Answer: t=2*±√(35)=±11.8322
Step-by-step explanation: STEP
1
:
t2
Simplify ——
20
Equation at the end of step
1
:
t2
(—— + 8) - 15 = 0
20
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 20 as the denominator :
8 8 • 20
8 = — = ——————
1 20
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
t2 + 8 • 20 t2 + 160
——————————— = ————————
20 20
Equation at the end of step
2
:
(t2 + 160)
—————————— - 15 = 0
20
STEP
3
:
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 20 as the denominator :
15 15 • 20
15 = —— = ———————
1 20
Polynomial Roots Calculator :
3.2 Find roots (zeroes) of : F(t) = t2 + 160
Polynomial Roots Calculator is a set of methods aimed at finding values of t for which F(t)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers t which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 160.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,5 ,8 ,10 ,16 ,20 ,32 ,40 , etc
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 161.00
-2 1 -2.00 164.00
-4 1 -4.00 176.00
-5 1 -5.00 185.00
-8 1 -8.00 224.00
Note - For tidiness, printing of 15 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
3.3 Adding up the two equivalent fractions
(t2+160) - (15 • 20) t2 - 140
———————————————————— = ————————
20 20
Trying to factor as a Difference of Squares:
3.4 Factoring: t2 - 140
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 140 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Equation at the end of step
3
:
t2 - 140
———————— = 0
20
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
t2-140
—————— • 20 = 0 • 20
20
Now, on the left hand side, the 20 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
t2-140 = 0
Solving a Single Variable Equation:
4.2 Solve : t2-140 = 0
Add 140 to both sides of the equation :
t2 = 140
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
t = ± √ 140
Can √ 140 be simplified ?
Yes! The prime factorization of 140 is
2•2•5•7
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 140 = √ 2•2•5•7 =
± 2 • √ 35
The equation has two real solutions
These solutions are t = 2 • ± √35 = ± 11.8322
A store manager paid $44.00 for a shirt. She marked up the price of the shirt by 80% and then sold the shirt what was the selling price of the shirt
Cost price = $44
mark up percent = 80% = 80/100 = 0.8
selling price = ?
The markup formula:
[tex]markup=\text{ }\frac{selling\text{ price - cost price}}{\cos t\text{ price}}[/tex][tex]\begin{gathered} 0.8=\text{ }\frac{selling\text{ price - 4}4}{44} \\ \text{cross multiply:} \\ \text{0.8(44) }=\text{ selling price - 44} \\ \end{gathered}[/tex][tex]\begin{gathered} 35.2\text{ = selling price - 44 } \\ 35.2\text{ + 44 = selling price } \\ \text{selling price = \$79.2} \end{gathered}[/tex]write an exponential function to model the situation. find the amount after the specified time. $1,000 principal, 3.6% compounded monthly for 10 years
We can model this problem by an exponential growth:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A is the amount accumulated, P is the principal, r is the interest rate, n is the number of times per year and t is the time. By substituting our given data, we get
[tex]\begin{gathered} A=1000(1+\frac{0.036}{12})^{12t} \\ A=1000(1+0.003)^{12t} \end{gathered}[/tex]therefore, the model is
[tex]A=1000(1.003)^{12t}[/tex]Now, by substituting t=10 years, we have
[tex]A=1000(1.003)^{120}[/tex]then, the amount will be
[tex]A=1432.55\text{ dollars}[/tex]110.4 ÷4 step bye step show me pictures
we ahve
110.4 ÷4
so
110.4/4
Multiply by 10/10 the expression
1104/40
simplify
1104/40=552/20=276/10=27.6
the answer is 27.6
Please help topic is geometry
Image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .
What do you mean by reflection in coordinate plane?
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context.
Given point is O(-2,-1)
It is given that point O has reflected twice,
Firstly point O has reflected across the line y= 5
So, it become ,
(-2,11)
Secondly, it is reflected across the line x = 2
So, it become,
(6,11)
Hence, image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .
To learn more about the reflection from the given link.
https://brainly.com/question/28824664
#SPJ1
William is 4 years older than three times Alex's age . William is 31 years old . How old is Alex
Answer:
13
Step-by-step explanation:
.
Answer:
Alex is 14 years old.
Step-by-step explanation:
You can take William's age and divide it by 3, because William is 3 times the age of Alex:
31 divided by 3 = 10.33.
So, we will just say 10 for now.
Now, we add 4 to the 10 because WIlliam is 4 years older than three times his age.
So, in conclusion, Alex is 14 years old.
May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Using the counting principle determine the number of elements in the sample space. Two digits are selected without replacement from the digits 1,2,3,4,5 and 6
Consider the experiment of picking one digit first from the initial set (digits from 1 t) 6, and then pgrabbing a second digit without eplace,ment.
As for the first part of the experiment, there are 6 digits to choose from; however, during the second round, there are only 5 digits available. Therefore, according to the counting principle, the sample space has
[tex]6*5=30[/tex]30 elements. he answer is 30 elements in the sampele space.
Follow the steps to solve the equation.
Given equation is
[tex] \sqrt[3]{x {}^{2} - 7 } = \sqrt[3]{2x + 1} [/tex]
to solve this equation we first need to cube both the sides . As this would remove the cube root on both the sides ,
[tex]\longrightarrow (\sqrt[3]{x^2-7})^3 = (\sqrt[3]{2x+1})^3[/tex]
This would become ,
[tex]\longrightarrow x^2-7=2x+1 \\[/tex]
[tex]\longrightarrow x^2-2x-7-1=0\\[/tex]
[tex]\longrightarrow x^2-2x-8=0\\[/tex]
[tex]\longrightarrow x^2 -4x +2x -8=0\\[/tex]
[tex]\longrightarrow x(x-4)+2(x-4)=0\\ [/tex]
[tex]\longrightarrow (x+2)(x-4)=0\\[/tex]
[tex]\longrightarrow \underline{\underline{ x = 4,-2}} [/tex]
And we are done!
Answer:
[tex]\textsf{To solve the given equation, $\boxed{\sf cube}$ both sides}.[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt[3]{x^2-7} =\sqrt[3]{2x+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies (x^2-7)^{\frac{1}{3}}=(2x+1)^{\frac{1}{3}}[/tex]
Cube both sides of the equation:
[tex]\implies \left( (x^2-7)^{\frac{1}{3}}\right)^3= \left((2x+1)^{\frac{1}{3}}\right)^3[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies (x^2-7)^{\frac{3}{3}}=(2x+1)^{\frac{3}{3}}[/tex]
[tex]\implies (x^2-7)^{1}=(2x+1)^{1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]
[tex]\implies x^2-7=2x+1[/tex]
Subtract 2x from both sides:
[tex]\implies x^2-2x-7=1[/tex]
Subtract 1 from both sides:
[tex]\implies x^2-2x-8=0[/tex]
Rewrite -2x as (-4x + 2x):
[tex]\implies x^2-4x+2x-8=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-4)+2(x-4)=0[/tex]
Therefore:
[tex]\implies (x+2)(x-4)=0[/tex]
Apply the zero-product property:
[tex]x+2=0 \implies x=-2[/tex]
[tex]x-4=0 \implies x=4[/tex]
Subtract 7x minus 8 from 2x^2- minus 1
Expression 2x²-(-1) - [7x-8] is equal to 2x² - 7x +9
Expression is combination of math operations , numbers and unknown variables.
Math operation can be subtraction , addition , multiplication or division.
There are two types of expression : numerical expression and algebraic expression . Expression consists of only numbers are numerical where expression containing numbers and variables are algebraic expression.
Subtract 7x-8 from 2x²-(-1)
2x²-(-1) - [7x-8]
product of two minus is plus
2x²+1 -[7x-8]
open the bracket and change the minus sign
2x²+1 - 7x + 8
there is no x² and x term so,
2x² - 7x +1+8
2x² - 7x +9 is our required expression
To know more about Expression here
https://brainly.com/question/14083225
#SPJ1
SOMEONE PLEASE ANSWER THIS QUESTION!
If you know that 84 is 70% of the whole, how can you use proportional reasoning to determine the whole?
70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 120.
70100 shows 70% as a ratio. The ratio 84x compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 58.8.
70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
70100 shows 70% as a ratio. The ratio x84 compares 84 to the whole, x. Write an equation so that the first ratio is equal to the second ratio. Solve for x : x = 58.8.
The value of x is 120.
70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
Given, that 84 is 70% of the whole.
Let the whole be x,
According to the question,
(70/100) × x = 84
On multiplying both the sides by 100/70, we get
x = 84×100/70
Now, on solving the expression, we get
x = 120
Hence, 70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.
Learn more about Percentages here https://brainly.com/question/24877689
#SPJ1
What is the volume of a hemisphere with radius 3 ft? What is the volume of a hemisphere with diameter 13 cm?
The volume of a sphere is given by
[tex]V_s=\frac{4}{3}\pi r^3[/tex]Since a hemisphere is half sphere, its volume is given by
[tex]\begin{gathered} V_{}=\frac{4}{6}\pi r^3 \\ \text{which is equivalent to} \\ V_{}=\frac{2}{3}\pi r^3 \end{gathered}[/tex]where r is the radius.
Case a.
In this part r=3 ft, then by substituting this values into our last formula we get
[tex]V=\frac{2}{3}(3.1416)(3^3)[/tex]which gives
[tex]V=56.55ft^3[/tex]Case b.
In this part r=(13/2) cm, then by substituting this values into our last formula we get
[tex]V=\frac{2}{3}(3.1416)(6.5^3)[/tex]which gives
[tex]V=287.59cm^3[/tex]The equations in elimination method are written in the standard form as _______________.ax - by = cax + by + c = 0Ax + By = Cax - by - c = 0
Step 1
Given; The equations in the elimination method are written in the standard form as ____
Step 2
Simultaneous linear equations can be solved using the elimination method. First of all, make sure that the equations are written in the standard form either Ax+By=C or Ax+By+C=0. In this method, we multiply both the equations with a non-zero number to make the coefficients of any one variable equal.
Thus the answer is; The equations are written in standard form as seen below
[tex]Ax+By=C[/tex]A writer counted the number of pages she wrote in one year. The graph shows the relationship between the number of short stories written, x, and the number of pages written, y. coordinate plane with the x axis labeled number of short stories and the y axis labeled number of pages with a line that passes through the points 0 comma 1 and 1 comma 3 Part A: Calculate the slope of the linear equation shown in the graph. Show all necessary work. (3 points) Part B: What does the slope mean for the relationship between the number of pages written and the number of short stories written? (3 points) Part C: Interpret the y-intercept in the situation. (3 points) Part D: Write the equation of the line shown on the graph in slope-intercept form. (3 points)
I hope this helps! Good luck! Lmk if you need more help dude.
Step-by-step explanation:
A. Slope formula: y2-y1/x2-x1
(0,1) and (1,3)
3-1/1-0=2
The slope is 2.
B. I think the slope means there are 2 pages for every 1 short story written.
C. y=2x+1
2 is the slope, we see the line crosses through at (0,1) so it is our y-intercept.
A. The slope of the linear equation is 2.
B. The slope indicates that the number of pages written increases by a constant rate of 2 pages.
C. The y-intercept means that the initial number of page is 1.
D. The equation of the line in slope-intercept form is y = 2x + 1.
How to determine the slope and equation of this graph?Part A. First of all, we would determine the slope of the line represented by this graph;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (7 - 3)/(3 - 1)
Slope (m) = 4/2 = 2.
Part B.
The meaning of the slope is that the number of pages written by this writer increases by 2 every year. Therefore, there are two number of pages for every (1) short story that is written by the writer.
Part C.
The y-intercept is located at point (0, 1) and in the context of the situation, it indicates that there is a page when the number of short story is equal to zero (0) or when there are no short stories written.
Part D.
In Mathematics and Geometry, the slope-intercept form of a straight line can be calculated by using the following mathematical equation:
y = mx + b
Where:
x and y represent the points.b is the y-intercept.m represent the slope.By substitution, a linear equation for the line is given by:
y = mx + b
y = 2x + 1
Read more on slope-intercept here: brainly.com/question/7889446
#SPJ2
A sector with a radius \maroonD{18\,\text{cm}}18cmstart color #ca337c, 18, start text, c, m, end text, end color #ca337c has an area of \goldE{234\pi\,\text{cm}^2}234πcm 2 start color #a75a05, 234, pi, start text, c, m, end text, squared, end color #a75a05.
The formula for the area (A) of the sector is,
[tex]A=\frac{\theta}{360^0}\times\pi r^2[/tex]Given
[tex]\begin{gathered} r=18cm \\ A=234\pi cm^2 \end{gathered}[/tex]Therefore,
[tex]234\pi=\frac{\theta}{360}\times\pi(18)^2[/tex]Solve for θ
[tex]\begin{gathered} \frac{θ}{360}\pi \left(18\right)^2=234\pi \\ \frac{9\pi θ}{10}=234\pi \\ \frac{10\times \:9\pi θ}{10}=10\times \:234\pi \\ 9\pi θ=2340\pi \\ \mathrm{Divide\:both\:sides\:by\:}9\pi \\ \frac{9\pi θ}{9\pi }=\frac{2340\pi }{9\pi } \\ \thereforeθ=260^0 \end{gathered}[/tex]Hence, the answer is
[tex]260^0[/tex]Between what two standard deviations of a normal distribution contain 95% of the data?
Approximately 95% of the data fall within 2 standard deviations of the mean. That is, 2 standard deviations below and 2 standard deviations above the mean as in the following picture:
Plssss help!
Geometry A
Brainliest
Answer:
18 ft.
Step-by-step explanation:
Find the value of x in the triangle shown below
The answer is C, the square root of 65 (8.062).
7. Compare Ann and Barry Lindale's expenses for renting versus owning a home inthe table below.a. Complete each table.b. Is it less expensive for them to buy or rent a home, and what is the difference?
To complete the tables, we multiply the given numbers:
First table:
[tex]\begin{gathered} Rent:\text{ 850}\times12=10200, \\ Phone,\text{ Internet \& Cable TV: }99\times12=1188. \end{gathered}[/tex]Second table:
[tex]Phone,\text{ Internet \& Cable TV: }99\times12=1188.[/tex]Now, to determine which option is less expensive we compute the total annual expenses for each case:
1.-Rental:
[tex]10200+45+180+1560+2400+1188=15,573.[/tex]2.- Homeowner:
[tex]6600+3600+480+1710+2400+1188+570+960+1180=18,688.[/tex]From the above calculations, we can conclude that the cheaper option based on the given annual expenses is to rent.
Answer:Renting is less expensive.
Im an older lady not the best at this type of math please help
We need to first find the intersection between Q and R, which is the common elements between both groups. We have:
[tex]Q\cap R=\mleft\lbrace r,e,x\mright\rbrace[/tex]Now we need to determine the union between them:
[tex]P\cup(Q\cap R)=\mleft\lbrace e,x,a,c,t,r,e,x\mright\rbrace[/tex]Solve the system using the substitution technique:(−6, −3.6)(0.6, 0.8)(6, 4.4)(−0.6, 0)
Given
The system of equations,
[tex]\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}[/tex]To find the solution using substitution technique.
Explanation:
It is given that,
[tex]\begin{gathered} -2x+3y=1.2\text{ \_\_\_\_\_}(1) \\ -3x-6y=1.8\text{ \_\_\_\_\_}(2) \end{gathered}[/tex]That implies,
[tex]\begin{gathered} (1)\Rightarrow-2x+3y=1.2 \\ \Rightarrow3y=1.2+2x \end{gathered}[/tex]And,
[tex]\begin{gathered} (2)\Rightarrow-3x-6y=1.8 \\ \Rightarrow-3x-2(3y)=1.8 \end{gathered}[/tex]Substitute 3y=1.2+2x in the above equation.
That implies,
[tex]\begin{gathered} -3x-2(1.2+2x)=1.8 \\ -3x-2.4-4x=1.8 \\ -7x=1.8+2.4 \\ -7x=4.2 \\ x=\frac{4.2}{-7} \\ x=-0.6 \end{gathered}[/tex]And, substitute x=-0.6 in (1).
That implies,
[tex]\begin{gathered} (1)\Rightarrow-2(-0.6)+3y=1.2 \\ \Rightarrow1.2+3y=1.2 \\ \Rightarrow3y=1.2-1.2 \\ \Rightarrow3y=0 \\ \Rightarrow y=0 \end{gathered}[/tex]Hence, the solution is (-0.6,0).
An = -8 - (n-1)2
what’s an equation equivalent
An = -2n-6
An = -2n-10
An = -8n -2
An = -2 - 8(1-n)
Write the coefficient of x in the following terms
3. xy
1. 24x
4. x
2. abx
5. 3xy
6. xyz
Answer:
1. 1
2. 24
3. 1
4. 1 [ab]
5. 3
6. 1
Step-by-step explanation:
Every variable or alphabet's coefficient is the number on the left of it.
e. g coefficient of x is 1.
or coefficient of 83x is 83
12. Jayden sold 103 tickets for the school play. Student tickets cost $9 and adult tickets cost $14. Jayden's sales totaled $1127. How many adult tickets and how many student tickets did Jayden sell?
The total number of student tickets which are sold is 63 and the total number of adult tickets which are sold is 40.
Let the students' tickets sold by Jayden be x. Then, the number of adult tickets which are sold be 103-x.
Now, one student ticket costs $9.
Total cost of student tickets which are being sold = $9x
Similarly, one adult ticket costs $14.
Total cost of adult tickets which are being sold = $14×(103-x)
Total sales done by Jayden = $1127
∵ $9x + $14×(103-x) = $1127
⇒ 9x + 14×(103-x) = 1127
⇒ 9x + 1442 - 14x = 1127
⇒ 14x - 9x = 1442 - 1127
⇒ 5x = 315
∴ x = 63
⇒ 103 - x = 103 - 63 = 40
Hence, the total number of student tickets which are sold is 63 and the total number of adult tickets which are sold is 40.
To find similar questions on 'tickets'
visit- https://brainly.com/question/24749333
#SPJ9
What is the slope of the line that passes through the points (5, 8) and (11, 5)? Write
your answer in simplest form.
The value of x equals the number of cubic units in a box that is 4 units high, 4 units deep, and 4 units wide. Which equation can be used to determine the value of x?Math item stem image3x=644x=64x−−√=4x−−√3=4
The value of x equals the number of cubic units in a box that is 4 units high, 4 units deep, and 4 units wide.
Recall that the volume of a cube is given by
[tex]V=l\cdot w\cdot h[/tex]Where l is the length, w is the width, and h is the height of the cube.
We are given that all three sides are 4 units.
So, the volume is
[tex]\begin{gathered} V=4\cdot4\cdot4\; \\ V=64\; \; cubic\; \text{units} \end{gathered}[/tex]x must be equal to this volume
[tex]x=64[/tex]Take cube root on both sides of the equation
[tex]\begin{gathered} \sqrt[3]{x}=\sqrt[3]{64} \\ \sqrt[3]{x}=\sqrt[3]{4^3} \\ \sqrt[3]{x}=4 \end{gathered}[/tex]Therefore, the correct equation is the last option.
[tex]\sqrt[3]{x}=4[/tex]Fence A is 1 1/2 yards long but is 1 4/5 inches long on the blueprint. What is the unit rate per yard on this blue print? If fence B is 10 yard king,how long is fence B on the blueprint
The unit rate per yard is 0.03yards per unit
The length of fence B is 0.3yards
What is unit rate?A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit.
Fence A which is 1 1/2yards but 1 4/5inches on blueprint. 1 inch = 0.0278 yards
blueorint reading = 9/5×0.0278=0.05=5/100yards
therefore the scale is 3/2 : 5/100 = 3/2÷5/100
= 3/2×100/5= 1:30 = 0.03 :1
therefore the unit rate / yard = 0.03yardperunit
if a fence B is 10yards then on the blueprint it will be 10×0.03= 0.3yards
learn more about unit rate from
https://brainly.com/question/4895463#
#SPJ1
(2x²+4-5x)-(-8x+2+x²) is a what kind of polynomial
Answer:
The degree of the polynomial is the greatest of its various terms' exponents (powers). This is a seconds degree polynomial.
Step-by-step explanation:
2x^2 - 3x^5 + 5x^6.
We observe that the above polynomial has three terms. Here the first term is 2x^2, the second term is -3x^5 and the third term is 5x^6.
Now we will determine the exponent of each term.
(i) the exponent of the first term 2x^2 = 2
(ii) the exponent of the second term 3x^5 = 5
(iii) the exponent of the third term 5x^6 = 6
Since the greatest exponent is 6, the degree of 2x^2 - 3x^5 + 5x^6 is also 6.
Therefore, the degree of the polynomial 2x^2 - 3x^5 + 5x^6 = 6.
Easy peasy, hope you understand now.
What is the probability of either event occurring when you spina spinner with the numbers 1 through 4 which are all evenlyrepresented?Event A: Spinning an odd numberEvent B: Spinning a 4
We are given an experiment, and we are asked about the probability that either event happens. Therefore, we use the addition rule of probability, which states that if A and B are two events in a probability experiment the probability that either one of the events to happen is:
[tex]P(A\text{ }or\text{ }B)=P(A)+P(B)\text{ - }P(A\text{ }and\text{ }B)[/tex]Therefore, in our specific case, we have that the probability of A is 1/2, since we have 2 odd numbers out of possible 4 outcomes. The probability of B is 1/4, since we have a number 4 out of 4 possible outcomes. The probability of A and B is 0, because obtaining a 4 and an odd number are two mutually exclusive events. Therefore we have that our probability simply is the sum of our two probabilities:
[tex]P(A\text{ }or\text{ }B)=\frac{1}{2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}[/tex]Therefore, our answer is 3/4
8−6÷2+3×5= 7×3−15÷5= 8+2(1+12÷2)^2=
Recall that the order of the operations PEMDAS
1. Parenthesis
2. Exponents.
3. Multiplication.
4. Division.
5. Addition.
6. Subtraction.
1. Given expression is
[tex]8-6\div2+3\times5[/tex]Multiply 3 and 5, we get
[tex]8-6\div2+3\times5=8-6\div2+15[/tex]Divide 6 by 2, we get
[tex]=8-3+15[/tex]Subtract 3 from 8, we get
[tex]=5+15[/tex]Add 5 and 15, we get
[tex]=20[/tex]The answer is
[tex]8-6\div2+3\times5=20[/tex]2.Given expression is
[tex]7\times3-15\div5[/tex]Multiply 7 and 3, we get
[tex]7\times3-15\div5=21-15\div5[/tex]Divide 15 by 5, we get
[tex]=21-3[/tex]Subtract 3 from 21, we get
[tex]=18[/tex]The answer is
[tex]7\times3-15\div5=18[/tex]3. Given expression is
[tex]8+2(1+12\div2)^2[/tex]First, we need to solve inside the parenthesis, divide 12 by 2, we get
[tex]8+2(1+12\div2)^2=8+2(1+6)^2[/tex]Add 1 and 6, we get
[tex]=8+2(7)^2[/tex]Solve exponent.
[tex]=8+2(49)[/tex]Multiply 2 and 49, we get
[tex]=8+98[/tex]Add 8 and 98, we get
[tex]=106[/tex]The answer is
[tex]8+2(1+12\div2)^2=106[/tex]If f(x) = x² +3,then f (x + h) =
The function is f(x) = x² +3,then f (x + h) = [tex]x^2+2xh +h^2+3[/tex].
Given,
In the question:
The function is given as:
f(x) = x² +3
To find the f (x + h) = ?
Now, According to the question:
Substitute x = x + h into f(x) = x² +3
f(x + h) = (x+ h)² +3
Expand the expression using:
[tex](a +b)^2 = a^2 +2ab+b^2[/tex]
f(x + h) = [tex]x^2+2xh +h^2+3[/tex]
Hence, The function is f(x) = x² +3,then f (x + h) = [tex]x^2+2xh +h^2+3[/tex].
Learn more about Function at:
https://brainly.com/question/17403806
#SPJ1