So, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or we can also write them as 24 × 3, where 2 and 3 both are prime numbers.
if (2i/2+i) - 3i(3+i) = a + bi then a= ____ and b=_____
A = 1/10, -10, 1/50, -1/10
B = i/10, -10i, -1/10, -1/50
The value of a and b in the given complex expression is 1/10 and -1/10 respectively.
This is a problem related to the complex numbers. The complex numbers has a general form of (a+bi) where 'i' is the imaginary number or √-1. The part without an 'i' is called Real Part and the part with an 'i' is called Imaginary Part.
(2i/2+i) - 3i/(3+i) = a + bi
{ 2i(3+i) - 3i(2+i) }/ (2 + i)(3 + i) = a+bi
6i + 2i² - 6i - 3i² / (2 + i)(3 + i) = a+bi
(-2 + 3) / (6 + 5i - 1) = s+bi
1 / (5 + 5i) = a+bi
Now we multiply top and bottom by 5 - 5i :
5 - 5i / (5 + 5i)(5 - 5i) = a+bi
5 - 5i / 25 -25i² = a+bi
5 - 5i / 50 = a+bi
1/10 - 1/10i = a+bi
On comparing the real and imaginary part on the both sides:
a= 1/10 , b= -1/10.
To know more about the complex numbers, refer:
https://brainly.com/question/20566728?referrer=searchResults
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (4, −1), and Monique's desk is located at (−4, 3). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
Answer:
the distance from Maria's desk to Monique's desk is approximately 8.94 feet.
Nicole, Miguel, and Samuel served a total of 115 orders Monday at the school cafeteria. Miguel served 3 times as many orders as Samuel. Nicole served 10 more orders than Samuel. How many orders did they each serve?
Answer:
Samuel = 21 orders
Nicole = 31 orders
Miguel = 63 orders
Step-by-step explanation:
Let N represent Nicole's orders, M represents Miguel's orders, and S represent Samuel's orders.
We know that the sum of their tree orders equals 115 as
N + M + S = 115
Since Miguel served 3 times as many orders as Samuel, we know that
M = 3S.
Since Nicole served 10 more orders than Samuel, we know that
N = S + 10
Samuel's Orders:
Now we can plug in 3S for M and S + 10 for N to find S, the number of Samuel's orders:
S + 10 + 3S + S = 115
5S + 10 = 115
5S = 105
S = 21
Thus, Samuel served 21 orders.
Nicole's Orders:
Now we can plug in 21 for S in N = S + 10 to determine how many orders Nicole served:
N = 21 + 10
N = 31
Thus, Nicole served 31 orders.
Miguel's Orders:
Now we plug in 19 for S in M = 3S to determine how many orders Miguel served:
M = 3(21)
M = 63
Thus, Miguel served 63 orders.
HELP ASAP!!!!!! LOOK AT THIS:
Alice, Raul, and Maria are baking cookies together. They need 3/4 cup of flour and 1/3 cup of butter to make a dozen cookies. They each brought the ingredients they had at home . Alice brought 2 cups of flour and 1/4 cup of butter, and Maria brought 1and1/4 cups of flour and 3/4 cup of butter. If the students have plenty of the other ingredients they need (sugar, salt, baking soda, etc.), how many whole batches of a dozen cookies can they make ?
,Alice, Raul, and Maria can make 1 whole batch of a dozen cookies together using the ingredients they brought.
To determine how many whole batches of a dozen cookies they can make, we need to compare the amount of flour and butter they have with the required amounts for each batch of cookies.
Let's calculate the total amount of flour and butter each student brought:
Alice:
Flour: 2 cups
Butter: 1/4 cup
Maria:
Flour: 1 1/4 cups
Butter: 3/4 cup
Now let's compare the amounts with the required ingredients for a batch of cookies:
Required amount per batch:
Flour: 3/4 cup
Butter: 1/3 cup
First, let's see how many batches of cookies Alice can make:
Flour: Alice has 2 cups, and each batch requires 3/4 cup. So she can make 2 cups / (3/4 cup) = 8/3 = 2 and 2/3 batches of cookies.
Butter: Alice has 1/4 cup, and each batch requires 1/3 cup. Since she doesn't have enough butter for a full batch, she can't make any batches of cookies with the butter she brought.
Next, let's see how many batches of cookies Maria can make:
Flour: Maria has 1 1/4 cups, and each batch requires 3/4 cup. So she canmake (5/4 cups) / (3/4 cup) = 5/3 = 1 and 2/3 batches of cookies.
Butter: Maria has 3/4 cup, and each batch requires 1/3 cup. So she can make (3/4 cup) / (1/3 cup) = 9/4 = 2 and 1/4 batches of cookies.
Now, to find the maximum number of whole batches they can make together, we take the minimum of the number of batches each student can make:
Alice: 2 and 2/3 batches
Maria: 1 and 2/3 batches
Raul: Not mentioned, so we assume he brought the required ingredients.
The minimum value is 1 and 2/3 batches, which means they can make 1 whole batch of a dozen cookies together.
For more such question dozen visit:
https://brainly.com/question/30948187
#SPJ8
The units of measurement for surface area are always cubed.
O False
O True
Answer:
False
Step-by-step explanation:
When calculating volume, units of measurement are cubed. When calculating surface area, units of measurement are squared.
Further explanation:
Let's say you are finding the area of a rectangle. The length is 5in and the width is 7 in.
since you know l*w is area, you need to multiply 5in and 7in. 5*7=35 and then the two units of measurement, in*in=in^2 so 5in*7in=35in^2. the unit is squared not cubed.
The units of measurement for surface area are always SQUARED. Hence the correct answer is FALSE.
In 2-D, the total space covered by any two-dimensional figure is called Area while if we talk about 3-D, the total area of all the outer surfaces when added, sums up to form the Surface Area. Hence, the surface area is the multiplication of any two of the physical quantities.
For example,
Area of a square=(side x side)
=(metre x metre) or (cm x cm) [in terms of units]
= [tex]metre^{2}[/tex] or [tex]cm^{2}[/tex]
Similarly,
Surface Area of cube=6x(side x side) [summation of the area of 6 faces of cube]
=(metre x metre) or (cm x cm) [in terms of units]
= [tex]metre^{2}[/tex] or [tex]cm^{2}[/tex] (again)
Therefore, The units of measurement for the surface area are always SQUARED. Hence the correct answer is FALSE.
When talking of volume, since volume is the amount of space taken by any object or any 3-Dimensional body, the units of measurement of Volume are always cubed. For example, [tex]metre^{3}[/tex] or [tex]cm^{3}[/tex].
To learn more about Surface Area and Units,
https://brainly.com/question/16519513
https://brainly.in/question/609711
Results from a marijuana drug test study showed 143 subjects with positive test results including 24 false positive results. There were 157 negative results, including 3 false negative results. What is the probability that a randomly selected subject did not use marijuana? Round to three decimal places as needed.
Part 1
A. 0.533
B. 0.593
C. 0.523
D. 0.477
Answer:
B. 0.593
Step-by-step explanation:
The table below represents the function, and the following graph represents the function g.
4 -3 -2 -1 0 1
X-6 -5
f(x) 8-2
-8 -10 -8 -2 8 22
Complete the following statements.
The functions f and g have
The y-intercept of fis
the y-intercept of g.
Over the interval [-6, -31, the average rate of change of fis
m. All rights reserved.
9
-6 -4
-2
6
4
2
4-
N
6
2
4 6
the average rate of change of g
The correct options to the questions posed are :
The functions f and g have the same axis of symmetry.The y-intercept of f is greater than the y-intercept of g.Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.Axis of symmetryFrom the given table of f(x) and x, from which we have;
The minimum point for f(x) as it's vertex as (-3, -10) = -3
For the function g(x). represented by the graph, the axis of symmetry is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
InterceptThe y-intercept, is the point on the graph where the line intersects the y-axis or where x = 0. Here , the point is (0,8) = 8
Over the interval [-6, -3]
The average rate of change of f(x) is
(-10 - 8)/(-3 -(-6)) = -6
Using the graph g(x)From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2) = -2
Over the interval [-6, -3]
The average rate of change = (6 - (-2))/(-3 -(-6)) = 8/3 = 2.67
Hence,
The functions f and g have the same axis of symmetry.
The y-intercept of f is greater than the y-intercept of g.
Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.
Learn more on functions : https://brainly.com/question/24320260
#SPJ1
In 1995, wolves were introduced into Yellowstone Park.
The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.
By what percent does the number of wolves change each year?
In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.
Percent calculation.
To determine the percentage change within the number of wolves each year, we ought to look at the development rate of the work w(x) = 14 * 1.08^x.
The development rate in this case is given by the example of 1.08, which speaks to the figure by which the number of wolves increments each year. In this work, the coefficient 1.08 speaks to a development rate of 8% per year.
To calculate the percentage change, we subtract 1 from the growth rate and increase by 100 to change over it to a rate:
Percentage change = (1.08 - 1) * 100 = 0.08 * 100 = 8%.
In this manner, the number of wolves changes by around 8 percentage 8% each year based on the given work.
Learn more about percentage below.
https://brainly.com/question/24304697
#SPJ4
0.059 and 0.01 which is greater?
I only need help with the f(0)= the equation is above all the rest is filled in thank you
f(0) = -3
I believe, since the graph has a closed circle/point at (0,-3), f(0) should equal -3. Also, the graph 3x-3 has a domain of x>=0.
However, in terms of limits, the limit approaching x-->0 does not exist since the left and right limits do not equal one another.
Hope this helps.
se logarithms to solve the problem.
The rule of 70 is a rule of thumb for estimating the doubling time of a quantity (e.g., investment, GDP, population) experiencing growth that is compounded continuously. The rule states that if the growth rate is r% per year, then the time it takes for the quantity to double is approximately 70/r years.
(a)
Use the rule of 70 to estimate the time it takes for an investment to double in value if it grows at the rate of 5% per year compounded continuously.
yr
(b)
What is the exact time it will take for the investment in part (a) to double in value? (Round your answer to two decimal places.)
yr
a. The investment to double in value take about 14 years for the funding to double in value.
b. The genuine time it will take for the funding to double in fee is about 13.86 years.
(a) To estimate the time it takes for an funding to double in cost the use of the rule of 70, we want to decide the increase rate. In this case, the increase price is given as 5% per 12 months compounded continuously.
Using the rule of 70, we can calculate the estimated doubling time:
Time to double ≈ 70 / boom rate
Time to double ≈ 70 / 5
Simplifying, we have:
Time to double ≈ 14 years
Therefore, it would take about 14 years for the funding to double in value.
(b) To decide the genuine time it will take for the funding to double in value, we can use the formulation for non-stop compounding:
Doubling time (exact) = ln(2) / (ln(1 + r))
where r is the increase fee as a decimal.
In this case, the increase charge is 5% per year, or 0.05 as a decimal.
Doubling time (exact) = ln(2) / (ln(1 + 0.05))
Doubling time (exact) ≈ 13.86 years (rounded to two decimal places)
Therefore, the genuine time it will take for the funding to double in fee is about 13.86 years.
For more related questions on investment:
https://brainly.com/question/34043637
#SPJ8
A file that is 268 megabytes is being downloaded if the download is 14.3% complete how many megabytes have been downloaded
Mr. Marshal spent his salary of $8 400 in the following manner: Rental .....1/5 Food.......1/10 Bank ......1/4 Miscellaneous ......... the remainder. what fraction of the money was spent on miscellaneous. how much did he spend on rental. if marshal spent 4/9 of miscellaneous on a trip what fraction of his entire salary was spent on the trip ?
Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.
To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.
Rental: 1/5
Food: 1/10
Bank: 1/4
To find the fraction spent on miscellaneous:
Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)
Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40
Fraction spent on miscellaneous = 1 - 17/40 = 23/40
So, Mr. Marshal spent 23/40 of his salary on miscellaneous.
To find the amount spent on rental, we multiply the fraction spent on rental by his salary:
Amount spent on rental = (1/5) [tex]\times[/tex] $8,400 = $1,680
Therefore, Mr. Marshal spent $1,680 on rental.
If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.
Fraction spent on the trip = (4/9) [tex]\times[/tex] (23/40) = 92/360 = 23/90
For similar question on fraction.
https://brainly.com/question/30154928
#SPJ8
The diagram shows a cuboid. 8 cm 15 cm 20 cm What is the volume of the cuboid?
Answer:
The answer is 2400 cm^3
Step-by-step explanation:
You just need to multiply the dimensions
Answer:
2400 cm³
Step-by-step explanation:
Volume of cuboid = length × width × height
Volume = 8 cm × 15 cm × 20 cm
Volume = 2400 cm³
So, the volume of the cuboid is 2400 cm³
what is question 4????
Answer:
2.2
Step-by-step explanation:
(1.85 x 2) - 1.50
...............
Study these equations:
f(x) = 2x – 4
g(x) = 3x + 1
What is h(x) = f(x)g(x)?
h(x) = 6x2 – 10x – 4
h(x) = 6x2 – 12x – 4
h(x) = 6x2 + 2x – 4
h(x) = 6x2 + 14x + 4
Answer:
6x2-10x-4
Step-by-step explanation:
hx=(2x-4)(3x+1)
hx=2x(3x+1)-4(3x+1)
hx=6x2+2x-12x-4
hx=6x2-10x-4
Type the correct answer in each box. Round your answers to the nearest thousandth.
A company has 200 machines. Each machine has 12% probability of not working.
If you were to pick 40 machines randomly, the probability that 5 would not be working is
and the probability that at least one machine would be working is
the probability that all would be working is
1) The probability that 5 will be working is: 0.187
2) The probability that at least one machine would be working is: 0.006
3) The probability that all would be working is : 1
How to find the probability of working?We are given the parameters as:
Total number of machines = 200
Probability that a Machine is working = 12% = 0.12
1) Now, you want to pick 40 machines and want to find the probability that 5 will be working.
This probability is given by the expression:
P(5 working) = C(40,5) * 0.12⁵·0.88³⁵ ≈ 0.187
where C(n, k) = n!/(k!(n-k)!)
2) The probability that at least one machine would be working is:
0.88⁴⁰ ≈ 0.006
3) The probability that all would be working is the complement of the probability that all have failed. Thus:
P(all working) = 1 - 0.12⁴⁰ ≈ 1
Read more about probability of working at; https://brainly.com/question/25870256
#SPJ1
Please help on question asap if you are correct with answer I'll give brainlie st, a thanks and five stars.
When we have a trapezium and w e are finding out the area , would it be possible to have a radius\diameter in the trapezium or is that just for 3D shapes
Is not possible to define a radius nor a diameter in a trapezium.
Is it possible to have a radius/diameter in the trapezium?Radius and diameter are two measures defined for circles.
Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).
At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.
To get the area use the formula:
Area = (base1 + base2)*height / 2
Learn more about trapeziums:
https://brainly.com/question/1410008
#SPJ1
Select the correct answer from each drop-down menu.
Given: Line segment WU is the perpendicular bisector of line TV.
Prove: Line TU ≠ Line VU
WU is the perpendicular bisector of TV and W is the midpoint of TV.
Statements:
WU is the perpendicular bisector of TV.
W is the midpoint of TV.
TW = VW.
∠ZTWU and ∠ZVWU are right angles.
∠ZTWU ≅ ∠LVWU.
WU = WU.
∠ATWU ≅ ∠AVWU.
TU = VU.
Reasons:
Given.
Definition of the perpendicular bisector: It divides a segment into two congruent parts, and W is the midpoint of TV.
Definition of midpoint: The segment TW is congruent to VW because W is the midpoint of TV.
Given that WU is the perpendicular bisector, it means that ∠ZTWU and ∠ZVWU are right angles.
All right angles are congruent.
Reflexive property of congruence: Any segment or angle is congruent to itself.
Corresponding parts of congruent triangles are congruent (CPCTC): Since ∠ATWU and ∠AVWU are corresponding parts of congruent triangles, they are congruent.
Corresponding parts of congruent triangles are congruent (CPCTC): Since TU and VU are corresponding parts of congruent triangles, they are congruent.
Therefore, the correct statements and reasons are:
Statements:
WU is the perpendicular bisector of TV.
W is the midpoint of TV.
TW = VW.
∠ZTWU and ∠ZVWU are right angles.
∠ZTWU ≅ ∠LVWU.
WU = WU.
∠ATWU ≅ ∠AVWU.
TU = VU.
Reasons:
Given.
Definition of the perpendicular bisector.
Definition of midpoint.
Given.
All right angles are congruent.
Reflexive property of congruence.
CPCTC.
CPCTC.
Learn more about triangle here:
https://brainly.com/question/17335144
#SPJ8
The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base.
O False
O True
Answer: True
Step-by-step explanation:
The lateral faces are the triangular faces that connect the apex of the pyramid to the edges of the base. The area of each lateral face can be calculated using the formula for the area of a triangle, which is [tex]\frac{1}{2} \times b \times h[/tex]. The area of the base is simply the area of the polygon that forms the base of the pyramid.
__________________________________________________________
The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. (True or False)
Answer:The correct answer is True.
Explanation:The surface area of a pyramid is the sum of the areas of the lateral faces and the area of the base. This can be represented by the formula:
[tex]\qquad\qquad\Large\boxed{\rm{\:SA = B + LA\:}}[/tex]
The lateral faces are the faces that are not the base, so their areas are calculated using the formula for the area of a triangle. The area of the base is calculated using the appropriate formula depending on the shape of the base.
Learn more about surface area here: https://brainly.com/question/32228774
if you borrow $1,000 for 4 years at an annual interest rate of 8% what is the total amount of money you will pay back
-Ready
Algebraic Expressions with Exponents-Instruction-Level F
Amelia is building 3 square garden beds that are all the same size. She arranges them side-
by-side to separate certain plants. Amelia wants to know the total area of the garden beds.
length (ft) of one side of a garden bed
Write an expression to show the total
area of the garden beds.
38²
What is the total area if each garden
bed has a length of 4 feet?
ft²
A = $²
7 8 9
6
3
4
51
1
1 2
X
1
t
X
The correct answer is each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.
To find the total area of the garden beds, we can use the expression:
Total area = (length of one side)^2 * number of garden beds
Given that each garden bed has a length of 4 feet, we substitute 4 for the length of one side in the expression:
Total area = (4)^2 * 3
Simplifying:
Total area = 16 * 3
Total area = 48 square feet
Therefore, if each garden bed has a length of 4 feet, the total area of the garden beds is 48 square feet.
Learn more about Algebraic Expressions here:
https://brainly.com/question/4344214
#SPJ8
Find the equation of the line in slope-intercept form, perpendicular to a line with a slope of
1
13 and passing through (-1,3).
The equation of the line perpendicular to a line with a slope of -- and passing through (-1,3) is.
(Simplify your answer. Type your answer in slope-intercept form.)
The equation of the line perpendicular to the line with a slope of 1/13 and passing through the point (-1, 3) is y = -13x - 10.
To find the equation of a line perpendicular to a line with a slope of 1/13 and passing through the point (-1, 3), we need to determine the slope of the perpendicular line.
The slope of a line perpendicular to another line can be found by taking the negative reciprocal of the given slope. The negative reciprocal of 1/13 is -13/1, or simply -13.
Now that we have the slope (-13) and a point (-1, 3) that the line passes through, we can use the point-slope form of a linear equation to find the equation of the perpendicular line.
The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Substituting the values (-1, 3) and -13 into the point-slope form, we get:
y - 3 = -13(x - (-1))
Simplifying:
y - 3 = -13(x + 1)
Expanding the equation:
y - 3 = -13x - 13
To convert the equation to slope-intercept form (y = mx + b), we can isolate y:
y = -13x - 13 + 3
y = -13x - 10
Therefore, the equation of the line perpendicular to the line with a slope of 1/13 and passing through the point (-1, 3) is y = -13x - 10.
for such more question on line perpendicular
https://brainly.com/question/18991632
#SPJ8
Which of the following steps indicates the addition property of equality while solving the equation –1 – 6x = x – 15?
A) x = 14∕2
B) –1 – 6x = x – 15
C) 23 – 6x – 24 = x – 15
D) –1 – 6x + 15 = x – 15 + 15
Answer:
-1 - 6x = x - 15
Add 15 to both sides using the addition property of equality.
14 - 6x = x
14 = 7x
2 = x
D) -1 - 6x + 15 = x - 15 + 15
Answer and Step-by-step explanation:
Please refer to the photo for the solution!
PLSSSS HELPPP I WILL FIVE BRAINLY!!!!
Answer:
The first box : -4 the second one : 6
Step-by-step explanation:
subtract 7 from 3 for the first box, then add 10 to -4 for the second one.
Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and express P(x) in the form dix) Q(x) R(x).
P(x)=x^3+3x²-8x+140
d(x)=x+7
P(x) = (x+7)( ) +
The polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0
What is a polynomialA polynomial is a mathematical expression which have a sum of powers in one or more variables with coefficients. The highest power of the variable in a polynomial is called its degree.
We shall divide the polynomial x³ + 3x² - 8x + 140 by x + 7 as follows;
x³ divided by x equals x²
x + 7 multiplied by x² equals x³ + 7x²
subtract x³ - x² from x³ + 3x² - 8x + 140 will result to -4x² - 8x + 140
-4x² divided by x equals -4x
x + 7 multiplied by -4x equals -4x² - 28x
subtract -4x² - 28x from -4x² - 8x + 140 will result to 20x + 140
20x divided by x equals 20
x + 7 multiplied by 20 equals 20x + 140
subtract 20x + 140 from 20x + 140 will result to a remainder 0
Therefore, the polynomial P(x) = x³ + 3x² - 8x + 140 divided by (x + 7), will give a quotient of x² - 3x + 2 and a remainder of 0 using the long division, we can write P(x) = (x + 7)(x² - 4x + 20) + 0
Read more about polynomial here:https://brainly.com/question/24729294
#SPJ1
Is the relation shown in the table below a function? (type in yes or no)
Answer:
Yes
Step-by-step explanation:
To know if a table is a function or not, we have to see if 1 input only has 1 output.
Looking at the table each input only has 1 output, so it is a function.
A bakery is making cupcakes using a cylindrical mold. The cupcake mold has a diameter of 8.5 centimeters and is 6 centimeters tall. Which of the following shows a correct method to calculate the amount of cupcake batter needed to fill the mold all the way to the top? Use 3.14 for π.
V = (3.14)(8.5)2(6)
V = (3.14)(6)2(8.5)
V = (3.14)(4.25)2(6)
V = (3.14)(6)2(4.25)
Answer:
V = (3.14)(4.25)²(6)
Step-by-step explanation:
4) AD is a common internal tangent to circles B and C. Find the length of the radius
of circle B. Round to the nearest hundredth. (Hint: Prove that the two triangles
are similar and use proportions to find missing lengths.) (10 points)
I
B
E
6
D
Both triangles in the image are similar based on the AAA similarity theorem. The radius of the circle B is therefore calculated as: AB = 12.
What are similar triangles?Similar triangles are geometric figures that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are in proportion to each other.
Since AD serves as a common tangent, angle BAE is equal to 90 degrees, which is also equal to angle CDE due to being opposite angles.
By the Angle-Angle-Angle (AAA) similarity criterion, triangles ABE and DCE are similar.
Therefore:
AB/EA = DC/ED
Substitute:
AB/18 = 4/6
Cross multiply:
AB = 18 * 4/6
AB = 12
Therefore, the radius of the circle B is: 12.
Learn more about Similar triangles on:
https://brainly.com/question/27996834
#SPJ1
find g[h(-2)] from f(x)=x^(2),g(x)=5x , h(x)=x+4
Explanation:
Plug x = -2 into h(x)
h(x) = x+4
h(-2) = -2+4
h(-2) = 2
This means g[ h(-2) ] = g(2) after replacing h(-2) with 2.
g(x) = 5x
g(2) = 5*2
g(2) = 10
Therefore, g[ h(-2) ] = 10
