Solve: 512^x-2/(1/64)^3x=512

Answer:

30

Step-by-step explanation:

unknown number = x

3/10 × x = 9

3x/10 = 9

3x = 90

x = 30

Answer:

2.7  or 2 7/10.

Step-by-step explanation:

9 * 3/10

= 27 / 10

= 2.7.

Answer:

$390

Step-by-step explanation:

3250 x 0.12 = 390

Answer:

The answer is $390

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image for the step by step explanation for the answer to the question

Answer:

height = 142.00 ft

height ≈ 200. 82 ft

height ≈ 245.95 ft

Step-by-step explanation:

The picture below represent the image of the draw bridge. The illustration will form a right angle triangle. The hypotenuse is each half of the drawbridge which is 284 ft long. The opposite side  of the triangle is facing the drawbridge half leg and the adjacent side is horizontal length. This is the side that made the angle with the drawbridge half leg(hypotenuse).

The question ask us to find the height of the drawbridge when it rise which is the opposite sides of the triangle when the angle is 30° , 45° and  60°.

Using SOHCAHTOA principle,

Angle 30°

sin 30° = opposite/hypotenuse

sin 30°  = height/284

cross multiply

height = 0.5 × 284

height = 142.00 ft

Angle 45°

sin 45° = height/284

height = 284 × 0.70710678118

height = 200.818325857

height ≈ 200. 82 ft

Angle 60°

sin 60 = height/284

cross multiply

height = 0.86602540378  × 284

height = 245.951214675

height ≈ 245.95 ft

The question asks about the height a drawbridge rises at different angles. This is a trigonometry problem that can be solved by using the sine of the angle to calculate the height of the bridge when raised. The height corresponds to the 'opposite' side in a right triangle formed by the raised drawbridge.

This question appears to be asking about how high a drawbridge rises based on an angle, x, which is a trigonometry problem. Assuming that the drawbridge forms a right triangle when it rises, the height can be calculated using the sine of the angle, x. Sine of x is equal to the opposite side (height of the bridge when it is raised) over the hypotenuse (half of the drawbridge's length).

Applying these trigonometric principles, calculations for each scenario would look like the following:

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Answer:A & B

Step-by-step explanation:

Answer:

[tex](-\infty, 0)[/tex]

Step-by-step explanation:

(w circle r) (x) is the composite function(w of r(x)), that is, w(r(x))[/tex]

We have that:

[tex]r(x) = 2 - x^{2}[/tex]

[tex]w(x) = x - 2[/tex]

Composite function:

[tex]w(r(x)) = w(2 - x^{2}} = 2 - x^{2} - 2 = -x^{2}[/tex]

[tex]-x^{2}[/tex] is a negative parabola with vertex at the original.

So the range(the values that y assumes), is:

[tex](-\infty, 0)[/tex]

The range of (w circle r) (x) will be (-∞,0). Option A is correct.

A connection between independent variables and the dependent variable is defined by the function.

Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.

The relation between them is shown as y if dependent and x is the independent variable;

Given functions;

[tex]\rm r(x) =2- x^2 \\\\ w(x) =x-2[/tex]

The composite function is found as;

[tex]\rm w(r(x))=w(2-x^2 = 2-x^2-2)\\\\ w(r(x))= -x^2[/tex]

-x² is graphed and shows the negative parabola

The range of (w circle r) (x) will be (-∞,0).

Hence, option A is correct.

To learn more about the function refer to the link https://brainly.com/question/12431044.

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Answer:

36/27

Step-by-step explanation:

simplified is  4/3

Answer:

For this case is the rectangle is dilated a factor of 2.2 we assume that the expansion is in all the dimensions so then the new length and width are:

[tex] L_f = 2.2 L_i= 2.2* 7.5 in = 16.5 in[/tex]

[tex] W_f = 2.2 w_i = 2.2 * 3 in = 6.6 in[/tex]

Step-by-step explanation:

The area of a rectangle is given by [tex] A = L *W[/tex]

For this case is the rectangle is dilated a factor of 2.2 we assume that the expansion is in all the dimensions so then the new length and width are:

[tex] L_f = 2.2 L_i= 2.2* 7.5 in = 16.5 in[/tex]

[tex] W_f = 2.2 w_i = 2.2 * 3 in = 6.6 in[/tex]

And the area would be (2.2)^2 times the initial area since is defined as [tex]A = L_f W_f [/tex]

Answer:

The length and the width of the new rectangle are 16.5 inches and 6.6 inches respectively

Step-by-step explanation:

Given

Shape: Rectangle

[tex]Length = 7.5 inches[/tex]

[tex]Width = 3 inches[/tex]

[tex]Scale factor = 2.2[/tex]

Required

Dimension of the new rectangle

The dimensions of the new rectangle can be solved by multiplying the scale factor by the old dimensions;

This means that

New Length = Scale factor * Old Length

and

New Width = Scale factor * Old Width

Calculating the new length

New Length = Scale factor * Old Length

Substitute 2.2 for scale factor and 7.5 for old length; This gives

[tex]New Length = 2.2 * 7.5 inches[/tex]

[tex]New Length = 16.5 inches[/tex]

Calculating the new width

New Width = Scale factor * Old Width

Substitute 2.2 for scale factor and 3 for old width; This gives

[tex]New Width = 2.2 * 3 inches[/tex]

[tex]New Width= 6.6 inches[/tex]

Hence, the length and the width of the new rectangle are 16.5 inches and 6.6 inches respectively

Answer:

96.12

Step-by-step explanation:

89x.0.08 is 7.12 add that to 89 gives you 96.12

Answer:

67%

Step-by-step explanation:

500=50*x*15

500=750*x

500/750=x

.666666666=x

.67=x

67%=x

Answer:

Average speed v = 83.8 km/h

Step-by-step explanation:

Given;

Distance travelled = 95 km

Time taken t = 12.23 - 11.15 = 1 hour 8 minutes

t = 1 + 8/60 hours = 1.133 hours.

Average speed v = distance travelled/time taken

substituting the values;

v = 95 km ÷ 1.133 hours

Average speed v = 83.8 km/h

Step-by-step explanation:

12 to the 2nd power=144

15 to the 2nd power =225

225-144=81

square root of 81 is 9

Answer:

11/15 pi radians

Step-by-step explanation:

To convert from degrees to radians, multiply by pi/180

132 * pi/180

11/15 pi

Answer:

2.304 radians

hope this helps :)

Answer:28 green and 35 red

Step-by-step explanation:

Given

If there are r red counter and g green counter then

Probability of drawing a green counter is [tex]P(g)=\frac{4}{9}[/tex]

and [tex]P(g)=\frac{\text{No of g counter}}{\text{Total no of counter}}[/tex]

Thus [tex]\frac{\text{No of g counter}}{\text{Total no of counter}}=\frac{4}{9}[/tex]

[tex]\frac{g}{g+r}=\frac{4}{9}[/tex]

[tex]\Rightarrow 9g=4g+4r[/tex]

[tex]\Rightarrow 5g=4r\quad \ldots(i)[/tex]

Also if 4 red and 2 green counter is added the probability of drawing a green counter is

[tex]P(g)=\frac{10}{23}=\frac{\text{No of g counter}}{\text{Total no of counter}}[/tex]

[tex]\Rightarrow \frac{10}{23}=\frac{g+2}{g+2+r+4}[/tex]

[tex]\Rightarrow \frac{10}{23}=\frac{g+2}{g+r+6}[/tex]

[tex]\Rightarrow 10g+10r+60=23g+46[/tex]

[tex]\Rightarrow 10r+14=13g\ quad \ldots(ii)[/tex]

Substitute the value of g in equation (ii)[/tex]

[tex]\Rightarrow 10\times \frac{5}{4}g+14=13g[/tex]

[tex]\Rightarrow \frac{25}{2}g+14=13g[/tex]

[tex]\Rightarrow g=28[/tex]

Therefore [tex]r=35[/tex]

Thus there 28 green counter and 35 red counter

Answer:

-23

Step-by-step explanation:

PEMDAS says to multiply first, so we multiply 4 by -4 and get -16.

Now the equation is -7 - 16. Change the subtraction sign into addition and the negative 16 into a positive, and the equation is -7 + -16.

-7 + -16 is -23.

We have been given that in △CDE , CD=10 , DE=7 , and m∠E=62 degrees. We are asked to find the measure of angle D.

We will use law of sines to solve our given problem.

[tex]\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}[/tex], where, a, b and c are opposite sides to angles A, B and C respectively.

First of all we will find measure of angle C as:

[tex]\frac{7}{\sin(C)}=\frac{10}{\sin(62^{\circ})}[/tex]

[tex]\sin(C)=\frac{7\cdot \sin(62^{\circ})}{10}[/tex]

[tex]\sin(C)=\frac{7\cdot 0.882947592859}{10}[/tex]

[tex]\sin(C)=0.6180633150013[/tex]

Now we will use arcsin to solve for C as:

[tex]C=\sin^{-1}(0.6180633150013)[/tex]

[tex]C=38.174844995363^{\circ}[/tex]

[tex]C\approx 38.2^{\circ}[/tex]

Now we will use angle sum property to find measure of angle D.

[tex]\angle D+\angle C+\angle E=180^{\circ}[/tex]

[tex]\angle D+38.2^{\circ}+62^{\circ}=180^{\circ}[/tex]

[tex]\angle D+100.2^{\circ}=180^{\circ}[/tex]

[tex]\angle D+100.2^{\circ}-100.2^{\circ}=180^{\circ}-100.2^{\circ}[/tex]

[tex]\angle D=79.8^{\circ}[/tex]

Therefore, the measure of angle D is approximately [tex]79.8^{\circ}[/tex].

  Measure of angle D will be 79.8°.

          [tex]\frac{c}{\text{sinC}}= \frac{d}{\text{sinD}}= \frac{e}{\text{sinE}}[/tex]

        Here, c, d and e are the sides and C, D, E are the angles opposite

        to these sides of the given triangle.

Given in the question,

In ΔCDE,

CD = 10 units

DE = 7 units

m∠E = 62°

By applying sine rule,

[tex]\frac{7}{\text{sinC}}= \frac{d}{\text{sinD}}= \frac{10}{\text{sin(62)}}[/tex]

[tex]\frac{7}{\text{sinC}}= \frac{10}{\text{sin(62)}}[/tex]

[tex]\text{sin(C)}=\frac{\text{sin(62)}\times 7}{10}[/tex]

          [tex]=0.618063[/tex]

C = [tex]\text{sin}^{-1}(0.618063)[/tex]

C = 38.175°

   ≈ 38.2°

By triangle sum theorem of a triangle,

m∠C + m∠D + m∠E = 180°

38.2 + m∠D + 62° = 180°

m∠D = 79.8°

       Therefore, measure of angle D will be 79.8°.

Learn more about the sine rule here,

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Answer:

Step-by-step explanation:

Hello!

Full text:

Here are the low temperatures (in degrees Fahrenheit) for one week in Montreal, Canada:

                          -3.5ºF, 5ºF, 1.5ºF, -0.5ºF, -2ºF, 2.5ºF, -4ºF

Compare the weather on two different days using an inequality. Then see if their comparisons change by finding the absolute value of each.

You have to choose two days at random and compare the values of temperature registered those days and compare them, for example:

Day 1: 3rd day: 1.5ºF

Day 2: 7nth day: -4ºF

Comparison of Day 1 and Day 2:

Remember:

"<" indicates that the value from the left is less than the value from the right.

">" indicates that the value from the left is greater than the value from the right.

The temperature registered on Day 1 is 1.5ºF and the temperature registered on Day 2 is -4ºF, as you notice the second temperature is negative and therefore is less than the first temperature:

                                            1.5ºF > -4ºF

Comparison of days with absolute value:

To compare absolute values you have to disregard the sign and consider only the number of the temperature:

|Day 1|= |1.5ºF|

|Day 2|= |4ºF|

Then the registered temperature of Day 1 is less than the registered temperature on Day 2:

                                              |1.5ºF| < |4ºF|

I hope this helps!

Answer:

-4ºF and 1.5ºF

Step-by-step explanation:

Answer:

t = 54 seconds

Step-by-step explanation:

The equation that models the path of a rocket into the air is given by :

[tex]h(t)= -16t^2+864t[/tex]

It is required to find the time after which the rocket will hit the ground. When it hits the ground, the height of the rocket will becomes zero. It means,

h(t) = 0

i.e.

[tex]-16t^2+864t=0\\\\16t(-t+54)=0\\\\16t=0, -t+54=0\\\\t=0\ and\ t=54\ s[/tex]

It means after 54 seconds, the rocket will hit the ground.

Answer:

(2,0)

Step-by-step explanation:

Solve by graphing:

Use a graphing tool to graph the lines y=2x -4 and y = -x+2.

The lines intercept at point (2,0).

Therefore, the solution to the set of equations is (2,0).

[tex]x=2\\y=0[/tex]

Brainilest Appreciated!

Answer:

(0, -4) and (2,0)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the limit function

Lim x → 2: f(x)

1. When f(x) = 9

Then,

From limit theorem

Lim x → xo: K = K

Where k is a constant. Then, the limit of a constant is that constant.

Lim x → 2: 9 = 9

So limit is 9.

2. Lim x → 2: f(x)

Lim x → 2: x

When x = 2

Lim x → 2: 2 = 2

Then, x = 2.

Answer:

2 nights

Step-by-step explanation:

We need to find how many nights Francesca will have to spend to knit the rest of the scarf.

First, we have to find how much she has left to knit, and then find how many nights it will take her.

She has already knit 28 centimeters of scarf.

She wants to knit a total of 42 centimeters of scarf.

Therefore, the length of scarf left to knit is:

42 - 28 = 14 centimeters

She can knit 7 centimeters each night.

Therefore, the number of nights more she needs to knit 14 centimeters is:

14 / 7 = 2 nights

She will spend 2 nights to knit a total of 42 centimeters of scarf.

Answer:

there are more magnets that  longer than 2 1/2

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

From the photo, we can see that:

Length of the magnet:

=> the total number of magnets that  longer than 2 1/2 are: 4+1+2 = 7

=> the total number of magnets that  shorter than 2 1/2 are: 1+2+3 = 6

Hence, there are more magnets that  longer than 2 1/2

Hope it will find you well.

Answer:

Step-by-step explanation:

Answer:

The restrictions partly depend on the type of function.

You can’t divide by  0

You can’t take the square (or other even) root of a negative number, as the result will not be a real number.

In what kind of functions would these two issues occur?

the function is a rational function and the denominator is  

0

for some value or values of x,  

f ( x ) = x + 1 2− x

is a rational function

the function is a radical function with an even index (such as a square root), and the radic and can be negative for some value or values of x.  

f ( x ) = √ 7 − x

is a radical function

The following table gives examples of domain restrictions for several different rational functions.

Hope this helped

Answer:

The answer is 6.

Step-by-step explanation:

Answer:

75 percent

Step-by-step explanation:

3/4 = 75%

75 - 56 = 19%

Answer:

  (a)  a maximum of 130 and a lower quartile of 10

Step-by-step explanation:

The whiskers of a box plot extend from the minimum to the maximum. The box ranges from the lower quartile to the upper quartile. The middle line divides the box at the median.

Your plot has ...

The maximum and lower quartile are correctly described as 130 and 10, respectively.

Answer:

A. a maximum of 130 and a lower quartile of 10

Step-by-step explanation:

Answer: D- 1,728

Step-by-step explanation: I did the quiz

Answer:

d

Step-by-step explanation:

Answer:

13n + 52 + 91m

Step-by-step explanation:

you multiply 13 by every number in the parenthesis

13×n=13n

13×4=52

13×7m=91m

Answer:

The answer is 20

Step-by-step explanation:

Given that the smallest angle of rotation for a regular hexagon is 18°. We are to find the number of sides of the polygon. Since the polygon is regular, so all its sides and angles are equal.

Answer:

its 20

Step-by-step explanation:

got it right on my test

Answer:

Value of h greater than 5.4 will make inequality false.

Step-by-step explanation:

This question is incomplete; here is the complete question.

The Jones family has saved a maximum of $750 for their family vacation to the beach. While planning the trip, they determine that the hotel will average $125 a night and tickets for scuba diving are $75. The inequality can be used to determine the number of nights the Jones family could spend at the hotel 750 ≥ 75 + 125h. What value of h does NOT make the inequality true?

From the given question,

Per night expense (expected) = $125

If Jones family stays in the hotel for 'h' days then total expenditure on stay = $125h

Charges for scuba diving = $75

Total charges for stay and scuba diving = $(125h + 75)

Since Jones family has saved $750 for the vacation trip so inequality representing the expenses will be,

125h + 75 ≤ 750

125h ≤ 675

h ≤ [tex]\frac{675}{125}[/tex]

h ≤ 5.4

That means number of days for stay should be less than equal to 5.4

and any value of h greater than 5.4 will make the inequality false.