a microwave oven has a capacity of 1.59ft³. the interior of the microwave of the is 14 in wide and 14 in deep. what is the height of the interior of the microwave, to the nearest tenth of a foot​

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°

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]

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!!

Answer:

444 pot soils

Step-by-step explanation:

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]

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].

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)

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.

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]

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

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.

add 2

multiply by six

subtract by 8

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

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

Answer:

20/60 = 33%

18/60 = 30%

21/60 = 35%

31/60 = 52%

Step-by-step explanation:

Just divide em'

Simple as that.

Answer:

I hope th is helps you I just divided the fractions by the way :)

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

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

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] .

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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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.

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

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]

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

he is [tex]\sf{3\sqrt{5} }[/tex] far from the starting point

Answer:

X= 40

Step-by-step explanation:

2(110 + 4x) = 220 + 8x = 540

8X = 320

X= 40

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)

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)

Learn more about Polynomial from:

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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

Answer:

[tex]y=-2(sin(2x))-7[/tex]

Step-by-step explanation:

1. Approach

Given information:

What conclusions can be made about this function:

Therefore, one has the following information figured out:

[tex]y=-n(sin(ax))+b[/tex]

Now one has to find the following information:

2. 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]

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

Answer:

0033

Step-by-step explanation:

.033 of a whole number so its .033

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＼*)