Answer:
No Real Solutions
Step-by-step explanation:
So we have:
[tex]x-2\sqrt{x-3}=0[/tex]
First, determine the domain restrictions. The expression under the radical cannot be less than 0. Therefore:
[tex]x-3\geq 0\\x\geq 3[/tex]
Therefore, our final answers must be greater than or equal to 3:
Now, going back to the original equation, subtract x from both sides:
[tex]-2\sqrt{x-3}=-x[/tex]
Now, square both sides:
[tex]4(x-3)=x^2[/tex]
Distribute:
[tex]4x-12=x^2[/tex]
Subtract 4x and add 12 to both sides:
[tex]0=x^2-4x+12[/tex]
This isn't factor-able. Let's use the quadratic formula. a is 1, b is -4 and c is 12:
[tex]x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute:
[tex]x=\frac{4\pm\sqrt{(-4)^2-4(1)(12)}}{2(1)}[/tex]
Simplify the radical:
[tex]x=\frac{4\pm\sqrt{-32}}{2(1)}[/tex]
The number under the radical is negative. In other words, there are no real solutions.
Simplify to create an equivalent expression. 8−4(−x+5) Choose 1 answer: A 4x−12 B −4x−12 C 4x+13 D 4x+5
Answer:
A (4x-12)
Step-by-step explanation:
Still think of PEMDAS: 8-4(-x=5)
a) Multiply -4(-x + 5)
* -4(-x) = 4x (remember a neg x neg = pos)
* -4(5) = - 20
b) Now it reads = 8 +4x - 20
c) put all like terms together
* 8 - 20 = -12
Which pairs of angles in the figure below are vertical angles?
Answer:
m∠BTD and m∠ATP
m∠ATN and m∠RTD
Answer:
ATN & RTD, BTD& ATP
Step-by-step explanation:
To find out which pairs of angles are vertical in the picture let's define it first
Vertical Angles: Opposite Angles
It can't be the first one because the angle vertical to RTP is BTN
ATN & RTD
It isn't the third option since the angle opposite to DTN is RTA
BTD& ATP
How do i solve this question?
Answer & step-by-step explanation:
Andy watches 10 television shows every week. He watches dramas, comedies, and reality shows. Dramas are 1 hour long, comedies are 30
minutes, and reality shows are 2 hours long. He spends 8 hours watching his shows and watches twice as many comedies as dramas. Which
system of equations could be used to determine how many of each type of show he watches each week?
Оа
b
d+C+r= 8 d + .5€ + 20 = 10 c = 2d
d+C+ r = 10 d + 5c + 2r = 8 d = 20
d+ C + r=10 d + 5c +2r = 8 C= 2d
d+C+ r = 8 d + C + 2r = 10 d = 20
с
d
Submit
Saved at 1:29 pm
Answer:
[tex]d+0.5c+2r=8\\\\ c=2d[/tex]
Step-by-step explanation:
Let d= dramas
c= comedies
r= reality shows
Dramas are 1 hour long, comedies are 30 minutes, and reality shows are 2 hours long.
Total time spent on watching = [tex]1 \times(d) + 0.5 \times (c) +2 \times(r)= d+0.5c+2r[/tex]
[ [tex]30\ minutes=\dfrac{30}{60} \ hours = 0.5 hour \ \ (1 hour = 60\ minutes)[/tex] ]
Since he spent 8 hours for this, that means
[tex]d+0.5c+2r=8[/tex] → First equation
He watches twice as many comedies as dramas.
i.e. [tex]c=2d[/tex] → second equation
So, the system of equations could be used to determine how many of each type of show he watches each week:
[tex]d+0.5c+2r=8\\\\ c=2d[/tex]
Joe’s boat rental rents paddle boats for $8.00 and the paddles rent for $5.00 for the day. If David has $45, what is the least amount of hours he could rent the paddle boat
Answer:
Well i haven't found the hours out because the problem doesn't specify how many hours you can rent the boat for. I did do the math and you can rent the boat and the paddles for 13 dollars. This means that David can rent the boat for 3 days and he will have 6 dollars left over. I hope this helped you.
What is the area of the figure composed of a parallelogram, a square and a rectangle ?
Answer : The area of the figure composed of a parallelogram, a square and a rectangle is 126 in².
Step-by-step explanation :
Area of composed figure = Area of parallelogram + Area of square + Area of rectangle
First we have to calculate the area of parallelogram.
Area of parallelogram = Base × Height
Given:
Base = 10 in
Height = 3.5 in
Area of parallelogram = 10 in × 3.5 in
Area of parallelogram = 35 in²
Now we have to calculate the area of square.
Area of square = (Side)²
Given:
Side = 4 in
Area of square = (4 in)²
Area of square = 16 in²
Now we have to calculate the area of rectangle.
Area of rectangle = Length × Breadth
Given:
Length = 12.5 in
Breadth = 6 in
Area of rectangle = 12.5 in × 6 in
Area of rectangle = 75 in²
Now we have to calculate the composed figure.
Area of composed figure = Area of parallelogram + Area of square + Area of rectangle
Area of composed figure = 35 in² + 16 in² + 75 in²
Area of composed figure = 126 in²
Therefore, the area of the figure composed of a parallelogram, a square and a rectangle is 126 in².
The area of the given figure is 126in²
Composite figuresThe given figure is a composite figure composed of a parallelogram, a square and a rectangle.
Get the area of the square
Area = L²
Area of the square = 4² = 16in²
Area of the rectangle = 6 * 12.5
Area of the rectangle = 75in²
For the parallelogram:
Area of the parallelogram = Base * Height
Area of the parallelogram = 10 * 3.5
Area of the parallelogram = 35 in²
Area of the figure = 75in² + 35in² + 16in²
Area of the figure = 126in²
Hence the area of the figure is 126in²
Learn more on area of composite figures here: https://brainly.com/question/10254615
Plz help ASAP WILL MARK YOU BRAINLIST IF UR ANSWER IS CORRECT Question #3
Answer: D
Step-by-step explanation:
A is a function because all quadratics are functions because it shows the graph of a parabola.
B is also a function because it is a quadratic equation
C is a function because it is a linear function
D which I don't know about doesn't looks like it represent a function.
it is given that 2/3, 8/d and n/39 are equivalent fractions. find the value of d and the value of n
Answer:
d = 12 and n = 26
Step-by-step explanation:
Given that the fractions are equivalent then
[tex]\frac{2}{3}[/tex] = [tex]\frac{8}{d}[/tex] ( cross- multiply )
2d = 24 ( divide both sides by 2 )
d = 12
--------------------------------------
and
[tex]\frac{2}{3}[/tex] = [tex]\frac{n}{39}[/tex] ( cross- multiply )
3n = 78 ( divide both sides by 3 )
n = 26
The fractions represent the same amount or value given that they are
equivalent.
The value of d is 12The value of n is 26Reasons:
Equivalent fractions are fractions that have equal values, therefore;
[tex]\displaystyle \frac{2}{3} = \frac{8}{d} =\frac{n}{39}[/tex]
Which by cross multiplying gives;
2 × d = 8 × 3 = 24
Therefore;
[tex]\displaystyle d = \frac{24}{2} = \mathbf{12}[/tex]
d = 12
Similarly, we have;
[tex]\displaystyle \frac{2}{3} =\frac{n}{39}= \frac{8}{d}[/tex]
Which gives;
2 × 39 = 3 × n
Therefore;
[tex]\displaystyle n = \frac{2 \times 39}{3} = \mathbf{26}[/tex]
n = 26
Learn more about equivalent fractions here:
https://brainly.com/question/13489708
which expression is equivalent to h+0.67h-0.36h
Answer:
= 1.31h
Step-by-step explanation:
h = 1h
then:
h + 0.67h 0.36h = (1+0.67-9.36)h
= 1.31h
HELP I NEED AN EXPLANATION IM CONFUSED |3x|>-12 is x>−4 or x<4 but I dont know how that is. I thought it was no solution.. can someone explain.
Answer:
see below (I hope this helps!)
Step-by-step explanation:
|3x| > -12
There are two cases, x is either positive (in which |3x| = 3x) or negative (in which |3x| = -3x). Therefore:
3x > -12 or -3x > -12
x > -4 or x < 4 (Remember, multiplying / dividing an inequality by a negative number flips the sign.)
Answer:
All real numbers.
Step-by-step explanation:
So we have the equation:
[tex]|3x|>-12[/tex]
Remove the absolute value bars. Definition of absolute value:
[tex]3x>(-12)\text{ or } 3x<-(-12)[/tex]
Note that we change the sign on the right because we multiplied by a negative.
Divide both sides by 3:
[tex]x>-4\text{ or }x<4[/tex]
Now, look at this inequality. This says that the solution is all the numbers to the right of -4 and all numbers to the left of 4.
I've provided a number line. The red line represents x>-4 and the blue line represents x<4.
As you can see, every value is covered both towards the left and the right.
In other words, our answer is all real numbers.
4p - 3(p + 5) = 3p - 17
Answer:
p=1
Step-by-step explanation:
4p - 3(p + 5) = 3p - 17
Distribute
4p -3p -15 = 3p -17
Combine like terms
p -15 = 3p -17
subtract p from each side
p-p -15 = 3p -17-p
-15 = 2p -17
Add 17 to each side
-15+17 = 2p -17+17
2 = 2p
Divide by 2
2/2 = 2p/2
1 =p
Answer:
Need points! Give brainliest! (a useless mod deleted all my answers for no reason)
Step-by-step explanation:
4p -3p-15 = 3p-17
2 = 2p
p = 1
28 POINTS HELP MEA pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution
A cylindrical water bottle with a height of 21 cm and diameter 6.5 cm is fully filled with water. Kelvin wants to pour all the water in the bottle into a cubic container. State thr minimum leght, to the nearest cm, the side of the cube.
Answer:
9 cm
Step-by-step explanation:
First, we need to find the volume of the cylindrical water bottle. The volume of a cylinder is πr²h where r = radius and h = height. In this case, r = diameter / 2 = 6.5 / 2 = 3.25 and h = 21 so the volume is π * 3.25² * 21 = 221.8125π ≈ 696.84. Let's call the length of the cubic container s. The volume of the cube (which is s³) must be at least the volume of the water bottle, therefore:
s³ ≥ 696.84
∛s³ ≥ ∛696.84
s ≥ 8.86566
The smallest integer value that satisfies this is 9 cm.
Use the diagram below to answer questions 1-6. All rooms are rectangular. 1. What is the value of side A? Explain your thinking. 2. What is the value of side B? Explain your thinking. 3. What is the value of side c? Explain your thinking. 4. What is the area of the vegetable garden? Show your thinking
(5x-3)(9x+2)
5x(9x+2)-3(9x+2)
45x^2+10x-27x-6
45x^2-17x-6
You could also use the FOIL rule to get this answer. The box method is another alternative.
Identify the type of conic section that is represented by the equation y^2- 1 = 4(x-7). DUE IN 2 HOURS, will give BRAINLIEST! A. Circle B. Hyperbola C. Parabola D. Ellipse
Answer:
Solution : Parabola
Step-by-step explanation:
As you can see only one variable is square in this situation, so it can only be a parabola. We can prove that it is a parabola however by converting it into standard form (x - h)^2 + (y - k)^2.
[tex]y^2-1=4\left(x-7\right) = y^2-1=4\left(x-7\right)[/tex]
Respectively it's properties would be as follows,
[tex]\left(h,\:k\right)=\left(\frac{27}{4},\:0\right),\:p=1[/tex]
divide 68 into two parts so that the larger number exeed the smaller one by 6
Answer:
31, 37
Step-by-step explanation:
Let the smaller number be x
Therefore, longer number = x + 6
According to the given information:
x + x + 6 = 68
2x + 6 = 68
2x = 68 - 6
2x = 62
x = 62/2
x = 31
x + 6 = 31 + 6 = 37
Thus, the two parts of 68 are 31 and 37.
(-12a^3b^5)/(4a^2b^7)
state any restrictions on the variable(s) if they exist.
PLEASE HELP (30 points)
Answer:
[tex]a\neq 0 \text{ and } b\neq 0[/tex]
Step-by-step explanation:
So we have the rational expression:
[tex]\frac{-12a^3b^5}{4a^2b^7}[/tex]
In rational expressions, the restrictions of the expression would be the zeros of the denominator Therefore, set the denominator equal to zero and solve for its zeros:
[tex]4a^2b^7=0[/tex]
Zero Product Property:
[tex]4a^2=0\text{ or } b^7=0\\[/tex]
Solve for a and b:
[tex]4a^2=0 \text{ or } b^7=0\\a\neq 0 \text{ or }b\neq 0[/tex]
Therefore, the restrictions on the variables are that a and b cannot equal zero.
30 \div \frac{1}{3} 30÷ 3 1
Answer:
90Step-by-step explanation:
[tex]30 \div \frac{1}{3} \\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:30=\frac{30}{1}\\=\frac{30}{1}\div \frac{1}{3}\\\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}\\=\frac{30}{1}\times \frac{3}{1}\\\\\mathrm{Apply\:rule}\:\frac{a}{1}=a\\=30\times \:3\\\\=90[/tex]
Answer:
90Step-by-step explanation:
[tex]30\div \frac{1}{3}\\\\=\frac{30}{1}\div \frac{1}{3}\\\\=\frac{30}{1}\times \frac{3}{1}\\\\=30\times 3 =90[/tex]
What is the simplest form of (4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x + 9)
Simplest form:
7 x^3 − 5 x^2 + x + 2
What is the equation of the line that passes through the point (-8,5) and has a slope of -1/4
Step-by-step explanation:
Using slope intercept for y = mx + b, substitute m = - 1/4, and (-8, 5) in for (x, y) to find the y-intercept
Please help
the value -2 is lower bound for the zeros of the function below
f(x)=4x^3-12x^2-x+15
True or False
Answer:
False
Step-by-step explanation:
f(x)=4x^3-12x^2-x+15
Using synthetic division
-2 4 -12 -1 15
-8 40 -78
--------------------------
4 -20 39 -63
Since this is not zero, this is not a lower bound
Answer:
[tex]\Large \boxed{\mathrm{False}}[/tex]
Step-by-step explanation:
[tex]\sf f(x)=4x^3-12x^2-x+15[/tex]
The zeros of the function is the values at which the function crosses the x-axis.
The value -2 is not a lower bound for the zeros of the function.
1
Spoints
Which is the image of vertex O after the triangle has been rotated 90 degrees counterclockwise about the origin?
6+
5
3
2
L
2
3
-653 -2.1
s! S6
o
w
s
.67
0 -1.2)
Answer:
(2, - 1 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) , thus
O(- 1, - 2 ) → (2, - 1 )
Under what operation are the set of integers closed? Explain your answer
Answer:
a set of integers is closed under addition, subtraction, and multiplication because when you add, subtract, or multiply any integers, the result is always an integer.
Step-by-step explanation:
The wire supporting a 20-foot tall phone pole is attached to the top of the pole, and to the
ground 12 feet from the pole. How long is the wire?
Answer:
22.36 feet
Step-by-step explanation:
This situation forms a right triangle, where the wire is the hypotenuse
Use the pythagorean theorem to find the hypotenuse/wire length:
a² + b² = c²
20² + 12² = c²
400 + 144 = c²
544 = c²
22.36 = c
So, the wire is 22.36 feet long
The function f(x) = 4x + 30 represents the length of a rectangle. The function g(x) = x - 1 represents the width of the rectangle. Use (fºg)
(5) to determine the area of the rectangle.
04
46
O 50
O 200
Answer:
The answer is 46Step-by-step explanation:
f(x) = 4x + 30
g(x) = x - 1
In order to find (fºg)(5) first find ( f • g)(x)
To find ( f • g)(x) substitute g(x) into f(x) that's for every x in f (x) replace it with g(x)
So we have
( f • g)(x) = 4(x -1) + 30
= 4x - 4 + 30
( f • g)(x) = 4x + 26
To find (fºg)(5) substitute the value of x that's 5 into (f • g)(x)
That's
(fºg)(5) = 4(5) + 26
= 20 + 26
We have the final answer as
(fºg)(5) = 46Hope this helps you
Answer:
46
Step-by-step explanation:
Determine if each statement is always, sometimes, or never true. Parallel lines are ____ coplanar. a) always b) sometimes c) never Perpendicular lines are ____ coplanar. a) always b) sometimes c) never Distance around an unmarked circle can ______be measured. a) always b) sometimes c) never
Answer:
Parallel - Always
Perpendicular - Always
Circle - Never
Step-by-step explanation:
Parallel lines always exist in the same plane.
Circle needs to be marked in order to be measured.
Quoteing from https://brainly.com/question/4854505#:~:text=As%20you%20can%20see%2C%20the%20red%20and%20blue,N.%20In%20conclusion%2C%20perpendicular%20lines%20are%20always%20coplanar.
" the red and blue lines are perpendicular. Notice that the red line lies on the plane M and also on the plane N, and the blue line only lies on the plane N. Therefore, both lines lie on the plane N. In conclusion, perpendicular lines are always coplanar."
Detailed answer here
https://brainly.com/question/4854505#:~:text=As%20you%20can%20see%2C%20the%20red%20and%20blue,N.%20In%20conclusion%2C%20perpendicular%20lines%20are%20always%20coplanar.
Please give brainliest thanks! Also I quoted it and listed where i took the info so brainly mods. please do not take this down
Parallel lines are always coplanar. Perpendicular lines are always coplanar and, Distance around an unmarked circle can never be measured.
What are parallel and perpendicular lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.
1. Parallel lines are always coplanar.
When two lines are parallel to each other it means that the two lines will never intersect each other and their plane is also the same.
2. Perpendicular lines are always coplanar.
From the definition that two lines will be perpendicular to each other their angle should be 90 degrees or they should intersect at 90 degrees angle to each other.
3. Distance around an unmarked circle can never be measured.
We need to have a marked circle to measure the distance. So, the distance from the centre of the circle to one point of it is the radius. Moreover, the distance between two points of the circle taking a line passing through the centre is the diameter of the circle.
To know more about parallel and perpendicular lines follow
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Kono divides The numerator and the denominator of 4872 by the greatest common factor to simplify the fraction in one step by what number does he divide
Complete question:
Kono divides The numerator and the denominator of 48 over 72 by the greatest common factor to simplify the fraction in one step by what number does he divide
Answer:
2/3
Step-by-step explanation:
Given the number : 48 / 72
Obtain the greatest common factor of 48 and 72
- - - - 48 - - - - 72
- 2-- 24 - - - - 36
- 2 - 12 - - - - - 18
- 2 - 6 - - - - - - 9
- 3 - 2 - - - - - - 3
The greatest common factor of 48 and 72 is hence (2 * 2 * 2 * 3) = 24
Hence, divide both the numerator and denominator by 24 ;
Numerator = 48/24 = 2
Denominator = 72 / 24 = 3
= 2/3
Given the graph below, which of the following statements is true? On a coordinate plane, a graph shows an image with three connected lines. The first line has a negative slope and goes from (negative 5, 6) to (negative 2, 0), the second line has a positive slope and goes from (negative 2, 0) to (2, 2), and the third line has a negative slope going from (2, 2) through (4, negative 2). The graph represents a one-to-one function because every x-value is paired with only one y-value. The graph represents a one-to-one function because it is defined for all x-values. The graph does not represent a one-to-one function because it does not pass through the origin. The graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
Answer:
The correct option is (D).
Step-by-step explanation:
A one-to-one function can be defined such the every value of x corresponds to exactly one value of y.
That is:
x₁ → y₁
x₂ → y₂
x₃ → y₃
.
.
.
and so on.
Consider the graph.
From the graph it can be seen that for y = 0 and y = 2 there are multiple x coordinates.
So, the graph does not represent a one-to-one function because the y-values between 0 and 2 are paired with multiple x-values.
According to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.
Given :
On a coordinate plane, a graph shows an image with three connected lines. The first line has a negative slope and goes from (-5, 6) to (-2, 0).The second line has a positive slope and goes from (-2, 0) to (2, 2).The third line has a negative slope going from (2, 2) through (4, -2).Draw the graph of the three lines in order to determine the function is one-one function or not.
The equation of the line passing through (-5,6) and (-2,0) is given by:
[tex]\dfrac{y-6}{x+5}=\dfrac{0-6}{-2+5}[/tex]
[tex]\dfrac{y-6}{x+5}=\dfrac{-6}{3}[/tex]
[tex]y-6=-2(x+5)[/tex]
y + 2x + 4 = 0 --- (1)
The equation of the line passing through (-2,0) and (2,2) is given by:
[tex]\dfrac{y-0}{x+2}=\dfrac{2-0}{2+2}[/tex]
2y = x + 2 ---- (2)
The equation of the line passing through (2,2) and (4,-2) is given by:
[tex]\dfrac{y-2}{x-2}=\dfrac{-2-2}{4-2}[/tex]
y - 2 = -2(x - 2)
y + 2x = 6 ---- (3)
Now, with the help of these three equations, the graph of the three lines can be plotted. The Graph is attached below.
So, according to the graph it can be concluded that the graph of three lines is not an one one function because the values of 'y' between 0 and 2 are paired with multiple 'x' values.
Therefore, the correct option is D).
For more information, refer to the link given below:
https://brainly.com/question/12465796
what are the solutions of |3x + 2| >9?
Answer
-11/3>x>7/3
Step-by-step explanation:
|3*7/3+2|=9
|7+2|=9
|9|=9
9=9
therefore, x must be > 7/3
|3*-11/3+2|=9
|-11+2|=9
|-9|=9
9=9
therefore, x must be < -11/3
(Picture of question below)
Answer:
Second option
Step-by-step explanation:
x^(3)-4x^(2)-13x-6= (x+1) (3x + 2) (x-3)