[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
If it passes through x, then let's find x when y = 0
[tex]\qquad \tt \dashrightarrow \:0 = {x}^{2} - x - 6[/tex]
[tex]\qquad \tt \dashrightarrow \: {x}^{2} - 3x + 2x - 6 = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:x(x - 3) + 2(x - 3) = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:(x - 3) (x + 2) = 0[/tex]
So, required values of x are 3 and -2
Now, let's differentiate the equation to get slope slope for tangent ~
[tex]\qquad \tt \dashrightarrow \: m = \dfrac{d}{dx} ( {x}^{2} - x - 6)[/tex]
[tex]\qquad \tt \dashrightarrow \: m = 2 x - 1[/tex]
Now, plug in the values of x to find slopes of tangents
[tex]\qquad \tt \dashrightarrow \: m _1 = (2 \times 3) - 1[/tex]
[tex]\qquad \tt \dashrightarrow \: m_1 = 6 - 1[/tex]
[tex]\qquad \tt \dashrightarrow \: m _1 = 5[/tex]
and
[tex]\qquad \tt \dashrightarrow \:m_2 = (2 \times - 2) - 1[/tex]
[tex]\qquad \tt \dashrightarrow \:m_2 = - 4- 1[/tex]
[tex]\qquad \tt \dashrightarrow \:m_2 = - 5[/tex]
We know, tangent are normal are perpendicular. so let's find out slopes of normals m1' and m2'
[tex]\qquad \tt \dashrightarrow \:m _1\cdot m_1 ' = - 1[/tex]
[tex]\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{m_1}[/tex]
[tex]\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{ 5}[/tex]
and
[tex]\qquad \tt \dashrightarrow \:m _2\cdot m_2 ' = - 1[/tex]
[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{m_2}[/tex]
[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{ -5}[/tex]
[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{1}{ 5}[/tex]
Now, write the equations of normals using point slope form :
Normal 1 : passing through (3 , 0), and slope = -1/5
[tex]\qquad \tt \dashrightarrow \:y - 0 = - \dfrac{1}{5} (x - 3)[/tex]
[tex]\qquad \tt \dashrightarrow \:5y = - (x - 3)[/tex]
[tex]\qquad \tt \dashrightarrow \:5y = - x + 3[/tex]
[tex]\qquad \tt \dashrightarrow \:x + 5y - 3 = 0[/tex]
and
Normal 2 : passing through (-2 , 0), and slope = 1/5
[tex]\qquad \tt \dashrightarrow \:y - 0 = \dfrac{1}{5} (x - ( - 2))[/tex]
[tex]\qquad \tt \dashrightarrow \:5y = x + 2[/tex]
[tex]\qquad \tt \dashrightarrow \ x - 5y + 2 = 0[/tex]
That's all for Aunty ~ hope it helps !
The percentage of executives in a certain industry receiving cash signing bonuses is increasing. the percentage is given by the function b(t)= 4.891(1.331)^t. where r is the number of years since 1996. find the percentage of executives receiving signing bonuses in 2000 and in 2001.
The function b(t)= 4.891(1.331)^t is an exponential function
The percentage of executives in 2000 is 15.35The percentage of executives in 2001 is 20.43The percentage of executives in 2000The function is given as:
b(t)= 4.891(1.331)^t.
2000 is 4 years from 1996.
This means that t = 4
So, we have:
b(4)= 4.891(1.331)^4
Evaluate
b(4)= 15.35
So, the percentage of executives in 2000 is 15.35
The percentage of executives in 20012001 is 5 years from 1996.
This means that t = 5
So, we have:
b(5)= 4.891(1.331)^5
Evaluate
b(5)= 20.43
Hence, the percentage of executives in 2001 is 20.43
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Last year a company spent a total of £2400 on advertising. This year they spent £2796 What was the percentage increase in their spending on advertising?
Answer:
16.5%
Step-by-step explanation:
[tex] \frac{396}{2400 } \times 100[/tex]The percentage increase in their spending on advertising will be 16.5%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Last year an organization spent a sum of £2400 on publicizing. This year they burned through £2796.
Then the percentage increase in their spending on advertising will be given as,
P = [(2796 - 2400) / (2400)] x 100
P = (396 / 2400) x 100
P = 0.165 x 100
P = 16.5%
The percentage increase in their spending on advertising will be 16.5%.
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Each week Samantha can pay as much $15 for her school at lunch. Write an inequality showing how much Samantha spends at lunch. Please help me!! I need an answer fast!
Answer:
To represent all the possible amounts that Samantha can pay, you will write that x is less than or equal to 15.
This means that any amount up to and including 15 is a possibility.
Step-by-step explanation:
Answer:
x≤15
Step-by-step explanation:
x means how much samantha is able to spend on lunch each week. she can spend only 15 dollars or less. -Crispin
are my answers correct?
1. 17× = 170 = 10
2. x = 23 = 2
___
11
3. 3X = 21 = 7
4. X = 17 = 3.4
____
5
1. x = 10 is correct
2. not sure
3. x = 7 is correct
4. not sure
3. Make Sense and Persevere The circumference of the inner
circle is 44 feet. The distance between the inner circle and the outer
circle is 3 feet. By how many feet is the circumference of the outer
22
circle greater than the circumference of the inner circle? Use ?
for . Round to the nearest hundredth of a foot.
Answer:
9.42 feet more
Step-by-step explanation:
the outer circle is 53.42 feet
hope this helps :)
What is the purpose of the QUADRATIC FORMULA?
N
A Determine the distance between two points
B Determine the zeros of a quadratic function
Calculate the axis of symmetry of a quadratic function
Calculate the y-coordinate of the vertex of a parabola
You roll a number cube 120 times. How many times can you expect the number cube to land on a six?
Answer:
10 or 6
Step-by-step explanation:
pls tell me if im wrong
The principal would like to assemble a committee of 8 students from the 12-member student council. How many different committees can be chosen?
Answer: 4 committees
Hope this helps! :)
I need brainliest please.
find the volume
of a rectangle
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Volume of Rectangular prism ~
[tex]\qquad \sf \dashrightarrow \:length \times width \times height[/tex]
[tex]\qquad \sf \dashrightarrow \:20 \frac{1}{2} \times 10 \frac{1}{2} \times 12 [/tex]
[tex]\qquad \sf \dashrightarrow \:\frac{41}{2} \times \frac{21}{2} \times 12 [/tex]
[tex]\qquad \sf \dashrightarrow \:{41}{} \times {21}{} \times3 [/tex]
[tex]\qquad \sf \dashrightarrow \:2583 \: \: {m}^{3} [/tex]
Select the expression that is equal to 3(7+x)
13x
21+4x
21+3x
10+3x
10+4x
I don't know
Answer:
21 + 3x
Step-by-step explanation:
3(7 + x) ← multiply each term in the parenthesis by 3
= 21 + 3x
PLEASE HELP!!!!! I need to pass algebra
Answer:
C
Step-by-step explanation:
find the area of the circle.
diameter=8 inches
Answer:
Area = 32 π in^2
Step-by-step explanation:
Area of the Circle : Area = 2 *π * r^2
diameter = 2 *radius
8 inches = 2 * radius
radius = 8 in/2 = 4 in
radius = 4 in
Area = 2 *π * r^2
Area = 2 *π * (4 in)^2
Area = 2 *π * 16 in^2
Area = 32 π in^2
Answer:
If you're using the exact number for pie then the answer is approximately 50.27. If you're using 3.14 for pie then the answer is 50.24.
I need help with this, question is in image.
Answer:
-75 ft
Step-by-step explanation:
Hope this helps! Have a great day!!
Answer:
-75
Step-by-step explanation:
hope this helped.
No explanation really is there to it.
Have a great day! :)
Solve the following ⇒ 8x-5=5(x-4)
Answer:
x = -5
Step-by-step explanation:
Given:
[tex]\displaystyle \large{8x-5=5(x-4)}[/tex]
Distribute 5(x-4):
[tex]\displaystyle \large{8x-5=5x-20}[/tex]
Add both sides by 5:
[tex]\displaystyle \large{8x-5+5=5x-20+5}\\\displaystyle \large{8x=5x-15}[/tex]
Subtract both sides by 5x:
[tex]\displaystyle \large{8x-5x=5x-15-5x}\\\displaystyle \large{3x=-15}[/tex]
Divide both sides by 3:
[tex]\displaystyle \large{\dfrac{3x}{3}=\dfrac{-15}{3}}\\\displaystyle \large{x=-5}[/tex]
Therefore, your solution is x = -5
Answer:
x = -5
Step-by-step explanation:
8x - 5 = 5(x - 4)Distributing the value in the RHS
5(x - 4)5(x) - 5(4)5x - 20Equating to the RHS
8x - 5 = 5x - 20Bring x terms to the left and numbers to the right.
8x - 5x = -20 + 53x = -15Divide both sides by 3.
3x/3 = -15/3x = -5Jill went shopping from 3:45 pm to 5:00 om for how long did she shop
Find the area of the parallelogram. 13 cm 20 cm Area cm?
Answer:
260 cm²
Step-by-step explanation:
A=b×h
A=b×h=20·13=260
Step-by-step explanation:
solution
b=20 cm
h =13 cm
Area (a) = b ×h
a=20cm ×13 cm
so , a =260 cm square
Find the value if x. PLS HELP ASAP
Answer: 90°
Step-by-step explanation:
(x°+90°)=180°(being the sum of angles of the triangle)
or, x°= 180°-90°
or x°= 90°
Does the graph shows a proportional relationship
Answer:
no
Step-by-step explanation:
a proportional relationship when graphed always is a straight line that goes through the origin (0,0)
The graph shown, shows a straight line but the line doesn't go through the origin therefore the graph does not show a proportional relationship.
Note that the origin is where the x and y axis cross , or the bottom right corner of the graph in this case
Ellie just accepted a job at a new company where she will make an annual salary of $62000. Ellie was told that for each year she stays with the company, she will be given a salary raise of $4000. How much would Ellie make as a salary after 6 years working for the company? What would be her salary after t years? Salary after 6 years: Salary after t years: t
Answer:
The answer is 86000
Step-by-step explanation:
This is because if she gets 4000 each yhear then that 4000 times 6 which is 24000. then you add that to the 62000 she initially got and you get youre answer, 86000.
work out size of angle x
Answer:
x = 105 degrees.
Step-by-step explanation:
The small polygon is a regular hexagon so each internal angle = 120 degrees while the large polygon is a regular octagon with internal angle =
135 degrees.
So angle x = 360 - ( 120 + 135)
= 360 - 255
= 105 degrees.
Note we use the fomula T = 180( n - 2) to find total internal angles in an n sided polygon. So for hexagon T = 180(6-2) = 180*4 = 720 so each internal angle in a regular hexagon = 720/6 = 120 degrees.
what is 2 multiplied 34 times plus 72 divided 3
Answer:
92
Step-by-step explanation:
2 × 34 + 72 ÷ 3
(2 × 34) + (72 ÷ 3)
68 + 24 = 92
I hope this helps!
Carmen's car used 11 gallons of gas to travel 462 miles. How many miles per gallon did his car travel? Show the steps for finding the unit rate
Answer:
I'm pretty sure it's 473 if that isn't correct Then what you do Is Divide it or Mutiply it if you still don't get your answer Be sure to Ask someone
Answer:
42miles per gallon
Step-by-step explanation:
since total gallons of fuel used is 11 gallons to travel 462miles,
per gallon will be 462/11 =42miles per gallon
Max went to a shopping mall with $35 in his wallet. He spent two fifths of the money he had in his wallet at the bookstore. How much money, in dollars, did he have left?
$21
$26
$10
$13
Answer:
$21
Step-by-step explanation:
1) Find the amount spent.
"Two fifths" = 2/5
So, he spent 2/5 of 35.
= 2 x 35 / 5
= 70 / 5
= 14
2) Subtract 14 from 35, since 35 is the total amount of money he had.
= 35 - 14
= 21
Answer:
$21
Step-by-step explanation:
Given that:
Max went to a shopping mall with $35 in his wallet.
He spent two fifths of the money he had in his wallet at the bookstore.
To Find:
How much money, in dollars, did he have left?
Solution:
Let the left money that max have = x
Base on the given:
$35-(2/5)×$35=x
⇒ $35-($2×7)=x
⇒ $35-$14=x
⇒ x=$21
Hence, max has $21 left.
Kavinsky
find the area please and thank you
Answer:
60 cm²
Step-by-step explanation:
area of trapezium = 1/2(a + b) × h
= 1/2(6+14) × 6
= 20/2 × 6 = 10 × 6
= 60 cm²
Santa seated his guests so that X number of people sat at each of Y number of tables. Mrs. Claus placed Y number of people at each table, but she had X number of tables. Compare the number of guests Santa and Mrs. Claus were able to seat.
Answer:
they are the same
Step-by-step explanation:
The number of guests seated were, in each case, ...
(guests per table) × (number of tables)
__
For Santa, this product is ...
X × Y
For Mrs. Claus, this product is ...
Y × X
The commutative property of multiplication tells you that ...
XY = YX
The numbers of guests were the same.
If 100 grams of water evaporated into a gas, how much mass will the gas have?
Answer: 100 grams
Step-by-step explanation:
Mass remains constant. So 100 grams of water will be 100 grams of water vapor
I NEED THIS ASAP WORK IS ABOUT TO BE DUE IN A COUPLE OF HOURS
Answer:
D
Step-by-step explanation:
The interquartile range is the difference between the last dot on the box and the first dot on the box.
20 - 40:
150 - 110 = 40
50 - 70:
125 - 95 = 30
Find the equation of line a and line b.
HELP PLEASE
Answer:
Blue-y=1/2-1
Red-x=-3
Step-by-step explanation:
The area of the Atlantic Ocean is 2.9638 x 107 mi? . The area of the
Pacific Ocean is 6.0061 x 107 mi? How much greater is the area of the
Pacific Ocean than the area of the Atlantic Ocean?
A 3.0423 x 10° mi?
B 3.0423 x 104 mi?
C 3.0423 x 106 mi?
D 3.0423 x 10? mi?
Answer:
Answer not in the listed options....did you enter all of the info correctly ?
Step-by-step explanation:
6.0061 / 2.9638 = 2.026 times bigger
A factor delivered 284 boxes of books to stores. There are 20 books in each box. How many books did the factor deliver?
Answer:
284*20
Step-by-step explanation:
since there are 284 boxes of each 20 books, 1box = 20 books then 284 boxes = (284*20) books
If factor delivered 284 boxes of books to stores and 20 books in each box then the total number of books deliver by factor are 5680.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a factor delivered 284 boxes of books to stores.
There are 20 books in each box.
We have to find the number of books the factor deliver
To find this we have to multiply the number of boxes with the number of books in a box
Number of books deliver = 284×20
Two hundred eighty four times of twenty
Number of books deliver =5680
Hence, if factor delivered 284 boxes of books to stores and 20 books in each box then the total number of books deliver by factor are 5680.
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