Find an equation in​ point-slope form for the line having the slope m=5 and containing the point (2,3).

Answer:

w=122

x=122

m<Z=58

Step-by-step explanation:

Answer:

4(x+y)

Step-by-step explanation:

x+y is one side length and there are 4 side lengths.

The area of a triangle is calculated using the formula A = 1/2bh, where b is the base and h is the height. If Charlie draws a second triangle with dimensions that are halved, then the base and height of the second triangle are half of the base and height of the first triangle.

This means that the area of the second triangle is 1/2(1/2bh) = 1/4bh, which is one-fourth of the area of the first triangle. In other words, the area of the second triangle is 25% of the area of the first triangle. Therefore, the relationship between the areas of the two triangles is that the area of the second triangle is one-fourth of the area of the first triangle.

When Charlie draws a triangle with given dimensions and then creates a second triangle with dimensions halved, the relationship between the areas of the two triangles is a ratio of 1:4. This is because the area of a triangle is calculated using the formula A = 0.5 * base * height. When both the base and height are halved, the new area becomes A = 0.5 * (base/2) * (height/2), which simplifies to A = 0.25 * base * height. Comparing the original area to the new area (1 * base * height versus 0.25 * base * height), we see that the area of the second triangle is one-fourth or 25% the area of the original triangle.

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5% of 5,000 interest rates equals to 250 interest rates.

Answer:

$94

Step-by-step explanation:

hope this helps

The interest on the loan is $1200.

Given,

In the question:

You get a loan from the loan star bank to help pay for your home.

and, if you borrowed $12,000 at 10% for one year.

To find the interest on the loan.

Now, According to the question;

Based on the given conditions:
Formulate:

Borrowed= $12,000

At 10% for one year

12000 x 10%

Convert percentage into decimal

12000 x 0.1

calculate the product or quotient:

= 1200

Hence, The interest on the loan is $1200.

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Answer:

\(\dfrac{1}{64}\)

Step-by-step explanation:

Hemi-, demi- and semi- are prefixes which mean half.

When applied to musical notation, each time a prefix is added it means the note's value is halved.

Therefore, if a quaver is one-eighth of a semibreve, then a semiquaver is half of a quaver, which means it's one-sixteenth of a semibreve.

\(\large \begin{aligned}\sf quaver & = \sf\dfrac{1}{8}\:of\:a\:semibreve\\\\\implies \sf hemisemidemiquaver & = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times quaver\\\\& = \sf \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{8}\\\\& = \sf \dfrac{1}{64}\:of\:a\:semibreve\end{aligned}\)

Therefore, a hemisemidemiquaver is one-sixty-fourth of a semibreve.

We have that, when testing a certain type of truck tire on rough terrain, it is observed that 25% of the trucks fail to complete the test without blowout, the probability that of the next 15 trucks tested, at least one will not able to complete the test run without an explosion is 0.987

Given that when testing a certain type of truck tire on rough terrain, it is found that 25% of the trucks do not complete the test without blowout.So, the probability that a truck completes the test without a blowout is:

P (A complete truck test without blowout) = 1 - P (A complete truck test without an explosion) = 1 - 0.25 = 0.75

Now, we need to find the probability that of the next 15 trucks tested, at least one will not complete the test without an explosion. This can be found using the complement rule. The complement of the probability that at least one truck does not complete the test without a blowout is the probability that all 15 trucks complete the test without a blowout.

P(All 15 trucks complete the test without a blowout) = P(One truck completes the test without a blowout) x P(A second truck completes the test without a blowout) x ... x P(The fifteenth truck completes the test without a blowout) = 0.75 x 0.75 x ... x 0.75 (15 times)= 0.75^15= 0.013

But we need the probability that at least one truck fails to complete the test without a blowout, which is the complement of the above probability.

P(At least one truck does not complete the test without blowout) = 1 - P(All 15 trucks complete the test without blowout)= 1 - 0.013= 0.987

Therefore, the probability that of the next 15 trucks tested, at least one will not be able to complete the test run without an explosion is 0.987.

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The formula for the nth term of the sequence \((-1)^n\) / (2n + 4) creates a sequence that alternates between positive and negative values and gets smaller as n increases.

First, let's break down what the formula for the nth term means. The \((-1)^n\) term is simply a way to alternate between positive and negative values, depending on the value of n. When n is an even number, \((-1)^n\) is equal to 1, and when n is an odd number, \((-1)^n\) is equal to -1.

The denominator, 2n + 4, increases as n increases. This means that as n gets larger, the fraction becomes smaller and smaller since the numerator \((-1)^n\) stays the same. In other words, the sequence alternates between positive and negative terms and becomes smaller as n increases.

To find the first six terms of the sequence, we simply substitute the values 1 through 6 for n in the formula and simplify each term. This gives us:

\(a_1 = (-1)^1 / (2(1) + 4) = -1/6\)

\(a_2 = (-1)^2 / (2(2) + 4) = 1/8\)

\(a_3 = (-1)^3 / (2(3) + 4) = -1/10\)

\(a_4 = (-1)^4 / (2(4) + 4) = 1/12\)

\(a_5 = (-1)^5 / (2(5) + 4) = -1/14\)

\(a_6 = (-1)^6 / (2(6) + 4) = 1/16\)

So the first six terms of the sequence are -1/6, 1/8, -1/10, 1/12, -1/14, and 1/16.

Overall, the formula for the nth term of the sequence \((-1)^n\) / (2n + 4) creates a sequence that alternates between positive and negative values and gets smaller as n increases. By substituting the values 1 through 6 for n, we can find the first six terms of the sequence.

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Answer:

Equivalent measurements: teaspoon, ounce, pint, pound

You will find a table of equivalent measurements in the back of many cookbooks:

1 tablespoon = 3 teaspoons  

      1 cup = 16 tablespoon = 8 ounces  

    1/4 cup = 4 tablespoons  

    1/3 cup = 5 tablespoons plus 1 teaspoon  

     1 pint = 2 cups = 16 ounces  

    1 quart = 4 cups (2 pints) = 32 ounces  

   1 gallon = 4 quarts

    1 pound = 16 ounces

  1/2 pound = 8 ounces

  1/4 pound = 4 ounces

Note that a pint is 16 ounces of volume, while a pound is 16 ounces of weight. The popular rhyme "A pint's a pound, the world around" can help you remember this, but keep in mind that they're not really equivalent.

Doubling a recipe can be easy (just put in two of each measurement), but what if you need to divide a recipe in half? Here are some measurements that may help:

Measurement    1/2 Measurement

1/8 teaspoon   just a dash

1 tablespoon   1 1/2 teaspoons

1/4 cup        2 tablespoons

1/3 cup        2 tablespoons + 2 teaspoons

3/4 cup        6 tablespoons

Step-by-step explanation:

The number that will complete the square to solve equation is 1/36.

What is completing the square?

For some values of h and k, completing the square is an elementary algebraic method for changing a quadratic polynomial of the form

ax^2 + bx + c to the form a^2 + k. In other words, the quadratic expression is completed by inserting a perfect square trinomial.

Consider, the given polynomial

3w^2 - w - 24 = 0

Rewrite the polynomial in the form ax^2 + bx = c

Add 24 on both sides,

3w^2 - w - 24 + 24 = 24

⇒ 3w^2 - w = 24

Divide both sides by 3,

\(w^2-\frac{1}{3}w = 8\)

To complete the square x^2 + bx, we add \((\frac{b}{2} )^2\)

Here, b = -1/3

So, \((\frac{b}{2})^2 = (\frac{-1/3}{2})^2 = (-\frac{1}{6})^2 = \frac{1}{36}\)

Adding to both sides of the equation, we have

\(w^2-\frac{1}{3}w+\frac{1}{36} = 8+\frac{1}{36}\)

Hence, the number that will complete the square to solve an equation is 1/36.

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The probability of selecting an even number from 1 to 100 is C) 0.5, or 50%.

There are 100 numbers to choose from, and half of them (50) are even numbers (2, 4, 6, 8, ... 98, 100), while the other half are odd numbers (1, 3, 5, 7, ... 97, 99). Since each number has an equal chance of being selected, the probability of selecting an even number is equal to the ratio of the number of even numbers to the total number of possible choices, which is 50/100 or 0.5. This means that in the long run, if we were to select numbers randomly from 1 to 100 using the same method, we would expect to get an even number about half of the time.

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Answer:

5!=120 ways

Step-by-step explanation:

1st colour 5 ways

2nd colour 4 ways

3rd colour 3 ways

4th colour 2 ways

5th colour 1 way

total no of ways = 5 × 4 × 3 × 2 ×1 =5! = 120 ways

Answer:

4.443*10^9

Step-by-step explanation:

pls heart and give brainliest much appreciated

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE

As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.

So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.

Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.

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The complete question is given below:

Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:

"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."

Answer:

40

Step-by-step explanation:

24 divided by 3 is 8.

8 times 5 is 40.

Answer:

nth term = 4 + n^2

Step-by-step explanation:

Sorry if the answer is long but I'm hoping my explanation can help.

In order to understand the issue, we should try to find the pattern between the terms given.

The terms given were 5, 8, 13, 20 and 29.

Between the first term and second term, the difference is 3.

Between the second and third term, the difference is 5.

The pattern goes on and we find out that the difference between the (n-1)th term and the nth term is

2n - 1.

Hence, we can determine the pattern of the numbers is

nth term = (n-1) term + 2n - 1

We can use this to find term 0 (before term 1) by plugging in the values for term 1

5 = 0th term + 2 (1) - 1

5 = 0th term + 1

Hence the 0th term = 4

If we expand on the summation,

We can find the nth term

nth term = 4 + 2 (1) - 1 + 2(2) - 1 + ... + 2(n-1) - 1 + 2n - 1

As we can see, the number 1 has been subtracted n times (excluding the -1 in 2(n-1)). Hence, we can split combine all of the subtracted ones into -n.

We can rewrite it as

nth term = 4 + 2 (1) + 2(2) + ... + 2(n-1) + 2n - n

Now, we will move 4 and n to one side.

nth term = 4 - n + 2 (1) + 2(2) + ... + 2(n-1) + 2n

We can factorize 2 out from every term to the right of -n. This would give out

nth term = 4 - n + 2 (1 + 2 + ... + (n-1) + n)

The term (1 + 2 + ... + (n-1) + n) can actually be rewritten by using the triangular formula.

The triangular formula is stated such that

Tn = (n*(n+1))/2

This heavily simplifies the equation into

nth term = 4 - n + 2 [(n*(n+1))/2]

This equation becomes

nth term = 4 - n + n^2 + n.

Now, we can finally simplify into the final equation

nth term = 4 + n^2

Answer:

>

Step-by-step explanation:

2 is greater than -4, so put >

2>-4

Answer:

2.5 times taller

Step-by-step explanation:

6+6=12 3+3=6 12+6=18  so the streetlight is 18 ft

Answer:

B. A washing machine.

Step-by-step explanation:

What's Electrical energy?

Electrical energy is energy derived from electric potential energy or kinetic energy. When used loosely, electrical energy refers to energy that has been converted from electric potential energy.

Hope this helps!

Answer:

to f(x) = 6x^2 - 13x + 5. One way to do this is to complete the square, which involves adding and subtracting a constant term to the quadratic expression to make it a perfect square trinomial. This can be done as follows:

f(x) = 6x^2 - 13x + 5

= 6(x^2 - (13/6)x) + 5

= 6(x^2 - (13/6)x + (13/12)^2 - (13/12)^2) + 5

= 6((x - 13/12)^2 - 169/144) + 5

= 6(x - 13/12)^2 - 101/24

Therefore, an equivalent function to f(x) is g(x) = 6(x - 13/12)^2 - 101/24.

Answer:

Step-by-step explanation: 1 you see white mice and grey mice 2 the bird goes for the white mice 3 the bird mainly ate the white mice ( i hope this helps you a little bit)

The event happening in figures 1-3 is that the bird is catching all the white mouse one by one.

Image description or picture discription is to figure out and express the image in the word form. In image description, one anlaze each point of the picture to identify that what is happning in it.

The given image has three part. Lets understands all the parts one by one.

Thus, the event happening in figures 1-3 is that the bird is catching all the white mouse one by one.

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Answer:

-3

Step-by-step explanation:

Let the number be x.

x^2 - 21 = 4x

x^2 - 4x - 21 = 0

(x - 7)(x + 3) = 0

x - 7 = 0 or x + 3 = 0

x = 7 or x = -3

Answer: -3

Answer:

-3

Step-by-step explanation:

I got it right

Answer:

5% of the time or in a decimal it's 0.05

Answer:

non of these choice are correct

Step-by-step explanation:

288.09-43.15+100.00-24.10 = 320.84

Answer:

Step-by-step explanation:

Because even if you keep trying to find the solution it won't give you the solution so that'll mean there is NO solution

I hope this helped, plz rate 5 stars, give thanks, and Mark as brainilest (Probably) That'll be much appreciated

Because, When x=9, the original equation 

\( \sqrt{x} + 1 + 5 = 3\)

does not hold true.

We will drop x=9 from the solution set.

thats why this this equation has no solution.

Answer:

C

Step-by-step explanation:

the one that the median is 14

Answer:

The one with a median of 13

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

Step 1: Write out equation

3x - 5 = 1

Step 2: Add 5 to both sides

3x = 6

Step 3: Divide both sides by 3

x = 2

3x - 5 = 1.

5 + 1 = 6

3x = 6

6 ÷ 3 = 2

x = 2.

We randomly select three apples from a crate at a farmer's market amount and ask the vendor to give them to us. Each student in a class rolls a die and those who get a certain number are randomly chosen to complete a special survey.

Scenario 1 describes a random sampling without replacement. This involves randomly selecting three apples from a crate at a farmer's market and asking the vendor to give them to us. This ensures that all apples in the crate are given an equal chance of being selected, and once one has been selected, it cannot be selected again.

Scenario 2 also represents random sampling without replacement. Each student in the class is randomly chosen to roll a die and those who get a certain number are selected to complete a special survey. This samplings ensures that all students in the class have an equal chance of being chosen and those who have already been chosen cannot be chosen again.

Finally, scenario 3 also represents random sampling without replacement. This involves randomly choosing ten patients each day from all patients who had an appointment that day. This ensures that patients with all kinds of ailments, including seasonal ones such as influenza, have an equal chance of being selected and those who have already been chosen cannot be chosen again.

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Answer:

see explanation

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

We require to find a₁ and d

given a₃ = 2 and a₅ = 32 , then

a₁ + 4d = 32 → (1)

a₁ + 2d = 2 → (2)

subtract (2) from (1) term by term to eliminate a₁

0 + 2d = 30

2d = 30 ( divide both sides by 2 )

d = 15

substitute d = 15 into (2) and solve for a₁

a₁ + 2(15) = 2

a₁ + 30 = 2 ( subtract 30 from both sides )

a₁ = - 28

Then

\(a_{n}\) = - 28 + 15(n - 1) = - 28 + 15n - 15 = 15n - 43

Explicit formula is \(a_{n}\) = 15n - 43

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

A recursive formula allows a term in the sequence to be found by adding d to the previous term, that is

\(a_{n}\) = \(a_{n-1}\) + 15 ; a₁ = - 28