According to estimates, FG has a magnitude of 2√5.
The vector direction of FG is given as = 63.43°. (angle formed in the 1st quadrant with anti-clockwise direction).
What exactly would a distance formula imply?The distance formula is used in complex numbers to show the plane in addition to its magnitude. Distance formulas can also be used to determine the actual the distances between two planes in three- and n-dimensional planes.
Now, in answer to the question posed;
F and G have coordinates of (-1,10) and (1,-12), respectively.
The formula for calculating the distance between points A and B is as follows:
FG² = (x₂ - x₁)² + (y₂ - y₁)²
FG = √[(x₂ - x₁)² + (y₂ - y₁)²]
The coordinates for the points F and G's are-
(x₁,y₁) = (-4,0) and (x₂,y₂) = (-6,-4).
Substituting the given values in the distance formula;
FG = √[(-6 + 4)² + (-4 + 0)²]
FG = √[(-2)² + (-4)²]
FG = √[4 + 16] = √20
FG = 2√5 (magnitude of the vector FG)
Estimate the direction of this same vector FG now. The angle formed by a vector with a horizontal line defines its direction.
Use one of the following formulas to calculate the direction of a vector.
tan Ф = Δy/Δx
Where, x = horizontal change
and, y = vertical change
tan Ф = (y₂ - y₁)/(x₂ - x₁)
= (-4 + 0)/(-6 + 4)
tan Ф = -4/(-2) = 2
Ф = 63.43° (angle lies with in the first quadrant with anticlockwise direction).
As a result, the distance between F and G is determined to be 2√5. (the same as the magnitude of a given vector FG).
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Help Please
Solve for y : | y | = 16 .
y= ____ , ____
For the geometric sequence 3,12,48,192, . . . . . , find the indicated term.17 th term
The 17th term of the given geometric sequence, 3, 12, 48, 192, . . . , is 1.288490189 x 10^10.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
r = ratio
Given the geometric sequence 3, 12, 48, 192, . . .
Find the ratio,
r = a(n)/a(n-1)
r = a(2)/a(1)
r = 12/3
r = 4
Notice that the ratio between two succeeding terms is always 4.
Use the formula to find the 17th term of the geometric sequence.
a(n) = a r^(n-1)
a(17) = 3[4^(17-1)]
a(17) = 3(4^16)
a(17) = 1.288490189 x 10^10
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The monthly cost of using a cell phone is $29.95 plus $0.035 per minute of talk time. An equation to
represent this monthly cost would be:
C = 29.95 + 0.035x, where C represents the monthly cost and x represents the number of minutes used.
How many minutes were used during a month if the cost amounted to $43.53 ?
O 506 minutes
O 426 minutes
O 388 minutes
438 minutes
Answer:
c) 388 minutes
Step-by-step explanation:
Given equation,
→ C = 29.95 + 0.035x
Then the call duration will be,
→ C = 29.95 + 0.035x
→ 43.53 = 29.95 + 0.035x
→ 0.035x = 43.53 - 29.95
→ x = 13.58/0.035
→ [ x = 388 ]
Hence, option (c) is correct.
CCSS ARGUMENTS Write a coordinate proof for each statement.The three segments joining the midpoints of the sides of an isosceles triangle form another isosceles triangle.
The triangle formed by joining the midpoint of an isosceles triangle is also an isosceles triangle.
What is an isosceles triangle?An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
An isosceles triangle XYZ is been made as shown below. Now, for the ΔXYZ, the midpoints of the line segment XY, YZ, and ZX are A, B, and C, respectively.
Further, the length of the sides of the ΔABC can be written as,
AB = √[(x₂-x₁)² + (y₂-y₁)² ]
= √[(3 - 1)² + (1 - 1)²]
= √4
= 2
BC = √[(x₂-x₁)² + (y₂-y₁)² ]
= √[(3 - 2)² + (1 - 0)²]
= √2
AC = √[(x₂-x₁)² + (y₂-y₁)² ]
= √[(1 - 2)² + (1 - 0)²]
= √2
Since, the length of the two sides is the same, while the length of the third side is different, thus, the triangle formed by joining the midpoint of an isosceles triangle is also an isosceles triangle.
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Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x)=11 x-11 for x=-11
f(-11) = -132 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= 11 x-11
Put x = -11 ⇒ 11 * - 11 - 11
⇒ - 121 - 11
⇒ -132
Therefore f (-11) = -132
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The midpoint of CD is M(–9, –8). One endpoint is D(–9, –7). Find the coordinates of the other endpoint C
Use the link below to answer your question:
https://www.omnicalculator.com/math/endpoint
Hope this helps!
|-a2|, given a = 5, b = -3, and c = -2.
10
25
-10
-25
The scatter plot shows the number of stamps Katie collected in different months:
plot ordered pairs 1, 30 and 2, 70 and 3, 110 and 4, 150 and 5, 190
What is the approximate predicted number of stamps she collected in the 25th month? (1 point)
980
990
1,000
1,010
Hello!
The approximate predicted number of stamps she collected in the 25th month is 990.
Step-by-step explanation:
The ordered pairs are as follows:
( 1, 30), ( 2, 70), ( 3, 110), ( 4, 150), and ( 5, 190).
The pattern visible is that each month the value increases by 40 from each previous month.
The equation you would have to do in order to see how many stamps she collected is:
[tex]30[/tex] + [tex]40[/tex] × [tex]24=30[/tex] + [tex]960=990[/tex]
Hope this helps!
Type the correct answer in the box. round your answer to the nearest whole number. dylan has two cubes of iron. the larger cube has twice the mass of the smaller cube. he measures the smaller cube. its mass is 20 grams, and its density is 7.87 g/cm3. what’s the larger cube’s volume? the larger cube’s volume is about cm3.
The larger cube's volume is 5.08 cm³.
As per the given information, expressing the relation between the mass of iron cubes -
Mass of large iron cube = 2×mass of small cube
Mass of large iron cube = 2×20
Performing multiplication to find the mass
Mass of large iron cube = 40 grams
Now calculating the volume of large iron -
Density = mass ÷ volume
Keep the values in formula to find the volume of cube -
Volume = mass ÷ density
Volume = 40 ÷ 7.87
Performing division to find the volume of cube -
Volume = 5.08 cm³
Hence, the volume of larger iron cube is 5.08 cm³.
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(3x + 4)(x + 2x + 3)
Answer:
9x^2 + 21x + 12
Step-by-step explanation:
(3x+4)(x+2x+3)
Combine x and 2x to get 3x.
(3x+4)(3x+3)
Apply the distributive property by multiplying each term of 3x+4 by each term of 3x+3.
9x^2 + 9x + 12x + 12
Combine 9x and 12x to get 21x.
9x^2 + 21x + 12
State the domain and range and determine if it’s a function
Answer:
Domain: 3, 6, 12, 18
Range: 5, 7, 9, 10
This is not a function.
Step-by-step explanation:
In a function there is a single y value for each x value. In this case, when x = 6, y can be both 5 and 10. If you were to plot all these points and graph them, you would see that the result would fail the "vertical line test" for a function.
whats 94 1/4 divided by 7 1/4 need steps pls
Which equation is parallel to 4x- 2y = 6 and passes through (0, 1)
The equation that is parallel to 4x- 2y = 6 and passes through (0, 1) is y = 2x + 1
How to determine the linear equation?The given parameters are
4x - 2y = 6
Divide through by 2
So, we have
2x - y = 3
Make y the subject of formula
So, we have
y = 2x + 3
A linear equation is represented as
y = mx + c
Where
Slope = m
This means that
m = 2
Parallel lines have equal slopes
So, the slope of the other line is
m = 2
The point on the line is given as (0, 1)
The equation is then calculated as
y = m(x- x1) + y1
So, we have
y = 2(x - 0) + 1
Evaluate
y = 2x + 1
Hence, the equation that is parallel to 4x- 2y = 6 and passes through (0, 1) is y = 2x + 1
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w+1/7z=4
z=3w-2 using substitution
Answer:
w = - 2/7 + 4
w = z/3 + 2/3
Step-by-step explanation:
18/12 pls??? Someone help
Answer:
3/2
Step-by-step explanation:
[tex]\frac{18}{12}=\frac{6(3)}{6(2)}=\frac{3}{2}[/tex]
draw base ten blocks to show the number 200 in the place value chart below
Answer:
Step-by-step explanation:
The base ten blocks to show the number 200 in the place value chart is shown below.
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 number 200 in the place value.
Now,
Since, the number 200 in the place value.
Hence, The figure for the base ten blocks to show the number 200 in the place value chart is shown in figure.
Thus, The base ten blocks to show the number 200 in the place value chart is shown below.
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Isaac saves 20% on a hard drive that costs $110 but must pay 6% sales tax. What is the total amount that he must pay at the store?
A. $93.28
B. $88.00
C. $106.00
D. $140.80
E. None of the above
The answer is 93.28
Step-by-step explanation:
The reason why is because 110 - 20% would leave you only paying 88 dollars. but when you add the 6% sales tax you get 93.28
Find the center and the radius of each circle. x²+y²-4 y-16=0
The center and radius of the circle given by the equation x^2 + y^2 - 4y - 16 = 0 is (0 , 2) and 2√5, respectively.
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in general form is x^2 + y^2 - 4y - 16 = 0, then the coefficients are:
D = 0
E = -4
F = -16
If D = -2h and D = 0, then
0 = -2h
h = 0
If E = -2k and E = -4, then
-4 = -2k
k = 2
If F = h^2 + k^2 -r^2 and F = -16, then
-16 = 0^2 + 2^2 - r^2
r^2 = 0 + 4 + 16
r^2 = 20
r = 2√5
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Which expression is equivalent to (3x^−4y^5) ^−2?
A: -9^8y^10
B: x^8/ 9y^10
C: -9x^8/ y^10
D: 1/ 9x^8y^10
(x's are variables not multiplication) (dashes resemble fractions) (^ resembles powers)
The equivalent expression to the given one is x^8/(9*y^10)
So the correct option is B.
Which expression is equivalent to (3x^−4y^5) ^−2?Here we just need to operate with the exponent properties that we know and love.
Remember that:
(a^n)^m = a^(n*m)
Then if we apply that to our case we will get:
(3x^−4y^5) ^−2 = (3^(-2)*x^(-4*-2)*y^(5*-2))
= (3^(-2)*x^8*y^(-10)
Now remember that negative exponents just "move" the number to the denominator position, this means that:
3^-2 = 1/3^2 = 1/9
Then we can rewrite our expression as:
(3^(-2)*x^8*y^(-10) = x^8/(9*y^10)
That is the equivalent expression to the given one.
The correct option is B.
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9. Writing to Explain Explain why you do not have to do any
computing to solve 15 X 0 X (13 + 7).
Answer:
because the answers 0 -
Explanation:
15 x 0 x (13+7)
= 15 x 0 x 20
= 0 x 20
= 0
Connor has a biased dice. The
probability of it landing on a
three is 0.8. Connor is going to
throw the dice 120 times.
Work out an estimate for the
number of times the dice will
land on a three.
Step-by-step explanation:
120×0.8
120/10)×8
=12×8
=96
The estimated number of times the dice will land on a three in 120 throws is 96 times.
We have,
To estimate the number of times the biased dice will land on a three, we can use the probability of getting a three in a single throw and multiply it by the total number of throws.
Probability of landing on a three in a single throw = 0.8
Total number of throws = 120
Estimated number of times the dice will land on a three
= Probability of landing on a three × Total number of throws
Estimated number of times = 0.8 × 120
Estimated number of times = 96
So, based on the biased dice with a probability of 0.8 for landing on a three, the estimated number of times the dice will land on a three in 120 throws is 96 times.
Thus,
The estimated number of times the dice will land on a three in 120 throws is 96 times.
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The battery power available to operate a deep space probe is given by the formula P=42 e°.°°5t , where P is power in watts and t is time in years. For how many years can the probe run if it requires 35 watts? Round the answer to the nearest tenth year.
The life of the battery is about 36.5 years, if it requires 35 watts.
What is termed as logarithmic functions?A logarithmic term is a number expressed in logarithmic form. Some other name for it is a log term.
A number could also be the sum of two or more numbers. As a result, a term can be the product of two or even more quantities, at least one of which should be in logarithmic form. These same terms are recognised as log terms in such cases.A quantity can also be described as the variation between two quantities. However, if a term contains a quotient of quantities, or if at least one of the amounts can also be conveyed in log form, the term is referred to as a log term.Consider some formulas used in log.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, as per the given question,
The function is written as;
P = 42e∧(-0.005t).
The value of the power P is mentioned in the question; (P = 35 watt).
Thus, substitute the value of the P in teh equation;
35 = 42e∧(-0.005t).
Now, divide both sides by 42.
0.8333 = e∧(-0.005t)
Taking natural log on both side;
㏒0.8333 = ㏒e∧(-0.005t)
㏒0.8333 = -0.005t
Solve the value of the log by using calculator,
-0.182 = -0.005t
t = 36.5
Therefore, the the life for which the battery will run is 36.5 years.
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Shelia starts with $50 in her checking account. She spends $45, deposits $32, spends $14, and finally desposits $30. What is her ending balance?
Write an equation of a circle with the given center and radius. Check your answers.
center (-1.5,-3) , radius 2
The equation of the circle with radius 2 and center at (-1.5 , -3) is (x + 1.5)^2 + (y + 3)^2 = 4.
The general form of the equation of circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-1.5 , -3)
r = 2
(x - -1.5)^2 + (y - -3)^2 = 2^2
(x + 1.5)^2 + (y + 3)^2 = 4
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Need help asap!!
Which of the following lists is in order from least to greatest?
√5 , 4, 3 2, -2
-2,√5 , 4, 3 2
-2, 4, 3 2, √5
-2, 3 2, 4, √5
Thanks!
The numbers in the second option is from the least to the greatest.
How to find the list from least to greatest?The numbers can be list from least to greatest as follows:
√5 , 4, 32, -2
32 is greater than -2.
Therefore, the numbers in first option is not from the least to the greatest.
-2,√5 , 4, 32
The number increases.
Therefore, the numbers in the second option is from the least to the greatest.
-2, 4, 32, √5
32 is greater than √5.
Therefore, the numbers in third option is not from the least to the greatest.
-2, 3 / 2, 4, √5
4 is greater than √5.
Therefore, the numbers in fourth option is not from the least to the greatest.
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what equation can represent 27 divided by 6 to represent the unknown quantity
Answer:
27÷6=? Answer is 4.5
Step-by-step explanation:
All you have to do is do 27/6 and the answer (unknown quantity) is 4.5.
find the area of the polygon
7 ft, 22 ft, 10 ft.
what is the area of the polygon?
Answer:1540
Step-by-step explanation: I hope this helps
Joshua decides to research the relationship between the length in inches and the weight of a certain species of catfish. He measures the length and weight of a number of specimens he catches then throws back into the water. After plotting all his data, he draws a line of best fit. What is the meaning of the x-value on the line when y=29?
The x value when y = 29 implies that the length in inches when the weight of the specie is 29
What is the meaning of the x-value on the line when y =29?The given parameters are:
The plot is about the relationship between the length in inches and the weight of a certain species of catfish
This implies that
x represents the length in inches y represents the weight of the speciesWhen the graph is plotted, the x value when y = 29 implies that the length in inches when the weight of the specie is 29
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What is the slope of the line passing through the following points? (2,4) and (4,2)
The slope of the line passing through the points (2,4) and (4,2) is -1
How do you determine a line's slope?
Determine the coordinates of two locations along the line that you choose. Find the difference between these two locations' y-coordinates (rise). Find the difference between these two locations' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
Formula to determine the slope is - y₂ - y₁ / x₂ - x₁
Given are the points -
(2,4) and (4,2)
slope of the line = 2 - 4 / 4 - 2
= -2 / 2
= -1
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Find the distance between the points (-5, -4) and (7, -4).
Answer:
12
Step-by-step explanation:
the distance would be 12 because if you see the y values they are both -4 so they dont have any distance between them. Now if u look in the x values you will see different values -5 and 7 what u have to do now is do the equation 7 - - 5 which will be 12 because minus and minus will be plus so 7 plus 5 is 12, the distance between those points is 12.
Hope this answers ur question.
