Answer:
If you mean only one rational solution, the answer is
[tex]k_1 = 8, k_2 = -8[/tex]
If you mean at least 1 rational solution, the answer is
[tex]k\in (-\infty, -8]\cup[8, \infty)[/tex]
Step-by-step explanation:
[tex]4x^2 + kx + 4 = 0[/tex]
Let's calculate the discriminant.
[tex]\Delta = b^2 - 4ac[/tex]
[tex]\Delta = k^2 -4 \cdot 4 \cdot 4[/tex]
[tex]\Delta = k^2 -64[/tex]
Now, remember that:
[tex]\text{If } \Delta > 0 : \text{2 Real solutions}[/tex]
[tex]\text{If } \Delta = 0 : \text{1 Real solution}[/tex]
[tex]\text{If } \Delta < 0 : \text{No Real solution}[/tex]
Therefore, I will just consider the first two cases.
[tex]k^2 - 64 > 0[/tex]
and
[tex]k^2 -64 = 0[/tex]
[tex]\boxed{\text{For } k^2 - 64 > 0}[/tex]
[tex]k^2 > 64 \Longleftrightarrow k>\pm\sqrt{64} \Longleftrightarrow k\in (-\infty, -8)\cup(8, \infty)[/tex]
[tex]\boxed{\text{For } k^2 - 64 = 0}[/tex]
[tex]k^2 = 64 \Longleftrightarrow k=\pm\sqrt{64} \implies k_1 = 8, k_2 = -8[/tex]
Sarah has 273 feet of wire to make bead necklaces. If each necklace requires 1 2/3 feet of wire, how many necklaces can she make?
Oh boy, here we go again
First we must convert 1 2/3 to an improper fraction. By doing this, we get 5/3 (3/3 + 2/3)
So now we have 273 / 5/3
To divide this easier we can do something that when I learned it was called (keep, change, flip) which basically means keep the first fraction, change the sign from division to multiplication, and flip the second fraction
This now turns into: 273/1 * 3/5
Combine 273 and 3/5
273⋅3/5
Multiply 273
by 3
819/5
is your answer
PLEASE HELP!! A classmate wrote the set notation for the values of the domain of a function {−5, −4, −3, −2, −1, 0} as {x | −5 ≤ x ≤ 0}. Explain the student's error.
A. The student should have listed 0 before −5
B. The set notation includes all values from −5 to 0, but the domain only includes the integer values.
C. The student should have used less than symbols rather than less than or equal to symbols.
D. The student should have used greater than or equal to symbols rather than less than or equal to symbols.
The set notation includes all values from -5 to 0, but the domain only includes the integer values
eg: something like -1.2 is in the second set, but it is not in the set {-5,-4,-3,-2,-1}
==========================================================
Further explanation:
Let's go through the answer choices one by one
A. This is false because 0 does not come before -5, but instead -5 is listed first. The order -5,-4,-3,-2,-1,0 is correct meaning that [tex]-5 \le x \le 0[/tex] is the correct order as well.B. This is true. A value like x = -1.2 is in the set [tex]\left\{x| -5 \le x \le 0\right\}[/tex] since -1.2 is between -5 and 0; but -1.2 is not in the set {-5, -4, -3, -2, -1, 0}. So the distinction is that we're either considering integers only or all real numbers in this interval. To ensure that we only look at integers, the student would have to write [tex]\left\{x| x\in\mathbb{Z}, \ -5 \le x \le 0\right\}[/tex]. The portion [tex]x \in \mathbb{Z}[/tex] means "x is in the set of integers". The Z refers to the German word Zahlen, which translates to "numbers". C. This is false. The student used the correct inequality signs to indicate x is -5 or larger and also 0 or smaller; basically x is between -5 and 0 inclusive of both endpoints. The "or equal to" portions indicate we are keeping the endpoints and not excluding them.D. This is false. Writing [tex]-5 \ge x \ge 0[/tex] would not make any sense. This is because that compound inequality breaks down into [tex]-5 \ge x \ \text{ and } \ x \ge 0[/tex]. Try to think of a number that is both smaller than -5 AND also larger than 0. It can't be done. No such number exists.Shirley picked out a lite for $3.50 if she gave the family ten-dollar bill what is the fewest number of bills and coins that she could receive as change
Answer:
2 bills and 1 coin
Step-by-step explanation:
Given
[tex]Lite = \$3.50[/tex]
Required
Fewest number of bills and coins she can get receive as change
FIrst, we need to calculate her change
Change = Amount Paid - Lite
[tex]Change = \$10 - \$3.5[/tex]
[tex]Change = \$6.5[/tex]
Next is to split the change to bills and coins
[tex]\$6.5 = \$5\ bill + \$1\ bill + 50 cents[/tex]
The $5 and $1 makes 2 bills while the 50 cents makes 1 coin.
Hence, the minimum she could receive is 2 dollar bills and 1 coin as change
You want to make a rectangular banner that is 18ft. Long with a trim around the entire border of the banner . You have no more than 48ft. Of trim of the banner. What are the possible widths of the banner?
Answer:
6 ft
Step-by-step explanation:
Given that:
Length of rectangular banner = 18 ft
Total trim of banner available = 48 ft
To find:
Possible widths of the banner = ?
Solution:
Maximum trim available of the banner around the entire border of the banner = 48 ft
i.e. we are given the total perimeter of the rectangular banner.
Formula for perimeter of a rectangle is given as:
[tex]Perimeter = 2 \times (Length + Width)[/tex]
Putting the values of perimeter and length to find the value of width.
[tex]48 = 2 \times (18 + Width)\\\Rightarrow 48 =36+2 \times Width\\\Rightarrow 2 \times Width = 48-36\\\Rightarrow 2 \times Width = 12\\\Rightarrow \bold{Width = 6\ ft}[/tex]
So, width possible is 6ft.
Kathy Crawford works as a freelance writer and editor. She charges $12 per page for editing services and $0.15 per word for writing. Kathy’s regular client has asked her to write a 500-word press release and edit a 12-page newsletter. what is the total pay for the job?
How many 1/8 pounds meatballs can Rory make
Plzzz helpppp fast
Answer:
6
Step-by-step explanation:
since he has 2 pounds of ground beef and we are dividing these pounds into 8th's he would have a total of 16/8 meaning 8/8 for each pound of ground beef.
and since he used 5/8 for each of the two huge meat balls that means he used a total of 10/8 in total leaving 6/8.
[tex]16/8 = 8/8 + 8/8\\[/tex]
[tex]5/8 + 5/8 = 10/8\\16/8-10/8=6/8[/tex]
so since he is making 1/8 pound meatballs and he has 6/8 pounds of ground beef left he can make 6 of the 1/8 pound meatballs
The chart below shows the points scored by two team members in their last five games.
Cynthia
Grace
Game 1
15
6
Game 2
7
10
Game 3
00
16
Game 4
12
17
Game 5
9
11
What is the median number of points scored by the two players?
11.1
O 11
O 10
10.5
Answer:
10.5
Step-by-step explanation:
Ordering the set of data by ascending order gives us the set {6, 7, 8, 9, 10, 11, 12, 15, 16, 17}. Since there are 10 terms and the median is the middle term, we know that the median will be the average of the 5th and 6th terms, which are 10 and 11. The average of 10 and 11 is (10 + 11) / 2 = 10.5.
The expression (√90 *√40) - (√8*√18) simplifies to what
Answer:
48
Step-by-step explanation:
[tex] \sqrt{90 \times 40} - \sqrt{8 \times 8} [/tex]
Answer 48
The blackpoll warbler migrates 2,376 miles, stops, and then flies another 3,289 miles to reach its destination. The arctic tern migrates 11,013 miles, stops, and then flies another 10,997 miles to reach its destination. How much farther is the arctic tern's migration than the blackpoll warbler's migration?
simply the equation-2(-3 + 2z)
Simply the equation -2(-3 + 2z)
6 − 4z
John bought 3 pants for 25 dollars each and paid with a one-hundred-dollar bill. Write a numerical expression to represent this situation and then find how much money John gets back from the cashier?
Answer:
x-25=75
Step-by-step explanation:
ANSWER
Answer:
$ 25
Step-by-step explanation:
Let the balance amount be 'x'
Price of 3 pants = 3* 25 = $ 75
Amount paid = $ 100
x = 100 - 75
x = 25
What is 4/10 - 2/15 simplify
A. 4/15
B. 2/5
C.8/18
D.2/3
solve 3/2 + t = 1/2
t = ___
Answer:
-1
Step-by-step explanation
1/2-3/2 = -1
Answer:
-1
Step-by-step explanation:
3/2+t=1/2
T=1/2-3/2
T=(1-3)/2
=-2/2
-= - 1
(4x2 + 7x - 4) + (x2 – 7x + 14)
What is the answer?
Answer:
[tex]5x^2 + 10[/tex]
Step-by-step explanation:
[tex]4x^2 + x^2 = 5x^2\\7x + (-7x = 0\\-4 + 14 = 10[/tex]
Here is a collection of dogs, mice, and cats: There are 6 dogs, 2 mice, and 4 cats. Write two sentences that describe a ratio of types of animals in this collection.
Answer:
The ratio of dogs to mice is
6 to 2; 6:2; 6/2
The ratio of cats to dogs is
4 to 6; 4:6; 4/6
Hope this helped~
Your smart local crackhead
The ratio of the dogs, mice, and cats is 3 : 1 : 2.
What is a Ratio?A ratio indicates the number of times one number contains another.
Given that, there are 6 dogs, 2 mice, and 4 cats.
The ratio of the collection is:
dogs : mice : cats
6 : 2 : 4
= 3 : 1 : 2
Hence, the ratio of the dogs, mice, and cats is 3 : 1 : 2.
To learn more about ratios, click here:
https://brainly.com/question/13419413
#SPJ5
1/3(9x+3)=3x+1 what does x equal
Step-by-step explanation:
1/3(9x+3)=3x+1 multiply inside the parenthesis with 1/3
(9x+3)/3 = 3x + 1 multiply both sides of the equation by 3
9x + 3 = 9x + 3 add like terms
0 = 0 which means there are infinitely many solutions for this equation therefore infinitely many values for x
Answer:
x is any number
infinite solutions
Step-by-step explanation:
1/3(9x+3)=3x+1
Distribute
3x+1 = 3x+1
Subtract 3x from each side
1=1
Since this is always true, x can be any value
The sum of two numbers is five more than twice the first. The sum of the number is 45. Find the numbers
Answer:
First number is 20, second is 25
Step-by-step explanation:
x + y = 5 + 2x = 45
solve for x first
5 + 2x = 45
x = 20
then solve for y
20 + y = 45
y = 25
hope this helps
Algebra Parent Functions Graph
Answer:
b. Cubic
Exponential and logarithmic graphs are the similar, logarithmic graphs just reflect exponential graphs. Cubic root is like the one shown, just horizontal.
Use the figure to find the Slant Height. 4 5 √(11)
Answer:
[tex]height = 4[/tex]
Step-by-step explanation:
By the Pythagorean Theorem, we know:
[tex]a^2 + b^2 = c^2[/tex]
Where [tex]c[/tex] is the slope.
Here we see the following:
[tex]a = 3\\b = ???\\c = 5[/tex]
Plug in the numbers:
[tex]3^2 + b^2 = 5^2\\9 + b^2 = 25\\b^2 = 16\\b = \sqrt{16}\\ b = 4[/tex]
In Crosby's model collection, 5/16 of the models are trains and 7/16 of the models are cars. What part of Crosby's model collection is trains and cars?
Answer:
3/4.
Step-by-step explanation:
5/16 + 7/16
= (5+7)/16
= 12/16
= 3/4.
ALGEBRA 2 100 POINTS STEP BY STEP EXPLANATION PLEASE!
solve the equation for b
= √4^2 + 4^2
Answer:
[tex]b=20[/tex]
Step-by-step explanation:
So we have the equation:
[tex]b=(\sqrt{4})^2+4^2[/tex]
The square root and the square cancels out for the first term.
And 4 squared is 16.
So:
[tex]b=4+16[/tex]
Add:
[tex]b=20[/tex]
Answer: 20
Solution Steps
Immersive Reader
sqrt4^2+42
Calculate 4 to the power of 2 and get 16.
sqrt16+4^2≈20
Calculate the square root of 16 and get 4.
4+4^2≈20
Calculate 4 to the power of 2 and get 16.
4+16=20
Add 4 and 16 to get 20.
20
If E is the midpoint of segment AB and AB = 30, what is AE?
Answer:
15
Step-by-step explanation:
its in the center so u devide it by 2
Answer:
AE = 15
Step-by-step explanation:
AB = 30
E is the midpoint of AB
AE + EB = AB
AE = EB
2AE = AB
2AE = 30
Divide by 2
AE = 15
Fabricio recibe el encargo de preparar 1000 moldes en forma de pirámide hexagonal regular de 10 cm de lado x 30 cm de altura. Además, le han pedido barnizar cada uno de los moldes por dentro y por fuera. Si el galón de barniz rinde para 45 m2, ¿Cuántos galones se requerirán para barnizar los moldes? ¿Cuál será la capacidad en litros de cada molde? a) 2 galones y 1500 litros b) 3 galones y 2200 litros c) 4 galones y 2568 litros d) 5 galones y 2600 litros
Answer:
a) 2 galones y 1500 litros
Step-by-step explanation:
La fórmula para el área de la superficie lateral de una pirámide hexagonal regular =
A = 3a × √ (h² + 3a² / 4)
Donde a = longitud lateral o borde de la base de la pirámide hexagonal = 10 cm
h = altura de la pirámide hexagonal = 30cm.
Resolviendo para 1 molde
A = 3 × 10 × √ (30² + 3 × 10² / 4)
A = 936,7497 cm²
Esto significa que Fabricio tiene que cubrir 936.7497cm² de 1 molde con barniz.
En la pregunta se nos dice que:
1 galón de barniz rinde o cubre 45m²
Por lo tanto, convertimos el área de la superficie de 1 molde a m²
1 cm² = 0,0001m²
936.7497cm² =
936.7497cm² × 0.0001m² / 1 cm²
= 0.09367497m²
Por tanto, si
45m² = 1 galón de barniz
0.09367497m² = x galón
x galón = 0.09367497m² / 45 m²
= 0.002081666 galones
Esto significa que 0,002081666 galones barnizarán 1 molde.
Recuerda, en la pregunta, nos dicen que Fabricio está barnizando 1000 moldes
Si. 1 molde = 0.002081666 galón de barniz
1000 moldes
1000 × 0,002081666
= 2.081666 galones de barniz
Aproximadamente = 2 galones de barniz.
De ahí la capacidad en litros de cada molde = 1500 litros.
Solve the factorial
5!/3!
Answer:
20
Step-by-step explanation:
(5x4x3x2x1)÷(3x2x1)=
120÷6=
20
One minus the quotient of one and a number x
Answer:
1/x-1
Step-by-step explanation:
If the relationship is proportional, what is the missing value from the table?
x
8
16
24
y
6
?
18
Answer:
The answer is 12.
Step-by-step explanation:
6 is 3/4 of 8 and 18 is 3/4 of 24. All you do is divide 16 by 4 which equals 4. Then multiple that answer by 3 which gives you 12.
Answer:
The answer is 12
Step-by-step explanation:
Simplfy... PLZ HELPPPP 3x^2 - 4x + 8 + 5x^2 + 9x - 10
Answer:
8x² + 5x - 2
Step-by-step explanation:
Given
3x² - 4x + 8 + 5x² + 9x - 10 ← collect like terms
= (3x² + 5x²) + (- 4x + 9x) + (8 - 10)
= 8x² + 5x - 2
I need help on these questions
Answer:
1. 21 hours
2. 21 hours
Step-by-step explanation:
1. If we add up all the time it takes them to build one dog house, we get 210 minutes or 3.5 hours. All we have to do is multiply this by 6 because they are building 6 of these exact dog houses. We would then get the answer 21 hours.
2. For this one, it would take Reece double the time it would take both friends. We know if they are both working it takes 3.5 hours so if it is just one of them working it would take 7 hours. So if she builds 3 it will take 21 hours.
Credit card companies use negative balances to represent when the credit card company owes the customer money and positive balances to represent when the customer owes the credit card company DIDIE. Sneha has a balance of 0 dollars with her credit card company, What does a balance of dollars represent?
Answer: Neither Sneha nor the credit card company owes money.
What is an expression that represents the area of the rectangular room? How can the expression be rewritten as a polynomial in standard form? Show your work. What is an expression that represents the area of the rectangular room? How can the expression be rewritten as a polynomial in standard form? Show your work. Expression: ______________________ Expression in Standard Form (Show your work): Expression: ______________________ Expression in Standard Form (Show your work):
Answer:
The answer is below
Step-by-step explanation:
The question is not complete, the correct question is:
The length of a rectangular room is 9 less than four times the width, w , of the room. What expression represents the area of the room? How can the expression be rewritten as a polynomial in standard form
Answer: A rectangle is a polygon that has for sides in which the opposite sides are equal. All angles in a rectangle are equal and the diagonals bisect each other. The area of a rectangle is given by the formula:
Area = Length × Width
Given that The length is 9 less than four times the width and the width is w, hence, the length is given as:
Area = 4w² - 9w
A polynomial is in standard if its terms are arranged from highest degree to lowest degree.
The polynomial in standard form is: 4w² - 9w