What is the value of x in 15x-15=30

Answer:

[tex]d) \ 55\textdegree[/tex]

Step-by-step explanation:

-we apply the relationship of chords intersecting within a circle:

-when two chords intersect to form a vertex of an angle within a circle, the measure of the angle is equal to one-half the sum of the measures of the two arcs intercepted by the angle and its vertical angle:

[tex]\angle AFE=0.5(arc\ EA +arc \ BD)\\\\=0.5(40+70)\\\\=55\textdegree[/tex]

Hence, the measure of ∠AFE is 55°

The volume of rotation of region R is [tex]192\pi[/tex] cubic units.

Given information:

Region R is bounded by the lines y=4, x=6, the y-axis and the x-axis.

Region R is rotated about the line y=-2.

So, the region R is a rectangle with length 6 units (x=0 to x=6), and the height of the rectangle is 4 units (y=0 to y=4).

After rotating this rectangle about y=-2, we will get a hollow cylinder.

The outer radius of the cylinder will be,

[tex]R=4-(-2)=6[/tex]

The inner radius of the cylinder will be,

[tex]r=0-(-2)=2[/tex]

And the length of the cylinder is 6 units.

So, the volume of the solid formed after the rotation will be,

[tex]V=\pi R^2L-\pi r^2L\\V=\pi L(R^2-r^2)\\V=\pi \times 6(6^2-2^2)\\V=\pi\times 6 \times 32\\V=192\pi[/tex]

Therefore, the volume of rotation of region R is [tex]192\pi[/tex] cubic units.

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To find the volume of the solid formed by rotating region R about the line y=-2, we use the washer method which results in a volume of 216π cubic units.

The problem involves calculating the volume of a solid of revolution, which is formed when a two-dimensional region is rotated around a line that does not intersect the region.

Region R is defined as the area bounded by y=4, x=6, the y-axis, and the x-axis. The volume of the solid formed by rotating this region around the line y=-2 can be calculated using the washer method, which involves integrating over the area of concentric washers.

The general formula for the volume V of a washer is given by V = π∫[R2(x) - r2(x)]dx , where R(x) and r(x) are the outer and inner radii of the washers, respectively. In this case, the outer radius is R(x) = 4 - (-2) = 6 and the inner radius is r(x) = -2 - (-2) = 0.

Therefore, the volume V is:

V = π∫06[62 - 02 ]dx = π∫0636dx = 36π∫06dx = 36π[6] = 216π cubic units.

Answer:

$0.41

Step-by-step explanation:

Take the total cost and divide by the number of cans

2.46/ 6

.41

The price is 41 cents per can or$.41

Answer:

0.65 kilograms

Step-by-step explanation:

Answer:

0.65 kg

Step-by-step explanation:

[tex] \because \: 1 \: gram = \frac{1}{1000} kg \\ \\ \therefore \: 650 \: grams = \frac{650}{1000} \\ \\ \red{ \boxed{\bold {\therefore \: 650 \: grams =0.65 \: kg} }}[/tex]

Answer:

-3,8

Step-by-step explanation:

1) we can factor this since this quadratic function is in the form of

ax^2+bx+c

where we need to find out what*what=c

and what+what=b

since c is -24 and b is -5 we need to figure out the factors of -24 which equal -5:

-8+3=-5

and

-8*3=-24

hence -8 and 3 is our factors, next we will substitute them in place of "b"

so

n^2-8n+3n-24

split this equation in two groups:

group 1) n^2-8n

group 2) 3n-24

gcf of group 1= n

so

n(n-8)

gcf of group 2: 3

so

3(n-8)

next take numbers outside of parentheses and group them together:

so (n+3) (n-8)=0

since  anything times 0 is equal to 0, either (n+3) is 0 or (n-8) is 0

so

n+3=0

n=-3

n-8=0

n=8

hence n=-3,8

Hope this helps!

Answer: r=0.8

Step-by-step explanation:

4r + 8 = 7.2 + 5r

-4r             -4r

8=7.2+r

8-7.2=r

0.8=r

Answer: [tex]r=0.8[/tex]

Step-by-step explanation:

-Solve:

[tex]4r+8=7.2+5r[/tex]

-Subtract [tex]5r[/tex] from both sides:

[tex]4r+8-5r=7.2[/tex]

Combine [tex]4r[/tex] and [tex]5r[/tex] to get [tex]-r[/tex]:

[tex]-r+8=7.2[/tex]

-Subtract [tex]8[/tex] from [tex]7.2[/tex] to get [tex]-0.8[/tex]:

[tex]-r=7.2-8[/tex]

[tex]-r=-0.8[/tex]

-Multiply both sides by [tex]-1[/tex]:

[tex]r=0.8[/tex]

-Result:

[tex]r=0.8[/tex]

Answer:

-0.95

Step-by-step explanation:

cos(theta) = sqrt(1 - sin²(theta))

= sqrt(1 - 0.312²)

= sqrt(0.902656)

= +/- 0.9500821017

Since cos is negative in quadrant 2,

cos(theta) = -0.95

To approximate the value of cos0, we can use the given value of sin0 and the Pythagorean identity. The approximate value of cos0 is -0.95022.

Since the given angle 0 lies in Quadrant II where cos0 is negative, we can approximate the value of cos0 using the given value of sin0.

Using the Pythagorean identity sin^2(0) + cos^2(0) = 1, we can find cos0.

sin^2(0) + cos^2(0) = 1

0.312^2 + cos^2(0) = 1

0.097344 + cos^2(0) = 1

cos^2(0) = 1 - 0.097344

cos^2(0) = 0.902656

cos0 = √0.902656

cos0 ≈ -0.95022

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Answer:

C. 100 cm

Step-by-step explanation:

2x-15=185

+15      +15

2x=200

/2    /2

x=100

Answer:

b

Step-by-step explanation:

The square root of b times the square root of b is simply b.

b^(1/2)*b^(1/2) = b^1 = b

Answer:

About 29

Step-by-step explanation:

575 cans of food / 20 days = About 28.75 cans a day, rounded to 29.

Answer:

28.7 cans

Step-by-step explanation:

We want to find the unit rate for cans per day

To find this, divide the number of cans by the number of days

cans/days

574/20

28.7

About 28.7 cans per day

Answer:

1. 2a

2. Vertex

3. Center

4. (c-a)

Step-by-step explanation:

The missing black in the paragraph will be 2a, vertex, center, and (c – a).

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of 2a.

2a is used in the equation because the Vertex is a point on the hyperbola, and it is the difference in the distances from this point to the foci.

This can be shown algebraically if we let a be the distance from the Center to the vertex. Then, the difference of the distances is (c + a) – (c – a).

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Answer:

F25 A B S14 BOTH S AND F IS 32IN THE MIDDLE

Step-by-step explanation:

14 study Spanish, 25 study French.

71 total students - 14 - 25 = 32

A 32 would be put in the middle where the circles overlap, which means 32 students are studying both languages.

B) only French would be the 25 shown in the circle marked F

C) 14 + 32 = 46 total students study Spanish

Answer:

(-35, 0)

step-by-step explanation:

The x-intercept of the line does not exist.

The x-intercept of a line represents the point where the line intersects the x-axis. To find the x-intercept, we need to look for a point on the graph where y is equal to zero. Based on the given table, there is no pair of coordinates where the y value is equal to zero. Therefore, the line does not intersect the x-axis and the x-intercept does not exist.

Answer:

80 minutes

Step-by-step explanation

24/3=8

8mins/1 mile

8 minsx10 miles= 80 mins for 10 miles

Answer:

t = 3 seconds

Step-by-step explanation:

This is a quadratic equation. First set it up and set it equal to 0 (the ground).

-16t² + 46t + 6 = 0

The quadratic formula is (-b ± √(b² - 4ac))/2a

a= -16

b = 46

c = 6

Plug those numbers into the equation and solve which will result in -.125 or 3.

The time of course can not be negative in this case. Therefore, t=3 seconds.

The ball will hit the ground after 3 seconds.

The problem deals with the quadratic equation representing the motion of the ball. When the ball hits the ground, the height (h) is 0. So, we need to solve the equation -16t^2 + 46t + 6 = 0 for (t). The roots of this quadratic equation can be found using the quadratic formula, t = [-b ± sqrt(b^2 - 4ac)]/2a. Substituting a=-16, b=46, and c=6 into the formula, you will find the solutions are t = 3 seconds and t = -0.375 seconds. Therefore, the ball will hit the ground after 3 seconds. The correct choice is A. 3.

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Write it as an equation:

X - 10 = 6x + 3

Now solve for x:

Subtract 3 from both sides:

x-13 = 6x

Subtract 1 x from both sides:

-13 = 5x

Divide both sides by 5:

x = -13/5

Answer:

x = -2.6.

Step-by-step explanation:

Let the number be x, then:

x - 10 = 6x + 3

x - 6x = 3 + 10

-5x = 13

x = -13/5

= -2.6.

Answer:

The wrong sampling method was used.

Step-by-step explanation:

In convenience sampling, first few responses are considered and not all parameters are considered. This is the easiest method of sampling but least effective

(D) The wrong sample method was used.

The term 'sample' can mean -

Therefore, the correct answer if the problem is (D) the wrong sample method was used.

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Answer:

Shelly paid $215 for the desk

Step-by-step explanation:

In this question, we are asked to calculate the price a particular desk was bought given the price at which it was sold and the percentage of profit associated with the sales of the desk. In other words, we are calculating the cost price

Mathematically,

% profit = (selling price - cost price)/cost price * 100%

Our percentage profit here is 35% and our selling price is $290.25, we are left with calculating the selling price. let’s input these values into the equation;

Before that, let’s say the cost price is $x

35 = (290.25-x)/x * 100

100(290.25-x) = 35x

29025 -100x = 35x

135x = 29025

x = 29025/135

x = $215

Answer:

A) (x²/127806.25) + (y²/76956) = 1

B) 451 miles

C) 715 miles

Step-by-step explanation:

Center is at (0,0) and focus is at (c,0) while vertex is at (a,0)

Thus, a - c = 132 miles

and a + c=583 miles

Adding both equations together, we have;

2a= 715 miles

Thus, a = 715/2

a = 357.5 miles

Since a+c=583

Thus, c = 583-357.5 = 225.5 miles

Now, for an ellipse it is defined by; a² = b² + c²

a² = 357.5² = 127806.25

c² = 225.5² = 50850.25

So, b² = 127806.25 - 50850.25

b² = 76956

b = √76956

b = 277.409

A) Equation of tangent to ellipse which is equation of orbit would be;

(x²/a²) + (y²/b²) = 1

Thus,

(x²/127806.25) + (y²/76956) = 1

B) distance between the earth and the other focus is = 2c = 2 x 225.5 = 451 miles

C) Length of other major axis = 2a = 2 x 357.5 = 715 miles

a) The equation of the orbit is \(\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\). b) The distance from the center to the other focus is calculated using the formula \(c = \sqrt{(583+3963)^2 - 132^2}\). c) The length of the major axis is \(2(583+3963)\).

a) To find an equation of the orbit, we can use the standard form equation for an ellipse:
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\] where \((h,k)\) represents the center of the ellipse, \(a\) represents the distance from the center to the vertices along the major axis, and \(b\) represents the distance from the center to the co-vertices along the minor axis. In this case, the center of the ellipse is the Earth's center, which is at the origin \((0,0)\). The highest point of the orbit is 583 miles above the Earth's surface, so the distance from the center to the vertices along the major axis is 583 miles + the radius of the Earth. The radius of the Earth is approximately 3963 miles. The lowest point of the orbit is 132 miles above the Earth's surface, so the distance from the center to the co-vertices along the minor axis is 132 miles. Substituting the values into the equation:
\[\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\]

b) The distance from the center to the other focus can be found using the relationship \(c = \sqrt{a^2 - b^2}\), where \(c\) represents the distance from the center to the foci. Substituting the values into the equation:
\[c = \sqrt{(583+3963)^2 - 132^2}\]

c) The length of the major axis can be found using the formula \(2a\), where \(a\) represents the distance from the center to the vertices along the major axis. Substituting the values into the equation:
\[2a = 2(583+3963)\]

Answer:

try using this it might help out with the question

Step-by-step explanation:

Y=2x+3

The one that is an the inverse of y = 3 Superscript x is y = 3x is f-1(x) = 1/3x.

The use of the idea of inverse function to look for the solution is given below:

Note that, y = 3x

Then let f(x) = y = 3x

One will need to Switch x and y and as such, x = 3y

Then one should express y in terms of x and as such, y = 1/3 x

Since f(x) = y ⇒ x = f-1(y)

Then f-1(y) = 1/3x

Therefore, the inverse of y = 3x is f-1(x) = 1/3x.

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Answer:

12 inches

Step-by-step explanation:

In this question, we are asked to calculate the width of a rectangle having a length 9 inches less than twice it’s width and given the area of the rectangle.

First, we identify that the length is 9 inches less than twice the width

meaning if length is l and width is w; then l = (2w-9) inches

Mathematically the area of the rectangle is l * w ; meaning w * (2w-9)

This has a value equal to 180

w * (2w-9) = 180

opening the bracket;

2w^2 -9w = 180

2w^2 -9w - 180 = 0

solving this quadratic equation;

w = 12 or -7.5

since width cannot be negative, w = 12 inches

Answer:

The width of the triangle is 18.65 inches

Step-by-step explanation:

From the question, we have;

Length, L = Width, W - 9

Also the area is given by

L × W = 180

Therefore, we have

(W - 9) × W= 180

W² - 9·W = 180

W² - 9·W - 180 = 0

Factorizing or solving with quadratic formula

[tex]\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

a = 1

b = -9 and

c = -180

we get

(W + 9.65)(W-18.65) =0

Therefore W = - 9.65 or  18.65

Therefore, the Width, W = 18.65 and the length = W - 9 = 18.65 - 9 =9.65

The width of the triangle = 18.65 inches.

Answer:

Sales Price = $21.00

New Price = $39.00

Step-by-step explanation:

Convert 35% into a decimal and multiply that with the $60.00. After you get the product, which is $21.00, you then need to subtract $21.00 from $60.00 and that gets you $39.00.

Using normal distribution concepts, we can conclude that the correct statement is:

B. Use t when the population is normal and the population standard deviation is not known

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Answer:

The angle is 84 degrees

Step-by-step explanation:

Let's call the angle by 'x'.

the supplement of x is equal to 180-x, and the complement of x is equal to 90-x.

If the supplement is sixteen times the complement, we can write the following equation:

(180 - x) = 16 * (90 - x)

180 - x = 1440 - 16x

16x - x = 1440 - 180

15x = 1260

x = 84

The angle is 84 degrees.

Answer:

84⁰

Step-by-step explanation:

Complement = 90 - x

Supplement = 180 - x

Given:

180 - x = 16(90 - x)

180 - x = 1440 - 16x

15x = 1260

x = 84

Step-by-step explanation:

Given

f(x) = 3x - 5

f(-2) = 3 * (-2) - 5

= -6 -5

= - 11

Answer:

f(×)=

Step-by-step explanation:

[tex] f(- 2 )= 3( - 2) - 5 [/tex]

[tex] - 2 = - 6 - 5[/tex]

[tex] - 2 = - 11[/tex]

Answer:

0.2x

Step-by-step explanation:

Answer:

0.2x---------------------------------------------------------------------------------------

Answer:

Therefore the probability that a pen from the first box and a crayon from the second box are selected is [tex]\frac5{16}[/tex]

Step-by-step explanation:

Probability:

The ratio of the number of favorable outcomes to the number all possible outcomes of the event.

[tex]Probability=\frac{\textrm{The number favorable outcomes}}{\textrm{The number all possible}}[/tex]

Given that,

Three plain pencils and 5 pens are contained by the first box.

Total number of pens and pencils is =(3+5)=8

The probability that a pen is selected from the first box is

=P(A)

[tex]=\frac{\textrm{The number pens}}{\textrm{Total number of pens and pencils}}[/tex]

[tex]=\frac{5}{8}[/tex]

A second box contains three colored pencils and three crayons.

Total number of pencils and crayons is =(3+3)=6

The probability that a crayon is selected from the second box is

=P(B)

[tex]=\frac{\textrm{The number of crayon}}{\textrm{Total number of crayons and pencils}}[/tex]

[tex]=\frac{3}{6}[/tex]

Since both events are mutually independent.

The required probability is multiple of the events

Therefore the required probability is

[tex]=\frac58\times \frac36[/tex]

[tex]=\frac5{16}[/tex]