Let $r$ and $s$ be the roots of $3x^2 + 4x + 12 = 0.$ Find $r^2 + s^2.$
Use a similar strategy as in your other question, [19925664].
3x² + 4x + 12 = 3 (x - r ) (x - s)
3x² + 4x + 12 = 3 (x² - (r + s) x + rs)
3x² + 4x + 12 = 3x² - 3 (r + s) x + 3rs
so that
r + s = -4/3
rs = 12/3 = 4
Recall that
(r + s)² = r² + 2rs + s²
so that
r² + s² = -2rs = -2(4) = -8
A 93 L batch of Ropivacaine is being made. The specific gravity is 1.01 g/mL. 196.42 g of Ropivacaine and 799.8g of sodium chloride are added. What is the weight of the water to be added to QS the solution?
Answer:
92.93378 kg
Step-by-step explanation:
Given that:
Volume of Batch = 93 L
= 93 × 1000 (since 1 L = 1000 mL)
= 93000 mL
Specific gravity = [tex]\dfrac{density \ of \ solution}{density \ of \ water}[/tex]
where;
density of water = 1 g/ml
specific gravity = 1.01 g/mL
Density of solution = (1.01 × 1) g/mL
Density of solution = 1.01 g/mL
[tex]Density \ of \ solution = \dfrac{mass \ of \ batch }{volume \ of \ batch}[/tex]
mass of batch = 1..01 g/mL × 93000 mL
mass of batch = 93930 g
Now, the mass of additional water = mass of (batch - Ropivaciance - sodium chloride)
= 93930 g - 196.42 g - 799.8 g
= 92933.78 g
Since 1kg = 1000 g
The weight of the water to be added to the QS solution is:
[tex]=\dfrac{92933.78}{1000}[/tex]
= 92.93378 kg
An airplane is flying from nyc to la. The distance it travels in miles,d, is related to the to the time in seconds, t, by the equation d=0.15t
Answer:
It will cover 4.5 miles in 30 seconds.
Step-by-step explanation:
An airplane is flying from nyc to la.
The distance it travels in miles,d, is related to the to the time in seconds, t, by the equation :
d=0.15t ...(1)
Let us assume we need to find the distance at t = 30 s.
Put t = 30 s in equation (1).
d=0.15 × 30
d = 4.5 miles
Hence, it will cover 4.5 miles in 30 seconds.
Which are the intercepts of the equation y+2=4(x+1) ?
Answer:
*3rd option*
y intercept (0, 2)
x intercept (-1/2 , 0)
Step-by-step explanation:
First, rearrange the equation so y is on one side, the rest of the terms on the other.
y+2 = 4x + 4
y = 4x+2
The y intercept is 2 because x=0, y = 2
rearrange where x is on one side
4x = -y + 2
x = -1/4y - 1/2
The x intercept is -1/2 because when y=0, x=-1/2
please give thanks :)
and brainliest :)
hope this helps
Using mental math, the approximate tip to leave for a bill of $81.79, if you tip 15% would be _____.. a. $8.20 b. $10.30 c. $12.30 d. $16.40 Please select the best answer from the choices provided A B C D
Step-by-step explanation:
The approximate tip is - 12.30$
Because bill is 81.79$
and tip - 15%
therefore bill amount divided by 15/100
==> 81.79* 15% is 12.30$
Comparing Linear Functions Written in Different Ways Compare the linear functions expressed below by data in a table and by an equation. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x. Which of the following statements are true? Select all that apply. If the equation were graphed, it would be a horizontal line. Both functions have the same slope. The origin is the y-intercept for the function expressed in the table. The linear equation does not have a y-intercept. The table and the graph express an equivalent function.
Answer:
#2
Both functions have the same slope.
#3
The origin is the y-intercept for the function expressed in the table.
#5
The table and the graph express an equivalent function.
Answer:
B, C, E
Step-by-step explanation:
I got it right on edge
this is algebra ,
what is the minimum unit cost?
Answer:
search it up
Step-by-step explanation:
Please answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answer:
30
Step-by-step explanation:
3 multiply 5 =15
so:
6 multiply 5=30
There are 5 red markers, 2 orange markers, 3 yellow markers, and 5 green markers in a desk drawer.What is the probability of choosing a red marker?
Answer:
the probability is 5/12 or 0.416 or 41%
Step-by-step explanation:
Hope I helped!
A submarine hovers at 66 and two-thirds yards below sea level. If it ascends 24 and StartFraction 1 over 8 EndFraction yards and then descends 78 and three-fourths yards, what is the submarine's new position, in yards, with respect to sea level?
Answer:
- 121 7/24
Step-by-step explanation:
Initial Position = 66 2/3 below sea level
Ascent = 24 1/8
Descent = 78 3/4
New position of submarine :
Since initial. Position is below sea level, we finite with a negative sign :
-66 2/3 = - 200 /3
Ascent is positive ; 24 1/8 = 193 / 8
-200 /3 + 193 / 8
(-1600 + 579) / 24
= - 1021 / 24
Descent = 78 3/4 (negative) downward
78 3/4 = - 315/ 4
-1021 / 24 - 315/4
(-1021 - 1890) / 24
= - 2911 / 24
= - 121 7/24
121 7/24 below sea level
Heyyyyy ah ha ha help I’m begging please someone god bless
Answer:
Step-by-step explanation:
Domain of a function is a set of x-values (input values) for which the function is defined.
Range of a function is a set of y-values (output values) for the given set of input values.
7). Domain → (-∞, ∞)
Range → (-∞, ∞)
8). Domain → (-∞, ∞)
Range → [-2, ∞)
9). Domain → [-2, 2]
Range → [-3, 3]
10). Domain → (-∞, ∞)
Range → [-1, 1]
Find the equation of the line
Use exact numbers
Y=blankx+blank
Step-by-step explanation:
The equation of the line is y = -1.5x + 3.
Enter the correct answer in the box.
Consider this rational equation.
Use the least common denominator to simplify the rational equation into a standard form quadratic equation.
Replace the values of b and c to create the equation.
Answer:
[tex]x^2-10x+8=0[/tex]
Step-by-step explanation:
[tex]\frac{1}{x} +\frac{1}{x-2}=\frac{1}{4} \\\\\frac{x-2+x}{x(x-2)} = \frac{1}{4} \\\\\frac{2x-2}{x(x-2)}=\frac{1}{4} \\\\4(2x-2)=x(x-2)\\8x-8=x^2-2x\\0=x^2-2x-8x+8\\0=x^2-10x+8\\x^2-10x+8=0\\[/tex]
Using the least common denominator in simplifying the rational equation, the result of in standard form is: [tex]\mathbf{x^2 -10x + 8 = 0}[/tex]
What is the Least Common Denominator (LCD)?Least common denominator is the smallest common multiple of the denominators of two or more fractions.It is useful when simplifying, adding, subtracting or comparing fractions.Given:
[tex]\frac{1}{x} + \frac{1}{x - 2} = \frac{1}{4}[/tex]
The least common denominator of the two fractions on the left side of the equation is x(x - 2).
Thus:
[tex]\frac{1(x - 2) + x(1)}{x(x - 2)} = \frac{1}{4}\\\\\frac{x - 2 + x}{x(x - 2)} = \frac{1}{4}\\\\\frac{2x - 2}{x^2 - 2x)} = \frac{1}{4}[/tex]
Cross multiply[tex]4(2x + 2) = 1(x^2 - 2x)\\\\8x + 8 = x^2 - 2x\\\\[/tex]
Rewrite in standard form[tex]0 = x^2 - 2x - 8x + 8\\\\0 = x^2 -10x + 8\\\\\mathbf{x^2 -10x + 8 = 0}[/tex]
Learn more about least common denominator on:
https://brainly.com/question/542317
A wire is attached to a 425-foot tower that is perpendicular to the ground. The wire makes an angle of 26.5o to the ground. what is the length of the wire in feet
Answer
952.49feet
Step-by-step explanation:
This set up will be a right angled triangle
Height = opposite side = 425foot
Length of wire = hypotenuse= x
Angle of elevation= 26.5°
Using the SOH identity
Sin 26.5 = opp/hyp
Sin26.5 = 425/x
x = 425/sin26.5
x =425/0.4462
x = 952.49feet
Hence the length of the wire is 952.49feet
what is the sum of all interior angles of a parallelogram
Can someone please help even bubbling in with no work is ok I just don’t understand.
Answer:
This is as much as I could do.
Step-by-step explanation:
Steps r in pic below
In a two digit number , the digits at tens place is 1 more than the digit at unit place .If the product of the digits is 20,find the numbers.
Determine if the result of each product is a positive or negative integer
Answer:
1. -13x9= -117 Negative
2. 4x14= 65 Positive
3. -6x(-31)= 186 Positive
4. -18x(54)= 4374 Positive
5. 55x7= 385 Positive
Step-by-step explanation:
At the beginning of the week, a stock was $82.73 per share.
On Monday, the stock gained $0.19 per share.
-On Tuesday, it gained $0.07 per share.
-On Wednesday, the stock lost $0.13 per share.
-On Thursday, it lost $0.25 per share.
On Friday morning, what was the price of the stock per share?
Which statement best explains why citizens are required to pay taxes to the government? (3 points)
A) If citizens do not pay taxes, they will lose their legal citizenship.
B) Citizens who pay taxes receive special benefits, such as free food.
C) Taxes help pay for the services government provides, such as education.
D) Taxes are paid back to the people evenly, helping spread money around.
Answer:
C.
Step-by-step explanation:
A. Is false because citizens do not lose their citizenship if they fail to pay taxes.
B. Is false because not every tax paying citizen receives government assistance gets benifits like food stamps.
D. Is false because taxes don't go directly back to the people as cash payouts.
Answer:
The real answer is c.
Step-by-step explanation:
Taxes that we pay goes tords goverment things such as school. Smiles have a good day!
Which phrases could n + 10 represent? Check all that apply.
the sum of a number and ten
the difference between a number and ten
a number plus ten
the difference between ten and a number
ten more than a number
Answer:
The sum of a number and ten
A number plus ten
Ten more than a number
Step-by-step explanation:
edg
Carlos has 38 apples. He puts 8 apples into each bag if he fills as many bags as possible, how many apples are left
Answer:
6
Step-by-step explanation:
What you need to do is 38 ÷ 8. The answer would be 4 with a remainder of 6, so there are six apples left
13 points!!
The table below shows the heights of five different people.
table shown below
Jackson has a height of 55 inches. Which is true if Jackson is added to the data set?
Answer:
The Mean Decreases.
Step-by-step explanation:
Answer:
the answer is Cindy and i dont understand what your trying to say but if your saying witch one is closer to Jackson then yeah Cindy
Identify the domain of the function shown in the graph.
A. -5<x<5
B. 0<x<5
C. x is all real numbers.
D. x > 0
Answer:
The answer is A choice.
Explanation:
By looking at the graph, we notice that at the left side, the domain/x-value stops at -5 and 5.
Thus, the domain is at the left end side to the right end side.
The domain stops at -5 on the left side and 5 on the right side. Thus the answer is
-5 < x < 5.
The A choice.
Understanding
The domain of a function is basically all the values where x is defined, and by defined, it means it has a y value corresponding to it. In this graph, x is defined from -5 to 5. If you look outside this range of numbers (from -5 to 5 on the x-axis) you will not find any y values for them. We can easily say the solution is A.
Solution:
[A] [tex]-5<x<5[/tex]
Note: From what I see from the picture -5 and 5 are included in the domain, either the question is incorrectly written, or the picture isn't clear enough. If so, the answer should be [tex]-5\leq x\leq 5[/tex].
Energy can be transferred from one form to another. We use many energy converters in our daily life. Observe carefully to find these energy converters in your home. Make a list of any 10 converters including their names along with their energy chains.
i don’t know what to do, please help!!
Answer:
b 7
Step-by-step explanation:
open the bracket and the power gets cancelled because it will be 5/5
then answer will be 7 to the power 1 which is equals to 7
Help! Thank youuuuu!!!!!
Answer:
scamming outta points
Step-by-step explanation:
Pls help I cant do this
Answer:
Here you go!
Step-by-step explanation:
Hope this helped!
Answer: a=7
d=2
Step-by-step explanation:
I NEED HELP PLZZ ANSWER PLUS GIVE STEPS
Answer:
1. y=-4/3x+9
2. y=-4x+6
Step-by-step explanation:
1.y=-4/3x+b
put in 3,5 into equation
5=-4/3(3)+b
5=-4+b
9=b
so y=-4/3x+9
2. y=4x+b
2=4(-1) +b
2=-4+b
6=b
y=-4x+6
Jason used 0.5 cup of kernels to make 16 cups of popcorn how many cups of popcorn would he make if he used 0.75 cup of kernels.
A. 32
B. 28
C. 24
D. 20
PLEASE HELP ME IM DAILING MATH
Answer:
Option C: 24 is the correct answer.
Step-by-step explanation:
Given that:
Jason used 0.5 cup of kernels to make 16 cups of popcorn
Ratio of cup of kernel to cups of popcorn = 0.5 : 16
Let,
x be the cups of popcorn made from 0.75 cups of kernel
Ratio of cups of kernel to cups of popcorn = 0.75 : x
This is a direct proportion as the cups of kernel is increasing.
0.5 : 16 :: 0.75 : x
Product of mean = Product of extreme
16*0.75 = 0.5x
12=0.5x
0.5x=12
Dividing both sides by 0.5
[tex]\frac{0.5x}{0.5}=\frac{12}{0.5}\\x=24[/tex]
Jason can make 24 cups of popcorn from 0.75 cups of kernel.
Hence,
Option C: 24 is the correct answer.