Answer:
Step-by-step explanation:
(a - b)² = a² -2ab + b²
Here, a = x and b = 1
(x -1)² = x² - 2 * x *1 + 1²
= x² - 2x + 1
[tex]\sf \longmapsto \:( x + 1) {}^{2} [/tex]
[tex]\sf \longmapsto(x+1)(x+1)[/tex]
[tex]\sf \longmapsto(x)(x)+(x)(1)+(1)(x)+(1)(1)[/tex]
[tex]\sf \longmapsto \: x {}^{2} +x+x+1[/tex]
[tex]\sf \longmapsto \: x {}^{2} +2x+1[/tex]
[tex] \boxed{ \boxed{ \red {\sf x {}^{2} +2x+1}}}[/tex]
(a) State whether each of the following is a function. (6, 2), (8,2), (6,3), (12,3) Yes / No
Answer:
Not a function.
Step-by-step explanation:
The definition of a function specifies that no value of x can be paired with two or more different values of y.
In the given relation: {(6, 2), (8, 2), (6, 3), (12, 3)},
The input value of x = 6 has two corresponding output values (y-coordinates): 2 and 3.
Therefore, the given relation is not a function.
[tex]-------------------[/tex]
12+2=
Which of the following is the midsegment of triangle ABC ?
Α. AL
B. LM
C. LB
D. MC
Answer:
LM
Step-by-step explanation:
a
Lucy has a coin collection. She keeps 3 of the coins in her box, which is 25% of the
collection. How many total coins are in her collection?
Multiply/scale up to solve.
coins
3
25
100
percent
Answer:
3x4=12
12 coins in her collection
Step-by-step explanation:
25x4=100%
The Western inventory was written by 4 different authors. Author A wrote 1/4 of the books, author b wrote 5/16 of the books, and author c write 3/8 of the books. What part of the inventory did author D write?
Answer:
Author D write 1/16 of the total number of books.
Step-by-step explanation:
Let the total number of books be b. Then the amounts written by the four authors would be represented by:
(1/4)A
(5/16)A
(3/8)A
( ? )A
Add these together, realizing that the LCD here is 16:
(4/16)A
(5/16)A
(6/16)A
( ? ) A
------------
(15/16)A must then equal the remainder of the work: (16/16)A
Thus, Author D wrote (1/16)A of the books. (Note that 4/16 + 5/16 + 6/16 + 1/16 = 1)
Author D write 1/16 of the total number of books.
Please help! I really need to get the answer correct
Answer:
x + 9y²
Step-by-step explanation:
A prime polynomial is simply an irreducible polynomial.
x + 9y² is a prime polynomial
First, we test the options.
x + 9y²
The above function cannot be reduced further.
Hence, x + 9y² is a prime polynomial
3m + 9n
Factor out 3
3 (m + 3n)
3m + 9n is not a prime because it can be factored as 3 (m + 3n)
8x^7 - 9x + 12x²
Factor out x
x(8x^6 - 9 + 12x)
8x^7 - 9x + 12x² is not a prime because it can be factored as x(8x^6 - 9 + 12x)
Hence, x + 9y² is a prime polynomial
miggy ask to solved the given quadratic equation x²+8x-20=0 using the quadratic formula,Help miggy to determine the following
roots of the quadratic 3
discriminant
nature of roots
sum of the roots
product of the roots
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
roots of the quadratic equation ~
[tex]2 \: \: \: \:a nd \: \: - 10[/tex]discriminant ~
[tex]144[/tex]nature of roots ~
[tex]real[/tex]sum of the roots ~
[tex] - 8[/tex]product of the roots ~
[tex] - 20[/tex][tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's solve he given quadratic equation using quadratic formula ~
Let's consider the following values ~
b (Coefficient of x) = 8 a (Coefficient of x²) = 1 c (Constant term) = -20According to quadratic formula, the roots are ~
[tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]where, ( b² - 4ac ) is known as it's discriminant ~
that is equal to ~
[tex](8) {}^{2} - (4 \times 1 \times - 20)[/tex][tex]64 - ( - 80)[/tex][tex]64 + 80[/tex][tex]144[/tex]Hence, Discriminant = 144
And since discriminant is positive, then the roots of the quadratic polynomial are real .
Let's find the roots now ~
[tex] \dfrac{ - b \pm \sqrt{b {}^{2} - 4ac} }{2a} [/tex][tex] \dfrac{ - 8 \pm \sqrt{144} }{2 \times 1}[/tex][tex] \dfrac{ - 8 \pm12}{2} [/tex][tex] \dfrac{ 2( - 4 \pm6)}{2} [/tex][tex] - 4 \pm6[/tex]So, the two roots are ~
[tex] - 4 + 6[/tex][tex]2[/tex]and
[tex] - 4 - 6[/tex][tex] - 10[/tex]Sum of roots ~
[tex] - 10 + 2[/tex][tex] -8[/tex]product of roots ~
[tex] - 10 \times 2[/tex][tex] - 20[/tex]What times -1/2 x what = -20?
Answer:
40
Step-by-step explanation:
Let the number be y
-1/2 × y = -20
y = -20 ÷ -1/2
y = 20 × 2
y = 40
Have i done this right, why did i not get the third mark
Answer:
because you are good with math
Step-by-step explanation:
its urgent please. my assignment is due in like 30 minutes
Answer:
( iii)
a-x/a+x =b
a-x=b(a+x)
a-x=ab+ax
a-ab=ax+x
a-ab=x(a+1)
a-ab/a+1=x(a+1)/a+1
x=a-ab/a+1
x=a(1-b)/a+1
There are only 9 counters in a bag. There are 2 red counters 3 green counters 4 blue counters Lethna takes at random a counter from the bag. (a) Write down the probability that she takes
(i) a blue counter,
A white counter
-1/3(2p-9) what does p equal
Answer:
-2p/3+3
Step-by-step explanation:
Which theorem does it offer proof of?
Answer:
vertical angles are =
Step-by-step explanation:
sharon ate 2 pieces of pie. if this was 25% of the whole pie, how many pieces were there were originally.
Answer:
8
Step-by-step explanation:
25 divided by 2 is 12.5.
100 divided by 12.5 is 8
Answer:
8
Step-by-step explanation:
2 is 25% so, 2 times 2 is 4
4 is 50% so, 2 times 3 is 6
6 is 75% so, 2 times 4 is 8
8 is 100% of the pie
Please help! I don't understand A-E its urgent :(
No links!!!! (picture included)
A. Name an alternate interior angle to angle 3
B. Name a corresponding angle to angle 8
C. Name a vertical angle to angle 2
D. Name a same side-interior angle to angle 5
E. Name an alternate exterior angle to angle 7
Step-by-step explanation:
A. 6 ---- Alternate interior angles are on opposite sides of the transversal while still between the other 2 lines
B. 4 ---- Corresponding angles are angles in matching corners when the transversal crosses over 2 other lines
C. 3 ---- Vertical angles are on opposite sides when 2 lines intersect
D. 6 ---- Side interior angles are the opposite of alternate interior angles, they are both on the same side
E. 2 ---- Alternate exterior angles are very similar to alternate interior angles, only that they are on the outside rather than on the inside of the 2 lines
11(5-8=-11 5-8=-1. S=
Complete the following proof. Given: (BD) is the perpendicular bisector of (AC) Prove: ∢A≅∢C
Statement Reason
1. (BD) is the perpendicular bisector of (AC) 1. Given
2. Point B is the midpoint of (AC) 2. Definition of perpendicular bisector
3. 3. Definition of midpoint
4. ∢ABD and ∢CBD are right angles 4. Definition of perpendicular bisector
5. ∢ABD and ∢CBD are congruent 5. All right angles are congruent.
6. 6. Reflexive property of congruence
7. 7.
8. ∡A≅∡C 8.
Answer:
I dont know if this is right but... i tried XD
Step-by-step explanation:
Angle A is congruent to angle C.
What is Triangle?A triangle in geometry is a polygon with three sides and three angles. The sum of the interior angles of a triangle is 180°.
If XYZ is a triangle, it is represented as ΔXYZ
Here, it is given that BD is the perpendicular bisector of AC.
Then by the definition of perpendicular bisector, B is the midpoint of AC.
Consider ΔABD and ΔCBD
ΔABD and ΔCBD are right triangles with ∡ABD = ∡CBD = 90°.
So, ∡ABD ≅ ∡CBD (∵ all right angles are congruent)
Now, by the reflexive property of congruence, every side or angles are congruent to itself.
So BD ≅ BD
Since B is the midpoint of AC, AB = BC.
Hence AB ≅ BC
By SAS theorem, if two sides and an angle of a triangle are congruent to two sides and angles of another triangle, then both triangles are congruent.
Hence ΔABD ≅ ΔCBD
So, Angle A is congruent to angle C.
Hence ∡A ≅ ∡C if BD is perpendicular bisector of AC.
To learn more about congruence of triangles, click:
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If 2x = 3y + 11 and 2 to the power of x = 2 to the power of 4(y+1), determine the value of x + y
Z = -2
Y = 5
is your answer
whats x
-5x + 2 = 67
Answer:
x=-13
Step-by-step explanation:
Subtract 22 from both sides.
-5x=67-2
Simplify 67-2 to 65.
-5x=65
3 Divide both sides by -5.
[tex]x=-\frac{65}{5}[/tex]
Simplify [tex]\frac{65}{5}[/tex] to 13.
x=−13
The temperature of a pan of water on the stove increases steadily from 22°C to 100°C at a rate of 8°C per minute. The temperature after 5 minutes is what.
Answer:
ui100
Step-by-step explanation:
125
The temperature of a pan of water on the stove after 5 minutes would be 40°C.
What is temperature?Temperature is the measure of the degree of hotness and coldness which is expressed in different scales.
The temperature of a pan of water increases steadily from 22°C to 100°C at a rate of 8°C per minute.
We need to find the temperature after 5 minutes.
Rate of temperature per minute = 8°C
Rate of temperature after 5 minutes = 8°C × 5
= 40°C
Therefore, the temperature after 5 minutes would be 40°C.
Learn more about temperature;
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PLEASE HURRY!
Nicholas started a canned-food drive at school. The equation representing this is y = 235x + 15, where x is the number of days, and y is the number of cans collected. Explain how to determine how many days it would take to collect 2600 cans.
Answer:
11 days
Step-by-step explanation:
because Nicholas was given a number of cans, which is y, and I need to find the number of days, which is x. To do this, I would substitute 2600 for y, to get 2600 = 235x + 15. Solving for x, I would get x = 11. Thus, it would take 11 days to collect 2600 cans.
Answer:
11 days
Step-by-step explanation:
1. A person who weighs 100pounds on Earth weighs 16.5 pounds on the Moon. If a boy
weighs 86pounds on Earth, how much does he weigh on the moon
Answer:
That person would weigh 14.22 lbs.
Each big square below represents one whole.
Answer:
103%
Step-by-step explanation:
each little box is 1%
What are the two pieces of information needed to write an equation, in slope-intercept
form, to model any linear relationship?
Answer:
Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information. All you need to know is the slope (rate) and the y-intercept. Continue reading for a couple of examples! Write the equation for a line that has a slope of -2 and y-intercept of 5.
Step-by-step explanation:
Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information. All you need to know is the slope (rate) and the y-intercept. Continue reading for a couple of examples! Write the equation for a line that has a slope of -2 and y-intercept of 5.
Answer:
The first piece of information you need is the slope number and the second piece of information you need is the y intercept
8x-3y=9
3x+2y=8
(Guys need help on this simultaneous equation)
Step-by-step explanation:
sorry that's all i know hehe
5. Find the triangle similar to AABC at the right. Question 5
Answer:
b
Step-by-step explanation:
If you multiple each side by 3 then they will equal the numbers that b has
help plss c:
a family wishes to determine the distance from their home to the nearest park. on a coordinate grid, the house sits at (0,0), and the park at (16,11)
using 1 unit = 10 yards, which vector represents the path from the house to the park, and what is the actual distance between them?
Answer:
components: {16,11}, distance: 194.16 yards
Step-by-step explanation:
to find the length of a point to another point that has different y and x points you use the pythagorean theorem (a^2 + b^2 = c^2)
16 and 11 are the distances from her house
16^2 + 11^2 = c^2
c^2 = 377
c = 19.416...
but we dont stop here
we have to convert this to yards by multiplying it by ten
19.416 * 10 = 194.16 yards
Answer:
B
Step-by-step explanation:
Just did the test
In 2005 a town with a population of 10,000 finds that its population is declining by a rate of 0.3% per year. Find the following
of the original population. He answered that it would never reach half, what is the incorrect assumptions Johnny made? (answer with a Johnny was asked how long it will take the population to reach complete sentence)
Johnny's assumption is that, none of the residents of the town will live up to 231 years.
The parameters are given as:
[tex]\mathbf{P_o = 10000}[/tex]--- the population in 2005
[tex]\mathbf{r = 0.3\%}[/tex] -- the rate at which the population declines
To model a population, we make use of the following exponential function
[tex]\mathbf{P = P_o \times(1 -r)^t}[/tex]
Where P is the current population in t years.
So, we have:
[tex]\mathbf{P = 10000 \times(1 -0.3\%)^t}[/tex]
When the population reaches half of the initial population, then P = 5000.
So, we have:
[tex]\mathbf{5000 = 10000 \times(1 -0.3\%)^t}[/tex]
Divide both sides by 10000
[tex]\mathbf{0.5 = (1 -0.3\%)^t}[/tex]
[tex]\mathbf{0.5 = (0.997)^t}[/tex]
Take logarithm of both sides
[tex]\mathbf{log(0.5) = log(0.997)^t}[/tex]
Rewrite the equation as
[tex]\mathbf{log(0.5) = tlog(0.997)}[/tex]
Make t the subject
[tex]\mathbf{t = \frac{log(0.5)}{log(0.997)}}[/tex]
[tex]\mathbf{t = 231}[/tex]
This means that the population will halve its initial population in 231 years.
Johnny's assumption is that, none of the residents of the town will live up to 231 years.
Read more about population functions at:
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sandra babysat for the millers for 4.5 hours. the millers gave her 40$. write and solve an equation to calculate how much sandra earned per hour. round to the nearest hundrefth.
Nadine received the same score on each turn in an online game. Her score on each turn was −24. She had 4 turns.
What was Nadine's final score?
Answer:
Step-by-step explanation:
-24 x 4 = -96