Find parametric equations for the line passing through (0,0,1) and parallel to the line passing through (3,1,5) and (1,−1,2). Use symbolic notation and fractions where needed.) x : y= z=

When a line L is perpendicular to two lines on the plane that intersects line L , then line L is perpendicular to the plane.

We know that two lines are perpendicular to each other if they intersects and these two lines are inclined at angle 90° (right angle)

Perpendicular lines are intersecting lines.

Mathematically, the perpendicular lines are represented by the symbol, ‘⊥‘.

When a line is perpendicular to two lines on the plane then it is perpendicular to the plane.

We can say that when the line L is perpendicular to every line in the plane that intersects line L, then we can say that a line and a plane are perpendicular.

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Answer:

-399.5

Step-by-step explanation:

You divide, add, then subtract.

Answer:

-399.5

Step-by-step explanation:

100/200 = 0.5

300 + 0.5 = 300.5

300.5 - 700 = -399.5

(actually did math properly this time)

The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.



To determine the number of significant figures in a calculation, we follow the rules for significant figures:

1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).

Now, multiplying this result by \(3.1416\) gives \(329.5719744\).

The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.

According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.

Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.

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The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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we can express the simplified form as (32)/(3x).

To simplify the complex fraction (4/x) / (3/8), we can follow these steps:

Step 1: Reciprocal of the denominator:

The reciprocal of (3/8) is (8/3). Therefore, the complex fraction can be written as (4/x) * (8/3).

Step 2: Simplify the numerator and denominator separately:

Multiply the numerators together: 4 * 8 = 32.

Multiply the denominators together: x * 3 = 3x.

Step 3: Simplify the fraction:

The simplified complex fraction is 32/3x.

Therefore, the simplified form of the complex fraction (4/x) / (3/8) is 32/3x. It is important to note that in complex fractions, it is generally preferred to rewrite them as a division of fractions rather than a complex fraction. So, alternatively, we can express the simplified form as (32)/(3x).

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Answer:

x=8

Step-by-step explanation:

x/4=12/6

x=12×4/6

x=48

x=8

Answer: f(-9)= 243

Step-by-step explanation:

f(x) = 4x²+7x -18

f(-9) = 4(-9)²+7(-9)-18

= 4(81) -63-18

= 324- 81

= 243

Answer:

144

Step-by-step explanation:

Answer:

52°

Step-by-step explanation:

it should always add up to 180°

Answer:

45

Step-by-step explanation:

The ratio of the horizontal change to the vertical change of a line would not be used to describe a slope. Thus the correct option is option C.

The slope of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run) of a line.

Slope=Vertical Change/Horizontal Change

This is also represented as the "ratio of rise to run of a line".

Slope=Rise/Run

In the given question, however, option C states that the "ratio of the horizontal change to the vertical change of a line".

Horizontal Change/ Vertical Change= 1/slope

This is an incorrect statement since the ratio of the horizontal change to the vertical change of a line is the reciprocal of the correct ratio.

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Answer:

B

Step-by-step explanation:

i took the assessment

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Answer:

Store B

Step-by-step explanation:

I got it right

Answer:

-2/15

Step-by-step explanation:

-2/5 × 1/3

Multiply the numerators

-2*1 = -2

Multiply the denominators

5*3 = 15

Put the numerator over the denominator

-2/15

Answer:-3.25

Step-by-step explanation:

Answer:

68.2

Step-by-step explanation:

if the triangles are similar then all of the angles are the same. The only thing that changes is the side lengths.

Answer:

\(63.2\)°

Step-by-step explanation:

since the triangles are similar they have identical angle measures are the same

however you could solve it this way too:

\(A+B+C=180\)

all measures of a triangle add up to 180

\(23.8+90+C=180\)

\(116.8+C=180\)

\(C=63.2\)

Answer:

A, B, C and E are true. Only D is false.

Step-by-step explanation:

Step-by-step explanation:

1: change 'sin²A' and 'cos²B' into (1-cos²A)and (1-sin²A) respectively.

2:open the brackets and put signs accordingly.

3: cancel (-1) and (+1).

4: remaining is your answer.

Answer:

D

Step-by-step explanation:

The question:

10^4= 10000

4^10=1048576

1048576x10000= 10485760000

4^5= 1024

10485760000/1024= 10240000

A. 262144 (NO)

B. 2.62144e+14 (NO)

C. 10000x1073741824= 1.0737418e+13 (NO)

D. 10000x1024= 10240000 (YES)

Hope this helps ^^

If the value stated by a null hypothesis is within the confidence interval, then the decision would have likely been to retain the null hypothesis.

In hypothesis testing, the null hypothesis represents the default assumption or the claim that there is no significant difference or relationship between variables. The confidence interval, on the other hand, provides a range of plausible values for the population parameter based on sample data. If the value stated by the null hypothesis falls within the confidence interval, it means that the null hypothesis value is considered plausible or consistent with the observed data.

In this case, there is insufficient evidence to reject the null hypothesis, and the decision would be to retain it. On the other hand, if the null hypothesis value is outside the confidence interval, it suggests that the null hypothesis is unlikely, and the decision would be to reject it in favor of an alternative hypothesis.

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Answer: Congruent triangles have congruent corresponding sides.

(Note): This is not the correct answer..This is an Example. :)

Step-by-step explanation: part a) draw two triangles, translating one of them to the right.

part b) Consider triangles ΔYXB and ΔYZA. In these triangles:

∠Y is common, then ∠XYB≅∠ZYA (additional information that is needed);

∠YXB≅∠YZA (given);

XY≅ZY (given).

Therefore, these two triangles have two congruent angles adjacent to congruent sides. By the ASA Postulate, ΔYXB≅ΔYZA.

ASA Postulate: If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

Hope This Was helpful..

Answer:

You could use the ASA theorem to prove that the congruent angles and side are congruent. Or you could use CPCTC which is Corresponding parts of congruent triangles are congruent. By using these two theorems you could prove that these triangles are congruent and not similar.

Step-by-step explanation:

To construct the inscribed and circumscribed circles of a triangle, follow these steps:

Inscribed Circle: The inscribed circle of a triangle is the circle that touches all three sides of the triangle from the inside. To construct it:

a. Take any two sides of the triangle and find their angle bisector using a compass and ruler.

b. The point where the two angle bisectors intersect is the center of the inscribed circle.

c. Using the compass, draw a circle centered at the intersection point with a radius equal to the distance between the center and any side of the triangle.

Circumscribed Circle: The circumscribed circle of a triangle is the circle that passes through all three vertices of the triangle. To construct it:

a. Find the midpoint of each side of the triangle using a compass and ruler.

b. Draw the perpendicular bisectors of any two sides of the triangle.

c. The point where the perpendicular bisectors intersect is the center of the circumscribed circle.

d. Using the compass, draw a circle centered at the intersection point with a radius equal to the distance between the center and any vertex of the triangle.

Regarding the opposite angles of inscribed quadrilaterals, we know the following:

In an inscribed quadrilateral (a quadrilateral with all four vertices lying on a circle), the opposite angles are supplementary. This means that the sum of the measures of the two opposite angles is always 180 degrees. In other words, if we label the angles of the inscribed quadrilateral as A, B, C, and D (in cyclic order), then angle A + angle C = 180 degrees, and angle B + angle D = 180 degrees. This property holds true for any inscribed quadrilateral.

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Answer: 4xy²(5-y)

Step-by-step explanation:

To factorize, we must take out common multiples in both parts of the equation. Think of 20xy² and -4xy³ as two completely separate parts. Now, we need to see which parts of the equation are found in both. For instance, 4 can go into both, an x can go into both, and y² can go into both. Now, we simply factor.

Bring the similarities out to the front: 4xy²()

Now, use division to find what would be inside the parenthesis: 5 - y

Now, combine these two parts: 4xy²(5-y)

To check your work, you can simply multiply the outside of the parenthesis by the inside, and you should get the same as what you started with. Hope this helps!

According to the question the enlarged design requires 450 feet of lights.

Design is the process of creating a plan or solution to a problem. It involves identifying users’ needs and creating a product, service, or system that meets those needs. Designers must consider how their solutions will function, how it will look, and how people will interact with it. Design thinking is a creative process that involves research, brainstorming, prototyping, and testing. Good design can improve user experience, increase engagement, and help businesses achieve their goals.

Let's assume the original design is X feet.
The enlarged design is 2X feet.
Therefore, the scale factor is 2.
The original design requires 225 feet of lights.
We can use the scale factor to calculate the amount of lights required for the enlarged design.
225 * 2 = 450 feet
Therefore, the enlarged design requires 450 feet of lights.

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Complete Question:

The probability that 5 hearts are chosen when 7 cards are drawn from a well-shuffled deck of 52 playing cards is option (d) 0.00000962.

Step 1: Determine the total number of ways to choose 7 cards from a deck of 52 playing cards, which can be calculated using the combination formula: C(52, 7) = 52! / (7! * (52 - 7)!), where "!" denotes the factorial.

Step 2: Determine the number of ways to choose 5 hearts from the deck. There are 13 hearts in a standard deck, so we can calculate the number of ways to choose 5 hearts from 13: C(13, 5) = 13! / (5! * (13 - 5)!).

Step 3: Calculate the probability by dividing the number of favorable outcomes (choosing 5 hearts) by the total number of possible outcomes (choosing 7 cards from the deck): P(5 hearts) = C(13, 5) / C(52, 7).

Step 4: Evaluate the probability numerically using a calculator or math software, and the result is approximately 0.00000962.

Therefore, the correct answer is option (d) 0.00000962.

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The two sets of angles are corresponding angles are angles p and s & angles q and r

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

The triangles

By definition, corresponding angles are angles that are at relative the same position

using the above as a guide, we have the following:

Angles p and s & angles q and r are corresponding angles

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Step-by-step explanation:

since they're Head opposite angles.

\((3x - 3) = (2x + 13) \\ 3x - 2x = 13 + 3 \\ x = 16\)

Answer:

1.) x= 3

2.) x=5

3.) x=2

Step-by-step explanation:

1) 7x+8=29

( -8). 7x=21. (-8)

(÷7). x=3. (÷7)

2). 6x+6=36

6x=30. subtract 6

x=5. divide by 6

3). 7+6x=19

6x+7=19. rearrange it

6x=12. subtract 7

x=2. divide by 6

\( \huge\mathbb\red{ANSWER} \)

\( \mathsf \purple{7x + 8 = 29}\)

\( \mathsf \pink{7x + 8 - 8 = 29 - 8}\)

\( \mathsf \purple{7x = 21}\)

\( \mathsf \pink{ \frac{7x}{7} = \frac{21}{7} }\)

\( \mathsf \purple{x = 3}\)

\( \mathsf \red{6x + 6 = 36}\)

\( \mathsf \green{6x + 6 - 6 = 36 - 6}\)

\( \mathsf \red{6x = 30}\)

\( \mathsf \green{ \frac{6x}{6} = \frac{30}{6} }\)

\( \mathsf \red{x = 5}\)

\( \mathsf \blue{7 + 6x = 19}\)

\( \mathsf \orange{ - 7 + 7 + 6x = 19 - 7}\)

\( \mathsf \blue{6x = 12}\)

\( \mathsf \orange{ \frac{6x}{6} = \frac{12}{6} }\)

\( \mathsf \blue{x = 2}\)