[tex]\bf \cfrac{x^5y^3}{x^2-x-6}\cdot \cfrac{x^2-9}{x^2y^4}\implies \cfrac{x^5y^3}{x^2-x-6}\cdot \cfrac{\stackrel{\textit{difference of squares}}{x^2-3^2}}{x^2y^4} \\\\\\ \cfrac{x^5y^3}{~~\begin{matrix} (x-3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+2)}\cdot \cfrac{~~\begin{matrix} (x-3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+3)}{x^2y^4}\implies \cfrac{x^5y^3}{x+2}\cdot \cfrac{x+3}{x^2y^4}[/tex]
[tex]\bf \cfrac{x^5y^3}{x^2y^4}\implies \cfrac{x^5x^{-2}}{y^4y^{-3}}\cdot \cfrac{x+3}{x+2}\implies \cfrac{x^{5-2}}{y^{4-3}}\cdot \cfrac{x+3}{x+2}\implies \cfrac{x^3(x+3)}{y(x+2)}\implies \cfrac{x^4+3x^3}{yx+2y}[/tex]
Which shows a perfect square trinomial?
502-4x2
100-36x?y
16x2+24 xy +9y2
49x2 - 70 xy +10y
Answer:
Third choice.
Step-by-step explanation:
Trinomial means you have 3 terms.
You don't have 3 terms in first two choices so let's not look at them.
Anything of the form [tex]a^2x^2+2abxy+ b^2y^2[/tex] is a perfect square trinomial because it can be written as [tex](ax+by)^2[/tex].
Let's this this:
[tex](ax+by)^2[/tex]
[tex](ax+by)(ax+by)[/tex]
Now foil!
First=ax(ax)=a^2x^2
Outer=ax*by=abxy
Inner=by*ax=abxy
Last=by*by=b^2y^2
Add together and this gives you a^2x^2+2abxy+b^2y^2.
So looking at third choice you can write it as 4^2x^2+24xy+3^2y^2.
Is 2*4*3 equal to 24? If it is then you have your answer. It is.
We have our answer.
Edgar accumulated $5,000 in credit card debt. If the interest is 20% per year and he does not make any payment for 2 years. How much will he owe on this debt in 2 years by compounding continously?
Answer:
$7,434.57
knewton alta 2023
Step-by-step explanation:
Edgar will owe approximately $6,360.92 on his credit card debt in 2 years with continuous compounding.
Explanation:To calculate the amount Edgar will owe on his credit card debt in 2 years with continuous compounding, we can use the formula for compound interest:
A = P*e^(rt)
Where:
A is the final amountP is the initial principal (the amount Edgar owes)e is Euler's number (approximately equal to 2.71828)r is the interest rate per year in decimal formt is the time in yearsPlugging in the values, we have:
A = $5,000 * e^(0.20*2)
Calculating this expression gives the approximate value of $6,360.92. Therefore, Edgar will owe approximately $6,360.92 on his credit card debt in 2 years with continuous compounding.
Solve y over negative 2 + 5 = 13
Answer: y=-16
Step-by-step explanation:
Y/-2+5=13
Y/-2=8
Y=-16
Which point is on the graph of f(x) = 3 • 4x? A. (0, 12) B. (0, 0) C. (1, 12) D. (12, 1)
Answer:
(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].
Please correct if I'm wrong about your expression.
Step-by-step explanation:
I think you mean [tex]f(x)=3 \cdot 4^x[/tex].
Let's test the point and see.
A. (0,12)?
(0,12)=(x,y)
What happens when x equals 0? Is the result 12?
[tex]3 \cdot 4^0[/tex]
[tex]3 \cdot 1[/tex]
[tex]3(1)[/tex]
[tex]3[/tex]
Yep that isn't 12 so (0,12) is not on the graph of f.
B. (0,0)?
(0,0)=(x,y)
What happens when x equals 0? Is the result 0?
[tex]3 \cdot 4^0[/tex]
We already this and got 3 so (0,0) is not on the graph of f.
C. (1,12)?
(1,12)=(1,12)
What happens when x equals 1? Is the result 12?
[tex]3 \cdot 4^1[/tex]
[tex]3 \cdot 4[/tex]
[tex]12[/tex]
The result is 12 so (1,12) is on the graph of f.
C. (12,1)
(12,1)=(x,y)
What happens when x equals 12? Is the result 1?
[tex]3 \cdot 4^{12}[/tex]
This will result in a really big number that isn't 1 so (12,1) is not on the graph of f.
(1,12) is correct if you meant [tex]3 \cdot 4^x[/tex].
Answer:
(1,12)
Step-by-step explanation:
ape x
PLS ANSWER THESE QUESTIONS. I WILL GIVE 20 POINTS AD BRAINLIEST.
1. Write an expression to represent the sum of three consecutive even numbers. Let x equal the first number.
2. Find the circumference of a circle that has a diameter of 1 4/5 inches. Use 22/7 for pi.
3. Divide. Write the quotient in simplest form. 1/7 divided by -2/7 = ?
THANK YOU
Answer:
1. 3x + 6
2. [tex]\frac{99}{14}[/tex] or 7.071
3. [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
1. 3 consecutive even integers
If the first is x, the 2nd is x+2, and the 3rd is x+4
x + (x+2) + (x+4)
= 3x + 6
2. The equation for circumference is
[tex]C=2\pi r[/tex]
If the diameter is [tex]1\frac{4}{5} = \frac{9}{5}[/tex]
The the radius is half of that.
So the circumference is
[tex]\pi * \frac{9}{4} *\frac{1}{2} * 2\\= \pi * \frac{9}{4}\\=\frac{22}{7} * \frac{9}{4}\\= \frac{198}{28}\\ =\frac{99}{14} \\=7.071[/tex]
3. To divide we multiply by the reciprocal. So flip the fraction that we are dividing by.
[tex]\frac{1}{7} / -\frac{2}{7}\\ = \frac{1}{7} * -\frac{7}{2} \\= -\frac{1}{2}[/tex]
If a fixed number is added to each term of an arithmetic sequence, is the resulting sequence an arithmetic sequence? explain
Answer:
Yes.
Step-by-step explanation:
If we add a fixed number to each term of an arithmetic sequence, we are still going to be having an arithmetic sequence.
For example, given the following sequence:
1, 3, 5, 7, 9, 11...
The difference between consecutive terms is 2, therefore the pattern is adding two to the previous term.
If we add a fix number, let's say '3':
1+3, 3+3, 5+3, 7+3, 9+3, 11+3...
4, 6, 8, 10, 12, 14...
We notice that the pattern is the same, and it's still an arithmetic sequence.
Write a linear equation giving the median salary y in terms of the year x. Then, use the equation to predict the median salary in 2047.
Answer:
[tex]y=\frac{1}{30}(x-7)+1.5[/tex]
2.8 million is what we get in 2047
Step-by-step explanation:
Ok I see the following given in 2007, the medium salary is 1.5 million and in 2013 the medium salary is 1.7 million.
It says let x=7 represent 2007 so that means x=13 would represent 2013.
It also says y is in millions so y=1.5 means 1.5 million and y=1.7 means 1.7 million.
So we have these points that we need to find a line for: (7,1.5) and (13,1.7).
The slope can be found by using the slope formula given two points. This looks like this (y2-y1)/(x2-x1).
I like to line the points up and subtract then put 2nd difference over 1st difference.
Let's do that.
(13, 1.7)
-(7, 1.5)
-----------
6 .2
The slope is .2/6 or 2/60 (after multiplying top and bottom by 10) or 1/30 (after dividing top and bottom by 2)
So point slope form for this line is [tex]y-1.5=\frac{1}{30}(x-7)[/tex].
To get the point slope form for this line I just entered my m (the slope) and point (x1,y1) I knew on the line (like (7,1.5) ). Point slope form is [tex]y-y_1=m(x-x_1)[/tex].
So adding 1.5 on both sides of [tex]y-1.5=\frac{1}{30}(x-7)[/tex] gives me [tex]y=\frac{1}{30}(x-7)+1.5[/tex]
So now it says what is the medium salary in 2047 I believe. So we are going to plug in 47.
This gives us
[tex]y=\frac{1}{30}(47-7)+1.5[/tex]
[tex]y=\frac{1}{30}(40)+1.5[/tex]
[tex]y=\frac{4}{3}+1.5[/tex]
[tex]y=2.833333333333333333333333[/tex]
So 2.8 million
A fraction reduces to 36 if its numerator is (6x)^5 what is it’s denominator
Set up an equation:
Numerator is the top number and denominator is the bottom number in a fraction.
(6x)^5 / d = 36
(6x)^5 can be rewritten as 6^5x^5
6^5x^5 / d = 36
Raise 6 tot he power of 5:
7776x^5 /d = 36
Multiply both sides by d:
7776x^5 = 36d
Divide both sides by 36:
d = 7776x^5 / 36
d = 216x^5
HELP I RLLY NEED IT
Answer:
93
Step-by-step explanation:
A quadrilateral's 4 angles add to 360 degrees
70 + 92+<1 + 105 = 360
Combine like terms
267 + <1 = 360
Subtract 267 from each side
267-267 + <1 = 360-267
<1 = 93
Answer:
93
Step-by-step explanation:
OK it's simple...
The interior angles of ANY quadrilateral (a shape with 4 sides) add up to 360.
So all you have to do is add up the angles you already know (70+92+105=267) and subtract that from 360. (360-267).
How many degrees would a square need to be rotated to map onto itself?
Answer:
360
Step-by-step explanation:
Given: ∆ABC, m∠C = 90°
m∠BAC = 2m∠ABC
BC = 24 cm,
AL− ∠ bisector
Find: AL
Answer:
16 un.
Step-by-step explanation:
In right triangle ABC:
m∠C = 90°;
m∠BAC = 2m∠ABC;
BC = 24;
AL is a bisector of angle A.
The sum of the measures of all interior angles in triangle is always 180°, then
In right triangle the leg that is opposite to tha angle 30° is half of the hypotenuse. This means that
By the Pythagorean theorem,
Let AL be the angle A bisector. By bisector property,
Use the Pythagorean theorem for the right triangle ACL:
Read more on Brainly.com - https://brainly.com/question/7723556#readmore
Answer:
AL=24 cm
Step-by-step explanation:
We are given that a triangle ABC,
[tex]m\angle C=90^{circ}[/tex]
[tex]m\angle BAC=2m\angle ABC[/tex]
BC=24 cm
AL is angle bisector
We have to find the value of AL
Let [tex]m\angle ABC=x[/tex]
In triangle ABC
[tex]m\angle BAC+m\angle ABC+m\angle ACB=180^{\circ}[/tex]
[tex]2x+90+x=180[/tex]
[tex]3x=180-90[/tex]
[tex]3x=90[/tex]
[tex]x=\frac{90}{3}=30[/tex]
[tex]m\angle ABC=30^{\circ}[/tex]
[tex]m\angle BAC=2\times 30=60^{\circ}[/tex]
AL is a bisector of angle A
Then [tex]m\angle CAL=30^{\circ}[/tex]
BL=LC=12 cm
In triangle ACL
[tex]sin\theta =\frac{perpendicular side }{hypotenuse}[/tex]
[tex]sin30^{\circ}=\frac{12}{AL}[/tex]
[tex]\frac{12}{AL}=\frac{1}{2}[/tex]
[tex]AL=12\times 2=24 cm[/tex]
Hence, AL=24 cm
poaching is causing a population of elephsnt to decline by 8% per year. what is the hakf life for the population? if there is 10,000 elephants today, how many will remain in 50 years?
Answer:
60,000/ -30,000 (read explanation)
Step-by-step explanation:
8% of 10,000 is 800, 800 x 50(years) = 40,000, 100,000 -40,000 = 60,000, I believe you meant 100,000, cause if not, the answer is -30,000
Hope this helped
What is the solution to the equation? 305p equals 1,525
Answer:
Step-by-step explanation:
305p=1,525
305 305
p=5
The solution of the linear equation 305p = 1525 will be 5.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The linear equation with one variable is given below.
305p = 1525
On simplifying, we have
305p = 1525
p = 1525 / 305
p = 5
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ2
HELP needs to be handed in at 3:30
The Jameses take out a mortgage on their $470,000 home. The mortgage has an interest rate of 4.6% and is amortized over 30 years by making monthly payments. How much will the James be paying each month on their home mortgage?
Answer:
$2322.59
Step-by-step explanation:
Given
mortgage amount=$470,000
Interest rate annually=4.6%
Time=30 years
Monthly payments=?
Formula to apply
[tex]M=\frac{P(1+r)^n*r}{(1+r)^n-1}[/tex]
where
M=monthly payment for the mortgage
P=Principal amount =$470,000
i=rate per month=4.6÷12=0.3833%
n=30×12=360
Applying the formula
[tex]M=\frac{P(1+r)^n*r}{(1+r)^n-1} \\\\\\M=\frac{470000(1+0.004)^{360}*0.004 }{(1+0.004)^{360} -1} \\\\\\M=\frac{7452.235}{3.209} =2322.59[/tex]
There are 134third grades and 167 fourth -grades at the annual school and family picnic. The number of students is 7 times the number of adults. Each picnic table can seat 9 people. How many picnic tables will need to be set up for the picnic????
Answer:
39 tables
Step-by-step explanation:
Given:
third grade= 134
fourth grade=167
total=134+167=301
Now no. of students is 7 times no. of adults,
no. of adults= 301/7
=43
Total no. of people =301+43
=344
Each picnic table can seat 9 people, so
No. of tables for 344 people= 344/9
=38.222
39 tables picnic tables will need to be set up for the picnic!
Will mark brainliest, please answer:)
Find the value of AG. Round to the nearest tenths if necessary. Explain work.
(Image of Question is above and use the 3D Pythagorean Theorem rule)
Check the picture below.
7. Mis the midpoint of QR and M has
coordinates (-2, 6). Q has coordinates
(8, -10). What are the coordinates of R?
nges to the original content are the responsibility of the instructor.
I need help on number 7 please
Answer:
R(- 12, 22 )
Step-by-step explanation:
Using the midpoint formula
[tex]\frac{1}{2}[/tex](8 + [tex]x_{R}[/tex] ) = [tex]x_{M}[/tex] = - 2
Multiply both sides by 2
8 + [tex]x_{R}[/tex] = - 4 ( subtract 8 from both sides )
[tex]x_{R}[/tex] = - 12
----------------------------------------------
[tex]\frac{1}{2}[/tex](- 10 + [tex]y_{R}[/tex] ) = [tex]y_{M}[/tex] = 6
Multiply both sides by 2
- 10 + [tex]y_{R}[/tex] = 12 ( add 10 to both sides )
[tex]y_{R}[/tex] = 22
The coordinates of R = (- 12, 22 )
Find the product (n^3)^2 x (n^5)^4
Answer:
[tex]\large\boxed{(n^3)^2\times(n^5)^4=n^{26}}[/tex]
Step-by-step explanation:
[tex](n^3)^2\times(n^5)^4\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=(n^{3\cdot2})\times(n^{5\cdot4})=n^{6}\times n^{20}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\=n^{6+20}=n^{26}[/tex]
produce a graph that represents a vertical translation by 4 units down of the function f(x)=2x
Answer:
Given a function f(x), the function f(x) + k will be translated k units down if k<0. In this case, if we want to produce a vertical translation by 4 units down of the function f(x) = 2x, therefore the new function is:
f(x) = 2x - 4.
Now, we can graph the function like we normally do. Attached you will find the graph made with the help of a graphing calculator.
Which polynomial is prime?
X2-36
X2-16
X2-7x + 12
X2-X-20
Answer:
Step-by-step explanation:
x^2 - 36 is the difference of two squares and factors as follows:
(x - 6)(x + 6)
x^2 - 16 is the difference of two squares and factors as follows:
(x - 4)(x + 4)
x^2 - 7x + 12 is an easily factored quadratic; the factors are
(x - 3)(x - 4)
x^2 - x - 20 is an easily factored quadratic; the factors are
(x - 5)(x + 4)
I conclude that none of the four expressions is prime.
Answer:
B. [tex]x^2+16[/tex]
Step-by-step explanation:
We are asked to find the prime polynomial from our given choices.
We know that a polynomial is prime, when it has only two factors that are 1 and polynomial itself.
Upon looking at our given choices, we can see that each polynomial can be factored except [tex]x^2+16[/tex].
We can see that [tex]x^2+16[/tex] is sum of squares and sum of squares cannot be factored, therefore, polynomial [tex]x^2+16[/tex] is a prime polynomial.
What is the average rate of change for the sequence shown below?
coordinate plane showing the points 1, 4; 2, 2.5; 3, 1; and 4, negative 0.5
Answer:
[tex]\large\boxed{-1\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The points on the graph are collinear (they lie on one straight line).
Therefore, average of change is the same as a slope.
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We choose two points and put the coordinates to the formula
[tex](1, 4), (3, 1)\\\\\dfrac{1-4}{3-1}=\dfrac{-3}{2}=-1\dfrac{1}{2}[/tex]
The average rate of change for the sequence given is [tex]-1\frac{1}{2}[/tex].
What is the average rate of change?The average rate of change formula is used to find the slope of a graphed function. To find the average rate of change, divide the change in y-values by the change in x-values.
The points on the graph are collinear (they lie on one straight line).
Therefore, average of change is the same as a slope.
The formula of a slope:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
We choose two points and put the coordinates to the formula
(1, 4), (3, 1)
[tex]\frac{1-4}{3-1} =\frac{-3}{2} =-1\frac{1}{2}[/tex]
The average rate of change for the sequence given is [tex]-1\frac{1}{2}[/tex].
Find out more information about average rate of change here
https://brainly.com/question/12531344
#SPJ2
Solve the right triangle, ΔABC, for the missing sides and angle to the nearest tenth given angle B = 39° and side c = 13.
Answer:
Part 1) [tex]b=8.2\ units[/tex]
Part 2) [tex]a=10.1\ units[/tex]
Part 3) [tex]A=51\°[/tex] and [tex]C=90\°[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
step 1
Find the side b
we know that
In the right triangle ABC
The function sine of angle B is equal to divide the opposite side angle B (AC) by the hypotenuse (AB)
[tex]sin(B)=AC/AB[/tex]
we have
[tex]AB=c=13\ units[/tex]
[tex]AC=b[/tex]
[tex]B=39\°[/tex]
substitute
[tex]sin(39\°)=b/13[/tex]
solve for b
[tex]b=(13)sin(39\°)[/tex]
[tex]b=8.2\ units[/tex]
step 2
Find the side a
we know that
In the right triangle ABC
The function cosine of angle B is equal to divide the adjacent side angle B (BC) by the hypotenuse (AB)
[tex]cos(B)=BC/AB[/tex]
we have
[tex]AB=c=13\ units[/tex]
[tex]BC=a[/tex]
[tex]B=39\°[/tex]
substitute
[tex]cos(39\°)=a/13[/tex]
solve for a
[tex]a=(13)cos(39\°)[/tex]
[tex]a=10.1\ units[/tex]
step 3
Find the measure of angle A
we know that
In the right triangle ABC
[tex]C=90\°[/tex] ----> is a right angle
[tex]B=39\°[/tex]
∠A+∠B=90° ------> by complementary angles
substitute the given value
[tex]A+39\°=90\°[/tex]
[tex]A=90\°-39\°[/tex]
[tex]A=51\°[/tex]
1. What is the equation of a line that contains the points (0, 8) and (8, 8)?
A y = 0
B x = 0
C x = 8
D y = 8
2. Write the equation of a line that goes through point (0, −8) and has a slope of 0.
A x = −8
B x = 0
C y = −8
D y = 0
Answer:
1. D y = 8
2. C y = −8
Step-by-step explanation:
1.
Both points have y-coordinate 8, so the line is horizontal.
A horizontal line has equation
y = k
where k is the y-coordinate of all of its points.
The y-coordinate of all points on this line is 8.
Answer: y = 8
2.
A line with 0 slope is a horizontal line. All points on a horizontal line have the same y-coordinate.
A horizontal line has equation
y = k
where k is the y-coordinate of all of its points.
The y-coordinate of the given point is -8, so all points must have -8 as the y-coordinate.
Answer: y = -8
The equation of a line through two given points can be found using the point-slope form. A slope of 0 indicates a horizontal line.
Explanation:To find the equation of a line that contains the points (0, 8) and (8, 8), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Here, (x1, y1) represents one of the points and m represents the slope. Since the y-coordinates of both points are 8, we can see that the line is horizontal. Therefore, the equation of the line is y = 8.
For the second question, a slope of 0 indicates a horizontal line. The equation of a horizontal line is y = b, where b is the y-coordinate of any point on the line. Since our point is (0, -8), the equation of the line is y = -8.
Learn more about Equations of lines here:https://brainly.com/question/30200878
#SPJ2
Which of the following is equal to the expression below?
(6^-8)^-4
Answer:
6^(32)
Also I don't see your choices.
Step-by-step explanation:
I'm going to apply this law of exponents: (x^a)^b=x^(a*b).
It justs says to multiply the exponents in this case so we have 6^(-8*-4)=6^(32).
Answer:
It would be 1/6^32
Step-by-step explanation:
Use the quadratic formula to solve the equation -3x^2-x-3=0
Answer:
[tex]x_{1=} \frac{-1+i\sqrt{35} }{6} \\\\x_{2=} \frac{-1-i\sqrt{35} }{6}[/tex]
Step-by-step explanation:
Using the quadratic formula:
[tex]x=\frac{-b+-\sqrt{b^{2}-4*a*c} }{2*a}[/tex]
We will have two solutions:
[tex]x_{1}\\ x_{2}[/tex]
-3x^2-x-3=0 a=-3 b=-1 c=-3
We have:
[tex]x_{1}=\frac{1+\sqrt{-35} }{-6}\\\\x_{2}=\frac{1-\sqrt{-35} }{-6}\\[/tex]
we can write:
[tex]x_{1}=\frac{-1+\sqrt{-35} }{6}\\\\x_{2}=\frac{-1-\sqrt{-35} }{6}\\[/tex]
The solutions are not real numbers.
So, we know: [tex]i=\sqrt{-1}[/tex]
Finally we have:
[tex]x_{1}=\frac{-1+i\sqrt{35} }{6}\\\\x_{2}=\frac{-1-i\sqrt{35} }{6}\\[/tex]
Terry has 2 more quarters than fines and has a total of $6.80. How many quarters and dimes does Terry have?
Answer:
Terry has 20 quarters and 18 dimes
Step-by-step explanation:
Let
x -----> the number of quarters
y ----> the number of dimes
Remember that
1 quarter=$0.25
1 dime=$0.10
we know that
x=y+2 ----> equation A
0.25x+0.10y=6.80 -----> equation B
Substitute equation A in equation B and solve for y
0.25(y+2)+0.10y=6.80
0.25y+0.50+0.10y=6.80
0.25y+0.10y=6.80-0.50
0.35y=6.30
y=18 dimes
Find the value of x
x=y+2 -----> x=18+2=20 quarters
therefore
Terry has 20 quarters and 18 dimes
To determine the number of quarters and dimes Terry has, set up two equations based on the information provided, solve one of the equations for one variable, and substitute this into the second equation. Solve the equation to get the number of dimes and substitute it into the first equation to get the number of quarters.
Explanation:To solve this, we can use algebra, setting up equations to represent the problem and then solve it.
Let F represent the number of dimes (since a dime is worth $0.10) and let Q represent the number of quarters (since a quarter is worth $0.25). We have two key pieces of information:
Terry has 2 more quarters than dimes: Q = F + 2The total amount of money Terry has equals $6.80: 0.10F + 0.25Q = 6.80From the first equation, we can substitute F + 2 for Q in the second equation: 0.10F + 0.25(F + 2) = 6.80.
Solve this equation to find the value of F, representing the number of dimes, Terry has. Then, substitute the value of F into the first equation to determine the number of quarters Terry has.
Learn more about Algebra here:https://brainly.com/question/24875240
#SPJ3
If y = x+ 5 were changed to y = x + 9, how would the graph of the new
function compare with the first one?
O
A. It would be shifted down.
O
B. It would be shifted up.
O
C. It would be shifted right.
O
D. It would be steeper.
Answer: B. It would be shifted up.
Step-by-step explanation: We are changing the last number only. This number determines where the y-intercept is, which is on the vertical axis. Since the number increases by 4, the y-intercept would be shifted up by 4, without changing the slope. Therefore, the answer would be B. It would be shifted up.
what are terms? how do you combine them? can you give me an example?
A term is any number, variable or combination of a number and a variable in an equation.
Examples:
In 2x + 5y + 8, 2x is one term, 5y is a second term and 8 is a 3rd term.
In the equation 2x + 3 + 5x -2
Combine the like terms 2x and 5x are like terms because they both have x as a variable, there is a plus sign in fron of the 5x, so you would have 2x +5x = 7x
Then 3 and 3 are like terms, because they are just numbers, there is a subtraction sign in front of the 2, so you have 3-2 = 1
The equation then becomes: 2x + 3 + 5x -2 : 7x + 1
Factorize a^2+b^2+2(ab-ac-bc)
Answer:
(a + b)(a + b - 2c)
Step-by-step explanation:
Note that
(a + b)² = a² + b² + 2ab
Given
a² + b² + 2(ab - ac - bc) ← distribute parenthesis
= a² + b² + 2ab - 2ac - 2bc
= (a + b)² - 2ac - 2bc ← factor out - 2c from each term
= (a + b)² - 2c (a + b) ← factor out (a + b) from each term
= (a + b) [ a + b - 2c ]
= (a + b)(a + b - 2c) ← in factored form
The expression a² + b² + 2(ab - ac - bc) cannot be factorized using standard factorization techniques over real numbers, as a² + b² is not factorizable over the reals and there's no common factor for all terms.
To factorize the expression a² + b²+ 2(ab - ac - bc). To factorize this, we will look for a common factor and regroup the terms. Let's see if there's a way to rearrange the terms to resemble a known pattern or factor by grouping.
First, let's rewrite the expression by grouping terms with a common factor:
a² + 2ab - 2ac
b² - 2bc
However, we notice that the expression does not fit into a perfect square or any other easily factorizable form like (a + b)² or (a - b)² due to the nature of the terms a², b², and 2(ab - ac - bc). The expression is already in its simplest factored form as it stands because a²+ b² is not factorizable over the real numbers, and there's no common factor for all terms.
Therefore, the expression a² + b² + 2(ab - ac - bc) does not factorize further using real numbers and the usual factorization techniques.
please help ive been stuck on this since yesterday
[tex]\huge{\boxed{y=-3x+4}}[/tex]
Slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] represents the slope and [tex]b[/tex] represents the y-intercept.
Substitute in the values. [tex]\boxed{y=-3x+4}[/tex]
Remember that the slope intercept formula is:
y = mx + b
m is the slope
b is the y-intercept
In this case the slope (m) is -3 and the y-intercept (b) is 4
Your equation is:
y = -3x + 4
Hope this helped!
~Just a girl in love with Shawn Mendes