The area of a rectangular wall on a barn is 80 ft². Its length is 6 feet longer than twice its width. Find the length and width of the wall of the barn.
Answers
The area of the rectangular barn is 80 ft².
Let "l" represent the length of the barn and "w" represent the width.
You know that the length is 6ft longer than twice the width.
The length of the wall can be expressed as follows:
[tex]l=2w+6[/tex]The area of the rectangular wall is equal to the product of the length and width:
[tex]A=lw[/tex]Write the formula using A=80 and l=2w+6
[tex]\begin{gathered} A=lw \\ 80=(2w+6)w \end{gathered}[/tex]Distribute the multiplication on the parentheses term:
[tex]\begin{gathered} 80=(2w+6)w \\ 80=2w*w+6*w \\ 80=2w^2+6w \end{gathered}[/tex]Zero the equation by subtracting 80 to both sides of the equal sign:
[tex]\begin{gathered} 80-80=2w^2+6w-80 \\ 0=2w^2+6w-80 \end{gathered}[/tex]The expression obtained is a quadratic equation, to determine the possible values of "w" you have to use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Where
a is the coefficient of the quadratic term
b is the coefficient of the x-term
c is the constant
For this exercise, the independent variable is "w" and the coefficients are:
a=2
b=6
c=-80
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ w=\frac{-6\pm\sqrt{6^2-4*2*(-80)}}{2*2} \end{gathered}[/tex]Simplify as much as possible:
[tex]\begin{gathered} w=\frac{-6\pm\sqrt{6^2-4*2*(-80)}}{2*2} \\ w=\frac{-6\pm\sqrt{36-640}}{4} \\ w=\frac{-6\pm\sqrt{676}}{4} \\ w=\frac{-6\pm26}{4} \end{gathered}[/tex]Next, solve the sum and difference separately:
- Sum:
[tex]\begin{gathered} w=\frac{-6+26}{4} \\ w=\frac{20}{4} \\ w=5ft \end{gathered}[/tex]-Difference
[tex]\begin{gathered} w=\frac{-6-26}{4} \\ w=-\frac{32}{4} \\ w=-8ft \end{gathered}[/tex]The possible values of w are 5ft and -8ft.
Now, the width is a dimension, and thus it cannot be negative. So, although w=-8ft is mathematically correct, it is not a valid value for the width of the wall.
Then, the width of the wall is w=5ft.
Related Questions
The following table gives the cost, C(n), of producing a certain good as a linear function of n, the number of units produced. Use the information in this table to answer the questions that follow it. a. Evaluate each of the following expressions. Give economic interpretation of each. C(200) = _______ C(200) - C(150) = ________ C(200) - C(150) / 200 - 150 = _______ b. Estimate C(0). _______ c. the fixed cost of production is the cost incurred before any goods are produced. The unit cost is the cost of producing an additional unit. Find a formula for C(n) in terms of n, given that: Total cost = fixed cost + unit cost x number of units C(n) = _________
Answers
a. Based on the table, when 200 units is produced, the cost of production is $12,100 hence, C(200) = $12,100.
On the other hand, when 150 units is produced, the cost of production is $12,000 hence, C(150) = $12,000.
Subtracting C(200) - C(150), we have $100.
Dividing this result $100 by the difference of 200 and 150, we get 2.
[tex]\frac{C(200)-C(150)}{200-150}=\frac{12,100-12,000}{50}=\frac{100}{50}=2[/tex]b. Estimate C(0).
Based on the answers in letter a, we can see that for every additional unit produced, the additional cost of production is $2.
So, if we subtract 100 units, there will be 2*100 = $200 less on the cost of production.
From $11, 900 total cost of production of 100 units as shown in the table, we remove 100 units that cost $200, the total cost of production will now be $11, 700. Hence, at 0 units produced, the cost of production is $11, 700. C(0) = $11, 700.
c. Based on the answer in letter b, with 0 units produced, there is already a fixed cost of $11, 700.
Based on the answer in letter a, the unit cost per number of units produced is $2. If "n" is the number of units produced, the additional cost is 2n.
With these information, the formula for the finding the total cost of production is:
[tex]\begin{gathered} C(n)=FixedCost+(UnitCost\times no.ofunits)\text{ } \\ C(n)=11,700+2n \end{gathered}[/tex]
For this question it is asking for the mean, standard deviation, Q1, Q3, lower fence, and upper fence
Answers
Step 1
Given;
[tex]10,\:15,\:19,\:52,\:34,\:44,\:47,\:20,\:60,\:25[/tex]Step 2
Find the mean
[tex]\begin{gathered} The\:arithemtic\:mean\:\left(average\right)\:is\:the\:sum\:of\:the\:values\:in\:the\:set\: \\ \begin{equation*} divided\:by\:the\:number\:of\:elements\:in\:that\:set. \end{equation*} \\ \mathrm{If\:our\:data\:set\:contains\:the\:values\:}a_1,\:\ldots \:,\:a_n\mathrm{\:\left(n\:elements\right)\:then\:the\:average}= \\ \frac{\sum x}{n}=\frac{326}{10}=32.6 \end{gathered}[/tex]Step 3
Find the standard deviation
[tex]S\mathrm{tandard\:deviation,\:}\sigma\left(X\right)\mathrm{,\:is\:the\:square\:root\:of\:the\:variance:}\sigma\left(X\right)=\sqrt{\frac{\sum(x_i-\mu)^2}{N}}[/tex][tex]Standard\text{ deviation=}17.28326[/tex]Step 4
Find Q1
[tex]\begin{gathered} The\:first\:quartile\:is\:computed\:by\:taking\:the\:median\:of\:the\:lower\:half\:of\:a\:sorted\:set \\ Arrange\text{ in ascending order} \\ 10,\:15,\:19,\:20,\:25,\:34,\:44,\:47,\:52,\:60 \\ Take\text{ the lower half of the ascending set} \\ 10,15,19,20,25 \\ Q_1=19 \end{gathered}[/tex]Step 5
Find Q3
[tex]\begin{gathered} \mathrm{The\:third\:quartile\:is\:computed\:by\:taking\:the\:median\:of\:the\:higher\:half\:of\:a\:sorted\:set.} \\ Arrange\text{ the terms in ascending order} \\ 10,\:15,\:19,\:20,\:25,\:34,\:44,\:47,\:52,\:60 \\ Take\text{ the upper half of the ascending term} \\ 34,44,47,52,60 \\ Q_3=47 \end{gathered}[/tex]Step 6
Find the lower fence
[tex]\begin{gathered} =Q_1-1.5(IQR) \\ IQR=Q_3-Q_1=47-19=28 \\ =19-1.5(28)=-23 \end{gathered}[/tex]Step 7
Find the upper fence
[tex]\begin{gathered} =Q_3+1.5(IQR) \\ =47+1.5(28)=89 \end{gathered}[/tex]GOF and DISERBUHVE PROPERE25 + 20
Answers
the given expression is
= 25 + 20
now we can break these numbers'
[tex]=5\times5+5\times4[/tex](we know that 5 x 5 = 25
and 5 x 4 = 20)
now we can take greatest common factor 5 as common, then
[tex]\begin{gathered} =5\times(5+4) \\ =5\times9 \\ =45 \end{gathered}[/tex]so the answer is 45
Page 112 question 7 part 8 which equation matched the following graph A f(x)=2^xBf(x)=-2^xC f(x)=-2^xDf(x)=-3x2^x
Answers
EXPLANATION
The given graph corresponds to the function f(x)= -2^x
Graph the system of equation on the grid below in the mark their point of intersections (point c )y = 3x + 3y = x + 5
Answers
Given
y=3x+3
y=x+5
Procedure
Choose the answer with the proper number of sig figs
Answers
the answer is
[tex]69\times10^9[/tex]tionables wiin two-step rulesFill in the table using this function rule.y=2x+3Xv2D6DIDIOD810
Answers
Evaluating a function means finding the value of a function that corresponds to a given value of x. To do this, simply replace all the x variables with whatever x has been assigned.
Our function is
[tex]y=2x+3[/tex]For the given values on the table, we have the corresponding y values
[tex]\begin{gathered} y(2)=2\cdot(2)+3=4+3=7 \\ y(6)=2\cdot(6)+3=12+3=15 \\ y(8)=2\cdot(8)+3=16+3=19 \\ y(10)=2\cdot(10)+3=20+3=23 \end{gathered}[/tex]I need to find area of them composite shape please
Answers
Answer:
[tex]A=1,026\imaginaryI n^2[/tex]Explanation: We have to find the total area of the figure shown, the total area would be the area of the triangle and the square:
[tex]\begin{gathered} A=A_T+A_S\rightarrow(1) \\ \\ A_T=\frac{1}{2}(B\times H) \\ \\ A_S=S^2 \end{gathered}[/tex]plugging in the unknowns in the equation (1) gives the answer as follows:
[tex]\begin{gathered} H=35in \\ \\ \\ B=\sqrt{37in^2-35in^2} \\ \\ \\ A_T=2\times\frac{1}{2}(BH)=(35in\times\sqrt{37\imaginaryI n^2-35\imaginaryI n^2}) \\ \\ \\ A_T=(35in\times\sqrt{37\mathrm{i}n^2-35\mathrm{i}n^2})=35in\times\sqrt{144}=35in\times12in^2 \\ \\ \\ A_T=420in^2 \\ \\ \\ A_S=S^2 \\ \\ \\ S=2\times B=2\times12in=24in \\ \\ \\ A_S=24in^2=576in^2 \\ \\ \\ A=A_T+A_S\Rightarrow A=420in^2+576in^2 \\ \\ \\ A=1,026in^2 \end{gathered}[/tex]Solve the following system of equations using an inverse matrix. You must alsoindicate the inverse matrix, A-1, that was used to solve the system. You mayoptionally write the inverse matrix with a scalar coefficient.2x-3y = -55x - 4y = -2Al=y =
Answers
The two equations given are:
[tex]\begin{gathered} 2x-3y=-5 \\ 5x-4y=-2 \end{gathered}[/tex]The coefficient matrix A is:
[tex]A=\begin{bmatrix}2 & -3 \\ 5 & -4\end{bmatrix}[/tex]The variable matrix X is:
[tex]X=\begin{bmatrix}x \\ y\end{bmatrix}[/tex]and the constant matrix B is:
[tex]B=\begin{bmatrix}-5 \\ -2\end{bmatrix}[/tex]Then, AX = B looks like,
[tex]\begin{gathered} AX=B \\ X=A^{-1}B \end{gathered}[/tex]So, the variables "x" and "y" are found my multiplying the inverse of A by the matrix B.
Let's find the inverse matrix of A:
Given, a 2 x 2 matrix,
[tex]A=\begin{bmatrix}a & b \\ c & d\end{bmatrix}[/tex]The inverse of this matrix will be,
[tex]A^{-1}=\frac{1}{ad-bc}\begin{bmatrix}d & -b \\ -c & a\end{bmatrix}[/tex]Using the formula, we have:
[tex]\begin{gathered} A^{-1}=\frac{1}{-8--15}\begin{bmatrix}-4 & 3 \\ -5 & 2\end{bmatrix} \\ =\frac{1}{7}\begin{bmatrix}-4 & 3 \\ -5 & 2\end{bmatrix} \\ =\begin{bmatrix}-\frac{4}{7} & \frac{3}{7} \\ -\frac{5}{7} & \frac{2}{7}\end{bmatrix} \end{gathered}[/tex]Now, we can solve for the matrix X, shown below:
[tex]X=\begin{bmatrix}-\frac{4}{7} & \frac{3}{7} \\ -\frac{5}{7} & \frac{2}{7}\end{bmatrix}\begin{bmatrix}-5 \\ -2\end{bmatrix}=\begin{bmatrix}(-\frac{4}{7})(-5)+(\frac{3}{7})(-2) \\ (-\frac{5}{7})(-5)+(\frac{2}{7})(-2)\end{bmatrix}=\begin{bmatrix}\frac{20}{7}-\frac{6}{7} \\ \frac{25}{7}-\frac{4}{7}\end{bmatrix}=\begin{bmatrix}\frac{14}{7} \\ \frac{21}{7}\end{bmatrix}=\begin{bmatrix}2 \\ 3\end{bmatrix}[/tex]The solution matrix, X, is
[tex]X=\begin{bmatrix}2 \\ 3\end{bmatrix}[/tex]This, means the solution to the system of equations is:
[tex]x=2,y=3[/tex]7x + 15+9x - 5 = It’s is negative-10 or 10
Answers
1) Solving for x, the following expression:
7x + 15+9x - 5 = 0 Combine like terms
7x +9x +15 -5 =0
16x +10 =0 Subtract 10 from both sides
16x = -10 Divide both sides by 16
x = -10/16 Simplify it
x=-5/8
Macmillan Learning
Suppose that your federal direct student loans plus accumulated interest total $33,000 at the time that you start repayment and the interest rate on all the loans is 5.23%.
(a) If you elect the standard repayment plan of a fixed amount each month for 10 years, what would your monthly payment be?
(b) How much would you pay in interest over the 10 years?
Answers
Using the monthly payment formula, it is found that:
a) Your monthly payment would be of $353.74.
b) You would pay $9,444.8 in interest over the 10 years.
What is the monthly payment formula?The monthly payment rule is presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the meaning of each parameter is given as follows:
P is the initial amount.r is the interest rate.n is the number of payments.In the context of this problem, the values of these parameters are:
P = 33000, r = 0.0523, r/12 = 0.0523/12 = 0.00435833, n = 10 x 12 = 120.
Hence the monthly payment is calculated as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 33000\frac{0.00435833(1.00435833)^{120}}{(1.00435833)^{120} - 1}[/tex]
A = $353.74.
The total amount paid is:
T = 120 x 353.74 = $42,444.8.
The interest paid is the total amount subtracted by the loan value, hence:
42444.8 - 33000 = $9,444.8.
More can be learned about the monthly payment formula at https://brainly.com/question/14802051
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Caitlin travels from 1 1/3 hours to visit a friend who lives 4 and 1/2 miles away Martin travels 4 1/4 miles to visit a friend it takes in 1 1/5 hours to get there who travels at a greater rate of 4 miles per hour
Answers
Caitlin travels 4.5 miles at 11/3 hours.
So his rate of travel will be
[tex]\frac{4.5}{\frac{11}{3}}=1.23[/tex]His rate is 1.23 mile/hour
Again Martin travels 4.25 miles at 11/5 hours
So his rate will be
[tex]\frac{4.25}{\frac{11}{5}}=1.93[/tex]Hence martins rate is 1.93 miles/hour.
SO Martin travels at a greater rate than Caitlin.
Answer:
Step-by-step explanation:
Write the next explicit form of this sequence, given a1 = 20 and r= 0.5 (1/2) and find n=15.
Answers
Given the first term, a1=20
Common ratio, r=0.5*1/2=0.25
A geometric sequence is represented by the following expression:
[tex]\begin{gathered} a_n=ar^{n-1} \\ \end{gathered}[/tex]We want to find the 15th term:
[tex]\begin{gathered} a_{15}=20(0.25)^{15-1} \\ a_{15}=7.45\times10^{-8} \end{gathered}[/tex]find three consecutive intergers whose sum is 276
Answers
If we need to find three consecutive integers, we have that they can be written as follows:
[tex]x,x+1,x+2[/tex]Since the sum of all of them is equal to 276, we can write the following equation:
[tex]x+(x+1)+(x+2)=276[/tex]Now, adding like terms, we have:
[tex]\begin{gathered} (x+x+x)+(1+2)=276 \\ 3x+3=276 \\ \end{gathered}[/tex]Now, we can subtract 3 from both sides of the equation, and then divide by 3 as follows:
[tex]\begin{gathered} 3x+3-3=276-3 \\ 3x=273 \\ \frac{3x}{3}=\frac{273}{3} \\ x=91 \end{gathered}[/tex]Then, we have that:
[tex]\begin{gathered} x=91 \\ x+1=92 \\ x+2=93 \end{gathered}[/tex]If we add these three consecutive integers, we will have:
[tex]\begin{gathered} 91+92+93=276 \\ 276=276\Rightarrow This\text{ is True.} \end{gathered}[/tex]In summary, the three consecutive integers whose sum is 276 are 91, 92, and 93.
need help asap got something I dont understand
Answers
Formula
[tex]\text{ Area = }\frac{B\text{ + b}}{2}\text{ h}[/tex]B = long base
b = short base
h = height
Counting the number of squares:
B = 8
b = 6
h = 4
Substitution
[tex]\begin{gathered} \text{ Area = }\frac{(8\text{ + 6)}}{2}4 \\ \text{ Area = }\frac{14}{2}4 \\ Area=\frac{56}{2}\text{ } \\ \text{Area = 28} \end{gathered}[/tex]Four more than eight times a number (written as a expression)
Answers
'Four more than' is written as 4+
Let n be 'a number'
Then, the whole expression is:
[tex]4+8n[/tex]a bus route takes about 45 minutes. the company's goal is mad of less than 0.5 minute. one drivers times for 9 runs of the route. did the driver meet the goal?44.2 , 44.9 , 46.1, 45.8 , 44.7 , 45.2 , 45.1 , 45.3, 44.6
Answers
Answer:
The driver meet the goal
Explanation:
We are given that a bus route takes about 45 minutes
If companys goal is made less than 0.5minute, then, the company's goal is 45 - 0.5 = 44.5minutes
If one drivers times for 9 runs of the route, as ahown;
44.2 , 44.9 , 46.1, 45.8 , 44.7 , 45.2 , 45.1 , 45.3, 44.6
We will have to calculate the mean data first as shown;
Mean time = 44.2 +44.9+46.1 +45.8+ 44.7+ 45.2+45.1+45.3+44.6/9
Mean time = 405.9/9
Mean time = 45.1minutes
Since the mean time(45.1minutes) is greater than the company's goal (44.5minutes), hence the driver meet the goal
O How many times greater is:the value of the digit 2 in234,567 than the value ofthe digit 2 in 765,432?
Answers
Given:
The given numbers are 234,567 and 765,432.
Required:
We need to find the number of times the value of the digit 2 in 234,567 is greater than the value of digit 2 in 765,432.
Explanation:
The value of digit 2 in 234,567 is 200,000.
The value of digit 2 in 765,432 is 2.
Divide 200,000 by 2.
[tex]\frac{200,000}{2}=100,000[/tex]200,000 is 100,000 times greater than 2.
The value of digit 2 in 234,567 is 100,000 times greater than the value of digit 2 in 765,432 is 2.
Final answer:
The value of digit 2 in 234,567 is 100,000 times greater than the value of digit 2 in 765,432 is 2.
[tex]100,000[/tex]Drag each tile to the correct box.Arrange the steps to perform this subtraction operation in the correct order.(1.93 x 10"- (9.7 x 105)(1.93x107)–(9.7x106)0.96x107(1.93x10?)–(0.97X107)10 (0.96X107)(1.93-0.97)x107(1.93x10?)–10(9.7x106)9.6x106
Answers
We make the subtraction following this order:
1.
[tex]1.93\times10^7-9.7\times10^6[/tex]2.
[tex]1.93\times10^7-\frac{10}{10}\times(9.7\times10^6)[/tex]3.
[tex]1.93\times10^7-0.97\times10^7[/tex]4.
[tex](1.93-0.97)\times10^7[/tex]5.
[tex](0.96)\times10^7[/tex]6.
[tex]\frac{10}{10}(0.96\times10^7)[/tex]7.
[tex](9.6)\times10^6[/tex]Select all polynomials that are divisible by (x-1)
Answers
Explanation
[tex]\begin{gathered} \frac{5x^4+9}{x} \\ \end{gathered}[/tex]Step 1
Split the fraction
[tex]\frac{5x^4+9}{x}=\frac{5x^4}{x}+\frac{9}{x}[/tex]Step 2
Simplify:
[tex]\begin{gathered} \frac{5x^4}{x}+\frac{9}{x}=5x^{4-1}\text{ +}\frac{9}{x\text{ }} \\ \frac{5x^4}{x}+\frac{9}{x}=5x^3\text{ +}\frac{9}{x\text{ }} \\ 5x^3\text{ +}\frac{9}{x\text{ }} \end{gathered}[/tex]so,the answer is
[tex]5x^3\text{ +}\frac{9}{x\text{ }}[/tex]I hope this helps you
Erika has a baking company and needs to purchase 17 pounds of flour for her cakes. The Baking Goods Store sells two different-sized bags of flour. The table shows the amounts of flour in the bag, the number of bags at the store, and the cost per bag of flour. Size Pounds 1 Bags for Sale 75 Cost per Bag Small $0.84 5 Large 4 4 $16.80 If Erika buys all of the large bags, how many small bags will she need? A. 7 small bags B. 12 small bags C. 28 small bags D. 71 small bags
Answers
There are 4 large bags, and each one has 4 pounds. Then, since she buys all of the large bags, she already has
[tex]4\times4=16[/tex]16 pounds. So, she only needs
[tex]17\text{ }\frac{2}{5}-16=1\text{ }\frac{2}{5}=\frac{5}{5}+\frac{2}{5}=\frac{7}{5}[/tex]1 2/5 pounds more, this fraction is equals to 7/5 pounds. Since the small bags only contains 1/5 pounds of flour, then, she needs
[tex]\frac{\frac{7}{5}}{\frac{1}{5}}=\frac{7}{5}\times\frac{5}{1}=\frac{7\times5}{5\times1}=7[/tex]7 small bags
What fraction is considered zero? when zero is on top o depends on the numerator when zero is on bottom no fraction is undefined
Answers
When the numerator of the fraction = 0 then the fraction is consider to be zero
If the diameter of a circle is changed from 5 cm to 10 cm, how will the circumference change?
Answers
Solution
Step 1
Write out an expression for the circumference of a circle
[tex]\begin{gathered} C\text{ =}\pi d \\ C\text{ is the circumference} \\ d\text{ is the diameter} \end{gathered}[/tex][tex]\begin{gathered} \text{when d = 5}cm \\ C=5\pi cm \end{gathered}[/tex][tex]\begin{gathered} \text{when d=10cm} \\ C=10\pi cm \end{gathered}[/tex]Thus, when the diameter changed from 5cm to 10cm, the circumference is twice the previous size
That is, the circumference when the diameter is 10cm is 2 times the circumference when the diameter is 5cm
Ava bought a rectangular rug for her hallway. The rug is į yards wide and 2 yards long 2 3 What is the area of the rug?
Answers
Answer:
Concept:
The area of the rectangle is given below as
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times width \\ A_{\text{rectangle}}=l\times w \\ \text{where,} \\ l=2\frac{3}{4}yd \\ w=\frac{2}{3}yd \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} A_{\text{rectangle}}=\text{length}\times width \\ =2\frac{3}{4}yd\times\frac{2}{3}yd \\ A_{\text{rectangle}}=\frac{11}{4}yd\times\frac{2}{3}yd \\ A_{\text{rectangle}}=\frac{11}{6}yd^2 \\ A_{\text{rectangle}}=1\frac{5}{6}yd^2 \end{gathered}[/tex]Hence,
The final answer is
[tex]1\frac{5}{6}yd^2[/tex]Look at this graph: 5 3 2 0 1 2 3 4 5 6 7 8 9 10 What is the slope?
Answers
Here, we want to find the value of the slope
To do this, we will need to select two points on the graph
Any two points selected will sufice as far as they are reasonably apart to draw the slope triangle
The points we are seecting are (6,3) and (9,4)
Mathematically, the slope formula is as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{4-3}{9-6} \\ \\ m\text{ = }\frac{1}{3} \end{gathered}[/tex]I need help finding the answer. I don't need astep-by-step explanation just the answer please.Thank you.
Answers
Find a using the theorem of sinus:
[tex]\sin(57°)=\frac{a}{29}[/tex][tex]a=\sin(57)*29=24.32[/tex]Now with the Pythagoras theorem find b:
[tex]a^2+b^2=29^2[/tex][tex]24.32^2+b^2=29^2[/tex][tex]b^2=29^2-24.32^2[/tex][tex]b^2=841-591.46[/tex][tex]b=\sqrt{841-591.46}=\sqrt{249.53}[/tex][tex]b=15.79[/tex]Finally, find B knowing that the sum of all internal angles of a triangle is equal to 180°:
[tex]B=180-57-90=33°[/tex]Describe how the formula is a transformation of a toolkit function. Then sketch a graph of the transformation.. Be sure to include labels for the increments on your x and y axis. Take a picture of that written work and upload it when submitting your answer. You may want to create a table of values to help you graph the function.p(x)=(\frac {1}{3}x)^3-3
Answers
Given the function:
[tex]p(x)=(\frac{1}{3}x)^3-3[/tex]The parent function to the given function is f(x) = x³
To get the function p(x) from f(x), we will perform the following translations:
1) Horizontal stretch with a factor of 1/3
2) Shift downward 3 units
The graph of f(x) and p(x) will be as shown in the following picture:
What is the solution set to the following system?x + y = 3x^2 = y^2 = 9
Answers
To solve the given system of equations:
1. Solve x in the first equation:
[tex]\begin{gathered} x+y-y=3-y \\ \\ x=3-y \end{gathered}[/tex]2. Use the value of x=3-y in the second equation:
[tex](3-y)^2+y^2=9[/tex]3. Solve y:
[tex]\begin{gathered} (a-b)^2=a^2-2ab+b^2 \\ \\ 3^2-2(3)(y)+y^2+y^2=9 \\ 9-6y+2y^2=9 \\ \\ 2y^2-6y=0 \\ 2y(y-3)=0 \\ \\ \end{gathered}[/tex]When the product of two factors is equal to zero, then you equal each factor to zero to find the solutions of the variable:
[tex]\begin{gathered} 2y=0 \\ y=\frac{0}{2} \\ y=0 \\ \\ y-3=0 \\ y-3+3=0+3 \\ y=3 \end{gathered}[/tex]Then, the solutions for variable y in the given system are:
y=0
y=3
4. Use the values of y to find the corresponding values of x:
[tex]\begin{gathered} x=3-y \\ \\ y=0 \\ x=3-0 \\ x=3 \\ \text{Solution 1: (3,0)} \\ \\ y=3 \\ x=3-3 \\ x=0 \\ \text{Solution 2: (0,3)} \end{gathered}[/tex]Then, the solutions for the given system of equations are: (3,0) and (0,3)quations4. Use the values of y to find the corresponding values of x:
[tex]undefined[/tex]4. Use the values of y to find the corresponding values of x:
[tex]undefined[/tex]sofia makes pies for sale the materials for each pie cost $4.00 and she sells the pies for $7.00. to find her profits, she writes the equation p=7.50X-4.00X explain what the variable x represents
Answers
Andrew, this is the solution:
Price of the pie materials = $ 4
Sale price of each pie = $ 7
Sofia writes this equation:
p= 7.50X - 4.00X
X represents the number of pies Sofia makes and sells
Andrew, the equation Sofia wrote is wrong.
This is the correct equation:
p= 7.00X - 4.00X
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Construct the 270° rotation of the square ABCD about point P.
Answers
We want to rotate square ABCD by 270° around point P, lets see
We can think that the square is "glued" to segment PC, so if we rotate the segment PC by 270°, the square will also be rotate by 270°, as follows
So, we have our rotation about point P.
Answer: the answer is B
Step-by-step explanation: just trust me, I got it right