Answer:
k=5
a= -5
Step-by-step explanation:
if the polynomial x^4-6x^3+16x^2-25x+10 is divided by x^2-2x+k the remainder comes out to be x+a,find k and a
Solution
x^4-6x^3+16x^2-25x+10 / x^2-2x+k = x-a
We have,
(4k-25+16-2k)x+[10-k(8-k)] = x+a
(2k+9)x + (10-8k+k^2)=x+a
2k-9=1
2k=1+9
2k=10
Divide both sides by 2
2k/2=10/2
k=5
And
10-8k+k^2=a
10-8(5)+(5^2)=a
10-40+25=a
-5=a
Therefore, a=-5
x^4-6x^3+16x^2-25x+10 divided by x^2-2x+5 = x-5
Please answer it in two minutes
Answer:
0.9
I guess.
If yes
.. Follow me..
EXPLANATION NEEDED:
In right triangle ABC, ∠ B is a right angle and sin ∠ C = x. cos ∠ A =
a. √x² - 1
b. √1 - x²
c. x
d. √x² + 1
e. x²
Answer:
C. xStep-by-step explanation:
AC denotes the length of the hypotenuse and AB and BC denote the lengths of the other two sides, so:
[tex]\cos(\angle A)=\dfrac{AB}{AC}=\sin(\angle C)=x[/tex]
Identify the ventez of the graph. Tell whether it is a minimum or maximum.
Answer:
2nd option: the lowest point on the graph is (-2, -2). this is where both sides of the parabola converge. from this point, both lines go up. this means the vertex is a minimum.
Please answer please question
Answer:38
Step-by-step explanation:multiple
2/3 (m-1/2) +3= m/3-7 Please Explain (Will give brainliest)
Answer:
m= -29
Step-by-step explanation:
This is a bit of a complex equation, but let's work through it.
2/3 (m-1/2) +3= m/3-7
First, we need to distribute the 2/3.
(2/3)(m)+(2/3)(−1/2)+3=m/3+−7
Now we simplify that.
2/3m+−1/3+3=1/3m+−7
We can now combine like terms.
2/3m+8/3=1/3m+−7
The goal is to isolate the variable, so we should subtract 1/3m from both sides.
1/3m+8/3=−7
Lets keep going! We can subtract 8/3 from both sides.
1/3m=-29/3
Well now we know what 1/3 of m is, but we want to know what m is. So we can multiply both sides by three to finally find out what m is!
m=-29
We did it! m=-29
An object traveled for 3 hours at a rate of 30 mile/hr, and then for another 2 1/4 hours at a rate of 10 1/2 miles/hr. How many total miles did the object travel?
Answer:
113.625 miles
Step-by-step explanation:
3 hours at a rate of 30 mile/hr : 3*30=90 miles
2 1/4 hours at a rate of 10 1/2 miles/hr= 2 1/4 *10 1/2= 2.25*10.5=23.625
total miles the object traveled : 90+23.625=113.625 miles
please help me with this math question
Answer:
5.50 years
Step-by-step explanation:
A = P[tex](1 + \frac{r}{n})^{nt}[/tex]
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
3178 = 2000(1+.086/2)^2t
t = 5.499904413
Which is a qualitative graph? On a coordinate plane, a line with positive slope goes through points (negative 1, 0) and (0, 3). On a coordinate plane, points are at (0, 2), (1, 3), (2, 2.5), (3, 3), (4, 4), and (4.5, 5). A graph has time on the x-axis and height on the y-axis. The graph increases to point A, increases to point B, and then decreases to point C. A graph has time on the x-axis and height on the y-axis. Segment A increases, segment B is increases, and segment C decreases.
Answer:
(-1,0), (0,3) and (2,2.25)
Step-by-step explanation:
The qualitative graph is as follows:
A(-1,0) ------> B(0,3) ------> C(2,2.25)
Hence, slope = (2.25 - 0)/(2 - (-1)) = 2.25/3
∴ slope = 0.75
Except for the option graph on a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), all the graph is qualitative. Options B, C, and D are correct.
What is a qualitative graph?The kind of graph that shows the quality curve such as decreasing and increasing events, is called a qualitative graph or curve.
Here,
1. On a coordinate plane, a line with a positive slope goes through points (negative 1, 0) and (0, 3), since this graph does not represent any data as well as also constantly increasing between two points so it is not a qualitative graph.
Similarly,
Graphs B, C, and D have an increasing and decreasing order, so all are qualitative graphs.
Thus, except for graph A all the graphs are qualitative graphs.
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if f(x)=4x-7 and g(x)=2x+4 evalvate f(x)+g(x) for x=-3
Answer:
-21
Step-by-step explanation:
We are told to find f(x) + g(x) for x= -3. Therefore, we must evaluate f(-3) and g(-3), then add them together.
First, evaluate f(-3).
f(x)=4x-7
To find f(-3), we need to substitute -3 in for x.
f(-3)= 4(-3)-7
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction First, multiply 4 and -3.
f(-3)= -12-7
Next, subtract 7 from -12
f(-3)= -19
Next, find g(-3).
g(x)=2x+4
To find g(-3), substitute -3 in for x.
g(-3)= 2(-3)+4
Solve according to PEMDAS. First, multiply 2 and -3.
g(-3)= -6+4
Next, add -6 and 4
g(-3)= -2
Now, we can add f(-3) and g(-3) together.
f(-3) + g(-3)
f(-3)= -19
g(-3)= -2
-19 + -2
Add
-21
Answer:
-21
Step-by-step explanation:
Adding f and g together, we get (f + g)(x) = 4x + 2x -7 + 4, or
= 6x - 3
Now replace x with -3. We get:
(f + g)(-3) = 6(-3) - 3 = -21
The slope of the line below is 4 . Which of the following is the point slope form of that line ? ( top answer gets )
Answer:
C
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 4 and (a, b) = (- 3, - 4) , thus
y - (- 4) = 4(x - (- 3)) , that is
y + 4 = 4(x + 3) → C
Dax is buying coffee for 5 5 people in his office. He also leaves a $2.00 $ 2.00 tip for the barista. If his total, with tip, is $18.25, $ 18.25 , how much is each cup of coffee, not including the tip? Enter your answer as a decimal, like this: 42.53
Answer:
$3.25
Step-by-step explanation:
To get the price of one cup of coffee without including Dax's two dollar tip, the first step is to subtract 2 from 18.25.
18.25 - 2= 16.25
16.25 is price of the five cups of coffee that Dax bought without the two dollar tip. The final step is to get the price of one cup of coffee which is basically:
16.25 ÷ 5 = 3.25
The cost of each cup of coffee is $3.25.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
To get the price of one cup of coffee without including Dax's two-dollar tip, the first step is to subtract 2 from 18.25.
18.25 - 2= 16.25
16.25 is the price of the five cups of coffee that Dax bought without the two-dollar tip. The final step is to get the price of one cup of coffee which is basically:
16.25 ÷ 5 = $3.25
Hence, the cost will be $3.25.
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The table below lists some of the characteristics of the houses on Katrina’s street. Characteristics of Homes For Sale on Katrina’s Street Bedrooms Acres of land Sale price Appraised value Property tax 2 0.17 $230,000 $200,000 $1,220 2 0.20 $210,000 $220,000 $1,232 3 0.20 $275,000 $250,000 $1,400 4 0.24 $275,000 $275,000 $1,540 4 0.52 $360,000 $310,000 $1,736 4 0.75 $350,000 $320,000 $1,792 5 1.23 $375,000 $350,000 $1,960 Which relationship describes a function?
Answer:
your welcome and hope this helps
I need this answered in ONE minute
Place the indicated product in the proper location on the grid. Write your answer in descending powers of x. (x^ 2 + 3x + 1)(x^2 + x + 2)
Answer:
[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]
Step-by-step explanation:
We are asked to multiply the given polynomials.
[tex](x^ 2 + 3x + 1) \times (x^2 + x + 2)[/tex]
Multiply each term of the first polynomial to each term of the second polynomial.
[tex]x^ 2 \times (x^2 + x + 2) = x^4 + x^3 + 2x^2[/tex]
[tex]3x \times (x^2 + x + 2) = 3x^3 + 3x^2 + 6x[/tex]
[tex]1 \times (x^2 + x + 2) = x^2 + x + 2[/tex]
Add the results
[tex](x^4 + x^3 + 2x^2) + (3x^3 + 3x^2 + 6x) + ( x^2 + x + 2)[/tex]
Combine the like terms
[tex]x^4 + 4x^3 + 6x^2 + 7x + 2[/tex]
The answer is written in descending powers of x.
What is the sum of the fractions? Use the number line to help find the answer. A. -2 B. -4/5 C. 4/5 D.2
Answer:
The answer is B.
Step-by-step explanation:
You solve it using the number line. Starting with the point at 3/5 then, you have to go backwards by 7 steps which is -4/5.
You can ignore the denorminator as all the denorminators are the same.
Answer:
-4/5
Step-by-step explanation:
The parentheses can be removed immediately since they do not affect the outcome in this problem.
then we have:
3/5 - 7/5 = -4/5
The mean one-way commute to work in Chowchilla is 7 minutes. The standard deviation is 2.4 minutes, and the population is normally distributed. What is the probability of randomly selecting one commute time and finding that: a). P (x < 2 mins) _____________________________ b). P (2 < x < 11 mins) _____________________________ c). P (x < 11 mins) ________________________________ d). P (2 < x < 5 mins) _______________________________ e). P (x > 5 mins)
Answer:
The answer is below
Step-by-step explanation:
Given that:
The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For x < 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
From normal distribution table, P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%
b) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337
c) For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(x < 11) = P(z < 1.67) = 0.9525
d) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) = 0.2033- 0.0188 = 0.1845
e) For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(x < 5) = P(z < -0.83) = 0.2033
Factor the polynomial.
X2-13x+30
Answer:
[tex] \ \boxed{(x - 3)(x - 10)}[/tex]Step-by-step explanation:
[tex] {x}^{2} - 13x + 30[/tex]
Write -13x as a difference
[tex] {x}^{2} - 3x - 10x + 30[/tex]
Factor out x from the expression
[tex]x(x - 3) - 10x + 30[/tex]
Factor out -10 from the expression
[tex]x(x - 3) - 10(x - 3)[/tex]
Factor out x-3 from the expression
[tex](x - 3)(x - 10)[/tex]
Hope I helped!
Best regards!!
Pls answer this question with steps (proof).
Answer:
Step-by-step explanation:
Since triangle BCE is a right angle triangle, we would determine angle BEC by applying the tangent trigonometric ratio. Therefore,
Tan BEC = 6/3 = 2
Angle BEC = Tan^-1(2)
Angle BEC = 63.4°
The sum of the angles on a straight line is 180°. This means that
Angle AED + angle DEC + angle BEC = 180
Angle AED = 180 - (45 + 63.4) = 71.6°
Angle ADE = angle AED = 71.6°
Angle CDE + angle ADE = 180(sum of angles on a straight line)
Angle CDE = 180 - 71.6 = 108.4°
To get line EC, we would apply Pythagoras theorem. Therefore
EC² = 3² + 6² = 45
EC = √45 = 6.71 cm
The sum of the angles in a triangle is 180°
Therefore,
Angle ECD = 180 - (45 + 108.4) = 26.6°
By applying sine rule,
6.71/sin108.4 = ED/sin26.6 = DC/Sin45
6.71/sin108.4 = ED/sin26.6
Cross multiplying, it becomes
6.71sin26.6 = EDsin108.4
ED = 6.71sin26.6/sin108.4
ED = 3.00608/0.949 = 3.18cm
The area of a triangle is
Area = 1/2abSinC
Therefore, area of triangle EDC = 1/2 ×
ED × EC × SinDEC
Area = 1/2 × 6.71 × 3.18 × sin45
Area = 1/2 × 6.71 × 3.18 × 0.707
Area = 7.54 cm²
ASAP PLEASE A box contains 6 red, 3 white, 2 green, and 1 black (in total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting at least one red ball?
Answer:
7 is the least.
Step-by-step explanation:
Their are 12 balls, and 6 of them are red. if you are to pick every single ball except the red ones, you cut the number of balls in half, and are left with 6 red balls, and 6 balls picked. Your next pick must be a red ball, making 7 picks.
PLEASE HELP!!!
These dot plots show the ages in years) for a sample of two types of fish.
Explanation:
The median is the center of the distribution. We see that the center of the shark's distribution is to the left compared to the koi's center. Therefore, the shark's median age is smaller. Choice A is one of the answers.
The spread is exactly what it sounds like: how spread out the data is. Mathematically we use the standard deviation, or sometimes the range, to find out how spread out things are. The koi distribution is more spread out. The shark's data is more clumped together. This is why choice B is the other answer.
Center: Sharks have lower median age than Koi.
Spreads: The ages of koi are more spread out.
What is dot plot?A dot plot is a standardized way of displaying the distribution of data based on a five number summary.
What is the median in a dot plot?The center line in the dot plot shows the median for the data .
What is the spread of data?Spread of data is measured in terms how far the data differs from the mean.
According to the given question
We have a dot plots for the two fishes sharks and Koi.
According to the given dot plot
Most ages of the sharks is lower than the koi.
⇒ Sharks are lower than koi.
So, the center: Sharks have lower median age than Koi.
Also, the ages of Koi are wide spreading.
⇒ The ages of koi are more spread out
Therefore, Spreads: The ages of koi are more spread out.
Hence, option A and B are correct.
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Three students used factoring to solve a quadratic equation? The equation was solve correctly by ______.The solutions of the equation are__________.
Answer:Keith
x=5,x=12
Step-by-step explanation:
Answer:
the answers are keith and -5,-12
Step-by-step explanation:
I just took the test and got a 5/5 the other person is incorrect.
Points A(-l, y) and B(5,7) lie on a circle with centre 0(2, -3y). Find the values of y. Hence, find the radius of the circle
Answer:
The answer is below
Step-by-step explanation:
Points A(-l, y) and B(5,7) lie on a circle with centre O(2, -3y). This means that AB is the diameter of the circle and OA = OB = radius.
For two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]), the coordinates of the midpoint (x, y) between the two points is given as:
[tex]x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}[/tex].
For A(-l, y) and B(5,7) with center O(2, -3y), the value of y can be gotten by:
[tex]For\ x\ coordinate:\\2=\frac{-1+5}{2}\\ 2=2.\\For\ y\ coordinate:\\-3y=\frac{y+7}{2}\\ -6y=y+7.\\-6y-y=7\\-7y=y\\y=-1[/tex]
The value of y is -1. Therefore A is at (-1, -1) and O is at (2, -3(-1))= (2, 3)
The radius of the circle = OA. The distance between two points X([tex]x_1,y_1[/tex]) and Y([tex]x_2, y_2[/tex]) is given as:
[tex]|OX|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\Therefore\ the\ radius \ |OA|\ is :\\|OA|=\sqrt{(2-(-1))^2+(3-(-1))^2}=\sqrt{25}=5[/tex]
The radius of the circle is 5 units
Instructions: Find the Measure of the indicated angle to the
nearest degree.
Answer:
? = 35
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan ? = opp /adj
tan ? = 33/48
Take the inverse tan of each side
tan ^ -1 ( tan ? ) = tan ^ -1 ( 33/48)
? =34.50852299
? = 35
The value 4 is a lower bound for the zeros of the function shown below.
f(x) = 4x^3 – 12x^2 – x + 15
A) True
B) False
Answer:
False roots are x = -1 or x = 5/2 or x = 3/2
Step-by-step explanation:
Solve for x:
4 x^3 - 12 x^2 - x + 15 = 0
The left hand side factors into a product with three terms:
(x + 1) (2 x - 5) (2 x - 3) = 0
Split into three equations:
x + 1 = 0 or 2 x - 5 = 0 or 2 x - 3 = 0
Subtract 1 from both sides:
x = -1 or 2 x - 5 = 0 or 2 x - 3 = 0
Add 5 to both sides:
x = -1 or 2 x = 5 or 2 x - 3 = 0
Divide both sides by 2:
x = -1 or x = 5/2 or 2 x - 3 = 0
Add 3 to both sides:
x = -1 or x = 5/2 or 2 x = 3
Divide both sides by 2:
Answer: x = -1 or x = 5/2 or x = 3/2
Answer:
False
Step-by-step explanation:
f(x) = 4x³ - 12x² - x + 15
Set output to 0.
Factor the function.
0 = (x + 1)(2x - 3)(2x - 5)
Set factors equal to 0.
x + 1 = 0
x = -1
2x - 3 = 0
2x = 3
x = 3/2
2x - 5 = 0
2x = 5
x = 5/2
4 is not a lower bound for the zeros of the function.
A recent national survey found that high school students watched an average (mean) of 7.8 movies per month with a population standard deviation of 0.5. The distribution of number of movies watched per month follows the normal distribution. A random sample of 30 college students revealed that the mean number of movies watched last month was 7.3. At the 0.05 significance level, can we conclude that college
Answer:
Step-by-step explanation:
Given that :
Mean = 7.8
Standard deviation = 0.5
sample size = 30
Sample mean = 7.3 5.4772
The null and the alternative hypothesis is as follows;
[tex]\mathbf{ H_o: \mu \geq 7.8}[/tex]
[tex]\mathbf{ H_1: \mu < 7.8}[/tex]
The test statistics can be computed as :
[tex]z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{7.3- 7.8}{\dfrac{0.5}{\sqrt{30}}}[/tex]
[tex]z = \dfrac{-0.5}{\dfrac{0.5}{5.4772}}[/tex]
[tex]z = - 5.4772[/tex]
The p-value at 0.05 significance level is:
p-value = 1- P( Z < -5.4772)
p value = 0.00001
Decision Rule:
The decision rule is to reject the null hypothesis if p value is less than 0.05
Conclusion:
At the 0.05 significance level, there is sufficient information to reject the null hypothesis. Therefore ,we conclude that college students watch fewer movies a month than high school students.
The FDA recommends that Americans get on average 3,000mg of salt in their daily diet. Suppose that you are interested in testing if Americans' average daily intake is different from 3,000mg. What is the correct null and alternative hypothesis statements?
Answer:
Null hypothesis; H0: μ = 3000
Alternative Hypothesis; Ha: μ ≠ 3000
Step-by-step explanation:
We are told that the FDA recommends that Americans get on average 3,000mg of salt in their daily diet.
Now we want to test this claim of whether Americans truly get an average of 3,000mg of salt in their daily diet.
Thus, the hypotheses is as follows;
Null hypothesis; H0: μ = 3000
Alternative Hypothesis; Ha: μ ≠ 3000
Null hypothesis; H0: μ = 3000
Alternative Hypothesis; Ha: μ ≠ 3000
Calculation of the null and alternative hypothesis:Since
The FDA recommends that Americans get on average 3,000mg of salt in their daily diet.
So, here the hypothesis be like
Null hypothesis; H0: μ = 3000
Alternative Hypothesis; Ha: μ ≠ 3000
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Find each product.
(5-x2+2)(-3)
PLEASE HELP!!! ASAP!!!
Answer:
[tex]3x^2 - 21[/tex] (did you mean for the equation to be [tex](5 - x^2 + 2) \cdot -3[/tex]?)
Step-by-step explanation:
Multiplying -3 by each term:
[tex]-3 \cdot 5 = -15[/tex]
[tex]-x^2 \cdot -3 = 3x^2[/tex]
[tex]-3 \cdot 2 = -6[/tex]
[tex]-15-6 = -21[/tex]
So the equation comes out to [tex]3x^2 - 21[/tex] .
Hope this helped!
In the figure, ABC is mapped onto XYZ by a 180° rotation. Angle B corresponds to which angle in XYZ?
Answer:
x
Step-by-step explanation:
Factor the polynomial.
X2+3x-54
Answer:
[tex] \mathrm{(x + 9)(x - 6)}[/tex]Step-by-step explanation:
[tex] {x}^{2} + 3x - 54[/tex]
Write 3x as a difference
[tex] {x}^{2} + 9x - 6x - 54[/tex]
Factor out x from the expression
[tex]x(x + 9) - 6x - 54[/tex]
Factor out -6 from the expression
[tex]x(x + 9) - 6(x + 9)[/tex]
Factor out x+9 from the expression
[tex](x + 9)(x - 6)[/tex]
Hope I helped!
Best regards!
Answer: (x + 9)(x - 6)
Step-by-step explanation:
x² + 3x - 54 Find 2 numbers whose product is -54 and sum is +3
∧
-1 + 54
-2 + 27
-3 + 18
-6 + 9 = +3 This works!
Place those digits in the parentheses and it is now factored.
(x - 6)(x + 9)
The revenue of selling a new video game is modeled by the equation can be modeled by the equation f(x)=-3x^2 + 21x + 54 where x is the price of the game and y is the revenue. Find the price of the game, x, that would result in no revenue.
Answer:
x = 9Step-by-step explanation:
Given the revenue of selling a new video game modeled by the equation f(x)=-3x² + 21x + 54 where x is the price of the game and y is the revenue, to calculate the price of game x that would result in no revenue, we will set the revenue f(x) to be zero and then solve the resultinf equation.
at f(x) = 0;
0 = -3x² + 21x + 54
0 = -x² + 7x + 18
Multiplying through by minus sign
x² - 7x - 18 = 0
Factorizing the resulting expression;
x² - 9x+2x - 18 = 0
(x² - 9x)+(2x - 18) = 0
x(x-9)+2(x-9) = 0
(x-9)(x+2) = 0
x-9 = 0 and x+2 = 0
x = 9 and -2
Neglecting the negaive value of x;
x = 9
Hence, the price of the game, x, that would result in no revenue is 9.
Please help find these angle for me plz!
Answer:
<DEF = 40°<EBF = <EDF = 56°<DCF = <DEF =40°<CAB = 84°Step-by-step explanation:
In triangle DEF, we have:
Given:
<EDF=56°
<EFD=84°
So, <DEF =180° - 56° - 84° =40° (sum of triangle angles is 180°)
____________
DE is a midsegment of triangle ACB
( since CD=DA(given)=>D is midpoint of [CD]
and BE = EA => E midpoint of [BA] )
According to midsegment Theorem,
. (DE) // (CB) "//"means parallel
. DE = CB/2 = FB =CF
___________
DEBF is a parm /parallelogram.
Proof: (DE) // (FB) [(DE) // (CB)]
AND DE = FB
Then, <EBF = <EDF = 56°
___________
DEFC is parm.
Proof: (DE) // (CF) [(DE) // (CB)]
And DE = CF
Therefore, <DCF = <DEF =40°
___________
In triangle ACB, we have:
<CAB =180 - <ACB - <ABC =180° - 40° - 56° =84° (sum of triangle angles is 180°)
[tex]HOPE \: THIS \: HELPS.. GOOD \: LUCK![/tex]