Unfortunately, due to a couple of pitiful people (some poor kids who got so lost in life, they resulted to spamming), I’m having to repost this:
OK, so I was learning about how to factorize a quadratic polynomial. And I also wrote notes on it. Now, even though I know that my notes are definitely correct, I’m getting stuck at a certain point. Please look at the attached photo, and explain why the variable X and the number 4 have been removed when we get the factors. I’d greatly appreciate it. Thanks!
Answers
Answer:
so when factorising, you first remove the common factors. in this case it is (x+3)
so what is remaining is the x and 4
you group that together.
my teacher explained that when factorising, after removing the common factor then you divide each term by the common factor, and then group the answers to that in brackets.
so it will be,
[tex]x(x + 3) + 4(x + 3) \\ (x + 3)( \frac{x(x + 3)}{x + 3} + \frac{4(x + 3)}{(x + 3)} [/tex]
so basically whats left after dividing, is x and 4 because the x+3 cancel off.
and thats how you get the answer of
(x+3)(x+4)
hope this helps;)
Related Questions
line RP and line RQ are tangent to point G at P and Q. if the measurement of angle PRG=35 degrees, find the measurement of angle PGR.
Answers
Answer:
55°
Step-by-step explanation:
By theorem of specific circle, the radius is perpendicular to the tangential lineSummation of all internal angles equal to 180°Thus from the atrachment, the angle PGR is 180°-35°-90°
= 55°
factorise fully the following expression (am-an+bm-bn)
Answers
Step-by-step explanation:
am-an+bm-bn
m(a+b)-n(a+b)
(m-n)(a-b)
Answer:
[tex] \small \sf \: ( m - n ) ( a + b )[/tex]
Step-by-step explanation:
( am - an + bm - bn)
Do the grouping= ( am - an ) + ( bm - bn )
Factor out a in the first and b in the second group= a ( m - n ) + b ( m - n )
factor out common term m - n by using distributive property= ( m - n ) ( a + b )
The present oge of a :b are in ratio 5: 6 three year ago , thier age were in the ratio 4:5 find there present age .
Answers
Answer:
Their present age are 15 and 18
Step-by-step explanation:
a : b = 5 : 6
[tex]\frac{a}{b} = \frac{5}{6} \\\\6a = 5b\\\\a = \frac{5b}{6} \\\\\frac{a-3}{b-3} = \frac{4}{5} \\\\5(a-3) = 4(b-3)\\\\5a - 15= 4b - 12\\\\5a - 4b = 15 - 12\\\\5a - 4b = 3\\\\substitute \ the \ value \ of \ a \ into \ the \ above \ equation;\\\\5(\frac{5b}{6} ) - 4b = 3\\\\25b - 24b = 18\\\\b = 18\\\\now, \ solve \ for \ a;\\\\a = \frac{5}{6} \times 18\\\\a = 15[/tex]
The seventh grade wants to break last year's record of 78 coats collected for the annual clothing drive. They have already collected 13 coats.
Which number line represents the graph of the solution to the inequality that represents the number of coats, c, that the seventh grade must still collect?
Answers
Answer:
The last number line or D.
Step-by-step explanation:
To find the remaining coats to be collected, subtract the coats that are collected from the total of coats needed.
So:
78 - 13= 65
They must collect a total of 65 and more to break the last year's record of 78 coats. Number line D, represents the solution of this inequality.
Hope this helps! Have a nice dayy! :)
Convert 3.5 ⋅ 104 to standard form.
Answers
Answer:
In standard notation [tex]3.5 \times 10^4 = 35000[/tex]
In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of 10.
----------------
If it was 3.5 x 104 it would equal 350.
Slopes of parallel lines
Answers
Answer:
2
Step-by-step explanation:
Parallel lines have the same slopes
If the slope of line a is 2, the slope of line b is 2
Answer:
slope of line b = 2
Step-by-step explanation:
The slopes of parallel lines are equal
Given slope of line a = 2 and parallel to line b , then
slope of line b = 2
4.2 To buy a new car is not a very good investment. In the first year the car will
decrease in value by 25%.
4.2.1
If the car costs R200 000, what will it be worth after 1 year?
Answers
Given:
In the first year, the car will decrease in value by 25%.
The cost of a car is Rs. 200,000.
To find:
The worth of the car after 1 year.
Solution:
The cost of a car is Rs. 200,000 and in the first year the car will decrease in value by 25%. So, the worth of the car after 1 year is:
[tex]Worth=200000-\dfrac{25}{100}\times 200000[/tex]
[tex]Worth=200000-\dfrac{1}{4}\times 200000[/tex]
[tex]Worth=200000-50000[/tex]
[tex]Worth=150000[/tex]
Therefore, the worth of the car after 1 year is Rs. 150,000.
A fitness club offers two membership plans.
Plan A: $30 per month
Plan B: $18 per month plus $2 for visit for each visit to the club
a) graph the linear system. When would the cost of the two membership plans be the same
B) describe a situation under which you would
Choose each plan
Help please
Answers
In a race, 23 out of 50 swimmers finished in less than 43 minutes. What percent of swimmers finished that race in less than 43 minutes?
Please help me on this T_T
Answers
Answer:
46%
Step-by-step explanation:
x : 100 = 23 : 50
x = (23 * 100)/50 = 46%
If a ball is thrown straight up with an initial velocity of 29.4 m/s, the
equation for the height "h" is given by h = -4.9t2 + 29.4t. When does the
ball return to the ground?
Answers
Answer:
6 sec
Step-by-step explanation:
when ball return to the ground, h is 0
0=at^2 +bt
0 = -4.9t^2+29.4t
factor: -4.9 times -6 is 29.4
0 = -4.9t(t-6)
set each equation to 0
-4.9t = 0 or t-6=0
t = 0 or t= 6
it's 6 seconds
Answer:
after 6 seconds in the air
Step-by-step explanation:
setting 'h' equal to zero will yield when the ball returns to the ground
you can factor out -4.9t to get:
-4.9t(t - 6) = 0
t = 0 (prior to ball being thrown)
t = 6 (this means, after 6 seconds, the height of the ball is back to zero)
Consider the graph of the function f(x) =
= 10^x
What is the y-intercept of function gif g(x)
=4f(x) + 12
Answers
Answer:
(0,8)
Step-by-step explanation:
Let X be 0 and solve for Y to get the intercept
y= - 4([tex]10^{x}[/tex]) + 12
y= - 4 * [tex]10x^{0}[/tex] + 12
y= - 4 * 1 + 12
y= - 4 + 12
y=8
when x=0, y=8
(0,8) is y intercept
The y-intercept of the given function is (0,8).
We have given that,
The graph of the function f(x) = 10^x
The y-intercept of function gif g(x)=4f(x) + 12
What is the intercept?
The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Let X be 0 and solve for Y to get the intercept
[tex]y= - 4(10^x) + 12[/tex]
[tex]y= - 4 (10^0) + 12[/tex]
[tex]y= - 4 * 1 + 12[/tex]
[tex]y= - 4 + 12[/tex]
[tex]y=8[/tex]
when x=0, y=8
The y-intercept of the given function is (0,8).
To learn more about the intercept visit:
https://brainly.com/question/1884491
#SPJ5
What is the area is square feet?
Answers
Answer:
A = 24
Step-by-step explanation:
Figure shown is a trapezoid
Area of a trapezoid = [tex]\frac{a+b}{2} h[/tex]
where a and b = base lengths and h = height
The trapezoid shown has the following dimensions
Shorter base length (a) = 6
Longer base length (b) = 10
Height (h) = 3
Using these dimensions , plug in the values into the area formula
A = [tex]\frac{6+10}{2} 3[/tex]
add 6 + 10 = 16
[tex]A=\frac{16}{2} 3[/tex]
divide 16/2 = 8
[tex]A = (8)(3)[/tex]
multiply 8 times 3
A = 24
A penny-farthing is a bicycle with a very large front wheel and a much smaller back wheel. Penny-farthings were popular in the 1800s and were available in different sizes. Suppose the diameter of one particular penny-farthing's front wheel is inches and the ratio of the diameter of the front wheel to the diameter of the back wheel is :1. What is the circumference of the back wheel? Use 3.14 for. The circumference of the back wheel is nothing inches.
Answers
Answer:
The circumference of the back wheel is 2.62 inches
Step-by-step explanation:
Given
[tex]d_1 = 5in[/tex] --- diameter of front wheel
[tex]d_1 : d_2 = 3:1[/tex] --- ratio of the diameters
Required
The circumference of the back wheel
First, we calculate the diameter of the back wheel.
We have:
[tex]d_1 : d_2 = 3:1[/tex]
Substitute: [tex]d_1 = 5in[/tex]
[tex]5in: d_2 = 3 : 1[/tex]
Express as fraction
[tex]\frac{d_2}{5in} = \frac{1}{3}[/tex]
Make [tex]d_2[/tex] the subject
[tex]d_2 =5in * \frac{1}{3}[/tex]
[tex]d_2 = \frac{5}{3}\ in[/tex]
So, the circumference (C) of the back wheel is:
[tex]C =\pi d[/tex]
[tex]C = 3.14 * \frac{5}{6}\ in[/tex]
[tex]C = \frac{3.14 * 5}{6}\ in[/tex]
[tex]C = \frac{15.7}{6}\ in[/tex]
[tex]C = 2.62\ in[/tex]
For the angle 0 = 150° moving counter-clockwise in standard position, determine which
primary trigonometric ratio is positive.
Answers
Answer: Start at the positive
x
-axis, then rotate left by the desired angle.
Explanation-
Standard position means the first arm of the angle is the positive
x
-axis, and the other arm is placed by rotating counter-clockwise from there, by the amount of the angle.
As a basic example, the symbol
∠
is about a 45° angle in standard position.
To get a feel for where the second arm (called the "terminal arm") will go, remind yourself that the axes themselves meet each other at 90°.
If our angle was 90°, the terminal arm would be on the positive
y
-axis.
If our angle was 180°, it would be on the negative
x
-axis.
Wait! 180° is more than 150°, so our angle is somewhere in quadrant 2. In fact, 150° is 2/3 of the way between 90° and 180°, so our terminal arm will be 2/3 of the way into quadrant 2.
graph{(y+tan(pi/6)x)(y^2-.00001x)=0 [-10, 10, -5, 5]}
(ignore the part of the line in quadrant 4)
Name the marked angle in 2 different ways.
Answers
1) angle RQP
2) angle PQR
I understand the problem
Answers
Answer:
c.100
Step-by-step explanation:
first draw a figure of rhombus EFGH to avoid confusions
given
angle E= 3x+5
angle H= 4x
here,
E=G and H=F ( opposite angles of rhombus are equal)
now,
E+G+H+F= 360 ( sum of interior angles in a rhombus)
3x+5+3x+5+4x+4x= 360
x= 25°
we know that,
F= H
F= 4x
F= 4 × 25
F= 100
pls help me..... the question is in the attachment.... thank you
Answers
Answer:
I added some attachments as well, I hoped I helped.
HELP PLEASEEEE !!!!!
Answers
Answer:
5%
Step-by-step explanation:
5 customers ordered large cold drinks so the probability would be 5/100
To convert 5/100 to percent, just do 5/100 x 100%
Questions in the image.
Answers
Answer:
Step-by-step explanation:
1). 3x + 10
3(2) + 10
= 16
2). 14 - 2y
14 - 2(-3)
= 20
3). 7x - 5y
7(2) - 5(-3)
= 29
4). 5x + 7
5(2) + 7
= 17
5). 2x + 3y
2(2) + 3(-3)
= -5
6). 6y - 5x
6(-3) - 5(2)
= -28
Consider the following system of two equations.
{y=−8x+10
y=x−8
What are the coordinates (x,y) of the solution to the system of equations?
Enter the coordinates in the space provided.
Answers
Expected value is: Group of answer choices the average probability of all possible outcomes of a future event occurring, weighted by each possible outcome individually the sum of all probabilities of all possible outcomes of a future event occurring the sum of all possible outcomes of a future event, weighted by its probability of occurring
Answers
Answer:
the average probability of all possible outcomes of a future event occurring, weighted by each possible outcome individually
Step-by-step explanation:
An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).
This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.
In Statistics, an expected value can be defined as the average probability of all possible outcomes of a future event occurring in an experiment, weighted by each possible outcome individually. Thus, an expected value in theory refers to the outcome an individual expect to obtain from an experiment in the long-run.
Mathematically, an expected value can be calculated by summing the products of each distinct outcome and their probability respectively.
Calculate the total surface area and the volume of a cone of base diameter 9cm and slant height of 12cm
Answers
Answer:
T.S.A = 233.29 cm²
volume of the cone = 235.84 cm³
Step-by-step explanation:
Given;
diameter of the cone, d = 9 cm
radius of the cone, r = 4.5 cm
slant height of the cone, l = 12 cm
The total surface of the cone is calculated as;
T.S.A = πr² + πrl
T.S.A = πr(r + l)
T.S.A = 3.142 x 4.5(4.5 + 12)
T.S.A = 233.29 cm²
The volume of the cone is calculated as;
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where;
h is height of the cone
h² = 12² - 4.5²
h² = 123.75
h = √123.75
h = 11.12 cm
[tex]V = \frac{1}{3} \pi \times (4.5)^2 \times 11.12\\\\V = 235.84 \ cm^3[/tex]
Apply the distributive property to create an equivalent expression.
\dfrac12(2a - 6b+ 8) =
2
1
(2a−6b+8)=start fraction, 1, divided by, 2, end fraction, left parenthesis, 2, a, minus, 6, b, plus, 8, right parenthesis, equals
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]a-3b+4[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Simplifying the Equation...}}\\\\\frac{1}{2}(2a-6b+8)\\----------------\\\rightarrow\frac{1}{2}* 2a = a\\\\ \rightarrow\frac{1}{2}*-6b = -3b\\\\\rightarrow\frac{1}{2}*8 = 4\\\\\text{\underline{Therefore:}}\\\\\frac{1}{2}(2a-6b+8)\rightarrow \boxed{a-3b+4}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer: a-3b+4
Step-by-step explanation:
Credits to guy up there
I don't understand help plz
Answers
In parallelogram GHJK if m∡GHJ=140˚ find m ∡KGH.
Answers
Answer: m∠x = 40°
Step-by-step explanation:
This works the exact same way as the other one
Being adjacent angles in a parallelogram, the two angles would be supplementary (add up to 180°).
140° + x° = 180°
x = 40°
a square garden has an area of 6400 square find its perimeter
Answers
Answer:
80
Step-by-step explanation:
Area of a square is LxL where L is the length of the side
so 6400 = LxL
L = 80
Jamal works at a sporting goods store on the weekends. Suppose last weekend he worked 12.5 hours and earned $110. How much money does Jamal earn per hour? Step I: Write an equation you can use to solve the problem. Be sure to define the variable you use. NOTE: If you are paid hourly, you must multiply your hourly rate by the number of hours worked in a week to find the amount of money made. (4
Answers
Answer:
$8
Step-by-step explanation:
12.5 hours earned him $110
then an hour will earn him less
12.5=$110
1=x then you cross multiply
12.5x=110
12.5x/12.5=110/12.5
x=8
therefore an hour will earn him $8
i need help...... ..
Answers
Problem 27)
Refer to the diagram that says "problem 27".
This is the graph of y = 5x where x is the time in years, and y is the amount of simple interest in the account.
This equation comes from the simple interest formula below
i = P*r*t
i = 100*0.05*x
i = 5x
y = 5x
Note: The graph is a straight line through (0,0) and (1,5)
=====================================================
Problem 28)
The abscissa is the x coordinate. For a point like (-3, -7), the abscissa is -3.
The ordinate is the y coordinate. For that point mentioned earlier, the ordinate is -7.
The graph of points is shown below in the figure labeled "problem 28".
When graphing any point, we always start at the origin (0,0) where the x and y axis meet up. Then for a point like (-3,-7) we move 3 units to the left on the x axis and 7 units down on the y axis to arrive at point A. The other points are plotted in a similar fashion. The labels A,B,C,D are optional. They were added to help keep track of the points.
Which of the following is NOT true about mathematical induction?
A.The first possible case is always n = 1.
B.Mathematical induction depends on a recursive process.
C.It can be used to prove that 1 + 2 + 3+...+n =
n(n+2)
2
D. Since Sn is valid for n = 1, it is valid for n = 2. Since it is valid for n = 2, it is valid for n = 3, and so on, indefinitely.
Answers
Answer:
A. the first possible case is always n = 1
Step-by-step explanation:
Mathematical induction is a technique used to provide proof for a statement such that the statement holds for all natural numbers which are the non-negative integers
Therefore, given that the natural numbers are 0, 1, 2..., we have that mathematical induction can start from n = 0
Therefore, the statement which is not true is that the first possible case is always n = 1
Compare the graph h(x)=1/4x^2 to the graph of f(x) = x2.
Answers
Answer:
h(x) is the image after f(x) is horizontally stretched by a scale factor of 4
Step-by-step explanation:
Given
[tex]h(x) = \frac{1}{4}x^2[/tex]
[tex]f(x) = x^2[/tex]
Required
Compare h(x) to f(x)
We have:
[tex]h(x) = \frac{1}{4}x^2[/tex]
Substitute [tex]f(x) = x^2[/tex]
[tex]h(x) = \frac{1}{4}f(x)[/tex]
This means that f(x) is stretched horizontally by a scale factor of 4 to get h(x)
