Answers
Answer:
(x + 2)(-8x + 1) or,
(-8x + 1)(x + 2)
Explanation:
To factor quadratic equations in the form ax² + bx + c that cannot be factored in your head, the first step is to find factors for the product of coefficient a and constant c whose sum equates to coefficient b. This may sound confusing, but it is easier in practice.
So, we find the product of -8 and 2 which is -16.
Now we list the factors of -16. I like to list them as factor pairs. These are:
1, -16, 2, -8, 4, -4, 8, -2, 16, -1
Next, we examine which combination of factor pairs has a sum of -15. These are -16 and 1. To check: -16 + 1 = -15
Then, we place these values as coefficients into the original equation as substitutes for -15x and find factor out the greatest common factor (GCF) of the equation terms:
-8x² - 16x + x + 2
(-8x² - 16x) + (x + 2)
The GCF between -8x² and -16x is -8x. The GCF between x and 2 is 1.
-8x(x + 2) + 1(x + 2)
If these binomials within the parenthesis match, then you have found the factors. The binomial within the parenthesis is one factor and the GCFs outside of each binomial are is the other factor. Thus, the factors of the original quadratic expression are:
(-8x + 1)(x + 2)
To check these factors for accuracy, we can use the FOIL method to expand the expression, combine like terms, and observe if it matches the original equation. FOIL stands for Firsts, Outsides, Insides, and Lasts, instructing which terms of each binomial are multiplied together.
Firsts: -8x(x) = -8x²
Outsides: -8x(2) = -16x
Insides: 1(x) = x
Lasts: 1(2) = 2
In an equation: -8x² - 16x + x + 2 → -8x² - 15x + 2
This is the original equation, therefore (-8x + 1)(x + 2) are accurate factors.
Related Questions
I know how to solve number 4 but I’m having a hard time with 1,2,3,5,6
Answers
angle b=112-------> by vertical angles
angle a+112=180-----> supplementary angles
angle a==180-112----> angle a=68
angle c=angle a-----> by vertical angles
angle c=68
the answer part 1) is
angle a=68°
angle b=112°
angle c=68°
part 2)
angle a+15+38=180-----> angle a=180-(15+38)----> angle a=127
the answer part 2) is
angle a=127°
part 3)
angle b=40-----> by vertical angles
angle d=70-----> by vertical angles
2*angle x+40+angle d=180----> 2*angle x=180-(40+70)
2*angle x=70------> angle x=35
angle a=angle x-----> by vertical angles
angle a=35
angle c=angle x-----> by vertical angles
angle c=35
the answer part 3) is
angle a=35°
angle b=40°
angle c=35°
angle d=70°
Part 4)
angle a+70=90------> are complementary angles
angle a=90-70----> angle a=20
angle a+angle b=90----> are complementary angles
angle b=90-angle a----> 90-20-----> angle b=70
angle d=70 -------> by vertical angles
angle d+angle e=180------> supplementary angles
angle e=180-angle d----> angle e=180-70----> angle e=110
angle a+angle b+angle c+angle d=180
angle c=180-(20+70+70)----> angle c=20
the answer part 4) is
angle a=20°
angle b=70°
angle c=20°
angle d=70°
angle e=110°
Part 5)
angle a+90=180------> supplementary angles
angle a=180-90----> angle a=90
angle a +angle b=180----> supplementary angles
angle b=180-angle a----> angle b=180-90----> angle b=90
angle e=132-----> by vertical angles
angle d+132=180-----> supplementary angles
angle d=180-132----> angle d=48
angle c+138=180-----> supplementary angles
angle c=180-138----> angle c=42
the answer part 5) is
angle a=90°
angle b=90°
angle c=42°
angle d=48°
angle e=132°
part 6)
angle a+110=180------> supplementary angles
angle a=180-110----> angle a=70
angle c=25-----> by vertical angles
angle b+100+25=180----> angle b=180-(100+25)----> angle b=55
the answer Part 6) is
angle a=70°
angle b=55°
angle c=25°
Please find perimeter and area. also show work plz. It's really easy. I will mark as brainliest.
Answers
The perimeter of an enclosure is the length around the enclosure, or the sum of all the outer sides added up (red+blue lines in picture).
1) We are told that the two vertical sides of the enclosure (shown in blue) are each 20ft, making it 20 + 20 = 40ft total. All we need to find is the sum of the lengths of the four sides of the triangles (shown in red).
2) We are given the height of the triangle, 16ft, and the length of the base of the triangle, 20ft. To find the length of the edge we're looking for, we need to find the hypotenuse of the right triangle shaded in green. One of the legs of the triangle is 10ft (half of the base of the larger triangle) and the other leg is 16ft (same as height of the larger triangle).
Use the pythagorean theorem, which says [tex] a^{2} + b^{2} = c^{2} [/tex].
a and b are the length of your legs, 10ft and 16ft, and c is the length of the hypotenuse, or the side we're looking for. Plug your numbers in and find c:
[tex]10^{2} + 16^{2} = c^{2} \\ c^{2} = 356\\ c = 18.868 ft[/tex]
3) Now you know each red side is 18.868 ft. There are 4 red sides, so 4 x 18.868ft = 75.472ft. Add this number to the length of your two blue sides to get the perimeter:
75.472ft + 40ft = 115.472ft.
--------------
Area: [tex]720ft^2[/tex]
The area of the enclosure is shaded in yellow. To find the area of the enclosure, you want to find the sum of the areas of all the shapes. Break the enclosure down into one square (in the middle) with two triangles on the top and bottom, find the area of those three shapes, and add those areas together.
1) The equation for the area of the square is [tex]A=s^2[/tex], where s = length of the side.
You're told that the length, s = 20ft. Plug that in and solve for the area of the square:
[tex]A=s^2\\ A=20^2\\ A = 400 ft^2[/tex]
2) The equation for the area of a triangle is [tex]A = \frac{1}{2} bh[/tex], where b = length of base and h = height of triangle.
You're told that the length of the base, b = 20ft and the height of the triangle, h = 16ft. Plug these values in and solve for area of one of the triangles:
[tex]A = \frac{1}{2} bh\\ A = \frac{1}{2} (20)(16)\\ A = 160 ft^2[/tex]
3) Since you have two identical triangles, multiply the area of one triangle by two to get the total area of the two triangles:
[tex]160 ft^2 \times 2 = 320 ft^2[/tex]
4) Add up the areas of the square and the two triangles to get the total area of the enclosure:
[tex]400 ft ^2 + 320 ft^2 = 720ft^2[/tex]
given the equation (x+a)^2(x-2)=x^3+bx^2+12x-72 find a and b
Answers
[tex]a=- \frac{ x^{2}- \sqrt{( x^{3} + x^{2} b+12x-72(x-2)-2x} }{x-2} ,- \frac{ x^{2}+ \sqrt{( x^{3} + x^{2} b+12x-72(x-2)-2x} }{x-2} [/tex]
Solve for b by simplifying both sides of the equation then isolating the variabel.
[tex]b= \frac{12}{x}+ \frac{72}{ x^{2} }-2+2a- \frac{4a}{x}+ \frac{ a^{2} }{x}- \frac{2a^{z} }{ x^{2} } [/tex]
Hopefully i helped ^.^ Mark brainly if possible
Simplify the expression.
2^2 • 2^3
A.
4^5
B.
4^6
C.
2^6
D.
2^5
Answers
[tex] 2^{2} 2^{3} = 2^{2*3} = 2^{6} [/tex]
The answer you're looking for is ( D ) because in exponents, the rule is..
║If the bases are the same, add the exponents║
2 ^2 * 2 ^3 = ? (Bases are the same, add the exponents)
Answer: D = 2^5
║Hope that helps :)║
Consider the attached diagram if the box weighs 100 N in what direction is the support force
A) up
B) down
C) left
D) right
Answers
There needs to be an equal amt of force exerted on the box from the bottom so that the box won't crash through the ground and into space. It needs to be kept on the ground by a force exerting upwards as gravity pulls it down.
Solve the system of equations algebraically.
3x-3y=6
6x-7y=5
a. (8,8)
b. (9,7)
c. many solutions
d. no solution
Answers
The system of equations has a solution at (9, 7), which is an option (b).
What are Systems of equations?Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
The given equations are:
3x-3y=6
6x-7y=5
Multiply the first equation by 2 to get rid of the coefficient of x in the second equation:
6x - 6y = 12
6x - 7y = 5
Subtract the first equation from the second equation to eliminate x:
0x - y = -7
y = 7
Substitute y = 7 into one of the original equations and solve for x:
3x - 3y = 6
3x - 3(7) = 6
3x - 21 = 6
3x = 27
x = 9
Therefore, the solution to the system of equations is (9, 7), which corresponds to option (b).
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A number cube is rolled 360 times , and the results are recorded as follows : 96 ones , 31 twos , 49 threes , 76 fours , 45 fives , and 63 sixes . What is the experimental probability of rolling a 2 or a 3 ?
1. 0.16
2. 0.22
3. 0.37
4. 0.78
Answers
Total number of 2s and 3s = 31 + 49 = 80
P(2 or 3) = 80/360 = 2/9 = 0.22 (nearest hundredth)
Answer: 0.22
The experimental probability of rolling a 2 or a 3 would be 0.22
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
We are given that number cube is rolled 360 times , and the results are recorded as follows : 96 ones , 31 twos , 49 threes , 76 fours , 45 fives , and 63 sixes .
Total number of times rolled = 360
Total number of 2s and 3s = 31 + 49 = 80
P(2 or 3) = 80/360 = 2/9
P(2 or 3) = 0.22 (nearest hundredth)
The answer is: 0.22
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0.8 x 3.15 it’s multiplying rational numbers
Answers
Let me know if you want me to show my work
The following data shows the low temperature in Vancouver, in degrees Celsius, for two weeks in January one year. 8.90, 8.35, 8.50, 8.65, 8.55, 8.20, 8.50, 8.32, 8.50, 8.60, 8.60, 8.30, 8.10, 8.65 Which box plot best represents this data?
Answers
8.10, 8.20, 8.30, 8.32, 8.34, 8.50, 8.50, 8.50, 8.55, 8.60, 8.60, 8.65, 8.65, 8.90
Lower extreme: 8.10
Upper extreme: 8.90
Median: 8.50
1st/lower quartile: 8.32
3rd/upper quartile: 8.60
Please see the attached picture for the boxplot.
A basket is filled with white eggs and brown eggs. Half of the white eggs are cracked. An egg is randomly selected from the basket. What is the probability that it is a cracked, white egg? Write your answer as a fraction in simplest form.
Answers
The probability of randomly picking a cracked white egg from a basket of white and brown eggs is calculated by dividing the number of cracked white eggs (half of the total white eggs) by the total number of eggs. However, specific numbers for the number of white and brown eggs are needed for an exact answer.
Explanation:In order to answer this question, we need to know the number of white eggs and brown eggs in the basket. However, assuming that there are 'w' white eggs and 'b' brown eggs in the basket, and half of the white eggs are cracked, the probability of randomly picking a cracked white egg would be calculated by dividing the number of cracked white eggs by the total number of eggs. Therefore, if 'w' over 2 represents cracked white eggs, the probability would be (w/2) / (w + b).
For example, if the basket had 10 white eggs and 20 brown eggs, and half the white eggs are cracked. There would be 5 cracked white eggs. Hence, the probability of picking a cracked white egg would be calculated as: (5 / (10 + 20)), which equals to 1/6.
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Does 21.6,28.8,36 equal a right triangle
Answers
if they are the lengths of the sides of a right triangle then:
[tex]21.6^2+28.8^2=36^2\\\\L_s=466.56+829.44=1296\\\\R_s=1296\\\\L_s=R_s[/tex]
therefore it's the right triangle.
Which expression gives the distance between the points (5, 1) and (9, -6)?
Answers
Answer:
[tex]d = \sqrt{65}\text{ units}[/tex]
Step-by-step explanation:
Let [tex](x_1,x_2)[/tex] and [tex](y_1, y_2)[/tex] be the two points.
We have to find the distance between the two points.
The distance Formula:
[tex]d = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2}[/tex]
Here, we are given [tex](x_1,x_2)[/tex] = (5,1) and [tex](y_1, y_2)[/tex] = (9,-6)
Then, the distance between these two points is given by:
[tex]d = \sqrt{(5 - 9)^2 + (1- (-6))^2}[/tex]
[tex]d = \sqrt{(-4)^2 + (7)^2}[/tex]
[tex]d = \sqrt{16 + 49}[/tex]
[tex]d = \sqrt{65}[/tex]
Thus, the distance between the given point is [tex]\sqrt{65}\text{ units}[/tex].
In a large apartment building, 35 of the apartments have a balcony and 55 do not. An apartment us randomly selected as part of a survey. What is the probably it has a balcony?
Answers
11/18 probability
90 apartments total
35/90=
11/18
Answer:
Thanks
Step-by-step explanation:
This person is correct peeps :DD
if the circumference of the base=126 cm and h=10 cm, find the volume
Answers
Consider a cylinder with radius 6 cm and a height of 11.5 cm. Describe how to calculate the surface area of the given cylinder and what the surface area means.
Answers
A net is an unfolded 3d shape.
To find the surface area you use the equation [tex]A= 2x \pi r h + 2 \pi r^{2} [/tex]
For this cylinder, the answer would be around 659.73
Surface area is the area you get from a shape's net.
A net is an unfolded 3rd shape.
To find the surface area you use the equation A = 2xπrh + 2πr²
The answer would be 659.73 cm²
Hope this helps have a wonderful day!
which numbers are rational numbers 2, -4.0, 8.1, 3/4, 0, -8
Answers
Keisha has one penny, one nickel, and one dime in her pocket. She randomly takes on coin out of her pocket. Without putting it back, she randomly takes out another coin. If Keisha lists all the possible outcomes of picking the two coins one at a time, how many outcomes are there?
Answers
Which of these expressions represent the sum of 3 and n?
Answers
"Sum of" tells you its addition and because it's addition the order of the two terms (the 3 and the N) don't matter.
Your correct expressions are:
3 + n
or
n + 3
Elizabeth has two gardens in her yard. The first garden is 8 feet long and 6 feet wide. The second garden is half the length of the first garden. the area of the second garden is twice the area of the first garden. What is the area of the second garden? Ask for details Follow Report by Beatrizsalazar 28.02.2018
Answers
The area of the second garden is 96 square feet.
Let's denote the length of the second garden as l (since it's half the length of the first garden) and the width of the second garden as w.
Given:
Length of the first garden [tex](\(L_1\))[/tex]= 8 feet
Width of the first garden [tex](\(W_1\))[/tex] = 6 feet
Length of the second garden [tex](\(l\)) = \(L_1/2\) = \(8/2 = 4\)[/tex] feet
Area of the first garden [tex](\(A_1\)) = \(L_1 \times W_1\) = \(8 \times 6 = 48\)[/tex] square feet
We are given that the area of the second garden [tex](\(A_2\))[/tex] is twice the area of the first garden:
[tex]\[A_2 = 2 \times A_1 = 2 \times 48 = 96\][/tex] square feet
use the given graph to determine the period of the function. 1 & 2 plz
Answers
We have then:
Part 1:
The period of the function is:
T = 3
Part 2:
The period of the function is:
T = 4
Answer:
The period of functions 1 and 2 respectively are:
T = 3
T = 4
3/7÷1/2 how do you graph this
Answers
Not sure what you mean by graphing it though. Like on a number line? There is no x or y in your equation.
a furnace is rated 4000 BTU per hour. How many foot pounds of energy are released in one hour?
- 5.1 foot pounds
- 2,456,000 foot pounds
- 0.2 foot pounds
- 3,112,000 foot pounds
Answers
Now we just need to multiply 4000 BTU by our conversion factor:
[tex]4000BTU*\frac{778foot-pound}{1BTU}=3112000foot-pound[/tex]
We can conclude that the furnace released 3,112,000 foot pounds of energy in one hour.
A cylinder has a circular base with a diameter of 12ft. The height of cylinder is 4 ft. What is the volume of the cylinder rounded to the nearest whole number? Use 3.14 for pi.
Answers
Volume = (3.14)(12÷2)²(4) = 452 ft³ (nearest whole number)
Answer: 452 ft³
Write each mixed numbers as a product of a whole number and a unit fraction
1 1/2
1 3/5
3 3/4
Answers
2. 1/5 x 8
3. 1/4 x 15
Kathy is baking cakes each cake requires 1/12 of a teaspoon of vanilla and she has 9/12 of a teaspoon how many cakes can she bake?
Answers
Tyrone factored the polynomial completely. What is the value of b? 12x^4+30x^3+4x^2+10x
Ax(Bx^2+1)2x+5
Answers
Given: 12x^4 + 30x^3 + 4x^2 + 10x
Req'd: B = ?
Sol'n:
*use elimination
solving for B:
= 2x (6x^3 +15x^2 + 2x +5)
= 2x (3x^2(2x + 5 +2x +5)
= 2x (3x^2 + 1) (2x + 5)
Answer:
[tex]B=3[/tex]
Step-by-step explanation:
We have been given an expression [tex]12x^4+30x^3+4x^2+10x[/tex].
Let us factor our given expression to answer the given problem.
Factor out [tex]2x[/tex] from all terms:
[tex]2x(6x^3+15x^2+2x+5)[/tex]
Now, we will make two groups of [tex]6x^3+15x^2+2x+5[/tex] as shown below:
[tex]2x((6x^3+15x^2)+(2x+5))[/tex]
[tex]2x((6x^3+15x^2)+(2x+5))[/tex]
Factor out [tex]3x^2[/tex] from 1st group:
[tex]2x((3x^2(2x+5))+(2x+5))[/tex]
[tex]2x(3x^2+1)(2x+5)[/tex]
Upon comparing [tex]2x(3x^2+1)(2x+5)[/tex] with [tex]Ax(Bx^2+1)(2x+5)[/tex], we can see that [tex]A=2[/tex] and [tex]B=3[/tex].
Therefore, the value of B is 3.
which of the following is equal to the rational expression.......
Answers
The expression equal to the rational expression is 3/(x + 6)
Calculating the value of the rational expression
from the question, we have the following parameters that can be used in our computation:
3(x + 2)/(x + 6)(x + 2)
Divide the fraction by x + 2
So, we have
3(x + 2)/(x + 6)(x + 2) = 3/(x + 6)
Hence, the value of the rational expression is 3/(x + 6)
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PLX HELP! Need this ASAP! Thx
One of the same side angles of two parallel lines is 20° smaller than the other one. Find all angles.
Answers
x+x+20^{0}=180^{0}
2x=160^{0}
x=80^{0}.
So measure of smaller angle is 80^{0} and measure of bigger angle is x+20^{0}=80^{0}+20^{0}=100^{0}.
Answer:
80° and 100 °
Step-by-step explanation:
The total of the two angles is 180°, and one angle is 20° smaller than the other, so the equation would be x+x-20°=180°, then all you need to do is find x, and x-20°.
DONT FORGET TO WRITE THE DEGREE SYMBOL OR IT WILL BE COUNTED AS INCORRECT!!!
-Char-
the first computer is usually regarded as one called ROACH completed in 1945. Email was invited in 1971. how many years after the computer was email invented
Answers
the first computer is usually regarded as one called ROACH completed in 1945. Email was invited in 1971. how many years after the computer was email invented
in this vase we will use soustraction
1971-1945=26
email was invented 26 years after computers
hopes this helped you well
may i please have the brainliest
have a wonderful day or night
Final answer:
Email was invented 26 years after the completion of the first recognized computer in 1945.
Explanation:
The first computer is often attributed to the work carried out during World War II, with machines like ENIAC, completed in 1945, incorporating vacuum tubes and filling entire rooms. However, the question references a machine called ROACH, which seems to be a typo or a misunderstanding; we usually refer to ENIAC as one of the first computers. Email, on the other hand, was invented in 1971 by Ray Tomlinson. Calculating the difference between the years when the first computer was completed and when email was invented gives us the number of years it took for email to be developed after the advent of the computer.
To find this, we subtract the year the first computer was completed, 1945, from the year email was invented, 1971:
1971 (the year email was invited) - 1945 (the year the computer was completed) = 26 years.Email was invented 26 years after the completion of the first computer.
what components make an ellipse an ellipse
Answers
An ellipse is a curved shape characterized by two foci and a major axis, with every point on the ellipse being at a constant sum of distances from the foci. The eccentricity, which is the ratio of the distance between the foci to the length of the major axis, determines the 'roundness' of the ellipse. The ellipse can be constructed using the gardener's method to showcase this constant sum property.
Explanation:An ellipse is a specific type of curve that is noticeably different from a circle in that it is elongated; it has two distinct foci instead of a single central point and a major axis that defines its longest diameter. The foci are two fixed points located within the ellipse such that the sum of the distances from any point on the ellipse to the two foci is constant. This consistent sum of distances is what gives an ellipse its characteristic shape. This property is often demonstrated by the 'gardener's method' of creating an ellipse by anchoring a string to two fixed points (the foci) and tracing a path with a marker keeping the string taut.
The eccentricity of an ellipse, which determines its 'roundness,' is the ratio of the distance between the two foci to the length of the major axis. If the foci are close together relative to the major axis, the ellipse will appear more circular; if they are further apart, the ellipse will be more stretched out. The major axis (2a) cuts the ellipse into two equal halves, and each half is referred to as the semimajor axis (a).
A crucial aspect of drawing an ellipse involves identifying the length of the major axis and the location of the two foci. Because these elements are so fundamental, an ellipse can be readily illustrated by the use of string and a couple of tacks representing the foci.