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The radius of circle is r = 8 cm.
The arc is of angle 270 degree.
The formula for the arc length is,
[tex]l=2\pi r\cdot\frac{\theta}{360}[/tex]Determine the length of the arc.
[tex]\begin{gathered} l=2\cdot3.14\cdot8\cdot\frac{270}{360} \\ =37.68 \end{gathered}[/tex]So lenth of the arc is 37.68.
Related Questions
The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certainday, 252 people entered the park, and the admission fees collected totaled 728 dollars. How many childrenand how many adults were admitted?Your answer isnumber of children equalsnumber of adults equalso
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Answer: Number of children = 112, number of adult = 140
Let the number of children = x
Let the number of adult =
According to the question, 252 people entered the park
Mathematically, the number of adult and children that entered the park sum up to 252
x + y = 252 ------- equation 1
$1.5 is charged for children for the admission fee into the park
$4 is charged for adult for the admission fee into the park
A totaled of $728 was realized from both children and adult that were admitted into the park
This implies that the total amount realized is equal to the number of children and adults inside the park per amount charged respectively
1.5* x + 4 * y = 728
1.5x + 4y = 728 -------- equation 2
Equation 1 and 2 can be solve simultaneously using substitution method
x + y = 252 ----- 1
1.5x + 4y = 728 ------ 2
Make x the subject of the formula in equation 1
x + y = 252
x = 252 - y ----- equation 3
Substitute equation 3 into equation 2
1.5(252 - y ) + 4y = 728
Open the parenthesis
1.5 x 252 - 1.5 x y + 4y = 728
378 - 1.5y + 4y = 728
Collect the like terms
-1.5y + 4y = 728 - 378
2.5y = 350
Divide both sides by 2.5
y = 350/2.5
y = 140
To find x, put the value of y into equation 1
x + y = 252
x = 252 - y
x = 252 - 140
x = 112
The number of children = 112
The number of adults = 140
How do I solve this problem?Mary reduced the size of a painting to a width of 3.3 inches. What is the new height of it was originally 32.5 inches tall and 42.9 inches wide? Round your answer to the nearest tenth.
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Given the follow equivalence
[tex]\frac{Oldwidth}{Oldheight}=\frac{Newwidth}{Newheight}[/tex]where
old width=42.9
Old height= 32.5
New width=3.3
then
[tex]\frac{42.9}{32.5}=\frac{3.3}{Newheight}[/tex][tex]Newheight=3.3*\frac{32.5}{42.9}[/tex][tex]Newheight=2.5[/tex]New height is 2.5 inches
Given the definitions of f(a) and g(x) below, find the value of (19)( 1),f (x) = x2 + 3x – 11g(x) = 3a + 6
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The given functions are,
[tex]\begin{gathered} f(x)=x^2+3x-11_{} \\ g(x)=3x+6 \end{gathered}[/tex]Fog can be determined as,
[tex]\begin{gathered} \text{fog}=f(g(x)) \\ =f(3x+6) \\ =(3x+6)^2+3(3x+6)-11 \\ =9x^2+36+36x+9x+18-11 \\ =9x^2+45x+43 \end{gathered}[/tex]The value of fog(-1) can be determined as,
[tex]\begin{gathered} \text{fog}(-1)=9(-1)^2+45(-1)+43 \\ =9-45+43 \\ =7 \end{gathered}[/tex]Thus, the requried value is 7.
A car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?
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A car can travel 28 miles per gallon of gas. How far can the car travel on 8 gallons of gas?
Applying proportion
28/1=x/8
solve for x
x=(28)*8
x=224 miles
the answer is 224 milesTranslate the following word phrases to an algebraic expression and simplify: “8 times the difference of 6 times a number and 3”
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SOLUTION:
Step 1:
In this question, we are meant to:
Translate the following word phrases to an algebraic expression and simplify:
“8 times the difference of 6 times a number and 3”
Step 2:
Assuming the unknown number be y, we have that:
[tex]\begin{gathered} 8\text{ ( 6y - 3 )} \\ =\text{ 48 y - 24} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]48y\text{ - 24}[/tex]
Mr Gregory drives a furniture delivery truck 4 days each week the table below shows the driving record for 1 week find the difference in meters between the distance Mr Gregory traveled on Wednesday and Thursday
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ANSWER:
6150 meters
STEP-BY-STEP EXPLANATION:
To calculate the difference between the two days we must calculate the subtraction of the values corresponding to the days Wednesday and Thursday.
[tex]80.75\text{ km}-74.6\text{ km}=6.15\text{ km}[/tex]Now, we convert this value in kilometers to meters, knowing that 1 kilometer is equal to 1000 meters:
[tex]6.15\text{ km}\cdot\frac{1000\text{ m}}{1\text{ km}}=6150\text{ m}[/tex]I need help with this practice problem I’m having trouble solving it
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A generic cosecant function is
[tex]f(x)=A\csc (kx+\theta)+C[/tex]We must find A, k, θ, and C using the information that we have.
Finding A:
To find A we can use the range of the function, we know there is a gap between -9 and 5, that's the crucial information, the value of A will be the mean of |-9| and |5| (in modulus!), therefore
[tex]A=\frac{|-9|+|5|}{2}=\frac{9+5}{2}=\frac{14}{2}=7[/tex]Therefore
[tex]f(x)=7\csc (kx+\theta)+C[/tex]Finding C:
We can use the fact that we know A and find C, let's suppose that
[tex]\csc (kx+\theta)=1[/tex]For an unknown value of x, it doesn't matter, using the range again we can use the fact that 5 is a local minimum of the function, therefore, when the csc(kx + θ) is equal to 1 we have that the function is equal to 5
[tex]\begin{gathered} 5=7\cdot1+C \\ \\ C=-2 \end{gathered}[/tex]And we find that C = -2. Tip: You can also suppose that it's -1 and use -9 = 7 + C, the result will be the same.
Finding k:
Now we will use the asymptotes, we have two consecutive asymptotes at x = 0 and x = 2π, it means that the sin(kx) is zero at x = 0 and the next zero is at x = 2π, we know that sin(x) is zero every time it's a multiple of π, which gives us
[tex]\begin{gathered} \sin (0)=0\Rightarrow\sin (k\cdot0)=0\text{ (first zero | first asymptote)} \\ \sin (\pi)=0\Rightarrow\sin (2k\pi)=0\Rightarrow k=\frac{1}{2}\text{ (second zero | second asymptote)} \end{gathered}[/tex]Therefore, k = 1/2
[tex]f(x)=7\csc (\frac{x}{2}+\theta)-2[/tex]Finding θ:
It's the easiest one, since we have a zero at x = 0 it implies that θ = 0
Therefore our function is
[tex]f(x)=7\csc (\frac{x}{2})-2[/tex]Final answer:
[tex]f(x)=7\csc \mleft(\frac{x}{2}\mright)-2[/tex]
5. Helen, Riley, and Derrick are on a running team. Helen ran 15 1/4 kilometers last week. Riley ran 4 1/12 less kilometers than Helen, and Derrick ran 7 3/8 more kilometers than Riley. If their goal is to run 60 kilometers in total, how much further do they need to run to meet their goal? I
Answers
Given in the scenario:
a.) Helen ran 15 1/4 kilometers last week.
b.) Riley ran 4 1/12 less kilometers than Helen.
c.) Derrick ran 7 3/8 more kilometers than Riley.
d.) Their goal is to run 60 kilometers in total.
To be able to determine how much further do they need to run to get 60 kilometers in total, we must first determine how many kilometers did Riley and Derrick run.
We get,
A.)
[tex]\text{Riley: }4\frac{1}{12}\text{ less kilometers than Helen}[/tex][tex]\text{ = 15 }\frac{1}{4}\text{ - 4 }\frac{1}{12}[/tex]Recall: To be able to subtract mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.
The LCM of 4 and 12 is 12. We get,
[tex]\text{ 15 }\frac{1}{4}\text{ = }\frac{1\text{ + (4 x 15)}}{4}\text{ = }\frac{1\text{ + 60}}{4}\text{ = }\frac{61}{4}\text{ = }\frac{(61)(3)}{12}\text{ = }\frac{183}{12}[/tex][tex]4\text{ }\frac{1}{12}\text{ = }\frac{1\text{ + (4 x 12)}}{12}\text{ = }\frac{1\text{ + 48}}{12}\text{ = }\frac{49}{12}[/tex]Let's now proceed with the subtraction,
[tex]15\frac{1}{4}-4\frac{1}{12}=\frac{183}{12}\text{ - }\frac{49}{12}\text{ = }\frac{183\text{ - 49}}{12}\text{ = }\frac{134}{12}\text{ = }\frac{\frac{134}{2}}{\frac{12}{2}}\text{ = }\frac{67}{6}\text{ or 11}\frac{1}{6}[/tex]Conclusion: Riley ran 11 1/6 kilometers.
B.)
[tex]\text{Derrick: }7\frac{3}{8}\text{ more kilometers than Riley}[/tex][tex]\text{ = 11}\frac{1}{6}\text{ + 7}\frac{3}{8}[/tex]Recall: To be able to add mixed numbers, you must first convert them into an improper fraction with a common denominator. The LCM of the two denominators must be their denominator when converted.
The LCM of 6 and 8 is 24. We get,
[tex]11\frac{1}{6}\text{ = }\frac{1\text{ + (11 x 6)}}{6}\text{ = }\frac{1\text{ + 66}}{6}\text{ = }\frac{67}{6}\text{ = }\frac{(67)(4)}{24}\text{ = }\frac{268}{24}[/tex][tex]7\frac{3}{8}\text{ = }\frac{3\text{ + (7 x 8)}}{8}=\frac{3\text{ + 56}}{8}=\frac{59}{8}=\frac{(59)(3)}{24}=\frac{177}{24}[/tex]Let's now proceed with the addition,
[tex]11\frac{1}{6}\text{ + 7}\frac{3}{8}\text{ = }\frac{268}{24}\text{ + }\frac{177}{24}\text{ = }\frac{268\text{ + 177}}{24}\text{ = }\frac{445}{24}\text{ or 18}\frac{13}{24}[/tex]Conclusion: Derrick ran 18 13/24 kilometers.
C.) To be able to determine how much further do they need to run to get 60 kilometers in total, we subtract 60 by the sum of distance the three people ran.
We get,
[tex]\text{ 60 - (15 }\frac{1}{4}\text{ + 11}\frac{1}{6}\text{ + 18}\frac{13}{24})[/tex]The same process that we did, convert all numbers into similar fractions.
The LCM of 4, 6 and 24 is 24. We get,
[tex]15\frac{1}{4}\text{ = }\frac{1\text{ + }(15\text{ x 4)}}{4}\text{ = }\frac{1\text{ + 60}}{4}\text{ = }\frac{61}{4}\text{ = }\frac{(61)(6)}{24}\text{ = }\frac{366}{24}[/tex][tex]11\frac{1}{6}\text{ = }\frac{1\text{ + (11 x 6)}}{6}\text{ = }\frac{1\text{ + 66}}{6}\text{ = }\frac{67}{6}\text{ = }\frac{(67)(4)}{24}\text{ = }\frac{268}{24}[/tex][tex]\text{ 18}\frac{13}{24}=\text{ }\frac{13+(18\text{ x 24)}}{24}\text{ = }\frac{13\text{ + 432}}{24}\text{ = }\frac{445}{24}[/tex][tex]60\text{ = }\frac{60\text{ x 24 }}{24}\text{ = }\frac{1440}{24}[/tex]Let's proceed with the operation,
[tex]\text{ 60 - (15 }\frac{1}{4}\text{ + 11}\frac{1}{6}\text{ + 18}\frac{13}{24})\text{ = }\frac{1440}{24}-(\frac{366}{24}\text{ + }\frac{268}{24}\text{ + }\frac{445}{24})[/tex][tex]\text{ }\frac{1440\text{ - (366 + 268 + 445)}}{24}\text{ = }\frac{1440\text{ - 1079}}{24}[/tex][tex]\text{ = }\frac{361}{24}[/tex]Therefore, they need to run a total of 361/24 kilometers to be able to meet their goal.
The equation for the line of best fit is shown below.What does the y-intercept represent? A. the cost to upload an unlimited amount of files B. the cost to enroll in the file sharing service C. the cost per file uploaded D. the cost per Mb uploaded
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Answer:
B. the cost to enroll in the file-sharing service
Explanation:
The y-intercept is the cost when x = 0. It means that it is the cost of the service when the customer uploads 0 Mb, so it should represent the cost to enroll in the file-sharing service.
add or subtract : x/4 + 3/4 =
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Answer:
x + 3 / 4
Explanation:
Solve the triangle with the given measures. More than one triangle may be possibletriangle ABCM
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then
[tex]undefined[/tex]The sum of three consecutive integers is -39. What are the three numbers? Enter your answer as three numbers separated by a comma.
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Answer:
-12, -13, and -14
Explanation:
x, y, and z are the three consecutive numbers and they sum -39, so we can write the following equation
x + y + z = -39
Since these numbers are consecutives, we get
y = x + 1
z = x + 2
So, replacing these equation on the first one and solving for x, we get
x + y + z = -39
x + (x + 1) + (x + 2) = -39
x + x + 1 + x + 2 = -39
3x + 3 = -39
3x + 3 - 3 = -39 -3
3x = -42
3x/3 = -42/3
x = -14
Then, y and z are
y = -14 + 1 = -13
z = -14 + 2 = -12
Therefore, the consecutive numbers are
-12, -13, and -14
Find the exact solution to the exponential equation. (No decimal approximation)
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Let's solve the equation:
[tex]\begin{gathered} 54e^{3x+3}=16 \\ e^{3x+3}=\frac{16}{54} \\ e^{3x+3}=\frac{8}{27} \\ \ln e^{3x+3}=\ln (\frac{8}{27}) \\ 3x+3=\ln (\frac{2^3}{3^3}) \\ 3x+3=\ln (\frac{2}{3})^3 \\ 3x+3=3\ln (\frac{2}{3}) \\ 3x=-3+3\ln (\frac{2}{3}) \\ x=-1+\ln (\frac{2}{3}) \\ x=-1+\ln 2-\ln 3 \end{gathered}[/tex]Therefore the solution of the equation is:
[tex]x=-1+\ln 2-\ln 3[/tex]Find the output, f, when the input, t, is 7 f = 2t - 3 f = Stuck? Watch a video or use a hint.
Answers
Answer:
f=11
Explanation:
Given the function:
[tex]f=2t-3[/tex]When the input, t=7
The value of the output, f will be gotten by substituting 7 for t.
[tex]\begin{gathered} f=2t-3 \\ =2(7)-3 \\ =14-3 \\ f=11 \end{gathered}[/tex]The output, f is 11.
in the figure shown MN is parallel to segment YZ what is the length of segment YZ
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We will solve this question using the similar angle theorem
The shape consist of two triangles which i am going to draw out,
One is a big triangle while the other is a small triangle
Let NZ = a
To find NZ We will equate the ratio of the big triangle to that of the small triangle
[tex]\frac{7.5\operatorname{cm}}{3\operatorname{cm}}=\frac{(a+5)cm}{5\operatorname{cm}}[/tex]We then cross multiply to get,
[tex]\begin{gathered} 3(a+5)=7.5\times5 \\ 3a+15=37.5 \\ by\text{ collecting like terms we will have that} \\ 3a=37.5-15 \\ 3a=22.5 \\ \frac{3a}{3}=\frac{22.5}{3} \\ a=7.5\operatorname{cm} \end{gathered}[/tex]Therefore XZ=XN+NZ
[tex]XZ=5+7.5=12.5\operatorname{cm}[/tex]To calculate YZ ,
We will use the pythagorean theorem,
[tex]\begin{gathered} XZ^2=YZ^2+XY^2 \\ 12.5^2=YZ^2+7.5^2 \\ 156.25=YZ^2+56.25 \\ YZ^2=156.25-56.25 \\ YZ^2=100 \\ YZ=\sqrt[]{100} \\ \vec{YZ}=10.0cm \end{gathered}[/tex]Therefore ,
The value of YZ is
[tex]\vec{YZ}=10.0\operatorname{cm}[/tex]Hence ,
The correct answer is OPTION B
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?
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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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Katherine bought à sandwich for 5 1/2 dollar and a adrink for $2.60.If she paid for her meal with a $ 10 bill how much money did she have left?
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To find out how much Katherin have left we need to substrac the amount she spent:
[tex]10-5\frac{1}{2}-2.6=10-5.5-2.6=1.9[/tex]Therefore she has $1.9 left.
To do this same problem in fraction form we need to convert the 2.6 in fraction, to do this we multiply the number by 10 and divided by ten. Then:
[tex]2.6\cdot\frac{10}{10}=\frac{26}{10}=\frac{13}{5}[/tex]then we have:
[tex]\begin{gathered} 10-5\frac{1}{2}-\frac{13}{5}=10-\frac{11}{2}-\frac{13}{5} \\ =\frac{100-55-26}{10} \\ =\frac{19}{10} \end{gathered}[/tex]Therefore, the answer in decimal form is 19/10 dollars.
an equation that shows that two ratios are equal is a(n)
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An equation that shows that two ratios are equal is referred to as a true proportion.
What is an Equation?This refers to as a mathematical term which is used to show or depict that two expressions are equal and is usually indicated by the sign = .
In the case in which the equation shows that two ratios are equal is referred to as a true proportion and an example is:
10/5 = 4/2 which when expressed will give the same value which is 2 as the value which makes them equal and is thereby the reason why it was chosen as the correct choice.
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i will drop a picture
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B) y= -1/2x -4
1) Let's start by picking two points from that line: (0,3) and (-2,-1). Now we can plug them into the slope formula and find out the slope of that line:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\Rightarrow m=\frac{-1-3}{-2-0}=\frac{-4}{-2}=2[/tex]2) Examining that graph we can see that when x=0 y=3, so the linear coefficient b is 3. Therefore we can write the equation as y= 2x-3.
2.2) Since the question wants a perpendicular line, then the slope of this perpendicular line must be reciprocal and opposite to m=2, so:
[tex]m\perp=-\frac{1}{2}[/tex]So, plugging the given point (6,-7) we can find out the linear coefficient of that perpendicular line:
y=mx +b
-7 = 6(-1/2) +b
-7 =-3 +b
-7+3 = b
b=-4
3) Hence, the answer is y= -1/2x -4
Find the equations (in terms of x) of the line through the points (-2,-3) and (3,-5)
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The general equation of a line passing through two points (xb₁,y₁)Pxb₂,y₂) is expressed as
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ m\Rightarrow slope\text{ of the line, expr}essed\text{ as }m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)\Rightarrow coordinate_{}\text{ of point P} \\ (x_2,y_2)\Rightarrow coordinate_{}\text{ of point Q} \end{gathered}[/tex]Given that the coordinates of the two points are (-2, -3) and (3, -5), we have
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(-2,\text{ -3)} \\ (x_2,y_2)\Rightarrow(3,\text{ -5)} \end{gathered}[/tex]Step 1:
Evaluate the slope o the line.
The slope is thus evaluated as
[tex]\begin{gathered} m\text{ = = }\frac{y_2-y_1}{x_2-x_1} \\ \text{ = }\frac{\text{-5-(-3)}}{3-(-2)} \\ =\frac{-5+3}{3+2} \\ \Rightarrow m\text{ = -}\frac{2}{5} \end{gathered}[/tex]Step 2:
Substitute the values of x₁,
Thus, we have
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ x_1=-2 \\ y_1=-3 \\ m\text{ =- }\frac{2}{5} \\ \text{thus,} \\ y-(-3)\text{ = -}\frac{2}{5}(x-(-2)) \\ y+3\text{ =- }\frac{2}{5}(x+2) \end{gathered}[/tex]Step 3:
Make .
[tex]\begin{gathered} y+3\text{ =- }\frac{2}{5}(x+2) \\ \text{Multiply both sides of the equation by 5 } \\ 5(y+3)\text{ = -2(x+2)} \\ \text{open brackets} \\ 5y\text{ + 15 =- 2x - 4} \\ \Rightarrow5y\text{ =- 2x - 4 -15} \\ 5y\text{ = -2x-1}9 \\ \text{divide both sides of the equation by the coefficient of y, which is 5.} \\ \text{thus,} \\ \frac{5y}{5}=\frac{-\text{2x-1}9}{5} \\ \Rightarrow y\text{ =- }\frac{2}{5}x\text{ - }\frac{19}{5} \end{gathered}[/tex]Hence, the equation of the line is
[tex]y\text{ = -}\frac{2}{5}x\text{ - }\frac{19}{5}[/tex]y₁ and m into the general equation of the line.
I ONLY need help with the last question help me with special Angles in a circle..GEOMETRY
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We want to know the measure of the angle BCD. In this case, we see that it is an inscribed angle, and then its measure is half of the arc it intercepts (in this case BD).
With this in mind,
[tex]m\measuredangle BCD=\frac{1}{2}m\hat{BD}=\frac{1}{2}(130^{\circ})=65^{\circ}[/tex]And then, the angle BCD has 65°.
In ∆PQR, p=13 inches, q=18 inches and r= 12 inches. Find the area of ∆PQR to the nearest square inch.
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Given data:
The first side of the triangle is p=13 inches.
The second side of the triangle is q=18 inches.
The third side of the triangle is r= 12 inches.
The semi-perimeter is,
[tex]\begin{gathered} s=\frac{p+q+r}{2} \\ =\frac{13\text{ in+18 in+12 in}}{2} \\ =21.5\text{ in} \end{gathered}[/tex]The expression for the area of the triangle is,
[tex]\begin{gathered} A=\sqrt[]{s(s-p)(s-q)(s-r)_{}} \\ =\sqrt[]{21.5\text{ in(21.5 in-13 in)(21.5 in-18 in)(21.5 in-12 in)}} \\ =\sqrt[]{(21.5\text{ in)(8.5 in)(3.5 in)(9.5 in)}} \\ =77.95in^2 \end{gathered}[/tex]Thus, the area of the given triangle is 77.95 sq-inches.
3: A Bunch of SystemsSolve each system of equations without graphing and show your reasoning. Then, check yoursolutions,
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Use the elimination method to solve the given system of equations.
To do so, multiply the first equation by -3 so that the coefficient of x in the first equation becomes the additive inverse of the coefficient of x in the second equation:
[tex]\begin{gathered} -3(2x+3y)=-3(16) \\ \Rightarrow-6x-9y=-48 \end{gathered}[/tex]Then, the system is equivalent to:
[tex]\begin{gathered} -6x-9y=-48 \\ 6x-5y=20 \end{gathered}[/tex]Add both equations to eliminate the variable x and to obtain an equation in terms of the variable y only:
[tex]\begin{gathered} (-6x-9y)+(6x-5y)=-48+20 \\ \Rightarrow-6x-9y+6x-5y=-28 \\ \Rightarrow-14y=-28 \\ \Rightarrow y=\frac{-28}{-14} \\ \therefore y=2 \end{gathered}[/tex]Replace y=2 into the first equation to find the value of x:
[tex]\begin{gathered} 2x+3y=16 \\ \Rightarrow2x+3(2)=16 \\ \Rightarrow2x+6=16 \\ \Rightarrow2x=16-6 \\ \Rightarrow2x=10 \\ \Rightarrow x=\frac{10}{2} \\ \therefore x=5 \end{gathered}[/tex]Replace y=2 and x=5 into the second equation to confirm the answer:
[tex]\begin{gathered} 6x-5y=20 \\ \Rightarrow6(5)-5(2)=20 \\ \Rightarrow30-10=20 \\ \Rightarrow20=20 \end{gathered}[/tex]Therefore, the solution to the system of equations is x=5, y=2.
The pro shop at the Hidden Oaks Country Club ordered two brands of golf balls. Swinger balls cost$2.10 each and the Supra balls cost $1.00 each. The total cost of Swinger balls exceeded the total costof the Supra balls by $330.00. If an equal number of each brand was ordered, how many dozens ofeach brand were ordered?AnswerHow to enter your answer (opens in new window)KeypadKeyboard Shortcutdozen
Answers
The Solution:
Given that equal number of each brand of golf ball was ordered.
Let the number of each brand ordered be represented with n
Each swinger ball cost $2.10
So, the total cost of the swinger ball ordered is:
[tex]2.10n[/tex]Each Supra ball cost $1.00
So, the total cost of the supra ball ordered is:
[tex]\begin{gathered} 1.00\times n \\ \text{which becomes}\colon \\ n \end{gathered}[/tex]Given that the total cost of the Swinger balls exceeded the total cost of the Supra balls by $330.00. We have the linear equation below:
[tex]2.1n=n+330[/tex]We are required to find the number of dozens of each brand of golf balls that were ordered.
So, we shall solve for n and then divide the value by 12.
[tex]\begin{gathered} 2.1n=n+330 \\ \text{collecting the like terms, we get} \\ 2.1n-n=330 \\ 1.1n=330 \end{gathered}[/tex]Dividing both sides by 1.1, we get
[tex]\begin{gathered} \frac{1.1n}{1.1}=\frac{330}{1.1} \\ \\ n=300\text{ balls} \end{gathered}[/tex]Dividing 300 by 12 (since 1 dozen = 12 balls), we get
[tex]\frac{300}{12}=25\text{ dozens of each brand of golf balls were ordered.}[/tex]Therefore, the correct answer is 25 dozens.
Which equation shows the commutative property? CLEAR SUBMIT (10+5) (30 + 6) = 15 x 36 36 x 15 = 15 X 36 (10 + 30) x (5 + 6) = 15 x 36 36 + 15 = 15 X 36
Answers
Explanation
The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication,hence
Let's check every option
Step 1
a)
[tex]\begin{gathered} (10+5)\cdot(30+6)=15\cdot36 \\ \end{gathered}[/tex]this does not show the commutative property
b)
[tex]\begin{gathered} 36\cdot15=15\cdot36 \\ \end{gathered}[/tex]as we can see the factor were moved, and by the commutative property the result is not afected, so
[tex]\begin{gathered} \\ 36\cdot15=15\cdot36 \end{gathered}[/tex]is the answer.
I hope this helps you
What is the value of the trig ratio sin A?
Answers
The sine relation is given by the length of the opposite leg to the angle over the length of the hypotenuse.
So, for the given triangle, we have:
[tex]\begin{gathered} \sin A=\frac{BC}{AC}\\ \\ \sin A=\frac{20}{29} \end{gathered}[/tex]Therefore the value of sin A is 20/29.
A) Write an expression for the given number trick B) Simplify the expression you came up with
Answers
a)
Since we need an Expression, we also need a variablel for the "number".
Let's use "n".
We will translate each of the lines:
Pick a number : n
Mutiply that number by 12, so it becomes: n x 12
Add 15 to that, so we put parenthesis around that expression and add "15" to it:
(n x 12) + 15
Divide by 3, then we simply divide whole thing by 3, so we have:
[tex]\frac{(n\times12)+15}{3}[/tex]b)
To simplify, let's re-write:
[tex]\begin{gathered} \frac{(n\times12)+15}{3} \\ =\frac{12n+15}{3} \\ =\frac{12n}{3}+\frac{15}{3} \\ =4n+5 \end{gathered}[/tex]This is the simplified form.
√64= A. 16 B. 8 C. 7 D. 9
Answers
Answer:
B. 8
Explanation:
[tex]64=8\times8[/tex]We can write this in index form as:
[tex]64=8^2[/tex]Therefore:
[tex]\sqrt[]{64}=\sqrt[]{8^2}[/tex]On the right-hand side, the square root sign cancels the square, so we have:
[tex]\sqrt[]{64}=8[/tex]The correct choice is B.
what is the domain and range of {(1,0), (2,0), (3,0) (4,0), (5,0)}
Answers
We have the following:
The domain is the input values or the values of x and the range is the output values or the values of y
Therefore:
[tex]\begin{gathered} D=\mleft\lbrace{}1,2,3,4,5\mright\rbrace \\ R=\mleft\lbrace0\mright\rbrace \end{gathered}[/tex]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 cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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