In Exercises 13 and 14, the solids are similar. Find the surface area of solid B. (See Example
Pyramid A
Pyramid B

14.
27 in.
S = 48 in.²
+
36 in.
●
I

Answer: Let u = ln(x). Then, we have:

y = y(u)

dy/dx = dy/du * du/dx = dy/du * (1/x)

d^2y/dx^2 = d/dx (dy/du * du/dx) = d^2y/du^2 * (1/x)^2 - dy/du * (1/x^2)

Substituting these into the original differential equation yields:

d^2y/du^2 - dy/du + (4 - e^u)y = e^(2u)

This is now a second-order ordinary differential equation in y with constant coefficients, which can be solved using standard methods such as the characteristic equation or undetermined coefficients.

Step-by-step explanation:

The simplest form of the radical expression (√2 + √3) / (√2 - √3) is -5 - 2√6.

Given the radical expression in the question;

(√2 + √3) / (√2 - √3)

To simplify the expression, we need to eliminate the radical in the denominator.

We can do this by multiplying both the numerator and denominator by the conjugate of the denominator, which is (√2 + √3):

[(√2 + √3) / (√2 - √3)] × [ (√2 + √3) / (√2 + √3) ]

= (2 + √6 + √6 + 3) / (2 - √9)

= (5 + 2√6) / (2 - 3)

= (5 + 2√6) / (-1)

= -5 - 2√6

Therefore, the simplified form is -5 - 2√6.

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Answer:

(x - 3)^2 = 8

x - 3 = + 2√2

x = 3 + 2√2

The values of x when the equation (x-3)² = 8 was solved is 3±2√2.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

solve  the equation means to find the value of x in the equation (x-3)² = 8.

To find the value of x, we following the steps below

Given equation = (x-3)² = 8.

Step 1:

Note: square root and square will cancel out.

Step 2

Hence, the values of x is 3±2√2.

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The balloon’s vertical distance above the ground will be 721.7 feet.

Given that:

Lan measures a 30° dip to a point that is 1250 feet distant from a hot air balloon while measuring horizontally.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The vertical height of the air balloon is calculated as,

tan 30° = h / 1250

h = 1250 x tan 30°

h = 721.7 feet

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To find the test statistic, we need to use the formula:

z = (p - P) / sqrt[(P * (1 - P)) / n]

where:

p = sample proportion = 15/20 = 0.75

P = hypothesized population proportion = 0.42

n = sample size = 20

Plugging in the values, we get:

z = (0.75 - 0.42) / sqrt[(0.42 * 0.58) / 20]

z = 2.11

Therefore, the test statistic is 2.11.

Answer:

[tex] \frac{ {m}^{4} \times { {m}^{3} }}{ {m}^{5} } = \frac{ {m}^{7} }{ {m}^{5} } = {m}^{2} [/tex]

So a = 2.

Answer:

Step-by-step explanation:

(4n+2m)(2n+3m)(n-m)(3n+2m)​

4n+2m=2(m+2n)

10n(m−n)(m+2n)(3m+2n)

Answer:

A and D

Step-by-step explanation:

The scatter plots that do not suggest a linear relationship between x any are A and D because A is a hill shape which isn't linear and d is just random things plotted so the answer is A and D

The calculated value of the area of the shape is 84.78 square units

From the question, we have the following parameters that can be used in our computation:

The three quarter circle

The area of the shape is then calculated as

Area = 3/4 * πr²

Where

Radius, r = 6 ( from the diagram)

substitute the known values in the above equation, so, we have the following representation

Area = 3/4 * 3.14 * 6²

Evaluate

Area = 84.78

Hence, the area is 84.78 square units

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Answer:

The surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.

Step-by-step explanation:

formulas:

Surface Area = 2B + Ph

Volume = Bh

where B is the area of the triangular base, P is the perimeter of the base, h is the height of the prism, and B and h are both in the same units (inches, feet, etc.).

Given:

Height of the triangular prism = 1 foot

Base of the triangular prism = 6 inches

Height of the triangular base = 4 inches

Length of the other two sides of the triangular base = 5 inches

First, we need to find the area of the triangular base (B):

B = (1/2) x base x height

B = (1/2) x 6 inches x 4 inches

B = 12 square inches

Next, we need to find the perimeter of the triangular base (P):

P = sum of all three sides

P = 6 inches + 5 inches + 5 inches

P = 16 inches

Now, we can use the formulas to find the surface area and volume:

Surface Area = 2B + Ph

Surface Area = 2(12 square inches) + (16 inches)(1 foot)

Surface Area = 24 square inches + 16 square feet

Surface Area = 16.222 square feet (rounded to three decimal places)

Volume = Bh

Volume = 12 square inches x 1 foot

Volume = 12 cubic feet

Therefore, the surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.

Answer:

Step-by-step explanation:

area of shaded region

[tex]=\pi r^2 \times\frac{121}{360} \\\\=\pi 8^2\times \frac{121}{360} \\=\frac{121 \pi }{45} \\\approx 8.447\\\approx 8.4~sq.~ft[/tex]

Answer: D

Step-by-step explanation: Cuz i just know

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 12000\\ P=\textit{original amount deposited}\dotfill & \$80000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 12000 = (80000)(\frac{r}{100})(1) \implies \cfrac{12000}{80000}=\cfrac{r}{100} \\\\\\ \cfrac{3}{20}=\cfrac{r}{100}\implies \cfrac{300}{20}=r\implies \stackrel{ \% }{15}=r[/tex]

Using the simplification of an equation we can get the value of x to be,

x = 10 2/11.

Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol. It'll be regarded as a term.

Here in the question,

The given equation is:

(x-4 8/11) + 1 9/11= 7 3/11

Simplifying it, we get:

(x - 52/11) + 20/11 = 80/11

Subtracting 20/11 from both sides:

x - 52/11 = 60/11

Adding 52/11 on both side:

x = 112/11

x = 10 2/11

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The  probability that all seniors will be chosen at random is 5/9.

We have,

Seniors = 5

Juniors = 4

Total number of people= 5 + 4 = 9

So, the probability that all seniors will be chosen at random is

= Number of senior/ total number of person

= 5 / 9

Thus, the required probability is 5/9.

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Answer:

Plot the points on the graphing calculator. Then generate an exponential regression model.

y = 14,220.322(.838^x)

After 10 years:

y = 14,220.322(.838^10) = 2,428.56

After 10 years, the value of the car is $2,428.56.

it will take you approximately 31.4 seconds  to run around the baseball field at a rate of 9 feet per second.

The time it takes to run around the baseball field will depend on the distance around the field.

Assuming the field is a perfect circle and has a diameter of 90 feet (which is a common size for a baseball field).

The circumference of a circle with diameter 90 feet is:

C = πd = π(90) = 90π feet

To run around the perimeter of the baseball field, you will need to cover a distance of 90π feet.

Using the formula:

time = distance / rate

we can calculate the time it takes to run around the baseball field:

time = (90π feet) / (9 feet/second)

time = 10π seconds

time ≈ 31.4 seconds (rounded to the nearest tenth of a second)

Therefore, it will take you approximately 31.4 seconds (rounded to the nearest tenth of a second) to run around the baseball field at a rate of 9 feet per second.

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Answer:  1 cm

Step-by-step explanation:

To find the length of arc, multiply the fraction of the circle to the Circumference

Looks like:

[tex]\frac{part of circle}{whole circle} (2\pi r)[/tex]

r=3/[tex]\pi[/tex]

length = [tex]\frac{120}{360} (2\pi)\frac{3}{\pi }[/tex]              pi's cancel, now reduce

        = 2 cm

According to the situation in the graph, the three inequalities will be: 7x + 2y < 40, y ≥ 4, x ≥ 2, where x is the wing packages and y is the hot dogs per pound.

Let x be the number of wing packages and y be the number of pounds of hot dogs.

Then the inequality equation is,

7x + 2y < 40

Inequality to represent at least 4 pounds of hot dogs,

y ≥ 4

Inequality to represent at least 2 packages of wings,

x ≥ 2

To graph it,

The graph will give the region that satisfies all the conditions and the shaded region represents the feasible region.

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The answer is C. 60(x-3)=45x. This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.

Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.

To solve this equation, we must use algebra and solve for x. First, we multiply both sides of the equation by 4/5. This gives us:

48x + 36 = 45x

-36 = 3x

Finally, we divide left side of the equation by 3, giving us the final solution:

x = -12

Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15. This equation shows the correct relationship between the two types of wood that the contractor purchased.

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Answer:

Step-by-step explanation:

17

-7

-1

2

8

2

0

Answer:

8 - -9 = 17

-4 + -3 = -7

-8 - -7 = -1

-4 + 6 = 2

5 - -3 = 8

5 - 3 = 2

-6 - -6 = 0

Answer:

A. The first one

Step-by-step explanation:

its just is

The value of the variable 'x' and 'y' will be 16 and 8√3, respectively. Then the correct option is A.

Given that:

Angle, θ = 30°

Perpendicular, P = 8

The length of the hypotenuse will be given as,

sin 30° = 8 / x

x = 8 / sin 30°

x = 16

The length of the base will be given as,

tan 30° = 8 / y

y = 8 / tan 30°

y = 8√3

The value of the variable 'x' and 'y' will be 16 and 8√3, respectively. Then the correct option is A.

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The height of the triangle is, 22 units.

WE know that triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that the area of a triangle is 154 square inches. The base is 14 inches.

Now, We get;

Base = 14 units

Height =h units

We know that;

Area of triangle = 1/2 x base x height

                 154       = 1/2 x 14 x h

              h = 154 / 7

              h = 22

Thus, The height is, 22 units.

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Answer:  The answer is 21 because for X: 23 + 2 = 25, 25 + 3 = 28, 28 + 4 = 32 

Step-by-step explanation: Please give Brainlist.

Hope this helps.

I can answer more questions for brainlists.

Answer:

Reading, writing, and mathematics are, or should be, inseparable. Hands-on mathematics can stimulate curiosity, engage student interest and build important prior knowledge before students read or write about the topic. The more students know about a topic, the better they comprehend and learn from text on the topic. Prior knowledge is the strongest predictor of student ability to make inferences from text.

Hands-on mathematics, though, must be combined with minds-on activities. Reading and writing activities can help students analyze, interpret and communicate mathematical ideas. These are skills needed to evaluate sources of information and the validity of the information itself, a key competency for mathematically literate citizens.

Many of the process skills needed for mathematics are similar to reading skills and, when taught together, would reinforce each other. Examples of common skills are predicting, inferring, communicating, comparing and contrasting, and recognizing cause and effect relationships. Teachers who recognize the interrelatedness of mathematics and literacy processes can design instruction that reflects these similarities. Becoming a Nation of Readers suggests that the most logical place for instruction in most reading and thinking strategies is in the content areas rather than in separate lessons about reading.

The importance of writing in the mathematics classroom cannot be overemphasized. In the process of writing, students clarify their own understanding of mathematics and hone their communication skills. They must organize their ideas and thoughts more logically and structure their conclusions in a more coherent way. Competency in writing can only be accomplished through active practice; solving mathematics problems is a natural vehicle for increasing students’ writing competence.

Step-by-step explanation:

Answer:

87

Step-by-step explanation:

Step-by-step explanation:

4 ^x  = 1/64     take LOG of both sides

x log 4 =  log (1/64)

x = log(1/64) / log4  =  - 3

The transformation that produce function g(x) from f(x) is that g(x) = 4 f(x).

Given graphs of f(x) and g(x).3

Both are v shaped graphs, which is probably modulus functions.

For the graph of f(x),

Vertex = (0, 0)

Other points = (-1, 1) and (1, 1)

For the graph of g(x),

Vertex = (0, 0)

Other points = (-1, 4) and (1, 4)

Here the coordinates can be related as,

(x, f(x)) transformed to (x, 4f(x))

So g(x) = 4 f(x).

Hence the transformation is g(x) = 4 f(x).

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The total number of players at the baseball game was 16.

To solve this problem, we can use a proportionality equation.

If we let "p" be the total number of players at the baseball game and "y" be the number of players who chose a bottle of water, we can set up the equation:

y ÷ p = 3 ÷ 4

According to the problem statement, 12 players chose a bottle of water, which is 3/4 of the total number of players.

So we can substitute that in:

12 ÷ p = 3 ÷ 4

To solve for "p", we can cross-multiply and simplify:

12 × 4 = 3 × p

48 = 3 × p

p = 48 ÷ 3

p = 16

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The number of months that it will take for the company to recover the investment is given as follows:

10.5 months.

The number of months that it will take for the company to recover the investment is obtained applying the proportions in the context of the problem.

The amount saved during the first year is of $40,000, hence the monthly amount is given as follows:

40000/12 = $3,333.33.

Hence the time needed to save $35,000 is given as follows:

t = 35000/3333.33

t = 10.5 months.

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