The required solution of the given quadratic equation are 2 or -2.
What is Quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x ax² +bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution.
According to question:We have,
b² -4=0
Here we will use identity a² - b² = (a+b)(a-b)
Then,
b² -4=0
b² - (2)² = 0
(b + 2)(b - 2) = 0
b + 2 = 0
b = -2
Or b - 2 = 0
b = 2
Thus,required solution of the quadratic function are 2 or -2.
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how to solve this equation?
Answer: 1
Step-by-step explanation:
Explanation and steps in photo
Astronomers often measure large distances using astronomical units (AU) where 1 AU is the average distance from Earth to the Sun. In the image, d
represents the distance from a start to the Sun. Using a technique called "stellar parallax," astronomers determined θ
is 0.00001389 degrees.
b) Write an equation to calculate d
for any star.
(Your response must include an equal sign, and the variables d
and θ.)
The trigonometric function can be used to calculate the distance (4124966.128 AU) between the star and also the sun.
d = 4124966.128
Define the term "stellar parallax"?Astronomers can determine the apparent shift in location of a star by measuring its position once, then again six months later. Stellar parallax refers to the apparent motion of the star.Given:
Astronomers frequently use astronomical units (AU), where 1 AU represents the typical distance between the Earth and the Sun.The graphic depicts the separation between the Sun and a star.Astronomers discovered that using a method known as "stellar parallax," is 0.00001389 degrees.The steps listed below can be used to calculate the astronomical unit distance between star and the Sun:Step 1: To calculate the distance in astronomical units here between star and the Sun, apply the trigonometric function.
The sine function is used to calculate the distance in step two.
sin Ф = P/ H
where H is the hypotenuse and P is the perpendicular.
Step 3: Replace the above expression with the known terms.
sin (0.00001389 ) = 1/d
Step 4: Condense the previous expression.
d = 4124966.128
Thus, the distance of star from the sun is found as d = 4124966.128.
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what is the greatest two-digit prime number with the property that the product of its digits is also a prime number?
The greatest two-digit prime number with the property that the product of its digits is also a prime number is 37, since 3 x 7 = 21.
The greatest two-digit prime number with the property that the product of its digits is also a prime number is 37, since 3 x 7 = 21. Prime numbers are those numbers greater than 1 that are divisible only by 1 and itself. Two-digit prime numbers are those number between 10 and 99. The prime numbers between 10 and 99 are 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. The product of the digits of 37 is 3 x 7 = 21, which is also a prime number. Therefore, the greatest two-digit prime number with the property that the product of its digits is also a prime number is 37.
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Solve the following problem by graphing -6 = -3y + 2x 4= -y + 8/3x
Answer:
y = 2/3x - 2
y = 8/3x - 4
Step-by-step explanation:
If you graph it you will intersect at (1 , -1 1/3)
Shane invested $3,500 in a savings account that pays 4% interest
semiannually (every 6 months). How much money will he have in his
account in 5 years?
The money in Shane's account after five years will be $4900.
The formula for simple interest is -
S.I. = PRT/100, where P is principal, R is rate of interest, T is time and SI is simple interest. Interest is calculated semi-annually then t will be 5×2 years.
Keep the values in formula -
S.I. = 3500 × 4 × 5 × 2/100
Performing multiplication in numerator on Right Hand Side of the equation
S.I. = 1,40,000/100
Cancelling common zero on Right Hand Side of the equation
S.I. = $1400
Total amount = Principal + Interest
Keep the values in formula -
Total amount = 3500 + 1400
Performing addition
Total amount = $4900
The total money in account will be $4900.
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I need help with this question please and thank you
The type of transformation and scale factor as required are;
16) Rotation
17) Reflection
18) Dilation
19) n = 5
20)P = r = 4
What is the type of transformation?There are different types of transformation as follows;
1) Translation: This type of translation is defined as moving the object in space by keeping its size, shape or orientation constant. In a translation, each point of the shape must be moved in the same direction and for the same distance
2) Dilation: This type of translation expands or contracts the object by keeping its orientation or shape the same. This is also known as resizing.
3) Rotation: This type of transformation has an object about a fixed point without changing its size or shape.
4) Reflection: This type of translation is called reflection because it flips the object across a line by keeping its shape or size constant.
16) This transformation is rotation based on the definitions above.
17) This type of transformation is a reflection as it is like the image was flipped across a line more like a mirror image.
18) This called dilation as the scale factor was adjusted to produce the new image.
19) Scale Factor = 6/3 = 2
Thus;
n = 10/2 = 5
20) Scale factor = 12/9 = 4/3
Thus;
P = r = 3 * 4/3
= 4
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Systems of Equations and Inequalities 2020-2021 / 5 of 18
Two students were shopping for school supplies. They need spirals which cost x dollars and pens which cost y dollars. One student bought
2 spirals and 3 pens for $8. 66. Another student bought 4 spirals and 5 pens for $15. 20. Find the unit cost of a spiral.
1
Each notebook is $5 and each thumb drive is $12.
To Locate:
The price per notebook and per flash drive
Explain x and y:
Let's say a notebook costs x dollars.
I'll pay whatever a thumb drive costs.
Form equations:
4x + y = 32 ------------------------ [ 1 ]
3x + 2y = 39 ---------------------- [ 2 ]
Equation [ 1 ] x 2:
8x + 2y = 64 ---------------------- [ 3 ]
[ 3 ] - [ 2 ] :
5x = 25
x = 5
Substitute x = 5 into [ 1 ]:
4(5) + y = 32
20 + y = 32
y = 32 - 20
y = 12
Find the cost of each notebook and each thumb drive:
notebook = x
notebook = $5
thumb-drive = y
thumb-drive = $12
Each notebook is $5 and each thumb drive is $12.
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suppose that the student scores on a test follow a bell-shaped distribution with mean 50 and standard deviation 10. using the empirical rule, what percent of students scored scored above 60?
Approximately 99.7% falls within three standard deviations.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
Since the mean score is 50 and the standard deviation is 10, this means that approximately 68% of the students scored between 40 and 60, approximately 95% scored between 30 and 70, and approximately 99.7% scored between 20 and 80. Therefore, approximately 32% of students scored above 60.
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What is the value of f(150)?
Answer:
Step-by-step explanation:So make sure you learn this in fifth grade so basically whatever your line go to let's say if it lands on 79 I mean 70 and that's like I mean 150 it depends on what you're using
Light travels at a speed of 3 x 10 8 metres per second
According to the universe in which light only moves at 3x10^8 meters/sec, it would take 3.333 x 10^-6 seconds to go 1 meter.
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
According to the universe in which light only moves at 3x10^8 meters/sec, it would take 3.333 x 10^-6 seconds to go 1 meter.
Given that light travels 3x10^8 m/s. So there . . .
The speed of light is in units of meters/sec.
If it is 3x10^8 meters/sec, we can also write the inverse:
1 sec/3x10^8 meters
Do the division to find seconds per 1 meter:
3.333 x 10^-9 seconds.
For Milky Way inhabitants,
It only requires 3.33 x 10^-9 second.
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The complete question is;
Light travels about 3 x 10^8 metres per second. Find the time it takes to travel 1 metre.
Using the substitution method,solve
4x-3y=25
6x+5y=9
Answer:
The correct answer is
x= 4
y=-3
Answer:
(x, y) = (4, -3)
Step-by-step explanation:
You want to solve this system of equations using substitution.
4x -3y = 256x +5y = 9SubstitutionThe substitution method requires that you find an expression for one of the variables that you can use to replace that variable in the other equation.
Here, we choose to use the second equation to write an expression for y. This makes the resulting coefficients be decimal values.
5y = 9 -6x . . . . subtract 6x
y = 1.8 -1.2x . . . . divide by 5
Substituting this for y in the first equation gives ...
4x -3(1.8 -1.2x) = 25
7.6x -5.4 = 25 . . . . . . . simplify
7.6x = 30.4 . . . . . . . . add 5.4
x = 4 . . . . . . . . . . divide by 7.6
y = 1.8 -1.2(4) = 1.8 -4.8
y = -3
The solution is (x, y) = (4, -3).
__
Additional comment
We could have used the first equation to write an expression for x. That would also make the coefficients be terminating decimal values. Using the first equation to write an expression for y leaves coefficients that are multiples of 1/3, not nice decimals. Similarly, solving the second equation for x would result in coefficients that are multiples of 1/6, also not nice decimals.
These "not nice" values can be used to get the same result. It just depends on what kind of arithmetic you want to do: fractions or decimals.
This set of coefficients would generally indicate that some other method would be more desirable to use: graphing, or matrix methods, for example. The attachment shows a matrix method.
HELP ME PLEASE THIS IS HALF MY GRADE
Answer: 2/7
Step-by-step explanation:
Go from point A to D by moving up 2 units and right 7 units. Since it slopes up it's a positive number.
The polygons are similar, but not necessarily drawn to scale. Find the value of x.
The value of x is 5.5
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
Given;
The two polygons are similar
So,
x-1/6=16/21
x/6-1/6=16/21
x/6=16/21+1/6
x=5.5
y+1/32=21/24
y/32+1/32=7/8
y=3
Therefore, the value of x in polygon will be 5.5
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enter the value of n for the eqation 5 n = 5 11 times 5 3
For the equation 5^n = 5^11 × 5³ the value of n using the exponents rule is obtained as n = 14.
What is an exponent?
The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
The given equation is 5^n = 5^11 × 5³
Since, the base of the exponents is same, so apply the operations on the powers of the base.
The value of n can be found by following the exponent rule.
The exponent rule is - a^(b) × a^(c) = a^(b + c)
Write the equation according to the rule -
5^n = 5^(11 + 3)
Use the arithmetic operation of addition -
5^n = 5^(14)
n = 14
Therefore, the value of n is obtained as 14.
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Arabella wants to buy 42 dresses.
Each dress costs £8.70.
Estimate the cost of Arabella's 42 dresses
Answer:
378 Euros
Step-by-step explanation:
A good way to estimate is to round to the nearest whole number or 10th and then multiply:
8.70 --> 9.00 (since 7 > 5 you round up to the nearest whole number, in this case 9)
then you multiply. A good way to do this in your head is doing:
split 42 into 2 numbers:
40, 2
then multiply by nine:
9 * 4 = 36 (9 * 40 = 360) added a zero since we multiplied by 40, its just easier to multiply by smaller numbers
9 * 2 = 18
then add the two numbers together:
360 + 18 = 378 Euros
The actual answer with a calculator is 365.4 Euros, so for an estimation its fairly close.
Another way you could solve it is to just round 8.70 --> 10 (rounding to the nearest 10th)
then:
10 * 42 = 420 (nice)
I don't recommend it since its way too off from the original value, but could be good for quick estimations.
hope this helped you :)
Given the triangle find x.
“Although part of your question is missing, you might be referring to this full question: In the given triangle with base length =[tex]8\sqrt{3}[/tex] and angles at vertices are 60°,90°, and 30° respectively find the length of side x ”
The length of side x in the given triangle is 4√3 units.
In the given triangle with a base length of 8√3 and angles at the vertices of 60°, 90°, and 30°, we can use trigonometry to find the length of side x.
Since we know that one angle is 90°, we can use the 30-60-90 triangle ratios to determine the other sides. The ratios for a 30-60-90 triangle are as follows:
Opposite side (x) / hypotenuse (8√3) = sin 30° = 1/2
Adjacent side (y) / hypotenuse (8√3) = cos 30° = √3/2
So, using these ratios, we can calculate the length of the opposite side (x):
x = (8√3) (1/2) = 4√3
Therefore, the length of side x in the given triangle is 4√3 units.
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Need assistance……………………….
Answer:
see attached.
Step-by-step explanation:
15. Use the given degree of confidence and sample data to find a confidence interval for the
population standard deviation c. Assume that the population has a normal distribution.
Round the confidence interval limits to the same number of decimal places as the sample
standard deviation.
College students' annual earnings: 98% confidence; n = 9, x = $3959, s = $886
Confidence interval will be between $831.57 and $1040.67.
To find a confidence interval for the population standard deviation, we can use the formula:
(sample standard deviation / square root of sample size) x t-multiplier
where t-multiplier is based on the degree of confidence and the sample size.
For a 98% confidence interval and a sample size of 9, the t-multiplier is 2.821 (from a t-table or a calculator with a t-distribution function).
So the confidence interval for the population standard deviation is:
(886 / sqrt(9)) x 2.821 = (886 / 3) x 2.821 = 295.33 x 2.821
= 831.57 to 1040.67
Therefore, we can be 98% confident that the population standard deviation of the annual earnings of college students falls between $831.57 and $1040.67.
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the value of
3(2x+3) when x=5
Answer:
39
Step-by-step explanation:
3(2x + 3) = 6x + 9 = 6(5) + 9 = 39
[tex]3(2x+3)[/tex] when x is 5
Substitute for x with the given value:
[tex]3(2(5)+3)[/tex]
[tex]3(10+3)[/tex]
[tex]3(13)[/tex]
[tex]=\fbox{39}[/tex]
Sixty three is the product of nine and a number
Sixty three is the product of nine and a number which is seven
What is multiplication?Multiplying in math is the same as adding equal groups.
The number of items in the group grows as we multiply. Parts of a multiplication problem include the product, the two components, and the answer.
In the multiplication problem involving 63 as the product of 9 and another number
let the number be x
9 * x = 63
9x = 63
isolating x by dividing both sides by 9
9x / 9 = 63 / 9
x = 7
the number is 7
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a numerical measure of linear association between two variables is the . a. standard deviation b. covariance c. coefficient of variation d. variance
option b is correct - covariance
The correlation coefficient (r ) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.
Covariance
A numerical measure of linear association between two variables.
Covariance is a measure of how changes in one variable are associated with changes in a second variable. Specifically, covariance measures the degree to which two variables are linearly associated. However, it is also often used informally as a general measure of how monotonically related two variables are. It is similar to variance, but where variance tells you how a single variable varies, covariance tells you how two variables vary together.
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I need help please, thanks so much
Answer:
g(- 1) = - 4
Step-by-step explanation:
g(- 1) means what is the value y when x = - 1
Locate - 1 on the x- axis, go vertically down to meet the line at (- 1, - 4 ) , so
when x = - 1 then y = - 4 , that is
g(- 1) = - 4
Answer:
[tex]g(x)=-4[/tex]
Step-by-step explanation:
1. Find the slope-intercept form of the equation
So to first solve this equation you need to find the slope of the line to find the slope you do [tex]\frac{rise}{run}[/tex] which means you count the number of boxes the line moves up or down which is 2 so that is the "rise" part of our equation. To find the run you find how much the equation moves left or right which is one. So the slope would be [tex]\frac{2}{1} x[/tex] or [tex]2x\\[/tex]. To find the y-intercept you look at where the line hits the y-axis which is at -2. So now you have your equation in a slope-intercept form which is [tex]g(x)=2x-2[/tex]
2. Find g(-1)
So... The slope-intercept form of the equation is [tex]g(x)=2x-2[/tex] that you replace the x in the g(x) with -1 so now you replace the x in the slope-intercept equation with -1. Then simplify!
[tex]g(-1)=2(-1)-2[/tex]
[tex]g(-1)= -2-2[/tex]
[tex]g(-1)=-4[/tex]
remember that we don't consider degenerate triangles unless specially instructed otherwise. two side lengths of a triangle are and . what is the longest possible integer length of the third side of the triangle?
The minimum value of the third side is 9 cm, and The maximum value of the third side is 6.7 cm.
The minimum value of the third side is when the triangle is a degenerate triangle, meaning that the third side is a line segment joining the two endpoints of the first two sides, which is equal to 3 cm + 6 cm = 9 cm.
The maximum value of the third side is when the triangle is a right triangle, and the two sides are the legs. According to the Pythagorean theorem, the third side (the hypotenuse) should be equal to the square root of 3² + 6² = 9 + 36 = 45, which is equal to 6.7 cm.
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--The given question is incorrect; the correct question is
"The length of two sides of a triangle are 3cm and 6cm. What could be the minimum and maximum value of its third side?"--
The length of a rectangle is 5/6 feet and the width is 1/8, how much greater is the length than the width
The length of the rectangle is 17/24 feet greater than the width.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
The length of a rectangle is 5/6 feet and the width is 1/8 feet.
So, The length of the rectangle is greater than the width is,
⇒ 5/6 - 1/8
⇒ (40 - 6)/48
⇒ 34/48
⇒ 17/24 feet.
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please help me find angle m< 4 (geometry)
Assuming the horizontal lines are parallel, we will see that the measure of angle 4 is m∠4 = 39°
How to find the measure of angle 4?First, we assume that the two horizontal lines are parallel, that will mean that the measures of angle 4 and 7 are equal, beacause both of them are on the same quadrant.
Also, notice that angle 7 and 141° should add up to 180° (a plane angle) thus, we will get:
m∠7 + 141° = 180°
m∠7 = 180° - 141°
m∠7 = 39°
The measure of angle 4 is also that, so we conclude that:
m∠4 = 39°
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MATH QUESTION is in the image (40 Points)
The numeric value of the expression 36x + 42y - 18x + 6 when x = 0.25 and y = -1 is given as follows:
-31.5.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The expression in this problem is given as follows:
36x + 42y - 18x + 6.
We want to find the numeric value at:
x = 0.25 and y = -1.
Hence:
The two instances of x are replaced by 0.25.The lone instance of y is replaced by -1.Then the numeric value is given as follows:
36(0.25) + 42(-1) - 18(0.25) + 6 = -31.5.
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Point A(-3, 5) is first reflected over the line y =x, then reflected over the line with equation y = -4. What are the coordinates of the image of A after the two reflections?
The two coordinate values are simply swapped in the reflection over the line y=x: A'' = (4, 1) (4, 1)
What are the positions of A's reflections after the two?The x-coordinate and y-coordinate of a point change positions when it is reflected across the line y = x.
The x- and y-coordinates shift positions and are negated when a point is mirrored across the line y = -x.
In light of this, the reflection of the point (x, y) across the line y = x is (y, x).
The first reflection's location across the vertical line x=-3 ensures that the y-coordinate is constant.
The point (-3, 4) on the line of reflection will become the halfway point between A and A' thanks to the x-coordinate of A':
(-3, 4) = (A +A')/2
2(-3, 4) (-3, 4)
-A = A' = (-6-(-7), 8 -4) = (1, 4) (1, 4)
The two coordinate values are simply swapped in the reflection over the line y=x: A'' = (4, 1) (4, 1)
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to classify fossils of an insect, archeologists measure the length of the body. the body length of a type a insect is distributed as and the body length of a type b insect is distributed as (in millimeters). the fossil is classified as type a if the length is less than millimeters and classified as type b if the length is larger than or equal to millimeters. find the value of that the probability of correctly classifying a type a insect equals the probability of correctly classifying a type b insect (round off to first decimal place).
The value that the probability of correctly classifying a type an insect equals the probability of correctly classifying a type b insect is 4.5 millimeters.
To find the value that the probability of correctly classifying a type A insect equals the probability of correctly classifying a type B insect, we need to find the point where the probability density functions of the two types of insects intersect.
For type A insects, the probability density function is given as -
f(x) = [tex](1/2)e^{-{x-3}^{2/2}}[/tex]
For type B insects, the probability density function is given as-
f(x) = [tex](1/4)e^{-{x-5}^{2/2}}[/tex]
We can set these two probability density functions equal to each other and solve for x as follows -
[tex](1/2)e^{-{x-3}^{2/2}}[/tex] = [tex](1/4)e^{-{x-5}^{2/2}}[/tex]
Solving for x, we get:
x = 4.5
So the value that the probability of correctly classifying a type A insect equals the probability of correctly classifying a type B insect and is 4.5 millimeters. This means that if the length of the insect is 4.5 millimeters or less, it will be classified as type A, and if it is greater than 4.5 millimeters, it will be classified as type B.
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Help me please thhhannkkk youuu
Answer:
25 . 3 %
Step-by-step explanation:
it has the circuits of the brain
The prom committee is decorating the venue for prom and wants to hang lights above the diagonals of the rectangular room. If DH=44.5 feet, EF=39 feet, and m∠GHF=128° , find m∠HEF .
The measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.
Define the term linear pair?A linear pair is just a pair of neighboring angles created by the intersection of two lines. 1 and 2 create a linear pair in the illustration. The same holds true for pairs 1, 2, 3, and 4. A linear pair's two angles are always supplementary, that means that the sum of their measurements is 180 degrees.The given data:
DH=44.5 feet, EF=39 feet, and m∠GHF=128°As, GE is the straight line.
Thus,
m∠EHF = 180 - 128 (sum of all angles of line is 180, linear pair)
= 52°
Now,
m∠HEF = 180 - 52 / 2 (isosceles triangle)
m∠HEF = 64°
Thus, the measure of the angle m∠HEF = 64°, for the diagonals of rectangular room.
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The diagram for the question is attached.