Select the correct answer.
What is the ratio of the length of DE to the length of BC?
A. 1/4
B. 1/3
C. 2/5
D. 1/5

Answer:

Step-by-step explanation:

\(x^2-5=-2x+3\\\\x^2+2x-8=0\\\\a=1\,,\ b=2\,,\ c=-8\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-2\pm\sqrt{2^2-4\cdot1\cdot(-8)}}{2\cdot1}=\dfrac{-2\pm\sqrt{4+32}}{2}=\dfrac{-2\pm\sqrt{36}}{2}=\dfrac{-2\pm6}{2}\\\\x_1=\dfrac{-2-6}2=\dfrac{-8}2=-4\\\\y_1=-2x_1+3=-2(-4)+3=8+3=11\\\\(-4\,,\ 11)\\\\x_2=\dfrac{-2+6}{2}=\dfrac{4}2=2\\\\y_2=-2x_2+3=-2\cdot2+3=-4+3=-1\\\\(2\,,\ -1)\)

Answer:

22. 3/8

23. 3/5

24. 0

Step-by-step explanation:

turn the 1 into a fraction for each of the problems.

for 22. it would be 8/8 because also trying to make the denominators the same.

8/8 - 5/8 = 3/8

try 23 and 24 now!

Answer:

pair c has the inverse functions

Now,

<2 = <3 [ vertically opposite angle]

Then,

<2 = <8 [corresponding angles]

Again,

<2 + <5 = 180° [straight angle]

◆ True A || B

I hope you understand...

Mark me as brainliest...

Answer:

True

Step-by-step explanation:

∠ 2 and ∠ 5 are same- side exterior angles and are supplementary, sum to 180°

Answer:

C.) =

Step-by-step explanation:

the absolute value of 5 is 5, and the absolute value of -5 is 5, so they will be equal

Answer:

=

Step-by-step explanation:

The absolute value of a number is how far the number is from zero on a number line.

Both 5 and -5 are 5 units from zero on a number line, so

|5| = |-5| since |5| = 5 and |-5| = 5.

Answer: X = 60 degrees.

60 + 60 + 65 - 5 = 180.

Answer:

AV of -15 is 15.

AV of 16 is 16.

Step-by-step explanation:

It turns the number positive.

Answer:

That is an obtuse scalene triangle

Step-by-step explanation:

Scalene- has no congruent sides

Obtuse - has an angle that is greater than 90

we can use Pythagorean theorem to confirm this

The Pythagorean theorem states that in an obtuse triangle the hypotenuse squared is greater than the two legs squared added together

so basically \(7^2>4^2+5^2\\7^2=49\\4^2=25\\5^2=25\\25+16=41\\49>41\)

therefore it is an obtuse scalene

Answer:

(Choice E) E Scalene triangle and (Choice F) F Obtuse triangle

Step-by-step explanation:

Aside from E, Scalene triangle (as all the sides are of different lengths, we can assume that the angles will also be), the answer can either be B, Isosceles triangle or F, Obtuse triangle, so let's figure that out using the cosine rule! If it is an obtuse triangle, this means Angle ABC is bigger than Angle BAC and Angle BCA. But we can clearly see it is, as it's an Obtuse Triangle is a triangle where 1 angle is bigger than 90 degrees. Let's work out Angles BAC and BCA to find out if the triangle is obtuse or isosceles.

\(a^{2} = b^{2} +c^{2} -2bcCosA\)  This is the cosine rule formula. Now all we need to do is substitute in the values. We are using the cosine rule because we aren't given any angle values. We use Further Trigonometry instead of SOHCAHTOA as this clearly isn't a right-angled triangle. SOHCAHTOA only applies to triangles with a 90 degree angle, also known as a right-angled triangle. Let's rearrange the cosine formula so that we have everything equal to A instead.

\(A = cos^{-1}(\frac{b^{2} + c^{2} - a^{2} }{2bc})\)

We will work out BAC first.

a = 5

b = 4

c = 7

\(A = cos^{-1}(\frac{4^{2} + 7^{2} - 5^{2} }{2(4)(7)})\)

A = 44.4 rounded to 3 significant figures

Next, we will work out BCA.

a = 4

b = 5

c = 7

\(A = cos^{-1}(\frac{5^{2} + 7^{2} - 4^{2} }{2(5)(7)})\)

A = 34.0 rounded to 3 significant figures

The answer is F, Obtuse triangle and E, Scalene triangle

If we just worked out BAC, we would have noticed that by assuming BCA was also 44.4, the obtuse angle would be 91.2 degrees, which is barely above 90 degrees, therefore we would have correctly guessed the triangle as obtuse from there-on. I just worked out BCA as evidence to support that Triangle ABC cannot be isosceles, therefore we can eliminate that option and classify this triangle as Obtuse.

I hope my explanation helps!!

Answer:

h-1(x) =

Step-by-step explanation:

In order to find the inverse of a function, you have to change "h(x)" into "y" (It's the same thing, but it will be easier to solve). Then, solve the equation for "x". Finally, substitute the "y" for "x" and the "x" for "h-1(x)":

h(x)=x3-4

y = x3 - 4

y + 4 = x3

x = \(\sqrt[3]{y + 4}\)

h-1(x) = \(\sqrt[3]{x+4}\)

From the given function as \(h(x) = x^3- 4\) the value of the expression

would be \(h-1(x) = \sqrt[3]{y+4}\).

Suppose that the given function is

\(f:X\rightarrow Y\)

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

\(f^{-1}: Y \rightarrow X\)

In order to find the inverse of a function, we have to change "h(x)" into "y"  Then, to solve the equation for "x".

Finally, substitute the "y" for "x" and the "x" for "h-1(x)":

\(h(x) = x^3- 4\\y = x^3 - 4\\y + 4 = x^3\\x = \sqrt[3]{y+4} \\h-1(x) = \sqrt[3]{y+4}\)

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We get the least-squares solutions for axe = b as x = [0.981, -0.196, 0.490, 0.079, -0.343, 0.412] by using the least-squares method on the vectors a and b that have been provided.

We must reduce the squared difference between the product of a and x and the vector b in order to get the least-squares solutions for the equation axe = b. This can be described mathematically as minimization of the objective function ||axe - b||2, where ||.|| stands for the Euclidean norm.

The matrix equation AT Axe = AT b can be expanded to create a system of equations given the values of a and b as [5, 8, 1] and [2, 1, 2, 0, 2, 3] respectively. In this case, the coefficients of the variables in the equation make up the rows of the matrix A.

We get the least-squares solution for x by resolving the equation AT Axe = AT b. To be more precise, we calculate the pseudo-inverse of A, designated as A+, allowing us to determine that x = A+b.

The matrix AT A is invertible in this situation, and we may locate its inverse. Therefore, we may determine x = A+ b by computing A+ = (AT A)(-1) AT.

We get the least-squares solution for axe = b as x = [0.981, -0.196, 0.490, 0.079, -0.343, 0.412] by using the least-squares method on the vectors a and b that have been provided.

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9514 1404 393

Answer:

  C.  D"(0, -1)

Step-by-step explanation:

The attachment shows the two transformations. The original figure is in quadrant III, so rotating it 270° CCW will put the first image in quadrant II. Translating it down and right will move most of it to quadrant IV.

As you can see in the attachment, the location of D" is now (0, -1).

Answer:

55.5 cm^2

Step-by-step explanation:

9x 9 x 1/1= 40.5

3x5= 15

40.5+15=55.5

Answer:

-cos α

is the answer-------

Answer: {Route2, Route3, Route4} (Total 3  outcomes)

Step-by-step explanation:

Given: There are 4 different routes from Ben's house back to their home in Garland.

Let Sample space for all outcomes: {Route1, Route2, Route3, Route4 }

Ben  chooses Route 1.

The possible outcomes of the routes taken by the family if Ben  chooses first:

{Route2, Route3, Route4}

Hence, the possible outcomes of the routes taken by the family if Ben  chooses first: {Route2, Route3, Route4} (Total 3 choices)

The system of equations solved by the elimination method gives (-2, 1)

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

y = -4x + 11

y = 1/2x + 2

Subtract the equations to eliminate y

So, we have the following representation

-4 1/2x - 9 = 0

So, we have

-4 1/2x = 9

Divide the equations

x = -2

Recall that

y = 1/2x + 2

So, we have

y = 1/2(-2) + 2

This gives

y = 1

Hence, the solutions are x = 2 and y = 1

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The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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where is the rest of the question??

When music has two beats in each measure, it is in duple meter or 2/4 meter.

Duple meter is characterized by a strong emphasis on the first beat and a secondary emphasis on the second beat. It is commonly used in many musical genres, including marches, polkas, and certain fast-paced dance rhythms.

The time signature 2/4 indicates that there are two quarter note beats in each measure, with the quarter note receiving one beat. This meter creates a sense of regularity and stability, providing a foundation for rhythmic patterns and musical phrases. Duple meter often lends a lively and energetic feel to music, allowing for clear and predictable rhythmic patterns.

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relational algebra is a sufficient tool for manipulating data in a distributed system because it provides a uniform and consistent way to access and manipulate data.

Regardless of where it is stored in the system, and because it is a declarative language that abstracts away implementation details, making it easier to maintain and evolve the system.

Relational algebra is a powerful mathematical tool used to manipulate data in a relational database. It provides a way to perform operations on data in a structured and organized manner.

In a distributed system, where multiple nodes store and process data, relational algebra is still sufficient because it provides a uniform and consistent way to access and manipulate data across the entire system.

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Simplifying:y = (-5/3)x The final answer is:y = (-5/3)x

To find the equation of the line passing through the origin and point (-3,5), we can use the point-slope form of the equation of a line, which is:y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

We know that the line passes through the origin, which is the point (0, 0).

Therefore, we have:x1 = 0 and y1 = 0We also need to find the slope of the line.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:m = (y2 - y1)/(x2 - x1)Using the given points, we have:

x1 = 0, y1 = 0, x2 = -3, y2 = 5Substituting these values into the formula, we get:m = (5 - 0)/(-3 - 0) = -5/3

Therefore, the equation of the line passing through the origin and point (-3, 5) is:y - 0 = (-5/3)(x - 0)Simplifying:y = (-5/3)x

The final answer is:y = (-5/3)x

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Answer:

y= -2

x= 0

Explanation

0 - 2 = -2

-2 - (-2) = 0

Answer:

I believe the answer you're looking for is 2

Step-by-step explanation:

Given the length and the expression that represents the width of a rectangle, you need to remember that:

• The area of a rectangle can be calculated by multiplying its dimensions:

Where "l" is the length and "w" is the width.

• The perimeter of a rectangle is:

Where "l" is the length and "w" is the width.

Then, knowing that:

- You can set up that the area of this rectangle is:

Simplifying, you get:

- And the perimeter is:

Hence, the answer is:

- The area is:

- The perimeter is:

Answer:

Yes

no

no

yes

Step-by-step explanation:

I hope it's serving

:v

Answer:

g(x) = \((x + 8)^{2}\)

Step-by-step explanation:

Answer:

Please leave more information regarding the question thank you

The probability that Alice leaves before Carol is 0.5 according to the given information.

Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur.

If X1 and X2 are both exponential distributions with parameters 1 and 2, respectively, then

P(X₁< X₂)= λ₁/(λ₁+λ₂ )

And P(X>s+t/x>s)=P(X>t), if X≈exp(μ)

Here, Let \(X_{A}\), \(X_{C}\) denote the service times for Alice and Carol

And also given that,

E[ \(X_{A}\)]=1/μ

E[ \(X_{A}\)]=4

E[ \(X_{C}\)]=4

E[ \(X_{A}\)]=E[ \(X_{C}\)]=4

So, \(X_{A}\), \(X_{C}\) ≈exp(1/4)

Now, when Betty completes his service, Alice is still being served, and the remaining time required to complete his service is exp(1/4).

Because the exponential distribution has no memory.

So, P( \(X_{A}\)< \(X_{C}\) )=  λ₁/ λ₁+ λ₂

=(1/4)/((1/4)+(1/4))

=(1/4)/(1/2)

=0.5

As a result, the probability that Alice leaves before Carol is 0.5.

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Answer:

I got 5/16 as my answer

Step-by-step explanation:

I used a calculator to solve the equation :/

Answer:

25%

Step-by-step explanation:

\(percentage \: increase = \frac{30 - 24}{24} \times 100 \\ \\ = \frac{6}{24} \times 100 \\ \\ = \frac{1}{4} \times 100 \\ \\ = 25\%\)