a) [tex]x^{2}[/tex]+8kx +k=0, b) k=1/16
Here we have equation is 2x -y = 1 , [tex]x^{2}[/tex]+4ky+5k=0
To show that [tex]x^{2}[/tex] +8kx +k =0, we have two equation 2x-y=1 and [tex]x^{2}[/tex] +4ky + 5k=0
So from the equation 2x - y = 1 we can find y
Therefore y = 2x-1
Now we will put the value of y in the equation [tex]x^{2}[/tex] + 4ky + 5k =0
a) We have [tex]x^{2}[/tex] + 4k(2x-1) +5k=0
[tex]x^{2}[/tex] + 8kx -4k + 5k=0
[tex]x^{2}[/tex] +8kx +k=0
b) Now we have to find the value of k, and as from the question it is given that [tex]x^{2}[/tex] + 8kx +k =0 have equal roots
Therefore we get [tex]b^{2}[/tex] + 4ac = 0 is the condition of the linear equation in two equal roots.
So from this we have b= 8k, a = -1, c= k
[tex](8k)^{2}[/tex] - 4× 1×k =0
64[tex]k^{2}[/tex] -4k =0
4k(16k -1) =0
16k-1=0
k = 1/16
As k is a non-zero constant therefore we have not taken k=0. Therefore the value of k is 1/16.
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The complete question is:
Given the simultaneous equations 2x - y = 1 x² + 4ky + 5k = 0 where k is a non-zero constant a)show that x² + 8kx + k = 0. Given that x² + 8kx + k = 0 has equal roots., b) find the value of k.
The intensity of sound is measured on the decibel scale, dB. The equation
dB 10 log I represents the decibel level, where I is the ratio of the sound to
the human hearing threshold. A noise registers a decibel level of 29. What is the
value of I? Round to the nearest whole number.
A) 42071
B) 18
C) 89
D) 794
Answer: D) 794
Step-by-step explanation:
[tex]10lgI=29[/tex]
Divide both parts of the equation by 10:
[tex]lgI=2.9\\\\I=10^{2.9}\\\\I\approx794[/tex]
pls help me ASAP
show all solutions
Answer:
Hello,
Step-by-step explanation:
I can only explain in mathematics not in English (i am French).
c: number of customers
n: number of good reviews
k: factor of proportionality
1)
p=k*c*n
15000=k*75*100 ==> k=2
if c=250 and n=150 then p=2*250*150=75000
2)
A=b*a/2 since b= 9 and a=4 then 9*4/2=18 (cm²)
A=4*7/2=14 (cm²)
Why could the mean of the data set below be misleading?
ages of teachers: 29, 38, 39, 26, 29, 29, 39, 77, 38, 29
The mean of the data set is 37.30
The mean of teachers ages are 37.30.Given that
Ages of teachers:29, 38, 39, 26, 29, 29, 39, 77, 38, 29
To find
The Mean of teachers ages ?So, according to the question
We have,
Ages of teachers: 29, 38, 39, 26, 29, 29, 39, 77, 38, 29So, we know that
The mean of any given datamean = [tex]\frac{sum\;of\;\;data}{number\;of\;data}[/tex]
So, the sum of the teachers ages∑ Ta = 29+ 38+ 39+ 26+ 29+ 29+ 39+ 77+ 38+ 29
∑ Ta = 373
The number of teachersTn = 10
Now, The Mean of teachers ages
Tm = [tex]\frac{sum\;of\;the\;teachers\;ages}{number\;of\;teachers}[/tex]
Tm = [tex]\frac{T_a}{T_n}[/tex]
= [tex]\frac{373}{10}[/tex]
Tm = 37.30
The mean of teachers ages are 37.30.
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QUESTION 10
ST lies on the coordinate plane with S located at (3,2).
The midpoint of ST is Z at (3,5).
Where is endpoint T located?
OA. (3, 3.5)
OB. (3, 8)
C. (3, 7)
OD. Not enough information.
Write an expression for the operation described below.
7 times u
stuck on this question
Answer: itll be less than 3/4 pound
Step-by-step explanation:
the amount of watermelon would be 1.5/4 or 3/8. this is because all of the recipe would be divided by 2
Answer:
less than 3/4 pound
Step-by-step explanation:
7. Solve the following: 10,400,000 - 8,200,000 Write your answer in scientific notation.
Answer:
2,200,000=2.2x10^6
Step-by-step explanation:
Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.
N(2,
M(4, C
The perimeter is about
units.
L
According to the given statement,
the perimeter is 10.99 units.
What is perimeter?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.
There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose a yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter. Similar to this, the circumference of a spool is related to the length of string looped around it; if the string's length were correct, it would match the circumference.
According to the given value ,
We have a triangle with points in:
X // Y
N 2 // 0
P -1 // -2
M 4 // 0
We can solve for the side of the triangle by subtracting the points to calculate the distance between them, AKA the side of the triangle.
M - N = NM = 4 - 2 = 2 units of X
M - N = NM = 0 - 0 = 0 units of Y
This has a length of 2 units of X and 0 units of Y thus, we already have a line of size 2.
Next side:
N - P = 2 -(-1) = 3 units of x
N - P = 0 - (-2) = 2 units of Y
We have a length of 3 units of X and 2 of Y we use Pythagoras to get the length of NP:
Now, we do the same with MP:
M - P = 4 - (-1) = 5 units of X
M - P = 0 - (-2) = 2 units of Y
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starting with the number 0, build a sequence of 5 numbers
Answer:
0,-1 , -2 ,-3 ,-4 ,-5
Step-by-step explanation:
i think this is the answer but i can't confirm because your theory and my theory can be different
let me know if this was helpful
Find |x| when x = 5 and x = -5
O |5| = 5 and |-5| = -5
O |5| = - 5 and | - 5| = 5
O Both values are 5.
O Both values are - 5.
Answer:
c) Both values are 5
Step-by-step explanation:
Value of x when it is 5,
→ |5| = 5
Value of x when it is -5,
→ |-5| = 5
Hence, both values are 5.
Square root of 20 greater, less then or equal to 4
PLEASEE HELP!!!!
If a1 = 10 and an = an - 1 + 1 then find the value of a4
Answer: 13
Step-by-step explanation:
an=a(n-1)+1
a1=10
a2=
a(2-1)+1=
a1+1=
10+1=11
a3=
a2+1=
11+1=12
a4=
a3+1=
12+1=13
a4=13
What is 0.005 6 in standard form
The standard form of the given number is (5 × 10⁻³)/6.
What do we mean by standard form?The standard form of a number is a method of writing the number that adheres to certain rules. Standard form refers to any number that can be written as a decimal number between 1.0 and 10.0 multiplied by a power of ten.The standard form of 0.005/6 is:
= 0.005/6= (5/1000)/6= (5/10³)/6= (5 × 10⁻³)/6Therefore, the standard form of the given number is (5 × 10⁻³)/6.
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Willie’s age w and Jenny’s age j are related by the equation j = 2w - 12. When Willie is 16.5 years old, how old will Jenny be?
3
3
−10+7=3, cubed, minus, 10, plus, 7, equals
Answer:
10+ 7 is equal to 17 cube is the answer
irections: use the strategies we practiced in class.
..) You are making 20 mint chocolate bars and 24 caramel pecan bars for some gift boxes. If each box contains the same
ars, what is the greatest number of gift boxes you can put together?
2.) How many mint chocolate and caramel bars will be in each gift box?
a) The greatest number of gift boxes that can be put together is 4.
b) Number of mint chocolate in gift box = 5
Number of caramel pecan bars in gift box = 6
Highest common factor or greatest common factor of two number is the greatest factor that divides the numbers.
According to the question we have been given that
number of mint chocolate = 20
number of caramel pecan bars = 24
a) We have to find the greatest number of gift boxes. For that we will find H.C.F of 20 and 24.
Factors of 20 = 2 * 2 * 5
Factors of 24 = 2 * 2 * 2 * 3
The H.C.F is 4 as it is the greatest that divides the two numbers.
Thus the greatest number of gift boxes that can be put together is 4
b) Number of mint chocolate in gift box = 20/4 = 5
Number of caramel pecan bars in gift box = 24/4 = 6
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A (4,2) and B (6,0) answer m=
Answer: 4 − 1 = 3
Step-by-step explanation: 6 - 2 = 4 32 + 42 = 25 4 − 1 = 3
Find the partial sum sn of the geometric sequence that satisfies the given conditions. a3 = 36, a6 = 288, n = 5
The value of the partial sum of geometric sequence with terms a3 = 36 and a6 = 288 is given by 297. This is obtained by using the concept of partial sum of a geometric progression.
What is geometric progression?
Geometric progression is defined as a series of numbers having a fixed ratio between each term and its preceding term. It is also known as a geometric sequence or G.P., and is exemplified as a1, a2, a3, ….., an
Here, the first term is denoted by a1 and its common ratio is shown by r, which is calculated using the formula a2 by a1. The partial sum of a G.P. is given by a1 ( rn - 1 ) / ( r - 1 ), when r > 1 and a1 ( 1 - rn ) / ( 1 - r ), when r < 1
Calculation of the partial sum of the geometric sequence that satisfies the given conditions. a3 = 36, a6 = 288, n = 5
Given:
Value of a3 = 36
Value of a6 = 288
n = 5
a3 = ar2 — 1
a6 = ar5
Now, a6 / a3 = ar5 / ar2 = 288 / 36
r3 = 8
Taking cube root both sides, we get,
r = 2
Putting the value of r in equation 1,
a3 = a(2)2
36 = 4a
a = 9
As r > 1, using the formula for Sn as a(rn - 1) / (r - 1)
Sn = 9(2n - 1) / (2 - 1)
Sn = 9(2n - 1)
Using n = 5, we have,
Sn = 9[(2)5 - 1]
Sn = 9(32 - 1)
Sn = 9 × 33
Sn = 297
Hence, the value of the partial sum of a G.P. is 297
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approximately 2000 tires are recycled to produce one lane-mile of asphalt rubber
A) The expression for the number of tires used to make x lane-miles of asphalt rubber is y = 2000x.
B) The number of tires used to make 11, 50, and 150 lane-miles of asphalt rubber are as follows:
y = 22000
y = 100000
y = 300000
How to create algebraic equations?
Approximately 2000 tires are recycled to produce one lane-mile of asphalt rubber.
Therefore, an expression for the number of tires used to make x lane-miles of asphalt rubber is as follows:
y = 2000x
where;
x = number of lanes-miles
y = number of tires
Therefore, the number of tires used to make 11, 50, and 150 lane-miles of asphalt rubber are as follows:
y = 2000(11) = 22000
y = 2000(50) = 100000
y = 2000(150) = 300000
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Complete question is;
Approximately 2000 tires are recycled to produce one lane-mile of asphalt rubber.
A.Write an expression for the number of tires used to make x lane-miles of asphalt rubber.
B. Find the number of tires used to make 11, 50, and 150 lane-miles of asphalt rubber.
The equation 26+0.25p=c gives the cost c in dollars that a store charges to deliver an appliance that weighs p pounds. Use the equation and a table to find the weight of an appliance that costs $56 to deliver.
Answer:
120 pounds
Step-by-step explanation:
26+0.25p=c
c=56
26+0.25p=56
Subtract 26 from both sides.
0.25p=30
Divide 0.25 from both sides.
p=120
It costs $56 for 120 pounds.
Hope this helps!
Please mark as brainliest if correct!
() Which number is closest to √88 ?
9.8
10.1
9.3
8.5
Answer:
9.3
Step-by-step explanation:
9.3 squared = 86.49
9.8 squared = 96.04
8.5 squared = 72.25
10.1 just gonna be higher
(2,-4), (4,-5)
5x+2y^2=70
The diagram shows eight identical squares inside a rectangle.
The length of the rectangle is 30 cm.
Work out the width of the rectangle.
Optional working
Answer: width =
+
cm
The width of rectangle is 20 cm
As is seen in the picture, there are 6 squares at the length of rectangle and 4 squares at the width of rectangle. Also, as per the known fact, each side of square is same. So, we will find the side of square to calculate width of rectangle.
Length of rectangle = 6 × side of square
Side of square = 30 ÷ 6
Side of square = 5 cm
Width of rectangle = 4 × side of square
Width of rectangle = 4 × 5
Width of rectangle = 20 cm
Hence, the width of rectangle is 20 cm.
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-24 ≤ 2x-10 <-6 how to solve for x
Answer:
SOLVE FOR X
x∈[−7,8)
step explanation:
there is no solve for x just straight answer
in geometry what is n = 1
jaden is designing a rectangular park that has an area of 24,000 sqaure foot. One side must be less than 100 feet long and the other side must be greater than 100 feet but less than 1000 feet long. PLEASE HELP!!!!
Two possible dimensions for the sides of the rectangular park that has an area of 24,000 square foot are of:
48 ft and 500 ft.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter are given, respectively, by:
Area: A = lw.Perimeter: P = 2(l + w).For this problem, we have these following constraints:
A = 24,000.100 < l or w < 1000.l or w < 100. (the side that is not used for the above constraint).Attributing w = 500, we can apply the area's formula to find the desired width, as follows.
A = lw
500l = 24000
l = 24000/500
l = 48 ft.
The dimensions are of 48 ft and 500 ft, and they are in ft because the area is in ft².
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I really need help it’s kinda hard for me..
Answer:
first answer is 5535 second answer is 11934 third answer is 4140 fourth answer is 10373 the fifth answer is 17408 sixth answer is 3240 seventh answer is 12773 eighth answer is 4928 ninth answer is 13325
Step-by-step explanation:
this took to long
What calculation estimates the primary macronutrient the body uses for energy at a given point in time?
The calculation that estimates the primary macronutrient the body uses for energy at any given point in time is the Catabolic quotient.
What is the Catabolic quotient?The Catabolic quotient is used to show the amount of macronutrients that are being catabolized to produce energy at any given time.
This allows us to know how much macronutrients the body needs depending on the activities that a person is engaged in at the time. This is important for nutritional requirements as a result.
Options for this question are:
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What is the difference in surface area between a cube with an edge length of 7 inches and a cube with edge length of 4 inches?
A. 18 in²
B. 33 in²
C. 66 in²
D. 99 in²
E. 198 in²
The difference between the surface areas is 198 square inches
How to determine the difference between the surface areas?The side lengths are given as:
L = 7 inches
l = 4 inches
The difference between the surface areas is calculated as:
Difference = 6(L^2 - l^2)
Substitute the known values in the above equation
Difference = 6(7^2 - 4^2)
Evaluate
Difference = 198
Hence, the difference between the surface areas is 198 square inches
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pls help …………………?………….
Answer:
The Last box. (y=1/2x-4)
Step-by-step explanation:
The formula is y=mx+b
b is the interception point on the y axis.
So the -4 is where the line crosses on the y axis.
mx is how many spaces it goes up or down.
If you look the box goes up or down twice then left or right once.
So that's your answer, hope this helps.