Write the absolute value equations in the form |x|=c (where b is a number and c can be either a number an expression) that has the following solution set.
Two solutions x=1/2, x=-1/3
Answers
According to the given information, the absolute value is |x - 7/6| = 5/6.
What is an algebraic expression?
A mathematical expression known as an algebraic expression can include variables, integers, and mathematical operations including addition, subtraction, multiplication, and division.
When expressing quantities or values that might change depending on the values given to the expression's variables, algebraic expressions are utilised. Expressions in algebra can include one or more variables and be simple or complex.
Two solutions x=1/2, x=-1/3
|x - 7/6| = 5/6.
We know that the absolute value of (1/2 - 7/6) equals the absolute value of (-1/3 - 7/6) because they are opposites and have the same absolute value. So we need an expression that equals 5/6 when either 1/2 - 7/6 or -1/3 - 7/6 is plugged in for x.
To get an expression that equals 5/6 when 1/2 - 7/6 is plugged in for x, we can subtract 7/6 from 1/2 and take the absolute value of the result:
|1/2 - 7/6| = |-1/6| = 1/6.
To get an expression that equals 5/6 when -1/3 - 7/6 is plugged in for x, we can subtract 7/6 from -1/3 and take the absolute value of the result:
|-1/3 - 7/6| = |-9/6| = 3/2.
Since both expressions have the same absolute value of 5/6, we can use either one as the absolute value expression in the equation. Thus,
|x - 7/6| = 5/6.
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Related Questions
A concrete pillar has the shape of a cylinder. It has a diameter of 4 meters and a height of 5 meters. If concrete costs $107 per cubic meter, how much did the concrete cost for the pillar?
For your calculations, do not round any intermediate steps, and use the pi button on a calculator. Round your answer to the nearest cent.
Answers
The cost of the concrete used to make the cylinder was approximately $6,776.89.
The problem is asking us to find the cost of the concrete used to make a cylindrical pillar, given its dimensions and the cost per cubic meter of concrete. We first need to calculate the volume of the cylinder using the formula for the volume of a cylinder:
[tex]V=pir^2h[/tex]
where V is the volume, r is the radius, h is the height, and π is the constant pi (approximately 3.14159).
In the problem, the diameter of the cylinder is given as 4 meters, which means the radius is half of that, or 2 meters. The height of the cylinder is given as 5 meters.
Substituting these values into the formula, we get:
[tex]V = \pi r^2h = \pi (2)^2(5) = 20\pi cubic meters[/tex]
Next, we need to find the cost of the concrete used to make the cylinder, given that the cost per cubic meter of concrete is $107. We can do this by multiplying the volume of the cylinder by the cost per cubic meter of concrete:
20π × $107 = $6,776.89
Rounding to the nearest cent, we get that the cost of the concrete used to make the cylinder was approximately $6,776.89.
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This time, make a simple coaster that "bumps" the axis at x = 500. remember to make sure that the track rises before it falls! y = ax(x – 1000 )
Answers
The coaster starts at a height of 250, then drops down to 0 at x=500, and then rises back up to a height of 250. The bump is located at x=500 and is the highest point on the coaster.
y = -0.0005(x-500)² + 250
The coaster starts at the highest point (y=250) when x=0 and then drops down to x=500 by following the equation y=ax(x-1000). To create the bump, we need to make the coaster rise before it falls, so we use a quadratic equation that has a vertex at x=500 and y=250 (the initial height).
The equation y = -0.0005(x-500)² + 250 is a downward-facing quadratic equation with a maximum value of y=250 at x=500. This means that as the coaster approaches x=500, it starts to rise, and then falls down again. The coefficient -0.0005 controls the steepness of the coaster's drop and the height of the bump.
Here's a graph of the coaster:
^
260| *
| *
| *
| *
| *
height | *
| *
| *
0 +--------------->
0 500 1000 x-axis
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Using identities evaluate :78x82
Answers
Answer:
6436
Step-by-step explanation:
78 x 82
= (80-2) * (80+2)
= (80^2 - 2^2)
= 6436
Given ab and be are diameter of circle P. Diameter whether the arc is a minor arc, a major arc or a semi-circle of circle P. The find the measure of the arc. A. CD b. AE c. BC d. AC e. ADC f.AED g.CE H. BAD
Answers
Answer:
a. m(arc) CD = 65°
b. m(arc) AE = 120°
c. m(arc) BC = 55°
d. m(arc) AC = 115°
e. m(arc) ADC = 245°
f. m(arc) AED = 180°
g. m(arc) CE = 125°
h. m(arc) BAD = 240°
Step-by-step explanation:
a.
m<CPD = 180 - 55 - 60 = 65
m(arc) CD = 65°
b.
m<APB = 60°
m<APE = 180° - 60° = 120°
m(arc) AE = 120°
c.
m(arc) BC = 55°
d.
m(arc) AC = 60° + 55° = 115°
e.
m(arc) ADC = 120° + 60° + 65 = 245°
f.
m(arc) AED = 180°
g.
m(arc) CE = 60° + 65° = 125°
h.
m(arc) BAD = 60° + 120° + 60° = 240°
Consider a scenario in which Romeo responds positively to Juliet's feelings, and Juliet responds equally to her own feelings, but responds negatively to Romeo's feelings. The corresponding system is: R = 1 j = -R+J (a) Use the (A,T) chart to classify the behavior of the system. (b) Calculate the eigenvalues and eigenvectors of the system. Sketch the behavior of the system in the phase plane. (c) Sketch in particular the solution curb that starts at R(0) = 1, J0) = 1. (d) Predict what will happen to the couple in the long term, if starting at this initial point.
Answers
The solution curve represents a spiral that converges towards the origin.
(a) To classify the behavior of the system, we can use the (A,T) chart. Here, A is the sum of the elements in each row of the system matrix and T is the sum of the absolute values of the off-diagonal elements.
The system matrix for this scenario is:
[ 0 1 ]
[-1 1 ]
So, A = 1 for both rows, and T = 1 (absolute value of the off-diagonal element).
Using the (A,T) chart, we can see that the system is a focus.
(b) To find the eigenvalues and eigenvectors of the system, we need to solve the characteristic equation:
| 0-lambda 1 | |u| |0|
| -1 1-lambda| [tex]\times[/tex] |v| = |0|
Expanding the determinant, we get:[tex]\lambda^2[/tex] -[tex]\lambda[/tex] + 1 = 0
Solving for lambda using the quadratic formula, we get:[tex]\lambda[/tex] = (1 +/- sqrt(3)i) / 2
So, the eigenvalues are complex conjugates with a real part of 1/2. The eigenvectors can be found by solving the system of linear equations:(0 - lambda)u + v = 0
(-1)u + (1 - lambda)v = 0
For lambda = (1 + sqrt(3)i) / 2, we get:u = [1, -1 + sqrt(3)i]
For lambda = (1 - sqrt(3)i) / 2, we get:u = [1, -1 - sqrt(3)i]
(c) To sketch the solution curve that starts at R(0) = 1, J(0) = 1, we can use the eigenvectors and eigenvalues. The general solution for the system can be written as:[x(t), y(t)] = [tex]c_1 \times u_1 \times e^(l \ambda1 \times t) + c2 \times u2 \times e^(\lambda2 \times t)[/tex]
where c1 and c2 are constants determined by the initial conditions, u1 and u2 are the eigenvectors, and lambda1 and lambda2 are the eigenvalues.
Plugging in the values, we get:
[tex][x(t), y(t)] = c_1 \times [1, -1 +\ sqrt(3)i] \times e^{((1 + \sqrt(3)i)t} / 2) + c_2\times [1, -1 - \sqrt(3)i] \times e^{((1 - \sqrt(3)i)t} / 2)[/tex]
Using the initial condition R(0) = 1, J(0) = 1, we get:
[tex]c_1 + c_2 = 1[/tex]
(-1 + sqrt(3)i)c1 + (-1 - sqrt(3)i)c2 = 1
Solving for [tex]c_1[/tex] and [tex]c_2[/tex], we get:
[tex]c_1[/tex] = (1 + sqrt(3)i) / (2[tex]\times[/tex] sqrt(3)i)
[tex]c_2[/tex]= (1 - sqrt(3)i) / (2 [tex]\times[/tex] sqrt(3)i)
Plugging in these values, we get:
[x(t), y(t)] = [1, 0] [tex]\times[/tex] e^((1 + sqrt(3)i)t / 2) + [0, 1] [tex]\times[/tex] e^((1 - sqrt(3)i)t / 2)
This solution curve represents a spiral that converges towards the origin.
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nelly has 250 discs. this is 14 less than 8 times the number of discs valerie has.
Answers
264 : 8 = 33
Valerie has 33 discs
Shen drove 603 miles in 9 hours. At the same rate, how long would it take him to drive 335 miles?
Answers
Answer:
5 hours
Step-by-step explanation:
Since Shen drove at the same rate for both distances, we can use a proportion to solve for the time it would take him to drive 335 miles:
[tex]\frac{d_{1} }{t_{1} }=\frac{d_{2} }{t_{2} }[/tex]
where d1 is 603 miles, t1 is 9 hours, d2 is 335, and t2 is the unknown value.
Thus, we can simply plug in everything to the equation and solve for t2:
[tex]\frac{603}{9}=\frac{335}{t_{2} }\\ 67=\frac{335}{t_{2} }\\ 67t_{2}=335\\ t_{2}=5[/tex]
(*Note that 9 divides evenly into 603 and becomes 67, which is why I didn't cross-multiply first with he 603 and t2 and the 335 and 9, although you'd still get the same result for t2)
Thus, it would take Shen 5 hours to drive 335 miles.
You can check by finding the rate for both equations since we know that distance is equal to the product of rate and time (d = rt):
First equation: 603 miles = 9 hours * r mph
67 mph = r
603 = 67 * 9
Second equation: 335 miles = 5 hr * r mph
67 mph = r
335 = 67 * 5
PLEASE HELP!!!
1.) Circle A has been transformed to Circle B. What is the translation rule for these circles?
A.) (x-2),(y+3)
B.) (x+2),(y+3)
C.) (x-1),(y+4)
D.) (x+4),(y+3)
*Please Show All Work***
2.) Circle A has been transformed to Circle B. What is the scale factor of Circle A to Circle B?
Answers
The translation of circle A to circle B is achieved using the translation rule
B.) (x + 2),(y + 3)The scale factor of Circle A to Circle B is 2
What is translation in geometry?In geometry, translation refers to a transformation that moves an object in a straight line without changing its size, shape, or orientation.
This movement is done by sliding the object along a line, which is called the axis of the translation.
The scale factor is solved by comparing the diameter
Circle A has diameter of 2 units
Circle B has diameter of 4 units
let the scale factor be k
diameter of circle A * k = diameter of circle B
2 * k = 4
k = 4 / 2
k = 2
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The length of a classroom is 7 meters. How many centimeters long is the classroom?
Answers
Answer:
700 cm
Step-by-step explanation:
Mutiply the value by 100.
a distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. find p81, which is the score separating the bottom 81% from the top 19%.
Answers
If the distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. the score separating the bottom 81% from the top 19% is 168.24.
The value of p81, which is the score separating the bottom 81% from the top 19%, can be calculated as follows:
The given, Mean = μ = 93.2
Standard deviation = σ = 87.4
We are supposed to find the score separating the bottom 81% from the top 19% which is nothing but the 81st percentile.
Let X be a random variable with a normal distribution, then the z-score of the 81st percentile is calculated as follows:
z = InvNorm(0.81)
z ≈ 0.8 (by standard normal distribution tables)
The 81st percentile in terms of X is given by:
p81 = μ + zσp81
= 93.2 + 0.8(87.4)p81
p81 = 168.24
Thus, the score separating the bottom 81% from the top 19% is 168.24.
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QUESTION 2 2.1 Determine the following products: 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9)
Answers
The products of 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9) is -3x² - 9x - 27
How to find the products: 2.1.1 x(x-1) 2.1.2 (-3)(x² + 3x + 9)2.1.1 x(x-1) can be simplified using the distributive property of multiplication:
x(x-1) = xx - x1 = x^2 - x
2.1.1 x(x-1):
Expanding the expression x(x-1) using the distributive property:
x(x-1) = x^2 - x
Therefore, the product of 2.1.1 is:
x(x-1) = x^2 - x
2.1.2 (-3)(x² + 3x + 9):
Expanding the expression (-3)(x² + 3x + 9) using the distributive property:
(-3)(x² + 3x + 9) = -3x² - 9x - 27
Therefore, the product of 2.1.2 is:
(-3)(x² + 3x + 9) = -3x² - 9x - 27
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PLS HELP IT IS DUE TODAY
Answers
Therefore, the equation in slope-intercept form that has a y-intercept at (0, -3) and also contains the point (4, 5) is y = 2x - 3.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. An equation is usually written with an equal sign (=) between the two expressions. Equations are used to represent mathematical relationships between quantities, to solve problems, and to model real-world situations. They can be used to find unknown values, to predict outcomes, and to test hypotheses. There are many types of equations, including linear equations, quadratic equations, polynomial equations, trigonometric equations, and differential equations. Each type of equation has its own rules and methods for solving it.
Here,
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given that the y-intercept is (0, -3), so b = -3. To find the slope, we can use the two given points (0, -3) and (4, 5).
slope = (y2 - y1)/(x2 - x1)
= (5 - (-3))/(4 - 0)
= 8/4
= 2
Now that we know the slope and the y-intercept, we can write the equation in slope-intercept form:
y = 2x - 3
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What is 1. 2 x 10 ^5 in standard form?
Answers
Answer: 0.000012
Step-by-step explanation: The exponent is -5, making it 10 to the power of negative 5. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 5 times
1.2 -> 0.000012
Find the area of the rectangle below:
What is the area?
Answers
Step-by-step explanation:
Find length b by using the Pythagorean theorem for right triangles
17^2 = 8^2 + b^2
b = 15
the area = L x W = 15 X 8 = 120 cm^2
Answer:
120
Step-by-step explanation:
Find out B- 17 squared- 8 squared ( square root) = 15
b = 15
8 X 15 = 120
we used the method of pythagoros - a squared + b squared = c squared
Have a nice day !
Harry buys a TV priced at £1200 plus 20% VAT. He pays £300 deposit and the balance in ten equal monthly payments. Calculate each monthly payment.
Answers
Answer:
Step-by-step explanation:
Step 1: Find the TV price:
£1200×(100%+20%)= £1440
Step 2: Find the final price Harry have to pay:
since he deposited £300 so the ammout he have to pay is:
£1440 - £300 = £1140
Step 3: Find the monthly payment
in this case he pays equally every month so we take the ammount he has to pay devided by 10 months
£1140÷10=£114
Conclusion: He has to pay £114 every month
There are 1600 students in school. 47. 5% are male. How many are female
Answers
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{47.5\% of 1600}}{\left( \cfrac{47.5}{100} \right)1600}\implies 760~\hfill \underset{ females }{\stackrel{1600~~ - ~~760 }{\text{\LARGE 840}}}[/tex]
in an experiment, once the independent and dependent variables are determined, we have a choice to make about the other variables. if we hold everything else constant, we are reducing what kinds of variables? a. intervening b. confounding c. random d. control
Answers
The correct option - d. control. After identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.
Explain about the control variables?Something kept constant or constrained in a research study is referred to as a control variable. Although not being relevant to the study's goals, this variable is controlled since it could have an impact on the results.
Variables can be controlled either directly by maintaining their value throughout a study (for example, by maintaining a constant room temperature in such an experiment) or indirectly by using techniques like randomization as well as statistical control . Research biases including omitted variable bias can be avoided by including control variables in your analysis.Thus, after identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.
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40.7 x 19.3 whats the product and explain how
Answers
Answer:
Step-by-step explanation:
the answer is 785.51
Use regrouping to solve. Make sure your answer is not an
improper fraction.
10-1-1-6-²-2--
69
Noitoont insloviups no son datin
Answers
-1
To use regrouping to solve, we need to add and subtract the numbers in the expression, taking care to keep track of any negative signs.
10 - 1 - 1 - 6 - ² - 2
= 10 - (1 + 1) - 6 - ² - 2 [Group the first two numbers together and add them]
= 10 - 2 - 6 - ² - 2 [Simplify the first three terms]
= (10 - 2) - 6 - ² - 2 [Group the first two terms together and subtract them]
= 8 - 6 - ² - 2 [Simplify the first two terms]
= 2 - ² - 2 [Simplify the first two terms]
= -1 [Simplify the expression by subtracting ² and 2 from -1]
Therefore, the final answer is -1.
A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0. 40 cubic foot per minute. At this rate how many hours will it take for the water level to drop 2 feet?
Answers
It will take 32 hours for the water level to drop 2 feet.The rate of leaking is 0.40 cubic feet per minute.
To calculate how many hours it will take for the water level to drop 2 feet, we can use the following formula:Time (in hours) = Volume of water (in cubic feet) ÷ Rate of leaking (in cubic feet per minute)In this case, the volume of water is equal to the volume of the pool, which can be calculated using the formula V = l × w × h, where l is the length of the pool, w is the width of the pool, and h is the height of the pool. In this case, l = 24, w = 8, and h = 4, so the volume of the pool is V = (24)(8)(4) = 768 cubic feet.The rate of leaking is 0.40 cubic feet per minute.Therefore, the time (in hours) it will take for the water level to drop 2 feet is equal toTime (in hours) = 768 cubic feet ÷ 0.40 cubic feet per minute Time (in hours) = 1920 minutes Time (in hours) = 32 hoursTherefore, it will take 32 hours for the water level to drop 2 feet.
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Assignment: Waves Math Exploration
What is the wave speed of a wave that has a frequency of 500 Hz and a wavelength of 0.40 m?
Please answer immediately if able to!
Answers
200 m/s is the wave speed of a wave that has a frequency .
What do you name a wave?
There are two different types of waves: longitudinal and transverse. Longitudinal waves are similar to those of sound in that they alternate between compressions and rarefactions in a medium, much like transverse waves in that the surface of the medium rises and falls.
The pattern of disruption brought about by the movement of energy through a medium (such as air, water, or any other liquid or solid matter) as it spreads away from the source of the sound is known as a sound wave.
The wave speed (v) of a wave can be calculated by multiplying its frequency (f) by its wavelength (λ). Mathematically, we can express this as
v = f x λ
Substituting the given values of frequency and wavelength into this formula, we get:
v = 500 Hz x 0.40 m
Multiplying these values, we get:
v = 200 m/s
Therefore, the wave speed of a wave that has a frequency of 500 Hz and a wavelength of 0.40 m is 200 m/s.
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Ms. Ibrahim travelled a total of 150 miles for work in 5 days. She traveled the same distance for work each day. Which 3 points lie on the line that represents the total distance in miles y, she traveled for work in x days. Circle three correct points.
Answers
Three pοints οn the line are: (0,0), (1,30), and (2,60)
what is slοpe-intercept fοrm?When yοu knοw the slοpe οf the line tο be investigated and the given pοint is alsο the y intercept, yοu can utilise the slοpe intercept fοrmula, y = mx + b. (0, b). The y value οf the y intercept pοint is denοted by the symbοl b in the fοrmula.
Tο sοlve the prοblem, we can start by using the fοrmula fοr the equatiοn οf a line in slοpe-intercept fοrm:
y = mx + b
We can use the given infοrmatiοn tο find the slοpe:
m = tοtal distance / number οf days = 150 miles / 5 days = 30 miles/day
b = 0 miles
Therefοre, the equatiοn οf the line representing the tοtal distance Ms. Ibrahim travels fοr wοrk in x days is:
y = 30x
When x = 0 (i.e., when Ms. Ibrahim dοes nοt wοrk), y = 0.
When x = 1 (i.e., οn the first day), y = 30 miles.
When x = 2 (i.e., οn the secοnd day), y = 60 miles.
Sο, three pοints οn the line are: (0,0), (1,30), and (2,60)
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Help please ! I’ll mark brainliest <333
Answers
Answer:
A) 6; B) 29∘; C) 29∘; D) 151∘
Step-by-step explanation:
A) Since ∠3 = ∠5 (opposite angles), we can make an equation:
5x - 1 = 3x + 11
5x - 3x = 11 + 1
2x = 12 / : 2
x = 6
B) ∠3 = 5x - 1 (x = 6)
∠3 = 5 × 6 - 1 = 29∘
C) ∠3 = ∠1 = 29∘ (cross angles)
D) ∠2 = 180∘ - ∠1 = 180∘ - 29∘ = 151∘
19. A piece of wire 44 cm long is cut into two parts.
Each part is bent to form a square. Given that
the total area of the two squares is 65 cm², find the
perimeter of each square.
Answers
4x + 4y = 44 cm
This is a system of equations where you can solve for one variable and then substitute to find the other.
4x = 44 - 4y
X= 11-y
Then, substitute.
(11-y)^2 + y^2 = 65
121-22y+2y^2=65
2y^2-22y+56= 0
Now factor and solve for y.
Y^2-11y+28=0
(Y-4) (y-7) =0
Y= 4 or 7
The perimeter is 4(x) + 4(y), so the perimeters of the squares would be 28 cm and 16 cm respectively.
Answer:28 and 16 cams
Step-by-step explanation: let the two parts be x cms and 44 -x cms.
So side of squares will be x/4 and (44-x)/4 resp
Area will be (x/4)^2 and ((44-x)/4)^2 resp
Equation is(x/4)^2 + ((44-x)/4)^2 = 65
(X-28)(x-16) = 0
X =28 or x = 16 cms
the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes. find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
Answers
The probability of a person being randomly choosing having waiting time greater than 4.25 is 0.2917 or 29.17%.
To answer this question we need to know about-
Probability is the measure of the likelihood of an event to happen. The probability value ranges between 0 and 1.
When the probability value is 0, it means that the event is impossible to happen.
When the probability value is 1, it means that the event is certain to happen.
Uniform distribution is when the values of a probability distribution are spread uniformly across the interval, it is called a Uniform distribution
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 6 minutes.
The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is found as follows:
Let X = Waiting time of a randomly selected passenger P(X > 4.25) = ?
Now we have to use the uniform distribution formula to find the probability:
P(C< X >D)=C-D/B-A
where C = lower value of the selected interval
D= upper value of the selected interval
B= highest value of the selected interval
A= lowest value of the selected interval
putting above values in the formula -
P(X > 4.25) = 6 - 4.25/6-0= 0.2917
Hence the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.2917.
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 7
Blue 6
Green 12
Yellow 19
Purple 19
Based on these results, express the probability that the next spin will land on blue as a fraction in simplest form.
Answers
Explanation
Add up the frequencies:
7+6+12+19+19 = 63
Out of those 63 total spins, 6 of them landed on blue.
The empirical (aka experimental) probability of landing on blue is therefore 6/63 = 2/21
Find the value of the discriminant for the quadratic:
x²- 7 + 6 = 0
Value of the discriminant?
How many zeros?
What type?
Answers
(a) The discriminant is positive (25)
(b) The quadratic equation has two zeros.
(c) The type of the zeros is real and distinct.
What is the discriminant of the quadratic equation?The given quadratic equation is: x² - 7x + 6 = 0
To find the discriminant, we use the formula:
Discriminant = b² - 4ac
Here, a = 1, b = -7, and c = 6.
So, the discriminant is:
b² - 4ac = (-7)² - 4(1)(6) = 49 - 24 = 25
Therefore, the discriminant is 25.
To determine the number of zeros, we use the discriminant as follows:
If the discriminant is positive (greater than zero), then the quadratic equation has two real and distinct roots.If the discriminant is zero, then the quadratic equation has one real and repeated root.If the discriminant is negative (less than zero), then the quadratic equation has two complex conjugate roots.Here, the discriminant is positive (25), so the quadratic equation has two real and distinct roots.
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A car travels at a constant speed
It travels a distance of 146.2m, correct to 1 decimal place. This takes 7 seconds,correct to the nearest second
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In winter, the price of apples suddenly went up by $0. 75 per pound. Sam bought 3 pounds of apples at the new price for a total of of $5. 88. Write an equation to determine the original price per pound
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The equation to determine the original price per pound is 3(x + 0.75) = 5.88, where x is original price per pound. so, the original price is $1.21.
Let x be the original price per pound of apples.
When the price increased, the new price became x + 0.75.
Sam bought 3 pounds of apples at the new price for a total of $5.88. This can be expressed as:
3(x + 0.75) = 5.88
Expanding the left side of the equation, we get:
3x + 2.25 = 5.88
Subtracting 2.25 from both sides, we get:
3x = 3.63
Dividing by 3, we get:
x = 1.21
Therefore, the original price per pound of apples was $1.21.
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what is the area of an equilateral triangle whose side length is 8 cm? leave your answer in simplest radical form.
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The area of the equilateral triangle with a side length of 8 cm is 16√(3) cm².
To find the altitude of an equilateral triangle with a side length of 8 cm, we can use the Pythagorean theorem.
The Pythagorean theorem is states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In these triangles, the side opposite the 60-degree angle is half the length of the hypotenuse, which is 8 cm. Using the Pythagorean theorem, we can find that the length of the altitude is:
Altitude = √(8² - (4²)) = √(48) = 4√(3)
Now that we know the altitude, we can plug it into the formula for the area of a triangle:
Area = (base x height) / 2 = (8 x 4√(3)) / 2 = 16√(3) cm²
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