The quadratic function g(x)=ax^2+bx+c has the complex roots (10+i) and (10-i). You may assume that a=1.
What is the value of b?
What is the value of c?
The values are [tex]b=-20\text{ and }c=101[/tex]
The quadratic function, expressed in factored form is
[tex](x-(10+i))(x-(10-i))=g(x)[/tex]
Expanding and simplifying
[tex]g(x)=(x-(10+i))(x-(10-i))\\=x^2-x(10-i)-x(10+i)+(10+i)(10-i)\\=x^2-10x+xi-10x-xi+100-i^2\\=x^2-10x-10x+100+1\\=x^2-20x+101[/tex]
since
[tex]g(x)=ax^2+bx+c=x^2-20x+101[/tex]
we can equate coefficients of like-terms and conclude that
[tex]a=1,b=-20,c=101[/tex]
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Ahem please some help please
[tex]4 \div 0.5[/tex]
If 7 out of 25 students have a pet, what percent of the class has a pet?
Answer:
28%
Step-by-step explanation:
(25%-7%)×4
100%-28%
A. Express the following in scientific notation 1.0.948901 2.11,000,000 3.0.08907
Answer:
answer should be c good luck
Does the point (–13, –1) satisfy the equation y = –3?
I’m very smart. My hair is dark. I love to eat honey, insects, and bark.
I don't understand the question your asking
Use the distributive property to remove the parentheses.
3(6-y)
Answer:
18-3y.
Step-by-step explanation:
3 x 6 = 18
3 x -1y= -3y.
Answer:
18 - 3y
Step-by-step explanation:
3(6-y)
(3)(6) + (3)(-y)
18 + (-3y)
18 - 3y
a local factory has to add a liquid ingredient to make there product at a rate of 13 quarts every 5 minutes. how many gallons per hour of the ingredient do they need to add
Per hour, they would need to add 147 quarts of the liquid ingredient. When converting to gallons, every 4 quarts is one gallon, so we need to divide 147 by 4.
36.75 Gallons Per Hour
They need to add 39 gallons of ingredients to make the production they desire.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know 4 quarts are one gallon.
∴ They would be making (13/4) = 3.35 gallons every 5 minutes Or (3.25/5) = 0.65 gallons per minute.
∴ In an hour or 60 minutes, they would be making (0.65×6) = 39 gallons per hour.
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Simplify:
(a^-2)^-3 divided by (a^5)^-1
Hi,
.
[tex]( { {a}^{b} })^{c} = {a}^{b \times c} [/tex]
.
[tex] \frac{ {a}^{b} }{ {a}^{c} } = {a}^{b - c} [/tex]
=>
[tex]\frac{ { ({a}^{ - 2} })^{ - 3} }{ { {(a}^{5}) }^{ - 1} } = \frac{ {a}^{ 6} }{ {a}^{ - 5} } = {a}^{ 11} [/tex]
.
.
I hope it helped ✅(•‿•)
The function P(t)=25,000(1.1023)t2 can be used to model the population in the town of Madison t years from now. Interpret the function in terms of the context for this situation.
Answer:
A growth function has the following form.
where = Original amount,
r = annual rate of change,
n = number of periods,
t = time in years
Since the time is in years, we need to convert t into days. We know that 1 year = 365 days. So t years = 365t days.
So in this case, n = 365, r = 0.0095.
Then the function is rewritten as follows.
The daily growth rate would be
Step-by-step explanation:
Lets find year wise population for example
let years be 3t=3[tex]\\ \sf{:}\longrightarrow P(3)=25,000(1.1023)3^2[/tex]
[tex]\\ \sf{:}\longrightarrow P(3)=27557.5(9)[/tex]
[tex]\\ \sf{:}\longrightarrow P(3)=248017.5[/tex]
Which of the following is a rational function?
A.
B.
C.
D.
Answer:
c
Step-by-step explanation:
c will be the answer g g g t g
Name two transformations that result in Figure ABCD being transformed back onto itself.
Answer:
(b) rotate 180°, then reflect across x and y axes
Step-by-step explanation:
A rotation of 180° cannot be "undone" by translation, or by reflection across the same line twice.
Reflection across the x- and y-axes, in either order, is equivalent to a rotation of 180° (or reflection across the origin). This pair of reflections will "undo" the rotation of 180°, putting the figure back in its original position
The transformation to map the figure to itself are ...
rotation 180°, reflection across the x-axis, reflection across the y-axis
whats the exact length of BC?
-..........The answer is b-
--------------------------------------------------------
(15)²= (9)²+(BC)²
225=81+(BC)²
BC=√144
BC=12
Answer:
B:12
Step-by-step explanation:
The length of BC is 12 because we can use the Pythagorean theorem to solve this. First, we know what the hypotenuse is 15 and the one of the side lengths which is 9. he equation to solve this is h^2-a^2 when h is 15 and a=9. So, we we plug in the info, we get 15^2-9^2 which is 15*15-9*9 which is 225-81 and that is 144. We are not done yet because we need to find the square root of 144 since we squared 15 and 9 in the first place. The √144 is 12 because 12*12 is 144. Now, we have to check! The equation is a^2+b^2=h^2 when a=12, b=9, and h=15! So, it will be 12^2+9^2=15^2 which simplifies to 144+81=225 and that is true!! So thats why it is B. Hope this helps!!!!!!
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Two plus two equal four
Answer:
Two plus two equals sixxxxxxx
Which of the following would be a correct first step to solve the equation, 5(y+12) = 25?
Answer:
divide both sides by 5
Step-by-step explanation:
y + 12 = 5
y = -7
What is the answer step by step explanation please.
w (3w + 2) + 5w
Answer:8w^2+2
w(3w+2)+5w
First distribute the w to the parentheses:
3w^2+w
Add on the 5w to the new equation:
3w^2+2w+5w
Combine like terms:
8w^2+2
Any help wit this ? Cause I’m kinda confused
Answer:
D. The hiker would climb up 46 meters
Step-by-step explanation:
It would make the negative cancel out and would make it 0. 0 is sea level
Answer:
D the hiker would climb up 46 meters.
Step-by-step explanation:
If the hiker is -46 meters from sea level, that means the hiker is 46 meters BELOW sea level. For them to return to sea level, they would have to increase their elevation 46 meters by going up 46 meters, to make it to sea level.
Which equation is NOT a linear? function
Answer:
A
Step-by-step explanation:
Because the x-intercept is zero and if you want to show it on a graph it is a quadratic function.
Hey! i need some help with a math question if anyone doesn't mind helping-
35 = 4x + 7
yes, this is a very simple equation but i have the brain of a 5th grader lol.
Given that T is the centroid of △DEF and FT=12
The centroid of a triangle divides the median of the triangle into 1 : 2
The measure of FQ is 18, while the measure of TQ is 6
Because point T is the centroid, then we have the following ratio
[tex]\mathbf{TQ : FT =1 : 2}[/tex]
Where FT = 12.
Substitute 12 for FT in the above ratio
[tex]\mathbf{TQ : 12 =1 : 2}[/tex]
Express as fraction
[tex]\mathbf{\frac{TQ }{ 12} =\frac{1 }{ 2}}[/tex]
Multiply both sides by 12
[tex]\mathbf{TQ =\frac{1 }{ 2} \times 12}[/tex]
This gives
[tex]\mathbf{TQ =\frac{1 2}{ 2}}[/tex]
Divide 12 by 2
[tex]\mathbf{TQ =6}[/tex]
The measure of FQ is calculated using:
[tex]\mathbf{FQ = FT + TQ}[/tex]
Substitute 12 for FT, and 6 for TQ
[tex]\mathbf{FQ = 12 + 6}[/tex]
Add 12 and 6
[tex]\mathbf{FQ = 18}[/tex]
Hence, the measure of FQ is 18, while the measure of TQ is 6
Read more about centroids at:
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Answer it please ❤❤❤❤❤❤❤❤❤❤ I really appreciate if u answer it !
Answer:
Josh has 60% of $600 that is $360
Daniel has $320
So Josh has more by $40
5)
Bianca has 43 votes
Carlos has 38% of the 150 vote that is 57
So Carlos has 14 more votes than Bianca
Step-by-step explanation:
You have learned that to find 1% of a number means finding 1/100 of it. Similarly, finding 60% of a number means finding 60/100 (or 6/10) of it. 60% of $600 → 60% × $600. 60% of $600 → 0.6 × $600.
Challenge Question Sally's bank account balance was $50 on Monday. On Tuesday, she bought a new pair of shoes for $45. On Thursday evening she earned $25 babysitting her neighbor's children. On Friday she spent $42 on pizza for her friends. She earned $20 dollars on Saturday raking leaves. What is her bank account balance on Sunday? ?
Answer:
$8
Step-by-step explanation:
After the shoe purchase, her balance was $50 -45 = $5.
After depositing her babysitting earnings, her balance was $5+25 = $30.
After buying pizza, her balance was $30 -42 = -$12.
Assuming no overdraft charge, her balance after depositing her earnings was ...
-$12 +20 = $8
Sally's balance on Sunday was $8.
HELP PLEASE!! ;-; !! TWO PART QUESTION!! 1) Consider the image. Are the two triangles congruent if a is congruent to d and b is congruent to e?
A) Yes, by the ASA postulate.
B) Yes, by the SAS postulate.
Yes, by the SSS postulate.
D) No, they are not congruent.
2) suppose that three corresponding angles are congruent for two triangles (AAA), why can’t congruence be proved between the two triangles?
A) the triangles could have the same shape but not the same size.
B) The triangles could have the same size but not the same shape.
C) with three equal angles, only the shortest side of the triangles can be congruent.
D)With three equal angles, only the longest side of the triangles can be congruent.
Answer:
A
Step-by-step explanation:
A
0.326
In stranded form pleasee
Answer:
0.326
The dot is going to move to the right which is going to be in between 3 and 2.
Then the answer will be 3.26 ×10^-1
Answer:
3.26 × 10-1 or
[tex] \frac{163}{500} [/tex]
I didnt know which one u needed
-33 less than or equal to -4x + 3
Step-by-step explanation:
-33 ≤ -4x + 3
Group like terms
4x ≤ 3 + 33
4x ≤ 36
Divide both sides by 4
4/4x ≤ 36/4
x ≤ 9
Final answer: x ≤ 9
Hope this helps.
Use the algebra tiles to help you solve 3x+6=12
Answer:
2
Step-by-step explanation:
We subtract both sides by 6 (3x=6)
And then we divide by 3 (x=2)
Hey there!
You have 3 x-tiles
+
6 = positive-tiles (+)
=
12 positive-tiles (+)
3x + 6 = 12
SUBTRACT 6 to BOTH SIDES
3x + 6 - 6 = 12 - 6
CANCEL out: 6 - 6 because it gives you 0
KEEP: 12 - 6 because it helps solve for the x-value
NEW EQUATION: 3x = 12 - 6
SIMPLIFY IT!
3x = 6
DIVIDE 3 to BOTH SIDES
3x/3 = 6/3
CANCEL out: 3/3 because it gives you 1
KEEP: 6/3 because it helps solve for the x-value
x = 6/3
SIMPLIFY IT!
x = 2
Therefore, your answer is: x = 2
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Find 6889 + 3088 + 9062.
1903
pls mark brainliest
if u want
Answer:
19039
Step-by-step explanation:
hope that help mark me brinilylist
you need to explain more
it was easy
What is 826x98= ?
826x98 is 80948
Answer:
im pretty sure we keeps the account sorry this isnt for the math question
Step-by-step explanation:
826×98=80948
Answer:
80,948
Step-by-step explanation:
that's the answer.
Owen is driving to a concert and needs to pay for parking. There is an automatic fee of $12 just to enter the parking lot, and when he leaves the lot, he will have to pay an additional $3 for every hour he had his car in the lot. How much total money would Owen have to pay for parking if he left his car in the lot for 5 hours? How much would Owen have to pay if he left his car in the lot for tt hours?
Answer:
27$
Step-by-step explanation:
I do not know what you mean by tt hours, but I can create an equation for the problem
Y=3x+12
Essentially, every X hours he spends in the lot you add 3$, but you start off with 12$. Please mark this brainliest or thank it.
you are taking a typing class and can now type 30 words er minute. set up a proportion to solve for the amount of time it would take you to type 400 words
Time needed to type 400 words is 13.3 minutes.
What is unit rate?A unit rate means a rate for one of something.
Given that, you are taking a typing class and can now type 30 words per minute.
For 30 word, you need 1 minute.
Let you need x minutes for 400 words,
Therefore, the proportion will be,
1/30 = x/400
x = 400/30
x= 40/3
x = 13.33333 ≈ 13.3
Hence, you need 13.3 minutes to type 400 words.
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