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;
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CAN SOMEONE HELP ME PLEASE
a store is having a sale where everyhting is 15% off. If Damien wants to buy an item that originally costs $50 how much will he save? What is his total cost?.
Answer:
35 because i had this problem before and the answer was 35 cuz yeah
C) {(0, 1), (2.1), (0.3) Function? Explain:
Is this a function or not
6. What is the 10th term of the geometric sequence -20, -10,-5, ... ?
Answer:
-0.0390625
Step-by-step explanation:
each is cut in half
so we do this
20, 10, 5, 2.5, 1.25, .625, .3125, .15625, 0.078125, 0.0390625
simplify and show your work
Answer
math way search it
Step-by-step explanation:
Simplify 5a + 5b - 6a + 8b
Answer:
-1a + 13b
Step-by-step explanation:
combine like terms and just be sure to change signs as needed
Step-by-step explanation:
-a+13b
colect like terms and solve
1
2
3
4
5
6
Which value of x will make the following statement false?
*<5.3
A. 16
B. 5.3
C. 0
D. -8.95
Answer:
A [and B]
Step-by-step explanation:
If x < 5.3 then anything higher than 5.3 makes the statement false.
16 is too high and therefore is the most obvious fallacy.
5.3 would actually make x=5.3 and therefore x wouldn't be less than 5.3 making it also false but this really depends on what your teacher is looking for.
0 is true.
-8.95 is true.
If there is any clarification in the problem you can provide I can give a more definite answer but now it is really a coinflip!
This is the question of 7 class opt math book. Write right answer.
Answer:
Step-by-step explanation:
x + 50 + 90 = 180
x + 140 = 180
x = 40 degrees
Find AB using the segment addition postulate.
Rotate triangle P 90° clockwise about the point (2, -1).
Please screenshot this and send me the answers cuz I really need help :(
Answer: (2,0), (2,1), and (6,1)
Step-by-step explanation: I just used the desmos graphing calculator to find the answer to your problem. I don't know any formulas to solve it so I just rotated the points by hand. I also made sure they were still equidistant from the point (2,-1) because if their distances from other points changed during the rotation, then the triangle would not be equal to the first triangle and the image would've been distorted.
I hope this helps! Have a nice day.
how would u get the solution to x/3 < -2
help me please [giving brainliest to best answer with step by step]
Hi there!
[tex]\large\boxed{3\text{ } \frac{3}{4} cm^3}[/tex]
Knowing that one cube has side-lengths of 1/2, we can calculate the dimensions for the prism:
Length: 1/2 × 5 = 2.5 cm
Height: 1/2 × 3 = 1.5 cm
Width: 1/2 × 2 = 1 cm
Use this formula to solve for the volume:
V = l × w × h
Thus:
V = 2.5 × 1.5 × 1 = 3.75 cm³
Convert to fraction:
75/100 = 3/4
Thus, the volume in mixed-numbers is 3 3/4 cm³.
what+js+the+sum+of+3(4v-1)+and+6(10+3v) when v = 8
Answer:
297
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
3(4v - 1) + 6(10 + 3v)
v = 8
Step 2: Evaluate
Substitute in v: 3(4(8) - 1) + 6(10 + 3(8))(Parenthesis) Multiply: 3(32 - 1) + 6(10 + 24)(Parenthesis) Subtract: 3(31) + 6(10 + 24)(Parenthesis) Add: 3(31) + 6(34)Multiply: 93 + 204Add: 297Acellus
Find the missing side of this right
triangle.
x
7
14
x= [?]
Enter the number that belongs in the green box.
Enter
Answer:
2 is the correct answer because 14 ÷7 is 2
Answer:
the answer in your question is √245
15.6524 ≈ 15.7
Step-by-step explanation:
[tex]x = \sqrt{{14}^{2} + {7}^{2} } \: = 15.6524 = 15.7[/tex]
i keep getting the wrong answer and have no idea what to do
Answer:
[C] 0
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFunctionsFunction NotationCalculus
Limits
Derivatives
Definition of a Derivative: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle\displaystyle g(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
[tex]\displaystyle f(x) = \frac{3}{5x^4 + 3}[/tex]
[tex]\displaystyle g(0)[/tex]
Step 2: Differentiate
Substitute in x [Function g(x)]: [tex]\displaystyle\displaystyle g(0) = \lim_{h \to 0} \frac{f(0 + h) - f(0)}{h}[/tex]Substitute in function f(x) [Function g(x)]: [tex]\displaystyle\displaystyle g(0) = \lim_{h \to 0} \frac{\frac{3}{5(0 + h)^4 + 3} - \frac{3}{5(0)^4 + 3}}{h}[/tex]Simplify: [tex]\displaystyle\displaystyle g(0) = \lim_{h \to 0} \frac{\frac{3}{5h^4 + 3} - 1}{h}[/tex]Rewrite: [tex]\displaystyle\displaystyle g(0) = \lim_{h \to 0} \frac{3}{h(5h^4 + 3)} - \frac{1}{h}[/tex]Rewrite: [tex]\displaystyle\displaystyle g(0) = \lim_{h \to 0} \frac{3}{h(5h^4 + 3)} - \frac{5h^4 + 3}{h(5h^4 + 3)}[/tex][Subtraction] Combine like terms: [tex]\displaystyle\displaystyle g(0) = \lim_{h \to 0} \frac{3 - 5h^4 + 3}{h(5h^4 + 3)}[/tex][Addition] Simplify: [tex]\displaystyle\displaystyle g(0) = \lim_{h \to 0} \frac{-5h^4 + 6}{h(5h^4 + 3)}[/tex][Distributive Property] Distribute h: [tex]\displaystyle\displaystyle g(0) = \lim_{h \to 0} \frac{-5h^4 + 6}{5h^5 + 3h}[/tex]Evaluate limit [Power Method]: [tex]\displaystyle\displaystyle g(0) = 0[/tex]Since the bottom polynomial has a higher degree than the top polynomial, the bottom polynomial will increase faster.
∴ If the bottom is approaching a bigger value, the fraction gets smaller and smaller, approaching 0.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Write the equation of a line that has a slope of 1/2 and passes through (6, -4). Write your answer in slope-intercept form. PLEASE HELP
Answer:
y = 1/2x - 7
Step-by-step explanation:
y = 1/2x + b
-4 = 1/2(6) + b
-4 = 3 + b
-7 = b
Madeleine owes $36,000 to a private lender. The debt grows with 12% annual interest that compounds every week. How much will Madeleine owe in one year?
Answer:
A= $40584.28
Step-by-step explanation:
P = 36000
r = 12% = 0.12
n = 52 weeks
t = 1
[tex]A = P(1 + \frac{r}{n})^{nt}\\[/tex]
[tex]=36000(1 + \frac{0.12}{52})^{52 \times 1}\\\\=36000 (1.002307)^{52}\\\\=36000 \times 1.12734\\\\=40584.28[/tex]
What is the midpoint between( -4,-5 )and( 6,2)
Answer:
(1, -1.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x values and divide by 2
(-4+6)/2 = 2/2 = 1
To find the y coordinate of the midpoint, add the y values and divide by 2
(-5+2)/2 = -3/2 = -1.5
WILL GIVE BRAINLIEST AND THANKS. find the value of x
Answer:
x = 48
Step-by-step explanation:
To solve this problem, one must assume that the segment with a length of (7) bisects the segment with a length of (x).
It is given that the segment with a length of (7) is perpendicular (forms a right angle with) the segment that has a length of (x). This is indicated by the box around one of the angles, signifiying that it is a right angle, or (90) degree angle. Therefore, the triangle with sides measuring (25) and (7) is a right triangle. Thus, one can use the Pythagorean theorem to solve for the base length. Then multiply it by (2) to find the total length of (x).
The Pythagorean theorem states the following:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs, or sides adjacent to the right angle, and (c) is the hypotenuse or side opposite the right angle.
[tex]a^2+(7)^2=(25)^2[/tex]
Simplify,
[tex]a^2+49=625[/tex]
Inverse operations,
[tex]a^2=576\\\\a=24[/tex]
Multiply this value by (2) to find the total side length of the segment (x),
2(a)
Substitute,
2(24)
Simplify,
48
Hello there! Please answer this question for me please. Brainliest and 35 points!
What is the area of figure ABCD?
A
104 square inches
B
120 square inches
C
136 square inches
D
168 square inches
Answer:
That's a Trapezium
Area =½( A + B)x H
A and B are the top and bottom of the shape.
H is the height.
Substituting...
Area = ½(13+17)8
=120 Square Inches
Answer:
B. 120 in.²
Step-by-step explanation:
13 × 8 = 104 in.²
17 - 13 = 4
4 × 8 = 32
32 ÷ 2 = 16
16 in.² + 104 in.²
120 in.²
Help urgent
I need this done quick
Answer:
It is supplementary.
Step-by-step explanation:
Supplementary angles are angles that have two angles adding up to 180°. You can tell by just finding the straight line that equals 180° then seeing a line that separates the whole measurement into two angles, but together making a 180° angle still. Hope this helps! :D
Meanings of the other Options:
Alternate Interior Angles - Angles formed when two parallel or non-parallel lines are intersected by a transversal. The angles are positioned at the inner corners of the intersections and lie on opposite sides of the transversal.
Corresponding Angles - Angles that are in the same relative position at an intersection of a transversal and at least two lines. If the two lines are parallel, then the corresponding angles are congruent.
Alternate Exterior Angles - Angles are the pair of angles that lie on the outer side of the two parallel lines but on either side of the transversal line. Exterior angles lie on opposite sides of the transversal but outside the two parallel lines.
Parallel Lines - Two lines that never intersect. Like an equal sign for example (=).
Transversal - A line the cuts through a parallel line. Like a non-equal sign for example (≠).
Chanda is planning to visit universities over the summer to help decide where she
wants to attend college. The first two universities on her proposed route are 6
inches apart on Claudias map. In real life, this distance is 30 miles. What scale
does the map use? 1 in = miles.
Scott starts off working for Dunkin Donuts at $11.15 per hour. He only gets scheduled for 20 hours per week. If he works all 52 weeks in a year, how much will he make (before taxes)? a) In one week? b) In a year?
Answer:
week: 223
Year: 11596
Step-by-step explanation:
Answer: a) $223; b) $11,596
Step-by-step explanation:
1 week: 11.15/hr * 20hrs/week = 223
Year = 52 weeks; 52 * 223 = 11,596
A quantity with an initial value of 670 decays continuously at a rate of 25% per hour.
What is the value of the quantity after 7 hours, to the nearest hundredth?
Answer:
89.43
Step-by-step explanation:
a = 670 * (1 * .25)^7
a = 670 * (.75)^7
a = 89.43
This Question: 1 pt
A triangle has a perimeter of 9x² + 7x - 2.
One side of the triangle measures 6x + 7. Another side of the triangle measures 8x?.
What is the measure of the third side of the triangle?
Answer:
9x² - 7x - 9
Step-by-step explanation:
Two sides
(6x + 7) + 8x = 14x + 7
total perimeter - two sides = Third side
9x² + 7x - 2
- (14x + 7)
––––––––––
9x² - 7x - 9
Question 10 of 10 Classify the following triangle. Check all that apply. 7 A. Right B. Acute C. Isosceles D. Scalene E. Equilateral F. Obtuse
D & F
Step-by-step explanation:
D scale because all sides are different lengths
F obtuse because one angle is greater than 90 degrees
Look up definition of the other properties and you will see they don't apply
The given triangle is a obtuse and scalene triangle
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given triangle is an obtuse triangle and scalene triangle.
A triangle whose any one of the angles is an obtuse angle or more than 90° is known as obtuse triangle.
A triangle in which all the three sides have different lengths then it is called as scalene triangle.
Hence, the given triangle is a obtuse and scalene triangle.
To learn more on Triangles click:
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SOMEONE PLEASE HELP ASAP!!
Answer:
YES SIR!
Step-by-step explanation:
its
x=4 y=6
x= 6 y=9
Answer:
4, 6
6, 9
Step-by-step explanation:
129x-33=112
solve for x
Answer:
x =145/129
Step-by-step explanation:
129x-33=112
Add 33 to each side
129x-33+33=112+33
129x = 145
Divide each side by 129
129x/129 = 145/129
x =145/129
Which of the following equations is equivalent to 5(2p – 6) = 40?
10p – 6 = 40
7p – 11 = 40
10p – 30 = 40
7p – 1 = 40
A $5.50
baseball hat is
marked up
150%. What is
the new price
of the hata
Answer:
13.75
Step-by-step explanation: