we have the function
[tex]F\mleft(x\mright)=\mleft[\csc \mleft(x^2\mright)+\mleft(x^6\mright)-5e^7x\mright]^{85}[/tex]perations on Whole NumbersT2(d) Three measuring tapes are 10, 15 and 25 m long. Find the shortest lengthwhich can be measured exactly by any one of these tapes. Som(e) Asick person has to take three types of medicines. He takes type-X in every3 hours, type-Y in every 4 hours and type-Z in every 6 hours. If he takes atypes of medicine at the same time at 6 a.m., at what time does he take athese types again at a time? 6pm(f) A book, a pen and a box cost Rs 36, Rs 45 and Rs 54 respectively. Find thesmallest sum of money with which the exact number of books, pens anboxes can be purchased. 120
(f) To find the smallest amount of money that would allow us to purchase an exact amount of any item, we need to find the Least Commom Multiple of the three values.
The first step is to factorate the numbers in their prime factors:
[tex]\begin{gathered} 36=2\cdot2\cdot3\cdot3 \\ 45=3\cdot3\cdot5 \\ 54=2\cdot3\cdot3\cdot3 \end{gathered}[/tex]Then, we pick the maximum number of times that each prime factors show up and create a new number:
[tex]\begin{gathered} \text{number 2: 2 times} \\ \text{number 3: 3 times} \\ \text{number 5: 1 time} \\ \text{new number: 2}\cdot2\cdot3\cdot3\cdot3\cdot5=540 \end{gathered}[/tex]So the smallest amount of money to purchase an exact number of any item is Rs 540
A cleaning company charged $125 to clean a 2500 square foot house. The same company charged $146 to clean a 3200 square foot house. Write an equation in slope-intercept form to represent the total cost, y, to clean a house with x square feet. Then. find the total cost to clean a house that is 4500 square feet.this is confusing me so badly I'm getting a headache step by step explanation and solving might help me thank you.
Answer:
• y=0.03x+50
,• $185
Explanation:
The slope-intercept form of the equation of a line is:
[tex]y=mx+b,m=\text{slope,b}=y-\text{intercept}[/tex]The number of square feet = x
The cost of cleaning x square feet = y
From the given information:
• When x=2500 square foot, y=$125; and
,• When x=3200 square foot, y=$146
First, we find the slope of the line.
[tex]\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{146-125}{3200-2500} \\ =\frac{21}{700} \\ m=0.03 \end{gathered}[/tex]Next, substitute the value of m.
[tex]\begin{gathered} y=0.03x+b \\ At\text{ (2500,125)} \\ 125=0.03(2500)+b \\ b=125-0.03(2500) \\ b=125-75 \\ b=50 \end{gathered}[/tex]The slope-intercept form representing the total cost, y, to clean a house with x square feet is:
[tex]y=0.03x+50[/tex](b) When the house is 4500 square feet.
[tex]\begin{gathered} y=0.03(4500)+50 \\ =135+50 \\ =\$185 \end{gathered}[/tex]The diagonal of a square is x units. What is the area of the square in terms of x?o įx square unitsO x? square unitsO 2x square unitso įx square units
We have
First,
we need to find the measure of the side
Graph the image of W -61 after a translation nine units down. Help would be appreciated
ANSWER:
STEP-BY-STEP EXPLANATION:
Given:
W (-6, 1)
[tex]undefined[/tex]Find the perimeter of the triangle to the nearest tenth of a meter.
You can identify that the triangle shown in the picture is a Right triangle.
You can use the following Trigonometric Identity:
[tex]\tan \alpha=\frac{opposite}{adjacent}[/tex]In this case:
[tex]\begin{gathered} \alpha=30\degree \\ opposite=5 \\ adjacent=x \end{gathered}[/tex]See the picture below:
Substitute values into
[tex]\tan \alpha=\frac{opposite}{adjacent}[/tex]And solve for "x":
[tex]\begin{gathered} \tan (30\degree)=\frac{5}{x} \\ \\ x\tan (30\degree)=5 \\ \\ x=\frac{5}{\tan(30\degree)} \\ \\ x=5\sqrt[]{3} \end{gathered}[/tex]To find the length of the hypotenuse, you can use the Pythagorean theorem:
[tex]a^2=b^2+c^2[/tex]Where "a" is the hypotenuse and "b" and "c" are the legs of the Right triangle.
In this case:
[tex]\begin{gathered} a=y \\ b=5 \\ c=5\sqrt[]{3} \end{gathered}[/tex]Substituting values into the equation and solving for the hypotenuse, you get that this is:
[tex]\begin{gathered} y^2=(5)^2+(5\sqrt[]{3})^2 \\ y=25+25(3) \\ y=\sqrt[]{100} \\ y=10 \end{gathered}[/tex]The perimeter of a triangle can be found by adding the lengths of its sides. Then, the perimeter of this triangle rounded to the nearest tenth, is:
[tex]\begin{gathered} P=5m+5\sqrt[]{3}m+10m \\ P=23.66m \\ P\approx23.7m \end{gathered}[/tex]The answer is: Option C.
Find the inverse of the function. I really need help!!
Given the function:
[tex]f(x)=8x-2[/tex]We will find the inverse of the function as follows:
[tex]\begin{gathered} y=8x-2 \\ y+2=8x \\ \frac{1}{8}(y+2)=x \end{gathered}[/tex]So, the inverse of the function will be:
[tex]f^{-1}(x)=\frac{x+2}{8}[/tex]So, the answer is the first option
ABC painting company is painting a house. They charge a travel and cleanup fee of $150.00 per hour to paint. Write an equation in slope-intercept form for this situation. Then tell what the slope and y-intercept represent (in words). Equation: _______________________________Slope (in words):________________________Y-intercept (in words): _________________________
Solution
The equation is given by:
y= 125x+150
Slope (in words): for each hour of increment the price of painting increase in 125 $
y- intercept (in words): represent the fixed cost and the initial fee for painting a house for this case 150$
A survey of a group of seventh graders and a group of teachers at a local middle school asked how many siblings they each have. The dot plots below show the results.
Students
A dot plot titled Students. A number line going from 0 to 9 labeled number of siblings. There are 2 dots above 0, 4 above 1, 7 above 2, 5 above 3, 2 above 4, and 0 above 5, 6, 7, 8, and 9.
Teachers
A dot plot titled Teachers. A number line going from 0 to 9 labeled Number of siblings. There is 1 dot above 0, 3 dots above 1, 2 above 2, 4 above 3, 5 above 4, 3 above 5, 1 above 6, 0 above 7, 1 above 8, and 0 above 9.
Which compares the modes of the data?
To obtain the information requested in the question, the following steps are necessary:
Step 1: Write out the values from the box plot as a sequence of numbers, as follows:
[tex]0,0,0,1,1,1,2,2,2,3,3,3,3,3,3,4,4,4,6[/tex]Step 2: Now, that we have the values written out as above, we can proceed to answering the questions, as follows:
a) To obtain the number of students that have at least 4 siblings (that is, more than 4 siblings), we count the number of times the numbers 4 and 6 occur.
By counting, we get: 5
Therefore, the number of students that have at least 4 siblings is: 5
b) To obtain the number of students that have no siblings (0 siblings), we count the number of times the number 0 occurs.
By counting, we get: 3
Therefore, the number of students that have at least 0 siblings is: 3
c) To obtain the mean (average) number of siblings, we proceed as follows:
[tex]average=\frac{sum\text{ of all the number of siblings}}{\text{total number of students}}[/tex]Therefore:
[tex]\begin{gathered} \text{average}=\frac{0+0+0+1+1+1+2+2+2+3+3+3+3+3+3+4+4+4+6}{20} \\ \text{average}=\frac{45}{20}=\frac{9}{4}=2.25 \\ \text{average}=2.25 \end{gathered}[/tex]Therefore, the mean (average) number of siblings is 2.25 (approximately 2)
What is the solution of the equation 2 = op – 8 5p? O p = -10 Op=-6 Op=2 O p = 10
To solve the equation, first, add similar terms
[tex]\begin{gathered} 2=6p-8-5p \\ 2=p-8 \end{gathered}[/tex]Now add 8 to both sides of the equation
[tex]\begin{gathered} 2+8=p-8+8 \\ 10=p \end{gathered}[/tex]Therefore, the solution of the equation is p = 10 and the correct answer is D.
express √180 as a mixed radical in simplest form
The expression is given as,
[tex]\sqrt[]{180}[/tex]Use the prime factorization of 180 as,
[tex]\begin{gathered} 180=2\cdot2\cdot3\cdot3\cdot5 \\ 180=2^2\cdot3^2\cdot5 \end{gathered}[/tex]Consider the formulae,
[tex]\begin{gathered} \sqrt[]{x}=(x)^{\frac{1}{2}} \\ (xy)^m=x^my^m \\ (x^m)^n=x^{mn} \end{gathered}[/tex]Then the given expression can be resolved as follows,
[tex]\begin{gathered} \sqrt[]{180} \\ =(180)^{\frac{1}{2}} \\ =(2^2\cdot3^2\cdot5)^{\frac{1}{2}} \\ =(2^2)^{\frac{1}{2}}(3^2)^{\frac{1}{2}}(5)^{\frac{1}{2}} \\ =(2^{2\cdot\frac{1}{2}})^{}(3^{2\cdot\frac{1}{2}})^{}(5)^{\frac{1}{2}} \\ =(2^1)^{}(3^1)^{}\cdot\sqrt[]{5} \\ =6\sqrt[]{5} \end{gathered}[/tex]Thus, the simplest form of the given expression is,
[tex]6\sqrt[]{5}[/tex]1 1 Yesterday, Jack drove 30 miles. He used 1- gallons of gasoline. What is the unit rate for miles per 4 gallon? The unit rate is miles per gallon. (Simplify your answer. Type an integer, fraction, or mixed number)
We have to remember that a unit rate is a rate (a fraction that compares two quantities with different units) with the unit in the denominator.
Then, to solve this question, we need to divide the given miles by the total of gallons to have the unit rate. Then, we have:
[tex]\frac{30miles}{4\text{gallons}}=\frac{15}{2}=\frac{14}{2}+\frac{1}{2}=_{}7+\frac{1}{2}=7\frac{1}{2}miles/gallons[/tex]Then, the unit rate is 7 1/2 miles per gallon.
Harry budgeted $180 per month for eating out. At an estimated $9 permeal, that allows him 20 meals per month. He would like to eat 28 mealsout per month. How much more would he have to budget?a. $36b. $120c. $72d. $180
From the information given,
Initial budget = $180
Amount per meal = $9
Cost of 20 meals per month = 9 x 20 = $180
This means that he has nothing left. If he would like to eat 28 meals out per month, the additional number of meals is
28 - 20 = 8
The cost of eating 8 meals is 8 x 9 = 72
Therefore, the additional amount that he needs to budget is $72
The graph of the reciprocal parent function, f(x) = is shifted 8 units down and 6 units to the left to create the graph of g(x). What function is g(x)?
Answer:
C.
Explanation:
The reciprocal parent function is:
f(x) = 1/x
If a function h(x) = f(x) - c, we can say that h(x) is f(x) shifted c units down. Additionally, if a function f(x) = f(x+c), we can say that h(x) is f(x) shifted c units to the left.
Therefore, the function g(x) that is equal to f(x) but shifted 8 units down and 6 unit to the left is:
[tex]\begin{gathered} g(x)=f(x+6)-8 \\ g(x)=\frac{1}{x+6}-8 \end{gathered}[/tex]Therefore, the answer is C.
Hello’ I need help with this practice problem in calculus
Answer:
Explanation:
Given the below;
[tex]\lim _{x\to-\infty}(2x^3-2x)=-\infty[/tex]We're to determine if the above is true or not.
Let us pick two negative values for x and see what we'll have.
When x = -1, we'll have;
[tex]2(-1)^3-2(-1)=2(-1)+2=-2+2=0[/tex]When x = -5, we'll have;
[tex]2(-5)^3-2(-5)=2(-125)+10=-250+10=-240[/tex]We can see from the above, that x tends to negative infinity, the function keeps getting smaller, also tending to negative infinity, therefore we can say that the given limit statement is true.
Given the below;
[tex]\lim _{x\to\infty}(-2x^4+6x^3-2x)=-\infty[/tex]To determine if the above is true or not, let's pick any two values of x and see what we'll have.
We'll only consider the term with the highest degree as this term can also show us what will happen to the polynomial just as the whole can;
When x = 1;
[tex]-2(1)^4=-2(1)=-2[/tex]When x = 10;
[tex]-2(10)^4=-2(10000)=-20000[/tex]We can see from the above, that x tends to positive infinity, the function keeps getting smaller, tending to negative infinity, therefore we can say that the given limit statement is true.
Given the below;
[tex]\lim _{x\to\infty}(9x^5-6x^3-x)=-\infty[/tex]To determine if the above is true or not, let's pick any two values of x and see what we'll have.
We'll only consider the term with the highest degree as this term can show us what will happen to the polynomial just as the whole function;
When x = 1;
[tex]9(1)^5=9(1)=9[/tex]When x = 10;
[tex]9(10)^5=9(100000)=900000[/tex]We can see from the above, that x tends to positive infinity, the function keeps getting larger, tending to positive infinity, therefore we can say that the given limit statement is false.
Explain why you could use a base 2 or a base 4 to solve the problem above and get the same answer. Show your work and explain.
Step 1. The expression that we have is:
[tex]4^x=16^{x-2}[/tex]To prove that we get the same answer if we use a logarithm base 2 and a logarithm base 4, we will solve the equation using both and check that the result is the same.
Step 2. To solve using a base 2 logarithm, we apply it to both sides of the equation:
[tex]log_2(4^x)=log_2(16^{x-2})[/tex]Using the following property of logarithms:
[tex]log(x^m)=mlog(x)[/tex]The expression is simplified as follows:
[tex]xlog_2(4)=(x-2)log_2(16)[/tex]The base 2 logarithm of 4 and 16 is:
[tex]\begin{gathered} log_2(4)=2 \\ log_2(16)=4 \end{gathered}[/tex]Substituting these values into the equation:
[tex]\begin{gathered} x(2)=(x-2)(4) \\ Simplifying: \\ 2x=4x-8 \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} 2x-4x=-8 \\ -2x=-8 \\ x=\frac{-8}{-2} \\ \boxed{x=4} \end{gathered}[/tex]Step 3. Now we repeat the process but this time we use the logarithm base 4.
The expression is:
[tex]4^{x}=16^{x-2}[/tex]Applying logarithm base 4 to both sides:
[tex]log_4(4^x)=log_4(16^{x-2})[/tex]Simplifying:
[tex]xlog_4(4)=(x-2)log_4(16)[/tex]The base 4 logarithm of 4 and 16 is:
[tex]\begin{gathered} log_4(4)=1 \\ log_4(16)=2 \end{gathered}[/tex]Substituting these values into our equation:
[tex]\begin{gathered} x(1)=(x-2)(2) \\ Simplifying\text{ and solving for x:} \\ x=2x-4 \\ x-2x=-4 \\ -x=-4 \\ \boxed{x=4} \end{gathered}[/tex]Answer: We have proven that we get the same result using a base 2 logarithm and a base 4 logarithm.
514508502497495507458477464515Find the mean and sample standard deviation of these data. Round to the nearest hundredth.meansample standard deviation
The number of observations in the data is n = 10.
Determine the mean of the data.
[tex]\begin{gathered} \mu=\frac{514+508+502+497+495+507+458+477+464+515}{10} \\ =\frac{4937}{10} \\ =493.7 \end{gathered}[/tex]So mean of the data is 493.7.
Determine the sum of square difference between observation and mean.
[tex]\begin{gathered} \sum ^n_{i\mathop=1}(x_i-\mu)^2=(514-493.7)^2+(508-493.7)^2+(502-493.7)^2+(497-493.7)^2 \\ +(495-493.7)^2+(507-493.7)^2+(458-493.7)^2+(477-493.7)^2+(464-493.7)^2+(515-493.7)^2 \end{gathered}[/tex][tex]=412.09+204.49+68.89+10.89+1.69+176.89+1274.49+278.89+882.09+453.69[/tex][tex]=3764.1[/tex]The formula for the standard deviation is,
[tex]\sigma=\sqrt[]{\frac{\sum ^n_{i=1}(x_i-\mu)^2}{n-1}}[/tex]Substitute the value in the formula to determine the standard deviation of the data.
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{3764.1}{10-1}} \\ =\sqrt[]{\frac{3764.1}{9}} \\ =20.4507 \\ \approx20.45 \end{gathered}[/tex]Answer:
Mean: 493.7
Standard deviation: 20.45
SF(A-B) Sabe Capes Career Card 5 kapsa Sant Card 6 Card 5 I C Card 6 Card 7 C Card 7 Sport Card 8 Card 8
By considering the grid lines in the image, you would see that 1 box represents 1 unit.
1 box = 1 unit
For card 5:
The small circle spans 2 boxes
Size of small circle (A) = 2 units
The big circle spans 6 boxes
Size of big circle (B) = 6 units
The Scale Factor, SF (A-B) = 2 / 6 = 1 / 3
Therefore, SF (A-B) = 1 : 3
For card 6:
Size of A = 9
Size of B = 3
SF (A-B) = 9 / 3 = 3 / 1
SF (A-B) = 3 : 1
For card 7:
Size of A = 4
Size of B = 2
SF (A-B) = 4 / 2 = 2 / 1
SF (A-B) = 2 :1
For card 8:
Size of A = 5
Size of B = 5
SF (A-B) = 5 / 5 = 1 : 1
SF (A-B) = 1
Angela is starting a new business, selling shirts and dresses that she sews herself. The materials for the skirts cost $13.56, and the materials for the dresses cost 18.79. She only has $80 to spend. She still has a regular job, so she is limited on the time she has to sew her products. She only wants to spend 15 hours sewing; it takes 2 hours to sew a skirt, and 4 hours to sew a dress. Answer the following questions below and show you work.1. Using the information above, write inequalities representing the constraints based on the amount she has for materials, and the amount of time she has to spend sewing.2. Graph each inequality on the same set of coordinate axes. Identify the number of skirts and dresses that could possibly maximize her profits. Round to the nearest whole number.3. Angela thinks she could sell each skirt for $30, and each dress for $40. Write an equation for the function S(x,y), the amount of money she will make in sales for x number of skirts and y number of dresses.4. Using the equation for the amount of money she could make, Identify the number of skirts and dresses that will maximize her sales, and find her total profit for selling that amount of skirts and dresses.
1.
Since the number of skirts is x and the number of dresses is y
Since the cost of the material of skirts is $13.56 and for the dresses is $18.79
Since she only has $80, then the 1st inequality is
[tex]13.56x+18.79y\leq80\rightarrow(1)[/tex]Since she takes 2 hours for one skirt and 4 hours for one dress
Since she can work only on them for 15 hours
Then the 2nd inequality is
[tex]2x+4y\leq15\rightarrow(2)[/tex]2.
We will graph the 2 inequalities
The red area represents inequality (1)
The blue area represents inequality (2)
The two lines red and blue intersected at the point (2.29, 2.605)
Then to get the maximum profit she has to make about 2 skirts and 3 dresses
3.
Since she will sell each skirt for $30 and $40 for each dress
The equation is
[tex]S=30x+40y[/tex]4.
The vertices of the common shaded area are
(0, 3.75), (2.29, 2.605), (5.9, 0)
Substitute them in the equation to find the maximum amount of profit
[tex]\begin{gathered} S=30(0)+40(4) \\ S=\text{ \$160} \end{gathered}[/tex][tex]\begin{gathered} S=2(30)+3(40) \\ S=60+120 \\ S=\text{ \$}180 \end{gathered}[/tex][tex]\begin{gathered} S=6(30)+0(40) \\ S=\text{ \$}180 \end{gathered}[/tex]Since the greatest amount of selling is $177, then
The number of skirts is 6
The number of dresses is 0
The total amount of profit is
[tex]\begin{gathered} P=160-4(18.79) \\ P=\text{ \$}84.84 \end{gathered}[/tex][tex]\begin{gathered} P=180-[2\times13.56+3\times18.79] \\ P=\text{ \$}96.51 \end{gathered}[/tex][tex]\begin{gathered} P=180-6(13.56) \\ P=\text{ \$}98.64 \end{gathered}[/tex]The greatest profit with 6 skirts and 0 dresses
The total amount of profit is $98.64
What is the standard form for g(x)= the square root of 6-x
The standard form of an Irrational function is given as:
[tex]\begin{gathered} y=\sqrt{a(x-p)}+q \\ \text{where:} \\ y\geqslant q\text{ and x}\geqslant p \end{gathered}[/tex]In the given function:
[tex]\begin{gathered} g(x)=\sqrt{6-x} \\ \text{Domain: }\left\lbrace x\in R\colon x\leqslant6\right\rbrace \\ \text{Range: }\left\lbrace y\in R,\text{ }y\geqslant0\right\rbrace \end{gathered}[/tex]Therefore, the standard form of g(x) is:
[tex]g(x)=\sqrt{-(x-6)}[/tex]A pescatarian is a person who eats fish and seafood but no other animal. An event planner does some research and finds that approximately 2.75% of the people in the area where a large event is to beheld are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the local population of about 150,000.Suppose the event planner assumes that 4% of the guests will be pescatarian so he orders 10 pescatarian meals. What is the approximate probability that more than 4% of the guests are pescatarianand that he will not have enough pescatarian meals? Round to three decimal places
SOLUTION:
Case:
Given:
Required:
Method:
Final answer:
find the LCD for 5/2n^2+21n+27, 8n/2n^2-n-6.
1) Examining the Polynomial
[tex]\begin{gathered} \frac{5}{2n^2+21n+27} \\ \frac{5}{(2n^2+21n)+27} \\ \frac{5}{n(2n+21)+27} \\ \frac{5}{(2n+3)(n+9)} \end{gathered}[/tex]Let's find the Least Common Divisor, we need to factor the polynomial, then look for what we get.
In this case, factoring the denominator we have that as the LCM since (2n+3)(n+9) is the simplest form.
b) Writing the equation and factoring we can have:
[tex]\begin{gathered} \frac{8n}{2n^2-n-6} \\ \frac{8n}{(2n^2-n)-6} \\ \frac{8n}{n(2n-1)-6} \\ \\ \frac{8}{(2n+3)(n-2)} \end{gathered}[/tex]So, in short, to find the LCM of a polynomial is simply factorizing a polynomial to its simplest form.
If the function y = sinx is transformed to v= 3.sin(x), how do the amplitude and period change?
Answer:
The amplitude changes from 1 to 3
The period is unchanged
Explanation:
Given that the function
[tex]y=\sin x[/tex]is transformed to
[tex]v=3\sin x[/tex]We want to know how the amplitude and period change.
Consider the transformation:
[tex]y=a\sin \mleft(bx+c\mright)+d[/tex]Where a is the amplitude
Period is:
[tex]\frac{2\pi}{b}[/tex]The amplitude changes from 1 to 3
The period is unchanged
9. The number of possible string sections (s) to be cut from a 4-inch piece of string variesinversely with the length (/) of each of these string sections. Which equation models thisrelationship?
ANSWER
[tex]s=\frac{4}{l}[/tex]EXPLANATION
We want to find the equation that models the relationship.
An inverse proportional relationship is generally given as:
[tex]y=\frac{k}{x}[/tex]where k = constant of proportionality
x and y = variables that are related
Therefore, given that the number of possible string sections, s, varies inversely with the length, l, the only option that is in this form is:
[tex]s=\frac{4}{l}[/tex]That is the correct answer.
A parallelogram is formed by the points A (2, 4), B (6,3), C (0,0), and D (4,1).What transformation could have occurred in order for A' to be (3, 6)?А.Dilation of 150%BReflection across the axis y = 5СRotation of 90° about the originDTranslation following the rule (x + 2,y+1)
You have the change in point A: (2,4) to A': (3,6)
You see that the change follows the rule:
[tex]undefined[/tex]What is the What is the value of z in the equation 2(4z − 9 − 7) = 166 − 46? (5 points)19212634
We will have the following:
[tex]\begin{gathered} 2(4z-9-7)=166-46\Rightarrow2(4z-16)=120 \\ \\ \Rightarrow8z-32=120\Rightarrow8z=152 \\ \\ \Rightarrow z=19 \end{gathered}[/tex]So, the value of z is 19.
One side of a rectangle is 6 centimeters shorter than six times another side. Find the length of the shorter side if we also know that the perimeter of the rectangle is 156 centimeters.
length of the shorter side is 12cm
Explanation:let one of the side of th rectangle = x
six times this side = 6x
Another side is 6cm shorter than six times the previous side
this side = 6x - 6
The perimeter of a rectangle = 2(length + width)
let the unknown side = width = x
let the length = 6x - 6
The perimeter of the triangle is given as 156 cm
Perimeter = 2(6x - 6 + x)
156 = 2(6x - 6 + x)
solve for x:
156 = 2(7x - 6)
divide both sides by 2:
[tex]\begin{gathered} \frac{156}{2}=2(\frac{7x -6}{2}) \\ 78\text{ = 7x - 6} \end{gathered}[/tex][tex]\begin{gathered} \text{Add 6 to both sides:} \\ 78\text{+ 6 = 7x } \\ 84\text{ = 7x} \end{gathered}[/tex][tex]\begin{gathered} \text{divide both sides by 7:} \\ \frac{84}{7}\text{ = }\frac{7x}{7} \\ x\text{ = 12} \end{gathered}[/tex]The width = x = 12
The length = 6x - 6 = 6(12) - 6
The length = 66
From the above, we see the length of the shorter side is 12cm
Solve the equation 60=3/4h.
60 = 3/4 h
multiply both-side of the equation by 4/3
60 x 4/3 = h
20 x 4 = h
80 = h
h = 80
The distance of the line segment is 36.True or False
Apply the pythagorean theorem:
c^2 = a^2 + b^2
Where:
c = hypotenuse
a & b = the other 2 sides of the triangle
Replacing:
x^2 = 6^2 + 8^2
x^2 = 36 + 64
x^2 = 100
x= √100
x= 10
Answer: FALSE
=========================================================
Explanation:
If you prefer the pythagorean theorem, then follow the method mentioned by the other response.
I'll use the distance formula as a slight alternative. In fact, the distance formula is a modified version of the pythagorean theorem.
[tex]A = (x_1,y_1) = (-5,5) \text{ and } B = (x_2, y_2) = (3,-1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-5-3)^2 + (5-(-1))^2}\\\\d = \sqrt{(-5-3)^2 + (5+1)^2}\\\\d = \sqrt{(-8)^2 + (6)^2}\\\\d = \sqrt{64 + 36}\\\\d = \sqrt{100}\\\\d = 10\\\\[/tex]
The result of the distance formula calculation shows the distance from A(-5,5) to B(3,-1) is exactly 10 units.
This means segment AB is exactly 10 units long.
Therefore, the statement "the line segment is 36 units long" is false
To inspect manufacturing processes, companies typically examine samples of parts for deficiencies. One company that manufactures ballpoint pens selected samples of 1000 pens on each of 18 days. The company recorded, for each sample of 1000 , the number of defective pens in the sample. Here are their data.
Hello! Let's solve the exercise:
First, let's write the data again:
1 1 2 2 2 3 3 3 5 5 6 6 7 10 10 14 15 18
(a)
[tex]\operatorname{mean}=\frac{\text{sum of all terms}}{\text{ number of terms}}[/tex]an evening flight had six less than twice the number of passengers that a morning flight had if the total number of passengers on both sides was 753 how many were on the morning flight
we write teo equations for each statement
an evening flight had six less than twice the number of passengers that a morning flight
[tex]e=2m-6[/tex]the total number of passengers on both sides was 753
[tex]e+m=753[/tex]where e is the passengers on evening flight and m the passengers on morning flight
we will solve two equations with two unknowns
[tex]\begin{gathered} e=2m-6 \\ e+m=753 \end{gathered}[/tex]we will use the substitution method
we wiil replace the value of e from the first equation on the second
[tex]\begin{gathered} e+m=753 \\ (2m-6)+m=753 \end{gathered}[/tex]now solve for m
[tex]\begin{gathered} 2m-6+m=753 \\ 3m-6=753 \\ 3m=753+6 \\ m=\frac{759}{3} \\ \\ m=253 \end{gathered}[/tex]the morning flight had 253 passengers