Answer:
[tex] {(x - 4)}^{2} + 6[/tex]
Step-by-step explanation:
[tex] {x}^{2} - 8x + 22 \\ \\ = {x}^{2} - 8x + 16 + 6 \\ \\ = {x}^{2} - 8x + {4}^{2} + 6 \\ \\ = {(x - 4)}^{2} + 6[/tex]
The completed square form of x² - 8x + 22 = 0 is (x - 4)² = - 6.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, a quadratic equation x² - 8x + 22 = 0.
We know (a - b)² = a² - 2ab + b².
∴ x² - 8x + 22 = 0 is
(x)² -2(x)(4) + 4² + 6 = 0.
(x - 4)² = - 6.
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Question
Under ideal conditions, the population of a certain species doubles every nine years. If the population starts
with 100 individuals, which of the following expressions would give the population of the species t years after
the start, assuming that the population is living under ideal conditions?
Answer: 100 x 2^ t/9
Step-by-step explanation:
The initial population of 100 that doubles in 9 years, gives the
expression for population as; [tex]\underline{ P = 100 \cdot e^{0.077 \cdot t}}[/tex].
How can the expression for the population be found?Given parameters are;
The time it takes the population to double = 9 years
The initial population count = 100
Required:
The expression that gives the population after t years.
Solution:
The population as a function of time can be expressed as an
exponential function as follows;
[tex]P = \mathbf{P_0 \cdot e^{c \cdot t}}[/tex]
At the start, t = 0, P = 100, we have;
[tex]100 = \mathbf{ P_0 \times e^{c \times 0} }= P_0[/tex]
Therefore;
P₀ = 100
After 9 years, we have;
P = 2·P₀
Therefore;
[tex]2 = \mathbf{ e^{c \times 9}}[/tex]
ln(2) = 9·c
[tex]c = \dfrac{ln(2)}{9} \approx 0.077[/tex]
The function that gives the population is therefore;
[tex]\underline{ P = 100 \cdot e^{0.077 \cdot t}}[/tex]Learn more about exponential functions here:
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What is the volume of the cone?
Answer:
70/3 πcm
Step-by-step explanation:
hope this helps
the sum of 22 and a number is 41
Answer:
19
Step-by-step explanation:
sum means answer to an addition problem, so 41 - 22 = 19, so 22 + 19 = 41
i need help.....plz.
hopefully u can solve the problem
but i need the answer asp
Answer:
I believe the answer would be 4 :) hope this helps
the answer is definitely 4
Complete the proof of the Triangle Angle Sum Theorem.
Answer:
In the proof above, reason 5 is Alternate Interior Angles Theorem, and reason 7 is Angle Addition Postulate.
Step-by-step explanation:
I took the quiz.
On a team 5 girls and 2 boys scored a total of 41 points. The difference between the number of points scored by the 5 girls and the number of points scored by the
2 boys is 29. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each
boy
Each girl scored points
Step-by-step explanation:
Let x be the number of points the 5 girls scored.
=> 41 - x is the number of points the 2 boys scored.
We have x + 29 = 41 - x or x - 29 = 41 - x.
=> 2x = 12 or 2x = 70
=> x = 6 or x = 35
We reject x = 6 as 6 is not a multiple of 5. (Each girl would have scored 1.2 points which is absurb)
So x = 35, each girl scored 35/5 = 7 points.
=> 41 - (35) = 6, each boy scored 6/2 = 3 points.
Find the measure of the indicated angle to the nearest degree.
1/6 + 7/9 + _____ = 1
Answer:
[tex] \frac{1}{18} [/tex]
Answer:
3/54
Step-by-step explanation:
6 and 9 both go into 54
1/6=9/54
7/9=42/54
42+9=51
3/54
Kwan has determined that he can use the expression 2(n+1)−3 to find the number of squares for any step number n. Find an equivalent expression that Kwan can also use. I need help
Answer:
the answer is 2n-1
Step-by-step explanation:
Answer: 2n-1
Step-by-step explanation:
Which of the following situations can be described by the equation 2x – 4 = 10?
Step-by-step explanation:
Add 44 to both sides.
2x=10+4
2x=10+4
2 Simplify 10+410+4 to 1414.
2x=14
2x=14
3 Divide both sides by 22.
x=\frac{14}{2}
x=
2
14
4 Simplify \frac{14}{2}
2
14
to 77.
x=7
x=7
Done
What is the value of 76 + (4 — 3) x 60?
Using trigonometric identities, the answer should be: 77
Answer: 4,620
Step-by-step explanation:
1. 76 + (1) x 60
2. 77 x 60
3. 4,620
If there is 1 person who needs to talk and there are hundreds of others out there, how many will the person probably talk to?
Answer:
10
Step-by-step explanation:
Answer:
...........1 person...........
The Math and Science Club sold candles for seven hours one Saturday. The bar graph shows the number of
candles sold during each hour.
Number of Candles Sold
30
25
20
No. of Candles
15
10
5
0
1
2
3
4
5
6
7
Hour
How many candles were sold during the fifth hour?
candles
Answer:
20 candles
Step-by-step explanation:
At Pizza Pi, 20% of the pizzas made last week had extra cheese. If 50 pizzas had extra cheese, how many pizzas in all were made last week?
Answer:
250 pizzas
Step-by-step explanation:
We can use the formula 50 = 20/100x. We multiply both sides by 100 to get 5000 = 20x. Now, we divide both sides by 20 to get 250 = x. That means 250 pizzas were made last week.
The length and breadth of a rectangle are in the ratio 3 : 1. If the breadth is 7 cm, then the length of the rectangle is
Answer:
the length would be 21
7x3=21
(0,0) (3,-2) in slope-intercept form
Answer:
y=2/3 +0
Step-by-step explanation:
xiokijhgfcxyuiuhygfdxsghjkmjnbv m,kjhgtfrdsxcvbnmkiuytredxcvbnfytumvjgcrdhg
Look at the problem above and please tell me which is correct
I think it's the third 4 ( а² + 2а ) + 9
9. Which company pays the most per pizza?
Papa Ron's made their offer in the form of this graph.
w
Bombinoes' Pizza is offering $56 per shift and $250
in commission for each pizza delivered.
Little Squeezer's showed Tony a table of salaries.
10
Pizzas 0
Salary | 48
2
54
4
60
78
1
Pizza Tent has given Tony his pay options in the
following function. Srepresents Tony's salary, and p
represents the number of pizzas he delivers.
S = 2.75p +52
A. Bombinoes' Pizza
B. Little Squeezer's
C. Pizza Tent
D. Papa Ron's
the correct answer is option a. bombinos pizza
How was your winter break and what would are your goals of 2021? What would you have done differently in 2020? lol i don't know what to say :(.
Answer:
Just look at the explanation
Step-by-step explanation:
My winter Break was really great. I got to spend time with my family! Looking back on 2020, I see that I would have iked to ask my parents for a dog before we figured out that they were allergic to them. But other than that, I am so glad that this year is over!
Tables
Х
у
6
4
8
12
12
24
16
30
Proportional
Not Proportional
Answer:
it's not proportional ...
please thnx my answer..
Sarah mailed her computer to Store B for repairs. Her bill was:
Initial Repair Cost = $1,350
Sales Tax of 7 percent = $94.50
Total Cost of Computer Repair = $1,444.50
Shipping = 2 percent of Total Cost
Answer:
D
Step-by-step explanation:
Answer:
0.02($1,444.50)
Step-by-step explanation:
Can someone help me please
Answer: D is located at point (-3, -4)
turn, Aklo earns 8 points. On his second turn, he loses 3 points.
The expression 8 + (-3) represents this situation.
Aklo is playing a board game. He starts with O points. On his first
a. Use a model to find 8 + (-3).
LESSON 7 / SESSION 2
Answer:
its 5
Step-by-step explanation:
translate the expression in to a sentence and simply
[tex] \sqrt{49} [/tex]
Answer:
Concept: Mathematical Computation
In plain text it is: square root of 49 [tex] \sqrt{49} [/tex]We need to values such that x × x = 49 Hence [tex] \sqrt{49} = 7[/tex]Rate brainlistMULTIPLY
3/5 •3/4
A: 9/20
B:4/10
C: 4/5
D: 5/4
Answer:
a
Step-by-step explanation:
3×3=9
5×4=20
hope this helps
Answer:
9/ 20
Step-by-step explanation:
hope it helps!
.....
what is the answer to this question
Answer:
9v + 14
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
7v + 2 + 12 + 2v
Step 2: Simplify
Combine like terms (v): 9v + 2 + 12Combine like terms (Z): 9v + 14What is the constant of proportionality in the equation 3y = 2x
Answer:k = 2/3
Step-by-step explanation:
When a variable y directly relates to another variable x, we can say:
y=kx
Given the equation, we can say
3y=2x
y= 2x/3
Putting the value of y from above discussion
kx = 2x/3
x is being cancelled on both sides of equation
k= 2/3
Answer:
k = 2/3
Step-by-step explanation:
i don’t know how to explain sorry I’m not good at explaining but I hope this helps
See your levels
A factory uses 3/4 of a barrel of raisins in each batch of granola bars. Yesterday, the factory
used 1 1/2 barrels of raisins. How many batches of granola bars did the factory make
yesterday?
Write your answer as a fraction or as a whole or mixed number.
batches
By solving a simple quotient with the mixed numbers/fractions, we will see that they made 2 batches.
How many batches of granola bars did the factory make yesterday?We know that the factory uses 3/4 of a barrel for a batch of granola bars.
In this case, we know that yesterday they used (1 + 1/2) barrels of raisins, to see how many batches of granola bars they made, we need to take the quotient between the total amount used and the amount needed for a single batch.
N = (1 + 1/2)/(3/4)
The quotient can be written as:
N = (1 + 1/2)*(4/3) = 4/3 + 4/6 = 4/3 + 2/3 = 6/3 = 2
They made 2 batches.
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Noah orders an extra-large pizza. It costs $12.49 for the pizza plus $1.50 for each topping. He orders an extra-large pizza with toppings that costs a total of dollars. Select all of the equations representing the relationship between the number of toppings and the pizza's total cost with toppings.
a. 12.49 + t = d
b.12.49 + 1.50d = d
c. 12.49 + 1.50 = t
d. 12.49 = d +1.50t
e. t = [tex]\frac{d-12.49}{1.5}[/tex]
f. t = d - [tex]\frac{12.49}{1.5}[/tex]
The equation to represent the given situation is 12.49+1.50d=t. Therefore, options B and E are the correct answers.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Noah orders an extra-large pizza. It costs $12.49 for the pizza plus $1.50 for each topping.
Let t be total money and d be the number of toppings.
So, the equation is 12.49+1.50d=t
1.50d=t-12.49
d=(t-12.49)/1.50
Therefore, options B and E are the correct answers.
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