1. If one zero of the quadratic polynomial kx² + 3x + k is 2 then the value of k is *
Answers
Answer:
Step-by-step explanation:
Given one zero of the quadratic polynomial kx² + 3x + k is 2,
Substitute x = 2 in the polyomial , we get
k(2)²+3×2+k = 0
=> 4k + 6 + k = 0
5k+6 = 0
5k= -6
k= -6/5
Therefore,
Value of k = -6/5
Related Questions
If y=26−(3x+2), then x = ?
Answers
Answer:
-1/3y +8 = x
Step-by-step explanation:
y=26−(3x+2)
Distribute
y = 26 -3x-2
Combine like terms
y = 24 -3x
Subtract 24 from each side
y -24 = -3x
Divide each side by -3
y / -3 -24/-3 = -3x/-3
-1/3y +8 = x
EXAMPLE 10 Show that the points (a, a),(-a, - a) and (-3a, 3a) are the vertices of an equilateral triangle. Also find its area.
Answers
Answer:
The triangle is not equilateral.
Step-by-step explanation:
Distance formula:
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Distance from (a, a) to (-a, -a):
[tex] d_1 = \sqrt{(-a - a)^2 + (-a - a)^2} [/tex]
[tex] d_1 = \sqrt{(-2a)^2 + (-2a)^2} [/tex]
[tex] d_1 = \sqrt{8a^2} [/tex]
Distance from (-a, -a) to (-3a, 3a):
[tex] d_2 = \sqrt{(-3a - (-a))^2 + (3a - (-a))^2} [/tex]
[tex] d_2 = \sqrt{(-2a)^2 + (4a)^2} [/tex]
[tex] d_2 = \sqrt{20a^2} [/tex]
Distance from (-3a, 3a) to (a, a):
[tex]d_3 = \sqrt{(-3a - a)^2 + (3a - a)^2}[/tex]
[tex]d_3 = \sqrt{(-4a)^2 + (2a)^2}[/tex]
[tex]d_3 = \sqrt{20a^2}[/tex]
The three sides do not have the same length, so the triangle is not equilateral.
please help !!! idk how to do this
Answers
Answer:
C
Step-by-step explanation:
Here, we want to state the interval that has the highest frequency.
What we are asked here is the range of values where we have the the most common salary.
For 0-10, we have 1 ( Estonia)
For 11-20, we have 1 (Israel)
For 21-30 , we have 0
For 31-40, we have 1 ( Greece)
For 41-50, we have 5
For 51-60, we have 3
For 61-70, we have 1 (Luxembourg)
So 41-50 is the class with the highest frequency
If JK = 28, JL = 20, KL = 13, and ML = 22, calculate NL. Image not set to scale.
Answers
Answer:
NL = 440 /13 or 33.85 (to two decimals)
Step-by-step explanation:
Consider triangles JKL and NML
angle JLK = angle NLM vertical angles
angle KJL = angle MNL given
Therefore triangles JKL and NML are similar
By proportion of corresponding sides of similar triangles,
NL / JL = LM / LK
Substitute given values
NL / 20 = 22 / 13
solve for NL
NL = 20*22 / 13 = 440 /13 or 33.85 (to two decimals)
Answer:
[tex]\huge \boxed{33.85}[/tex]
Step-by-step explanation:
JL is similar to NL. KL is similar to ML.
We can use ratios to solve.
JL/KL = NL/ML
Let the length of NL be x.
20/13 = x/22
Cross multiply.
13 × x = 22 × 20
13x = 440
Divide both sides by 13.
(13x)/13 =440/13
x = 440/13 = 33.846154...
What is this used for and how do i use it..?
Answers
you have to solve each one to get your answer and I think that your answer will be inside the circle
Answer:
This is called the Unit Circle. It is used in trigonometry. It had a radius of 1.
It helps you when using the trig function of sin cos and tan.
Hope this helps!!!!
Step-by-step explanation:
Given the two figures are similar, calculate the value of y
Answers
Answer:
y+1/12.5=2/5
or,5y+5=25
ory=20/5
so, y=4
Step-by-step explanation:
hope it helps you
Can any kind soul help me please
Use the cosine rule
Answers
Answer:
M = 45°
Step-by-step explanation:
a²=b²+c²-2bc Cos A
m² = n² + p² - 2np cos M
(5.1)² = (7.2)² + (5.3)² - 2(7.2)(5.3) cos M
26.01 = 51.84 + 28.09 - 76.32 cos M
-53.92 = -76.32 cos M
0.7065 = cos M
M = [tex]cos^{-1 }[/tex](0.7065)
M = 45°
use the given information to find the new price
wholesale price: $35
markup: 95%
Answers
Answer:
i think the answer is either $68.25 or $110
i hope this helped
Why is it important to consider scale when graphing inequalities?
Answers
Answer:
Because to get a straight line you need a scale. Otherwise you will not be able to graph a straight line.
Hope this helps:)
If a square has a side of length 3, then it’s area is 9. This square has a side of length 3, so it’s area is 9. Is it valid or invalid?
Answers
Answer:
Yes it is valid
Step-by-step explanation:
A square is a geometric shape which is also known as a Quadrilateral. This means that it has 4 sides.
For a square, it's 4 sides are equal to one another or we can put it in other words as the length of the 4 sides of a square are congruent to one another.
From the above question, we are asked that:
"If a square has a side length of 3, it's area is 9. Is it valid or invalid?"
The above statement is valid. This is because, the formula for the Area of a Square is given as
L × L = L²
Where L = Side length = 3
Area = 3 × 3 = 3²
Area = 9
Therefore, the statement is valid.
How many and of which kind of roots does the equation
f(x) = x5+ 3x4 + 8x3 + 14x2 + 16x + 8 have?
A. 2 real; 3 complex
B.5 real
C. 3 real;2 complex
D.1 real;4 complex
Answers
Answer:
D. 1 real; 4 complex
Step-by-step explanation:
1. Calculate the total number of roots
The fundamental theorem of algebra states that any polynomial of degree n has n roots.
Your polynomial is fifth degree, so it has five roots.
2. Calculate the number of real roots
We can use Descartes' rule of signs to determine the number of real roots:
The number of positive real roots is the same as the number of changes in the sign of the coefficients of ƒ(x) or less than by an even number.
The number of negative real roots is the same as the number of changes in sign of the coefficients of the terms of f(-x) or less than this by an even number.
(a) Number of positive real roots
The coefficients of ƒ(x) are
+1 +3 +8 +14 +16 + 8
There are no changes of sign, so there are no positive real roots.
(b) Number of negative real roots
(i) Find f(-x)
f(-x) = -x⁵+ 3x⁴ - 8x³ + 14x² - 16x + 8
(ii) Count the changes of sign
The coefficients of f(-x) are
-1 ∥ +3 ∥ -8 ∥+14 ∥ -16 ∥ +8
There are five changes of sign.
Thus, the number of negative roots is five, three, or one.
So far, we know that we have five roots. None is positive, and there could be one, three, or five negative real roots.
3. Confirm by sketching the graph
The real roots are the points at which the graph crosses or touches the x-axis.
The graph (see below) crosses the x-axis at only one point.
Thus. we have
one real root (negative) four complex roots
after allowing 5 percent discount on the marked price of a radio 10 percent vat is charged on it , then its price became rs 1672 .how much amount was given in the discount
Answers
Answer:
Hi, there!!!
The solutions in pictures will help you.
Best of luck....
write as an expression: a number that is equal to five less than b
Answers
Answer:
[tex]\huge\boxed{a = b-5}[/tex]
Step-by-step explanation:
Let the number be a
So, the given condition is:
a = b-5
Answer:
[tex]\Huge \boxed{a=b-5}[/tex]
Step-by-step explanation:
Let the number be [tex]a[/tex].
[tex]a[/tex] is equal to 5 less than [tex]b[/tex].
5 is subtracted from [tex]b[/tex].
24 is 75% percent of what number?
Answers
Answer:
32
Step-by-step explanation:
We can call the number x. 75% can be expressed as 0.75 so we can write the following equation: 0.75x = 24. Dividing both sides by 0.75 to get rid of the coefficient of x, we get that x = 32.
Answer:
32.
Step-by-step explanation:
Let's say the number we are trying to find is x.
24 = 0.75x
0.75x = 24
x = 24 / 0.75
x = 32
Hope this helps!
A circular hall has a hemispherical roof.
The greatest height is equal to the
inner diameter. If the capacity of
the hals is
the
floor is.
43510 m^3
then
area
of the
Answers
Answer:
Area=1,288.88m²
Step-by-step explanation:
A circular hall(big room) has a hemispherical roof.The greatest height is equal to the inner diameter.Find the area of the floor,given that the capacity of the hall is 43510 cubic meter
Solution
let
diameter = D
radius,r = D/2
Greatest height = D
height of cylindrical part (h)= D-r = r
radius of cylindrical part = r
area of floor = πr²
volume = volume of cylindrical part + volume of hemispherical part
= πr²h + 2/3 πr³
Recall h=r
volume = πr³ + 2/3 πr³
43510=5/3πr³
Make r the subject
r=3√(43510*3)/5π
=3√(130,530/15.7
=3√8,314.01
=20.26
Area of floor = πr²
=3.14*(20.26)²
=3.14*410.47
=1,288.88m²
a police car drives a constant speed of 64 mph.how far can it travel in 2 hours
Answers
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Dr. Green has to multiply the weight of the team's bug spray bottles, 7 x 90 grams. To solve this, he writes out the equation 7 x 9 x 10. Why does this strategy work?
Answers
Because 9 × 10 equals 90
Then 7×90=7×9×10
Please answer this question now
Answers
Answer:
76 degrees.
Step-by-step explanation:
Let as consider O is the center of the circle . So from the figure it is clear that
[tex]\angle AOB=44^{\circ}[/tex]
[tex]\angle COD=118^{\circ}[/tex]
By central angle theorem, central angle subtended by an arc is twice of inscribed angle of the same arc.
We know that, [tex]\angle BAD=97^{\circ}[/tex] and angle BOD is the central angle subtended by arc BD.
[tex]\angle BOD=2\times \angle BAD[/tex]
[tex]\angle BOD=2\times 97^{\circ}[/tex]
[tex]\angle BOD=194^{\circ}[/tex]
Now,
[tex]\angle BOD=\angle BOC+\angle COD[/tex]
[tex]194^{\circ}=\angle BOC+118^{\circ}[/tex]
[tex]194^{\circ}-118^{\circ}=\angle BOC[/tex]
[tex]76^{\circ}=\angle BOC[/tex]
[tex]m(arc(BC))=76^{\circ}[/tex]
Therefore, the measure of arc BC is 76 degrees.
A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line?
Answers
Answer:
y = -x +2
Step-by-step explanation:
y =x has a slope of 1
Perpendicular lines have slopes that multiply to -1
m* 1 = -1
The slope of the perpendicular line is -1
We have a slope and a point
y = mx+b
y= -1x+b
Substitute the point into the equation
-3 = -1(5) +b
-3 =-5 +b
Add 5 to each side
-3+5 = b
2 =b
y = -x +2
reduce to simplest form -7/12+3/8 =_____
Answers
Answer:
-5/24
Step-by-step explanation:
make the denominators the same!
Terri graphed a system of linear inequalities. Which ordered pairs are a part of the solution set for this system of linear inequalities? Select two that apply.
(-1, 5)
(2, -4)
(7, -1)
(4, 6)
(5, 2)
Answers
Answer: (2, -4) and (7, -1)
Step-by-step explanation:
Ok, the solutions of the system of inequalities are all the points that lie on the blue shaded part of the graph or in the solid line.
So, in order to see if the points are solutions of the system, then you need to locate the point in the graph and see if it is inside the shaded region or in the solid line (only in the segment that "touches" the shaded region).
Now, we want to find the equation of the solid line, we can see that it passes through the points (0, 6) and (6, 0)
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Then, in this case, the slope is:
a = (0 - 6)/(6 - 0) = -1.
And to find the value of b, we have that when x = 0, y = 6.
y = 6 = -1*0 + b
6 = b
The equation is:
y = -1*x + 6
(-1, 5) is not in the blue region nor in the solid line, so this is not a solution.
(7, - 1) this point is near the solid line, let's test it:
y(7) = -1*7 + 6 = -1
So the point (7, -1) is on the solid line, and is the other solution of the system.
The distance between two points on a number line can be found by taking the ____A_____ of the ____B_____ of the coordinates. Fill in the blanks in the previous sentence by matching the letter for each blank with the correct answer.
Answers
Answer:
The distance between two points on a number line can be found by taking the absolute value of the difference of the coordinates.
Step-by-step explanation:
Every point can be paired with a number on a number lineThe coordinate is the number associated with a pointTo find the distance between point A and B you subtract the coordinates in any order you like and take the absolute value.9. You run a business making birdhouses. You spend $600 to start your business, and it costs you $5.00
to make each birdhouse.
# of birdhouses
1
2
3
4
5
6
7
Total cost to build
Answers
Answer:
$635
Step-by-step explanation:
$5x7 birdhouses=$35want
So, $35+$600=$635 total!
I hope this helps you!
Multiplication is the process of multiplying. The cost of building 7 birdhouses will be $635.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
The cost of the birdhouse is the sum of the fixed cost, which is the setup cost of the business of $600, and the variable cost is the cost that is needed to make a single house, therefore, $5.
Now, the total cost of making n number of houses will be,
Cost of making n house = Fixed cost + variable cost
= $600 + $5(n)
Further, the table can be filled using the above formula by substituting the value of n for the number of houses. Therefore,
Number of bird houses Total cost to build
1 $600+$5(1) = $605
2 $600+$5(2) = $610
3 $600+$5(3) = $615
4 $600+$5(4) = $620
5 $600+$5(5) = $625
6 $600+$5(6) = $630
7 $600+$5(7) = $635
Hence, the cost of building 7 birdhouses will be $635.
Learn more about Multiplication here:
https://brainly.com/question/14059007
#SPJ2
Evaluate the expression below for x =4 and y = 5.
x2 + 3(x + y)
When x = 4 and y = 5, x2 + 3(x + y)= |
(Type an integer or a decimal.)
Answers
Answer:
positive 35
Step-by-step explanation:
x2 + 3(x + y) given
4(2) + 3(4+5) problem
4(2) + 3(9)
8 + 27= 35
I need Help please answer :((
Answers
Answer:
Second option is the correct answer
[tex] {3}^{ - 4} [/tex]
Step-by-step explanation:
[tex] {3}^{ - 8} . {3}^{4} = {3}^{ - 8 + 4} = {3}^{ - 4} [/tex]
Answer:
The answer is D because you multiply the exponents so -8 times 4 is -32
Hope this helps and plz mark branliest!
Step-by-step explanation:
PLEASE ANSWER QUICKLY
Answers
Answer:
Hi ! Answers given in the pictures below
Step-by-step explanation:
7a - 3 = 3 - 2a What does a equal?
Answers
Answer:
2/3
Step-by-step explanation:
1) Move the 7a to the other side
2) Move the 3
3) Combine like terms
4) Divide by 9
5) Answer is 2/3
Answer:
a=2/3
Step-by-step explanation:
All this problem needs is some knowledge of how an = sign and basic equations work
7a-3=3-2a
7a+2a=3+3 (Sign becomes opposite on the other side of the equation)
9a=6
a=2/3
Thank you for your time!
which choice is the solution set for the inequality below
x < 3
Answers
Answer:
B) x < 9
Step-by-step explanation:
√x < 3
(√x)² > 3²
x < 9
Write an equation in slope-intercept form for the line the road will follow. (The road is the dashed line.)
Answers
Answer:
x=6
Step-by-step explanation:
The crocodile river is y = 4
The road will intersect at ( 6,4)
We have two points on the line
(6,7) and (6,4)
The slope is
m = (y2-y1)/(x2-x1)
= (4-7)/ (6-6)
= -3/0
The slope is undefined
That means the equation is in the form
x=
Since the x coordinate is 6
x=6
What is the answer to (6/7)/(12/21) = 4/x Algebra plz help
Answers
Answer:
(6/7)/(12/21) = 4/x
the first part of the expression :
when divide fraction: turn the sign from ÷ to × and flip the second fraction
(6/7)×(21/12)=4/x
126/84=4/x ( simplify the fraction 126/84)
GCF of 126 and 84 is 42 ( 126/48=3 and 84/42=2)
3/2=4/x ( cross multiplication ( butterfly)
1.5=4/x
1.5x=4
x=4/1.5=2.6666.......
