Answer:
x² + 3x - 10 = 0
x² - 25 = 0
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
A. In 2 - In x
B. In 1 + In 2 - ln x
C. 1 + In 2 - In x
D. In 2 + ln x
Answer:c
Step-by-step explanation:
The equivalent expression is 1 + In 2 - In x.
How to estimate an equivalent to the given expression?Given:
[tex]$\ln \left(\frac{2 e}{x}\right)$[/tex]
Apply log rule:
[tex]$$\log _{C}\left(\frac{a}{b}\right)=\log _{c}(a)-\log _{c}(b)$[/tex]
[tex]$&\ln \left(\frac{2 e}{x}\right)=\ln (2 e)-\ln (x) \\[/tex]
= ln (2e) - ln (x)
Apply log rule:
[tex]$\log _{c}(a b)=\log _{c}(a)+\log _{c}(b)$[/tex]
ln (2e) = ln (2) + ln (e)
= ln (2) + ln (e) - ln (x)
Apply log rule:
[tex]$\log _{a}(a)=1$[/tex]
= ln (2)+1-ln (x)
Therefore, the correct answer is option C. 1 + In 2 - In x.
To learn more about log rule
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simpify 20/[(5-{24/2-(7-5of3)}]
Answer:
Why do we need an order of operations?
Example: In a room there are 2 teacher's chairs and 3 tables each with 4 chairs for the students. How many chairs are in the room?
We know there are 14, but how do we write this calculation? If we just write
2 + 3 x 4
how does a reader know whether the answer is
2 + 3 = 5, then multiply by 4 to get 20 or
3 x 4 = 12, then 2 + 12 to get 14?
There are two steps needed to find the answer; addition and multiplication. Without an agreed upon order of when we perform each of these operations to calculate a written expression, we could get two different answers. If we want to all get the same "correct" answer when we only have the written expression to guide us, it is important that we all interpret the expression the same way.
One way of explaining the order is to use brackets. This always works. To say that the 3 x 4 is done before the adding, we would use brackets like this:
2 + (3 x 4)
The brackets show us that 3 x 4 needs to be worked out first and then added to 2. However, we can also agree on an order of operations, which is explained below.
Another example: Calculate 15- 10 ÷ 5
If you do the subtraction first, you will get 1. If you do the division first, which is actually correct according to the rules explained below, you will get 13. We need an agreed order.
1. Estimate the area of the irregular shape. Explain your method and show your work.
2. The coordinates of the vertices of △LMN are L (-2, 4), M (3, -1), and N (0, -4). Determine whether △LMN is a right triangle and support your decision. Show all work.
3. The coordinates of the vertices of quadrilateral PQRS are P (-6, 2), Q (-1, 4), R (2, 2), and S (-3, 0). Alexandra states that quadrilateral PQRS is a parallelogram. Prove or disprove Alexandra’s statement. Show all work.
Answer:
Step-by-step explanation:
1. Do not see a figure, and unsafe to download and execute .docx.
2. Vectors LM<5,-5>, NM<3,3>, NL<2,-8>
Since LM.NM = 15-15 = 0, LM and NM are orthogonal, hence the given points form a right triangle.
3. A parallelogram has opposite sides parallel.
Slope PQ = (4-2) / (-1 - -6) = 2/5
Slope RS = (2-0) / (2- -3) = 2/5
Therefore PQ || RS
Slope PS = (2-0)/(-6- -3) = -2/3
Slope QR = (4-2)/(-1 -2) = -2/3
Therefore PS | QR
Since opposite sides are parallel, PQRS is a parallelogram
Answer:
Step-by-step explanation:
1. There are 31 complete are almost complete squares.
Top line is about 3.5 squares
Right side is about 1.8
Bottom about 3.5 and left side about 1.2.
Total approximately 41 square units.
2. If it is a right triangle then 2 sides will be perpendicular.
Slope of LM = (-1-4)/(3 +2 = -1
Slope of MN = (-4+1)/ -3 = -3/-3 = 1.
So as the product of the slope = -1 * 1 = -1 the angles between LM and MN is a right angle and LMN is a right triangle.
3(x - 4) = -3. Solve for x.
Answer:
x = 3
Step-by-step explanation:
3(x - 4) = -3
Divide by 3
3/3(x - 4) = -3/3
x-4 = -1
Add 4 to each side
x-4+4 = -1+4
x = 3
Answer:
x = 3
Step-by-step explanation:
Divide each term by 3 and simplify.
x - 4 = [tex]\frac{-3}{3}[/tex]
Cancel the common factor of 3 .
x - 4 = -1
Move all terms not containing x to the right side of the equation.
x = -1 + 4
Add -1 and 4.
x = 3
Hope this helps!
A boat can carry 22 people 940 people went on the boat how many trips did the boat do
In triangle ABC, the measure of angle B is 22° more than three times the measure of angle A. The measure of angle C is 53° more than the measure of angle A. Find the measure of each angle.
Answer:
105
Step-by-step explanation:
53+22=75, 180-75=105
109.06 in scientific notation is
Which expression is equivalent to 3/x5y?
Answer:
option B
Step-by-step explanation:
[tex]\sqrt[3]{x^5 \ y} = (x^5 \ y )^\frac{1}{3} \ \ \ \ \ \ \ \ \ \ \ \ [ \ \sqrt[n]{x} = x^\frac{1}{n} \ \ , \ (xy)^a = x^a y^a]\\\\[/tex]
[tex]= x^{ (5 \times \frac{1}{3} )} \ y ^{\frac{1}{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ ( x^a )^b = x^{ab} \ ]\\\\\\[/tex]
[tex]= x^{\frac{5}{3} }\ y^{\frac{1}{3}}[/tex]
The area of a circle is 64 pi ft squared. What is the circumference, in feet? Express your answer in terms of pi
HELP I HAVE TO PASS!
What is the average rate of change for this quadratic function for the interval from x=0 to x=2?
A) -4
B) -2
C) 2
B) 4
Answer:
At X = 0 Y = 10
At X = 2 Y = 6
Rate of change = change in Y / change in X = -4 / 2 = -2 or B
Calculate the BMI for a woman who is 165 cm tall and weighs 65 kg.
Charlie weighed 8 lbs. 11 oz. at birth given that 1 pound is equivalent to 16 ounces what is Charlie’s birthweight expressed in ounces
Answer:
139 oz.
Step-by-step explanation:
If 1 pound equals 16 ounces, multiply 8 by 16 and you will get 128, then add the original 11 ounces to get 139.
Eden has a part-time job
She is paid £7.20 per hour
This week she worked for 18½ hours
Work out Eden's total pay for this week
Answer:
$133.20
Step-by-step explanation:
You make 7.20 an hour for 18 1/2 hours. You must multiply to know how much she made that week
7.20/hr = ?/18 1/2 hr
7.20 x 18 1/2
7.20 x 18.5=
133.20
find the coordinates of 6x² + 6x = 12
Answer:
1 , -2
Step-by-step explanation:
6x^2 + 6x = 12
6x^2 + 6x - 12 = 0
using middle term break method
6x^2 + (12 - 6)x - 12 = 0
6x^2 + 12x - 6x - 12 = 0
6x(x + 2) - 6(x + 2) = 0
(x + 2)(6x - 6) = 0
either (x + 2) = 0 OR (6x - 6) = 0
x + 2 = 0
x = 0 -2
x = -2
6x - 6 = 0
6x = 6
x = 6/6
x = 1
therefore , x = 1 , -2
1. Two-thirds of the sum of the number x and 5 is written
2x+5
a.
2
-x+ 5
3
b. §
(5x) <(x+5)
d.
e. x+ķ(x+5)
{(+5)
3
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Answer:
cbaStep-by-step explanation:
This is as much about English comprehension as it is about math. When you read an English sentence, you need to figure out what each of the pronouns, phrases, and modifiers is referring to. When the sentence refers to math operations, you need to determine what each math operation is being applied to. In most cases, a math operation involves two operands, so the trick is to figure out what those are.
__
1. "Two-thirds of the sum ..." will look like 2/3( + ). "The sum of a number and 5" will look like (x+5). So, the words are describing ...
2/3(x +5) . . . . matches C
__
2. "Seven decreased by ..." will look like 7 -( ). "The quotient of a number and 3" will look like (n/3). So, the words are describing ...
7 -n/3 . . . . matches B
__
3. Consider the order of operations. When you evaluate 2x²+9, the last operation you perform is addition. That is, the result is a sum. One of the elements of that sum is 9 (the second one). The other element of that sum is the product 2x². The elements of that product are 2 and the square of x. So, one way to describe this expression is ...
the sum of the product of 2 and the square of a number, and 9.
The order of operations requires that squares be evaluated before multiplication and division, so it is not unreasonable (if slightly more ambiguous) to write this as ...
the sum of 2 times a number squared and 9 . . . . choice A
Consider the following. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) Three coins are tossed; the result is at most one tail. What sets of elements are included in the sample space?
Answer:
a) [tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]
b) [tex]n=(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).[/tex]
Step-by-step explanation:
From the question we are told that:
3 coin are tossed
Therefore
Sample space [tex]n=(HHH, HHT, HTH, HTT, THH, THT, TTH, TTT).[/tex]
Generally the sets that correspond with the result of at most one tail is therefore given as follows
[tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]
Therefore
The result is at most one tail when
[tex]P(<1)=(HHH,HHT,HTH,THH)[/tex]
Find the Surface Area and the Volume.
Answer:
Surface area = 850 cm²
Volume = 1000 cm³
Step-by-step explanation:
Applying,
A = h(a+b+c+d)................ Equation 1
Where A = Surface area of the trapezoidal prism, a, b, c, d = length of the four sides the trapezium respectively, h = height of the prism.
From the diagram in the question,
Given: h = 25 cm, a = 6 cm, b = 14 cm, c = 7 cm, d = 7 cm
Substitute these values into equation 1
A = 25(6+14+7+7)
A = 25(34)
A = 850 cm²
From the volume,
V = A'h...................... Equation 2
Where A' = Area of the base.
From the diagram,
A' = 1/2(6+14)4
A' = 40 cm²
Therefore,
V = 40×25
V = 1000 cm³
A custodian has 5 1/2 gallons of paint. Each of the bookcases she is painting requires 1/2 gallon of paint. How many bookcases will the custodian be able to paint with that amount of paint
A. 3
B. 4
C. 11
D. 15
Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on all 7 days of a given week,and the average​ (mean) value is 120.7 volts.
A. The given value is a parameter for the week because the data collected represent a population.
B. The given value is a statistic for the week because the data collected represent a population.
C. The given value is a statistic for the week because the data collected represent a sample.
D. The given value is a parameter for the week because the data collected represent a sample
Answer:
A. The given value is a parameter for the week because the data collected represent a population
Step-by-step explanation:
Parameters in a study refers to the numbers that are used to summarize the data for the entire population. Whereas, a statistic are used to summarize the data from a sample only.
In the context, it is given that a person measures the voltage supply to his home for all the seven days and finds the average value of the voltage. The homeowner here considers the population of his sample to make his study.
Thus it is a parameter for the entire week as the data represents a population.
How many side of the triangle are congruent? Explain.
A) 0
B) 2
C)3
D) not enough information given
Answer:
Option B
Step-by-step explanation:
In the given triangle,
Two sides of the triangle measure 2 cm and one side measures 3 cm.
Therefore, in this triangle two sides measuring 2 cm are congruent.
Option B is the correct option.
One evening Papa John’s sold a total of 33 pizzas topped with pepperoni, sausage, or pepperoni and sausage. There were 29 pizzas that had pepperoni. Of these, 15 also had sausage. How many more pizzas had pepperoni only than had sausage only?
Answer:
10
Step-by-step explanation:
Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33
Number of pizzas with pepperoni = 29
Number of pizzas with pepperoni and sausage = 15
Pizza with pepperoni only = 29 - 15 = 14
Pizza with sausage only = 33 - 29 = 4
Pepperoni only than sausage only :
14 - 4 = 10
i need to know how to solve this
Answer:
C
Step-by-step explanation:
I think you have to call a = 14/32 and b = 7/4
3a = 3 * 14/32 = 42/32
b = 1 3/4 = (4 + 3)/4 = 7/4
42/32 // 7/4 Invert and multiply
42/32 * 4/7 Cancel 4 into 32 and 7 into 42
6/8 = 3/4
I make the answer C
Answer:
So the square seems to multiply the first number by three and then divide it by the second number.
So,
14/32 * 3
=
42/32
Simplify
21/16
And now for division, we flip the diveding fraction and multiply.
21/16 * 4/7
Which is after some fraction simplifing:
3/4
Which expression can be used to convert 22 Australian dollars to US dollar
Answer:26.4
Step-by-step explanation:1.2 x22
How many one-to-one functions are there from the set {A, B, C} to the set {x, y, z, t, w, k}?
Answer:
120 different one-to-one functions
Step-by-step explanation:
A one-to-one function means that each element from the domain can be mapped into only one element from the range (like for a typical function), and each element from the range can be mapped only once.
This means that, for two different inputs x₁ and x₂, we can't have:
f(x₁) = f(x₂)
Because that would mean that two different values of the domain are being mapped into the same element from the range.
Ok, now that we know this, let's count the number of possible "mappings" for each element in the domain.
For the first element, A, we have the options {x, y, z, t, w, k} (a total of 6 options).
For the second element, B, we will have an option less (because one was already taken) so here we have 5 options.
For the last element on the domain, C, there will be again an option less than in the previous case, so here we have 4 options.
The total number of combinations (each combination defines a different one-to-one function) is equal to the product between all the options for each case, then the total number of one-to-one functions is:
C = 6*5*4 = 120
There are 120 different one-to-one functions.
HELP ASAP PLEASE Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45. If Alaina makes the purchase, which integer will represents the amount of money in Alaina's account?
Answer:
-17
Step-by-step explanation:
28-45= -17 dollars in her account
A comet travels at an average speed of 273,000 km/h.
It takes 8 days for the comet to reach Earth.
Find the distance, in km, the comet travelled
Answer: 52,416,000 km
Step-by-step explanation:
If a comet travels 273,000 km/hr
1) Multiply 273,000 km by 24 hours to find how far the comet travels in one day
2) multiply the answer from 1 by 8 to determine how far it travels in 8 days
1) [tex]\frac{273,000 km}{hr}[/tex]*[tex]\frac{24 hr}{1 day}[/tex] = [tex]\frac{6,552,000km}{day}[/tex] (hours cancel out)
2)[tex]\frac{6,552,000km}{day}[/tex]*8 day= 52,416,000 km in 8 days
The comet approximately travelled 52,416,000km from when it began to travel to when it reached Earth. Hope this helped :)
Describe the transformation of f(x) = sin x to g(x) = sin x – 7.
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Answer:
C. 7 units down
Step-by-step explanation:
The y-coordinate of a point on a graph is the function value. It tells how far up from the x-axis the point is located. When 7 is subtracted from the function value, the y-coordinate is 7 less than it was. That is, the point has moved 7 units down.
Find the investment value when compounded anually.
P = $120,000, r= 5.3%, t = 8 yr
Given:
[tex]P=\$120,000[/tex]
[tex]r=5.3\%[/tex]
[tex]t=8\text{ years}[/tex]
To find:
The value of the investment when the interest is compounded annually.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is the principal, r is the rate of interest in decimal, n is the number of time interest compounded in an years, and t is the number of years.
The interest is compounded annually. So, [tex]n=1[/tex].
Substituting [tex]P=120000, r=0.053, n=1, t=8[/tex] in the above formula, we get
[tex]A=120000\left(1+\dfrac{0.053}{1}\right)^{1(8)}[/tex]
[tex]A=120000\left(1.053\right)^{8}[/tex]
[tex]A=181387.85936[/tex]
[tex]A\approx 181387.86[/tex]
Therefore, the value of the investment after 8 years is $181,387.86.
Listed below are the top 10 salaries (in millions of dollars) of television personalities in a recent year.
38 36 35 27 15 13 12 10 9.6 8.4
Use the sample data to construct a 95% confidence interval for the population mean and correctly interpret your answer.
Answer:
The correct answer is "(11.69, 29.11)".
Step-by-step explanation:
Given:
[tex]38 \ 36\ 35\ 27\ 15\ 13\ 12\ 10\ 9.6\ 8.4[/tex]
[tex]n=10[/tex]
As per the question,
Mean,
[tex]\bar x=20.40[/tex]
Standard deviation,
[tex]s=12.17[/tex]
or,
[tex]df=10-1[/tex]
[tex]=9[/tex]
For 95% confidence interval,
[tex]t^*=2.262[/tex]
hence,
The 95% confidence interval will be:
= [tex]\bar x \pm \ t^*\times \frac{s}{\sqrt{10} }[/tex]
By substituting the values, we get
= [tex]20.40 \pm 2.262\times \frac{12.17}{\sqrt{10} }[/tex]
= [tex](11.69, 29.11)[/tex]
A shopkeeper bought bycicle for rs 3520 and a mobile for rs 4690 . he sold both the items for rs 8650 calculate how much money did he gain
Answer:
Rs 440
Step-by-step explanation:
Price of bicycle = 3520
Price of mobile = 4690
Cost Price of both mobile and bicycle = 3520 + 4690
=> 8210
Selling price of both mobile and bicycle = 8650
Profit = selling price - cost price
= 8650 - 8210
= 440
Therefore he gained Rs 440