The perimeter of a rectangle is given by:
P = 2w + 2h
Where:
w = width = 2x
h = height = x
P = 18
Replacing the data into the equation:
18 = 2(2x) + 2(x)
18 = 4x + 2x
18 = 6x
Solving for x:
x = 18/6
x= 3
Therefore:
w = 2(3) = 6m
h = 3m
---------------------------------------------------------------------------------
P = x + 2x + (x + 3)
23 = 3x + x + 3
23 = 4x + 3
Solving for x:
23 - 3 = 4x
20 = 4x
20/4 = x
5 = x
Therefore its sides are:
x = 5 ft
2x = 2(5) = 10ft
x + 3 = 5 + 3 = 8ft
Consider the rectangle. IT 4 x+1 Which two expressions represent the area of the rectangle?
sides of the rectangle:
4
x+1
Area of the rectangle = product of the sides
4 (x+1 )
Apply distributive property:
4(x)+4(1)
4x+4
So, the correct options are:
C. 4x+1
E.4x+4
Ron bought two comic books on sale. Each comic book was discounted $1 off the regular price r. Write an expression to find what Ron paid before taxes. If each comic book was regularly $2.50, what was the total cost before taxes?
Step 1
Given;
[tex]\begin{gathered} A\text{ regular price of r for a comic book on sale} \\ A\text{ discount of \$1 before tax} \end{gathered}[/tex]Required; To
1) write an expression to find what was paid by Ron before taxes
2)Find the total cost before taxes of the comic books, if each one costs $2.50
Step 2
Write the expression of what Ron paid before taxes
[tex]\begin{gathered} \text{\$}2(r-1) \\ \text{Note; One book costs \$(r-1)} \\ \text{\$}(2r-2) \end{gathered}[/tex]Step 3
If each book was regularly $2.50, find the total cost before taxes
[tex]\begin{gathered} r=\text{\$}2.50 \\ \text{Total cost=\$(2(2.50)-2)} \\ \text{Total cost=\$(5-2)=\$}3 \end{gathered}[/tex]Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval. x2 + 2x + 2 x2 The area is 54 (Type an integer or a simplified fraction.)
To find this area, it is necessary to solve an integral, actually the sum of 2 integrals
[tex]\int (x^2+2x+2)dx+\int (3x+4)dx[/tex]The first one must be evaluated from -3 to 2 and the second one from 2 to 3
[tex]\begin{gathered} \int (x^2+2x+2)dx+\int (3x+4)dx \\ (\frac{x^3}{3}+x^2+2x)+(\frac{3x^2}{2}+4x) \\ \end{gathered}[/tex]Evaluate the first integral
[tex]\begin{gathered} \frac{x^3}{3}+x^2+2x\text{ (From -3 to 2)} \\ (\frac{2^3}{3}+2^2+2\cdot2)-(\frac{(-3)^3}{3}+(-3)^2+(2\cdot-3)) \\ \frac{8}{3}+4+4-(-\frac{27}{3}+9-6) \\ \frac{35}{3}+5=\frac{50}{3} \end{gathered}[/tex]Evaluate the second integral
[tex]\begin{gathered} \frac{3x^2}{2}+4x\text{ (From 2 to 3)} \\ (\frac{3\cdot(3^2)}{2}+4\cdot3)-(\frac{3\cdot(2^2)}{2}+4\cdot2) \\ (\frac{27}{2}+12)-(\frac{12}{2}+8) \\ \frac{15}{2}+4=\frac{23}{2} \end{gathered}[/tex]Now, solve the sum
[tex]\begin{gathered} \frac{50}{3}+\frac{23}{2} \\ \frac{100+69}{6}=\frac{169}{6} \end{gathered}[/tex]The area is 169/6
solve: 10+7-4y=-5+6y+22 and decide whether it has infinite solutions or no solutions or one solution
answer is one solution
Solve the equation for c: 52 = 4(c + 5)
Given:
[tex]52\text{ = 4(c + 5)}[/tex]Solution
We are required to solve the equation for c.
First, we open the bracket:
[tex]52\text{ = 4c + 20}[/tex]Next, we make c the subject of formular:
[tex]\begin{gathered} 4c\text{ = 52 - 20} \\ 4c\text{ = 32} \\ \text{Divide both sides of the equation by 4} \\ c\text{ = 8} \end{gathered}[/tex]Answer: c = 8
A sociology teacher asked her students to complete a survey at the beginning of the year. One survey question asked, "How responsible are you?" Another question asked, "How many siblings do you have?" Irresponsible Responsible O siblings 6 3 1 sibling 4 5 What is the probability that a randomly selected student has 0 siblings and is irresponsible? Simplify any fractions.
Answer: Probability is 1/3
Step by step explanation:
The probability (P) of an event is:
[tex]P=\frac{\text{Number of ways it can happen}}{\text{Total number of outcomes}}[/tex]The probability that a randomly selected student has 0 siblings and is iiresponsible is:
[tex]P=\frac{6}{6+3+4+5}=\frac{6}{18}=\frac{1}{3}[/tex]Determine the domain and range Express your answer in interval notation
The domain of a function is the set of all values that the x-variable can take.
On the other hand, the range of the function is the set of all values that the function takes when it is evaluated at elements of the domain.
For the given expression:
[tex]p(x)=-\frac{1}{(x-1)^2}[/tex]The denominator is (x-1)^2. Since the denominator must be different from 0, then:
[tex]\begin{gathered} (x-1)^2\ne0 \\ \Rightarrow x-1\ne0 \\ \Rightarrow x\ne1 \end{gathered}[/tex]Then, the only restriction for the variable x is not to be equal to 1. Then, the domain of p(x) is the set of all real numbers except 1, which can be written using interval notation as:
[tex](-\infty,1)\cup(1,\infty)[/tex]Since the exponent of the denominator is 2, then the denominator is always positive. Since the coefficient of the term 1/(x-1)^2 is -1, then the whole expression must always be negative. Additionally, there is no way in which the expression can be equal to 0.
Then, the range of the function is the set of all negative numbers, which can be expressed using interval notation as:
[tex](-\infty,0)[/tex]Therefore, the answers are:
[tex]\begin{gathered} \text{ Domain: }(-\infty,1)\cup(1,\infty) \\ \\ \text{ Range: }(-\infty,0) \end{gathered}[/tex]How wide is the space betweeneach number on this clock?
Solution:
Given:
We have the angle between each hands of the clock to be
[tex][/tex]Alex is 12 years older than George, Carl is three times older than Alex, The sum of their ages is 68. Find the ratio of George's age to Carl's age to Alex's age.
Firstly, let x represent Alex's age, y represent George's age and z represent Carl's age.
from the question;
Alex is 12 years older than George, So;
[tex]x=y+12\ldots\ldots\ldots\ldots.1[/tex]Carl is three times older than Alex, So;
[tex]z=3x\ldots\ldots\ldots..2[/tex]The sum of their ages is 68, So;
[tex]x+y+z=68\ldots\ldots\ldots\ldots\ldots3[/tex]Now we have three equations and three unknowns, so it is solvable.
Let us substitute equation 2 into equation 3; that is replace z with 3x in equation 3.
[tex]\begin{gathered} x+y+3x=68 \\ 4x+y=68\ldots\ldots\ldots\ldots\ldots\ldots4 \end{gathered}[/tex]Next, let us substitute equation 1 into equation 4. that is replace x with y+12 in equation 4.
[tex]\begin{gathered} 4(y+12)+y=68 \\ 4y+48+y=68 \\ 5y+48=68\ldots\ldots\ldots.5 \end{gathered}[/tex]we can now solve for the value of y from equation 5.
[tex]\begin{gathered} 5y+48=68\ldots\ldots\ldots.5 \\ \text{subtract 48 from both sides.} \\ 5y+48-48=68-48 \\ 5y=20 \\ y=\frac{20}{5} \\ y=4 \end{gathered}[/tex]let us now replace y with 4 in equation 1 to get the value of x. since y = 4;
[tex]\begin{gathered} x=y+12\ldots\ldots\ldots\ldots.1 \\ x=4+12 \\ x=16 \end{gathered}[/tex]then, since x =16 let us replace x with 16 in equation 2 to get z.
[tex]\begin{gathered} z=3x\ldots\ldots\ldots..2 \\ z=3(16) \\ z=\text{ 48} \end{gathered}[/tex]so we have;
[tex]\begin{gathered} \text{Alex's age = x = 4 years} \\ George^{\prime}sage_{}=y=16\text{ years} \\ Carl^{\prime}sage=z=48\text{ years} \\ \end{gathered}[/tex]We now need to find the ratio of George, Carl and Alex's age.
[tex]\begin{gathered} 16\colon48\colon4 \\ \text{dividing through by 4 we have;} \\ 4\colon12\colon1 \end{gathered}[/tex]So the ratio of their ages are;
[tex]4\colon12\colon1[/tex]hello this is a plane trigonometry question hopefully you can help I did every thing else it's just the last one I can't get the reference angle for five in this question
Find the solution of the system of equations. 3x + 3y = 6 9x - 5y = -24
3x + 3y = 6 (eq. 1)
9x - 5y = -24 (eq. 2)
Multiplying equation 1 by 3,
3(3x + 3y) = 3*6
3(3x) + 3(3y) = 18
9x + 9y = 18 (eq. 3)
Subtracting equation 2 to equation 3,
9x + 9y = 18
-
9x - 5y = -24
---------------------
14y = 42
y = 42/14
y = 3
Replacing this result into equation 1,
3x + 3(3) = 6
3x + 9 = 6
3x = 6 - 9
3x = -3
x = -3/3
x = -1
a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
a pet store has c tanks of fish. Each tank has 24 fish. Using c, write an expression for the total number of fish in the store
the equation is equal to
Multiply the number of tanks by 24
so
24c
the answer is 24cPart 2
1/13 is the reciprocal of 13
because
(13)(1/13)=1
a number multiplied by its reciprocal is equal to 1
choose the expression that is represented by the following phrase:"the square of Y decreased by the quotient of 8 and y"
The price of televisions has dropped dramatically over the last three years. Three years ago, a 32 inch television was $500. This year the tv was on sale for $199. What is the percent change?
it is due today!!! 7th honers
The percent change in the price of television from initial price $500 to final price $199 is 60.2.
What are Percentages?
The term 'per cent' means 'out of a hundred'.
Percentage is a way to define parts of a whole.
To convert fraction to a percentage, first convert fraction to decimal,
then multiply decimal value with 100, with '%' sign.
So, Percentage change = [tex]\frac{initial-final}{initial}[/tex]×100%
Percentage change = { ( $500 - $199 ) / $500 } × 100%
= { $301 / $500 } × 100%
= .602 × 100%
= 60.2%
Hence, the percentage change in tv price is 60.2%.
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I need help describing the sequence of transformations for 12 and 13.
12. For the first part we rotate 90° and reflect on the y-axis
Then we reflect on the x-axis
13. First we reflect on the y-axis, then we rotate 90° and finally we reflect on the x-axis
Question 9, on which interval is the graph negative ?
The intervals where the graph is negative are those where it goes below the x-axis. With the figure we can easily identify the following negative portion of the graph:
As you can see, these negative values are located for all the points within (-5, -1), this is equivalent to the interval -5 < x < -1. Then option B is the correct answer
The taxes on a house assessed at 90,000 are $3420 a year. If the assessment is raised to 119,000 and the tax rate did not change, how much would the taxes be now?
The amount of tax to be paid on the assessment of the house is $4522.
How to calculate the tax?Given that the taxes on a house assessed at 90,000 are $3420 a year, the tax rate will be:
= Tax / Total value.
= 3420 / 90000
= 3.8%
Therefore, when the assessment is raised to 119,000 and the tax rate did not change, the value of the tax will be:
= Tax percentage × New assessment
= 3.8% × 119000
= $4522
The tax is $4522.
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Daig 20. Sample Problem using Daum Equation Editor 4 - [3 :) and B - [: 6 51 Determine -3A + 2B Show all work using the Daum Equation Editor. Insert your image here:
The question is given as : -3A +2 B
[2 5] + { 6 5 }
[7 0 } { 1 1 }
For the first matrix , multiply by -3 and the second matrix multiply by 2
To multiply a matrix, every value in the bracket is multiplied by the scalar.
For -3A multiply the values in the bracket with -3 as;
[tex]\begin{bmatrix}{2} & {5} & \\ {7} & {0} & {} \\ {} & {} & \end{bmatrix}\times-3\text{ = }\begin{bmatrix}{-6} & {-15} & \\ {-21} & {0} & {} \\ {} & {} & {}\end{bmatrix}=-3A[/tex]For 2B
[tex]\begin{bmatrix}{6} & {5} & {} \\ {1} & {1} & {} \\ {} & {} & {}\end{bmatrix}\times2=\begin{bmatrix}{12} & {10} & \\ {2} & {2} & {} \\ {} & {} & {}\end{bmatrix}=2B[/tex]Now perform the addition as; -3A + 2B
[tex]\begin{bmatrix}{-6} & {-15} & \\ {-21} & {0} & {} \\ {} & {} & {}\end{bmatrix}+\begin{bmatrix}{12} & {10} & \\ {2} & {2} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-6+12} & {-15+10} & \\ {-21+2} & {0+2} & {} \\ {} & {} & {}\end{bmatrix}[/tex]This will give the following;
[tex]\begin{bmatrix}{6} & {-5} & {} \\ {-19} & {2} & {} \\ {} & {} & {}\end{bmatrix}[/tex]According to the histogram, what is the least number of broken light bulbs received in a shipment?
Responses
A 0
B 1
C 10
D 50
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DIoll Solve the equation x³ + 2x² - 5x-6=0 given that 2 is a zero of f(x)= x³ + 2x² - 5x-6.The solution set is(Use a comma to separate answers as needed.)
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
f(x) = x³ + 2x² - 5x - 6
zero:
x = 2
Step 02:
roots:
solution set:
2 | 1 2 -5 -6
| 2 8 6
________________
1 4 3 0
x² + 4x + 3 = 0
(x + 3)(x + 1) = 0
x = - 3
x = - 1
The answer is:
solution set:
{-3 , -1 , 2}
how do I find the central angle for turn b?
We will to use the formula to a sector areaa, which is given for:
[tex]A=r^2\theta/2[/tex]Where r is the radius and θ is the central angle.
We can rewrite the formula to obtain the central angle like this:
[tex]\theta=\frac{2A}{r^2}[/tex]We replace with the values of the track:
[tex]\theta=\frac{2\ast51\pi}{20\ast3^2}=\frac{17\pi}{30}[/tex]Then we change radians to degrees:
[tex]\frac{17\pi}{30}\ast\frac{180}{\pi}=102\text{ \degree}[/tex]Then the correct answer is 102°.
Please help will mark Brainly
Answer:
Below
Step-by-step explanation:
A yes all values of y
B yes slope is undefined for a vertical line
C no there is no y axis intercept for this line
D yes the line intercepts the x-axis at x = -2
E no the domain is only x = -2
i need help trying to write a system of linear equations for the graph below
We need to find the equation in slope-intersect form
[tex]y=mx+b[/tex]of the given lines.
For the horizontal line, we can see that it passes through points
[tex]\begin{gathered} (x_1,\text{y}_1)=(0,7) \\ (x_1,y_2)=(4,6) \end{gathered}[/tex]the its slope (m) is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-7}{4-0}=\frac{-1}{4}=-\frac{1}{4}[/tex]Then, the line equation has the form
[tex]y=-\frac{1}{4}x+b[/tex]where b is the y-intercept. From the picture, we can see that the line crosses the y-axis at y=7, therefore, b=7. Then, the line equation for the horizontal line is
[tex]y=-\frac{1}{4}x+7[/tex]Similarly, we can apply the same procedure for the other line. We can see that it passes through points
[tex]\begin{gathered} (x_1,\text{y}_1)=(0,-2) \\ (x_2,\text{y}_2)=(4,6) \end{gathered}[/tex]Then, the slope (m) of this line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-(-2)}{4-0}=\frac{6+2}{4}=\frac{8}{4}=2[/tex]Then, the line equation has the form
[tex]y=2x+b[/tex]Since this line crosses y-axis at y=-2 then b=-2. Hence, the equation is
[tex]y=2x-2[/tex]In summary, the system of linear equations is:
[tex]\begin{gathered} y=-\frac{1}{4}x+7 \\ y=2x-2 \end{gathered}[/tex]If f(x) = x2 + x, find f(-3).-123O6
To find f(-3) we have to substitute x = -3 in the equation.
[tex]\begin{gathered} f(-3)=(-3)^2+(-3) \\ f(-3)=9-3 \\ f(-3)=6 \end{gathered}[/tex]If the line joining the points (a,4) and (2,-5) is parallel to the line with given equation 2x-3y=12 find the value of a
Parallel lines have the same slope, thus, using the equation of the parallel line, we can find out the slope of the line that passes through the given points.
To find the slope of a line given its equation, we have to put the equation into the slope-intercept form, whcih we can do by solving the equation for y:
[tex]\begin{gathered} 2x-3y=12 \\ -3y=-2x+12 \\ y=\frac{-2}{-3}x+\frac{12}{-3} \\ y=\frac{2}{3}x-4 \end{gathered}[/tex]The slope of the line is the coefficient multiplying x, which is 2/3 in this case.
So, let's name the slope m:
[tex]m=\frac{2}{3}[/tex]Since the lines are parallel, both have the same slope m.
Also, if we want to find the slope given two numbers on the line, we can use the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, we have the points (a, 4) and (2, -5) and we have the slope m = 2/3. Substituting these, we have:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}_{} \\ \frac{2}{3}=\frac{-5-4}{2-a} \\ \frac{2}{3}=\frac{-9}{2-a} \\ 2(2-a)=3\cdot(-9) \\ 4-2a=-27 \\ -2a=-27-4 \\ -2a=-31 \\ a=\frac{31}{2} \end{gathered}[/tex]Thus, the value of a is 31/2.
How many ounces of water must be added to 85oz of a 40% salt solution to make a solution that is 17% salt?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested value, so we obtain the following:
Accordingly, since the amount of salt remains the same, then we have the following equality, where x represents the amount of water that must be added:
0.4(85)=0.17(x+85)
Let's solve for x:
34=0.17x+14.45
0.17x=34-14.45
0.17x=19.55
x=19.55/0.17
x=115
Finally we obtain that must be added 115 ounces of water to make a solution that is 17% salt.
The table represents the cost to eat at a buffet-style restaurant.Number ofPeople (p)2Cost (C)(including tax)27.5441.3155.0868.85345682.62Which equation could be used to calculate the cost. C, for any number of people, p, to eat at the restaurant?
We need to take the values of the table and check which of the options fit with the results.
In the first line of the table we have p=2 and C=27.54.
Using the equation in option A, for p=2 we would get:
[tex]\begin{gathered} C=p+27.54 \\ C=2+27.54 \\ C=29.54 \end{gathered}[/tex]Which is not value for C in the table. Thus we discard option A.
Using the equation for option B, for the value of p=2, we would get:
[tex]\begin{gathered} C=13.77p \\ C=13.77(2) \\ C=27.54 \end{gathered}[/tex]Which is indeed the value of the table.
To confirm, we try now with the next value of p, p=3, and check if we get the same result with equation B as with the table:
[tex]\begin{gathered} C=13.77p \\ C=13.77(3) \\ C=41.31 \end{gathered}[/tex]Which is also the value for C in the table.
Thus we confirm that option B is the correct equation
could i have a fast answer please? if not it’s ok
Given:
Strip diagrams are given.
Option D represents the 175% .
Option D is the correct answer.
What is the quotient in simpilest form? 3/4÷5/16
the given expression is
[tex]\frac{\frac{3}{4}}{\frac{5}{16}}[/tex][tex]\frac{3\times16}{5\times4}=\frac{12}{5}=2.4[/tex]so the quotient will be 2.4
Find the values of x and y in the parallelogram.A46x+2211 BO x= 11, y = 24O x = 24, y = 11Ox=-11, y = 46O x=46, Y =-11
Since the opposite sides of a parallelogram are congruents, we can write the following equations:
[tex]\begin{cases}DA=BC \\ AB=CD\end{cases}[/tex]From the first one, we have:
[tex]y=11[/tex]From the second one, we have:
[tex]\begin{gathered} x+22=46 \\ x=46-22 \\ x=24 \end{gathered}[/tex]So we have x = 24 and y = 11, therefore the correct option is the second one.