When a line bisects another in a certain point it creates two segments, these must be equal in length. So the sum of their lengths is equal to the length of the whole line. In this case the line QR was divided in PQ and PR, so we have:
[tex]QR=PQ+PR[/tex]We want to find the length of PR, so we need to isolate it on the left side:
[tex]PR=QR-PQ[/tex]Applying the expressions for QR and PQ we have:
[tex]\begin{gathered} PR=8x-12-(2x) \\ PR=8x-2x-12 \\ PR=6x-12 \end{gathered}[/tex]The segment PR measures "6x - 12".
Solve the system of equations below using any method you learned in this unit. Show all work (even if you are using your calculator). elmianation method would be preferred but whatever works
Given
[tex]\begin{gathered} 3x-4y=11...Equation\text{ i} \\ 2x+3y=-1...Equation\text{ ii} \end{gathered}[/tex]Using Elimination method
Solution
Multiply the first equation by 3 and multiply the second equation by 4.
[tex]\begin{gathered} 3\left(3x−4y=11\right) \\ 4\left(2x+3y=−1\right) \end{gathered}[/tex]Becomes
[tex]\begin{gathered} 9x−12y=33 \\ 8x+12y=−4 \end{gathered}[/tex]Add these equations to eliminate y:
[tex]17x=29[/tex]Divide both sides by 17
[tex]\begin{gathered} \frac{17x}{17}=\frac{29}{17} \\ \\ x=\frac{29}{17} \end{gathered}[/tex]Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
[tex]\begin{gathered} 3x−4y=11 \\ \\ \\ Substitute\text{ x=}\frac{29}{17} \\ \\ 3(\frac{29}{17})-4y=11 \\ \\ \frac{87}{17}-4y=11 \\ \\ solve\text{ for y} \end{gathered}[/tex][tex]\begin{gathered} −4y=11-\frac{87}{17} \\ -4y=\frac{100}{17} \\ \\ divide\text{ both sides by} \\ y=-\frac{25}{17} \end{gathered}[/tex]The final answer
[tex]x=\frac{29}{17},\:y=-\frac{25}{17}[/tex]An interior designer wants to decorate a newly constructed house. The function f(c) - 49x^2 - 200 represents the amount of money he earns per room decorated, where xrepresents the number of rooms he designs. The function g(x) = 1/7x represents the number of rooms the Interior designer decorates, where x is the number of hours he works.Part A: Determine the amount of money the Interior designer will make decorating the house as a function of hours he works.Part B: If the newly constructed house requires 50 hours of work, how much will the interior designer earn? Show all necessary calculations. Part C: Determine an expression to represent the difference quotient for the function found in Part A. Show all necessary work.
Part A:
to find the amount of money the interior designer will make as a function of hours we need to find f(g(x)), so:
[tex]\begin{gathered} g(x)=\frac{1}{7}x \\ f(g(x))=49(\frac{1}{7}x)^2-200 \\ f(g(x))=49(\frac{1}{49}x^2)-200 \\ f(g(x))=x^2-200 \end{gathered}[/tex]so the answer is: x^2-200
Part B:
we can use the equation we just found, so x is the number of hours so x=50 and we need to find f(g(x))
[tex]50^2-200=2300[/tex]so the answer is: 2300
The scatter plot shows the average monthly temperature, x, and the monthly heating cost of a family, y, for 25 different months
a) the predicted heating cost is $66.85
b) the predicted heating cost is $97.10
c) for an increase of 1 °F, the predicted decrease in heating cost is $1.21
Explanation:Given:
A scatter plot that shows the average monthly temperature, x, and the monthly heating cost of a family, y, for 25 different months
[tex]\begin{gathered} the\text{ line of best fit is given as:} \\ y\text{ = -1.21x + 97.10} \end{gathered}[/tex]To find:
a) the predicted heating when the average temperature is 25 °F
b) the predicted heating when the average temperature is 0°F
c) the predicted decrease in monthly heating cost for an increase in 1°F
a) We will substitute x with 25 °F to get the predicted heating
[tex]\begin{gathered} y\text{ = -1.21\lparen25\rparen + 97.10} \\ y\text{ = \$66.85} \end{gathered}[/tex]b) To get the predicted heating, we will substitute x with 0 °F
[tex]\begin{gathered} y\text{ = -1.21\lparen0\rparen+ 97.10} \\ y\text{ = 0 + 97.10} \\ y\text{ = \$97.10} \end{gathered}[/tex]c) To get the decrease per monthly heating cost, we will find the predicted heating cost between two consecutive values of x
let x = 0, 1
when x = 0, y = $97.10
when x = 1 (this is an increase of 1 °F from the previous temperature)
y = -1.21(1) + 97.1
y = 95.89
The difference in heating cos when there is an increase of 1 °F:
difference = 95.89 - 97.10
difference = -1.21
Hence, for an increase of 1 °F, the predicted decrease in heating cost is $1.21
In a museum there is a sculpture in the shape of a cylinder. The cylinder has a diameter of12 feet and a height of h feet, which equation can be used to find V, the volume of thecylinder in cubic feet?A V = (6YhBV = (hy'CV = *(12y' hDV = (12h
Volume of a cylinder = π (radius)^2 heigth
V = π r^2 h
Since the diameter = 2 x radius
12 = 2r
12/2 =r
r= 6 ft
Replacing:
V = π (6)^2 h
The sum of two consecutive numbers is 89. What are the two numbers?A.43 and 46B.44 and 45C.38 and 51D.45 and 46
We know that:
- the sum of two consecutive numbers is 89
And we must find the two numbers
To find them, we can use equations to represent the situation.
1. We can use the next equation
[tex]n+m=89[/tex]Where, n is the smallest number and m is its consecutive number
2. Since m is the number after n, we can write m as
[tex]m=n+1[/tex]3. We must replace m = n + 1 in the first equation
[tex]\begin{gathered} n+(n+1)=89 \\ \text{ Solving for }n, \\ n+n+1=89 \\ 2n+1=89 \\ 2n=89-1 \\ 2n=88 \\ n=\frac{88}{2} \\ n=44 \end{gathered}[/tex]4. Finally, we must replace n = 44 in the equation for m
[tex]\begin{gathered} m=44+1 \\ m=45 \end{gathered}[/tex]ANSWER:
B.44 and 45
According to one study, an average payout for slots machines is 90 cents on each dollar. What is the percent return on every dollar spent in playing slots?The percent return on every dollakspent in playing slots is %.
90 %
Explanation
we can easily solve this by using a rule of three
let
x represents the percentage
also, we need to know
[tex]1\text{ dollar = 100 cents}[/tex]so
[tex]\begin{gathered} if \\ 100\text{ cents}\rightarrow100\text{ \%} \\ \text{then} \\ 90\text{ cents}\rightarrow x \end{gathered}[/tex]so, we can make a proportion
[tex]\frac{100\text{ cents}}{100\text{ \%}}=\frac{90\text{ cents}}{x}[/tex]finally,solve for x
[tex]\begin{gathered} \frac{100\text{ cents}}{100\text{ \%}}=\frac{90\text{ cents}}{x} \\ \frac{100}{100}=\frac{90}{x} \\ 100x=90\cdot100 \\ x=\frac{90\cdot100}{100} \\ x=90\text{ \%} \end{gathered}[/tex]therefore, the return on every dollar is
90 %
I hope this helps you
Evaluate the expression,in simplest form.W=10.5X= -3Y=7.4Expression: w-x+y
The given expression is
[tex]w-x+y[/tex]Where w = 10.5, x = -3, and y = 7.4.
Replacing all given values, we have
[tex]10.5-(-3)+7.4=10.5+3+7.4=20.9[/tex]Therefore, the simplest form is 20.9.Which of the following quadratic equations has the solutions2+1322X2Required: Choose an answer!A. 3x2 + 4x + 1 = 0OB. 4x2 – 8x + 1 = 0C. x2 + 3x + 2 = 0D. x2 - 4x + 3 = 0PrevNext
Given the solution of the equation:
[tex]x=\frac{2\pm\sqrt[]{3}}{2}[/tex]Let's check which quadratic equations has the given solution,
[tex]\begin{gathered} A)3x^2+4x-1=0 \\ \text{compare with ax}^2+bx+c=0 \\ a=3,b=4,c=-1 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-4\sqrt[]{4^2+12}}{2\cdot3} \\ =\frac{-4\pm\:2\sqrt{7}}{2\cdot\:3} \\ x_{}=\frac{-2+\sqrt{7}}{3},\: \frac{-2-\sqrt{7}}{3} \end{gathered}[/tex][tex]\begin{gathered} B)4x^2-8x+1=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-\left(-8\right)\pm\sqrt{\left(-8\right)^2-4\cdot\:4\cdot\:1}}{2\cdot\:4} \\ x=\frac{-\left(-8\right)\pm\:4\sqrt{3}}{2\cdot\:4} \\ x=\frac{2\pm\sqrt{3}}{2} \end{gathered}[/tex]Hence, the correct option is B) 4x²-8x+1=0
How do I find the answer to this math equation?
The given equation is expressed as
- (2x + 4) = 3x - 5
The first step is to open the bracket on the left habd side of the equation by multiplying each term inside the bracket by - 1 which is outside the bracket. Thus, we have
- 1 * 2x + - 1 * 4 = 3x - 5
- 2x - 4 = 3x - 5
Collecting liketerms, we have
- 2x - 3x = - 5 + 4
- 5x = - 1
Dividing both sides of the equation by - 5, it becomes
- 5x/- 5 = - 1/- 5
x = 1/5
Find the area of the triangle Can you please show me step by step so I understand?
To solve this question we will use the following diagram:
Notice that triangles ABD and BCD are right triangles.
Using the Pythagorean theorem we get:
[tex]\begin{gathered} x^2+7^2=11^2, \\ x^2+y^2=9^2\text{.} \end{gathered}[/tex]Simplifying the above equations we get:
[tex]\begin{gathered} x^2+49=121, \\ x^2+y^2=81 \end{gathered}[/tex]Subtracting 49 from x²+49=121 we get:
[tex]\begin{gathered} x^2+49-49=121-49, \\ x^2=72. \end{gathered}[/tex]Therefore:
[tex]x=\sqrt[]{72}=\sqrt[]{36\cdot2}=6\sqrt[]{2}\text{.}[/tex]Substituting x²=72 in x²+ y²=81 we get:
[tex]72+y^2=81.[/tex]Subtracting 72 from the above equation we get:
[tex]\begin{gathered} 72+y^2-72=81-72, \\ y^2=9. \end{gathered}[/tex]Therefore:
[tex]y=3.[/tex]Therefore the measure of the base of the original triangle is:
[tex]y+7=3+7=10,[/tex]and its height is:
[tex]x=6\sqrt[]{2}\text{.}[/tex]Using the formula for the area of a triangle:
[tex]A=\frac{bh}{2},[/tex]we get:
[tex]A=\frac{10\cdot6\sqrt[]{2}}{2}=\frac{60\sqrt[]{2}}{2}=30\sqrt[]{2}\text{.}[/tex]Answer: The area of the original triangle is:
[tex]30\sqrt[]{2}\text{ square units.}[/tex]ALTERNATIVE SOLUTION.
To be able to use trigonometric functions first we have to determine at least one angle of the triangle. To do that, we will use the trigonometric function cosine, recall that:
[tex]\cos \alpha=\frac{\text{adjacent side}}{\text{hypothenuse}}\text{.}[/tex]Now, we will use triangle ADB and angle A, then:
[tex]\cos A=\frac{7}{11}\text{.}[/tex]Therefore:
[tex]A=\cos ^{-1}(\frac{7}{11}).[/tex]Once we have the angle, now we use another trigonometric function, the sine:
[tex]\sin \alpha=\frac{opposite\text{ side}}{\text{hypothenuse}}\text{.}[/tex]Then:
[tex]\begin{gathered} \sin A=\frac{x}{11}, \\ x=\sin A(11)\text{.} \end{gathered}[/tex]Once we have x we do the same to find y but with angle C:
[tex]\begin{gathered} \cos C=\frac{y}{9}, \\ y=\cos C\times9. \end{gathered}[/tex]Finally, we use the formula for the area of a triangle, and get:
[tex]A=\frac{(7+y)x}{2}=\frac{(7+3)\times11\sin A}{2}\approx42.5\text{ square units.}[/tex]The ratio of the longer side of a rectangle to its shorter side is 4 to 3. If the shorter side of the rectangle is 21 ft, what is the length of its longer side? Group of answer choices 26 ft 30 ft 24 ft 28 ft
The longer side of the rectangle is 28 feet
How to determine the length of its longer side?From the question, the given parameters are:
Ratio of the longer side of a rectangle to its shorter side is 4 to 3
This can be represented as
Ratio = 4 : 3
Also it can be represented as
Longer side : Shorter side = 4 : 3
From the question, another parameter is given as:
Shorter side = 21 ft
Substitute Shorter side = 21 ft in the ratio Longer side : Shorter side = 4 : 3
So, we have the following equation
Longer side : 21 = 4 : 3
Express as fraction
So, we have the following equation
Longer side/21 = 4/3
Multiply by 21
So, we have the following equation
Longer side = 28
Hence, the length of its longer side is 28 feet
Read more about ratio at
https://brainly.com/question/29146883
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1. A rectangular room measures 13 feet by 15 feet. It is going to be carpeted 1 point with carpeting that sells for $31.50 per SQUARE YARD. (A square yard is 3 feet by 3 feet, or 9 square feet)... So, this carpet sells for 31.50/9 or $3.50 per square foot. a. What is the area of the room in square feet? *
According to the question, the rectangular room has dimensions of 13 and 15 feet. Use the formula to find the area of a rectangle to find the area of the room in square feet.
[tex]\begin{gathered} A=b\cdot h \\ A=13\cdot15 \\ A=195 \end{gathered}[/tex]The rectangular room's area in square feet is 195ft^2.
What type of number is 12.5 + 27i?Choose all answers that apply:A RealB ImaginaryC Complex
Hello!
We can say that the number 12.5 + 27i is a complex number because it has two parts: a real number + an imaginary number.
A sample with a sample proportion of 0.4 and which of the following sizeswill produce the widest 95% confidence interval when estimating thepopulation parameter?
As a sample size increases, the confidence interval increases too, so, to have the widest confidence interval we have to choose the smallest size for the sample.
In this case B. 50
Solve y = 4x + 8x for x.X=
For this problem we want to solve for x from this equation:
[tex]y=4x+8x=12x[/tex]We can divide both sides of the equation by 12 and we got:
[tex]x=\frac{y}{12}[/tex]And that would be the final answer.
Determine the center and radius of the following circle equation: x² + y2 + 4x – 6y + 9 = 0 Center: Radius:
The center of the circle is (2,-3) while the radius of the circle is 2 units
Here, we want to determine the center and the radius of the given circle
Generally, we have the equation of a circle as follows;
[tex](x-a)^2+(y-b)^2=r^2[/tex]Where (a,b) represents the center of the circle and r is the radius of the circle
We have this as follows by dividing the coefficients of x and y by 2
[tex]\begin{gathered} (x+2)^2+(y-3)^2-4\text{ = 0} \\ \text{where (x+2)}^2=x^2+4x\text{ + 4} \\ (y-3)^2=y^2-6y+9 \\ By\text{ subtracting 4 from the sum 13, we have -4} \\ so\text{ we have;} \\ (x+2)^2+(y-3)^2\text{ = 4} \\ (x+2)^2+(y-3)^2=2^2 \end{gathered}[/tex]The center of the circle is (2,-3) while the radius of the circle is 2 units
Tickets to the local carnival cost $5.50 for adults and $3.00 for children under the age of 12. A group of 8 people bought tickets to the carnival for $36.50. Write a system of equations to represent this scenario. How many adult tickets were sold? Just type in the ONE number answer.Single line text.
Solution
For this case let :
x= number of adults
y= number of children
We can create the following equations:
x +y =8
5.5 x + 3.0 y=36.50
Then we can solve for x and we got:
x = 8-y
And replacing in the second equation we got:
5.5*(8-y)+ 3y = 36.50
44 -5.5y +3y = 36.50
44-36.50 =2.5y
7.5 =2.5y
y= 3
And for x we got:
x = 8- 3=5
Then the solution would be:
5 adult tickets
how to express the result of the equation in percentage? 9.7 x 10 to the power of 5 minus 8.73 x 10 to the power of 5 = 9.7 x 10 to the power of 49.7 x 10 to the p of 5 was given as the total output, the result of the equation, so 9.7 x 10 to the p of 4, is to be expressed in percentage
Solution:
Given:
To convert a number into a percent, multiply it by 100 and then add the percent sign.
Hence, the result as a percentage of the total output;
[tex]\begin{gathered} \frac{9.7\times10^4}{9.7\times10^5}\times100\text{ \%} \\ =0.1\times100\text{ \%} \\ =10\text{ \%} \end{gathered}[/tex]Therefore, the answer is 10%
A bakery produces 734 cookles a week. How many cookies will it make in 175 days? Number sentence used to solve the problem: _____________________________________ The bakery will make_________ shoes.
A bakery produces 734 cookles a week. How many cookies will it make in 175 days?
Remember that
1 week=7 days
so
734 cookles in 7 days
Applying proportion
734/7=x/175
solve for x
x=(734/7)*175
x=18,350 cookies
In the year 2014, Lee was 3 years older than Kim who was a year younger than Annie. If
Annie was born in 1989, how old were Annie, Lee and Kim?
Answer:
(Please try to show working so that I can understand what u did)
There's probably some other part of the question too. I didn't expected it to be this simple!
XDXDXD
Perform the indicated operations. Simplify your answer. 4/9 + 1/4
Use the following formula:
[tex]\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}[/tex]so:
[tex]\frac{4}{9}+\frac{1}{4}=\frac{4\cdot4+9\cdot1}{9\cdot4}=\frac{16+9}{36}=\frac{25}{36}[/tex]can you just tell me which answer choice it is you don't need to explain it
The function f(p) is used to model the amount of money spent on the project.
The domain is "p" that is the number of people working on this project.
So the question is asking what should be the type of this domain "p"
Let me ask you can the number of people be negative?
Is it possible to say there are -3 people working ?
No, the number of people must be a positive number
Now one more question.
Can the number of people be in fraction?
is it possible to say there are 0.5 people working?
No, the number of people must be whole numbers like 1, 2, 3 etc
So the correct answer is "positive integers"
Because real numbers also include fractions so that is incorrect
complete the sequence of sums on the diagonals shown in the figure what pattern do the sums make? what is the name of this important sequence of numbers
a=8
b=13
c= 21
d=34
This sequence of numbers is given by the pascal triangle
7. Chelsea conducted a survey to determine which candidate is leading the race for ninth-grade class president byasking 50 ninth-grade girls in the cafeteria how they would vote in the election ?
Answer
Option B is correct.
The only reason why Chelsea's prediction might be wrong is that She did not include all of the ninth graders in the survey.
Explanation
Surveys provide an idea of how the entire group of people feel about a subject matter. So, picking 50 ninth grade girls to survey will provide an idea of how the election results will be like.
But since everyone is voting in the election, the prediction using the survey results might be wrong, since it doesn't include all the ninth graders in the survey.
Hope this Helps!!!
22Select the correct answer.The domain of function ris(-00,-7) (-7.5) U (5.00), and the value of the function approaches 1 as x approaches --o0 and oo. Which functioncould be function ?
The function f is a rational function.
Since the function has a horizontal asymptote given by
y = 1
then the only possible relationship between the degree of the numerator, N, and the degree of the denominator, D, is as given below
[tex]\begin{gathered} N=D \\ \text{and } \\ y=\frac{a}{b}=1 \\ \text{ Where} \\ a\text{ is the leading coefficient of the numerator} \\ b\text{ is the leading coefficient of the denominator} \end{gathered}[/tex]With these conditions, we can eliminate option B.
This is because in the case of option B, 1 = N ≠ D = 2
Of all the remaining options, only the function in the case of option C,
has vertical asymptotes at x = -7 and x = 5. Which implies that the domain of f in option C is given by
Dom(f) = (-∞,-7) U (-7, 5) U (5, ∞ )
Hence, the correct choice is option C
A person earns $86,000 per year and is an 814% income tax bracket how much does he pay in taxesThey are in the 14% percent bracket
Given:
A person earns $86,000 per year.
[tex]\begin{gathered} \text{Amount to pay as tax=86000}\times\frac{14}{100} \\ \text{Amount to pay as tax= }860\times14 \\ \text{Amount to pay as tax= \$12040} \end{gathered}[/tex]If you apply the changes below to the exponential parent function f(x) = 2*,what is the equation of the new function?Shift 4 units to the right.• Shift 6 units up.O A. g(x) = 2(x+6) + 4B. g(x) = 2(x– 6) + 4C. g(x) = 2(x – 4) + 6O D. g(x) = 2(x+4) + 6
You need to remember the following Transformation rules for functions:
1. If
[tex]f(x+h)[/tex]The function is shifted "h" units to the left.
2. If
[tex]f(x-h)[/tex]The function is shifted "h" units to the right.
3. If
[tex]f(x)+k[/tex]The function is shifted "k" units up.
4. If
[tex]f(x)-k[/tex]The function is shifted "k" units down.
In this case you have the following Exponential parent function:
[tex]f\mleft(x\mright)=2^x[/tex]You know that it is shifted 4 units to the right and then 6 units up, then you can identify that the transformations are:
[tex]f(x-h)+k[/tex]Where
[tex]\begin{gathered} h=4 \\ k=6 \end{gathered}[/tex]Then, the equation is:
[tex]g\mleft(x\mright)=2^{(x-4)}+6[/tex]The answer is: Option C.
4#The mean diastolic blood pressure for a random sample of 60 people was 81 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 8 millimeters of mercury, find a 95% confidence interval for the true mean diastolic blood pressure of all people. Then give its lower limit and upper limit.Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit:??Upper limit: ??
In this case we want to estimate the mean of the population; since the sample size is larger than 60 and we know the standard deviation of the population the confidence interval is given by:
[tex]\begin{gathered} \bar{x}\pm z\sigma_{\bar{x}} \\ \text{ where} \\ \sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}} \end{gathered}[/tex]Now, from a normal distribution table we know that the z-value for a 95% confidence interval is 1.96; plugging these and the values of the mean and standard deviation given we have that:
[tex]81\pm(1.96)(\frac{8}{\sqrt{60}})=81\pm2.024[/tex]Choosing the negative sign we can calculate the lower limit:
[tex]81-2.024=79[/tex]Choosing the positive sign we can calculate the upper limit:
[tex]81+2.024=83[/tex]Threfore, the lower and upper limits of the confidence interval are 79 and 83, respectively.
Expree the ratio in simplest form400g : 1kg how do I solve this
Answer:
2:5
Explanation:
Given the ratio:
[tex]400g\colon1\operatorname{kg}[/tex]In order to reduce the ratio, both must be in the same unit.
[tex]\begin{gathered} 1\operatorname{kg}=1000g \\ \implies400g\colon1\operatorname{kg}=400g\colon1000g \end{gathered}[/tex]We can then express it in the simplest form.
[tex]\frac{400}{1000}=\frac{2\times200}{5\times200}=\frac{2}{5}[/tex]The ratio in simplest form is 2:5.
$8850 is invested at 8,0% compounded continuously, How long will it take for the balance to reach $17,700 Round your answer to two decimal placesKeypadAnswer
Formula:
• A= P *e^(rt)
Where:
A = future value of investment = 17,700
P= principal investment = 8850
r= interest rate = 8% = 8/100 =0.08 (decimal form)
t = years
Replacing:
17,700 = 8,850 * e^(0.08t)
Solve for t:
17,700/8,850 = e^(0.08t)
2 = e^(0.08t)
Take natural log
Ln 2 = Ln e^(0.08t)
Ln2= 0.08t * Ln e
Ln2 = 0.08t
Ln2/0.08 = t
t = 8.66 years
Answer:
It will take 8.66 years for the balance to reach $17,700.