The equations which are true for the values of x given are; x²-4 =0 and 4x²= 16.
Which equations are true for the values of x?The values of x given according to the task content are; x = –2 and x = 2.
By considering equation; x²-4 =0
x² = 4
x = ±2
Also, by considering 4x²= 16;
x² = 16/4 = 4
x = ±4.
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Which expression is equivalent to?
3/2
Answer:
D
Step-by-step explanation:
simplified is 1 1/2, 1.5 or 3/2
Subject
mathematics, 06.11.2020 05:30 tonya3498
2. (15 points) sheila needs to hire a babysitter for the evening. the babysitter charges $10 for each
hour and also charges for the time she spends driving to and from the house. she thinks it will take
1.5 hours of total driving time. sheila is willing to spend $80 for the night for babysitting.
a. write an equation to determine for how many hours sheila can afford to hire the babysitter.
b. use the guess-and-check method to determine how many hours of babysitting sheila can
afford.
c. sheila finds another babysitter that lives much closer to her and would only need 1 hour of
driving time. however, she charges $15 per hour. write an equation to determine how many hours
of babysitting sheila could buy from her.
d. can sheila afford the same amount of babysitting from the second sitter as she could from the
first sitter?
a. The equation we get is 10(1.5 + x) = 80, where x is the number of hours Sheila can afford to hire the babysitter.
b. Sheila can afford the babysitter for 6 hours and 30 minutes.
c. The equation we get is 15(1 + x) = 80, where x is the number of hours Sheila can afford to hire the new babysitter.
d. Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.
Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.
a. We assume the hours affordable to Sheila be x hours.
Per hour charge of the babysitter = $10.
Time taken by the babysitter traveling = 1.5 hours.
Therefore, total chargeable time = 1.5 + x.
Therefore, the total charge by the babysitter = $10(1.5 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 10(1.5 + x) = 80.
b. We are asked to determine the hours Sheila can afford to hire the babysitter.
We have got the equation 10(1.5 + x) = 80, where x is the hours Sheila can afford to hire the babysitter.
Thus, by solving this equation, we can determine the hours Sheila can afford to hire the babysitter.
10(1.5 + x) = 80,
or, 1.5 + x = 8,
or, x = 8 - 1.5 = 6.5 = 6 hours and 30 minutes.
Thus, Sheila can afford the babysitter for 6 hours and 30 minutes.
c. Per hour charge of the new babysitter = $15.
Time taken by the new babysitter traveling = 1 hour.
Therefore, total chargeable time = 1 + x.
Therefore, the total charge by the new babysitter = $15(1 + x).
This needs to be equal to the amount Sheila is willing to spend, that is, $80.
Thus, the equation we get is: 15(1 + x) = 80.
d. We are asked whether Sheila affords the same amount of babysitting from the second sitter as she could from the first sitter.
To determine this, we need to find the hours she affords from the second babysitter, for which, we solve the equation 15(1 + x) = 80 as follows:
15(1 + x) = 80,
or, 1 + x = 80/15,
or, x = 80/15 - 1 = 65/15 = 13/3 = 4 hours and 20 minutes.
Sheila can afford to hire the new babysitter for 4 hours and 20 minutes, while the first babysitter was hired for 6 hours and 30 minutes.
Thus, Sheila can't afford the same amount of babysitting from the second sitter as she could from the first sitter.
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If three different orders are selected, find the probability that they are all from Restaurant B
If three different orders are selected, find the probability that they are all from Restaurant B is; 0.026
How to find the probability?Total orders both accurate and not accurate = 1131
Total orders from restaurant B (both accurate and not accurate) = 337
Probability of first order from B = 337/1131
Probability of second order from B = 336/1130
Probability of third order from B = 335/1129
Probability of the first three orders from B = 337/1131 × 336/1130 × 335/1129
Probability of the first three orders from B = 0.026
Complete question is;
Use the data in the following table , which lists drive - thru order accuracy at popular fast food chains Assume that orders are randomly selected from those included in the table Drive thru Restaurant A B C D Order Accurate 312 277 250 144 Order Not Accurate 32 60 37 19 If three different orders are selected , find the probability that they are all from restaurant A
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Circle 1 is centered at (-4,
2) and has a radius of 3 centimeters. Circle 2 is centered at (5, 3) and has a radius of 6 centimeters.
What transformations can be applied to Circle 1 to prove that the circles are similar?
Enter your answers in the boxes.
The circles are similar because you can
translate Circle 1 using the transformation rule C, ) and then
dilate it using a scale factor of
The transformation for circle 1 exists (x+9), (y+5) and the scale factor of circle 1 exists 2.
What is a scale factor?Scale exists described as the ratio of the length of any object on a model to the actual length of the exact object in the entire world.
What is the transformation rule?The function transformation rules: f(x)+b changes the function b units upward. f(x)−b shifts the function b units downward. f(x + b) shifts the function b units to the left.
Circle 1
center: (−4, −2)
Radius: 3 centimeters
Circle 2
center: (5, 3)
Radius: 6 centimeters
Transformations can be used to circle 1 to verify that the circles exist similar.
As circle 2 and circle 1 do not contain the exact coordinates
So, circle 1 has to utilize transformation rules.
The difference between the coordinates of circle 2 and circle 1 exists
[tex]$x_2 - x_1 = 5 - (-4 ) = 9[/tex]
[tex]y_2 - y_1 = 3 - (-2) = 5[/tex]
Therefore, transformation for circle 1: (x+9), (y + 5)
The scale factor between circle 2 and circle 1 exists
The radius of Circle 2 = 2 [tex]*[/tex] radius of circle 1
Therefore, the scale factor of circle 1 = 2
Therefore, the transformation for circle 1 exists (x+9), (y+5), and the scale factor of circle 1 exists 2.
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Use the ideal gas law (PV=nRT) to find P. Round answer to 1 d.p.
Given: V = 3 L, n = 2 mol, T = 300 K, R = 0.0821
Answer:
P = 16.4
Step-by-step explanation:
Given the equation PV = nRT and the values we know, we need to isolate P .
Thus, we have:
[tex]PV=nRT\\3P=2*0.0821*300\\P=49.26/3\\P=16.42=16.4[/tex]
Bill and jenna are solving the quadratic equation x 2 - x = 12. bill solved this way jenna solved this way x 2 - x = 12 x(x - 1) = 12 x = 12 or 13 x 2 - x = 12 x 2 - x - 12 = 0 (x - 4)(x 3) = 0 x = 4 or x = -3 which student is correct? what error did the other student make when solving?
Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.
Form of quadratic equationThe form of quadratic equations is given as
ax2 + bx + c = 0
So, for the quadratic equation, we have
x² - x = 12
Let's make it into quadratic form
x² - x - 12 = 0
Bill solved it as
x(x - 1) = 12
This is wrong, because quadratic equations must be written in the form before solving for the variables
Jenna solved it as
x 2 - x - 12 = 0
Jenna is correct because she converted the equation to a quadratic form before solving for the variables.
Thus, Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.
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How many significant digits are there in the number 1.00250? A.7 B. 6 C. 5 D. 4
Answer:
B.6 is the significant digits of number 1.00250
I HOPE IT HELP YOU
The number of significant figures that are available in 1.00250 are; B: 6
What is the significant figure?
Significant figures are defined as the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value.
Now, in the question we are given the decimal number 1.00250.
Now, it should be noted that when dealing with significant numbers as regards decimals, any zero digit to the left of the decimal is a non-significant figure while any zero digit to the right of the decimal is a significant figure.
Thus, the significant figures in the question are all the numbers which are 6 in number.
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When solving the following system of equations, which variable would be the easiest to solve for? 2x + y = 9 3x - 2y = 17
Answer:
In my opinion, it would be 'y', since it is already on its own (in the first equation) without any coefficients.
Answer:
x.
Step-by-step explanation:
x because if you multiply the first equation by 2 and add the result to equation 2 , the y's will cancel out.
2x + y = 9 Times 2:-
4x + 2y = 18
3x - 2y = 17 Adding:-
7x = 35
x = 5.
(14x2 + 13x + 12) + (7x2 + 20x + 4)
Answer:
21x^2 + 33x + 16
Step-by-step explanation:
(14x^2 + 13x + 12) + (7x^2 + 20x + 4)
Combine like terms:
14x^2 + 7x^2 = 21x^2
13x + 20x = 33x
12 + 4 = 16
Thus:
21x^2 + 33x + 16
Answer:
21x^2 + 33x + 16.
Step-by-step explanation:
(14x2 + 13x + 12) + (7x2 + 20x + 4) Remove the parentheses:
= 14x2 + 13x + 12 + 7x2 + 20x + 4 Bring like terms togethher:
= 14x^2 + 7x^2 + 13x + 20x + 12 + 4
= 21x^2 + 33x + 16.
(Lesson 1.3) Use properties to find the sum or product. (3,5,7,9,11 only)
The values when the given numbers are multiplied will be:
230
78
3
91
1800
How to compute the values?3. 5 × 23 × 2
It should be noted that the given information simply means that we should multiply 5 by 23 by 2. This will be:
= 5 × 23 × 2
= 230
5. 34 + 0 + 18 + 26
This information simply means that we should add thirty four, eighteen, and twenty six together. This will be:
34 + 0 + 18 + 26 = 78
7. (3 × 10 × 8) = ....... × (10 × 8)
(3 × 10 × 8) = 3 × (10 × 8)
9. 0 + ...... = 91
It simply means the number that will be added to zero that will give ninety one. This will be 91.
11. The total income for the theater will be:
= (20 × 18) × 5
= 1800
Therefore, the correct values based on the computation will be 730, 78, 3, 91, and 1800.
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a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. -1/1.06
The required answers are:
a. The linear approximating polynomial at a = 1: P₁(x) = x - 2
b. The quadratic approximating polynomial at a = 1: P₂(x) = -3 + 3x - x²
c. Appromating the given quantity -1/1.06 for P₁(x) and P₂(x): -3.06 and -7.30 respectively.
Using Taylor polynomial series, the required approximating polynomials are calculated.
What is the Taylor polynomial series?The Taylor polynomial series is
Pₙ(x) = ∑ [tex]\frac{f^n(a)}{n!}[/tex](x - a)ⁿ; limits from 0 to n
Where fⁿ(a) is the nth derivation of f(x) at a
The first order(linear) Taylor polynomial series is
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
The second order(quadratic) Taylor polynomial series is
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
Calculation:The given function is f(x) = -1/x at a = 1
f(a) = f(1) = -1
f'(x) = -(-1/x²) = 1/x²; f'(a) = f'(1) = 1
f''(x) = -2/x³; f''(a) = f''(1) = -2
a. Linear approximating polynomial:
From the Taylor series, we have
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
On substituting,
P₁(x) = -1 + (1/1!)(x - 1)¹
= -1 + (x - 1)
= x - 2
b. Quadratic approximating polynomial:
From the Taylor series, we have
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
On substituting,
P₂(x) = f(1) + (1/1!)(x - 1) + (-2/2!)(x - 1)²
= -1 + (x - 1) - (x - 1)²
= -1 + x - 1 - (x² - 2x + 1)
= x - 2 - x² + 2x - 1
= -3 + 3x - x²
c. Approximating the given quantity -1/1.06:
Substituting x = -1.06 in P₁(x) and P₂(x),
P₁(x) = x - 2
⇒ P₁(-1.06) = (-1.06) - 2 = -3.06
P₂(x) = -3 + 3x - x²
⇒ P₂(-1.06) = -3 + 3(-1.06) - (-1.06)² = -7.30
Therefore, the approximating polynomials are calculated by using Taylor polynomial series.
Disclaimer: The given question is incomplete. Here is the complete question.
Question:
a. Find the linear approximating polynomial for the following function centered at the given point a.
b. Find the quadratic approximating polynomial for the following function centered at the given point a.
c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.
f(x) = -1/x , a = 1; approximate -1/1.06
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THIS IS VERY HARD PLSSS
Answer:
[tex]y=3\sqrt{x-1}-7[/tex]
Step-by-step explanation:
We are given the function [tex]y=\sqrt{x}[/tex]. Let's apply each transformation separately and see what we get. First, let's apply the vertical shift. We are told that the graph shifts downwards by 7 units. In other words, when x is 0, y should be -7 instead of 0. We can accomplish that by changing the y-intercept of the graph and subtracting our function by 7: [tex]y=\sqrt{x} -7[/tex]. Notice that the -7 is outside the square root.
Next, we can apply the horizontal transformation. We are told that the graph shifts to the right 1 unit. This means that, for [tex]y=\sqrt{x}[/tex], if y is 0, x should be 1. We can accomplish this by doing [tex]y=\sqrt{x-1}[/tex] (if x = 1, y will be 0). Now, we can combine the two transformations we have done so far: [tex]y=\sqrt{x-1}-7[/tex].
Lastly, we need to vertically stretch the function by a factor of 3. All we have to do here is multiply sqrt(x) by 3 (this way, if x is equal to 1, y should be 3 instead of 1 (3 times x)). So, we get something like this: [tex]y=3\sqrt{x}[/tex]. Now, we can combine all of the transformations we did to get our final answer:
[tex]y=3\sqrt{x-1}-7[/tex]
Does this graph show a function?
Answer:
I think that is is C
Step-by-step explanation:
The Vertical Line Test determines whether or not a curve on the graph is a function. This one passes the vertical line test because no vertical line can intersect the curve more than once. I hope that helps!
The typical pole for pole vaulting is 17 feet long. How fast would a pole vaulter have to run (in the direction of the pole) in order for a spectator sitting in the stands to see it 15 feet long
A pole vaulter have to run at 18m/s speed.
According to the statement
The typical pole for pole vaulting is 17 feet long
we use the formula
1/2 m(v)^2 = mgh
Now rearrange the terms
(v)^2 = 2gh
here g = 10 and h = 15 then
substitute the values
(v)^2 = 2*10*15
v = 17.32
So, A pole vaulter have to run at 18m/s speed.
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If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?
Haven worked on an externship in a prosecutor’s office, the legal support position which you would be best suited for is: paralegal.
What is paralegal?Paralegal can be defined as a person who has been trained in subsidiary legal matters (issues), but not fully qualified to act as an attorney or lawyer.
In this context, we can infer and logically deduce that paralegal is a legal support position which you would be best suited for a person who has worked on an externship in a prosecutor’s office.
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Complete Question:
If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?
mediator
paralegal
legal secretary
court reporter
Marina correctly simplified the expression StartFraction negative 4 a Superscript negative 2 Baseline b Superscript 4 Baseline Over 8 a Superscript negative 6 Baseline b Superscript negative 3 Baseline EndFraction, assuming that a not-equals 0, b not-equals 0. Her simplified expression is below.
Negative one-half a Superscript 4 Baseline b Superscript empty box
What exponent should Marina use for b?
The exponent Marina should use for b is: D. 7.
How to Divide Exponents with the same Base?When dividing, you subtract the exponents. I.e. [tex]a^m \div a^n = a^{m - n}[/tex].
Using the rule, we would also subtract the exponents of b in the simplified expression. Thus:
[tex]b^4 \div b^{-3}[/tex]
Subtract the exponents
4 -(-3) = 4 + 3 = 7.
Therefore, the Maria should use the exponent b = 7.
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Answer: D
Step-by-step explanation:
Help me please with this question
Answer:
[tex]y = \sqrt{ \frac{\pi \: x - A {}^{} }{\pi} } [/tex]
Step-by-step explanation:
To make y subject of formular, we place y in terms of other variables.
[tex] A = \pi \: x {}^{2} - \pi \: y {}^{2} \\ making \: y \: subject \\ A + \pi \: y {}^{2} = \pi \: x {}^{2} \\ \pi \: y {}^{2} = \pi \: x {}^{2} - A \\ Dividing \: bothsides \: by \: \pi \\ y {}^{2} = \frac{\pi \: x { - A}^{} }{\pi} \\ Squarerooting \: bothsides \\ y = \sqrt{ \frac{\pi \: x - A {}^{} }{\pi} } [/tex]
Evaluate 3x for x = -2, x = 1, and x = 3.
Answer: A. 1/9, 3, 27
Step-by-step explanation:
3^x for x = -2
= 3^-2 = 1/9
3^x for 1
= 3^1 = 3
3^x for 3
= 3^3 = 27
hope this helped
Katie has 100 apples, and she plans on eating 2 of them every day.
True or false...the number of apples Katie has left is proportional to the number of days that pass.
Can someone help me please. (TROLLS WILL BE REPORTED!!!)
Answer:
B.) 54π units²
Step-by-step explanation:
First, we need to find the height of the cone. We can do this using the Pythagreom Theorem.
a² + b² = c² <----- Pythagreom Theorem
3² + b² = 15² <----- Insert side lengths
9 + b² = 225 <----- Solve 3² and 15²
b² = 216 <----- Subtract 9 from both sides
b = 14.7 units <---- Take square root of 216
Now, we can use the surface area of a right cone equation to find the final answer.
r = 3 units
h = 14.7 units
SA = πr(r + √(h² + r²)) <----- Surface Area equation
SA = π(3)(3 + √(14.7² + 3²)) <----- Insert values
SA = π(3)(3 + √(216 + 9)) <----- Solve 14.7² and 3²
SA = π(3)(3 + √225) <----- Add 216 and 9
SA = π(3)(3 + 15) <----- Take square root of 225
SA = π(3)(18) <----- Add 3 and 15
SA = 54π units² <----- Multiply 3 and 18
Which expression could help you find the distance between –1 and 3 on the number line?
Answer:
|-1| + |3|
Step-by-step explanation:
We can use absolute values to find the distance between positive and negative numbers on a number line.
|-1| + |3| =
Keep in mind that
- the absolute value of a positive number is positive and
- the absolute value of a negative number is positive
1 + 3 =
4 units
X: -1/2
-6(x-2)
pls i need a result
Answer:
15
Step-by-step explanation:
First, we can plug -1/2 into the equation and get -6(-1/2 -2). Then, we can convert -2 into a fraction to get -4/2. If we subtract -4/2 from -1/2, we get -6(-5/2). We then multiply this and get 30/2 which simplifies to 15
HELP! what is this? what’s the answer?!
D. not continuous at X=0
if you trace the function you'll find a jump in the graph. To be continuous the line can't have any breaks in it. In this example, it's discontinuous when X=0
If is any positive two-digit integer, what is the greatest positive integer that must be a factor of
Answer:
23
Step-by-step explanation:
small brain
according to the graph, what is the value of the constant in the equation below?
Answer: B
Step-by-step explanation:
The product of height and width is constant.
If we take the point (0.5,1), we get the product to be 0.5.
In London, the charge of a tour bus consists of a fixed rental price plus a per kilometre rate, that depends on the distance of the trip.
The per kilometre rate is $12/km. You decide to go on a 5 km trip, and it costs you $70.
a) What is the fixed rental cost? Show your work.
b) Determine the equation relating the cost, C, in dollars, and the distance, d, in km.
d) What is the cost of an 18 km trip?
e) What is the distance travelled if the total cost is $250?
PLEASEEEEEEEE
Using a linear function, we have that:
a) The fixed cost is of $10.
b) The equation is: C = 10 + 12d.
c) The cost of an 18 km trip is $226.
d) The distance traveled is of 20 km.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the slope is of m = 12. When d = 5, C(d) = 70, hence we find the fixed cost as follows:
C(d) = 12d + b
70 = 60 + b
b = 10.
Hence the equation is:
C(d) = 12d + 10.
For a trip of 18 km, d = 18, hence the cost is:
C(12) = 12 x 18 + 10 = $226.
When the cost is of $250, the distance is found as follows:
250 = 12d + 10
12d = 240
d = 240/12
d = 20 km.
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Help please you don’t know how much this means to me
[tex]db {}^{2} - ab {}^{2} = ab {}^{2} - ae {}^{2} \\ db {}^{2} = 2ab {}^{2} - ae {}^{2} \\ (ac + bc) {}^{2} = 2ab {}^{2} - ae {}^{2} \\ ac {}^{2} + bc {}^{2} + 2ac.bc = 2ab {}^{2} - ae {}^{2} \\ 2ac.bc = ab {}^{2} - ae {}^{2} [/tex]
[tex]2ac.bc = ab {}^{2} - (ac {}^{} - ce) {}^{2} \\ 2ac.bc = ab {}^{2} - ac {}^{2} + 2ac.ce - ce {}^{2} \\ 2ac.bc = ab {}^{2} - ac {}^{2} - cb {}^{2} + 2ac.ce \\ but \: ab {}^{2} - ac {}^{2} - cb {}^{2} = 0 \\ 2ac.bc = 2ac.ce \\ bc = ce \\ which \: is \: true[/tex]
Find the discriminant of the quadratic equation x2 6x 14 = 0 and use it to determine the number and types of solutions. b2 − 4ac −20; two nonreal solutions −20; one real solution 92; two real solutions 92; one real solution
The discriminant of the quadratic equation is -20 and there are two non real solutions.
The discriminant of a quadratic equation uses the equation:
[tex]b^{2} -4ac[/tex]
Where the value of this calculation can tell you what solutions there are, plug known values in:
[tex]x^{2} +6x+14[/tex]
a=1
b=6
c=14
[tex]b^{2} -4ac[/tex]
which is equal to -20 on putting the values of a,b and c in the equation
As -20 < 0, this means that there is not a real solution, resulting in the first option being correct.
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i need help finding all of this stuff
Answer:
Axis Of Symmetry = -2
Vertex = (1,-2)
Min (0,-2)
Domain = All Real #'s
Range = Y is greater than or equal to -2
Volume=
Help me please
I appreciate it so much :)
The volume of the given solid is 6322.75 cubic units.
What is the volume of the given figure?
It is given that,
The area of the regular pentagonal base, a = 35 units
Altitude of the given pyramid, h = 9 units
The formula for the volume of a pyramid with regular pentagonal base is given by,
V = (5/12) × tan(54°)ha²
Substituting the given values of a and h, we get the volume as,
V = (5/12) × tan(54°) × 9 × (35)²
V = (5/12) × (1.376) × 9 × 1225
V = (5/4) × (1.376) × 3 × 1225
V = (5/4) × 5056.8
V ≈ 6322.75 units³
Thus, the volume of the given figure comes out to be approximately equal to 6322.75 cubic units.
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