Answer:
#4 x = 3 ± i√31
2
Step-by-step explanation:
Solve by completing the square
x² - 3x + 10 = 0
x² - 3x = -10
x² - 3x + 9/4 = -10 + 9/4 half of 3 and square the answer (half of 3 = 3/2
and square the number (3/2)² = 9/4
x² - 3x + 9/4 = -31/4
[tex](x - \frac{3}{2} )^2 = \frac{-31}{4}[/tex]
[tex]\sqrt{(x-\frac{3}{2})^2 } =\sqrt{\frac{-31}{4} }[/tex]
[tex]x - \frac{3}{2} = \frac{i\sqrt{31} }{2}[/tex]
x = 3/2 ± i[tex]\sqrt{31}[/tex] /2
x = 3 ± i√31
2
A cook has 32 ounces of a 5% apple cider vinegar that she wants to
dilute to a 3% apple cider vinegar. How much water does she need
to add to obtain that concentration?
The cook needs to add 21.333 ounces of water to obtain a 3 % concentration.
In matter of units, concentration equals to to the mass of cider vinegar ([tex]m_{c}[/tex]) divided by mass of water ([tex]m_{w}[/tex]), both expressed in ounces. A reduction on concentration implies that mass of cider vinegar remains constant while mass of water is increased.
Now we derive expressions for the initial and final concentrations for cider vinegar:
Initial concentration
[tex]c_{i} = \frac{m_{c}}{m_{w}+m_{c}}[/tex] (1)
Where:
[tex]m_{w}[/tex] - Initial water mass, in ounces. [tex]c_{i}[/tex] - Initial concentration ratio, no unit.Final concentration
[tex]c_{f} = \frac{m_{c}}{m_{c}+m_{w}'}[/tex] (2)
Where:
[tex]m_{w}'[/tex] - Initial water mass, in ounces. [tex]c_{i}[/tex] - Initial concentration ratio, no unit.Then, if we know that [tex]c_{i} = 0.05[/tex], [tex]c_{f} = 0.03[/tex], [tex]m_{w}+m_{c} = 32\,oz[/tex] and [tex]m_{c}+m_{w}' = 32 + x[/tex], then the addition of water is:
[tex]0.05 = \frac{m_{c}}{32}[/tex] (1b)
[tex]0.03 = \frac{m_{c}}{32+x}[/tex] (2b)
Then we eliminate [tex]m_{c}[/tex] in (1b) and (2b):
[tex]0.05\cdot 32 = 0.03\cdot 32 + 0.03\cdot x[/tex]
[tex]0.02\cdot 32 = 0.03\cdot x[/tex]
[tex]x = 21.333\,oz[/tex]
The cook needs to add 21.333 ounces of water to obtain a 3 % concentration.
To learn more on concentrations, we kindly invite to check this question: https://brainly.com/question/492238
share $ 4,500 between Ben and Jenny in the ratio 4:5
What is the equation for the line in slope-intercept form?
Answer:y=4x+4
Step-by-step explanation:
Domain and Range of {(0,2), (2,4), (-1,1)}
Bu sorunu nasil olur?
how can i solve this problem?
Answer:
i can't see your handwriting
are 6y + 12 and 6 (y + 2) equal?
I NEED HELP
Find the value
Answer:
7 and 2?
Step-by-step explanation:
i think because f(2) : f(x)= 5+2x = 7
Given that D, E, and F are the midpoints of their respective sides, which of the following is a true statement?
Answer:
I'm pretty sure its the 1st one.
Step-by-step explanation:
1) -64÷16+[12x{6÷(16÷10-2)}]
Answer:
= -30[tex]x^{6}[/tex]-4
i hope that helps and is right
If that is a multiplication sign then it is -184
if that is an x then it would be -4 -180x
Simplify:
-5x - 2(3x - 7) + 4(3x - 5) - (6x -9)
Answer:
7x+3
Step-by-step explanation:
-5x+6x+14+12x-20-6x+9
combine like terms
7x+3
Bernie had $30 in his bank account. Today, he withdrew d dollars but tomorrow he will
bank account after tomorrow.
deposit $15. Write an expression to represent how much money Bernie will have in his
Answer:
Step-by-step explanation:
Bernie had $30 in his bank account.
Today he withdrew $d
Now he has = $30 — $d
Because from $30 he took away $d that’s why $d have to subtract from the $30.
Tomorrow he’ll deposit $15 and that will be added up with current balance $30 —$d.
So, the expression to represent how much money Bernie will have in his bank account is $30 —$d + 15
Please help meeeeeeeeeeeeeeeeeee
Answer:
[tex]\frac{3^{12}}{3^{10}}[/tex]
Step-by-step explanation:
+ or x you plus the indices
- or divide you minus the indices
so 3^8 x 3^4 would be 3^12
and 3^2 x 3^8 would be 3 ^10
Need help l don’t understand new topic
7x - 2 = 5x + 14
7x - 5x = 14 + 2
2x = 16
x = 16/2
x = 8
______
Hope it helps ⚜
Answer:
x = -8
Step-by-step explanation:
[tex]7x - 2 = 5x + 14 \\ 5x - 7x = 14 + 2 \\ - 2x = 16 \\ \frac{ - 2x}{ - 2} = \frac{16}{ - 2} \\ x = - 8[/tex]
In mosquito, more itchy bites are dominate to less itchy bites. If a male mosquito with a heterogeneous, more itchy bite mates with a less itchy, homologous female, what will the offspring likely be like?
4 Points Total:
Key (assign letters and traits) 1
Correct Punnet square 1
Correct phenotype 1
Correct prototypes 1
Answer:
a rash
Step-by-step explanation:
I need the answers to a b c and d PLZ DUE AT 11:59PM ITS 9:23PM
Answer:
do u even still need the answer its been aweek since you asked it and it was due that same day
Step-by-step explanation:
Which statement is true about the equation f(x)=g(x) given f(x)=2x+3 and g(x)=x^2? please help
Answer:
x=3 and x=-1
Step-by-step explanation:
If f(x)=g(x), then 2x+3=x^2:
x^2-2x-3=0
(x-3)(x+1)=0
x=3 and x=-1
We can conclude that the statement:
There are values of x for which f(x) = g(x)" is true.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To determine which statement is true about the equation f(x) = g(x) given f(x) = 2x + 3 and g(x) = x²,
We can substitute the expressions for f(x) and g(x) into the equation and simplify:
f(x) = g(x)
2x + 3 = x^2
Now we have a quadratic equation.
We can rearrange it to standard form and solve for x using the quadratic formula:
x² - 2x - 3 = 0
a = 1, b = -2, c = -3
x = (-b ± √(b² - 4ac)) / 2a
x = (2 ± √(16)) / 2
x = (2 ± 4) / 2
x = -1 or x = 3
Therefore,
The equation f(x) = g(x) is true for some values of x, namely x = -1 and x = 3.
Thus,
Based on this, we can conclude that the statement "There are values of x for which f(x) = g(x)" is true.
Learn more about functions here:
https://brainly.com/question/28533782
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PLSS HELP MEE WILL MARK BRAINLIEST
What would be the point in between the 700 and 800?
Answer:
750
Step-by-step explanation:
NEED ANSWERS PLEASEEE! PROGRESS REPORTS GO IN SOON.
Answer:
1. they both are the same length and diameter, the difference is thw diameter is a different direction.
2. 4 cm
3. EB and 8 cm
Step-by-step explanation:
Diameter is the length of the circle aross, hope this helps!
pls help me I need it ASAP
Answer:
1) 1600cm² 2 )4095cm² 3) 550cm²
Step-by-step explanation:
Because area is length times width, you can use that on these problems.
1) 40*40=1600
2)65*63=4095
3)25*22=550
Which expressions are equivalent to 25 + 3(a - 5) + 7a?
A. 10a + 20
B. 8a + 23
C. 5(2a + 2)
D. 10a + 10
E. 2(5a + 10)
Answer:
This is what I got 10(a+1)
I don't think you need this but there you go.
Step-by-step explanation:
In the rectangle below,
Answer:
EI = FI and EG is twice the length of EI. Try setting up algebraic equations 3x + 8 = 6x -4 to find the value of x. Then substitute it back into the equation to find the length.
Step-by-step explanation:
Jack was the science Museum in sabotage the recycling plant had an average speed of 26KM/H. Sometime later Aaliyah love traveling in the opposite direction with an average speed of 57KM/H. After Jack had traveled for four hours they were 332KM a part. How long did Aaliyah travel?
Please help me.......................
Answer:
D) 53.1
Step-by-step explanation:
we can use the soh,cah,toa rule
sin = opp/hyp
cos = adj/hyp
tan = opp/adj
we would use tan because the opposite side of the angle is revealed as 12
the adjacent side of the angle is revealed as 9
there for
tan(theta) = 12/9
theta = arctan(12/9) = 53.1
arctan = tan^-1 = inverse of tan
Can somebody help me pleaseeeeee
The answer: a° = 180° - 62° = 118° , b° = 62° , c° = (180° - 62°) ÷ 2 = 59°
Ok done. Thank to me :>
Define a variable for the number of cars, and define a variable for the number of vans or trucks. You will need to choose x for one and y for the other.
Answer:
See below!
Step-by-step explanation:
I don't think you included the entire question, but maybe you were just stuck on this part, so I'm happy to help!
You include variables in a math equation to give meaning to a word, phrase, or situation in a shortened way.
For example, if I say, "I run 2 miles every day. How many miles will I run in x days?", your equation should look like this:
miles=2x
Notice that the 2 is a number, because that is the one thing that we know for sure. We know, no matter what, I run 2 miles a day. However, we don't know for how many days. So, for this, we need to put something as a sort of placeholder until we are told how many days.
Variables can be any letter, from A-Z! It is reccomended to stay with letters that avoid s, and i(among others) to make sure that you are using letters that can't be mistaken as letter on accident. For example, s could look like 5. In some cases, i could look like 1.
For your question, you could use:
#of cars=x
#of trucks/vans=y
HELP PLEASE...........
Answer:
B. slope -5, y-intercept (0, 7)
Step-by-step explanation:
The y-intercept is the first (x, y) pair shown in the table: (0, 7). (This eliminates choices C and D.)
The slope is ...
change in y / change in x
(-13 -7) / (4 -0) = -20/4 = -5 . . . slope
This matches choice B.
i need 20 characters, but the question is the photo
Answer: The answer is in the first image.
Explanation: The explanation is in the second image.
what do I do here? please help
Answer:
x = 10
Step-by-step explanation:
8x - 12 and 6x + 8 are corresponding angles and are congruent , then
8x - 12 = 6x + 8 (subtract 6x from both sides )
2x - 12 = 8 ( add 12 to both sides )
2x = 20 ( divide both sides by 2 )
x = 10
Write an equation in point-slope form of the line that passes through the point (-6,6) and has a slope of m=3/2
Answer:
y=3/2 x+15
Step-by-step explanation:
A salad dressing recipe calls for ¾ cup of oliva oil for every ½ cup of vinegar. How many cups of vinegar are needed for 2 cups of olive oil?
Answer:
[tex]1\frac{1}{3}[/tex]
Step-by-step explanation:
Write a proportion comparing the Oliva Oil to Vinegar = Oliva Oil to Vinegar.
[tex]\frac{3/4}{1/2} = \frac{2}{?}[/tex]
3/4 ? = 2(1/2)
3/4? = 1
? = 1 ÷ 3/4
? = 1 × 4/3
? = 4/3
[tex]? = 1\frac{1}{3}[/tex]