Select the correct answer.
What is the approximate solution to this equation?
4lni - 8 = 12
ОА.
59,874
OB.
I 10.5
Ос.
IÑ148.4
OD.
I 1.61

The true statement about the axis of rotation is the option;

It is parallel to a side of the equilateral triangle, but is separate from the equilateral triangle.

The axis of rotation is a straight line around which all points on a rotating body rotates.

The diagram shows a figure with a hollow cylindrical cross section and triangular cross section on the left and right, which indicates that the figure is created by the rotation of the equilateral triangle about height of the cylinder, such that the axis of rotation is a vertical line through the center of the hollow cylinder. Therefore, the axis of rotation is parallel to the height of the cylinder, and therefore, it is parallel to the base of the equilateral triangle, but it it seperate from walls of the cylinder, and therefore, separate from the equilateral triangle

Learn more on the rotation of plane figures here: https://brainly.com/question/12688268

#SPJ1

the surface area of the above triangular prism is 156 square inches.

Step-by-step explanation:

multiply the sum of the triangle sides by the height of the prism and add the values together for the answer, remembering to include the correct unit of measurement.

Here, we just need to add x and y and subtract it from 180.

x + y = 91 + 42 = 133.

180 - 133 = 47.

Hence, z = 47 degrees.

Answer:

Step-by-step explanation:

straight line = 180° we remove the angles x and y and find z

180 - 91 - 42 =

47°

Answer:

1.6cm

Step-by-step explanation:

80/50=1.6 cm

Good Luck!

Answer:

The slope of the line is 1/6.

Step-by-step explanation:

y=mx+b

0=m(0)+b

0=0+b

b=0

---------------

0.5=3m+b

0.5=3m+0

0.5=3m

1/2=3m

m=(1/2)/3

m=(1/2)(1/3)

m=1/6

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

We have,

Let's start by finding the total number of points that Carlos can earn in the class:

Total points

= 5 quizzes x 20 points per quiz

= 100 points

If Carlos needs an average of 90% or greater, that means he needs to earn at least 90 points out of 100.

Total points earned.

= 18 + 19 + 17 + 20

= 74 points

To find the minimum score Carlos needs on the final quiz, we can set up an inequality:

(74 + x) / 5 ≥ 0.9

where x is the score on the final quiz.

Simplifying this inequality.

74 + x ≥ 90

x ≥ 16

Therefore,

Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ1

Answer:

[A] $1500

[B] 1/4

[C] 375

Step-by-step explanation:

Given:

Priced at $1499.80

Sale for 25% off

Solve:

[A] Rounded MacBook Price:

$1499.80 → $1500

Hence, Rounded MacBook Price is $1500

[B] Estimated Discount Price:

25% ⇒ 25/100

Simplify

1/4

Hence, Estimated Discount Price: 1/4

[C] Estimated Sale Price AFTER DISCOUNT ( Do NOT include tax):

$1500 x 1/4 = 375

Hence, Estimated Sale Price after discount( not include tax) is 375.

[RevyBreeze]

R=

\({ \)

(x,y):y=

\( {x}^{2} \)

\(}\)

Step-by-step explanation:

Amongal medhanite motwal

Answer:

$466.93

Step-by-step explanation:

I multiplied by 26.50 & 17.62 and that got me $466.93. Or you can divide that into 17.62 = $1.50

Answer:

The image below is the graph of y = -4x + 2

Hope this helps! :)

Answer:

E. 35/4

Step-by-step explanation:

Multiply denominator (4) to the whole number (8) then add to the numerator (3)

(8× 4 + 3)/ 4

(32 + 3)/4

35/4

.

Step-by-step explanation:

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

Learn more on volume of a solid obtained by rotating curve here;

https://brainly.com/question/32301706

#SPJ1

Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

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

Answer:

k+5=11

Step-by-step explanation:

Answer:

k=6

Step-by-step explanation:

k+5=11 (this is an algebraic expression)

k=11-5 (you move 5 to the left)

k=6

Answer:

12x+4

Step-by-step explanation:

M A T H W A Y

Answer:

12x+1

Step-by-step explanation:

4(3x+1)

(4 x 3x)+1

12x+1

A) the angle ( 7π)/4 is in the third quadrant.

B)  the reference angle is π/4 radians or 45°

C) sin(7π/4) = -√2/2

D) cos(7π/4) =  - √2/2

1) The 3rd quadrant is located in the graph's lower left-hand corner. It has negative values for both x and y. The fourth quarter is in the lower right-hand corner, with a positive x and a negative y value.

2) For the angle ( 7π) /4, the nearest multiple   of 2π is 2π.

2π -  (7 π ) /4 = (8π) / 4 - (7π)/4   = π/4

hence  the reference angle is π/4 radians or 45 degrees.

3)  The reference angle for (7π)/4 is π/4.

sin(7π/4) = - sin(π/4) = -1/√2

= -√2/2

cos(7π/4) = -  cos(π/4) = -1/√2

=  

- √2/2

Learn more about quadrants:
https://brainly.com/question/26426112
#SPJ1

Answer:

When doing multiplication or division with measured values, the answer should have the same number of significant figures as the measured value with the least number of significant figures. Procedure to determine significant figures after multiplication or division: 1.

Step-by-step explanation:

The required solution is multiplication or division.

It is required to find the fill in blanks.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

When doing multiplication or division with measured values, the answer should have the same number of significant figures as the measured value with the least number of significant figures.

Therefore, the required solution is multiplication or division.

Learn more details about arithmetic here:

https://brainly.com/question/11559160

#SPJ2

Answer:

2/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3.

Step-by-step explanation

Similarly, if we divide the numerator and denominator of 12/18 by 6 we get. 12/18 = 12÷6 / 18÷6 = 2/3. So 12/18 is an equivalent fraction of 2/3 as well.

Answer:

5 sides

Step-by-step explanation:

the sum of the interior angle and exterior angle = 180°

sum the parts of the ratio, 2 + 3 = 5 parts , then

180° ÷ 5 = 36° ← value of 1 part of the ratio

exterior angle = 2 × 36° = 72°

the sum of the exterior angles of a polygon = 360°

since the polygon is regular then the exterior angles are congruent , so

number of sides = 360° ÷ 72° = 5

EXPLANATION

We need to use the Compounding Interest Equation as shown as follows:

Where P=Principal = 14,000 r=rate in decimal form = 3.4/100 = 0.034 n=number of times interest is compounded per unit 't' = 1 t= time = 2029 - 2011 = 18 years

Plugging in the terms into the expression:

Adding numbers:

Computing the power:

Multiplying numbers:

In conclusion, in the year 2029 the value will be $14,476

Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

Answer: b=-2

Step-by-step explanation:

3(b+3)-4(-2+b)=19

3b+9+8-4b=19

-b+17=19

-b=19-17

-b=2

-b/-1=2/-1

b=-2

Answer:

sknsonsknsknsknskdnksndksn?

\( \huge\boxed{\sf \green{ Given : }}\)

\(\red {\underline{ \sf \: Let's \: Solve \: For \: Eqn \: 1 : }}\)

_____________________________________

\(\orange {\underline{ \sf \: Let's \: Solve \: For \: Eqn \: 2}}\)

____________________________

[Eqn 3]

f(x) = x³ + 3x² + 6x - 11 when x = 5

____________________________

[Eqn 4]

f(x)=x³ - x² + 12x - 15 when x = 1

____________________________

[Eqn 5]

f(x) = 2x³ + 6x² + 4x + 8 when x = 2

\( \boxed{\sf \purple{ Hope \: It's \: Helpful!}}\)

Evaluating the polynomial using direct substitution method will give the following :

f(x) = 2x³ - 5x² - x when x = 3

f(3) = 6

f(x) = -4x³ + 3x - 5 when x = 2

f(2) = -31

Substitution simply means to put in place of another.  Therefore,

f(x) = 2x³ - 5x² - x when x = 3

f(3) = 2(3)³ - 5(3)² - 3

f(3) = 2(27) - 5(9) - 3

f(3) = 54 - 45 - 3

f(3) = 6

f(x) = -4x³ + 3x - 5 when x = 2

f(2) = -4(2)³ + 3(2) - 5

f(2) = -4(8) + 6 - 5

f(2) = -32 + 6 - 5

f(2) = -32 + 1

f(2) = -31

learn more on substitution here: https://brainly.com/question/15200459

B. 1/2

The blue marbles are half of the marbles that there are, so that makes it 1/2 which is also counted as 50%.

Hope that helped:)

Answer:

1.176 ounces per dollar

Step-by-step explanation: