Kelly, this is the solution:
We have the following system of equations:
y = 1/4x + 4
x + y = - 1
___________
Solving it algebraically:
x + (1/4x + 4) = -1
5/4x + 4 = -1
5/4x = -1 - 4
5/4x = -5
x = -4
-4 + y = -1
y = -1 + 4
y = 3
Solving it graphically:
which one is X value the proceeds from a carwash are directly proportional to the number of cars washed. The total after 9 cars with $180. How much can be raised if 60 cars were washed
Answer:
$1200 would be raised if 60 cars were washed.
Step-by-step explanation:
This question can be solved using a rule of three.
The total after 9 cars was of $180. How much would be raised with 60 cars washed?
9 cars - $180
60 cars - $x
Applying cross multiplication
9x = 180*60
9x = 10800
x = 10800/9
x = 1200
$1200 would be raised if 60 cars were washed.
Convert the following units as indicated.2,250 watts to horsepower (Round answer to the nearest thousandth.)
The question given is to convert
[tex]2250\text{ watts to horse power}[/tex]From a conversion calculator,
[tex]1\text{ horse power = }745.699872\text{Watt}[/tex]Therefore,
[tex]1\text{ watts = }\frac{1}{745.699872}\text{horse power}[/tex]Therefore,
2250 watts will be
[tex]\begin{gathered} =2250\times\frac{1}{745.699872} \\ =\frac{2250}{745.699872}\text{horse power} \\ =3.0172997\text{ horse power} \\ \approx to\text{ the nearest thousandth} \\ =3.017\text{ horsepower} \end{gathered}[/tex]Hence,
The final answer = 3.017 horse power
Which of the following equations does the graph below represent?
A. -3x - 6y = 36
B. -3x + 6y = 36
C. x + 6y = 36
D. 3x + 6y = 36
The equation of the line which represents the given graph is -3x + 6y = 36
We can infer from the graph that the equation of the line passes through the points (0,6) and (-12,0).
Therefore the slope of the line passing through these two points is given by:
m = (0-6)/(-12-0)
or, m = 1 / 2
Now we can use the general equation of the line to get the required equation.
y-6 = 1/2 (x-0)
or, 2y - x = 12
Now we will multiply throughout by 3 we get:
6y - 3x = 36
or, -3x + 6y = 36
The general equation for a straight line is y = mx + c, where m stands for the line's slope and c for its y-intercept. The most frequently used straight line equation is one that has to do with geometry.
There are numerous ways to express the equation of a straight line, such as slope-intercept form, point-slope form, standard form, general form, etc.
Hence the required equation is -3x + 6y = 36 .
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a rectangle with a base of 6 and height of 4 has been scaled with a scale factor of 3. what is the area of the scaled copy?
We have a rectangle of base 6 and height 4. We have a rectangle like this:
Now, we have a scale factor of 3. We need to multiply each side by 3:
Now the rectangle has a height of 12 and a base of 18.
The area of a rectangle is h*b. Then, the area of the scaled copy is:
[tex]A=12\cdot18\Rightarrow A=216[/tex]Therefore, the scaled copy has an area of 216 square units.
Claire took part in a cross country race
and completed the course in 1 hour and 12
minutes. Her average speed for the race
was a sound 17.5 km per hour. What was
the distance that she ran
Claire who took part in a cross-country race ran 21 km in 1 hour and 12 minutes.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Claire took part in a cross-country race and completed the course in 1 hour and 12 minutes which is (1 + 12/60) = (1 + 1/5) = 6/5 = 1.2 hours.
Her average speed for the race was 17.5 km per hour.
∴ The total distance she ran is,
= (17.5×1.2) km.
= 21 km.
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Find X and RDB:
X =
RDB =
[tex]\frac{13x+7-60}{2}=5x-10 \\ \\ 13x-53=10x-20 \\ \\ 3x-53=-20 \\ \\ 3x=33 \\ \\ \boxed{x=11} \\ \\ m\angle RDB=5(11)-10=\boxed{45^{\circ}}[/tex]
And each diagram below, right, the 2 number on the sides of the acts that are multiplied together to get the top number of the x, but added together to get the bottom number of the x.
-34 = x*y
15 = x +y
17 and -2
__________________________
_____________
9 = x*y
6 = x +y
_
Determine the slope of the line between (-6,13) and (1,11)
We can find the slope using the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Let:
[tex]\begin{gathered} (x1,y1)=(-6,13) \\ (x2,y2)=(1,11) \\ \end{gathered}[/tex]Therefore:
[tex]m=\frac{11-13}{1-(-6)}=\frac{-2}{7}=-\frac{2}{7}[/tex]Answer:
[tex]-\frac{2}{7}[/tex]The expression to represent the decrease in temperature then the explanation and it’s meaning
The expression would be:
[tex]\frac{10}{1000}\cdot x[/tex]Where x are the meters climbed.
For 2,000 m we'll have:
[tex]\frac{10}{1000}\cdot2000\rightarrow20[/tex]A 20°C decrease in temperature.
Ivanna is on her way home in her car. Her drive is 12 miles long. She has finished one-fourth of the drive so far. How far has she driven?miles
Fractions
Ivanna has to drive 12 miles. She has already driven 1/4 so far.
The distance she has driven is:
[tex]\frac{1}{4}\cdot12=\frac{12}{4}=3[/tex]Ivanna has driven 3 miles so far
Consider a die rolling game that costs $15 per play. Rolling a 6 wins you $40, rolling a 5 gets you$25, and rolling anything else gets you nothing. Find the expected value and determine if the gameis fair.
Explanation
We need to present the information given in a table as follows:
The second column shows the probability of obtaining each event. Since they are equiprobable events, their probability are 1/6.
The next column determine the cost of obtaining each event; keeping in mid that each play costs $15.
The last column shows the expected value.
We know that If the value of the game is zero i.e. there is no loss or gain for any player, then the game is fair.
According to the table, there is a loss of 25/6, hence, the game is not fair.
How is the series 7 + 13 + 19+...+ 139 represented in summation notation?
Each term is 6 greater than the previous term.
First term is "7".
So,
a = 7
d = 6
Let's find the formula for the series,
[tex]\begin{gathered} a+(n-1)d \\ 7+(n-1)(6) \\ 7+6n-6 \\ 6n+1 \end{gathered}[/tex]We can immediately eliminate the firsst and third choice.
The variable is "t", so the general formula will be:
[tex]6t+1[/tex]How many terms are there?
The series starts from t = 1,
since 6(1) + 1 = 6 + 1 = 7
and 6(2) + 1 = 12 + 1 = 13
The terms match!
So, 2nd answer choice is correct!!
Answer[tex]\sum ^{23}_{t\mathop=1}(6t+1)[/tex]find the area of the white region ...blue region has a 150 degree triangle with 7cm side and the circle has a radius of 7
First, let's find the area circular sector:
[tex]A=\frac{r^2\theta}{2}[/tex]Where:
r = radius = 7cm
θ = angle (in radians) = 5/6 π
so:
[tex]\begin{gathered} A=\frac{7^2(\frac{5}{6}\pi)}{2} \\ A=\frac{245}{12}\pi \end{gathered}[/tex]Now, let's find the area of the triangle, that triangle is an isosceles triangle, so, we can use the following formula in order to find its area:
[tex]\begin{gathered} At=\frac{1}{2}s^2\cdot\sin (\theta) \\ \end{gathered}[/tex]where:
s = one of the equal sides = 7
θ = angle = 150
so:
[tex]\begin{gathered} At=\frac{1}{2}(7^2)\sin (150) \\ At=\frac{49}{4} \end{gathered}[/tex]Therefore, the area of the white region will be, the area of the circular sector minus the area of the isosceles triangle, so:
[tex]Area_{\text{ }}of_{\text{ }}the_{\text{ }}white_{\text{ }}region=\frac{245}{12}\pi-\frac{49}{4}=51.9cm^2[/tex]taxes :2.69 * 10 ^ 5 square miles Rhode Island:1.21 * 10 ^ 3 square miles Determine the differences in square miles between the area Texas and the area Rhode Island. write your answer in scientific notation
Explanation:
The difference is:
[tex]2.69\cdot10^5-1.21\cdot10^3[/tex]To solve this we need the exponent of 10 be the same for both terms of the substraction. It is better is we change the exponent of the area of Texas, by moving the decimal point two places to the right:
[tex]2.69\cdot10^5-1.21\cdot10^3=269\cdot10^3-1.21\cdot10^3[/tex]Now we can substract the numbers and leave the 10³ out:
[tex]269\cdot10^3-1.21\cdot10^3=(269-1.21)\cdot10^3=267.79\cdot10^3[/tex]Scientific notation has always only one place with a number before the decimal point. Therefore 267.79x10³ is not in scientific notation, we have to move the decimal point two places to the left and add 2 to the exponent of 10:
Answer:
The difference is 2.6779 x 10⁵ square miles
witch is an equation in point slope form the given point and slope point (1, 9) point 5
The formula for equation of line pasing through point (x_1,y_1) with slope m is,
[tex]y-y_1=m(x-x_1)[/tex]Substitute point and slope in the equation to obtain the equation of line.
[tex]\begin{gathered} y-9=5(x-1) \\ y-9=5x-5 \\ y=5x+4 \end{gathered}[/tex]So equation of line is y=5x+4.
A farmer has 36 ft of fencing and wants to enclose the maximum rectangular area for his llamas. Find the dimensions of three possible areas he could enclose. What do you think the maximum area is? Why?
The farmer would like to eclose a rectangle
First we know that the perimeter of the rectangle is
[tex]P=2x+2y[/tex]We also know that we have 36 ft of fence, that is we only can enclose a rectangle of 36 ft of perimeter. Then
[tex]36=2x+2y[/tex]From this we can find y
[tex]\begin{gathered} 36=2x+2y \\ 36-2x=2y \\ y=\frac{36-2x}{2} \\ y=18-x \end{gathered}[/tex]The area of the rectangle is
[tex]A=xy[/tex]But we know the value of y, plugging this value into the last equation we have that
[tex]A=x(18-x)[/tex]To find three possible values for the area we only have to give values to x. This values have to be positive (since we can't have a negative lenght). We also notice that the value can't exceed 18 since that would mean a zero area. With those point in consideration we choose three values between zero and 18.
If x=3, then the area is
[tex]\begin{gathered} A=3(18-3) \\ =3(15) \\ =45 \end{gathered}[/tex]If x=9, then the area is
[tex]\begin{gathered} A=9(18-9) \\ =9(9) \\ =81 \end{gathered}[/tex]if x=15, then the area is
[tex]\begin{gathered} A=15(18-15) \\ =15(3) \\ =45 \end{gathered}[/tex]Then we have three possible areas for the rectangle.
The maximum value for the area is 81, and we see that because the equation for the area is a parabola that opens down with vertex in the point (9,81)
We use absolute value to find distances in the real world. Suppose you travel 10 miles north to the grocerystore, then 6 miles south to the post office. From there, you travel 8 miles north to the nearest bank. What isthe total distance you have traveled?A. 4 milesB. 8 milesC.12 milesD. 24 milesPlease select the best answer from the choices providedOAOBOCOD
Given:
Thesis about question is given
Required:
To select which option is correct
Explanation:
assumption S1 is the distance to the grocery store
assumption S2 is the distance to the south post office
assumption S3 is the distance to the north bank
assumption S is the total distance
according to the question
S1= 10 miles S2=6 miles S3=8 miles
S=S1+S2+S3=10+6+8=24 miles
Required answer:
option D
What is the surface area of a right square pyramid with height of 3 centimeters and a base that measures 8 centimeters by 8 centimeters?
Okay, here we have this:
Considering the provided measures, we are going to calculate the requested surface area, so we obtain the following:
So to calculate the surface area we will use the following formula:
A = a(a + √(a^2 + 4h^2))
A = 8 cm(8cm + √((8 cm)^2 + 4(3 cm)^2))
A = 8 cm(8cm + √(64 cm^2 + 4*9 cm^2))
A = 8 cm(8cm + √(64 cm^2 + 36 cm^2))
A = 8 cm(8cm + √(100 cm^2))
A = 8 cm(8cm + 10 cm)
A = 8 cm(18 cm)
total surface areaA = 144 m^2
Finally we obtain that the total surface area is equal to 144 m^2
I need help converting to logarithmic equation e^-t = 125
Apply ln to both sides:
Ln e^-t = ln 125
Ln e (125) = -t
The population of one country changed from 23 million to 54 million. Use the information to find the unknown values in the bar diagrams a = L.347 b
The population of one country changed from 23 million to 54 million. Use the information to find the unknown values in the bar diagrams a = L.347 b
y
Question 4 of 10Select the correct product of the exponential expression.35A. 5.5.5B. 3.5C. 15D. 3.3.3.3.3SUBMIT
You have the following expression:
[tex]3^5[/tex]it means that the number 3 is multipled by itself five times (because of the exponent), then, the previous expression can be written as follow:
[tex]3^5=3\cdot3\cdot3\cdot3\cdot3[/tex]At an important meet, Hassan won the men's 400 meters in 47.36 seconds. Hassan ran an average rate of__ meters per minnearest hundredth
506.78 meters per min
Explanation:distance = 400 m
time = 47.36 seconds
The result is meant to be in meters/min
We need to convert the seconds to minute:
60 seconds = 1 min
47.36 seconds = 47.36/60 = 0.7893
The average rate will be distance divided by time
[tex]\begin{gathered} \text{Average rate =}\frac{400}{0.7893} \\ \text{Average rate =}\frac{400}{0.7893}\text{ = }506.7782 \\ \\ \text{Average rate = }506.78\text{ meters per min (nearest hundredth)} \end{gathered}[/tex]8. Select the equation that has no real solution.12x + 15 = 12x - 157x +21= 21-5x-25 = 5x + 2512x+ 15 = 3(4x+5)
We will have that the equation with no real solution is:
[tex]12x+15=12x-15[/tex]Because:
[tex]12x-12x=-15-15\Rightarrow0\ne-30[/tex]Can you pls help me with this question thank you
I) We have to convert the temperature from Celsius to Farenheit, using the formula:
[tex]F=\frac{9}{5}\cdot C+32[/tex]The temperature in the Poconos is 15 °C, so we have C = 15. We can then calculate the temperature as:
[tex]\begin{gathered} F=\frac{9}{5}\cdot15+32 \\ F=27+32 \\ F=59 \end{gathered}[/tex]The temperature in Canada is 5 °C, so we can calculate the temperature in Farenheit as:
[tex]\begin{gathered} F=\frac{9}{5}\cdot5+32 \\ F=9+32 \\ F=41 \end{gathered}[/tex]II) We have to find the expression for the cost for each hotel in function of "n", the number of nights.
Holiday inn costs $80 per night plus $10 for parking.
We can express the total cost in function of n as:
[tex]undefined[/tex]A survey asked "Do you think the president is doing a great job?" Of the 1200 Americans surveyed, 800 responded yes. For a 95% level of confidence find the sample proportion and the margin of error associated with the poll.
We have here working with estimating a population proportion.
We have the following information from the question:
• The sample size, n, is equal to 1200 (n = 1200).
,• We have that the fraction that responded "Yes" is 800.
,• We need to find a 95% level of confidence for the margin error associated with the poll.
Now, we have the sample proportion for the sample size, n = 1200 is as follows:
Sample Proportion[tex]\begin{gathered} \hat{p}=\frac{800}{1200}=\frac{2}{3}\approx0.666666666667\approx0.67 \\ \\ \hat{p}=\frac{800}{1200}\approx0.67 \end{gathered}[/tex]Therefore, the sample proportion for the sample size is 800/1200, which is, approximately, 0.67.
The margin of error associated with the pollThe margin of error, in this case, is given by the next formula:
[tex]E=Z_c\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]Where:
[tex]\begin{gathered} Z_c\text{ is the critical value for a 95\% level of confidence} \\ \\ n\text{ is the sample size \lparen n = 1200\rparen} \\ \\ \hat{p}\text{ is the sample proportion \lparen800/1200\rparen} \\ \end{gathered}[/tex]Now, we have that, for a level of confidence of 95%, the critical value is equal to z = 1.96:
Now, using all of the values at our disposal, we can use the formula to find the margin of error as follows:
[tex]\begin{gathered} E=Z_c\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ \\ E=1.96\sqrt{\frac{\frac{8}{12}(1-\frac{8}{12})}{1200}} \\ \\ E=0.0266722216436\approx0.027 \end{gathered}[/tex][tex]\begin{gathered} E=Z_c\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ \\ E=1.96\sqrt{\frac{\frac{8}{12}(1-\frac{8}{12})}{1200}} \\ \\ E=0.0266722216436\approx0.027 \end{gathered}[/tex]Therefore, in summary, we have that:
1. The sample proportion is:
[tex]\hat{p}=\frac{800}{1,200}\approx0.67[/tex]2. The margin of error associated with the poll is:
[tex]E=0.0266722216436\approx0.027[/tex]2705 is compound annually at a rate of 8% for 1 year
The formula of compound interest is,
[tex]\begin{gathered} A=P(1+i)^n \\ \text{Here, A=2075, i=8\%, n=1 year} \\ 2075=P(1+\frac{8}{100})^1 \\ P=1921.3 \end{gathered}[/tex]when Thanos snapped his fingers in Avengers endgame he put a circular hole in this Square what is the area of the Shaded region last left?
Calculate the area of the square (A1), and then subtract the area of the circle (A2).
Square area = side length ^2
A1 = 12^2 = 144 ft2
Area of a circle = π r^2
where:
r= radius = diameter /2 = 12/2 = 6
Replacing:
A2 = π 6^2 = 113.09 ft^2
Area of the shaded region = A1- A2 = 144-113.09 = 30.92 ft2
Greetings, i need help with this math problem. Thank you
The numerator of the left hand side can be rewritten as:
[tex]x^2+6x+9=(x+3)^2[/tex]Then, the given equation can be written as:
[tex]\frac{(x+3)^2}{x+3}=0[/tex]Since
[tex](x+3)^2=(x+3)(x+3)[/tex]we have
[tex]\frac{(x+3)(x+3)}{x+3}=0[/tex]We can to can cancel out one term x+3 and get
[tex]x+3=0[/tex]which gives
[tex]x=-3[/tex]Finally, in order to check that this value corresponds to a real answer, we need to subsitute this value into the equation and compute the limit when x approaches to -3, that is,
[tex]lim_{x\rightarrow-3}\frac{x^2+6x+9}{x+3}[/tex]which gives
[tex]l\imaginaryI m_{x\operatorname{\rightarrow}-3}\frac{x^{2}+6x+9}{x+3}=\frac{0}{0}[/tex]Since the limit has the form 0/0 we can to apply L'Hopital rule, that is,
[tex]l\imaginaryI m_{x\operatorname{\rightarrow}-3}\frac{\frac{d}{dx}(x^2+6x+9)}{\frac{d}{dx}(x+3)}[/tex]which gives
[tex]l\imaginaryI m_{x\operatorname{\rightarrow}-3}\frac{\frac{d}{dx}(x^{2}+6x+9)}{\frac{d}{dx}(x+3)}=l\imaginaryI m_{x\operatorname{\rightarrow}-3}\frac{2x+6}{1}=\frac{0}{1}=0[/tex]Since the limit exists and is equal to zero then the solution of the equation is: x= -3
Find the exact value of s in the given interval that has the given circular function value.
Recall that:
[tex]\tan x=\frac{\sin x}{\cos x}\text{.}[/tex]Therefore:
[tex]\tan s=1\Leftrightarrow\frac{\sin s}{\cos s}=1.[/tex]Then:
[tex]\sin s=\cos s\text{.}[/tex]Now, notice that:
[tex]\sin s-\cos s=-\sqrt{2}\cos (s+\frac{\pi}{4}).[/tex]Then:
[tex]-\sqrt[]{2}\cos (s+\frac{\pi}{4})=0.[/tex]Therefore:
[tex]\cos (s+\frac{\pi}{4})=0.[/tex]Then:
[tex]\begin{gathered} s+\frac{\pi}{4}=\frac{\pi}{2}+n\pi, \\ s+\frac{\pi}{4}=\frac{3\pi}{2}+n\pi\text{.} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} s=\frac{\pi}{4}+n\pi, \\ s=\frac{5\pi}{4}+n\pi\text{.} \end{gathered}[/tex]Since:
[tex]s\in\lbrack\pi,\frac{3\pi}{2}\rbrack^{},[/tex]we get that:
[tex]s=\frac{5\pi}{4}\text{.}[/tex]Answer:
[tex]s=\frac{5\pi}{4}\text{.}[/tex]please help me Solve for a6=a/4+2-6+x/4=-59x-7=-70=4+n/5-4=r/20-52(n+5)=-2-9x+1=-80144=-12(x+5)10-6v=-104
6=a/4+2
Subtract 2 from both sides of the equation:
6-2 = a/4+2-2
4 = a/4
Multiply both sides by 4
4 (4) = a/4 (4)
16 = a
a= 16