Answer:
10,596 cubic inches
Step-by-step explanation:
The shape of the prism with which the sand castle can be modelled = Square prism
The arrangement of the square prism = One on top of the other
The given height of each prism, h = 6 inches
The side length of the base of the bottom prism, s₄ = 30 inches
The side length of the base of the other prism = The side length of the base of the prism below each prism - 7 inches
Therefore;
The side length of a prism = 7 inches + The side length of the prism above it
Given that the side length of the base prism (The fourth prism), s₄ = 30 inches
The side length of the prism, directly above the base prism (The fourth prism), s₃ = (30 - 7) inches = 23 inches
The side length of the prism, directly above the third prism (The second prism), s₃ = (23 - 7) = 16 inches
The side length of the top most prism, s₁ = (16 - 7) inches = 9 inches
The volume of the sand castle, V = h × (s₄² + s₃² + s₂² + s₁²)
∴ V = 6 × (30² + 23² + 16² + 9²) = 10,596
The volume of the sand castle, V = 10,596 in.³
Heyo!
The volume of the sandcastle above is 10,596 cubic inches.
Hope this helps! If so, please lmk! Tysm and good luck guys!
Mind helping if you have time on your hands that is
Answer:
C. 2%
Step-by-step explanation:
when you have a decimal and are looking for the percentage, simply move the decimal two places to the right. so .0201= 2%
Answer: C. 2%
Step-by-step explanation:
STEP ONE: Convert the decimal into a percentage
Percentage = Number × 100%
Percentage = 0.0201 × 100%
Percentage = 2.01%
STEP TWO: Round to the nearest ones
2.01% ≈ 2%
Hope this helps!! :)
Please let me know if you have any questions
x + 3x/2 = 35. Find x.
[tex]\large\sf \: x + \frac{3x}{2} = 35[/tex]
Find x
________________
[tex]\sf \: x + \frac{3x}{2} = 35 \\ \sf \: \frac{x}{1} + \frac{3x}{2} = 35 \: (take \: LCM \: = 2) \\ \sf \: \frac{2x}{2} + \frac{3x}{2} = 35 \\ \sf \: \frac{2x + 3x}{2} = 35 \\ \sf \: 2x + 3x = 35 \times 2 \\ \sf \: 5x = 70 \\ \sf \: x = \frac{70}{5} \\ \sf \: x = \boxed{ \underline{ 14}}[/tex]
_________________
Answer ⟶ [tex]\boxed{\bf{x= 14}}[/tex]
Which of the following is the equation of a line that passes through the point
(1.4) and is parallel to the x-axis?
A.x=1 B.y=4 C.x=4 D.y=1
Given:
A line passes through the point (1,4) and is parallel to the x-axis.
To find:
The equation of the line.
Solution:
If a line is parallel to x-axis, then the line is a horizontal line. We know that the slope of a horizontal line is always 0. So, the slope of the required line is 0.
The point-slope form of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
Where, m is the slope and [tex](x_1,y_1)[/tex] is the point.
The slope of the required line is 0 and it passes through the point (1,4). So, the equation of the line is:
[tex]y-4=0(x-1)[/tex]
[tex]y-4=0[/tex]
[tex]y-4+4=0+4[/tex]
[tex]y=4[/tex]
The required equation is [tex]y=4[/tex].
Therefore, the correct option is B.
Graph the function f(x) = - squared x + 2
One of the ways to graph this is to use plug in a few x-values and get an idea of the shape. Since the x values keep getting squared, there is an exponential increase on either side of the y-axis. You can see this by plugging in a few values:
When
x=0,f(x)=0
x=1,f(x)=1^2=1
x=2,f(x)=2^2=4
x=3,f(x)=3^2=9
x=4,f(x)=4^2=16
The same holds true for negative x-values to the left of the y-axis since a negative value squared is positive. For example,
x=−1,f(x)=(−1)2=1*−1=1
x=2,f(x)=(−2)2=−2*−2=4
The graph of f(x)=x^2 is called a "Parabola." It looks like this:
Jeanette wants to raise $3,200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
Total amount she wants to raise = $3200
Amount she'll get for each kilometer = $35
So, number of kilometers she need to run
= Total amount she wants to raise/Amount she'll get for each kilometer
= $3200/$35
= 91.42....
Since her sponser is will donate only for whole kilometers she'll have to run 92 km.
For the expression 6 − y + 3, determine the coefficient for the variable term.
−1
0
3
6
Answer:
-1
Step-by-step explanation:
The only variable in this expression is y and it's coefficient, which is the number and it's sign before the term, is -1.
In the expression, 6 and 3 are constants. This is because they have a fixed value and they do not change.
However, the algebraic term y can have different values depending on the equation it is in and is thus known as a variable term.
Although the number '1' is not written, it is implied that the digit 1 (or in this case -1) is there. For example, instead of writing 1x, we can simply write x. The coefficient cannot be zero as if there is zero y, the y term would not exist in the first place.
Help Now!!!!
The Base Of A triangle prism
Answer:
Volume=Area × height
=35×7
volume = {245} m³
OAmalOHopeO
Answer:
Since the area of the triangle(base) is known we now multiply it to the height so we can get the volume.
7 x 35 = 245 m3 is your answer
You can picture it too:
(sorry my drawing is bad with the marker)
Dilate the figure by the scale factor. Then enter
the new coordinates.
A(1,3)
B(4,2)
K=3
A'([?],[ ]
B'([ ],[])
c'[[)
C(1,-3)
Answer:
i think (4,2)
Step-by-step explanation:
I need help with this I don't understand
Answer:
Sin ? = 4/7
? = arcSin (4/7)
? = 35° (rounded to the nearest degree)
So the answer is 35°
Answered by GAUTHMATH
write a expression to represent 6 fewer then the quotient of 8 and a number
Answer:
8/x-6
Step-by-step explanation:
When it says a number fewer, that means to put it behind rather than in the front.
Hope this helps!!:)
Answer:
The expression to represent the phrase is 8/x - 6.
Will give brainiest
∆ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form ∆PQR. The side lengths of ∆ABC are , 5 units; , 4.2 units; and , 4 units. Match each side of ∆PQR to its length.
see file attached
Answer:
QR=5.25 units
PR=5 units
PQ=6.25 units
At the bulk food store, Jerry bought 200 g of mixed nuts that cost $2.50.
What is the price of 450 g of nuts show ur work pls lol
Given:
Cost of 200 g of mixed nuts = $2.50.
To find:
The price of 450 g of nuts.
Solution:
We have,
Cost of 200 g of mixed nuts = 2.50 dollars
Cost of 1 g of mixed nuts = [tex]\dfrac{2.50}{200}[/tex] dollars
Cost of 450 g of mixed nuts = [tex]\dfrac{2.50}{200}\times 450[/tex] dollars
= [tex]\dfrac{2.50}{4}\times 9[/tex] dollars
= [tex]5.625[/tex] dollars
Therefore, the price of 450 g of nuts is $5.625.
last question. 50 points!
w=-1.5
w=2
Answer:
Solution given:
[tex]\sqrt{2w²-19w+31}+2=7-2w[/tex]
again
keep square root alone
[tex]\sqrt{2w²-19w+31}=7-2w-2[/tex]
solve subtraction of 7-2
[tex]\sqrt{2w²-19w+31}=5-2w[/tex]
Squaring on both side
[tex](\sqrt{2w²-19w+31})²=(5-2w)²[/tex]
2w²-19w+31=5²-2*5*2w+4w²
take terms one side
2w²-19w+31-25+20w-4w²=0
-2w²+w+6=0
2w²-w-6=0
doing middle term factorisation
2w²-(4-3)w-6=0
2w²-4w+3w-6=0
take common from each two term
2w(w-2)+3(w-2)=0
(w-2)(2w+3)=0
either
w=2
or
W=-3/2=-1.5
In the xv-plane, the line determined by the
points (2,k) and (k, 32) passes through the origin.
Which of the following could be the value of k ?
Answer:
8
Step-by-step explanation:
If the diagonal line passes through the origin, that means it is proportional. That means that for every point on the line y/x is constantly the same value. So we have k/2=32/k.
Cross multiply: k^2=64
Square root both sides: k=8
Find the measure of the missing angle using the triangle angle sum theorm.
Answer:
20 degrees
Step-by-step explanation:
One angle is 70 degrees and the other is 90. Angles of a triangle add up to 180. 180 - 70 - 90 = 20. The final angle is 20 degrees.
see ss below
spam answers will be reported
Answer:
G = 9y
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
Identify
18y² = G(2y²)
Step 2: Solve for G
Option 1: Factor
Factor: 18y² = (2y²)(9y)Option 2: Isolate
Divide both sides by 2y² to isolate G: 18y³ / 2y² = GSimplify: G = 9yAnswer:
[tex]\boxed {\boxed {\sf G= 9y}}[/tex]
Step-by-step explanation:
We are given the following equation and asked to find the missing factor that makes the equality true.
[tex]18y^3=(G)(2y^2)[/tex]
Essentially, we need to solve for the variable G.
1. Factoring
One method we can use is factoring.
We could factor the expression 18y³ because we know one factor is 2y². Since this is one of the factors, the other must be 9y.
[tex]18y^3=(9y)(2y^2)[/tex]
If we compare this factored version of the expression with the original equation we see that 9y and G correspond, so they must be equal.
[tex]G=9y[/tex]
2. Solving
Another method we could use is solving.
We can solve the original equation for G by isolating the variable.
[tex]18y^3= (G)(2y^2)[/tex]
G is being multiplied by 2y³. The inverse of multiplication is division, so we divide both sides of the equation by 2y³.
[tex]\frac {18y^3}{2y^2}=\frac{(G)(2y^2)}{2y^2}[/tex]
[tex]\frac {18y^3}{2y^2}= G[/tex]
The coefficients are divided as usual and the exponents are subtracted.
[tex]9y= G[/tex]
Which of the following exponential functions represent the graph?
Answer:
dodndbdie9ejrnfudowp2ejdnsmwo2oeidndndoep
Given the following equation where A = Area of a rectangle and w = width of the rectangle, what value of 'w' would maximize the area?
A = LW
P = 2L+2W
P = 100
w should be 625 units
w should be 25 units
w should be 0 units
w should be 50 units
Answer:
the second option : w should be 25 units
Step-by-step explanation:
the area of the rectangle is length×width = L×W
the perimeter of a rectangle = 2L + 2W
now, we know that the perimeter is 100 units.
and we have to find the best length of W, that will then define L (to keep the 100 units of perimeter) and maximizes the area of the rectangle.
in other words, what is the maximum area of a rectangle with perimeter of 100 (and what are the corresponding side lengths)?
now, w = 625 is impossible. that side alone would be bigger than the whole perimeter.
W = 0 would render the whole rectangle to a flat line with L = 50 because of
100 = 2L + 2W = 2L + 0 = 2L
L = 50
and A = L×W = 50×0 = 0
an area of 0 is for sure not the largest possible area.
w = 50 would cause L = 0
100 = 2L + 2W = 2L + 2×50 = 2L + 100
0 = 2L
L = 0
and with L = 0 the same thing happens as with W = 0 : a flat line with 0 area.
so, the only remaining useful answer is W = 25
100 = 2L + 2W = 2L + 2×25 = 2L + 50
50 = 2L
L = 25
A = L×W = 25×25 = 625 units²
and indeed, the maximum area for a given perimeter is achieved by arranging the sides to create a square.
Can someone help me with this math homework please!
Answer:
The answers are options A and C.
They are (-2,0) and (0,0).
Step-by-step explanation:
x-intercept
(-2,0) and (0,0)
American airlines requires that total outside dimensions (length+width+height) of a checked bag not exceed 62 inches.Suppose you want to check a bag whose height is same as its width.What is the biggest volumn bag of this shape that you can check on an american flight
Answer:
The maximum volume is 35316.4 in^3.
Step-by-step explanation:
Length + width + height is less than equal to 62 inches
Height = width = W
Let the length is L .
[tex]L + W + W = 62 \\\\L= 62 - 2 W\\\\Volume, V = L W H\\\\V = (62 - 2 W)\times W \times W\\\\V = 62 W^2 - 2 W^3\\\\\frac{dV}{dW}=124 W - 6 W^2\\\\So, \frac{dV}{dW} =0\\\\124 = 6 W\\\\W = 20.67 inches[/tex]
So, the maximum volume is
[tex]V =124\times 20.67\times 20.67 - 2 \times 20.67^3\\\\V =52978.86 - 17662.46 = 35316.4 inch^3[/tex]
In a recent storm, an 18-foot utility pole broke and fell leaving a 5-foot tall portion upright. How far is the top of the pole from the base of the pole?
Answer: [tex]12\ ft[/tex]
Step-by-step explanation:
Given
Total height of utility pole is 18 ft
After breakage, only 5 foot tall portion is standing
The fallen part is [tex]18-5=13\ ft[/tex] in length
From the figure, apply the Pythagoras theorem
[tex]\Rightarrow 13^2=x^2+5^2\\\Rightarrow x^2=169-25\\\Rightarrow x=\sqrt{169-25}\\\Rightarrow x=\sqrt{144}\\\Rightarrow x=12\ ft[/tex]
Thus, the fallen part is [tex]12\ ft[/tex] away from the base of the pole.
Identify the transformations of the graph of f(x) = x3 that produce the graph of the given function
g(x). Then graph g(x) on the same coordinate plane as the graph of f(x) by applying the
transformations to the reference points (-1,-1),(0,0), and (1,1).
Answer:
Step-by-step explanation:
Find the interior angle sum for the following polygon
Answer:
140 degrees
Step-by-step explanation:
(n-2) times 180
9-2 times 180
7 times 180
1260
1260/9 = 140
Interior angle sum of the given regular polygon of 9 sides is 1260°.
A regular polygon is a closed figure where all sides are equal. Interior angles of a regular polygon are the angles formed between the edges of the polygon. The formula for calculating the sum of interior angles of a regular polygon = (n-2) * 180
where, n is the number of sides of a regular polygon.
Number of sides in the regular polygon = 9
n = 9
Sum of interior angle of the regular polygon =
(n-2) * 180 = (9-2) * 180 = 7 * 180 = 1260°
Learn more about polygon here
https://brainly.com/question/17756657
#SPJ2
Point A is the incenter of △PQR. Find each measure
Answer:
[tex]\angle ARU=40^{\circ}[/tex]
AU=20 units
[tex]m\angle QPA=35^{\circ}[/tex]
Step-by-step explanation:
We are given that
[tex]\angle ARQ=40^{\circ}[/tex]
AT=20 units
Point A is the incenter of triangle PQR.
Incenter is that point where three angle bisector of triangle meets.
AR is the bisector of angle R of triangle PQR.
Therefore, [tex]\angle ARQ=\angle ARU=40^{\circ}[/tex]
All right triangles are similar when two triangles are similar then the ratio of their corresponding sides are equal.
Right angled triangle ATP and Right triangle AUP are similar.
Therefore,
[tex]\frac{AT}{AU}=\frac{AP}{AP}=1[/tex]
[tex]\frac{20}{AU}=1[/tex]
[tex]AU=20[/tex]units
AP is the angle bisector of angle P of triangle PQR
[tex]\angle APQ=\angle APU[/tex]
[tex]3x+2=4x-9[/tex]
[tex]2+9=4x-3x[/tex]
[tex]x=11[/tex]
Using the value of angle x
[tex]\angle APQ=3x+2=3(11)+2[/tex]
[tex]\angle APQ=35^{\circ}[/tex]
Hence, the measure of angle QPA=35 degree
The incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle. This point is equidistant from the sides of a triangle.
Angle ARU = 40 degree
Length of AU = 20
Angle QPA = 35 degree
Here a figure is attached.
Since, AR is angle bisector of angle URK.
So, ∠ARU = ∠ARK = 40 degree
Since, incenter point is equidistant from the sides of a triangle.
So, AT = AU = AK = 20
Since, PA is angle bisector of angle QPU.
So, ∠QPA = ∠UPA
3x + 2 = 4x - 9
4x - 3x = 9 + 2
x = 11
Substituting value of x in angle 3x + 2
We get, ∠QPA = 3(11) + 2 = 35 degree
Learn more:
https://brainly.com/question/1620555
Find the value of x. Write your answer in simplest form. WILL MAKE BRAINLIEST
============================================
Explanation:
Since we have an isosceles right triangle, the the length of the hypotenuse (let's call it y) is equal to sqrt(2) times the leg length x.
In other words, [tex]y = x*\sqrt{2}[/tex]
If we replaced y with 3*sqrt(2), then we could say,
[tex]y = x*\sqrt{2}\\\\3\sqrt{2} = x*\sqrt{2}[/tex]
in which we can see that x = 3 must be the case. Or you could divide both sides of that last equation by sqrt(2) to find x = 3.
-------------------------
Another method:
We'll use the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\x^2+x^2 = \left(3\sqrt{2}\right)^2\\\\2x^2 = 3^2*\left(\sqrt{2}\right)^2\\\\2x^2 = 9*2\\\\2x^2 = 18\\\\x^2 = 18/2\\\\x^2 = 9\\\\x = \sqrt{9}\\\\x = 3\\\\[/tex]
We get the same answer as before.
How do I find this? Please help.
Answer:
a.) r = 60ft
b.) ball_distance = 68ft
Step-by-step explanation:
Use Pythagorean theorem:
(r^2) + (32ft)^2 = (r + 8ft)^2
r^2 + 1024sqft = r^2 + (16ft)×r + 64sqft
960sqft = r×(16ft)
(960sqft) / (16ft) = r
r = 60ft
Radius is green. Ball is 8ft further than green. 68ft.
Show that 4^(x+2)+4^(x+1)+4^x is divisible by 7 for all positive integers of x.
Answer:
Below.
Step-by-step explanation:
4^(x+2)+4^(x+1)+4^x
= 4^x*4^2 + 4^x*4 + 4^4
= 4^x(16 + 4 + 1)
= 21*4^x.
As 21 is divisible by 7, 21*4^x is also divisible by 7 for all positive integers of x.
Thus the original expression must be also divisible by 7 for all positive integers of x.
3. Simplify the expression 5a - 4b - 2[a - (2b + c)]
Answer:
[tex]{ \tt{5a - 4b - 2{ (a - (2b + c))}}} \\ = { \tt{5a - 4b - 2a + 4b - 2c}} \\ { \tt{ = (5 - 2)a + ( - 4 + 4)b - 2c}} \\ { \tt{ = 3a - 2c}}[/tex]
Answer:
Step-by-step explanation:
5a - 4b -2[a - 2b + c] = 5a - 4b -2a + 4b - 2c {Distributive property}
= (5a - 2a) + (4b - 4b) - 2c {Group like terms}
= 3a - 2c
Find the missing segment in the image below
Answer:
If there are two line which is parallel in a triangle the triangle has a ratio
Step-by-step explanation:
So we can see one side has 6cm and 4cm length. and other side has 20cm in totally. But we know that the small line divided the side with 6/4 ratio and we can say ?=12 and other is 8
Answer:
Step-by-step explanation:
find the value of 2/5 - 3
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
[tex]\sf{\dfrac{2}{5}-3 }[/tex] [tex]\sf{\dfrac{2-10}{5} }[/tex] [tex]\sf{\dfrac{-8}{5} }[/tex][tex]\sf{ }[/tex]
