The expression square root 3x is equivalent to the expression x square root 3
True
False
Answer:
Second option: False
Step-by-step explanation:
We need to remember this property:
[tex]\sqrt[n]{x^n}=x^{\frac{n}{n}}=x[/tex]
In this case we have the following expressions provided in the exercise:
[tex]\sqrt{3x}[/tex] and [tex]x\sqrt{3}[/tex]
Based on the property mentioned before the expression [tex]\sqrt{3x}[/tex] cannot be simplified. So 3 and [tex]x[/tex] stays inside the square root.
Therefore, the conclusion is: The expression [tex]\sqrt{3x}[/tex] is not equivalent to the expression [tex]x\sqrt{3}[/tex]
Deciphering the expressions reveals that 'square root 3x' is not equivalent to 'x square root 3'. They interpret differently on the terms inside and outside of the square root, thus they are not the same.
Explanation:The statement 'the expression square root 3x is equivalent to the expression x square root 3' is False. To understand why, we need to understand the properties of square roots and multiplication. The expression square root 3x means that the square root is being taken over the entire product of 3x. This is not the same as x square root 3, where the square root is only being applied to 3, and then that result is being multiplied by x.
Learn more about Square Roots here:https://brainly.com/question/29286039
#SPJ3
1. From a total yearly budget of
$360,000, the Kimball Foundation
spends $30,000 on leasing office
space. What is the ratio of dollars
spent on office space to dollars spent
on other costs?
A. 12:1
B. 11:1
C. 1:11
D. 1:12
Answer:
Option C. 1:11
Step-by-step explanation:
Let
x-----> dollars spent on office space
y ----> dollars spent on other costs
we know that
x+y=$360,000 -----> equation A
x=$30,000 ----> equation B
substitute equation B in equation A and solve for y
30,000+y=360,000
y=360,000-30,000=$330,000
Find the ratio of dollars spent on office space to dollars spent on other costs
Divide the dollars spent on office space by the dollars spent on other costs
so
x/y
substitute
30,000/330,000=1/11
An animal shelter estimates that it costs about $6 per day to care for each dog. If y represents the total cost of caring for a single dog for x days, which table models the situation?
Answer:
x y
6 36
9 54
12 72
Step-by-step explanation:
The options are shown in the pictures attached.
Data:
a single dog costs about $6 per day
y-variable represents the total cost
x-variable represents days
So, 1 day costs $6, 2 days costs 2*$6 = $12, 3 days costs 3*$6 = $18 and so on. Then, the table is:
x y
6 6*6 = 36
9 9*6 = 54
12 12*6 = 72
Jack and Jillian sell apples at a produce stand. Jillian earns $2 for each bag of apples she sells. At the end of the week, Jack has earned $8 less than Jillian. The following expression shows Jack's earnings: 2x − 8 In the expression, what does the first term represent? Jack's earnings at the end of the week The number of bags of apples Jillian sold Jillian's earnings at the end of the week The number of bags of apples Jack sold
Answer:
The first term (2x) represents Jillian's earnings at the end of the week. Where the 2 represents the amount of money she earns per pag, and the 'x' is the number of bags sold.
Let us explain this with an example: if Jillian sells 36 bags, then she will earn 2×36 = $72
Answer:
option C is true.
Step-by-step explanation:
We are given that Jack and Jillian sell apples at a produce stand .
We are given that an expression which shows Jack's earning=2x-8
We have to find that first term what represent in the given expression
Jillian earns for each bag of apples she sells=$2
Let Jillian sold number of bags of apples =x
Then ,Jillian earn total at the end of the week =[tex]2\timesx=$2x[/tex]
Jack has earned $ 8 less than Jillian earn
Therefore, total earning of jack=[tex]2x-8[/tex]
In the given expression the first term 2x represent the earning of Jillian.
Hence, option C is true.
Answer: C: JIllian's earning at the end of the week
Don’t understand this word problem!!!
Answer:
b) L+S=80 and 2.75L+3.25S=245
Step-by-step explanation:
L stands for larger softballs. S stands for smaller softballs.
If you are ordering 80 softballs, then L and S represent the number of softballs of each one (large or small) to get a total of 80.
2.75 is the price of a large softball
3.25 is the price of a small softball.
You multiply the amount of each softball to how many of those kinds of softballs you get, you will then get the sum of the amount you ordered for 80 softballs: 245 dollars.
So thus the answer is B
Answer:
L+S=80
2.75L+3.25S=245
Choice B
Step-by-step explanation:
Larger ball costs $2.75.
Smaller ball costs $3.25.
You order a total of 80 softballs for $245.
So L is for number of large balls.
S is for number of small balls.
So we have 80 balls in all, some are small and some are large. This means the number of large plus the number of small equals 80.
So we have this equation L+S=80.
Now if you buy L balls, you spend 2.75 times L on large balls altogether.
If you buy S balls, you spend 3.25 times S on small balls altogether.
So together you spend 2.75L+3.25S. They gave us that this amount should be equal to 245.
So this equations is 2.75L+3.25S=245
We are looking for the choice that contains these equations:
L+S=80
2.75L+3.25S=245
If f(x)=2x^2+3x−4, and g(x)=−8x−4, what does f(x)+g(x) equal?
f(x)=2x^2+5x+8
f(x)=2x^2−5x−8
f(x)=2x^2+11x−8
f(x)=2x^2+5x
[tex]\( f(x) + g(x) \) equals \( 2x^2 - 5x - 8 \).[/tex] (option b)
To find [tex]\( f(x) + g(x) \)[/tex], we need to add the functions f(x) and g(x):
[tex]\[ f(x) + g(x) = (2x^2 + 3x - 4) + (-8x - 4) \][/tex]
[tex]\[ = 2x^2 + 3x - 4 - 8x - 4 \][/tex]
[tex]\[ = 2x^2 + (3x - 8x) + (-4 - 4) \][/tex]
[tex]\[ = 2x^2 - 5x - 8 \][/tex]
Therefore, the correct answer is:
[tex]\[ f(x) = 2x^2 - 5x - 8 \][/tex]
Complete question: If f(x)=2x²+3x−4, and g(x)=−8x−4, what does f(x)+g(x) equal?
a-f(x)=2x²+5x+8
b-f(x)=2x²−5x−8
c-f(x)=2x²+11x−8
d-f(x)=2x²+5x
What is the value of b in the equation below: 5^6/5^2=a^b
Step-by-step explanation:
for x^a/x^b = x^(a-b)...eqn 1
thus for 5^6/5^2 = a^b,
if a = 5, following eqn 1...
then b = 6-2 = 4
What is the value of 4a^3–2b^2+5 when a = 3 and b =–2
Answer:
105
Step-by-step explanation:
Evaluate 4 a^3 - 2 b^2 + 5 where a = 3 and b = -2:
4 a^3 - 2 b^2 + 5 = 4×3^3 - 2×(-2)^2 + 5
3^3 = 3×3^2:
4×3×3^2 - 2×(-2)^2 + 5
3^2 = 9:
4×3×9 - 2×(-2)^2 + 5
3×9 = 27:
4×27 - 2×(-2)^2 + 5
(-2)^2 = 4:
4×27 - 24 + 5
4×27 = 108:
108 - 2×4 + 5
-2×4 = -8:
108 + -8 + 5
| | 1 |
| 1 | 0 | 8
+ | | | 5
| 1 | 1 | 3:
113 - 8
| | 0 | 13
| 1 | 1 | 3
- | | | 8
| 1 | 0 | 5:
Answer: 105
Answer:
105
Step-by-step explanation:
4a^3 -2b^2 +5
Let a=3 and b= -2
4 (3)^3 -2 (-2)^2 +5
4 *27 -2 (4) +5
108 -8+5
105
Which sequence is modeled by the graph below? (1 point) coordinate plane showing the points 1, 5; 2, 0.5; and 3, 0.05 an = 5(−10)n − 1 an = 0.5(10)n − 1 an = one tenth (5)n − 1 an = 5( one tenth )n − 1
Answer:
[tex]\large\boxed{a_n=5\left(\dfrac{1}{10}\right)^{n-1}}[/tex]
Step-by-step explanation:
Check:
[tex]n=1\\\\a_1=5\left(\dfrac{1}{10}\right)^{1-1}=5\left(\dfrac{1}{10}\right)^0=5(1)=5\qquad\bold{CORRECT}\ (1,\ 5)\\\\n=2\\\\a_2=5\left(\dfrac{1}{10}\right)^{2-1}=5\left(\dfrac{1}{10}\right)^1=5\left(\dfrac{1}{10}\right)=\dfrac{5}{10}=0.5\qquad\bold{CORRECT}\ (2,\ 0.5)\\\\n=3\\\\a_3=5\left(\dfrac{1}{10}\right)^{3-1}=5\left(\dfrac{1}{10}\right)^2=5\left(\dfrac{1}{100}\right)=\dfrac{5}{100}=0.05\qquad\bold{CORRECT}\ (3,\ 0.05)[/tex]
[tex]a_{n}[/tex] [tex]= 5 (\frac {1}{10} )^{n-1}[/tex]
Mathematical sequences are the set of numbers that makes a pattern or can be simple and complicated, finite and infinite. Explore sequences, terms in a sequence, and the different kinds of mathematical sequences, including the famous Fibonacci sequence.
Check:
n=1
[tex]a_{1} = 5 (\frac {1}{10} )^{1-1} = 5 (\frac {1}{10} )^{0} = 5 (1)=5[/tex] True (1,5)
n=2
[tex]a_{2} = 5 (\frac {1}{10} )^{2-1} = 5 (\frac {1}{10} )^{1} = 5 \frac{1}{10} = 0.5[/tex] True (2, 0.5)
n=3
[tex]a_{3} = 5 (\frac {1}{10} )^{3-1} = 5 (\frac {1}{10} )^{2} = 5 \frac{1}{100} = 0.05\\[/tex] True (3, 0.05)
sequence chart is a series of the events and actions set in the order in which they take place. this is considered to be a fantastic way to represent the necessary steps taken to reach to the outcome.
Learn more about the sequence chart here https://brainly.com/question/444154?
#SPJ2
Which ratio is equivalent to 8:6
Answer:
4:3
Step-by-step explanation:
You divide 8 and 6 by 2 to simplify it
Will mark brainliest, please answer :)
The question is in the picture above
Answer:
6√10 ≈ 19.0
Step-by-step explanation:
The length of the diagonal is:
d² = w² + l² + h²
Given d = 36, l = 30, and h = 6:
36² = w² + 30² + 6²
1296 = w² + 900 + 36
w² = 360
w = 6√10
w ≈ 19.0
The box should be approximately 19 inches wide.
what is
x+y+z=8
3x+y-z=4
4x-y+2z+6
[1, 4, 3]
Solve for the first variable in one of the equations, then substitute the result into the other equation.
**For more information on how to solve a system of equations in three variables, paste and copy this link:
https://youtu.be/zcC7wsn3b2g
Subscribe to my channel [USERNAME: MATHEMATICS WIZARD].
I am joyous to assist you anytime.
***By the way, in the final line, that "+" next to the 6 should be replaced with an "=".
Anja divides (8x3 - 36x2 + 54x - 27) by (2x - 3) as shown below. What error does Anja make?
4x2 - 12x+9
2x-3) 8x2 – 36x2 + 54x-27
8x3–1282
-24x2 + 54 x
-24x2 + 36%
18x-27
18x+27
-54
She makes a subtraction error
She makes an error choosing the x-term in the quotient.
She makes a multiplication error
She makes an error rewriting the problem in long division
Answer:
There is a multiplication error
Step-by-step explanation:
Long division method is used to divide greater number by a smaller number.
Here, greater number is known as the dividend and smaller number is known as divisor.
As per division algorithm,
Dividend = Divisor [tex]\times[/tex] quotient + remainder
Here, dividend = [tex]8x^3-36x^2+54x-27[/tex]
Divisor = [tex]2x-3[/tex]
Here, we need to find the error in the long division .
In step:
[tex]18x+27[/tex] , it should be 18x-27 as [tex]-3\times 9=-27[/tex] not +27
So, there is a multiplication error .
The correct option is c) she makes a multiplication error.
Step-by-step explanation:
Given :
Dividend = [tex]8x^3-36x^2+54x-27[/tex]
Divisor = [tex]2x-3[/tex]
Solution :
In step [tex]18x +27[/tex] there is mistake. It should be [tex]18x - 27[/tex] because [tex]-3 \times 9= -27[/tex] not +27.
Therefore the correct option is c) she makes a multiplication error.
For more information, refer the below link
https://brainly.com/question/21416852?referrer=searchResults
Translate "the sum of 6 and the product of 8 and x” into a mathematical expression
The mathematical expression is 6 + 8x
The sum of 6 and the product of 8 and x can be written mathematically by first getting the product of 8 and x which equals 8x
Sum means addition( +)
So the sum of 6 is written as 6 +
We thus have the mathematical expression Translated as 6 + 8x
See related answer using this link: https://brainly.com/question/12593943
The mathematical expression for 'the sum of 6 and the product of 8 and x' is 6 + 8x.
Explanation:A mathematical expression is a combination of numbers, variables, and mathematical operators (e.g., +, -, *, /) that represents a calculation or relationship. Expressions can be simple, like 2x + 3, or complex, serving various purposes in mathematical modeling, calculations, and problem-solving.
To translate the phrase 'the sum of 6 and the product of 8 and x' into a mathematical expression, we can use the symbols and operations of algebra. The sum of 6 and the product of 8 and x can be written as 6 + 8x. Here, 8x represents the product of 8 and x, and the addition symbol, '+', represents the sum of 6 and 8x.
Learn more about Translating phrases into mathematical expressions here:https://brainly.com/question/29174775
#SPJ11
Round 20.155 to the nearest tenth
Answer:
20.2
The thousandth position doesn't affect the rounding of the numbers. Since the hundredth position contains a 5, you will round up, meaning the tenth position will change from a 1 to a 2.
Answer:
20.2
AMG Mark as brainlist!
(–1) + 5 – (–6) – 5 =
Answer:
5
Step-by-step explanation:
(-1) + 5 - (-6) - 5 =
v
4 - (-6) - 5 =
v
10 - 5 =
v
5
Evaluate P(5, 3). 15 20 60
Answer:
20.
Step-by-step explanation:
P(5,3) = 5! / 3!
= (5*4*3*2*1) / (3*2*1)
= 20.
A scale model of a rectangle building lot measures 7 ft by 5ft. Id the actual house will be built using a scale factor of 12. What is the area of the actual building lot?
Answer:
5040 ft^2
Step-by-step explanation:
The area of rectangle is: 7 ft by 5 ft
The scaling is done by multiplying the dimensions with the sale factor.
so,
The area of actual house will be:
(7*12) x (5*12)
= 84 * 60
= 5040 ft^2
So the area of actual building is 5040 ft^2 ..
which of the following is most likely the next step in the series?
HELP ME FAST PLEASE!!!!!!APEX
Answer:
A is most likely the next step in the series
Step-by-step explanation:
Each step, the number of sides is increasing by 1.
4,5,6 means that the next number of sides would be 7. Option A has 7 sides.
A, B, C, and D have the coordinates (-8, 1), (-2,4),(-3,-1) and (-6,5), respectively. Which sentence about the points is true?
A. A, B, C, and D lie on the same line
B. AB and CD are perpendicular lines.
c. Ag and are parallel lines.
D. AB and CD are intersecting lines but are not perpendicular.
E. AC and B are parallel lines.
Answer:
B. [tex]^\leftrightarrow_{AB}[/tex] and [tex]^\leftrightarrow_{CD}[/tex] are perpendicular lines.
Step-by-step explanation:
We can quickly plot the points in the cartesian plane as shown in the attachment.
A visual representation will help us see that A,B,C, and D do not lie on the same line.
The slope of AB is [tex]\frac{4-1}{-2--8} =\frac{3}{6}=\frac{1}{2}[/tex]
The slope of CD is [tex]\frac{5--1}{-6--3} =\frac{6}{-3}=-2[/tex]
The two slopes are negative reciprocals of each other.
It is true that line AB and line CD are perpendicular.
These two lines cannot be perpendicular and parallel at the same time.
It is also not possible that, the two lines are perpendicular but will not intersect
Therefore the correct choice is B
Answer:
B
Step-by-step explanation:
plato/edmentum
Which equation is equivalent to 2^4x = 8^x-3?
2^4x = 2^2x-3
2^4x = 2^2x-6
2^4x = 2^3x-3
2^4x = 2^3x-9
Answer:
[tex]\large\boxed{2^{4x}=2^{3x-9}}[/tex]
Step-by-step explanation:
[tex]8=2^3\to 8^{x-3}=(2^3)^{x-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{3(x-3)}\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=2^{(3)(x)+(3)(-3)}=2^{3x-9}[/tex]
If you want a solution of this equation:
[tex]2^{4x}=8^{x-3}\\\\2^{4x}=2^{3x-9}\iff4x=x-3\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x=-3\qquad\text{divide both sides by 3}\\\\x=-1[/tex]
Answer: the correct option is
(D) [tex]2^{4x}=2^{3x-9}.[/tex]
Step-by-step explanation: We are given to select the correct equation that is equivalent to the following equation :
[tex]2^{4x}=8^{x-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Equivalent equations means two equations that can be obtained from one another using some properties of formula.
We will be using the following formula :
[tex](a^b)^c=a^{b\times c}.[/tex]
From equation (i), we have
[tex]2^{4x}=8^{x-3}\\\\\Rightarrow 2^{4x}=(2^3)^{x-3}\\\\\Rightarrow 2^{4x}=2^{3\times(x-3)}\\\\\Rightarrow 2^{4x}=2^{3x-9}.[/tex]
Thus, the required equivalent equation is [tex]2^{4x}=2^{3x-9}.[/tex]
Option (D) is CORRECT.
Which expression is equivalent to (2mn)^4/6m^-3n^-2? assume m and n cannot equal 0
Answer:
=8/3m⁷n⁶
Step-by-step explanation:
Given the expression (2mn)⁴/6m⁻³n⁻², we first solve the numerator
(2mn)⁴ = 16m⁴n⁴
The new expression becomes 16m⁴n⁴/6m⁻³n⁻²
We now divide the coefficients and the exponents as follows:
=16/6ₓ(m⁴/m⁻³)×(n⁴/n⁻²)
Division between indices to the same base we subtract the powers.
4-⁻3=7
4-⁻2=6
=8/3m⁷n⁶
Answer:
the asnwer is A
Step-by-step explanation:
Given that (-3,7) is on the graph of f(x), find the
corresponding point for the function f- 3/4x
Answer:(4, 7)
Step-by-step explanation:
This question is about changing the coordinates of the function.
They want you to choose a value of x that will make the sentence inside the function (-3x/4) equal to -3.
-3 x / 4 = -3
x = 4
Hence, the correspondig point is (4, 7)
Select the correct answer.
Which set of vertices forms a parallelogram?
A.
A(2, 4), B(3, 3), C(6, 4), D(5, 6)
B.
A(-1, 1), B(2, 2), C(5, 1), D(4, 1)
C.
A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)
D.
A(-1, 2), B(1, 3), C(5, 3), D(1, 1)
Answer:
Step-by-step explanation:
Option 3 is correct
A(-5, -2), B(-3, 3), C(3, 5), D(1, 0) set of vertices forms a parallelogram
Step-by-step explanation:
Slope formula is given by:
slope = y2-y1
over x2-x1
Properties of the parallelogram:
Opposite sides are equal and parallel.Diagonals are unequalSlope of the opposite sides are equal.Opposite angles are equal.Consider the set of vertices:A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)
⇒Slope of AB =Slope of CD and Slope of BC = Slope of AD
By property of parallelogram:
⇒A(-5, -2), B(-3, 3), C(3, 5), D(1, 0) set of vertices forms a parallelogram
Answer: OPTION C.
Step-by-step explanation:
A parallelogram is defined as a quadrilateral which has two pairs of parallel sides.
Attached is shown in the parallelogram obtained by plotting the vertices provided in Option C.
If that figure is a parallelogram, then:
[tex]Slope\ AB=Slope\ CD\\\\Slope\ BC=Slope\ AD[/tex]
Let's check this:
[tex]Slope\ AB=\frac{-2-3}{-5-(-3)}=\frac{5}{2}[/tex]
[tex]Slope\ CD=\frac{0-5}{1-3}=\frac{5}{2}[/tex]
[tex]Slope\ BD=\frac{3-5}{-3-3}=\frac{1}{3}[/tex]
[tex]Slope\ DA=\frac{-2-0}{-5-1}=\frac{1}{3}[/tex]
Therefore, the set of vertices that forms a parallelogram is:
[tex]A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)[/tex]
Lisa's barn has 20 animals that have 62 legs in total. She only has cows and geese. How many cows and how many geese does she have?
Answer:
9 geese
11 cows
Step-by-step explanation:
Say x is cows, and y is geese.
x + y = 20 animals
x * 4 + y * 2 = 62
x = 20 - y
(20 - y) * 4 + y * 2 = 62
80 - 4y + 2y = 62
- 2y = -18
y = 9 geese
x = 20 - 9 = 11 cows
Lisa has 11 cows and 9 geese.
To solve the problem involving Lisa's barn with 20 animals having 62 legs in total, and knowing she only has cows and geese, we can use a system of linear equations. We can denote the number of cows as c and the number of geese as g. Cows have 4 legs and geese have 2 legs.
We can then set up the following equations based on the information given:
Cows and geese equation: c + g = 20 (since there are 20 animals in total)
Legs equation: 4c + 2g = 62 (because cows have 4 legs and geese have 2 legs)
Now, let's solve the system of equations:
Multiply the first equation by 2 to match the number of geese legs in the second equation: 2c + 2g = 40
Subtract the modified first equation from the legs equation: (4c + 2g) - (2c + 2g) = 62 - 40, which simplifies to 2c = 22, and then c = 11. Lisa has 11 cows.
Substitute the number of cows back into the first equation to find the number of geese: 11 + g = 20, which leads to g = 9. Lisa has 9 geese.
Therefore, Lisa has 11 cows and 9 geese.
What is the equation of the line that passes through the point (-1, -3) and has a slope of -5?
A) y=-5x-8
B) y=-5x-16
C) y=-5x+16
D) y=-5x+8
Answer:
A) y = -5x - 8Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have the slope m = -5, and the point (-1, -3). Substitute:
[tex]y-(-3)=-5(x-(-1))\\\\y+3=-5(x+1)[/tex]
Convert to the slope-intercept form (y = mx + b):
[tex]y+3=-5(x+1)[/tex] use the distributive property
[tex]y+3=-5x-5[/tex] subtract 3 from both sides
[tex]y=-5x-8[/tex]
HELP ASAP!!!! Please tell me the steps and answer on how to do it.
Answer:
71.4
Step-by-step explanation:
For this, we will use Heron's Formula, or
[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex],
with p as the perimeter divided by 2, and a, b, and c are the side lengths.
Plugging our values in, (11.6+20+13)/2 = 22.3 = p, and
[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex] = [tex]\sqrt{5103.8679} =71.4[/tex] rounded to the nearest tenth
Your income last year was $27,000 from your main job, $2,200 from a part time job and $600 from interest earned on investments. If your state income tax is 3% of your gross income, what was your state tax for last year?
Answer:
$894
Step-by-step explanation:
$27,000+$2,200+$600= $29,800
$29,800*0.03=$894
Make a table with the domain of {2,3,4,5,6} and draw a graph of the absolute value function y = 2|x-4| + 3.
Answer:
Table for y = 2|x-4| + 3 on domain {2,3,4,5,6} is given as:
x y
2 2|x-4| + 3 = 2|2-4| + 3 = 7
3 2|x-4| + 3 = 2|3-4| + 3 = 5
4 2|x-4| + 3 = 2|4-4| + 3 = 3
5 2|x-4| + 3 = 2|5-4| + 3 = 5
6 2|x-4| + 3 = 2|6-4| + 3 = 7
The graph of the absolute value function y = 2|x-4| + 3 for the given domain is attached.
Step-by-step explanation:
The absolute value parent function, written as function(x) = | x |, is defined as:
|x| = x and |-x| = x
In our case;
For x = 2
y = 2|x-4| + 3
= 2|2-4| + 3
= 2|-2| + 3
= 2*2 + 3
= 4 + 3
= 7
Similarly, for all other values of x in the given domain, value of y can be calculated.
Answer:
In the attachment.Step-by-step explanation:
[tex]|a|=\left\{\begin{array}{ccc}a&for\ a\geq0\\-a&for\ a<0\end{array}\right[/tex]
Put each value of x from the set {2, 3, 4, 5, 6}
to the equation y = 2|x - 4| + 3:
x = 2 → y = 2|2 - 4| + 3 = 2|-2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (2, 7)
x = 3 → y = 2|3 - 4| + 3 = 2|-1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (3, 5)
x = 4 → y = 2|4 - 4| + 3 = 2|0| + 3 = 2(0) + 3 = 0 + 3 = 3 → (4, 3)
x = 5 → y = 2|5 - 4| + 3 = 2|1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (5, 5)
x = 6 → y = 2|6 - 4| + 3 = 2|2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (6, 7)
Mark the points in the coordinates system.
The domain is only five numbers, therefore the graph of this function is only five points.
Using the discriminant, how many real solutions does the following quadratic
equation have?
x^2 - 8x + 16 = 0
A. Three real solutions
B. No real solutions
C. Two real solutions
D. One real solution
Answer:
D one real solution
Step-by-step explanation:
x^2 - 8x + 16 = 0
This is in the form
ax^2 +bx + c = 0
so we can use the discriminant to determine the number of solutions
b^2 -4ac
(-8)^2 -4(1)(16)
64 - 64
0
Since the discriminant is zero, there is one real solution.