Answer:
The amount of time it would take 160 workers to build 16 miles of Highway is;
[tex]15\text{ weeks}[/tex]Explanation:
Given that the amount of time it takes to build a highway varies directly with the length of the highway and inversely with the number of workers.
Let t represent the time in weeks, l represents the length of the highway in miles, and n represent the number of workers;
So, we have;
[tex]\begin{gathered} t\propto\frac{l}{n} \\ t=k\frac{l}{n} \\ k=\frac{nt}{l} \end{gathered}[/tex]Given;
it takes 100 workers 6 weeks to build 4 miles of Highway
[tex]\begin{gathered} n=100 \\ t=6 \\ l=4 \\ k=\frac{nt}{l} \\ k=\frac{100\times6}{4} \\ k=150 \end{gathered}[/tex]so, for 160 workers to build 16 miles of Highway the time it will take is;
[tex]\begin{gathered} n=160 \\ l=16 \\ k=150 \\ t=k\frac{l}{n} \\ t=150\times\frac{16}{160} \\ t=\frac{150}{10} \\ t=15 \end{gathered}[/tex]Therefore, the amount of time it would take 160 workers to build 16 miles of Highway is;
[tex]15\text{ weeks}[/tex]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]Select the correct answer.Which expression has a value closest to 1? (Use 3.14 as the value of T.)OA.77V10OB. V75-V74OC. 37-V26OD3V5 V20V2
the expression has a value closest to 1 is √37 - √26 (option C)
Explanation:
To determine the expression, we need to solve each of the options.
a) 7π/√10 = 7(3.14) /√10 = 21.98/3.1623
= 6.95
b) √75 - √74 = 8.66 - 8.60
= 0.06
c) √37 - √26 = 6.083 - 5.099
= 0.984
d) (3√5 - √20)/√2 = (6.708 - 4.472)/1.414 = 2.236/1.414
= 1.58
√37 - √26 = 0.984 is closest to 1
From the above, the expression has a value closest to 1 is √37 - √26 (option C)
Enter values for alien base of the system of equation shown has one solution
we have the system of equations
y=3x+4 ----> equation 1
y=ax+b ----> equation 2
Remember that
The only condition for the system, to have only one solution is that the slopes of both lines are different
so
The values for a are all real numbers except for a=3
The values for b are all real numbers
Therefore
A solution could be
a=2 and b=4The solution is (0,4)
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.
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:
Which of the equations shown have infinitely many solutions? Select all that apply. A. 3x – 1 = 3x + 1 B. 2x – 1 = 1 – 2x C. 3x – 2 = 2x – 3 D. 3(x – 1) = 3x – 3 E. 2x + 2 = 2(x + 1) F. 3(x – 2) = 2(x – 3)
The equation with infinitely many solutions are 3(x – 1) = 3x – 3 and 2x + 2 = 2(x + 1) .
How to find equation that shows infinitely many solution?An infinite solution has both sides equal to each other.
It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.
Therefore, the equation with infinitely many solution are as follows:
D.
3(x – 1) = 3x – 3
open the brackets on the left side of the equation
3x - 3 = 3x - 3
E.
2x + 2 = 2(x + 1)
open the brackets on the right side of the equation
2x + 2 = 2x + 2
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What is debt? How does debt create financial risk and instability?
Debt can be defined as a sum of money that is owed or due.
Debt creates financial risk and instability by:
a) spreading economic pain and hardship to the country's citizens and to other countries.
b) causing Financial losses, market turmoil, and sharp slowdowns in trade and economic growth are some of the ways countries can feel the effects of a debt crisis in other countries.
c)Creating a heavy debt load that you can’t pay off, your credit score will start to go down resulting in a bad credit score and report.
d) leading to stress by limiting your ability to enjoy life. This can result in various health issues.
Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. Debt is a deferred payment, or series of payments, differentiating it from an immediate purchase. It can lead to financial risk and instability for both individuals and the state at large.
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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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The price of tuition has tripled since my parents went to school - that’s a 200% increase
in price.
The statement makes sense. This is because A 200 percentage increase in price corresponds to a price that is 300% of the original price
How to illustrate the information?You can express a fraction of something using percentages. A change in something can be described using percentages. As an illustration, the price of milk increased by 5% last month.
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage.
A figure or ratio stated as a fraction of 100 is called a percentage. The % sign is frequently used to indicate it. In this case, 200% of something implies that it will give 300% of the initial amount.
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The price of tuition has tripled since my parents went to school thats a 200% increase in price corresponds to a price that is 300% of the original price. Does this makes sense?
Rectangular Prism: a. The measures: I =5, w = 7, h = 8 .. b. The measures: h =7, w = 7,1 = 7. C. W = 3.6, I = 4.2, h = 8.3
ANSWER:
a. 280 cm^3
b. 343 cm
STEP-BY-STEP EXPLANATION:
The formula for the volume of the rectangular prism is as follows:
[tex]V=l\cdot w\cdot h[/tex]We replace for each case:
a.
[tex]\begin{gathered} V=5\cdot7\cdot8 \\ V=280 \end{gathered}[/tex]b.
[tex]\begin{gathered} V=7\cdot7\cdot7 \\ V=343 \end{gathered}[/tex]c.
[tex]undefined[/tex]Factor. v2 + 22v - 23
we can factor this quadratic expression finding the zeros, as follows:
[tex]\begin{gathered} v_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ v_{1,2}=\frac{-22\pm\sqrt[]{22^2-4\cdot1\cdot(-23)}}{2\cdot1} \\ v_{1,2}=\frac{-22\pm\sqrt[]{484+92}}{2} \\ v_{1,2}=\frac{-22\pm\sqrt[]{576}}{2} \\ v_1=\frac{-22+24}{2}=1 \\ v_2=\frac{-22-24}{2}=-23 \end{gathered}[/tex]Then, the quadratic expression can be expressed as
[tex]\begin{gathered} a(v-v_1)(v-v_2) \\ v^2+22v-23=(v-1)(v+23) \end{gathered}[/tex]use a system of equations with two variables and two equations to solve.A number is 11 more than another number.twice the sum of the two numbers is 42. find the two numbers
"A number is 11 more than another number" can be expressed as
[tex]x=y+11[/tex]"Twice the sum of the two numbers is 42" can be expressed as
[tex]2(x+y)=42[/tex]So, these two equations for a system. Let's combine them to find y in the first place
[tex]\begin{gathered} 2(x+y)=42 \\ 2(y+11+y)=42 \\ 2(2y+11)=42 \\ 2y+11=\frac{42}{2} \\ 2y+11=21 \\ 2y=21-11 \\ 2y=10 \\ y=\frac{10}{2} \\ y=5 \end{gathered}[/tex]Then, we find x
[tex]x=y+11=5+11=16[/tex]The solution is (16, 5).The inner core is solid because the inner core consists of a lot of pressure and high temperatures. And the more pressure and high temperatures the more dense the substance gets.
The inner core is solid because the inner core consists of a lot of pressure and high temperatures. This is true.
How to illustrate the information?The pressure surrounding the inner core, as well as the planet's atmosphere, keeps the iron from melting. The iron atoms cannot migrate into a liquid form due to the pressure and density, which are simply too high.
Temperature is a measure of how hot or cold something is, more particularly the average kinetic energy of the particles in an object, which is a sort of energy related with motion. Temperature is a measure of how hot or cold something is represented in terms of one of several scales, including Fahrenheit and Celsius.
Because the inner core is under intense pressure and is extremely hot, it is solid. And the stuff becomes denser as pressure and temperature increase. Therefore, the inner core's high heat and pressure are what are solidifying it since the denser the stuff is, the more solidified it becomes.
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The inner core is solid because the inner core consists of a lot of pressure and high temperatures. And the more pressure and high temperatures the more dense the substance gets. True or false?
What else would need to be congruent to show that. abc xyz by aas
a circular garden has a diameter of 8 yards. what is the area of the garden? use 3.14 for piπ.
To calculate the area of a circle you have to use the following formula:
[tex]A=\pi r^2[/tex]Where
A is the area
π is the number pi, for this exercise you have to use up to its two first decimal values: 3.14
r is the radius.
The radius of a circle is half its diameter, so the radius of the circular garden will be
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{8}{2} \\ r=4\text{yards} \end{gathered}[/tex]Next, you can calculate the area of the circular garden as follows:
[tex]\begin{gathered} A=3.14\cdot(4^2) \\ A=3.14\cdot16 \\ A=50.24yd^2 \end{gathered}[/tex]The area of the circle is 50.24yd²
What do you know about the role of financial accounting standard setting in the United States? This is actually for an intermediate accounting course in college
The role of financial accounting standard setting in the United States is to establish and improve financial accounting and reporting standards to provide useful information to those who need it.
What is the Financial Accounting Standard?The Financial Accounting Standard is a term to refer to an institution established in 1973 that was created with the objective of establishing financial reporting and accounting standards for public and private companies and non-profit organizations.
What is the role of this institution?The main role of this institution is to create accounting standards focused on public companies. This process of creating accounting standards is focused on promoting financial information in the financial field for different institutions and people interested in investing.
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what is the GCF (-3x, 6x, 12x)
Answer:
3x
Explanation:
First, find the prime factorization of each of the terms:
[tex]\begin{gathered} -3x=-1\times3\times x \\ 6x=2\times3\times x \\ 12x=2\times2\times3\times x \end{gathered}[/tex]Next, pick the term that is common in the three products:
[tex]\begin{gathered} \text{GCF}=3\times x \\ =3x \end{gathered}[/tex]The GCF of -3x, 6x, and 12x is 3x.
g(x) = 4x+5f(x) = 2x - 2Find (g•f )(x)
The value of the function (g•f )(x) is 8x-3.
Given the functions are:
g(x) = 4x+5
f(X) = 2x-2
we are asked to determine (g•f )(x) = ?
⇒ g(x) = 4x+5
⇒ f(x) = 2x-2
⇒ (g•f )(x), substitute the value for f(x)
⇒ g(f(x))
⇒ g(2x-2)
now put the value g(2x-2) in g(x)
⇒ g(2x-2) = 4x+5
⇒ g(2x-2) = 4(2x-2) + 5
⇒ g(2x-2) = 8x - 8 + 5
⇒ g(2x-2) = 8x - 3
Hence we get the value of (g•f )(x) as 8x-3
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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.
please help me out quickly
[tex]A^{-1} =\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right][/tex]
[tex]x =\left[\begin{array}{ccc}108\\-14\\22\end{array}\right][/tex]
Given matrix A:
[tex]\left[\begin{array}{ccc}5&-15&-44\\-1&2&6\\1&-3&-9\end{array}\right][/tex]
To find the inverse of the matrix we start by finding the determinant of the matrix.
|A| = 5(-18+18) + 15(9-6) - 44(3-2)
= 0 + 15(3) - 44 = 45 - 44 = 1
As the determinant 1 ≠ 0, hence the inverse of the matrix exists.
Now, we find the minors of each element of the matrix.
m₁₁ = [tex]\left[\begin{array}{ccc}2&6\\-3&-9\end{array}\right][/tex] = 0
m₁₂= [tex]\left[\begin{array}{ccc}-1&6\\1&-9\end{array}\right][/tex] = 3
m₁₃ = [tex]\left[\begin{array}{ccc}-1&2\\1&-3\end{array}\right][/tex] = 1
m₂₁ = [tex]\left[\begin{array}{ccc}-15&-44\\-3&-9\end{array}\right][/tex] = 3
m₂₂ = [tex]\left[\begin{array}{ccc}5&-44\\1&-9\end{array}\right][/tex] = -1
m₂₃ = [tex]\left[\begin{array}{ccc}5&-15\\1&-3\end{array}\right][/tex] = 0
m₃₁ = [tex]\left[\begin{array}{ccc}-15&-44\\2&6\end{array}\right][/tex] = -2
m₃₂ = [tex]\left[\begin{array}{ccc}5&-44\\-1&6\end{array}\right][/tex] = -14
m₃₃ = [tex]\left[\begin{array}{ccc}5&-15\\-1&2\end{array}\right][/tex] = -5
The cofactor matrix can be obtained as:
[tex]\left[\begin{array}{ccc}0&3&1\\3&-1&0\\-2&-14&-5\end{array}\right][/tex]
Now the adjoint of matrix A (written as adj A) by taking the transpose of the cofactor matrix of A is,
[tex]\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right][/tex]
To determine the inverse of a square matrix A, we use the formula:
A⁻¹ = adj(A) / |A|
Therefore, the inverse of the given matrix is:
A⁻¹ = 1/1 [tex]\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right][/tex]
It is given, Ax = b
and b = [tex]\left[\begin{array}{ccc}-2\\-2\\-2\end{array}\right][/tex]
Let x be [tex]\left[\begin{array}{ccc}a\\b\\c\end{array}\right][/tex]
Putting values in Ax = b equation,
[tex]\left[\begin{array}{ccc}0&-3&-2\\-3&-1&14\\1&0&-5\end{array}\right]\left[\begin{array}{ccc}a\\b\\c\end{array}\right]=\left[\begin{array}{ccc}-2\\-2\\-2\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-3b-2c\\-3a-b+14c\\a-5c\end{array}\right]=\left[\begin{array}{ccc}-2\\-2\\-2\end{array}\right][/tex]
Equating the three equations with the respective values,
So, -3b - 2c = -2
-3a -b + 14c = -2
a - 5c = -2 ⇒ a+2/5 = c
Solving the above equations we obtain the values of a,b, and c as 108, -14, and 22.
So, the matrix x is
[tex]x =\left[\begin{array}{ccc}108\\-14\\22\end{array}\right][/tex]
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Fill out this whole column in an organized manner please
We can calculate the slope as:
[tex]S=\frac{{\Delta}Y}{\Delta X}[/tex]From this, we have: (FIRST ANSWER)
[tex]\begin{gathered} S_{ZY}=\frac{0-\mleft(-3\mright)}{1-6}=-\frac{3}{5} \\ S_{YX}=\frac{-6-(-3)}{1-6}=\frac{3}{5} \\ S_{XW}=\frac{-3-(-6)}{-4-1}=-\frac{3}{5} \\ S_{WZ}=\frac{-3-0}{-4-1}=\frac{3}{5} \end{gathered}[/tex]The length of the non-parallel sides can be measured as:
[tex]L=\sqrt[]{(\Delta Y)^2+(\Delta X)^2}[/tex]From this, we have: (SECOND ANSWER)
[tex]\begin{gathered} L_{ZW}=\sqrt[]{(1-(-4))^2+(0-(-3))^2}_{}=\sqrt[]{25+9}=\sqrt[]{34} \\ L_{ZY}=\sqrt[]{(6-1)^2+(-3-0)^2}=\sqrt[]{25+9}=\sqrt[]{34} \end{gathered}[/tex]From the figure in the beginning and the values we found, this is a Rhombus.
Which of the following is the complete factorization of the polynomial below? x3 -7% +7x+15 O A. (x + 1)(x+3)(x+5) O B. (x-1)(x-3)(x-5) (C. (x-1)(x+3)(x+5) OD. (16-3 D. (x+1(x-3)(x-5)
Given the polynomial:
[tex]x^3-7x^2+7x+15[/tex]You can factorize it as follow:
1. Rewrite the term with exponent 2 in this form:
[tex]-7x^2=x^2-8x^2[/tex]2. Rewrite the x-term in this form:
[tex]7x=-8x+15x[/tex]3. Rewrite the expression:
[tex]=x^3+x^2-8x^2-8x+15x+15[/tex]4. Make three groups of two terms each using parentheses:
[tex]=(x^3+x^2)-(8x^2+8x)+(15x+15)[/tex]5. Identify the Greatest Common Factor (GCF) of each group (the largest factor that all the terms in the group have in common):
- For:
[tex](x^3+x^2)[/tex]The Greatest Common Factor is:
[tex]GCF=x^2[/tex]- For:
[tex](8x^2+8x)[/tex]The Greatest Common Factor is:
[tex]GCF=8x[/tex]- And for:
[tex](15x+15)[/tex]It is:
[tex]GCF=15[/tex]6. Factor the GCF of each group out:
[tex]=x^2(x^{}+1)-8x(x+1)+15(x+1)[/tex]7. Notice that each expression is common in all the terms:
[tex]x+1[/tex]Then, you can factor it out:
[tex]=(x^{}+1)(x^2-8x+15)[/tex]8. In order to factor the Quadratic Polynomial in the second parentheses, you can find two numbers whose Sum is -8 and whose Product is 15. These are -3 and -5. Then, you get:
[tex]=(x^{}+1)(x-3)(x-5)[/tex]Hence, the answer is: Option D.
solve for the unknown angle measure given that f || g
Find x to the nearest tenth.
The value of x = 42
Given : A right angled triangle with the below mentioned measures :
angles ∠ 1 = 28 °
∠ 2= 25° and the length is 600
To find : the value of x
Let us assume the rest of the length is y that is the side opposite of the angle will now be x + y
thus tan 28 ° = [tex]\frac{x+y}{600}[/tex]
tan 28 °= 0.53 thus the equation after cross multiplying becomes ;
0.53 × 600 = x + y
318 = x + y ------------------ equation 1
And tan 25° = [tex]\frac{y }{600}[/tex]
tan 25 ° = 0.46
After cross multiplying we get : 0.46 × 600 = y
=> 276 = y
Substituting this value in equation 1 we get : 318 = x + 276
=> x = 318 - 276
=> x = 42
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X+2=2x-1.equations with variables on both sides
Answer:
X = 3
Step-by-step explanation:
To solve this you want to first make the X variable alone by itself by moving it to the left or right it doesn't really matter, for this I moved it to the left making the new equation
-x = -1 - 2
I then make the 2 a negative using the order of operations and a negative adding a negative makes -3 making the following
-x = -3
then I change the signs making it
x = 3
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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One positive number is 5 times another number. The difference between the twonumbers is 148. Find the numbers.0 20 and 100O 37 and 1850 1 and 5O 50 and 250
Let L and M represent two positive numbers.
Since one positive number is 5 times another number, we can make the statement:
[tex]L=5M[/tex]Since the difference between those numbers is 148, we can write down:
[tex]L-M=148[/tex]Where we have chosen L-M instead of M-L since L is greater than M and both are positive numbers (by using M-L, the difference would be negative).
Substitute 5M for L in the second equation:
[tex]5M-M=148[/tex]Solve for M:
[tex]\begin{gathered} 4M=148 \\ \Rightarrow M=\frac{148}{4} \\ \Rightarrow M=37 \end{gathered}[/tex]Once knowing M, multiply by 5 to get L:
[tex]\begin{gathered} L=5\cdot37 \\ =185 \end{gathered}[/tex]Therefore, those two numbers are 37 and 185.
Please find the square root. Round your answer to the nearest thenth.√121=
Explanation
Step 1
A square root of a number is a value that, when multiplied by itself, gives the number.
hence, we need to find a value(s) that when multiplied by itself gives 121,so
[tex]\sqrt[]{121}=\pm11[/tex]because
[tex]\begin{gathered} 11\cdot11=121 \\ or \\ -11\cdot-11=121 \end{gathered}[/tex]I hope this helps you
1 1/6 divided by 2 2/3
Answer:
7/16
Step-by-step explanation:
Convert "mixed numbers" into "improper fractions":
1 1/6 = 7/6
2 2/3 = 8/3
1 1/6 divided by 2 2/3 = 7/6 divided by 8/3
Apply the KFC rule:
1) Keep the first
7/6
2) Flip the second
8/3 becomes 3/8
3) Change the sign
7/6 multiplied by 3/8
7/6 × 3/8
= 7×3 / 6×8
= 21/48
= 7/16
