Answer:First, we can simplify the equation a^2 = 3a + 1 by subtracting 3a and 1 from both sides, to get:
a^2 - 3a - 1 = 0
Now we can factor the left side:
(a-1)(a+1) = 0
This equation tells us that either a-1 = 0 or a+1 = 0. So, a = 1 or a = -1.
Next, we can substitute these values into the expression (a+1/a)^2
For a = 1, (1+1/1)^2 = 2^2 = 4
For a = -1, (-1+1/(-1))^2 = 0^2 = 0
So, the value of (a+1/a)^2 is 4 when a = 1, and 0 when a = -1
Step-by-step explanation:
The distance around the wheel of a truck is 10.45 feet. What is the diameter of the wheel?
The diameter of the wheel of the truck is 3.33 feet.
What is a diameter?A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.
The distance around the wheel of a truck is 10.45 feet.
Let the diameter of the wheel = d feet.
Circumference of the wheel
= Distance around the wheel,
πd = 10.45 feet.
d = (10.45/π) feet.
Here, we take the π = 3.14.
So,
d = 3.326
d = 3.33
Therefore, the diameter is 3.33 feet.
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1. Amanda is attempting to launch a model rocket over the roof of her two-story house.
The path of the rocket, without consideration of the house, can be modeled by a
quadratic equation, where y represents the distance above the ground in yards
and x represents the horizontal distance in yards away from Amanda.
•The rocket will be launched from the ground 1 yard in front of Amanda.
•The rocket will reach a maximum height of 16 yards above the ground when the
rocket is 5 yards in front of Amanda as measured along the ground.
• The rocket would land on the ground 9 yards in front of Amanda.
Which equation represents the rocket's path?
A model rocket is launched from the roof of a building. It's flight path is modeled by -5t^2 + 30t + 10 and the Distance from ground = 10 + height after 3 sec
How to determine when is lands?Where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds.
Ans as h = -5t2+30t+10
at t=0, H = 10, which is height of the building from the ground
at t= 2 sec
h= -5.4+30.2+10
= -20+60 +10 = 50 m
For max height dh/dt = 0
-10t+30 = 0
t=3 sec
Therefore, the Distance from ground = 10 + height after 3 sec
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20 people fit comfortably in a 10 feet by 10 feet area. Use this value to estimate the size of a crowd that
is 12 feet deep on ONE side of the street along a 1 mile section of a parade route.
Answer:
1267 people
Step-by-step explanation:
The area of the 10 feet by 10 feet square is 100 square feet. If 20 people fit comfortably in this area, we can use this information to estimate the number of people in a larger area.
Since we know that 20 people fit in 100 square feet, we can calculate how many people would fit in a larger area by multiplying the number of square feet by 20.
A 1 mile section of a parade route is approximately 5280 feet long and 12 feet deep (on one side of the street). Therefore, the area that the crowd is occupying is approximately 5280*12 = 63,360 square feet.
So, the number of people that would fit in this area would be approximately:
63,360 square feet * 20 people/100 square feet = 1267.2 people.
So we can estimate that 1267 people will comfortably fit in a 1 mile section of a parade route that is 12 feet deep on one side of the street.
Answer:
389 people
Step-by-step explanation:
Step 1 we convert 1500 inches to feet
A parking lot began with two times as many spaces in a row as rows. After being expanded, 7 more rows were added and 9 more spaces in each row. The maximum number of spaces that the parking lot will hold is 582.
If r represents the original number of rows, which of the following represents this situation?
A.
2r2 + 63 > 582
B.
2r2 < 645
C.
2r2 + 23r + 63 < 582
D.
2r2 + 23r > 645
Answer:
D. 2r2 + 23r > 645
Step-by-step explanation:
The equation "2r^2 + 23r > 645" represents the situation because it states that the number of spaces in the parking lot, represented by the left-hand side of the equation (2r^2 + 23r), is greater than the maximum number of spaces that the parking lot can hold (645). This is consistent with the information given in the problem, which states that the parking lot has been expanded and can now hold more spaces.
The other equations given (A, B, C) do not accurately represent the situation because they do not take into account the expansion of the parking lot and the addition of new rows and spaces.
graph the equation.
H
-2
-1
0
2
4y + 16x = 28
Y
Ordered Pair
10
-5
10+
5
-S
-10-
Clear All
y
5
५
IC
The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: The equation as 4y+16x=28 or y+4x=7
putting (1,3) in the equation we get 3+4×1=7
Similarly we can find the ordered pair as (2, -1) , (3,-5) , (4,-9)
Hence, The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)
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(Look at picture) and ty for the help btw………….lol
Answer:
Step-by-step explanation:
1 inch is to 4 miles as inches is to 56 miles.
Answer:
14 inches is to 56 miles
Step-by-step explanation:
First, let's convert the question into an "equation"
1in : 4mi as xin:56mi
Since we need to multiply 4mi by 14 to 56mi, we will multiply 1in by 14 to find the value of x. 1 * 14 = 14. So, x must be equal to 14 and 1 inch is to 4 miles as 14 inches is to 56 miles.
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It is given to us in the question that we have a proportion of 1 inch is to 4 miles.
The proportion we need to solve is, 1 : 4 :: x : 56 as given in the question.
To solve this,
If 1 inch is equal to 4 miles, that means 4 miles is equal to 1/4 inch.
i.e. 1x = 4y; where x is inches and y is miles
1y = 1x/4....................(i)
Similarly, from the above-given proportion, we see that
x = 56y;
Taking the value of y from (i),
x = 56 * (1/4)
= 14
So the proportion becomes,
1 inch : 4 miles :: 14 inch : 56 miles
Hence, it can be determined that 1 inch is to 4 miles as 14 inches is to 56 miles.
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casey draws a rectangle array that is 1,167 units long and 7 units wide. what is the area of caseys array?
The Casey's rectangular array that is 1,167 units long and 7 units wide has an area of
8169 square unitsHow to calculate the area of the rectangleThe formula for the area of a rectangle is the product of length and wide. This is written mathematically as
= length * wideness
In the problem the rectangular array made by Casey has a the following dimensions
length = 1167 units
wide = 7 units
Area of rectangle = length * wideness
substituting the values
Area of rectangle = 1167 * 7
Area of rectangle = 8169 square units
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Factor polynomial 81bsquared minus 16csquared
Answer:
(9b-4c)(9b+4c)
Step-by-step explanation:
81b^2-16c^2
Using the the difference of square formula: a^2-b^2=(a-b)(a+b)
(9b-4c)(9b+4c)
Need help explain to me please?
Answer:
$101.75
Step-by-step explanation:
You work 4 hours in the morning from 8-12 and 5 hours and 15 minutes in the afternoon from 12:45 to 5:30 (a.k.a. 17:30)
15 minutes is a quarter of an hour. 1/4 = 0.25
4 + 5.25 = 9.25
You worked for 9.25 hours
Multiply that by $11 per hour.
9.25 · 11 = 101.75
You make $101.75 on Monday.
PLEASE HELPPPPPPPPP!!!!!!!
Answer:
A 10
Step-by-step explanation:
a proportional relationship is defined as
y = kx
k is the constant of proportionality, because it is constant for this function for any value of x.
it is usually called the slope of the line or rate of change.
these are special lines : lines that go through the origin (0, 0).
and for these lines people often call k the constant of proportionality.
as we can see right in the given equation, this constant of proportionality is 10.
what is the slope of line t in the graph?
Answer:
Step-by-step explanation:
y2-y2/x2-x1
find the y-intercept(s) of f(x)=(3x+4)^(4)(x-5)^(5)
The y - intercept of the function f(x) = (3x + 4)⁴(x - 5)⁵ is (0, -800,000)
What is Y - Intercept of EquationWhen an equation's graph crosses the y-axis, that location is known as the y-intercept. When x = 0, it is y's value.
A linear equation's constant term serves as a representation for the y-intercept. The y-intercept of the equation y = 2x + 3 is 3, for instance. This indicates that the coordinate plane point (0, 3) is at y = 3 when x = 0.
y= mx + b, where m is the slope and b is the y-intercept, is another way to express a linear equation.
For instance, the equation y = -2x + 5 can be written as y = -2x + 5, and since the y-intercept is 5, the point (0, 5) is on the graph of the equation.
The y-intercept of an equation, or the value of y when x = 0, is the point at which the graph of the equation crosses the y-axis. It can be represented by b in the slope-intercept form of a linear equation as well as by the constant term in the equation.
In the function given;
f(x) = (3x + 4)⁴(x - 5)⁵
Substitute the value of 0 for x and solve to find the y - intercept.
f(0) = (3(0) + 4)⁴(0 - 5)⁵
f(0) = -800000
The value of y - intercept(s) is (0, -800000)
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The y-intercept of the function f(x) = (3x + 4)^4(x - 5)^5 is given as follows:
-800,000.
How to obtain the y-intercept of a function?The function for this problem is defined as follows:
f(x) = (3x + 4)^4(x - 5)^5
Graphically, the y-intercept of a function represents the value of y assumed by the function when the graph of the function crosses the y-axis.
Hence, algebraically, the y-intercept of a function is given by the numeric value of the function when the input x assumes a value of zero.
The numeric value of the function at x = 0 is calculated replacing the two instances of x in the function by zero, hence the y-intercept of the function is defined as follows:
f(0) = (3(0) + 4)^4(0 - 5)^5
f(0) = 4^4 x (-5)^5
f(0) = -800,000.
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The test scores for the analytical writing section of a particular standardized test can be approximated by a normal distribution, as shown in the figure.
(a) What is the maximum score that can be in the bottom 5% of scores?
(b) Between what two values does the middle 90% of scores lie?
the mean is 3.6
the standard deviation is 0.75
The maximum score that can be in the bottom 5% of scores is 2.64
The middle 90% of scores lie between 2.88 and 4.56.
What is the maximum score that can be in the bottom 5% of scores?(a) To find the maximum score that can be in the bottom 5% of scores, we need to find the score that corresponds to the 5th percentile of the normal distribution.
Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28. To convert this back to the original scale, we can use the formula:
x = mu + z * sigma
Where
x is the original score, mu is the mean (3.6), z is the standard normal score (-1.28), and sigma is the standard deviation (0.75).Plugging in the values, we get:
x = 3.6 + (-1.28) * 0.75
x= 2.64
(b)
To find the range of scores that the middle 90% of scores lie between, we need to find the 5th and 95th percentiles of the normal distribution.
Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28 and the 95th percentile corresponds to a standard normal score of 1.28. To convert these back to the original scale, we can use the formula:
x = mu + z * sigma
Where
x is the original score, mu is the mean (3.6), z is the standard normal score, and sigma is the standard deviation (0.75).Plugging in the values, we get:
x = 3.6 + (-1.28) * 0.75
= 2.88 for the 5th percentile
x = 3.6 + 1.28 * 0.75
= 4.56 for the 95th percentile
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Which of the following inequalities is modeled by the graph? (5 points)
Ox + 4y = 15; y ≥ 0
Ox - 4y ≥ 15; y ≥ 0
Ox+4y ≤ 15; y ≥ 0
O-x - 4y ≥ 15; y ≥ 0
The graph shows that the x-values increase as the y-values increase, which is consistent with the inequality x+4y ≤ 15. The y-values are all greater than or equal to 0, which is consistent with the inequality y ≥ 0.
What is inequality?Inequality is the unequal distribution of resources or opportunities among different individuals, groups, or social classes. It is a situation in which some individuals or groups have significantly more resources or opportunities than other individuals or groups. Inequality can be seen in terms of income, wealth, social class, access to education and health care, political power, or other factors. Inequality can be caused by systemic oppression and discrimination, or by the unequal distribution of resources within a society. It can have a negative impact on the ability of individuals and groups to meet their basic needs and achieve their full potential.
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Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.
A(2, 2) and C(6, - 2)
The coordinates are ?
The coordinates of the square are 2.8
What is a square?A square is a polygon whose all sides are equal. the if the sides are equal, the coordinates of the vertices are also equal to each other.
The length of the diagonal of the square is gotten by the use of the formula for distance between two points
d = √(y₂-y₁)²+(x₂-x₁)²
distance = √(6-2)²+(-2-2)²
distance = √4²+-4²
Distance = √16+16
distance = √32 = 5.7 units
This implies that the sides of the square = 5.7/2 = 2.8
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evaluate -
[tex]\int \:{tan}^{ - 1} x \: dx[/tex]
tysm! :)
Write a polynomial equation with integer coefficients that has the given roots. x=-2 x=3
Answer:
[tex]\boxed{x^2 - x - 6}[/tex]
Step-by-step explanation:
If a is the root of a polynomial then x-a is a factor of that polynomial
Since - 2 is a root, x -(-2) = x + 2 is a factor
Since 3 is a root, x - 3 is a factor
Multiplying the factors of a polynomial gives you the polynomial equation
So the polynomial equation is
[tex](x + 2)(x-3)[/tex]
Apply FOIL method:
[tex](x + 2)(x-3) \\\\= x\cdot x+ x\left(-3\right)+2x+2\left(-3\right)\\\\= x^2 -3x + 2x -6\\\\x^2 - x - 6\\\\Answer: \boxed{x^2 - x - 6}[/tex]
I WILL MARK BRAINLIEST RNN
Answer:
maximum value = 2
Step-by-step explanation:
the maximum value of the function is the y- coordinate of its vertex
given a quadratic function in standard form
y = ax² + bx + c (a ≠ 0 )
then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = - x² + 2x + 1 ← is in standard form
with a = - 1 and b = 2 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{2}{-2}[/tex] = 1
to find the y- coordinate of the vertex, substitute x = 1 into y
y = - 1² + 2(1) + 1 = - 1 + 2 + 1 = 2
then maximum value of the function is 2
9n - 7 = ______________________________________
Answer: 9n-7
Step-by-step explanation:
9n-7 because there are no like terms
Simply the ratio of univariate monomials
32y^6/20y^2
The simplified form of the univariate monomial expression as requested in the task content is; 1.6 y⁴.
What is the simplified form of the univariate monomial?It follows from the task content that the simplified form of the univariate monomial expression is to be determined.
Since the given expression is;
32 y⁶ / 20 y²
The expression can be simplified as follows;
( 32 / 20 ) • y⁶ / y²
= 8/5 • y⁴
= 1.6 y⁴.
On this note, it can be inferred that the simplified form of the expression is; 1.6 y⁴.
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please help very important
Therefore , the solution of the given problem of triangle comes out to be tangent angle ∠B = 41/9 .
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
Here,
Given :
=> B = 8
=> S = 40
Tangent :
=> Angle ∠A = 40/9
For tangent ∠B:
=> Angle ∠B = 41/9
Therefore , the solution of the given problem of triangle comes out to be tangent angle ∠B = 41/9 .
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PLEASSEEEE HELPPPPPPPP
Answer:
third option
Step-by-step explanation:
Instead of having a constant rate of change, the third option does not as it goes up by 1 then 3 then 5
Find the annual percentage yield in (APY) in the following situation. A banks offers an APR of 4.86% compounded daily. The annual percentage yield is what percent?
Answer:
The annual percentage yield (APY) is the effective annual rate of return on an investment, taking into account the effects of compounding. To calculate the APY, we can use the formula:
APY = (1 + (APR / n))^n - 1
Where APR is the annual percentage rate (the stated interest rate), and n is the number of times the interest is compounded per year.
In this case, the APR is 4.86% and the interest is compounded daily, so n = 365 (the number of days in a year).
APY = (1 + (0.0486 / 365))^365 - 1
Plugging in the numbers, we get:
APY = (1 + 0.000132876712328767123)^365 - 1
APY ≈ 4.87%
So, the annual percentage yield is 4.87%
There are 1,000,000 nanometres in a milimetre
Molecules of water can be modelled as spheres with a diameter of 0.275 nanometres. What is the measurement in millimetres. Write your answer in standard form
On solving the provided question we can say that 1,000,000 nanometers = 1 millimeter; 1e-6 millimeter = nanometers
what is nanometers?A nanometer, often known as a nanometer, is a unit of measurement that is one billionth of a metre and one thousandth of a picometre in the International System of Units. In scientific notation, a nanometer is represented by the numbers 1 109 m and 1/1000000000 metres. The prefix "nano" refers to one billionth, or 10-9, in the International System of Units. An nanometer is therefore one billionth of a metre. The metric unit of length known as a nanometer is one billionth of a metre (0.000000001 m). It is a small length unit, abbreviated as nm. One billionth of a metre or one billionth of a micrometre is what is known as a nanometer (nm), which is 109 metres. Atoms and the molecules they make up are measured using this scale.
1,000,000 nanometers = 1 millimeter
1e-6 millimeter = nanometers
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Please help me out I need help
Answer:
DE = 9
Step-by-step explanation:
Given quadrilateral DEFG with DG≅EF, ∠FDG≅∠DFE, and markings EF=(6x+4), DG=(4x+8), and FG=(4x+1), you want the measure of DE.
ParallelogramThe given congruences mean that the figure DEFG is a parallelogram. Opposite sides are the same length.
EF = DG
6x +4 = 4x +8
2x = 4 . . . . . . . . subtract (4x+4)
x = 2 . . . . . . . . divide by 2
Now, we can find FG.
FG = 4x+1 = 4(2) +1 = 9
Opposite side DE is the same length:
DE = 9
__
Additional comment
You can prove ΔEFD ≅ ΔGDF using SAS. Then CPCTC tells you corresponding parts of the triangles are congruent: DE≅FG.
all the factors of 14 that are odd
Answer:
1, 2, 7, 14
Step-by-step explanation:
its all of those
Tell whether (2, 23) is solution of y = 9x + 5.
Answer:
Yes.
(2, 23) is a solution for the equation y = 9x + 5
Step-by-step explanation:
(2, 23) means that for an x value of 2, the y value should be 23
The equation is y = 9x + 5
Substitute x = 2 on the right side
y = 9(2) + 5 = 18 + 5 = 23
Since this matches the given value of y =23, we can conclude that
(2, 23) is a solution for y = 9x + 5
Graph the equation y=|x-1|-2
Answer:
if it is bracket than see explanation
darw a table with
x 3 5 -4
y 0 2 -7
taking x as 3 so
y= (3-1)-2
= 0
so like this do by 5 also and -4 too
and after solving plot in in the graph
Set up and solve a proportion for the following application problem. If 3 pounds of grass seed cover 403 square feet, how many pounds are needed for 6045 square feet? HELP
I'LL GIVE 50 POINTS
There are 45 pounds are needed for 6045 square feet.
What is pounds?
The United Kingdom and nine of its associated territories use the sterling as their currency. The pound is the primary unit of sterling, and the term "pound" is also frequently used to refer to the British pound or the pound sterling in international contexts.
Given:
3 pounds of grass seed cover 403 square feet.
We have to find the how many pounds are needed for 6045 square feet.
As 3 pounds of grass seed cover 403 square feet.
⇒ 403/3 = 134.33
⇒ 1 pound of grass seed cover 134.33 square feet.
Let x pounds needed for 6045 square feet.
⇒ x = 6045 / 134.33 = 45
Hence, there are 45 pounds are needed for 6045 square feet.
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