Step-by-step explanation:
The easiest way to do this is to imagine the microwave as a box. Ignore the turntables, whether or not something will spin if it touches an edge, and anything else that would make the fact that we're talking about a microwave confusing. This is a box now. :)
The capacity of our box is 1.59 ft^3, which means it can hold that much of "things" inside it. Instead of a capacity, we'll think of it as the box's total area. A tricky thing to note, is the area is given in ft, where the interior values are given as inches. So we'll need to turn the inches into feet.
To get the area of a box, we do length x width x height.
We're already given the length, 14 (inches), and the width, 14 (inches), so all we need to find now is the height (feet). To turn the lengths into feet, we'll divide them by 12, because there are 12 inches in 1 foot, or Feet = Inches / 12.
To finally turn it into math:
Area (A) = length (L) * width (W) * height (H)
[tex]A = L * W * H[/tex]
Insert known values.
[tex]1.59 = \frac{14}{12} * \frac{14}{12} * H[/tex]
Multiply.
[tex]1.59 = \frac{196H}{144}[/tex]
Simplify.
[tex]1.59 = \frac{49H}{36}[/tex]
Multiply both sides by 36.
[tex]1.59*36 = \frac{49H}{36}*36[/tex]
Simplify.
[tex]57.24 = 49H[/tex]
Divide both sides by 49.
[tex]\frac{57.24}{49} = \frac{49H}{49}[/tex]
Simplify.
[tex]1.16816326... = H[/tex]
To turn make this the nearest Tenth, we round up to the first decimal place.
Answer:
H = 1.2 ft
The zeros of polynomial function g are -5, -1, and 7. Complete the factors to write an equation for function g. Assume that g has only three zeros and three factors.
Answer:
g(x) = (x + 5)(x + 1)(x - 7)
Step-by-step explanation:
i know for a fact im right
The complete equation of function whose zeros are given;
f(x) = (x+5)(x+1)(x-7)
What is Polynomial?
A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number.
Here, given zeros are;
-5, -1, 7
then we can write;
x = -5, x = -1; x = 7
x +5 = 0 ; x + 1 = 0 ; x - 7 = 0
On multiplying all the terms we get;
(x+5)(x+1)(x-7) = 0
Thus, The complete equation of function whose zeros are given;
f(x) = (x+5)(x+1)(x-7)
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If the outliers are not included what is the mean of the data set 76,79,80,82,50,78,79,81,82
Answer:
The answer is 80
Step-by-step explanation:
we know that
the outlier is 50, as it is not around the other numbers in the data set.
therefore
mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9
mean=[720]/9
mean=80
Answer:
80
Step-by-step explanation:
mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9
mean=[720]/9
mean=80
enlarge shape a by 1/3 with the centre enlargement (3,-3)
(-9,9) (-9,6) (-3,6)
Answer:
0033
Step-by-step explanation:
.033 of a whole number so its .033
Translate into algebra,
the sum of twice the number x and 25 more than 3 times the number y
Answer: The expression would look like 2x+(25+3y).
Step-by-step explanation:
Let the number be x
2x+(25+3y)
The algebraic expression will be [tex]2x+(25+3y)[/tex] .
What is expression ?Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
We have,
A number [tex]x[/tex]
Number [tex]y[/tex],
The sum of twice the number [tex]x[/tex] and [tex]25[/tex] more than [tex]3[/tex] times the number [tex]y[/tex] ,
So,
According to the question,
sum of twice the number [tex]x[/tex] [tex]=2x[/tex]
And,
ore than [tex]3[/tex] times the number [tex]y[/tex] [tex]=25+3y[/tex]
Now,
The whole algebraic expression,
[tex]2x+25+3y[/tex]
Hence, we can say that the algebraic expression will be [tex]2x+(25+3y)[/tex] .
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Niko wants to put soil in his garden shown below. If soil comes in bags that fill 6 square yards each, how many bags of soil should Niko buy? Hint: you may have some leftover soil.
Answer:
444 pot soils
Step-by-step explanation:
help asap no wrong answers----------------------
Answer:
[tex]y=-2(sin(2x))-7[/tex]
Step-by-step explanation:
1. Approach
Given information:
The graph intersects the midline at (0, -7)The graph has a minimum point at ([tex]\frac{\pi}{4}[/tex], 9).What conclusions can be made about this function:
The graph is a sine function, as its y-intercept intersects the midlineThis graph has a negative coefficient, this is because after intersecting the midlines at the y-intercept, the function has a minimum.This graph does not appear to have undergone any horizontal shift, as it intercepts the midlines with its y-interceptTherefore, one has the following information figured out:
[tex]y=-n(sin(ax))+b[/tex]
Now one has to find the following information:
amplitudemidlineperiod2. Midline
The midlines can simply be defined as a line that goes through a sinusoidal function, cutting the function in half. This is represented by the constant (b). One is given that point (0, -7) is where the graph intersects the midline. The (y-coordinate) of this point is the midline. Therefore, the midline is the following:
y = -7
2. Amplitude
The amplitude is represented by the coefficient (n). It can simply be defined by the distance from the midline to point of maximum (the highest part of a sinusoidal function) or point of minimum (lowest point on the function). Since the function reaches a point of minimum after intercepting the (y-axis) at its midlines, the amplitude is a negative coefficient. One can find the absolute value of the amplitude by finding the difference of the (y-coordinate) of the point of minimum (or maximum) and the absolute value of the midline.
point of minimum: [tex](\frac{\pi}{4},9)[/tex]
midline: [tex]y=-7[/tex]
Amplitude: 9 - |-7| = 9 - 7 = 2
3. Period
The period of a sinusoidal function is the amount of time it takes to reach the same point on the wave. In essence, if one were to select any point on the sinusoidal function, and draw a line going to the right, how long would it take for that line to reach a point on the function that is identical to the point at which it started. This can be found by taking the difference of the (x- coordinate) of the intersection point of the midline, and the (x-coordinate) of the point of minimum, and multiplying it by (4).
point of minimum: [tex](\frac{\pi}{4},9)[/tex]
midline intersection: [tex](0, -7)[/tex]
Period: [tex]4(\frac{\pi}{4}-0)=4(\frac{\pi}{4})=\pi[/tex]
However, in order to input this into the function in place of the variable (a), one has to divide this number by ([tex]2\pi[/tex]).
[tex]a=\frac{2\pi}{\pi}=2[/tex]
4. Assemble the function
One now has the following solutions to the variables:
[tex]n =-16\\a=2\\b=-7\\[/tex]
Substitute these values into the function:
[tex]y=-2(sin(2x))-7[/tex]
simplify.
[tex]( { - 2})^{ - 3} [/tex]
options:
8
1/8
-8
-1/8
Answer:
-1/8
Step-by-step explanation:
Apply exponent rule ^a^-b = 1/a^B
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{2}\mathsf{^{-3}}\\\\\\\mathsf{= \dfrac{1}{-2\times-2\times-2}}\\\\\\\mathsf{-2\times-2\times-2 =\bf (-2)^{3}}\\\\\mathsf{(-2)^3}\\\mathsf{= -2\times-2\times-2}\\\mathsf{= 4\times-2}\\\mathsf{\mathsf{= \bf -8}}\\\\\\\mathsf{= -2^{-3} \rightarrow\boxed{\bf -\dfrac{1}{8}}}\large\checkmark[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: Option D. }\mathsf{\bf - \dfrac{1}{8}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the measure of arc BC?
Answer:
129
Step-by-step explanation:
Since,
AD = BC
AD = 3x + 24
BC = 4x - 11
3x + 24 = 4x - 11
4x - 11 = 3x + 24
4x - 3x = 24 + 11
x = 35
BC = 4x - 11
= 4 ( 35 ) - 11
= 140 - 11
BC = 129
Answer:
[tex]AB=BC[/tex]
[tex]3x+24=4x-11[/tex]
[tex]3x-4x=-11-24[/tex]
[tex]x=35[/tex]
[tex]BC=4\times 35-1[/tex]
[tex]=140-11[/tex]
[tex]=129[/tex]
--------------------------
Hope it helps..
Have a great day!!
In Australia, road distance is measured in kilometres.
In the USA, road distance is measured in miles.
5 miles is about the same distance as 8 kilometres.
About how many miles is 120 kilometres?
Answer:
75
Step-by-step explanation:
5 miles-8km
x miles-120 km
x=120×5÷8
x=75 (miles)
Answer:
s
Step-by-step explanation:
since 5 miles is the same as 8 kilometers,how many miles is 120 kilometers..use ratio and proportion
5miles:8kilometers
x. :120kilometers
8x/8=600/8
x=75miles
I hope this helps
WORD PROBLEM -
Sohanlal is a gardener He is paid 160 daily find how much money will he get in the month of September
GIVE ME UR ANSWERS SOON PLS
Jernel has to figure out the area of her square garage. She knows that one side of the garage is equal to the length of her rabbit pen. The dimensions of the rectangular rabbit pen are 13 by 10.
Answer:169
Step-by-step explanation:13 x 13 = 169
You would take the larger side of the pen (13) or else it wouldn’t fit if you chose 10.
HELP!!! 15 points. picture below
Step-by-step explanation:
[tex] \sin( \alpha ) = \frac{ \sqrt{5} }{3} \\ \alpha = 48.19 \: degrees \\ \cos( \alpha ) = \frac{2}{3} [/tex]
Answer:
cos theta =± 2/3
Step-by-step explanation:
sin theta = sqrt(5) /3
sin theta = opp side / hypotenuse
We know that
a^2 + b^2 = c^2 from the pythagorean theorem
opposite side ^2 + adjacent side ^2 = hypotenuse ^2
( sqrt(5)) ^2 + adjacent side ^2 = 3^2
5 + adjacent side ^2 = 9
Subtract 5 from each side
5-5 + adjacent side ^2 = 9-5
adjacent side ^2 = 4
Taking the square root of each side
adjacent side = ±2
We know that
cos theta = adj side / hyp
cos theta =± 2/3
How would I answer this: How many minutes are in a 30-day month.... use vertical multiplication to get the right answer
Answer:
There are 43200 minutes in a 30-day month.
Step-by-step explanation:
We know that:
60 minutes = 1 hour
24 hours = 1 day
Thus to determine the minutes in a 30-day month, let us first determine the number of hours in the month.
30
x 24
_______
120
60
_______
720 hours
The 30-day month has a total of 720 hours.
So that the number of minutes that make up 720 hours can be determined by;
720
x 60
_______
000
4320
_______
43200
Therefore, there are 43200 minutes in a 30-day month.
Help fast please in a test and don’t know the answer I have tried Googling and everything please help
Answer:
Surface Area = 3,543.7 cm²
Step-by-step explanation:
Surface area of the cylinder = 2πr(h + r)
Where,
radius (r) = 12 cm
height (h) = 35 cm
Plug in the values into the surface area formula
S.A = 2*π*12(35 + 12)
S.A = 24π(47)
S.A = 3,543.71651 cm²
≈ 3,543.7 cm² (approximated to the nearest tenth)
Evaluate (5.6 x 10^-4 ) - (9.3x10^-6)
Give your answer in standard form to 3SF
Answer:
I got 5.51x10^-4
Step-by-step explanation:
Answer:
.0005507
Step-by-step explanation:
5.6 x [tex]10^{-4}[/tex]
9.3 x [tex]10^{-6}[/tex]
560 x [tex]10^{-6}[/tex]
- 9.3 x [tex]10^{-6}[/tex]
550.7 x [tex]10^{-6}[/tex]
.0005507
look at photo! please help needed! 1.
Answer:
5/12
Step-by-step explanation:
it says in the question that 1/4 +1/3 is used so in order to make it simple we have to find the common denominator that is 12. so converting 1/4 is 3/12 and 1/3 is 4/12.so u add the numerator and u get 7 over 12 .so now the whole container of peanuts is 12/12 but 7/12 is used so 12-7= 5. so ur ans is 5/12
Ross walked 3 m east and 6 m north. How far is he from the starting point
Answer:
3 sqrt(5) meters
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem.
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2+6^2 = c^2
9+36 = c^2
45 = c^2
Taking the square root
sqrt(45) = sqrt(c^2)
sqrt(9*5) = c
sqrt(9) sqrt(5) =c
3sqrt(5) = c
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Given:-Ross walked 3 m east and 6 m north. Find:-How far is she from the starting point?solution:-Ross walked 3 m east and 6 m north.
so her path is a right angle triangle path.
we know that,
in a right angle triangle, According to the Pythagorean theorom,
[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]
where
l= legs b=baseh=hypotenuse According to the question, [tex]\sf{3^2+6^2=f^2 }[/tex] [tex]\sf{9+36=f^2 }[/tex] [tex]\sf{ f^2=45 }[/tex] [tex]\sf{f=\sqrt{45} }[/tex] [tex]\sf{f=3\sqrt{5} }[/tex] Therefore:-he is [tex]\sf{3\sqrt{5} }[/tex] far from the starting point
A side of the triangle below has been extended to form an exterior angle of 72°. find the value of x.
Answer:
108°
Step-by-step explanation:
The sum of angles on a straight line is 180°
Therefore:
x + 72° = 180°
x = 180° - 72°
x = 108°
Therefore, the value of x is 108°
solve: 5y +12 - 3y + 12 = 18
Answer:
5y-3y+12+12=18
2y = 18 - 24
y = -6/2
y = -3
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{5y + 12 - 3y + 12 = 18}\\\\\large\text{COMBINE the LIKE TERMS}\\\\\large\textsf{(5y - 3y) + (12 + 12) = 18}\\\\\large\text{NEW EQUATION: \textsf{2y + 24 = 18}}\\\\\large\text{SUBTRACT 24 to BOTH SIDES}\\\\\large\textsf{2y + 24 - 24 = 18 + 24}\\\\\large\text{Cancel out: \textsf{24 - 24} because it gives you 0}\\\\\large\text{Keep: \textsf{18 - 24} because it helps solve it helps solve for y}\\\\\large\textsf{18 - 24 = \bf -6}[/tex]
[tex]\large\text{NEW EQUATION: \textsf{2y = -6}}\\\\\large\text{DIVIDE 2 to BOTH SIDES}\\\\\mathsf{\dfrac{2y}{2y}=\dfrac{-6}{2}}\\\\\large\text{Cancel out: }\mathsf{\dfrac{2}{2}}\large\text{ because it gives you 1}\\\\\large\text{KEEP: }\mathsf{\dfrac{-6}{2}}\large\text{ because it gives you the y-value}\\\\\large\textsf{y = }\mathsf{\dfrac{-6}{2}}\\\\\mathsf{\dfrac{-6}{2}= \bf -3}\\\\\\\\\\\boxed{\boxed{\huge\textsf{Answer: y = \bf -3}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
Find the percentage of the following:
20/60
18/60
21/60
31/60
Answer:
20/60 = 33%
18/60 = 30%
21/60 = 35%
31/60 = 52%
Step-by-step explanation:
Just divide em'
Simple as that.
Answer:
20/60 = 33%18/60 = 30%21/60 = 35%31/60 = 51.67%I hope th is helps you I just divided the fractions by the way :)
Suppose that a1, a2, a3, . . . is an arithmetic sequence, in which a3 = 19 and a14 = 96. Find a1.
What are the coordinates of the image of L for a dilation with center (0, 0) and scale factor ?
Answer:
The vertices of ABCD:
A ( - 3, 1 )
B ( 4 , - 3 )
C ( 1, 3 )
D ( - 1 , 4 )
∴ ( 4 x, 4 y ):
A ` ( - 12, 4 )
B ` ( 16, - 12 )
C ` ( 4, 12 )
D ` ( - 4 , 16 )
Step-by-step explanation: I hope this helps! ™(*/ω＼*)
Q5. Evaluate this expression when a=6
Q6. Which option shows this expression simplified correctly?
Q7. Which option shows this expression simplified correctly?
Q8. Find the following:
Q9. Which option shows this expression expanded correctly?
3 of 9
Express the ratio below in its simplest form.
2:4:2
Answer:
1 : 2 : 1
Step-by-step explanation:
2:4:2
Divide each term by 2
2/2:4/2:2/2
1 : 2 : 1
2. A cylindrical candle has a volume of 785 cm. Determine the minimum amount of plastic which is needed to cover
the outside of the candle for packaging and find the dimensions of the candle which produce this surface area
3. A company which produces pizza ovens has had complaints about their ovens losing too much heat to be
efficient. They have decided to redesign their ovens. The ovens must have a volume of 0.512 m. Find the
optimal design for the oven so that the surface is as small as possible to minimize heat loss Calculate that
surface area.
Answer:
2. Candle dimensions: x = 6.3 cm h = 6.29 cm
A (min) = 373.49 cm²
3. Cylindrical oven dimensions: x = 0.54 m h = 0.55 m
A (min)= 1.4747 m²
Step-by-step explanation:
2.A The volume V of the cylindrical candle is 785 cm³
V = π*x²*h x is the radius of the base and h the heigh of the cylinder
The surface area A is area of the base π*x² . plus lateral area 2*π*r*h
then . A = π*x² + 2*π*x*h . h = V/π*x²
A as a function of x . is
A(x) = π*x² + 2*π*x*785/π*x²
A(x) = π*x² + 1570/x
Taking derivatives on both sides of the equation we get:
A' (x) = 2*π*x - 1570/x²
A'(x) = 0 . 2*π*x - 1570/x² = 0 . 2*π*x³ = 1570
x³ = 250
x = 6.3 cm . and . h = 785/π*x² . h = 785/124.63
h = 6.29 cm
Then dimensions of the cylindrical candle:
x = 6.3 cm h = 6.29 cm
A (min) = 3.14 * (6.3)² + 6.28*6.3*6.29
A (min) = 124.63 + 248.86
A (min) = 373.49 cm²
3. For a cylindrical oven V = 0.512 h = 0.512/ π*x²
Following the same procedure
A(x) = π*x² + 2*π*x*0.512/π*x² .A(x) = π*x² + 1024/x
A'(x) = 2* π*x - 1.024/x²
A'(x) =0 . 2* π*x - 1.024/x² =0 . 2* π*x³ . = 1.024
x³ = 0.512/π . x³ = 0.163
x = 0.54 m h = 0.512/π*x² . h = 0.55 m
A(min) = 3.14*(0.54)² + 1024/x
A(min)= 0.9156 + 0.5591
A (min)= 1.4747 m²
plzzz helpppp dont ignoreeee
Answer:
X= 40
Step-by-step explanation:
2(110 + 4x) = 220 + 8x = 540
8X = 320
X= 40
If f(x) =3x^2 +1 and g(x) = 1 -x, what is the value of (f-g) (2)?
Answer:
(f-g)(2) = 14
Step-by-step explanation:
f(x) =3x^2 +1 and g(x) = 1 -x
f(2) = 3(2)^2 +1 = 3(4)+1 = 12+1 = 13
g(2) = 1-2 = -1
f(2) - g(2) = 13 - -1 = 13+1 =14
Answer:
14
Step-by-step explanation:
(f-g)(2) means f of x minus g of x when x equals 2.
To solve, first set up the equation
[tex](3x^2}+1)-(1-x)[/tex]
Change the signs in the second part. {because this is subtraction}
[tex]3x^2}+1-1+x[/tex]
Replace x with 2.
[tex]3(2^2})+1-1+2[/tex]
Solve.
[tex]3(4)+2[/tex]
[tex]12+2[/tex]
[tex]14[/tex]
solve for x−4 + x ≤ 9
Answer:
x ≤ 6.5
Step-by-step explanation:
x−4 + x ≤ 9
Combine like terms
2x-4≤ 9
Add 4 to each side
2x-4+4≤ 9+4
2x≤ 13
Divide by 2
2x/2 ≤ 13/2
x ≤ 6.5
The function f(x) = log4x is dilated to become g(x) = f (1/3x).
What is the effect on f(x)?
Given:
The functions are:
[tex]f(x)=\log_4x[/tex]
[tex]g(x)=f\left(\dfrac{1}{3}x\right)[/tex]
The function f(x) is dilated to become g(x).
To find:
The effect on f(x).
Solution:
Transformation is defined as:
[tex]g(x)=f(kx)[/tex] ...(i)
Where, k is the factor of horizontal stretch and compression.
If 0<k<1, then the graph of f(x) stretched horizontally by factor [tex]\dfrac{1}{k}[/tex].
If k>1, then the graph of f(x) compressed horizontally by factor [tex]\dfrac{1}{k}[/tex].
It is given that
[tex]g(x)=f\left(\dfrac{1}{3}x\right)[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]k=\dfrac{1}{3}[/tex]
Therefore, the graph of f(x) stretched horizontally by factor [tex]3[/tex].
Strat with k add 2 multiply by 6 then subtract 8
Answer:
6(k+2) -8
Step-by-step explanation:
Start with k
k
Add 2
(k+2)
Multiply by 6
6(k+2)
Then subtract 8
6(k+2) -8
6(k+2)-8 is a required answer.
Answer:
Solution given:
Start with k.
Kadd 2
k+2multiply by six
(k+2)*6subtract by 8
6(k+2)-8