Explanation:
Polynomials of degree 1, aka linear polynomials, are the highest allowed for the divisor when using synthetic division. If the divisor is degree 2 and larger, then you'll need to use polynomial long division instead.
An example divisor of degree 1 is something like [tex]x+5[/tex], which can be written as [tex]x^1+5[/tex]. That exponent of 1 determines the degree.
1.
Find the slope and intercepts of 3x + 4y = 12. Sketch a graph.
The slope of 3x + 4y = 12 is m = -3/4
To get the slope, you must use the slope-intercept form y = mx + b to find the slope.
The x-intercept of 3x + 4y = 12 are located at: (4,0)
To find the x-intercept, you must substitute in 0 for y and solve for x.
The y-intercept of 3x + 4y = 12 are located at: (0,3)
To find the y-intercept, you must substitute in 0 for x and solve for y.
Please view the graph attached below that has the slope and intercepts of 3x + 4y = 12 sketched.
:)
Which one is the answer!
Solve for b.
Help pls thank u !!!!
Step-by-step explanation:
3b - 3.76 = 1.34
3b = 3.76+ 1.34
3b = 5.1
b= 5.1/3
= 1.7
Find the x- and y-intercepts of the graph of the function f(x)=−4|x+5|+8 .
Answer:
x-intercept(s): (−3,0),(−7,0)
y-intercept(s): (0,−12)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute i 0 for x and solve for y.
show your solution need an answer, please need an answer, please.
complete answer pls:(
Answer:
1. x = -1
2. y = -1, y = 2
3. y = -½ + i [tex]\frac{\sqrt{3} }{2}[/tex]; y = -½ - i [tex]\frac{\sqrt{3} }{2}[/tex]
4. x = -3; x = -6
Step-by-step explanation:
I will only produce work for questions 1 through 4, and you could follow the same steps for questions 5 and 6 so that you could learn and get used to solving quadratic equations. I am practically using the same techniques in solving questions 1 through 4 anyway.
1.) x² + 2x + 1 = 0
where a = 1, b = 2, c = 1
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = 2² - 4(1)(1) = 4 - 4 = 0
This means that the equation has one real root.
Next, determine the factors of the quadratic equation.
Use the perfect square trinomial factoring technique:
u² + 2uv + v² = (u + v)²
From the equation, x² + 2x + 1 = 0
where a = 1, b = 2, c = 1
Find factors with product a × c and sum b:
Possible factors:
product a × c : 1 × 1 = 1
sum b : 1 + 1 = 2
Therefore, the binomial factors of x² + 2x + 1 = 0 is (x + 1)²
To find the roots, set x = 0:
x + 1 = 0
Subtract 1 from both sides to isolate x:
x + 1 - 1 = 0 - 1
x = -1 (This is the root of the equation).
2) y² - y - 2 = 0
where a = 1, b = -1, and c = -2
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = (-1)² - 4(1)(-2) = 9
Since b² - 4ac > 0, then it means that the equation will have two real roots.
From the equation, y² - y - 2 = 0
where a = 1, b = -1, and c = -2:
Find factors with product a × c and sum b:
Product a × c :
1 × -2 = -2
-1 × 2 = -2
Sum b:
1+ (-2) = -1
-1 + 2 = 1
Therefore, the possible factors are: 1 and -2:
(y + 1) (y - 2)
To find the roots, set y = 0:
y + 1 = 0
Subtract 1 from both sides:
y + 1 - 1 = 0 - 1
y = -1
y - 2 = 0
Add 2 to both sides:
y -2 + 2 = 0 + 2
y = 2
Therefore, the roots of the quadratic equation, y² - y - 2 = 0 are: y = -1 and y = 2.
3.) y² + y + 1 = 0
where a = 1, b = 1, and c = 1
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = (1)2 - 4(1)(1) = -3
Since b² - 4ac < 0, then it means that the equation will have two complex roots.
Use the Quadratic Formula:
[tex]y = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]y = \frac{-1 +/- \sqrt{1^{2} - 4(1)(1)} }{2(1)}[/tex]
[tex]y = \frac{-1 +/- \sqrt{1 - 4} }{2}[/tex]
[tex]y = \frac{-1 +/- \sqrt{-3} }{2}[/tex]
[tex]y = \frac{-1 +/- i\sqrt{3} }{2}[/tex]
Therefore, the roots of the quadratic equation, y² + y + 1 = 0 are:
y = -½ + i [tex]\frac{\sqrt{3} }{2}[/tex]; y = -½ - i [tex]\frac{\sqrt{3} }{2}[/tex]
4) x² + 9x + 18 = 0
where a = 1, b = 9, and c = 18.
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = (9)2 - 4(1)(18) = 9
Since b² - 4ac > 0, then it means that the equation will have two real roots.
Use the Quadratic Formula:
[tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]x = \frac{-9 +/- \sqrt{9^{2} - 4(1)(18)} }{2(1)}[/tex]
[tex]x = \frac{-9 +/- \sqrt{9} }{2}[/tex]
[tex]x = \frac{-9 + 3}{2}; x = \frac{-9 - 3}{2}[/tex]
[tex]x = \frac{-6}{2}; x = \frac{-12}{2}[/tex]
x = -3; x = -6
Therefore, the roots of the quadratic equation, x² + 9x + 18 = 0
are: x = -3 and x = -6.
NO LINKS OR ASSESSMENT!!!
Write a rule to describe each transformation: #10 & #12
Answer:
Step-by-step explanation:
10
You are rotating the the triangle 180 degrees about the origin. The rule for that is (x,y) ----> (-x,-y)
So X starts at (-4,1) and rotates until it hits (- - 4, -1 or (4,-1). Question is that where X' is? Yes.
Now try the next two points
W(-3,-4) ------> W'(- - 3, - -4) = W'(3,4)
Y(-1,-2) =====> y'(- - 1 , - - 2) = Y'(1,2)
Is that where these points are? Yes it is
12
This given triangle GFH rotates 90 anticlockwise. The rule for that (x,y) ===>(-y,x)
This means that you interchange x and y and make the y value minus. All you have to do is obey the rule.
F(-3,0) becomes F'(0,-3)
G(4,0) becomes G'(0,-4)
H(-3,3) becomes H'(-3,-3)
What should you be convinced of? You should think there is no stretch taking place -- the triangles are not getting bigger or smaller. You should see that the shape remains the same. If you cut both out with a pair of scissors and put one on top of the other, you could not tell which came from where.Answer:
10) (x, y) ⇒ (-x, -y) . . . . rotation 180° about the origin
12 (x, y) ⇒ (-y, x) . . . . . rotation 90° CCW about the origin
Step-by-step explanation:
10) The order of the points WXY is CW in both figures, so no reflection (or an even number of reflections) across a line will be involved. Each image point is the same distance from the origin as its preimage point, so no dilation is involve. Those distances are in opposite directions, so rotation 180° about the origin is indicated.
The transformation describing that is ...
(x, y) ⇒ (-x, -y)
__
12) The order of points GHI is CW in both figures, so reflection across a line is not involved. Each image point is the same distance from the origin as its preimage, so no dilation is involved. The direction from the origin is different by 90°, so there has apparently been a 90° CCW rotation about the origin. This transformation is described by the rule ...
(x, y) ⇒ (-y, x)
Which of the following is the correct graph of the linear equation below?
y+3 = -(x-4)
=-
PRII
A.
5 -4 -3
-2.1
2
3
4
-1
-2
+-3
-4
T'
Find the measure of the missing angles.
no links Use the hundreds grid to answer the question.
A 10 by 10 grid is shown with the first 9 columns shaded. The top row is also shaded in a different color. The first 9 squares of the top row overlap with the 9 shaded columns.
Give the decimal multiplication equation shown by the model. Explain how each part of the equation is shown on the model. Include the final product.
Answer:
9%
Step-by-step explanation:
There are 100 boxes and only 9 are shaded so a fraction of that would be 9/100 so if you convert that to a percentage it would be 9% of the boxes
so therefor 9% is you answer
hope this helped
BRANLIEST?
The model is considered to be expressing the equation "9 x 0.1 = 0.9".
What is the equation?The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.
A 10 by 10 grid is shown with the first 9 columns shaded. The top row is also shaded in a different color. The first 9 squares of the top row overlap with the 9 shaded columns.
It looks like the model is showing the equation "9 x 0.1 = 0.9".
The "9" is shown by the 9 shaded columns on the grid. The "0.1" is shown by the top row of the grid, which is shaded differently from the rest of the grid. The "0.9" is shown by the 9 shaded squares in the top row, which overlap with the 9 shaded columns.
The final product of the equation is 0.9.
Learn more about the equations here:
brainly.com/question/10413253
#SPJ2
An elevator was at floor24. It was down 6 floors, up 10 floors, and then down 8 floors. At what floor did it stop?
please help!
The freezing point of seawater is -2 °C. The freezing
point of nitric acid is -42 °C. How much greater is the freezing
point of seawater than the freezing point of nitric acid?
Answer:
Express concentrations of solution components using mole fraction and molality
Describe the effect of solute concentration on various solution properties (vapor pressure, boiling point, freezing point, and osmotic pressure)
Perform calculations using the mathematical equations that describe these various colligative effects
Describe the process of distillation and its practical applications
Explain the process of osmosis and describe how it is applied industrially and in nature
Step-by-step explanation:
i helped
What is the measure of
Answer:
30
Step-by-step explanation:
because 3 times 30 is 90,and 2 times 30 is 60 plus 30 would be equal to 180
Please help
Solve for w
What's 9 + 10 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answer:
19
Step-by-step explanation:
9 + 10 = 19
Answer:
19
Step-by-step explanation:
21
HELP ME AND PLEASE HURRY
Am i correct on this problem if not please tell me why im not.
9514 1404 393
Answer:
A
Step-by-step explanation:
Reflection across a line reverses the orientation of the figure from CW to CCW, or vice versa. Each point on the image is the same distance from the line of reflection as the corresponding point on the preimage.
These characteristics are manifested in figure A.
__
Figure B represents a translation to the right; Figure C represents both rotation and translation. Figure D is translation up and to the right.
_____
Additional comment
When vertices of a figure are labeled, their orientation (CW or CCW) is easy to identify. When they are not, it isn't always easy. It helps when the figure has no particular symmetry, as here. We can, for example, consider the sides in order from shortest to longest. That would make the orientation CCW on the left of figure A, and CW on the right. Figure A is the only figure in which the orientation changes.
CW=clockwise; CCW=counterclockwise
si a+b = 10; ab= 3 calcula a2 + b2
94
In 8 hours, Keiko reads 24 chapters of a book.
What is her rate in chapters per hour?
Answer:
3 chapters per hour
Step-by-step explanation:
24/8 = 3 chapters per hour
write 3.01 as a mixed number
Sarah's grandmother has a square blanket that covers an area of 25 square feet. Sarah wants to put a string of pearls around the sides of the blanket. How many feet long will the string of pearls have to be for Sarah to complete the job?
Answer:
20 ft
Step-by-step explanation:
area of square = (side)^2
area of square = 25 ft^2
(side)^2 = 25 ft^2
side = 5 ft since (5 ft)^2 = 25 ft^2
The side of the square measures 5 ft.
All around the square is the perimeter.
perimeter = 4 * side
perimeter = 4 * 5 ft
perimeter = 20 ft
Answer: 20 ft
A park has a grassy section that covers 2 1/3 acres. Denny mowed half of the grassy section. What is the number of acres that Danny mowed?
Answer:
7/6 (1 1/6)acres
Step-by-step explanation:
The grassy section covers 2 1/3 acres overall. To find half of that, we divide it by two because half of an amount or object is one of the two equal parts that together make up the whole amount or object.
To turn a mixed number (in this case, 2 1/3) into an improper fraction, multiply the whole number with the denominator of the proper fraction.
2*3 = 6Add the numerator to this product to obtain the numerator of the improper fraction.
6 + 1 = 7
so the improper fraction is 7/3
then we multiply that fraction by 1/2 because we are trying to find half of the overall section
7/3 * 1/2 = 7/6
A box contains 10 light bulbs, of which 3 are defective and the other 7 work. If two bulbs are drawn in succession without replacement, what is the probability of getting 1 working bulb and 1 defective bulb?
Answer:
Working: 7/10
defective:3/10
Step-by-step explanation:
Just trust me
A rare disease has been discovered that affects 2 out of every 10,000 trees in a forest, what percent of trees are affected? Plz show work if you can
[tex]\sqrt50 + \sqrt18\\[/tex]
Answer:
8\sqrt2=\sqrt128
Step-by-step explanation:
[tex] \sqrt{50} = 5 \sqrt{2} \\ \sqrt{18} = 3 \sqrt{2} [/tex]
[tex]3.2a-1-4 \frac{1}{3}a+7-a[/tex]
"keep-change-flip" is a strategy used to dividing fractions.
always change the mix fraction to a improper fraction and you slove.
I'll do the first one and the rest is basically done the same way.
for the last fraction equation I cross multiply the 4 divided into 4 gives you 1 and the 3 divided into 21 gives you 7.
Find a10, for the geometric sequence an = 3(4)^n-1.
A. 262,144
B. 786,432
C. 1,048,579
D. 3,145,728
What is the distance between the points (−7, −3) and (−7, −9) ?
A 12 units
B 10 units
C 6 units
D 4 units
Answer:
C. 6 unitsStep-by-step explanation:
Since the points have same x- coordinate of -7, the distance is the difference in y - coordinates:
d = -3 - (-9) = -3 + 9 = 6Correct choice is C
Distance
[tex]\\ \sf\longmapsto \sqrt{(-7+7)^2+(-9+3)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{(-6)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{36}[/tex]
[tex]\\ \sf\longmapsto 6[/tex]
if a child weighs 83 pounds how many ouces would she weigh
Answer:
1,328
Step-by-step explanation:
1 pound = 16 ounces
83 pounds X 16 ounces = 1,328 ounces
1 pound is 16 ouces
83 pounds x 16 ounces equals 1328
A parabola can be drawn given a focus of (-9,6) and a directrix of x = -1. What
can be said about the parabola?
1.8331 to nearest hundred
Answer:
1.83 because hundredth would be in the second place after the period
Step-by-step explanation:
