For example, let's expand out (x+3)*(2x+1). Use of the FOIL rule should get to you 2x^2 + 7x + 3.
Now imaging that you handed 2x^2 + 7x + 3 to a friend to be factored. They do not know the factorization yet.
They would see that a = 2, b = 7, c = 3.
The friend needs to find two numbers u,v such that they multiply to a*c = 2*3 = 6 and add to b = 7
Through trial and error (I recommend making a table of values), your friend would get
u*v = 1*6 = 6u+v = 1+6 = 7But as you mentioned, your friend could easily swap the order of addition and multiplication to say
u*v = 6*1 = 6u+v = 6+1 = 7----------------------
If we go with the first option, then the factor by grouping looks like this
2x^2 + 7x + 3
2x^2 + 1x + 6x + 3 ... break up 7x into 1x+6x
(2x^2+1x) + (6x+3) .... group up the terms into pairs
x(2x+1) + 3(2x+1) .... factor each grouping
(x+3)(2x+1) ..... factor out the overall GCF
---------------------
Or we could have the factor by grouping looks like this
2x^2 + 7x + 3
2x^2 + 6x + 1x + 3 ... break up 7x as 6x+1x
(2x^2+6x) + (1x+3)
2x(x+3) + 1(x+3)
(2x+1)(x+3)
(x+3)(2x+1)
We end up with the same factorization.
The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).
Answer:
Area of the shaded region = 16(π - 2) in²
Perimeter of the shaded region = 4(π + [tex]2\sqrt{2}[/tex]) in
Step-by-step explanation:
Since, BDC is a quarter of the circle with radius = 8 in.
Area of the quarter of the circle = [tex]\frac{1}{4}(\pi)(r)^2[/tex]
= [tex]\frac{1}{4}(64)\pi[/tex]
= 16π in²
Area of ΔBCD = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(8)(8)[/tex]
= 32 in²
Since, area of the shaded part = Area of quarter of the circle - Area of triangle BCD
= (16π - 32)
= 16(π - 2) in²
Therefore, area of the shade region = 16(π - 2) in²
Similarly, length of arc BD = [tex]\frac{1}{4}(2\pi r)[/tex]
= [tex]\frac{8\pi }{2}[/tex]
= 4π in.
Length of the diagonal of a square = (Side)√2
= 8√2 in
Perimeter of the shaded region = Length of arc BD + Length of diagonal BD
= 4π + 8√2
= 4(π + 2√2) in.
The new pastry chef at Jackson's Bakery specializes in sheet cakes for parties. She sold 17 small, 11 medium, and 20 large sheet cakes in one week. How much money did Jackson's Bakery make in one week from sheet cakes?
Answer:
Therefore the total amount that Jackson's Bakery made in one week from sheet cakes is: = $2,238
Step-by-step explanation:
Step One:
To arrive at the total amount made from the sheet cakes, we have to assign the prices of each type of cake. They are:
Small Sheet Cake - $36Medium Sheet Cake - $46Large Sheet Cake - $56Step Two:
If the new pastry sold 17 small, 11 medium and 20 large sheet cakes respectively, the total money made comes to the following:
= (36 x 17) + (11 x 46) + (56 x 20)
= 612 + 506 + 1120
Therefore the total amount that Jackson's Bakery made in one week from sheet cakes is:
= $2,238
Cheers!
Simplify (right answer only ) : 2(x – 9)
Answer:
2x-18
Step-by-step explanation:
2(x-9)
distribute the 2 in the ( )
2x-18
Hope this Helps!!!
The sales tax rate is 5%. If Rebecca buys a lawn mower priced at $61, how much tax will she pay?
Answer:
3.05
Step-by-step explanation:
Step-by-step explanation:
(9a4 + 2a2 + 5) – (16a4 – 7a2 + 1)
A. 25a4 – 5a2 – 4
B. –7a4 – 5a2 + 6
C. 25a8 + 9a4 + 6
D. –7a4 + 9a2 + 4
5.Multiply 9x2(2x2 + 8x).
A. 18x4 + 72x3
B. 18x2 + 72x3
C. 11x4 – 17x3
D. 90x4
On a coordinate plane, three of the four vertices of a rectangle are located at the points (0,0). (5,5), and (6,2). What is the area, in square units of the rectangle?
Using the distance formula and the area of a rectangle, the area of the rectangle in square units is: B. 10√5
What is the Area of a Rectangle?Area of rectangle = length × width.
What is Distance Formula?Distance Formula is given as: [tex]d = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].
Thus:
Length of rectangle = distance between (0, 0) and (5, 5)
[tex]d = \sqrt{(5 - 0)^2 + (5 - 0)^2}\\\\d = \sqrt{50}[/tex]
Width of rectangle = distance between (5, 5) and (6, 2)
[tex]d = \sqrt{(2 - 5)^2 + (6 - 5)^2}\\\\d = \sqrt{10}[/tex]
Area of rectangle = √50 × √10
= √500
Area = 10√5
Therefore, using the distance formula and the area of a rectangle, the area of the rectangle in square units is: B. 10√5
Learn more about area of rectangle on:
https://brainly.com/question/25292087
The expression (2x2)3 is equivalent to _____.
a.6x2
b.6x5
c.8x6
Answer:
A
Step-by-step explanation:
(2x2)3
= (4)3
=12
6x2 = 12
So the answer is A
7x (6 x t) and (7 x 6) x t
If your question is which propperty is used in that opperation
Answer: The commutative property of multiplication
Step-by-step explanation: The comutative property of multiplication says that the order in which elements are multiplied the result is the same.
A parabola can be drawn given a focus of (8, 6) and a directrix of x=4. Write the equation of the parabola
Answer:
The equation of the Parabola
(y - 6 )² = 8 (x -6)
Step-by-step explanation:
Step(i):-
Given directrix x = 4
we know that x = h - a = 4
h -a = 4 ...(i)
Given Focus = ( 8,6)
we know that the Focus of the Parabola
( h + a , k ) = ( 8,6)
comparing h + a = 8 ...(ii)
k = 6
solving (i) and (ii) and adding
h - a + h+ a = 8 +4
2 h = 12
h =6
Put h = 6 in equation (i)
⇒ h - a =4
⇒ 6 - 4 = a
⇒ a = 2
Step(ii):-
The equation of the Parabola ( h,k) = (6 , 6)
( y - k )² = 4 a ( x - h )
(y - 6 )² = 4 (2) (x -6)
(y - 6 )² = 8 (x -6)
Sophia scored 33 points in a basketball game. She scored four more two-point baskets than three-point baskets. Write a system of equations in standard form that models this situation.
How many three-point baskets did Sophia make?
please right step by step :)
Answer:
33=2(4)+3x
8 Three Points
Evaluate the expression. (343)^-1/3
Answer:
1/7
Step-by-step explanation:
Issa jogged two-thirds of the way home from school. Then he was tired, so he walked the remaining 3,200 m.
How many kilometers did Issa travel from school to his house?
Answer:
9.6km
Step-by-step explanation:
3200/(1/3)=
3200*3/1=9600 m=9.6km
lua is creating a rectangular prism the base of her prism is shown below she plans to have a height of 7 cubes
what will the volume of the completed figure be?
_______ cubic units
Answer:
63
Step-by-step explanation:
hhehehehhehehehehh hope this helps
What makes a linear pair with 84°?
Answer:
as per linear pair axiom it will be X + 84= 180
this answer is 106 degrees
10
Mr. Jones purchased a new Bluetooth speaker for $89.99. Sales
tax is 8%. How much will Mr. Jones pay for the speaker with
sales tax?
A. $82.79
B. $90.08
C. $97.19
D. $107.20
Answer:
I believe the answer is C. hope this helps
Answer:
C
Step-by-step explanation:
uh i DD this answer on a test so ya
helpppppppppppp???????????????????????????????????????????????\\
A company sells bottles of vitamin capsules. The graph and table show the linear relationship between the cost per capsule in cents and the number of bottles ordered.
A. y= -5x – 70
B. y= 5x +70
C. y=-5x + 70
D. y= 70x - 5
Answer:
C
Step-by-step explanation:
Trust me and vote brainliest
Two cylindrical soup cans have a volume of 40 cubic inches. Can their surface areas be unequal?
You must be at least 42 inches tall to ride the bumper cars at an amusement park. Write an inequality that represents this situation. Let x represent the heights of people who are allowed to ride the bumper cars.
Answer:
x ≥ 42
Step-by-step explanation:
If you must be at least 42 inches tall to ride the bumper cars at an amusement park, this means that the minimum average height you can have is 42in i.e you can be more than 42inches tall.
The right inequality sign to represent this situations is a "greater than or equal to sign"(≥)
If x represent the heights of people who are allowed to ride the bumper cars, the required inequality expression will be x ≥ 42
Set up the equation you would use to solve the problem.Do not actually solve the equation.
A plane flies 390 miles with the wind and 325 miles against the wind in the same length of time. If the speed of the wind is 10 miles per hour, fine the speed of the plane in still air. (Let x = speed of the plane.)
A. 390/x+20 = 395/x
B. 390/x+10 = 325/x-10
C. 390/x = 325/x-20
D. 390/x-10 = 325/x+10
1. Find the volume of the cylinder. (no units-round to nearest tenth
7 km
8 km
Answer:
1407.43 would be your answer
Step-by-step explanation:
The formula is [tex]\pi r^2h[/tex], so plug 8 and 7 into the equation, and you'll get your answer. Hope this helps :)
Select the table that represents a proportional relationship between X and Y
The answer is A
Step-by-step explanation:
Which equation is true?
O 1150) = - 150
01 - 150 = 150
- 150 = 150
O-1 - 150= 150
THe 3rd equation is true
Which equation is equivalent to 8x + 2y = 10?
Answer:
y=-4x+5
Step-by-step explanation:
8x+2y=10
2y=10-8x
divide by 2
y=5-4x
y=-4x+5
What is the equation of the line that passes through the point (-5,5)and has a slope of -1
Answer:
y = - xStep-by-step explanation:
The point-slope form of the equation is y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope:
m = -1
(-5, 5) ⇒ x₀ = -5, y₀ = 5
The point-slope form of the equation:
y - 5 = -1(x + 5)
So:
y - 5 = -x - 5 {add 5 to both sides}
y = -x ← the slope-intercept form of the equation
A family went out to eat. The bill is $65.82. The family wants to leave a 20% tip. How much tip will be added on to the cost of dinner?
Answer:
$13.16
Step-by-step explanation:
Graph the line.
Y+4=1/5(x-1)
Answer:
graph the point (0, -5) and from that point go up 1 unit and to the right 5 units (5, -4) and plot that point; connect the two points
Step-by-step explanation:
help , read the question. please help me
BRAINLIEST !
Answer:
9.76 years turns 900 dollars into 1200 dollars.
Step-by-step explanation:
A(t) = 900*(1.03)^t
1200 = 900 * (1.03)^t Divide by 900
1200/900 = (1.03)^t
1.333 = 1.03^t Take the log of both sides.
log(1.3333) = t * log(1.03)log 1.3333 = .1249log 1.03 = .01281.249 = 0.0128*t
1.249/0.0128 t = 9.76 years.
Alicia drew a map of Texas. In the scale Alicia used for the map, 1/2 inch represents 20 miles. What is the distance between two cities on the map if the actual distance between the two cities is 360 miles?
Answer:
9 inches
Step-by-step explanation:
Given that,
For the graph, 1/2 inch represents 20 miles.
We need to find the distance between the cities on the map if the actual distance between the two cities is 360 miles.
1/2 inch = 20 miles
1 mile = [tex]\dfrac{\dfrac{1}{2}}{20}=0.025\ \text{inches}[/tex]
For 360 miles, = 0.025 × 360
= 9 inches
Hence, the required answer is 9 inches.
Last one... hehe- sorry
Answer:
113
Step-by-step explanation:
I have no idea Imao
helpppp plzzzzzzzzzzzzzzz
Answer:
y= 0.2(0.05)^x