the equation t² = 3 x + 1 will be written as x = t² / 3 - 1 / 3 with the subject as x.
We are given an equation:
t² = 3 x + 1
We need to solve it so that the subject becomes x.
For this, we will first subtract 1 from both the sides:
t² - 1 = 3 x + 1 - 1
3 x = t² - 1
Now, we will divide both the sides by 3
3 x / 3 = (t² - 1) / 3
x = t² / 3 - 1 / 3
So, the subject is being made as x now.
Therefore, we get that, the equation t² = 3 x + 1 will be written as x = t² / 3 - 1 / 3 with the subject as x.
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If a lighthouse's shadow is 36ft what is the lighthouse height?
Answer:
I think its 48 feet
Step-by-step explanation:
Answer:
wouldn't u need another object and that objects shadow?
What is the inequality shown
Answer:
it shows that the answer is (-2,8(
the brackets are the symbols of inequality
(2y to the power of -3)(3y)to the negative 2 power) (6y to the negative 2 power)to the power of 2)
Evaluation of the equation is [tex]\frac{y^{-14} }{6718464}[/tex]
Here from the question, we get the evaluation
[tex][(2y)^{-3} (3y)^{-2} (6y)^{-2}]^{2}[/tex]
Now evaluate it in the simple form we have
[tex][(\frac{1}{2y} )^{3} (\frac{1}{3y} )^{2} (\frac{1}{6y} )^{2} ]^{2}[/tex]
[tex][\frac{1}{8y^{3} } \frac{1}{9y^{2} } \frac{1}{36y^{2} } ]^{2}[/tex]
[tex][\frac{1}{2592y^{7} } ]^{2}[/tex]
[tex]\frac{1}{6718464y^{14} }[/tex]
[tex]\frac{y^{-14} }{6718464}[/tex]
Therefore we get the simplest form of the evaluation.
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select translation, reflection, or rotation to identify the single transformation that transforms ∆rst to ∆r′s′t′.
The single transformation that transforms ∆RST to ∆R'S'T' is a reflection.
Part A:
For the first figure it is visible that the orientation of the pre-image (∆RST) is similar to that of the image (∆R'S'T').The image is received from the pre-image through moving the pre-image a few units down. Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a translation.
Part B:
For the second figure ,it is visible that the orientation of the pre-image (∆RST) is similar to that of the image (∆R'S'T').The image is received from the pre-image through moving the pre-image a few units down and a few units to the right. Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a translation.
Part C:
For the third figure it is visible that the orientation of the pre-image (∆RST) isn't similar to that of the image (∆R'S'T').The image is received from the pre-image through rotating the pre-image a few 180 degrees. Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a rotation.
Part D:
For the fourth figure it is visible that the orientation of the pre-image (∆RST) isn't similar to that of the photograph (∆R'S'T').The image is received from the pre-image through reflecting the pre-image.
Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a reflection.
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Prove that the value of the expression (n+8)(n-4) - (n+3)(n-2) + 27 is not divisible by 3 for any whole number n.
The value of the expression (n+8)(n-4) - (n+3)(n-2) + 27 is not divisible by 3 for any whole number n
How to prove that the value of the expression (n+8)(n-4) - (n+3)(n-2) + 27 is not divisible by 3 for any whole number n?The expression is given as
(n+8)(n-4) - (n+3)(n-2) + 27
Open the brackets
So, we have
n^2 + 8n - 4n - 32 - n^2 - 3n + 2n - 6 + 27
Collect the like terms
So, we have
n^2 - n^2 - 3n + 8n - 4n + 2n - 32 - 6 + 27
Evaluate the like terms
So, we have
3n - 11
The above expression cannot be expressed as a factor of 3
Hence, the value of the expression (n+8)(n-4) - (n+3)(n-2) + 27 is not divisible by 3 for any whole number n
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a list of measurements in increasing order is 4, 5, 6, 8, 10, and x . if the median of these measurements is six sevenths times their arithmetic mean, what is the value of x ?
In a list of measurements in increasing order: 4, 5, 6, 8, 10, and x, the value of x is 16.
To get the value of x, we will use algebraic expressions to demonstrate the given relationships.
If the median of these measurements is six sevenths times their arithmetic mean, then:
median = 6/7 x mean
Median (Md), is a single value at the middle of the data values arranged in increasing or decreasing order. On the other hand, arithmetic mean (μ) is the sum of the data values divided by its total number.
For the list of measurements in increasing order is 4, 5, 6, 8, 10, and x,
The median is between 6 and 8.
Md = 6+8/2
Md = 7
Evaluating the first equation using Md = 7:
median = 6/7 x mean
7 = 6/7 x mean
mean = 49/6
By definition,
mean = (4 + 5 + 6 + 8 + 10 + x)/6
Equating both equations for the mean:
49/6 = (4 + 5 + 6 + 8 + 10 + x)/6
49 = 33 + x
x = 16
Hence, the value of x is 16.
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John made a nut mixture that contains
90% peanuts by mixing 5 oz. of mixed
nuts with 20 oz. of peanuts. The mixed
nuts contained what percent peanuts?
The percentage of peanuts which this mixed nuts contained is 40%.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
In order to determine the percentage of peanuts which this mixed nuts contained, we would develop a table of proportion to model the word problem as follows:
5 oz + 25 oz = 30 oz
5x + 25 = 30(0.9)
x + 5 = 6(0.9)
x + 5 = 5.4
x = 5.4 - 5
x = 0.4 ⇒ 40%.
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What is the value of f(15) if the function is f(x)=(x)(2x+5)
Answer:
525
Step-by-step explanation:
f(x)=(x)(2x+5)
f(x)=2x^2+5x
f(15)=2*(15)^2 + 5*15
= 2*225 + 75
=450 + 75
=525
You are solving a measurement problem where the numbers 4.0286 × 109 and 3.1 × 10−4 are divided. How many significant digits should the quotient have?
2
3
4
5
From the result you can see that the result must have a significant figure of 2 since that is the lowest significant figure in question
Dividing scientific notationsThe standard scientific notations is expressed according to the expression A * 10^n
where
A is any value from 1 to 10
Given the following quotient
4.0286 × 10^9/3.1 × 10^−4
This can also be expressed as:
4.0286 × 10^9/3.1 × 10^−4 = (4.0286/3.1) × 10^9+4
4.0286 × 10^9/3.1 × 10^−4 = 1.2995 × 10^13
From the result you can see that the result must have a significant figure of 2 since that is the lowest significant figure in question
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Answer: The answer is 2
Step-by-step explanation: Hope this helps :)
What are the domain and range of the function h(x) = –12 (x − 4)2 + 3? A. The domain is all real numbers and the range is y ≤ 3. B. The domain is x ≥ 4 and the range is y ≥ 3. C. The domain is all real numbers and the range is y ≥ 3. D. The domain is x ≥ −4 and the range is y ≤ −3.
For the given quadratic function we have that:
Domain: Set of all real values.Range: y ≤ 3.What is the domain and range of the quadratic function?For a function h(x), we define the domain as the set of the inputs (values of x) and the range is the set of the outputs (values of y).
Generally, for all quadratic functions, the domain is the set of all real numbers, so we already know the domain.
Now let's look at the range.
The given function is:
h(x) = -12*(x - 4)^2 + 3
Remember that if a quadratic function has a vertex (h, k), then the vertex form is:
f(x) = A*(x - h)^2 + k
So the vertex here is (4, 3)
And we also can see that the leading coefficient of the quadratic function is negative. This means that the function opens downwards, so the vertex is the maximum.
Then the range is the set of all real values smaller than or equal to 3, then the range is:
R: y ≤ 3.
Concluding:
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What is a real word situation for 10y-3
The real world situation will be , Ram buys y pens and each pen costs $10 . How much he need to pay if he has already paid $3.
It is given that an equation is 10y - 3.
We have to write a real world situation representing above equation.
What is algebra ?
Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.
As per the question ;
The expression given is 10y - 3.
Let's write a real world situation representing the above equation.
Ram buys y pens and each pen costs $10 . How much he need to pay more if he has already paid $3.
Let's assume no. of pens be 4 i.e., y = 4.
So ;
He need to pay more ;
= 10 × 4 - 3
= 40 - 3
= $ 37
Thus , the real world situation will be , Ram buys y pens and each pen costs $10 . How much he need to pay if he has already paid $3.
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lee jogged 3 1/11 laps in teh morning and 2 3/22 laps in the evening how many laps did lee jog in all? simlify and write the answer as a improper fraction
Lee jogged a total of 5 3/22 laps
How to calculate the total laps ?
Lee jogged 3 1/11 laps in the morning
He then jumped 2 3/22 laps in the evening
Therefore the total laps jogged can be calculated by adding both values together
3 1/11 + 2 3/22
34/11 + 47/22
= 113/22
= 5 3/22
Hence the total laps jogged is 5 3/22 laps
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what percent of 54 is 23? explained
Answer: 42.59
Step-by-step explanation:
Step 1: First, write the problem as an equation: P% = X/Y
Step 2: Here, X is 23, Y is 54, so the equation is P% = 23/54
Step 3: A percent is a ratio of a number expressed out of 100. So P% means P/100
Step 4: Substitute P/100 instead of P% in the above equation, then P% = 23/54 becomes P/100 = 23/54
Step 5: Solve for P
P/100 = 23/54
P = (23/54) * 100 = 42.59
Therefore, 23 is 42.59 percent of 54
If h(x)=-4/5x+6/7 find the following values. Simplify your answer.
h(1)=
h(2)=
h(-1/2)
Hence , on solving the given expression , we get values of h(1) = 58/35 , h(2) = 86 /35 and h(-1/2) =26 /35.
A operate in maths may be a special relationship among the inputs (i.e. the domain) and their outputs (known because the codomain) wherever every input has specifically one output, and therefore the output are often derived back to its input.We have given an expression h(x)=-4/5x+6/7 .
Putting x = 1 in h(x) , we get
h(1) = 4/5(1) +6/7
= 4/5 +6/7
= 28 + 30 /35
= 58 /35
Putting x = 2 in h(x) , we get
h(2) = 4/5(2) +6/7
= 8/5 + 6/7
= 56 + 30 /35
= 86 /35
Putting x = -1/2 in h(x) , we get
h(-1/2) = 4/5(-1/2) +6/7
= -2/5 + 6/7
= -14 + 30 /35
= 26 /35
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If h(x)=-4/5x+6/7 find the following values. Simplify your answer.
h(1)=
h(2)=
h(-1/2)
Evaluate the following expressions a) (3 + 2i) - (8 - 5i) b) (4 - 2i)*(1 - 5i) c) (- 2 - 4i) / i d) (- 3 + 2i) / (3 - 6i)
a) 3 - 8 + 2i - (-5i) = -5 + 2i +5i = -5 + 7i
b) 4 - 20i - 2i + 10i² = 4 - 22i + 10([tex]\sqrt{-1}[/tex])² = 4 - 22i + 10(-1) = 4 - 10 -22i
= -6 -22i
c) Multiply both numerator and denominator by i
[tex]\frac{i(-2-4i)}{i^{2} }[/tex] = [tex]\frac{-2i - 4i^{2} }{i^{2} }[/tex] = [tex]\frac{-2i - 4(\sqrt{-1})^{2} }{(\sqrt{-1})^{2}}[/tex] = [tex]\frac{-2i - 4(-1)}{-1}[/tex] = [tex]\frac{-2i+4}{-1}[/tex] = 2i - 4 = -4 + 2i
d) Multiply both numerator and denominator by (3+6i)
[tex]\frac{(3+6i)(-3+2i)}{(3+6i)(3-6i)}[/tex] = [tex]\frac{-9+6i-18i+12i^{2} }{9-36i^{2} }[/tex] = [tex]\frac{-9-12i+12(\sqrt{-1} )^{2} }{9-36(\sqrt{-1} )^{2} }[/tex] = [tex]\frac{-9-12i+12(-1)}{9-36(-1)}[/tex] = [tex]\frac{-9-12-12i}{9+36}[/tex]
= [tex]\frac{-21-12i}{45}[/tex] = [tex]-\frac{21}{45} - \frac{12}{45}i[/tex]
A theater is showing a ballet performance. Tickets are available on three levels in the performance hall. Lower level tickets cost $35, mezzanine tickets cost $25, and upper balcony tickets cost $15. For a certain performance the theater sold 5 times as many lower level tickets as upper balcony tickets. The theater sold $37,500 in tickets for that performance. The money made from mezzanine tickets alone was 4 times the money made from upper balcony tickets. How many lower level tickets were sold for that performance?
Based on the calculation done below, the number of lower level tickets sold is 750.
How do we calculate the number of units sold from a word problem?Let:
L = number of lower-level tickets sold = 5U
M = number of mezzanine tickets sold
U = number of upper balcony tickets sold
We therefore have:
35L + 25M + 15U = 37,500 ...................... (1)
25M = 4 * 15U = 60U
Substituting L = 5U and 25M = 60U into equation (1) and solve for U, we have:
35(5U) + 60U + 15U = 37,500
175U + 60U + 15U = 37,500
250U = 37,500
U = 37,500 / 250
U = 150
Susbstituting U = 150 into L = 5U, we have:
L = 5 * 150
L = 750
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3/5 ÷ 2
help please! (10 points)
Answer:
i think the answer is 0.3 but im not sure i just used a calculator
You add a mixture of salt, sugar, and cooking oil to a glass of water. You stir everything together and wait a few minutes. What will you see in the glass? (2 points)
a
All of the parts of the mixture will disappear because they are all soluble in water.
b
The salt and sugar will seem to disappear, and the oil will float on the surface of the water.
c
The salt and sugar will settle to the bottom of the glass, and the oil will float on top of the water.
d
The salt will settle to the bottom of the glass, and the sugar and oil will disappear in the glass.
Answer:b. the salt and sugar will disappear and the oil will float on the surface of water
Step-by-step explanation: If you stir salt and sugar it will dissapear but oil in thick and if you know it will float to the surface
an airplane is taking off headed due north with an air speed of 173 miles per hour at an angles of 18
The vector that represents the resultant velocity of the plane will be V = 30.72 i + 135.89 j + 53.46 k.
What is a vector?The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.
An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of S 47° E.
Let north be the y-axis and east be the x-axis. Then the vector equation will be given as,
V = (42 sin 47°) i + (173 cos 18° - 42 cos 47°) j + (173 sin 18°) k
V = 30.72 i + 135.89 j + 53.46 k
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What is the surface area of the cuboid below?
If it takes my car 2.2 seconds to accelerate from 8.9 m/s to 35.76 m/s, what is my cars average acceleration in that time?
Your cars average acceleration in that time is 12.21m/s^2
What is my cars average acceleration in that time?The given parameters are
Initial velocity, u = 8.9 m/s
Final velocity, v = 35.76 m/s
Time, t - 2.2 seconds
The average acceleration is calculated using
v = u + at
So, we have
35.76 = 8.9 + 2.2a
Evaluate the like terms
26.86 = 2.2a
Divide by 2.2
a = 12.21
Hence, your cars average acceleration in that time is 12.21m/s^2
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What is the greatest common factor of 35 and 25
Answer:
5
Step-by-step explanation:
5 |35 | (5 is the divisor and 35 is the dividend)
= 7|
For 25;
5 |25|
=5
35 = 5 * 7
25 = 5 * 5
Now, common factor =5
A group of 24 students and 3 adults visited the zoo. The admission fee for an adult was $4 more than the fee for a student. The total amount due
was $133.50.
What was the cost of each type of admission fee?
Select from the drop-down menus to correctly complete the statement.
Adult admission fees cost $___ and student admission fees cost $___
la razon de hombres a mujeres que trabajan en una campañia es de 4 a 7. Si hay 143 empleados en total ¿Cuantas mujeres trabajan en la compañia?
In a company of 143 employees, the number of women working in the company is 91.
The quantitative relation is outlined because the comparison of 2 quantities of a similar units that indicates what proportion} of 1 amount is gift within the alternative quantity.Ratios may be classified into 2 varieties. One half|is a component|is an element} to part quantitative relation and also the alternative is an element to whole quantitative relation.Given,
Men : Women = 4 : 7
Total number of employees = 143
Let us take a multiplying factor of x
This implies, Number of men = 4x , Number of women = 7x
Using the given data, we get 4x + 7x = 143
11x = 143
x = 143 / 11
x = 13
Number of men = 4x = 4 (13) = 52
Number of women = 7 (13) = 91
Therefore, using the concept of RATIO, we get the number of women working in the company as 91.
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The complete question is given below.
The question given in Spanish when translated in English states that :The ratio of men to women working in a company is 4 to 7. If there are 143 employees in total, how many women work in the company?
a 17-inch candle is lit and steadily burns until it is burned out. let b represent the burned length of the candle (in inches) and let r represent the remaining length of the candle (in inches). write a formula that expresses r in terms of b .
b r = 17 - b
when it is 8 inches tall after 9 inches have burned from the candle.
What do you mean by formula?A formula in mathematics is an assertion of a fact, rule, or principle using mathematical symbols. Equations, equalities, identities, inequalities, and asymptotic expressions are a few examples of formulae.
In the theory of logic, the word "formula" is also frequently used to refer to a sentential formula, also known as a propositional formula, or a formula in propositional calculus.
A 17 inch candle is lit and steadily burns until it is burned out.
Let b represent the burned length of the candle (in inches ) and let r represent the remaining length of the candle (in inches) .
Write a formula that expresses r in terms of b r = 17 - b
Preview b. When 6.8 inches have burned from the candle, the remaining length of the candle is 10.2 inches.
Therefore the point should be on the graph of r in terms of b. c. On the graph below:
i, represent the linear relationship between l and b ii. plot the point that represents the candle when it is 8 inches tall after 9 inches have burned from the candle.
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The graph of y = f(x) is shown. Draw the graph of y = 2f(x) .
if the given graph is f(x)= [tex]x^{2}[/tex], then the new graph is y= [tex]2x^{2}[/tex] and we have drawn the graph
Given,
The graph of the function y =f(x)
From the graph we can say that
f(1)=1
f(2)=4
f(-1)=1
f(-2)=4
So,
f(x)= [tex]x^{2}[/tex]
Then,
y= 2f(x)
y= [tex]2x^{2}[/tex]
draw the graph
Hence, if the given graph is f(x)= [tex]x^{2}[/tex], then the new graph is y= [tex]2x^{2}[/tex]
and we have drawn the graph
The complete question is:
The graph of y = f(x) is shown. Draw the graph of y = 2f(x) .
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in what rate of interest rupees 4000 amount to Rupees 6000 in 2 years find it
with full process
A 25% rate of interest is required for Rupees 4000 amount to Rupees 6000 in 2 years.
Here we are given the following-
Principal amount = Rs 4000
Amount received after 2 years = Rs 6000
Time period = 2 years
Let the rate of interest = r%
Then, according to the simple interest formula-
Simple interest = Principal × time period × rate/100
and Simple interest = Final amount - principal amount
Here, simple interest = 6000 - 4000 = Rs 2000
Thus,
2000 = 4000 × 2 × r/100
2000/4000 = 2 × r/100
1/2 = 2 × r/100
1/4 = r/100
r = 100/4
r = 25
Thus, the rate of interest is 25%.
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the owner of the good deals store opens a new store across town. for the new store, the owner estimates that, during business hours, an average of 909090 shoppers per hour enter the store and each of them stays an average of 121212 minutes. the average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (note: ignore the percent symbol when entering your answer. for example, if the answer is 42.1\b.1b, point, 1, percent, enter 42.142.142, point, 1.)
The answer is 60%
According to the original information given, the estimated average number of shoppers in the original store at any time(x) is 45.
In the question, it states that, in the new store, the manager estimates that an average of 90 shoppers per hour(60 minutes) enter the store, which is equivalent to 1.5 shoppers per minute(s).
The manager also estimates that each shoppers stays in the store for an average of 12 minute (t). Thus, by Little's law there are, on average,
x = s x t
=> x = 1.5 x 12
=> x = 18
Hence, there are 18 shoppers at any time in the new store.
Now, Percentage of shoppers
[tex]\frac{45-18}{45}[/tex] x 100 = 27/45 x 100 = 2700/45 = 60%
Therefore, the answer is 60%
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Which expressions have a value of less than 3 when x = 6 ?
An expression that has a value of less than 3 when x = 6 is; 20 - 3•x
How can the required expression be found?An expression is a symbol collection that together expresses a quantity.
An expression consists of variables, numbers and operators placed together to express a quantity.
A possible expression that have a value of less than 3 when x = 6, is presented as follows;
20 - 3•xThe above expression satisfies the given condition (have a quantity less than 3), given that we have;
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