The equation 5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0 is a quadratic equation
The value of x is 8 or 1
How to determine the value of x?The equation is given as:
5/2 - x + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0
Rewrite as:
-5/x - 2 + x - 5/x + 2 + 3x + 8/x^2 - 4 = 0
Take the LCM
[-5(x + 2) + (x -5)(x- 2)]\[x^2 - 4 + [3x + 8]/[x^2 - 4] = 0
Expand
[-5x - 10 + x^2 - 7x + 10]/[x^2 - 4] + [3x + 8]/[x^2 - 4] = 0
Evaluate the like terms
[x^2 - 12x]/[x^2 - 4] + [3x + 8]/[x^2 - 4 = 0
Multiply through by x^2 - 4
x^2 - 12x+ 3x + 8 = 0
Evaluate the like terms
x^2 -9x + 8 = 0
Expand
x^2 -x - 8x + 8 = 0
Factorize
x(x -1) - 8(x - 1) = 0
Factor out x - 1
(x -8)(x - 1) = 0
Solve for x
x = 8 or x = 1
Hence, the value of x is 8 or 1
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Joana prepared 6 kilograms of dough after working 3 hours. How many hours did joana work if she prepared 8 kilograms of dough?
Answer:
4 hours
brainliest please?
The heights of 100 people in an office building were recorded and the results were normally
distributed. Which histogram shows a normal distribution that could represent this data?
Answer:
d
Step-by-step explanation:
Math question 10 points
Answer:
D.
Step-by-step explanation:
242-44
198/2 = inequality
10 records in her collection. Now she has 12 records. What is the percent increase of her collection?
10 records in her collection. Now she has 12 records. The percentage increase of her collection is by 20%.
Percentage:
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is usually represented by the percent sign "%", although 'it is abbreviated "pct.", "pct.", and sometimes "pc". Percentage is a dimensionless number (pure number); it is unmeasured Unit.
Example :
If 50% of the total number of pupils in a class are boys, this means that 50 out of 100 pupils are boys. If there are 500 students, 250 of them are men.
According to the Question:
We can use the rule of three to solve this problem.
If 100% is 10 records, the percentage of 12 records:
= 12 × 100%/10
= 120%
Then if subtracted 120% -100%, there will be a difference of 20%, i.e. 12 is 20% more, i.e. his collection has increased by 20%.
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I bought 5 gallons of gas for 1770 what is the unit price for gas per gallon
Answer:
Brainleist!Step-by-step explanation:
1770/5 = the unti price
1770 / 5 = 354
354
\(solution \\ cost \: of \: 5 \: gallons \: of \: gas = 1770 \\ cost \: of \: 1 \: gallons \: of \: gas = \frac{1770}{5} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 354 \\ \)
hope it helps...
good luck on your assignment
What is the inverse of FX =- 3x?
The inverse of FX =- 3x is FX = (1/3)x.
The inverse of FX = -3x is a mathematical equation that finds the inverse of a given function.
In this case, the inverse of the given equation is FX = (1/3)x.
The inverse of an equation is the equation that, when solved, produces the same result as the original equation. In this case, when using the inverse equation, the x-value is multiplied by 1/3 to find the corresponding y-value.
The inverse of the equation FX = -3x is the equation x = 1/3Fx.
In mathematics, inverse meaning is the concept of reversing a given equation or operation.
This can be done by switching the terms and operations in the equation, so that the result of the equation is the opposite of what it was before.
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The area of a square is 25 square meters. what is the length of one side of the square
Answer:
6.25.
Step-by-step explanation:
25 divided by 4 is 6.25.
some hikers set on a hike at noon. At some point, they turn around and follow the same path back to where began, and arrive there at 8:00pm. Their speed is 4mi/hr on level ground, 3mi/hr uphill and 6 mi/hr downhll. How many miles dyd they hike
The total distance they hiked is 2x + y + z = 2x + 24 - x = x + 24 miles.
Let's denote the distance they hiked on level ground, uphill, and downhill as x, y, and z, respectively. Since they turned around at some point, we know they hiked a total distance of x + y + z + x = 2x + y + z.
We can use the formula: time = distance/speed, to write the time they spent on each part of the hike as follows:
Time spent hiking on level ground = x / 4
Time spent hiking uphill = y / 3
Time spent hiking downhill = z / 6
Since they started at noon and arrived at 8:00 pm, we know they hiked for a total of 8 hours. Therefore, we can write the equation:
\(\frac{x}{4} + \frac{y}{3} + \frac{z}{6} + \frac{x}{4} + \frac{y}{3} + \frac{z}{6} = 8\)
Simplifying this equation, we get:
x + y + z = 24
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what are the coefficients in the expression (2x+15)(9x-3) need it asap
Answer:
2x and 9x are the coefficients.
Step-by-step explanation:
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c ).
i need help asap. rn
Answer:
4
Step-by-step explanation:
For this, you need to find the scale factor of two sides that are already given to you.
So, we will have to use the hypotenuse and one of the legs to make sure there is an accurate scale factor.
Hypotenuse:
15 / 5 = 3
Leg:
6 / 2 = 3
____________
So the scale factor is 3.
Using the leg (with the x) we need to divide 12 by the scale factor (3) to give us what x is equal to.
12 / 3 = 4
So, the answer is 4.
If correct I’ll give brainlist
Answer:
y=x4
Step-by-step explanation:
Answer:
y-intercept = 0
Step-by-step explanation:
Check all that apply for the series [infinity] 12 n n=1 Diverges by the Divergence Test (nth term test). Convergent Geometric series. Divergent Geometric series. Divergent Harmonic series. Convergent Alternating Harmonic Series. Convergent p-series. Divergent p-series. Convergent by Comparison/Limit Comparison Test. Divergent by Comparison/Limit Comparision Test. Convergent by Alt. Series Test. Convergent by Ratio/Root Test. Divergent by Ratio/Root Test.
In general, the Divergence Test (nth term test) only allows us to determine whether a series diverges or not. It does not help us to determine the convergence of a series. Therefore, none of the other tests apply to this series.
The Divergence Test (nth term test) states that if the limit of the nth term of a series is not equal to zero, then the series diverges.
The series [infinity] 12 n n=1 is defined as follows:
[infinity] 12 n n=1 = 12¹ + 12² + 12³ + ...
The nth term of this series is given by:
aₙ = 12ⁿ As n → ∞, aₙ → ∞,
which means the limit of the nth term of the series does not exist.
Therefore, the series [infinity] 12 n n=1 diverges by the Divergence Test (nth term test).
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If a cup of coffee is 275 mL, what is the volume of 4 cups of coffee, in milliliters?
Answer:
1100 milliliters.
Step-by-step explanation:
First, separate the numbers 275, it will be 200, 70, and 5.
Second, multiply 4x200, it equals 800
Third, multiply 4x70, it equals 280
Fourth, multiply 4x5, it equals 20.
Fifth, add them all together one by one like 280+20=300, then add 280+800 which is 1100.
PART A (1 point)
The dimensions of Riley's rectangular backyard are (3x-8) by (2x-1). Riley is planning to put a rectangular garden in
their backyard with the dimensions (x+5) by (x-3).
For Part A, draw a picture of Riley’s backyard with the garden inside. Please make sure to label all of the dimensions:
PART B (1 point)
Find the total area of Riley’s backyard.
Show ALL work step by step.
PART C (1 point)
Find the total area of Riley’s garden.
Show ALL work step by step.
PART D (1 point)
What is the area of Riley’s backyard, NOT including the garden?
Part B: The total area of Riley's backyard is 6x² - 14x + 8 Part C: The total area of Riley's garden is x² + 2x - 15 Part D: The area of Riley's backyard not including the garden is 5x² - 16x + 23
What is area?
The word "area" refers to a free space. A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc. But a shape's area is a two-dimensional measurement. As a result, it is expressed in square measurements like square inches.
To find the total area of Riley's backyard, we need to multiply the length and width:
Total Area = length × width
Total Area = (3x-8) × (2x-1)
Total Area = 6x² - 6x - 8x + 8
Total Area = 6x² - 14x + 8
PART C:
To find the area of Riley's garden, we need to multiply the length and width:
Garden Area = length × width
Garden Area = (x+5) × (x-3)
Garden Area = x² + 2x - 15
PART D:
To find the area of Riley's backyard not including the garden, we need to subtract the garden area from the total area of the backyard:
Backyard Area (without garden) = Total Area - Garden Area
Backyard Area (without garden) = (6x² - 14x + 8) - (x² + 2x - 15)
Backyard Area (without garden) = 6x² - 14x + 8 - x² - 2x + 15
Backyard Area (without garden) = 5x² - 16x + 23
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Graph the line y = -8. HELPPPP
Answer:
a horizontal line on -8 (y-axis)
Step-by-step explanation:
7. The quality control division of Rothschild's Blueberry Farm randomly inspects 100 of the containers in the truck being
sent to Stop and Shop. Identify the population and sample given in this scenario.
The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Population: The containers of blueberries that are being sent to Stop and Shop.
Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
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Roger has a credit card with an APR of 19.40% and a billing cycle of 30 days. The following table shows his transactions with that credit card in the month of June
Date 611 6/6 Amount ($) Transaction 265.40 Beginning balance 90.00 Payment 43.33 Purchase 37.71 Purchase 6/16 6/22 If Roger's finance charge for June is $3.56, which method of calculating the finance charge does Roger's credit card company use?
daily balance method
b. adjusted balance method previous balance method
d. there is not enough information to determine which method was used
Answer:
The daily balance method
Step-by-step explanation:
The method of calculating the finance charge that Roger's credit card company uses is A. daily balance method.
What is the daily balance method?The daily balance method of calculating credit card's finance charge uses the actual daily balance of the billing cycle instead of being based on an average of the balance throughout the billing cycle.
Using the daily balance method, the finance charges are calculated by summing daily balance multiplied by the daily rate or APR/365.
Data and Calculations:APR = 19.40%
Monthly APR = 1.62% (19.4%/12)
Daily APR = 0.053%
Date Transaction Amount ($)
6/6 Beginning balance 90.00
6/11 Payment 43.33
6/16 Purchase 37.71
6/22 Purchase 265.40 $349.78
Finance charge = 3.56
Ending balance = $353.34
Thus, the method of calculating the finance charge that Roger's credit card company uses is A. daily balance method.
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Consider the expression 4(8x+5)4(8x+5)4, left parenthesis, 8, x, plus, 5, right parenthesis.
The given expression is 4(8x + 5). This is a product of a coefficient and a binomial expression. In mathematics, a binomial is a polynomial with two terms.
They are represented as ax + b or a + bx or (a + b) etc. Given expression is 4(8x + 5). We can simplify this by applying the distributive property. It is given as follows; The distributive property of multiplication states that a(b + c) = ab + ac To simplify the given expression, we need to multiply the coefficient 4 with each term in the parentheses.
It can be done as follows; 4(8x + 5) = 4*8x + 4*5 We multiply 4 with 8x and 4 with 5 to obtain; 32x + 20 This is the main answer. Therefore, the simplified form of 4(8x + 5) is 32x + 20. To simplify the given expression 4(8x + 5), we can use the distributive property. According to this property, the product of a number with the sum of two or more terms is equal to the sum of the products of that number with each term of the sum. In other words, a(b + c + …) = ab + ac + … In the given expression, 4 is multiplied with the binomial (8x + 5). Hence,
4(8x + 5) = 4*8x + 4*5
= 32x + 20
Hence, the simplified form of 4(8x + 5) is 32x + 20.
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What is the rate of change of y=-4/9x+5
Answer:
Rate of change of y is \(- \frac{4}{9}\)
Step-by-step explanation:
\(y = - \frac{4}{9} x + 5 \\ \\ differentiating \: with \: respect \: to \: x \\ \\ \frac{dy}{dx} = - \frac{4}{9} \frac{d}{dx} x + \frac{d}{dx} 5 \\ \\ \frac{dy}{dx} = - \frac{4}{9} .1 + 0 \\ \\ \huge \red{\frac{dy}{dx} = - \frac{4}{9} } \\ \\ rate \: of \: change \: of \: y =- \frac{4}{9}\)
2. Find the value of x and y.
(2x+7)
(12y+1)
Ox= 15, y = 12
Ox=14, y = 11
(3-7)
(1 point)
The value of x and y are x=14 and y=12
We can use 2x + 7 = 3x - 7 to solve for the corresponding measures.
Let's solve for x:
2x + 7 = 3x - 7
2x + 7 - 2x = 3x - 7 - 2x
7 = x - 7
7 + 7 = x - 7 + 7
14 = x
We can use (2x + 7) + (12y + 1) = 180 to solve for the straight angle.
Substitute for x
(2(14) + 7) + (12y + 1) = 180
(28 + 7) + (12y + 1) = 180
35 + 12y + 1 = 180
Now solve for y:
36 + 12y = 180
36 + 12y - 36 = 180 - 36
12y = 144
12y/12 = 144/12
y = 12
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Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (6,5) and parallel to the line whose equation is 78-6y-5=0 The equation of the line in point-stope form is ____
(Type an equation Use integers or fractions for any numbers in the equation) The equation of the line in general form is ____ =0 (Type an expression using x and y as the variables Simplify your answer. Use integers or fractions for any numbers in the expression.)
The equation of the line passing through (6, 5) and parallel to the given line in general form is:36x + y - 221 = 0
Given the coordinates of a point and the equation of a parallel line, we will find the equation of the line in point-slope and general form.
Point-slope form The equation for a line in point-slope form is given by
y - y₁ = m(x - x₁)
Where(x₁, y₁) are the coordinates of the point and m is the slope of the line.
As the line is parallel to 6y - 78 + 5 = 0, we need to find the slope of the given line.
6y - 78 + 5 = 0
⇒ 6y = 73
⇒ y = 73/6
So, the slope of the given line is m = 6/(-1/6) = -36
Therefore, the equation of the line passing through (6, 5) and parallel to the given line is:
y - 5 = -36(x - 6) ⇒
y - 5 = -36x + 216
⇒ y = -36x + 221
General form ,The equation of a line in general form is given by: Ax + By + C = 0
Where A, B, and C are constants.
Rearranging the equation y - 5 = -36(x) + 216,
we get: 36x + y - 221 = 0
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Assume AEFG AJKL. If m2 J= 90°, mz K= 26, and m2 L = 64°, what is
the measure of ZE?
O A. Cannot be determined
OB. 64°
O C. 90°
OD. 26°
SUBMIT
The measure of angle ∠E is 90 degrees. Therefore, the answer is C.
How to find the angle of a congruent triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Therefore, the triangles EFG and JKL are congruent and that means the side and angles are congruent.
Therefore,
ΔEFG ≅ ΔJKL
where
∠E = ∠J = 90 degrees
∠F = ∠K = 26 degrees
∠G = ∠L = 64 degrees
Therefore, let's find ∠E as follows:
Using the congruency as follows:
∠E = 90 degrees
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9-x^2 y = Given x = 4
Answer:
9-16y
Step-by-step explanation:
9-x^2y when x=4
plus in 4: 9- (4)^2y
=9-16y
Using a pencil, pair of compasses, ruler and protractor, construct a triangle with angles 67° and 54° and side between of 6cm. Measure the length of the other side adjacent to the 67° angle.
Answer:
To construct a triangle with angles 67° and 54° and a side length of 6 cm, follow these steps:
Using a ruler, draw a horizontal line segment of length 6 cm. This will be the base of the triangle.
Using a pair of compasses, set the distance to 3 cm (half the length of the base). Place the point of the compasses on one end of the base line, and draw an arc above the line.
Repeat step 2 on the other end of the base line. The two arcs should intersect at a point above the base line.
Using a protractor, measure the angle between the base line and one of the arcs. It should be 67°.
Using a pencil, draw a line segment connecting the intersection of the arcs to one end of the base line. This line segment will be one of the sides of the triangle.
Measure the length of this line segment using a ruler. This will be the length of the side adjacent to the 67° angle.
The resulting triangle should have angles of 67°, 54°, and 109° (the sum of the angles in any triangle is 180°). The length of the side adjacent to the 67° angle can be measured using a ruler.
QUICK HELP PLEASE TIME IS ALMOST UP!!
Answer: first one
Step-by-step explanation:
Hey I need to point of rotation for this question. Need the answer asap :)
Answer:
see explanation
Step-by-step explanation:
the vertices of S under the translation \(\left[\begin{array}{ccc}0\\-3\\\end{array}\right]\) are
(2, 3 ) → (2, 0 )
(6, 3 ) → (6, 0 )
(4, 5 ) → (4, 2 )
Under an anticlockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) then the above coordinates become
(2, 0 ) → (0, 2 )
(6, 0 ) → (0, 6 )
(4, 2 ) → (- 2, 4 )
which are the coordinates of the vertices of the image T
then the rotation is 90° anticlockwise about the origin , point (0, 0 )
Answer:
Below
Step-by-step explanation:
the vertices of S under the translation are
(2, 3 ) → (2, 0 )
(6, 3 ) → (6, 0 )
(4, 5 ) → (4, 2 )
Under an anticlockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) then the above coordinates become
(2, 0 ) → (0, 2 )
(6, 0 ) → (0, 6 )
(4, 2 ) → (- 2, 4 )
which are the coordinates of the vertices of the image T
then the rotation is 90° anticlockwise about the origin , point (0, 0 )
Need help asap.
The GDP of a country goes down as people spend more money and businesses make more products.
True or false
Answer:
I'm gonna say false
GDP or Gross Domestic Profit is the money that is being spent/made inside the country. So it stands to reason that if people are spending more, the GDP would go up.
Hope this helps!
You decide to save up for a big trip and deposit 1491 in a special vacation account today. If your account earns 5.07% annually, how much will you have available to spend in 6 years? Round to two decimal places (Ex. $0,000.00)
You will have approximately $1929.29 available to spend in 6 years.
To calculate the future value of your deposit after 6 years, we can use the formula for compound interest:
Future Value = Present Value * (1 + Interest Rate)^Time
Plugging in the values:
Present Value (PV) = $1491
Interest Rate = 5.07% = 0.0507
Time = 6 years
Future Value = $1491 * (1 + 0.0507)^6
Calculating the expression:
Future Value = $1491 * (1.0507)^6
Future Value ≈ $1929.29
Therefore, you will have approximately $1929.29 available to spend in 6 years.
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three numbers are in the ratio 1:2:1 find the largest number if the sum of their cubes is 1000
Answer:
Given,
The ratio of the three numbers are 1:2:3 . Let the numbers are x , 2x and 3x.
According to the question,
x³+(2x)³+(3x)³=4,500
⟹x³+8x³+27x³=4,500
⟹36x³=4500
⟹x³=4,50036
⟹x³=125
⟹x=125−−−√3
⟹x=5
So the numbers are 5,5×2=10,5×3=15
Therefore, 5 is the smallest number.
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pls help me 13 minute left 10 POINTS
Answer:
The answer is 6.28.
Step-by-step explanation:
The formula for finding the circumference is C=2 times 3.14 times the radius of the circle. 3.14 times 2 equals 6.28 times the radius which is 1 feet (because half of 2 feet equals 1 feet). 6.28 times 1 equals 6.28.