X -5x+4 =015.x+6=0A rectangular painting is 3 feet shorter in length than it is tall (height).12. Write a polynomial to represent the area of the painting.13. Write a polynomial to represent the perimeter of the painting.14. The painting has the unique quality of having an area that has a value that is equal to the value of theperimeter. Find the height of the painting.15. What is the extraneous solution to the polynomial created when the area is set equal to the perimeter?
Answers
The rectangular painting is 3 feet shorter in length than in height.
Let "x" represent the painting height, then its length can be expressed as "x-3"
12.
The area of the rectangular painting can be calculated by multiplying its length by its height.
[tex]A=l\cdot h[/tex]For the painting
h=x
l=x-3
-Replace the formula with the expressions for both measurements:
[tex]A=(x-3)x[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} A=x\cdot x-3\cdot x \\ A=x^2-3x \end{gathered}[/tex]The polynomial that represents the area of the painting is:
[tex]A=x^2-3x[/tex]13.
The perimeter of a rectangle is calculated by adding all of its sides, or two times its length and two times its height. You can calculate the perimeter of the painting as follows:
[tex]P=2l+2h[/tex]We know that
h=x
l=x-3
Then the perimeter can be expressed as follows:
[tex]P=2(x-3)+2(x)[/tex]-Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} P=2\cdot x-2\cdot3+2x \\ P=2x-6+2x \end{gathered}[/tex]-Order the like terms together and simplify them to reach the polynomial:
[tex]\begin{gathered} P=2x+2x-6 \\ P=4x-6 \end{gathered}[/tex]14.
The painting has the unique quality of having an area that is equal to the value of the perimeter, then we can say that:
[tex]A=P[/tex]-Replace this expression with the polynomials that represent both measures:
[tex]x^2-3x=4x-6[/tex]To solve the expression for x, first, you have to zero the equation, which means that you have to pass all therm to the left side of the equation. Do so by applying the opposite operation to both sides of the equal sign.
[tex]\begin{gathered} x^2-3x-4x=4x-4x-6 \\ x^2-7x=-6 \\ x^2-7x+6=-6+6 \\ x^2-7x+6=0 \end{gathered}[/tex]We have determined the following quadratic equation:
[tex]x^2-7x+6=0[/tex]Using the quadratic formula we can calculate the possible values for x. The formula is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where
a is the coefficient that multiplies the quadratic term
b is the coefficient that multiplies the x term
c is the constant of the quadratic equation
For our equation the coefficients have the following values:
a=1
b=-7
c=6
Replace these values in the formula and simplify:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4\cdot1\cdot6}}{2\cdot1} \\ x=\frac{7\pm\sqrt[]{49-24}}{2} \\ x=\frac{7\pm\sqrt[]{25}}{2} \\ x=\frac{7\pm5}{2} \end{gathered}[/tex]Next is to calculate the addition and subtraction separately:
-Addition
[tex]\begin{gathered} x=\frac{7+5}{2} \\ x=\frac{12}{2} \\ x=6 \end{gathered}[/tex]-Subtraction
[tex]\begin{gathered} x=\frac{7-5}{2} \\ x=\frac{2}{2} \\ x=1 \end{gathered}[/tex]The possible values of x, i.e., the possible heights of the painting are:
x= 6ft
x=1 ft
15.
To determine the extraneous solution created when the area was set equal to the perimeter you have to calculate the corresponding length for both possible values of the height:
For the height x= 1ft, the corresponding length of the painting would be -2ft. This value, although mathematically correct, is not a possible measurement for the painting's length since these types of measures cannot be negative.
Related Questions
How many terms do you have in the expression 7x - 2y + 8?
Answers
Answer:
3 terms we have constant ,Y and X terms
The height of a diver above the water’s surface can be modeled by the function h(t)= –16t^2+ 8t + 48. How long does it take the diver to hit the water? Solve by factoring
Answers
Given the function:
[tex]h(t)=-16t^2+8t+48[/tex]Where h(t) is the height of the diver above the surface of the water and t is the time.
Let's find how long it takes the diver to hit the water.
When the diver hits the water, the height h(t) = 0.
Now substitute 0 for h(t) and solve for the time t.
We have:
[tex]0=-16t^2+8t+48[/tex]Rearrange the equation:
[tex]-16t^2+8t+48=0[/tex]Solve for t.
Let's factor the expression by the left.
Factor 8 out of all terms:
[tex]8(-2t^2+t+6)=0[/tex]Now, factor by grouping.
Rewrite the middle term as a sum of two terms whose product is the product of the first term and the last term:
[tex]\begin{gathered} 8(-2t^2+4t-3t+6)=0 \\ \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 8((-2t^2+4t)(-3t+6))=0 \\ \\ 8(2t(-t+2)+3(-t+2))=0 \\ \\ 8(2t+3)(-t+2)=0 \end{gathered}[/tex]Hence, we have the factors:
[tex]\begin{gathered} 2t+3=0 \\ -t+2=0 \end{gathered}[/tex]Solve each factor for t:
[tex]\begin{gathered} 2t+3=0 \\ \text{ Subtract 3 from both sides:} \\ 2t=-3 \\ \text{ Divide both sides by 2:} \\ \frac{2t}{2}=-\frac{3}{2} \\ t=-\frac{3}{2} \\ \\ \\ -t+2=0 \\ t=2 \end{gathered}[/tex]Hence, we have the solutions:
t = -3/2
t = 2
The time cannot be negative, so let's take the positive value.
Therefore, the will take 2 seconds for the diver to hit the water.
ANSWER:
2 seconds.
14 Tom can whitewash a fence alone in 4 hours, and Huck can whitewash the same fence in 5 hours working by himself. Tom whitewashes with Huck for 1 hour and then leaves. How long will it take Huck to finish whitewashing the fence?
Answers
Given:
Time it takes Tom = 4 hours
Time it takes Huck = 5 hours
Tom then whitewashes with Huck for 1 hour and then leaves.
Let's find how long it will take Huck to finish whitewashing the fence.
We have:
Tom's rate = 1/4
Huck's rate = 1/5
Total rate:
[tex]\frac{1}{4}+\frac{1}{5}=x[/tex]Now, let's find the time it will take them to whitewash together.
[tex]\begin{gathered} \frac{1}{T}=\frac{5+4}{20} \\ \\ \frac{1}{T}=\frac{9}{20} \\ \\ T=\frac{20}{9} \\ \\ T=2.22 \end{gathered}[/tex]It will take them 2.22 hours to whitewash together.
Now they both whitewash together for 1 hour before Huck leaves.
We have:
[tex]2.22-1=1.22[/tex]When Huck leaves after one hour, the time left for both of them to finish together is 1.22 hours.
Since only Huck will finish whitewashing the fence, the time it will take him will be:
[tex]5(1-\frac{1.22}{2.22})=2.25[/tex]Therefore, it will take Huck to finish whitewashing the fence is 2.25 hours.
ANSWER:
2.25 hours
5. Find the arclength that subtends a central angle of 175° in a circle with radius 3 feet.
Answers
As given by the question
There are given that the central angle is 175 degrees and the radius is 3 feet.
Now,
The length of an arc given it subtends a known angle at the centre is:
[tex]\text{arc length=2}\times\pi\times r\times\frac{175}{360}[/tex]Then,
[tex]\begin{gathered} \text{arc length=2}\times\pi\times r\times\frac{175}{360} \\ \text{arc length=2}\times3.14\times3\times\frac{175}{360} \\ \text{arc length=}9.16 \end{gathered}[/tex]Hence, the arclength is 9.16.
Find the average rate of change of the following function from t = 1 to t=2.5h(t) = 148 – 16t
Answers
The average rate of change of the function from t=1 to t=2.5 is given by:
[tex]\frac{h(2.5)-h(1)}{2.5-1}=\frac{h(2.5)-h(1)}{1.5}[/tex]It is given that:
[tex]\begin{gathered} h(t)=148-16t \\ h(2.5)=148-16\times2.5=108 \\ h(1)=148-6=142 \end{gathered}[/tex]Substitute the values to get:
[tex]\frac{h(2.5)-h(1)}{1.5}=\frac{108-142}{1.5}=\frac{-68}{3}\approx-22.6667[/tex]Hence the rate of change is -22.6667.
in a 30 60 90° triangle giving the short leg equals 5 find a hypotenuse of the triangle
Answers
To answer this question we need to remember that the longest and shortest side in any triangle are always opposite to the largest and smallest angle, respectively.
With this in mind we can draw the triangle:
Now, we need to find the hypotenuse. To do this we can use the cosine function for the angle 60. Remember that the cosine function is given as:
[tex]\cos \theta=\frac{\text{adj}}{\text{hyp}}[/tex]In this case we have that:
[tex]\begin{gathered} \cos 60=\frac{5}{\text{hyp}} \\ \text{hyp}=\frac{5}{\cos 60} \\ \text{hyp}=10 \end{gathered}[/tex]Therefore the hypotenuse is 10.
Hey there Mr or Ms could you help me out here with this problem? Just a head up this isn't a quiz, it's my homework assignment for today it's about Squares and Rhombi.
Answers
please see the attched figure o better understand the problem
Applying the Pythgorean Theorem
d^2=b^2+b^2
we have
b=10 units
substitute
d^2=10^2+10^2
d^2=100+100
d^2=200
[tex]d=\sqrt[]{200}[/tex]simplify
[tex]d=10\sqrt[\text{ }]{2\text{ }}\text{ units}[/tex]the diagonal is
[tex]d=10\sqrt[\text{ }]{2\text{ }}\text{ units}[/tex]Need answer for 3a please. This is for homework :)
Answers
Given the supplementary angle below for 3a,
Supplementary angles is 180°,
To find x,
[tex]\begin{gathered} 132^0+2x^0+3=180 \\ 2x^0+135^0=180^0 \\ 2x^0=180^0-135^0 \\ 2x^0=45^0 \\ x=\frac{45^0}{2}=22.5^0 \\ x=22.5^0 \end{gathered}[/tex]Hence, x = 22.5°
Vera cut a piece of fabric into 5 equal-length pieces. Then she cut another 3 centimeters off one piece, leaving 6 centimeters of fabric. How many centimeters long was her original piece of fabric? Write two equations with letters for the unknowns. Solve.
Answers
We have
fabric cut into 5 equal -length pieces
she cut 3 cm
l=length of one piece of the 5 equals pieces
l=6+3
l=9
the original piece of fabric is
o= length of the original fabric
o=5l
o=5(9)
o=45 cm
the original piece of fabric is 45 cm
how many hours did the plumber work to fix the plumbing
Answers
The total cost of the fix is C = $375.
The plumber charges a fixed rate per call of F = $50 and charges a variable rate of v = $25 per hour, if h is the number of hours he worked, we can write:
[tex]\begin{gathered} C=F+v\cdot h \\ 375=50+25\cdot h \end{gathered}[/tex]This equation shows that the total cost is equal to the fixed cost plus the variable cost. The variable cost is equal to the hourly rate times the number of hours of work.
Then, we can calculate h as:
[tex]\begin{gathered} 375=50+25h \\ 375-50=25h \\ 325=25h \\ h=\frac{325}{25} \\ h=13 \end{gathered}[/tex]Answer: he worked 13 hours.
NOTE:
Table of values:
If we need to use a table of values to solve this, we will have two columns: one for the number of hours and the other for the total cost.
We can make the table have more detail and separate the cost column in 3: one for the fixed cost, one for the variable cost and the last one for the total cost.
Then, we would write in each column:
1) Hours: the number of hours, from 0 to the amount we consider.
2) Fixed cost: this column will have the value $50 for all the rows, as it is independent of the number of hours.
3) Variable cost: this column will have values proportional to the hours. This values will be 25 times the number of hours.
4) Total cost: this column will add both the fixed cost and variable cost.
Then, we will obtain the following table.
We can now look for the value $375 in the Total cost column.
We find that this cost correspond to 13 hours:
Graph:
We can now use the data from the table to graph the total cost in function of the number of hours.
Adele opens an account with $140 and deposits $35 a month. Kent opens an account with $50 and also
deposits $35 a month. Will they have the same amount in their accounts at any point? If so, in how many
months and how much will be in each account? Complete the explanation.
have the same amount in their accounts at a certain point. Setting the expressions equal
which is (select)
and solving them gives 140=
They (select)
to each other gives 140 + 35x =
View Exampl
Step-by-Stepm
Textbook
Print
Turn it in
Save & Close
Answers
Answer: No
Step-by-step explanation:
If Adele opens an account with more money than Kent, and they deposit the same amount each month, Adele will always have more money than Kent.
9. As a speed skater, Kyle cycles between sprinting and recovering on the 111.12-meter short track during practice every day for 50 minutes. Let t be the time in hours that Kyle sprints during a practice. A. Write the unsimplified expression to represent the total distance Kyle skates. It may help you to make a verbal model to represent the total distance Kyle skates. Be sure to use compatible units.
Answers
SOLUTIONS
As a speed skater, Kyle cycles between sprinting and recovering on the 111.12 meter short track during practice every day for 50 minutes.
Let t be the time in hours that Kyle sprints during practice.
Sprint Speed: 48 km/hr
Recovery: 18 km/hr
(a)
Write an unsimplified expression to represent the total distance Kyle skates.
[tex]speed=\frac{distance}{time}[/tex]If t= time sprinting then (50-t)= time recovering
Distance = rate x time= t(48) + (50-t)18
Distance = 111.2m
(c) Simplifying the expression
A) equation in center radius form B) equation in general form
Answers
The equation of a circle in center-radius form, is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]-Where the coordinates of the center of the circle are (h,k) and the radius of the circle is r.
From the given graph, we can see that the coordinates of the center are (-2,4) and the radius of the circle is 2.
a)
To determine the equation of the circle in center-radius form, replace h=-2, k=4 and r=2
[tex]\begin{gathered} \Rightarrow(x-(-2))^2+(y-(4))^2=2^2 \\ \Rightarrow(x+2)^2+(y-4)^2=4 \end{gathered}[/tex]Therefore, the equation of the circle in center-radius form is:
[tex](x+2)^2+(y-4)^2=4[/tex]b)
To find the equation of the circle in general form, expand the parentheses and take all the terms to the left member:
[tex]\begin{gathered} (x+2)^2+(y-4)^2=4 \\ \Rightarrow x^2+2(2)(x)+(2)^2+y^2-2(4)(y)+4^2=4 \\ \Rightarrow x^2+4x+4+y^2-8y+16=4 \\ \Rightarrow x^2+4x+y^2-8y+20=4 \\ \Rightarrow x^2+4x+y^2-8y+20-4=0 \\ \Rightarrow x^2+4x+y^2-8y+16=0 \end{gathered}[/tex]Write the quadratic terms first:
[tex]\Rightarrow x^2+y^2+4x-8y+16=0[/tex]Therefore, the equation of the circle in general form, is:
[tex]x^2+y^2+4x-8y+16=0[/tex]1/4×3/2×8/9 whats the answer?
Answers
Multiply the given fractions to find the answer, use the given example:
Now, solve the given multiplication:
[tex]\frac{1}{4}\cdot\frac{3}{2}\cdot\frac{8}{9}=\frac{1\cdot3\cdot8}{4\cdot2\cdot9}=\frac{24}{72}=\frac{1}{3}[/tex]The answer is 1/3.
Using the Distributive Property, which of the following expressions are equivalent to 7 x 6? Select all that apply. A. (6 x 7)+(6 x 7)
B. (5×6) + (2 × 6)
C. (7 x 6) + (1 x 6)
D. (7 x 6) + (2 x 6)
E. (2 x 6)+(5 x 6)
Answers
By using the Distributive Property, the equivalent expression to 6 x 7 is option (B) (5 x 6) + (2 x 6) and option (E) (2 x 6) + (5 x 6).
Distributive property:
The distributive Property defines that when a factor is multiplied by the addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.
This property can be stated symbolically as:
A ( B+ C) = (A x B) + (A x C)
Where A, B and C are three different values.
Given,
Here we have the expression 7 x 6.
Now, we need to find the equivalent expression by using the distributive expression.
AS per the definition of distributive property,
First we have o identify in which term is got separated,
Here they separated the term 7.
So, there three way for dividing it,
They are,
6 + 1 = 7
2 + 5 = 7
3 + 4 = 7
Based on these, we have two way to write the expression,
one is,
(5 x 6) + (2 x 6)
Another way is,
(2 x 6) + (5 x 6)
So, the correct options are option (B) and (E).
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Can u guys simplify this?
(2x^-3y^5)^2*(x^7y^-11)
Answers
Choose all true inequalities from the list below.3 < 8-8 < -3-5 < -2118 > 4
Answers
ANSWER and EXPLANATION
We want to identify which of the inequalities are correct.
For the inequality to be correct, the left and right-hand sides of the inequality must agree with
molly has 12 stickers 1/3 of her stickers are blue exactly how many stickers are not blue
Answers
Answer:
8 stickers
Step-by-step explanation:
beacuse 1/3 =4 4x3 =12 12-4=8 here you go:)
what is the domain of this exponential function y=2x-8+2
Answers
The given function is
[tex]y=2^{x-8}+2[/tex]The domain is all real numbers, but the range would be all the real numbers greater than 2 because the function approximates to y = 2.
Hence, the answer is the first option.Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
Answers
The amount by which the cost of 1 liter of permimum gasoline is greater is $0.43.
By how much is permimum gasoline greater?The first step is to determine the cost of 1 liter of each type of gasoline. In order to determine the cost of 1 liter, divide the total cost by the number of liters of gasoline bought.
Cost of 1 liter of gasoline = total cost / total liters bought
Cost of 1 liter of regular gasoline = $58.98 / 25 = $2.36
Cost of 1 liter of permimum gasoline = $69.73 / 25 = $2.79
Difference in price = $2.79 - $2.36 = $0.43
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Why is it important to
line up the digits in each place-value position when subtracting?
Answers
Answer: it’s important because when you do that it makes it easier to remember what’s not a whole number and what is
Step-by-step explanation: the answer is basically the explanation
simplify-6u^2 v-u^v^2-22u^2v^2
Answers
simplify-6u^2 v-u^v^2-22u^2v^2
we have
[tex]undefined[/tex]how much of each ingredient would you need to make an identical recipe that serves 8 people explain your reasoning
Answers
LITERS OF SODA
24 people calls for 4 liters of lemon soda
18 people calls for x liters of lemon soda
24 people = 4 liters
18 people = x
cross multiply
24x = 72
Divide both-side of the equation by 24
x = 3
18 peoples calls for 3 liters of soda
PINT OF SHERBET
24 people calls for 2 pint of sherbet
18 people calls for x pint of sherbet
24 people = 2 pint
18 people = x
cross-multiply
24x = 36
Divide both-side of the equation by 24
x =1.5
18 peoples calls for 1.5 pint of sherbet
CUPS OF RICE
24 peoples calls for 6 cups of rice
18 people calls for x cups of rice
24 people = 6 cups of rice
18 people = x
cross multiply
24x = 108
Divide both-side of the equation by 24
x=4.5
18 people calls for 4.5 cups of rice
Hence, 18 people calls for; 3 liters of soda, 1.5 pint of sherbet and 4.5 cups of rice
I really need help please
Answers
The surface area of the given figure is the sum of the area of the six faces.
Two of them have an area A1:
A1 = 2.5 x 4 ft² = 10 ft²
Other two have an area A2:
A2 = 1.25 x 2.5 ft² = 3.125 ft²
and the other two have an area A3:
A3 = 1.25 x 4 ft² = 5 ft²
Then, the total surface area is:
AT = 2(A1) + 2(A2) + 2(A3)
AT = 2(10 ft²) + 2(3.125 ft²) + 2(5 ft²)
AT = 36.25 ft²
Hence, the total surface area of the given figure is 36.25 ft²
how many cheese pizzas can the girls buy if they pool all their money together? inequality form for each scenario. CHEESE PIZZA IS 7.25 DOLLARS.
Answers
Since we have 5 girls and their parents give each other $10, they have in total $50.
Now, let x be the number of pizzas they buy, since each pizza cost $7.25 the total cost for x pizzas is:
[tex]7.25x[/tex]this should be less or equal to $50 (otherwise the girls go over budget), then the inequality that represents this situation is:
[tex]7.25x\leq50[/tex]Now, solving the inequality we get:
[tex]\begin{gathered} 7.25x\leq50 \\ x\leq\frac{50}{7.25} \\ x\leq6.9 \end{gathered}[/tex]Therefore, they can buy a maximum of 6 pizzas without going over budget.
In 2002, the population of Isosceles City was 200,000. If expected growth is 10% per year, what will the expected population be in 2010?
Answers
The expected population in [tex]2010[/tex] will be [tex]428,717.762[/tex].
In [tex]2002[/tex] the population of Icosceles city was [tex]200,000[/tex].
The expected growth per year [tex]=10%[/tex]%
We have to find the expected population in [tex]2010[/tex].
From [tex]2002[/tex] to [tex]2010[/tex] the total years are [tex]8[/tex].
Since the population is increased every year so the population of previous year added. So we can see that the population is increased compound. We can find the total population by multiplying the population in 2002 with the rate assembled by one. So we can use the formula
Total population in [tex]2010=[/tex]Population in [tex]2002(1+\frac{rate}{100})^{year}[/tex]
Total population in [tex]2010=[/tex] [tex]2010=200,000(1+\frac{10}{100})^{8}[/tex]
Total population in [tex]2010=200,000(1+\frac{1}{10})^{8}[/tex]
Total population in [tex]2010=200,000(\frac{11}{10})^{8}\\[/tex]
Total population in [tex]2010=200,000(\frac{214,358,881}{100000000} )[/tex]
Total population in [tex]2010=200,000(2.14,358,881)[/tex]
Total population in [tex]2010=428717.762[/tex]
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In the similaritytransformation of AABCto ADEF. ABC was dilatedby a scale factor of 1/2reflected across the !? 1,and moved through thetranslation [1.
Answers
Solution: C. Y-Axis
Analysis: In this case, the triangle is reflected across the Y-Axis. That's the reason why the triangle changes the orientation of the initial triangle.
Example: Point B reflects Point E. X=2 to X=-2. And the value of Y stands.
can you help me with discount tax tip and markup
Answers
Answer:
Final Price = $24.5
Explanation:
To found the final price, we first need to find 30% of $35 as follows:
[tex]35\times30\text{ \% = 35}\times\frac{30}{100}=10.5[/tex]So, there will be a discount of $10.5
Then, the final price will be the original price less the 30% of $35, so the final price will be equal to:
Final Price = Original Price - Discount
Final Price = $35 - $10.5
Final Price = $24.5
So, the answer is $24.5
GEOMETRY Draw the next two figures in the pattern shown below. OOO
Answers
Given , the pattern
O , OO , .....
so, the first term is 1 circle
The second is 2 circles
So, the next two figures are:
OOO , OOOO
Camden, a florist, is dividing 56 flowers equally into 8 bouquets. He uses division to find that he can put 7 flowers in each bouquet. Which subtraction equation could he use to check his answer?
Answers
The subtraction equation that Camden could use to check his answer is, x = 56 - 8 x 7.
What is a subtraction equation?A subtraction equation is an equation, which is a mathematical statement that two mathematical expressions share equality, which involves the use of the subtraction operation.
The result of a subtraction operation is known as the difference. The other parts of a subtraction operation are the minuend and the subtrahend.
The total number of flowers for the bouquets = 56
The number of bouquets = 8
The number of flowers for each bouquet = 7 (56/8)
Check:
x = 56 - 7 x 8
x = 56 - 56
x = 0
To check if the answer is correct, Camden should multiply 7 by 8 and then subtract the product from 56.
Thus, the difference in the subraction equation x = 56 - 8 x 7 that Camden used is zero, showing that his earlier division operation was correct.
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