A polynomial is a mathematical expression formed by variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponentiation of variables.
The expression:
[tex]x^5+x^2+x[/tex]Is formed by the addition of three terms, each consisting of the variable x raised to a positive integer quantity. Therefore, the given expression is a polynomial.
Part I: Domain and Range-identify the domain and range of each graph. Problem / Work Answe 2+ 6+ 2+ 1. Week 15 Homework Packet pdf 2003
Domain is the set of input values,
In the graph x axis show the domain
Where the x values is lies at -2,-1,0,1,2
Sothe domain will be :
[tex]\text{Domain =-2}\leq x\leq2[/tex]Range is the set of output values,
In the graph the value of function at y axis is : 0,2,4,6,8-2,-4.....
So, the range will be :
[tex]\text{Range = -}\infty\leq y\leq\infty[/tex]determine the number of real solutions for the following quadratic equation using the discriminate
Given equation:
[tex]y=x^2-3x-4[/tex][tex]a=1,b=-3,c=-4[/tex]Discriminant:
[tex]\begin{gathered} b^2-4ac \\ (-3)^2-4(1)(-4) \\ =9+16 \\ =25 \end{gathered}[/tex]Number of real solutions:
Since the discriminant is > 0 (that is ,it is a positive value)
Brett colors 25% of the total shapes on his paper. He colors 14 shapes. How many total shapes are there on Brett’s paper?
Answer:
56 i think because if 25% = 1/4 and 14 is 25% you would need to multiply 14 by 4 to get 100% or 4/4
i need help solving this with the statements and reasons
Given that:
[tex]\bar{AB}\mleft\Vert \mright?\bar{DC}[/tex]To prove that:
[tex]\Delta ABE\cong\Delta\text{CDE}[/tex]We know that congruent parts of congruent triangles are congruent
[tex]\angle\text{AEB }\cong\angle CDE\text{ (vertically opposite angles)}[/tex]Given that E is the midpoint of AC, therefore,
[tex]\begin{gathered} EA=EC\text{ } \\ EB=ED \end{gathered}[/tex]By the SAS congruency theorem as illustrated above, it is sufficient to prove that the triangles are congruent
Erin is buying produce at a store. She buys c cucumbers at $0.89 each and a apples at $0.99 each. What does the expression 0.89c + 0.99a represent? The expression represents the
One cucumber costs $0.89, so with Erin buys "c" cucumbers, the price he will pay for the cucumbers is the unitary price (0.89) times the number of cucumbers ("c"), so the price is 0.89c.
One apple costs $0.99, so with Erin buys "a" apples, the price he will pay for the apples is the unitary price (0.99) times the number of apples ("a"), so the price is 0.99a.
Then, to find the final price Erin will pay, we just need to sum both prices: all the cucumbers and all the apples:
Final price = 0.89c + 0.99a
So the expression represents the final price (or cost) Erin will pay for all products.
The high school soccer booster club sells tickets to the varsity matches for $4 for students and $8
for adults. The booster club hopes to earn $200 at each match.
what does the slope mean in terms of the situation?
May I please get help with this. For I have tried multiple times but still can’t get the right answer or the triangle after dilation?
Solution:
Given the triangle ABC as shown below:
To draw the image,
step 1: Determine the coordinates of the vertices of the triangle.
In the above graph,
[tex]\begin{gathered} A(6,7) \\ B(9,9) \\ C(8,6) \end{gathered}[/tex]step 2: Evaluate the new coordinates A'B'C' of the triangle after a dilation centered at the origin with a scale factor of 2.
After a dilation centered at the origin with a scale factor of 2, the iniatial coordinates of the vertices of the triangle are multiplid by 2.
Thus,
[tex]\begin{gathered} A(6,7)\to A^{\prime}(12,14) \\ B(9,9)\to B^{\prime}(18,18) \\ C(8,6)\to C^{\prime}(16,12) \end{gathered}[/tex]step 3: Draw the triangle A'B'C'.
The image of the triangle A'B'C' is as shown below:
Use the give right triangle to find ratios. In reduced form, for sin A, cos A, and tan A
From the figure given, if theta = A
opposite = 28 and hypotenuse =53
substitute the values into the formula
[tex]\sin A=\frac{28}{53}[/tex][tex]\cos A=\frac{adjacent}{\text{hypotenuse}}[/tex][tex]\cos A=\frac{45}{53}[/tex][tex]\tan \theta=\frac{opposite}{adjacent}[/tex][tex]\tan A=\frac{28}{45}[/tex]I wanted to know if this is the right answer
Notice that angles 6 and 4 are alternate exterior angles, therefore:
[tex]m\measuredangle4=m\measuredangle6.[/tex]Answer: m<4=66.
Find sin 2x, cos 2x, and tan 2x if tan x= -3/2 and x terminates in quadrant IV.
• sin 2x = -12/13
,• cos 2x = -5/13
,• tan 2x = 12/5
Explanation:Given that
[tex]\tan x=-\frac{3}{2}[/tex]Then
[tex]\begin{gathered} \sin2x=\frac{2\tan x}{1+\tan^2x} \\ \\ =\frac{2(-\frac{3}{2})}{1+(-\frac{3}{2})^2}=\frac{-3}{\frac{13}{4}} \\ \\ =-3\times\frac{4}{13}=-\frac{12}{13} \end{gathered}[/tex][tex]\begin{gathered} \cos2x=\frac{1-\tan^2x}{1+\tan^2x}=\frac{1-(-\frac{3}{2})^2}{1+(-\frac{3}{2})^2} \\ \\ =\frac{1-\frac{9}{4}}{1+\frac{9}{4}}=\frac{-\frac{5}{4}}{\frac{13}{4}}=-\frac{5}{4}\times\frac{4}{13}=-\frac{5}{13} \end{gathered}[/tex][tex]\begin{gathered} \tan2x=\frac{2\tan x}{1-\tan^2x}=\frac{2(-\frac{3}{2})}{1-(-\frac{3}{2})^2} \\ \\ =\frac{-3}{1-\frac{9}{4}}=\frac{-3}{-\frac{5}{4}}=-3\times\frac{-4}{5}=\frac{12}{5} \end{gathered}[/tex]The confidence interval on estimating the heights of students is given as (5.4, 6.8). Find the sample mean of the confidence interval. A.6.8B.6.1C. 5.4D. 0.7
Solution
- The formula for finding the sample mean from the confidence interval is given below
[tex]\begin{gathered} \text{Given the Confidence interval,} \\ (A_1,A_2) \\ \\ \therefore\operatorname{mean}=\frac{A_1+A_2}{2} \end{gathered}[/tex]- Thus, we can find the sample means as follows
[tex]\begin{gathered} A_1=5.4 \\ A_2=6.8 \\ \\ \therefore\operatorname{mean}=\frac{5.4+6.8}{2} \\ \\ \operatorname{mean}=\frac{12.2}{2} \\ \\ \operatorname{mean}=6.1 \end{gathered}[/tex]Final Answer
The sample mean is 6.1 (OPTION B)
What value n makes the eauqation n x 3/4 = 3/16
Answer:
N = 1/4
Step-by-step explanation:
Okay, so 1/4 is equal to N.
3/4 x1/4=3/16
A cannery needs to know the volume-to-surface-area ratio of a can to find the size that will create the greatest profit. Find the volume-to-surface-area ratio of a can.Hint : For a cylinder, S = 2πr2 + 2πrh and V = πr2h.a. 1/2b. 2(r+h) / rhc. πr(2r + 2h − rh)d. rh / 2(r+h)
SOLUTION
[tex]Volume\text{ }of\text{ }can=\pi r^2h[/tex][tex]Surface\text{ }area\text{ }of\text{ }can=2\pi r^2+2\pi rh[/tex]The ratio can be established as shown below
[tex]\begin{gathered} \frac{\pi r^2h}{2\pi r^2+2\pi rh} \\ \frac{\pi r^2h}{2\pi r(r+h)} \\ \frac{rh}{2(r+h)} \end{gathered}[/tex]The correct answer is OPTION D
hi I need on this. $6000 invested at 5.5% interest, compounded annually. how how would i have in 6years?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
principal = $6000
rate (interest) = 5.5%
time = 6 years
Step 02:
compound interest:
n = annually
n = 1
r = 5.5 % = 5.5 / 100 = 0.055
A = amount
[tex]A\text{ = P \lparen1 + r/n\rparen}^{nt}[/tex][tex]A\text{ = 6000 * \lparen1 + }\frac{0.055}{1})\placeholder{⬚}^{1*6}[/tex][tex]A\text{ = 6000 * \lparen1.3877\rparen = 8273.06}[/tex]The answer is:
$8273.06
3.2 Similar FiguresIf ASRT - ACBD, find the value of x.Show all work.Hint: Don't let your eyes deceive you pay attention tothe similarity statement.
Find the ratio of corresponding sides:
SRT to CBD =
70/50 = 1.4
SR / 60 = 1.4
SR = 60 x 1.4
SR = 84
84= 11x-4
Solve for x:
84+4 = 11x
88= 11x
88/11 = x
8=x
please help ………………. …………. ………… i already have the answer for part A but im having trouble with Parts B and C
In part B we must perform the following operation:
[tex](5a^3+4a^2-3a+2)+(a^3-3a^2+3a-9)[/tex]The key here is to group the terms according to the power of a they have:
[tex](5a^3+4a^2-3a+2)+(a^3-3a^2+3a-9)=(5a^3+a^3)+(4a^2-3a^2)+(-3a+3a)+(2-9)[/tex]Then, we can use the distributive property of the multiplication but in reverse:
[tex]b\cdot a+c\cdot a=(b+c)\cdot a[/tex]If we do this in each of the terms between parenthesis we get:
[tex]\begin{gathered} (5a^3+a^3)+(4a^2-3a^2)+(-3a+3a)+(2-9)= \\ =(5+1)a^3+(4-3)a^2+(-3+3)a-7 \\ (5+1)a^3+(4-3)a^2+(-3+3)a-7=6a^3+a^2-7 \end{gathered}[/tex]Then the answer for part B is:
[tex]6a^3+a^2-7[/tex]In part C we must simplify:
[tex](4y^3-2y+9)-(2y^3-3y^2+4y+7)[/tex]Here is important to remember that a negative sign before a parenthesis means that you have to change the sign of all the terms inside it. Then we have:
[tex](4y^3-2y+9)-(2y^3-3y^2+4y+7)=4y^3-2y+9-2y^3+3y^2-4y-7[/tex]Now we can do the same thing we did in part B, we group the terms according to the powers of y:
[tex]4y^3-2y+9-2y^3+3y^2-4y-7=(4y^3-2y^3)+3y^2+(-2y-4y)+(9-7)[/tex]Then we apply the distributive property in reverse:
[tex]\begin{gathered} (4y^3-2y^3)+3y^2+(-2y-4y)+(9-7)=(4-2)y^3+3y^2+(-2-4)y+2 \\ (4-2)y^3+3y^2+(-2-4)y+2=2y^3+3y^2-6y+2 \end{gathered}[/tex]Then the answer for part C is:
[tex]2y^3+3y^2-6y+2[/tex]Which of the following shows the division problem down below
Question:
Solution:
Synthetic division is a quick method of dividing polynomials; it can be used when the divisor is of the form x-c. In synthetic division, we write only the essential parts of the long division. Notice that the long division of the given problem is written as:
thus, the synthetic division of the given problem would be:
Writing 6 instead of -6 allows us to add instead of subtracting. We can conclude that the correct answer is:
A.
Ingrid is preparing a budget. She is first calculating her income. She makes $2,000 a month as a tutor, but she is going to school to become a lawyer who will eventually make close to $10,000 a month. What is the BEST thing for Ingrid to do to prepare an accurate budget?A. She should use the difference between both incomes--$8,000.B. She should average both incomes and use $6,000.C. She should use her future income of $10,000.D. She should use her current income of $2,000.
Given:
Ingrid is preparing a budget. She is first calculating her income.
She makes $2,000 a month as a tutor.
And she is going to school to become a lawyer.
Eventually, she will make close to $10,000 a month
So, the best thing is to calculate her earnings when she becomes a lawyer.
So, the answer will be option A
She should use the difference between both incomes--$8,000.
State the rational number represented by each letter on the number line as a decimal.
The rational number represented by the letter D is -43/100 and by the letter R is -46/100.
What is rational number?
A rational number is one that can be written as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
Here the number line is divided into 10 division with equal distance.
Each division is of the distance 0.01
So, the decimal number represented by letter D is -0.43 and by the letter R is -0.46.
To convert decimal number into rational number,
-0.43 = -43/100
-0.46 = -46/100
Therefore, the rational number represented by each letter on the number line as a decimal are D = -43/100 and R = -46/100.
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Solve for x. Write the reasons next to each step.Submit723x+10
x = 26/3
Explanation:We would apply the mid-segment theorem:
The base of the smaller triangle = 1/2 (the base of the bigger triangle)
The base of the smaller triangle = 3x + 10
the base of the bigger triangle = 72
3x + 10 = 1/2(72)
Reason: Mid segment is parallel to the base of the large triangle. And it is equal to half the length of the base of the large triangle
simplifying:
3x + 10 = 72/2
3x + 10= 36
subtract 10 from both sides:
3x + 10 - 10 = 36 - 10
3x = 26
DIvide both sides by 3:
3x/3 = 26/3
x = 26/3
or x = 8 2/3
Determine whether 17y = 3x − 19 is quadratic or not. Explain.No; there is no x2 term, so a = 0.No; there is no x-term, so b = 0.No; there is no constant term, so c = 0.Yes; it can rewritten in the form y = ax2 + bx + c.
The standard form of quadratic equation is given as,
[tex]ax^2+bx\text{ + c = 0 where a }\ne\text{ 0}[/tex]The equation is given as,
[tex]17y\text{ = 3x - 19}[/tex]Therefore,
[tex]\text{From the given equation x}^2\text{ is not present and also a = 0.}[/tex]Thus the given equation is not a quadratic equation.
Monica did an experiment to compare two methods of warming an object. The results are shown in thetable below. Which statement best describes her results?
The correct answer is,
The temperature using method 2 changed exponentially.
Go on the head 120 eggs delivered to her bakery she used to 98 eggs to bake cakes which equation can she use find the number of eggs r she has left
Yolanda has 120 eggs, but she used 98 eggs
r represents the equation for the number of eggs that she left:
To find this, subtract the total of eggs by the eggs used
Then, r = 120 - 98
Complete each equation so that it has infinitely many solutions. 12x - x + 8 + 3x = __x + __ (__ are blanks)
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
What are a definition and an example of a linear equation?Linear formula first-degree algebraic equation with the variables y = 4x + 3 or similar (that is, raised only to the first power). Such an equation has a straight line for its graph.
-12-x=8-3x
Add what is to the right of the equal sign to both sides of the equation, then rewrite the equation as follows:-12-x-(8-3*x)=0
Take like variables away:-20 + 2x = 2 • (x - 10)
Solve: 2 = 0There is no answer to this equation.A constant that is not zero can never equal zero.x-10 = 0
On both sides of the equation, add 10:x = 10.
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In 1990, the cost of tuition at a large Midwestern university was $104 per credit hour. In 1998, tuition had risen to $184 per credit hour.
We have to find the linear relationship for the cost of tuition in function of the year after 1990.
The cost in 1990 was $104, so we can represent this as the point (0, 104).
The cost in 1998 was $184, so the point is (8, 184).
We then can calculate the slope as:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{184-104}{8-0} \\ m=\frac{80}{8} \\ m=10 \end{gathered}[/tex]We can write the equation in slope-point form using the slope m = 10 and the point (0,104):
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-104=10(x-0) \\ y=10x+104 \end{gathered}[/tex]We can then write the cost c as:
[tex]c=10x+104[/tex]We then can estimate the cost for year 2002 by calculating c(x) for x = 12, because 2002 is 12 years after 1990.
We can calculate it as:
[tex]\begin{gathered} c=10(12)+104 \\ c=120+104 \\ c=224 \end{gathered}[/tex]Now we have to calculate in which year the tuition cost will be c = 254. We can find x as:
[tex]\begin{gathered} c=254 \\ 10x+104=254 \\ 10x=254-104 \\ 10x=150 \\ x=\frac{150}{10} \\ x=15 \end{gathered}[/tex]As x = 15, it correspond to year 1990+15 = 2005.
Answer:
a) c = 10x + 104
b) $224
c) year 2005.
The cost of a laptop computer decreased from $600 to $480. By what percentage did the cost of the computer decrease?
Initial value= $600
new value = $ 480
[tex]\begin{gathered} =\frac{600-480}{480}\times100 \\ =\text{ }\frac{120}{480}\times100 \\ =\text{ 25\%} \end{gathered}[/tex]25% decrease is the answer
solve 6 + 5 on the sqr root of 249 - 2x = 7
ANSWER
x = 124
EXPLANATION
First we have to clear the term that contains x in the equation. In this case, this term is the second term. So we have tu subtract 6 from both sides of the equation:
[tex]\begin{gathered} 6-6+\sqrt[5]{249-2x}=7-6 \\ \sqrt[5]{249-2x}=1 \end{gathered}[/tex]Then, we have to eliminate the root. Note that in the expression inside the root there are two terms. To do this, we have to apply the "opposite" operation on both sides of the equation, which in this case is exponent 5:
[tex]\begin{gathered} (\sqrt[5]{249-2x})^5=1^5 \\ 249-2x=1 \end{gathered}[/tex]Now we do something similar to the first step. We want to leave on one side of the equation only the term that contains x and the rest on the other side. To do this we can either add 2x on both sides, or subtract 249 from both sides. We'll apply the first option because then we'll have a positive coefficient for x:
[tex]\begin{gathered} 249-2x+2x=1+2x \\ 249=1+2x \end{gathered}[/tex]However, we now have to subtract 1 from both sides of the equation:
[tex]\begin{gathered} 249-1=1-1+2x \\ 248=2x \end{gathered}[/tex]Finally, to find x, we have to divide both sides by 2:
[tex]\begin{gathered} \frac{248}{2}=\frac{2x}{2} \\ 124=x \end{gathered}[/tex]Hence, the solution to the equation is x = 124.
Liam's monthly bank statement showed the following deposits and withdrawals.If Liam's balance in the account was $62.45 at the beginning of the month, what was the account balance at the end of the month?
First, let's take the inital balance and add all the deposits:
[tex]62.45+32.35+63.09+98.79=256.68[/tex]Then, we'll take this amount and substract all the withdrawals:
[tex]256.68-114.95-79.41=62.32[/tex]This way, we can conclude that the account balance at the end of the month was $62.32
4-10x = 3+5x subtract 4 from both sides
S={1/15}
1) Solving that expression
4-10x = 3+5x Subtract 4 from both sides
4-4-10x=3-4+5x
-10x =-1+5x Subtract 5x from both sides, to isolate x on the left side
-10x -5x = -1 +5x -5x
-15x=-1 Divide both sides by -15 to get the value of x, not -15x
x=1/15
S={1/15}
Inside. Make sure you don’t enter any spaces in your answers. This answer needs to be rounded to the nearest hundredth.
ANSWER
c = 14.14
EXPLANATION
To find the length of side AB, which is the hypotenuse of the right triangle ABC, we have to apply the Pythagorean Theorem,
[tex]AB^2=AC^2+BC^2[/tex]Replace the known values and solve for c,
[tex]c^2=10^2+10^2=100+100=200\Rightarrow c=\sqrt{200}\approx14.14[/tex]Hence, the value of c is 14.14, rounded to the nearest hundredth.