If triangle HJK has a centroid P then we know that the side HP will be the double of PM so we can made an equation for HM
[tex]\begin{gathered} HM=HP+PM \\ HM=2PM+PM \\ HM=3PM \end{gathered}[/tex]Now we can replace the value of HM and solve for PM so:
[tex]\begin{gathered} \frac{39}{3}=PM \\ 13=PM \end{gathered}[/tex]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
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]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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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 inequality 6x^2 + 5x < 4
Answer: -4/3 < x< 1/2
Step-by-step explanation: inequality form
Donna De Paul is raising money for the homeless. She discovers that each church group requires 2 hours of letter writing and 1 hour of follow-up, while for each labor union she needs 2 hours of
letter writing and 3 hours of follow-up. Donna can raise $150 from each church group and $200 from each union local, and she has a maximum of 12 hours of letter writing and a maximum of 12
hours of follow-up available per month. Determine the most profitable mixture of groups she should contact and the most money she can raise in a month.
Let x, be the number of church groups, and let x2₂ be the number of labor unions. What is the objective function?
z = 150 x₁ + 200 x₂
(Do not include the $ symbol in your answers.)
She should contact
(Simplify your answers.)
church group(s) and labor union(s), to obtain a maximum of $ in donations.
Answer:
x = 7
y = 3
z (max) = 4950/3 = 1650
Step-by-step explanation:
Let call
x numbers of church goup and
y numbers of Union Local
Then
First contraint
2*x + 2*y ≤ 20
Second one
1*x + 3*y ≤ 16
Objective Function
z = 150*x + 200*y
Then the system is
z = 150*x + 200*y To maximize
Subject to:
2*x + 2*y ≤ 20
1*x + 3*y ≤ 16
x ≥ 0 y ≥ 0
We will solve by using the Simplex method
z - 150 *x - 200*y = 0
2*x + 2*y + s₁ = 20
1*x + 3*y + 0s₁ + s₂ = 16
First Table
z x y s₁ s₂ Cte
1 -150 -200 0 0 = 0
0 2 2 1 0 = 20
0 1 3 0 1 = 16
First iteration:
Column pivot ( y column ) row pivot (third row) pivot 3
Second table
z x y s₁ s₂ Cte
1 -250/3 0 0 200/3 = 3200/3
0 - 4/3 0 -1 2/3 = -20/3
0 1/3 1 0 1/3 = -20/3
Second iteration:
Column pivot ( x column ) row pivot (second row) pivot -4/3
Third table
z x y s₁ s₂ Cte
1 0 0 750/12 700/6 = 4950/3
0 1 0 3/4 -1/2 = 7
0 0 1 -1/4 1/2 = 9/3
Step-by-step explanation:
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
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
4√7 - 9i
Write the trigonometric form of the complex number. (around your angle to two decimal places. Let 0< theta < 2pi
[tex]\stackrel{a}{4\sqrt{7}}~~ - ~~\stackrel{b}{9}i ~~ \begin{cases} r=\sqrt{a^2 + b^2}\\\\ \theta =\tan^{-1}\left( \frac{b}{a} \right) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ r=\sqrt{(4\sqrt{7})^2 + 9^2}\implies r=\sqrt{16(7)+81}\implies r=\sqrt{193} \\\\\\ \theta =\tan^{-1}\left( \cfrac{9}{4\sqrt{7}} \right)\implies \theta \approx 40.38^o \\\\[-0.35em] ~\dotfill\\\\ z~~ = ~~\sqrt{193}( ~~ \cos(319.62^o)~~ + ~~i\sin(319.62^o) ~~ )\qquad \textit{\LARGE IV Quadrant}[/tex]
let's take a quick look at the (a , bi) pair, "a" is positive whilst "b" is negative, that means the IV Quadrant, now let's keep in mind that tan⁻¹(x) has a range that lies on the I and IV Quadrants, so, if you check in your calculator for tan⁻¹(x) for those values, you'll notice it gives the one in the I Quadrant, namely 40.38°, however our coordinate pair is on the IV Quadrant, so we need its twin.
Make sure your calculator is in Degree mode.
Can anyone help me solve
The function that we want to get is:
t(h) = √(-h + 500)/4
And the height is 250 ft after 3.95 seconds.
How to express t as a function of h?Here we have the height function defined as:
h(t) = 500 - 16t²
And we want to write t as a function of h, so we just need to isolate the variable t.
h - 500 = -16*t²
(-h + 500)/16 = t²
√((-h + 500)/16) = t
√(-h + 500)/4 = t
This is the function that defines h as a function of t. Notice that we only care for the positive solution of the square root.
The time at which the height is 250ft is given by:
√(-250 + 500)/4 = t
√(250)/4 = 3.95
So the height after 3.95 seconds is 250ft.
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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
please help me. The photo above shows the question.80% of the picture frame is glass a photo shows a picture frame of length 10 3/4 inches of width 8 1/2 inches, hanging on the wall. The border of the frame is labeled with molding what is the area of the molding?
The area of the moulding is;
[tex]18\frac{11}{40}in^2[/tex]Here, we want to get the area of the moulding
From the question, we are told that the 80% of the frame is a glass photo
What this mean is that 20% of the picture frame will be that of the moulding
Mathematically, by calculating 20% of the area of the frame, we get the area of the moulding
As we can see that the frame is a rectangular shape, the area is the product of its length and its width
We have this as;
[tex]\begin{gathered} 10\frac{3}{4}\times8\frac{1}{2} \\ =\text{ }\frac{43}{4}\times\frac{17}{2}\text{ = }\frac{731}{8\text{ }}in^2 \end{gathered}[/tex]The area of the moulding is 20% of this which is the same as one-fifth or 1/5
we have this as;
[tex]\begin{gathered} \frac{731}{8}\text{ divided by 5} \\ \\ =\text{ }\frac{731}{8}\text{ }\times\text{ }\frac{1}{5}\text{ = }\frac{731}{40}\text{ = 18}\frac{11}{40\text{ }}\text{ square inches} \end{gathered}[/tex]Fight men can do a piece of work in 12days. How long will 6 men take to do thesame work if they work at the same rate?A.14 daysB. 16 daysC.18 daysD.20 days
To solve this
QUESTION
Eight men can do a piece of work in 12
days. How long will 6 men take to do the
same work if they work at the same rate?
SOLUTION
Let X be thr time taken for 6 men to work at the same rate
Looking at the question, it is an indirect proportion
because as the number of men increases, the time taken to do the work decreases
So therefore;
8 men = 6 men
X days = 12 days
cross-multiply
6 x X = 12 x 8
6X = 96
divide both-sidde of the equation by 6
6X/6 = 96/6
X = 16 days
Therefore, it takes 16 days for 6 men men to do the work at the same rate.
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:
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]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.
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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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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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]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.
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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Use the roster method to write the given set. You may need to consult a reference, such as the Internet or an encyclopedia. (Enter EMPTY for the empty set.)
The set of lowercase letters in the English alphabet, except the letter y, that are vowels.
The vowel is the Roster method representation of all lowercase English letters except 'y'.
={a, e, i, 0, u}
This is further explained below.
What is a set?Generally, A set comprises elements or members that may be mathematical objects of any sort, including integers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is a mathematical model for a collection of various things.
In conclusion, the Roster method representation of a set of all lowercase letters in the English alphabet except the letter 'y' is Vowel.
={a, e, i, 0, u}
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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
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
An old man is giving out meals to the less fortunate. He starts off by giving out five meals and every day afterwards, he gives out an additional 3 meals. What kind of relationship is this? discrete or continuous
1) As the number of meals is integer, 5, 8, 11, and so on
2) Then we have a discrete relationship between the numbers of meals.
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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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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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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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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