The Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ] is ( 5/√2, -5/√2)
The polar cordinates given are (r,θ)=(5,− π/4)
And we need to find the cartesian coordinates
We have,
x=rcosθ, y=rsinθ
x=5cos(− π/4) ,y=5sin(− π/4)
x= 5/√2 ,y=− 5/√2
So, the cartesian form is ( 5/√2, -5/√2)
The Cartesian coordinate of the point where polar coordinates are [5√2, π/4 ] is ( 5/√2, -5/√2)
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what is -3 > -2x + 7 ?
Which is the correct answer ????
f(x)=x^2-1, g(x)=x+2
The composite function ( f. g(x)) is x² + 4x + 3
What is a function?A function can be described mathematically as a rule, law or equation that explains, shows and elaborates the relationship between to variables.
The variables are known as;
The independent variableThe dependent variableFrom the information given, we have the functions as;
f(x)=x^2-1g(x)=x+2To determine the composite function ( f. g(x)), we have to substitute the value of g(x) as a function in the function f(x) as the variable 'x', we get;
( f. g(x)) = (x + 2)² - 1
Now, let's expand the square
( f. g(x)) = (x + 2) ( x+ 2) - 1
Expand the bracket
( f. g(x)) = x² + 2x + 2x + 4 - 1
Now, let's collect like terms, we get
( f. g(x)) = x² + 4x + 3
Thus, the function is x² + 4x + 3
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The complete question:
Find ( f. g(x)) if f(x)=x^2-1, g(x)=x+2
(q − 10) (q² + q +1)
What is the slope of the line that passes through the points (−4, −4) and (6, 4
Answer: no slope
Step-by-step explanation:
m= y2-y1/x2-x1
m= 6-(-6)/4-4
m=12/0
m= no slope
Answer:
y = 0.8x - 0.8
Step-by-step explanation:
Δy ÷ Δx = gradient (x)
4 - -4 = 8
6 - -4 = 10
8 ÷ 10 = 0.8
equation of line; y = mx + c
substitute one of the coordinates into the equation
(6, 4) y = 4, x = 6
4 = 0.8(6) + c
4 = 4.8 + c
- 4.8 to get the y intercept on it's own
-0.8 = y intercept (c)
confirmation
substitute the new values to get the other y
(-4, -4) y = -4 <-- should be the answer, x = -4
y = mx + c
y = 0.8(-4) - 0.8
y = -3.2 - 0.8
y = -4 the gradient and the y intercept have been proven right
Which statement is most likely to be true for this distribution?
O A. The mean is less than the median.
• B. The mean is greater than the median.
• C. The mean is the same as the median.
The statement that is most likely correct for the negatively skewed data distribution given is B. The mean is less than the median.
What is a Negatively Skewed Data Distribution?
A negatively skewed data distribution has the tail to the left of the number line, and therefore its median is usually greater than its mean.
The dot plot shows a data distribution that is negatively skewed. Therefore, the statement that is most likely to be true is B. The mean is less than the median.
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A triangle has a base of 8 inches and a height of 12 inches. What is the area?
Helpful conversion fact: A=1/2b•h
96 inches
96 square inches
48 inches
48 square inches
Answer:
48 square inches
Step-by-step explanation:
A=1/2 bh
A=(1/2)(8)(12)
A=(4)(12)
A=48 square inches
you can also multiply 8 x 12 then divide by 1/2 or 2 which is still 48. either way is correct but since the formula is half of the base times height that is the step i followed. Also area is always whatever measurement used (in this case inches) squared.
Elijah read his book from 4:30pm until 6:00pm. He read 1 chapter every 10 minutes.
How many chapters total did Elijah read?
Answer:
he read 9 chapters
Step-by-step explanation:
4:30 pm to 6:00 pm is 1:30 hours, which is 90 minutes
90/10=9
Mrs Ali baked some cookies.
She gave away 250 cookies and packed the remaining cookies into bags of 12.
Each bag of cookies was sold for $8.
She received $2016 from the sale of all bags of cookies.
How many cookies did she bake at first?
Answer: 3274 cookies
Step-by-step explanation:
She sold : 2016 ÷ 8 = 252 ( bags )
The remaining cookies : 12 × 252 = 3024 ( cookies )
She baked : 3024 + 250 = 3274 ( cookies )
Which of the following is the graph of (x+1)2/9 - (y+4)2/4 = 1?
The answer will be the graph of the straight line.
What is the equation straight line?
Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.
Using the equation we can plot the graph in 2D.
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Use the given information to find the number of degrees of freedom, the critical values χ2L and χ2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.
Nicotine in menthol cigarettes 95% confidence; n=23, s=0.25 mg.
The critical values of the chi statistic are; χ²R = 8.643 and χ²L = 42.796
The confidence interval estimate of σ is; 0.20 < σ < 0.45
How to find the critical value of Chi - Statistics?We are given the following data;
Sample size; n = 23
Degree of freedom; df = n - 1 = 23 - 1 = 22
Confidence level; α - level = 99%
Sample standard deviation; s = 0.25 mg
For χ²R;
The significance level is; 1 - (1 - 0.99)/2= 0.995
The degree of freedom is; df = 22
From critical value tables, we know that; χ²R = 8.643
For χ²L ;
The significance level is; (1 - 0.99)/2 = 0.005
The degree of freedom is; df = 22
From critical value tables, we know that; χ²L = 42.796
The confidence interval estimate of σ is;
s * √[(n-1)/χ²L] < σ < s * √[(n-1)/χ²R)]
Plugging in the relevant values gives;
0.28 * √(22/42.796) < σ < 0.28 * √(22/8.643)
0.2008 < σ < 0.4467
0.20 < σ < 0.45
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Drag each tile to the correct box. Not all tiles will be used.
Find the equations with unit rates greater than the unit rate of the graph. Then arrange these equations in order from least to greatest unit rate.
The equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x
How to determine the equations with unit rates greater than the unit rate of the graph?
On a graph, the unit rate is obtained by calculating the slope of the line. The slope is the change in y divided by the change in x:
Slope = y2-y1 / x2-x1
Thus, we can any two convenient points on the graph and use it calculate the slope:
Let's pick points (5, 10) and (12, 25)
This implies x1 = 5, y1 = 10 and x2 = 12, y2 = 25
Slope = y2-y1 / x2-x1
Slope = 25-10 / 12-5 = 15/7
Thus, the unit rate of the graph is 15/7 = 2.143
Find the equations with unit rates greater than the unit rate of the graph:
y = 19/8x: unit rate = 19/8 = 2.375
y = 27/13x: unit rate = 27/13 = 2.077
y = 21/9x: unit rate = 21/9 = 2.333
y = 11/5x: unit rate = 11/5 = 2.200
y = 15/17x: unit rate = 15/17 = 0.882
y = 31/15x: unit rate = 31/15 = 2.067
y = 13/6x: unit rate = 13/6 = 2.167
The equations with unit rates greater than the unit rate of the graph are y = 19/8x, y = 21/9x, y = 11/5x and y = 13/6x
Therefore, the equations in order from least to greatest unit rate are y = 13/6x,y = 11/5x, y = 21/9x and y = 19/8x. Drag each tile to the correct box accordingly
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The kitchen is a square and has an area of 169 square feet.whatis the length of one side of Tito’s kitchen?
The length of one sides of the square Tito's Kitchen is 13 feet.
How to find the length of a square?A square is a quadrilateral with 4 sides equal to each other. The opposite sides of a square is parallel to each other.
The sum of angles in a square is 360 degrees. Each angle is 90 degrees.
The kitchen is a square and has an area of 169 square feet.
The length of one side of the kitchen can be calculated as follows:
area of the square kitchen = l²
where
l = side lengthTherefore,
area of the square kitchen = 169 ft²
169 = l²
square both sides of the equation
√169 = √l²
l = 13 ft
Therefore,
length of the square kitchen = 13 feet.
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screenshot included with question
Answer:
48 fl oz = 6 c
4 gal = 16 qt
Step-by-step explanation:
4 times 4 is 16
48 divided by 8 is 6
Find the GCF of 21 and 28.
Answer: 7
Step-by-step explanation:
Answer:
7 is the GCF of 21 and 28
Step-by-step explanation:
The GCF of 21 and 28 is 7. To calculate the greatest common factor (GCF) of 21 and 28, we need to factor each number (factors of 21 = 1, 3, 7, 21; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 21 and 28, i.e., 7.
Mid point of AB is M (1,-4). If the coordinates of A are (-3,-6) what are the coordinates of B?
The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2).
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
The coordinate of midpoint between two points (x₁, y₁) and (x₂, y₂) is given by,
( (x₁ + x₂)/2 ,(y₁+ y₂)/2)
Given that, M is the midpoint of A and B.
Let's say the coordinate of point B is B(x,y).
Then,
1 = (-3 + x)/2
x = 2 + 3 = 5
And,
(-6 + y)/2 = -4
y = -8 + 6 = -2
Hence "The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2)".
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Please help me with the attached question
The expression equivalent to [tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex] is m - 2.
How to find equivalent expression?Equivalent expressions are expressions that work the same even though they look different.
In other words, equivalent expressions are expressions that have the same value.
Therefore, the expression that is equivalent can be calculated as follows:
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m[/tex]
Hence, let's simplify the expression to find it's equivalent,
open the bracket
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m[/tex]
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = -\frac{21}{2}+2m+\frac{17}{2}-m = -\frac{21}{2}+\frac{17}{2}+2m-m[/tex]
[tex]-\frac{21}{2}+\frac{17}{2}+2m-m=-\frac{4}{2} + m[/tex] = m - 2
Therefore,
[tex]-3(\frac{7}{2} -\frac{2}{3}m )+\frac{17}{2} -m = m-2[/tex]
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d) Three bus services A, B and C arrive at a station. Service A arrives at the station every 15 minutes, service B arrives every 20 minutes and service C arrives every 30 minutes. All three buses arrive at the station together at 9 a.m. At what time will the three buses next arrive at the station. (Decide which will you use to find the answer: GCF or LCM)
The time that the three buses will next arrive at the station, given the time between their individual arrivals is 10 am.
How to find the time of arrival?Service A arrives every 15 minutes. Service B arrives every 20 minutes. Service C arrives every 30 minutes.
The goal is to find the time when all services arrive at the same time. This can be found by finding the LCM of all three times. This will show the shortest time till all services arrive.
The LCM of 15 minutes, 20 minutes, and 30 minutes is 60 minutes.
The three bus services will arrive at the same time in 60 minutes which is:
= 9 am + 60 minutes
= 10 am
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what is the measure of arc XY in the diagram below ?
The measure of the intercepted arc, [tex]\widehat{XY}[/tex], formed by the secants ZW and ZV is 30°
What is a secant of a circle?A secant line is a straight-line which has two points of intersection with a circle.
From a similar question on the internet, the figure consists of an outside angle of 41° formed by two secants and two intercepted consisting of [tex]\widehat{XY}[/tex]and [tex]\widehat{VW}[/tex] which measures 112°
The outside angles of a circle theorem states that the outside angle formed by two secants or two tangent or a combination of a secant and a tangent is the difference of the measure of the difference of the angles of the intercepted arcs divided by two.
Mathematically;
[tex]m\angle z = \dfrac{\widehat{VW} - \widehat{XY}}{2}[/tex]
Where;
The outside angle formed by the secant ZW and ZV, m∠z = 41°
[tex]\widehat{VW}[/tex] = 112°
Which gives;
[tex]41^{\circ}= \dfrac{112^{\circ}- \widehat{XY}}{2}[/tex]
2 × 41° = 112° - [tex]\widehat{XY}[/tex]
82° = 112° - [tex]\widehat{XY}[/tex]
[tex]\widehat{XY}[/tex] = 112° - 82° = 30°
[tex]\widehat{XY}[/tex] = 30°
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How do I solve the following equation?
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (-2 , 5.5)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5.5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5.5}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -5.5= -\cfrac{1}{3} (x +2)[/tex]
[tex]y-5.5=-\cfrac{1}{3}x-\cfrac{2}{3}\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+5.5\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{55}{10} \\\\\\ y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{11}{2}\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x+\cfrac{29}{6} \end{array}}[/tex]
Please help! What is the standard form of the following equation?
y= 5x+0.5
-5x+y=-0.5
-5x+y=0.5
-5x-y=0.5
-5x+y= 0.5
The standard form of the equation, 3y = 9x -12, is -5x + y = 0.5. The correct option is the third option -5x+y=0.5
Writing an equation is standard formFrom the question, we are to write the given equation is standard form.
The given equation is
y = 5x + 0.5.
The standard form of a linear equation is
Ax + By = C
Where A, B, and C are constants
x and y are variables
Now, we will write the given equation is the standard form of a linear equation.
y = 5x + 0.5
Subtract 5x from both sides of the equation
y - 5x = 5x - 5x + 0.5
y - 5x = 0.5
Rewrite the equation, so that it would correspond to the standard form of a linear equation
-5x + y = 0.5
Hence, the standard form is -5x + y = 0.5
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The width of a rectangle measures (9.6w+4.7x) centimeters, and its length
measures (7.8w - 2.1x) centimeters. Which expression represents the perimeter,
in centimeters, of the rectangle?
Answer:
[tex]34.8w+5.2x[/tex] cm
Step-by-step explanation:
If the width of a rectangle measures [tex](9.6w+4.7x)[/tex] cm and its length measures [tex](7.8w-2.1x)[/tex] cm, then the perimeter of the rectangle is:
[tex]2(9.6w+4.7x)+2(7.8w-2.1x)[/tex]
[tex](19.2w+9.4x)+(15.6w-4.2x)[/tex]
[tex]19.2w+9.4x+15.6w-4.2x[/tex]
[tex]19.2w+15.6w+9.4x-4.2x[/tex]
[tex]34.8w+5.2x[/tex]
Pls help I’m giving brainliest
Using prime factorization, the LCM and GCF of numbers are
1) For 46 and 4
GCF = 2
LCM = 92
2) For 2 and 34
GCF = 2
LCM = 34
3) For 32 and 4
GCF = 4
LCM = 32
What is meant by prime factorization?A natural number other than 1 with just the number 1 and itself as factors is known as a prime factor. Actually, 2, 3, 5, 7, 11, and so on are the first few prime numbers. For numbers, we may now also employ what is known as prime factorization, which really involves utilizing factor trees.
When a number is expressed as the product of its prime factors, this is known as prime factorization.
1) The factors of the numbers are
46 = 2 × 23
4 = 2 × 2
GCF = 2
LCM = 2 × 2 × 23
= 92
2) The factors of 34 are
34 = 2 × 17
GCF = 2
LCM = 2 × 17
=34
3) The factors of the numbers are
32 = 2 × 2 × 2 × 2 × 2
4 = 2 × 2
GCF = 2 × 2
= 4
LCM = 2 × 2 × 2 × 2 × 2
= 32
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Solve for x
150µ=0.694(x+7.2K)*10^-9
[tex]x=2.16*10^{11}u-7.2k[/tex].
Side note: This answer could be more precise if made usage of more significant figures. For practicality reasons, in this solution we reduced the amount of significant figures to use.
Step-by-step explanation:1. Write the expression.[tex]150u=0.694(x+7.2K)*10^-9[/tex]
2. Solve the parenthesis using the distributive property of multiplication.[tex]150u=[(0.694*x)+(0.694*7.2K)]*10^-9\\\\150u=[0.694x+4.9968k]*10^-9\\ \\150u=10^-9*0.694x+10^-9*4.9968k[/tex]
3. Subtract "10^-9*0.694x" from both sides of the equation.[tex]150u-10^-9*0.694x=10^-9*0.694x-10^-9*0.694x+10^-9*4.9968k\\ \\150u-10^-9*0.694x=10^-9*4.9968k[/tex]
4. Subtract "150µ" from both sides of the equation.[tex]-150u+150u-10^-9*0.694x=10^-9*4.9968k-150u\\ \\-10^-9*0.694x=10^-9*4.9968k-150u[/tex]
5. Divide both sides by "-10^-9*0.694".
[tex]\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k-150u}{-10^-9*0.694} \\ \\\frac{-10^-9*0.694x}{-10^-9*0.694} =\frac{10^-9*4.9968k}{-10^-9*0.694}-\frac{150u}{-10^-9*0.694} \\ \\x=-7.2k-(-2.16*10^{11} u)\\ \\x=-7.2k+2.16*10^{11}u\\ \\x=2.16*10^{11}u-7.2k[/tex]
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question attached, it's trig
The value of sin 3° will be;
⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The values are,
sin 18° = √(3 - √5) / 2√2
cos 18° = √ (5 + √5) / 2√2
Now,
Find the value of sin 3° as;
⇒ sin 3° = sin (18 - 15)°
= sin 18° cos 15° - cos 18° sin 15°
= √(3 - √5) / 2√2 × (√3 + 1) / 2√2 - √(5 + √5) / 2√2 × (√3-1)/2√2
= 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)
Thus, The value of sin 3° will be;
⇒ sin 3° = 1/8 (√(3 - √5) (√3 + 1) - √ (5 + √5) (√3- 1)
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The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Find
(a) the co-ordinates of the mid-point of the line PQ,.
The co-ordinates of the mid-point of the line PQ are (6,4).
From the question, we have
The point P has co-ordinates (10, 12) and the point Q has co-ordinates (2,-4).
Mid-point of the line PQ =(10+2)/2 , (12-4)/2
= (6,4).
Midpoint:
A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places. When we know the coordinates of two points, we can apply the midpoint formula to get the midpoint between them. If we know the coordinates of the other endpoint and the midpoint, we can use the midpoint formula to obtain the coordinates of the endpoint as well.
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Question 13(Multiple Choice Worth 2 points)
(Multi-Step Percent Problems MC)
A gaming system costs $600 and is on sale for 35% off. After the discount, there is a 5% tax. What is the final price of the gaming system?
$409.50
$390.00
$220.50
$210.00
What is the y-intercept of a line that has a slope of and passes through point (8, 3)?
000
3
5
11
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The y-intercept of a line that has a slope of and passes through points (8, 3) is (0,1).
what is the slope-intercept?
A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.
The slope-intercept form: y = mx + b
m - a slope
b - y-intercept
Here, we have
A slope m = 1/4.
Substitute: y = 1/4 x + b
We know that
the line passes through the point (8, 3) → x = 8, y = 3.
Put the values of x and y into the slope of the line:
1/4 · 8 + b = 3
2 + b = 3 |-2
b = 1
Hence, the y-intercept is (0, 1)
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15. Mohammed has $8376 in his bank account. In the next month he takes out $4595 to buy a car. He then buys some new tires for his car for $1200. The next day, he receives his salary of $2709 in his bank account. How much is in his account at the end of the month?
By doing addition and subtraction of integers, the result obtained is
Mohammed had $5290 at the end of the month
What is addition and subtraction of integers?
At first it is important to know about integers
Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.
Suppose there are many integers, and we need to find the sum total of all those integers, then the operation used in this case is called addition.
To find how big or small one integer is from the other, then the operation used is called subtraction of integers.
Here we will use addition and subtraction of integers
Bank balance of Mohammed = $8376
Amount of money taken out by Mohammed next month to buy a car = $4595
Amount of money needed to buy new tires for his car = $1200
Amount of salary received by Mohammed next day = $2709
Amount of money Mohammed had at the end of the month =
$(8376 - 4595 - 1200 + 2709)
= $5290
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Students in two classrooms were given a mathematics test. The first classroom had 25 students and their average score was 86%. The second classroom had 15 students and their average score was 94%. If the teacher combined the test scores of students in both classes, what is the average score for both classes?
Answer:
Step-by-step explanation:
