How is the graph of y= (x-1)^2-3 transformed to produce the graph of y= 1/2(x+4)^2?
Answers
The graph of y=(x-1)^2-3 can be transformed to the graph of y=1/2(x+4)^2 by stretching it vertically and shifting it horizontally to the left.
Explanation:The graph of y=(x-1)^2-3 transformed to produce the graph of y=1/2(x+4)^2 can be done by manipulating the equation and observing its effect on the graph.
Step 1: Identify the transformation of the parent function y=x^2
Step 2: The transformation y=1/2(x+4)^2 indicates a vertical stretch by a scale factor of 1/2 and a horizontal shift to the left by 4 units.
Therefore, the graph of y=(x-1)^2-3 is transformed to the graph of y=1/2(x+4)^2 by stretching it vertically and shifting it horizontally to the left.
A: The graph is translated left 5 units, compressed vertically by a factor of One-half, and translated up 3 units.
B: The graph is stretched vertically by a factor of One-half, translated left 5 units, and translated up 3 units.
C: The graph is translated left 5 units, compressed horizontally by a factor of One-half, and translated down 3 units.
D: The graph is stretched horizontally by a factor of One-half, translated left 5 units, and translated down 3 units.
Answer:
The graph is stretched horizontally by a factor of 1/2, translated left 5 units and up 3 units.
Step-by-step explanation:
I put both equations into a graphing calculator and compared them. Five units left and 3 up agree with answers A and B. The second equation showed a wider parabolic than the first one, which agrees only with answer C. Therefore, it is my opinion that neither answer is correct. I chose D, but since this is a unit test I can't go in and see if I was correct or not.
Related Questions
Which expression represents the prime factorization of 96?
A. 2 x 2 x 3 x 8
B. 2 x 2 x 2 x 12
C. 2 x 2 x 2 x 2 x 2 x 3
D. 2 x 2 x 2 x 2 x 2 x 3 x 3
Answers
It is not A. because 8 is not a prime number.
It is not B. because 12 is not a prime number.
C. 2 x 2 x 2 x 2 x 2 x 3 = 4*4*6= 96
D. 2 x 2 x 2 x 2 x 2 x 3 x 3= 4*4*6*3=16*18= 288
Answer is C. -2 x 2 x 2 x 2 x 2 x 3 : 96 ( not D. = 298 , 298 is greater than 96)
The prime factorization of the number 96 is 2 x 2 x 2 x 2 x 2 x 3. The correct option is C.
What is prime factorization?A number can be expressed as a product of its prime factors through the process of prime factorization. Prime factorization is the process of factorizing the bigger numbers in a way that all the numbers are prime.
Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is any natural number greater than one that is not prime.
The given number is 96. The factorization of the number 96 will be done as below:-
96 = 2 x 2 x 2 x 2 x 2 x 3
Therefore, the prime factorization of the number 96 is 2 x 2 x 2 x 2 x 2 x 3. The correct option is C.
To know more about prime factorization follow
https://brainly.com/question/18187355
#SPJ2
use the substitution method to solve the system of equations choose the correct orderd pair. 3x-y=7 2x-2y=2
Answers
Answer:
(3,2)
Step-by-step explanation:
We are given the system:
3x-y=7
2x-2y=2.
We are asked to solve this by substitution. We need to pick an equation and pick a variable from that equation to solve for that variable.
I really like either for this. Some people might go with the first one though. Let's do that. I will solve the first one for y.
3x-y=7
Subtract 3x on both sides:
-y=-3x+7
Divide both sides by -1:
y=3x-7
Now we are ready for substitution. We are going to plug this equation into the second equation giving us:
2x-2y=2 with y=3x-7 gives us:
2x-2(3x-7)=2
Distribute:
2x-6x+14=2
Combine like terms:
-4x+14=2
Subtract 14 on both sides:
-4x =2-14
Simplify:
-4x =-12
Divide both sides by -4:
x =-12/-4
Simplify:
x =3
So using y=3x-7 and x=3, I will find y now.
y=3x-7 if x=3
y=3(3)-7 (I inserted 3 for x since we had x=3)
y=9-7 (Simplified)
y=2 (Simplified)
The answer is (x,y)=(3,2).
What is the value of "c" in the quadratic equation 3x 2 + 5x + 7 = 0?
3
5
7
Answers
Answer:
[tex]c=7[/tex]
Step-by-step explanation:
They are just asking you to compare
[tex]ax^2+bx+c=0[/tex] to
[tex]3x^2+5x+7=0[/tex].
What constant values are in the place of [tex]a,b, \text{ and } c[/tex].
[tex]a=3[/tex]
[tex]b=5[/tex]
[tex]c=7[/tex]
3x^2+5x+7
ax^2+bx+C
Ivan's gas tank is 1/5 full. After he buys 7 gallons of gas, it is 7/10 full. How many gallons can Ivan's tank hold?
Answers
Answer: 14 gallons of gas.
Step-by-step explanation: For the fractions, find a common denominator, which would be 10. To get 1/5 to have a denominator of 10, multiply each number by 2. You would get 2/10. 7 gallons fills his tank from 2/10 to 7/10. Subtract the two fractions.
7/10 - 2/10 = 5/10.
7 gallons filled his tank half way. We are trying to find the amount to fill his tank all the way. So multiply 7 by 2.
7 x 2 = 14
14 gallons of gas will fill his tank all the way.
I hope this helps!
Ivan's gas tank can hold 17.5 gallons when full after being 1/5 full and then adding 7 gallons.
The total capacity of Ivan's gas tank:
From 1/5 to 7/10 full means it increased by 4/10 or 2/5 of its capacity.Since 7 gallons represent 2/5, to find the total capacity, we divide 7 by 2/5 or multiply by 5/2.Therefore, the total capacity of Ivan's gas tank is 17.5 gallons.The surface area of the prism is ______ square units. All measurements in the image below are in units. (Input whole number only.) A triangular prism is shown with 2 right triangular sides having legs 3 and 4 and hypotenuse 5. The length of the prism is 3.5 Numerical Answers Expected! Answer for Blank 1:
Answers
Answer:
54
Step-by-step explanation:
Answer:
54 square units
Step-by-step explanation:
In order to calculate the surface area of the prism you have to calculate the area of each face of the prism, and you have to remember the different formulas to calculate the areas:
[tex]Rectangle=Length*Width[/tex]
[tex]Triangle=\frac{Base*Height}{2}[/tex]
So you just have to insert the values into the formulas:
[tex]Rectangle1=4*3.5[/tex]
[tex]Rectangle1=14[/tex]
[tex]Rectangle2=5*3.5[/tex]
[tex]Rectangle2=17.5[/tex]
[tex]Rectangle3=3*3.5[/tex]
[tex]Rectangle3=10.5[/tex]
[tex]Triangle1=\frac{4*3}{2}[/tex]
[tex]Triangle1=6[/tex]
[tex]Triangle2=\frac{4*3}{2}[/tex]
[tex]Triangle2=6[/tex]
If you add up all the faces, you get the surface area of the prism:
14+17.5+10.5+6+6=54
Multiply.
(x + 7)(3x - 2)
( please answer with
A.
B.
C.
D.
Answers
Answer:
A. 3x^2+19x-14
Step-by-step explanation:
Applying the distributive property the given expression is equal to 3x²+19x-14 (Letter A).
Properties of MultiplicationThe properties of multiplication are:
Distributive: a(b±c)= ab±acCommutative: a . b = b. aAssociative: a(b+c)= c(a+b)Identity: b.1=bZero= b*0=0For evaluating the given question, you should apply the distributive property.
The question gives the expression (x+7)(3x-2). Thus, from the distributive property, you have:
3x²-2x+21x-14
3x²+19x-14
From the given options of the question, 3x²+19x-14 is shown in option A.
Read more about the distributive property here:
brainly.com/question/4077386
#SPJ6
Which statements are true for the functions g(x) = x^2 and h(x) = –x^2 ? Check all that apply.A.For any value of x, g(x) will always be greater than h(x).B.For any value of x, h(x) will always be greater than g(x).C.g(x) > h(x) for x = -1. D.g(x) < h(x) for x = 3. E.For positive values of x, g(x) > h(x). F.For negative values of x, g(x) > h(x)
Answers
Answer:
C, E, F
Step-by-step explanation:
The range of the function [tex]g(x)=x^2[/tex] is [tex]y\in [0,\infty)[/tex], the range of the function [tex]h(x)=-x^2[/tex] is [tex](-\infty,0][/tex]
This means that for any value of x, the value of [tex]g(x)[/tex] is always greater or equal to the value of [tex]h(x)[/tex] (the values are equal at x=0).
So, options A and B are false, because at x=0 the values are equal and h(x) cannot be greater than g(x)
Options C, E and F are true, because for all non-zero x, g(x)>h(x).
Option D is false (the reason is the same as for option B)
Solve F(x) for given domain. Include all of your work in your final work submit your solution
F(x)=x^2+2
F(x^2)=
PLEASE HELP I'AM SCREAMING FOR HELP!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
Actually, you have not "given" the domain.
The domain of F(x)=x^2+2 is "the set of all real numbers," because F(x)=x^2+2 is a polynomial.
F(x^2) = (x^2) + 2 = x^4 + 2. Again, this is a polynomial and the domain is "the set of all real numbers."
Double check to ensure that you have copied down this problem correctly.
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 56 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 7000 batteries, and 1% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
Answers
Answer:
98.1% chance of being accepted
Step-by-step explanation:
Given:
sample size,n=56
acceptance condition= at most 2 batteries do not meet specifications
shipment size=7000
battery percentage in shipment that do not meet specification= 1%
Applying binomial distribution
P(x)=∑ᵇₐ=₀ (n!/a!(n-a)!)p^a (1-p)^(n-a)In this formula, a is the acceptable number of defectives;
n is the sample size;
p is the fraction of defectives in the population.
Now putting the value
a= 2
n=56
p=0.01
[tex]\frac{56!}{0!\left(56-0\right)!}\left(0.01\right)^0\:\left(1-0.01\right)^{\left(56-0\right)} + \frac{56!}{1!\left(56-1\right)!}\left(0.01\right)^1\:\left(1-0.01\right)^{\left(56-1\right)} +[/tex][tex]\:\frac{56!}{2!\left(56-2\right)!}\left(0.01\right)^2\:\left(1-0.01\right)^{\left(56-2\right)}[/tex]
=0.56960+0.32219+0.08949
After summation, we get 0.981 i.e. a 98.1% chance of being accepted. As this is such a high chance, we can expect many of the shipments like this to be accepted!
Given that a function, g, has a domain of -20 sxs 5 and a range of -5 s g(x) s 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be
true for g.
A g(-4)=-11
B. g(-13) = 20
C. g(7)=-1
D. g(0) = 2
Answers
Answer:
s(x) = f(x) + g(x) = (5x + 2) + (7x + 4) = 12x + 6
p(x) = 6*g(x) = 6(7x + 4) = 42x + 24
Step-by-step explanation:
What is the solution to the equation 1/4x- 1/8=7/8+1/2x
Answers
Answer:
4
Step-by-step explanation:
Start by multiplying both sides by 4.
[tex]\frac{1}{4} x-\frac{1}{8} =\frac{7}{8} +\frac{1}{2} x\\x-\frac{1}{2} =\frac{7}{2}+2x[/tex]
Next, combine like terms.
[tex]x-\frac{1}{2} =\frac{7}{2}+2x\\-\frac{1}{2} =\frac{7}{2} +x\\x=\frac{8}{2} \\x=4[/tex]
1. does a linear function have to have an x value of 0?
2. what is a constant rate?
3. does a linear function need to be all positive, or can it have some negative values?
Answers
Answer:
yes
Step-by-step explanation:
let me explain more in depth. 1: yes, it's the point where the function crosses the x axis. 2: the absence of acceleration. 3: I think it can be negative
7. Which two equations are equivalent?
A. y = (x + 3)2 and y = x2 + 6
B. y = (x – 5)2 and y = x2 – 25
c. y = (x – 3)2 and y = x2 - 6x + 9
D. y = (x + 5)2 and y = x2 + 25x + 10
Answers
Answer:
C. [tex]y=(x-3)^2[/tex] and [tex]y=x^2-6x+9[/tex]
Step-by-step explanation:
before answering the problem let us remind the formula for square of sum and differences
[tex](a+b)^2=a^2+2 \times a \times b + b^2[/tex]
[tex](a-b)^2=a^2-2 \times a \times b + b^2[/tex]
We are going to use the above two formulas to solve each part and come to an answer
A. [tex]y = (x + 3)^2[/tex]
[tex](x + 3)^2=x^2+2 \times x \times 3 + 3^2[/tex]
[tex](x + 3)^2=x^2+6x+9[/tex]
Hence this option is not correct pair
B. [tex]y = (x-5)^2[/tex]
[tex](x - 5)^2=x^2-2 \times x \times 5 + 5^2[/tex]
[tex](x -5)^2=x^2-10x+25[/tex]
Hence this option is also not correct pair
C. [tex]y = (x -3)^2[/tex]
[tex](x - 3)^2=x^2-2 \times x \times 3 + 3^2[/tex]
[tex](x -3)^2=x^2-6x+9[/tex]
Hence this option is correct as it have equivalent pair
D. [tex]y = (x + 5)^2[/tex]
[tex](x + 5)^2=x^2+2 \times x \times 5 + 5^2[/tex]
[tex](x + 5)^2=x^2+10x+25[/tex]
Hence this option is also not correct pair
sollve for x (x-5)=4x-5
Answers
Answer:
x=0
Step-by-step explanation:
(x-5)=4x-5
Subtract x from each side
x-5-x=4x-x-5
-5 = 3x-5
Add 5 to each side
-5+5 = 3x-5+5
0 = 3x
Divide by 3
0/3 = 3x/3
0 =x
x=0
Raina brought a table for 627 the price was 35%less than the original price
Answers
Answer:
964.62
Step-by-step explanation:
Let x = the original price
35% less than means we pay 65% of the original price
627 = 65% x
Changing to decimal form
627 = .65x
Divide each side by .65
627/.65 = .65x/.65
964.6153846 =x
Rounding to the near cent
964.62
The table represents a linear equation. Which equation correctly uses point (–2, –6) to write the equation of this line in point-slope form? y – 6 = (x – 2) y – 6 = (x – 2) y + 6 = (x + 2) y + 6 = (x + 2)
Answers
Answer:
[tex]y+6=m(x+2)[/tex]
where I would have to look at the table to know [tex]m[/tex].
Step-by-step explanation:
Point-slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
where [tex]m \text{ is the slope and } (x_1,y_1) \text{ is a point on that line}[/tex]
You are given [tex](x_1,y_1)=(-2,-6) \text{, but no value for }m[/tex].
So we know we are looking for an equation that looks like this:
[tex]y-(-6)=m(x-(-2))[/tex]
If you simplify this looks like:
[tex]y+6=m(x+2)[/tex]
Answer:
d
Step-by-step explanation:
Only a few minutes please help!!
A) 20
B) 50
C) 90
D) 120
Answers
Answer:
C 90
Step-by-step explanation:
Answer: OPTION B.
Step-by-step explanation:
You can observe in the figure provided that the angle 3 and the angle that measures 70° , share the same vertex, therefore, you can conclude that they are Vertical angles and they are congruent. Then:
[tex]m\angle 3=70\°[/tex]
You can notice that the angle 1 and the angle that measures 70° are Complementary angles (They add up to 90°), then you can find the measure of the angle 1:
[tex]m\angle 1+70\°=90\°\\\\m\angle 1=90\°-70\°\\\\m\angle 1=20\°[/tex]
Then:
[tex]m\angle 3-m\angle 1=70\°-20\°\\\\m\angle 3-m\angle 1=50\°[/tex]
7hr= how many minutes
Answers
Answer:
420 minutes
Step-by-step explanation:
1 hour = 60 minutes
7 * 1 hour = 7 * 60 minutes
7 hours = 420 minutes
We know that 1 hour = 60 minutes
To find how many minutes is in seven hours, we can multiply 60 by 7 and we will get a product of 420.
1 hour = 60 minutes
2 hours = 120 minutes
3 hours = 180 minutes
4 hours = 240 minutes
5 hours = 300 minutes
6 hours = 360 minutes
7 hours = 420 minutes
Which of the following reveals the minimum value for the equation 2x^2 + 12x − 14 = 0?
Answers
The equation that reveals the minimum value for the equation is 2(x + 3)² = 32
Which reveals the minimum value for the equation
From the question, we have the following parameters that can be used in our computation:
2x² + 12x − 14 = 0
Rewrite as
2x² + 12x = 14
So, we have
2(x² + 6x) = 14
Take the coefficient of x
k = 6
Divide by 2
k/2 = 3
Square both sides
(k/2)² = 9
So, we have
2(x² + 6x + 9) = 14 + 2 * 9
2(x² + 6x + 9) = 32
Express as squares
2(x + 3)² = 32
Hence, the equation that reveals the minimum value for the equation is 2(x + 3)² = 32
Question
Which of the following reveals the minimum value for the equation 2x^2 + 12x - 14 = 0?
2(x + 6)^2 = 26
2(x + 6)^2 = 20
2(x + 3)^2 = 32
[tex]( \sqrt{5x + 6} ) ^{2} [/tex]
multiply
Answers
[tex]\bf (\sqrt{5x+6})^2\implies \sqrt{(5x+6)^2}\implies 5x+6[/tex]
The fraction four-fifths is equivalent to what percent?
Answers
The answer is:
The fraction is equivalent to 80%.
Why?To solve the problem, we need to remember that if we want to convert from numbers to percentual values, we need to multiply the given number by 100.
So, if we have the fraction four-fifths which is:
[tex]\frac{4}{5}=0.8[/tex]
If we need to convert it to percent, we need to multiply it by 100:
[tex]0.8*100=80(percent)[/tex]
Hence, we have that the fraction is equivalent to 80%.
Have a nice day!
Answer:
80%
Step-by-step explanation:
We know 4/5 is the same as 4 divided by 5 then using long division for 4 divided by 5 gives us 0.8 converting our number to a percent
0.8 x 100 = 80%
Sketch the graph of y= (x - 2)2 - 16, then select the graph that corresponds
to your sketch.
-20
O A. Graph A
O B. Graph B
O C. Graph c
O D. Graph D
Answers
If there was an illustration, I would be happy to assist you.
What is the solution of this equation
4x-6=10x-3
Answers
Answer:
x=[tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
4x-6=10x-3 (add 6 to both sides)
4x=10x+3 (subtract 10x from both sides)
-6x=3 (divide both sides by -6)
x=[tex]\frac{-1}{2}[/tex]
Answer: X = -1/2
Step-by-step explanation: Your goal is to isolate x. First, subtract 4x from each side.
-6 = 6x - 3
Add 3 on both sides.
-3 = 6x
Divide by 6 on each side.
X = -1/2
Select all that apply.
Which numbers are not perfect squares?
25
20
18
36
16
14
24
Answers
Answer:
14, 18, 20, and 24 are not perfect squares.
The numbers that are not perfect squares are:
1. 20
2. 18
3. 14
4. 24
These numbers do not have integer square roots, which means they are not perfect squares.
A perfect square is a number that can be expressed as the product of an integer multiplied by itself. For example, 25 is a perfect square because [tex]\(5 \times 5 = 25\).[/tex]
Let's examine each number:
1. 25 - This is a perfect square because [tex]\(5 \times 5 = 25\).[/tex]
2. 20 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.
3. 18 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.
4. 36 - This is a perfect square because [tex]\(6 \times 6 = 36\).[/tex]
5. 16 - This is a perfect square because [tex]\(4 \times 4 = 16\).[/tex]
6. 14 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.
7. 24 - This is not a perfect square. It cannot be expressed as the product of an integer multiplied by itself.
Therefore, the numbers that are not perfect squares are 20, 18, 14, and 24. They cannot be represented as the square of an integer. The other numbers, 25, 36, and 16, are perfect squares as they can be expressed as the square of an integer.
The complete question is here.
Which numbers are not perfect squares? 25 20 18 36 16 14 24
Factor completely 2x3 + x2 − 18x − 9.
(x2 − 9)(2x + 1)
(x − 3)(x + 3)(2x − 1)
(x − 3)(x + 3)(2x + 1)
(2x − 3)(2x + 3)(x − 1)
Answers
X2(2x+1) -9(2x+1)
(X2-9)(2x+1)
Answer:
Option C: (x − 3)(x + 3)(2x + 1)
Step-by-step explanation:
NEED HELP WITH A MATH QUESTION
Answers
Answer:
87.88 ft^2.
Step-by-step explanation:
Area = 1/2 * base * height
= 1/2 * 16.9 * 10.4
= 87.88 ft^2.
Answer:
87.88 ft²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 16. 9 and h = 10.4, so
A = 0.5 × 16.9 × 10.4 = 87.88 ft²
A gardener is planting two types of trees:Type A is three feet tall and grows at a rate of 15 inches per year.Type Bis four feet tall and grows at a rate of 10 inches per years. Determine exactly How long many years it will take for these trees to be the same height
Answers
Answer:
2.4 years
Step-by-step explanation:
you have to first convert the trees' heights into inches. three feet is equivalent to 36 inches and four feet is equivalent to 48 inches. Since three A grows at 15 inches a year it'll become a the expression 15x+36 and the expression for tree B will be 10x+48. You set them up to each other and simplify it.
15x+36=10x+48
-10x -10x
5x+36=48
-36 -36
5x=12
/5 /5
x=2.4
So it'll be 2.4 years
Which is an exponential decay function?
Answers
Step-by-step explanation:
exponential decay functions are written in the form :
[tex]y=ab^{x}[/tex]
where b is less than 1
if we look at the 3rd choice and consider the term on the right.
[tex](8/7)^{-x}[/tex]
= [tex](7/8)^{x}[/tex]
If we compare this to the general form above,
b = 7/8 (which is less than 1)
hence the 3rd choice is correct.
The function which is an exponential decay function is:
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
Step-by-step explanation:We know that an exponential function is in the form of:
[tex]f(x)=ab^x[/tex]
where a>0 and if 0<b<1 then the function is a exponential decay function.
and if b>1 then the function is a exponential growth function.
a)
[tex]f(x)=\dfrac{3}{4}(\dfrac{7}{4})^x[/tex]
Here
[tex]b=\dfrac{7}{4}>1[/tex]
Hence, the function is a exponential growth function.
b)
[tex]f(x)=\dfrac{2}{3}(\dfrac{4}{5})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{2}{3}(\dfrac{5}{4})^x[/tex]
Here
[tex]b=\dfrac{5}{4}>1[/tex]
Hence, the function is a exponential growth function.
c)
[tex]f(x)=\dfrac{3}{2}(\dfrac{8}{7})^{-x}[/tex]
We know that:
[tex]a^{-x}=(\dfrac{1}{a})^x[/tex]
Hence, we have the function f(x) as:
[tex]f(x)=\dfrac{3}{2}(\dfrac{7}{8})^x[/tex]
Here
[tex]b=\dfrac{7}{8}<1[/tex]
Hence, the function is a exponential decay function.
d)
[tex]f(x)=\dfrac{1}{3}(\dfrac{9}{2})^x[/tex]
Here
[tex]b=\dfrac{9}{2}>1[/tex]
Hence, the function is a exponential growth function.
a cars fuel efficiency is no less the 45 mpg use F to find the cars fuel efficiency. how do i turn this into an inequality math problem
Answers
Answer:
F ≥ 45
Step-by-step explanation:
"No less than" means "greater than or equal to", so you can write the expression as ...
F ≥ 45 . . . . . miles per gallon
A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents this scenario?
Answers
Answer:
The graph that representss this scenario is attached.Explanation:
You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.
1. Determine the expression that relates the variables.
a) The name of the variables is given:
x: number of solved puzzlesy: number of solved riddlesb) Point rules:
Each solved puzzle is worth two points: 2x Each solved riddle is worth 1 point: 1y = ySum of points: 2x + yThe video game requires at least 4 points to advance: this means that the number of points must grater than or equal to 4 ⇒ 2x + y ≥ 4 .In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.
2) Building the graph
Solve algebraically for y: y ≥ 4 - 2xYou want to draw the border line of the function, that is y = 4 - 2xYou have a linear function, so you need only two points to draw it. It is generally easier to work with the intercepts.x-intercept (y = 0) ⇒ 2x + 0 = 4 ⇒ 2x = 4 ⇒ x = 2 ⇒ point (2, 0)y-intercept (x = 0) ⇒ 2(0) + y = 4 ⇒ y = 4 ⇒ point (0, 4).In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.
Addtional constrains: x and y cannot be negative, so add the constrains:x ≥ 0 and y ≥ 0
The set of solutions of y ≥ 4 - 2x is the same line y = 4 - 2x and the region over the line, so you have to shade that portion of the graph, but only in the first quadrant (since x and are greater than or equal to zero).The resulting graph is attached.
Answer:
D
Thank me later!! Just did the test on edge