By the Intermediate Value Theorem, since f(-4) = 51/4 > 0 and f(-3) = -3/4 < 0, there exists a value c between -4 and -3 such that f(c) = 0. Approximating the zero using bisection method yields c ≈ -3.7321.
The Intermediate Value Theorem states that if a continuous function f(x) changes sign over an interval [a, b], then it has a zero in that interval. In this case, we have shown that f(x) = 3x^2/(9x^2-3x+9) changes sign over the interval [-4,-3], meaning that it has a zero in that interval.
To approximate the zero, the bisection method is used. This method involves repeatedly dividing the interval in half and testing which half the zero lies in. In this case, we start with the interval [-4,-3] where we know a zero exists, and we test the midpoint of the interval, which is (-4-3)/2 = -3.5.
If f(-3.5) is positive, then we know the zero lies in the interval [-3.5,-3]. If f(-3.5) is negative, then we know the zero lies in the interval [-4,-3.5]. We continue dividing the interval in half and testing until we reach a desired level of accuracy.
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a) If the newspaper charges $44 for the first three lines and $8 for each extra line, how much will this ad cost Leslie? b) Ruth buys the car for 8% less than the advertised price. How much does she pay? c) Ruth must pay her state 7% sales tax on the sale. How much must she pay in sales tax?
Answer:
$3687
Step-by-step explanation:
Hope this helps!!!!
please help!!! ITS URGENT!1
answer the following questions:
1)Which functions have graphs with y-intercepts greater than −2?
(Check all that apply.)
Function 1 Function 2 Function 3 Function 4
2)Which function has the graph with a y-intercept farthest from 0?
Function 1 Function 2 Function 3 Function 4
3)Which function's graph is the steepest?
Function 1 Function 2 Function 3 Function 4
Answer:
answer was 3)
Step-by-step explanation:
Because function was star with 1,2,3,4,
in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4. in how many ways can places 1 through 4 be determined?
In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.
Define permutation.The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations. Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation could be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!
Given,
Ways 7 runners can places 1 through 4 be determined:
By using permutation:
7!
7 ×6 × 5 ×4×3×2×1
5040
In 5040 different ways, 7 runners can places 1 through 4 be determined if in a race there are 7 runners. trophies for the race are awarded to the runners finishing in places 1 through 4.
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Ellen has two pizzas left after a party. One is whole and one has been half-eaten. The whole pizza has a radius of 7 inches. The half eaten pizza has a diameter of 20 inches.
Which pizza has a greater circumference?
Answer:
half eaten pizza has greater circumference
Step-by-step explanation:
full eaten pizza's circumference = 2πr
= 2 * 3.14 * 7 = 43.96 inches
half eaten pizza's circumference = πd
= 3.14 * 20
=62.8 inches
Which expression represents the quotient of the sum of a number (n) and 4, divided by
2?
Answer:
(n+4) ÷ 2
Step-by-step explanation:
An equation you can use to solve this problem is:
(n + 4) ÷ 2Therefore, the answer is listed above.
Answer:
n+4divided by 2
Step-by-step explanation:
Complete the equation so that it has solutions of –5 and 7. x2 x = 0
The equation it has solutions of –5 and 7 is x^2-2x-37=0
We have equation
solutions of equation are –5 and 7.
We have to find complete the equation.
We have given that solutions of the equation are -5, 7.
The standard form of a quadratic equation.
What is the factor of the quadratic equation?
\((x -\alpha) (x- \beta)\)
Where we have
\(p = -(\alpha+\beta) and q = (\alpha\times \beta)\)
So, roots are
\(( x- (-5)) (x-7)\)
\(p = -( -5+7)\) , \(q =(-5)(7).\)
\(p = -2 and q = -35.\)
On substituting p and q in equation
\(x^2+(-2)x-37=0\)
\(x^2-2x-37=0\)
Therefore,x^2-2x-37=0 is the equation of solution -5,7.
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Answer:
-2, -35
Step-by-step explanation:
Complete this statement with an expression in terms of m. 18m^3 + 9m^2 + 4m + 7 = (9m^2 + 7) (...........................)
Step-by-step explanation:
18m^3+ 9m^2 + 4m + 7=(9m^2 + 7)
18m^3+9m^2+4m+7=9m^2 + 7
18m^3+9m^2+4m+7-7=9m2+7-7
18m^3+9m^2+4m=9m^2
18m^3+9m^2+4m-9m^2-9m^2
18m^3+4m=0
factor 18m^3+4m:. 2m(9m^2+2)
2m (9m^2+2)=0
using the zero factor principle: if an=0 then a=0 or b=0
m=0 or 9m^2+2=0
solve 9m^2+2=0:. m= i√2 m= -i√2
__, __
3 3
The solutions are:
m=0, m= i√2 m= -i√2
__, __
3 3
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Write an equation in point-slope form of the line that passes through the given point and has the given slope. (12, 5); m = -3
Answer:
y - 5 = -3(x - 12)
Step-by-step explanation:
Point slope form is: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.
Plug in the point and the slope:
y - y1 = m(x - x1)
y - 5 = -3(x - 12)
So, y - 5 = -3(x - 12) is the equation in point slope form of the line.
Answer:
y-5 = -3(x-12)
Step-by-step explanation:
Find the measure of angle K.
Answer:75
Step-by-step explanation:
First solve for x. That will get you 13. Then plug 13 in 8x-29. So you'd multiply 13 times 8. 104 then you have to subtract 29 so you'd get 75. Have a great day
Which graph is defined by the function given below?
y = (x-3)(x-3)
Answer: graph b
Step-by-step explanation:
Vertex: ( 3 ,0 )
Focus: ( 3 , 1 4 )
Axis of Symmetry: x = 3
Directrix: y = − 1 4
Which of the following describes how the graph of y = |x| transforms to obtain the graph of y = |x + 1| + 4.
Answer:
See explanation
Step-by-step explanation:
The graph of y = |x| is a graph of the absolute value function, which is a piecewise defined function. The graph of this function is a V-shaped curve, with the vertex of the V at the origin (0,0). The graph of y = |x + 1| + 4 can be obtained by shifting the graph of y = |x| to the right by 1 unit, and then shifting it up by 4 units.
The resulting graph of y = |x + 1| + 4 will be a V-shaped curve with the vertex at the point (1,4). The curve will be shifted to the right and up compared to the graph of y = |x|, and it will have the same general shape as the original graph.
what is the graph of y=1/4x^3
What is not true about any right angle
Answer:
Step-by-step explanation:
Not true: Right angle is not 90 degrees because all right angles must be 90 degrees
you are interested in knowing what proportion of college students smoke. in a big university, you take a small random sample of 650 students and find that 25 of them smoke. based on the results of your survey, construct a 99% confidence interval for the proportion of college students who smoke.
A 99% confidence interval for the proportion of college students who smoke for the given standard deviation is (0.021. 0.045).
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
formula for confidence interval is :
m = p-bar ± z*√p(1-p)/n
given information =
n= 650
p - bar = 25/650 = 1/26
C.I. = 99% = 0.99
we need to find value of 0.99 in z -table
z = 2.33
substituting value ,
0.038 ± 2.33√( 0.038(1-0.038))/650
0.038 ± 2.33 * 0.075
0.038 ± 0.017
(0.021. 0.045)
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Solve for x in the diagram below.
Answer:
x = 45
Step-by-step explanation:
180 = (2x + 45) + x
135 = 2x + x
135/3 = 3x/3
45 = x
Answer:
x = 45
Step-by-step explanation:
The 2 given angles are adjacent snd sum to 180° , then
2x + 45 + x = 180 , that is
3x + 45 = 180 ( subtract 45 from both sides )
3x = 135 ( divide both sides by 3 )
x = 45
What is this rational function?
Answer:
A rational function is any function which can be written as the ratio of two polynomial functions, where the polynomial in the denominator is not equal to zero. The domain of f(x)=P(x)Q(x) f ( x ) = P ( x ) Q ( x ) is the set of all points x for which the denominator Q(x) is not zero.
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9514 1404 393
Answer:
f(x) = (x^2+2)/(x-1)
Step-by-step explanation:
In simplest form, it will be a quadratic divided by (x-1). The quadratic must have no zeros, and a y-intercept of 2.
One such could be ...
f(x) = (x^2 +2)/(x -1)
__
The numerator polynomial must have no zeros in order to prevent the rational function from having zeros. It must be a function that has a degree an odd number greater than the denominator function. The denominator function can have only one zero, at x=1. The ratio of the functions must have a net odd degree and the overall leading coefficient must be positive in order to make the end behavior match the requirement.
After substituting, what is the first step when evaluating x + 3 x minus 4.2 when x = 5?
Multiply 3 by 5
Add 5 and 3
Subtract 4.2 from 5
Add 3 and 4.2
Answer:
Multiply 3 by 5
Step-by-step explanation:
the P and M in PEMDAS because there’s multiplication inside the parentheses
5 + 3(5) - 4.2
Apples are $1.79 per lb at Food Lion. If I purchase 3.8 lbs, how much sure I expect to pay?
Answer:
$6.80
Step-by-step explanation:
1.79 x 3.8 = 6.802
So $6.80
How many people did vote, but are not Republicans? Of the people who voted, how many are not Republicans? How many people did vote? Of the Republicans, how many did not vote?
Solution:
Given:
From the table, the following can be deduced.
79 people voted that are not Republicans.
Of the 148 people who voted, 79 people are not Republicans.
148 people in total voted.
Of the 139 Republicans, 70 people did not vote.
Find the value of x.
Personally, I would say 5.
Step-by-step explanation:
Because it's a little bit shorter than the length 6.
Please help with this geometry question
It has been proven that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
How to prove a Line Segment?We know that in a triangle if one angle is 90 degrees, then the other angles have to be acute.
Let us take a line l and from point P as shown in the attached file, that is, not on line l, draw two line segments PN and PM. Let PN be perpendicular to line l and PM is drawn at some other angle.
In ΔPNM, ∠N = 90°
∠P + ∠N + ∠M = 180° (Angle sum property of a triangle)
∠P + ∠M = 90°
Clearly, ∠M is an acute angle.
Thus; ∠M < ∠N
PN < PM (The side opposite to the smaller angle is smaller)
Similarly, by drawing different line segments from P to l, it can be proved that PN is smaller in comparison to all of them. Therefore, it can be observed that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
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The spinner below is incomplete. If the numbers in the sections of the spinner represent the probabilities of spinning
each section, what fraction is missing?
1/3
1/4
1/8
3/12
Answer:
i believe its a 1/4 because youre taking a quater of a chance of a spinner spinning everytime you try
the vertices of an isosceles triangle are a(-10, 1), b(-6, 3) and c(-4, 7). what is the equation of the triangle's line of symmetry?
The equation of the triangle's line of symmetry is Y= X+10.
Equation: The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Symmetry: Symmetry means that one shape is identical to the other shape when it is moved, rotated, or flipped. If an object does not have symmetry, we say that the object is asymmetrical. The concept of symmetry is commonly found in geometry.
Isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
It is given that an isosceles triangle with sides A(-10,1) ; B (-6,3) ; C(-4,7) is drawn and we notice that, the mid point of AB is the perpendicular bisector of the line AB.
Mid point of AB = (-8,2)
Slope of AB = [(-10) - (-6)] / (1 - 3)
=> -4 / -2
=> 2
Slope of perpendicular bisector of AB = 1
Equation of the line of symmetry = (Y - 2) = 1 [X - (-8)]
=> Y - 2 = X + 8
=> Y= X+10
Therefore, the equation of the triangle's line of symmetry is Y= X+10.
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There were 234 roses growing in the back garden. If 50% of the roses were red. How many were not red?
Answer:117
Step-by-step explanation:
I’m good at math
Answer:
117 Roses
Step-by-step explanation:
234 *0.5 = 117
i need help please i have been stuck on this problem for 2 months
Answer:
$8
Step-by-step explanation:
Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −33? flvs
Isolating the variable x we will get the simplified inequality (which is equivalent to the given one)
3 < x ≤ 5.2
How to get an equivalent inequality?Sadly, the options are not given, so we can get a trivial equivalent inequality which is the one where the variable x is isolated, and it gives the solution set for the inequality.
So let's isolate the variable:
-22 > -5x - 7 ≥ −33
First, we can add 7 everywhere, so we get:
-22 + 7 > -5x - 7 + 7 ≥ −33 + 7
-15 > -5x ≥ −26
Now we can divide everywhere by -5, because it is a negative number, it changes the direction of the symbols.
-15/-5 < -5x/-5 ≤ -26/-5
3 < x ≤ 5.2
That is the equivalent inequality, and the solution set is:
(3, 5.2]
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2) At age 22, Joseph places $4,500 in a retirement account with a fixed annual interest rate 7%,compounded continuously. He never places any additional money in the account. What will hisbalance be at age 55 ?
lets remember what it means compound continuously,
the interest never stopped, the balance is earning interest at all time
Joseph is 22 and he wants to know how much money he will have at 55
55-22=33
his balance will gain interest for 33 years, this is our time
there is a 7% rate
the formula is
P(t)= P(0) e ^rt
our t is 33
rate=7%
Joseph will have a balance at age 55, 45,334.99 dollars
Geoff goes to the shop and buys a packet of crisps for 25p, a can of soup
for 68p and a watermelon for £1.47. He pays with a £5 note. How much
change does he get? Give your answer in pounds (£).
CRISPS
Salt & Vinegar
25p
SOUP
68p
£1.47
Answer:
Step-by-step explanation:
Geoff is feeling peckish, so he decides to pop into the shop and grab some snacks. He picks up a packet of crisps for 25p, a can of soup for 68p and a watermelon for £1.47. He wonders why the watermelon is so cheap, but he doesn't question it. He goes to the cashier and hands over a £5 note. The customer behind Geoff wonders "how much change does he get back?"
To figure this out, we need to add up the price of the snacks and take it away from the money Geoff gave. We can use a dot to show the pence as parts of a pound. For example, 25p = 0.25 pounds.
The price of the snacks is:
0.25 + 0.68 + 1.47 = 2.40 pounds
The money Geoff gave is:
5.00 pounds
The change is:
5.00 - 2.40 = 2.60 pounds
So, Geoff gets £2.60 in change and a bargain watermelon.
Answer:
Answer:
2.60
Step-by-step explanation:
25+68+147=240
500-240=260
turn into pounds 2.60
Step-by-step explanation:
WILL GIVE BRAINLIEST
Quadrilaterals PQRS and TUVW are similar
What is the value of b in yards?
O 0.5 yd
0 3.2 yd
O 12.5 yd
0 28.8 yd
Answer:
3.2
Step-by-step explanation:
depending on what W-T looks like it seems the best answer
♡ The Question ♡
Quadrilaterals PQRS and TUVW are similar.
What is the value of b in yards?
* ୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer ♡
3.2 yd!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
No Explanation/Step-By-Step provided!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tips ♡
-No tips provided!
ABC company has just purchased a life truck that has a useful life of 5 years. The engineer estimates that maintenance costs for the truck during the first year will be $2,000. As the truck ages, maintenance costs are expected to increase at a rate of $300 per year over the remaining life. Assume that the maintenance costs occur at the end of each year. The firm wants to set up a maintenance account that earns 10% interest per year. All future maintenance expenses will be paid out of this account. How much does the firm have to deposit in the account now? $9,640.11
$11,500.00
$9,920.21
$9,127.02
The amount the firm needs to deposit in the account now is 9,640.11. Given that the company has purchased a life truck with a useful life of 5 years, the maintenance costs for the truck during the first year are 2,000.
Also, maintenance costs are expected to increase at a rate of 300 per year over the remaining life, which is for four years. Assume that the maintenance costs occur at the end of each year.
The future maintenance costs for the truck can be calculated as shown below:
Year 1:\($2,000Year 2: $2,300Year 3: $2,600Year 4: $2,900Year 5: $3,200\)The maintenance account that earns 10% interest per year has to be set up, and all future maintenance expenses will be paid out of this account. The future value of the maintenance costs, i.e., the amount that the firm needs to deposit now to earn 10% interest and pay the maintenance costs over the next four years is given by:
\(PV = [C/(1 + i)] + [C/(1 + i)²] + [C/(1 + i)³] + [C/(1 + i)⁴] + [(C + FV)/(1 + i)⁵]\),where PV is the present value of the future maintenance costs, C is the annual maintenance cost, i is the interest rate per year, FV is the future value of the maintenance costs at the end of year 5, which is $3,200, and 5 is the total number of years, which is
5.Substituting the given values in the above equation:
\(PV = [2,000/(1 + 0.1)] + [2,300/(1 + 0.1)²] + [2,600/(1 + 0.1)³] + [2,900/(1 + 0.1)⁴] + [(3,200 + 3,200)/(1 + 0.1)⁵] = 9,640.11\)Therefore, the firm needs to deposit 9,640.11 in the account now. Hence, option (A) is the correct answer.
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