Consider points R, S, and T. Which statement is true about the geometric figure that can contain these points? No line can be drawn through any pair of the points. One line can be drawn through all three points. One plane can be drawn so it contains all three points. Two planes can be drawn so that each one contains all three points.

Answers

Answer 1

Hello,

c- one plane can be drawn so it contains all three points.
(i just took this on a mastery test)

Answer 2

Answer: The answer is (c) One plane can be drawn so that it contains all three points.

Step-by-step explanation: We are given three points R, S and T in a coordinate plane. Considering all these three points to be distinct and non-collinear, we can draw the following conclusions.

(i) Since each pairs of points. i.e., (R,S), (S,T) and (T,R) give rise to a straight line when joined, so option (a) is incorrect.

(ii) Through any two given points, we can always draw a line. If we consider a third point and since we are dealing with non-collinear points, so one line cannot be drawn through three points.

(iii)We can always draw a line by joining two points and when we join the two ends of the line to a third point which does not lie on the line, it will give rise to a plane. So, option (c) is correct.

(iv) We cannot draw two different planes through three given points. If we do so, the new plane will coincide with the previous one. This proves that option (d) is not correct.

Please see the attached figure, where P, Q and R are three non-collinear points. They give rise to a plane.

Thus, the correct option is (c).

Consider Points R, S, And T. Which Statement Is True About The Geometric Figure That Can Contain These

Related Questions

If r = x, y, z and r0 = x0, y0, z0 , describe the set of all points (x, y, z) such that |r − r0| = 5.

Answers

We are concern about the vector (x-x0, y-y0, z-z0) equaling to 5.

This happens when √(x-x0)^2 + (y-y0)^2 + (z-z0)^2 = 5

Square both side:

(x-x0)^2 + (y-y0)^2 + (z-z0)^2 = 25 , a sphere

Which you will recognize as a circle of radius one centered at (x0, y0, z0)

Answer:

Point [tex]\left ( x,y,z\right )[/tex] represents a sphere

Step-by-step explanation:

Take [tex]r=\left ( x,y,z \right )\,,\,r_0=\left ( x_0,y_0,z_0 \right )[/tex]

We need to describe the set of all points (x, y, z) such that [tex]\left | r-r_0 \right |=5[/tex]

Solution :

For [tex]r-r_0=\left ( x,y,z \right )-\left ( x_0,y_0,z_0 \right )[/tex], we will subtract the respective elements .

[tex]r-r_0=\left ( x,y,z \right )-\left ( x_0,y_0,z_0 \right )=\left ( x-x_0,y-y_0,z-z_0 \right )[/tex]

Therefore, [tex]\left | r-r_0 \right |=\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}[/tex]

As [tex]\left | r-r_0 \right |=5[/tex], we get

[tex]\sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2}=5[/tex]

On squaring both sides, we get

[tex]\left ( \sqrt{(x-x_0)^2+(y-y_0)^2+(z-z_0)^2} \right )^2=5^2\\(x-x_0)^2+(y-y_0)^2+(z-z_0)^2=25[/tex]

The general equation of a sphere is (x - a)² + (y - b)² + (z - c)² = r², where (a, b, c) denotes the center of the sphere and r represents the radius .

So, [tex](x-x_0)^2+(y-y_0)^2+(z-z_0)^2=25[/tex] represents a sphere with center as [tex]\left ( x_0,y_0,z_0 \right )[/tex] and radius equal to 5 units

In winter, the price of apples suddenly went up by \$0.75$0.75dollar sign, 0, point, 75 per pound. Sam bought 333 pounds of apples at the new price for a total of \$5.88$5.88dollar sign, 5, point, 88.
Write an equation to determine the original price per pound (p)(p)left parenthesis, p, right parenthesis.

Answers

Your formula would be 3(p+0.75)=5.88

Because you have 3 pounds and 0.75 for each.

Solving the equation by distributing, you will get P=1.21

Hope this helps!

The equation will be 3 (p + 0.75) = 5.88. Then the original price per pound p will be 1.21.

What is the solution to the equation?

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

In winter, the price of apples suddenly went up by a $0.75 dollar sign per pound. Sam bought 3 pounds of apples at the new price for a total of $5.88 dollar sign.

The original price per pound p will be

3 (p + 0.75) = 5.88

p + 0.75 = 1.96

p = 1.96 - 0.75

p = 1.21

The equation will be 3 (p + 0.75) = 5.88. Then the original price per pound p will be 1.21.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

There is 6/8 of a birthday cake leftover after a birthday party. How many 1/4 pieces can be made from the leftover cake?

Answers

divide both 6 & 8 by 2 6/2 = 3

8/2 = 4

so 6/8 = 3/4

there is 3 pieces

It takes the earth 24 hours to complete a full rotation. It takes mercury approximately 58 days, 15 hours, and 30 minutes to complete a full rotation. How many hours does it take mercury to complete a full rotation?

Answers

To answer this question you need to convert the mercury rotation time from 58 days, 15 hours, and 30 minutes into hours.
First, try to convert the days into hours. The calculation would be=
58 days x 24 hours/day= 1392 hours.
Then convert the 30 minutes into the hours.
30 minutes / (60 minutes/hour)= 0.5 hours

After that you just need to add them all, then hours need for mercury to complete a full rotation: 1392 hours + 15 hours+ 0.5 hours= 1407.5 hours.

Final answer:

Mercury takes approximately 1407.5 hours to complete a full rotation, calculated by converting 58 days, 15 hours, and 30 minutes entirely into hours.

Explanation:

To calculate how many hours it takes for Mercury to complete a full rotation, we need to convert the given time of approximately 58 days, 15 hours, and 30 minutes into hours. Here are the step-by-step calculations:

First, convert the days into hours. Since there are 24 hours in a day, we multiply 58 days by 24 hours per day.58 days × 24 hours/day = 1392 hoursNext, add the additional hours to the total from the days.1392 hours + 15 hours = 1407 hoursFinally, convert the minutes to hours. There are 60 minutes in an hour, so we divide 30 minutes by 60.30 minutes ÷ 60 minutes/hour = 0.5 hoursAdd this to the total number of hours.1407 hours + 0.5 hours = 1407.5 hours

Therefore, it takes Mercury approximately 1407.5 hours to complete a full rotation.

Stan and hilda can mow the lawn in 35 min if they work together. if hilda works twice as fast as stan, how long would it take stan to mow the lawn alone?

Answers

105 minutes "Stan and Hilda can mow the lawn in 35 min" 35 = 1/(S + H) "Hilda works twice as fast as Stan" H = 2S "how long would it take Stan to mow the lawn alone?" T = 1/S First, let's determine what S is, so 35 = 1/(S + H) Substitute 2S for H 35 = 1/(S + 2S) Solve for S 35 = 1/(3S) 35(3S) = 1) 105S = 1 S = 1/105 Now solve T = 1/S with S = 1/105 T = 1/S T = 1/(1/105) T = 1/1 / 1/105 T = 1/1 * 105/1 T = 105 So it will take Stan 105 minutes to mow the lawn alone.

Which pair of angles are interior angles?

A. 1 and 8

B. 3 and 6

C. 3 and 4

D. 3 and 5

Answers

B. 3 and 6 opposite sides of the transversal but inside the two lines

3 & 5 are the interior angles

Answer is D

If x represent a number , then write an expression for one half the sum of x and 7

Answers

Hello there!

It would be (x + 7) / 2

Hope This Helps You!
Good Luck :)

the sum of x and 7 would be x+7

then to get half of that you would divide by 2

so equation is (x+7)/2

Round 90608.5881594 to 1 decimal place

Answers

90608.6 is the answer

Remember if the number after this line is less than 5 round down, or round up if the number is 5 or above.

Answer:

90608.6

Step-by-step explanation:

Round 90608.5881594 to 1 decimal place

To round the answer to 1 decimal place , we round the answer to nearest tenth.

In the given number , 5 after decimal point is in tenths place

8 is in hundredths place

Here 8 in hundredths place is greater than 5. If it is greater than 5 then we add 1 in tenths place

So 5 in tenths place becomes 6

90608.5881594 to 1 decimal place is 90608.6

70 is 20% of what number

Answers

350 is the answer to the question

x*0.20= 70
x=70/0.20
x=350

make sense?

Using graphite furnace atomic absorption spectrometry, the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2 (assume that s is a good approximation of σ). calculate the 90% and 95% confidence intervals (ci) for: (a) two analyses and (b) five analyses of this homogenized sample.

Answers

Part A1:

Given that the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2

The 90% confidence interval for a sample of size n, with sample mean [tex](\bar{x})[/tex] and a standard deviation of s is given by:

[tex]90\%\ C.I.=\bar{x}\pm1.645\left( \frac{s}{ \sqrt{n} } \right)[/tex]

Thus, the 90% confidence intervals (ci) for two analyses is given by:

[tex]7.50\pm1.645\left( \frac{0.52}{ \sqrt{2} } \right)=7.50\pm1.645(0.3677) \\ \\ =7.50\pm0.6049=(6.90, \ 8.1)[/tex]

Part A2:

Given that the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2

The 95% confidence interval for a sample of size n, with sample mean [tex](\bar{x})[/tex] and a standard deviation of s is given by:

[tex]95\%\ C.I.=\bar{x}\pm1.96\left( \frac{s}{ \sqrt{n} } \right)[/tex]

Thus, the 95% confidence intervals (ci) for two analyses is given by:

[tex]7.50\pm1.96\left( \frac{0.52}{ \sqrt{2} } \right)=7.50\pm1.96(0.3677) \\ \\ =7.50\pm0.7207=(6.78, \ 8.22)[/tex]

Part B1:

Given that the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2

The 90% confidence interval for a sample of size n, with sample mean [tex](\bar{x})[/tex] and a standard deviation of s is given by:

[tex]90\%\ C.I.=\bar{x}\pm1.645\left( \frac{s}{ \sqrt{n} } \right)[/tex]

Thus, the 90% confidence intervals (ci) for five analyses is given by:

[tex]7.50\pm1.645\left( \frac{0.52}{ \sqrt{5} } \right)=7.50\pm1.645(0.2326) \\ \\ =7.50\pm0.3825=(7.12, \ 7.88)[/tex]

Part B2:

Given that the mean cadmium (cd2 ) content value in a homogenized sample of 40 zebra mussles was found to be 7.50 ppb cd2 with a standard deviation (s) of 0.52 ppb cd2

The 95% confidence interval for a sample of size n, with sample mean [tex](\bar{x})[/tex] and a standard deviation of s is given by:

[tex]95\%\ C.I.=\bar{x}\pm1.96\left( \frac{s}{ \sqrt{n} } \right)[/tex]

Thus, the 95% confidence intervals (ci) for five analyses is given by:

[tex]7.50\pm1.96\left( \frac{0.52}{ \sqrt{5} } \right)=7.50\pm1.96(0.2326) \\ \\ =7.50\pm0.4559=(7.04, \ 7.96)[/tex]

The Hamptons family has a fish tank holding 10,450 ml of water. The water is leaking at a rate of 270 ml per minute. Define the input and output in the given scenario

Answers

The input is any variable which goes into the system. In this case there is no input.

While the output is any variable going out of the system. In this case the output is the amount of water which leaked out.

Answer:

The number of minutes represents input and remaining water represents output.

Step-by-step explanation:

Given,

The original quantity of the water in the tank = 10,450 ml,

Also, the quantity of the water leaked per minute = 270 ml,

Thus, the quantity water leaked in x minutes = 270x

∵ Remaining water in the tank ( say y ) = Original water - leaked water

⇒ y = 10450 - 270x,

Which is the equation that shows the given scenario.

In this equation, x represents the input value and y represents the output value,

Hence, the number of minutes represents input and remaining water represents output.

how do you write the decimal 0.7 as a fraction in simplest form

Answers

0.7 is 7/10 in fraction form

It is also already in simplest form

7/10 is your answer

hope this helps

Let −→ ab= h2, −3, −1i. if the coordinates of a are (2, −1, 5), what are the coordinates of the point b?

Answers

the answer to that is -2 and -3

Elton pours 41 1/4 ounces of water from a large pitcher into a bottle. That amount is 2/5 of the water that was in the pitcher. There were _____ ounces of water in the pitcher.

Write your answer as a mixed number in lower terms.

Answers

Okay. 41 1/4 is 2/5 if what was previously in the pitcher. In this case, we have to divide to see how much was previously in the pitcher. We convert 41 1/4 to an improper fraction, which is 165/4. Then we must keep that fraction the same, change the sign to a multiplication sign, and flip the second fraction over. So turn 2/5 into 5/2. 165/4 * 5/2. When you do that, you should get 825/8 or 103 1/8 when simplifies. There were 103 1/8 ounces of water in the pitcher.

About 36,100,000 households in the U.S. have cats and about 43,300,000 households have dogs. About how may more households dogs and cats

Answers

theres about a 7,200,000 difference between household dogs vs household cats

???????????????????????????

Answers

y=×+8
×+×+8=10
×=1
y=9
(X.Y)(1.9)

Grandpa Schmidt is 75 years old this is nine years less than seven times the age of Junior submit how old is Junior

Answers

Let the age of Junior be x,

age of grandpa schmidt = 7x + 9
7x + 9 = 75
7x = 66
x = 66/7
= 9.43 (to three significant figures)

Junior is 9.43 years old.

Add.

(6x3+3x2−2)+(x3−5x2−3)
pleaseeeeeee answer in standard form!!!!

Answers

I believe the answer is
7x^3-2x^2-5

Whats the rule for this pattern, 3,1.5,0,-1.5,-3

Answers

The pattern subtracts 1.5 for each number in the pattern. 3-1.5 is 1.5. 1.5 minus 1.5 is zero. 0 minus 1.5 is -1.5. -1.5 minus 1.5 is negative 3. If we apply this rule to the next value, it would be -3 minus 1.5 which is equal to 4.5. The value after that would be 6, applying the same rule.

Final answer:

The rule for the pattern 3, 1.5, 0, -1.5, -3 is to subtract 1.5 from the previous term in the sequence.

Explanation:

The rule for the number pattern 3, 1.5, 0, -1.5, -3 is subtracting 1.5 from the previous number each time. To identify this, observe the difference between consecutive terms:

From 3 to 1.5 we subtract 1.5 (3 - 1.5 = 1.5).

From 1.5 to 0 subtract 1.5 (1.5 - 1.5 = 0).

From 0 to -1.5 subtract 1.5 (0 - 1.5 = -1.5).

And from -1.5 to -3, again subtract 1.5 (-1.5 - 1.5 = -3).

This pattern consistently decreases by 1.5, and it can be continued indefinitely by keeping this rule in mind.

Each marble bag sold by jenny's marble company contains 3 yellow marbles for every 5 orange marbles. if a bag has 15 yellow marbles, how many orange marbles does it contain?

Answers

it would contain 25 Orange marbles

The total cost CC (in dollars) to participate in a ski club is given by the literal equation C=85x+60C=85x+60, where xx is the number of ski trips you take
How many ski trips do you take if you spend a total of $315? $485?

Answers

First of all why is there 2 similar equation connected to one another?

Second in order to solve this all you need to do is plug in the number and solve for x

For 485

85x+60=485
85x=420
X=5

Do the same thing and you get 3

Answer:

The total cost C (in dollars) to participate in a ski club is given by the literal equation :

[tex]C=85x+60[/tex]

Where x is the number of ski trips you take.

1. When C = 315 ;substituting the value of C in the above equation.

[tex]315=85x+60[/tex]

=> [tex]85x=315-60[/tex]

=> [tex]85x=255[/tex]

x = 3 trips.

2. When C = 485

[tex]485=85x+60[/tex]

=> [tex]85x=485-60[/tex]

=> [tex]85x=425[/tex]

x = 5 trips.

if a=b then ac=bc. this called the of quality.(2words)

Answers

I'm not sure how this is 2 words, as the answer is the Multiplication Property of Equality.

Hope this helps!

Which represents a rational Number and how can you tell?[tex] \sqrt{17} \sqrt{36} \sqrt{50} \sqrt{101} [/tex]

Answers

[tex]\bf \begin{array}{llll} \sqrt{17}\\\\ \sqrt{101} \end{array}\impliedby \textit{17 and 10 are both prime numbers} \\\\\\ \sqrt{36}\implies \sqrt{6^2}\implies \pm 6 \\\\\\ \sqrt{50}\implies \sqrt{25\cdot 2}\implies \sqrt{5^2\cdot 2}\implies 5\sqrt{2}\impliedby \textit{2 is a prime number}[/tex]

if a number is a prime number, it has no two equal factors that can produce a product of such a number, and therefore such value is an irrational number.

now, the last one, 5 is being multiplied by an irrational, and therefore the product will yield the same irrational, just a bit larger.

so, the only rational there is the ±6 really.

Find an equation of a linear function given h(1)=6 and h(4)=-3

Answers

We can rewrite this in the form of h (t):

at t = 1, h = 6

at t = 4, h = -3

The linear equation is in the form of:

h = mt + b

where m is the slope and b is the h-intercept

So calculating for the slope m:

m = [-3 – 6] / (4 – 1)

m = (-9) / 3

m = -3

So,

h = -3t + b

Solving for b by plugging in any pair:

6 = -3(1) + b

b = 9

Therefore:

h = -3t + 9

A soccer player runs 1 5/6 miles during the first half of a match and 2 1/2 miles during the second half. How many miles does he run during the match in total?

Answers

is he runs 1 5/6 miles during the half and 2 1/2 during the second half u will get
1.83

1 5/6 = 1 5/6
2 1/2 = 2 3/6
1 5/6 + 2 3/6=3 8/6
3 4/3 = 4 1/3
so your answer is 4 1/3

simplify
14+4(12−34)2

Answers

The answer for that is -162

Answer: The required simplified answer is 1950.

Step-by-step explanation: We are given to simplify the following algebraic expression :

[tex]E=14+4(12-34)^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To simplify the given expression, first we evaluate the square term, multiply it by 4 and add the result to 14.

From expression (i), we get

[tex]E\\\\=14+4(12-34)^2\\\\=14+4(-22)^2\\\\=14+4\times484\\\\=14+1936\\\\=1950.[/tex]

Thus, the required simplified answer is 1950.

Which word describes the slope of the line?

positive
negative
zero
undefined

Answers

Since the line, from left to right, is going upward, the slope is positive.

Answer:

positive

Step-by-step explanation:

The slope is the inclination of the line with respect to the x-axis. It is denoted by the letter [tex]m[/tex]. In mathematical language, the slope [tex]m[/tex] of the line is defined as the difference on the y-axis divided by the difference on the x-axis for two different points [tex]P_1(x_1,y_1)[/tex] and [tex]P_2(x_2,y_2)[/tex] on the line:

[tex]m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}[/tex]

If:

[tex]m>0[/tex] The slope is positive and the line is increasing from left to right

[tex]m<0[/tex] The slope is negative and the line is decreasing from left to right

If a line is vertical the slope is undefined

[tex]m=0[/tex] is a constant function.

Since the graph of the linear function shown is increasing from left to right, we can conclude that the slope is positive.

Dos angulos consecutivos de un paralelogramo estan e la relacion de 2 a 7. calcula el mayor angulo del paralelogramo

Answers

Can you translate to English?

Which expression is equivalent to x6 – 9?

Answers

x⁶ – 9, it could be written as x⁶ - 3², which expression is the difference of 2 squares (a² - b²) = (a-b)(a+b)

x⁶ - 3³ = (x³-3)(x³+3)

Answer:

(x3)2 – 32

Step-by-step explanation:

what is the solution of 1/3b = -3

Answers

simplify 1/3b to b/3

b/3 = -3

multiply both sides by 3

b = -3 * 3

multiply 3 * 3 so it can = 9

Answer: b = -9

The answer would be b= -9. To do so you need to multiply the equation by 3 so you can get rid of the fraction. You then end up with 1b= -9. Then you divide both sides by 1 and there you go. I hope this helps love! :)

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