (negative 4, negative 4). The image of a figure is shown. What are the coordinates of X in the pre-image of the figure if the rule that created the image was T–5.2, 1.4(x, y)? X =

Answers

Answer:

(3.2, 0.6)

Step-by-step explanation:

[tex]T_{-5.2, 1.4} [/tex] means a translation of (x, y) → (x - 5.2, y + 1.4)

Suppose X has coordinates (a, b), after the translation is applied, X' has coordinates (a - 5.2, b + 1.4). X' is located at (-2, 2), therefore:

a - 5.2 = -2

a = -2 + 5.2

a = 3.2

b + 1.4 = 2

b = 2 - 1.4

b = 0.6

Answer:

(3.2, 0.6)

Step-by-step explanation:

edg 2021

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Simplify 2a^2b^3(4a^2+3ab^2-ab)=? A. 8a^4b^5+3a^3b^5-2a^3b^4 B. 8a^4b^3+6a^3b^5-2a^3b^4C. 8a^4b^5+3a^3b^5-2a^3-ab= Simplify 12-(-8)x4=? A. 44 B. -20 C. 16 D. 80 One day when Terry went to school the temperature outside was -15 degrees Fahrenheit. In Terry's classroom the temperature was 68 degrees Fahrenheit. How many more degrees was it inside the building than outside? A. +53 degrees B. +83 degrees C. -53 degrees D. -83 degrees If Juan purchased thee 24-ounce cans of motor oil for 410.80, how much did he pay per ounce? A. $3.60 B. $.45 C. $2.59 D. $.15 Simplify (x^2+16)(x^2-16)=? A.x^4-32 B. x^4+256 x^4-256 D. x^4+32 If the value of b is 7, then what is the value of the expression -3b^2+25=? A. 122 B .17 C. 172 D. -122 what are all the rays that come from the sun called List all? (Displaying a Sentence with Its Words Reversed) Write an application that inputs a line of text, tokenizes the line with String method split and outputs the tokens in reverse order. Use space characters as delimiters. Which type of transformation is shown? The transformation is a what action made Louis XVI Such an unpopular ruler ?( he entered France into an unpopular war) (he married Australian princess)(he did not support government reform) (he refused to let the third estate own land) A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 4 feet. The area of the logo must be at most 14 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle. Use b for the base length of the triangular logo. Miss Christina deposits her monthly salary $9000 in a bank which pays 7% interest compounded half yearly.How much will she get after 10 years? A.)18,122 B.)18,014 C.)17,908 D.)17,704 Between July 1, 2000 and July 1, 2007, the estimated population of a city declined from 3487 to 2653. What was the percent decrease to the nearest tenth? Re-read lines 482-490. Whatdo you predict Rainsford willdo next? Someone please help please Please can answer my question . When you flip a biased coin the probability of getting a tail is 0.3. How many times would you expect to get tails if you flip the coin 160 times? Please answer this question Which statement best illustrates A claim of fact? Which title is most appropriate for this table? ANSWERS: Uses of Functional Groups Involving Oxygen Natural Sources of Functional Groups Involving Oxygen Uses of Functional Groups Involving Halides and Amines Natural Sources of Functional Groups Involving Halides and Amines An arhaeologist, exploring the pyramidsof Africa, discovers a mummy. He findsthat it contains 53 % of original amountof C-14. Find age of the mummy. Which one is correct? No chores or obligations faced us. We actually had time to enjoy the holidayO A. No chores or obligations faced us therefore we actually had time to enjoy the holidayOB. No chores or obligations faced us, therefore we actually had time to enjoy the holidayOC. No chores or obligations faced us, therefore, we actually had time to enjoy the holiday. A relay with n laps was run by 4 people. The 1st runner ran half the laps. The 2nd runner ran half the number of laps the 1st runner ran. The 3rd runner ran half the number of laps the 2nd runner ran. The remaining laps were completed by the 4th runner. How many laps did the 4th runner complete? Explain with examples following characteristics of chemical reactions: a. Change of colour b. Evolution of gas c. Change of smell d. Change of state the focal length F of a lens made by combining two lenses of focal length U and V is given I/F=I/U+I/VA.make V the subject of the formula.B.find V when F=6,U=10 Find the slope through each pair of two points. Report answers in simplest form.(0,0) and (0.5,0.25)m =