Answer:
Step-by-step explanation:
14: k^-3/k^4= 1/k^7
15: answer : 1/3²
16: n^-4
17: f-g^4 = 3-(-5)^4 = -622
18: (x^5-y^2)²+x³ =
(2^5-8^2)²+2³ =1032
19: m²-n³
6²-2³ = 36-8=28
20 : 2²×3²×5³= 4500
4500/10 = 450 islands
(Please this is URGENT!) On a computer screen, Jennifer just created a triangular design of a banner with vertices at A(-4,3), B(-1,5) and C(-1,2). She can use the computer software to perform transformations on this design.
Which sequence of two transformations could she perform so that the transformed vertices become A'(4,-5), B'(7,-7), and C'(7,-4)?
a. translating 6 units down, followed by translating 8 units to the right
b. reflecting about the line y = -2, followed by translating 8 units to the right
c. reflecting about the line y = -1, followed by reflecting about the y-axis
d. reflecting about the line y = -1, followed by translating 8 units to the right
Answer:
The correct option is;
d. Reflecting about the line y = -1, followed by translating 8 units to the right
Step-by-step explanation:
The coordinates of the vertices of the banner Jane created = A(-4, 3), B(-1, 5) and C(-1, 2)
By reflecting across the line y = -1, we get
A(-4, 3) by reflection across the line y = -1 gives A(-4, -5)
B(-1, 5) by reflection across the line y = -1 gives B(-1, -7)
C(-1, 2) by reflection across the line y = -1 gives C(-1, -4)
By translating 8 units to the right get
A(-4, 3) by translation 8 units right gives A prime (4, -5)
B(-1, 5) by translation 8 units right gives B prime (7, -7)
C(-1, 2) by translation 8 units right gives C prime (7, -4)
Therefore, the two transformation that she could perform so that the transformed vertices become A prime (4, -5), B prime (7, -7), and C prime (7, -4) are;
1) Reflection across the line y = -1
2) An horizontal translation 8 units to the right get.
Transformation involves changing the size and position of a shape.
The sequence of two transformations are: (d). reflecting about the line y = -1, followed by translating 8 units to the right
The coordinates of ABC are given as:
\(\mathbf{A =(-4,3)}\)
\(\mathbf{B =(-1,5)}\)
\(\mathbf{C =(-1,2)}\)
First, the coordinates of ABC are reflected across the line \(\mathbf{y =-1}\)
The transformation rule is:
\(\mathbf{(x,y) \to (x,-y -2 \times 1)}\)
So, we have:
\(\mathbf{A' = (-4,-3 -2 \times 1)}\)
\(\mathbf{A' = (-4,-5)}\)
\(\mathbf{B' =(-1,-5 - 2 \times 1)}\)
\(\mathbf{B' =(-1,-7)}\)
\(\mathbf{C' =(-1,-2 -2 \times 1)}\)
\(\mathbf{C' =(-1,-4)}\)
Next, the shape is translated 8 units right.
The rule of this transformation is:
\(\mathbf{(x,y) \to (x + 8, y)}\)
So, we have:
\(\mathbf{A" = (-4 + 8, -5)}\)
\(\mathbf{A" = (4, -5)}\)
\(\mathbf{B" =(-1+8,-7)}\)
\(\mathbf{B" =(7,-7)}\)
\(\mathbf{C" =(-1+8,-4)}\)
\(\mathbf{C" =(7,-4)}\)
Hence, the sequence of two transformations are:
(d). reflecting about the line y = -1, followed by translating 8 units to the right
Read more about transformations at:
https://brainly.com/question/13801312
Carlos and his brother each made 72 cookies for the church bake sale. They sold the same amount of cookies each day over a three day period. Between the two of them how many cookies did the boys sell each day? A. 24 B. 48 C. 72 D. 144
Answer:
the answer is 144
Step-by-step explanation:
just add 72+72=144
2x+2y=6 3x-y=5 equivalent equation
Answer:
x = 2, y = 1
Step-by-step explanation:
Given:
\(\begin{bmatrix}2x+2y=6\\ 3x-y=5\end{bmatrix}\)
Solve:
\(\mathrm{Isolate\;x\;for\;2x+2y=6:x=3-y}\)
\(\mathrm{Substitute\:}\)
\(\begin{bmatrix}3\left(3-y\right)-y=5\end{bmatrix}\)
\(\mathrm{Simplfy}\)
\(\begin{bmatrix}9-4y=5\end{bmatrix}\)
\(\mathrm{Isolate\;y\;for\;9-4y=5:y=1}\)
\(\mathrm{For\:}x=3-y\;\mathrm{Substitute\:}y=1\)
\(x=3-1\)
\(\mathrm{Simplify}\)
\(x=2\)
\(\mathrm{The\:Answers\:to\:the\:system\:of\:equations\:are:}\)
\(x=2,\:y=1\)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check Answer:
Since \(x =2 , y =1\)
\(2(2)+2(1)\)
\(4 + 2\)
\(= 6\)
True
\(3(2) - (1)\)
\(6 -1\)
\(5\)
True
Hence, \(x = 2, y = 1\)
~Lenvy~
If m∠XWY=20∘,m∠XWZ=40∘, and XY = 16, what is the value of YZ?
Answer:
YZ=16
Step-by-step explanation:
Because they are parallel
Please help. Look at the triangle below.
Answer:
See below.
Step-by-step explanation:
Side BC is adjacent to <B and is 11 units long.
Side BA is the hypotenuse and is x units long.
Point
�
′
(
6
,
−
5
)
B
′
(6,−5)B, prime, left parenthesis, 6, comma, minus, 5, right parenthesis is the image of
�
(
−
5
,
−
2
)
B(−5,−2)B, left parenthesis, minus, 5, comma, minus, 2, right parenthesis under a translation.
B' is 11 right and 3 down from B.
What is an image translation?A shape is translated when it is moved up, down, left, or right without turning. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.
Here, we have
Given: Point B′(6,−5) is the image of B(−5,−2) under a translation.
The translation is from (-5, -2) to (6, -5). That is the values (h, k) was added to the coordinates where ...
-5 +h = 6
h = 11 . . . . . . . a translation of 11 to the right
and
-2 +k = -5
k = -3 . . . . . . . a translation of -3 upward is a translation of 3 downward.
Hence, B' is 11 units to the right and 3 units down from B.
To learn more about the image translation from the given link
https://brainly.com/question/17172292
#SPJ1
Mr.Shand had $50 in his wallet on Friday after school.That night,He spent $11.50 on a pizza $3.75 on ice cream.One his way home,He found $5 on the ground ,How much money does Mr.Shand have at the end of the night?
Answer:
39.75
Step-by-step explanation:
so first we do 50-11.50-3.75+5. to simplify it 55-15.25
if u do the math that equals 39.75
to double check 39.75+15.25=55
A single piecewise-defined function f(x) has been
graphed for you on the display to the left.
At how many values c on the interval x€[−6, 4) is it
true that the limx→cf(x) = 1?
Answer: 1
Step-by-step explanation:
\(\lim_{x \to -6} f(x) \neq -1\) because the left and right hand limits are not the same.
\(\lim_{x \to -1} f(x) \neq -1\) because the left and right hand limits are not the same.
However, somewhere between 1 and 2, the limit does equal -1 because the left and right hand limits are the same.
1. AC is a diameter of the circle.Find measure of AEDFind measure of BCEFind length of ABFind length of CD2. AC is tangent to circle O.Find the lengths of the segments to the nearest hundredth.AO=DC=
80+x+45=180 (sum of angles on a straight line)
x=180-80-45
x=55.
\(\begin{gathered} \text{Thus,} \\ i)\text{ measure of AED=80+x} \\ m\text{ AED=80+55} \\ mAED=135^O \end{gathered}\)\(\begin{gathered} ii)\text{ measure of BCE=90+45+55} \\ \text{m BCE=190}^0 \end{gathered}\)\(\begin{gathered} iii)\text{Length of arc AB=}\frac{\theta}{360}\times2\pi r \\ \text{where }\theta\text{ is the angle subtended by the arc} \\ ^{\prime}r^{\prime}\text{ is the radius.} \\ \text{The radius of AB is 16. The angle subtended by AB is 'y'. Let's find 'y'.} \\ y=360-90-45-55-80=90^0 \\ \text{Thus,} \\ L_{arc\text{ AB}}=\frac{90}{360}\times2\times3.142\times16.\text{ Take }\pi\text{ to be 3.142} \\ L_{arc\text{ AB}}=25.136 \end{gathered}\)\(\begin{gathered} \text{Length of arc CD=}\frac{\theta}{360}\times2\pi r \\ \theta=45^0,\text{ for arc CD.} \\ r=16.\text{ The radius is constant} \\ L_{arc\text{ CD}}=\frac{45}{360}\times2\times3.142\times16 \\ L_{arc\text{ CD}}=12.568 \end{gathered}\)11) Stephanie makes $ 50 a week babysitting. She spends $ 25, saves $ 15, and uses the rest to pay off a $ 100 loan from her brother. After six weeks, how much has Stephanie spent, how much has she saved, and how much still owes her brother?
Answer:
She saved 90 dollars and she owes her brother 40 still.
Step-by-step explanation:
The engineer's model of a sugar factory has a floor area of 30 inches by 52 inches. The floor area of the model is __________ square feet.
The floor area of the engineer's model of the sugar factory is 10.825 square feet.
To determine the floor area of the engineer's model of a sugar factory in square feet, we need to convert the given measurements from inches to feet. Since there are 12 inches in a foot, we can divide both dimensions by 12 to convert them.
The length of the model in feet is 30 inches / 12 = 2.5 feet, and the width is 52 inches / 12 = 4.33 feet.
To find the floor area, we multiply the length by the width:
Area = Length × Width
= 2.5 feet × 4.33 feet
= 10.825 square feet
It's important to note that the given measurements are not a standard aspect ratio or scale for a sugar factory. The given dimensions may be scaled down for the model's convenience, so the calculated floor area is only applicable to the scale of the model.
In actuality, a sugar factory would have much larger dimensions.
For more such questions on floor area
https://brainly.com/question/32436570
#SPJ8
At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least 16 tickets. The system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys.
Answer:
4 is the maximum number of ride tickets she can buy
Step-by-step explanation:
Here, r represents the number of ride tickets and f represents number of food tickets.
The system of inequalities is given as:
r+f\geq 16 ....[1]
4r+2f\leq 40 .....[2]
To solve Mathematically:
Multiply equation [1] by -2 we have;
-2r-2f \leq -32 .....[3]
Add equation [2] and [3] we have;
2r \leq 8
Divide both sides by 2 we have;
r \leq 4
Since r must be less than or equal to 4.
You can also see the graph of the given system of inequalities as shown below.
The intersection point is, (4, 12)
Therefore, the maximum number of ride tickets she can buy is, 4
Answer:
A. 4
Step-by-step explanation:
edg2021 hope this helps :>
Find the area of the shaded polygon.
To find the area of the shaded polygon, we had to assume that each dotted line was one unit. In which case, the coordinates are:
A(1,4)B (5,6)C (6, 3)D (3, 2)Hence, the area of the polygon is A \(\approx\) 11.15 units.
To get the area of the polygon, we must determine the length of all it's sides.
a) A-B is given by the distance formula:
distance = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using this formula, we can calculate the distance between points A(1,4) and B(5,6) as follows:
distance = √((5 - 1)² + (6 - 4)²)
= √(16 + 4)
= √(20)
A-B = 4.47213595
A-B \(\approx\) 4.47
b)
To find B-C we use the same method:
B-C = 3.16 units.
c)
To find C- D we use the same method:
C- D \(\approx\) 3.16 units.
d) to find D-A we use the employ the same method:
D - A \(\approx\) 2.83
Since this is an irregular quadrilateral, we will require the use of the
length of one of it's diagonals which is also computed using the distance formula to get: 4.47 Units.
Calculate the perimeter of ABCD
Perimeter of ABCD = AB + BC + CD + AD
Perimeter of ABCD = 4.4721359549996 + 3.1622776601684 + 3.1622776601684 + 2.8284271247462
Perimeter of ABCD = 13.625118400083
Calculate the semi-perimeter (s) of ABCD
s = Perimeter ÷ 2
s = 13.625118400083 ÷ 2
s = 6.8125592000413
Calculate the Area (A) using Brahmagupta's Formula
A = √[(s - a)(s - b)(s - c)(s - d)]
A = √(6.8125592000413 - 4.4721359549996)(6.8125592000413 - 3.1622776601684)(6.8125592000413 - 3.1622776601684)(6.8125592000413 - 2.8284271247462)
A = √(2.3404232450417)(3.6502815398729)(3.6502815398729)(3.9841320752951)
A = √(124.24555320337)
A = 11.14654893693
A \(\approx\) 11.15 units.
Learn more about area at:
https://brainly.com/question/30493388
#SPJ1
Quadrilateral GHIJ is similar to quadrilateral KLMN. Find the measure of side KL. Round your answer to the nearest tenth if necessary.
The measure of side KL is 65.4 to the nearest tenth.
What is common ratio?If the side on one form is a and the side on the other form is b, then there will be a common ratio r between the two forms, such that a = b x r. Simply divide the length of one comparable side by the other to arrive at a similar ratio, r = a / b.
We have the quadrilaterals, GHIJ is similar to KLMN.
That means, the common ratio is constant.
To find the common ratio:
Side of GHIJ / Side of KLMN = k (let),
here we choose similar sides.
Substituting the value of sides to the formula,
48 / 11 = k
k = 4.363636
So, the length of KL = k x similar side of GHIJ
The length of KL = 4.363636 x 15
The length of KL = 65.4
Therefore, side KL = 65.4.
To learn more about the common ratio;
brainly.com/question/13637951
#SPJ1
A student is assessing the correlation between the number of workers in a factory and the number of units produced daily. The table below shows the data:
Number of workers
(x) 0 10 20 30 40 50 60 70 80 90
Number of units
(y) 2 52 102 152 202 252 302 352 402 452
Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer. (4 points)
Part B: Write a function which best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate? (3 points)
The number of units produced increases from 2 to 452 as the number of factory workers increases from 0 to 90, which gives;
Part A:
Yes there is a strong positive correlationPart B:
The function is y = 5•x + 2Part C:
The slope indicates the number of units produced by each worker dailyThe y-intercept indicates that two units can be produced without workers.How can the existence of a correlation and the best fit function for the data be found?Part A:
The correlation is the relationship between variables based on statistical data.
From the given table, the difference between consecutive terms of the x and y-values are constant, therefore as the x-values increases, the corresponding y-value increases.
Change in x-values, ∆x = 10 - 0 = 20 - 10 = 30 - 20 = 10
Change in y-values, ∆y = 52 - 2 = 102 - 52 = 152 - 102 = 50
Therefore;
There is a strong positive correlation between the number of workers, x, and the number of units produced, y.Part B:
Given that the rate of change of the x-values is constant, and the rate of change of the y-values is a constant, the function relating the x and y-values is a linear function, which can be found as follows;
Slope of the equation, m = ∆y/∆x
Which gives;
m = 50/10 = 5
y - 2 = 5•(x - 0)
The function that best fits the data is therefore;
y = 5•x + 2Part C:
The slope of the function is the coefficient of the variable x in the equation, y = m•x + c
The slope of the plot, 5, indicates that each worker produces 5 units dailyThe y-intercept of the function is the value of the constant term, c, in the equation, y = m•x + c
The y-intercept of the linear equation, y = 5•x + 2, which is 2, indicates that the initial number of units of products at the factory before workers arrive is 2.Learn more about finding relationship between variables here:
https://brainly.com/question/4219149
#SPJ1
For each set of angles or sides lengths, determine whether they could form a unique triangle, more than one triangle, or no triangle.
5 cm, 10 cm, 12 cm
8 ft, 12 ft, 20 ft
40°, 50°, 80°
28°, 51°, 101°
Answer: They can form one triangle.
Step-by-step explanation: Since all triangle must have 180 degrees, there’s only one set of degrees that sum up to 180.
28+51+101=180
I’m sorry, but the feet/centimeters part you have to solve on your own. Remember, this is a learning community! No stress :) I can guarantee you won’t get it wrong though.
There’s many different triangles, and I’m sure from these feet/centimeters you can make at least one of the listed: Scalene (none of the sides are equal), isosceles (only 2 sides are equal) or equilateral triangle (all sides are equal). There’s also right triangles (which are triangles with one right angle also known as 90 degrees) that are either isosceles or scalene or both! Try your best and remember, no stress :)
Which of the following would be the most appropriate unit to measure the volume of iced tea in a glass?
A. kilogram
B. fluid ounce
C. inches
D. gallon
Answer:
B. fluid ounce
Step-by-step explanation:
Just do this as a process of elimination if you're not sure. A glass isn't very big, so gallons wouldn't be the most appropriate. Same thing for kilograms. Inches could work quite well, but fluid ounces are even better as they specifically measure liquids, therefore why it would be the most appropriate.
However, keep in mind that they could all be used to measure liquids/volumes.
(20m + 3) - (7 m - 5)
Find the difference
Answer:
This can be done in two ways -
- horizontal
- vertical
so I chose Vertical :
The sum of fifteen and six times a number t is eighty-one.
Answer:
11
Step-by-step explanation:
15 + (6 multiplied by x) = 81
81 - 15 = 66
66 / 6 = 11
During the rebuilding after World War II, we were short of tractors. The machine and tractor stations would lend each other equipment as needed. Three machine and tractor stations were neighbors. The first lent the second and third as many tractors as they each already had. A few months later, the second lent the first and third as many as they each had. Still later, the third lent the first and second as many as they each already had. Each station now had 24 tractors.
How many tractors did each station originally have?
The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;
The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors
What are simultaneous equations?Simultaneous equations are a set of two or more equations that have common variables.
Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station
According to the details in the question, after the first transaction, we get
Number of tractors at the first station = x - y - z
Number of tractors at the second station = y + y = 2·y
Number of tractors at the third station = z + z = 2·z
After the second transaction, we get;
Number of tractors at the first station = 2·x - 2·y - 2·z
Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z
Number of tractors at the third station = 2·z + 2·z = 4·z
After the third transaction, we get;
Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z
Number of tractors at the second tractor station = 6·y - 2·x - 2·z
Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y
The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)
6·y - 2·x - 2·z = 24...(2)
7·z - x - y = 24...(3)
Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;
12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24
16·y - 8·x = 24...(4)
Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;
14·z - 2·x - 2·y = 48
42·y - 14·x - 14·z = 168
42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168
40·y - 16·x = 216...(5)
Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;
40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168
8·y = 168
y = 168/8 = 21
The number of tractors initially at the second station, y = 21
16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24
8·x = 16 × 21 - 24 = 312
x = 312 ÷ 8 = 39
The number of tractors initially at the first station, x = 39
7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24
7·z = 24 + 39 + 21 = 84
z = 84/7 = 12
The number of tractors initially at the third station, z = 12
Learn more about simultaneous equations here:
https://brainly.com/question/21902579
#SPJ1
Use the following equation:
(x + 4)² + (y + 6)² = 9
What is the x and y value of the center of the circle?
Answer:
(-4, -6)
Step-by-step explanation:
Six students, Michelle, Nadir, Olivia, Parvi, Quinn, and Richard, are running for four identical positions on student council. What is the theoretical probability that Nadir will be chosen as part of the group
The theoretical probability of Nadir being chosen as part of the group of four students for the student council is 4/6, which simplifies to 2/3.
To calculate the theoretical probability, we need to determine the number of favorable outcomes (Nadir being chosen) and divide it by the total number of possible outcomes (all combinations of four students out of the six).
First, let's calculate the number of favorable outcomes. Since we want Nadir to be chosen, we can consider Nadir as one of the positions to be filled. This leaves us with three remaining positions to be filled by the remaining five students (Michelle, Olivia, Parvi, Quinn, and Richard). Therefore, the number of favorable outcomes is the number of ways to choose three students out of the five, which is given by the combination formula: 5 choose 3 = 5! / (3! * (5-3)!) = 10.
Next, let's determine the total number of possible outcomes, which is the number of ways to choose four students out of the six. Using the combination formula again, we have 6 choose 4 = 6! / (4! * (6-4)!) = 15.
Finally, we divide the number of favorable outcomes by the total number of possible outcomes: 10 / 15 = 2/3. Therefore, the theoretical probability of Nadir being chosen as part of the group is 2/3.
Learn more about theoretical probability here:
https://brainly.com/question/30604977
#SPJ11
Condense
2loga(4)+3loga(X-4)loga(4)
Log(x+3)+log(x-3)
Answers should be log a x^3/16 and log (x^2-9)
SHOW WORK
URGENT
The steps to condensing the expressions
2loga(4)+3loga(X-4)loga(4)
Log(x+3)+log(x-3) is given below.
To condense the expressions, we can apply the properties of logarithms. Here are the condensed forms of the given expressions.
2loga (4) + 3loga(X - 4) - loga 4 )
By using the product and quotient rules of logarithms, we can simplify this expression as follows
2 loga( 4) + 3 loga( X-4) - log a(4)
= loga(4 ²) + loga((X-4)³) - loga (4) = loga (16 ) + loga((X-4)³) - loga (4)
Combining the logarithms using the power rule and quotient rule we have
= loga(16(X-4)³/4)
log(x+3) + log (x-3)
By using the product rule of logarithms, we can combine these logarithms
log (x +3) +log (x - 3) = log ((x +3 )(x -3 ))
Simplifying further, we get
= log (x² - 9 )
So this means that the condensed forms of the given expressions are
2loga( 4) + 3loga(X -4) - loga (4) = loga(16 (X-4) ³/4)
log (x+ 3) + log(x- 3) = log(x² - 9)
Learn more about condensed expressions:
https://brainly.com/question/13729452
#SPJ1
Jakim deposited $10,000 in an account that earned simple interest annually.
- He did not make additional deposits nor withdrawals.
-At the end of 7 years, the balance was $12,100.
What is the interest rate on this account?
Answer:
Step-by-step explanation:
Simple interest is a method for calculating the percentage of interest paid on a sum over a predetermined time period at a predetermined rate. The annual simple interest rate on the principal amount of 10000 at the end of 7 years would be 3%.
What exactly is simple interest?In simple interest, the principal amount doesn't change. Simple interest is a clear-cut and simple method for figuring out how much money has earned interest. It is a way to figure out how much interest will be charged.
Simple interest can be computed by multiplying the principal amount by the rate multiplied by the time period. In banks and other financial institutions, simple interest is frequently used to complete a variety of calculations. The total amount of cash that was spent on interest during the course of the loan is described.
Simple Interest = ( Principal × Rate × Time ) / 100
First, we need the Simple Interest (S.I)
Total = Principal + Simple Interest
T = P + S.I
$10,000 = $12,100. + S.I
S.I = $12,100 - $10,000
S.I = 2100
Simple Interest = (Principal × Rate × Time) / 100
S.I = (P × R × T) / 100
2100 = (10000 × R × 7) / 100
2100 = 70000R / 100
2100 = 700R
R = 2100 / 700
R = 3
Thus, The annual interest rate is 3%
To learn more about simple interest, visit:
https://brainly.com/question/16161499
#SPJ1
Somebody plz help ????? I need the answer to this
Answer:
I was thinking it should be -1,2 but that'd not an awnser so B
a. Solve over [0, 2π]: sin 2x = cosx
b. Given f(x) = - 4 / x + 3, find and simplify f(x) - f(a) / x -
a
a) the solutions to the equation sin(2x) = cos(x) over [0, 2π] are x = π/6, π/2, 5π/6, and 3π/2., b) The simplified expression for (f(x) - f(a))/(x - a) is -(a - x)/(ax).
a. To solve the equation sin(2x) = cos(x) over the interval [0, 2π], we can use trigonometric identities and algebraic manipulations. Let's begin:
sin(2x) = cos(x)
Using the double angle formula for sine, we have:
2sin(x)cos(x) = cos(x)
Rearranging the equation, we get:
2sin(x)cos(x) - cos(x) = 0
Factoring out the common term cos(x), we have:
cos(x)(2sin(x) - 1) = 0
Now we can set each factor equal to zero:
cos(x) = 0 or 2sin(x) - 1 = 0
For cos(x) = 0, the solutions over [0, 2π] are x = π/2 and x = 3π/2.
For 2sin(x) - 1 = 0, we have:
2sin(x) = 1
sin(x) = 1/2
The solutions for sin(x) = 1/2 over [0, 2π] are x = π/6 and x = 5π/6.
b. To find and simplify (f(x) - f(a))/(x - a), where f(x) = -4/x + 3, we'll substitute the values into the expression and simplify:
(f(x) - f(a))/(x - a) = (-4/x + 3 - (-4/a + 3))/(x - a)
To simplify further, we can find a common denominator for -4/x and -4/a:
(-4/a + 3a/a - (-4/x + 3x/x))/(x - a)
= (-4a + 3a - (-4x + 3x))/(ax)
= (-a + x)/(ax)
= -(a - x)/(ax)
Learn more about trigonometric identities at: brainly.com/question/24377281
#SPJ11
Solve for g: 6 - 2g = 12
Answer:
g = -3
Step-by-step explanation:
subtract 6 on both sides
-2g = 6
divide by -2
g = -3
Answer:
G=-3
Step-by-step explanation:
I have used an online algebra calculator to check my answer against and I got the answer g= -3 both times so I am 100% positive that the answer is correct.
PLEASE MARK BRAINLIEST
what is 40 times 8 minus 10 to the power of 2
Answer:
220
Step-by-step explanation:
40 x 8 = 320
\(10^{2}\) = 100
320- 100 = 220
Hope that helps and have a great day!
Answer:
220
Step-by-step explanation:
Rewritten in numerical terms, the problem is:
40 * 8 - 10^2
Remember PEMDAS:
10^2 = 100
40*8 = 320
320 - 100 = 220
220
plz help me
The container below contains 2 gray. 1 white, and 4 black marbles. Without looking, if Eric chooses a marble from the container will the probability be closer to O or to 1 that Eric will select a white marble? A gray marble? A black marble? Justify each of your predictions.
Step-by-step explanation:
Probability of Grey ball = 2/7 or 0.285. It is closer to 0
Probability of White marble = 1/7 or 0.142. It is closer to 0
Probability of Black marble = 4/7 or 0.571. It is closer to 1
The diameter of a circular pizza is 24 in. How much pizza is eaten (in square inches) if half of it is consumed? (Pie and л... hmmmm...interesting...)
Using the formula of area of a circle, about 226.08in² has been eaten
How much pizza is eaten?The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:
Area = π * r²
where π is approximately 3.14 and r is the radius of the circle.
Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.
Let's calculate the area of the entire pizza first:
Area = 3.14 * 12²
Area = 3.14 * 144
Area ≈ 452.16 square inches
Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:
Area of half of the pizza = 452.16 / 2
Area of half of the pizza ≈ 226.08 square inches
Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.
Learn more on area of a circle here;
https://brainly.com/question/15673093
#SPJ1