An equation for the plane consisting of all points that are equidistant from the points (1,4,4) and (-4, 1, 2) is 5x+3y+2z-6=0
Given, the points are (1, 4, 4) and (-4, 1, 2).
We have to find an equation for the plane consisting of all points that are equidistant from the given points.
Let the parametric point be (x, y, z) on the plane which is equidistant from the given points.
Using the distance formula:
[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1} )^2 } }[/tex]
Distance between the points (x, y, z) and (1, 4, 4)
=[tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}[/tex]
Distance between the points (x, y, z) and (-4, 1, 2)
=[tex]\sqrt{(x-(-4)^2+(y-1)^2+(z-2)^2}\\\\ \sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]
Given, [tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}=\sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]
By using algebraic identity,
(a-b)² = a²-2ab+b²
(a+b)² = a²+2ab+b²
(x² - 2x + 1)+(y²-8y+16)+(z²-8z+16)=(x²+8x+16)(y²-2y+1)+(z²-4z+4)
x²+y²+z²-2x-8y-8z+1+16+16=x²+y²+z²+8x-2y-4z+16+1+4
By grouping,
-2x-8x-8y+2y-8z+4z+33-21
-10x-6y-4z+12=0
Dividing by -2 into both sides,
5x+3y+2z-6=0
Therefore, the equation of the plane is 5x+3y+2z-6=0
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If m∠5 = x°, which angles also have a measure of x°? Select all that apply.
The angle that are equal to m∠5 are ∠9 and ∠12, therefore, C and D.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
As per the given image, the two streets 1st ave and 2nd ave are parallel to each other while D street acts as a transverse and intersects both 1st ave and 2nd ave. Therefore, the angle that will be equal to m∠5 are:
m∠5 = m∠9, Becuase the two angles are the corresponding angles
m∠5 = m∠9m = m∠12, Becuase ∠9 and ∠12 are vertically opposite angles.
Hence, the correct options are C and D.
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soit B(x)=4x²-12x. Résoudre dans R l'équation B(x)=-9
Answer:
B(-9) = 432
Step-by-step explanation:
B(x) = 4x² - 12x
B(-9) = 4(-9)² - 12(-9)
B(-9) = 4(81) + 108
B(-9) = 324 + 108
B(-9) = 432
Answer:
432
Step-by-step explanation:
B(x) = - 9
Replacing the value of x in the equation,
4x² - 12x
= 4 * (-9)² - 12 * (-9)
= 4 * 81 + 108
= 324 + 108
= 432
_________
hope this helps!
Find the slope. Find the slope.
Answer:
Step-by-step explanation:
Hello! The slope formula is rise over run, or (y2 - y1)/(x2 - x1). You can choose either y-coordinate for y2 and y1 and either x-coordinate for x2 and x1. Since you are given two points already, use those. The first coordinate in a coordinate pair is always x, and the second coordinate is always y (x, y). (0, 0) is the origin, or the point where both lines x and y meet up. The leftmost point is 3 squares below that, and y is a vertical line. The coordinates of the leftmost point on the line is (0, -3). The rightmost point on the line is located at the coordinate pair of (1, 0). Any point located below or left of the origin is negative. A point below the origin means the y is negative, and a point left of the origin means the x coordinate is negative. You now have two coordinate pairs, which is all you need to figure out the slope of the line. Use the formula (y2 - y1)/(x2 - x1) to get your answer. Substitute the y values in for the first part. The two y values are 0 and -3. The two x values are 0 and 1. You now have (0 - (-3)/(1 - 0). 0 - (-3) = 3 because two negatives make a positive. You now have 3/1. If you have to simplify this, then the slope is 3. Another easy way is shown below:
Hope this helped you solve slopes!
What is one over three to the fifth power?
six over eight
five over fifteen
one over one hundred twenty-five
one over two hundred forty-three
What is the value of the expression mnp+(−n) if m = 5, n = 8, and p = –2?
Answer:
The answer is -88.
Step-by-step explanation:
We can substitute the given values into the expression to find its value:
mnp + (-n)
= (5)(8)(-2) + (-8)
= -80 + (-8)
= -88
So, the value of the expression mnp + (-n) if m = 5, n = 8, and p = -2 is -88.
I would greatly appreciate Brainliest.
Have a nice day.
How do you find the x and y coordinates of the vertex of a parabola?.
The process of find the x and y coordinates of the vertex of a parabola is y = -b/2a
Coordinates in math is known as a number on the x-axis called an x-coordinate and a number on the y-axis called a y-coordinate.
Here we need to write down the process of finding the x and y coordinates of the vertex of a parabola.
The first step is to Get the equation in the form y = ax² + bx + c.
And then we have to calculate -b / 2a ad this is the x-coordinate of the vertex.
In order to find the y-coordinate of the vertex, then we have to simply plug the value of -b / 2a into the equation for x and solve for y.
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Which expressions are equivalent to
4
�
−
2
+
(
−
8
�
)
4m−2+(−8m)4, m, minus, 2, plus, left parenthesis, minus, 8, m, right parenthesis ?
The equivalent expression is -4m -2
What is an algebraic expression?An algebraic expression can be defined as an expression that is composed of terms, variables, coefficients, factors and constants.
These algebraic expressions are also known to consist of some arithmetic operations, such as;
Floor divisionAdditionMultiplicationSubtractionDivisionBracketParenthesesFrom the information given, we have that;
4m−2+(−8m)
Now, expand the bracket
4m - 2 - 8m
Collect like terms, we get;
4m - 8m - 2
Subtract the like terms
-4m - 2
Hence, the expression is -4m - 2
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If you are paid $236. 64 for 24 1/2 hour of work what amount hould you be paid for 32 hour of work at thi time ame rate to pay
I would be paid $310.4 for 32 hour of work at the same rate
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Hours worked = 24 1/2 hPaid = $236.64Hours = 32 hPaid (32h)= ?We transform the mixed fraction into improper fraction and we have:
24 1/2 =
[(24*2) + 1)] /2=
[48+1] /2=
49/2
Calculating the amount of dollars paid for 1 hour worked:
Dollar per hour = Paid / Hours worked
Dollar per hour = $236.64 / (49/2)
Dollar per hour = $236.64 * 2 / 49
Dollar per hour = $473.28/49
Dollar per hour = $9.70
Calculating the amount of dollars paid for 32 hours worked:
Paid (32h) = Dollar per hour * Hours
Paid (32h) = $9.70/h * 32 h
Paid (32h) = $310.4
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Use distributive property to rewrite each algebraic expression: 4(10 + x
Answer:40+4x
Step-by-step explanation:
1) distribute the 4 to each term
4(10+x)
40+4x
this is what truthfully struggle with can someone explain how i do this please then imma try it on my own
The radian measure of an angle θ is the length of the?
a) opposite side
b) diameter
c) hypotenuse
d) arc
The radian measure of an angle theta is the length of the arc that subtended angle 2Pi
We can measure angle in two form degrees or Radian.
What is the meaning of radian?
Radian can be described as a measure of angle subtended by a circular arc. It can be defined as the ratio of the arc length subtending angle to the radius of circle.
One radian is the measure of angle subtended by by an arc that is equal to the radius of circle.
Therefore,the radians measure an angle theta the length of arc.
Θ =s/r ,
where, theta is the angle subtended, s is the arc length and r is the radius of circle.
We know that the 2π radians = 360 degrees.
That subtends the angle in a circle of radius 2Pi
Therefore ,The radian measure of an angle theta is the length of the arc that subtended angle 2 Pi
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How do you write 300000000 in standard form?.
To write 300000000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point.
300000000 in standard form would be written as 3 x 10^8.
To arrive at this form, we move the decimal point 8 places to the left (since there are 8 zeros in 300000000) and add the power of 10 notation, indicating that we moved the decimal point 8 places to the left. The number 3 is the coefficient and 8 is the exponent. This way, we get 3 x 10^8 which is the standard form of 300000000.
Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers.
When a number is written in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point. The number of places the decimal point is moved is indicated by a power of 10.
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solve 2y = -3x and y = -2x + 2 using elimations
If anybody could help explain how to solve this as well that would be great! I have a quiz on this tomorrow so any explanation on how to solve it is helpful
The solutions to the system of equations are x = 4 and y = -6
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
2y = -3x
Divide by 2 on both sides of the equation , we get
y = ( -3/2 )x be equation (1)
Let the second equation be represented as B
Now , the value of B is
y = -2x + 2 be equation (2)
Substituting the value of y from equation (1) in equation (2) , we get
( -3/2 )x = -2x + 2
Adding 2x on both sides of the equation , we get
2x - ( 3/2 )x = 2
( 4x - 3x ) / 2 = 2
x/2 = 2
Multiply by 2 on both sides of the equation , we get
x = 4
Substitute the value of y in equation (1) , we get
y = ( -3/2 ) 4
y = -3 ( 2 )
y = -6
Therefore , the value of x and y is 4 and -6 respectively
Hence , the equations are solved
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How do you draw a triangle XYZ?.
A ruler and a pencil may be used to quickly create the triangle XYZ.
The length of the sides and the angle of the triangle XYZ are the fundamental concepts needed to start.
The steps to design a triangle whose three sides are known are as follows:
1. Mark point A, which will serve as one of the triangle's vertices.
2. Set the required length AB for the compass breadth.
3. Cut an arc by setting the compass's width to the required length of the side AC.
4. Cut an arc by setting the compass's width to the appropriate length of side BC.
You may thus obtain the needed triangle.
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What is isosceles angle theorem?.
Isosceles Triangle Theorem: If two triangle sides are similar, then their corresponding angles must also be similar. The sides of a triangle that correspond to two angles that are congruent are also congruent.
According to the isosceles Angle Theorem, the angles in an isosceles triangle that face congruent sides are also congruent.
A triangle with two equal sides is said to be isosceles. Isosceles triangle is basically such triangle which have two sides equal in magnitude. It is to be noted that because two angles should also be equal because of the two equal sides.
Angles opposing two triangle sides are congruent if their two sides are as well.
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In 1997, a city had a population of 220,000 people. Each year ince, the population ha grown by 6. 2%. Let t be the number of year ince 1997. Let y be the city’ population. Write an exponential function howing the relationhip between y and t
An exponential function is a mathematical function that models a relationship between a variable (in this case, t) and a constant multiplied by the power of another variable (in this case, y). The general form of an exponential function is y = ab^t, where
a is the initial valueb is the growth factor (also called the base)t is the independent variable (in this case, the number of years since 1997).In this specific scenario, we are told that in 1997, the population of a city was 220,000 people and that each year since then, the population has grown by 6.2%. We can use this information to find the values of a and b in the exponential function.
The initial value, a, is simply the population of the city in 1997, which is given as 220,000.
To find the value of b, we need to determine how much the population increases each year as a proportion of the current population. We are told that the population grows by 6.2% each year. This means that if the population is currently P, the population will be (1 + 0.062)P the next year. We can write this as P(1.062) as the growth factor b.
So, combining the values of a and b, we have:
y = 220,000 * (1.062)^t
This equation tells us that the population of the city, y, is equal to the initial population of 220,000 multiplied by the growth factor of 1.062 raised to the power of t, where t is the number of years since 1997. This equation expresses the relationship between population and time.
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Julianne and Vito caught 6 flounders, which was 75% of the fish they caught. How many fish did Julianne and Vito catch altogether?
Answer:
8 FISHES
Step-by-step explanation:
There are several ways to solve this but lets use proportion cus I feel it's easier. So what you are looking for is simply 100% of the fish they caught.!
So therefore, 75% = 6
100% = (100 × 6) ÷ 75
= 600 ÷ 75
= 8 FISHES
How do you graph y =- 2x 6?.
To determine the x-intercept, solve for x while replacing y with 0. To obtain the y-intercept, solve for y while replacing x with 0.
( 3, 0 ) are the x-intercepts.
(0, 6) are the y-intercepts.
What does Y = - 2x 6's y-intercept represent?6. Y-intercept In order to find x, set x = 0 in the equation y = 2x - 6. It is -6 for the y-intercept. By selecting "New Example" below, you may read some additional examples.
What on a graph does Y = - 6 mean?The Y-value of every point 6 units below the X-axis is actually equal to -6. As a result, the plane's points that are 6 units below the X-axis form the graph of y = -6.
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Rachel plays a game where she can randomly select 1 of 3 cards. If she selects Card A, she will win $10. If she selects Card B, she will win $15. If she selects Card C, she will win $50. What is the expected value of winning?
Therefore , the solution of the given problem of probability comes out to be the probability is 1/3 = 0.33 so the least value is winning $10.
What specifically does the probability method entail?Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Probabilities can be expressed using the numbers 0 , 1, fractions with just a range of 0% - 100%, or an another few characters. the proportion of occurrences among a group of equally likely options out of all conceivable outcomes.
Here,
Given :
In a game, Rachel has the option of picking any one of three cards at random. She will receive $10 if she chooses Card A.
Choosing Card B will earn her $15.
She will receive $50 if she chooses Card C.
Thus ,
expected value of winning is $10 which is the least prize that is $10 on selected card A.
As the probability is 1/3 = 0.33
Therefore , the solution of the given problem of probability comes out to be the probability is 1/3 = 0.33 so the least value is winning $10.
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Answer:
Step-by-step explanation:
$25
Jocelynn rode her motorcycle at an average speed of 45 miles per hour for 4.5 hours then rode at an average speed of 50 per hour for 2.5 hours. What was the total distance in miles that Jocelynn rode her motorcycle during this time?
Answer:
327 miles
Step-by-step explanation:
Answer:
327.5 miles
Step-by-step explanation:
45 times 4.5 + 50 times 2.5 = 327.5
Please solve the question correctly
Answer:
5x + 7y + 4
Step-by-step explanation:
5x + (6y+y) ( 3+1)
5x + 7y + 4
What is tan formula?.
The tangent formula is thus written as follows:
tan θ = (opposite side) / (adjacent side)
where "opposite side" refers to the side that is across from angle x and "adjacent side" refers to the side that is right next to it.
The tangent (tan) function is discussed in the tangent formulas. Let's assume a right-angled triangle where x is the acute angle.
The tangent formulas are trigonometric formulas that describe the tangent function. One of the six trigonometric functions, the tangent function, also known as "tan," is the ratio of the opposite side to the adjacent side.
Numerous trigonometric identities and formulas can be used to obtain numerous tangent function-related formulas.
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When given three side measures of a triangle, when will you be able to create a unique triangle, no triangle, and/or many triangles? Explain you reasoning.
The key is to check whether the given side measures satisfy the triangle inequality theorem or not, if yes then we can create a unique triangle, if no then no triangle can be created, and if the given measures are the perimeter of a triangle, we can create many triangles.
When will you be able to create a unique triangle, no triangle, and/or many triangles?When given three side measures of a triangle, the following scenarios can occur:
Unique triangle: If the three side measures given are the lengths of the three sides of a triangle and they satisfy the triangle inequality theorem, then we can create a unique triangle. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
No triangle: If the three side measures given do not satisfy the triangle inequality theorem, then it is not possible to create a triangle with those side lengths.
Many triangles: If the three side measures given are the perimeter of a triangle, and we are allowed to vary the lengths of the three sides of the triangle within a certain range, then we can create infinitely many triangles.
Example: A triangle with perimeter 12cm, we can create a unique triangle with sides 3,4,5, or we can create many triangle with sides (2,5,5), (4,4,4),(3,4,5) and so on.
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show your work to get brainliest
what is the value of m?
Answer:
m = 0.28
Step-by-step explanation:
you can create a proportion as follows:
[tex]\frac{2.8}{m}[/tex] = [tex]\frac{4}{5.4}[/tex]
cross-multiply to get:
4m = 2.8(5.4)
4m = 15.12
m = 15.12/4
m = 3.78
Answer:
m = 3.78
Step-by-step explanation:
Find the factor of how much bigger the second triangle is:
5.4 - 4 = 1.4
1.4/4 = 0.35
Then, multiply it by the top side
0.35 x 2.8 = 0.98
Finally, add the top number and the product
0.98 + 2.8 = 3.78
There is your answer!
Geometry 6.2
What is m∠N
Check the picture below.
How do you prove 3 angles of a triangle is 180?.
If the two lines crossed are parallel, the alternate angles are equal. It is proven that the sum of the three angles of a triangle is equal to 180 degrees.
We have to prove that ∠A + ∠B + ∠C is equal to 180 degrees.
The measure of A = ∠1
B = ∠2
C = ∠3
Given, l || BC
We know that the alternate angles are equal in parallel lines.
∠2 = ∠4 -------------- (1)
∠3 = ∠5 -------------- (2)
Adding (1) and (2),
∠2 + ∠3 = ∠4 + ∠5
By adding ∠1 on both sides,
∠1 + ∠2 + ∠3 = ∠4 + ∠5 + ∠1
From the figure,
The sum of the angles at a point on a line is equal to 180 degrees.
∠4 + ∠1 + ∠5 = 180°
So, ∠1 + ∠2 + ∠3 = 180°
Therefore, ∠A + ∠B + ∠C = 180°
Thus, If the two lines crossed are parallel, the alternate angles are equal. It is proven that the sum of the three angles of a triangle is equal to 180 degrees.
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Ivan tart with 150$ and ave 5 each week uma ha 45 and ave 20 each week write linear equation to repreaent ivan and uma aving
The equation that represent Ivan having is: 150+ 5x and Uma having is: 45 + 20x
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
To solve this problem, we have to state the equation using the information of the problem:
Information about the problem:
Ivan start = 150$Ivan's weekly profit= 5$Uma start = 45$Uma's weekly profit= 20$Ivan equation = ?Uma equation= ?Writing the equation according to the information gave, we have:
y(Ivan) = 150+ 5x
y(Uma) = 45 + 20x
Where:
Amount earned = yNo. weeks passed = xThe relationship between the No. weeks passed and the amount earned is: linear and direct because when the number of weeks increases (x), the amount earned (y) will decrease.
The "y" variable is the dependent variable, because it will change according to the number of weeks passed (x).
The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of weeks passed.
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Zayn has a garden that is 86 metres long and x metres wide. He decides to build a fence around the garden. If the perimeter of the garden is 268 m, what is the width? Remember to write the algebraic expression.
Step-by-step explanation:
the perimeter of a rectangle is
2×length + 2×width
in our case we have
268 = 2×86 + 2x = 172 + 2x
96 = 2x
x = 96/2 = 48 m
Work out 656 divided by 3. Give your answer as a whole number and a remainder
Bookwork code:K27
Answer:
218 with a remainder of 2
Step-by-step explanation:
656 divided by 3 = 218.6666667
218 times 3 = 654
656 - 654 = 2
When 656 is divided by 3 is 218 with a remainder of 2.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation.
To divide 656 by 3, we can perform long division as follows:
3 ) 656 (218
-6
____
15
-12
_____
35
- 33
_____
2
We first divide the first digit of 656 (which is 6) by the divisor 3, which gives us 6 with a remainder of 15.
We then bring down the next digit (which is 56) to form the dividend 18, and we perform the division again.
This gives us 218 with a remainder of 2.
Therefore, 656 divided by 3 is 218 with a remainder of 2.
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please show the Mod base Work
Pretend that it's 3:00 now. Answer the following
questions, but don't worry about AM/PM.
A
What time will the clocks minutes show 220 minutes from
now?
Time after 220 minutes will be 6:40 on the clock.
Add 60 minutes to the end minutes and take an hour off the end time hours if the start minutes are greater than the end minutes. Subtract the start time minutes from the final minutes as you go. Add the hours from the start to the end. To find the solution, combine the results for hours and minutes.
1 hour = 60 mins
220 minutes = hours?
⇒ 220 / 60
⇒ 3 4/6
⇒ 3 hours and 40 minutes
At present, it's 3:00,
The time after 220 minutes will be -
⇒ 3 + 3.7 hours
⇒ 6.7 hours
The clock will show time 6: 40.
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