Part A
Use the FOIL rule to expand out the expression below
(2x+7)(5x+9)
2x*5x + 2x*9 + 7*5x + 7*9
10x^2 + 18x + 35x + 63
10x^2 + 53x + 63 is the final answer for part A
==========================================================
Part B
The degree is 2. This is a quadratic trinomial.
The degree is simply the largest exponent after expanding everything out. The degree directly determines the type of polynomial. Since the degree is 2, we have a quadratic. The polynomial is a trinomial because it has 3 terms.
==========================================================
Part C
Imagine we had a machine in which we deposit 2 coins into it. One would happen on either side. After the coins are deposited, a third coin pops out. The 2 coins going in and the third coin coming out are the same currency. This represents an example of closure.
In mathematics, the idea of closure is taking any two objects of the same type, applying an operation on them, and getting the same type of object as the input.
For example, we could take two whole numbers and multiply them together. The result is always a whole number. The set of whole numbers is closed under multiplication because you can't leave the set (hence the gate is closed not letting anything out).
Similarly, taking any two polynomials and multiplying them together will always lead to some other polynomial. Part A shows this in action because (2x+7), (5x+9) and 10x^2 + 53x + 63 are all polynomials.
[tex]\rm 10x^{2} + 53x + 63[/tex] is the expression that represents the area of the rectangle. This is a trinomial expression.
What is a quadratic equation?A quadratic equation is the polynomial of second degree in one variable only. The standard form of a quadratic equation is [tex]\rm ax^{2} +bx+c=0[/tex]
Where, x is the variable and a,b, and c are real numbers.
Part A
Let length of a rectangle = (2x+7)
Let width of a rectangle = (5x+9)
The area of the rectangle = length × width
= (2x+7)(5x+9)
= 2x × 5x + 2x × 9 + 7 × 5x + 7 × 9
= [tex]\rm 10x^{2} + 18x + 35x + 63[/tex]
Therefore, [tex]\rm 10x^{2} + 53x + 63[/tex] is the expression that represents the area of the rectangle.
Part B
The degree is 2 in the expression. This is a trinomial expression.
The degree is simply the largest exponent. The degree directly represents the type of polynomial. Since the degree is 2. The polynomial is a trinomial because it has 3 terms.
Part C
Applying multiplication operations such that taking any two polynomials and multiplying them together will always lead to some other polynomial. Part A shows this multiplication because (2x+7), (5x+9) and [tex]\rm 10x^{2} + 53x + 63[/tex] are all polynomials.
Learn more about quadratic equations;
https://brainly.com/question/2263981
what two numbers that multiply to 20 and add to 9
Answer:
4 and 5
Step-by-step explanation:
4+5=9
4*5=20
Answer:
5 an 4
Step-by-step explanation:
If you add 5+4 you get 9
And if you multiple 5×4 you get 20
can you help me with these problems i need them ASAP!!!!!!
Answer:look it up on quizlet its easier
Step-by-step explanation:
If you were to pick one day of the year at random, is it more likely that the day would be a Tuesday or that the day would fall during the month of January?
Answer and explain in your own words why you chose what you chose.
Answer: It's more likely it's a Tuesday
========================================================
Explanation:
The odds of it being a Tuesday is 1/7 since there's 1 day of the week that's Tuesday out of 7 total.
The odds of it being January is 1/12 because we have 1 month we want out of 12 total.
Now the question is: which fraction is larger?
For now, assume they are equal. We'll cross multiply like so
1/7 = 1/12
1*12 = 7*1
12 = 7
We get a false statement at the end, but we can fix things by replacing the equal sign with a greater than sign to get this new set of steps
1/7 > 1/12
1*12 > 7*1
12 > 7
which leads us to a true statement. Therefore, 1/7 is the larger fraction and the more likely event.
-----------------
Alternatively, you can use your calculator to find that:
1/7 = 0.143 approximately1/12 = 0.083 approximatelyThen for each decimal, move the decimal point 3 spots to the right. The values 0.143 and 0.083 become 143 and 83 respectively. We can see that 143 is larger, which means 0.143 is larger, and lastly 1/7 is larger. Think of it like a chain.
what is the ordered pair for 90 degrees on a unit circle
Calculate the value of c in the following square using the information given.
с
W.
Х
10.6 cm
b
Z
0
c = 15 cm
c = 16 cm
c = 17 cm
O c = 18 cm
9514 1404 393
Answer:
c = 15 cm
Step-by-step explanation:
The congruent diagonals are perpendicular bisectors of each other, so ∆WVX is an isosceles right triangle. The length of c is √2 times the length WV, so is ...
c = (√2)(10.6 cm) ≈ 15.0 cm
the area of a circle is 100 square miles. What is the diameter?
Answer:
The diameter of a circle with an area of 100 square miles is 20/√π miles.
Step-by-step explanation:
Area =100 = πr^2.
diameter = d = 2r.
100 = πr^2.
100/π = r^2.
√(100/π) = r.
10/√π = r.
d = 2r.
d = 2 * 10/√π.
d = 20/√π
A 50 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jack
grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the
side of the house will the ladder reach now? (The answer is not 44 ft.) Round to the
nearest tenth of a foot.
1.4 feet
let me know if you get it right hope i helped!
Answer:
14
Step-by-step explanation:
a2+(48)2=
502\,\,50^{2}502
Use the Pythagorean Theorem.
a2+2304=a^{2}+2304=a2+2304=
2500\,\,25002500
Simplify.
−2304-2304\phantom{=}−2304=
−2304\,\,-2304−2304
Subtract 2304 from both sides.
a2=a^{2}=a2=
196\,\,196196
a2=\sqrt{a^{2}}=a2
=
±196\,\,\pm\sqrt{196}±196
Square root both sides.
a=a=a=
14\,\,1414
Simplify. Ignore negative root, as length must be positive.
Identify an equation of a line in slope-intercept form that passes through (1, 2) with a slope of -8
Answer:
y = -8x + 10
Step-by-step explanation:
y = -8x + b
2 = -8(1) + b
2 = -8 + b
10 = b
9514 1404 393
Answer:
y = -8x +10
Step-by-step explanation:
The y-intercept can be found from the equation ...
b = y -mx
Using the given point and slope, this is ...
b = 2 -(-8)(1) = 10
Then the slope-intercept equation is ...
y = mx +b
y = -8x +10
help now
options on second pic
Answer:
D. -8√70 + 7√2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Simplifying radicalsStep-by-step explanation:
Step 1: Define
Identify
√7(-8√10 + √14)
Step 2: Simplify
[Distributive Property] Distribute √7: -8√70 + √98Reduce: -8√70 + 7√2Which of the following is equivalent to 3 cm??
A.
B.
6 mm2
30 mm
90 mm-
300 mm
C.
D.
Answer:
30mm
Step-by-step explanation:
Find the length of the third side. If necessary, round to the nearest tenth 10 20
if only i knew I would love to help you sorry
please answer its due tomorrow ill give brainiest no links or scam
Answer:
4: 1 2/3
5. 5/21 b. 1/4 c. 11/18 d. 3/20
6. 11/12 b. 10/12 < 11/12
7. 4/45
Step-by-step explanation:
4. 1/3 times 5
6. just add
7. 1/5 minus 1/9
Answer:
hey this is my alt acount im doing this so i can give brainiest
Step-by-step explanation:
Choose all points that lie on a circle with Center (2, -3) and diameter 10 units.
Answer:
the points that lie on a circle is (2,2) and (5,-7)
-\frac{1}{10}-x^3+x^4+3x
−
10
1
−x
3
+x
4
+3x
Answer:
Its really simple
Step-by-step explanation:
first you take the 10 then turn it into joe then mama
Answer:
-1/10 - 1x^3 + x^4 + 3x
Step-by-step explanation:
negative one tenth minus 1x exponet 3 plus x exponent 4 plus 3x
find the unique permutations of the letters of the word : CEASELESS
Answer:
There are 2,520 unique permutations.
Step-by-step explanation:
When we have a set of N different elements, the total number of permutations is given by:
P = N! = N*(N - 1)*(N - 2)*...*(2)*(1)
Particularly, if out of these N elements, there are a given element that is repeated K times, then the permutations of these K elements actually do not add new unique permutations, then in that case the total number of unique permutations is:
P = N!/K!
And if we have another element that is repeated L times, then with the same reasoning than above, the total number of unique permutations is:
P = N!/(K!*L!)
Now, we have the set:
{C, E, A, S, E, L, E, S, S}
So we have a set of 9 letters, then:
N = 9
And, the letter S is repeated 3 times
The letter E is repeated 3 times
Then, using the above notation, we can define:
K = 3
L = 3
The total number of permutations is then:
[tex]P = \frac{9!}{3!*3!} = \frac{9*8*7*6*5*4*3*2*1}{3*2*1*3*2*1} = \frac{9*8*7*6*5*4}{3*2*1} = 2,520[/tex]
So there are 2,520 unique permutations.
Find value of x
A.)46
B.)80
C.)15
D.) 26
The two angles are supplementary angles, which when added together equal 180 degrees.
6x -10 + 6x +10 = 180
Combine like terms:
12x = 180
Divide both sides by 12:
x = 180/12
x = 15
The answer is C) 15
Suppose you want to save $1000 for a down payment on your first car purchase. You have $750 right now. You invest it in an account that pays %5 annually. How many years will it take until you have enough for your down payment.
Answer:
6 years
Step-by-step explanation:
750+5%=787.5 (repeat add 5% to the sum of the previous till you reach 1000)
!!!REMEMBER TO GIVE BRAINLIEST IF THIS HELPED!!!Given y = 3x + 1 State the quadrants in which this graph is in. (Use the numbers 1-4)
The graph of y = 3x + 1 lies in quadrants I and III. The graph of the equation y = 3x + 1 is a straight line with a positive slope.
To determine the quadrants in which the graph lies, we need to analyze the signs of the x and y coordinates in different regions of the coordinate plane.
Quadrant I: In this quadrant, both the x and y coordinates are positive. When we substitute positive values for x into the equation, we obtain positive values for y. Since the slope is positive, the line rises as we move from left to right. Therefore, the graph lies in quadrant I, where both x and y are positive.
Quadrant III: In this quadrant, the x coordinate is negative, while the y coordinate is positive. If we substitute negative values for x into the equation, we still obtain positive values for y. The positive slope ensures that the line rises from right to left. Hence, the graph also lies in quadrant III.
The graph does not pass through quadrants II and IV because the signs of the coordinates do not align with the equation. In quadrant II, the x coordinate is negative, but the y coordinate is negative as well. In quadrant IV, both the x and y coordinates are positive, which contradicts the equation. Therefore, the graph of y = 3x + 1 is confined to quadrants I and III.
For more questions on quadrants
https://brainly.com/question/1548800
#SPJ8
DO IT ASAP! Thank you very much!
Answer:
a = 5
Step-by-step explanation:
According to the factor theorem, if x + 2 is a factor, then by dividing the polynomial by the binomial, we are meant not to have a remainder
In this case, the remainder would be zero
So, if we set the binomial equals zero and substitute the x-value into the polynomial, we are supposed to have 0
So we have this as;
x + 2 = 0
x = -2
-2^3 -2(-2)^2 -2(a) + 6 = 0
-8-8-2a + 6 = 0
-16 + 2a + 6 = 0
2a -10 = 0
2a = 10
a = 10/2
a = 5
You have 90 degree triangle and the adjacent is 24, the opposite is 32, and the hypotenuse is 40. What is the value of tan W rounded to the nearest hundredth, if necessary.
Answer:
sorry need points Step-by-step explanation:
sorry need points sorry need points
What is an equation of the line that passes through the points
(
0
,
−
4
)
(0,−4) and
(
−
4
,
6
)
(−4,6)?
Answer:
[tex]y=-\frac{5}{2}x-4[/tex]
Step-by-step explanation:
[tex]slope=\frac{6-(-4)}{-4-0}=\frac{10}{-4}=-\frac{5}{2}[/tex]
[tex]y-6=-\frac{5}{2}[x-(-4)] \\\\y-6=-\frac{5}{2} (x+4)\\\\y-6=-\frac{5}{2}x -10\\\\y=-\frac{5}{2}x-4[/tex]
Jake buys an oven and discovers that its temperature can vary out to 2.5 Fahrenheit from his settings. If Jake set the temperature to 345 Fahrenheit to bake a cake, from an inequality to represent the possible temperatures of the oven, tea, and degrees Fahrenheit. Then determine the range of possible temperatures when the oven is set at 345 Fahrenheit. Select a correct any quality and range on the table
Answer:
Answer in the image
If 8n = -40, then n =
Answer:
n=-5
Step-by-step explanation:
Answer:
Step-by-step explanation:
8n=-40
n=-40/8
n=-5
Given complex numbers z^1= 12 + 6i and 2=-8+ 2i, find z^1+ z^2.
a.20 +4i
b.-4+4i
c. 10 - 2i
d. 4+8i
Answer:
answer is a 20+4i
Step-by-step explanation:
what is the answer help me pls ASAP
What is the surface area of this right cone?
Answer:
Step-by-step explanation:
Slant height s = 12
Radius r = 8
Lateral area of cone = πrs = 96π units²
Base area of cone = πr² 64π units²
Surface area = 96π + 64π = 160π units²
Find (from (3)
f(x) = x^2 - x
Answer:
I think the answer is 6.......
Find the area of this circle. Use 3.14 for . 84in
Answer:
22155.84 in
Step-by-step explanation:
r = 84 in
π = 3.14
then area if circle = r² × π
… A = 84² × π = 22155.84 = ( 22.15584 min )
Question I need to Answer: How many beats can a heart pound in 20 minutes?
Answer:
1300
Step-by-step explanation:
4 times 5 = 20
260 times 5 = 1300
Answer:
1300 times
Step-by-step explanation:
195 is is 3 X 65 so dividing 195 by 3 gets you 65
65 X 20 = 1300
Which is the domain of the function f(x) =
12
- 2?
Vx+4
O A. x20
O
B. x>-4
o
C. x>-2
D. x>-4
E. all real numbers
The domain of the function is x> -4.
The correct option is B.
We have the function
f(x) = 12/ √(x+ 4) - 2
Now, putting f(x) = 0
12/ √(x+ 4) - 2 = 0
12 - 2√(x+ 4) = 0
-2√(x+ 4) = -12
√(x+ 4) = 6
Taking Square on both side we get
x+ 4 = ±36
x = ± 36 - 4
x = 32 or x= -40
Thus, the domain of the function is x> -4.
Learn more about Function here:
https://brainly.com/question/12431044
#SPJ7
