[tex]~~(x^2 -3x)^2 -14(x^2 -3x) +40\\\\=u^2-14u+40~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Let}~ u = x^2 -3x]\\\\=u^2 - 10u-4u +40\\\\=u(u-10)-4(u-10)\\\\=(u-4)(u-10)\\\\=(x^2 -3x -4)(x^2 -3x -10)~~~~~~~~~~~~~;[\text{Substitute back}~ u = x^2 -3x]\\\\=(x^2 -4x+x-4)(x^2 -5x+2x-10)\\\\=\textbf{[}x(x-4) +(x-4) \textbf{]} \textbf{[}x(x-5) +2(x-5) \textbf{]} \\\\=(x+1)(x-4)(x+2)(x-5)[/tex]
XY and BD are parallel lines
X is a point on AB and C is a point on BD.
XB = XC
a) Complete this sentence.
Angle XBC = 55° because = ?
b) Work out angle BXC.
Give a reason for each angle you work out.
Answer:
a) they are corresponding angles
b) B=55° (proven)
C=55 (Angles opposite equal sides)
B+C+X=180° ( sum of angles of a triangle)
55°+55°X=180
110°+X=180°
X=180°-110°
X=70°
What is the derivative of the function f(x)= 4cos2x + logx + x?
Answer:
[tex]f'(x)=-8\sin2x+\frac{1}{x} +1[/tex]
Step-by-step explanation:
I assume by [tex]\log(x)[/tex], the base is [tex]e[/tex], so let [tex]\log_e(x)=\ln(x)[/tex]:
[tex]\displaystyle f(x)=4\cos2x+\ln x+x\\\\f'(x)=\frac{d}{dx}(4\cos2x+\ln x + x)\\\\f'(x)=\frac{d}{dx}(4\cos2x)+\frac{d}{dx}(\ln x)+\frac{d}{dx}(x)\\\\f'(x)=-8\sin2x+\frac{1}{x}+1[/tex]
Remember that by the chain rule, to find the derivative of [tex]4\cos2x[/tex], you must find the derivative of the inside, which is [tex]\displaystyle \frac{d}{dx}(2x)=2[/tex], and multiply it by the outside derivative. Recall that [tex]\displaystyle \frac{d}{dx}\cos(x)=-\sin(x)[/tex], so replace [tex]-\sin(x)[/tex] with [tex]-4\sin(2x)[/tex], and multiply by 2 to get [tex]-8\sin(2x)[/tex] as your derivative.
Also remember that [tex]\displaystyle \frac{d}{dx}\ln(x)=\frac{1}{x}[/tex], one of the more basic derivatives.
The derivative of the function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given function is four times of cos2x plus logx plus x.
f(x)= 4cos2x + logx + x
We need to find the derivative of it f'(x)
d/dxf(x)=d/dx(4cos2x)+d/dx(logx)+d/dx(x)
f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)
We know that
d/dx(cosx)=-sinx
d/dx(logx)=1/x
d/dx(x)=1
Apply in above equation
f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)
f'(x)=4.2(-sin2x)+1/x+1
f'(x)=-8sin2x+1/x+1
Hence the derivative of function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.
To learn more on Differentiation click:
https://brainly.com/question/24898810
#SPJ2
Sara made hot chocolate mix to give to
her neighbors. She mixed 4 cups of sugar
with 2 cups of cocoa. Then she poured 12/2
cups of the mix in each jar. How many jars
did she fill?
Ryder used front-end estimation to estimate the product of (–24.98)(–1.29). What was his estimate?
–32
–20
20
32
Answer:
(d) 32
Step-by-step explanation:
An estimate is a value that is intended to approximate the result of a detailed calculation. Often, the target is an estimate that is within about 10% of the actual value. A "rough order of magnitude" (ROM) estimate is intended to be within about a factor of 3 of the actual value.
__
An estimate is generally made by using a reduced number of significant figures in the calculations. Often, the numbers used will be rounded to 1 or 2 significant figures. The math is often accomplished mentally, so methods of mental arithmetic are often used to simplify the calculations.
rounded valuesWe are asked for an estimate of the product (-24.98)(-1.29). We notice there are an even number of minus signs, so the result will be positive. The values are (25)(1.3) when rounded to 2 significant figures.
Along with the rounded values, it is often useful to make note of the direction and magnitude of the errors due to rounding. Here, we have rounded both numbers up. The number 25 is high by 0.02, and the number 1.3 is also high by 0.01. These can be used to estimate the error in the estimated value.
the productThe desired product can be computed several different ways. Either or both of the numbers 25 and 1.3 can be represented in a fashion that facilitates the (mental) arithmetic. Here are three (3) methods that could be used.
(25)(1.3) = 25(1 +0.3) = 25 +7.5 = 32.5 (a little high, so we can choose to round down to 32)(25)(1.3) = (100/4)(1.3) = 130/4 = 65/2 ≈ 64/2 = 32 (again, rounding down because we know 32.5 is too high)(25)(1.3) = 2.5(13) = 2(13) +13/2 = 26 +6.5 = 32.5 ≈ 32Ryder's estimate was 32.
_____
Additional comment
The actual product is ...
(25 -0.02)(1.3 -0.01) = (25)(1.3) -0.02(1.3) -0.01(25) +(0.02)(0.01).
As a first approximation of the error in the product 32.5, we can sum the middle two terms:
-0.02(1.3) and -0.01(25) = -0.026-0.25 = -0.276.
Then the first refinement of the estimate will give us ...
32.500 -0.276 = 32.224
The actual value is obtained by adding the final error term:
32.224 +0.0002 = 32.2242 . . . . the actual product with estimate errors resolved.
Answer:
yo
Step-by-step explanation:
its C, or 20
edge
ur welcome
Matthew is grocery shopping for a taco Tuesday Bloc Party he is expecting 60 people including himself, and for each person to have 1 soft and 1 crispy taco. Soft tortillas coke in packs of 10. Crispy taco shells come in packs of 12. How many packages of each tortilla type does Mathew need to feed everyone?
The number of each tortilla type that Mathew would need to feed everyone is = 6 packages of Soft tortillas and 5 packages of Crispy taco shells.
Calculation of number of tortillaThe number of people Matthew is expecting including himself = 60
The Soft tortillas coke appear = 10/pack
The Crispy taco shells appear = 12/pack
Since each person is to get 1 soft and 1 crispy taco, the number of tortilla type that Mathew would need to feed everyone is
= 60/10 = 6 packages of Soft tortillas
= 60/12 = 5 packages of Crispy taco shells
Learn more about addition here:
https://brainly.com/question/25421984
#SPJ1
Find the missing side of this right
triangle.
X
28
[?]
X =1
Enter the number that belongs in the green box.
Applying the Pythagorean theorem, the missing side of the right triangle is: √788.
What is the Pythagorean Theorem?To find the hypotenuse (c) of a right triangle, having two other legs a and b, the Pythagorean theorem states that, c = √(a² + b²).
Given the following:
c = xa = 2b = 28Plug in the values
x = √(2² + 28²)
x = √788
Missing side is: √788.
Learn more about the Pythagorean theorem on:
https://brainly.com/question/343682
#SPJ1
Describe how the product of 0.08 x 8 would look on a one hundred-square grid.
The product would have ____
squares shaded out of 100.
Find the volume of the prism.
9km 8km 6km
The correct answer is option B which is the volume of the prism is 216 km³.
What is the volume of the prism?A prism is a three-dimensional solid with a triangular base called a triangular prism. The volume of the triangular prism is equal to the product of the area of the base and the height of the prism.
The volume of the prism will be calculated by using the formula below:-
V = Area of the base x Height
Since the base is a right-angle triangle so we will calculate the area of the right-angle triangle.
V = Area of the triangle x Height
V = ( 1/2 ) x 8 x 6 x ( 9 )
V = 216 km²
Therefore the correct answer is option B which is the volume of the prism is 216 km³.
To know more about volume follow
https://brainly.com/question/1972490
#SPJ1
Solve for x in the triangle. Round your answer to the nearest tenth.
X
5
22°
Which of the following rules is the composition of a dilation of scale factor 2, then a translation of three units to the right? a) (2x+3,y) b) (2x+6, 2y) c) (2x +3, 2y) d) (2x+6, y)
Answer:
The answer is C: (2x +3, 2y)
Step-by-step explanation:
When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.
Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.
(x, y) -----> (2x, 2y)
Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.
Translation 2 units right:
(2x, 2y) -----> (2x +3, 2y)
6. Solve the equation: h/9 = 7.
A. h = -63
B. h=63
C. h=127
D. h = 7/g
Answer:
B) h=63
Step-by-step explanation:
Multiply both sides by 9.
h/*9=9*7
Simplify
h=63
[tex]\bf{\dfrac{h}{9}=7 \ \ \to \ \ \ Exercise \ to \ solve }[/tex]
Multiply both sides by 9.
h = 7 × 9Multiply 7 and 9 to get 63.
h = 63 ===> AnswerTherefore, the correct option is "B".
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Find the slope of the line.
Answer:
2
Step-by-step explanation:
we know the line goes through the origin, so we have point (0,0). next, find another point the line goes through. for example, point (2,4)
the slope formula for points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1). plug in the 2 points to get (4-0)/(2-0) = 4/2 = 2
If a prism is placed into a basin of water (density: 32.5 lbs/ft^3 ) displaces 3.3 lbs of water, what is the volume of the water that was displaced (in cubic inches)?
Please help
The volume of water that was displaced is 0. 000019 cubic meters.
What is volume?Volume is known to be the amount of space or capacity occupied by a three-dimensional solid shape.
It is denoted in cubic units.
How to calculate the volumeThe formula for calculating volume is;
Volume = mass ÷ density
Given that mass = 3. 3 Ibs and density = 32. 5Ibs/ ft∧3
Volume = 3. 3 ÷ 32. 5 = 0. 10 Ibs
How to covert Ibs to cubic meters
Ibs = 0. 00019 m∧3 (cubic meters)
Then, 0. 10 Ibs = 0. 00019 × 0.10 ÷ 1 = 0. 000019 cubic meters.
Therefore, the volume of the water displaced is 0.000019 cubic meters.
Learn more on volume here:
https://brainly.com/question/1972490
#SPJ1
I am not divisible by 2,3,5 or 7. My two digits are not the same, but they are both squares. What two numbers could I be?
I NEED HELP FASTTT
Answer:
19 is suitable no in which 1 is square of itself and 9 is of 3
Between which two tenths is the decimal approximation of √7?
Answer:
2.6 and 2.7
Step-by-step explanation:
The actual square root of 7 is 2.64 and that is between 2.6 and 2.7.
is f(x)=x^(2)-4 and f(x)=3(2-x) functions?
Answer:
Yes
Step-by-step explanation:
There is only one output value for each input value, which is the definition of a function.
Why is y = 63?? Isn’t (x-5)+51+(y-6)=180??
Answer:
coz it is
Step-by-step explanation:
the angle is 57° , so y is 63 as 63-6 = 57
PLEASE HELP ME WITH THIS!!!
Answer:
68 inches
Step-by-step explanation:
y = x + 2
x = 66
y = 66 + 2
y = 68
which equation represents circle n? (17 points & will mark branliest)
Answer:
c. (x+7)^2+(y-6)^2=50
Step-by-step explanation:
The equation of a circle is; (x+7)²+(y-6)² = 50
What is circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The points on the circle are L(-2, 11) and centre is N(-7, 6)
Find the radius,
D = √(-7+2)²+(6-11))²
D = √25+25
D = √50
We know that, the equation of a circle is given by,
( x − a )² + ( y − b )² = r² , where ( a , b ) represents the centre of the circle,
Here, centre is N(-7, 6)
Therefore, the equation of a circle is;
(x+7)²+(y-6)² = 50
Hence, the required equation is (x+7)²+(y-6)² = 50
For more references on circle, click;
https://brainly.com/question/29142813
#SPJ2
please help i need to turn this in
Answer:
a) -3
b) 9
c) -3
Step-by-step explanation:
a)
[tex]2^5 * 2^{-8} = 2^a[/tex]
In cases where we have a multiplication with exponents we keep the integer as it is and we add the exponents. 5 + -8 = -3. Therefore a is 3.
b)
[tex]\frac{4^7}{4^-{2}} = 4^b[/tex]
In cases when we have a division with exponents we keep the integers as it is and we subtract the exponents. 7 - (-2) = 7 + 2 = 9. Therefore, b is 9
c)
[tex]\frac{7^9}{7^c} = 7^{12}[/tex]
We are dividing again however we are finding the denominator.
9 - (c) = 12
Subtract from both sides: -c = 3, To make c positive we just make the value negative, c = -3. Therefore c is -3
Urgent! Brainliest to whoever solves it
Quadrilateral HGFJ is a rhombus
Answer:
16cm and 48 degrees
Step-by-step explanation:
The equation of line LM is y = 5x + 4. Write an equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2).
The box is 450 square. The length is 10 inches and the width is 5 inches. What is the height of the box
Answer:
9 inches
Step-by-step explanation:
I assume you mean the volume of the box is 450.
In that case, to figure out for the volume we multiply 10 by 5. This gives us 50.
450/50=9
The height of the box is 9 inches
Give brainliest please!
hope this helps :)
Submitting a Bid
You want to bid on a project for the pool shown. The project involves ordering and installing the brown tile that borders the pool, and ordering a custom-made tarp to cover the surface of the pool. In the figure, each grid square represents 1 square foot.
You pay $5 per linear foot for the tile.
You pay $4 per square foot for the tarp
It takes about 15 min to install each foot of the tile
A) estimate the total cost for the tile and the tarp
Answer:
5,125
Step-by-step explanation:
What is the probability of rolling a 6 sided die 4 times and getting an even number all 4 times?
Find the slope and the y-intercept of the following linear equation. 5. 3x + 2y = 14
The slope and y-intercept of the equation are - 3 / 2 and 7 respectively.
How to find slope and y-intercept?The slope and y-intercept of an equation can be easily found using slope intercept equation.
y = mx + b
where
m = slopeb = y-interceptTherefore,
3x + 2y = 14
2y = -3x + 14
y = -3 / 2 x + 7
Therefore,
slope = - 3 / 2
y-intercept = 7
learn more on slope here: https://brainly.com/question/3605446
#SPJ1
An arithmetic sequence has this recursive formula:
What is the explicit formula for this sequence?
Answer:
C
Step-by-step explanation:
the explicit formula for an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
from the recursive formula in the form
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d
given
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 7
with d = - 7 and a₁ = 4 , then explicit formula is
[tex]a_{n}[/tex] = 4 + (n - 1)(- 7)
3z+35=47 solve
help, i need answer
Answer:
z=4
Step-by-step explanation:
subtract 47-35
3z=12
divide both sides by 3
z=4
Paul and Krystal spent 1 1/2 hours at the pool
Answer:
Paul and Krystal spent 13 hours at the pool
Step-by-step explanation:
I Thank
4gal 2qt - 3gal 3qt=
I need help with this one, it's just subtracting as is. Thank you
Answer:
= .75 gallons or 3 quarts
Step-by-step explanation:
Known
1 gallon = 4 quartsProblem:
4 gallons 2 quarts - 3 gallons 3 quarts
⇒ 2 quarts: 0.5 gallons
⇒ 3 quarts: 0.75 gallons
Add on both sides
4 + 0.5 = 4.5 gallons
3 + 0.75 = 3.75 gallons
This leaves the equation at:
4.5 gallons - 3.75 gallonsThis equals 3 quarts or 0.75 gallons.