Answer:
10 ounces of water
Step-by-step explanation:
16=8/5
z=1
16*1=16
8/5*z=8/5z
16=8/5z
16/1.6z=10
z = 10
Answer:
10 ounces of water
Step-by-step explanation:
What are the zeros of the quadratic function f(x) = 6x2 + 12x – 7?
x = –1 – and x = –1 +
x = –1 – and x = –1 +
x = –1 – and x = –1 +
x = –1 – and x = –1 +
It an expression or a way of saying f(x)=6x2+12-7
Answer:
[tex]x=-1+\frac{\sqrt{78} }{6}[/tex] and
[tex]x=-1-\frac{\sqrt{78} }{6}[/tex]
Step-by-step explanation:
[tex]f(x) = 6x^2 + 12x - 7[/tex]
To find out the zeros of the quadratic function, we apply quadratic formula
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
From the given f(x), the value of a=6, b=12, c=-7
Plug in all the values in the formula
[tex]x=\frac{-12+-\sqrt{12^2-4(6)(-7)}}{2(6)}[/tex]
[tex]x=\frac{-12+-\sqrt{312}}{2(6)}[/tex]
[tex]x=\frac{-12+-2\sqrt{78}}{2(6)}[/tex]
Now divide each term by 12
[tex]x=-1+-\frac{\sqrt{78} }{6}[/tex]
We will get two values for x
[tex]x=-1+\frac{\sqrt{78} }{6}[/tex] and
[tex]x=-1-\frac{\sqrt{78} }{6}[/tex]
How many degrees are there in angle C?
** multiple choice question
There are 50 degrees in angle c
Answer: A. 50°
Step-by-step explanation:
Since the measure angles of a triangle add up to 180° and the right triangle=90°, therefore when you subtract 180-90-40, you get 90-40, which then equals to 50°.
before school began mrs. weeks bought a total of 86 balls us the information below to help you write a numerical expression
For this case we have that the total of the balls is 86. We know there are 8 footballs then:
Basketball: Two more than twice the number of footballs are basketballs, that is:
[tex]2 + 2 (8) = 2 + 16 = 18[/tex]
There are 18 Basketballs.
Baseballs: Four less than 5 times the number of footballs are baseballs, that is:
[tex]5 (8) -4 = 40-4 = 36[/tex]
There are 36 Baseballs.
Softballs: Six more than half of baseballs are softballs. That is to say:
[tex]6+ \frac {36} {2} = 6 + 18 = 24[/tex]
There are 24 Softballs
If we add we must get 86.
[tex]8 + 18 + 36 + 24 = 86[/tex]
ANswer:
There are 8 Footballs
There are 18 Basketballs.
There are 36 Baseballs.
There are 24 Softballs
What is the solution to this system of equations?
x + 2y − z = 3
2x − y + 2z = 6
x − 3y + 3z = 4
Answer: The system of equations has no solutions.
Step-by-step explanation:
Identify the equation as:
[tex]x + 2y - z=3[/tex] [Equation 1]
[tex]2x -y + 2z=6[/tex] [Equation 2]
[tex]x - 3y + 3z=4[/tex] [Equation 3]
Multiply [Equation 1] by -2 and add this to [Equation 2] :
[tex](-2)(x + 2y - z)=3(-2)[/tex]
[tex]\left \{ {{-2x - 4y +2z=-6} \atop {2x -y + 2z=6}} \right.\\ ..........................\\-5y+4z=0[/tex]
Find another equation of two variables: Multiply [Equation 3] by -2 and add this to [Equation 2]:
[tex](-2)(x - 3y + 3z)=4(-2)[/tex]
[tex]\left \{ {{2x -y + 2z=6} \atop {-2x +6y -6z=-8}} \right.\\........................\\5y-4z=-2[/tex]
Then you get this new system of equations. When you add them, you get:
[tex]\left \{ {{-5y+4z=0} \atop {5y-4z=-2}} \right.\\..................\\0=-2[/tex]
Since the obtained is not possible, the system of equations has no solutions.
The solution to the system of equations x + 2y - z = 3, 2x - y + 2z = 6, and x - 3y + 3z = 4 is (-1, 1, 2) utilizing substitution method.
Explanation:The subject of this question is to find a solution to the system of linear equations. We can solve this system by methods of either substitution, elimination or matrix - but let's use substitution. First, let's isolate x in the first equation: x = 3 - 2y + z. Then we substitute x into the second and the third equation:
2(3 - 2y + z) − y + 2z = 6(3 - 2y + z) − 3y + 3z = 4
After simplifying these equations, we find y = 1 and z = 2. Plugging these back into x = 3 - 2y + z, we get x = -1. Therefore, the solution to the system is (-1, 1, 2).
Learn more about System of Equations here:https://brainly.com/question/21620502
#SPJ3
What is the value of m in the equation 1/2m-3/4n=16, when n = 8?
A. 20
B. 32
C. 44
D. 48
Answer:
44
Step-by-step explanation:
0.5 m - 0.75 n = 16
Substitute n = 8 into the equation
0.5 m - ( 0.75 × 8 ) = 16
0.5 m - 6 = 16
( Add 6 to both sides )
0.5 m = 26
( Divide by 0.5 )
m = 52
A bag contains 10 pieces of flavored candy 4 lemon 3 strawberrys 2 grape and 1 cherry one piece of candy will be randomly picked from the bag what is the probability the candy picked is not grape flavored
Answer:
The probability that the candy picked is not grape flavored would be 4/5
Step-by-step explanation:
We are given that a bag contains 10 pieces of flavored candy. 4 lemon, 3 strawberry, 2 grape and 1 cherry. The probability that the candy picked is not grape flavored is calculated as;
(number of candy that are not grape flavored)/ ( total number of candy in the bag)
= (4+3+1)/(10)
= 8/10
=4/5
Therefore, the probability that the candy picked is not grape flavored would be 4/5
To find the probability that a randomly picked candy is not grape flavored, we will follow these steps:
1. Count the total number of pieces of candy in the bag. This is the sum of all the different flavors of candy:
- 4 lemon candies
- 3 strawberry candies
- 2 grape candies
- 1 cherry candy
The total number is 4 + 3 + 2 + 1 = 10 candies.
2. Count the number of candies that are not grape flavored. Since there are 2 grape candies, the number of candies not grape flavored is the total minus the grape candies:
10 (total candies) - 2 (grape candies) = 8 candies that are not grape flavored.
3. Calculate the probability of picking a non-grape flavored candy. Probability is the number of favorable outcomes divided by the total number of possible outcomes. In our case, the favorable outcomes are the instances where we pick a non-grape flavored candy, and the total possible outcomes are picking any candy from the bag:
Probability (not grape flavored) = Number of non-grape flavored candies / Total number of candies
Probability (not grape flavored) = 8 / 10
4. Simplify the fraction, if needed. In this case, the fraction 8/10 can be simplified to 4/5 by dividing both the numerator and denominator by the greatest common divisor, which is 2.
Therefore, the probability of picking a candy that is not grape flavored from the bag is 4/5, or 80% if expressed as a percentage.
In triangle ABC AB =BC and m
the length of DE is 9/2 units and m<CAB is 45
The measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.
What is a triangle?A triangle is a polygon with three angles and sides.
Given that, a right triangle ABC, right-angled at B,
Here D and E are midpoints of AB and BC, and also AB = AC, CB = 9 units.
We need to find the measurements of DE and angle CAB in the given triangle ABC,
Since, the two sides are equal in the triangle then it is a right-isosceles triangle,
In a right-isosceles triangle, the two acutes angles are measured 45°
Therefore, ∠ CAB = ∠ ACB = 45°
Hence, ∠ CAB = 45°
Now, using the midpoint theorem, we will get. CB = 2DE
Therefore,
9 = 2DE
DE = 4.5 units
Hence, the measurements of DE and angle CAB in the given triangle ABC are 4.5 units and 45° respectively.
Learn more about triangles, click;
https://brainly.com/question/2773823
#SPJ7
Elijah spends 5 hours each week working out in a pool. This is twice the
amount of time he spends working out in the weight room. How much time
does he spend in the weight room each week?
Answer: he spends 2.5 hours in the weight room each week.
Step-by-step explanation: 2.5 multiplied by 2 (which is the twice amount of time spent working out in the pool) is 5.
So the answer is 2.5
(1.1•10^-5)(3 •10^-2)
A. 4.1 • 10 ^-7
B. 4.1 • 10^10
C. 3.3 • 10^-7
D. 3.3 • 10^10
Answer:
C. 3.3 • 10^-7
Step-by-step explanation:
(1.1•10^-5)(3 •10^-2)
Multiply the numbers out front of the powers of ten, then add the exponents on the powers of 10
1.1 * 3 * 10 ^(-5+-2)
3.3 ^ (-7)
Answer:
C
Step-by-step explanation:
If 1 dish of craft paint covers an area of 720 square centimeters, how many dishes of paint are required to paint the top surface and the lateral faces of the table shown in the diagram? Ignore the bottom of the tabletop and the legs.
(540 + 540 + 900 + 900) + (2160) = (Surface area of Lateral faces) + (Top) = 5040 sq cm.
5040 / 720 = dishes of craft paint = 7 dishes
Answer:
7 dishes
Step-by-step explanation:
Ivan is putting books in his bookcase. He has
already put 74 books in the bookcase but he has
225 books. How many more books does he have to
put in the bookcase?
Answer:
151
Step-by-step explanation:
because 225-74 =151
151 books
There are 225 books, and 74 have already been placed on the shelf. Subtract 225 minus 74 to find that Ivan needs to place 151 more books on the shelf.
A survey find that 61% of people are married. They ask the same group of people and 75% of them have at least one kid. If 48% are married and have one kid what is probability that a person in a survey is married or has a child?
Answer:
22/25
Step-by-step explanation:
The overlap between the 61% and the 75% is the 48%, which means that 13% of the people are married and have no kids (61-48=13)
The 75% includes the people who have one or more kids, and the people who have one or more kids and are married.
Now all we have to do is 13% + 75% = 88% = 22/25
Using Venn probabilities, it is found that there is a 0.88 = 88% probability that a person in a survey is married or has a child.
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In this question, the events are:
Event A: Person is married.Event B: Person has a child.The probabilities are given by:
[tex]P(A) = 0.61, P(B) = 0.75, P(A \cap B) = 0.48[/tex]
Hence:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]P(A \cup B) = 0.61 + 0.75 - 0.48[/tex]
[tex]P(A \cup B) = 0.88[/tex]
0.88 = 88% probability that a person in a survey is married or has a child.
More can be learned about Venn probabilities at https://brainly.com/question/25698611
Find the Exact value of each equation between [tex]0\leq theta\leq2\pi[/tex]
15) [tex]cos(-\frac{13\pi }{3} )[/tex]
16)[tex]csc(\frac{23\pi }{4}[/tex])
17)[tex]sec-(\frac{7\pi }{2}[/tex])
18)[tex]cot(-\frac{29\pi }{6}[/tex])
Use the fact that the co/sine functions are [tex]2\pi[/tex]-periodic and that the tangent function is [tex]\pi[/tex]-periodic. Also, recall that [tex]\cos x[/tex] is even (so that [tex]\cos(-x)=\cos x[/tex]) and [tex]\sin x[/tex] is odd (so that [tex]\sin(-x)=-\sin x[/tex].
15.
[tex]\cos\left(-\dfrac{13\pi}3\right)=\cos\dfrac{13\pi}3=\cos\left(\dfrac\pi3+4\pi\right)=\cos\dfrac\pi3=\boxed{\dfrac12}[/tex]
16.
[tex]\sin\dfrac{23\pi}4=\sin\left(\dfrac{3\pi}4+5\pi\right)=\sin\left(\dfrac{3\pi}4+\pi\right)=\sin\dfrac{7\pi}4=-\dfrac1{\sqrt2}[/tex]
[tex]\implies\csc\dfrac{23\pi}4=\boxed{-\sqrt2}[/tex]
17.
[tex]\cos\left(-\dfrac{7\pi}2\right)=\cos\dfrac{7\pi}2=\cos\left(\dfrac\pi2+3\pi\right)=\cos\left(\dfrac\pi2+\pi\right)=\cos\dfrac{3\pi}2=0[/tex]
[tex]\implies\sec\left(-\dfrac{7\pi}2\right)=\boxed{\text{undefined}}[/tex]
18.
[tex]\tan\left(-\dfrac{29\pi}6\right)=\dfrac{\sin\left(-\frac{29\pi}6\right)}{\cos\left(-\frac{29\pi}6\right)}=-\dfrac{\sin\frac{29\pi}6}{\cos\frac{29\pi}6}[/tex]
[tex]\sin\dfrac{29\pi}6=\sin\left(\dfrac{5\pi}6+4\pi\right)=\sin\dfrac{5\pi}6=-\dfrac12[/tex]
[tex]\cos\dfrac{29\pi}6=\cos\dfrac{5\pi}6=\dfrac{\sqrt3}2[/tex]
[tex]\implies\tan\left(-\dfrac{29\pi}6\right)=-\dfrac{-\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}[/tex]
[tex]\implies\cot\left(-\dfrac{29\pi}6\right)=\boxed{\sqrt3}[/tex]
Can the three segments below form a triangle
Answer:
Step-by-step explanation:
The sum of the two shorter sides must be greater than the longest side.
5 + 8 = 13
13 is not greater than 14, so the three segments cannot form a triangle.
Answer: No
Step-by-step explanation:
A triangle can be formed only if the sum of 2 sides of the triangle is bigger than the length of the third side of this triangle.
In this case we have AB = 5, BC = 8 and AC = 14.
AB + AC > BC → 5 + 14 > 8 →1 9 > 8 ok!
AB + BC > AC → 5 + 8 > 14 → 13 > 14 false!
BC + AC > AB → 8 + 14 > 5 → 22 > 8 ok!
As we have that AB + BC > AC FALSE, this segments cannot form a triangle.
Find the perimeter of an isosceles triangle ABC. Side AB=4, and the base BC=3. Angles B & C are both 70 degrees.
Answer:
11 units
Step-by-step explanation:
Since ∆ABC is isosceles, it means that at least two sides are congruent/equal in length.
Sides CA and AB are congruent, since BC is the base. So, CA = 4.
That means the perimeter is 4 + 4 + 3 = 11 un
A company that produces video games has hired you to set the sale price for its newest game. based on the production costs and consumer demands , the company has concluded that the equation p(x) = -0.3x^2 + 45x - 1000 represents the profit p (in dollars) for x individual games sold. What will the company's profit be if 100 games are sold?
Answer: 500 dollars
You just plug in 100 to the x’s in the equation
The company's profit be if 100 games are sold is $41100
The profit function is given as:
[tex]p(x) = -0.3x^2 + 45x - 1000[/tex]
When the number of games is 100, it means that
x = 100
So, we substitute 100 for x in the profit function
[tex]p(x) = -0.3x^2 + 45x - 1000[/tex] becomes
[tex]p(100) = -0.3(100)^2 + 45(100) - 1000[/tex]
Evaluate the exponents
[tex]p(100) = -0.3(10000) + 45(100) - 1000[/tex]
Open all brackets
[tex]p(100) = -3000 + 45100 - 1000[/tex]
Evaluate like terms
[tex]p(100) = 41100[/tex]
Hence, the company's profit be if 100 games are sold is $41100
Read more about quadratic functions at:
https://brainly.com/question/11441586
Kane is saving money. He starts with $14. The next day he has $21 and the third day he has $28. Assuming this pattern continues, what is the equation for the nth term of the arithmetic sequence?
Answer:
x+7
Step-by-step explanation:
let x= the amount of money he got that day
he gains $7/day
x+7
5(x+y)-3(y/x) plz help me
Answer:
[tex]\large\boxed{5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}}[/tex]
Step-by-step explanation:
[tex]5(x+y)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=5x+5x\\\\3\left(\dfrac{y}{x}\right)=\dfrac{3y}{x}\\\\5(x+y)-3\left(\dfrac{y}{x}\right)=5x+5y-\dfrac{3y}{x}[/tex]
write the comparison below as a ratio in it's simplest form using a fraction, a colon and the word to. _____ 15 dollars to 27 dollars
Answer:
Step-by-step explanation:
15/27 - 5/9
5:9
5 to 9 ratio
2. What percent of rolling a 2
3 probability of getting HH
Answer:
2. The correct answer option is 25%.
3. The experimental probability is 3% greater than the theoretical probability.
Step-by-step explanation:
2. We are given that a number cube is rolled 20 times out of which 5 times it lands on the number 2.
We are to find the experimental probability of getting the number 2.
P (2) = [tex]\frac{5}{20} \times 100 =\frac{1}{4} \times 100[/tex] = 25%
3. The theoretical Outcomes are: HH HT TH TT
So theoretical probability of getting HH = [tex]\frac{1}{4} \times 100[/tex] = 25%
Total number of outcomes = [tex]28+22+34+16[/tex] = 100
So experimental probability of getting HH = [tex]\frac{28}{100} \times 100[/tex] = 28%
Therefore, the experimental probability is 3% greater than the theoretical probability.
Which is the better buy?
A. 3-yard piece of cotton cloth for $4.41
B. 3-foot piece of cotton cloth for $1.05
Answer:
Step-by-step explanation:
It’s is a because if you divide 4.41 divide by 3 you will get 1.47
Step-by-step explanation:
1 yard = 3 feet
So 3 yards = 9 feet
$4.41 / 9 feet = $0.49 per foot
$1.05 / 3 feet = $0.35 per foot
The second one is cheaper, so that's the better buy.
Find k and the roots if
3x^2+kx+4=0 and the sum of the roots is 3
Answer:
k = -9roots: (9±√33)/6Step-by-step explanation:
In the form ...
ax^2 +bx +c = 0
the sum of the roots is -b/a. Here, that is -k/3. You want that value to be 3, so we have ...
-k/3 = 3
k = -9
__
The solution can be found by completing the square. We choose to start by making the leading coefficient be 1.
x^2 -3x +4/3 = 0
(x^2 -3x +9/4) + (4/3 -9/4) = 0 . . . . . . . add and subtract (3/2)^2
(x -3/2)^2 = 11/12 . . . . . . . . . . . . . . . . . . add 11/12, write as square
x = 3/2 ± √(11/12) = (9±√33)/6 . . . . . . . .simplify
simplify
[tex](x^{2} + 3x - 4) + (4^{2} - 5) - (7x + 3)[/tex]
X^2-4x+4 is the answer, to save you points next time, use an app called M8thw8y
First you want to drop the parenthesis. If there is a “+” sign, you do not have to change anything. If there is a “-“ sign, you have to distribute the negative in order to simplify, so imagine you are distributing -1 to 7x + 3 to make it -7x -3.
So, you now have x^2 + 3x - 4 + 16 -5 - 7x -3. (I evaluated the 4^2 to 16)
Now, what you want to do now is to combine like terms. Notice that there is only one x^2, so it is the same. There are two terms that have “x”. 3x and -7x react like normal numbers and they form -4x. The numbers who don’t have x on them you combine like terms.
Answer is x^2 - 4x - 12
Determine whether f(x) = -5x2 - 10x + 6 has a maximum or a minimum
value. Find that value and explain how you know.
Answer:
The function has a maximum
The maximum value of the function is
[tex]f (-1) = 11[/tex]
Step-by-step explanation:
For a quadratic function of the form:
[tex]ax ^ 2 + bx + c[/tex] where a, b and c are the coefficients of the function, then:
If [tex]a <0[/tex] the function has a maximum
If [tex]a> 0[/tex] the function has a minimum value
The minimum or maximum value will always be at the point:
[tex]x=-\frac{b}{2a}\\\y=f(-\frac{b}{2a})[/tex]
In this case the function is: [tex]f(x) = -5x^2 - 10x + 6[/tex]
Note that
[tex]a = -5,\ a <0[/tex]
The function has a maximum
The maximum is at the point:
[tex]x=-\frac{-10}{2(-5)}[/tex]
[tex]x=-1[/tex]
[tex]y=f(-1)[/tex]
[tex]y= -5(-1)^2 - 10(-1) + 6[/tex]
[tex]y= 11[/tex]
The maximum value of the function is
[tex]f (-1) = 11[/tex]
The function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum value at the vertex of its parabola. The maximum value is f(x) = 11 when x = -1.
To determine whether the quadratic function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum or a minimum value, we need to examine the coefficient of the [tex]x^2[/tex]term. The general form of a quadratic function is [tex]f(x) = ax^2 + bx + c.[/tex] If 'a' is negative, the parabola opens downwards, and the function has a maximum value at its vertex. In this case, 'a' is -5, which is negative, so the function has a maximum value.
To find the vertex of the parabola, we use the formula for the x-coordinate of the vertex, which is given by -b/(2a). Here, a = -5 and b = -10. Plugging these values into the formula gives us:
x = -(-10) / (2 * (-5))
x = 10 / -10
x = -1
Now that we have the x-coordinate of the vertex, we can find the y-coordinate (the maximum value) by substituting x = -1 into the original function:
[tex]f(-1) = -5(-1)^2 - 10(-1) + 6[/tex]
f(-1) = -5(1) + 10 + 6
f(-1) = -5 + 10 + 6
f(-1) = 5 + 6
f(-1) = 11
Therefore, the maximum value of the function [tex]f(x) = -5x^2 - 10x + 6[/tex] is 11 when x = -1. This is the value at the vertex of the parabola, confirming that it is the maximum value since the parabola opens downwards.
is 3-6x=y proportional
Answer:
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
The equation of a proportional relation is of the form
y = kx,
where k is a number.
Here you have
3 - 6x = y,
which can be rewritten as
y = -6x + 3
Because of the +3, your equation is not for the form y = kx, and it is not a proportional relation.
find the measure of an angle between 0 and 360 coterminal coterminal with the given angle 495 degrees
Answer:
135 degrees
Step-by-step explanation:
Coterminal means it ends at the same spot around the circle.
To calculate the resulting angle we need to reduce/increase the started value to arrive to a value between 0 and 359 degrees.
If the starting angle is greater or equal to 360, we subtract 360 until we get below 360.
If the starting angle is below 0, we add 360 until we get equal or greater than 0.
So, starting with 495, we subtract 360 a first time....
A = 495 - 360 = 135
We're already in the desired range (0-359)... so we have our answer.
In the diagram, what is the measure, of
For this case we have that by definition, a flat angle is the space included in an intersection between two straight lines whose opening measures 180 degrees.
Now, according to the figure we have that from V to S there are 180 degrees, like this:
[tex]5x + 25x + 30 = 180[/tex]
We add similar terms:
[tex]30x + 30 = 180[/tex]
Subtracting 30 from both sides of the equation:
[tex]30x = 150[/tex]
Divide by 30 on both sides of the equation:
[tex]x = \frac {150} {30}\\x = 5[/tex]
Answer:
[tex]x = 5[/tex]
In a marathon 90% runner were managed to complete it and 30% were men if 270 men completed it how many total runner began the marathon
Answer:
1000 runners
Step-by-step explanation:
Take total number of runners to be -----------x
90% of x managed to complete the marathon= 90/100 × x =0.9x
30% of those who completed the marathon were men= 30% × 0.9x
=0.3×0.9x= 0.27x
=270 men completed the marathon; this means
0.27x=270--------------------------------find x by dividing both sides by 0.27
x= 270/0.27
x=1000 runners
Answer:
1000
Step-by-step explanation:
Given : In a marathon 90% runner were managed to complete it and 30% were men.
To Find: If 270 men completed it how many total runner began the marathon.
Solution:
Let x be the number of total runners
Now we are given that 90% runner were managed to complete it
So, number of runners managed to complete = [tex]90\% \times x =\frac{90}{100}x=0.9x[/tex]
Now we are given that out of 90% , 30% were men
So, Numbers of men runners = [tex]30\% \times 0.9x=\frac{30}{100} \times 0.9x =0.27x[/tex]
Now we are given that 270 men completed it
So, [tex]0.27x=270[/tex]
[tex]x=\frac{270}{0.27}[/tex]
[tex]x=1000/tex]
Hence 1000 runners began the marathon.
Which of the following piecewise functions is graphed above?
The answer is:
The piecewise function that represents the graph, is the option A (first option):
f(x) (piecewise function):
[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]
Why?To find the correct option, we need to look for the piecewise function that contains the following functioncs existing in the determined domains (inputs).
From the graph, we know that we need the following functions:
- A horizontal line, which exists from -∞ to -1, givind as input 8.
The function will be:
[tex]y=8[/tex]
Then, the piecewise function it will be:
[tex]8; x\leq -1[/tex]
- A quadratic function (convex parabola) which y-intercept is equal to 1, exists from -1 to 5, and it vertex (lowest point for this case) is located at (2,-3)
The function will be:
[tex]y=x^{2}-4x+1[/tex]
Finding the y-intercept, we have:
[tex]y=0^{2}-4*80)+1[/tex]
[tex]y=1[/tex]
Finding the vertex of the parabola, we have:
[tex]x_{vertex}=\frac{-b}{2}\\\\x_{vertex}=\frac{-(-4)}{2}=\frac{4}{2}=2[/tex]
[tex]y_{vertex}=x_{vertex}^{2}-4x_{vertex}+1[/tex]
[tex]y_{vertex}=2^{2}-4*2+1=4-8+1=-3[/tex]
The vertex of the parabola is located at the point (2,-3).
Then, for the piecewise function it will be:
[tex]x^{2} -4x+1;-1<x<5[/tex]
- A negative slope function, which evaluated at x equal to 5 (input), gives as output -4.
The function will be:
[tex]y=-x+1[/tex]
Proving that it's the correct equation by evaluating "x" equal to 5, we have:
[tex]y=-5+1[/tex]
[tex]y=-4[/tex]
It proves that the equation is correct.
Then, for the piecewise function it will be:
[tex]-x+1\geq 5[/tex]
Hence, we have that the piecewise function that represents the graph, is the option A (first option):
f(x) (piecewise function):
[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]
Have a nice day!
Four expressions are shown below:
4(8x + 2)
4(7x + 3)
32x + 8
28x + 12
Which two expressions are equivalent to 4(7x + 2 + x)?
It’s the first one and the third one
Answer: A and C
Step-by-step explanation: