Yes, the equation defines the value of y in terms of x which is ±10x.
What is the equation?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
Given, the equation defines y as a function of x.
100x² = y²
Hence,
Y² = (10x)²
Taking square root on both sides.
y = ±10x
Since the value of the y is in the term of x. Therefore, The value of y is defined in terms of x, which is 10x, in the equation.
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solve for the length of the diagonal of the rectangular prism
The diagonal can be written as -
d = √{(L)² + (B)² + (H)²}
What is a right rectangular prism? What is a mathematical equation? What is constant of proportionality?The right rectangular prism has two parallel end faces and four lateral faces, each one of which is a rectangle; the faces are perpendicular to each of its bases. The faces of a non-right rectangular prism (oblique prism) are parallelograms. A right rectangular prism is also called a cuboid.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a graph as shown in the figure.
Since the dimensions of a right rectangular prism are not given, assume the length, width and height to be [L], [W] and [H]. Then the diagonal can be written as -
d = √{(L)² + (B)² + (H)²}
Therefore, the diagonal can be written as -
d = √{(L)² + (B)² + (H)²}
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Solve the following inequality
8n+4n< -4+8n
Answer:
n < –1
Step-by-step explanation:
8n + 4n < –4 + 8n
12n < –4 + 8n
12n – 8n < –4
4n < –4
divide both sides by (4) to obtain
n < –1
i hope this helps please rate the answer as brainliest
Evaluate. Write your answer as a fraction or whole number.
(1/2)²=___
Answer: 0.25 or 1/4
Hope this helps :)
Step-by-step explanation:
Answer:
0.25 or 1/4
Step-by-step explanation:
1/2 as a decimal is 0.50 and that squared is 0.25, which as a fraction is 1/4.
Express the confidence interval 71.6% ± 8.2% in the form of a trilinear inequality.
The confidence interval, expressed as a trilinear inequality, is 71.6%
What does a confidence interval mean?
The range of values we see in our sample and expect to find the value that most accurately represents the population are referred to as a confidence interval.
The lower bound is 71.6% - 8.2% = 63.4% and the upper bound is 71.6% + 8.2% = 79.8%.
Thus the confidence interval, expressed as a trilinear inequality, is 63.4% < p < 79.8%, where p= 71.6%.
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The cost of buying gas varies directly with the number of gallons
Suppose that Lena bought 12.2 gallons of gas for $35.99. Write an equation that could be
used to find the unit cost per gallon of gas. Then find out how much 9.5 gallons of gas
would cost. Round to the nearest cent.
Answer:
1 gallon of gas is $2.95
9.5 gallons of gas is $28.025
Step-by-step explanation:
[tex]\frac{12.2}{35.99} =\frac{1}{y}[/tex]
Cross Multiply.
12.2 · y = 1 · 35.99
12.2y = 35.99
12.2y ÷ 12.2 = 35.99 ÷ 12.2
y = 2.95
1 gallon of gas is $2.95.
[tex]\frac{1}{2.95} =\frac{9.5}{y}[/tex]
1 · y = 2.95 · 9.5
y = 28.025
9.5 gallons of gas is $28.025.
y varies inversely as x. y = 18 when x = 7. Find y when x = 6.
The value of y is 21, when x = 6.
What are Inverse variations?
The link between two variables known as "inverse variation" occurs when the value of one variable rises while the value of the other variable falls.
Here, we have
Inverse variations look like this: y = k/x
We need to make our own inverse variation given y = 18 and x = 7. We can plug this into the standard inverse variation with variables.
y = k/x
18 = k/7
k = 126
We've determined that k =126. Now we have what it takes to create an inverse variation. This is our final equation:
y = 126/x
We still need to find what y equals when x is 6. Let's plug in 6 for x
y = 126/6
y = 21
Hence, the value of y is 21, when x = 6.
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If M is the centroid of triangle ABC, AM = 44, CE =54, and DM
= 23, find each missing measure.
The missing sides of triangle ABC, If M is the centroid of triangle ABC, AM = 44, CE =54, and DM = 23, are FM = 22, AM = 44.
What is the centroid of the triangle?Three medians of a triangle intersect to produce the centroid of the triangle. It is one of a triangle's four points of concurrency. When the midpoints of the triangle's opposite sides are linked, the triangle's vertices become the triangle's medians.
Given:
The [tex]M[/tex] is centroid of triangle ABC, AM = 44, CE = 54, and DM = 23,
The centroid of a triangle divides the median in the ratio [tex]2 : 1[/tex]
Therefore, [tex]AM : FM = 2 : 1[/tex]
Let AM = 2x and FM = x
Since, AM = 44
Hence, 2x = 44
x = 44 / 2
x = 22
FM = 22
Therefore, the missing sides are FM = 22 and AM = 44.
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The missing figure is attached below.
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours
ŷ= 6.45x + 31.5 is the equation of the regression line for the given data
How to find the equation of the regression line for a given data?Construct the table of the data as follows:
x >>>> y >>>> x² >>>> y² >>>> xy
1 39 1 1521 39
2 45 4 2025 90
3 52 9 2704 156
4 49 16 2401 196
5 61 25 4096 305
5 72 25 5184 360
................................................................................................
20 318 80 17931 1146
.................................................................................................
∑x = 20, ∑y = 318, ∑x²= 80, ∑xy = 1146, n = 6 (number data points)
The linear regression equation is of the form:
ŷ = ax + b
where a and b are the slope and y-intercept respectively
a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )
a = (6×1146 - 20×318) / ( 6×80-20² )
a = 6876-6360 / 480-400
a = 516 / 80
a = 6.45
x' = ∑x/n
x' = 20/6 = 10/3
y' = ∑y/n
y' = 318/6 = 53
b = y' - ax'
b = 53 - 6.45×(10/3)
b = 53 - 21.5
b = 31.5
ŷ = ax + b
ŷ= 6.45x + 31.5
Thus, the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)
(a) x=3 hours
ŷ= 6.45(3) + 31.5 = 50.85
(b) x=4.5 hours
ŷ= 6.45(4.5) + 31.5 = 60.525
(c) x=13 hours
ŷ= 6.45(13) + 31.5 = 115.35
(d) x=1.5 hours
ŷ= 6.45(1.5) + 31.5 = 41.175
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Write the sentences as an equation. 140 is the same as a multiplied by 319
140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.
What is an equation?An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.
Hence, the sentence as an equation for 140 is the same as multiplying by 319 is, 140 = a x 319.
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To express the given numbers in equation form it can be written as =
140 is the same as multiplying by 319 as an equation can be written as 140 = a x 319.
What is an equation?
An equation is a mathematical expression that contains an equal symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculation.Hence, the sentence as an equation for 140 is the same as multiplying by 319 is, 140 = a x 319.A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.To know more about equations check out,
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Complete the square by adding the correct missing term on the left, then factor as indicated:
x²+x+________=(______)²
Answer:
Missing term [tex]\dfrac{1}{4}[/tex]
Factored term on RHS: [tex]$(x+\dfrac{1}{2})^{2}$[/tex]
Step-by-step explanation:
Write an equation in solve-intercept form of the line that passes through the point (2, -2) and is parallel to the line y= -x-2.
The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as,
ax + by + d = 0
The equation of the line is given below.
y = - x - 2
x + y + 2 = 0
Then the equation of the line that is parallel to x + y + 2 = 0 is given as,
x + y + d = 0
The line is passing through (2, -2), then we have
2 + (-2) + d = 0
d = 0
The equation of the line that is parallel to the line x + y + 2 = 0 and passing through (2, -2) will be x + y = 0.
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It takes Stacy 0.75 hours to drive to school. Her route is 40km long. What is Stacy’s average speed on her
drive to school?
Answer:
Step-by-step explanation:
160/3
Line t passes through points (9, 9) and (2, 5). Line u is perpendicular to t. What is the slope of line u?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
To convert Celsius temperatures to Fahrenheit temperatures, the function F defined by F(x) = 32 + 1.87 is useful. Confirm this, then find a formula for the function C (which could also be called F-1) that converts Fahrenheit temperatures to Celsius temperatures.
Answer: The function F(x) = 32 + 1.87x converts Celsius temperatures to Fahrenheit temperatures. To confirm this, you can plug in a few different values for x (the Celsius temperature) and see if the corresponding value of F(x) (the Fahrenheit temperature) is correct.
For example, if x = 0, the function gives us F(0) = 32 + 1.87 * 0 = 32, which is the correct conversion from Celsius to Fahrenheit for 0 degrees Celsius.
If you want to find a formula for the function C that converts Fahrenheit temperatures to Celsius temperatures, you can start by rearranging the formula for F(x). The Fahrenheit temperature is equal to the Celsius temperature plus 32, multiplied by 1.8.
If we solve for the Celsius temperature, we get:
x = (F - 32) / 1.8
This is the formula for the function C that converts Fahrenheit temperatures to Celsius temperatures. To use this function, you would plug the Fahrenheit temperature into the function as the input, and it will give you the corresponding Celsius temperature as the output.
For example, if you want to convert 100 degrees Fahrenheit to Celsius, you would plug 100 into the function as the input:
C(100) = (100 - 32) / 1.8 = 37.78 degrees Celsius.
9 + a - 5b - 2 combine The like terms to create an equivalent expression
Answer:
Your answer is 7 + a - 5b.
Step-by-step explanation:
All you have to do is subtract the numbers.
Hope this helped! :D
Simplify 6.5m(3m + 1.8) using the distributive property.
19.5m + 11.7m
19.5m + 1.8
19.5m2 + 11.7m
19.5m2 + 1.8
Answer:
C.
19.5m2+11.7m
Step-by-step explanation:
hope this helps
Answer:
C.
19.5m2+11.7m
Step-by-step explanation:
what i got on the test
Solve linear differential equations.
a. (x + 2)² (dy/dx) = 5-8y - 4xy
The value of y for the linear differential equation is:
y= [5(x³+6x²+12x)/3(16+32x+24x²+8x³+4x⁴)] + c₁ /(16+32x+24x²+8x³+x⁴)
How to solve the differential equation?You should know that a differential equation is in which we find the value of y with respect to x
The given parameter is
(x-2)² dy/dx = 5-8y-4xy
Differentiate y with respect to x to have
y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]
Recall that the differential equation is (x-2)² dy/dx = 5-8y-4xy
Solving the Ordinary Differential Equation we have
y= y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]
In conclusion, the value of y is: y= [5(x³+6x²+12x)]/[3(16+32x+24x²+8x³+x⁴)] + c₁/(16+32x+24x²+8x³+x⁴)]
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Jacob wants to save $175 for a trip to an amusement park. He sets aside $14 of his allowance at the end of each week. How many weeks will it take him to save enough money for the whole trip?
The price of a CD player was reduced from $80to $52. What was the decent decrease in the price of the CD player?
Answer:
it was decreased by $28
Step-by-step explanation:
$80 – x = $52
–x = $52 – $80
–x = $28
x = $28
i hope this answer helped
The sum of a number and seven is one more than twice the number. What is the number
Answer: x+7=1+2x
Step-by-step explanation:
If x represents the number,The sum of a number and 7 is x + 7One more than twice the number is 1 + 2xThe IS in the middle of the sentence means =So, x + 7 = 1 + 2x Solve this equation,If you need further assistance message me.
Give the prime factorization of 300 in exponential form
Answer: 2^2*3^1*5^2
Step-by-step explanation:
1st step: find the factors
2 x 2 x 3 x 5 x 5
2nd step: simplify
2^2*3^1*5^2
there are 80 houses being built in a neighborhood last month 1/4 of them were sold. This month 2/5 of the remaining houses were sold. How many houses are left to be sold?
36 houses are left to be sold.
Step-by-step explanation:Here are the steps to find out the answer to your question:We need to convert 1/4 and 2/5 into decimals. We do this by dividing the numerator by the denominator:
1 ÷ 4 = 0.25
2 ÷ 5 = 0.4
Now, we can set up this equation to find out how many were sold in the first month:
0.25 x 80 = 20
Now, 20 isn't the answer, it is 60 houses left, because 80 - 20 = 60.
Let's do the next one:
0.4 x 60 = 24
60 - 24 = 36
Solution:
36 houses are left to be sold.
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
During a fireworks display, a shell is shot into the air with a velocity of 58 m/s, its height in meters after t seconds is given by y=58t-20t^2
Find velocity when t=0.5
The velocity of a shell shot into the air with a velocity of 58 m/s, its height in meters after t seconds is given by y=58t - 20t² is 38 m / s.
What is velocity?When anything is moving, its velocity tells us how quickly that something's location is changing from a certain vantage point and as measured by a particular unit of time.
If a point moves along a path and covers a certain distance in a predetermined amount of time, its average speed over that period of time is equal to the distance covered divided by the travel time. A train traveling 100 kilometers in two hours, for instance, is doing it at an average speed of 50 km/h.
Given:
Height equation, y = 58t - 20t²,
The time, t = 0.5 seconds,
The initial velocity, u = 58 m/s,
Calculate the height at 0.5 sec,
y = 58 × 0.5 - 20 × 0.5²
y = 24 m
Calculate the acceleration at 0.5 sec by using the motion equation given below:
[tex]s = ut+1/2at^2[/tex]
24 = 58 × 0.5 + 1 / 2 × a × 0.5²
-5 = 0.125 × a
a = - 40 m / s²
Calculate the velocity by using the formula given below,
[tex]v = u + at[/tex]
v = 58 + (-40) × 0.5
v = 38 m /s
Therefore, the velocity of a shell shot into the air with a velocity of 58 m/s, its height in meters after t seconds is given by y = 58t - 20t² is 38 m / s.
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Can someone please help me? I’ll give brainly thank you so much :)
Answer:
B (192 ft^2)
Step-by-step explanation:
The area of the blue shaded region: total area - small rectangle
This is:
(11x20) - (4x7)
= 220 - 28
= 192 ft^2
Hope this helps,
:]
Answer:
A.
Explanation:
20*11=220
Please vote for Brainliest and I hope this helps!
ASAP!!!
Find the perimeter of the square
Answer:
156
Step-by-step explanation:
4x + 3 = 3(2x - 5)
4x + 3 = 6x - 15
3 = 2x - 15
2x = 18
x = 9
4(9) + 3
= 36 + 3
= 39
39 * 4 = 156
Hope it helps!
Answer: 156 inches
Step-by-step explanation:
So we know that all of the sides are equal to each other.
Now we need to know what x equals.
4x + 3 = 3(2x -5)
4x + 3 = 6x - 15
3 = 2x -15
18 = 2x
9 = x
Plug 9 into one of the equations.
4(9) + 3
36 + 3 = 39
39 * 4 = 156
Perimeter = 156 inches
Hope this helps!!! :)
How many different roots does the polynomial function, y= (x+4)(x-2)^2(x+7) have?
The polynomial function, y= (x+4)(x-2)²(x+7) has three different roots
How to determine the number of roots?From the question, we have the following parameters that can be used in our computation:
y = (x+4)(x-2)^2(x+7)
Rewrite the equation properly
So, we have the following representation
y= (x+4)(x-2)²(x+7)
Set the factor to 0
So, we have
x + 4 = 0, x - 2 = 0 and x + 7 = 0
When these equations are solved, we have
x = -4 , x = 2 and x = -7
See that the counts of the values of x is 3
Hence, it has three different roots
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Question 1: Write down the square numbers from the list below
91 101 1024
81 200
How much money does Dana Jones have after 7 years if she invests $ 1100 at 5 % interest compounded continuously? Use the formula A =Pе⁺ to solve.
Dana Jones has $____ after 7 years.
(Simplify your answer. Type an integer or a decimal. Round to the nearest cent as needed.)
The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
When compounded continuously , the Compound Interest Amount is calculated by the formula ,
A = Pe^rt
Given data ,
Let the investment be P
The value of P = $ 1100
The rate of interest r = 5 %
The number of years t = 7 years
The Compound Interest Amount when compounded continuously is calculated by the formula ,
A = Pe^rt
Substituting the values in the equation , we get
A = 1100 x e ^ 0.05 x 7
A = 1100 x e ^ 0.35
A = 1100 x 2.718 ^ 0.35
A = 1100 x 1.419067
A = $ 1560.97
Therefore , the value of the amount is A = $ 1560.97
Hence ,
The amount of money Dana Jones have after 7 years with an investment of $ 1100 at 5 % interest compounded continuously is $ 1560.97
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Jo leaves some money in a bank account that pays
interest. Each year, the balance of her account is
15% more than it was the year before.
If she starts with £400 in her account, work out
her balance for the next three years. Give your
answers in order and rounded to the nearest
pound.
If she starts with £400 in her account, her balance for the next three years IS; $608.35
How to solve exponential equation?
The general formula for exponential equation is;
y = a(b)ˣ
where;
a represents an initial value or amount
b is the constant multiplier, is a growth factor or factor of decay.
We are given;
Initial value; a = £400
constant multiplier; b = an increase of 15% yearly = 1.15
Thus, her balance for the next three years is;
y(3) = 400(1.15)³
y(3) = $608.35
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Ride and simplify two division expressions they have a negative quotient used to fractions -2/3 5/6 and negative one show your work
The simplification of complex fraction -⅔/⅚ is - 4/5
What are complex fractions?A complex fraction is a rational expression that has a fraction in its numerator, denominator or both. In other words, there is at least one small fraction within the overall fraction.
In fraction when the numerator is bigger than the denominator , then it is called improper fraction, when a fraction consist of whole number and proper fraction is called mixed fraction
-2/3 ÷ 5/6
= -2/3×6/5
= -4/5
Therefore -⅔/⅚ can be simplified to -⅘
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