You can eliminate fractions by multiplying the whole thing by 7.
... -x +28 ≥ 21x
Now, add x to get all x-terms on the right. Then, divide by the coefficient of x.
... 28 ≥ 22x
... 28/22 ≥ x
This fraction can be reduced, so we have ...
... A. x ≤ 14/11
Write the equation of a line that is perpendicular to x = 3 and that passes through the point ( 0 , − 4 )
We have to write the equation of a line that is perpendicular to the line [tex]x=3[/tex] and that passes through the point [tex](0,-4)[/tex].
The general equation of a line in the slope-intercept form is given by:
[tex]y=mx+b[/tex]
Where, 'm' is the slope and 'b' is the y-intercept.
Now, we need to find the slope first,
The required line is perpendicular to the line [tex]x=3[/tex]. Slope of the line [tex]x=3[/tex] is undefined. A line perpendicular to that must have slope of '0'. That implies, our required line is parallel to the x-axis.
Therefore, m=0
Now that line is passing through the point [tex](0, -4)[/tex].
We can plug in the points to the find the value of y-intercept. After plugging the values, we get:
[tex]y=0 \times 0+(-4)=-4[/tex]
Hence, the equation of the required line is [tex]y=-4[/tex].
find the following
f(x)=x^2 - 4x - 12
A) f(a+2)
B) f(a+h)
(A) f(a + 2) = a² - 16
substitute x = a + 2 into f(x)
f(a + 2) = (a + 2)² - 4(a + 2) - 12
= a² + 4a + 4 - 4a - 8 - 12
= a² - 16
(B ) f(a + h) = a² + 2ah + h² - 4a - 4h - 12
substitute x = a + h into f(x)
f(a + h) = a² + 2ah + h² - 4a - 4h - 12
What is the remainder of (x 3 + 5x 2 − 32x − 7) ÷ (x +3)
What is the decimal equivalent of -11/9
In ∆ABC, the altitudes from vertex B and C intersect at point M, so that BM = CM. Prove that ∆ABC is isosceles.
Answer:
Given: ∆ABC with the altitudes from vertex B and C intersect at point M, so that BM = CM.
To prove:∆ABC is isosceles
Proof:-Let the altitudes from vertex B intersects AB at D and from C intersects AC at E( with reference to the figure)
Consider ΔBMC where BM=MC
Then ∠CBM=∠MCB......(1)(Angles opposite to equal sides of a triangle are equal)
Now Consider ΔDMB and ΔCME
∠D=∠E.......(each 90°)
BM=MC...............(given)
∠CME=∠BMD........(vertically opposite angles)
So by ASA congruency criteria
ΔDMB ≅ ΔCME
∴∠DBM=∠MCE........(2)(corresponding parts of a congruent triangle are equal)
Adding (1) and (2),we get
∠DBM+∠CBM=∠MCB+∠MCE
⇒∠DBC=∠BCE
⇒∠B=∠C⇒AB=AC(sides opposite to equal angles of a triangle are equal)⇒∆ABC is an isosceles triangle .
Answer:
m∠MBC = m∠MCB
by reason: Base Angles
Step-by-step explanation:
:)
The tables show the high and low temperatures in Chicago over a 15-day period. Which set of data has the greatest RANGE?
I would say the low I’m just guessing so get it checked
Answer:
the answer is C
Step-by-step explanation:
The low temperatures have the greater range. The range for the highs is 6, the range for the lows is 8.
there are 14 girls on the volleyball team if this represents 25% of the girls who tried out how many girls tried out for the volleyball team show work mark braniest
The answer would be 56 because 14X4 = 56
There were 56 girls who tried out for the volleyball team, found by dividing the number of girls on the team (14) by the percentage that made the team (25%), which equals 14 divided by 0.25.
Explanation:The question asks us to find the total number of girls who tried out for the volleyball team if 14 girls (making up 25% of those who tried) made the team. To calculate the total number of girls who tried out, we can set up the equation based on the percentage:
25% of total girls = 14
We can rewrite 25% as 0.25 in decimal form:
0.25 × total girls = 14
To find the total number of girls, we divide both sides of the equation by 0.25:
total girls = 14 ÷ 0.25
total girls = 56
Therefore, 56 girls tried out for the volleyball team.
What is the solution of the equation when solved over the complex numbers?
x^2+27=0
Thanks!
Try this option:
x²+27=0;
[tex](x+\sqrt{-27})(x- \sqrt{-27})=0; \ => \ \left[\begin{array}{ccc}x=3 \sqrt{3}i\\x=-3 \sqrt{3}i \end{array}\right[/tex]
x = ± 3i√3
given x² + 27 = 0 (subtract 27 from both sides )
x² = - 27 ( take the square root of both sides )
x = ±[tex]\sqrt{-27}[/tex] = ± √(9 × 3 × -1 ) ← (i = √-1 )
= ± (√9 × √3 ×√-1 ) = ±3i√3
What is the value of x?
Enter your answer in the box.
x =
PLEASEEE HELPP!!!!!!
Since the triangle is equilateral (you can tell by the tick on each side), all angles have the same measure as well.
The angles of a triangle sum up to 180 degress, so three equal angles must measure 60 degrees each.
So, in particular, we have
[tex] 7x+4 = 60 \iff 7x = 56 \iff x=8[/tex]
x = 8 and y = 6
ΔRST is an equilateral triangle
with all 3 sides equal in length and all 3 angles = 60°, hence
7x + 4 = 60 ( subtract 4 from both sides )
7x = 56 ( divide both sides by 7 )
x = 8
similarly
8y + 12 = 60 ( subtract 12 from both sides )
8y = 48 ( divide both sides by 8 )
y = 6
I need help with this!
Answer:
<L = 50 degrees
Step-by-step explanation:
B and C are given. There should be a one to one Correspondence. <A should = <L
Since there are 180o in any triangle
<L = <A = 180 - 35 - 95
<L = <A = 50 degrees
Use the given information to find the lengths of the other two sides of the right triangle if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
cos(B) = 4/5, a = 8
SOH CAH TOA tells you
... cos(B) = a/c
... 4/5 = 8/c
... c = 10 . . . . . multiply by 5c/4
By the Pythagorean theorem,
... b = √c² -a²) = √(10² -8²) = √36 = 6
The lengths of the other two sides are: b = 6, c = 10.
_____
You can tell from the value of the cosine that this is a 3-4-5 right triangle. You can tell from the value of "a" that the scale factor is 2. That means the other two sides are 6 and 10.
To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem and the cosine function. Side a is given as 8 and the cosine of angle B is given as 4/5. Using the cosine function, we can find the length of side b. Then, using the Pythagorean theorem, we can find the length of side c. The lengths of the other two sides are approximately 6.4 and 10.24, respectively.
Explanation:To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we are given that side a is opposite angle A and has a length of 8, and we are given the cosine of angle B, which is 4/5. We can use the cosine function to find the length of side b, and then use the Pythagorean theorem to find the length of side c.
Step 1: Use the cosine function to find the length of side b:
cos(B) = 4/5
b/a = cos(B)
b/8 = 4/5
b = (4/5) * 8
b = 32/5
b = 6.4
Step 2: Use the Pythagorean theorem to find the length of side c:
a² + b² = c²
8² + 6.4² = c²
64 + 40.96 = c²
104.96 = c²
c = √104.96
c ≈ 10.24
Therefore, the lengths of the other two sides of the right triangle are approximately 6.4 and 10.24, respectively.
*EASY POINTS!*
How many times larger is 6 × 10^10 than 2 × 10^-3?
(Its an exponent question!)
If you need to, you can write and solve an equation for the factor you seek.
... 6×10^10 = factor × 2×10^-3
Divide by 2×10^-3 to find the value of the factor:
... (6×10^10)/(2×10^-3) = factor
... factor = (6/2)×10^(10-(-3))
... factor = 3×10^13
The first number is 3×10^13 times the second number.
_____
An exponent signifies repeated multiplication.
... 10×10×10 = 10³
Just as you cancel common factors when you do division, you can subtract exponents.
[tex]\dfrac{10\cdot 10\cdot 10}{10\cdot 10}=\dfrac{10}{1}=10\\\\\dfrac{10^3}{10^2}=10^{3-2}=10^1=10[/tex]
The same process works regardless of the signs of the exponents. When multiplying, we add exponents; when dividing we subtract the exponent of the denominator.
what is the equation in point-slope form of the line that passes through the point (1,-2) and has a slope of 3?
point slope form
y-y1 = m (x-x1)
y- (-2) = 3(x-1)
y+2 = 3(x-1)
y + 2 = 3(x - 1)
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 = 3 and (a, b) = (1, - 2), hence
y + 2 = 3(x- 1) ← in point-slope form
Write an equation of the line passing through each of the following pairs of points. c (5, 6), (3, 4)
The point-slope form of a line:
[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (5, 6) and (3, 4). Substitute:
[tex]m=\dfrac{4-6}{3-5}=\dfrac{-2}{-2}=1\\\\y-6=1(x-5)\\\\y-6=x-5\qquad|\text{add 6 to both sides}\\\\y=x+1\qquad|\text{subtract x from both sides}\\\\-x+y=1\qquad|\text{change the signs}\\\\x-y=-1[/tex]
Answer:
slope-intercept form: y = x + 1
point-slope form: y - 6 = 1(x - 5)
standard form: x - y = -1
Hey there!
Given points:
...(5,6) and (3,4)
Slope-intercept form:
... y=mx+b
'm' is the slope and 'b' is the y-intercept.
Slope:
... (y₂-y₁)/(x₂-x₁)
... (4-6)/(3-5)
... -2/-2
...1
:
... y = x + b
... 4 = 3 + b
... b = 1
Slope-intercept form:
... y = x + 1
Hope helps!
A movie theater charges $5 per ticket and averages 300 customers each night. If prices are raised to $7 per ticket, the theater estimates that average nightly ticket sales will be $1,750. What is the percentage change in the average number of customers the theater has each night? (Express your answer in whole numbers; round decimals up or down).
Attendance with the higher ticket price is ...
... $1750/$7 = 250
So the percentage change in attendance is ...
... change = (new - original)/original × 100%
... = (250 -300)/300 × 100% = -1/6×100% ≈ -17%
Final answer:
The percentage change in the average number of customers after the movie theater raises ticket prices is approximately -17%.
Explanation:
The movie theater originally charges $5 per ticket and has an average of 300 customers each night. After raising the price to $7, the average nightly ticket sales amount to $1,750. To find the new number of customers, divide the total sales by the price per ticket: $1,750 / $7 = 250 customers.
The change in the number of customers is the new amount minus the original amount, which is 250 - 300 = -50. To find the percentage change, divide the change by the original amount and multiply by 100: (-50 / 300) x 100 = -16.67%. After rounding the decimal, the percentage change is approximately -17%.
An object dropped from a height of 600 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t) = 600 − 16t 2 . Express t as a function of height h, and find the time to reach a height of 400 feet.
given h = 600 - 16t ( add 16t to both sides )
16t + h = 600 ( subtract h from both sides )
16t = 600 - h ( divide both sides by 16 )
t = [tex]\frac{600-h}{16}[/tex]
when h = 400
t = [tex]\frac{600-400}{16}[/tex] = [tex]\frac{200}{16}[/tex] = 12.5 seconds
Answer:
The required time is 3.54 seconds approximately or [tex]\frac{5}{2}\sqrt{2}[/tex] seconds.
Step-by-step explanation:
Consider the provided function.
[tex]h(t) = 600-16t^2[/tex]
Where t represents the time in seconds and h represents the height.
It is given that we need to find the time to reach a height of 400 feet.
Substitute h(t)=400 in the above function.
[tex]400= 600-16t^2[/tex]
[tex]400- 600=-16t^2[/tex]
[tex]-200=-16t^2[/tex]
[tex]200=16t^2[/tex]
[tex]\frac{50}{4}=t^2[/tex]
[tex]t=\sqrt{\frac{50}{4}} \\t=\frac{5}{2}\sqrt{2}[/tex]
Neglect the negative value as time should be a positive number.
Or
[tex]t\approx 3.54[/tex]
Hence, the required time is 3.54 seconds approximately.
What is the value of cosA ?
Answer:
cos(A) = 24/25 = 0.96
Step-by-step explanation:
SOH CAH TOA tells you that ...
... cos(A) = AB/AC
We are given AB = 24, but we must calculate AC using the Pythagorean theorem.
... AC² = AB² + BC²
... AC² = 24² + 7² = 576 + 49 = 625
... AC = √625 = 25
Now, we have sufficient information to find cos(A):
... cos(A) = 24/25 = 0.96
The value of cosA is used in trigonometry and physics to calculate the horizontal component of vectors or the angle of right triangles. For example, if we have a vector A, at an angle θ, then Ax = A cos θ, where Ax is the horizontal component of the vector. So in this way, cosA provides a crucial part in vector calculations.
Explanation:The value of cosA refers to the cosine of angle A. In trigonometry, this is often used in the context of right triangles or in the calculation of vectors. For example, if you have a vector A and an angle θ (theta), the horizontal component of that vector can be found by multiplying the magnitude of the vector (Ax) by cos(θ). This is often denoted as Ax = A cos θ.
To use an example, let's say we have a vector A with a magnitude of 10.3 blocks and an angle of 29.1° from the x-axis. We can find the x-component (Ax) of that vector by calculating (10.3 blocks) * cos(29.1°), which gives us a value of approximately 9.0 blocks.
Therefore, the value of cosA in this context would be used to provide a component part of a vector based on an associated angle.
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Manuel's bus ride to school is 9/10 of a mile and Jessica's bus ride is 3/10 of a mile. How much longer is Manuel's bus ride than Jessica's?
A)
6
0
of a mile
Eliminate
B)
12
0
of a mile
C)
6
10
of a mile
D)
12
20
of a mile
The answer us C. 9/10 minus 3/10 is 6/10 simplified to 3/5 if you need it.
I need help with this problem please
In a video game, Gate 3 is open 40% of the time and Gate 4 is open 20% of the time. The chance of both gates being open at the same time is 15%. Draw a tree and Venn diagram (with probabilities labeled) to model the scenario. What is the P(Gate 3 and Gate 4 are both open)?
A.60%
B.15%
C.100%
D.0%
The answer to "What is the P(Gate 3 and Gate 4 are both open)?" is
B: 15%
It is because they state that the chance of both gates being open at the same time is 15% and that chance is indeed the probability.
A 12-foot ladder rests against a brick wall at angle of 60°. Which expression gives the value of x, the height on the brick wall where the ladder rests?
Using Pythagorean's Theorem we know that a^2 + b^2 = c^2
C is the length of the ladder, and we are given one of the sides, let's call that side b
_________
we have a^2 + b^2 = c^2, and a^2 = c^2 - b^2, so a = √ c^2 - b^2
_________ ______ ____
a = √12^2-3^2 = √ 144-9 = √ 135 = 11.61895
so the top of the ladder is 11.6 feet above the ground
here u go hope this helps
Answer:
12 sin60°
Remember SOHCAHTOA.
sinθ =
opposite
hypotenuse
sin60° =
x
12
x = 12 sin60°
The graph shows the distance Julian drives on a trip. What is Julian's speed?
Answer:
B. 80 km/h
Step-by-step explanation:
The graph is linear and goes through the origin, so distance is proportional to time, and the constant of proportionality is speed. The desired answer can be read from the point on the graph at time = 1 hour: 80 km.
Julian's speed is 80 kilometers per hour.
B
speed = [tex]\frac{distance}{time}[/tex]
From the graph the distance travelled = 480 Km
and time taken = 6 hours
speed = [tex]\frac{480}{6}[/tex] = 80 Km / hour
What part of 35 is 56? *not a percent* help pls
Expressed as a fraction 56 is 56/35 of 35. That fraction can be reduced, and expressed several ways.
56/35 = 8/5 = 1 3/5 = 1.6
56 is 1 3/5 of 35
56 is 1.6 times 35
Consider the enlargement of the pentagon.
Not drawn to scale
What is the value of x, rounded to the nearest tenth?
2.1 centimeters
3.3 centimeters
7.0 centimeters
15.0 centimeters
"Enlargement" here implies that the two pentagons are similar. Because of similarity, the following equation of ratios must be true: 7/15 = x/7. Then 15x=49, and x = 49/15 = 3.27 cm, approximately.
Rounded to the nearest tenth, that comes to 3.3 cm.
Answer:
B
Step-by-step explanation:
y=x+1
y=x^2-1
please help i don't understand
ANSWER
The solution is
[tex](x=1,y=2),(x=2,y=3)[/tex]
EXPLANATION
We have
[tex]y=x+1---(1)[/tex]
and
[tex]y=x^2-1---(2)[/tex]
Let us substitute equation (1) in to equation (2). This gives us,
[tex]x+1=x^2-1(2)[/tex]
We rewrite this as a quadratic equation as the highest degree is 2.
[tex]x^2-x-1-1=0[/tex]
This implies that
[tex]x^2-x-2=0[/tex]
we factor to obtain,
[tex]x^2+x-2x-2=0[/tex]
[tex]x(x-1)-2(x-1)=0[/tex]
[tex](x-1)(x-2)=0[/tex]
This means,
[tex](x-1)=0\:\: or\:\:(x-2)=0[/tex]
[tex]x=1\:\: or\:\:x=2[/tex]
We substitute this values into any of the above equations, preferably equation (1)
When, [tex]x=1[/tex], [tex]y=1+1=2[/tex]
When, [tex]x=2[/tex], [tex]y=2+1=3[/tex]
The solution is
[tex](1,2),(2,3)[/tex]
The cost of making 15 handbags is 1,615. The cost of making 27 handbags is 2,635. What is the cost per handbag ?
Assume that random guesses are made for 7 multiple-choice questions on a test with 2 choices for each question, so that there are nequals7 ...
Answer:
14
Step-by-step explanation:
Jessica is making gift baskets.each basket has 1 jarof salsa and 1 bag of tortilla chips.she buys the salsa in cases of 6 jars.she buy the tortilla chips in cases of 4 bags what is the least numbers of baskets Jessica can make
The least number of gift baskets Jessica can make, given that she has 6 jars of salsa and 4 bags of tortilla chips in each case, is 12. This is calculated by finding the Least Common Multiple of 6 and 4.
Explanation:Jessica is working with two different quantities: 6 jars of salsa in a case and 4 bags of tortilla chips in a case. In each gift basket, she places 1 jar of salsa and 1 bag of tortilla chips, meaning that she needs the same number of jars and bags for an even number of gift baskets.
Therefore, to find the least number of baskets she can make, we need to find the Least Common Multiple (LCM) of 6 and 4, which the smallest number that both numbers divide evenly into. The LCM of 6 and 4 is 12. Hence, the least number of gift baskets Jessica can make is 12.
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Given: △ABC, m∠A=60° , m∠C=45°, AB=8 Find: Perimeter of △ABC and the Area of △ABC
Try this solution (all the details are in the attached picture, answers are underlined with colour).
The perimeter of triangle of ABC is [tex]\boxed{28.73}[/tex] and the area of triangle ABC is [tex]\boxed{37.86}.[/tex]
Further explanation:
Given:
The measure of angle A is [tex]\angle A = {60^ \circ }.[/tex]
The measure of angle C is [tex]\angle C = {45^ \circ }.[/tex]
The length of side AB is [tex]AB = 8[/tex]
Calculation:
The sum of all angles of a triangle is [tex]{180^ \circ }.[/tex]
[tex]\begin{aligned}\angle A + \angle B + \angle C &= {180^ \circ }\\{60^ \circ } + \angle B + {45^ \circ } &= {180^ \circ }\\{105^ \circ } + \angle B &= {180^ \circ }\\\angle B&= {180^ \circ } - {105^ \circ }\\\angle B&= {75^ \circ }\\\end{aligned}[/tex]
The sine rule in triangle ABC can be expressed as,
[tex]\begin{aligned}\frac{{BC}}{{\sin {{60}^ \circ }}}&=\frac{8}{{\sin {{45}^ \circ }}}\\BC&=\frac{8}{{\frac{1}{{\sqrt2 }}}}\times\frac{{\sqrt 3 }}{2}\\BC&= 9.80\\\end{aligned}[/tex]
The length of AC can be calculated as follows,
[tex]\begin{aligned}\frac{{AB}}{{\sin {{45}^ \circ }}} &= \frac{{AC}}{{\sin {{75}^ \circ }}}\\\frac{8}{{\sin {{45}^ \circ }}} \times \sin {75^ \circ }&= AC\\10.93 &= AC\\\end{aligned}[/tex]
The perimeter of triangle ABC can be obtained as follows,
[tex]\begin{aligned}{\text{Perimeter}}&= AB + BC + AC\\&= 8 + 9.80 + 10.93\\&= 28.73\\\end{aligned}[/tex]
The area of triangle ABC can be obtained as follows,
[tex]\begin{aligned}{\text{Area}}&=\frac{1}{2} \times AB \times AC \times \sin \left( A \right)\\&= \frac{1}{2} \times 8 \times 10.93 \times \sin {60^ \circ }\\&= 4 \times 10.93 \times \frac{{\sqrt3 }}{2}\\&= 37.86\\\end{aligned}[/tex]
The perimeter of triangle of ABC is [tex]\boxed{28.73}[/tex] and the area of triangle ABC is [tex]\boxed{37.86}.[/tex]
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2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: angles, ABC, angle A=60 degree, perimeter, area of triangle, triangle ABC.
According to the synthetic division below, which of the following statements are true?
Check all that apply.
Answer:
Correct options are A and D
Step-by-step explanation:
According to the synthetic division in the diagram you can write down the result of division:
[tex]2x^2+9x-7=(x-(-6))(2x-3)+11,\\ \\2x^2+9x-7=(x+6)(2x-3)+11.[/tex]
Therefore,
when [tex]2x^2+9x-7[/tex] is divided by [tex]x+6,[/tex] the remainder is 11 (option D is correct). To find the remainder after division by [tex]x-6,[/tex] you have to use another synthetic division. Actually, [tex]2x^+9x-7=(x-6)(2x+21)+119,[/tex] then the remainder is 119 (option C is false).when [tex]x=-6,[/tex] the expression [tex]x+6[/tex] is [tex]-6+6=0[/tex] and [tex]2x^2+9x-7=0\cdot (2x-3)+11=11[/tex] (option A is correct). You cannot state the same when [tex]x=6[/tex] (option B is false).neither [tex]x-6[/tex] nor [tex]x+6[/tex] is a factor of [tex]2x^2+9x-7,[/tex] because the remainders in both cases are not equal to 0 (options E and F are false).When [tex]x= - 6,2{x^2} + 9x -7= 11[/tex] and when [tex]2{x^2} + 9x -7[/tex] is divided by [tex]\left( {x + 6} \right)[/tex], the remainder is 11.Option (A) is correct and option (D) is correct.
Further Explanation:
Given:
Explanation:
The synthetic division can be expressed as follows,
[tex]\begin{aligned}- 6\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,9\,\,\,\,\,\,\,\,\,\,\, - 7} \,}} \right. \hfill\\\,\,\,\,\,\,\underline {\,\,\,\,\,\,\,\, - 12\,\,\,\,\,\,\,\,\,\,\,\,18} \hfill\\\,\,\,\,\,\,\,\,2\,\,\,\,\,\, - 3\,\,\,\,\,\,\,\,\,\,\,\,11 \hfill \\\end{aligned}[/tex]
The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is 11. Therefore, the remainder of the synthetic division is 11.
When [tex]x= - 6, 2{x^2} + 9x -7= 11[/tex] and when [tex]2{x^2} + 9x -7[/tex] is divided by [tex]\left( {x + 6} \right)[/tex], the remainder is 11. Option (A) is correct and option (D) is correct.
Learn more:
Learn more about inverse of the functionhttps://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Synthetic Division
Keywords: division, factor (x+5), remainder 12, statements, true, apply, divided, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.