Answer:
2a. ((500x +200)x +600)x
2b. $1350.68
3. -1
Step-by-step explanation:
2. You want to know the balance in an account at the end of 3 years with deposits at the beginning of successive years being $500, $200, and $600, and with deposits having an annual growth factor of x. You want (a) an expression for the balance in terms of x, and (b) the balance when x=1+2%.
3. You want the value of p(-2) for p(x) = 5x³ +8x² -3x + 1.
2. Account Balancea. Expression$500 is deposited at the beginning of the first year. The problem statement tells us that this has been multiplied by growth factor x by the end of the year, so the balance at that point is 500x.
At the beginning of the second year, $200 is added to the account, and the entire amount is multiplied by the growth factor for the year. That makes the balance at the end of the second year be ...
(500x +200)x
Then $600 is added, and again the account grows by a factor of x. At the end of the third year, the balance is ...
balance = ((500x +200)x +600)x
b. Balance for r=2%The growth factor is given as x = 1 +r. When r = 2%, this becomes x = 1.02. Then the balance at the end of year 3 is ...
((500·1.02 +200)·1.02 +600)·1.02 = 1350.68
The amount in the account at the end of three years is $1350.68.
__
3. Polynomial valueThe value of p(x) = 5x³ +8x² -3x +1 for x=-2 is found by substituting -2 where x is found. Evaluation can be easier by rewriting the polynomial to Horner form:
p(x) = ((5x +8)x -3)x +1
p(-2) = ((5(-2) +8)(-2) -3)(-2) +1 = ((-2)(-2) -3)(-2) +1 = (1)(-2) +1 = -1
The value of the function for x=-2 is -1.
__
Additional comment
You will note that the expression in problem 2 is also written in Horner form. If it were expanded, it would be 500x³ +200x² +600x. Evaluation takes fewer steps when Horner form is used.
The functions f(x), g(x), and h(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 3≤x≤7 goes from least to greates
Given
Function f(x) , g(x) and h(x)
Find
Order of the function according to average rate of change
Explanation
Average rate of change can be given by
[tex]\frac{f(b)-f(a)}{b-a}[/tex][tex]3\leq x\leq7[/tex]for f(x)
[tex]\begin{gathered} \frac{f(7)-f(3)}{7-3} \\ \\ \frac{-10-(-8)}{4} \\ \\ -\frac{2}{4} \\ \\ -\frac{1}{2} \end{gathered}[/tex]for g(x)
[tex]\begin{gathered} \frac{g(7)-g(3)}{7-3} \\ \\ \frac{7-(27)}{4} \\ \\ -\frac{20}{4} \\ \\ -5 \end{gathered}[/tex]for h(x)
[tex]\begin{gathered} \frac{h(7)-h(3)}{7-3} \\ \\ \frac{60-24}{4} \\ \\ \frac{36}{4} \\ 9 \end{gathered}[/tex]Final Answer
least to greatest = g(x) , f(x) . h(x)
correct option is 2.
Evaluate XYZ squared if x = -2, y = 7, and z= -4.
The required value of XYZ squared would be 3136 which is determined by substituting x = -2, y = 7, and z = -4.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
We have to evaluate xyz squared if x = -2, y = 7, and z = -4.
⇒ (xyz)²
Substitute the values of x = -2, y = 7, and z = -4 in the above expression
⇒ [(-2) × (7) × (-4)]²
Apply the multiplication operation and we get
⇒ (56)²
⇒ 3136
Therefore, the obtained value of XYZ squared would be 3136 if x = -2, y = 7, and z = -4.
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write an equation in form of y=mx+b for a line with slope =7 and y-intercept =4
2334567Happy Paws charges $19.00 plus $2.50 per hour to keep a dog during the day. Woof Watchers charges$10.00 plus 53.75 per hour. Complete the equation and solve it to find for how many hours the total costof the services is equal. Use the variable h to represent the number of hours.The equation isThe total cost of the services will be equal athours.
Let h be the hours and y the total charge. Then, for Happy Paws, we have
[tex]y=2.50h+19[/tex]and for Woof Watches, we have
[tex]y=3.75h+10[/tex]Then, we need to solve these equations.
Solving by elimination method.
If we multiply by -1 the first equation, we have the equivalent system of equations:
[tex]\begin{gathered} -y=-2.50h-19 \\ y=3.75h+10 \end{gathered}[/tex]If we add both equations, we obtain
[tex]0=(3.75-2.50)h+10-19[/tex]because y-y=0. Then, it yields,
[tex]0=1.25h-9[/tex]If we move -9 to the left hand side as -9, we have
[tex]\begin{gathered} 9=1.25h \\ h=\frac{9}{1.25} \\ h=7.2 \end{gathered}[/tex]Hence, to find the total cost, we must substitute this values into one of the 2 equations. If we choose the first one, we obtain
[tex]\begin{gathered} y=2.50(7.2)+19 \\ y=18+19 \\ y=37 \end{gathered}[/tex]Then, the answers are:
The equation is
[tex]2.50h+19=3.75h+10[/tex]and, the total cost of the services will be equal at 7.2 hours
-2 1/3+ 1 4/7 what is the solution of this equation?
Answer:
[tex]-\frac{16}{21}[/tex]
Step-by-step explanation:
lets organize the equation so it becomes easier to see
[tex]-2\frac{1}{3} + 1\frac{4}{7}[/tex]
switch the spots so that it becomes even easier to read (this does not affect the result in any way)
[tex]1\frac{4}{7}-2\frac{1}{3}[/tex]
now make them both improper fractions
[tex]\frac{11}{7} -\frac{7}{3}[/tex]
and make them both have the same denominator (21)
[tex]\frac{33}{21} -\frac{49}{21}[/tex]
and solve
([tex]33-49= -16[/tex])
[tex]\frac{33}{21} -\frac{49}{21} =\frac{-16}{21}[/tex]
can we simplify [tex]\frac{-16}{21}[/tex]? does 16 and 21 have a common factor?
No.
so our result is
[tex]-\frac{16}{21}[/tex] or 0.761904762
What is the remainder of 5x3 - 7x² + 2x + 1 divided by (x - 3)?
A.) 126
B.) 79
C.) 203
D.) 205
Answer: A
Step-by-step explanation:
Can someone give me the answer to this pls?
Answer: x= -3
Step-by-step explanation:
1) Set up the equation with triangle sum
35 + x + 58 + 90 = 180
2) Solve
183 + x = 180
x = -3
the product of a number and -3 increased by 16 is 31
In ΔEFG, is it possible for segment GE to measure 6 units?
According to the triangle inequality theorem, the measure for the third side can be GE = 6 units, because: A. 3 + 5 > 6, 5 + 6 > 3, and 6 + 3 > 5.
What is the Triangle Inequality Theorem?The triangle inequality theorem states that the set of side measurements that will form a triangle will be the set of side lengths whereby the sum of any two sides will be greater than the third side of the triangle.
For example, if a, b, and c are the side lengths of a triangle, then:
a + b > ca + c > bb + c > aThus, we have the given lengths:
FE = 3 units
FG = 5 units
Therefore, the third side length would be GE = 6 units based on the triangle inequality theorem because:
3 + 5 > 6
5 + 6 > 3
6 + 3 > 5
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Write a condition Pls
3. Is x^5 + x² + x? a polynomial? Explain why or why not.
ANSWER:
A polynomial is an algebraic expression of ordered addition, subtraction, and multiplication made up of variables, constants, and exponents.
Polynomials are made up of finite terms. Each term is an expression that contains one or more of the three elements they are made of variables, constants, or exponents.
In this case, for each term, the variable is x, the constant is 1, and the exponents are 5, 2, and 1, respectively.
This means that we have a sum of monomials, that is, that the expression is a polynomial.
If f (x) = x/2 - 3 and g(x) = 4 x^2 + x-4, find (f+g)(x).
The sum of the two functions can also be expressed as follows;
[tex](f+g)(x)=f(x)+g(x)[/tex]This is not a difficult process. We just put the terms of the two functions together.
We have to be careful to add or subtract the coefficients of similar terms, taking into account their signs.
[tex]f(x)=\frac{x}{2}-3[/tex][tex]g(x)=4x^2+x-4[/tex][tex](f+g)(x)=f(x)+g(x)[/tex][tex](f+g)(x)=4x^2+x+\frac{x}{2}-7[/tex]Answer:
Step-by-step explanation:
x2 – 2x – 8
What type of reasoning is used to find the next amount of train cars? Explain your answer.
Answer: It's using the table of 2 to continue the pattern of trains.
in the first fig the no. of carton is 0.
for the next one it is 2 and the next 4.
the pattern will thus continue with the multiplication table of 2.
At a restaurant, Hamburgers cost $2.50 each and French Fries cost $1.20 each. If I went to this restaurant, and bought $8.60 worth of food,
write an equation which models how many hamburgers and french fries I purchased.
Let H represent Hamburgers
Let F represent French Fries.
Answer:
2.50h+1.20f=8.60
Step-by-step explanation:
Since the total cost of food costs $8.60, add together the costs of however many burgers and however many fries you bought. 2.50 and 1.20 are multiplied by the amount of food you purchase
The mass of Mars is 6.42 x 1023 kilograms. The mass of Mercury is 3.3 x 1023 kilograms.
Answer:
Im unaware what you are asking?
Step-by-step explanation:
hmmmm
what is 14+7.2n=11+7.5n (whole number)
Hello!
Let's solve:
[tex]\text{Copy down the equation}\\14+7.2n=11+7.5n\\\\\\\text{Move all the variables to one sides and constants to the other}\\14-11=7.5n-7.2n\\7.5n-7.2n = 14-11\\0.3n = 3\\\\\\\text{Divide both sides by 0.3}\\\dfrac{0.3n}{0.3} =\dfrac{3}{0.3} \\\\n = 10[/tex]
Answer: 10
Hope that helps!
Trixie exclaimed , “hey! Arithmetic sequences are just name for linear functions.” What do you think ? justify your idea based on multiple representations
An arithmetic progression is a sequence in which each number is a fixed amount larger (or smaller) than the one before it. The common difference is the sum in question.
"Arithmetic sequences are just name for linear functions", what you think?An arithmetic progression is a sequence in which each number is a fixed amount larger (or smaller) than the one before it. The common difference is the sum in question.
By picking two consecutive words in the sequence and deducting the first from the second, we may get the common difference for a particular sequence.
The graph of linear function is a straight line. A function with the formula y=f(x)=ax+by=f(x)=ax+b is said to be linear.
Although not quite the same, arithmetic progressions resemble linear functions.
If the value nn is a full number, then the expression t(n)=2n-4t(n)=2n4 denotes a series, and the graph of this sequence will have distinct points (as shown below).
The expression f(x)=2x-4f(x)=2x4, where xx is any real number, on the other hand, denotes a function, and this function's line graph will be continuous (as shown below).
Although not quite the same, arithmetic progressions resemble linear functions.
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Solve for the value of w. * (8w+8)(9w-5)°
The solution for the value w is 13 in the equation 8w+8 = 9w-5.
What is an angle?Two rays, referred to as the angle's sides and vertex, come together to form an angle. Angles created by two rays are located in the plane where the rays are located.
Dihedral angles are formed when two planes intersect. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can also be used to define an angle between two intersecting curves.
Angle is a term used to describe the size of an angle or of a rotation. This metric represents the proportion of a circular arc's length to radius. In the case of a geometric angle, the arc is centred at the vertex and is bound by the sides.
We know that vertical angles of intersection are equal, so here
⇒ (8w+8) = (9w-5)
⇒ 8w+8 = 9w-5
⇒ 9w - 8w = 8 + 5
⇒ w = 13
Angle measure = 8(13)+8
= 112°
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Which 2 of the following are correct equations of the line passing through (2, -3) with a slope of five?
y+3 = 5 (x-2)
y= 5x -3
y= 5x + 13
y-3= 5 (x+2)
y= 5x -13
Answer:
The two equations that passes through (2, -3) and has a slope of five are:
y + 3 = 5(x - 2) and y = 5x - 13
Step-by-step explanation:
For the first equation, you get y equal to itself. To do that, you need to simplify the right side of the equation. For 5(x - 2), you will distribute the 5 to the x and -2, equalling to 5x - 10. Next, we subtract 3 from both sides to cancel out the 3 on the left side. The equation is now y = 5x - 13. The -13 is the y intercept so we start at the point (0, -13). Since the slope goes up by 5 for every one point it moves to the right, it will eventually reach the point (2, -3). In other words, you add 1 to the x value and 5 to the y value. The points will look like this: it starts at (0, -13) and goes to (1, -8) and goes to (2, -3). The second equation is equivalent to the first equation. Hopefully this helps you out!
Given the equations y=x+7 and y=x^2+4 how many times do they intercept?
According to the following graph, the equations y=x+7 and y=x²+4 will intercept 2 times at the points (-1.3, 5.7) and (2.3, 9.3).
Intercept:
The point where the line or curve crosses the axis of the graph is known as intercept.
That is, if a point crosses the x-axis, then it is known as the x-intercept. Similarly, if a point crosses the y-axis, then it is called as the y-intercept.
Given,
Here we have the equation y=x+7 and y=x²+4.
Now, we need to find the number of times the equation is intercepts.
First, we have to plot the graph for the given equations,
Then based on that one we have easily identify the intercepting points in order to get the results.
In the following graph, the blue line represents the equation y=x²+4 and the red line represents the equation y = x + 7.
While we looking into the graph we have identified that the two lines are intersecting at two point they are (-1.3, 5.7) and (2.3, 9.3).
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what is 7.6 x 10^4 in standard form?
Answer: 76,000
Step-by-step explanation:
You move the decimal point to the right 4 times because of the positive exponent.
Write your answer as a fraction in simplest form. 4/25x10
Thenegative interval(3) of the functiony=-X²+1 are
We are given the following function
[tex]y=-x^2+1[/tex]We are asked to find the negative interval of this function.
A negative interval means that where the y values of the function are negative.
Let us have a look at the graph of this function.
As you can see,
For x = 0, the interval is positive.
For x = 1 and x = -1 the y value is 0 (we don't consider 0 as either positive or negative that's why 0 is not included in the negative or positive interval)
The y values of the function are negative for
x > 1 and x < -1
Therefore, the negative interval of the function y = x² + 1 is
[tex]1Find the value of x *
55°
X
Step-by-step explanation:
Since right angle is equal to 90°,
90°-55°=35°
please help me on this
S. SURVEY In a survey of their favorite
subjects, 390 students said math was
their favorite. One tenth as many...
students said that history was their
favorite subject. How many students
said history was their favorite?
The total number of students who participated in the survey are 100.Given to us The number of students who choose other as their favorite subject = 20 studentsMath = 30%English = 45%Let the total number of students in the survey be x.What is the percentage of students who choose other as their favorite subject?We know that percentage is always 100%, therefore,Total number of students in the survey = other + Math +English100% = other + 30% + 45%100% - 30% - 45% = otherother = 25%Thus, the percentage of students who choose another as their favorite subject is 25%.What is the total number of students who participated in the survey?We know that the number of students who choose English as their favorite subject in the surveys is 20, therefore,25% of the total number of students = 20Hence, the total number of students who participated in the survey is 100.
2x - 3y = -6please solve and graph
2x - 3y = -6
Solve for y:
-3y= -6-2x
y= (-2x-6) /-3
y= 2/3x+2
Slope intercept form:
y= mx+b
Where:
m= slope (2/3)
b= y-intercept (2)
So, to graph the function, we have to draw a line that crosses the y axis at 2, and for every 3 units moved to the right along the x-axis it goes up 2 units along the y-axis.
x/8 = 12.8 solve for x
Answer:
x = 102.4
Step-by-step explanation:
x/8 = 12.8 | * 8
x = 12.8 * 8
x = 102.4
Answer: x=102.4
Step-by-step explanation:
(x/8)*8=12.8*8
x=102.4
simplify the expression 22(5) − 8
Answer:The answer to the expression is 102.
Step-by-step explanation:
Answer:
102
Step-by-step explanation:
22(5)-8=102
Multiply and divide (left to right) 22(5) : 110
= 110 - 8
Add and subtract ( left and right) 110 - 8 : 102
2.if the m∠5 is 63° , find the measure of ∠3.
Show your work
Answer:
117°
Step-by-step explanation:
180-63=117°
so hope it help