Answer: y=0 y=-1 y=1
Step-by-step explanation:
[tex]\displaystyle\\f(y)=y^5-2y^2+y\\\\y^5-2y^2+y=0\\\\y(y^4+2y^2+1)=0\\\\y((y^2)^2+2(y^2)(1)+1^2)=0\\\\y(y^2-1)^2=0\\\\y=0\\\\(y^2-1)^2=0\\\\y^2-1-0\\\\(y+1)(y-1)=0\\\\y+1=0\\\\y+1-1=0-1\\\\y=-1\\\\y-1=0\\\\y-1+1=0+1\\\\y=1[/tex]
A sequence is defined by f(0) = -3, f(n) = f(n-1) + 0.5 for n ≥ 1.
1.
Write the first five terms of this sequence, starting with term 0.
2.
Write the nth term definition of this sequence.
Answer:
1.
f(0) = -3
f(1) = f(0) + 0.5 = -3 + 0.5 = -2.5
f(2) = f(1) + 0.5 = -2.5 + 0.5 = -2
f(3) = f(2) + 0.5 = -2 + 0.5 = -1.5
f(4) = f(3) + 0.5 = -1.5 + 0.5 = -1
2.
f(n) = 0.5n - 3
This function is linear.
hi helpppppppppppppppppppppppppppppppppppp
Answer:
with what?
Step-by-step explanation:
a. Solve a³ = 11.
b. Solve c² = 27.
Answer: a = 2.2
C = 5.1,-5.1
Alex, Cameron and Sam are all taking part in a 400 m race.
They are each running at a different constant speed.
Alex is running 12% faster than Cameron, whilst Sam is running 2% slower than Cameron.
When Alex crosses the finish line, how many metres is Sam from the finish line?
Answer:
A= C + 12%C = 1.12C
S=.C -2%C = .98C
A,C and S are the speeds of Alex, Cameron and Sam
400 meter race
how far is Sam from the finish line when Alex crosses the finish line?
distance = speed times time
400 = AT where T=Alex' finish time
400=1.12T
400=CU where U = Cameron's finish time
400=SV where V = Sam's finish time
T<U<V
Alex' finish time is less than Cameron's finish time is less than Sam's finish time
if Cameron runs at 20 meters per second, finishing in 20 seconds
then Sam is about 50 meters from the finish line when Alex finishes
sorry if i´m too late, hope this helps!
Please only answer : The horizontal scale should be X-scale and The vertical scale should be Y-scale
Regarding the scales to plot the points on the table, we have that:
The horizontal goes from X-min = -7 to X-max = 6.The horizontal scale should be X-scale = 1.The vertical goes from Y-min = -1500 to Y-max = 1200.The vertical scale should be Y-scale = 200.What are the ideal scales for the graphs?To find the ideal scales, we have to verify which are the extrema values of each variable, that is, the minimum and maximum value of each x and y.
From the table, the minimum and maximum values of X are given as follows:
X-min = -7.X-max = 6.This is a small range of values, hence the horizontal scale should be of 1.
From the same table, second column, the minimum and maximum values of Y are given as follows:
Y-min: -1500.Y-max: 1200.This is a large range of values, hence an ideal vertical scale is of 200, as then the number of traces would be almost the same as the number of traces of x.
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the value of y is directly proportional to the value of x. when x = 20, the value of y = 16/5. the value of y is incline choice 1 when x = 50 incline choice 1:
1. 312.5
2. 1160
3. 3
4. 3200
Since y is directly proportional to x then the value of y is 8
In a proportional relationship, one variable is always equal to the constant value of the other.
The "constant of proportionality" is the name of this constant.The ratio between the constant values of two proportional quantities is known as the proportionality constant.When the ratio or product of two fluctuating values results in a constant, we say that two values are in proportion.The Direct Variation and Inverse Variation types of proportions between the two provided values determine the value of the proportionality constant.It is clear that y increases in proportion to x by applying the direct proportionality formula, y = kx.
Given y is directly proportional to x.
Therefore y = kx
now at x = 20 , y = 16/5
∴16/5 = 20 k
or, k = 16 /100
Now at x = 50 ,
Y = 16 /100 × 50
or, y = 8
Therefore that value of y is 8.
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A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels at this speed in t hours.
a. What does the 65 tell us in this situation?
The car travels
miles in 1 hour.
b. How many miles does the car travel in 1.5 hours?
The car travels
miles in 1.5 hours.
c. How long does it take the car to travel 26 miles at this speed?
It takes the car
hours to travel 26 miles.
(a) 65 means the car will travel 65 miles in 1 hour .
(b) The car will travel 97.5 miles in 1.5 hours .
(c) The car will take 0.4 hours to travel 26 miles at his speed .
In the question ,
it is given that
the car is traveling down a highway at a constant speed
and the equation representing is d =65*t
Part(a)
On comparing , the given equation with the equation of speed , time and distance
which is , distance = speed × time
on comparing both the equations , we get speed = 65 mph .
hence , 65 means the car will travel 65 miles in 1 hour .
Part(b)
substituting the value t = 1.5 hours in the given equation , we get
d = 65×1.5
= 97.5
hence , The car will travel 97.5 miles in 1.5 hours
Part(c)
Substituting the value of d = 26 miles in the given equation , we get
26 = 65×t
t = 26/65
t = 0.4 hours
hence , It takes the car 0.4 hours to travel 26 miles.
Therefore , (a) 65 means the car will travel 65 miles in 1 hour .
(b) The car will travel 97.5 miles in 1.5 hours .
(c) The car will take 0.4 hours to travel 26 miles at his speed .
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What is the equation of the line that passes through the point (8, 1) and has a slope of -3/4?
Answer:
y-1= -(3/4)(x-8)
Step-by-step explanation:
y -1 =(-3/4)(x-8)
Distribute
y -1= (-3/4)x+6
Get rid of -1 by adding 1 to both sides
y=(-3/4)x+7
Hope this helps :)
1. How many ways can you flip a coin and roll four-sided tetrahedron dice?
Draw the tree diagram in the space provided below.
Answer:
Step-by-step explanation: I cant do the tree Diagram, however, I will help if you flip a coin (Heads or tails) The chances of it landing on heads will divide by 2 every time its heads or tails again and vise versa .
MANUFACTURING At a factory, molten glass is poured into molds to make
paperweights. Each mold is a rectangular prism with a height 4 inches
greater than the length of each side of its square base. Each mold holds
63 cubic inches of molten glass. What are the dimensions of the mold?
The dimensions of the mold are a length and width of 3 inches and a height of 7 inches.
What is the volume of a rectangular prism?The volume of a rectangular prism is the space that it contains. We know that the volume of any prism is calculated by multiplying its base area by its height.
Given :
Let's assume that the length and the width of the "box" is x.
It is said that the height is 4 inches greater, so the height is x+4.
The volume of the mold is:
V = (x)(x)(x +4)
V = x²(x +4 ) using the Distributive Property.
V = x³ + 4x²
Since from the question we have Volume = 63 cubic inches
The equation we have is,
63 = x³ + 4x²
Subtracting 63 from both sides of the equation,
x³ + 4x²- 63 = 0
The cubic equation can be written as,
(x−3)(x²+7x+21) = 0
The solution of the quadratic equation (x²+7x+21) is,
x = -b ±√(b² - 4ac) / 2a
a = 1 , b =7 and c = 21
Substituting the values in the formula,
x = -7 ±√(7² - 4(1(21)) / 2(1)
x = -7 ±√-35 / 2
Hence,there are no real solutions to the quadratic equation.
There is only one real solution to the equation x = 3.
Therefore, the length and width of the rectangular prism are 3 inches and the height is x+4 = 3+4 = 7 inches.
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The personal assets and liabilities of a carpenter are listed below.
What is the carpenter's net worth?
$139,450
$145,228
$281,313
$284,678
$139,450
==========================================================
Explanation:
asset = an item that is either cash or can be turned into cash
liability = something that needs to be paid back (eg: truck loan)
A = total assets
A = (homeValue) + (workEquipment) + (carValue) + (investments)
A = ( $175,742 ) + ($3,365) + ($44,346) + ($61,225)
A = $284,678
B = total liabilities
B = (mortgage)+(credit card balance)+(truck loan)
B = ($76,765)+($2,055)+($66,408)
B = $145,228
C = net worth
C = A - B
C = ($284,678) - ($145,228)
C = $139,450 which points us to choice A as the final answer.
The net worth of the carpenter is $144,633.
Given that, Home value = $175,742, Mortgage = $76,765, Credit card balance = $2,055, Owned work equipment = $3,365 and Car value = $44,346.
What is the net worth?Net worth is the value of all the non-financial and financial assets owned by an individual or institution minus the value of all its outstanding liabilities.
Here,
Net worth = Financial assets - Liabilities
= (175,742+3,365+44,346) - (76,765+2,055)
= 223,453 - 78,820
= $144,633
Therefore, the net worth of the carpenter is $144,633.
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The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons is 9 to 11. There are 55 gallons of gasoline. How many ounces of oil are there?
Given:
Ratio of ounces of oil to gallons of gasoline = 9 : 11
Gallons of gasoline = 55 gallons
Let's find the ounces of oil.
To find the ounces of oil, we have the equation:
[tex]\begin{gathered} \frac{\text{Ratio of ounces of oil}}{Ratios\text{ of gallons of gasoline}}=\frac{\text{Ounces of oil}}{\text{Gallons of gasoline}} \\ \\ \end{gathered}[/tex]Thus, we have:
[tex]\frac{9}{11}=\frac{x}{55}[/tex]Let x represent the ounces of oil.
Cross multiply:
[tex]\begin{gathered} 11x=9(55) \\ \\ 11x=495 \\ \\ \text{Divide both sides by 11:} \\ \frac{11x}{11}=\frac{495}{11} \\ \\ x=45 \end{gathered}[/tex]Therefore, there are 45 ounces of oil.
ANSWER:
45 ounces of oil
En una circunferencia señalamos diez puntos. ¿Cuál es la diferencia entre el número de heptágonos y el de triángulos cuyos vértices son algunos de esos puntos?
Answer:
ok wirrudi 123 alf8 434 21 3dis w
Springfield Mini Golf offers its customers a
25-round pass for $84, or they can pay
$3.25 per round. Which option has the
lesser price per round?
Find the height, if area is 24cm2 and the base is 6cm.
Answer:
4cm..............................
Step-by-step explanation:
24/6=4
4x6=24
Evaluate (-3)^8 and (-3)^9
The evaluation of the numbers (-3)^8 and (-3)^9 will be (-3)^17.
How to calculate the value?Based on the information given, it should be noted that this illustrates that the numbers are raised to power.
In this case, it should be noted that we want to multiply the powers, this illustrates that we gave to add the powers. This will be:
Evaluate (-3)^8 × (-3)^9
Note that 8 + 9 = 17. Therefore,
Evaluate (-3)^8 and (-3)^9
= -3^17.
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Evaluate (-3)^8 × (-3)^9
Please help. quickly
The total surface area of the triangular prism is 756 meter²
Given,
A triangular prism and its net.
We have to find the surface area of the triangular prism.
First we can consider the right angled triangle.
Height = 9 meter
Base = 12 meter
Hypotenuse = 15 meter
Area of the right angled triangle = (1/2 bh)
Here,
Area = 2 × (1/2 bh) = 2 × (1/2 × 12 × 9) = 2 × 6 × 9 = 108 meter²
Now, area of right rectangle.
Area of rectangle = length × breadth
Here, the breadth of the rectangle is the height of the triangle = 9 meter
Length = 18 meter
Area = length × breadth = 9 × 18 = 162 meter²
Then, area of middle rectangle.
Length = 18 meter
Breadth = 12 meter
Area = length × breadth = 18 × 12 = 216 meter²
Next, area of left rectangle.
Length = 18 meter
Breadth = Hypotenuse of the triangle = 15 meter
Area = length × breadth = 18 × 15 = 270 meter²
Now, lets calculate the total surface area of the triangular prism.
Surface Area of triangular prism = 108 + 162 + 216 + 270 = 756 meter²
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Form a polynomial whose zeros and degree are given.
Zeros: -7, multiplicity 1; -2, multiplicity 2; degree 3
MODE
Type a polynomial with integer coefficients and a leading coefficient of
f(x) = (Simplify your answer.)
Let p(x) be the required polynomial.
we are given that p(x) has a zero 1 with multiplicity 2
in other word, this means that (x-1) occurs twice as a factor of p(x).
How Do Polynomial Functions Work?Expressions with polynomial functions include variables with various degrees, non-zero coefficients, positive exponents (of variables), and constants. A polynomial in "b" of degree 2 is, for instance, f(b) = 4b2 - 6.
Likewise, (x-3) appears as a factor of p(x) once.
we are also given that the degree of p(x) is 3.
So, p(x) can not have more than 3 linear factors.
Altogether,
p(x) = k(x-1)^2 (x-3), where constant k ∈ R - {0}.
We may take k = 1 and get the desired polynomial,
p(x) = ( x-1)^2 ( x-3) = x^3 - 5x^2 +7x -3
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1) Work out the area and the perimeter of the shape below.
10 cm
12 cm
4 cm
Diagram NOT
accurately dr
Answer: 10 cm
Step-by-step explanation: because i am alwauys right about your mom
Write an equation of the line passing through the point (2, -9) that is perpendicular to the line y=x+6.
Answer:
y = -x - 7
Step-by-step explanation:
Perpendicular to the slope m = 1 is the slope -1/m = -1.
y = m * (x - Px) + Py
y = -1 * (x - 2) + (-9)
y = -x + 2 - 9
y = -x - 7
Provide the missing reasons for the following proof:
(In the picture)
Options
- Transitive Property of
Congruence
- Subtraction Property of
Equality
- Vertical Angles Theorem
(VAT)
- Division Property of
Equality
- Given
- Angle Congruence
Postulate
- Substitution Property of
Equality
The missing reasons are for the given two triangles VXW and VYZ are found.
What is defined as the congruent triangles?The assessments of the sides and angles of two or so more triangles determine their congruence. A triangle's size is determined by its three sides, and its shape is determined by its three angles. Two triangles have been shown to be congruent if the pairs of their corresponding angles and sides are equal. They are the same size and shape.The missing reasons for the following proof are -
∠XVW ≅ ∠W ; - Given∠XVW ≅ ∠ZVY ; Vertical Angles Theorem (VAT)m ∠ZVY ≅ ∠W ; Transitive Property of Congruence80x + 13 = 75x + 28 ; Angle Congruence Postulate5x = 15 ; Substitution Property of Equalityx = 3 ; Division Property of EqualityThus, the missing reasons are for the given two triangles VXW and VYZ are found.
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is (0,-4) a solution to the equation y = -10x + -4?
Yes, it is a solution
Explanation:y = -10x + - 4
The given point: (0, -4)
To know if it is a solution, we need to replace the y and x with the points given.
If the result on the left hand side is the same as the right hand side then, it is a solution
x =0, y = -4
-4 = -10(0) + -4
-4 = 0 + (-4)
Multiplication of same sign gives positive number. Multiplication of opposite signs give negative number.
-4 = 0 - 4
-4 = -4
The left hand side is the same as the right hand side. Hence, it is a solution
Answer:
Yes it is a solution
Step-by-step explanation:
y = -10x + - 4
Point: (0, -4)
100 times my number is 12.6 more than 5,000.
Answer:
50.126
Step-by-step explanation:
hope this helps
The solution is 50.126
What is Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
100 times my number is 12.6 more than 5000
Let the number be x
100 times the number = 100x
Now, 100x is 12.6 more than 5000
100x = 5000 + 12.6
100x = 5012.6
Divide by 100 on both sides , we get
x = 50.126
Hence , the solution is 50.126
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Determine whether the given function is even, odd or neither. *(1 Point)f(x) = x3 - 2x
Given:
The function is,
[tex]f(x)=x^3-2x[/tex]Replace x by -x in the given function,
[tex]\begin{gathered} f(x)=x^3-2x \\ f(-x)=(-x)^3-2(-x) \\ =-x^3+2x \\ =-(x^3-2x) \\ =-f(x) \end{gathered}[/tex]It is observed that, when the x is replace by -x the function end up with exactly opposite of the given function.
Thus, the given function is odd.
1. consider a lottery with three possible outcomes: $125 will be received with probability 0.25, $100 will be received with probability 0.3 and $50 will be received with probability 0.45. a. what is the expected value of the lottery? b. what is the variance of the outcome? c. what would a risk-neutral person pay (at most) to play the lottery?
The lottery's anticipated worth is $80.
Given that,
The probability of receiving $125 is 0.25; the likelihood of receiving $100 is 0.3; and the likelihood of receiving $50 is 0.45.
A) EV=125*.2+100*.3+50*.5=$80
The lottery's anticipated worth is $80.
The expected value is obtained by multiplying each result by its likelihood.
The expected value of the lottery is then calculated by adding up all of these.
This is what we have: ;;
125(0.2) + 100(0.3) + 50(0.5) (0.5)
= 25 + 30 + 25 = $80
B) This is the formula for variance is shown in figure :
So, we can calculate the variance as follows:
.2*(125-80)^2+.3*(100-80)^2+.5*(50-80)^2=975
C) A risk-neutral person would pay $80 or less to play the lottery.
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Answer:
Step-by-step explanation:
Expected value of the lottery is $83.75.
Variance of the outcome is 909.6.
A risk-neutral person would pay $83.75 or less to play the lottery.
a) The expected value is obtained by multiplying each result by its likelihood.
The expected value of the lottery is then calculated by adding up all of these.
This is,
125(0.25) + 100(0.3) + 50(0.45)
= $83.75
b) we can calculate the variance as follows:
Variance=.25*(125-83.75)^2+.3*(100-83.75)^2+.45*(50-80)^2=909.6
c) A risk-neutral person would pay $83.75 or less to play the lottery.
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I don’t get it I have to find the exterior angle (t+20)
Answer:
110
Step-by-step explanation:
To find the measure of the exterior angle we first need to find the value of t.
The sum of interior angles in a triangle is equal to 180° so we can write the following equation:
t + 10 + t + t + 20 = 180 add like terms
3t + 30 = 180 subtract 30 from both sides
3t = 150 divide both sides by 3
t = 50
The exterior angles and the angle represented with t + 20 make a straight line
and they are supplementary angles so their sum is equal to 180
t + 20 = 70 to complete this to 180 we need 110
3. If it costs $3.50 per pound of sliced ham at the
deli and Weylan spent $2.90, how many pounds
did he buy? Round to the nearest hundredth of a
pound.
The amount in pounds of sliced ham he can buy is 083 pounds.
How to find the number of pounds he bought?It costs $3.50 per pound of sliced ham at the deli and Weylan spent $2.90.
The number of pounds of sliced ham he bought can be calculated as follows:
Hence,
3.50 dollars = 1 pounds of sliced ham
2.90 dollars = ?
cross multiply
amount of pounds he bought = 2.90 × 1 / 3.50
amount of pounds he bought = 2.90 / 3.50
amount of pounds he bought = 0.82857142857
amount of pounds he bought = 0.83 pounds
Therefore, the amount of pounds bought to the nearest hundredth is 0.83 pounds.
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Write the equation for the line that passes through the given point and is perpendicular to the given line (1,7); x - 4y = 8
The equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3
Given : x - 4y = 8
4y = x- 8
On dividing by 4 we get;
y= x/4 - 2
This is of the form y = mx + c
Thus m in this case on comparing we get m= 1/4
We know the formula of the slope ;
y - y₁ =m ( x - x₁ )
y - 1 = 1/4 ( x- 7)
On cross multiplying we get ;
x- 4y = 3
Thus the equation for the line that passes through the given point and is perpendicular to the given line is x - 4y = 3 .
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Explore Part 2
Drag the number cards to create three points that represent a proportional relationship.
Use the sketch tool if it helps you with your thinking.
Please help I give 10 pt
Answer:
Step-by-step explanation:
1,3 2,6 4,8
I hope it helps, thank you!
Find the surface area and volume of the following solids , a cylinder with radius 5 m and height 0.5 m
The radius of the cylinder is 5 m and the height is 0.5 m.
Then, the total surface area is
[tex]\begin{gathered} A=2\pi r(r+h) \\ =2\pi(5)(5+0.5) \\ =55\pi\text{ squared meter} \end{gathered}[/tex]So, the surface area is
[tex]55\pi=172.79\text{ squared meter}[/tex]Now, the volume is
[tex]\begin{gathered} V=\pi(r^2)h \\ =\pi(5)^2(0.5) \\ =39.27\text{ cubic meter} \end{gathered}[/tex]So, the volume of the cylinder is 39.27 cubic meters.