First, we have to calculate the length of the sides of the pool, we are told that the scale factor of the backyard to the pool size equals 1/2, then we can find the length of the sides of the pool by multiplying the lengths of the sides of the backyard by 1/2, like this:
length of the pool = length of the yard * 1/2
width of the pool = width of the yard * 1/2
By replacing the 60 m for the length of the yard and 50 m for the width, we get:
length of the pool = 60 * 1/2 = 30
width of the pool = 50 * 1/2 = 25
Let's call x1 to the distance from the base of the pool to the bottom side of the yard and x2 to the distance from the top side of the pool to the top side of the yard, then we can formulate the following equation:
width of the yard = width of the pool + x1 + x2
Since we want the edges to be at an equal distance, x1 and x2 are the same, then we can rewrite them as x:
width of the yard = width of the pool + x + x
width of the yard = width of the pool + 2x
Replacing the known values:
60 = 30 + 2x
From this equation, we can solve for x to get:
60 - 30 = 30 - 30 + 2x
30 = 2x
30/2 = 2x/2
15 = x
x = 15
Now, let's call y1 to the distance from the right side of the corresponding side of the yard and y2 to the distance from the left side of the pool to the left side of the yard, with this, we can formulate the following equation:
length of the yard = length of the pool + y1 + y2
Since we want the edges to be at an equal distance, y1 and y2 are the same, then we can rewrite them as y:
length of the yard = length of the pool + y + y
length of the yard = length of the pool + 2y
Replacing the known values:
50 = 25 + 2y
50 - 25 = 25 - 25 + 2y
25 = 2y
25/2 = 2y/2
12.5 = y
y = 12.5
Now, we know that the pool must be at a distance of 15 m from the horizontal sides of the pool to the horizontal sides of the yard and that it must be at a distance of 12.5 m from the vertical sides of the pool to the vertical sides of the yards.
Here is a figure that depicts the results:
Find the hcf of 14,21,27 in prime factor
Answer:
Factors for 14: 1, 2, 7, and 14
Factors for 21: 1, 3, 7, and 21
Factors for 27: 1, 3, 9, and 27
It is hard for me
And I struggle in math it’s very hard for me
Answer:
i totally get you, math is hard
Step-by-step explanation:
Answer:
understandable
Step-by-step explanation:
but whats the question
Solve the problem. All of the values of functions g and f are shown in the given table.
Given:- All the values of function g and f are shown in the table.
To find:- The value of:
[tex](f\circ g)(3)[/tex]Solution:-
Solving the function as:
[tex](f\circ g)(3)=f(3)\times g(3)[/tex]Now from the table, the values are:
[tex]undefined[/tex]A system of linear equations is given below.
x+y=-10
x=y=20
Is (-5,-5) a solution to the system? Give a reason for your answer.
(-5,-5) a solution to the system 1 which is x + y = -10.
What is a coordinate system?An approach of pinpointing a point's location on the planet is to use a coordinate system. To pinpoint a point's location, most coordinate systems use two numbers, called a coordinate. Each of these numbers represents the distance between the point and the origin, a fixed point of reference. How far left or right the point is in relation to the origin is indicated by the first integer, also referred to as the X value. How much above or below the origin the point is can be determined by the second integer, called the Y value. The origin is located at the coordinates 0, 0.
Because they indicate locations on a sphere or globe, longitude and latitude belong to a specific category of coordinate systems called spherical coordinate systems.
The reason is that if we put the values of x and y in the given equation it results up to be the same for the first one .
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I just need help understanding this.__Consider the function represented by the following formula:F=9/5C+32Describe the input values, output values and the rule that relates an input value to an output value.
The input values for the function are any number replaced in C.
The output values of the functions are the numbers obtained after applying the rule for each value in C
The rule is the expression that allows C to become F
[tex]\frac{9}{5}C+32[/tex]Solve the inequality 6x^2 + 5x < 4
Answer: -4/3 < x< 1/2
Step-by-step explanation: inequality form
yvette read a word problem that uses the phrase 10 less than the product of 4 and a number which expression represents the phrase
10 less than the product of 4 and a number is the same as:
[tex]10-4n[/tex]use your graphing calculator to check whether r= -9 and r= -11 are solutions to the equation r^2 + 11r + 28 = 10
y1=
y2=
proposed solutions | x | y1 | y2
-9 | ? | ?
-11 | ? |?
r= -9 is/is not a solution?
r= -11 is/is not a solution?
The value of r = -9 is a solution, and r = -11 is not a solution.
We are given a quadratic equation.
r² + 11r + 28 = 10
We need to verify whether r = -9 and r = -11 are the solutions of the above quadratic equation or not.
We will first simplify the quadratic equation.
r² + 11r + 28 = 10
r² + 11r + 28 - 10 = 0
r² + 11r + 18 = 0
Now, we will draw the graph of the equation :
y = r² + 11r + 18
Now, we will see the roots of the equation.
We will see the x-coordinates of the intersection points of the graph and the x-axis.
The graph is attached below.
We can see that the roots of the equation are r = -9 and r = -2.
So, r = -9 is a solution, and r = -11 is not a solution.
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A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program?A. 2,520B. 6,720C. 15,210D. 35
To solve the present problem we can just use a formula use the following strategy:
For the first choice, there are 7 possibilities (all the 7). For the second choice, there are 6 possibilities (all the 7 less the first already chosen). For the third choice 5, then 4, and 3. From this, we know that the number of possible arranges is the multiplication of these numbers.
[tex]\begin{gathered} N=7\times6\times5\times4\times3 \\ \\ N=2,520 \end{gathered}[/tex]Because the order is something thar is important, we concluded that the correct answer is: A. 2,520
If a dozen of eggs cost ₹20, how many eggs can bought for ₹40
Answer:
Ur mommy
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
2 dozen = 24
I need geometry help?
Take into account that only reflection over lines which cross the center of the polygon and the midpoints of opposite sides, will map the polygon onto itself (the same for lines which cross opposite vertex of the figure).
Then, from the given answer choices, the following ones are true:
- A reflecion across line b, trough one vertex, the center d.
- A reflection across line c, trough the midpoints of opposite sides.
Now, related to the rotation, if θ (the angle of rotation) is such an angle that 360/θ is an integer, and the number of sides of the figure is multiple of the integer, then, the polygon will map onto itself after the transformation.
For θ = 60 degrees, 360/60 = 6
For θ = 120 degress, 360/120 = 3
Then, the following is true:
- A rotation of 60 degrees around the center point d.
- A rotation of 120 degrees around the center point d.
if the linear function is f(x) =3x +10 then the value of 3 could represent?
Answer: slope
Step-by-step explanation:
In the linear function, f(x) =3x +10 the 3 represents the slope of the line
How many 5/8 cup servings are in 3/4 cup of pudding
Answer:
3/4 divided by 5/8 =
3/4 * 8/5 = 24/20 = 12/10 = 6/5
Step-by-step explanation:
so it can be not correct
hope it helps have a nice day
Answer:1
Step-by-step explanation: How many times does 5/8 fit in 3/4?
Well, 3/4 also equals 6/8. So that means 5/8 fits 1 time in 6/8.
Maria is taking a multiple-choice
exam in which
there are five possible answers for each question.
The instructions indicate that she will be rewarded
2 points for each correct response, that she will lose
half a point for each incorrect response and that no
points will be added or subtracted for answers left
blank.
A. If Maria does not know the correct answer to a
question, is it to her advantage or disadvantage to
guess at an answer?
B. If she can eliminate one of the possible choices, is it
to her advantage or disadvantage to guess at the
answer?
Since there is no expected value, there is neither a benefit nor a drawback to making an educated prediction.
Expected value (EV), which is based on a random variable's probability distribution, refers to the long-term overall average of that variable.The expected value of a company or even other investment is a crucial factor in investing and is taken into account while performing scenario analysis.To create optimum portfolios, modern portfolio theory combines anticipated value with the standard deviation of an investment's risk.Correct Probability P(Correct) Equals 1/5 = 0.20
P(Wrong) = 4/5 = 0.80.
Expected Value is equal to P(Correct) * Marks given for Correct Questions plus P(Incorrect) * Marks given for Incorrect Questions.
Value Expected Equals 0.20*2 + 0.80* (-0.50)
Value Expected = 0
Since there is no expected value, there is neither a benefit nor a drawback to making an educated prediction.
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21. You need to work a total of 44 hours per week at your two jobs. Your job os a store clerk pays $5.50 an hour, and your job as a landscaper pays $6.00 an hour. You need to earn $250.00 per week to cover your expenses. Which system of equations shows the various numbers of hours you can work at each job. C is the number of hours worked as a clerk, while Lis the number of hours worked as a landscaper.
In this problem you can work a maximun of 44 hour so the sum of C and L must be 44:
[tex]C+L=44[/tex]Now if you need to do 250 dollar then the equation will be C tiems the payment in C plus L time the payment in L so:
[tex]5.50C+6.00L=250[/tex]So the answer was A
I need help 0.259 written out as a fraction or mixed number?
1) To write 0.259 as a fraction let's firstly rewrite as
[tex]\frac{259}{1000}[/tex]2) Count the digits the dot has gone to the left. Each digit to the left means divided by ten. Like this:
3) Since it starts with a zero then it can't be a Mixed number. So it is an improper fraction. No further simplification could be done.
Solving a word problem with three unknowns using a linear... The sum of three numbers is 104. The first number is 6 less than the second. The third number is 3 times the second. What are the numbers?
Let the unknown numbers be x, y, and z where
• First number = x
,• Second number = y
,• Third number = z
If the sum of the three numbers is 104, then;
[tex]x+y+z=104[/tex]If the first number is 6 less than the second, hence;
[tex]\begin{gathered} x=y-6 \\ \end{gathered}[/tex]Also, if the third number is 3 times the second, then;
[tex]z=3y[/tex]Substitute equations 2 and 3 into equation 1 to reduce the variables to the function of "y" only:
[tex]\begin{gathered} x+y+z=104 \\ (y-6)+y+3y=104 \\ y-6+4y=104 \\ 5y-6=104 \\ 5y=104+6 \\ 5y=110\rbrack \\ y=\frac{110}{5} \\ y=22 \end{gathered}[/tex]Get the first number "x"
[tex]\begin{gathered} x=y-6 \\ x=22-6 \\ x=16 \end{gathered}[/tex]Get the third number "z"
[tex]\begin{gathered} z=3y \\ z=3(22) \\ z=66 \end{gathered}[/tex]Therefore the three numbers are 16, 22, and 66.
Read the description of a proportional relationship.
In The Tall Tales of Timothy Toad, a witch brews a magical invisibility potion. There is a proportional relationship between the amount of potion the witch drinks (in milliliters), x, and the amount of time she is invisible (in minutes), y.
The equation that models this relationship is y=4x.
How much potion does the witch drink to be invisible for 16 minutes? Write your answer as a whole number or decimal.
Using the equation that models the proportional relationship, the amount of portion the witch drinks to be invisible for 16 minutes is: 64 ml.
What is a Proportional Relationship Equation?The equation that represent a proportional relationship between two variables, x and y, is given as y = kx, where the unit rate of the relationship is represented as k in the equation.
Given the following:
x = amount of portion in milliliters that the witch drinks.y = the amount of time in minutes that the witch is invisible.The equation for this relationship is given as y = 4x.
To find the amount of portion (y) the witch drank to be invisible for 16 minutes (x), substitute x = 16 into y = 4x:
y = 4(16)
y = 64
The witch will drink 64 ml of the portion.
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Solve k over negative 1.6 is greater than negative 5.3 for k. k > −8.48 k < −6.9 k > −6.9 k < 8.48
The required inequality is k > 8.48. Option A is correct.
Given that,
To determine the equivalent expression to the k / -1.6 > -5.3
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
As per the given condition, we have to simplify the given expression to get the equivalent expression,
k / -1.6 > -5.3
k > -1.6 (-5.3)
k > 8.48.
Thus, the required inequality is k > 8.48. Option A is correct.
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How do you determine if an ordered pair is a solution to a given equation? (there's no data)
The equation contains two unknown variables. They are usually x and y. The ordered pair would be written as (x, y). To determine if the ordered pair is a solution of the equation, we would substitute the value of x into the equation. If the resulting value of y is the same as the one in the ordered pair, then the ordered pair is a solution to a given equation
Which number line represents the solution to 5x < 30? F t 8 0 2 4 6 10 G =N + 4 H 8 0 6 10 H + 0 + 8 2 4 6 10 J + 2 + 4 0 6 8 10
Answer:
Line H, the third option
Step-by-step explanation:
First, find the value of x
5x < 30Divide both sides by 55x/5 < 30/5x < 6X is strictly less than 6, so the answer cannot include 6
This means the answer needs to have an open circle as an endpointThe less than sign (<) tells you the line should be pointing to the left
HELPPPPThe data is matricesCalculate a) A + B, b) CD
Answer:
Given that,
a)A+B
we get,
b)CD
What is the wavelength change of a radio signal changes if the emitting source is moving away at 3,000 km/s. The lab (rest) wavelength of this radio signal is 1 meter
The change in wavelength of the radio signal is 100m.
What is Wavelength ChangeThe change in wavelength of the radio can be calculated using the velocity of the given radio signal.
[tex]c = v \lambda\\[/tex]
c = speed of lightv = velocity y = wavelengthLet's substitute the values and solve.
But then, we have to convert the velocity from km to m
[tex]1km = 1000m\\3000km = x\\x = 3000000m[/tex]
we solve the wavelength here by
[tex]c = \lambda v\\3.0*10^8 = \lambda * 3.0^6\\\lambda = \frac{3.0*10^8}{3.0*10^6} \\\lambda = 1.0*10^2m\\\lambda = 100m[/tex]
The wavelength of the radio signal is 100m.
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Students were asked to prove the identity (tan x)(sin x) = sec x − cos x. Two students' work is given.Student AStep 1: sine x over cosine x times sine x equals secant x minus cosine xStep 2: sine squared x over cosine x equals secant x minus cosine xStep 3: 1 minus cosine squared x over cosine x equals secant x minus cosine xStep 4: 1 over cosine x minus cosine squared x over cosine x equals secant x minus cosine xStep 5: sec x − cos x = sec x − cos xStudent BStep 1: tangent x times sine x equals 1 over cosine x minus cosine xStep 2: tangent x times sine x equals 1 over cosine x minus cosine squared x over cosine xStep 3: tangent x times sine x equals 1 minus cosine squared x over cosine xStep 4: tangent x times sine x equals sine squared x over cosine xStep 5: tangent x times sine x equals sine x over cosine x times sine xStep 6: tan x sin x = tan x sin xPart A: Did either student verify the identity properly? Explain why or why not. (10 points)Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 points)
The identities used by student A is
1 - sin²x= cos²x
sin x/ cos x = tan x
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have to prove (tan x)(sin x) = sec x − cos x.
Now, student A and student B perform the proof.
Student A starts with tan x sin x then approaches to prove sec x - cos x.
So, Student A complete the proof.
But, student B starts with tan x sin x but failed to prove sec x - cos x.
The identities used by student A is
1 - sin²x= cos²x
sin x/ cos x = tan x
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Find the values of x and y that maximize the objective function
P = 3x + 2y for the graph. What is the maximum value?
Step-by-step explanation:
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeee
thank you
The domain is [1,∞) and the range is [0,∞).
The relation given on the graph is a function for which the domain and the range are asked to be identified.
Examining the graph, the function has values corresponding the x-values from 1 (including 1). That is, at x = 1, the function value is 0. From there, the function continues without any break and extends to infinity. So the function is continuous.
Hence the domain and range can be best described in interval notation.
The domain of a function is the set of x-values for which the function has values or the function is defined.
As the function has values from x = 1 and extends to infinity, the domain is [1,∞).
The range of a function is the images of the function corresponding to the domain values.
Considering the y-values corresponding to the domain, which are the function values, the range is [0,∞).
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Compute the value of the discriminant and give the number of real solutions of the quadratic equation.-2x² + 6x - 3=0Discriminant:12Number of real solutions:
The formula for the value of discriminant in a quadratic equation in the form ax^2 + bx + c = 0 is :
[tex]d=b^2-4ac[/tex]Where d is the discriminant and
a, b, c are the coefficients in the quadratic equation.
From the given problem,
[tex]ax^2+bx+c=0\Rightarrow-2x^2+6x-3=0^{}[/tex]a = -2, b = 6 and c = -3
Using the formula above,
[tex]\begin{gathered} d=b^2-4ac \\ d=6^2-4(-2)(-3) \\ d=36-24 \\ d=12 \end{gathered}[/tex]Note that if the discriminant is greater than 0, the number of real solution is 2.
The answer is
discriminant = 12
Number of real solutions = 2
Answer:
[tex]2[/tex]
[tex]x[/tex]
change to Ax+By=c form 2y=3x
We want to write the equation 2y=3x in the form Ax+By=C.
[tex]\begin{gathered} 2y=3x \\ -3x+2y=0 \\ So,\text{ A=-3, B=2 and C=0} \end{gathered}[/tex][tex]0 \div - 2[/tex]I am having trouble with this and every time I put it in the answer box it says I am wrong
Let's begin by listing out the information given to us:
[tex]\begin{gathered} 0\div-2 \\ \Rightarrow\frac{0}{-2}=0 \\ \therefore The\text{ ans}wer\text{ is zero (0)} \end{gathered}[/tex]Any number that is dividing zero always gives a result of zero
Determine if the table shows a proportional relationship.
x 36.75 16.8 77.1
y 12.25 5.6 25.7
Yes, it is proportional because the ratios for y over x are all equivalent to one half.
Yes, it is proportional because the ratios for y over x are all equivalent to one third.
No, it is not proportional because 12.25 over 36.75 is not equal to 16.8 over 5.6.
No, it is not proportional because 36.75 over 12.25 is not equal to 25.7 over 77.1.
The ratios of y over x are all equal to 1/3, thus we may infer that: B. the table is proportionate.
What is a Proportional Relationship?
Any pair of values in a table that depicts a proportionate relationship have the same value for the proportionality constant, k, where k = y/x.
Check each pair of values in the table to see if k is the same:
(36.75, 12.25):
k = 12.25/36.75 = 0.33
(16.8, 5.6):
k = 5.6/16.8 = 0.33
(77.1, 25.7):
k = 25.7/77.1 = 0.33
It is proportionate because the ratios of y across x are all equal to 1/3, which implies that the value of k is identical for all values.
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