Answer:
Fernando does not have enough clay to finish the structure since, the expressions for the volume left are not the same.
Step-by-step explanation:
Let w be the length of the longest slab. Since each slab is 2 inches less than the one beneath it, we have the width of the other 3 slabs as w - 2, w - 2 - 2 = w - 4 and w - 4 - 2 = w - 6 respectively.
Since the base of each slab is a square and has thickness 2 inches, the volume of each slab from largest to smallest is thus 2w², 2(w - 2)², 2(w - 4)² and 2(w - 6)² respectively.
We have that we have half of the container of clay left after forming the first two slabs(which are the bottom-most slabs). Let V be the volume of each clay container. Since we have half left, that is V/2, we have used 2V - V/2 = 3V/2 to make the two bottom-most slabs.
So, 3V/2 = 2w² + 2(w - 2)²
= 2w² + 2(w² - 4w + 4)
= 2w² + 2w² - 8w + 8
= 4w² - 8w + 8
= 4(w² - 2w + 2) (1)
Also we want to know if V/2 is equal to the volume of the two top-most slabs.
So, V/2 = 2(w - 4)² + 2(w - 6)²
= 2(w² - 8w + 16) + 2(w² - 12w + 36)
= 2w² - 16w + 32 + 2w² - 24w + 72
= 4w² - 40w + 104
= 4(w² - 10w + 26)
From (1) V/2 = 4(w² - 2w + 2)/3 ≠ 4(w² - 10w + 26)
Since the expressions for the remaining volume are not the same, Fernando does not have enough clay to finish the structure.
The bear moves closer, so Rick decides to go to the other side of the lake. Since there is a forest, he can only spotpoint A when angle C measures 50'. What trigonometric function would Rick
use to find AB if he knows the measure of BC ?
Answer:
Tangent
Step-by-step explanation:
Given
[tex]\angle C = 50[/tex]
See attachment for complete question
Required
Function to calculate BC
If AB is known, BC is calculated as:
[tex]\tan(C) = \frac{AB}{BC}[/tex]
Substitute d for AB and 50 for C
[tex]\tan(50) = \frac{d}{BC}[/tex]
Make BC the subject
[tex]BC = d * \tan(50)[/tex]
Hence, BC can be found using tangent
2/5 + 2/5
Help my sister
Step-by-step explanation:
2/5+2/5(2+2)/54/50.8stay safe healthy and happy...Answer:
4/5
Step-by-step explanation:
2 + 2 = 4
5 + 5 = 5
4/5
Pleaseeeeeeeee helppppp someone pleaseeeeeee I’m begging uuuuuuuuuuuu
Answer:
x=6
ABC= 135 degrees
Step-by-step explanation:
ABE and CBD are congruent angles (don't remember the theorem)
therefore
3x+27=45
solve for x
x=6
ABC and CBD are supplementary (meaning they add to 180)
Answer:
6
Step-by-step explanation:
zuma took a loan of 630 000 from the bank. he will repay the loan over 48 months at 9.5% per annum simple interest. how much interest will zuma pay on the loan
Answer:
Interest amount = 239400
Step-by-step explanation:
Below is the calculation of interest amount:
Given the loan amount or present value = 630000
Time period = 48 months or 4 years
Interest rate give = 9.5%
Total amount = P ( 1 + rt)
P = 630000
r = 9.5%
t = 4 years
Total amount = 630000 ( 1 + 9.5% x 4)
Total amount = 869,400
Interest amount = 869400 - 630000
Interest amount = 239400
what is the shape called??
Answer:
This is called a Trapezoidal prism
Number of faces: 5
Number of edges: 9
Number of vertices: 6
Hope this helps!!
PLEASE I NEEED HELP!!! YOU DONT HAVE TO AWNSER NUMBER 6
Answer:
6942-8.7 or 26/3-3.5 or -7/2What is an equation of the line that passes through the point (-6,-8) and is parallel to the line x-2y=6?
Answer:
[tex]y=\frac{1}{2}x-5[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope and different y-intercepts1) Determine the slope (m)
[tex]x-2y=6[/tex]
Rearrange this equation into slope-intercept form (this will help us find the slope)
Subtract x from both sides
[tex]x-2y-x=6-x\\-2y=-x+6[/tex]
Divide both sides by -2
[tex]y=\frac{1}{2} x-3[/tex]
Now, we can identify clearly that the slope of the given line is [tex]\frac{1}{2}[/tex] since it's in the place of m. Because parallel lines always have the same slopes, the line we're currently solving for would therefore have a slope of [tex]\frac{1}{2}[/tex] as well. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{1}{2}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{1}{2}x+b[/tex]
Plug in the given point (-6,-8)
[tex]-8=\frac{1}{2}(-6)+b\\-8=-3+b[/tex]
Add 3 to both sides to isolate b
[tex]-8+3=-3+b+3\\-5=b[/tex]
Therefore, the y-intercept is -5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:
[tex]y=\frac{1}{2}x-5[/tex]
I hope this helps!
Pleas help!
WILL THANKS YOUR ACCONT and MARK BRAINLIEST
Find the surface area. 10 ft 3 ft 5ft
Answer:
5.7 feet i think
Step-by-step explanation:
Carlitos purchased $13.90 of roasted almonds to make his own almond milk.He purchased 5 pounds of almonds.Assuming the cost per pound is the same,what was the cost per pound of the almonds?
Helpppppp pleaseeeer
Answer:
D is the answer
Step-by-step explanation:
Solve the trigonometric equation over the interval [0, 2π)
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
Show your work, thanks!
Answer:
θ = 0° , 60°
Step-by-step explanation:
[tex]\cos^2\theta + \sqrt{3}\sin \theta \cos \theta = 1[/tex]
Substract both the sides from 1.[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 1 - 1[/tex]
[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 0[/tex]
Rearrange the terms in L.H.S.[tex]=> (\cos^2 \theta - 1 )+ \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Replace the terms in brackets with '-sin²θ' by using the identity (sin²θ + cos²θ = 1).[tex]=> -\sin^2 \theta + \sqrt{3} \sin \theta \cos \theta = 0[/tex]
Take 'sinθ' common from the whole expression in L.H.S.[tex]=> \sin \theta(- \sin \theta + \sqrt{3}\cos \theta) = 0[/tex]
Now solve each part separately :-
1) [tex]\sin \theta = 0[/tex]
[tex]=> \theta = \sin^{-1}0 = 0[/tex]
2) [tex]-\sin \theta + \sqrt{3} \cos \theta = 0[/tex]
Divide both the sides by 'cosθ'.[tex]=> \frac{-\sin \theta + \sqrt{3}\cos \theta }{\cos \theta} = \frac{0}{\cos \theta}[/tex]
[tex]=> \frac{-sin \theta}{\cos \theta} + \frac{\sqrt{3} \cos \theta}{\cos \theta} = 0[/tex]
[tex]=> -\tan \theta + \sqrt{3} = 0[/tex]
Add both the sides with 'tanθ'.[tex]=> -\tan \theta + \sqrt{3} + \tan \theta = 0 + \tan \theta[/tex]
[tex]=> \tan \theta = \sqrt{3}[/tex]
[tex]=> \theta = \tan^{-1}\sqrt{3} = 60[/tex]
∴ θ = 0° , 60°
Answer:
Solution given:
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
[tex] 1-sin^{2} \theta+\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] 1-1 +sin^{2}\theta=\sqrt{3} sin \theta cos \theta = 1[/tex]
[tex] Sin\theta(sin\theta -\sqrt{3}cos\theta)[/tex]
Either
[tex] sin\theta=\sqrt{3} cos \theta [/tex]
[tex] \sqrt{sin\theta}{cos \theta}=\sqrt{3} [/tex]
[tex] Tan \theta =\sqrt{3}[/tex]
[tex] Tan \theta =Tan 60,Tan(180+60),Tan (360+60)[/tex]
[tex] \theta =60°,240°,420°[/tex]
in terms of π is
[tex] \theta =⅓π,\frac{4}{3}π,[/tex]
Or
[tex] Sin\theta=1[/tex]
[tex]Sin\theta=Sin0° ,Sin180°[/tex]
In terms of π is
[tex]\theta=0π,π[/tex]
so
[tex]\theta=0π,⅓π,π,\frac{4}{3}π,[/tex]
please help! 20 points. if you guess or just comment to take my points i will make sure ur account gets banned. thanks! i want a simple explanation
Answer:
x = 9
Step-by-step explanation:
Of course I'll do very simple explanation!
every time you see a straight line (nondiagonal) it measures 180°.
so if we're trying to solve for x in this case, we'll subtract 180° - 40° = 140°.
Then use the statement to solve for x
[tex]10x+50=140[/tex]
[tex]10x-50[/tex] = - 50 Subtract 50 from both sides
[tex]10x[/tex] [tex]=[/tex] 90 Divide 10 from both sides
x = 9
What is 1/3 minus 1/6
Answer:
Step-by-step explanation:
1/3 - 1/6
take the lcm of 3 and 6
lcm=6
=1*2-1/6
=2-1/6
=1/6
what is the difference between 1089 and 4445
Answer:
If it is:
1,089-4,445= -3,356
but if it is the other way:
4,445-1,089= 3,356
Hope it helped!
Answer:
Its a Subtraction problem
4445-1089
=3356
Taylor invested $2500 in an account that pays 3.7% interest compounded monthly. If Taylor does not touch the money, what will the balance of the account be after 7 years?
Answer:
hehe
Step-by-step explanation:
Convert 3.12 mm into cm, m and km.
Answer:
3.12mm= 31,2cm
3.12= 0.312m
3.12 = 0.000312km
6. Find the sum of the geometric series.
a1=-9 a5=-729 r=-3
Answer:
Sn = -9(1-(-3)^n)/4
Step-by-step explanation:
Since r < 1, the sum of nth term of a geometric sequence is expressed as;
Sn = a(1-r^n)/1-r
a is the first term
n is the number f terms
r is the common ratio
An = -9(1-(-3)^n)/1-(-3)
Sn = -9(1-(-3)^n)/4
Hence the sum of the nth term of the series is Sn = -9(1-(-3)^n)/4
P L E A S E A N S W E R A S A P
P L E A S E E E E E E
Answer:
d
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
like the guy above me said
atus
view
The Pythagorean Identity states that:
(sin x)2 + (cos x)2 = 1
Given cos 0 = Ź, find sin 0.
sin 0 =
V 역
Simplify the fraction.
Enter
Answer:
√7 / 4
Step-by-step explanation:
Trigonometrical identity are used to show the relationship between the sides and angles of a right angled triangle. Some trigonometric identities are:
sinΘ = opposite / hypotenuse, cosΘ = adjacent / hypotenuse, tanΘ = opposite / adjacent.
Given that cosΘ = 3 / 4
Therefore, cosΘ = adjacent / hypotenuse = 3 / 4
adjacent = 3, hypotenuse = 4. Let x be the opposite side, to get the opposite side, we use Pythagoras theorem:
opposite² + adjacent² = hypotenuse²
x² + 3² = 4²
x² + 9 = 16
x² = 7
x = √7
sinΘ = opposite/hypotenuse = √7 / 4
1 2/3 -2/9st step by step
Answer:
stay safe healthy and happy...You bought a new water glass. The glass is cone-shaped and has a circular base. It has a
diameter of 3 inches and a height of 7.5 inches. What is the volume of the glass? Use 3.14 to
approximate pi. Round your answer to the nearest tenth.
Answer:
TO find the answer, first you have to find the formula for volume of a cone-
The formula is
V= 1/3 times base times height
So V= (1/3) (pi3^2) (12)
V= 113.04
By the way for the base you have to find the volume of a circle. I divided the diameter by 2 to find the radius.
and pi is 3.14
I keep getting the wrong answers someone help please.
Answer:
1. 8.9
2. 14.5
3. 10.3
4. 18.8
5. 8.0
6. 15.0
(All to the nearest tenth)
The code is the sum of all missing sides
So adding all
=75.5
Simplify the following expression completely.
{x^2+11x+28}
{x^2+x-12}
wrote like division
Answer:
[tex] \frac{x + 7 }{x - 3} [/tex]
Step-by-step explanation:
First factorize both expressions
[tex] \frac{ {x }^{2} + 11x + 28 }{x { }^{2} + x - 12} \\ \frac{x {}^{2 } + 7x + 4x + 28 }{x { }^{2} + 4x - 3x - 12 } \\ \frac{x(x + 7) + 4(x + 7)}{x(x + 4) - 3(x + 4) } \\ \frac{(x + 7)(x + 4)}{(x + 4)(x - 3)} [/tex]
Now you can cross out x+4
and you'll be left with
[tex] \frac{x + 7}{x - 3} [/tex]
is "6x – (3x + 8) = 16x" a no solution
Answer:
no x = -8/13
Step-by-step explanation:
6x – (3x + 8) = 16x
Combine like terms
6x -3x -8 = 16
3x-8 = 16
Subtract 3x from each side
3x-8-3x = 16-3x
-8 = 13x
Divide by 13
-8/13 = 13x/13
-8/13 =x
Answer:
No, the answer would be -8/13
Step-by-step explanation:
6x-(3x+8)=16x
6x-3x-8=16x
3x-16x=8
-13x=8
x=-8/13
Can someone help me with this ?
Help out on the bottom part
Answer:
x+2y=-3
x+2(-1)=-3
x-2=-3
x=-3+2
x=-1
Find the midpoint
(1,-8) (-7,0)
Answer:
(-3, -4)
Step-by-step explanation:
Handy fact: the average of two numbers is exactly halfway between them.
To find the midpoint, average the x-coordinates; average the y-coordinates.
(1 + -7)/2 = -6/2 = -3
(-8 + 0)/2 = -8/2 = -4
The midpoint is (-3, -4).
The graph of quadratic function is shown on the grid.
Which of these best represents the domain of f?
A.
[tex]y \geqslant 5.5[/tex]
B.
All real numbers
C.
All real numbers less than -3 or greater than 2
D.
[tex] - 3 \leqslant x \leqslant 2[/tex]
What's the volume to this prism?
Answer:
36 cubic inch
Step-by-step explanation:
The formula for the volume of a rectangular prism is:
[tex]V=whl[/tex]
----------------------------------------------------------------------------------------------------------------
So:
6 × 3 × 2 = 36
----------------------------------------------------------------------------------------------------------------
Have a good day :)