Quadrilateral ABCD is a parallelogram. ,  bisects , and . What is the best name for quadrilateral ABCD?
A.
rectangle
C.
isosceles trapezoid
B.
rhombus
Using the graph, find this information about the child’s movement in the vertical (y) direction:
1. the best trigonometric function to start with
2. the amplitude
3. the period
4. any horizontal displacement of the graph.
5. any vertical displacement of the graph.
Type your response here:
HELP! Type the correct answer in each box. Use numerals instead of words, if necessary, use / for the fractions bar(s)
The piecewise function is:
[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]
To determine the piecewise function represented by the given coordinates, let's examine the points and their corresponding intervals.
The coordinates are (-1, 4), (1, 4), (3, 2), and (5, 4).
The points (-1, 4) and (1, 4) have the same y-coordinate, indicating that on the interval [tex]\(-1 \leq x \leq 1\)[/tex], the function has a constant value of 4. Therefore, the piecewise function for this interval is f(x) = 4 for [tex]\(-1 \leq x \leq 1\).[/tex]
The points (3, 2) and (5, 4) indicate that on the interval [tex]\(3 \leq x \leq 5\)[/tex], the function is a line passing through these two points. We can find the slope (m) and y-intercept (b) for this line.
[tex]\[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{4 - 2}{5 - 3} = \frac{2}{2} = 1 \][/tex]
Using the point (3, 2), we can find the y-intercept:
2 = 1(3) + b
b = -1
Therefore, the equation for the line on the interval [tex]\(3 \leq x \leq 5\) is \(f(x) = x - 1\) for \(3 \leq x \leq 5\).[/tex]
Putting it all together, the piecewise function is:
[tex]\[ f(x) = \begin{cases} 4 & \text{if } -1 \leq x \leq 1 \\ x - 1 & \text{if } 3 \leq x \leq 5 \end{cases} \][/tex]
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A student performed the following steps to find the solution to the equation x^2-2x-8=0. Where did the student go wrong?
Step 1. Factor the polynomial into (x-4) and (x-2)
Step 2. x-4=0 and x-2=0
Step 3. x=4 and x=3
A. The student did not make any mistakes, the solution is correct
B. in step 1
C. in step 2
D. in step 3
Evaluate f(x) when x=9
A line passes through the point (-8,3) and has a slope of 5/4.
Write an equation in slope-intercept form for this line.
The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.
Applying Newton's cooling model, the temperature of the tea after 2 hours will be ___
ºF. round to the nearest integer.
Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.
Therefore when expressed mathematically, this is equivalent to:
dT = - k (T – Ts) dt
dT / (T – Ts) = - k dt
Integrating:
ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)
Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.
R = ˚F + 460
T1 = 200 + 460 = 660 R
Ts = 70 + 460 = 530 R
ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)
T2 = 569.16 R
T2 = 109 ºF
Answer: After 2 hours, it will be 109 ºF
Answer:
109 degrees
Step-by-step explanation:
A gardener has 27 pansies and 36 daisies. He plants an equal number of each type of flower in each row.What is the greatest possible number of pansies in each row?
A dresser contains six pairs of shorts one each in the colors, red, black, blue, green, khaki, and gray. The dresser also contains four shirts one each in the colors black, navy, red, gray. Melanie has to get dressed in the dark, so she grabs A pair of shorts and a T-shirt at random. What is the probability that she selects a green pair shorts and a gray T-shirt?
(First of all, Melanie, you should really get a lamp. And second why is it you own more shorts than shirts?)
I need help with #18 c-i
Can someone help me
2.89-2.84 = 0.05 cent increase
0.05/2.84 = 0.0176
0.0176 = 1.8% increase
Identify the cross section shown.
circle
trapezoid
rectangle
pentagon
The cross section shown in the picture below include the following: B. rectangle.
In Mathematics and Euclidean Geometry, a rectangle refers to a type of quadrilateral or polygon in which its opposite sides are equal and all the angles that are formed are right angles.
Generally speaking, a circle has no edge or sides. A trapezoid is a type of quadrilateral that has one pair of parallel sides and one pair of non-parallel sides. Additionally, a pentagon is a regular polygon that comprises 5 sides.
By critically observing the cross section shown in the picture below, we can logically deduce that it represents a rectangle because its opposite sides are equal.
You invest an initial $2,000 in an account that has an annual interest rate of 6%, compounded daily. How much money will you have in the account after 15 years? Round your answer to the nearest whole number.
Find the greatest common factor of the following monomials 28g5h2 12g6h5
Also explain step by step how to solve these problems please
For the polynomial 8x3y2 – x?y2 + 3xy2 – 4y3 to be fully simplified and written in standard form, the missing exponent on the
Answer: 2
Step-by-step explanation: this answer is 100% correct for edge.nuity
Find the angle between the given vectors to the nearest tenth of a degree. u = <-5, 8>, v = <-4, 8>
Answer: 5.4 degrees
Step-by-step explanation:
look up online "how to find the angle between 2 vectors, and it'll show you how"
Given the function f(x) = log3(x + 4), find the value of f−1(3
Answer:
23
Step-by-step explanation:
Given : [tex]f(x) = log_3(x + 4)[/tex]
To Find: [tex]f^{-1}(3)[/tex]
Solution:
[tex]y = log_3(x + 4)[/tex]
Replace y with x and x with y
[tex]x = log_3(y + 4)[/tex]
[tex]3^x = y + 4[/tex]
[tex]3^x-4 = y [/tex]
So, [tex]f^{-1}(x)=3^x-4[/tex]
Now substitute x= 3
[tex]f^{-1}(3)=3^(3)-4 [/tex]
[tex]f^{-1}(3)=27-4 [/tex]
[tex]f^{-1}(3)=23[/tex]
Hence the value of [tex]f^{-1}(3)[/tex] is 23
When a line has an undefined slope what will any two points on the line have in common
The rectangle below has an area of x^2-15x+56 x 2 −15x+56 x, start superscript, 2, end superscript, minus, 15, x, plus, 56 square meters and a length of x-7x−7x, minus, 7 meters. what expression represents the width of the rectangle
The expression that represents the width of the rectangle is x - 8
Area of a rectangle:area = lwl = length
w = width
area = x² + 15x + 56
length = x - 7
Therefore,
x² - 15x + 56 = (x - 7) w
divide both sides by x - 7
w = x² - 15x + 56 / x - 7
w = (x - 7)(x - 8) / x - 7
w = x - 8
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A surface on which all points are at the same potential is referred to as
The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.
The sum of 2 numbers is 7. if one number is subtracted from the other, the result is -1. find the numbers
Evaluate. 5.4 - 1.3
Two containers, one for 3 liters and one for 5 liters, how would you measure 4 liters
Use Gauss-Jordan elimination to solve the following linear system: 5x – 2y = –2 –x + 4y = 4 A. (–6,–5) B. (2,0) C. (0,1) D. (–1,0)
The answer is C.(0,1)
5x - 2y = -2 -x + 4y = 4
5(0) - 2(1) = -2 -(0) + 4(1) = 4
What is the equation of the line?
If four times a number plus 3 is 11, what is the number
Which is a counterexample that disproves the conjecture? After completing several multiplication problems, a student concludes that the product of two binomials is always a trinomial.
Solve cos x +sqrt2 = -cos x for x over the interval (0,2pi) .
Final answer:
The equation cos x + sqrt(2) = -cos x is solved by combining like terms and isolating cos x, resulting in the solutions x = 3π/4 and 5π/4 over the interval (0,2π).
Explanation:
To solve the equation cos x + sqrt(2) = -cos x for x over the interval (0,2π), first combine like terms by adding cos x to both sides of the equation, resulting in:
2 cos x + sqrt(2) = 0
Isolate cos x by subtracting sqrt(2) from both sides:
2 cos x = -sqrt(2)
Divide both sides by 2 to solve for cos x:
cos x = -sqrt(2)/2
The value of cos x = -sqrt(2)/2 corresponds to angles in the second and third quadrants. So, the solutions for x in the interval (0,2π) are:
x = 3π/4, 5π/4
Can you use the ASA Postulate or the AAS Theorem to prove the triangles congruent?
Answer:
ASA only
Step-by-step explanation:
Given is a picture of two triangles with one side and one angle congruent.
Comparison of these two triangles given
side = side
one angle = one angle (given)
Second angle = second angle (Vertically opposite angles)
Thus we find here that two angles and one corresponding side are congruent.
HEnce we say that these two triangles are congruent by ASA theorem
ASA theorem can be applied here because the equal side is between the two congruent angles.
Instead if the side is not between the congruent angles but corresponding side then we can only use AAS
SO here ASA is correct.
Answer:
ASA only
Step-by-step explanation:
We are given that two triangles in which
An angle of triangle is equal to its corresponding angle of second triangle.
One side of a triangle is equal to one side of other triangle.
ASA postulate: It states that two angles and included side of one triangle are congruent to its corresponding angles and corresponding side of other triangle , then the two triangles are congruent.
AAS postulate: It states that two angles and non- included side of one triangle are congruent to its corresponding two angles and its corresponding side of another triangle, then the triangles are congruent by AAS postulate.
In triangle AOB and COD
[tex]\angle AOB= \angle COD[/tex] (Vertical angles are equal )
[tex]\angle ABO=\angle CDO[/tex] ( Given )
[tex]OB=OD[/tex] (Given )
[tex]\triangle AOB\cong \triangle COD[/tex] ( ASA Postulate )
Answer: ASA only