Answers
Answer:
Step-by-step explanation:
AB ≅ BC. So, ΔABC is an isosceles triangle
Opposite angles of equal sides are equal.
∠BAC = ∠BCA = x°
In ΔABC,
∠ABC + ∠BAC + ∠BCA = 180 {Angle sum property of triangle}
56 + x + x = 180
56 + 2x = 180
2x = 180 - 56
2x = 124
x = 124/2
x = 62°
∠BAC = ∠BCA = 62°
∠DCF = ∠BCA {Vertically opposite angles}
∠DCF = 62°
CDEF is a parallelogram.
In parallelogram, opposite angles are congruent.
∠DEF = ∠DCF
∠DEF = 62°
In a parallelogram, sum of adjacent angles = 180
∠DEF + ∠CDE = 180
62 + ∠CDE = 180
∠CDE = 180 - 62
∠CDE = 118°
∠CFE = ∠CDE {In parallelogram, opposite angles are congruent}
∠CFE = 118°
Related Questions
. Find two polynomial expressions whose quotient, when simplified, is 1/x . Use that division problem to determine whether polynomials are closed under division.
Answers
Answer:
The two polynomials are:
(x + 1) and (x² + x)
Step-by-step explanation:
A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.
Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.
Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.
So,
Let's multiply both numerator and denominator by (x + 1) to get;
(x + 1)/(x(x + 1))
This gives; (x + 1)/(x² + x)
Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.
A 2-column table with 8 rows. The first column is labeled x with entries negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 34, 3, negative 10, negative 11, negative 6, negative 1, negative 2, negative 15. Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing? (–6, –3) (–3, –1) (–3, 0) (–6, –5)
Answers
Answer:
Step-by-step explanation:
The only place that the function is increasing is [-3, -1] (learn your interval notation). At x = -3, y = -11; at x = -2, y = -6 (-6 is greater than -11); and at x = -1, y = -1 (-1 is greater than -6). The next x value, 0, returns a y value of -2. But -2 is less than -1, the value before it, so it begins deceasing again at x = 0.
Based on the values given in the table for f(x), the interval of x-values that show the function increasing is (-3, -1).
Which interval shows the function increasing?The value of f(x) was decreasing from 34 until it got to -11 where it then started to rise again. The relevant value of x here is -3.
The value then began to rise until it reached -1 where it then fell to -2. The x value here is -1.
The interval of x-values where the function is increasing is therefore (-3, -1).
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The length of country & western songs has mean 151 seconds and standard deviation 30 seconds. Determine the probability (as percent) that a random selection of 20 songs will have mean length of less than 149.75 seconds.
Answers
Answer:
48.514%
Step-by-step explanation:
The formula for calculating a z-score is is z = (x -μ)/σ,
where x is the raw score = 149.75
μ is the sample mean = population mean = 151 seconds
σ is the sample standard deviation
= Population standard deviation/√n
Where n = 20 songs
Population standard deviation = 30
Hence, sample standard deviation
30/√20
= 6.7082039325
z = (x -μ)/σ
z = 149.75 - 150/6.7082039325
z = -0.03727
Using the z score table to find the probability, we have :
P(x<149.75) = 0.48514
In percent = 0.48514 × 100
= 48.514%
Therefore, the probability (as percent) that a random selection of 20 songs will have mean length of less than 149.75 seconds is 48.514%
what is 32 – 21 + 10x – 12x
Answers
Answer:
11 - 2x
Step-by-step explanation:
Given
32 - 21 + 10x - 12x ← collect like terms
= 11 - 2x
Change y = – 2/3 x + 7 into standard form
Answers
Answer:
2x + 3y = 42
Step-by-step explanation:
Standard form should be like:
=> ax + by = c
To make an equation like the above one, we need to do the point-slope form first.
=> y - y1 = slope (x - x1)
Slope = -2/3
Y-intercept -> to find the y-intercept, we need to make the 'x' as 0.
=> y = -2/3 * 0 + 7
=> y = 7
X-intercept -> to find the x-intercept, we need to make 'y' as 0.
=> 0 = -2/3x + 7
=> -7 = -2/3x
=> -21/2 = -x
=> -10.5 = -x
=> 10.5 = x
So, x and y intercepts are 10.5 and 7.
We can now write the point-slope form:
=> y - 7 = -2/3 (x - 10.5)
=> y - 7 = -2/3x + 21/3
=> y = -2/3x + 7 + 7
=> y = -2/3x + 14
=> 2/3x + y = 14
=> Multiply all numbers by 3
=> 2x + 3y = 42
n/6=9/3? i dont what this is can someone please help me!!!!
Answers
Answer:
[tex]\boxed{n=18}[/tex]
Step-by-step explanation:
[tex]\frac{n}{6} =\frac{9}{3}[/tex]
[tex]\sf Divide \ 9 \ by \ 3.[/tex]
[tex]\frac{n}{6} =3[/tex]
[tex]\sf Multiply \ both \ sides \ by \ 6.[/tex]
[tex]\frac{n}{6} \times 6 =3 \times 6[/tex]
[tex]n=18[/tex]
Answer:
n = 18
Step-by-step explanation:
n/6 = 9/3
Simplify the right side
n/6 = 3
Multiply each side by 6
n/6 *6 = 3*6
n = 18
When the factors of a trinomial are (x-p) and (x+q) then the constant teen of the trinomial is
Answers
(x-p)(x-q)
y(x-q) .... let y = x-p
yx - yq ... distribute
x(y) - q(y)
x(x-p) - q(x-p) ... replace y with x-p
x^2 - px - qx + pq .... distribute
x^2 + (-p-q)x + pq
The last expression is in the form ax^2+bx+c with a = 1, b = -p-q and c = pq
The constant term is the term without any variable x attached to it (either x or x^2), so the constant term is pq
HELP ASAP
Points $A(-1, -2)$ and $B(3, 2)$ are the endpoints of a diameter of a circle graphed in a coordinate plane. How many square units are in the area of the circle? Express your answer in terms of $\pi$.
Answers
Answer:
8π units²
Step-by-step explanation:
center=((-1+3)/2,(-2+2)/2)=(1,0)
[tex]radius~r=\sqrt{(3-1)^2+(2-0)^2} =\sqrt{4+4} =\sqrt{8} \\area~of~circle=\pi r^2=\pi \times (\sqrt{8} )^2=8\pi ~square~units.[/tex]
Anyone know the answer to this... Thanks
Answers
Answer:
coefficients are the number attached to the variables :75d+8w+25
75 , 8 and the constant is 25. the variables are d and w
if he works for 5 days(d) and installed 48 windows(w)
75 d + 8 w+25
75(5)+8(48)+25= 784 dollars
if Javier get increase of 40 dollars for snack, only the constant change, because the coefficient depends on work days and the number of windows installed, and since only the increase in his stipend, therefor the increase will be the constant value only.
Help c/8+5 = 24 a) 192 b) 3 c) 7 d) 152
Answers
Answer:
c = 152
Step-by-step explanation:
c/8+5 = 24
Subtract 5 from each side
c/8+5-5 = 24-5
c/8 = 19
Multiply each side by 8
c/8*8 = 19*8
c =152
Answer:
D. 152
Step-by-step explanation:
First, subtract 5 from both sides:
c/8 + 5 = 24
c/8 = 19
Multiply both sides by 8:
c = 152
So, the correct answer is D, 152
Find the surface area and volume of cone. A = rs + r2 V = 1/3r2 h A cone's slant height (s) is 15 cm and its radius is 8 cm. Surface area (to the nearest tenth) = cm2 Volume (to the nearest tenth) = cm3
Answers
Answer:
a) 483.6cm²b) 850.1 cm³Step-by-step explanation:
Given the slant height 's' and its radius 'r' to be 15cm and 8cm respectively.
the total surface of the cone A = πrs+πr² and the volume is expressed as
V = 1/3πr²h
For the surface area of the cone;
Given parameters
radius = 8 cm and slant height s = 15 cm
Total surface area A = π(8)(15) + π(8)²
A = 90π+64π
A = 154π
If π = 3.14
A = 154(3.14)
A = 483.56cm²
A = 483.6cm²
Hence the total surface area of the cone to the nearest tenth is 483.6cm²
For the volume of the cone;
V = 1/3πr²h
Using pythagoras theorem to get the height of the cone;
l² = h²+r²
h² = l²-r²
h² = 15²-8²
h² = 225-64
h² = 161
h = √161
h = 12.69cm
V = 1/3π* (8)² * 12.69
V = 1/3π* 64 * 12.69
V = 1/3*3.14* 64 * 12.69
V = 2550.1824/3
V = 850.06 cm³
V = 850.1 cm³
Hence, the volume of the cone is 850.1 cm³ to the nearest tenth.
How much did it cost Mark to drive 775 miles? If his car makes 31 mpg and fuel cost $2.00 per gallon.
Answers
Answer:
$50.00
Step-by-step explanation:
775/31=25
25x2=50
The sales tax for an item was $15.60 and it cost $390 before tax. Find the sales tax rate. Write your answer as a percentage.
Answers
Answer:
15.60 times 100 divided by 390=4%
Step-by-step explanation:
The required sales tax rate percentage is 4%.
The sales tax for an item was $15.60 and it cost $390 before tax. To find the sales tax rate. Write your answer as a percentage.
the percentage is defined as, the composition of something out of whole inbounds of 100.example 10% of 150 = 10 * 150/100
= 15
It shows that 10 percent of 150 is 15.
sales tax = $15.60
cost = $390
To get the sales tax percentage we have to find out the tax composition of tax to the cost. So,
Sale tax percent = sale tax/cost * 100
= 15.60/390 * 100
= 0.04 * 100
= 4 %
Thus, the required sales tax rate percentage is 4%.
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Part C Now try this one. Write a description of the partitioned function using known function types, including transformations.
Answers
Answer:
Following are the function description to the given question:
Step-by-step explanation:
In the given-question, three functions are used, that can be defined as follows:
In function 1:
This function is also known as the modulus on the absolute value function, for example:
[tex]f(x)=| x| \left \{ {{x , \ \ \ x>0} \atop {-x, \ \ \ \x<0 }} \right.[/tex]
In the given in the above graph, that is [tex]f(x) = -x , \ \ x<0[/tex]
In function 2:
In this function, It is an algebraic function that is [tex]y=x^2[/tex]
It is also a part of the quadratic polynomial function, and its value is [tex]y=x^2 , \ \ \ x> 0[/tex]
In function 3:
In this function, it is the cubic polynomial equation that's value is [tex]y=x^3[/tex]
In the graph its value is:
[tex]y=-x^3\\\\and \\ \\\to y= f(x) \\\\ \to y=-f(x)\\[/tex]
Can someone help me find the amount on year 11
Answers
Answer:
525 dollars
Step-by-step explanation:
simple interest yearly ( year 11 does not count because the question asking at the amount at the beginning of year 11)
interest=300*0.075*10= 225
the amount in the account : 300+225=525 dollars
Find the product (4x-3y)(2x+5)
Answers
Answer:
8x²−6xy+20x−15y
Step-by-step explanation:
(4x−3y)(2x+5)
=(4x+−3y)(2x+5)
=(4x)(2x)+(4x)(5)+(−3y)(2x)+(−3y)(5)
=8x²+20x−6xy−15y
=8x²−6xy+20x−15y
How many solutions does this system of inequalities have graphed below
Answers
Answer:
There is only one solution set.
Step-by-step explanation:
The set can contain any number of solutions or none.
This is all I know, hope it helps.
The graph of f(x) = 2x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3.
Answers
Average rate of change of a function f(x) between any x values a and b = slope of the secant line connecting f(a) and f(b). This means (f(b)-f(a))/ (b-a). If a=0 and b=3, the average rate of change equals (f(3)-f(0))/(3-0).
f(3)=8+1=9, and f(0)= 1+1=2. So the average rate of change is (9-2)/3= 7/3.
Who’s salary represents the median of the data in the table?
Answers
Answer:
Rajesh salary is the median
Step-by-step explanation:
Am not good in explanation
Answer:
1: Ram
Step-by-step explanation:
The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values
if we put these salaries in order we can find out what the median salary is.
32,701 , 45,600 , 52,000 , 67,250 , 71860.
The number in the centre or the middle is 52,000. That is Ram's salary.
The answer is 1. Ram
I hope you find this useful, rate me the brainliest if you did ;)
How many of the positive integer factors of 15552 are perfect squares?
Answers
There are 12 factors which are perfect squares is 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
What is factors?Factors can be define splitting the value in multipliable values.
Factorization of 15552
= 1 * 4 * 4 * 4* 9 * 9 * 3
Perfect squares can be formed by above factors are
= 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
Thus, there are 12 factors which are perfect squares is 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
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The graph of y=3x^2-3x-1 is shown. Use the graph to find estimates for the solutions of i)3x^2-3x+2=2 ii) 3x^2-3x-1=x+1
Answers
Intersection point of graph of function is known as solution of the function.
Graph is attached below, in which solution is shown.
1. Here, given that [tex]3x^2-3x+2=2[/tex]
It can be written as, [tex]y=3x^2-3x+2\\\\y=2[/tex]
Intersection point of graph of above two equation will be the solution of given function,
Solutions are (1, 2) and (0, 2)
2. Given that , [tex]3x^2-3x-1=x+1[/tex]
It can be written as
[tex]y=3x^2-3x-1\\\\y=x+1[/tex]
Intersection of graph of above two equation will be the solution of given equation.
Solutions are (1.721, 2.721) and (- 0.387, 0.613)
Both graph attached below,
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how many are 4 raised to 4 ???
Answers
Answer:
256Step-by-step explanation:
The expression 4 raised to 4 can be written in mathematical term as [tex]4^4[/tex] and this means the value of 4 in four places as shown;
[tex]4^4\\\\= 4 * 4* 4* 4\\\\= (4 * 4)* (4* 4)\\\\= 16*16\\\\= 256\\\\[/tex]
Hence the expression 4 raised to 4 is equivalent to 256
the area of a square is given by s2 and the perimeter is given by 4s, where s is the side length of the square if the side length of a square is 4 inches its area is ... square inches and its perimeter is ... inches
Answers
Answer:
Area = s² = 4² = 16 sq. In.
Perimeter = 4s = 4(4) = 16 in.
Help plz ASAP!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
The volume (V) of the prism is calculated as
V = lbh ( l is length, b breadth and h is height )
Here l = 7, b = 2 and h = 4 , thus
V = 7 × 2 × 4 = 56 in² → D
Pls answer this question as soon as possible
Answers
Answer:
The answer is -½.
✌ yeah it is ✌
Given f(x) = 2x - 7, complete parts (a) through (c).
A. Solve f(x)=0.
B. What do the answers to parts (a) and (b) tell you about the graph of y=f(x)
Answers
Answer:
a) x=7/2
Step-by-step explanation:
a) since f(x) is=0, plug in 0 to → f(x)=2x-7 [this f(x)]. you would get 0=2x-7. solve for x by adding 7 and dividing by 2 which you get x=7/2.
Then value of [tex]x[/tex] is 7/2
What is function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input . Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters. The domain is defined as the set of all the values that the function can input while it can be defined. The range is all the values that come out as the output of the function involved. Co-domain is the set of values that have the potential of coming out as outputs of a function.
given function:
[tex]f(x)[/tex]= 2[tex]x[/tex] -7
So,[tex]f(x)[/tex]= 0
2[tex]x[/tex] -7=0
2[tex]x[/tex]= 7
[tex]x[/tex]= 7/2
The graph is attached below.
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(48. PERSEVERE Wha
PERSEVERE What is the greatest number of planes determined using any three of
the points A, B, C, and D if no three points are collinear?
Answers
Answer: 4
Step-by-step explanation:
We know that a plane is 2 dimensional surface that extends infinitely far.
The number of points required to define a plane = 3
Here , we have 4 points A, B, C, and D.
So, the number of possible combinations of 3 points to make a plane from 4 points = [tex]C(4,3)[/tex]
[tex]=4[/tex] [ [tex]C(n,n-1)=n[/tex] ]
Hence, the greatest number of planes determined using any three of the points A, B, C, and D if no three points are collinear = 4.
Sketch the graphs y=1/3x+2
Answers
Answer:
mark a dot 2 on the y axis and from there go up one right 3 until you can anymore then go back to the two and go down one left 2
Step-by-step explanation:
Two fractions equivalent to 1/3
Answers
Answer:
2/6 or 3/9
Step-by-step explanation:
1/3 x 2 = 2/6
1/3 x 3 = 3/9
Answer:
2/6 3/9
Step-by-step explanation:
to find equivalent fractions you can just multiply, or count by the denominator for example, 3 , 6 , 9 and so on and then with the numerator you count how much you went like, if you went to sixths than it was 2 because you skip counted.
A golf ball is hit off a tee toward the green. The height of the ball is modeled by the function h(t) = −16t2 + 96t, where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground. t = 3; It takes the ball 3 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 6 seconds to fall back to the ground.
Answers
Answer:
t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.
Step-by-step explanation:
To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.
h(t) = -16t² + 96t
= -16(t² - 6t)
= -16(t² - 6t + 9) - (-16) * 9
= -16(t - 3)² + 144
Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".
The time will be t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.
What is Function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable the dependent variable.
To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.
h(t) = -16t² + 96t
= -16(t² - 6t)
= -16(t² - 6t + 9) - (-16) * 9
= -16(t - 3)² + 144
Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum.
We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground.
The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".
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