Answer:
[tex]\fbox{Gradient of curve = -6}[/tex]
Step by step explanation:
Given:
Equation of curve ↦ xy = 6
Point ↦(1,6)
To find:
The gradient of curve = ?
Solution:
[tex]Using \: the \: equation, \\ xy = 6 \\ [/tex]
Taking log both the side,
[tex]log(xy) = log(6) \\ log(x) + log(y) = log(6) \\ Taking \: derivative \: both \: the \: side \\ \frac{1}{x} + \frac{1}{y} \cdot\frac{dy}{dx} = \: 0 \\ (Derivative \: of \: any \: constant =0) \\ \frac{1}{y} \cdot\frac{dy}{dx} = - \frac{1}{x} \\ \frac{dy}{dx} = - \frac{y}{x} \\ To \: find \: gradient \: at \: point (1,6) \\ \frac{dy}{dx} \mid_{(1,6)} = \frac{ - 6}{1} \\ \frac{dy}{dx} \mid_{(1,6)} = - 6 \\ \fbox{Gradient of curve = -6}[/tex]
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use the terms 8 , 3x , 3/2 and 4x to complete the expression below so that’s is equivalent to 9x - 12
Answer:
A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).
Hello people ~
factorise ↷
x^2 + 6x + 8
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer}}[/tex]
Let's solve ~ ☂
⧠ Here, I'm using middle term split method :
[tex] \qquad\rightarrowtail \sf {x}^{2} + 6x + 8[/tex]
[tex] \qquad\rightarrowtail \sf {x}^{2} + 4x + 2x+ 8[/tex]
[tex] \qquad\rightarrowtail \sf {x(x}^{} + 4) + 2(x+ 4)[/tex]
[tex] \qquad\rightarrowtail \sf (x + 2)(x+ 4)[/tex]
[tex]\\ \rm\rightarrowtail x^2+6x+8[/tex]
[tex]\\ \rm\rightarrowtail x^2+4x+2x+8[/tex]
[tex]\\ \rm\rightarrowtail x(x+4)+2(x+4)[/tex]
[tex]\\ \rm\rightarrowtail (x+2)(x+4)[/tex]
Done!
Terrence measured an Italian restaurant and made a scale drawing. The scale of the drawing was 7 centimeters = 2 meters. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Answer:
200/7
Step-by-step explanation:
(2 meters)/(7 centimeters) or (2m/7cm)
1 meter = 100 cm
(2m/7cm)*(100cm/1m) = 200/7 (or 28.57) scale factor.
What is the area of this figure?
Use 3.14 for TT.
Please help
Answer:
406.08
Step-by-step explanation:
First FInd the area of the rectangle : which is short side * long side
-> 15*12=180m
Then find the area of the half circle, the formula of the area of a circle is [tex]\pi r^2[/tex]
here it's half a circle so it's [tex]\frac{\pi r^2}{2}[/tex] where r is 12
-> [tex]3.14\cdot \frac{\left(12\right)^2}{2}=226.08 m[/tex]
Finally just add the area of the rectangle with the area of the half circle
-> [tex]180+226.08=406.08 m[/tex]
what is AxBxD and A=130 B=300 and D=? and when do the multiplication do the answer x 900 and than we are done :)
Do problems #4-6. Your answer choices are in a table below. Type your answer numbers the blank to move on! No spaces, no commas. Put it all together. *
I need help with 5
[tex]\frac{1}{2a}[/tex]
Step-by-step explanation:Simplify or expand
[tex](2a)^{-1}[/tex]
Simplify using negative exponent rule [tex]a^{-n}=\frac{1}{a^n}[/tex]
[tex]\frac{1}{2a}[/tex]
I hope this helps you
:)
Which of the following statements is FALSE?
AO = 7.8 cm
c1 = 40°
BO = 7.8 cm
a2 = 40°
Parallelogram is a quadrilateral with equal diagonals. The statement BO = 7.8 cm is the only false statement
Properties of a parallelogramFrom the given diagram, the opposite sides and angle of the figure are the same but the diagonals are not equal. This shows that:
m<B = m<D
m<A = m<C
Since the diagonals are not equal that is BD is not equal to AC, hence:
OB ≠ OC
Hence the statement BO = 7.8 cm is the only false statement
Learn more on parallelogram here: https://brainly.com/question/970600
Answer:BO = 7.8 cm
Step-by-step explanation: just did the quiz
The question is in the image. I really need help, please.
Answer:
(b) 65/27
Step-by-step explanation:
Here, we notice the index for the summation runs from 0 to 3, so there are a total of 4 terms.
The sum represented by the summation symbol is ...
5(-2/3)^0 +5(-2/3)^1 +5(-2/3)^2 +5(-2/3)^3
= 5(1 -2/3 +4/9 -8/27)
= 5/27(27 -18 +12 -8)
= 5(13/27) = 65/27
__
There is a formula for the sum of a geometric series:
Sn = a1×(1 -r^n)/(1 -r)
Here, the first term is a1 = 5(-2/3)^0 = 5. The common ratio is the base of the exponential, r = -2/3. So, the sum of n=4 terms is ...
S4 = 5×(1 -(-2/3)^4)/(1 -(-2/3)) = 5×(1 -16/81)/(5/3) = 65/27
Benjamin has 3 dimes and 4 nickels. What percent of a dollar does he have?
Answer:
50%
Step-by-step explanation:
Hope this helped
Maybe mark brainiest
Dime = 10 cents
Nickel = 5 cents
Total value of coins = 3(10) + 4(5) = 30 + 20 = 50
To find the percent, first create a fraction. The fraction will be the amount of money that Benjamin has over the total (one dollar).
50 / 100 = 5 / 10 = 0.5
0.5 x 100 = 50
50%
Answer: 50% of a dollar
Hope this helps!
Factor completely.
x2 - 10x + 24
Answer:
[tex]\boxed{\sf{(x-4)(x-6)}}[/tex]
Step-by-step explanation:
In order to solve this problem, all you have to do is multiply their expressions by their factors.
To begin, you must group these expressions.
[tex]\sf{x^2-10x+24=\left(x^2-4x\right)+\left(-6x+24\right)}[/tex]
After that, you factor.
Solve.
[tex]\sf{x^2-4=x(x-4)}[/tex]
-6x+24=-6(x-4)
Then rewrite the problem down.
x(x-4)-6(x-4)
Factor by the common term.
(x-4)(x-6)
Therefore, the final answer is (x-4)(x-6).
I hope this helps you! Let me know if my answer is wrong or not.
Simplify the following if x = 3 & y = 4:
1. 2x + y =
2. 3x + 2y =
3. 3y + 2x =
4. 10x + 4y + 2x =
5. 6y + 5x =
6. 7x + 4y =
Use your knowledge about parentheses and substitution to solve the following:
q = 1; r = 2; s = 3; t = 4; x = 5; y = 6
7. 2(x+4) + 10 =
8. 3(4x) + 4 =
9. 10(xy) =
10. 2(x + y) =
11. 3(rs) + 4(x)
12. 2(q) + 2(x + t) =
13. 6(3t + 4s) =
14. 10(10x) + 10y =
15. x(xy) =
16. r(s)(t) =
17. (r)(s)(t)(x)(y) =
18. 6(2x + 3Y) =
Answer: (All below)
Step-by-step explanation:
1. 2x + y = 10
2(3) + 4) = 10
6 + 4 = 10
2. 3x + 2y =
3(3) = 2(4) =
9 + 8 = 17
3. 3y + 2x = 18
3(4) + 2(3) = 18
12 + 6 = 18
4. 10x + 4y + 2x = 52
10(3) + 4(4) + 2(3) = 52
30 + 16 +6 = 52
46 + 6 = 52
5. 6y + 5x =39
6(4) + 5(3) = 39
24 + 15 = 39
6. 7x + 4y = 37
7(3) + 4(4) = 37
21 + 16 = 37
7. 2(x+4) + 10 = 28
2( 5 + 4) + 10 = 28
2(9) + 10 = 28
18 + 10 = 28
8. 3(4x) + 4 = 64
3(4(5)) + 4 = 64
3(20) + 4 = 64
60 + 4 = 64
9. 10(xy) = 300
10(5(6)) = 300
10(30) = 300
10. 2(x + y) = 22
2(5 + 6) = 22
2(11) = 22
11. 3(rs) + 4(x)
3(2(3)) + 4(5) =
3(6) + 20 =
18 + 20 = 38
12. 2(q) + 2(x + t) = 20
2(1) + 2(5 + 4) = 20
2 + 2(9) = 20
2 + 18 = 20
13. 6(3t + 4s) = 84
6(3(1) + 4(3)) = 84
6(2 + 12) = 84
6(14) = 84
14. 10(10x) + 10y = 560
10(10(5)) + 10(6) = 560
10(50) + 60 = 560
500 + 60 = 560
15. x(xy) = 150
5(5(6)) = 150
5(30) = 150
16. r(s)(t) = 24
2(3(4)) = 24
2(12) = 24
17. (r)(s)(t)(x)(y) =720
(2)(3)(4)(5)(6)= 720
6(20)(6) = 720
120(6) = 720
18. 6(2x + 3Y) = 1080
6(2(5) + 3(6)) = 1080
6(10 + 18) = 1080
6(180) = 1080
please help me with this question , we are now just learning it .
Answer:
angle 1=angle 4 ( vertical opposite angle)
Find the median and mean of the data set below:
Answer:
27=mean. 30=Median
Step-by-step explanation:
trust me I know what I'm doing
Select the values that would satisfy the following inequality:
K ≤ 12.75
|12.75|
|-12.75|
13
|-15|
0
Answer:
If it is a conjunction that uses the word and, the solution must work in both inequalities and the solution is in the overlap region of the graph. If it is a disjunction that uses the word or, the solution must work in either one of the equations.
Step-by-step explanation:
f(x) = 4x -8;{-2, -1,0,1,2}
What is the range? Choose the correct answer below.
A. {-16,- 11,-8, -3,0)
B. {-16, -12,-8, -4,0}
C. {-17, -12,- 8, -4,1}
D. {-16, -11, -9,-3,0)
Answer:
B
Step-by-step explanation:
4(-2)-8 = -16, so not C
4(-1)-8 = -12, so not A or D
4(0)-8 = -8, so not D
4(1)-8 = -4, so not A or D
4(2)-8 = 0, so not D
If the cost of a dozen pencil is ₹ 159.48, what will be the cost of 24 such pencil?
Answer:
₹ 318.96.
Step-by-step explanation:
24/12 = 2 , so twice as much;
159.48 * 2 = 318.96
7. Find the volume of a rectangular prism if the height is 14 inches and the area of the base is 30 square inches. Type your answer without units.
Answer:
420
Step-by-step explanation:
V = whl is the volume of a rectangular prism. w*h is the area, so V is area times height.
This gives us: V = 30 * 14 = 420.
50
The graph shows a proportional relationship between the
number of kilometers traveled by a bicycle (y) and the number of
minutes (x).
45
40
35
30
Distance traveled (km)
What is the unit rate, expressed in kilometers per minute?
25
20
O 0.30 km/min
15
(40, 12)
O 0.33 km/min
03.10 km/min
->
5 10 15 20 25 30 35 40 45 50
Time (min)
3.33 km/min
1
2
3
4
5
6
7
8
Next
9
10
Given a graph with a line running through coordinates (0,0) and coordinates (40,12), the unit rate of the relationship between the number of kilometers traveled by a bicycle (y) and the number of minutes (x) is given by the slope of the line.
What will be the sales price of the car if it has a regular price of $16 000 and is on sale for 20% off? Determine the cost of the car including 13% tax.
Answer:
14,464
Step-by-step explanation:
16,000 - 20% = 12,800
12,800 + 13% = 14,464
I hoope this is correct. Have a wonderful day and dream a good dream of good people. :)
Help will give brainleiest
Answer:
40" by 50"
Step-by-step explanation:
From inspection of the diagram,
height of 2 squares of the quilt ≈ height of doll plus a little bit
⇒ height of 2 squares of the quilt ≈ 18 + 2 = 20 in
⇒ height of 1 square of the quilt ≈ 20 ÷ 2 = 10 in
As the height of a square = width of a square
⇒ width of 1 square of the quilt ≈ 10 in
Dimensions of the quilt
width = 4 squares = 4 × 10 = 40 in
height = 5 squares = 5 × 10 = 50 in
Ratios
We can also work out the width and height by using ratios.
The ratio of width to height of the quilt = 4 squares : 5 squares
If we multiply by 10, the ratio becomes 40 : 50
Final Solution
40" by 50"
Please help i am confused
Answer: 12.16
Step-by-step explanation:
A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.
Write an equation to model the height h, in feet, of the ball t seconds after it has been punted.
The football is caught at 5.5 feet above the ground. How long was the football in the air?
Answer:
1.451 seconds. Hurry.
Step-by-step explanation:
The position(height, h) of the foot ball will be given by the equation:
h = -32.2t^2 + 45t + 2.5
The term -32.2t^2 consists of the acceleration caused by gravity at Earth's surface ( -32 ft/sec^2) and the term +45t accounts for the initial velocity. The + is assigned since the ball is moving vertically from ground. The negative sign in -32t^2 is due to the acceleration being towards ground. The term 2.5 accounts for the fact that the initial height of the ball is 2.5 feet above ground.
We can either calculate or graph with this function to find the time the ball spends in the air:
Calculate:
h = -32.2t^2 + 45t + 2.5
We need a value of t that would cause h to be 5.5 feet, the level it was caught:
5.5 = -32.2t^2 + 45t + 2.5
-32.2t^2 + 45t + 2.5 = 5.5
-32.2t^2 + 45t -3.0 = 0
Solve for t using the quadratic formula. I get a value of 1.33 seconds.
Graph:
See the attached graph. It confirms the 1.33 second value
What is the length of a diagonal of rectangle EFGH?
Answer:
[tex]\sqrt{53}[/tex]
Step-by-step explanation:
First, we find out the length of EH, which is 7. And then, we find the length of GH, which is 3. If we square both the numbers and add them, we get 53. And then we square root that to get [tex]\sqrt{53}[/tex]
Hope this helps <:)
Don't forget to put brainliest!
Y= x + 6
y= -x+2
solve each system of equations by substitution
Answer:
x= -2
y=4
Step-by-step explanation:
Since we have an equation set equal to y, we can plug it in for either value of y.
I will be using y= x+6 in this case.
Plug in x+6 for the other equation, so instead of y=-x+2 it will now be that x+6 = -x+2
Now add x to both sides, and that will remove the x on the left side leaving us with 2x+6 = 2
Now, subtract 6 from both sides to get 2x isolated, and you will get 2x= -4
Divide both sides by 2 to get x= -2
Not plug x= -2 in back for the top (or bottom) equation and get that y=4
Hope this helps and isn't too complicated!
On Monday, Payton rode 7 miles on a bike. On Tuesday, she rode 23
miles. On Wednesday, she rode 3 times as much as she did Monday
and Tuesday combined. What equation could you use to find how
many miles Payton rode on Wednesday, r?
Answer:
483
Step-by-step explanation:
I really really pray and hope this helpss.
Answer:
X=3(7+23)
Step-by-step explanation:
!!!!!:!:!:!:!:!!:!’dmemdmsmsms
DI AKO KRINUSHBAK SANA KAYO DIN
Ben and Cam are scuba diving. Ben is 15.8 meters below the surface of the water. Cam is 4.2 meters below
Ben. Andrew is a further 16 meters.
Part 1 Write an expression That'll allow you to find Andrew's depth.
Part 2: What's Andrew's depth?
Answer:
27.6
Step-by-step explanation:
1) Say bens depth is x
Cam's depth is x + 4.2
Andrew's depth is x + 4.2 + 16 or x + 11.8
1) andrew's depth = x + 11.8, where x is 15.8.
Therefore, his depth is 27.6 meters.
Please help, I’ll mark your answer as brainliest.
Answer:
it'sssssss 2.51
Step-by-step explanation:
========≈==================
A box of 15 cookies costs $9dollar sign, 9. What is the cost for 1 cookie?
Answer:
$1.66 or $1.70 if you round up
Step-by-step explanation:
OMG I NEED HELP LIKE RIGHT NOW
Answer:
x coordinate is +3 and y coordinate is +1
Step-by-step explanation:
just count three squares right and one square down from D