Answers
Given:
The polynomial is:
[tex]P(x)=ax+b[/tex]
To find:
Whether [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial or not.
Solution:
We have,
[tex]P(x)=ax+b[/tex]
Putting [tex]x=-\dfrac{b}{a}[/tex], we get
[tex]P(-\dfrac{b}{a})=a(-\dfrac{b}{a})+b[/tex]
[tex]P(-\dfrac{b}{a})=-b+b[/tex]
[tex]P(-\dfrac{b}{a})=0[/tex]
Since the value of the given polynomial is 0 at [tex]x=-\dfrac{b}{a}[/tex], therefore [tex]x=-\dfrac{b}{a}[/tex] is a zero of the given polynomial.
Related Questions
Given that sin ø 21/29, what is the value of cos ø, for 0° < ø < 90%
Answers
Answer:
[tex] \frac{20}{29} [/tex]
Step-by-step explanation:
Let x replace theta.
Apply pythagorean trig identity
[tex] \sin {}^{2} (x) + \cos {}^{2} (x) = 1[/tex]
[tex] (\frac{21}{29} ) {}^{2} + \cos {}^{2} (x) = 1[/tex]
[tex] \frac{441}{841} + \cos {}^{2} (x) = 1[/tex]
[tex] \cos {}^{2} (x) = 1 - \frac{441}{841} [/tex]
[tex] \cos {}^{2} (x) = \frac{400}{841} [/tex]
[tex] \cos(x) = \frac{20}{29} [/tex]
Cosine is positve in 1st quadrant so the answer is
[tex] \frac{20}{29} [/tex]
What is the slope-intercept equation of the line below? y-intercept=(0,2) slop=-1/4
Answers
Answer:
y=-1/4x+2
Step-by-step explanation:
So the forumla for slope/intercept equation is:
y=mx+b
Y equals the y coordinates on the graph. This is the value that you plug in x to solve for.
m equals the slope of the graph. (In this case -1/4)
x equals the x coordinates. This will always be just x when writen in a slope intercept equation, since x is the value you plug in to solve for y.
b equals the y intercept. This is different from the y coordinates. This is a known value, which can be found when x=0. (In this case 2)
Now, using this lets plug in our numbers for the differet variables:
y=mx+b
We know that m, the slope, is -1/4. So:
y=-1/4x+b
We also know that b, the y inteercept, is 2. Since we have the coordiantes (0x, 2y). So:
y=-1/4x+2
This is all you have to do! This is because y is the number you solve for, and x is the value you plug.
Hope this makes sense and helps! :)
A student purchased a used car for $5,000. Three months later, the student discovers the car needs major repairs which will cost $2,000. The student must decide whether to repair the car or purchase another car. Which statement is correct?
Answers
Answer:
The relevants cost are $2,000
Step-by-step explanation:
Based on the information given in a situation where the student have to decide whether to repair the car or purchase another car the correct statement is: THE RELEVANTS COST ARE $2,000 because the cost of repairs of the Amount of $2,000 represent the RELEVANT COST.
Therefore RELEVANT COSTS are costs or expense that can be incurred due to some certain decisions and on the other hand RELEVANT COSTS which is also known as AVOIDABLE COST can be seen as the cost or expense a person or an individual can do away with depending on other alternative such person choose to pick.
Answer:
2000
Step-by-step explanation:
Find the missing angle.
Answers
Answer:
=180-50-70
=50
Step-by-step explanation:
=180-50-70
50
Quadratic below
2^2−7−4
Vertex -
Y-Intercept -
X-Intercept -
Answers
Answer:
The y-intercept is y = -4.
The x-intercepts are [tex]x = 4[/tex] and [tex]x = -\frac{1}{2}[/tex]
The vertex is [tex](\frac{7}{4},-\frac{81}{8})[/tex]
Step-by-step explanation:
Quadratic equation:
Has the following format:
[tex]y = ax^2 + bx + c[/tex]
The y-intercept is c.
Finding the x-intercepts:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
Vertex:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
In this question:
The quadratic equation is [tex]2x^2 - 7x - 4[/tex], which has [tex]a = 2, b = -7, c = -4[/tex]. This means that the y-intercept is y = -4.
x-intercepts:
[tex]\Delta = (-7)^2-4(2)(-4) = 81[/tex]
[tex]x_{1} = \frac{-(-7) + \sqrt{81}}{2*2} = 4[/tex]
[tex]x_{2} = \frac{-(-7) - \sqrt{81}}{2*2} = -\frac{1}{2}[/tex]
The x-intercepts are [tex]x = 4[/tex] and [tex]x = -\frac{1}{2}[/tex]
Vertex:
[tex]x_{v} = -\frac{(-7)}{2*2} = \frac{7}{4}[/tex]
[tex]y_{v} = -\frac{81}{4(2)} = -\frac{81}{8}[/tex]
The vertex is [tex](\frac{7}{4},-\frac{81}{8})[/tex]
When solving for y, in which step did Ramon make a mistake?
a) step one,Ramona re-wrote the system incorrectly
b) step two,Ramona should have multiplied the first equation by -4 instead of -2
c) in step three Ramona simplify -28+10 as -18 instead of simplifying to 18
d) in step four, Ramona should have divided by -6 instead of dividing by 6
show work
Answers
Express this decimal 0.8 as a fraction
Answers
Answer: 4/5
How to: Convert to a mixed number by placing the numbers to the right of the decimal over 10 . Reduce the fraction.
Have a great day and stay safe ! so sorry if wrong
Answer:
8/9
Step-by-step explanation:
i got it righttt
Which numbers are equal to 24
8 divided by 1/3
6 divided by 1/8
9 divided by 1/4
4 divided by 1/6
12 divided by 1/2
Answers
Answer:
The first one
Step-by-step explanation:
I did this and got it right and I solved it
8×3 equal 24/1 so make it to a whole number 24
4 divided by 1/6= 24
12 divided by 1/2= 24
All of these :)
Whats the answer?This is trigonometry
Answers
Answer:
100
Step-by-step explanation:
Please help and thanks whoever helps me!!
Answers
Answer:
2/3 km per minute
Step-by-step explanation:
kilometers
1 1/3 - 2/3 = 2/3km
Minutes
2 - 1 = 1 minute
----------------------------
Spped
(2/3 km) / (1 minute)
2/3 km per minute
What is the shift from in the parent function y=x^2 to this function: y=(x+2)^2+3
A. The parent function would shift 3 units to the left and 2 units down.
B. The parent function would shift 3 units to the right and 2 units down.
C. The parent function would shift 2 units to the right and 3 units down.
D. The parent function would shift 2 units to the left and 3 units up.
Answers
Answer:
Shift to the right by 2 units, vertical translation upwards by 3 units.
Step-by-step explanation:
Danny is measuring two pyramids whose bases are squares. Given the height hhh and volume VVV of the first pyramid, Danny uses the formula a=\sqrt{\dfrac{3V}{h}}a= h 3V a, equals, square root of, start fraction, 3, V, divided by, h, end fraction, end square root to compute its base's side length aaa to be 555 meters. The second pyramid has the same volume, but has 444 times the height. What is the side length of its base?
Answers
Answer: THE ONE ABOVE IS WRONG
A= 3V/h
Step-by-step explanation:
Formulas may contain multiple variables, along with known numbers and letters that stand for known constants like \piπpi.
We can highlight a certain variable in the formula by treating the formula as an equation where we want to solve for that variable.
In this case, we need to solve the equation V =\dfrac{1}{3}AhV=
3
1
AhV, equals, start fraction, 1, divided by, 3, end fraction, A, h for AAA.
Hint #22 / 3
\begin{aligned} V&=\dfrac{1}{3}Ah \\\\ \dfrac{3V}{h}&=A \end{aligned}
V
h
3V
=
3
1
Ah
=A
Hint #33 / 3
This is the result of rearranging the formula to highlight the base area:
A=\dfrac{3V}{h}A=
h
3V
It works I did it in Khan
at lunch four friends drink 8 pints of milk. How many fluid ounces is this equal to? 1) 128 FL oz 2)64 FL oz 3)32oz 4) 16 FL oz
Answers
at lunch four friends drink 8 pints of milk. how many fluid ounces is this equal to?
128 FL
Answer:
The answer is choice #1 or 128 Fluid ounces
Step-by-step explanation:
8 pints = 128 oz
The ages of job applicants for a security guard position are uniformly distributed between 25 and 65. Could a 25-year-old job applicant be two standard deviations below the mean (or more than two standard deviations)?
Answers
Answer:
No, a 25-year-old job applicant cannot be two standard deviations below the mean
Step-by-step explanation:
There are two frequencies 25 and 65
Mean of the two frequencies = 25+65/2 = 45
Standard deviation =
[tex]\frac{65-25}{\sqrt{12} } \\= 11.55[/tex]
Mean - 2 x standard deviation [tex]= 45 - 2 * 11.55 = 21.9[/tex]
[tex]21.9 < 25[/tex]
Thus, a 25-year-old job applicant cannot be two standard deviations below the mean
In which choice do all three points lie on the
same straight line?
A А.
(0, 1), (-1, 3), (1, 3)
B.
(4, 2), (2, 1), (4, -2)
C (0, 0), (8, 0), (0, 8)
D
(1, 2), (2, 4), (4,8)
Answers
Answer:
D (1, 2), (2, 4), (4,8)
Step-by-step explanation:
Points lying on the same line:
If three points lie on the same line, the change in y has to be always the same when x changes by 1.
А. (0, 1), (-1, 3), (1, 3)
(-1,3) to (0,1): x changes by 1, y by -2
(0,1) to (1,3): x changes by 1, y by 2
So these points are not on the same line.
B. (4, 2), (2, 1), (4, -2)
Two values for y when x = 4, so not on the same straight line.
C (0, 0), (8, 0), (0, 8)
Two values for y when x = 0, so not on the same straight line.
D (1, 2), (2, 4), (4,8)
Here, when x changed by 1(from 1 to 2), y changed by 2.
When x changed by 2(from 2 to 4), y changed by 2*2 = 4.
So these points are on a straight line, and D is the correct answer.
Lincoln buys milk and oranges at the store.
He pays a total of $41.63.
He pays a total of $4.19 for the milk.
• He buys 6 bags of oranges that each cost the same amount.
.
Write and solve an equation which can be used to determine x, how much each bag
of oranges costs.
Answers
Answer:
$6.24
Step-by-step explanation:
equation: $41.63 - 4.19 = 37.44
solve: 37.44 ÷ 6 = 6.24.
hope this helped!
Answer:
He pays a TOTAL of $41.63. Meaning everything is equal to that value
He pays 4.19$ for Milk
He buys 6bags of Oranges and each of these cist the same amount.. let's say x.
So 6 bags would cost 6x
So Total is
6x + 4.19 =41.63
6x= 41.63-4.19
6x=37.44
x=37.44/6
x=$6.24
To check this
6x + 4.19 should equal 41.63$
6(6.24) + 4.19= $41.63
Which expressions are equivalent Log 2- log 8
Answers
Answer:
log(.25)
Step-by-step explanation:
[tex]log(a)-log(b)=log(\frac{a}{b})\\log(2)-log(8)=log(\frac{2}{8})\\log(\frac{1}{4})[/tex]
What is the period of the parent cosine function, y=cos(x)? degrees
What is the period of the cosine function shown in the graph? degrees
Answers
Answer: first 360 second 1080 third horizontal stretch
Step-by-step explanation:
The period of this parent cosine function [y=cos(x)] is equal to 360 degrees.
What is the period of a cosine function?The period of a cosine function can be defined as the overall length of the interval of values on the x-axis over which a graph lies and it's repeated. Mathematically, the period of this parent cosine function [y=cos(x)] is given by:
T = 2π/A
Where:
A is the coefficient of the x.When A = 1, we have:
T = 2π/1 = 360 degrees.
For the graphed function, the period of this cosine function is given by:
T = 6π
T = 6 × 360
T = 1080 degrees.
Read more on cosine function here: https://brainly.com/question/4599903
Lisa scored 85, 92, 87, 93 and 90 on 5 tests. What is the minimum score she needs to make on her 6th test to guarantee a 90 average in math class? The
Answers
Answer:
93
Step-by-step explanation:
(85 + 92 + 87 + 93 + 90 + x)/6 = 90
(447 + x)/6 = 90
multiply both sides of the equation by 6:
447 + x = 540
subtract 447 from both sides:
x = 93
What's the Area for each shape?
Answers
Answer:
[tex](6 \times 5) + (2 \times 3) \\ 30 + 6 \\ = 36cm^{2} [/tex]
Please help asap urgent! 20 pts!
Answers
Answer:
the mean of those numbers is 17.1
Answer:
The M.A.D (mean absolute deviation) is 2.3
Bonus (Just in case you need it): The Mean is 17.1
Have a good day!
Can someone help me?
Answers
Answer:
7. D) 61in
8. A) 57in
9. A) 47in
Step-by-step explanation:
The perimeter is the distance around the area of a 2-dimensional figure. it can be found by adding up all of the sides of the figure. One can use this to solve for the value of the parameter (x). Then substitute the value back in to find the value of the side.
7.
AB + BC + AC = 145
Substitute,
2x + 2x + 5 + x = 145
Simplify,
5x + 5 = 145
Inverse operations,
5x + 5 = 145
-5
5x = 140
/5
x = 28
Substitute,
AC = 2x + 5= 2(28) + 5 = 61
8.
AB + BC + AC = 135
Substitute,
2x + 2x + 5 + x = 135
Simplify,
5x + 5 = 135
Inverse operations,
5x + 5 = 135
-5
5x = 130
/5
x = 26
Substitute,
AC = 2x + 5 = 2(26) + 5 = 57
9.
AB + BC + AC = 122
Substitute,
x + 22 + 2x + x = 122
Simplify,
4x + 22 = 122
Inverse operations,
4x + 22 = 122
-22
4x = 100
/4
x = 25
Substitute,
AB = x + 22 = 25 + 22 = 47
A container has a 6 litres of juice. If 3⅕ litres are poured from it, How many juice is left in the container?
Answers
Answer:
2.8 liters
Step-by-step explanation:
6 - 3.20 = 2.8
Answer:
2 4/5
Step-by-step explanation:
6-3 1/5 = 2 4/5
Use Euler's formula to find the missing number.
Vertices: 13
Edges: 26
Faces: ?
A.14
B.15
C.16
D.17
Answers
Answer:
15
Step-by-step explanation:
trust me bro
Find an angle coterminal to 746°, where 0° < 0 < 360°
Answers
Answer:
26º
Step-by-step explanation:
746 - 360 = 386
386 - 360 = 26
1. Divide
1 point
1. On a standardized examination, Laura received a
score of 85, which was exactly 2 standard
deviations above the mean. If the standard
deviation for the examination is 4, what is the mean
for this examination?
Answers
Answer:
656×756÷765+656+65=
Step-by-step explanation:
it was soo easy now i get what it is talking about no
which equation best represents the relationship between x and y in the graph
Answers
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line
m = [tex]\frac{3-0}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3
The line crosses the y- axis at (0, 3 ) ⇒ c = 3
y = 3x + 3 ← equation of line → A
if you answers this question correctly i'll give you brainliest
Answers
Answer:
D. Both of the dot A and B have the same mean
Consider the equation x2 – 12x + 49 = 22. Which equation has the same solution(s) as the given equation?
Answers
Answer:
The correct solution is "x=3 or x=9".
Step-by-step explanation:
The given equation is:
⇒ [tex]x^2 - 12x + 49 = 22[/tex]
On subtracting "22" from both sides, we get
⇒ [tex]x^2-12x+49-22=22-22[/tex]
⇒ [tex]x^2-12x+27=0[/tex]
On factorizing the above equation, we get
⇒ [tex]x^2-9x-3x-27=0[/tex]
By taking common, we get
⇒ [tex]x(x-9)-3(x-9)=0[/tex]
⇒ [tex](x-3)(x-9)=0[/tex]
⇒ [tex]x-3=0[/tex]
[tex]x=3[/tex]
Or,
⇒ [tex]x-9=0[/tex]
[tex]x=9[/tex]
It took gigi 1 hour and 20 minutes to complete a bicycle race It took Johnny twice as long because he got a flat tire. How many minutes did it take Johnny to finish the race?