Answer:
The answer is (5x2 – 2)(25x4 + 10x2 + 4)
Find the equation of the line . Write in slope intercept form and in standard form. (SHOW YOUR SOLUTION)
1. m = -5, b=1
2. ( 1, -2), (3, 3)
3. (-2, 0) and (0, 5)
4. a = 2, b = -7
5, m = 2, (3, -1)
Answer:
1) The slope-intercept and standard forms are [tex]y = -5\cdot x + 1[/tex] and [tex]5\cdot x +y = 1[/tex], respectively.
2) The slope-intercept form of the line is [tex]y = \frac{5}{2}\cdot x -\frac{9}{2}[/tex]. The standard form of the line is [tex]-5\cdot x +2\cdot y = -9[/tex].
3) The slope-intercept form of the line is [tex]y = \frac{5}{2}\cdot x + 5[/tex]. The standard form of the line is [tex]-5\cdot x +2\cdot y = 10[/tex].
4) The slope-intercept and standard forms of the family of lines are [tex]y = \frac{2}{7}\cdot x -\frac{c}{7}[/tex] and [tex]2\cdot x -7\cdot y = c[/tex], [tex]\forall \,c \in \mathbb{R}[/tex], respectively.
5) The slope-intercept form of the line is [tex]y = 2\cdot x-7[/tex]. The standard form of the line is [tex]-2\cdot x +y = -7[/tex].
Step-by-step explanation:
From Analytical Geometry we know that the slope-intercept form of the line is represented by:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]m[/tex] - Slope, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
In addition, the standard form of the line is represented by the following model:
[tex]a\cdot x + b \cdot y = c[/tex] (2)
Where [tex]a[/tex], [tex]b[/tex] are constant coefficients, dimensionless.
Now we process to resolve each problem:
1) If we know that [tex]m = -5[/tex] and [tex]b = 1[/tex], then we know that the slope-intercept form of the line is:
[tex]y = -5\cdot x + 1[/tex] (3)
And the standard form is found after some algebraic handling:
[tex]5\cdot x +y = 1[/tex] (4)
The slope-intercept and standard forms are [tex]y = -5\cdot x + 1[/tex] and [tex]5\cdot x +y = 1[/tex], respectively.
2) From Geometry we know that a line can be formed by two distinct points on a plane. If we know that [tex](x_{1},y_{1})=(1,-2)[/tex] and [tex](x_{2},y_{2}) = (3,3)[/tex], then we construct the following system of linear equations:
[tex]m+b= -2[/tex] (5)
[tex]3\cdot m +b = 3[/tex] (6)
The solution of the system is:
[tex]m = \frac{5}{2}[/tex], [tex]b = -\frac{9}{2}[/tex]
The slope-intercept form of the line is [tex]y = \frac{5}{2}\cdot x -\frac{9}{2}[/tex].
And the standard form is found after some algebraic handling:
[tex]-\frac{5}{2}\cdot x +y = -\frac{9}{2}[/tex]
[tex]-5\cdot x +2\cdot y = -9[/tex] (7)
The standard form of the line is [tex]-5\cdot x +2\cdot y = -9[/tex].
3) From Geometry we know that a line can be formed by two distinct points on a plane. If we know that [tex](x_{1},y_{1})=(-2,0)[/tex] and [tex](x_{2},y_{2}) = (0,5)[/tex], then we construct the following system of linear equations:
[tex]-2\cdot m +b = 0[/tex] (8)
[tex]b = 5[/tex] (9)
The solution of the system is:
[tex]m =\frac{5}{2}[/tex], [tex]b = 5[/tex]
The slope-intercept form of the line is [tex]y = \frac{5}{2}\cdot x + 5[/tex].
And the standard form is found after some algebraic handling:
[tex]-\frac{5}{2}\cdot x+y =5[/tex]
[tex]-5\cdot x +2\cdot y = 10[/tex] (10)
The standard form of the line is [tex]-5\cdot x +2\cdot y = 10[/tex].
4) If we know that [tex]a = 2[/tex] and [tex]b = -7[/tex], then the standard form of the family of lines is:
[tex]2\cdot x -7\cdot y = c[/tex], [tex]\forall \,c \in \mathbb{R}[/tex]
And the standard form is found after some algebraic handling:
[tex]-7\cdot y = -2\cdot x +c[/tex]
[tex]y = \frac{2}{7}\cdot x -\frac{c}{7}[/tex], [tex]\forall \,c\in\mathbb{R}[/tex] (11)
The slope-intercept and standard forms of the family of lines are [tex]y = \frac{2}{7}\cdot x -\frac{c}{7}[/tex] and [tex]2\cdot x -7\cdot y = c[/tex], [tex]\forall \,c \in \mathbb{R}[/tex], respectively.
5) If we know that [tex](x,y) = (3,-1)[/tex] and [tex]m = 2[/tex], then the y-intercept of the line is:
[tex]3\cdot 2 + b = -1[/tex]
[tex]b = -7[/tex]
Then, the slope-intercept form of the line is [tex]y = 2\cdot x-7[/tex].
And the standard form is found after some algebraic handling:
[tex]-2\cdot x +y = -7[/tex] (12)
The standard form of the line is [tex]-2\cdot x +y = -7[/tex].
Jessica added the two distances in the table to get a sum
of 26.95 miles.
Jessica's Running Journal
Week 1
11.9 miles
Week 2
15.05 miles
Explain the steps you use to determine if Jessica's
answer is reasonable.
LOTS OF POINTS HELP ASAP
Answer:
Round to the nearest whole number and then add the numbers. The estimate should be close in value to the actual sum.
Step-by-step explanation:
Grades 1 through 6 at Eastwood Elementary School raised $5,492 towards repairs for the gymnasium floor. How much did each grade raise if they each collected about the same amount of money? Choose the best estimate
Answer:
[tex]Each\ Grade = \$915[/tex]
Step-by-step explanation:
Given
[tex]Total = \$5492[/tex]
[tex]Grades = 6[/tex] i.e. 1 to 6
Required
Determine the amount raised by each grade
From the question, we understand that each grade raised the same amount.
This implies that.
[tex]Each\ Grade = \frac{Total}{Grades}[/tex]
[tex]Each\ Grade = \frac{\$5492}{6}[/tex]
[tex]Each\ Grade = \$915.33333333[/tex]
[tex]Each\ Grade = \$915[/tex] (approximated)
Which quadrant does the complex number -4 - 9i lie in?
a. Quadrant I
b. Quadrant III
c. Quadrant II
d. Quadrant IV
Answer:
Quadrant III
Step-by-step explanation:
because in quadrant III there is both negative terms
Simplfy 7xy + 8x + 5xy + 6x
Answer:
2xy+2x
Step-by-step explanation:
7xy-5xy = 2xy
8x-6x= 2x
combine:
2xy+2x
Answer:
12xy+14x
Step-by-step explanation:
They're just hired a new employee to work in your bike shop in one hour the employee burns 55 chocolate chip cookies if this represented 22% of the days production how many cookies did you plan on producing that day
Answer:
250 cookies
Step-by-step explanation:
The employee burns 55 chocolate chip cookies
if this represented 22% of the days production
Let x = the total production of cookies for the day
how many cookies did you plan on producing that day?
22% of x = 55
22 / 100 * x = 55
0.22x = 55
Divide both sides by 0.22
x = 55 / 0.22
= 250
x = 250 cookies
Therefore, the total production of cookies for the day is 250
Where is the circumcenter of this acute triangle located?
O on a side of the triangle
O inside the triangle
O at a vertex of the triangle
O outside the triangle
!!Will give 90 points and brainiest!!
Answer:
inside of the triangle
Step-by-step explanation:
In school the ratio of the number of pupils to the number of teachers is 20:1 of the number of pupils is 840 how many teachers are there
Answer:
Step-by-step explanation:
Given ration of pupils and teachers =20:1
Let the no. Of teachers =X
So no.of pupils =20X
No.of pupils=840
20X=840
X=840/20
X=42
No.of teacher =X
=42.
Write the equation of a line that passes through (4, 6) and is parallel to y = 4x + 4.
Answer:
y = 4x - 10
Step-by-step explanation:
6 = 4 (4) + b
-10 = b
The percentage of sprouted seeds for a single crop can be modeled by a logistic function that is represented by y=100/1+99e^-0.89x. Which statements about the scenario are true? Check all that apply.
Answer:
A, B, and C
Step-by-step explanation:
Explain why x2 + 25 is not equal to (x + 5)2.
Step-by-step explanation:
Because in (x + 5)2 you have to multiply 2 by each term in the parentheses, and that is not equal to x2 + 25. itll be 2x + 10 and that is not equivalent.
x² + 25 is not equal to (x+5)² because the later has an extra term 10x in it.
What is a quadratic equation ?A quadratic equation has a highest degree of 2 and it has two solutions or roots which satisfies ax² + bx + c = 0.
According to the given explain why x² + 25 and (x+5)² are not equal.
We know (a+b)² = a² + 2ab + b².
So, (x+5)² = x² + 10x + 25.
On the other hand x² + 25 can be written as x² + 5².
∴ (x+5)² ≠ x² + 5².
There is an extra term 10x in (x+5)² or we can say x² + 25 is 10x less than (x+5)².
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DUE IN 2 minutes
pls help
Answer: I can’t see the numbers dude.
Step-by-step explanation:
Sorry
ILL GIVE BRAINLY FOR RIGHT ANSWER HELP!!!!!
Answer:
3 apples.
Step-by-step explanation:
Answer:
6 apples? maybe
Step-by-step explanation:
Is 12 even or odd? Pick you choice
Answer:
Even
Step-by-step explanation:
Help me solve this problem please
Answer:B. is your
Step-by-step explanation: make sure you thank me and rate this with 5 stars please I'm begging you
help me its an algebra 2 question 2. John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours. How long will it take them to mow their lawn if they work together?
A. 1 hour 12 minutes
B. 1 hour 15 minutes
C. 1 hour 20 minutes
D. 1 hour 30 minutes
E. 1 hour 35 minutes
Answer:
A
Step-by-step explanation:
John can mow the same lawn in 3 hours.
In 1 hour he can mow 1/3rd of the lawn.
In 1 hour they can together mow (1/2+1/3)=5/6th of the lawn.
Together they can mow the lawn in 6/5 hours=1.2 hours.
I hope this helped, please mark Brainliest, thank you!!
Time taken to mow the lawn together is 6/5 hours i.e., 1.2 hours.
The correct option is (C).
What is a algebra ?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Given:
John can mow his lawn in 3 hours.
Julie can mow same lawn in 2 hours.
In 1 hour = 1/3rd of the lawn.
In 1 hour, together they can mow
= (1/2+1/3)
=5/6th of the lawn.
Hence, time taken to mow the lawn together is 6/5 hours i.e., 1.2 hours.
Learn more about Algebra here:
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Given the sum of the interior angles of a polygon, tell the number of sides of the polygon.
If the interior angle sum is 360°, the polygon has _
sides.
If the interior angle sum is 540°, the polygon has _
sides.
If the interior angle sum is 900°, the polygon has _
sides.
If the interior angle sum is 1260°, the polygon has _
sides.
Answer:
[tex] \underline{the \: sides \: are} \: \to \\ \underline{ \boxed{ n= 4}} \\ \: \underline{ \boxed{ n= 5}} \\ \:\underline{ \boxed{ n= 7}} \\ \: \underline{ \boxed{ n= 9}} \\ \: [/tex]
Step-by-step explanation:
[tex] \\ the \: sum \:o f \: the\: interior \: angles \: of \: aregular \: polygon \: \\ is \: generaly \: given \: by \to \: 180(n - 2)\\ \underline{ \boxed {case \:( 1) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 360°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 360 \\ n - 2 = 2 \\ \underline{ \boxed{ n= 4}} \\ \: \underline{ \boxed {case \:( 2) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 540°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 540 \\ n - 2 = 3 \\ \underline{ \boxed{ n= 5}} \\ \: \underline{ \boxed {case \:( 3) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 900°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 900 \\ n - 2 = 5 \\ \underline{ \boxed{ n= 7}} \\ \: \underline{ \boxed {case \:(final ) \to}} \\ If \: the \: interior \: angle \: sum \: is \: 1260°, \\ then : \: the \: polygon \: has \to \: \\ 180(n - 2) = 1260 \\ n - 2 = 7\\ \underline{ \boxed{ n= 9}} \\ \: [/tex]
♨Rage♨
Answer:
4,5,7,9
Step-by-step explanation:
Got it right on edge
the polygons in each pair are similiar. help find the missing side length???
Answer:
[tex]x=12[/tex]
Step-by-step explanation:
Since the polygons are similar, we can use the formula: [tex]\frac{x}{15}=\frac{32}{40}[/tex]. Using cross-multiplication , we obtain: [tex]40x=15*32\\x=\frac{15*32}{40}= 12[/tex].
Writing the Inverse of a Function
What is the inverse of f(x) = **+ 2?
o h(x) = 2x+2
O h(x) = {x-2
O h(x) = 3x - 2
Oh(x) = 3x - 6
it is o h(x)= 2×+2 because if you look at the question and you see that the answer i got would match with the question
Can two people with blue eyes have a child with brown eyes? Why or why not? also i really don´t really know the subject so i put it in math.
Answer:
Yes
Step-by-step explanation:
In the family the blue eyed people may have had a gene with brown eyes. So if both parents carry that gene even if they don't display it, it can be still shown because brown eyes are the most dominant trait.
BR Elder 1: BL BR BL Elder 2: BL BL BL Elder 1: BL BL BL Elder 2: BR BL
I I I I
I I
Parent 1: Blue gene brown gene Parent 2: Blue gene brown gene
I I
I
Child Brown eyes: BR BL
Because the brown gene is dominant if the gene shows up in both parents the child would be more likely to have brown eyes than blue.
calculate the volume of of a cylinder of diameter 5.93cm and length 10cm in log and antilog
3.14 × 6.25..............
Answer:
calculator says 19.625
Answer:
19.625
Step-by-step explanation:
Help please!!!!!! And explain ur answer.. I will mark as BRAINLIEST
Answer:
Nu 4550
Step-by-step explanation:
Commission of 5% only applies to the first 70,000 so
[tex]70,000*\frac{5}{100} = 3500[/tex]
That leaves 15,000 left in sales where the 7% commission applies.
[tex]15,000*\frac{7}{100}=1050[/tex]
Adding these two together we get a total of
[tex]3500 +1050=Nu4550[/tex]
15+ Points, Plus Brainliest if your right!
A summer camp has 20 boys and 20 girls. Each day, all camper names are put in a hat, and one name is drawn to receive a prize. What are the odds in favor of boys names being drawn on three out of three nights?
A. ) 1:1
B. ) 1:7
C. ) 1:8
D. ) 7:1
Answer:
A
Step-by-step explanation:
Because there are a same number of boys and girls, the odds are 20:20 which can be simplified to 1:1
Hope that helps
Once again the answer is A
Bye have a great time :D
Pls anyone help i will give brainlist
Answer:
D
Step-by-step explanation:
sry if im wrong i tried
Answer:
0; 1; 2; 3. The slopes are 2, 0, 1, 3 from top to bottom, but from least to greatest it is 0, 1, 2, 3
You triple your account balance by making a deposit. Then you withdraw $125.00 to buy groceries. Your account is overdrawn $5.00 write an equation to find your account balance before you made the deposit
Answer:
3x - 125 = -5
Step-by-step explanation:
the 3 is the triple, x is the deposit and -125 is the withdrawn and -5 is what's left over in the bank account
3) g(t) = 31 - 5; Find g(9)
A) -5
B) -23
C) 22
D) 1
Answer:
C. 22
Step-by-step explanation:
Which quadratic equation models the situation correctly?
h(t) = –16t2 + 61
h(t) = –16t2 + 202.5
h(t) = –16t2 + 56t + 5
h(t) = –16t2 + 56t + 6.5
Answer:
D
Step-by-step explanation:
Edge 2020-2021
The quadratic equation {y = - 16t² + 202.5} correctly represents the given graph.
What is a quadratic equation?A quadratic equation is of the form -
f(x) = ax² + bx + c
Given is the graph as shown in the image attached.
The graph given in the image is correctly represented by the quadratic equation -
y = - 16t² + 202.5
Due to the negative coefficient of {a}, it opens downwards. The [y] intercept is at 202.5.
Therefore, the quadratic equation {y = - 16t² + 202.5} correctly represents the given graph.
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(EASY) I WILL MARK THE BRAINLYEST !!!
so, these problems are currently my last two problems. There were two rude people that answered them and didn't actually give me an answer and responded with "no". Can you guys please help me? These are the only two questions giving me problems at the moment. Thank you for taking the time to help me.
1) |5x+5|+22>57
solve for both absolute values
( it would help if you could include how to graph it on a number line as well as the interbal notation )
2) I= prt
solve for I
Answer:
-8>x>6
Step-by-step explanation:
I 5x+5I +22> 57subtract 22 on both sides
I5x+5I >35
SPLIT
5x+5>35 5x+5< -35 ( flip sign and 35 negative)
5x>30 5x< -40
x>6 x< -8
Draw a number line Write zero in the middle
From zero count to the left until- 8 make an open circle because- 8 is not included From -8 draw an arrow to the left (because x is less than -8)
From zero count to the right until 6 Make an open circle bc 6 is not included. From 6 draw an arrow to the right (because x is more than 6)
PART 2 is not already solved?
If you need to solve fot t
Divide both parts by pr
t= (l/ pr)
Joe wants to buy a pair of pants that cost $48. He has a coupon and after the coupon is applied, his jeans cost $40.80. What percent off was his coupon?
need answer asap
Answer:
85%
Step-by-step explanation:
I learned about it and did the problem so to check my answer i searched it up on Google
Step-by-step explanation:
Percent Change Formula
(New value- Original Value)/ original value multiplied by 100.
So (40.8-48)/48
This gives us a decimal of -.15.
Multiply by 100
And we get 15 percent off
