Answer:
[tex] 2w^2(w + 2)(4w - 3) [/tex]
Step-by-step explanation:
[tex] 8w^4 + 10w^3 − 12w^2 = [/tex]
First, factor out the GCF of all terms, 2w^2:
[tex] = 2w^2(4w^2 + 5w - 6) [/tex]
Now we work on the trinomial.
Think of ax^2 + bx + c.
Multiply ac
ac = 4 * (-6) = -24
Now we need two numbers whose product is -24 and whose sum is 5.
They are -3 and 8.
We break up the middle term, 5w, into a sum using these two numbers.
5w = 8x - 3w
[tex] = 2w^2(4w^2 + 8w - 3w - 6) [/tex]
Now we factor by parts. We factor a common factor out of the first two terms, and we factor a common factor out of the last two terms.
[tex] = 2w^2[4w(w + 2) - 3(w + 2)] [/tex]
[tex] = 2w^2(w + 2)(4w - 3) [/tex]
this is a calculus question.
The volume of a cube increases at a constant rate of 10 cm^3 per second. find the rate of change in its total surface area at the instant when its when its sides are 20 cm long.
Answer:
2 cm^2/sec
Step-by-step explanation:
side of cube ---- x cm
volume = x^3
d(volume)/dt = 3x^2 dx/dt
when c = 20, d(volume)/dt = 10 cm^3/sec
10 = 3(20^2) dx/dt
dx/dt = 10/1200 = 1/120 cm/sec
Surface area = SA = 6x^2
d(SA)/dt = 12x dx/dt
so when x = 20, as above
d(SA)/dt = 12(20)(1/120) cm^2/sec
= 2 cm^2/sec
I need help... please help me through this trigonometry. I need full answer.
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
tan(x + y) = [tex]\frac{tanx+tany}{1-tanxtany}[/tex] , tan(x - y) = [tex]\frac{tanx-tany}{1+tanxtany}[/tex], tan [tex]\frac{\pi }{4}[/tex] = 1
tan2x = [tex]\frac{2tanx}{1-tan^2x}[/tex]
Consider the left side
tan([tex]\frac{\pi }{4}[/tex] + Θ ) - tan([tex]\frac{\pi }{4}[/tex] - Θ )
= [tex]\frac{tan\frac{\pi }{4}+tan0 }{1-tan\frac{\pi }{4}tan0 }[/tex] - [tex]\frac{tan\frac{\pi }{4}-tan0 }{1+tan\frac{\pi }{4}tan0 }[/tex]
= [tex]\frac{1+tan0}{1-tan0}[/tex] - [tex]\frac{1-tan0}{1+tan0}[/tex]
= [tex]\frac{(1+tan0)^2-(1-tan0)^2}{(1-tan0)(1+tan0)}[/tex]
= [tex]\frac{1+2tan0+tan^20-1+2tan0-tan^20}{1-tan^20}[/tex]
= [tex]\frac{4tan0}{1-tan^20}[/tex]
= 2 [tex]\frac{2tan0}{1-tan^20}[/tex]
= 2 tan2Θ = right side
What’s x ?? Help plzzz
Answer:
x = 69°
Step-by-step explanation:
1). JFGHI is a pentagon, every angle in a Pentagon is equal to 108°.
2). angle JIH + angle HIE = 180°; angle JIH = 108, so angle HIE = 72°.
3). angle JDI is equal to 39° and angle IEH; so angle IEH = 39°
4). Now we know 2 out of the three angles in the triangle IHE, so we can find x!
5). x + angle HIE + angle IEH = 180°
x + 72° + 39° = 180°
x = 69°
PLEASE HELP!! URGENT
A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° Use the
information provided and the diagram below to determine the height of the tree. Round to the nearest
whole foot.
532 it
256 ft
479 ft
231 ft
13672 ft
< Previous
Next >
Answer:
The answer is option 1.
Step-by-step explanation:
You have to apply Tangent Rule, tanθ = opposite/adjacent. Then, you have to substitute the following values into the formula :
[tex]tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: θ = 25.7 \: , \: oppo. = h \: , \: adj. = 532[/tex]
[tex] \tan(25.7) = \frac{h}{532} [/tex]
[tex]532 \tan(25.7) = h[/tex]
[tex]h = 256 \: feet \: (3s.f)[/tex]
The value of height of tree is,
⇒ h = 256 feet
We have to given that,
A Giant Redwood tree cast a shadow that is 532 feet long, with an angle of elevation of 25.7° .
Hence, By given figure we get;
By using trigonometry formula, we get;
⇒ tan 25.7° = Opposite / Adjacent
⇒ tan 25.7° = h / 532
⇒ 0.4812 = h / 532
⇒ h = 0.4812 × 532
⇒ h = 256 feet
Therefore, The value of height of tree is,
⇒ h = 256 feet
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please help me with this questions. Will Mark brainliest.
Answer: 355
And 33 eggs
Step-by-step explanation:
8 × 40 = 320
7/8 × 40= 35 Add 35+320 = 355
2 × 12= 24 3/4 of 12 = 9
Add 9+24=33
You can also make an improper fraction. Multiply the denominator by the whole number then add the numerator.
2 3/4 becomes 4×2=8
8+3=11 Divide the other factor by the denominator: 12÷4=3
Then multiply by the "improper" numerator 3×11=33
8 7/8 becomes 71/8
40/8=5
5×71=355
Answer:
355
Step-by-step explanation:
So, you first multiply 8 with 8 = 64
Then 64 + 7 = 71
So, 71 is the numerator and 8 stays the denominator.
Now you have 71/8 *40.
You "cut" 40 into five and 8 into 1, Because 40 divided by 8 is 5, so 40 becomes 5 and 8 becomes 1.
Now we have 71 * 5 = 355
hope it helps!
PLEASE brainliest me!
Create diagrams to represent the possible cases for common tangents between two circles. Your diagram can be created using multimedia sources or drawn by hand. They should not be copied and pasted from a website. Explain why your diagrams satisfy the given criteria. One Common Tangent (10 points) Diagram: Justification:
Answer:
draw 2 lines and draw 2 circles in the lines with the edge touching the line
Step-by-step explanation:
In between two circles, there might be 0, 1, 2, 3, and 4 tangents are there.
What is the tangent of a circle?"A tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior.
1. When one circle is in between another and one circle does not touch the other one, then tangent is not possible.
2. When one circle is in between another and one circle touches the other one at a point inside the circle, then only one tangent is possible.
3. When one circle intersects the other one, then two tangents are possible.
4. When one circle touches the other one at a point outside, then three tangents are possible.
5. When one circle neither intersects the other one nor inside the other one, then four tangents are possible.
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A furniture shop refinishes cabinets. Employees use one of two methods to refinish each cabinet Method I takes 1 hour and the material costs $6. Method II takes 2 hours, and the material costs $5. Next week, they plan to spend 260 hours in labor and $986 in material for refinishing cabinets. How many cabinets should they plan to refinish with each method?
Answer:
They should refinish 96 tables using method 1
They should refinish 82 tables using method 2
Step-by-step explanation:
Let
a = number of tables refinished using method 1
b = number of tables refinished using method 2
Time equation
a+2b=260 (1)
Cost equation
6a+5b=986 (2)
a+2b=260 (1)
6a+5b=986 (2)
Multiply (1) by 5 and (2) by 2
5a+10b=1,300 (3)
12a+10b=1,972 (4)
Subtract (3) from (4)
7a=672
Divide both sides by 7
a=96
Recall,
a+2b=260
96+2b=260
2b=260-96
2b=164
Divide both sides by 2
b=164/2
=82
They should refinish 96 tables using method 1
They should refinish 82 tables using method 2
(07.05 LC)
Which statement is true for the equation 4n − 3 = 4n − 2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
Answer:
The answer is (A); there is no solution.
Step-by-step explanation:
It doesn't require any calculations, really, just logic. Look, 4n = 4n wil be equal because they are the same numbers multiplied by the same variable - no matter the variable's value. However, if you subtract both values by different numbers, you won't get the same number:
Let's say n = 5
4n = 4n
= 4(5) = 4(5)
= 20 = 20
Now,
4n - 3 = 4n - 2
= 4(5) - 3 = 4(5) - 2
= 20 - 3 = 20 -2
= 17 ≠ 18
Hope this helps! Tell me if I was wrong!
Answer:
It has no solution.
Step-by-step explanation:
If we try and solve it we end up with nonsense, so it has no solutions:
4n - 3 = 4n - 2
4n - 4n = - 2 + 3
0 = 1
- which is, of course, absurd.
Also, just by looking at the equation we can see that the term 4n -3 cannot in any way be equal to 4n - 2.
jodi has $8,525 in her savings account earning 1.8% annually. how much is in jodi’s account after 8 years? round answer to the nearest cent.
Answer: $32,207,620.36
Step-by-step explanation:
What you need to do is use the formula A = P(1+r)^n
A = Your answer
P = Is the amount Jodi started with.
R = Is the annual interest
N = Number of years
Then plug in your numbers. Always make sure you use PEMDAS. This means parenthesis, exponents, multiplication, division, addition, and subtraction. You always start with the things in the parenthesis and go on down the list. Once you finish the (1 + (1.8)) = 2.8 you will have. A = 8,535 (2.8)^8. You then multiply 2.8 with the exponent 8. Then multiply 8,535 and your answer for 2.8 times 8 and you get your answer.
Good luck on other questions kid
GUYS PLEASE HELP WILL MARK BRAINLIEST
Answer:
14 yards²
Step-by-step explanation:
To find the area of this complex shape, we can break it down into two parts.
I've broken it down into the left shape (with side lengths of 2, 2, 4 and 4) and the right shape (with side lengths of 2, 2, 2 and 3).
Looking at the shape on the left, the width is 4 yards and the length is 2 yards. Multiplying these numbers will get the area for that shape.
[tex]2\cdot4=8[/tex] yards².
Now in the right shape, the length is 3 and the width is 2, so:
[tex]3\cdot2=6[/tex] yards².
Now we can add both of these to get the total area of the figure.
[tex]6+8=14[/tex] yards².
Hope this helped!
Answer:
14 yds^2
Step-by-step explanation:
We can split this into two rectangles
There is a vertical rectangle on the left, 4 yds by 2 yds
The area is 4*2 = 8 yd^2
There is a horizontal rectangle on the right 3 yds by 2 yds
The area is 3*2 = 6 yd ^2
Add the areas together
8+6 = 14
Step 2 Using Proportional Relationships
Answer:
a ( 567 miles to unit)
b( looks like 2 units so i would say 1134 miles
Answ: the scale is
Step-bstep explanatio
How does 4D shape look like?
Answer:
here you go
i hope i helped you
Step-by-step explanation:
Answer:
It would look like these shapes on the picture
Step-by-step explanation:
It is a shape with another one of it inside it, you should see it on the pictturres.
Hope this helped you
Please mark as brainlist.
An architect maps two buildings, which are located on a piece of land, onto a coordinate plane. He wants to build a wall at the diagonal AC to divide the piece of land into two parts. What will be the length of the wall? A. 65–√ units B. 6 units C. 237−−√ units D. 2 units
Answer:
[tex] 6\sqrt{5} units [/tex]
Step-by-step Explanation:
The length of the wall = diagonal AC = distance between point A (-6, -2) and point C (6, 4).
Distance formula between two points on a graph (d) = [tex] \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Where,
[tex] A(-6, -2) = (x_1, y_1) [/tex]
[tex] C(6, 4) = (x_2, y_2) [/tex]
[tex] d = \sqrt{(6 - (-6))^2 + (4 -(-2))^2} [/tex]
[tex] d = \sqrt{(6 + 6)^2 + (4 + 2)^2} [/tex]
[tex] d = \sqrt{(12)^2 + (6)^2} [/tex]
[tex] d = \sqrt{144 + 36} [/tex]
[tex] d = \sqrt{180} [/tex]
[tex] d = \sqrt{36*5} [/tex]
[tex] d = 6\sqrt{5} [/tex]
The length of the wall = [tex] 6\sqrt{5} units [/tex]
*LAST QUESTION, PLEASE ANSWER I NEED HELP* What will be the new volume of the prism if a scale factor of 2.5 is applied to the dimensions?
Answer:
10,500 cubic inches
Step-by-step explanation:
1. Find the new lengths after the scale factor
6 · 2.5 = 15
8 · 2.5 = 20
14 · 2.5 = 35
2. Solve for the volume (length · width · height
15 · 20 · 35 = 10500
The required volume of the prism after the scale factor is 2.5 is applied to the dimensions is 10,500 cubic inches. Option D is correct.
DImension for prism,
Length = 14
width = 8
Height = 6
Scale factor = 2.5
New volume to be determined.
The scale factor is defined as the ratio of modified change in length to the original length.
Applying scale factor 2.5 to the dimensions,
Length = 2.5 * 14 = 35
width = 8 * 2.5 = 20
Height = 6* 2.5 = 15
The new volume of the prism = length * width *height
= 35 * 20 * 15
= 10, 500
Thus, The required volume of the prism after the scale factor is 2.5 is applied to the dimensions is 10,500 cubic inches. Option D is correct.
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Each half-inch of a ruler is divided evenly into eight divisions. What is the level of accuracy of this measurement tool?
Answer:
The level of accuracy of the measurement ruler measurement tool is 1/16 of an inch
Step-by-step explanation:
The accuracy of a measurement tool is determined by the ability of the tool measure the accurate value of the actual or standard measurement. The accuracy of a measurement tool depends on its ability to take small measurements
The parameter given includes;
The number of divisions on each 1/2 inch of the ruler = 8
Therefore, the smallest divisions on the ruler = (1/2) inch ÷ 8 = 1/16 inch
Therefore, the level of accuracy of the measurement ruler measurement tool = 1/16 of an inch.
pls help!! Consider the sequence below.
-34, -21, -8, 5...
Complete the recursively defined function to describe this sequence.
Answer:
a₁= -34
aₙ = 13n - 47
Step-by-step explanation:
This is an AP with the first term of -34 and the common difference of 13.
The nth term is:
aₙ= a₁ + (n-1)daₙ= -34 + (n-1)*13aₙ = 13n - 47This is the required formula.
165°
145
x =
Please Help!!!!
Answer:
15°
Step-by-step explanation:
The 165° and x forms a straight line or a supplementary angle. Supplementary angles add up to 180°. Therefore:
[tex]165+x=180[/tex]
Solve for x:
[tex]165+x=180\\x=15\textdegree[/tex]
Answer:
15 degress
165 and x lie on a 180 degress.
and 180 - 165 is 15.
Bye!
Step-by-step explanation:
WILL GIVE BRAINLY!!!!!! NEED HELP ASAP!!!!!!!! what is the range of f(x)=3^x+9
Answer:
y > 9
Step-by-step explanation:
The range of a function is the interval of all possible y-values that make the function true.
Here, one way to figure this out is to look at a graph of the function (see attachment).
From the graph, we can see that y-values approach very closely the value 9 and then the line rises beyond 9 forever. Thus, we can conclude that the range for f(x) is y > 9.
~ an aesthetics lover
Find X. Round your answer to the nearest tenth of a degree.
Answer:
48.6 degrees
Step-by-step explanation:
The sine function is appropriate here:
9
sin x = ------------- = 0.75
12
The inverse sine function arcsin x provides with the angle measurement:
arcsin 0.75 = 0.848 radian, or 48.6 degrees
Explain how to solve 5x2-3x = 25 by completing the square. What are the solutions?
Answer:
x= 3 +√509/10
Or
x= 3 - √509/10
Step-by-step explanation:
Given:
5x2-3x = 25
Using completing the square method of solving quadratic equation
Step 1: Factor out the coefficient of the x^2 term.
5(x^2 - 3x/5) = 25
Step 2: Add a number that would complete the square inside the parenthesis and also add this to the other side of the equation.
Take (1/2) of (3/5)
1/2 × 3/5
= 3/10
Square 3/10
We have, 9/100
We have,
5(x^2 - 3x/5 + 9/100) = 25 + 9/100
Step 3: Simplify
x^2 - (3/5)x + 9/100 = 25 + 9/100
5(x^2 - 3x/5 + 9/100) = 5 + 9/20
Step 4:
factor the right side
(x - 3/10)^2 = 509/100
Take both roots
√ (x - 3/10)^2 = √509/100
x - 3/10 = ±√ [509/100]
x = [ 3 ±√509 ] / 10
x= 3+√509/10
Or
x= 3 - √509/10
Lance can paint the room in 5 hours, while Kim can paint the same room in 4 hours.
How many hours would it take for them to paint the room together?
Answer:
1.5 hours
Step-by-step explanation:
what is the value of x
Answer:
x = 78
Step-by-step explanation:
The angles are vertical angles and vertical angles are equal
Answer:
78 degrees
Step-by-step explanation:
According to vertical angles theorem (vertical angles, angles that are opposite to each other and formed by two intersecting straight lines, are congruent) 78 and x are congruent
In a certain country, the heights and depths of a road are measured in relation to sea level. Sea level has a value of 0. The lowest point of the country lies at −8 feet. The highest point of the country lies at +107 feet. Which of the following statements best describes the lowest and the highest points?
The lowest point is 8 feet above sea level, and the highest point is 107 feet below sea level.
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
The lowest point is 8 feet below sea level, and the highest point is 107 feet above the lowest point.
The lowest point is 8 feet above sea level, and the highest point is 107 feet below the lowest point.
A negative value would mean it is below sea level. A positive value would be above sea level.
-8 is 8 feet below sea level
+107 is 107 feet above sea level.
The answer Is:
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
Answer:
Step-by-step explanation:
The lowest point is 8 feet below sea level, and the highest point is 107 feet above sea level.
Using the function f(x)=-x^2+8x-13 find f(4)
Answer:
f(4) = 3
Step-by-step explanation:
f(x) = -[tex]x^{2}[/tex] + 8x - 13
To find f(4), substitute 4 for all instances of x:
f(4) = -(4[tex])^{2}[/tex] + 8(4) - 13
Simplify the exponent:
f(4) = -16 + 8(4) - 13
Multiply:
f(4) = -16 + 32 - 13
Combine terms:
f(4) = 3
Answer:
3
Step-by-step explanation:
You plug in 4.
f(4)= -(4)^2+8(4)-13
f(4)= -16+32-13
f(4)= 16-13
f(4)=3
Ms. Canton has a book case. On three of the shelves there are the same amount of books. On another shelf there are four of her favorite books. Write an expression to represent all of the books in Ms. Canton's book case. Explain your answer
Answer:
y=3x+4
Step-by-step explanation:
x= the equal amount of books on 3 bookshelves
+4=the other 4 books on the fourth bookshelf
y=the total amount of books
Convert .23 Kiloliters to liters
what’s the answer?
Answer:
230 liters
Step-by-step explanation:
1000 liters is 1 kiloliter
Multiplying by the conversion factor
.23 kiloliters * 1000 liter/ 1 kiloliter= 230 liters
Answer:
= 230litres
Step-by-step explanation:
know that
1000liters makes 1 kilometer
if 1000liters make 1kilometer then we will multiply 0.23 by 1000litres
that is,
0.23 x 1000
= 230litres
2) A furlong is 1/8 of a mile. What part of a mile is 4 furlongs?
Answer:
1/2 mile
Step-by-step explanation:
(1/8)*4 = 1/2 mile
Answer:
4/8 or 1/2
Step-by-step explanation:
becuase 4 times 1/8 is 4/8 which is 1/2
solve for m. √m-7 = n+3 It is worth like 40 points
Answer:
sqrt of (m-7) = n+3
m = (n+3)^2 + 7 or m= n^2 + 6n + 16
sqrt of (m)-7 = n+3
m = (n+10)^2 or m =n^2 + 20n + 100
Step-by-step explanation:
(2) move the constants to the other side, and square
or (1) square and move constants
then you can solve for m
Answer:
[tex]n^2+6n+16[/tex]
Step-by-step explanation:
I'm going to assume you meant [tex]\sqrt{m-7} = n+3[/tex], not [tex]\sqrt{m} - 7 = n+3[/tex].
[tex](\sqrt{m-7}) ^2 = (n+3)^2\\\\(\sqrt{m-7}^2) = (n+3)^2\\\\(m-7)^{\frac{2}{2} } = (n+3)^2\\\\m - 7 = (n+3)^2\\\\m - 7 = n^2 + 2n\cdot3 + 3^2\\\\m - 7 = n^2 + 6n + 9\\\\m - 7 + 7 = n^2 + 6n + 9 + 7\\\\m = n^2 + 6n + 16[/tex]
Hope this helped!
A bag contains red, white, and blue marbles. If 1/4 of the marbles are red and 2/3
of the marbles are white, what fractional part of the marbles are blue?
Answer: 1/12
Step-by-step explanation: 1/4=3/12. 2/3=8/12. 3/12+8/12=11/12. The remaining 1/12 is blue.
PLEASE HELP!! A 5×5×5 wooden cube was painted and then sawed into 1×1×1 cubes. How many 1×1×1 cubes have exactly two faces painted?
Answer:
36
Step-by-step explanation:
There would be three on each edge. (Five, minus the two ends that have 3 sides painted.)
A cube has 12 edges.
12x3=36
