To determine the number and type of solutions to the quadratic equation x^2 - x = -1/4, we can use the discriminant, which is the part of the quadratic formula that determines the number of solutions. The quadratic formula is:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation. In this case, the coefficients of the equation are a = 1, b = -1, and c = -1/4. Plugging these values into the formula gives us:
x = (1 +/- sqrt(1^2 - 4(1)(-1/4))) / (2(1))
x = (1 +/- sqrt(1 + 1)) / 2
x = (1 +/- sqrt(2)) / 2
Therefore, the quadratic equation has two solutions: x = (1 + sqrt(2)) / 2 and x = (1 - sqrt(2)) / 2. These solutions are both real numbers.
A person invests 10000 dollars in a bank. The bank pays 6.5% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 29500 dollars?
Answer: 3000 years
Step-by-step explanation:
Let y be the number of money and x be the number of years
So we have the equation
y= 6.5x + 10000
Now we put 29500 in the y
29500 = 6.5x + 10000
Subtracted 10000 from both sides
19500 = 6.5x
Divided both sides by 6.5
x = 3000 years
Anna is knitting hats to give as gifts. Each one will use 1.2 skeins, and she has 6 skeins of yarn available. With the yarn available, how many hats can Anna knit?
Answer:
5
Step-by-step explanation:
There are 6 total skeins, and 1.2 is needed to make one
So you would divide 6 by 1.2
6 / 1.2 = 5
And to confirm it is 5, you can now multiply 5 by 1.2
5 x 1.2 equals 6
choose the equation of the graphed function.
Answer:
J
Step-by-step explanation:
shifts to the right by 1
The owner of a small computer repair business has
one employee, who is paid an hourly rate of $22.
The owner estimates his weekly profit using the
function P(x) = 8600 - 22x. In this function, x
represents
the number of
Answer:
employee's hours worked per week
Step-by-step explanation:
check answer
Answer:
In this function, x represents the number of 2) HOURS WORKED PER WEEK.
The theoretical probability of an event occurring is two-fifths. which best describes the experimental probability associated with this event?
The correct option is B. Out of every 5 trials, the desired outcome will occur approximately 2 times.
Explain the term experimental probability?The number of times an event happened during the experiment as a percentage of all the times the experiment was run is known as that of the experimental probability of that event occurring.The ratio between the number of favorable events and the total number of conceivable outcomes is known as the theoretical probability.For the stated question -
The first claim asserts that it will occur exactly twice, yet probability never assures success.
The second and fourth statements refer to "out of 7," which is false because "out of 7" is equivalent to "out of 2 to 5"
Thus, conclusion is out of every 5 trials, the desired outcome will occur approximately 2 times.
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The complete question is-
The theoretical probability of an event occurring is Two-fifths. Which best describes the experimental probability associated with this event?
A. Out of every 5 trials, the desired outcome will occur exactly 2 times.
B. Out of every 5 trials, the desired outcome will occur approximately 2 times.
C. Out of every 7 trials, there will be 2 desired outcomes and 5 undesired outcomes.
D. Out of every 7 trials, there will be 5 desired outcomes and 2 undesired outcomes.
If you have an average of 31 and you have the numbers 63,53,20,10, what is the missing value?
Answer: 9
Step-by-step explanation:
Let's start with what we know. If we have the data set:
63, 53, 20, 10, x
The average is:
(63+53+20+10+x)/5 = 31
We multiply both sides by 5
(65+53+20+10) = 155
146 + x = 155
x = 9
Diego is making sandwiches for a picnic. He uses 2 slices of cheese to make each sandwich,
and he has a package of cheese with 24 slices.
Write an equation that shows how the number of slices of cheese remaining, y, depends on
the number of sandwiches Diego makes, x.
Answer:
y = 24
y = 2x
I need help with this question
please help
Answer:£84.45
Step-by-step explanation:
10 single packs costs £97.5
9.75x10
3 packs of 3 plus a single costs £84.45
24.90x3+9.75
2 packs of 5 costs £86.5
43.25x2
Answer:
pack of 3 rolls
Step-by-step explanation:
Two 5 packs is 86.50
Ten 1 packs are 97.50
Three 3 packs is 74.70 + 8.3 (1/3 of 3 pack) = £83
What equation represents Twenty five is one sixth of the number n
The equation that represents "Twenty five is one sixth of the number n" is:25 = (1/6) * n
The equation "25 = (1/6) * n" represents the relationship between the number 25 and an unknown number, n. It states that 25 is equal to one sixth of n. In other words, if we multiply the unknown number n by one sixth (or divide n by 6), we will obtain the value of 25. This equation can be used to solve for the value of n by multiplying 25 by 6, which would give us the unknown number. It provides a clear mathematical expression of the given relationship and allows us to find the value of n based on the given condition.The equation states that 25 is equal to one sixth of the number n. This means that if we take one sixth of the value of n, we will get 25 as the result. In other words, if we divide the value of n by 6, the quotient will be 25.
To understand it conceptually, imagine that we have a number n and we want to find one sixth of that number. By dividing the number by 6, we can determine how many equal parts make up the whole number, and one of those parts is equal to 25.
This equation is useful in various situations, such as solving problems involving proportions or determining unknown values when given a fraction of a number.
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of
he
ne.
st
Simplify the following:
Holiday Bonus Problem
(5 Points)
X
{²+ + + ²x - 3X ICE +
R-X
{[(X + A)(X-A)M+A²M]E}
7
ruc
4AS
4AS
+
3X[(E+Y)²-(E-Y)²] * 3E[(Y + X)² – (Y-X)²] 3Y[(X + E)²-(X-E)²]
- BA}Y
4AS
Answer:
99987766554446677765
sketch the region enclosed by the given curves. y = 4/x, y = 16x, y = 1 16 x, x > 0
In order to plot the region enclosed by the given graphs we have to find the intersection points of all the 3 graphs taking 2 at a time
so finding intersection point of the y=4/x and y=16x
4/x=16x
=> [tex]x^{2}[/tex] = 1/4
=> x = 1/2 as x>0
and y=16x
=> y =8
now finding intersection point of y=4/x and y=1/16x
=> 4/x =x/16
=> [tex]x^{2}[/tex] = 64
=> x = 8 as x>0
and y= 4/x
=> y=1/2
now finding intersection point of y=16x and y=1/16x
the intersection point of both line is x=0
so y=16x
=> y=0
so we will get the intersection point of all the lines now after plotting all the points below we will get the graph as attached below.
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For the data in the table, does y vary directly with x? If it does, write an equation for the
direct variation.
x y
8 11
16 22
24 33
Answer:
Below in bold.
Step-by-step explanation:
The definition of direct variation is y = kx where k is a constant.
So, if y/x is a constant for the data, we have direct variation.
So, checking the rows in the given table:
y/x = 11/8
y/x = 22/16 = 11/8
y/x = 33/24 = 11/8
- we see that this is direct variation.
So, k = 11/8 and
The equation is
y = (11/8) x
or
y = 11x/8
or
y = 1.375x in decimal form.
Answer:
y = (11/8)x----------------------------------
Direct variation equation:
y = kx, where k- variation coefficientUse the pairs of coordinates and find the value of k, then compare:
11 = 8k ⇒ k = 11/822 = 16k ⇒ k = 22/16 = 11/833 = 24k ⇒ k = 33/24 = 11/8The value of k is same with all ordered pairs and the equation is:
y = (11/8)xMr waton buy 4 gallon of paint that cot 34 per gallon how much did mr waton pend on paint
Mr. Watson spent a total of $136 on the paint.
When taking on a painting project, it's important to factor in the cost of the paint. Mr. Watson was savvy enough to purchase 4 gallons of paint, which will likely be enough to cover a large area or multiple rooms. Not only did he save money by buying in bulk, but he also saved time by not having to go back to the store for more paint.
For those planning to take on a painting project, it's important to consider the cost of the paint as well as some other factors. It's important to research different brands and types of paint to make sure you're getting the best quality for the best value. Additionally, it's important to factor in the cost of supplies, such as brushes, rollers, and other tools.
Ultimately, Mr. Watson made a smart decision by purchasing 4 gallons of paint. He was able to get the job done while saving money and time.
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the diameter of a circle is 16. by what number must the radius be decreased in order to decrease the area of the circle by $48\pi$?
To decrease the area of the circle by $48\pi$, we need to decrease the radius by a factor of $\sqrt{48\pi}$.
Since the original radius of the circle was 8, the radius must be decreased to
$\frac{8}{\sqrt{48\pi}} = \frac{8}{\sqrt{48}\sqrt{\pi}} = \frac{8}{\sqrt{48}} \approx \frac{8}{6.9282} \approx 1.1547$.Therefore, to decrease the area of the circle by $48\pi$, the radius must be decreased by a factor of about 1.1547.
This means that the radius must be decreased by a number that is about 1.1547 times smaller than the original radius of 8, or by about $8 \times (1 - 1.1547) = -0.6158$.
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1. Here are some examples of data. Answer whether each is discrete or continuous data.
a. The number of customers in a shop.
b. The weight of a baby.
c. Shoe sizes.
d. The length of a leaf.
Answer:
discrete and continuous data
Answer:
a. Discrete data
b. Continuous data
c. Discrete data
d. Continuous data
Step-by-step explanation:
a. It is always possible to count the number of customers in a line, this is a type of discrete random variable.
b. The weight of a baby in its first year or the temperature in a room throughout the day.
c. Shoe sizes can be decimals (7.5 or 8.5) but there are still a fixed set of possible values with gaps between them (there is no 7.9 shoes size). Therefore shoe size is a discrete random variable.
d. The length is typically considered a continuous variable, since, a sea otter will typically not measure exactly 5 feet, but the length will differ by some fraction of a foot.
1. Is the relation on the right a function? Explain.
2. Can you state the domain and range of a relation that is not a function? If yes, what is the domain and range of the relation on the right?
3. Angelo states that all functions are relations but not all relations are functions. Do you agree with Angelo? Support your answer using an example.
1) The relation in the right is not a function.
2) domain
D: {-60, 20, 70}
range
R: {-6, 3, 2, 5}
3) Angelo is correct.
What is a function?A function is a relation that maps elements from one set called the domain into another set called the range, such each element from the domain is mapped into only one of the elements of the range.
Thus, if an element of the domain is being mapped into two or more elements of the range, then the relation is not a function.
1) If you look at the relationship in the right, you can see that the input -60 is being mapped into two different outputs, this, it is not a function.
2) The domain is the set in the left:
D: {-60, 20, 70}
And the range is the set in the right side:
R: {-6, 3, 2, 5}
3) Angelo is correct, functions are relations, but not all relations are functions, only the relations that meet the condition written above.
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Select the correct anwer. What i the value of thi expreion when c = -4 and d = 10?
A. 2
B. 9
C. 21
D. 41
Reet
The expression be 1/4(c³+ d²) then the value exists 9.
What is meant by PEMDAS order of operations?The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication and division (left to right), addition and subtraction (from left to right).
The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations.
Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are in the following order: PEMDAS (from left to right).
Let the given expression be 1/4(c³+ d²)
The value of c = -4 and d = 10
substitute the values in the above equation, we get
Follow the PEMDAS order of operations
Calculate within parentheses ((-4)³ + (10)²) = 36
1/4((-4)³ + (10)²)
simplifying the above equation, we get
= 1/4 × 36
= 9
Therefore, the correct answer is option B. 9.
The complete question is:
What is the value of this expression when c = -4 and d = 10?
1/4(c³+ d²)
A. 2
B. 9
C. 21
D. 41
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Help appreciated!!!
Consider a dilation of polygon ABCDEF from center O with scale factor r resulting in its image, polygon A'B'C'D'E'F'.
If EDC measures 117° then the measure of E'D'C' is___ If AB measures 1.8 inches and A'B' measures 4.5 inches, then the scale factor r is____
Name one segment from polygon ABCDEF and one segment from polygon A'B'C'D'E'F' that are parallel.
Step-by-step explanation:
in a dilation all the angles stay the same. only the lengths of lines (like sides or heights) change - and all with the same scale factor (which makes the original and the dilated result similar objects).
angle EDC = 117°.
therefore angle E'D'C' = 117°.
AB = 1.8 in
A'B' = 4.5 in
the scale factor r is
r = 4.5 / 1.8 = 2.5
every segment of A'B'C'D'E'F' is parallel to its original counterpart in ABCDEF.
like
AB to A'B'
as well as
BC to B'C'
CD to C'D'
DE to D'E'
EF to E'F'
that is the reason why projections work (even at an inclined angle of the projection screen the picture might seem strangely stretched, but the angles are still all the same, parallel lines remain parallel, perpendicular lines remain perpendicular, ... - and the viewer still recognizes the pictures).
helppp please i dont know how to do this
The solution of the pairs of lines are as follows,
(1) Line 1 and line 2 are perpendicular to each other.
(2) Line 1 and line 3 are parallel to each other.
(3) Line 2 and line 3 are perpendicular to each other.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Calculate the slope of each line,
LIne 1
3y = 2x + 5
y = 2/3x + 5/3
Compared with the standard equation of line y = mx + c,
Slope m = 2/3
Similarly.
The slope of line 2 = -3/2
The slope of line 3 = 2/3
Now. properties of pair of lines state that the slope of parallel lines is equal and the slope of perpendicular lines are negative reciprocal of each other,
So
Slope of line 1 = slope of line 3
But,
The slope of line 2 is the negative reciprocal of the slope of lines 1 and 3.
Thus, the solution of the pair of lines has been shown above.
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If the m<2 = 58° and the m<13 = 111°, find the measures of angles 1, 5, 8, 14, 18.
Note: x || m and z || y
The value of angle 1 is 122°.
The value of angle 5 is 58°
The angle of angle 8 is 58°
The angle of angle 14 is 122°
The angle 18 is 58°
How to calculate the angles?It should be noted that this information deals with angles. It should be noted that the value of angle on a straight line is 180°.
In this situation, the value of angle 1 will be:
= 180° - 58°
= 122°
Also it should be noted that vertically opposite angles are equal. Therefore, angle 5 will be 58°.
In this situation, it should also be noted that alternate angles are the same. Hence, Thai gives the value of the angles for angles 8, 14 and 18.
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Urgent help guysssss
Answer: A
Step-by-step explanation:
How do you measure the length of a line segment using a ruler or a compass? Explain the steps and show your work.
To measure the length of a line segment AB, place the zero marking of the ruler along the beginning of the line and measure its length.
A line segment has two definite endpoints in a line, and the line segment is fixed, which is the distance between two fixed points. The length can be measured by metric units such as centimeters, and millimeters.
A line segment with two endpoints A and B and is denoted by the bar symbol (—).
Using Ruler and Compass:
There are some markings on the ruler beginning from zero as shown in the figure. these markings divide the ruler into equal parts.
Each part is equal to a length of 1 cm and these units are measured in centimeters and are further subdivided into 10 parts and each sub-part is equivalent to 1 millimeter.
To measure a line segment AB, place the zero marking of the ruler along the beginning of the line and measure its length accordingly.
ln the figure, the length of line segment AB is 8 cm.
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A water balloon is thrown upward from a height of 5 feet with an initial velocity of 35 feet per second. The quadratic function \large h\left(t\right)=-16t^2+35t+5 represents the height of the balloon, h, in feet t seconds after it is thrown. When does the water balloon reach the height of 20 feet? round your answer to the nearest thousandth.
Since, The equation of the height with the time is provided and the balloon is thrown upwards against gravity from 5 feet, The answer is 0.255 sec.
What do you mean by equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definition of an equation in algebra is a mathematical statement 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.
What is initial and final velocity?When gravity first exerts force on an object, its initial velocity defines how quickly the object moves. The final velocity, on the other hand, is a vector number that gauges a moving body's speed and direction after it has reached its maximum acceleration.
initial height = 5
final height =20
height to travel =20-5 =15
[tex]15 = 16t^{2}+35t+5\\16t^{2}+35t-10 =0[/tex]
solving we get, t = 0.255 or -2.44
since, -2.44 is not possible,
t = 0.255 seconds.
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Select the correct answer. Circle F is represented by the equation (x + 6)2 + (y + 8)2 = 9. What is the length of the radius of circle F? A. 3 B. 9 C. 10 D. 81
Considering a circle whose equation is (x + 6)² + (y + 8)² = 9. The radius of the circle is 3 units
How to determine the radius of the circleInformation given in the question
Circle F is represented by the equation (x + 6)² + (y + 8)² = 9
Equation of a circle is given as
(x - h)² (y - k)² = r²
The equation of the circle is written in standard form is sown above comparing the equation with the given question gives
rewriting the equation
(x + 6)² + (y + 8)² = 9
(x + 6)² + (y + 8)² = 3²
comparing shows that r = 3
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a deck is shuffled well, what is the probability that the top card is ace of spades and the bottom is queen of hearts?
The probability that the top card is an Ace of Spades and the bottom card is a Queen of Hearts is extremely low, as there are 52 cards in a standard deck of cards and only two of those cards are an Ace of Spades and a Queen of Hearts.
Therefore, the probability of the top card being an Ace of Spades and the bottom card being a Queen of Hearts is 1/2652 or approximately 0.000038%.The probability of getting an Ace of Spades as the top card and a Queen of Hearts as the bottom card is 1/52 x 1/52 = 1/2652. This can be expressed as a percentage by multiplying the fraction by 100 which gives us 0.000038%. The probability that the top card is an Ace of Spades and the bottom card is a Queen of Hearts is extremely low, as there are 52 cards in a standard deck of cards and only two of those cards are an Ace of Spades and a Queen of Hearts.
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Autumn has a smart phone data plan that costs $50 per month that includes 9 GB of data, but will charge an extra $10 per GB over the included amount. How much would Autumn have to pay in a month where she used 3 GB over the limit? How much would Autumn have to pay in a month where she used went over by xx GB?
Answer:
1. $80 dollars for the month she used 3 GB over her data limit.
2. 10x + 50.
Explanation:
1. Autumn used 3 GB data more than her plan offered. $10 dollars a gigabyte of data times 3 gigabytes equals 30, plus 50 dollars for the base smartphone plan (which, off topic, sucks) equals 80 dollars for the month.
2. 10x + 50 means 10 dollars per X gigabytes, plus the base 50 dollars a month Autumn has to pay.
make this graph into y=mx+b form
Answer: y=-3x-5
Step-by-step explanation:
(0,-5) (-1,-2)
[tex]\displaystyle\\\frac{x-x_1}{x_2-x_1} =\frac{y-y_1}{y_2-y_1}[/tex]
x₁=0 x₂=-1 y₁=-5 y₂=-2
[tex]\displaystyle\\\frac{x-0}{-1-0}=\frac{y-(-5)}{-2-(-5)} \\\\\frac{x}{-1} =\frac{y+5}{-2+5} \\\\-x=\frac{y+5}{3}[/tex]
Multiply both parts of the equation by 3:
[tex]-3x=y+5\\\\-3x-5=y+5-5\\\\-3x-5=y[/tex]
[tex]Thus,\ y=-3x-5[/tex]
Determine which answer in the solution set will make the equation true.
4f − 10 = 3f − 18
S: {−18, −8, 3, 8}
A. −8
B. 8
C. −18
D. 3
The answer in the solution set that makes 4f − 10 = 3f − 18 true is (a) -8
How to determine the answer in the solution set?From the question, we have the following parameters that can be used in our computation:
4f − 10 = 3f − 18
And we have the solution set to be
S: {−18, −8, 3, 8}
Subtract 3f from both sides of the equation
So, we have the following representation
f - 10 = - 18
Add 10 to both sides of the equation
This gives
f = -8
Hence, the solution is (a) -8
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Examine the linear graph below. Which equation represents this graph?
Answer:B) -2x + 3y = 12 represents the graph.The y-intercept is 4, and the line intercepts the x-axis at -6. Therefore, the slope of the line is 4/6=2/3. The format for a linear equation is y=(slope)x+y intercept. So the equation would be y=2/3x+4. We can see that option B simplifies that. Adding 2x from both sides of the equation and we get 3y=2x+12.
a rectangular room is 3 3 times as long as it is wide, and its perimeter is 56 56 meters. find the dimension of the room.
Consequently, the room has a 7 meter width. The room's length is
[tex]= 7 * 3 meters = 21 meters[/tex]
What is rectangle?
A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.
Given that the length of the rectangular space is three times its breadth
The chamber has a 56-meter perimeter.
Assume that the room's width is x.
As a result, the room is three times as long.
The room's perimeter is now equal to 2(3x + x).
[tex]Here, 2(3x + x) = 56\\ 2 * 4x = 56\\ 8x = 56\\ x = 7.[/tex]
Consequently, the room has a 7 meter width.
The room's length is
[tex]= 7 * 3 meters\\= 21 meters[/tex]
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