Given the expression:
[tex]\frac{y^3+0y^2-1}{y+4}[/tex]Step 1:
Divide the leading term of the dividend by the leading term of the divisor. Multiply the result by the divisor and subtract the final result from the dividend as follows:
[tex]\begin{gathered} \frac{y^3}{y}=y^2 \\ \\ \\ y^2(y+4)=y^3+4y^2 \\ \\ \\ (y^3-1)-(y^3+4y^2)=-4y^2-1 \end{gathered}[/tex]Step 2: Divide the leading term of the obtained remainder by the leading term of the divisor, multiply it by the divisor, and subtract the remainder from the obtained result:
[tex]\begin{gathered} \frac{-4y^2}{y}=-4y \\ \\ \\ -4y(y+4)=-4y^2-16y \\ \\ \\ (-4y^2-1)-(-4y^2-16y)=16y-1 \end{gathered}[/tex]Step 3: Divide the leading term of the obtained remainder by the leading term of the divisor, multiply it by the divisor, and subtract the remainder from the obtained result:
[tex]\begin{gathered} \frac{16y}{y}=16 \\ \\ \\ 16(y+4)=16y+64 \\ \\ \\ (16y-1)-(16y+64)=-65 \end{gathered}[/tex]Since the degree of the remainder is less than the degree of the divisor, we would stop.
Therefore, the answer is:
[tex]\frac{y^3-1}{y+4}=y^2-4y+16+\frac{-65}{y+4}[/tex]what is the inverseof f(x)=x/5+6
Let's begin by listing out the information given to us:
[tex]\begin{gathered} f\mleft(x\mright)=\frac{1}{5}x+6 \\ f(x)=y \\ y=\frac{1}{5}x+6 \end{gathered}[/tex]To find the inverse, of this equation, we have to interchange the two variables (x for y). We have:
[tex]\begin{gathered} y=\frac{1}{5}x+6\Rightarrow x=\frac{1}{5}y+6 \\ x=\frac{1}{5}y+6 \\ \text{Multiply through each element by 5, we have:} \\ 5\cdot x=\frac{1}{5}y\cdot5+6\cdot5 \\ 5x=y+30 \\ \text{Subtract 30 from both side, we have:} \\ 5x-30=y+30-30 \\ 5x-30=y\Rightarrow y=5x-30 \\ y=5x-30 \\ f(^{-1})=5x-30 \end{gathered}[/tex]what is the x intercept?
Answer:
the x intercept is -2
Step-by-step explanation:
Dean has a table with a circular top. What isthe area, in square feet, of the table top?Use 3.14 for Pi. Round your answer to thenearest tenth.
Answer
124.7 ft²
Step-by-step explanation
The area of a circle is calculated as follows:
[tex]A=\frac{\pi D^2}{4}[/tex]where D is the diameter of the circle.
From the diagram, the diameter of the circular top is 12.6 ft, then its area is:
[tex]\begin{gathered} A=\frac{\pi(12.6)^2}{4} \\ A=124.7\text{ ft}^2 \end{gathered}[/tex]The answer wasn't clear for me
Find the number of 5-digit numbers that contain only digits 1, 2, 3, 4, 5, and use each digit exactly once. the digits 1 and 2 cannot be neighbors. the digits 3 and 4 cannot be neighbors.
The number of 5 - digit number that contain only digits 1, 2, 3, 4, 5, and use each digit exactly once will be;
⇒ 35241
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The number of 5-digit numbers that contain only digits 1, 2, 3, 4, 5.
And, Use each digit exactly once. the digits 1 and 2 cannot be neighbors. the digits 3 and 4 cannot be neighbors.
Now,
The number of 5-digit numbers that contain only digits 1, 2, 3, 4, 5 and the digits 1 and 2 cannot be neighbors. the digits 3 and 4 cannot be neighbors will be;
⇒ 35241
Thus, The number of 5 - digit number that contain only digits 1, 2, 3, 4, 5, and use each digit exactly once will be;
⇒ 35241
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solve for x 8/9x +4=12
hello
to solve for x, we have to simplify this equation
step one
collect like terms
[tex]\begin{gathered} \frac{8}{9}x+4=12 \\ \frac{8}{9}x=12-4 \\ \frac{8}{9}x=8 \\ \end{gathered}[/tex]step two
cross multipy both sides
[tex]\begin{gathered} \frac{8}{9}x=8 \\ 8x=8\times9 \\ 8x=72 \end{gathered}[/tex]step three
divide both sides by the coefficient of x
[tex]\begin{gathered} 8x=72 \\ \frac{8x}{8}=\frac{72}{8} \\ x=9 \end{gathered}[/tex]from the calculation above, the value of x is equal to 9
what is the y- intercept when x =-1,0,1,2,3,4, and y= -4,-3.5,-3,-2.5,-2,-1.5
The y - intercept will be - 7/2.
What is Equation of line?
The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The values are,
x = -1, 0, 1, 2, 3, 4,
y = -4, -3.5, -3, -2.5, -2, -1.5
Now,
Take two points on the line as;
⇒ (x, y) = (- 1, - 4) , (1, - 3)
Hence, The slope of the line passing through the points (- 1, - 4) , (1, - 3) is;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
⇒ m = (- 3 - (-4)) / (1 - (-1))
⇒ m = 1 / 2
So, The equation of line with slope 1/2 will be;
⇒ y - (-4) = 1/2 (x - (-1)
⇒ y + 4 = 1/2 (x + 1)
⇒ y + 4 = 1/2x + 1/2
⇒ y = 1/2x + 1/2 - 4
⇒ y = 1/2x - 7/2
Thus, The y - intercept will be - 7/2.
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For an equation with fractions,why is it helpful to multiply both sides of theequation by the LCD?
When you multiply both sides of an equation with fractions with the lowest common denominator, it simplifies the equation, so that adding/subtracting/multiplying and or dividing makes it easier.
A landscaper is designing a flower garden in the shape of a right triangle. She wants 10ft of a perennial border to form the hypotenuse of the triangle, and one leg is to be 2ft longer than the other. Find the lengths of the legs?
Let the length of one leg be x, then other leg length is (x+2).
Determine the length of leg of triangle by using the pythagoras theorem.
[tex]\begin{gathered} (10)^2=(x)^2+(x+2)^2 \\ 100=x^2+x^2+4x+4 \\ x^2+2x-48=0 \\ x^2+8x-6x-48=0 \\ x(x+8)-6(x+8)=0 \\ (x-6)(x+8)=0 \end{gathered}[/tex]So values of x is 6 and -8. Negative length is not possible. The value of x is 6.
Determine the length of other leg.
[tex]\begin{gathered} x+2=6+2 \\ =8 \end{gathered}[/tex]Thus length of legs of triangle are 6 ft and 8 ft.
Banana Cupcakes
makes 10 cupcakes
1 cup granulated sugar
cup vegetable oil
1 large egg
4 tablespoons sour cream
2 medium-sized ripe bananas, mashed
1 cups all-purpose flour
1 teaspoon baking soda
teaspoon salt
1 teaspoon vanilla extract
pinch of nutmeg
You will use the recipe above to answer the following questions:
This recipe serves 10, but you need to serve 30. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?
How much vegetable oil do you need for 30 cupcakes?
How much flour do you need for 30 cupcakes?
What is the difference in the amount of vanilla extract you would need for 30 cupcakes?
What is the difference in the amount of salt you would need for 30 cupcakes?
In the real world, even though you make adjustments to a recipe to accommodate the number of people you need to serve, you sometimes round the amount of an ingredient instead of using an exact amount. Which ingredient would it make more sense to round rather than coming up with the exact amount? Why?
For 30 cupcakes we need 3 cups of vegetable oil, and 3 cups of flour, for 30 cupcakes we need 3 teaspoons of vanilla, the difference is 3 - 1 = 2.
Here we have a recipe that works for 10 serves.
Then, if we want to make 30 servings, we need to use that recipe 3 times. (because x*10 = 30, then x = 30/10 = 3)
This would be equivalent to multiplying each ingredient by 3.
for 30 cupcakes we need:
3 cups of vegetable oil.
3 cups of flour.
(because for each one of these ingredients we needed only 1 cup to make 10 cupcakes).
for 10 cupcakes we need 1 teaspoon of vanilla.
for 30 cupcakes we need 3 teaspoons of vanilla, the difference is 3 - 1 = 2.
So the difference is 2 teaspoons.
Hence, for 30 cupcakes we need 3 cups of vegetable oil, and 3 cups of flour, for 30 cupcakes we need 3 teaspoons of vanilla, the difference is 3 - 1 = 2.
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Complete the square to rewrite the equation into standard form, show all work please x^2+6x+y^2-4y=-9
1) The first step is to divide the coefficient b by 2
[tex]\begin{gathered} b=6\therefore\frac{6}{2}=3 \\ b=-\frac{4}{2}\therefore=-\frac{4}{2}=-2 \end{gathered}[/tex]2) So now, let's add to both sides those squared numbers to both sides of the equation and then write them as binomials:
[tex]\begin{gathered} x^2+6x+3^2+y^2-4x+(-2)^2=-9+9+4 \\ (x+3)^2+(y-2)^2=4 \end{gathered}[/tex]Note that this is the Equation of the Circle in its standard form, whose radius is 4
y-(-10) = 2/3 (x- (-12))what is y
We have the expression:
[tex]y-(-10)=\frac{2}{3}(x-(-12))\Rightarrow y=\frac{2}{3}x-2[/tex]From this we have that y equals to 2/3x-2 and therefore y represents a line with slope of 2/3 and with a y-intercept of -2.
A number decreased by 7 is less than -6. Find the number.
Answer:
The number is less than 1.
[tex]x<1[/tex]Explanation:
Let x represent the number.
When the number is decresed by 7, it becomes;
[tex]x-7[/tex]From the question, When the number is decresed by 7 it is less than -6.
So;
[tex]x-7<-6[/tex]Solving the inequality by adding 7 to both sides of the equation. we have;
[tex]\begin{gathered} x-7+7<-6+7 \\ x<1 \end{gathered}[/tex]Therefore, the number is less than 1.
[tex]x<1[/tex]translate the following into an equation:five increased by triple a number results in 52
Answer:
3n+5=52
Explanation:
• Let the number = n
,• Triple the number = 3n
,• Five increased by triple a number = 3n+5
,• The result is 52.
The equation is:
[tex]3n+5=52[/tex]Р(А) = 1/2 P(В) = 1/3 If A and B are independent, what is P(A n B)?1/6 5/61/21/3
Given that events A and B are independent.
It follows that the probability of the occurrence of both events is equal to the product of occurrence of each event independently,
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]According to the given problem,
[tex]\begin{gathered} P(A)=\frac{1}{2} \\ P(B)=\frac{1}{3} \end{gathered}[/tex]Substitute the values,
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]Determine whether the system of equations below has one solution, infinitely many solutions, or no solution. 10x +9y = 25 20x + 6y = - 10 [classify]show work too please and will give brainliest for the right answer with work shown
Let's try to solve the system:
Taking the first equation and solving for x, we get:
[tex]\begin{gathered} 10x+9y=25 \\ 10x=25-9y \\ x=\frac{25-9y}{10} \\ x=2.5-0.9y \end{gathered}[/tex]Replacing it on the second and solving for y, we get:
[tex]\begin{gathered} 20x+6y=-10 \\ 20(2.5-0.9y)+6y=-10 \\ 50-18y+6y=-10 \\ 50-12y=-10 \\ -12y=-10-50 \\ -12y=-60 \\ y=\frac{-60}{-12} \\ y=5 \end{gathered}[/tex]Now, we can calculate x, replacing y by 5 as follows:
[tex]\begin{gathered} x=2.5-0.9y \\ x=2.5-0.9(5) \\ x=2.5-4.5 \\ x=-2 \end{gathered}[/tex]It means that x = -2 and y = 5 is the solution for the system.
Answer: The system has one solution and it is x = -2 and y = 5
which expression is equivalent to ^3 square root 54x + 3^3 square root 2x if x does not equal 0?
You have the following expression:
³√54x + 3(³√2x), x ≠ 0
In order to simplify the previous expression, write 54x as 27(2x). Moreover, take into account that 27 = 3³ and ³√27(2x) = ³√(3³(2x)) = 3(³√2x). Then, you have:
³√54x + 3(³√2x)
= 3(³√2x) + 3(³√2x)
= 6(³√2x)
Hence, the equivalent expression is
A. 6(³√2x)
Write a function that represents the sequences 7,14,21,28
Given:-
[tex]7,14,21,28,\ldots[/tex]To find the sequence inside the pattern.
Since the number are the numbers in 7th table the function can be,
[tex]f(n)=7n[/tex]So the required function is f(n)=7n
15.A snack bar sells scoops of strawberry, chocolate, andvanilla ice cream. On Monday, the snack bar sold100 scoops in total of these flavors of ice cream. Thesnack bar sold 3 times as many scoops of chocolate asit did strawberry and 2 times as many scoops ofvanilla as it did chocolate. How many scoops ofchocolate ice cream did the snack bar sell onMonday?
54 scoops of chocolate.
1) Gathering the data from the question
Monday = 100 scoops in total
Snack bar sells 3x chocolate
x strawberry
1.5x Vanilla ( 3 : 1.5 = 2)
How many chocolate scoops?
2) Setting the expression:
3x+x+1.5x=100
4x +1.5x=100
5.5x=100
x=18.1 approximately then x = 18
Answer
3x = Chocolate
3*18 = 54 chocolate scoops
A home improvement store advertises 60 square feet of flooring for $305.00 including an $80.00 installation fee. How much does each square foot of flooring cost? The variable s represents: Equation: Each square foot of floring costs $
Each square foot of flooring costs $ 6.41
What is algebraic expressions?Algebraic expressions contain numbers, operations, and variables. Suppose you have at least $4 in your piggy bank, but an unknown amount of more in your bank. We can use the algebraic expression 4+x to represent the total amount in the piggy bank. where x is an unknown amount. If you find that the unknown amount is $6, you can evaluate the expression 4+x and replace x with 6. The result is 4 + 6 = 10, so you have $10 in your piggy bank.
Each square foot of flooring costs $6.41
The total cost of flooring is $305.00 + $80.00 = $385.00
Now, since the total are to be floored in the mentioned cost is 60 ft²
So, for the cost of flooring each square which we are assuming as (s); we have the following equation:
Total cost of flooring = Area of floor × cost of flooring each square
$385.00 = 60 ft² × s
s = [tex]\frac{385}{60}[/tex]
s = $ 6.41
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SHOW THE EQUATION YOU SET UP.91 is what percent of 14?
1) Given that we want to know how much in percentage is 91 to 14 we can write out:
[tex]\begin{gathered} 14-------100\% \\ 91--------x \\ 14x=9100 \\ \frac{14x}{14}=\frac{9100}{14} \\ x=650\% \end{gathered}[/tex]Note that we crossed multiply that. And since 91 is way over 14, then it is clearly greater than 100%
Thus, 91 corresponds to 650% of 14
Graph the solution set of the following linear inequality:2 - 4y > - 14 - 8xAnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.AYChoose the type of boundary line:Dashed -O Solid (-) O--)SEnter two points on the boundary line:X10-5310-5Select the region you wish to be shaded:ОАOB10
The inequality is given
[tex]2-4y>-14-8x[/tex]ExplanationTo determine the graph of the inequality,
Solve the expression.
[tex]\begin{gathered} 2-4y>-14-8x \\ -4y+8x>-16 \end{gathered}[/tex]The inequality is given greater than -
That means
Find the measure of the arc.А1460EB.MABC = [ ? ]°
The measure of the arc m ABC is given by the central angles:
mBC = 360 - (146 + 90) (We have a right angle in the figure).
mBC = 360 - (236)
mBC = 124
The total length of the circle is the circumference:
C = 2*pi * r
If we use for pi = 22/7 (approximation)
Then the arc is given by the fraction that multiplies C:
(2 * pi * r) (mBC+m/360) =
Because 2/360 = 180, we have:
( pi * r) * (124/180)
(22/7) * r * (124/180)
Simplifying the fraction 124/180 by 4 (this is the greatest common divisor), we have:
22/7 * r * 31/45
Then, the measure for the arc is given by (a function of r):
m
22/7 * r * 31/45
For instance, if r = 3, then
6v =792 how I do dat
In order to solve the equation 6v = 792 for v, we just need to divide both sides of the equation by the coefficient multiplying the variable v, that is, the number 6.
So we have that:
[tex]\begin{gathered} 6v=792 \\ \frac{6v}{6}=\frac{792}{6} \\ v=132 \end{gathered}[/tex]Therefore the value of v that is solution of this equation is v = 132.
Estimate the product. Round each factor to the nearest whole number, and then mult 4.6 x 4.1 The product is approximately Submit O
We need to multiply:
[tex]4.6\cdot4.1=\text{???}[/tex]But first, we will round each term to the nearest whole number
so,
4.6 will be rounded to 5 ( because 0.6 > 0.5 )
4.1 will be rounded to 4 ( because 0.1 < 0.5 )
so,
4.6 x 4.1 ( approximately ) = 5 * 4 = 20
how long must $217 be invested at a rate of 6% to earn 78.12 dollars and interest
In ths case the answer is very simple.
Step 01:
Data:
p = investment = $217
r = interest rate = 6% = 0.06
I = interest = $78.12
t ( years) = Time = ?
Step 02:
Simple Interest
I = p * r * t
78.12 = 217 * 0.06 * t
[tex]\begin{gathered} \frac{78.12}{217\cdot0.06}=t \\ 6\text{ = t} \end{gathered}[/tex]The answer is:
t = 6 years
On October 23, 2011, one U.S. dollar was worth 13.65 Mexican pesos.(a) On that date, how many pesos was 81.35 dollars worth?Round your answer to the nearest hundredth of a peso.pesos(b) On that date, how many dollars was 91.03 pesos worth?Round your answer to the nearest hundredth of a dollar.
Solution
We are given that
[tex]\text{ \$}1=13.65\text{ }pesos[/tex]a.
[tex]\begin{gathered} \text{ \$}81.35=81.35\times13.65\text{ }pesos \\ \\ \text{ \$}81.35=1110.43\text{ }pesos\text{ \lparen to the nearest hundredth\rparen} \end{gathered}[/tex]b.
[tex]\begin{gathered} 1\text{ }pesos=\text{ \$}\frac{1}{13.65} \\ \\ 91.03pesos=\text{ \$}\frac{1}{13.65}\times91.03 \\ \\ 91.03pesos=\text{ \$}6.67\text{ \lparen to the nearest hundredth\rparen} \end{gathered}[/tex]2+32 + 3 + 5 + 5 + 5
Solution
We have the following expression:
2+32+3+5+5+5
And we can do this:
34 +3+5+5+5
37 + 5 +5 +5
42 +5+5
42+10 =52
Finala answer : 52
Suppose that the speed at which cars go on the freeway is normally distributed with mean 73 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(73Correct,9Correct) b. If one car is randomly chosen, find the probability that it is traveling more than 74 mph. 0.4558Correct c. If one of the cars is randomly chosen, find the probability that it is traveling between 72 and 76 mph. 0.17478Correct d. 69% of all cars travel at least how fast on the freeway? 68.5Incorrect mph.
Answer:
68.536 mph
Explanation:
Part D
• Mean Speed = 73 mph
,• Standard deviation = 9 mph.
Since we are supposed to find at least how fast on the freeway, then:
[tex]\begin{gathered} P(X\geq x)=0.69 \\ 1-P(XFrom the z-table, the z-value at 31% is -0.496.[tex]\begin{gathered} z=\frac{X-\mu}{\sigma} \\ -0.496=\frac{X-73}{9} \\ \text{ Cross multiply} \\ X-73=9\times-0.496 \\ X=73+(9\times-0.496) \\ X=68.536 \end{gathered}[/tex]69% of all cars travel at least 68.536 mph on the freeway.
The recursive formula, an = an-1 - 12 with a0 = 84 describes the amount of water left, in gallons, in a bathtub n after the drain stopper was pulled. Find a5, he amount of water left in the tub after 5 minutes.
After 5 minute, the water left in the bath tub is 24 gallons.
What is recursive relation?A recurrence relation is an equation that applies a rule to the previous phrase or terms in the series to produce the next term in the sequence.
The given recursive formula for amount of water,
aₙ = aₙ₋₁ - 12
Also given that,
a₀ = 84,
To find a₅, the amount of water left in bath tub after 5 minutes,
Follow the steps,
a₁ = a₀ - 12 ⇒ a₁ = 84 - 12 ⇒ a₁ = 72
a₂ = a₁ - 12 ⇒ a₂ = 72 - 12 ⇒ a₂ = 60
a₃ = a₂ - 12 ⇒ a₃ = 60 - 12 ⇒ a₃ = 48
a₄ = a₃ - 12 ⇒ a₄ = 48 - 12 ⇒ a₄ = 36
a₅ = a₄ - 12 ⇒ a₅ = 36 - 12 ⇒ a₅ = 24
Therefore, after 5 minute, the water left in the bath tub is 24 gallons.
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Find the value of a.
In the given triangle, the measure of ∠a is 18°.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.Triangles can be divided into three sorts based on the lengths of their sides, and they are Scalene, Isosceles, and Equilateral.So, we know that the sum of all 3 angles of a triangle is 180°.
Then, calculate for ∠a as follows:
63 + 99 + a = 180162 + a = 180a = 180 - 162a = 18°Therefore, in the given triangle, the measure of ∠a is 18°.
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