what is the perimeter of a triangle with the points (-9,4) (7,4) and (7, -8)

The solution of the system of equations is

A system of equations is a pair of equations containing two unknowns.

Since we have the system of equations

4y² - 16x + 3y + 67 = 0  (1)

3x + y - 4 = 0   (2)

From equation (2),

y = -3x + 4        (3)

substituting equation (3) into equation (1), we have

4y² - 16x + 3y + 67 = 0

4(-3x + 4)² - 16x + 3y + 67 = 0

Expanding the terms in the brackets, we have

4(9x² -24x + 16) - 16x + 3(-3x + 4) + 67 = 0

Removing the brackets, we have

4(9x² -24x + 16) - 16x + 3(-3x + 4) + 67 = 0

36x² - 96x + 64 - 16x - 9x + 12 + 67 = 0

Collecting like terms, we have

36x² - 96x - 16x - 9x + 64  + 12 + 67 = 0

36x² - 121x + 143 = 0

Using the quadratic formula, we solve for x

So, \(x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}\)

where

So, substituting the values of the variables into the equation, we have

\(x = \frac{-(-121) +/-\sqrt{(-121)^{2} - 4 \times 36 \times -143} }{2\times 36}\\= \frac{121 +/-\sqrt{14641 - 20592} }{72}\\= \frac{121 +/-\sqrt{-5951} }{72}\\= \frac{121 +/- 77.14i}{72}\\= 1.681 +/- 1.071i\)

So, x = 1.681 ± 1.071i

Since y = -3x + 4, substituting x into y, we have

y = -3(1.681 ± 1.071i)

y = 5.043 ± 3.213i

So,

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Answer:

A

Step-by-step explanation:

its A its AAAAAAAAAAAAA

Answer:

x = 3

Step-by-step explanation:

2(x+4) + 2 = 5x + 1

2x + 8 + 2 = 5x + 1

2x + 10 = 5x + 1

-3x + 10 = 1

-3x = -9

x = 3

To solve for x, we need to simplify the equation and isolate the variable. Let's proceed with the given equation:

2(x + 4) + 2 = 5x + 1

First, distribute the 2 to the terms inside the parentheses:

2x + 8 + 2 = 5x + 1

Combine like terms on the left side:

2x + 10 = 5x + 1

Next, let's move all terms containing x to one side of the equation and the constant terms to the other side. We can do this by subtracting 2x from both sides:

2x - 2x + 10 = 5x - 2x + 1

Simplifying further:

10 = 3x + 1

To isolate the x term, subtract 1 from both sides:

10 - 1 = 3x + 1 - 1

9 = 3x

Finally, divide both sides of the equation by 3 to solve for x:

9/3 = 3x/3

3 = ×

Therefore, the solution to the equation is x = 3.

The rose gold bracelets sold by Chantel's fine jewelry store are considered price elastic, as an increase in price resulted in an apparent increase in demand and sales.

Based on the information provided, Chantel raised the price of her rose gold bracelets by $75 to cover unexpected expenses. Surprisingly, she observed an increase in sales at the higher price point. This suggests that the rose gold bracelets are price elastic.

Price elasticity of demand refers to the responsiveness of the quantity demanded to changes in price. When a product is price elastic, an increase in price leads to a proportionately larger decrease in quantity demanded, resulting in a decrease in total revenue. Conversely, a decrease in price would lead to a proportionately larger increase in quantity demanded and total revenue.

This suggests that the demand for these bracelets is relatively elastic, meaning that customers are responsive to changes in price and perceive the higher price as an indicator of increased value, exclusivity, or quality.

Several factors may contribute to this phenomenon. The rose gold bracelets may have unique design elements or craftsmanship that customers are willing to pay a higher price for.

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Answer:

The Answer is 18

Hope this helps! :)

Step-by-step explanation:

This question is Incomplete

Complete Question

The bakery bought 4 bags of flour containing 3.5 kg each. 0.475 kg of flour is needed to make a batch of muffins, and 0.65 kg is needed to make a loaf of bread.

a. If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your answer in kilograms.

b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour? Explain your answer.

Answer:

a. 8.85kg of flour is left.

b. 2.95 bins

Step-by-step explanation:

The bakery bought 4 bags of flour containing 3.5 kg each.

Total kg of flour the Bakery bought : 4 × 3.5kg

= 14 kg of flour

0.475 kg of flour is needed to make a batch of muffins

1 batch of muffin = 0.475kg of flour

4 batches of muffins = ???

Cross Multiply

4 batches × 0.475kg/ 1 batch

= 1.9kg of flour was used.

0.65 kg is needed to make a loaf of bread.

1 loaf of bread = 0.65kg of flour

5 loaves of bread = ???

Cross Multiply

5 loaves × 0.65/1 loaf

= 3.25 kg of flour.

Total kg of flour used = 1.9kg + 3.25kg

= 5.15kg of flour.

The amount of flour left = 14kg - 5.15kg

= 8.85kg of flour is left.

b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour?

3 kg of flour is stored = 1 bin

8.85 kg of flour is stored = x

Cross Multiply

3kg × x = 8.85kg × 1 bin

x = 8.85 kg × 1 bin/3kg

x = 2.95 bins

SOLUTION

Step 1: Write out the formula for percentage increase

Step2: Identify the parametrs

Step3: substitute into the formula in step1

Therefore the percentage increase is 33.3% to the nearest tenth

Answer:

76,

Step-by-step explanation:

If you divide 57 by 3, you get 19. If you times 19 by 4 that is the total number of students there were in all.

The original activity of the sample can be calculated using the equation A=A0e^(-kt), where A0 is the initial activity, k is the decay constant, and t is the elapsed time.

1. Identify the given values: Half-life (t1/2) = 3.8 days, Activity level (A) = 0.17 bq/L, and Elapsed time (t) = 5.0 days.

2. Calculate the decay constant (k) using the equation k = ln(2)/t1/2.

k = ln(2)/3.8 days

k = 0.1815

3. Calculate the original activity (A0) using the equation A0 = A/e^(-kt).

A0 = 0.17 bq/L/e^(-0.1815)

A0 = 0.21 bq/L

Therefore, the original activity of the sample was 0.21 bq/L.

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Answer:

2 4/5

Step-by-step explanation:

Answer:

It is 1 19/30. Hope that helped

Answer:

True

Right angles measure 90° . So each vertical angle = 90° and hence they are equal

Step-by-step explanation:

The ball reaches the skydiver at 2.81 seconds.

Height of sky diver

          h(t) = -300t + 1000

Height of ball

           h(t) = -16t² + 100t

We need to find out when the ball reach the skydiver

That is both heights are equal

              -300t + 1000 = -16t² + 100t

                16t² - 400t + 1000 = 0

                t = 22.18 s   or t = 2.81 s  

The ball reaches the skydiver at 2.81 seconds.

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The probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.

The probability of a randomly selected student having at least two siblings can be calculated by adding the probabilities of having two and three or more siblings.

Using the given probabilities, the calculation is as follows:

P(at least 2 siblings) = P(2 siblings) + P(3 or more siblings)

= 0.121 + 0.039

= 0.160

Therefore, the probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.

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The z-score for an observation of 200 is approximately -2.000.

Here are the steps to calculate the z-score for an observation of 200 based on a normal distribution with a mean of 500 and a standard deviation of 150:

        x - μ = 200 - 500 = -300

        -300 / 150 = -2

        -2 ≈ -2.000

So, the z-score for an observation of 200 is approximately -2.000.

A z-score is a measure of how many standard deviations a given value is from the mean of a dataset. It is calculated by subtracting the mean of the dataset from a given value and dividing the result by the standard deviation of the dataset.

In the case of a normal distribution with a mean of 500 and a standard deviation of 150, a z-score of -2 would indicate that an observation of 200 is 2 standard deviations below the mean. This information can be used to determine the proportion of data within the dataset that is above or below a certain value, or to make comparisons between different datasets.

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Of the following one that is not considered a guideline for developing visualizations is vary the scale to conserve space whenever possible. (Option B)

Data and information visualization refers to an interdisciplinary field that focuses on the graphic representation of data and information. It is an efficient way of communicating when the data or information is numerous. It aims to present the data in a clear manner and with a clear purpose. The aim of the texts and labels should be to clarify and not clutter. According to the guidelines for developing visualization, it is not recommended to vary the scale to conserve space whenever possible.

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The polynomial as constant, linear, quadratic, cubic, or quartic, and determine the leading term, the leading coefficient, and the degree of the polynomial  is Leading term=  x

Leading coefficient= -6

Degree of the polynomial = 1

Taking = g(x) = - 6x - 9

It is a linear function which has an intercept with the y - axis at x= 0, y= -9.

Where m= -6.

Leading term=  x

Leading coefficient= -6

Degree of the polynomial = 1

What are cubic and quadratic constant polynomials?

A variable is a constant polynomial if its highest exponent is 0. It is a linear polynomial if the highest exponent is 1. It is a quadratic polynomial if the largest exponent of a variable is 2, and a cubic polynomial if the maximum exponent is 3.

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The range in which 95% of the scores lie is between 75 and 95.

According to the Empirical Rule: For a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% of the data falls within 2 standard deviations of the mean, and approximately 99.7% of the data falls within 3 standard deviations of the mean.

So, about 95% of the scores lie between 75 and 95. T

This is because the mean score is 85 and one standard deviation is 5, so one standard deviation below the mean is 80 (85-5) and one standard deviation above the mean is 90 (85+5).

Two standard deviations below the mean are 75 (85-2*5) and two standard deviations above the mean is 95 (85+2*5).

Therefore, the range in which 95% of the scores lie is between 75 and 95.

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The missing word is "modulus". The statement should read: Twelve is congruent to 60 (modulus 8) because both 12 and 60 have 4 as a remainder when divided by 8.

The modulus function, also known as the modulo operation or mod function, is a mathematical operation that returns the remainder when one integer is divided by another. The modulo operation is a quick and efficient way to find the remainder of a division. For example, if we want to know the remainder when 23 is divided by 5, we can simply compute 23 % 5, which equals 3. The symbol "%" is often used to represent the modulo operation in computer programming, while "mod" is used in mathematical notation to indicate congruence. In either case, the statement means that 12 and 60 leave the same remainder when divided by 8.

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The direction cosines and direction angles will be - \(\frac{x}{r},\frac{y}{r},\frac{z}{r}\) and

cos⁻¹(\(\frac{x}{r}\)), cos⁻¹(\(\frac{y}{r}\)),cos⁻¹(\(\frac{z}{r}\)) respectively.

The direction cosines of a specified vector, m = xi + yj + zk, are the cosines of the angles it makes well with x, y, and z axes.

The direction cosines of m are cos a, cos b, and cos c  in the x, y, and z axes, respectively, if a forms the angles a,b and c (which are the direction angles) with the x, y, and z axes, respectively.

Let us consider equation as =  \(xi + yj +zk\)

vector of the equation will be - (x,y,z)

r = length of vector = \(\sqrt{x^{2} +y^{2} +z^{2} }\)

The direction cosines will be -

\(\frac{x}{r},\frac{y}{r},\frac{z}{r}\)

angles will be - cos⁻¹(\(\frac{x}{r}\)), cos⁻¹(\(\frac{y}{r}\)),cos⁻¹(\(\frac{z}{r}\))

Let us consider an example,

If we have vector as (1,2,3)

= i + 2j + 3k

= r = \(\sqrt{1^{2} +2^{2} +3^{2} }\)

= \(\sqrt{14}\)

Direction cosines will be -

\(\frac{1}{\sqrt{14} } , \frac{2}{\sqrt{14} }, \frac{3}{\sqrt{14} }\)

Angles will be -

cos⁻¹(\(\frac{1}{\sqrt{14} }\)), cos⁻¹(\(\frac{2}{\sqrt{14} }\)),cos⁻¹(\(\frac{3}{\sqrt{14} }\))

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The number of waffles can be made from 15 eggs are, 20 waffles.

the waffles can be calculates as follows

4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles

we need 6 eggs to make 8 waffles

So, the waffles can we make from 15 eggs = \(\frac{8}{6} X 15 = 20\) waffles

Hence, the number of waffles can be made from 15 eggs are 20 waffles.

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150.72

...............

Answer:

3/7=€24/? 24*7/3? Therefore Hannah received €56 as tip.

Step-by-step explanation:

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

Answer:

Step-by-step explanation:

1. Write your formula

2. Plug it in

3. Solve

these steps will help you out with all of your surface area problems.

Like this

Since it is a diameter you have to divide the diameter by 2. That will get you your radius. Then you write your formula for a cylinder. Your formula is...

V = Bh                            (Pie is also known as 3.14)

your big (B) is (pie times r squared) Then you add your height.

so your formula will look like this...

V = pie times r squared...

the full formula will be...

V = (3.14) times (2.5 squared) times the height which in this case is (12)

everything together will be...

V = (3.14) (2.5^2) (12)

all you have to do is multiply all of that and you will get your answer.

The answer is...

V = 236 inches ^2                        (Just a tip, the ^ sign means to the power of)

Both AB and BA exists and AB = [30] and BA= \(\left[\begin{array}{cccc}1&2&3&4\\2&4&6&8\\3&6&9&12\\4&8&12&16\end{array}\right]\)

To multiply two matrices we need to check if the number of columns of first matrix is equal to number of rows in second matrix. Then the multiplication exists.

Hence the order of the resulting matrix formed will be equal to number of rows of first matrix and number of columns of second matrix.

Thus AB exists since, Number of columns in matrix A = Number of rows in matrix B.

Therefore, AB = [ 1 2 3 4 ] \(\left[\begin{array}{ccc}1\\2\\3\\4\end{array}\right]\)

⇒AB = [ (1)(1) +(2)(2) +(3)(3) + (4)(4)]

⇒ AB = [ 1+ 4+ 9+ 16]

⇒AB = [30]

Thus BA exists since, Number of columns in matrix B = Number of rows in matrix A.

Therefore, BA =\(\left[\begin{array}{ccc}1\\2\\3\\4\end{array}\right]\) [ 1 2 3 4 ]

⇒BA = \(\left[\begin{array}{cccc}(1)(1)&(1)(2)&(1)(3)&(1)(4)\\(2)(1)&(2)(2)&(2)(3)&(2)(4)\\(3)(1)&(3)(2)&(3)(3)&(3)(4)\\(4)(1)&(4)(2)&(4)(3)&(4)(4)\end{array}\right]\)\({4*4}\)

⇒BA= \(\left[\begin{array}{cccc}1&2&3&4\\2&4&6&8\\3&6&9&12\\4&8&12&16\end{array}\right]\)

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Answer:

m<PQT= 94°

Step-by-step explanation:

If line QS bisect <PQR

m<PQS = m < SQR

7x-6= 4x+15

7x-4x= 15+6

3x= 21

X= 21/3

X= 7

m<PQS= 7x-6

m<PQS= 7(7)-6

m<PQS= 49-6

m<PQS= 43°

m<PQS= m<SQR

<mSQR=43°

m<PQR= m<PQS + m < SQR

m<PQR=43+43

m<PQR= 86°

BUT

m<PQR= m<TQW

m<PQT= m<RQW

m<PQR+m<TQW +m<PQT+ m<RQW

= 360°

Let m<TQW= x

86+86+x+x= 360

2x+172= 360

2x= 188

X= 94°

m<PQT= 94°

Answer: 24x² + 44x + 16

We have a vector that which location is true bearing of 140°.

We have to express the quadrant bearing.

True bearing is a directional measurement where the angle is measured clockwise from North.

We can graph this vector as:

Then, as the vector is close to the South direction, we measure the angle of the vector from the South direction. in this case, the angle goes to the East.

The angle has to complete 180° between S and N, so the angle for the quadrant bearing is 180-140 = 40°.

We then can express the quadrant bearing as: S 40° E.

NOTE: if the vector was closest to the N, we should have used the N direction to measure the quadrant bearing, to the East or to the West depending on the vector.

Answer: S 40° E.

Using Tap working problem solving,

when faucet and drain working together, the time to fill up the tub is 60 minutes.

We have the following information about question,

The time taken by faucet to fill up the tub

= 15 minutes

The time taken by drain to empty the tub

= 20 minutes

we have to calculate the time in which the tub is fully fill the tube with drain open.

Rate of fill up the tub by faucet = 1/15 i.e 1/15 th of tub in one minute .

Rate of empty the tub by drain = 1/20 i.e 1/20 th of tub in one minute.

In one minute both are working together and will fill the tub = 1/15 - 1/20 = 1/60 i.e 1/60 th of tub

Since, it takes one minute to fill 1/60th of the tub and it will take 60 minutes to fill the tub.

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