Answer:
Factored form: [tex](x-3)(x+1)(x^2+9)[/tex]
Expanded form: [tex]x^4-2x^3+6x^2-18x-27[/tex]
Step-by-step explanation:
[tex](x-3)(x+1)(x^2+9)[/tex]
[tex](x^2-2x-3)(x^2+9)[/tex]
[tex]x^4+9x^2-2x^3-18x-3x^2-27[/tex]
[tex]x^4-2x^3+6x^2-18x-27[/tex]
[tex]x-3=0[/tex] has a solution of [tex]x=3[/tex]
[tex]x+1=0[/tex] has a solution of [tex]x=-1[/tex]
[tex]x^2+9=0[/tex] has a solution of [tex]x=\pm 3i[/tex]
309,303,297 find the 33rd term
Answer:
111
Step-by-step explanation:
multiply 33 by 6 because 6 is being subtracted every time and then subtract 198 from 309
Answer:
117
Step-by-step explanation:
Hope this helps!
What is the range of the given function?
Answer:
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. .The range is the resulting y-values we get after substituting all the possible x-values.
Step-by-step explanation:
e. Find the slope of the line that passes through the points (1, 3) and (9,7),
Answer:
0.5
Step-by-step explanation:
→ Find the difference in y
7 - 3 = 4
→ Find the difference in x
9 - 1 = 8
→ Divide the results
4 ÷ 8 = 0.5
Answer:
The slope is 1/2 (m=1/2)
Step-by-step explanation:
Use the slope formula: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] to solve for the slope. y2 is 7, y1 is 3, x2 is 1, x1 is 9. [tex]\frac{7-3}{9-1}=\frac{4}{8} = \frac{1}{2}[/tex]
How do you write 750% as a fraction or mixed number
Answer:
750/100 or 7 1/2 whichever way u need
Step-by-step explanation:
When solving a system of equations graphically, when would you need to estimate the solution? Explain.
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
Factor
y=x² + 4x + 3
Answer:
[tex]y=(x+3)(x+1)[/tex]
Step-by-step explanation:
[tex]y=x^2+4x+3[/tex] <-- Given
[tex]y=x^2+x+3x+3[/tex] <-- Expand middle term
[tex]y=x(x+1)+3(x+1)[/tex] <-- Factor into two parts
[tex]y=(x+3)(x+1)[/tex] <-- Combine like terms
There are 222 red marbles in a box. Amit takes out 6 red marbles and replaces them with 12 blue
marbles. He continues doing this till all the red marbles are replaced with blue marbles.
Which of the following expressions gives the total number of blue marbles he put in the box?
A (222 + 6) = 12 B (222 - 6) + 12 C (222 - 6) + 12 D (222 + 6) x 12
Answer:
(222 - 6) + 12
Step-by-step explanation:
You put B and C as the same thing but the correct option is this because first you take away 6 (subtract 6) from the 222 marbles then you replace them with 12 (add 12).
Write an equation of the line that passes through the point (3,-5) and has the slope of 2
Answer:
Y-Y1=M(x-x1)
that's the formula then fixing in your values we have
y + 5 =2(x-3)
y+5 =2x-6
Crossing over we have
y-2x=-6-5
equation of the line equals
y-2x-11 =0
Can someone please tell me the answer
(20 points)
Answer:
the aswer is B
Step-by-step explanation:
A palm tree is 30 feet tall and casts a 48 foot shadow. The woman standing next to the palm tree casts a shadow similar to that of the palm tree. How tall is the woman if she casts an 8 foot shadow?
Answer:
48 feet foot I took the testttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt oh yeah yeah yeah
Step-by-step explanation:
Find the gradient of the line segment between the points (-3,1) and (2,5). Give your answer in its simplest form.
Answer:
[tex]\displaystyle m = \frac{4}{5}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Step-by-step explanation:
Step 1: Define
Identify points.
Point (-3, 1)
Point (2, 5)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m.
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{5 - 1}{2 - -3}[/tex][Order of Operations] Evaluate: [tex]\displaystyle m = \frac{4}{5}[/tex]What is a2-b2 equal to?
determine whatever ABCD is a parallelogram by using the midpoint formula.
A(3,3) B (1.2) C(-3.1) D (-1.4)
Answer:
Not a parallelogram.
Step-by-step explanation:
By the midpoint formula, the midpoint of a segment between [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] is:
[tex]\begin{aligned} \left(\frac{x_{0} + x_{1}}{2},\, \frac{y_{0} + y_{1}}{2}\right)\end{aligned}[/tex].
A quadrilateral is a parallelogram if and only if the midpoints of the two diagonals are the same.
The two diagonals of quadrilateral [tex]{\sf ABCD}[/tex] are segment [tex]\sf{AC}[/tex] and segment [tex]{\sf BD}[/tex], respectively.
Using the midpoint formula, the midpoint of segment [tex]{\sf AC}[/tex] (between [tex]{\sf A}\; (3,\, 3)[/tex] and [tex]{\sf C}\; (-3,\, 1)[/tex]) would be:
[tex]\begin{aligned} & \left(\frac{3 + (-3)}{2},\, \frac{3 + 1}{2}\right) \\ =\; & (0,\, 2)\end{aligned}[/tex].
Likewise, the midpoint of segment [tex]{\sf BD}[/tex] (between [tex]{\sf B}\; (1,\, 2)[/tex] and [tex]{\sf D}\; (-1,\, 4)[/tex] would be [tex](0,\, 3)[/tex].
Thus, quadrilateral [tex]{\sf ABCD}[/tex] would not be a parallelogram since the midpoints of its two diagonals are not the same.
An 8 ounce steak costs $12.80. How much would a 32 ounce steak cost?
Answer:
12.80 divided by 8 = 1.60
1.60 x 32 = 51.20
Step-by-step explanation:
pleeeeeeeeeeeease help :)
ty
Answer:
y = 3x + 16
Step-by-step explanation:
If it is parallel to y = 3x + 8, then it has the same slope of 3.
y = 3x + b. Substitute the x and y values into the equation to solve for b.
7 = 3(-3) + b
7 = -9 + b
16 = b
y = 3x + 16
Write the equation from the table below.
x y
0 -5
1 -2
2 1
3 4
4 7
Answer:
hope this helped
Step-by-step explanation:
y = mx + b
b, the y-intercept, = 3 because when x is 0, y is 3
find m, slope:
(0,3) (2,2)
2 - 3/2 - 0
-1/2
-0.5 or -/2
y = -1/2x + 3
or
y = -0.5x + 3
How many solutions?
No solution
One Solution
Infinitely Many Solutions
Answer:
no solution
Step-by-step explanation:
solution would occur where the lines intersect; parallel lines will never intersect
Convert ratio to fraction simplified. 25:45
Suppose TD=SG and what additional information is needed to prove the two triangles congruent SAS
a)
PLEASE HELP
Answer:c
Step-by-step explanation:
Answer:
If TD = SG and MD = SL, then angle D would have to equal angle S in order to prove the triangles congruent by SAS.
Step-by-step explanation: C
Two times 3X times Y times 4Z times X times Y times Z
Answer:
24*(X^2)*(Z^2)*(Y)
Step-by-step explanation:
2*(3X)*(4Z)*(X)*(Y)*(Z)
2*(3X^2)*(4Z)*(Y)*(Z) [Combine like terms (X)]
2*(3X^2)*(4Z^2)*(Y) [Combine like terms (Z)]
24*(X^2)*(Z^2)*(Y) [Combine like terms (2*3*4)]
If 10 plus 2 equals 12 the what does 10 times 8 times 12 times 1 mean
Answer:
960
Step-by-step explanation:
(10 + 2) = 12
"10 times 8 times 12 times 1"
what does 10 times 8 times 12 times 1 mean
10 * 8 * 12 * 1 = (10)(8)(12)(1)
= (80) * 12
= 960
Line g is dilated by a scale factor of 1/2 from the origin to create line g'. Where are points E' and F' located after dilation, and how are lines g and g' related?
(See attatchment)
ANSWER OPTIONS:
A- The locations of E' and F' are E' (−8, 0) and F' (0, 4), and lines g and g' intersect at point F.
B- The locations of E' and F' are E' (−4, 0) and F' (0, 2), and lines g and g' are the same line.
C- The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' are parallel.
D- The locations of E' and F' are E' (−1, 0) and F' (0, 0), and lines g and g' are not related.
Answer:
The locations of E' and F' are E'(-2,0) and F'(0,1), and lines g and g' are parallel.
Step-by-step explanation:
I got it right on my test! :)
The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' are a parallel option (C) is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
As we know,
The dilation is transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.
From the graph:
The coordinate for E and F are:
E = (-4, 0)
F = (0, 2)
The scale factor = 1/2
E' = (-4/2, 0) = (-2, 0)
F' = (0, 2/2) = (0, 1)
Thus, the locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' are a parallel option (C) correct.
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ2
A skyscraper is 396 meters tall. At a certain time of day, it casts a shadow that is 332 meters long. At what angle is the sun above the horizon at that time?
Step-by-step explanation:
there is a right-angled triangle.
its legs (enclosing the 90° angle) are the height of the skyscraper (396 m) and the shadow (332 m).
so, we know the third side (the Hypotenuse, which is the line of sight between the end of the shadow and the top of the skyscraper) too by using Pythagoras :
c² = a² + b²
line² = 396² + 332² = 156816 + 110224 = 267040
line = sqrt(267040) = 516.7591315... m
and we know 1 angle : the 90° angle between the legs.
the other angles we can now get by using the law of the sines :
a/sin(A) = b/sin(B) = c/sin(C)
where the angles are opposite of the lines.
the line of sight is opposite of the 90° angle.
and the height of the skyscraper is opposite of the angle between the line of sight and the shadow. this angle is also the angle of the sun above the horizon, as the extended line of sight would lead directly to the sun.
so, we have
516.7591315.../sin(90) = 396/sin(angle)
as sin(90) = 1
516.7591315... = 396/sin(angle)
sin(angle) = 396 / 516.7591315... = 0.76631447...
angle = 50.02407526...°
Is this relation a function? {(3, 2), (5, 9), (11, 25)}
Answer:
Yes
Step-by-step explanation:
None of the X values are the same number.
Write 110% as a mixed number in simplest form.
110% = $$
Answer:
50
Step-by-step explanation:
you select a marble at random and then put it back. If you do this 8 times, what is the best prediction possible for the number of
times you will pick a red marble?
8 marble in total and 4 are green, 3 blue, and 1 red hope it help the problem :)
HELPPPPPP PLLSLLSLSLLSSS!!!
Cereal is on sale this week. Is it a better buy to get the 10-ounce box for $1.95 or the 14-ounce box for $2.81?
Answer:
It is better to buy the 10-ounce box for $1.95
Step-by-step explanation:
1.) Set up a ratio to represent this problem.
Ounces : Price
10 : 1.95
14 : 2.81
2.) Find the unit price for the first ratio.
10 : 1.95
/10 /10
1 : 0.195
This means that a one-ounce box of cereal will cost $0.12
3.) Find the unit price for the second ratio.
14 : 2.81
/14 /14
1 : 0.20071428571
This means that a one-ounce box of cereal will cost $0.20
4.) Compare prices
$0.12 < $0.20
Therefore, it is better to buy the 10-ounce box for $1.95.
Select all of the following that are ordered pairs of the given function.
ƒ(x) = 3 - 2x
(-2, -1)
(1, 0)
(2, -1)
(0, 3)
(-1, 5)
Answer:
(-2,-1)
Step-by-step explanation:
f(x)=3 - 2x
y = 3 - 2x
if x = - 2
y =3 - 2(-2)
= -1
Required ordered pair is (-2,-1)
Answer:Answer:
(-2,-1) (2,-1) (-1,5)
Step-by-step explanation:
f(x)=3 - 2x
y = 3 - 2x
if x = - 2
y =3 - 2(-2)
= -1
Required ordered pair is (-2,-1)
Step-by-step explanation:
A river flows at the rate of 12 feet per minute. What is the rate in second per foot?
X/2 = Y/3 = Z/4. prove that :2X-Y+5Z / 3Y-X =3. note :: (/) is for a fraction aka divide. help pls I've been stuck on it for a few days
The given equation
x/2 = y/3 = z/4
can be broken into three separate equations which I'll call equations (A), (B) and (C)
x/2 = y/3 ..... equation (A)y/3 = z/4 .... equation (B)x/2 = z/4 .... equation (C)We'll start off solving for z in equation (C)
x/2 = z/4
4x = 2z ... cross multiply
2z = 4x
z = 4x/2 ... divide both sides by 2
z = 2x
Now let's solve for y in equation (A)
x/2 = y/3
3x = 2y
2y = 3x
y = 3x/2
y = (3/2)x
y = 1.5x
The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.
We won't be using equation (B) at all.
---------------------
The key takeaway from the last section is that
z = 2xy = 1.5xLet's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:
(2x-y+5z)/(3y-x)
(2x-y+5(2x))/(3y-x) ..... plug in z = 2x
(2x-y+10x)/(3y-x)
(12x-y)/(3y-x)
(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x
(12x-1.5x)/(4.5x-x)
(10.5x)/(3.5x)
(10.5)/(3.5)
3
We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.