Solve for x to find the value that makes these ratios proportional. x/12 = 5/7 ​

Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Answer:

(x + 4)^2 + (y + 7)^2 = 36

Step-by-step explanation:

The given information describes a circle with its center at (-4, -7) and tangent to the vertical line x = 2. To determine the radius of the circle, we need to find the distance between the center and the tangent line.

The distance between a point (x1, y1) and a line Ax + By + C = 0 is given by:

d = |Ax1 + By1 + C| / sqrt(A^2 + B^2)

In this case, the equation of the line is x = 2, which can be written as 1x + 0y - 2 = 0. Therefore, A = 1, B = 0, and C = -2. The center of the circle is (-4, -7), so x1 = -4 and y1 = -7. Substituting these values into the formula, we get:

d = |1*(-4) + 0*(-7) - 2| / sqrt(1^2 + 0^2)

d = |-6| / sqrt(1)

d = 6

Therefore, the radius of the circle is 6 units. The equation of a circle with center (h,k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values we have found, we get:

(x + 4)^2 + (y + 7)^2 = 36

This is the equation of the circle that satisfies the given conditions.

Answer:

True

Step-by-step explanation:

15/7 is about 2.14 which is less than 3

Answer:

\(P = 48 in\),\(A= 120in^2\)

Step-by-step explanation:

Again we can use Pythagorean theorem to find the missing side

x^2 + 15^2 = 17^2

x^2 + 225 = 289

Subtract 225 from both sides

x^2 = 64

Find the square root of both sides

√x^2 = √64

x = 8

So

l = 15in, w = 8in

P=2(15) + 2(8)

P = 30 + 18

P = 48 in

A= 15(8)

A= 120in^2

The total volume of the continental Antarctica ice sheet, as a basic numeral. 31,000,000 km³.

The space occupied by any solid in a three-dimensional space is called the volume of the solid. For Antarctica, the volume will be the space occupied by the ice present in three-dimensional space.

Let us first gather the information needed Land area of Antarctica = 14,000,000 KM squared

The average thickness of Antarctic ice = 2.15 KM

Earth’s oceans cover a total surface area of 340,000,000 KM²

The ice melts into water, the resulting water volume is about 5/6 of the original ice.

(5/6) x  (14,000,000 km) x (2.15 km) = 340,000,000 km

14,000,000km² x 2.15km = 31,000,000 km³

Therefore, the total volume of the continental Antarctica ice sheet is a basic numeral. 31,000,000 km³.

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Answer: the correct value of x in this will be 6.

Step-by-step explanation: According to the equation given ,

f(x) = 64

so , f(x) = 11x - 2 now putting the value of f(x) in this equation

therefore , 64 = 11x - 2

now solving the equation , 11x= 64+2

11x = 66

x = 66/11

x = 6

thus, the value of x obtained from the equation is 6

Answer:

About 8.2 years.

Step-by-step explanation:

The minivan was purchased for $35,000 and it depreciates according to the function:

\(\displaystyle V(t)=35000\Big(\frac{1}{2}\Big)^{t/3}\)

Where t is the time in years.

And we want to determine how long it will take for the minivan to depreciate to 15% of its initial value.

First, find 15% of the initial value. This will be:

\(0.15(35000)=5250\)

Therefore:

\(\displaystyle 5250=35000\Big(\frac{1}{2}\Big)^{t/3}\)

Solve for t. Divide both sides by 35000:

\(\displaystyle 0.15=\Big(\frac{1}{2}\Big)^{t/3}\)

We can take the natural log of both sides:

\(\displaystyle \ln(0.15)=\ln(0.5^{t/3})\)

Using logarithmic properties:

\(\displaystyle \ln(0.15)=\frac{t}{3}\ln(0.5)\)

Therefore:

\(\displaystyle t=\frac{3\ln(0.15)}{\ln(0.5)}=8.2108...\)

So, it will take about 8.2 years for Tenzin's minivan to depreciate to 15% of its initival value.

Answer:

a. For the function:

f(x) = { sin x/3, if x ≤ π

{ x√3/2π, if x > π

I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:

lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2

II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:

lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2

III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:

lim f(x) as x approaches π = √3/2

b. For the function:

f(x) = (x^2 - 36)/√(x^2 - 12x + 36)

I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0

Substituting x = 6 - h into the function, we get:

f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]

= [h^2 - 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 - h) = h(h - 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12

II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:

lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0

Substituting x = 6 + h into the function, we get:

f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]

= [h^2 + 12h]/√[h^2]

Simplifying the numerator and denominator separately, we get:

f(6 + h) = h(h + 12)/|h|

Since h approaches 0 from the positive side, we have:

lim f(6 + h) as h approaches 0+ = lim h(h +

Step-by-step explanation:

SOLUTION:

Case: Rate

Method:

2/3 of the wind distance is:

Since the direction is against the wind, the speed with during the wind is:

Speed without the wind

The rate of the wind is:

24 - 16 = 8 m per min

Final answer:

8 meters per minute

Answer:

Step-by-step explanation:

Answer:

\(\fbox{\begin{minipage}{4em}Yes, it is\end{minipage}}\)

Step-by-step explanation:

3x - 6y = 24

Divide both sides by 6:

(3/6)x - (6/6)y = 24/6

Simplify:

(1/2)x - y = 4

Move y to the right side, 4 to the left side, and change sign of y and 4:

(1/2)x - 4 = y

Rearrange both sides:

y= (1/2)x - 4

Hope this helps!

:)

The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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Answer:

C

Step-by-step explanation:

Aaron received four stamps. He already had eight times as much. 32 + 4. Before pasting the stamps into albums, Aaron divides them equally into three envelopes. (32 + 4) ÷ 3.

The 19th term of a geometric sequence is 1048576.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

a = 4 and r = 2

The nth term of a geometric sequence.

= a\(r^{n-1}\)

Now,

The 19th term of a geometric sequence.

= a\(r^{n-1}\)

Substituting a and r values.

= 4 x \(2^{19 - 1}\)

= 4  x \(2^{18}\)

= 4 x 262144

= 1048576

Thus,

The 19th term of a geometric sequence is 1048576.

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Answer:

-6x

Step-by-step explanation:

2x - 8x = -6x

The restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.

Sale refers to the transfer of ownership of goods or services from one person to another in exchange for money or other consideration.

The total purchase price of the franchise naming rights and physical property was $1,250,000.

To calculate the amount paid for each individual element of the sale, the total purchase price must be divided by the two elements.

The total purchase price of $1,250,000 divided by two elements equals $625,000.

This means that the restaurant chain paid $625,000 for the franchise naming rights and $625,000 for the physical property.

The amount of money paid for the franchise naming rights (four times the cost of buying the physical property) can be calculated by multiplying the cost of the physical property, which is

$625,000/4 .

When the cost of the physical property is multiplied by four, the result is $2,500,000.

This means that the restaurant chain paid $2,500,000 for the franchise naming rights.

In summary, the restaurant chain paid $625,000 for the physical property and $2,500,000 for the franchise naming rights, for a total purchase price of $1,250,000.

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The decimal number that is multiplied by 10 must be less than a two-digit number.

We move the decimal point to the left for this problem and stop where the decimal is less than a two-digit number.

So, 956.3 becomes 9.56 after moving two places to the left. Moving to the left makes the exponent of 10 positive. Moving to the right, makes the exponent of 10 negative.

We want our answer in the form

(decimal number) x 10^(n).

Answer: 9.56 x 10^2

Understand???

Answer:

angle 10

FYI:

angle 10 or 12 is adjacent to 9

(they share an adjacent arm)

angle 11 is opposite adjacent to angle 9.

1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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Yes, it is significant evidence of a difference between the age distribution of jurors and the countrywide age distribution.

No, there is no age bias in the selection of jurors.

P             Oi       Ei        ( Oi-Ei) ^2/Ei

0.421     399     421     1.149643705

0.229     231     229     0.017467249

0.157     158     157     0.006369427

0.193     193     193     1.870466321

  1         1000  1000    3.043946702

The above can be represented in graphs.

Now,

Ei = n × pi

TS = 3.04394672

From TS < value

Value (7.81472)

We fail to reject the null hypothesis at 5% value of significance

No, there is no age bias in the selection of jurors.

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The area of the region enclosed by the curves can be found to be 1/6 square units.

To find the area enclosed by the curves y = x, y = 5x, and y = -x + 2, we first need to find the points where these curves intersect.

Intersection points of y = x and y = 5x: (0, 0)

Intersection points of y = x and y = -x + 2: Intersection point: (1, 1)

Intersection points of y = 5x and y = -x + 2: Intersection point: (1/3, 5/3)

Now we have the three intersection points: (0, 0), (1, 1), and (1/3, 5/3). The area enclosed by the curves is a triangle with vertices at these points.

To find the area of the triangle, we can use the Shoelace Formula:

Area = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Area = (1/2)|0(1 - 5/3) + 1(5/3 - 0) + (1/3)(0 - 1)|

Area = 1 / 6 square units

The area enclosed by the curves is 1/6 square units.

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Answer:

No.

Step-by-step explanation:

Associative property, for example, is the process of grouping numbers to find the sum. With this law, you also can multiply/add these numbers together and it will not affect your final answer. In this case, that's not the case. So, the statement is false.

Answer:

2, 3  and 5

Step-by-step explanation:

Answer:

2,3,5

Step-by-step explanation:

Answer:

The depth is 127 inches.

Step-by-step explanation:

The stairway and its depth can be compared to a right angled triangle. Let the depth be represented by d.

But,

12 inches = 1 foot

20 ft 6 in = 20 + \((\frac{6}{12} )\)

               = 20.5 feet

So that applying the appropriate trigonometric function, we have;

Sin θ = \(\frac{opposite}{hypotenuse}\)

Sin 31º = \(\frac{d}{20.5}\)

d = 20.5 x Sin 31º

   = 20.5 x 0.5150

d = 10.5575

d ≅ 11 feet

Therefore,

d = 10.5575 feet = (10.5575 x 12) inches

  = 126.69 inches

The depth is 127 inches.

Answer:

A it's a because 45 x 10³ is 75

The solutions for the quadratic equation:

x^2 - 8x = -3

Are:

Here we want to solve the quadratic equation:

x^2 - 8x = -3

First we can move all the terms to the left side so we get:

x^2 - 8x + 3 = 0

Using the quadratic formula (or Bhaskara's formula) we can get the solutions for x as:

\(x = \frac{8 \pm \sqrt{(-8)^2 - 4*¨1*3} }{2*1} \\\\x = \frac{8 \pm 7.2 }{2}\)

Then the two solutions for the quadratic equation are:

x = (8 + 7.2)/2 = 7.6

x = (8 - 7.2)/2 =0.4

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The area above x axis is 12.6 sq units while the area under the y-axis is 42.443 sq units. The change in the average phone bill is 29.843 units.

a) Here we see that the graph is in the shape of a right-angled triangle above the x-axis

The area of a triangle = 1/2 X Base X Height

Here the base will be the measure of the distance of co-ordinates on the x-axis

The height is the distance between the coordinates on the axis for that triangle

= 1/2 X (16 - 8) X (3.15 - 0)

= 1/2 X 8 X 3.15

= 12.60 sq units

b)

Below the x-axis, the graph is a rectangle and a triangle

The area of the rectangle = length X width

Here length is the distance of the co-ordinates of the y-axis and width is the distance between the coordinates for the x-axis

Hence we get

(0 - (-5.14))(8 - 0)

= 5.14 X 8

= 41.12 sq units for the rectangle.

The area of the triangle will be

1/2 X (18 - 15.48) X (0 - (-1.05))

1/2 X 2.52 X 1.05

= 1.323 sq unit

Hence, the total area is

41.12 + 1.323

= 42.443 sq unit

c)

Since the area under the graph represents change,

Here we see that the change in the average cell phone bill will be

42.443 + 12.6

= 55.043

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Complete Question

(Image Attached)

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation: