The value of x in the interval 0 ≤x≤ pi is 2.083 so the graph f and g have parallel tangent lines
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x) = tan x
and, g(x) = x²
Now, f(x) = t g(x)
and, g(x) = x²
On differentiating f(x) we get
f'(x) = t g²(x) + 1
and, g(x) = 2x
Now, the parallel tangent line
f' (x) = g'(x)
t g²(x) + 1 = 2x
since the interval for x is 0 ≤x≤ pi.
So, the value of x = 2.083
Hence, the value of x is 2.083.
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derek borrowed at 10% per annum coumpounded quarterly. how much money he repay after 5 years
The total amount Derek repaid after 5 years of quarterly payments at 10% per annum is $12,829.40.
How are the quarterly payments determined?The quarterly payments represent periodic payments made every three months to offset the credit.
The periodic payments can be computed using an online finance calculator.
Where the periodic payment is given, the total payment made can be determined as the product of the periodic payments and the number of periods involved.
N (# of periods) = 20 quarters (5 years x 4)
I/Y (Interest per year) = 10%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $-641.47
Results:
FV = $-0.03
Sum of all periodic payments = $-12,829.40
Total Interest = $2,829.43
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Question Completion:Derek borrowed $10,000 at 10% per annum compounded quarterly and repays $641.47 quarterly. How much money did he repay after 5 years?
2x-1 with a translation 1 unit left followed by a reflection in the x-axis
2x-1 with a translation 1 unit left followed by a reflection in the x-axis is -2x -1.
What is translation and reflection?
Flipping an object across a line without causing it to change in size or shape is called reflection. An object can rotate around a fixed point without changing its size or shape. Changing a figure's size, shape, or orientation does not constitute translation.
Reflections and translations are two of the most popular types of transformations. An object moves from one location to another through translation, remaining the same size and orientation.
One unit left means -1 shift on x-axis leads to F(x+1)
Reflection on x-axis means rotating the graph upside down on x-axis which leads -F(x+1)
-F(x + 1) = -2(x + 1) + 1 = -2x - 2 + 1 = -2x -1
Hence, 2x-1 with a translation 1 unit left followed by a reflection in the
x-axis is -2x -1.
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Which other expression has the same value as(-14)-8 ? Explain your
reasoning.
a. (-14)+8
b. (-14)- (-8)
c. (-14)+(-8)
d. (-14)+ (-8)
The dimensions of a rectangle are shown. Write the area of the rectangle as a sum of cubes. Question content area bottom Part 1 The area of the rectangle as a sum of cubes is enter your response here. x^2-3x+9 x+3
The area of the rectangle represented as the sum of cubes is x³ + 3³
What is an equation?An equation is an expression showing the relationship between numbers and variables.
The sum of cubes of a polynomial is in the form a³ + b³ while A the difference of cubes of a polynomial is a³ - b³
The area of rectangle = length * width
From the diagram, length = x² - 3x + 9; width = x + 3, hence:
The area of rectangle = length * width = (x² - 3x + 9)(x + 3)
Area = x³ - 3x² + 9x + 3x² - 9x + 27 = x³ + 27
Area = x³ + 3³
The area of the rectangle is x³ + 3³
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The parent function f(x) = 1.5x is translated such that the function g(x) = 1.5x + 1 + 2 represents the new function. Which is the graph of g(x)?
Four consecutive even integers sum to 332. Which integers are they?
Answer:
86
Step-by-step explanation:
let the numbers be x,x+2,x+4,x+6
Then x+x+2+x+4+x+6=332
4x=332-12=320
x=320/4=80
so numbers are 80,82,84,86
Answer:86
Step-by-step explanation:
Catarina’s boat has come untied and floated away on the lake. She is standing atop a cliff that is 35 feet above the water in a lake. If she stands 10 feet from the edge of the cliff, she can visually align the top of the cliff with the water at the back of her boat. Her eye level is 5½ feet above the ground. Approximately how far out from the cliff is Catarina’s boat? Round to the nearest foot.
If Catarina’s boat has come untied and floated away on the lake. She is standing atop a cliff that is 35 feet above the water in a lake. Approximately the distance from the cliff is Catarina’s boat is : 63.6ft.
What is distance?Distance can be defined as how far an object is from another object.
Now let find the distance:
AE/CD = BC/DE
Hence,
5.5/3.5 = 10/DE
Cross multiply
AE = 350/5.5
AE = 63.6ft
Therefore we can conclude that the distance is 63.6ft.
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Kris had 22 stickers and got 16 more Matt had 18 stickers.then he got some number of stickers.how many stickers did Matt get .
Answer:
20 Stickers
Step-by-step explanation:
Set up for the problem
22+16= 38
38-18=20
So, Overall=20...
HELP ME PLEASE!!
i need to find the j and k values and if you could explain that would be amazing!! Please and thank youu!! :))
Answer:
[tex]j = \dfrac{9}{2} = 4,5 \\\\\\k = 2[/tex]
Step-by-step explanation:
I am working on the assumption that the figure shown is a parallelogram, otherwise my answer will not be valid
The diagonals of a parallelogram bisect each other
In the above figure, the top left-bottom right diagonal is bisected by the top right - bottom-left diagonal
This means
[tex]3j = 5j - 9[/tex]
Subtract 5j from both sides:
[tex]3j - 5j = -9[/tex]
[tex]-2j = -9[/tex]
[tex]j = \dfrac{-9}{-2} = \dfrac{9}{2} = 4,5 \\[/tex]
I am not sure if you want it in fraction or decimal
Similarly
[tex]k + 10 = 6k\\\\[/tex]
Subtract k from both sides:
[tex]10 = 6k-k\\\\\\10 = 5k\\\\\\\textrm{Switching sides,}\\5k = 10\\\\k = \dfrac{10}{5} = 2\\\\[/tex]
given: ab=bc, ae=fc
prove m
rsm problem pls help
The triangles ∆AEC ≅ ∆AFC by Side-Angle-Side theorem
How to determine the proof of the trianglesThe complete question is added as an attachment
With the given information and the image attached below, we can state that the two triangles are congruent by SAS,
Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.
The proof is given as:
Statement Reason
1. AB ≅ BC, AE ≅ FC 1. Given2. AC ≅ AC 2. Reflexive property of congruence3. <BAC ≅ <BCA 3. Base angles of isosceles ∆BAC4. ∆AEC ≅ ∆AFC. 4. SAS5. <AEC ≅ <AFC. 5. CPCTCRead more about congruence proof at:
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Solve these equations.
Oki and Stephen are making bags of trail mix to sell. Oki’s trail-mix recipe requires 3 cups of nuts and 3 cups of dried fruit per bag. Stephen’s trail-mix recipe requires 4 cup of nuts and 2 cups of dried fruit per bag. Together, they want to make as many bags of trail mix as possible. They have exactly 120 cups of nuts and 90 cups of dried fruit. Find the maximum number of bags of trail mix Oki and Stephen can make together.
Oki and Stephen can only produce 0.75 bags of trail mix in total.
How can division be used?Two numbers can have a division symbol (") added between them to indicate that they have been divided. Therefore, we can write 36 6 if we need to demonstrate the division of 36 by 6. A fractional representation is 366, which we can also use.
Compared to multiplication, division is the opposite. When you divide 12 into three equal groups, you get four in each group if three groups of four add up to 12, which they do when you multiply.
The primary objective of division is to count the number of equal groups that are created or the number of individuals in each group after a fair distribution.
According to question:-
3/3 : 4/2 =1:2
90/120 = 0.75.
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g(x)
10
8
6
4
2
fo
-10-8-64-22
-4
-6
-8
-10
f(x)
2 4 6
8 10 x
What is the equation of the translated function, g(x), i
f(x) = x²?
g(x) = (x-4)² +6
Og(x) = (x + 6)²-4
g(x) = (x-6)²-4
Og(x) = (x+4)² + 6
O
Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6
What does the term function refer to?The study of numbers, their variations, mathematics and the regional tissue, structures, and both their actual and imagined locations, is known as mathematics. A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input. Each function is given a city, town, or scope, which is frequently referred to as a realm.
Here,
Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).
Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).
The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).
Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).
=> f(x) = (x-h)² + k
The outcome of translating a unit to the right with b unit up is
=>f'(x) = (x-h-a)² + k + b
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Pls help needed tyyy who lives farther? Easy
Sawyer lives 12.7 km farther from the soccer field.
How to find who lives farther from the soccer fields?Jabar lives 5 miles from the soccer fields, Sawyer lives 12.7 km from the same soccer fields .
The person that lives farther form the soccer field can be calculated as follows;
Let's convert Jabar distance from the soccer field to km.
1 miles = 1.60934
5 miles = ?
cross multiply
distance of Jabar from the soccer field = 5 × 1.60934
distance of Jabar from the soccer field = 8.0467 km
Therefore, jabar lives 8.0467 km from the soccer field.
Hence, Sawyer lives 12.7 km farther from the soccer field.
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The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees (in thousands) is given by the equation y=3.6x+442, and for women, the equation is y=14.3x+318, where x is the number of years after 1970
PLEASE HELP IS AN EMERGENCY
The solution to the system of equations for this problem is given as follows:
(11.59, 479).
How to solve the system of equations?The system of equations for this problem is defined as follows:
y = 3.6x + 442.y = 14.3x + 318.The solution for x is obtained when the two equations are equal, hence:
14.3x + 318 = 3.6x + 442
10.7x = 124
x = 124/10.7
x = 11.59.
Applying the substitution in any of the equations, the solution for y is obtained as follows:
y = 3.2(11.59) + 442
y = 479.
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Which answers describe the shape below? Check all that apply.
0
A. Rectangle
B. Rhombus
C. Parallelogram
D. Trapezoid
E. Quadrilateral
F. Square
Answer:
Rectangle, parallelogram, trapezoid, quadrilateral
Step-by-step explanation:
because the properties of the rhomboid(that is what it is called) match with those different shapes listed above
Which describes a relationship that varies directly?
t = 85-5h, where t represents temperature and h represents number of hours between temperature readings
b = 1.2m + 120, where b represents the bank account balance and m represents the number of months
C = 12k, where C represents the cost on the electrical bill and k represents the electricity used
T = 120, where T represents the time to prepare dinner for a dinner party
C = 12k, where C represents the cost on the electrical bill and k represents the electricity used is a relationship that varies directly. Option C is correct.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
A standard directly proportional relationship is given as,
y = kx
Now,
comparing the above equation with the equation among the option,
If the equation in options matches with the above equation, so that equation will be a relationship that varies directly.
Thus, C = 12k, where C represents the cost on the electrical bill and k represents the electricity used is a relationship that varies directly. Option C is correct.
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please help me with math i’ll give you brainlist
Answer:
it's a function
Step-by-step explanation:
to test if it's a function or not you do the vertical line test if it intersects the function at more than one point then it's not a function,, but here in the given function when you do the vertical test it'll only intersect it at one point so it's a function
7 = 3(5 + x) solve for x
Answer: x = -8/3
Step-by-step explanation:
7 = 3(5+x)
3(5+x)=7
apply the distributive property
15+3x=7
rearrange the variables to the left side of the equation
3x=7-15
3x=-8
divide on both sides
x=-8/3
Answer:
x = -8/3
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 7 = 3(5 + x)
Then the value of x will be,
→ 7 = 3(5 + x)
→ 7 = 3(5) + 3(x)
→ 7 = 15 + 3x
→ 7 - 15 = 3x
→ -8 = 3x
→ 3x = -8
→ [ x = -8/3 ]
Hence, the value of x is -8/3.
What shape results from a plane passing through a cone that is perpendicular to the base?
Isosceles Triangle
Circle
Parabola
Ellipse
The shape that results from a plane passing through a cone that is perpendicular to the base is a B. Circle
How is the Circle Formed?A circle intersects a cone when a plane passes through it perpendicular to the base. This is due to the plane cutting through the cone's circular cross-section at a 90-degree angle to the base of the cone.
As a result, if the plane were to be slanted or angled, the intersection would have the shape of an ellipse, which is a circle that has been flattened.
This is due to the fact that an ellipse is the shape created when a plane crosses a cone at an angle other than perpendicular to the base.
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Two angles are complementary. The larger angle is 50∘ more than the smaller angle. Find the measure of the larger angle.
The measure of the smaller complementary angles is 40°
What are complementary anglesWhen two angles add up to 90°, we say they complement each other in terms of mathematics. Hence in geometry, complementary angles are defined as two angles whose sum is 90 degrees.
The larger angle = 50°
we shall represent the smaller angle with the letter x so that;
x + 50° = 90°
subtract 50° from both sides of the equation
x + 50° - 50° = 90° - 50°
x = 40°
Therefore, the smaller complementary angle has a measure of 40°.
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Use synthetic division to show that x=-3 is a root of the polynomial function f(x)=x^3-4x+15 and say the other remains roots!!!!
The given function has one root i.e. -3.
Synthetic division: What is it?The Synthetic approach can speed up polynomial division, especially when the result needs to be divided by a linear factor. It is often used to find polynomial roots or zeroes rather than dividing components.
In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.
We've f(x) = x³-4x+15
= (x+3) ( x²-3x+5) + 0
which implies that it has remainder as 0, So -3 is a root of given f(x).
Since x²-3x+5 can't be factorized more, the given function has only one root i.e. -3.
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George is 48 inches tall and growing at a rate of 2 inches a year his sister is 42 inches tall and growing at a rate of 3 inches in a year if their growth rate continues how long will it be before Georgia sister is taller than he is
Answer: It will take 7 more years for George’s sister to be taller than him.
Step-by-step explanation:
Answer:
Step-by-step explanation:
7 years
I NEED HELP ASAP WITH THIS MATH HOMEWORK PLEASE
Answer: 1. 7a 2. 5r 3. 8y+4 4. 12m-7 5. 7u+5 6. 8q+6 7. 3w+5x 8. 4j + 4k 9. 5d+6
Step-by-step explanation: Add the coefficients of the terms with same variables. ex. 5a+4a+7... 5a and 4a have same variable which is a so add the 5 and 4 and you get 9a and the 7 doesn't match so leave it out and you get 9a + 7
Answer:
1) 7a
2) 5r
3) 8y +4
4) 12m-7
5) 7u+5
6) 8q+6
7) 3w+5x
8) 4j +4k
9) 5d+6
Step-by-step explanation:
you just add or subtract the number with the same letter after it (if there is no letter just leave it as is, unless there are two or more numbers with no letter after, then add or subtract as normal)
I need help with this ASAP! (will be giving brainliest to the correct answer.
The solution is
a) The motor boat traveled a displacement of
b) The velocity of the tugboat
c) The negative distances and velocities means the boat is traveling down a river
What is Velocity?Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time. It is a vector quantity. Velocity is the change in displacement of an object with respect to time
Velocity = Displacement / Time
Given data ,
Some boats are traveling up and down a river
So , when the boat is traveling up a river , the velocity will be positive and when the boat is traveling down a river , the velocity will be negative
a)
The velocity of motor boat = - 3.4 mph
The time taken by the boat = 0.75 hours
Velocity = Displacement / Time
Substituting the values in the equation , we get
Displacement = Velocity x Time
Displacement D = - ( 3.4 ) x 0.75
On simplifying the equation , we get
Displacement D = -2.55 miles
Therefore , the boat traveled -2.55 miles down
b)
The displacement of the tugboat D = -1.5 miles
The time taken by the tugboat T = 0.3 hours
So , velocity of the tugboat V = ( -1.5 ) / 0.3
On simplifying the equation , we get
Velocity V = -5 mph
Therefore , the velocity of the tugboat is -5 miles per hour
c)
When the boat is traveling down a river , the velocity will be negative
Hence , the equations are solved
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Which of the following are irrational numbers?
Choose the two correct answers.
Responses
100−−−√ 100 ,
28−−√ 28 ,
11−−√ 11 ,
2.78¯¯¯¯
The value of an irrational numbers are,
⇒ √28
⇒ √11
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 numbers are,
⇒ √100
⇒ √28
⇒ √11
⇒ 2.78⁻⁻⁻
Now, We know that;
An irrational number is a number that cannot be expressed as a fraction for any integers.
Hence, We get;
The correct value of an irrational numbers are,
⇒ √28
⇒ √11
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2b.) Determine the average rate of change between the
sixth and fourteenth hours, explain what it means in
context of the problem.
The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.
what is slope ?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).
given
slope = y2- y1 / x2 - x1
= -120/8 = -15
( 6 , 120 )
( 14 , 0 )
The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.
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A school uses a phone tree to communicate updates to families. First, the 3 school administrators decide when an announcement is needed. They each call 5 people in the first round of calls. Then, each of those people calls 5 people in the second round. In every round, each person who received a call in the previous round makes calls to 5 new people. Let x be the number of rounds, and let y be the number of people called during the round. Write and graph a function that models this situation. Label the y-intercept, and explain what it represents.
The exponential function that models this situation is given as follows:
y = 3(5)^x.
The y-intercept of the exponential function represents the number of people that were called by the administrators.
The graph of the exponential function is given by the image presented at the end of the answer.
How to define the exponential function?The general format of an exponential function is given as follows:
y = a(b)^x.
In which:
a is the initial value.b is the rate of change.First, the 3 school administrators decide when an announcement is needed, hence the parameter a, representing the y-intercept, is given as follows:
a = 3.
In each round, each person inserted into the conversion calls 5 more people, hence the parameter b is given as follows:
b = 5.
Meaning that the function is defined as follows:
y = 3(5)^x.
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According to the frequency chart below, how many people have a dog or cat as their favorite pet?
Answer:
22
Step-by-step explanation:
as you can see at the bottom, they have added up all of the tallies. so all you need to use addition to add 10 + 12 which is equal to 22.
The difference of twice a number and three is -21
Write into an equation
Answer:
Step-by-step explanation:
2n -3 =-21
2n-3+3=-21+3
2n=-19
n=-9.5