The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]
In this question, we use the concept of the solution of a quadratic equation to solve it, considering that a quadratic equation in the format:
[tex]ax^2 + bx + c = 0[/tex]
has two equal solutions if [tex]\Delta = b^2 - 4ac[/tex] is 0.
------------------------------------
In this question:
The equation is:
[tex](2k+1)x^2 + 2x = 10x - 6[/tex]
Placing in the correct format:
[tex](2k+1)x^2 + 2x - 10x + 6 = 0[/tex]
[tex](2k+1)x^2 - 8x + 6 = 0[/tex]
Thus, the coefficients are: [tex]a = 2k + 1, b = -8, c = 6[/tex]
------------------------------------
Delta:
We want it to be positive, so:
[tex]\Delta = b^2 - 4ac[/tex]
[tex]\Delta = 0[/tex]
[tex]b^2 - 4ac = 0[/tex]
[tex](-8)^2 - 4(2k+1)(6) = 0[/tex]
[tex]64 - 48k - 24 = 0[/tex]
[tex]-48k + 40 = 0[/tex]
[tex]-48k = -40[/tex]
[tex]48k = 40[/tex]
[tex]k = \frac{40}{48}[/tex]
[tex]k = \frac{5}{6}[/tex]
The equation has two real and equal roots for [tex]k = \frac{5}{6}[/tex]
A similar question is found at https://brainly.com/question/12144265
help me please to solve this 2 questions pleasee faster.. i will mark you as brainliest
Answer:
1. x=72, y=, 108
2.x=30, y=72
Step-by-step explanation:
Brainliest please~
Sue has 3 cats. Each cat eats 1 4 of a tin of cat food each day. Sue buys 4 tins of cat food. Has Sue bought enough cat food to feed her cats for 5 days? You must show how you get your answer
Answer:
3 3/4 tins of food
Step-by-step explanation:
Number of cats = 3
Quantity of food for each cat per day = 1/4 of a tin
Total tins of cat food sue bought = 4 tins
Has Sue bought enough cat food to feed her cats for 5 days?
Quantity of food 3 cats eat per day = Quantity of food for each cat per day × Number of cats
= 1/4 × 3
= 3/4 of a tin
Total Quantity of food 3 cats eat for 5 days = Quantity of food 3 cats eat per day × 5 days
= 3/4 × 5
= (3 * 5) / 4
= 15/4
= 3 3/4 tins of food
Total Quantity of food 3 cats eat for 5 days = 3 3/4 tins of food
Recall,
Total tins of cat food sue bought = 4 tins
Therefore, Sue bought enough cat food to feed her cats for 5 days
The length of a rectangular playing field is 5m longer than its width. If the perimeter of the field is 150m,find it's width
Answer:
35
Step-by-step explanation:
Make equations, l = w+5 and 2l + 2w = 150
Substitute w+5 into 2l + 2w = 150
Simplify to get 4w + 10 = 150
Subtract 10 from both sides to get 4w = 140
Divide both sides by 4 and you get 35 as width
Answer:
The width of the field is 35 meters.
Step-by-step explanation:
Recall that the perimeter of a rectangle is given by:
[tex]\displaystyle P = 2(w+\ell)[/tex]
Where w is the width and l is the length of the rectangle.
We know that the perimeter is 150 meters. Thus:
[tex]150=2(w+\ell)[/tex]
Divide both sides by two:
[tex]75=w+\ell[/tex]
We are given that the length is five meters longer than the width. So:
[tex]\ell = w+5[/tex]
Substitute:
[tex]75=w+(w+5)[/tex]
Combine like terms:
[tex]75=2w+5[/tex]
Subtract five from both sides:
[tex]70=2w[/tex]
And divide both sides by two. Hence:
[tex]w=35[/tex]
Thus, the width of the rectangular field is 35 meters.
Express 3.023 in P form where p and q are integers and q= 0 D
Given:
The number is 3.023.
To find:
The given number in the form of [tex]\dfrac{p}{q}[/tex], where [tex]q\neq 0[/tex].
Solution:
The given number is 3.023. It can be written as:
[tex]3.023=3.023\times \dfrac{1000}{1000}[/tex]
[tex]3.023=\dfrac{3023}{1000}[/tex]
It cannot be simplified further because 3023 and 1000 have no common factors.
Therefore, the given number 3.023 can be written as [tex]\dfrac{3023}{1000}[/tex].
Enter the coordinates of the point
on the unit circle at the given angle. 0°
The points are ( 1,0) (0,1) .
The coordinates of the point on the unit circle -The coordinates for the points lying on the unit circle and also on the axes are (1,0), (–1,0), (0,1), and (0,–1). These four points (called intercepts) are shown here. When you square each coordinate and add those values together, you get 1. They're the sine and cosine values of the most common acute-angle measures.a.) We seek the coordinates on the unit circle that represent an angle of 0 degrees.
The points on the unit circle are often provided by,
( cosθ, sinθ )
In order to do so,
θ= 0
to acquire,
(cos(0),sin(0))
(1,0)
b. With regard to the location on the unit circle where the angle is 90 degrees,
We swap out
θ = 90
to acquire,
(cos(90),sin(90))
This is condensed to, (0,1)
Learn more about the coordinates of the point on the unit circle brainly.com/question/10169163
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Answer: 1,0
is the actual answer
Căn 84 bình phương trừ 37 bình phương chia 47
Answer:
[tex]\sqrt{84^{2} } -37^{2} /47[/tex]=257 9/47
Step-by-step explanation:
Help,anyone can help me do quetion,I will mark brainlest.
5.
1m = 0.001 km
So, 1m² = 10^-6
Area = 5027 m² = 5027 × 10 ^-6 km²
6.
1mm = 0.1 cm
1mm² = 10^-2
Area = 210× 297 mm² =62370 mm² = 62370 ×10^-2 cm²
SOMEONE HELP ME PLEASE
9514 1404 393
Answer:
1/12
Step-by-step explanation:
The probability of any given outcome is the ratio of the number of ways that outcome can happen to the total number of outcomes.
P(4) = 1/6 . . . . . roll = 4 is one of 6 possible outcomes
P(odd) = 3/6 = 1/2 . . . . . of the 6 possible outcomes, 3 are odd
__
The two rolls of the die are presumed to be independent, so the probability of the two outcomes is the product of their individual probabilities.
P(4 & odd) = (1/6)(1/2) = 1/12
20 POINTS AND BRAIN LIESTJ ulia s urveyed the pl ayers on her so ccer team to see how many hou rs each mem ber prac ticed during the week. Her data is shown in the histo gram.
A histogram titled Prac tice Time has number of hours on the x -axis and number of players on the y-axis. 0.1 to 0.5 hours is 5 players, 0.6 to 1: 6, 1.1 to 1.5: 5, 1.6 to 2: 2, 2.1 to 2.5: 1, 2.6 to 3: 2, 3.1 to 3.5: 2, 3.6 to 4: 1, 4.1 to 4.5: 1.
Which of the following best describes the histogram?
The histogram is evenly distributed.
The histogram is symmetrical.
The left side of the histogram has a cluster.
The left side of the histogram is the mirror image of the right side.
Answer:
the left side of the histogram is the mirror image of the right side.
1/x^-2 x=7 yeet yeet
Answer:
49
Step-by-step explanation:
x = 7
1 / x^-2
= x^2
= 7^2
= 49
Answer: 49
Step-by-step explanation: yeet
find the value of x.
2+3
12
5
1.2
6.6
07
12
Answer:
x = 7
Step-by-step explanation:
The triangles are similar
12/8 = (x+3+5)/(x+3) cross multiply expressions
12x + 36 = 8x + 64
12x - 8x = 64 - 36
4x = 28 divide both sides by 4
x = 7
What is the distance between (4, -10) and (4,-4)?
Answer:
For x there is no distance since they are both for. For y, they are -6 apart.
Step-by-step explanation:
Answer:
Fox x Diya is no distance since they are both for they are six apart
Step-by-step explanation:
(4-10)
and= just opposite size (10- 4) .
10 -4 = 6 answer 6
and (4-4)
answer is
0
the answer is six apart
understand
Find sin R.
a. sin R= 29/21
b. sin R= 21/20
c. sin R= 20/29
d. sin R= 21/29
Answer:
sin R = 20 / 29
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin R = opp / hyp
sin R = 20 / 29
Find the surface area of this cylinder.
Round to the nearest tenth.
r = 3 cm
3 cm
SA = [ ? ] cm2
PLEASE HELP
Formula for the surface area of a cylinder: 2 x pi x r^2 + 2 x pi x r x h
Radius (r) = 3
Height (h) = 3
2 x pi x 3^2 + 2 x pi x 3 x 3
2 x pi x 9 + 2 x pi x 9
18pi + 18pi
36pi = 113.1 cm^2
Hope this helps!
The surface area of the cylinder is 113.0973 square centimeter.
What is surface area of a geometric shape ?The surface area of a solid object is a measure of the total area that the surface of the object occupies. The surface area can only be present in any three dimensional geometric shape.
How to find the surface area of the cylinder ?The surface area of the cylinder is given by - 2*π*r*h + 2*π*r*r
where r is the radius of the cylinder and h is the height of the cylinder from its base.
In the given problem, r = 3cm and h = 3cm .
⇒ Surface area = 2*π*3*3 + 2*π*3*3 square centimeters.
= 36π = 113.0973 square centimeters.
∴ Surface area = 113.0973 square centimeters.
Thus the surface area of the cylinder is 113.0973 square centimeter.
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Instructions: Find the measure of the indicated angle to the nearest degree.
50
?
25
Answer:
theta = 30 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp side/ hypotenuse
sin theta = 25/50
sin theta = 1/2
Taking the inverse sin of each side
sin ^-1 (sin theta) = sin ^-1 (1/2)
theta = sin ^-1 (1/2)
theta = 30 degrees
calculate the value of 120 is increased by 120%
Answer:
144
Step-by-step explanation:
currect answer for simple question
Answer:
264
Step-by-step explanation:
First find the amount of increase
120 * 120%
120 * 1.2
144
Add this to 120
120 +144
264
Using long division, what is the quotient of this expression?
X^4+4x^3-5x^2+x-3/x^2+x-3
Answer:
Using long division method the answer is B
Step-by-step explanation:
x²+3x-5+(15x-18)/x²+x-3
A company rents water tanks shaped like cylinders. Each tank has a radius of 6 feet and a height of 2 feet. The cost is $30 per cubic foot. How much does it cost to rent one water tank
Step-by-step explanation:
Volume of tank = (pi)×(radius squared)×(height)
= 3.14×(6×6)×2
= 3.14×36×2
= 226.08 cu.ft
Each cu.ft is rented for $30
So, for 226.08 cu.ft is,
=226.08×$30
=$6782.3
What is the simplified form of the complex fraction? 2x2+7x+6x2+x−64x2−9x2−5x+6
Answer:
3x - 124
Step-by-step explanation:
kindly find solutions in the picture above
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The simplified form of the complex expression 2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6 is
-65x² + 2x + 6
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6
Combine all like terms.
(2x² + 6x² - 64x² - 9x²) + (7x - 5x) + 6
(8x² - 73x²) + 2x + 6
-65x² + 2x + 6
There are no common factors or like-terms to simplify.
So,
The simplified form is -65x² + 2x + 6
Thus,
The simplified form of the complex expression 2x² + 7x + 6x² + x - 64x² - 9x² - 5x + 6 is
-65x² + 2x + 6
Learn more about expressions here:
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What is the area of this triangle
Answer:
17.5 units
Step-by-step explanation:
im not good at explaining sorry
Mrs.Click has a strawberry patch in her garden. It's border is 4/5 meters wide and 3/2 meters long. What is the area of Mrs.Clicks Garden?
Answer
Mrs. Click's Garden is 6/5 or 1 1/5 square meters.
Explanation
Mrs. Click's has a rectangular garden. To find the area of a rectangle, you multiply the width by the length. To find the area of Mrs. Click's Garden, you multiply 4/5 by 3/2.
To multiply fractions, you multiply the numerator by the denominator.
4×3 is 12 and 5×2 is 10. You get the fraction 12/10, which can be simplified to 6/5, or 1 1/5.
When the focus and directrix are used to derive the equation of a parabola, two distances were set equal to each other. = StartRoot (x minus x) squared + (y minus (negative p)) squared EndRoot = StartRoot (x minus 0) squared + (y minus p) squared EndRoot The distance between the directrix and is set equal to the distance between the and the same point on the parabola.
Answer:
The answer is "A point on the parabola and Focus".
Step-by-step explanation:
[tex]= \sqrt{(x - x)^2 + (y- (-p))^2} = \sqrt{(x-0)^2+ (y-p)^2} \\\\= \sqrt{(0)^2 + (y+p))^2} = \sqrt{(x)^2+ (y-p)^2} \\\\= \sqrt{(y+p))^2} = \sqrt{(x)^2+ (y-p)^2} \\\\= (y+p) = (x)+ (y-p) \\\\= y+p = x+ y-p \\\\=2p=x\\\\=x=2p[/tex]
Whenever the focus and also the guideline are utilized in determining the parabolic formula, two distances have indeed been equal.
The distance from the direction, as well as a parabolic point, was equal to the distance from the center to a parabolic point.
Answer:
The distance between the directrix and a point on the parabola is set equal to the distance between the focus and the same point on the parabola.
Step-by-step explanation:
Hope this helps! :)
Pleasee help me with this!!
Answer:
#1 is f.
#2 is d.
#3 is a.
#4 is b.
#5 is c.
#6 is g.
#7 is e.
Step-by-step explanation:
The digit "9" is in the ten's place because it is two numbers/spaces left from the decimal. If you make all the other digits "0", you'll be left with a value of 90.
The digit "1" is in the one's place because it is one number/space left from the decimal. Applying the same concept of making all the other digits "0", you'll be left with a value of 1.
The type of digits to the right of the decimal, starting from left to right, are the tenths place, hundredths place, thousandths place, ten-thousandths place, and millionths. Remember and know those digit types based on their position away from the decimal. The value will be there for you to see afterward.
What product is positive (2/5)(-8/9)(-1/3)(-2/7). (-2/5)(8/9)(-1/3)(-2/7). (2/5)(8/9)(1/3)(-2/7). (-2/5)(-8/9)(1/3)(2/7)
Answer:
d
Step-by-step explanation:
a. (2/5)(-8/9)(-1/3)(-2/7)= - 32/945
b. (-2/5)(8/9)(-1/3)(-2/7) = -32/945
c. 2/5 * 8/9 * 1/3 * - 2/7 = - 32/945
d. -2/5 * - 8/9 * 1/3 * 2/7 = 32/945
Answer:
D
Step-by-step explanation:
32/945 is the final answer
Two cars that are 600km apart are moving towards each other. Their speeds differ by 6km per hour and the cars are 123km apart after 4.5 hours. Find the speed of each car
Answer: [tex]56\ kmph,\quad 50\ kmph[/tex]
Step-by-step explanation:
Given
Two cars are 600 km apart moving towards each other
Difference in their speed is 6 kmph
After 4.5 hr, they are 123 km apart that is, they covered a distance of [tex]600-123=477\ km[/tex] in 4.5 hours
Suppose their speeds is [tex]v_1\ \text{and}\ v_2[/tex]
[tex]\therefore v_1-v_2=6\quad \ldots(i)[/tex]
Also, distance traveled is given by
[tex]\Rightarrow 477=[v_1+v_2]4.5\\\Rightarrow v_1+v_2=106\quad \ldots(ii)[/tex]
Solve, (i) and (ii) , we get [tex]v_1=56\ kmph\ \text{and}\ v_2=50\ kmph[/tex]
Solve the following system of equations. -5x - 4y= -11 7x + 3y = 18
Step-by-step explanation:
-5x - 4y= -117x + 3y = 18
-5x +117x = 3y + 4y = 18
112x = 7y = 18
A machine with velocity ratio of 5 is used to raise a load with an effort of 500N . If the machine is 80% efficient , determine the magnitude of the load.
Answer:
Solutions given:
Velocity ratio V.R =5
effort =500N
efficiency =80%
magnitude of load=?
mechanical advantage [M.A ]
we have
efficiency =M.A/V.R*100%
80=M.A./5*100
80/100*5=M.A
M.A.=4
again
we have
M.A =load/effort
4=load/500
load=500*4
load=2000N
the magnitude of the load is 2000N.Use the data in the table to complete the sentence.
х
-2
-1
0
1
y
7
6
5
4
The function has an average rate of change of ______.
Answer:
-1
Step-by-step explanation:
Increasing the x-value by one results in the y-value decreasing by 1. Therefore, the average rate of change is -1.
Answer: -1
Step-by-step explanation: ;)
It cost David $16.75 to fill his 5-gallon gas can.
1. Write two different rates.
2. What is the best unit rate to use?
3. If David decided to fill up his car that has a 22-gallon gas tank, would $73 be enough to cover it? If so, how much does he have leftover? If not, how much is he short?
Answer: I divided 16.75 by 5
Step-by-step explanation:
For every 1 gallon hes using 3.35
So 22 x 3.35 is 73.70 so hell need 70 cent more
Ayuda
Which of the following represents the isolate the variable "r" from the following formula?
V = K * q / r
Answer:
r = K * q / V
Step-by-step explanation:
V = K * q / r
