( 0 , -1 , 5) point lies on xyz plane .
What is xyz plane ?The xy-plane is the plane that houses the x- and y-axes, while the yz-plane and the xz-plane house the y- and z-axes, respectively. Space is divided into eight sections known as octants by these three coordinate planes. The positive axes determine the first octant, which is in the front.
To be expressed, everything needs a perspective and a point of view. The three spatial dimensions are represented by the X, Y, and Z coordinates. These stand for length, width, and depth. We employ the same X, Y, and Z denotations when referring to machines, but we assign them different values or meanings. Even more intriguingly, there are no clear laws defining the meaning, which makes it difficult to converse on these levels.
Calculationthis given point lies on xyz plane bcz the point itself shows coordinates which is only possible in xyz plane .
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9. There is so much water in the world, that we normally measure large bodies of water in cubic
miles or cubic kilometers instead of gallons. Cayuga Lake in upstate New York contains an
estimated 9.4 km³. How many cubic miles of water does Cayuga Lake contain?
Answer:
Step-by-step explanation:
12.5km
i made that up sorry
Find a polynomial function of least degree having only real
coefficients, a leading coefficient of 1, and zeros of 4 and
3 + i.
The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Given,
In the question:
A leading coefficient of 1, and zeros of 4 and 3 + i.
To find the polynomial function of least degree having only real coefficients.
Now, According to the question;
The function has 4 and 3 + i .
As, i's roots
So, 3 - i is also its root a leading coefficient of 1 .
So, The function of polynomial is :
f(x) = (x - 4) [tex][(x - 3)^2 + 1][/tex]
To solve the function;
f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
Hence, The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]
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will give u brainliest!
Answer:
3.46
Step-by-step explanation:
[tex]\sqrt{21-9}[/tex]
[tex]\sqrt{12}[/tex]
3.46
Hopes this helps please mark brainliest
The exponential model describes the population, A, of a country in millions, t years after 2003. Use the model A=384. 7e^0. 018t to determine when the population of the country will be 513 million.
The population of the country will be 513 million in __. (Round to the nearest year as needed. )
The population of the country will be 513 million in 2016 with The exponential model A=384. 7e^0. 018t describes the population, A, of a country in millions, t years after 2003.
What is exponential model?The exponential model represents the degrading failure process using an equation like: where Y = degradation, T = time, and A and B = parameters to be predicted using the regression approach using historical data. Exponentials are frequently utilized when the rate of change of a quantity is proportional to its beginning amount. Y represents exponential decay if the coefficient associated with b and/or d is negative. Y represents exponential growth if the coefficient is positive.
Here,
A = 384. 7e^0. 018t
513=384. 7e^0. 018t
513/384.7= e^0.018t
ln(513/384.7) = 0.018t
ln(513/384.7)/0.018 =t
t=15.9895575229 years
t=16 years
2003+16= 2019
In 2016, the country's population will be 513 million people. The exponential model A=384. 7e^0. 018t explains a country's population, A, in millions, t years after 2003.
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What is the area of the figure?
17.5 yd2
20.0 yd
19.1 yd
35.0 yd2
The area of the triangle is A. 17.5yd².
How to find the area?Using this formula to find the area
Area = 1/2 ( b × h)
Where:
b = base = 5
h = Height = 7
Hence,
Area = 1/2 (5 ×7)
Area = 1/2 (35)
Area = 1× 35/2
Area = 35/2
Area = 17.5yd²
Therefore the correct option is A.
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Kelly has 97 apples, Jason has 72. How may proportional relationships are there?
There are 6984 inverse proportional relationships and the direct proportional relationships are 97/72.
Given that:
Kelly has 97 apples, and Jason has 72.
The relationship between two variables, X and Y, is directly proportional if it can be expressed in terms of Y/X = k or Y = Xk.
Y/X = k
Substitute the given X and Y values and solve for k.
Suppose, Y = 97, X = 72
then k = 97/72
Distinguish a proportional relationship from other relations, including an inverse relationship (XY = k or Y = k/X).
An inverse proportional relationship is one in which two quantities vary inversely with respect to each other. We say that the variable Y changes inversely with X if
Y = k/X
Substitute the given X and Y values and solve for k.
Suppose, Y = 97, X = 72
then k = 97 x 72
=> k = 6984
Hence, there are 6984 inverse proportional relationships and direct proportional relationships are 97/72 between Kelly which has 97 apples, and Jason which has 72.
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What is the solution set for 5 - 5 = 15, given the replacement set {0, 1, 2, 3, 4}? O x = 4 O x = 3 O x = 2 O x = 1 x = 0
The solution set for the given equations is x = 4.
What is a set?
A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
Here,
we put the value of x in the given equation and justify our answer
when we x=4, we get
5x−5=15
5(4) - 5 = 15
20 - 5 = 15
15 = 15
Hence, the solution set for the given equations is x = 4.
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In 2001 there were 6680 electric-powered vehicles in use in the United States. In 1998 only 4760 electric vehicles were being used. (Source: U. S. Energy Information Administration)
a. Assume that the relationship between time, x, and number of electric-powered vehicles, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (years past 1998 comma number of vehicles).
An equation of slope-intercept form describing this relationship. Use ordered pairs of the form the equation, y = 640x + 4760
Since there were 4760 electric vehicles in 1998, when x=0 (indicating 0 years have passed since 1998), y=4760. There were 1,920 more electric vehicles on the road after three years. 1920 / 3 = 640 is the average rate of change every year. Between 1998 and 2001, there were 640 more automobiles every year.Our slope measures m=640. By dividing the change in y by 4760, or 1920, we can determine the slope.The y-intercept is just the starting point, or x=0. At this point, x=0. The y-intercept is shown here: (0, 4760). Equation of slope intercept: y = 640x + 4760 where b=4760.
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Write an equation of the line, in point-slope form, that passes through the two given points.
points: (-2,10), (10 -14)
The required equation of the line will be y = 2x + 6 which passes through the points (-2,10), (10 -14).
What is the slope of the line?The slope of a line is defined as the gradient of the line.
Given that line passes through the points (-2,10), (10 -14)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -2, y₁ = 10
x₂ = 10, y₂ = -14
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 10 = (-14 - 10)/(10-(-2))[x -(-2)]
⇒ y - 10 = (-24)/(12 )[x +2]
⇒ y - 10 = -2(x +2)
⇒ y = -2x - 4 + 10
⇒ y = -2x + 6
Therefore, the equation of the line would be y = 2x + 6 which passes through the points (-2,10), (10 -14).
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Question
Graph x=−6.
A graph of the given mathematical expression (x = -6) is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
In this scenario, a number line would be used to graph the given mathematical expression because it only contains one (1) variable.
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If f(x) = 10 - 200 and g(x) = 25x2 + 90, the value of f (4) - g (2) is:
As function f(x) is not completely right i assume it to be like f(x)= 10x-200.
Acc. to which the answer is -350.
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X.
Main Body:
f(x)= 10x-200
f(4)= 10*4-200
= 40-200
=-160
g(x)= 25[tex]x^{2}[/tex]+90
g(2)= 25*(2)² +90
= 25*4+90
=190
So, f(4)-g(2) = -160-190
= -350
Therefore the answer is -350.
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multiply
(−5 2/5) ⋅ 3 7/10.
a. −19 49/50
b. −15 7/25
c. −9 1/10
d. −1 7/10
Answer: -19 49/50 ==> a
Step-by-step explanation:
(−5 2/5) ⋅ 3 7/10=
(−5 - 2/5) ⋅ (3 + 7/10)=
(−25/5 - 2/5) ⋅ (30/10 + 7/10)= ==> make the terms have like denominators
((-25-2)/5) ⋅ ((30+7)/10)=
-27/5 ⋅ 37/10 =
-27 ⋅ 37 / (5 ⋅ 10) =
-999/50=
(-950-49)/50=
-950/50 - 49/50=
-19 - 49/50=-19 49/50 ==> a
Which inequality represents the phrase "nine less than two
times a number is no more than 45?"
The expression of the inequality is [tex]9 < 2x\le45[/tex]. It can be obtained using the operations of inequality.
What is inequality?
In matmathematics if two numbers are not equal even then there is a relationship. This relationship can be defined by inequality relationship.
According to the pharase, 9 is less than two times a number. Hence, consider the number is x and its two times means 2x. Now, 9 should be less than this number. Hence, 9<2x. Now, again the number 2x is not more than 45. Means, it can be equal to 45. Hence, it will give the expression [tex]2x\le45[/tex].
Now, combine the two expressions as follows:
9<2x
[tex]2x\le45[/tex]
[tex]9 < 2x\le45[/tex]
Hence, the expression of the inequality is [tex]9 < 2x\le45[/tex].
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A pool takes 3,185 gallons to fill. After 2.5 hours the pool is filled with 1,625 gallons how long will it take to fill the whole thing
[tex]\begin{array}{ccll} hours&gallons\\ \cline{1-2} 2.5 & 1625\\ h& 3185 \end{array} \implies \cfrac{2.5}{h}~~=~~\cfrac{1625}{3185}\implies \cfrac{2.5}{h}=\cfrac{25}{49} \\\\\\ (2.5)(49)=25h\implies \cfrac{(2.5)(49)}{25}=h\implies 4.9=h\qquad \textit{4 hours and 54 minutes}[/tex]
A manager of a fast food chain wants to know how his customers rate their service at the restaurany that day. after randomly picking the 9th customer, he surveys every 5th customer that exits the restaurant. which sampling method? your answer: simple random systematic stratified cluster volunteer
The sampling method used in this scenario is random Systematic random sampling
Systematic random sampling
Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.
If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.
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HELP MEEE PLEASEEEE
Answer:
5.8 cm
Step-by-step explanation:
the Pythagorean theorem states that a^2=b^2+c^2, where a is the hypotenuse, and b and c are the legs. Plugging in your values, we get:
4^2 + 4.2^2 = a^2
Simplify: 16 + 17.64=a^2
Simplify again: 33.64 = a^2
Square root both sides: 5.8 = a
f(-10) = 4, ƒ(8) = -5
Answer: f(x)=-.5x-1
Step-by-step explanation:
I believe this is the answer you are looking for. Because if you plug in -10 for x and it gives you 4. Do the same with 8 and you get -5
Hope this helps :)
What is the radius of the circle made by anas brother in the blue car? use 3. 14 and round your answer to the nearest tenth
The radius of Ana's brother's circle in the blue car is 35 feet.
Define the term radius of the circle?A radius is a line segment that connects the center towards the perimeter of a circle or sphere. The radius length remains constant as from center either to point on the circle or sphere's perimeter.For the given question-
The total distance covered by the Ana's brother in the blue car = 220 feet.
Total distance = circumference of the circle.
circumference of the circle = 2 π r
r = radius of the circle.
π = 3.14
Thus,
220 = 2 x 3.14 x r
r = 220 / (3.14 x 2)
r = 35.03
r = 35 feet.
As a result, the radius of Ana's brother's circle in the blue car is 35 feet.
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The complete question-
The missing data from the question is given in diagram attached.
Use the distributive property to remove the parentheses.
3c³(7c8 +8c+7)
Simplify your answer as much as possible.
Answer: 21 c^16 + 24c^9+ 21 c^8
Step-by-step explanation: To multiply exponents with the same base, add them.
Answer:
3c^3(7c^8+8c+7)
=(3c^3)(7c^8+8c+7)
=(3c^3)(7c^8)+(3c^3)(8c)+(3c^3)(7)
=21c^11 + 24c^4 + 21c^3
Step-by-step explanation:
Remember.... ^ is for power
Determine the slope of the graph of x2 = ln(xy) at the point (1, e).
The slope of the given graph x^2 = ln (xy) at the point (1, e) is e
We have been given a graph x^2 = ln (xy) and a point (1, e)
Differentiate the given graph on both sides
d/dx x^2 = d/dx (ln (xy))
⇒ 2x = 1/xy × d/dx (xy)
⇒ 2x × xy = x.dy/dx + y.dx/dx
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y - y = x.dy/dx
⇒ (2x^2y - y)/x = dy/dx … (1)
The slope at the point (1, e)
m = dy/dx at x = 1, y = e
Substitute the values in Equation (1)
⇒ m = (2(1)^2 (e) - e)/1
⇒ m = (2e - e)/1
⇒ m = e/1
⇒ m = e
Hence, the slope of the given graph is e.
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please help lol I need help
The expression can be expanded as 125/64
Evaluating an ExpressionTo evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.
To solve this problem, we need to evaluate the expression given;
For this, we can find the cube of the numerator and cube of the denominator.
(5/4)³ = 125/64
The solution to the problem is 125/64
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The angles of elevation of the top of a tower with respect to points A and B are 30° and 75°respectively. Points A and B are 175 feet apart and at equal elevations, and the base of the tower lies on the line between them. Find the height of the tower. Round your final answer to the nearest ten thousandth.
The height of the tower is 87.4870 feet
What is Angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The body of the calculation is contained in the attached file.
In conclusion, the height of the tower to the nearest ten thousandth is 87.4870 feet
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you cannot remember your 5-digit bike-lock combination. what is the probability that you guess the combination correctly? (enter your probability as a fraction.)
The probability that you guess the combination correctly 0.00001.
We know that the probability of an event is (possible outcome/total outcome)
I will assume that repeats are allowed as in most combination locks so the number of possible codes
= 10⁵ = 100000
We also know that there is only one correct combination so the probability that you guess the combination correctly
= 1/10⁵ = 1/100000 = 0.00001
Orchestrating individuals, digits, numbers, letters in order, letters, and tones are instances of changes. Choice of menu, food, garments, subjects, and group are instances of combination.
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What is the value of blank and 40.01 is close to 1
The number that is the numerator of a fraction with denominator of 40.01 and is equals to a coefficient of one is:
40.01.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:
Fraction = x/y.
The terms are named as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.Hence the quotient of the division is the numerator divided by the denominator.
In this problem, interpreting the blank variable as x, the fraction that represents the situation is:
x/40.01 = 1.
Applying cross multiplication, the numeric value of the variable x is obtained as follows:
x = 40.01 x 1
x = 40.01.
Missing InformationThe complete problem asks for which number divided by 40.01 is close to 1.
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a journalist for an automotive magazine wants to determine how the weight of a passenger vehicle, in kilograms, is related to its length, in centimeters; the maximum number of passengers; and its safety rating on a 5-point scale. what is the correct format for a multiple regression equation?
the correct format for a multiple regression equation is
ŷ= [tex]b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}[/tex]
multiple regression: The relationship between a single dependent or criterion variable and multiple independent or predictor variables is typically explained by multiple regression. The constant term and multiple independent variables with their corresponding coefficients are used to model a dependent variable. The term "multiple regression" refers to the fact that it requires two or more predictor variables.
because, the weight of a passenger vehicle, in kilograms, is related to its length, in centimeters; and the maximum number of passengers.
thus, ŷ=[tex]b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}[/tex] is the multiple regression equation.
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What value of b will complete the square in the expression below and make the
expression a perfect square trinomial?
x²+bx+144
Enter the perfect square trinomial as a squared binomial.
At b= 24 will complete the square in the expression x^2 + bx + 144.
What is perfect square trinomial?
A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b^2 = 4ac has the form ax^2 + bx + c, it is said to be a perfect square. The formula for the perfect square trinomial is (ax)^2 + 2abx + b^2 = (ax + b)^2.
Consider the given expression
x^2 + bx + 144
For this type of expression [tex]b = 2\sqrt{c}[/tex] will complete the square.
Here, c = 144
√144 = 12
So, b√c = 2(12) = 24
The expression becomes,
x^2 + 24x + 144 = (x + 12)^2
This is the perfect square.
Hence, b = 24 will complete the square in the expression x^2 + bx + 144.
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Triangle ABC has vertices A(0, -1), B(6, 5), and C(-4, 3). Which statement about triangle ABC is true?
The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.
What is a right triangle?A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.
The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;
d² = (x₂ - x₁)² + (y₂ - y₁)²
The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;
[tex]\overline{AB}^2[/tex] = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2
[tex]\overline{AC}^2[/tex] = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2
[tex]\overline{BC}^2[/tex] = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)
72 + 32 = 104
Therefore; [tex]\overline{AB}^2[/tex] + [tex]\overline{AC}^2[/tex] = [tex]\overline{BC}^2[/tex]
ΔABC is a right triangle
The slopes of the equation of the lines of the sides of the triangle are;
Slope of side AB = (5 - (-1))/(6 - 0) = 1
Slope of side BC = (3 - 5)/(-4 - 6) = 0.2
Slope of side AC = (3 - (-1))/(-4 - 0) = -1
Therefore;
[tex]\overline{AB}[/tex] ⊥ [tex]\overline{AC}[/tex]
Which gives;
A true statement about triangle ΔABC is that ΔABC is a right triangle a nd the lengths of the sides of the triangle are differentLearn more about the Pythagorean theorem in mathematics here:
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Three students ran for class president. lisa got 36 votes for class president. she got six times more votes than lauren. chandler got seven times more than lauren. how many votes did lauren get?
Lauren got 5 votes in class president election.
Number of votes Lisa got = 36
Let the number of votes of Lauren be x. So, forming the equation between the number of votes of Lisa and Lauren.
36 = x + 6x
Calculating the value of x from mentioned equation
36 = 7x
Rewriting the equation with 7 as denominator
x = 36/7
Performing division on Right Hand Side of the equation
x = 5.14
Rounding off the digits as number of votes will be whole number
x = 5
Based on the mentioned information, Lauren got 5 votes.
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solve for x and y
picture provided
The value of x will be 15 and the value of y will be 4.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Here in the image, we have a triangle having sub-triangles. The value of x is calculated by considering two right-hand triangles.
x / ( x + 5 ) = 18 / ( 18 + 6 )
x / ( x + 5 ) = 18 / 24
24x = 18x + 90
6x = 90
x = 15
The value of y will be calculated by considering the two left-hand triangles.
12 / ( 12 + y) = 15 / 20
240 = 180 + 15y
15y = 60
y = 60 / 15
y = 4
Therefore, the value of x will be 15 and the value of y will be 4.
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Decide whether each equation is true for all, one, or no values of x.
1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.
2. 9(x + 3) = 9x + 12 ; This is true for no values of x.
3. 4(2x + 3) = 12 + 8x ; True for any values of x.
Given,
The equations;
1. 3x + 9 = -4.5x + 20
2. 9(x + 3) = 9x + 12
3. 4(2x + 3) = 12 + 8x
We have to find whether each equation is true for all, one or no values of x.
Here,
1. 3x + 9 = -4.5x + 20
Solve for x;
3x + 4.5x = 20 - 9
7.5x = 11
x = 11/7.5
x = 1.47
Then,
This is true for one value of x.
2. 9(x + 3) = 9x + 12
Solve using distributive property;
9x + 27 = 9x + 12
9x - 9x = 12 - 27
0 = -15
This is true for no values of x.
3. 4(2x + 3) = 12 + 8x
Use distributive property and solve;
8x + 12 = 12 + 8x
8x - 8x = 12 - 12
0 = 0
True for any values of x.
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