Answers
The value of x are 4 and 2.4 after simplifying and applying the quadratic formula.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The equation is:
4/(x - 2) + 3/(x - 3) = 5
4(x - 3) + 3(x - 2) = 5(x -2)(x - 3)
4x - 12 + 3x - 6 = 5x² - 25x + 30
5x² - 32x + 48 = 0
After solving the above quadratic equation by the formula:
[tex]\rm x = \dfrac{-(-32) \pm\sqrt{(-32)^2-4(5)(48)}}{2(5)}[/tex]
x = 4
x = 2.4
Thus, the value of x are 4 and 2.4 after simplifying and applying the quadratic formula.
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Related Questions
Samuel orders four DVDs from an online music store. Each DVD costs $9.96. He has a 25% discount code, and sales tax is 7.75%. Round sales tax amounts to the nearest cent. What is the total cost of his order?
The total cost of Samuel's order is $
Answers
Samuel's order will ultimately cost $39.84.
One DVD Samuel purchased cost $9.96.
He purchased four DVDs in total.
as a result, his total outlay will be 4 * 9.96 = $39.84.
The 7.75% sales tax that must be paid is disclosed to us.
Adding 7.75% to $39.84 yields
39.84 x 7.75/(100) (100)
= $3.0876
Consequently, the total amount of tax due is $3.0876.
Using 25% of 39.84 to calculate a 25% discount,
39.84 x 25/100
= 996/100
=$9.96
Consequently, the total discount on the total of $39.84 will be $9.96.
as a result, the updated purchase price will be,
39.84-9.96
=$29.88
adding the tax to the updated price,
9.96+29.88
= $39.84
Consequently, Samuel's order will ultimately cost $39.84.
How are percentages calculated?One must compute percentage in order to determine the proportion of a whole that is stated in terms of 100. A percentage can be determined using one of two methods:
using the unitary method.
by changing the fraction's denominator to 100.
It should be noted that the second method of percentage computation is not used when the denominator is not a factor of 100. In these circumstances, we make use of the unitary approach.
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AB and BC are perpendicular lines.
Find the value of x.
Answers
First put it into an equation:
25 + 2x = 90
Then subtract 25 from both sides:
2x = 65
Finally divide by 2 on both sides:
X = 32.5
Write an
equation of a parabola with the given vertex and focus.
vertex (5,-2); focus (5, -1)
Answers
Answer:
[tex](x-5)^2=4(y+2)[/tex]
Please note that alternative forms of this equation (vertex and standard) are in the explanation.
Step-by-step explanation:
Standard form of a parabola with a vertical axis of symmetry:
[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]
Vertex = (h, k)Focus = (h, k+p)Given:
Vertex = (5, -2)Focus = (5, -1)Therefore:
h = 5k = -2k + p = -1Calculate p:
[tex]\implies -2+p=-1[/tex]
[tex]\implies p=-1+2[/tex]
[tex]\implies p=1[/tex]
Substitute the values of h, k and p into the formula to create an equation of the parabola with the given parameters:
[tex]\implies (x-5)^2=4(1)(y-(-2))[/tex]
[tex]\implies (x-5)^2=4(y+2)[/tex]
In vertex form:
[tex]\implies y=\dfrac{1}{4}(x-5)^2-2[/tex]
In ax² + bx + c form:
[tex]\implies y=\dfrac{1}{4}x^2-\dfrac{5}{2}x+\dfrac{17}{4}[/tex]
there are 5 students in mun elligible for a particular event at the next conference however, only two can compete. they are equally qualified, so it is decided that the contestants will be randomly selected. what is the probability that the first two students alphabetically will be selected?
Answers
The probability of selecting two students has 10 ways
Total number of students = 5
Only two students can be selected for the conference who are equally qualified.
The probability that the first two students selected alphabetically is derived from the combinations.
Therefore, the final probability for selecting the students randomly is,
x = ⁵C₂
x = [tex]\frac{5!}{2!*(5 - 2)!}[/tex]
x = 10
Hence, the probability of selecting two students has 10 ways.
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Graph each function f(x)=1/4 x
Answers
Graph f(x)=14.
Plot each graph on the same coordinate system.
f(x)=14x
image of graph
the jasmine family kept a log of the distance they traveled during a trip, as represented by the graph below
during which interval was their average speed the greatest
Answers
Answer:
I would say its 4, the eighth to tenth hour.
………………………………………………….
Answers
Answer:
i don't know if this is fully correct but I believe that the answer is both because both elements are used it this piece of art. one the art is in color. two it uses both horizontal and vertical lines.
(2x^2+3x+8) (x^2-x-4) multiply the polynomials and simplify the answer
Answers
Step-by-step explanation:
(2x² + 3x+8) (x²-x-4)
= (2x² + 3x+8) (x² +-x²+-4)
= (2x²) (x²) + (2x²) (-x) + (2x²) (-4) +(3x) (x²) + (3x) (-x) + (3x) (-4) + (8) (x²) + (8) (-x) + (8) (-4)
= 2x⁴ - 2x³ -8x² + 3x³ -3x² - 12x + 8x² - 8x - 32
=2x⁴ + x³ - 3x² - 20x - 32
∠A and ∠B are vertical angles. If ∠A = (x-29) and m∠B = (6x-11), then find the value of x.
Answers
The required value of x is -3.6 which is determined by the substitute that equals the vertical angles.
What are the vertical angles?When two lines intersect at a location, vertical angles are generated. They are always equal to each other.
Since ∠A and ∠B are vertical angles then they are congruent, thus
⇒ (x - 29) = (6x - 11)
Subtract 6x from both sides of the above equation,
⇒ x - 29 - 6x = 6x - 11 -6x
⇒ -5x - 29 = - 11
Add 29 to both sides of the equation,
⇒ -5x - 29 + 29 = - 11 + 29
⇒ -5x = 18
Divided by 5 to both sides of the equation,
⇒ x = - 18/5
⇒ x = - 3.6
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how to find the greatest number of students to whom 135pens 225 books and 315 copies can be divided equally also find the shares of each item . maths
Answers
Answer:
The items can be equally shared between 45 students.
Each student will get 3 pens, 5 books and 7 copies.
Step-by-step explanation:
We have to find the GCF (Greatest common factor) of 135 , 225 and 315.
135 = 5 * 3 * 3 * 3 = 45 * 3
225 = 5 * 5 * 3 * 3 = 45 * 5
315 = 5 * 3 * 3 * 7 = 45 * 7
GCF = 5 * 9 = 45
The items can be equally shared between 45 students.
Each student will get 3 pens, 5 books and 7 copies.
On May 8, 2010, a team of kayakers sets a record time for 5h 19 min 17 sec to kayak across the length of Loch Ness, Scotland, UK, a distance of 20.5 mi. When the kayakers were four times as far from the starting point as from the finish, how many miles were traveled?
Answers
Answer:
16.4
Step-by-step explanation:
The time is irrelevant to the problem
fraction42 *20.5= 16.4
Hope this helps
Someone answer this please!
Answers
Answer:
Answer down below!
Step-by-step explanation:
The correct answers are as follows:
2^381 over 1/2^3Answer: 2nd, 3rd, 5th
Step-by-step explanation:
Solve the problem
1/2*1/2*1/2 = 1/1/8
1 * 8/1
8
Check each answer
1) -(1/2)^3
-(1/2*1/2*1/2)
-(1/8)
-1/8
No
2) 2^3
2 * 2 * 2
8
Yes
3) 1/1/2^3
[tex]\frac{1}{\frac{1}{2} *\frac{1}{2} *\frac{1}{2} }\\ \frac{1}{\frac{1}{8} }\\1 * \frac{8}{1} \\8[/tex]
Note: Flip fraction when dividing a fraction.
Yes
4) 1/8
1/8
No
5) 8
8
Yes
I am confused my old teacher got fired so we are learning stuff completely different and I am rlly confused in this assignment please help me.
Answers
Hello!
First, let's analyze these two quadrilaterals:
• Notice that the quadrilateral AB'C'D is ,smaller ,than the quadrilateral ABCD.
Let's try to solve it using the lines AB and AB':
• The measurement of the ,line AB is 14 units,.
,• The measurement of the ,line AB' is 7 units,.
Knowing it, let's write the scale factor as:
[tex]\text{ScaleFactor}=\frac{AB^{\prime}}{AB}=\frac{7}{14}=\frac{1}{2}[/tex]Answer: alternative D.
Multiply.
40.631⋅1.07
Responses
4.347517
43.47517
434.7517
4347.517
Answers
Answer: 43.47517
Step-by-step explanation:
Considering orders of magnitude, we see that Option 2 is the only reasonable answer.
Answer for bothering x and y giving brainliest. Need help asap!!!
Answers
Answer: x = 77 - 2y y = -x/2 + (77/2)
Step-by-step explanation:
Noah is studying a type of sea sponge that grows at a constant rate. They measured the age and height of 333 pieces of the sponge. Here's what they found:
Answers
Answer:
a = h/2 would be the answer.
Step;-
Find slope:-
m = rise/run = (16-8)/(8-4) = 8/4 = 2
Now,
y = mx + b
or, 8 = 2(4) + b
so, b = 0
So,
y = mx + b
or, h = 2a + 0
so, h = 2a
hence,a = h/2.
The sea sponges's height grows 2cm every 1 year, so you can write an equation to find the height at any age [tex]a = \frac{h}{2}[/tex]
Anna spent half her weekly allowance at the movies to earn more money her parents let her wash the car for $8 what is her weekly allowance if she ended with $18
Answers
This situation can be expressed by the equation [tex]x-\frac{x}{2} +8=18[/tex], her weekly allowance is $20.
What is an equation?
The description of an equation in algebra is a mathematical proposition that demonstrates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.Let the weekly allowance of anna be = X
Allowance spent on movies= X/2
The extra money from the car wash = 8
Allowance retained with anna = 18
This situation can be expressed by the equation,
[tex]x-\frac{x}{2} +8=18[/tex]
Solving the above equation, we get,
[tex]\frac{x+16}{2} =18[/tex]
x+16=36
x=20
Therefore, her weekly allowance is $20.
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I need help figuring out the answer … I’m confused
Answers
1st step. Calculate the area of the parallelogram
We can use the following formula:
[tex]A=b\cdot h[/tex]where,
base, b = 9 km
height, h = 5 km
Therefore,
[tex]A=9\cdot5=45[/tex]The area of the parallelogram is 45 km^2
2nd step. Calculate the area of the triangle
Let's use this formula:
[tex]A=\frac{b\cdot h}{2}[/tex]where,
base, b = 6 km
height, h = 3 km
Therefore,
[tex]A=\frac{6\cdot3}{2}=9[/tex]The area of the triangle is 9 km^2
3rd step. calculates the ratio of the area of the parallelogram to the area of the triangle
[tex]r=\frac{A_P}{A_T}=\frac{45}{9}=5[/tex]Answer: the area of the parallelogram is 5 times greater than the area of the triangle.
I dont understand this
Identify all pairs of parallel segments. Arrange letters in
C
ALPHABETICAL
orders (AC. DF)
)//(
)//(
)//(
Answers
All pairs of parallel segments are given below.
What are parallel 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. Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible. Examples of parallel lines can be found everywhere, including zebra crossings, rows of notebooks, and the nearby railroad tracks.
Given,
a) Line segment = AC and FD
Parallel = AC ║FD
b) Line segment = AE and BD
Parallel = AE ║BD
c) Line segment = EC and FB
Parallel = EC ║FB
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Megan is in a musical production. She was at practice for 2 3/4 hours yesterday and 3 1/2 hours today. Altogether she spent 1/3 of her practice hours dancing. How many total hours did Megan spend dancing yesterday and today?
Answers
Megan spent 2 1/12 hours dancing both yesterday and today
How to calculate the number of hours Megan spent dancing ?Megan is involved in a musical production
Yesterday, she practiced for 2 3/4 hours
Today she practiced for 3 1/2 hours
The first step is to calculate the total number of hours she spent at the practice
2 3/4 + 3 1/2
= 11/4 + 7/2
The LCM between both fractions is 4
11/4 + 7/2
11 + 14/4
= 25/4
Megan spent 25/4 hours yesterday and today practicing
Out of this 25/4 hours, she spent 1/3 hours dancing
Therefore the hours she spent dancing can be calculated as follows
= 25/4 × 1/3
= 25/12
= 2 1/12
Hence Megan spent 2 1/12 hours dancing yesterday and today
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List the first 5 multiples.
18:
20:
16:
32:
Answers
Answer: 18: 18, 36, 54, 72, 90
20: 20, 40, 60, 80, 100
16: 16, 32, 48, 64, 80
32: 32, 64, 96, 128, 160
Step-by-step explanation:
multiply each number by 1 2 3 4 5 respectivly to get the answer.
Write the following number in standard decimal form.six tenths
Answers
Rewriting the words mathematically:
[tex]\text{Six tenths = }\frac{6}{10}[/tex]Next we will write in standard decimal form:
[tex]\begin{gathered} In\text{ decimal, 6/10 = 0.6} \\ We\text{ have one decimal place} \\ 0.6\text{ }is\text{ standard decimal = 6 }\times10^{n\text{ umber of movement})} \end{gathered}[/tex][tex]\begin{gathered} \text{movement from left to right will have a negative sign in front of the number of movement} \\ \text{movement from right to left will be positive} \\ \\ AS\text{ result, 0.6 = 6 }\times10^{-1} \end{gathered}[/tex]The ordered pairs below represent a function.
{(−4,2), (−2,1), (0,0), (2,−1)}
What is the RANGE of the function?
Answers
The range of the function is -1 ≤ y ≤ 2
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the range of the function?The ordered pair is given as
{(−4,2), (−2,1), (0,0), (2,−1)}
Rewrite as
(x, y) = {(−4,2), (−2,1), (0,0), (2,−1)}
Remove the y values
So, we have
y = {2, 1, 0,−1}
Express as an inequality
-1 ≤ y ≤ 2
Hence, the range is -1 ≤ y ≤ 2
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Zack and Zane were floating down the river. They climbed to the top of the rock, which was 14.6 feet above the water level. When Zack jumped in, he got down to a depth of 6.8 feet underwater. What was the total distance from his highest point to his lowest point?
Answers
The total distance from his highest point to his lowest point is 21.8 feet.
Height H climbed by Zack and Zane is 14.6 feet.
The depth D underwater that Zack got down to is 6.8 feet.
The distance between the highest and the lowest point can be found by assuming the coordinates axis.
Let us assume the origin is on the water surface,
So, going by this logic, highest point is at +14.6 feet.
The lowest point is at -6.8 feet.
The distance L between lowest and highest point is,
L = H - D
L = 14.6 -(-6.8) feet
L = (14.6 + 6.8) feet
L = 21.8 feet
So the distance L is 21.8 feets.
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Equivalent equation to 2(x +3)=16
Answers
A paintball court charges an initial entrance fee plus a fixed price per ball. Suppose it costs $18 to use 2 balls and $23 to use 4 balls. What is the entrance fee?
Answers
The entrance fees is 13 dollars charges by the paintball court.
Let us assume that the entrance fees is $X and the actual cost of using one ball is $Y charged by the paintball court.
According to one situation,
Total cost of using to ball = Cost of entry fees + actual cost of using two ball.
So, we can write,
X + 2Y = 18
Let us say that this is our equation 1,
Also, it is provided,
Total cost of using 4 balls = cost of entry fees + actual cost of using four balls.
X + 4Y = 23
Let us say that this is our equation 2,
Both of our equations are linear equations with two variables,
Now, substracting equation 1 from equation 2,
X + 4Y -(X + 2Y) = 23 - 18
2Y = 5
Y = $2.5.
Putting the value of Y = 2.5 in equation 1,
X + 2(2.5) = 18
X = 18 - 5
X = $13.
So, the entry fees is 13 dollars.
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When are reciprocals used to solve an equation?
Answers
It's important to know that reciprocals are the multiplicative inverse of a numbers, for example, the reciprocal of 7 is 1/7.
As you can observe, using reciprocals would help to solve equations when we have to get rid off a factor. For example, if we have the equations 4x = 8, we would use the reciprocal of 4 to isolate the variable x: (4x)/4 = 8/4 then x = 2.
Therefore, reciprocals are used to move factors across the equation to isolate the variable.The store is trying to get rid of their Game of Thrones Season 8 sets and is marking them down by 25%. The original price was $55. What is the new price before sales tax?
Answers
Help please I don’t knowwww
Answers
The corn's height when the fertilizer was applied is 13 centimeters and it grows at a rate of 13 centimeters each day.
What is the interpretation of the linear equation?The equation that is given is known as a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
A linear equation increases or decreases at a constant rate. When a linear equation is drawn on a graph, it is a straight line that curves either upward or downward.
A linear equation usually has this form y = mx + b
Where:
m = slope = rate of change of the equation with respect to x b = interceptH = 13 + 13t
Where:
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Write the equation of a line perpendicular to 8x−5y=−9 that passes through the point (−8,3).
Answers
Considering the definition of perpendicular line, the equation of a line perpendicular to 8x−5y=−9 that passes through the point (−8,3) is y=-5/8x-2 .
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseIn this case, the line is 8x-5y= -9. Expressed in the form y = mx + b, you get:
-5y= -9 - 8x
y= (-8x -9)÷ (-5)
y= 8/5x +9/5
The line has a slope of 8/5. If you multiply the slopes of two perpendicular lines, you get –1. In this case:
8/5× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (8/5)
slope perpendicular line= -5/8
So, the perpendicular line has a form of: y= -5/8x + b
The line passes through the point (-8, 3). Replacing in the expression for perpendicular line, you get:
3= -5/8× (-8) + b
3= 5 + b
3- 5 = b
-2= b
Finally, the equation of the perpendicular line is y= -5/8x -2 .
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