Find the volume of this triangular prism

Answer:

Step-by-step explanation:

The equation factors into

(x^2 + 14x + 49) =16                      Factor

(x + 7)^2 = 16                                 Take the square root of both sides

√(x + 7)^2 = √16

x + 7 = +/- 4

x + 7 = + 4                                      Subtract 7 from both sides

x  = 4 - 7

x = - 3

x + 7 = - 4                                      Subtract 7 from both sides.

x = - 4 - 7

x = - 11

x1 = -11

x2 = - 3

Step-by-step explanation:

When you have a ratio, you put one number as the numerator and than one number as the denominator.

so it would be (12/34)=(x/68)

In this example I made the ratio you are comparing it to have 68 dollars, so when you solve for the amount of quarters you need it should be 24, since all of the numbers in this example are just being doubled.

To solve for x, you multiply 68 on both sides of the equation, 68×(12/34)=x

24=x

So this proves that this is how ratios, are used. It also does not matter what number you place on the numerator or denominator.

Answer:

100°

Step-by-step explanation:

the lower right angle is 180-149 = 31°

the sum of all three angles in a triangle is 180°.

so the solution is 180-31-49

The relationship between logarithms and exponential functions is fundamental and provides a powerful tool for finding solutions in various mathematical and scientific contexts.

Logarithms are the inverse functions of exponential functions. They allow us to solve equations and manipulate exponential expressions in a more manageable way. By taking the logarithm of both sides of an exponential equation, we can convert it into a linear equation, which is often easier to solve.

One of the key properties of logarithms is the ability to condense multiplication and division operations into addition and subtraction operations. For example, the logarithm of a product is equal to the sum of the logarithms, and the logarithm of a quotient is equal to the difference of the logarithms.

Logarithms also help us solve equations involving exponential growth or decay. By taking the logarithm of both sides of an exponential growth or decay equation, we can isolate the exponent and solve for the unknown variable.

This is particularly useful in fields such as finance, population modeling, and radioactive decay, where exponential functions are commonly used.

Furthermore, logarithms provide a way to express very large or very small numbers in a more manageable form. The logarithmic scale allows us to compress a wide range of values into a smaller range, making it easier to analyze and compare data.

In summary, the relationship between logarithms and exponential functions enables us to simplify and solve equations involving exponential expressions, model exponential growth or decay, and manipulate large or small numbers more effectively.

For more such question on logarithms visit:

https://brainly.com/question/25993029

#SPJ8

Differentition of \(y=log_{2}x^{3}.(5x^{4}+2)\) is \(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}\)

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

\(y=log_{2}x^{3}.(5x^{4}+2)\)

We have to differentiate with respect to x.

y'=xy'+yx'

\(x=log_{2}x^{3}\)

\(y=5x^{4}+2\)

\(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x^{3}} .3x^{2}\)

\(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}\)

Hence, differentiation of \(y=log_{2}x^{3}.(5x^{4}+2)\) is \(y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}\)

To learn more on Differentiation click:

https://brainly.com/question/24898810

#SPJ1

Answer:

Option 3

(3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

Step-by-step explanation:

Factorize polynomials:

Use exponent law:

                   \(\boxed{\bf a^{m*n}=(a^m)^n} \ & \\\\\boxed{\bf a^m * b^m = (a*b)^m}\)

9x²y⁶ = 3²* x² * y³*² = 3² * x² * (y³)² = (3xy³)²

25x⁴y⁸ = 5² * x²*² * y⁴*² = 5² * (x²)² * (y⁴)² = (5x²y⁴)²

Now use the identity:  a² - b² = (a +b) (a -b)

Here, a = 3xy³ & b = 5x²y⁴

9x²y⁶ - 25x⁴y⁸ = 3²x²(y³)² - 5²(x²)² (y⁴)²

                       = (3xy³)² - (5x²y⁴)²

                      = (3xy³ + 5x²y⁴)  (3xy³ - 5x²y⁴)

The probability that none of the selected adults say that they were too young to get tattoos is 0.3512

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

14​% say that they were too young when they got their tattoos.

So, p= 0.14.

Six adults who regret getting tattoos are randomly​ selected

So, n=6.

Now, the probability that none of the selected adults say that they were too young to get tattoos.

P(X=0) = \(C_ {6.0} (0.14)^{0} (0.86)^{6}\)

             = 0.3512

Learn more about this concept here:

https://brainly.com/question/24123162

#SPJ1

Answer:

y=−x2+8x−7

Step-by-step explanation:

Answer: 2.72 i guess

Answer:

x = -1/3

Step-by-step explanation:

step one - Simply both sides of the equation

step two - Multiply both side by 4/(-3)

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

For more such questions on parking cost

https://brainly.com/question/18091509

#SPJ8

Answer:

Answer:

w = 22 in, h = 8 in.

Step-by-step explanation:

Reading the problem, I immediately see two equations. This hints me towards a system of equations problem.

Statement 1 is The width of a triangle is six more than twice the height.

The width (w) of a triangle is (=) six (6) more (+) than twice (2) the height (h).

Equation 1: w = 6 + 2h

Statement 2 is The area of the triangle is 88 in2.

The formula for the area of a triangle is \(\frac{wh}{2}\). So, we get our second equation.

Equation 2: wh/2 = 88

We see that we have the same number of equations as unknowns, two. This is important as it lets us know that we can find two unknowns in the two equations. If there are more unknowns than equations, then we cannot find the values of all the variables. Look for another equation in the problem. However, if the # equations greater than or equal to number of unknowns, then we are ready to start solving!  So, we can now move to solving.

Equation 1 isolates one of the unknowns (w). So, we can replace w in the second equation with the right side of eq 1. Then, we simplify for h.

\(\frac{wh}{2} = 88\)

\(\frac{(6 + 2h)h}{2} = 88\)

\(\frac{6h + 2h^2}{2} = 88\)

\(6h + 2h^2 = 176\)

\(2h^2 + 6h - 176 = 0\)

\(h = -11, 8\) (assuming you know how to solve quadratics)

Since we know that heights of triangles cannot be negative, we find that \(h = 8\) in.

For the final step, we plug \(h\) into our first equation to find \(w\).

\(w = 6 + 2h\)

\(w = 6 + 2(8)\)

\(w = 6 + 16\)

\(w = 22\)

So, the answer is w = 22 in, h = 8 in.

To check if we were right, we can plug the values into both equations to see if they are equal. I will skip equation 1 since we used that equation "as-is" to find w.

\(\frac{wh}{2} = 88\)

\(\frac{22 * 8}{2} = 88\)

\(11 * 8 = 88\)

\(88 = 88\)

The solution checks out!

Answer:

the answer is 20% so good luck

A

(a) You're looking for

\(P(X\le 8) = \displaystyle \sum_{x=0}^8 P(X=x)\)

where

\(P(X=x) = \begin{cases}\dfrac{\lambda^x e^{-\lambda}}{x!}&\text{if }x\in\{0,1,2,\ldots\}\\0&\text{otherwise}\end{cases}\)

Customers arrive at a mean rate of 6 customers per 10 minutes, or equivalently 12 customers per 20 minutes, so

\(\lambda = \dfrac{12\,\rm customers}{20\,\rm min}\times(20\,\mathrm{min}) = 12\,\mathrm{customers}\)

Then

\(\displaystyle P(X\le 8) = \sum_{x=0}^8 \frac{12^x e^{-12}}{x!} \approx \boxed{0.155}\)

(b) Now you want

\(P(X\ge4) = 1 - P(X<4) = 1 - \displaystyle\sum_{x=0}^3 P(X=x)\)

This time, we have

\(\lambda = \dfrac{6\,\rm customers}{10\,\rm min}\times(10\,\mathrm{min}) = 6\,\mathrm{customers}\)

so that

\(P(X\ge4) = 1 - \displaystyle \sum_{x=0}^3 \frac{6^x e^{-6}}{x!} \approx \boxed{0.849}\)

B

(a) In other words, you're asked to find the probability that more than 1 customer shows up in the same minute, or

\(P(X > 1) = 1 - P(X \le 1) = 1 - P(X=0) - P(X=1)\)

with

\(\lambda = \dfrac{6\,\rm customers}{6\,\rm min}\times(1\,\mathrm{min}) = 1\,\mathrm{customer}\)

So we have

\(P(X > 1) = 1 - \dfrac{1^0 e^{-1}}{0!} - \dfrac{1^1 e^{-1}}{1!} \approx \boxed{0.264}\)

C

(a) Similar to B, you're looking for

\(P(X \le 1) = P(X=0) + P(X=1)\)

with

\(\lambda = \dfrac{12\,\rm customers}{6\,\rm min}\times(1\,\mathrm{min}) = 2\,\mathrm{customers}\)

so that

\(P(X\le1) = \dfrac{2^0e^{-2}}{0!} + \dfrac{2^1e^{-2}}{1!} \approx \boxed{0.406}\)

Answer: The missing value from the data set is 4.

Step-by-step explanation: Let's put it from least to greatest to figure it out...

2, 2, (4, 4,) 5, 8,

It would have to be 4, because 8 divided by 2 will equal 4. And because there's an even amount of numbers we have to add two numbers then divide it by 2.

4 + 4 = 8

8 ÷ 2 = 4

The mean is 4, and the missing value from the data set is 4.

I hope this helps!

On Julie's door, the images will span 210 square inches.

As Julie printed six images, the total space that the images cover is:

6 x 35 square inches = 210 square inches

Inches are measured as 1/36 of a yard in both British Imperial and American Customary measurement systems. According to some sources, the term "inch" comes from the Old English "ince" or "ynce," which in turn is said to have originated from the Roman "uncia" unit.

The name of another English unit, the ounce, is derived from the Roman word uncia. According to legend, King David I of Scotland defined the old English word "ynce" as the width of a man's thumb at the base of the nail in the year or thereabouts 1150 AD.

From the question:

Six images total, each measuring 5 by 7 inches, were printed by Julie. We must first calculate the area of each image in order to add up the overall area that these photographs cover.

One image's area is as follows:

5 inches x 7 inches = 35 square inches

As Julie printed six images, the total space that the images cover is:

6 x 35 square inches = 210 square inches

Consequently, 210 square inches of Julie's door will be covered by the images.

To know more about inch visit:

https://brainly.com/question/16311877

#SPJ1

Answer:

29 degrees

Step-by-step explanation:

Note how both triangles are isosceles triangles, which mean two angles will be equivalent. In the triangle with the marked angle measurement, since the total of angles in a triangle is 180, then the measurement of the unmarked angles have a sum of 180-64, which is 116. Then, as stated before, this triangle is isosceles, so the measurement of each unmarked angle is 116/2, which is 58.
Next, notice how the angle below angle x in that triangle shares a line with one of the 58 degree angles. This means that angle is 180-58, which is 122. Now, since the total of angles in a triangle is 180 and the triangle is isosceles, then angle x is (180-122)/2, which is 58/2, or 29 degrees

The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

Read more on triangle here: brainly.com/question/22891315

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

you did not provide enough information to answer the question

Answer:

29 legs I believe

The motivations for producers and consumers in the black market are largely driven by financial incentives and a desire to avoid legal consequences.

The black market refers to the illegal trade of goods and services that are not permitted by law, such as drugs, counterfeit items, and stolen goods. Producers and consumers in the black market are motivated by a variety of factors, including:

High profits, Producers in the black market can earn higher profits than they would in legal markets due to the lack of regulation and taxes.

Escaping legal consequences: Producers and consumers may participate in the black market to avoid legal consequences, such as fines or imprisonment, for engaging in illegal activities.

Limited availability, Some goods and services are only available on the black market due to legal restrictions or limited supply.

Low prices, Consumers in the black market can often purchase goods and services at lower prices than in legal markets due to the lack of taxes and regulations.

Desire for anonymity, The black market can provide anonymity for both producers and consumers, allowing them to engage in illegal activities without fear of detection or retribution.

However, participating in the black market also comes with significant risks, including the possibility of arrest, fines, and even violence.

To learn more about financial incentives here:

https://brainly.com/question/29767675

#SPJ1

Hello.

First of all, let the number be t.

8 times t can be written like this:

\(\mathrm{8t}\)

Notice that the number is before the variable and the times sign (×) is not there.

We can write it as 8×t, but we usually write it as 8t.

The sum of means we add:

8t+21

Now, "less than" is "<" :

\(\mathrm{8t+21 < -16}\)

Therefore, the answer is

\(\mathrm{8t+21 < -16}\)

I hope it helps.

Have a nice day.

\(\boxed{imperturbability}\)

Answer:

7.083

Step-by-step explanation:

well there's the ones place, tenths, hundredths, and thousandths. easy math, unless i'm stoopid and this is wrong :D

Answer:

162

Explanation:

[ replace 9 with p ]

  [ 9 * 9 = 81 ]

  [ multiply ]

Step-by-step explanation: I know its right because i have problem solver and pls brainliest

Answer:

B. 57

Step-by-step explanation:

Answer:

57

Step-by-step explanation:

If there are 24 wins and 19 losses, that leaves 9 games in a tie. So, insert each number where it belongs in the equation.

P=2x+y

P=2*24+9

P=57

Answer:

d(3) = - 25

Step-by-step explanation:

Using the recursive formula with d(1) = 3, then

d(2) = d(1) - 14 = 3 - 14 = - 11

d(3) = d(2) - 14 = - 11 - 14 = - 25

Thus the 3 rd term in the sequence is - 25

Answers:

==========================================

Explanation: