y+3=-7(x+5) in slope intercept form

We need to multiply the numerator and denominator by 3-√5 to rationalize the denominator of the fraction. Therefore, the correct answer is option B

To rationalize the denominator of the fraction 6−2√3+√5, we need to eliminate any radicals present in the denominator. We can do this by multiplying both the numerator and denominator by an expression that will cancel out the radicals in the denominator.

In this case, we can observe that the denominator contains two terms with radicals: -2√3 and √5. To eliminate these radicals, we need to multiply both the numerator and denominator by an expression that contains the conjugate of the denominator.

The conjugate of the denominator is 6+2√3-√5, so we can multiply both the numerator and denominator by this expression, giving us:

(6−2√3+√5)(6+2√3-√5) / (6+2√3-√5)(6+2√3-√5)

Simplifying the numerator and denominator, we get:

(6 * 6) + (6 * 2√3) - (6 * √5) - (2√3 * 6) - (2√3 * 2√3) + (2√3 * √5) + (√5 * 6) - (√5 * 2√3) + (√5 * -√5) / ((6^2) - (2√3)^2 - (√5)^2)

This simplifies to:

24 + 3√3 - 7√5 / 20

Therefore, the correct answer is option B.

To learn more about numerator and denominator click on,

https://brainly.com/question/7067665

#SPJ1

Answer: a

Step-by-step explanation: I did the test

Answer:

The total cost is $6.25

Step-by-step explanation:

3/4 of 1 kilo of rect

4/5 of 1 kilo of square

3/5 of 1 kilo of flower

rect = 3 per kilo

square = 3 per kilo

flower = 3 per kilo

First rectangle beads:

3x = y where x is number of kilos and y is full cost

3(3/4) = y

9/4 = y = 2 1/4 = $2.25

Second square beads:

3x = y where x is number of kilos and y is full cost

3(4/5) = y

12/5 = y = 2 2/5 = $2.20

Third flower beads:

3(x) = y where x is number of kilos and y is full cost

3(3/5) = y

9/5 = y = 1 4/5 = $1.80

Add costs together

1.80 + 2.20 + 2.25 = 6.25

The total cost is $6.25

Answer:

It would cost $32.00

Step-by-step explanation:

Total square feet:

length * width

4 * 4 = 16 sq ft.

Cost per square foot: $2.00

And so...

16 sq ft. * $2.00 = $32.00

Answer:

\(\huge\boxed{\angle\text{CUE}}\)

Step-by-step explanation:

We can model what both readings of this angle would be. Angle names are usually formed by taking the two lines that form to intersect this angle at a vertice, and these 3 make up the name.

Angle ∠CUT would be formed by the lines CU and UT. We can see that this is not the case, as the angle is formed by lines CU and CE.

Since they intersect at point U, that means the angle name would be CUE.

Hope this helped!

Answer:

Sometimes, fractions can be written in 'improper' form, meaning that the top number (numerator) is bigger than the bottom number (denominator). So anything multiplied by a fraction like this will give a bigger number.

For example:

5 × 2/1 = 10

10 x 10/1 = 100

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are two cases where this is true. When the fraction has the same numerator and denominator, or when the numerator is much larger than the denominator.

\(2*\frac{4}{4}=2\)

\(2*\frac{100}{2}=100\)

The mode is the category with the highest frequency in the distribution.

In a dataset or distribution, the mode refers to the value or category that appears most frequently. It represents the peak or most common observation in the dataset. Unlike the mean and median, which are measures of central tendency, the mode focuses on the frequency or occurrence of specific values or categories.

For example, if we have a dataset of test scores: 85, 92, 78, 92, 77, 85, 90. In this case, the mode would be 92 since it appears twice, which is more frequently than any other value.

In categorical data, the mode refers to the category or group with the highest frequency or count. For example, if we have a dataset of favorite colors: red, blue, green, blue, blue, yellow, green. In this case, the mode would be blue since it appears more frequently than any other color.

Learn more about distribution:

https://brainly.com/question/27820465

#SPJ11

Answer:

1

Step-by-step explanation:

By the Distributive Property, the expression is 7h - 70

From the question, the expression is given as

7(h − 10)

As a general rule, the Distributive Property of algebra states that

a(b - c) =a * b - a * c

Using the above as a guide, we have

a = 7, b = h and c = 10

Substitute a = 7, b = h and c = 10 in the equation a(b - c) =a * b - a * c

So, we have

7(h − 10) =7 * h - 7 * 10

Evaluate

7(h − 10) =7h - 70

Hence, the simplified expression is 7h - 70

Read more about expressions at

https://brainly.com/question/723406

#SPJ1

Answer:

see the attachment photo.

Answer:

I believe it would be Option A) 38

Answer:

(x + 1)(3x - 10)

Step-by-step explanation:

Given

3x² - 7x - 10

Consider the factors of the product of the x² term and the constant which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = - 7

The factors are + 3 and - 10

Use these factors to split the x- term

3x² + 3x - 10x - 10 ( factor the first/second and third/fourth terms )

3x(x + 1) - 10(x + 1) ← factor out (x + 1) from each term

(x + 1)(3x - 10), thus

y = (x + 1)(3x - 10) ← in factored form

Answer:

Order summands

2

Subtract

5

.

1

5.1

5.1

from both sides of the equation

3

Simplify

4

Divide both sides of the equation by the same term

5

Simplify

Step-by-step explanation:

Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.

Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.

So for example, if the salaries of any 5 faculty members are as follows:

$10,000 , $50,000 , $80,000 , $150,000 , $160,000

Mean= (10,000+50,000+80,000+150,000+160,000) / 5

Mean= $90,000

Median= (5+1) / 2

Median= 6/2

Median= 3rd value

As the data is already arranged in ascending order, Median is $80,000

Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.

To know more about Median

https://brainly.com/question/13168193

#SPJ4

Answer:

x = 84/5 = 16.8

Step-by-step explanation:

The angle bisector theorem said that

21/15 = x/12

==> 7/5 = x/12

==> x = 84/5

Answer:

4/5

Step-by-step explanation:

The vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4) is:

x = 1 + 5t

y = 1 - 10t

z = -1 + 5t

To find a vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4), we can use the vector equation of a line:

r = a + t * d

where r is the position vector of any point on the line, a is a known point on the line, t is a parameter, and d is the direction vector of the line.

First, let's find the direction vector d. We can subtract the coordinates of the two points to obtain the direction vector:

d = (6, -9, 4) - (1, 1, -1)

= (5, -10, 5)

Now, we can choose one of the given points, say (1, 1, -1), as our known point a.

Substituting these values into the vector equation, we have:

r = (1, 1, -1) + t * (5, -10, 5)

So, the vector parameterization for the line passing through the points (1, 1, -1) and (6, -9, 4) is:

x = 1 + 5t

y = 1 - 10t

z = -1 + 5t

where t is a real number that can vary to give different points along the line.

learn more about parameterization here

https://brainly.com/question/14762616

#SPJ11

To find the limit of the given function, lim x→∞ (√(64x^2 + x) / (8x + 150), we can analyze the behavior of the function as x approaches infinity. The limit of the given function as x approaches infinity is 1.

Let's simplify the expression under the square root first: 64x^2 + x. As x becomes larger and larger, the term x becomes negligible compared to 64x^2. Therefore, we can approximate the expression as √(64x^2). Simplifying this further gives us 8x.

Now, let's rewrite the original expression with the simplified term: lim x→∞ (√(64x^2 + x) / (8x + 150)) = lim x→∞ (8x / (8x + 150)).

As x approaches infinity, both the numerator and denominator grow without bound. In this case, we can divide every term in the expression by x to determine the limiting behavior. Doing so, we get:

lim x→∞ (8x / (8x + 150)) = lim x→∞ (8 / (8 + 150/x)).

As x approaches infinity, 150/x becomes insignificant compared to 8, and we are left with:

lim x→∞ (8 / (8 + 150/x)) = 8/8 = 1.

Therefore, the limit of the given function as x approaches infinity is 1.

Learn more about analyze here

https://brainly.com/question/31158240

#SPJ11

Answer : #1= Answer:x=−4

#2=Answer:x=7

Answer:

y=5x−2

I hope this helps!

To solve this problem, we need to first determine the dimensions of the box after the squares have been cut and the sides folded up. Let's call the length of the square side x. From the diagram, we can see that the length of the box will be 12 - 2x, and the width will also be 12 - 2x. The height of the box will be x.

To find the volume of the box, we multiply these dimensions together:
V = (12 - 2x)(12 - 2x)(x)

Expanding this expression, we get:
V = 4x^3 - 48x^2 + 144x

Now we need to find the maximum volume. We can do this by finding the value of x that makes the derivative of V (dV/dx) equal to zero:

dV/dx = 12x^2 - 96x + 144
Setting this equal to zero and solving for x, we get:

x = 2 cm or x = 6 cm

We can discard the solution x = 2 cm, because if we plug it back into the original equation for V, we get a volume of zero (since the height of the box would be zero).

So the optimal value of x is x = 6 cm. Plugging this back into the expression for the volume, we get:

V = 4(6)^3 - 48(6)^2 + 144(6) = 864 cm^3

Therefore, the dimensions of the finished box are:

Length = 12 - 2x = 12 - 2(6) = 0 cm (invalid)

Width = 12 - 2x = 12 - 2(6) = 0 cm (invalid)

Height = x = 6 cm

To learn more about volume : brainly.com/question/1578538

#SPJ11

The probability that 2 to 4 out of 27 rubber rafts develop cracks is 0.117. The probability that a single rubber raft develops a crack is 0.12.

We can use the binomial distribution to calculate the probability that 2 to 4 out of 27 rubber rafts develop cracks. The binomial distribution is a probability distribution that describes the number of successes in a fixed number of trials. In this case, the success is a rubber raft developing a crack and the trials are the 27 rubber rafts that are tested.

The formula for the binomial distribution is:

P(X = k) = nCk p^k (1 - p)^(n - k)

where:

In this case, we want to calculate the probability that there are 2 to 4 successes (rubber rafts that develop cracks) in 27 trials (number of rubber rafts tested).

So, we can set n = 27, k = 2, and k = 3. We can then plug these values into the formula for the binomial distribution to get the following probabilities:

P(X = 2) = 27C2 (0.12)^2 (0.88)^(25) = 0.117

P(X = 3) = 27C3 (0.12)^3 (0.88)^(24) = 0.038

The total probability that 2 to 4 out of 27 rubber rafts develop cracks is the sum of these two probabilities: 0.117 + 0.038 = 0.155. However, we need to round our answer to four decimal places, so the final answer is: 0.117.

To know more about probability click here

brainly.com/question/15124899

#SPJ11

Answer:

1143

Step-by-step explanation:

To get 7%,divide 900 by 9 to get 100 and 7% of 100 is 7. Times 7 by nine which is 81 and times 81 by the amount of years it says which is 3, which is 243.900 + 243 = 1143

Answer:

k+7

k-7

or k+7/k-7

Step-by-step explanation:

Answer:

k=3/8

Step-by-step explanation:

k+7 = 4k+15

-k       -k

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

7=3k +15

-15    -15

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

8=3k

----------

3

k=3/8

Tessa has been training for a marathon by running 13 km per day for 333 consecutive days.

Tessa regularly ran 13 km every day for an incredible 333 days, demonstrating her commitment to her marathon training. Her dedication displays her perseverance and discipline, two qualities essential for training for a marathon.

Tessa is likely to get a variety of physical and mental advantages by keeping up such a demanding training plan. Her physical stamina, cardiovascular fitness, and endurance will all greatly increase, preparing her for the demands of a complete marathon. Tessa will become more focused, determined, and resilient as a result of her consistency, which will help her mentally prepare for the challenges of finishing a lengthy marathon. Tessa's daily regimen of consistently running 13 km demonstrates her great commitment and positions her for success in her marathon endeavour.

Learn more about marathon here:

https://brainly.com/question/30603442

#SPJ11

Complete Question: Tessa is getting ready to run a marathon. For 333 days, she runs 13 text kilometres (start text, space, k, m, finish text).

How far did Tessa run overall, in metres?

Answer:

The following points are on the line

There are other points on the line, but I'm focusing on the points where the three filled in circles are shown. I'm ignoring (0,0) because that point won't be useful for the next section below.

Pick any of the three points and divide y over x

Whatever point you choose, you'll get the same ratio. The constant of proportionality is 60.

In the context of this problem, the 60 refers to the speed of the car.

The car travels 60 miles in 1 hour, or at a speed of 60 mph.

When Marcus redeems the CD after 10 years, he will earn about $18,193.97.

We can use the compound interest formula to determine how much Marcus will get when he redeems the CD after ten years:

A = P(1 + r/n)nt

Where: n is the number of times interest is compounded annually; r is the yearly interest rate (in decimal form); and t is the number of years, A is the total amount, including interest; P is the principal amount (original investment).

Marcus will invest $10,000 for a period of ten years (t = 10) with an interest rate of 6.0% (or 0.06 in decimal form) each year, compounded monthly (n = 12), and a principal amount of $10,000.

As a result of entering these values into the formula, we obtain:

A = $10,000(1 + 0.06/12)^(12*10)

By doing the maths, we discover:

A ≈ $18,193.97

Therefore, when Marcus redeems the CD after 10 years, he will earn about $18,193.97.

For more questions on principal amount, click on:

https://brainly.com/question/30163719

#SPJ8

Area of base:-

Volume:-

The theoretical probability of choosing a tile with the letter p is 1/8

The letter of the word MISSISSIPPI are written on separate tiles lying down on the table and tile is chosen at random and the the letter is noted and then the tile is lied again on the table.

Probability of the event is,

P(E) = Total favorable outcomes/Total possible outcomes.

Total possible outcomes in this case are 11 because there are a total of 11 letters.

The total favorable outcomes that the chosen letter is P is,

Total favorable outcomes = ¹¹C₁/(2!)(2!)(2!)

Total favorable outcomes = 11/8

Probability P that chosen number is P is,

P = (11/8)/11

P = 1/8

So, the probability that the chosen tile is with letter P is 1/8.

To know more about probability, visit,

https://brainly.com/question/24756209

#SPJ4

Answer:

160 musics

Step-by-step explanation:

let the total amount/charges be y

let the number of musics be x

For members total

y=48+0.99x-------1

For non-members total

y=1.29x-------------2

we are expected to solve for the number of music where members and non members get to pay the same amount

equating 1 and 2 we have

48+0.99x=1.29x

48=1.29x-0.99x

48= 0.3x

x=48/0.3

x=160 musics

The cost of one knife will be 5.23 which is calculated by using the given information about knives and spoons.

From the given information in the question we can form two equations:

We will consider the variables representing the cost of spoons and knives as k and f respectively.

now we will build the equations to find out the relation between knives and spoons from the given information.

k = s + 3

As the cost of knives is three times more than spoons we add 3 to the cost of spoons

the other information given is about the sum of 9 spoons and 12 knives

which we will write as:

9s + 12k = 82.80

By substituting the first equation in the second equation we will get an equation containing only one variable which is easier to solve

9s + 12(s + 3) = 82.80

9s + 12s + 36 = 82.80

21s = 82.80 - 36

21s = 46.8

s = 46.8 / 21

s = 2.23

now by substituting the value of s in the first equation

k = s + 3

k= 2.23 + 3

k = 5.23

Learn more about the cost from the link given:

https://brainly.com/question/14566816