Answers
Given:-
The sides of the rectangle are 5 and 9.
To find the area after each side is increased by x.
So after each side is increased by x. we get the side lengths as,
[tex](2x+5),(2x+9)[/tex]So now we use the formula,
[tex]\begin{gathered} A=l\times b \\ A=(2x+5)(2x+9) \\ A=4x^2+18x+10x+45 \\ A=4x^2+28x+45 \end{gathered}[/tex]So our required area is,
[tex]4x^2+28x+45[/tex]Related Questions
Find the sum of x^2 + 3x -2 and x^2 - x -4
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
x² + 3x - 2
x² - x - 4
Step 02:
polynomials (sum):
x² + 3x - 2 + (x² - x - 4)
x² + 3x - 2 + x² - x - 4
2x² + 2x - 6
The answer is:
2x² + 2x - 6
Look at this geometric sequence0.0625, 0.125, 0.25, 0.5, 1, ...What is the common ratio for the given sequence?
Answers
Given 0.0625, 0.125, 0.25, 0.5, 1, ...
The common ratio of a geometric sequence is the ratio between two consecutive terms.
[tex]\begin{gathered} r=\frac{T_2}{T_1}=\frac{T_3}{T_2}_{} \\ r=\frac{0.125}{0.0625}=2 \end{gathered}[/tex]Thus, the common ratio r is 2
on the next play the team gained 5 yards and then lost 6 yard what is the total change in yard
Answers
So in a play a team gains 5 yards but then they lose 6. One way to represent the total change in yards is given by adding the gained yards and substracting the lost yards:
[tex]5-6=5+(-6)=-1[/tex]Then the total change in yards is -1 and the total loss is 6. Then the boxes must be completed like:
Rewrite the polynomial in the form ar? + b3 + cand then identify thevalues of a, b, and c.- 92 - 2a =beSubmit Answer
Answers
a = -1
b = -9
c = -1/8
Explanation:
The given polynomial:
[tex]\frac{-1}{8}\text{ - 9x }-x^2[/tex]Rewritting in the form:
[tex]\begin{gathered} ax^2\text{ + bx + c} \\ -x^2\text{ - 9x -}\frac{1}{8} \end{gathered}[/tex]where a is the coefficient of x²
b is the coefficient of x
c is the constant (only number)
Comparing both equation:
ax² = -x²
If you divide through by x², a = -1
a = -1
bx = -9x
if you divide through by x, b = -9
b = -9
c = -1/8
Solve the following system of equations.x² + y² = 20x² + 5y²=48
Answers
Given the system of equations:
[tex]\begin{cases}x^2+y^2={20...(1)} \\ x^2+5y^2={48...(2)}\end{cases}[/tex]We subtract equation (1) from equation (2):
[tex]\begin{gathered} x^2+5y^2-x^2-y^2=48-20 \\ \\ 4y^2=28 \\ \\ y^2=7 \\ \\ \Rightarrow y=\pm\sqrt{7} \end{gathered}[/tex]We use this value to find the corresponding x-values. Using (1):
[tex]\begin{gathered} x^2+(\pm\sqrt{7})^2=20 \\ \\ x^2+7=20 \\ \\ x^2=13 \\ \\ \Rightarrow x=\pm\sqrt{13} \end{gathered}[/tex]Finally, the solutions are:
[tex]\begin{gathered} (x_1,y_1)=(-\sqrt{13},-\sqrt{7}) \\ \\ (x_2,y_2)=(-\sqrt{13},\sqrt{7}) \\ \\ (x_3,y_3)=(\sqrt{13},-\sqrt{7}) \\ \\ (x_4,y_4)=(\sqrt{13},\sqrt{7}) \end{gathered}[/tex]#8A 90-foot rope from the top of a tree house to the ground forms a 45° angle of elevation from the ground. How high is the topof the tree house? Round your answer to the nearest tenth of a foot.feet
Answers
Given: A 90-foot rope from the top of a tree house to the ground forms a 45° angle of elevation from the ground.
Required: To determine the height of the tree house.
Explanation: The given problem can be represented as follows-
In the figure, AC represents the rope, and AB is the tree house. We need to determine the length of AB.
Recall the trigonometric ratio-
[tex]sin\theta=\frac{OppSide}{Hypotenuse}[/tex]Thus, for triangle ABC we have-
[tex]sinC=\frac{AB}{AC}[/tex]Substituting the values and solving for AB as-
[tex]\begin{gathered} AB=90\cdot sin45\degree \\ =90\times\frac{1}{\sqrt{2}} \\ =63.6396\text{ ft} \\ \end{gathered}[/tex]Thus,
[tex]AB\approx63.6\text{ ft}[/tex]Final Answer: The top of the tree house is 63.6 ft high.
The height (in centimeters) of a candle is a linear function of the amount of time in hours) it has been burning. When graphed, the function gives a line with aslope of -0.5. See the figure below.Suppose that the height of the candle after 17 hours is 16.5 centimeters. What was the height of the candle after 13 hours?
Answers
From the question
The slope of the graph is
[tex]m\text{ = -0.5}[/tex]using the equation of a line
[tex]y\text{ = mx + c}[/tex]we can find the intercept C, where m is the slope of the line
From the question,
the height of the candle after 17 hours is 16.5 centimeters implies
[tex]\begin{gathered} x\text{ = 17 hours} \\ y\text{ = 16.5cm} \end{gathered}[/tex]Using this information we can get the intercept C.
Substitute the values of x, y and m into the equation of line
[tex]\begin{gathered} \text{x = 17, y = 16.5 , m = -0.5 } \\ y\text{ = mx + c} \\ 16.5\text{ = -0.5(17) + C} \\ 16.5\text{ = -8.5 + C} \\ 16.5\text{ + 8.5 = C} \\ C\text{ = 25} \end{gathered}[/tex]Now we need to find the height of the candle after 13hours
therefore, x = 13, m = -0.5, C = 25
[tex]\begin{gathered} y\text{ = mx + c} \\ y\text{ = -0.5(13) + 25} \\ y\text{ = -6.5 + 25} \\ y\text{ = 18.5} \end{gathered}[/tex]Therefore,
The height of the candle after 13hours is 18.5 centimeters
Question 1 of 10
Calculate the difference and enter it below.
-1-(0)
Answer here
Answers
multiply first the numbers
[tex]1\cdot7=7[/tex]then multiply the signs,
[tex]-\cdot-=+[/tex]according to this
[tex]-1\cdot-7=7[/tex]Parentheses are placed differently in each of the following expressions. Drag the tiles to match the correct answer with each of the expressions. Tiles may be used once, more than once, or not at all.16, 28, 88, 196,30 - 2 x 3 + 4 = ________( 30 - 2 ) x 3 + 4 = _______30 - 2 x ( 3 + 4) = ________(30 - 2) x (3 + 4 ) = ________
Answers
SOLUTION
[tex]\begin{gathered} 30-2\times3+4 \\ 30-6+4 \\ 24+4=28 \\ \\ \therefore30-2\times3+4=28 \end{gathered}[/tex]Next:
[tex]\begin{gathered} (30-2)\times3+4 \\ 28\times3+4 \\ 84+4=88 \\ \\ \therefore(30-2)\times3+4=88 \end{gathered}[/tex]Next:
[tex]\begin{gathered} 30-2\times(3+4) \\ 28\times7 \\ =196 \\ \\ \therefore30-2\times(3+4)=196 \end{gathered}[/tex]Lastly:
[tex]\begin{gathered} (30-2)\times(3+4) \\ 28\times7 \\ =196 \\ \\ \therefore(30-2)\times(3+4)=196 \end{gathered}[/tex]solve for x: x/5 - 6 = 8
Answers
EXPLANATION
Given the equation:
x/5 - 6 = 8 (Adding +6 to both sides)
x/5 -6 +6 = 8 +6 (Simplifying)
x/5 = 14 (Isolating x)
x = 14*5 (Multiplying)
x=70
Answer is x=70
You ate 8 apples in 5 days. At this rate how many apples will you eat in 20 days? Your answer
Answers
We can apply the rule of three to solve this:
[tex]\begin{gathered} 5\text{ days}\longrightarrow8\text{ apples} \\ 20\text{ days}\longrightarrow\frac{8}{5}\cdot20=8\cdot4=32\text{ apples} \end{gathered}[/tex]Answer: 32 apples.
Kala, Deandre and Hans sent a total of 104 text messages during the weekend. Hans sent 3 times as many messages as Kala. Deandre sent 9 more messages than Kala. How many messages did they each send?Solve by using linear equation
Answers
The first thing we have to do to solve this is to formulate equations that led us solve for the number of text each member of the group sent. By calling K, D and H to the texts sent by Kala, Deandre and Hans respectively, we can start writing an equation for the total number of texts, which was 104, the messages sent by each member of the group must add up to 104then we can write:
K + D + H = 104
We are also told that Hans sent 3 times as many messages as Kala, then the number of messages sent by Hans must equal the messages sent by Kala multiplied by 3 and we can write the following equation:
H = 3K
Lastly, we are told that Deandre sent 9 more messages than Kala, then the messages sent by Deandre must equal the messages sent by Kala added to 9 and we can write the following equation:
D = K + 9
By replacing 3K for H, K + 9 for D in K + D + H = 104, we get:
K + D + H = 104
K + (K + 9) + 3K = 104
From this equation we can solve for K like this:
K + K + 9 + 3K = 104
5K + 9 = 104
5K + 9 - 9 = 104 - 9
5K = 95
K = 95/5
K = 19
Then, Kala sent 19 text messages. In order to find the messages sent by the other members of the group we just have to replace 19 for K in H = 3K and D = K + 9, then we get:
H = 3(19) = 57
D = 19 + 9 = 28
SummaryNumber of text messages Kala sent: 19
Number of text messages Deandre sent: 28
Number of text messages Hans sent: 57
How many shares can you buy today with $20,000 of the company of your choice? I choose PepsiCo. and I belive the price share is $147.87 unless I'm wrong. I don't fully understand this question.
Answers
Since the CURRENT listed share price currently is given as $146.63.
With $20,000, we can buy;
[tex]\begin{gathered} \frac{20,000}{146.63}=136.39\approx\text{ 136 shares} \\ \end{gathered}[/tex]Therefore, we can buy 136 shares with $20,000
The table represents a function, Which value is an output of the function? O -6 X f(x) O-2 -6 co O 7 7 3 4 -5 3 -2 -5 12 Cauta
Answers
The outputs of the function are the values of f(x) once we give an specific value of x, in a table we find them at the right column.
Looking at the values and the options given we notice that the only output in the options is -2, the other opitons are inputs.
Therefore the answer is -2.
Can I help with this problem. If z varies inversely as w^2 and z = 10 when w = 2. Find z when w = 6
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First, we need the find the value of the constant k:
[tex]z=\frac{k}{w^2}[/tex]Then, we use the given values to find k. Therefore:
z = 10 when w = 2
[tex]10=\frac{k}{2^2}[/tex]And solve for k:
[tex]\begin{gathered} 10=\frac{k}{4} \\ 10\cdot4=4\cdot\frac{k}{4} \\ k=40 \end{gathered}[/tex]Now, when w = 6, z will be:
[tex]z=\frac{k}{w^2}=\frac{40}{6^2}=\frac{40}{36}=\frac{10}{9}[/tex]Answer:
[tex]z=\frac{10}{9}[/tex]4). Write "4 less than the product of a number and 5" as and algebraic expressions.Help I need ASAP
Answers
Problem
Write "4 less than the product of a number and 5" as and algebraic expressions.
Solution
Let x the number of interest we can write:
5x -4
help please on this question
Answers
To find x, first, we have to calculate the second leg of the bigger triangle using Pythagorean's Theorem.
[tex]\begin{gathered} 18^2=12^2+z^2 \\ z=\sqrt[]{324-144} \\ z=\sqrt[]{180}\approx13.4 \end{gathered}[/tex]Then, we find the acute angle in the triangle on the right.
[tex]\begin{gathered} \tan \theta=\frac{12}{18} \\ \theta=\tan ^{-1}(\frac{12}{18})\approx34 \end{gathered}[/tex]Now, using this angle, we find the other part that sums 18 with x.
[tex]\begin{gathered} \cos \theta=\frac{y}{13.4} \\ y=13.4\cdot\cos 34\approx11 \end{gathered}[/tex]Then, we subtract to find x
[tex]x=18-11=7[/tex]Hence, x = 7.Lucia paints a certain room in 5 hours, and Marie paints the same room in 8 hours. How long does it take them to paint the room if they work together? Round to the nearest tenth. _(blank)_ hoursType your numerical answer below.
Answers
We need to find the time, t, that it takes them to paint the room working together.
In order to do so, notice that rate at which each of them paint the room, assuming it has an area A to be painted, is:
[tex]\begin{gathered} \text{ Lucia: }\frac{A}{5h} \\ \\ \text{Marie: }\frac{A}{8h} \end{gathered}[/tex]Now, when they work together, Lucia will paint an area A₁, and Marie will paint an area A₂, such that
[tex]A_1+A_2=A[/tex]Also, notice that the area each one paints is given by the rate at which they paint multiplied by the time t they spend painting. So, we have:
[tex]\begin{gathered} A_1=\frac{A}{5h}\cdot t \\ \\ A_2=\frac{A}{8h}\cdot t \end{gathered}[/tex]Then, using those expressions for A₁ and A₂ in the equation relating their sum to A, we obtain:
[tex]\begin{gathered} \frac{A}{5h}\cdot t+\frac{A}{8h}\cdot t=A \\ \\ \frac{t}{5h}+\frac{t}{8h}=1\text{ (dividing both sides by A)} \\ \\ \frac{8t}{40h}+\frac{5t}{40h}=1 \\ \\ \frac{13t}{40h}=1 \\ \\ 13t=1\cdot40h \\ \\ 13t=40h \\ \\ t=\frac{40h}{13} \\ \\ t\cong3.1h \end{gathered}[/tex]Therefore, rounded to the nearest tenth, it takes them to paint the room working together
3.1 hours
Help An elevator can carry 39adults or 40 children at one time. During the course of a day, the elevator carries a full passenger load 53times. If all the passengers were children, how many more people would the elevator carry than if all the passengers were adults?
Answers
Solution:
Given:
[tex]\begin{gathered} An\text{ elevator can carry 39 adults at a time} \\ \\ OR \\ \\ It\text{ can also carry 40 children at a time} \end{gathered}[/tex]In a day, it carries a full passenger load 53 times.
If all passengers were children, then the elevator carried a total of;
[tex]53\times40=2120c\text{hildren}[/tex]If all passengers were adults, then the elevator carried a total of;
[tex]53\times39=2067\text{ adults}[/tex]Hence, to get how many more people the elevator will carry than if all passengers were adults, we get the difference in the two.
[tex]\begin{gathered} \text{Thus,} \\ \\ 2120-2067=53 \end{gathered}[/tex]Therefore, the elevator will carry 53 more people than if all the passengers were adults.
Find a polynomial with rational coefficients that has the given numbers as roots -4,-2, 2
Answers
Solution
We are told to find the polynomial that has the following roots -4, -2, 2.
Explanation
- In order to solve this question in the easiest manner, we will make use of the following rules:
1. Sum of roots
2. Product of roots
3. Sum of Product of roots.
1. Sum of roots:
The sum of roots of a cubic equation is defined as follows:
[tex]\begin{gathered} \text{Given the cubic equation:} \\ y=ax^3+bx^2+cx+d \\ \text{If the roots of the equation are: }\alpha,\beta,\gamma \\ \text{then,} \\ \\ \alpha+\beta+\gamma=-\frac{b}{a} \end{gathered}[/tex]2. Product of roots:
The product of roots of a cubic equation is defined as follows:
[tex]\alpha\times\beta\times\gamma=-\frac{d}{a}[/tex]3. Sum of Product of roots:
[tex]\alpha\beta+\alpha\gamma+\beta\gamma=\frac{c}{a}[/tex]- We have been given these roots to be -4, -2, and 2. Thus, we can apply the 3 formulas defined above to find the correct equation.
- This is done below:
[tex]\begin{gathered} Let\alpha=-4,\beta=-2,\text{ and }\gamma=2 \\ Also,\text{ let }a=1 \\ \\ -4+(-2)+2=-\frac{b}{a}=-\frac{b}{1} \\ -6+2=-b \\ \\ \therefore b=4 \\ \\ -4(-2)(2)=-\frac{d}{a}=-\frac{d}{1} \\ \therefore d=-16 \\ \\ -4(-2)+(-4)(2)+(-2)(2)=\frac{c}{a}=\frac{c}{1} \\ 8-8-4=c \\ \\ \therefore c=-4 \end{gathered}[/tex]Now that we have all the coefficients, we can write out the equation as follows:
[tex]f(x)=x^3+4x^2-4x-16[/tex]Final Answer
The answer is
[tex]f(x)=x^3+4x^2-4x-16\text{ (OPTION 4)}[/tex]In an elastic collision, an object with momentum of 25kg.m/s collided with another object with a momentum of 35kg.m/s moving to the right. After collision both objects are still moving to the right. But the first object’s momentum is now 10kg.m/s. What is the final momentum of the second object?
Answers
This is a situation about momentum conservation.
The total momentum of both objects must conserve, the, total momentum before collision and total momentum after collision must be equal:
p before = p after
p1 + p2 = p1' + p2'
where p1 and p2 are the momenta of both objects before the collision. p1' and p2' are the momenta of the same both objects after the collision.
p1 = 25kg.m/s
p2 = 35kg.m/s
p1' = 10kg.m/s
p2' = ?
In order to calculate the value of the momentum of the second object after the colliwion you solve the equation for p2', as follow:
p1 + p2 = p1' + p2'
p2' = p1 + p2 - p1' replace the values of all parameters
p2' = 25kg.m/s + 35kg.m/s - 10kg.m/s
p2' = 50kg.m/s
Hence, the final momentum of the second object is 50kg.m/s
f(x)=(x+3)^2 vertex___^a=____ y-int.___ does the parabola open up or down? Is the vertex a max or min? axis of symmetry
Answers
vertex (0,9)
a=1
y-int=9
As a>1 we get the parabola opens up
and the vertex is a min
and the axis of symmetry is x=0
Hi I need help with the rate of change part please
Answers
As we can see on the question, in 1997 we had a level of 3827 and as the time passes in 2001 we just have a level of 3417.8 which means The surface elevation of Lake Powell is decreasing. Now to calculate the decay rate we just need to calculate how many years was passed (2001 - 1997 = 4 year) and the amount that has decreased (3827 - 3517.8 = 309.2), Now we can calculate the rate as follows:
[tex]\text{DecayRate}=\frac{309.2}{4}=77.3[/tex]So our final answer is:
The surface elevation of Lake Powell is decreasing at a rate of 77.3 feet per year.
Find the volume of this squarebased pyramid.10 in12 in[ ? Jin
Answers
Given data:
The given figure.
The volume of the square pyramid is,
[tex]\begin{gathered} V=\frac{1}{3}(12\text{ in)(12 in)(10 in)} \\ =480in^3 \end{gathered}[/tex]Thus, the volume of the square pyramid is 480 cubic-in.
The height of a tree grows by four inches every year.Select the recursive rule which represents this situation.
Answers
We know that the tree grows by four each inches every year.
Then, we can say that the height of the tree in year n (an) is 4 inches more than the heignth of the tree in year (n-1) (a_n-1).
Then, we can write the recursive rule as:
[tex]a_n=a_{n-1}+4[/tex]3x-y=0.6 x-2y=-1.3 what would be the graphical solutuon for this system
Answers
A sketch of the graph that represents the solution to the system of equations is as shown below:
Option B (the second) is the correct graph
For what values of b will F(x) = log, xbe a decreasing function? O A. 0 < b< 1 O B. O> b>-1 b O c. bco O D. b>
Answers
Recall that a function is called decreasing if:
F(x)>F(y)
when y>x.
Let
[tex]xThen:
[tex]b^{log_bx}If 0[tex]log_bx>log_by,[/tex]Answer:
[tex]02. How much will it cost you to buy enough ham to serve 85 lb of cookedsliced ham if whole, bone-in hams weigh 18 lb AP, have an AP to ASwaste percentage of 44%, and cost $1.83 per AP pound?
Answers
What number reduced by 44% gives us 85?
We write:
x - 0.44x = 85
0.56 x = 85
x = 85/0.56
x = 151.79
Now,
We need to buy 151.79 pounds of ham, which is 152 pounds.
1.83 * 152 = $278.16
through: (2, -5), perp. to y= 1/4x+5
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Find the domain of the function ? what is the only value of x not in the domain answer in fraction form
Answers
Notice that f(x) is a rational function. In general, a rational function is defined for all values of the variable except for those that make the denominator equal to zero.
In our case,
[tex]f(x)=\frac{1}{6x-2}[/tex]Suppose that the denominator is equal to zero; then,
[tex]\begin{gathered} 6x-2=0 \\ \Rightarrow6x=2 \\ \Rightarrow x=\frac{2}{6} \\ \Rightarrow x=\frac{1}{3} \end{gathered}[/tex]Therefore, the only value of x not included in the domain of f(x) is x=1/3. The answer is 1/3.