Step-by-step explanation:
The leading term is -5x^4, which tells us the highest degree of the polynomial.
The leading term in the equation tells us about the degree and whether the curve opens outwards on inwards
What is an equation in one variable?
An equation is a polynomial in one variable with a finite degree
We are given an equation
[tex]-5x^4+4x^3-6x^2+8[/tex]
In this the leading term is -5x^4
Here the coefficient is negative this tells us that the curve opens downwards. if the coefficient has been positive then the curve would open outwards.
Also from the leading term we can find out the degree of the highest variable. the degree of highest variable in this case is 4
Hence, The leading term in the equation tells us about the degree of the variable and whether the curve opens outwards on inwards
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On average, Adrian's salary is 1.05 times the previous year's salary.If Adrian initially has $52,000 and n denotes the number of years, which recursive equation gives Adrian's annual income, /(7), as a function ofthe year?
Given:
Adrian initially has $52,000 and n denotes the number of years
Required:
Adrian's annual income, /(7), as a function of
the year?
Explanation:
Initially has $52,000, therefore
[tex]f(1)=52,000\text{ Exclude B,D}[/tex]The salary is 1.05 times the previous year's salary.
[tex]f(n)=1.05.f(n-1),\text{ for n}\ge2[/tex]Required answer:
Option D
I need Help with this question... the asnwer should not be a decimal... it's about special right triangles.
Below is the figure of the triangle
We have three unkown variables which are x, y, and z
Firstly, let us find the unknown side z
To find z, we will be applying SOH CAH TOA
The longest side is z
The opposite sides is 39
[tex]\begin{gathered} \text{ applying SOH} \\ \text{ Sin }\theta\text{ = }\frac{opposite}{\text{hypotenus}} \\ \sin \text{ 45 = }\frac{39}{z} \\ \text{Introduce cross multiply} \\ z\text{ x sin 45 = 39} \\ \text{Divide both sides by sin 45} \\ \frac{z\cdot\text{ sin45}}{\sin\text{ 45}}\text{ = }\frac{39}{\sin \text{ 45}} \\ z\text{ = }\frac{39}{\sin \text{ 45}} \\ \text{ According to speciaal triangles; sin 45 = }\frac{\sqrt[]{2}}{2} \\ z\text{ = }\frac{39}{\frac{\sqrt[]{2}}{2}} \\ z\text{ = }\frac{39\text{ x 2}}{\sqrt[]{2}} \\ z\text{ = }\frac{78}{\sqrt[]{2}} \\ \text{Rationalize the expression} \\ z\text{ = }\frac{78\text{ x }\sqrt[\square]{2}}{\sqrt[]{2}\text{ x }\sqrt[]{2}} \\ z\text{ = }\frac{78\sqrt[]{2}}{2} \\ z\text{ = 39}\sqrt[]{2} \end{gathered}[/tex]Find x
X can be find by applying the SOH CAH TOA
Let z = opposite
let x = adjacent
[tex]\begin{gathered} \text{ Applying TOA} \\ \text{Tan}\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \text{opposite = z = 39}\sqrt[]{2} \\ x\text{ = adjacent} \\ \text{Tan 60 = }\frac{39\sqrt[]{2}}{x} \\ \text{Introduce cross multiply} \\ x\cdot\text{ tan 60 = 39}\sqrt[]{2} \\ \text{Divide both sides by tan 60} \\ \frac{x\cdot\text{ tan 60}}{\tan\text{ 60 }}\text{ = }\frac{39\sqrt[]{2}}{\tan\text{ 60}} \\ \text{According to special triangles}\colon\text{ Tan 60 }=\text{ }\sqrt[]{3} \\ x\text{ = }\frac{39\sqrt[]{2}}{\sqrt[]{3}} \\ \text{Rationalize the above surd} \\ x\text{ = }\frac{39\sqrt[]{2}\text{ x }\sqrt[]{3}}{\sqrt[]{3}\text{ x }\sqrt[]{3}} \\ x\text{ = }\frac{39\sqrt[]{6}}{3} \\ x\text{ = 13}\sqrt[]{6} \end{gathered}[/tex]Find y
let y = adjacent
x = Hypotenus
Applying SOH, CAH TOA
[tex]\begin{gathered} \text{ cos }\theta\text{ = }\frac{adjacent}{\text{Hypotenus}} \\ \text{Adjacent = y} \\ \text{Hypotenus = x = 13}\sqrt[]{6} \\ \text{Cos 60 = }\frac{y}{13\sqrt[]{6}} \\ \text{Cross multiply} \\ y\text{ = cos 6}0\text{ x 13}\sqrt[]{6} \\ \text{According to special angles : cos 60 = }\frac{1}{2} \\ y\text{= }\frac{1}{2}\text{ x 13}\sqrt[]{6} \\ y\text{ = }\frac{13\text{ x }\sqrt[]{6}}{2} \\ y\text{= }\frac{13\sqrt[]{6}}{2} \end{gathered}[/tex]A used car dealership is interested in the age of a used car and the price of the vehicle. The manager collects a simple random sample of vehicles as shown in the table.
The equation of the least-squares regression line is
ŷ = 19.2 – 0.868x, where ŷ is the price of the vehicle (in thousands of dollars) and x is the age (in years). Which shows the residual plot?
ANSWER: A
Answer:
The Answer is A
Step-by-step explanation: Edge
10) Given that a=4 b=2 and C=-1
find the value of:
1) a - b + c
11) 20
Answer:
1 is the answer
Step-by-step explanation:
a-b+c Substitute values into the equation
4-2+(-1)
2+(-1)
2-1
1 Answer
The value of: 1) a - b + c is, 1 is the solution.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
a=4 b=2 and C=-1
now,
a-b+c
Substitute values into the equation
we get,
4-2+(-1)
=2+(-1)
=2-1
=1 (Answer)
Hence, The value of: 1) a - b + c is, 1 is the solution.
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Given: m//n
Prove: m2 + m28 = 180
Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.
If m2 + m28 = 180 then we get ∠2 + ∠8 = 180°
What are the theorems for parallel lines?Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines.
Two lines are said to be parallel if a transversal and two matching angles it forms are congruent.
Verification of Parallel Lines
that which contradicts the alternate interior angles theorem.the opposite of the theorem relating comparable angles.the converse of the same-side interior angles hypothesis.alternative exterior angles theorem's opposite.When two lines are intersected by a transversal and the opposing interior angles line up, the intersected lines are said to be parallel. Two lines are said to be parallel if they are divided by a transversal such that their opposing exterior angles are equivalent.
Therefore,
Given line m is parallel to line m
Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.
Alternate Exterior Angles are congruent if a transversal cuts two parallel lines. When a transversal cuts two parallel lines, the resulting angles are congruent.
Therefore, ∠2 = ∠6
∠2 + ∠4 = 180° ( Sum of the angles on a straight line is 180°)
∠6 + ∠8 = 180° ( Sum of the angles on a straight line is 180°)
∵ ∠2 = ∠6
∴ ∠6 + ∠8 = 180° ⇒ ∠2 + ∠8 = 180°
∠2 + ∠8 = 180° , Hence Proved.
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Hello, can anyone please help me with my practice? Be very much appreciated
Answer:
The solution to the inequality is;
[tex]x<-81[/tex]Explanation:
Given the inequality;
[tex]-\frac{1}{9}x>9[/tex]Firstly, let's multiply both sides of the equation by 9;
[tex]\begin{gathered} -\frac{1}{9}x\times9>9\times9 \\ -\frac{9}{9}x>81 \\ -x>81 \end{gathered}[/tex]Then we can multiply both sides by -1.
Note that when we multiply both sides by a negative number(-1) the sign will change;
[tex]>\rightarrow<[/tex]So;
[tex]\begin{gathered} -x\times-1>81\times-1 \\ x<-81 \end{gathered}[/tex]The solution to the inequality is;
[tex]x<-81[/tex]Which one is the correct answer I need help on this
Given the function below,
[tex]f(x)=x^3+2x^2-5x-6[/tex]Let us now plot the graph in order to obtain the end behaviours.
From the graph above, we can conclude that
[tex]\mathrm{as}\: x\to\: +\infty\: ,\: f\mleft(x\mright)\to\: +\infty\: ,\: \: \mathrm{and\: as}\: x\to\: -\infty\: ,\: f\mleft(x\mright)\to\: -\infty[/tex]Hence, the correct answer is Option D.
what is the answer of this problem ? help me to find
Given:
Total invested amount = $9000
One account = 5%
Another account = 6%
Find-:
Invested amount of each equation
Explanation-:
Let in 5% account invested amount is x
then amount in 6% account is (9000-x)
Then,
[tex]5\%\text{ of }x+6\%\text{ of }(9000-x)=510[/tex]Then the value of "x" is:
[tex]\begin{gathered} \frac{5}{100}\times x+\frac{6}{100}\times(9000-x)=510 \\ \\ 0.05x+0.06(9000-x)=510 \\ \\ 0.05x+(0.06\times9000)-0.06x=510 \end{gathered}[/tex]The "x" is:
[tex]\begin{gathered} 0.05x-0.06x+540=510 \\ \\ -0.01x=510-540 \\ \\ -0.01x=-30 \\ \\ x=\frac{-30}{-0.01} \\ \\ x=3000 \end{gathered}[/tex]The value of x is 3000 the mean amount in 5% invested amount is 3000.
6% invested amount is:
[tex]\begin{gathered} =9000-3000 \\ \\ =6000 \end{gathered}[/tex]So each account invested amount is:
[tex]\begin{gathered} 5\%\rightarrow3000 \\ \\ 6\%\rightarrow6000 \end{gathered}[/tex]Write the statement in "If p, then q" form. We will be in good shape for the ski trip provided we take the aerobics class.
Answer: If we take the aerobics class, then we will be in good shape for the ski trip
===============================================
Explanation:
The conditional statement in bold is of the form "If P, then Q" where
P = we take the aerobics classQ = we will be in good shape for the ski tripP and Q are placeholders for logical statements, in much a similar fashion that x = 2 has x as a placeholder for the number 2.
Jason has 22 strawberry scones and 55 blackberry scones. He wants to make as many identical bags of scones as possible. Each bag should have an equal number of raspberry scones and an equal number of blackberry scones. What is the greatest number of bags Jason can fill? Explain how you know.
11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.
In this question we have been given Jason has 22 raspberry scones and 55 blackberry scones.
We need to find the maximum number of bags Jason can fill with equal number of raspberry scones and blackberry scones.
We will be using Greatest common factor (GCF) for knowing the number of bags.
22 = 2 × 11
and 55 = 5 × 11
So, the greatest common factor of 22 and 55 is 11
GCF(22, 55) = 11
Therefore, 11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.
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P(t) models the number of people on a beach, t hours past midnight on a certain day.What does P(10) = N mean?Group of answer choicesThere were an equal number of people on the beach at 10:00 AM and at N hours past midnight.There were N people on the beach at 10:00 AM.There were 10 people on the beach at N hours past midnight.
Since P(t) models the number of people on a beach, t hours past midnight, hence P(10)=N means that there were N people on the beach at 10 am
10.Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7. 11.Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2. 12.Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4. (Your equation must only have integer coefficients, meaning no fractions or decimals.) 13. Write a quadratic equation that will have a solution of only x = 0. Note: this means there will be a double solution of x = 0. 14. Write a quadratic equation that cannot be factored.
Explanation
Question 10
We are asked to write the quadratic eqation that has the solutions of x=3 and x =-7
To do so, we will make use of
[tex]y=x^2-(sum\text{ of roots})x+product\text{ of roots}[/tex]So we will follow the steps below
[tex]\begin{gathered} Sum\text{ of roots = 3+}-7=-4 \\ product\text{ of roots =3\lparen-7\rparen=-21} \end{gathered}[/tex]substituting the above, we will have
[tex]\begin{gathered} x^2-(-4)x+(-21)=0 \\ \\ x^2+4x-21=0 \end{gathered}[/tex]Therefore, the quadratic equation is
[tex]x^2+4x-21[/tex]PLEASE SOLVE THIS IM GIVING 40 POINTS
The coordinates of the point P lying between AB is found as (7, -2/5).
What is termed as the section formula?The Section formula is used to calculate the coordinates of a point that separates a line segment either internally or externally into a certain ratio. When a point separates a line segment in some ratio, we just use section formula to determine the coordinates of the that point.For the given question;
The two end coordinates are;
(x₁, y₁) = (8, 0)
(x₂, y₂) = (3, -2)
The ratio of the division is;
AP/PB = 1/4
OR
m:n = 1:4
The Formula for finding the coordinates of P for internally crossing is;
x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Put the values;
x = (mx₂ + nx₁)/(m + n)
x = (1×3 + 4×8)/(1 + 4)
x = (3 + 32)/5
x = 7
Now for y coordinates.
y = (my₂ + ny₁)/(m + n)
y = (1×(-2) + 4×0)/(1 + 4)
y = -2/5
Thus, the coordinates of the point P lying between AB is found as (7, -2/5).
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How many graduates in the sample came from University A?
The number of graduates in the sample that came from University A is:
35 + 90 + 35 = 160 graduates
what is the unit price for 10 stickers for $1.50?
We can find the unit price of a ticket by dividing the number of purchased tickets by the total price, like this:
[tex]\frac{1.5}{10}=0.15[/tex]Then, the unit price of the tickets is $0.15
1 The circumference of the circle is approximately feet. (Use 3.14 as an approximation for 7.) A 5 ft. B В
The circumference of the circle is
[tex]\begin{gathered} \text{circumference= 2}\pi\text{r}^2 \\ =2\times3.14\times5^2 \\ =157\text{ fe}etsquare \end{gathered}[/tex]PLEASE HELP!!!
Simplify the expression to a polynomial in
standard form:
(3x² + x − 5) (2x² + x + 3)
The standard form is 6x⁴+5x³-2x-15.
Here the term polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as subtraction, addition, division, and multiplication. the standard form of a polynomial is :
P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ +aₙ₋₂xⁿ⁻² + ………………. + a₁x + a₀
Where aₙ, aₙ₋₁, aₙ₋₂, ……………………, a₁, a₀ are the coefficients of xⁿ, xⁿ⁻¹, xⁿ⁻², ….., x and are to a real number.
The polynomial given to us is (3x² + x − 5) (2x² + x + 3)
=3x²(2x² + x + 3) + x (2x² + x + 3) − 5 (2x² + x + 3)
= 6x⁴ + 3x³+9x²+2x³+x²+3x-10x²-5x-15
= 6x⁴+3x³+2x³+9x²+x²-10x²+3x-5x-15
= 6x⁴+5x³-2x-15
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What is the value of the Missing angle
Answer: 120
Step-by-step explanation:
All angles in a triangle add up to 180. The third angle in the triangle is 60. A straight line is always 180, and line TU intersects it. So, subtract 60 from 180 and you get 120.
Answer:
120 degrees
Step-by-step explanation:
70 + 50 = 120 (exterior angle of a triangle)
Mike can be paid in one of two ways based on the amount of merchandise he sells:Plan A: A salary of $850.00 per month, plus a commission of 10% of sales, ORPlan B: A salary of $1,050.00 per month, plus a commission of 14% of sales in excess of $7,000.00.For what amount of monthly sales is plan B better than plan A if we can assume that Mike's sales are always more than $7,000.00Write your answer an an inequality involving x, where a represents the total monthly sales.
We are looking for the point at which the compensation from Plan A is less than the compensation from Plan B.
Plan A = 850 +0.1x
Plan B= 1050+(x-7000)(0.14)
Plan A < Plan B
850 +0.1x <1050+(x-7000)(0.14)
then we sill simplify
850+0.1x < 1050+0.14x-980
850+0.1x<70+0.14x
then we isolate the x
0.1x-0.14x<70-850
-0.04x<-780
x>-780/-0.04
x>19500
In this case the monthly sales x need to be greater than 19500 (x>19500), in order that Plan B were better than plan A.
The sum of the interior angles of a polygon with 10 sides can be expressed as 360n. What is the value of n? O 2 04 O 6 08
The sum of the interior angle of a polygon with 10 sides is equal to 1440°
If it can be expressed as 360n, then n is
[tex]\begin{gathered} 360n=1440 \\ \\ \text{Divide both sides by 360} \\ \frac{360n}{360}=\frac{1440}{360} \\ \frac{\cancel{360}n}{\cancel{360}}=\frac{1440}{360} \\ n=4 \\ \\ \text{Therefore, }n\text{ is equal to }4 \end{gathered}[/tex]Graph the inequality on the number line.
3x−10>5
The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.
what is inequality?
Inequality is a declaration of an exact relation between two numerals or algebra expressions, such as greater at, above to, below than, or lesser than or equal to. Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.Given inequality,
3x−10>5
3x>5+10
3x>15
x> (15/3)
x>5
The solution of 3x−10>5 inequality is x>5 and is graphed with the image attached.
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A group of tourists visiting a skyscraper boards an elevator headed up from the ground floor. The elevator moves at a speed of 200 meters per minute. At the same time, a second group of tourists boards an adjacent elevator which is on the top floor and is headed down. This one is traveling 250 meters per minute. If the elevators were originally separated by a distance of 450 meters, how long will it take for them to pass each other
Answer: 1 minute
Step-by-step explanation:
First elevator's rate is 200 meters per second
Second's rate is 250
In one second, they would travel 450 meters
Answer:
Step-by-step explanation:
Which relation is a function?
let's recall the vertical line test, if a vertical line hits the graph or points twice, then is NOT a function. Check the picture below.
A very easy way to find out if a graph is a function is to use the vertical line test.
Look at each graph and mentally draw a vertical line that goes through each of its points.
If that line goes through more than one point (2, 3, 4...) then that graph is not a function.
That's because a function, is an equation for which each input (x value) has exactly one output (y value). There cannot be two points of the same x value, with two different y values.
with a vertex of (-7,-2) and directrix of x=-1, is this a vertical or horizontal parabola?
answer step by step please
Considering a parabolic equation with a vertex of (-7,-2) and directrix of x = -1. This is a horizontal parabola
What is directrix of a parabola?The directrix of a parabola is a straight line perpendicular to the axis of symmetry of the parabola.
The directrix does not touch the parabola
How to determine if a parabola is vertical or horizontal using the directrixA parabolic equation is also called quadratic equation.
Since the directrix is perpendicular to the axis of symmetry of the parabola it means that if:
when the directrix is given at x, the directrix runs in the vertical direction and the parabola is a horizontal parabolawhen the directrix is given at y, the directrix runs in the horizontal direction and the parabola is a vertical parabolaThe axis of symmetry says if the parabola is vertical or horizontal, when the axis of symmetry is parallel:
the y direction the parabola is a vertical parabolathe x direction the parabola is a horizontal parabolaIn the given problem, the directrix is given at x, the axis of symmetry is along the x direction and hence a horizontal parabola
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Week 14 (12/7 - 12/11) - Homework Packet 3.13 - 4.1 3.13- Homework (due Tues. 12/8) Part I: Fill in the blank representation for each inequality. Words Algebra Graph 1) ** xis greater than or equal to 7 and xis less than or equal to 9 2) 3 < x or -2> X 3) 0 1 2 4 rah the following inequalities in the
1.
Algebra:
[tex]7\leq x\leq9[/tex]Graph:
2.
Words:
x is greater than 3 or x is less than minus 2
Graph:
3.
Words:
x is greater than minus 1 and x is less than 2.
Algebra:
[tex]-1√3(√6+√15) please simplify, thanks
Answer: [tex]3\sqrt{2}+3\sqrt{5}[/tex]
===================================================
Work Shown:
[tex]\sqrt{3}\left(\sqrt{6}+\sqrt{15}\right)\\\\\sqrt{3}*\sqrt{6}+\sqrt{3}*\sqrt{15}\\\\\sqrt{3*6}+\sqrt{3*15}\\\\\sqrt{18}+\sqrt{3*3*5}\\\\\sqrt{9*2}+\sqrt{9*5}\\\\\sqrt{9}*\sqrt{2}+\sqrt{9}*\sqrt{5}\\\\3\sqrt{2}+3\sqrt{5}\\\\[/tex]
-------------------
Explanation:
I distributed and used the idea that sqrt(A*B) = sqrt(A)*sqrt(B) to combine square roots, but also to break them up when factor out the largest perfect square factor.
Optionally for the last step, you could factor out 3, but your teacher may want you to leave it like shown.
Hey can someone help me for q2 and onwards with step by step working out on paper so that I can understand them better. Thank u!!!
Answer:
f
Step-by-step explanation:
You deposit $500 into a savings account that is compounded annually. The function g(x) = 500(1.02)x can be used to find the amount of money in the savings account after x years. What is the constant percent rate of change? (2 points)
102%
98%
1.02%
2%
Answer: 2%
Step-by-step explanation:
Exponential growth functions are of the form [tex]P(1+r)^t[/tex], where r is the rate of change. From the equation, we see that r=0.02, and converting this to a percentage, we get 2%.
A pancake stall sells sweet pancakes and savoury pancakes. The savoury pancakes can have three toppings (eggs, ham, tomato) which may be used in any combination. The sweet ones come with orange, lemon or strawberry jam with either ice cream or fresh cream. How many combinations does the stall sell?
The pancakes stall sells total 12 combinations of pancakes.
What is Combination?
Combinations are mathematical operations that count the number of potential permutations for a set of elements when the order of the selection is irrelevant.
According to the given data:
Savory pancakes can have 3 toppings in any combination.
Therefore, total number of savory pancake combinations = 3 x 2 x 1 = 6
For sweet pancakes jams can either have ice cream or fresh cream.
Therefore combinations with ice cream = 3
And combinations with fresh cream = 3
Hence total combinations for sweet pancakes = 3 + 3 = 6
Now, total pancakes combination = 6 + 6 = 12
So, the stall sells 12 combinations of pancakes.
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F varies jointly as D and E. Determine F when D=3 E =10 and k =7
The equation for F is,
[tex]\begin{gathered} F\propto DE \\ F=kDE \end{gathered}[/tex]Determine the value of F.
[tex]\begin{gathered} F=7\cdot3\cdot10 \\ =210 \end{gathered}[/tex]Thus value of F is 210.