Answer:
We have the following function:
F(x) = x^2 + 3x - 2
Factorizing, we have: F(x) = (x+ 3.562)(x -0.562)
Then, the solution to the system of equation is:
x1 = -3.562
x2 = 0.562
Now, let's work with F(x - 1) = (x-1)^2 + 3(x-1) - 2
F(x - 1) = (x+2.562)(x-1.562)
Then, the solution to the equation is:
x1 = -2.562
x2 = 1.562
answer :
we have the following function
F(x) = x^2 + 3x - 2
Factorizing, we have: F(x) = (x+ 3.562)(x -0.562)
Then, the solution to the system of equation is:
x1 = -3.562
x2 = 0.562
Now, let's work with F(x - 1) = (x-1)^2 + 3(x-1) - 2
F(x - 1) = (x+2.562)(x-1.562)
Then, the solution to the equation is:
x1 = -2.562
x2 = 1.562
Please answer the question from the picture above:)
Answer:
It's the red figure. This is because it is rotated 180 degrees.
Step-by-step explanation:
Please mark for Brainliest!! :D Thanks!!
For more questions or more information, please comment below!
50 points?with explanation
Answer:
a = b
b = c
So they're all equal, therefore a would be the same as c
Step-by-step explanation:
Answer: True
Step-by-step explanation: Since a||b and b||c, a||c is correct a is b and b is c.
Which statements describe a parabola? Check all that apply.
A parabola is the set of all points equidistant from the directrix and focus.
The fixed line is called the vertex of a parabola.
The focus is a fixed point inside the parabola.
The line of symmetry intersects the focus and directrix.
The line of symmetry and the directrix are perpendicular.
The parabola intersects the directrix.
Answer:
First, third, fourth and fifth statements describe a parabola
Step-by-step explanation:
The correct statements are:
A parabola is the set of all points equidistant from the directrix and focus.
The focus is a fixed point inside the parabola.
The line of symmetry intersects the focus and directrix.
The line of symmetry and the directrix are perpendicular.
Answer:
1, 3, 4, and 5 are the correct answers.
2 and 6 are not.
for each figure, find the missing side lengths. leave your answer as radicals in simplest form.
Answer:
4
Step-by-step explanation:
I'm not sure what question you are asking about but the one you had answer is incorrect.
You are given the long side which is 2sqrt(3).
Compare this to xsqrt(3) and hopefully you see x is 2 and is the short side.
The hypotenuse is twice the short side measurement so 2(2)=4.
Answer: 4
Answer:
Step-by-step explanation:
48
This is a 30-60-90 triangle, and we are given the [tex]x[/tex] value for the triangle, which makes it easier.
The hypotenuse for a 30-60-90 triangle will always be [tex]2x[/tex], while the adjacent side for a 30-60-90 triangle will always be [tex]x*\sqrt{3}[/tex].
So the hypotenuse is 14, and the adjacent side is [tex]7*\sqrt{3}[/tex]/
49
This is also a 30-60-90 triangle, and we can use the rules explained above.
The x value is [tex]5*\sqrt{3}[/tex] so the hypotenuse is [tex]10*\sqrt{3}[/tex] and the adjacent side is 15.
51
This is also a 30-60-90 triangle, and the root three value is [tex]2*\sqrt{3}[/tex], making the x value 2 and the hypotenuse 4.
52
This is a 45-45-90 triangle, and the same side value is [tex]4*\sqrt{2}[/tex].
This means that the adjacent side is also [tex]4*\sqrt{2}[/tex] and the hypotenuse is 8.
find missing term w+9/6=12
Answer: The missing term for W is 10.5.
Step-by-step explanation:
W + 9/6 = 12
W +9/6 - 9/6 = 12- 9/6
W = 12 - 1.5
W = 10.5
write 3/5 with denominator 10 and 20
Answer:
Answer is 6/10 and 12/20
Step-by-step explanation:
Let the numerator be x.
3/5=x/10
x=30/5
x=6
The required fraction is 6/10
Now same method applies for taking 20 as denominator
3/5=x/20
x=60/5
x=12
The required fraction is 12/20
Kathy distributes jelly beans among her friends. Alia gets 4^2 fewer jelly beans than Kelly, who gets 3^3 jelly beans. How many jelly beans does Alia get? A. 4^2 − 3^3 B. 3^3 + 4^2 C. 4 − 3^3 D. 3^3 − 4^2 E. 3^2 − 4^3
Answer:
Option D. Alia gets 3³ - 4² = 11 jelly beans.
Step-by-step explanation:
Kathy gives Kelly 3³ jelly beans.
Kathy gives Alia 4² fewer jelly beans than Kelly. This means that Alia gets the number of jelly beans obtained by Kelly decreased by 4².
To summarize:
#Kelly = 3³ = 27
#Alia = #Kelly - 4² = 3³ - 4² = 27 - 16 = 11
Then, option D is correct.
Choose the Domain & Range of the Relation shown in the graph:
Domain: -1, 0, 1, 2, 3
Range: -3, -1, 0, 3
Domain: -3, -1, 0, 3
Range: -3, -1, 0, 3
Domain: -3, -1, 0, 3
Range: -1, 0, 1, 2, 3
Domain: 3, 1, 0, 3
Range: -1, 0, 1, 2, 3
Answer:
C) Domain: -3, -1, 0, 3
Range: -1, 0, 1, 2, 3
Step-by-step explanation:
Domain is using x values
Range is using y values
some one help me pleaseeeeeeeeeee
Answer:
slope = [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (2, 4) ← 2 points on the line
m = [tex]\frac{4+1}{2-0}[/tex] = [tex]\frac{5}{2}[/tex]
Louise calculated the height of a cylinder that has a volume of 486 x cubic centimeters and a radius of 9 centimeters. Her work
is shown below
V=Bh
Step 1: 486x - R9?h
Step 2: 486 181 sch
486% 81
Step 3: 812 813
Step 4: h=6x cm
What error did Louise make when calculating the height of the cylinder?
In step 1, she substituted into the volume formula incorrectly.
In step 2, she calculated g2 incorrectly.
In step 4, the should have canceled, making the correct answer 6 cm.
Louise correctly calculated the height of the cylinder.
Answer:
Option C.
Step-by-step explanation:
we have that
The correct question is
Louis calculated the height of a cylinder that has a volume of 486pie cubic centimeters and a radius of 9 centimeters her work is shows below
V=BH
STEP 1: 486pie=pie9^2h
STEP 2: 486pie=81pieh
STEP 3: 486pie/81pie=81pie/81pie h
STEP 4: h=6pie cm
what error did Louise make when calculating the height of the cylinder
A. in step 1 she substituted into the volume formula incorrectly
B. in step 2 she calculated 9^2 incorrectly
C. in step 4 the pie should have canceled making the correct answer 6 cm
D. Louise correctly calculated the height of the cylinder
we know that
The volume of the cylinder is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the cylinder
we have
[tex]V=486\pi\ cm^{3}[/tex]
[tex]r=9\ cm[/tex]
Find the area of the base B
[tex]B=\pi r^{2}[/tex]
substitute
[tex]B=\pi (9)^{2}[/tex]
step 1
substitute the values in the formula of volume
[tex]486\pi=\pi (9)^{2}h[/tex]
step 2
[tex]486\pi=81\pi h[/tex]
step 3
Divide both sides by 81π
[tex]486\pi/81\pi=81\pi h/81\pi[/tex]
step 4
Simplify
[tex]6=h[/tex]
rewrite
[tex]h=6\ cm[/tex]
therefore
In step 4 the pie should have canceled making the correct answer 6 cm
Answer:
In step 4, the x should have canceled, making the correct answer 6 cm.
Which represents the solution(s) of the graphed system of equations, y = x2 + 2x – 3 and y = x – 1?
(1, 0) and (0, –1)
(–2, –3) and (1, 0)
(0, –3) and (1, 0)
(–3, –2) and (0, 1)
Answer:
Second option: (-2,-3) and (1,0)
Step-by-step explanation:
Given the system of equations [tex]\left \{ {{y = x^2 + 2x-3} \atop {y = x - 1}} \right.[/tex], you can rewrite them in this form:
[tex]x^2 + 2x-3= x - 1[/tex]
Simplify:
[tex]x^2 + 2x-3-x+1=0\\\\x^2+x-2=0[/tex]
Factor the quadratic equation. Choose two number whose sum be 1 and whose product be -2. These are: 2 and -1, then:
[tex](x+2)(x-1)=0\\\\x_1=-2\\\\x_2=1[/tex]
Substitute each value of "x" into any of the original equation to find the values of "y":
[tex]y_1= (-2) - 1=-3\\\\y_2=(1)-1=0[/tex]
Then, the solutions are:
(-2,-3) and (1,0)
ANSWER
The solutions are (-2,-3) and (1,0).
EXPLANATION
The given system has equations:
[tex]y = {x}^{2} + 2x - 3[/tex]
and
[tex]y = x - 1[/tex]
We equate both equations:
[tex] {x}^{2} + 2x - 3 = x - 1[/tex]
[tex] {x}^{2} + 2x - x - 3 + 1 = 0[/tex]
[tex] {x}^{2} + x - 2 = 0[/tex]
[tex](x - 1)(x + 2) = 0[/tex]
This implies that,
[tex]x = - 2 \: or \: x = 1[/tex]
When x=-2 , y=-2-1=-3
When x=1, y=1-1=0
The solutions are (-2,-3) and (1,0)
The amount of blueberries picked, in pounds, varies directly as the number of hours worked. After
10
hours,
30
pounds were picked.
What is the constant of proportionality
k
? Do not include units in your answer.
Answer:
3
Step-by-step explanation:
3 pounds were picked per hour
Answer: Hello there!
We know that the number of blueberries picked varies directly as the number of hours worked.
Direct variation means that: b = kh
where b is the number of blueberries, k is a constant of proportionality and h is the number of hours worked.
we know that in 10 hours there are 30 pounds of blueberries collected, then we can replace these numbers in the equation and solve it for k. And you want that I don't include units in the answer, so I will not include them.
30 = k*10
k = 30/10 = 3
Then the constant of proportionality is 3, whit is the amount of punds of blueberrys collected in one hour.
A survey asked people if they prefer to read books or e-books. The results are shown in the table below. What is the
marginal relative frequency of the number of people who prefer to read books?
Male Female Total
Read books
Read e-books
D
0.57
0.49
0.43
0.42
The marginal relative frequency of the number of people who prefer to read books is 0.42
Answer:
.42
Step-by-step explanation:
write the product using exponents
(-2) x (-2) x (-2)
Answer:
(-2)3 = -8
-2 × -2 = 4
4 × -2 = -8
Step-by-step explanation:
-2 multiply 3 times
negative times a negative equals a positive
negative times positive equals a negative
see results below
-2 × -2 = 4
4 × -2 = -8
If f(x)=4x+3 and g(x)= the square root of x-9, which is true? 2 is in the domain of f of g or 2 is not in the domain of f of g?
Answer:
2 is not in the domain of f of g
Step-by-step explanation:
* Lets revise at first the meaning of f of g (composite function)
- A composite function is a function that depends on another function
- A composite function is created when one function is substituted into
another function
- Example:
# f(g(x)) is the composite function that is formed when g(x) is
substituted for x in f(x).
- In the composition (f ο g)(x), the domain of f becomes g(x)
* Now lets solve the problem
∵ f(x) = 4x + 3
∵ g(x) = √(x - 9)
- Lets find f(g(x)), by replacing x in f by g(x)
∴ f(g(x)) = f(√(x - 9)) = 4[√(x - 9)] + 3
∴ f(g(x)) = 4√(x - 9) + 3
∵ The domain of f is g(x)
- The domain of the function is the values of x which make the
function defined
∵ There is no square root for negative values
∴ x - 9 must be greater than or equal zero
∵ x - 9 ≥ 0 ⇒ add 9 for both sides
∴ x ≥ 9
∴ The domain of f of g is all the real numbers greater than or equal 9
∴ The domain = {x I x ≥ 9}
∵ 2 is smaller than 9
∴ 2 is not in the domain of f of g
find five solutions of the equation y=20x. select integers for values for x starting with -2 and ending with 2
Five solutions of y = 20x with integer values for x ranging from -2 to 2 are (-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).
To find five solutions of the equation y = 20x , we can choose integer values for x starting with -2 and ending with 2, and then calculate the corresponding values of y using the given equation.
Starting with x = -2 :
y = 20(-2) = -40
So, the first solution is (-2, -40).
Moving to x = -1:
y = 20(-1) = -20
So, the second solution is (-1, -20).
At x = 0 :
y = 20(0) = 0
So, the third solution is (0, 0).
Proceeding to x = 1 :
y = 20(1) = 20
So, the fourth solution is (1, 20).
Finally, for x = 2 :
y = 20(2) = 40
So, the fifth solution is (2, 40).
Therefore, the five solutions of the equation y = 20x with integer values for x ranging from -2 to 2 are:
(-2, -40), (-1, -20), (0, 0), (1, 20), and (2, 40).
Help please!
x=
4
9
16
Answer:
16
Step-by-step explanation:
cos60°=8/x
x=8/cos60°
A scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live
for one week without producing any additional offspring. Each replicated organism also replicates at the same rate. At hour one,
there is one organism. At hour two, there are five more organisms. How many total organisms are there at hour seven?
2,801
19,531
19,607
97.655
Answer:
B. 19,531
Step-by-step explanation:
Answer:
The correct answer is option (2) 19,531
Step-by-step explanation:
Given Data;
a = 1 (first term)
r = 5 (five offspring)
n = 7 ( number of hours)
Using the formula of a geometric progression, we have
S₇ = [tex]\frac{a(r^{n} - 1) }{r -1}[/tex]
Substituting, we have
S₇ = [tex]\frac{1(5^{7} -1) }{5-1}[/tex]
S₇ = 78124/4
= 19531
Therefore, there are 19531 number of organisms at hour seven.
Please help me with this problem ASAP!!!!
For this case we have a function of the form [tex]y = f (x)[/tex]
They ask us to find the value of the function when[tex]x = 2[/tex], that is, [tex]f (2).[/tex]
If we look at the figure, and we mark x = 2 in the graph, we obtain a value of[tex]y = 4[/tex]
So, we have that the function has a value of 4 when[tex]x = 2[/tex]
Answer:
Option C
Write as an algebraic expression and then simplify if possible The distance traveled by a train in three hours with a constant speed of r miles per hour.
Answer:
Distance = 3r
Step-by-step explanation:
We are to write an algebraic expression and then simplify it for the given situation:
The distance traveled by a train in three hours with a constant speed of r miles per hour.
We know the formula of distance linking the speed and the time.
Distance = speed × time
Substituting the given values to get:
Distance = r × 3
Distance = 3r
A cable company claims that the average household pays $78 a month for a basic cable plan, but it could differ by as much as $20. Write an absolute value inequality to determine the range of basic cable plan costs with this cable company.
A. |x − 78| ≥ 20
B. |x − 20| ≥ 78
C. |x − 20| ≤ 78
D. |x − 78| ≤ 20
Answer:
D. |x − 78| ≤ 20
Step-by-step explanation:
Given,
The monthly charges for a basic cable plan = $ 78,
Also, it could differ by as much as $20,
So, the maximum charges = $(78 + 20) ,
And, the minimum charges = $(78 - 20),
Let x represents the monthly charges ( in dollars ),
78 - 20 ≤ x ≤ 78 + 20
⇒ 78 - 20 ≤ x and x ≤ 78 + 20
⇒ -20 ≤ x -78 and x-78 ≤ 20
⇒ 20 ≥ -(x-78) and x-78 ≤ 20 ( ∵ a > b ⇒ -a < -b )
⇒ |x-78| ≤ 20
Which is the required absolute value inequality to determine the range of basic cable plan costs,
Option 'D' is correct.
eighteen million, one hundred two thousand, seven hundred eighty-three as a whole number?
Answer:
18,102,783
Step-by-step explanation:
What is the sum of the fractions below? 3/5x+9/5x
[tex]\dfrac{3}{5x}+\dfrac{9}{5x}=\dfrac{12}{5x}[/tex]
The sum of the given expression will be equal to 12 / 5x.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression is:-
[tex]=\dfrac{3}{5x}+\dfrac{9}{5x}[/tex]
[tex]= \dfrac{3+9}{5x}[/tex]
[tex]=\dfrac{12}{5x}[/tex]
Therefore the sum of the given expression will be equal to 12 / 5x.
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three of the 15 people in the Latin club are chosen at random to wear togas to school to promote the club. What is the probability that Joseph, Heldi, and Katy are chosen
The probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is 1/455.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that three of the 15 people in the Latin club are chosen at random to wear togas to school to promote the club. Therefore, the number of ways 3 people can be chosen out of 15 is,
Number of ways to choose 3 people = ¹⁵C₃ = 455
Now, the number of ways Joseph, Heidi, and Katy can be chosen in only one way. Therefore, the probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is,
Probability = 1 /455 = 0.002197
Hence, the probability that Joseph, Heidi, and Katy are chosen out of 15 people in the Latin club to wear togas to school to promote the club is 1/455.
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At the beginning of year 1, Jonah invests $300 at an annual
compound interest rate of 4%. He makes no deposits to or
withdrawals from the account.
Which explicit formula can be used to find the account's
balance at the beginning of year 6?
The explicit formula that can be used to find the account's balance at the beginning of year 6 is B = P(1 + r/n)^(nt), which gives the value as [tex]300(1.04)^6[/tex]
Explanation:The explicit formula that can be used to find the account's balance at the beginning of year 6 is:
[tex]B = P(1 + r/n)^(nt)[/tex]
Where:
B is the balance after a certain number of yearsP is the principal amount (initial investment)r is the annual interest rate (as a decimal)n is the number of times that interest is compounded per yeart is the number of yearsIn this case, Jonah's initial investment is $300, the annual interest rate is 4%, interest is compounded annually (n = 1), and the number of years is 6 (t = 6). Plugging these values into the formula:
[tex]B = 300(1 + 0.04/1)^(1*6)[/tex]
[tex]B = 300(1 + 0.04)^6[/tex]
[tex]B = 300(1.04)^6[/tex]
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Solve each problem by writing and solving an equation.
For his son’s birthday party, Mr. Mori bought four equally-priced pizzas and a $3 bag of potato chips. If he spent $39, find the cost of each pizza.
Question 2 options:
Answer:
Each pizza costs for $9.
Step-by-step explanation:
We are given that Mr. Mori bought four equally-priced pizzas and a $3 bag of potato chips.
Given that he spent a total $39, we are to find the cost of each pizza.
This can be represented by an equation:
[tex]4x+3=39[/tex]
Solving it to find x.
[tex]4x=39-3[/tex]
[tex]4x=36[/tex]
[tex]x=\frac{36}{4}[/tex]
x = 9
Therefore, the cost of each pizza is $9.
Answer:
C.X=9
Step-by-step explanation:
Fracisco's game involves 3 green, 2 yellow, 4 red, and 3 black marbles. If he randomly draws three marbles from the
bag, without replacement, what is the probability that he will draw yellow, and then red, and then black?
A)1/192
B)1/72
C)3/220
D)1/55
Answer:1/55
Step-by-step explanation:
Answer: The answer is 1/55
Step-by-step explanation: because i got it right on edge. Can you mark brainliest?
Help answer this please
Answer:
B
Step-by-step explanation:
translation means to transcribe or change from on language/definition/understanding to another.
A student factors 10x^2+3x-27 to the following
A. The expression is equivalent, and it is completely factored
Find the product of (4x + 3y)(4x − 3y).
16x2 − 24xy + 9y2
16x2 − 9y2
16x2 + 24xy + 9y2
16x2 + 9y2
Answer:
It's B
Step-by-step explanation:
B, 16x2-9y2
Answer: The correct option is (B) [tex]16x^2-9y^2.[/tex]
Step-by-step explanation: We are given to find the following product :
[tex]P=(4x+3y)(4x-3y)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the given product, we will be using the following formula :
[tex](a+b)(a-b)=a^2-b^2.[/tex]
The product (i) can be calculated as follows :
[tex]P\\\\=(4x+3y)(4x-3y)\\\\=(4x)^2-(3y)^2\\\\=16x^2-9y^2.[/tex]
Thus, the required product is [tex]16x^2-9y^2.[/tex]
Option (B) is CORRECT.