consider the points below. p(1, 0, 1), q(−2, 1, 3), r(7, 2, 5) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
(b) Find the area of the triangle PQR.

Answer:

we know that,

y intercept exist when x = 0

so,

⇢y = -4x +98

⇢y = -4 x 0 +98

⇢y = 98

so , the expected test score is 98

when x = 0

y = -4(0) +98

when x = 1

y= -4(1) +98 = 94

when x = 2

y= -4(2) +98 = 90

we can see the decresement of 4 points

We can see that the increament in absent days lead to lower scores ( one class = 4 points)

For 0 clases

Option A is certified as correct

So it decreasing not increasing

Option C is correct

Yes as the missed classes increase expected test decreasing as slope is negative.

Option F is correct

Answer:

The second one !!

Step-by-step explanation:

You always start from the origin... (0, 0) !! From the bottom of that function, from the origin, you would move to the right 1, down 4 in order to get where the graph is in the picture !!

i hope this made sense... have a good day !

Franco can read approximately 1.875 chapters of his history book in 1 hour, assuming his reading rate remains constant.

Franco read 3/8 of a chapter in 1/5 of an hour. To find out how many chapters he can read in 1 hour, we need to first determine his rate of reading.

To do this, we can set up a proportion:

3/8 of a chapter = x chapters
1/5 of an hour = 1 hour

Cross-multiplying, we get:

3/8 * 1 hour = x * 1/5

Simplifying:

3/8 = x/5

Cross-multiplying again:

15/8 = x

So Franco can read 15/8 or 1 7/8 chapters in 1 hour.

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1. coefficient

2. constant

3. variable

4. equation

5. inequality

6. two - step

-- let me know if you have any questions regarding this.

By applying the algebra concept, it can be concluded that Leona ordered 25 boxes of pens.

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems.

We have this information:

The price of a box of pens = $8

The price of a box of rubber bands = $4

Total order = 30 boxes

Total payment = $220

Let p symbolize the number of pens and r symbolize the number of rubber bands. Now we have the following equations:

p + r = 30 ....................... (1)

8p + 4r = 220 ............... (2)

To find the value of p and r, we can do it by simplifying the first equation as follows:

p + r = 30

r = 30 - p

Then we can substitute this value into the second equation:

         8p + 4r = 220

8p + 4(30 - p) = 220

8p + 120 - 4p = 220

                 4p = 220 - 120

                      = 100

                   p = 100/4

                      = 25 boxes of pens

So we can calculate the value of r as well:

r = 30 - p

 = 30 - 25

 = 5 boxes of rubber bands

Thus, it can be concluded that Leona ordered 25 boxes of pens.

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Answer:

-15

Step-by-step explanation:

An integer is a whole number from positive and negative (no decimal no fraction)

In this case 15 degrees below is -15

Answer:

no

Step-by-step explanation:

if we put the ratios as fractions, we would get 2/1, or just 2, and 1 4/5. these are not equivalent, so the ratios are not equivalent either.

Answer:

No.

Step-by-step explanation:

2:1 has multiple equivalents, for example:

2:1

4:2

6:3

5:10

...

The 1st number will always be double of the 2nd number,

2 is double of 1

4 is double of 2

6 is double of 3

...

9 is not double of 5.

Using a calculator, it can be found that

Rounding to three decimal places,

The point P where the line intersects the given plane as P(3, 6, 3).

Let's apply this method to the specific provided in the question. We have the line defined by the equations:

x = 4 + 2t

y = 7 + 2t

z = 5 + 4t

And the plane given by the equation:

x + y - z = 2

To find the point of intersection, we substitute the parametric equations of the line into the equation of the plane:

(4 + 2t) + (7 + 2t) - (5 + 4t) = 2

Simplifying the equation, we get:

t = -1/2

This tells us that the line intersects the plane at t = -1/2. To find the point of intersection, we substitute this value of t into the parametric equations of the line:

x = 4 + 2(-1/2) = 3

y = 7 + 2(-1/2) = 6

z = 5 + 4(-1/2) = 3

Therefore, the line intersects the plane at the point P(3, 6, 3).

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Answer:

15

Step-by-step explanation:

basic math.

Answer:

its 15 i believe

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

2/4 of an hour is 30 min

2/3 of an hour is 40 min

So he jogged less than he played soccer

Answer:

D

Step-by-step explanation:

Answer:

It's the B

Step-by-step explanation:

The arithmetic sequence here is made by subtracting 3 every time

Hope this helps, have a good day

Answer:760

Step-by-step explanation:

Answer:

760

Step-by-step explanation:

Answer: Choice D) \(180 - (41+58) = m \angle H\)

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

Explanation:

Choice A isn't particularly useful because while it is a true statement, it doesn't help tie together the two triangles. It only helps us find angle A. It doesn't help is determine any connection to the other triangle. So we can rule choice A out.

Choice C is a similar story, but for the other triangle. So we can rule choice C out.

Choice B is a false statement because 180-(41+58) simplifies to 81; while 180-(41+75) simplifies to 64. This means the equation 180-(41+58) = 180-(41+75) simplifies to 81 = 64, which is false. We can rule choice B out.

The only thing left is choice D. If angle H was the measure of 180-(41+58) = 81, then we could conclude the triangles are similar. Recall that similar triangles have corresponding congruent angles. In the first triangle, the missing angle is A = 180-(41+58) = 81. If we can show that angle H is 81, then this forms one pair of congruent angles. The other pair would be angle F = angle B = 41. All we need at minimum are two pairs of congruent corresponding angles to prove the triangles similar. The theorem we would use is the AA (angle angle) Similarity Theorem.

So this is why choice D is the answer despite the fact that angle H in the diagram is shown to be 75. We would need to rewrite that angle in order to get the triangles to be similar. Currently the diagram shows two triangles that are not similar.

Answer:

-1/2

Step-by-step explanation:

We can see the points (0, 3) and (2, 2) on the graph given.

We can use the formula [ y2-y1/x2-x1 ]

2-3/2-0

-1/2

Best of Luck!

After approximately 84 minutes, the food will contain 9,600 bacteria based on the given growth rate.

The initial population is 150 bacteria, and this number doubles every 14 minutes. Therefore, the growth rate per unit of time is 2 (since it doubles) and the time period is 14 minutes.

The exponential growth equation for this scenario can be expressed as:

P(t) = P₀ * (2^(t/h))

Where:

P(t) is the population at time t

P₀ is the initial population

t is the time elapsed

h is the time period for the population to double (in this case, 14 minutes)

We want to find the value of t when the population reaches 9,600 bacteria, so we can set up the equation:

9600 = 150 * (2^(t/14))

To solve for t, we need to isolate the variable t. We can start by dividing both sides of the equation by 150:

9600/150 = 2^(t/14)

64 = 2^(t/14)

Next, we can take the logarithm (base 2) of both sides to solve for t:

log₂(64) = log₂(2^(t/14))

6 = (t/14)

Multiplying both sides by 14:

84 = t

After approximately 84 minutes, the food will contain 9,600 bacteria based on the given growth rate.

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Answer:

6 > z(10 - z)

6 > 10z - z^2

z^2 - 10z^2 + 6 < 0

z > 9.36, z < 0.64

Therefore, option (0) is the correct answer.

Step-by-step explanation:

HOPE IT HELP

Answer:

C) postulate

An axiom or a postulate is an accepted statement of fact.

OAmalOHopeO

Answer:

Im pretty sure its definition

Answer:

3:2

Step-by-step explanation:

For every 3 girls : there is 2 boys, so it's 3:2

3:6 in simplest form=1:2

Answer:

Explanation:

Answer:

C

Step-by-step explanation:

√9 = 3

3 • √5 • √2 = 3√10

Alternatively, √9 • √5 • √2 = √90 = 3√10

Answer:

C

Step-by-step explanation:

First, multiply all the square roots.

So, sqrt(9) x sqrt(5) x sqrt(2) = sqrt(9x5x2) =sqrt(90)

Think of two numbers that multiply to 90. One possible pair is 9x10.

So, sqrt(90) = sqrt(9x10)

Using the properties of surds,

Sqrt(9x10) = sqrt(9) x sqrt (10)

We know that sqrt(9) = 3

So, sqrt(90) = 3 x sqrt(10)

Hope this helps

Step-by-step explanation:

i hope you will get the answer

Step-by-step explanation:

Answer:

The total number of winners is 17.

Step-by-step explanation:

Let's assume that the number of winners is "x". Then the number of participants who did not win is "45 - x".

The amount of money awarded to the winners is 1000x rupees.

The amount of money awarded to the participants who did not win is 200(45 - x) rupees.

According to the question, the total amount of prize money distributed is 22600 rupees. So we can write:

\(\sf\implies 1000x + 200(45 - x) = 22600 \)

Simplifying this equation:

\(\sf\implies 1000x + 9000 - 200x = 22600 \)

\(\sf\implies 800x = 13600 \)

\(\sf\implies x = 17 \)

Therefore, the total number of winners is 17.

Hope it helps!

Data collected over several time periods are called time series data.

Time series data refers to data that is collected over several time periods. It captures a sequence of observations of a variable of interest over time, such as sales figures, stock prices, temperature, and so on. The observations are usually taken at regular intervals, such as daily, weekly, monthly or yearly, and the data reflects the changes in the variable over time.

Time series data is useful for identifying trends, patterns, and seasonality in the data, and for making predictions about future values. It's often used in economic forecasting, weather forecasting, and other fields where understanding how a variable changes over time is important.

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Answer:

draw a straight horizontal line that crosses 2

Step-by-step explanation:

The total amount of lemonade consumed was 6 * 0.75 = 4.5 quarts.

An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. Algebraic expressions are used to represent a wide range of mathematical problems and are an essential tool in algebra.

In examples, x, y, a, b, and c are variables, and 3, 2, 5, 7, 2, 2, 3, 4, 1, and 2 are constants. The operations used are addition (+), subtraction (-), multiplication (* or ·), division (/), exponentiation (^), and taking the square root (√).

Algebraic expressions can be simplified by combining like terms and using the rules of arithmetic. They can also be evaluated by substituting specific values for the variables.

Each person drank 24/32 = 0.75 quarts of lemonade (since 1 quart = 32 oz).

Therefore, the total amount of lemonade consumed was 6 * 0.75 = 4.5 quarts.

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Answer:

1

in this *represents x

8*-¹=2/16*

8*-¹= 2/(2)⁴*

8*-¹=2/2⁴*

on comparing quantities , we get

x-1=0/4x

x-1=0

x=1