Answer:
The number of tickets that cost $ 10 is 923
The number of tickets that cost $ 20 is 1205
The number of tickets that cost $ 30 is 1111
Step-by-step explanation:
Given as :
The total number of three different tickets cost $ 10 , $ 20 and VIP seats $ 30
The total number of all tickets sold = 3239
The sale price for the tickets = $ 63720
Let The type of ticket for $ 10 = x
And The type of ticket for $ 20 = y
And The type of VIP ticket = v
According to question
The number of $ 20 tickets = The number of $ 10 tickets + 282
I.e y = x + 282
And x + y + v = 3239
Or, v = 3239 - ( x + y )
I.e v = 3239 - ( x + x +282 )
Or, v = 2957 - 2 x
Now ,
x × $ 10 + y × $ 20 = v × $ 30
Or, x × $ 10 + ( x + 282 ) × $ 20 = ( 2957 - 2 x ) × $ 30
or, 10 x + 20 x + 5640 = 88710 - 60 x
Or, 30 x + 60 x = 88710 - 5640
or, 90 x = 83070
∴ x = [tex]\frac{83070}{90}[/tex]
I.e x = 923
So, The number of tickets that cost $ 10 = x = 923
Similarly
y = x + 282
or, y = 923 + 282
I.e y = 1205
So, The number of tickets that cost $ 10 = y = 1205
And
v = 2957 - 2 x
∴ v = 2957 - 2 × 923
I.e v = 1111
So, The number of tickets that cost $ 30 = v = 1111
Hence
The number of tickets that cost $ 10 is 923
The number of tickets that cost $ 20 is 1205
The number of tickets that cost $ 30 is 1111
Answer
Answer:
1021 of the $10 tickets, 1303 of the $20 tickets and 915 of the $30 tickets.
Step-by-step explanation:
We have 3 types of tickets:
ones that cost $10, others that cost $20 and others that cost $30.
If A is the number of $10 tickets sold, B is the number of $20 tickets sold and C is the number of $30 tickets sold we have that:
A + B + C = 3239
B = A + 282
A*10 + B*20 + C*30 = 63720
We need to solve this system of equations.
From the second equation we have B isolated, we can replace it in the other equations:
A + (A + 282) + C = 3239
A*10 + (A + 282)*20 + C*30 = 63720
Now we can isolate one of the variables in the first equation and replace it in the second, lets isolate C.
C = 3239 - 2*A - 282 = 2957 - 2*A
the third equation is now:
A*10 + (A + 286)*20 + (2957 - 2*A)*30 = 63720
Now we solve it for A:
A*10 + A*20 - A*60 + 282*20 + 2957*30 = 63720
-A*30 + 94350 = 63720
A*30 = - 63720 + 94350 = 30630
A = 30639/30 = 1021
So they sold 1021 tickets of $10.
Now we can replace it in the equation:
C = 2957 - 2*A = 2957 - 2*1021 = 915
They sold 915 $30 tickets
They sold 1303 tickets of $20.
B = A + 282 = 1021 + 282 = 1303.
A farm is rectangular with an area of 1/2 square
miles. If the length of the farm is 1/3 miles, what
is its width? Input your answer as a fraction.
The width of a rectangular farm with area of 1/2 square mile and length of 1/3 mile is 1 1/2 miles.
Explanation:The area of a rectangle is found by multiplying length times width. In this case, we know that the area is 1/2 square mile and the length is 1/3 mile.
So we have the equation (Length) * (Width)= Area; so 1/3 * W = 1/2. To solve for W (width), you need to divide both sides of the equation by 1/3.You might remember that dividing by a fraction is the same as multiplying by its reciprocal. So, we divide 1/2 by 1/3, which is the same thing as 1/2 * 3/1. Doing this, we end up with the fraction 3/2, or 1 1/2.
So the width of the farm is 1 1/2 miles.
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5 different mathematics books, 4 different French books and 2 different biology books are to be arrange on a shelf. How many different arrangements are possible, if
1. The books in each particular subject must all stand together?
2. Only the mathematics books must stand together.
Problem 1
A = 5! = 5*4*3*2*1 = 120 ways to arrange the math books
B = 4! = 4*3*2*1 = 24 ways to arrange the French books
C = 2! = 2*1 = 2 ways to arrange the biology books
D = 3! = 3*2*1 = 6 ways to arrange the three blocks of books, each block a different subject
E = A*B*C*D = 120*24*2*6 = 34560 different ways to arrange the books such that the subjects stick together
-------------
Answer: 34560========================================
Problem 2
Group all the math books to form one "book". This is the same as taking out the 5 math books and replacing it with one single math book. This single math book acts as a placeholder for all of the five books together as one block.
We have
1 math "book"
4 French books
2 biology books
So there are 1+4+2 = 7 "books" total and
7! = 7*6*5*4*3*2*1 = 5040 different ways to arrange those "books"
Within the math block of books, there are 5! = 120 ways to arrange things.
So overall we have 120*5040 = 604800
-------------
Answer: 604800Jasmine has 3/4 cup of flour in a mixing bowl. After adding more flour to the mixing bowl, Jasmine says that she now has 5/8 cup of flour.
Why is her statement incorrect?
Answer:
6/8
Step-by-step explanation:
3/4 into eighths would be 6/8. She said she had 5/8 cups of flour.
Deja has two baskets of berries. One of the baskets has 3 3/8 pounds of berries and the other basket has 2 7/8 pounds of berries. She is going to split the berries evenly among 4 people. Witch measure is the best estimate for the number of pounds of berries each person would receive.
A) 1 1/4 pounds
B) 1 5/8 pounds
C) 2 7/8 pounds
D) 3 3/16 pounds
Answer:
(b) The number of pounds of berries each person would receive is [tex]1\frac{5}{8}[/tex]pounds.
Step-by-step explanation:
The amount of berries in first basket = 3 3/8 pounds
Now, [tex]3\frac{3}{8} = 3+\frac{3}{8} = 3 + 0.375 = 3.375[/tex]
So, the amount of berries in first basket = 3.375 pounds
The amount of berries in second basket = 2 7/8 pounds
Now, [tex]2\frac{7}{8} = 2+\frac{7}{8} = 2 + 0.875 = 2.875[/tex]
So, the amount of berries in second basket = 2.875 pounds
Now, the total berries = Berries in ( First + Second) basket
= 3.375 pounds + 2.875 pounds
= 6.25 pounds
So, the number of pounds each person would have = [tex]\frac{\textrm{Total weight of viable berries}}{\textrm{4}} = \frac{6.25}{4} = 1.5625[/tex]
Now, [tex]1.5625 = 1 + 0.5625 = 1 + \frac{5625}{10000} = 1 + \frac{5}{8} = 1\frac{5}{8}[/tex]
So, the number of pounds of berries each person would receive is [tex]1\frac{5}{8}[/tex]pounds.
The line segment shown is rotated 90° clockwise about the origin. What are the new coordinates of point B?
(3, - 4)
Imagine a rectangle with one corner on the origin and the opposite on the point. Rotate the rectangle about the origin and see where the point lands.
To find the new coordinates of point B after a 90° clockwise rotation around the origin, you apply the rotation rule: (x, y) becomes (y, -x). The original coordinates are needed to calculate the exact new position of point B.
Explanation:The student is asking about the result of a 90° clockwise rotation of a point around the origin in the Cartesian coordinate system. To find the new coordinates of point B after the rotation, we use the rule for 90° clockwise rotation, which is (x, y) becomes (y, -x). If the original coordinates of point B are (x₂, y₂), the new coordinates after the rotation will be (y₂, -x₂).
Without knowing the original coordinates of point B, we cannot give the exact new coordinates. However, if the student provides the initial coordinates, the new coordinates can be calculated using the rotation rule mentioned.
Which comparison is true?
O A. 0.3 > 0.09
B. 0.04 > 0.2
OC. 0.29 > 0.38
OD. 0.24 > 0.67
O E. 0.55 > 0.600
Answer:
0.3 > 0.09
Step-by-step explanation:
The comparison 0.3 > 0.09 is true.
0.3 = 0.300
0.300 > 0.009
All other options are false. They should have a less than sign instead of a greater than sign.
Final answer:
Upon comparison of decimal values in the given options, Option A (0.3 > 0.09) is the true comparison as 0.3 is greater than 0.09 when comparing the tenths place.
Explanation:
When comparing decimal numbers, you should look at the largest place value first and work your way to smaller place values to determine which number is larger. Let's evaluate each option:
A. 0.3 > 0.09: Comparing the tenths place, 3 is greater than 0. Therefore, this statement is true.
B. 0.04 > 0.2: Comparing the tenths place, 0 is less than 2. Therefore, this statement is false.
C. 0.29 > 0.38: Comparing the tenths place, both numbers are equal, but in the hundredths place, 9 is less than 8. Therefore, this statement is false.
D. 0.24 > 0.67: Comparing the tenths place, 2 is less than 6. Therefore, this statement is false.
E. 0.55 > 0.600: Comparing the tenths place, both numbers are equal, and in the hundredths place, 5 is equal to 0 followed by an additional 0, thus both numbers are equal and this statement is false.
Based on the above analysis, the correct answer is Option A. 0.3 > 0.09.
The measure of the vertex angle of an isosceles triangle is 92. Find the measure of a base angle
Answer:
44°
Step-by-step explanation:
The sum of the angles in a triangle = 180°
In an isosceles triangle the base angles are equal, thus
base angle = [tex]\frac{180-92}{2}[/tex] = [tex]\frac{88}{2}[/tex] = 44°
(-4,6); slope = -3/4
Answer:
y-6=-3/4(x+4)
Step-by-step explanation:
y-y1=m(x-x1)
m=-3/4
y-6=-3/4(x-(-4))
y-6=-3/4(x+4)
A barn silo, excluding the top, is a cylinder. The silo is 7 m in
diameter and the height is 12 m. What is the volume of the silo?
The volume of the silo is 461.81 m³
Step-by-step explanation:
A barn silo, excluding the top, is a cylinder
The silo is 7 m in diameterIts height is 12 mWe need to find the volume of the silo
∵ The silo is shaped a cylinder
∵ The volume of a cylinder = base area × height
∵ The base is shaped a circle
∵ Area a circle = π r², where r is the radius of the circle
∴ The volume of the silo = π r² × h
∵ The diameter of the silo = 7 m
∵ The radius of a circle is half the diameter
∴ The radius of the silo = [tex]\frac{1}{2}[/tex] × 7 = 3.5 m
∵ The height of the silo = 12 m
- Substitute the values of r and h in the rule of volume
∴ The volume of the silo = π (3.5)² × 12
∴ The volume of the silo = 147 π = 461.81 m³
The volume of the silo is 461.81 m³
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Final answer:
The volume of a barn silo that is shaped like a cylinder with a diameter of 7 meters and a height of 12 meters is approximately 461.7 cubic meters.
Explanation:
To calculate the volume of the silo which is in the shape of a cylinder, we use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. The diameter of the silo is given as 7 meters, so the radius is half of that, which is 3.5 meters. The height of the silo is 12 meters. Plugging these values into the formula gives:
V = π × (3.5 m)² × 12 m
V = π × 12.25 m² × 12 m
V = π × 147 m³
Assuming π to be approximately 3.14159, the calculation results in:
V = 3.14159 × 147 m³ = 461.7 m³ (approx)
So, the volume of the silo is approximately 461.7 cubic meters.
Given that LON is a right angle, find the measure of x.
Answer:
[tex]x=30\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
m∠LOM+m∠MON=m∠LON ----> by angle addition postulate
we have
m∠LOM=2x°
m∠MON=x°
m∠LON=90° ----> is a right angle
substitute the values
[tex]2x+x=90[/tex]
solve for x
[tex]3x=90[/tex]
[tex]x=30\°[/tex]
In a recipe for double chocolate every 1/2 cup of milk calls for 2 cups of chocolate. if the recipe were increased to include 4 cups of chocolate, how much milk would be needed?
Answer:1 C milk
Step-by-step explanation:
1/2 C milk = 2 C chocolate
1 C milk = 4 C chocolate
Answer:
1 cup of milk
Step-by-step explanation:
If 1/2 cup of milk is needed for 2 cups of chocolate, and you need to find how much milk is needed for 4 cups, then you'd follow the same steps as going from 2 cups to 4, multiplying by 2.
2 cups chocolate x 2 = 4 cups chocolate
1/2 cup milk x 2 = 1 cup
pls use the diagram to answer the question thanks
Answer:
A) The smaller angle between 12 and 3 is 90° and that is [tex]\frac{1}{4}[/tex]th coordinate
B) The smaller angle between 2 and 3 is 30°
C) The angle between 4 and 6 is 60°
D) the angle between 6 and 9 is 90°
D) The angle between 6 and 12 is 180°
E) The angle between 7 and 8 is 30°
Step-by-step explanation:
Given as :
It is shown in diagram as ;
The circle with different angles from angle 1 to angle 12
Now, The figure is the complete circle, and the measure of all angles in a circle = 360°
The measure of semicircle = 180°
and each quadrant is divided in to 3 angles
Each right angle is further divided into three 30° angles
Again ,
A) The smaller angle between 12 and 3 is 90° and that is [tex]\frac{1}{4}[/tex]th coordinate
B) The smaller angle between 2 and 3 is 30°
C) The angle between 4 and 6 is 60°
D) the angle between 6 and 9 is 90°
D) The angle between 6 and 12 is 180°
E) The angle between 7 and 8 is 30° Answer
it took jack 360 seconds to walk home from school how many min did it take him
1 minute has 60 seconds. So dividing the number of seconds jack has to walk from school to home by 60 will give us minutes.
[tex]t=\dfrac{360\mathrm{s}}{60}=\boxed{6\mathrm{min}}[/tex]
Hope this helps.
Your get a haircut that cost $23.if you tip the barber 10%,what is the final bill?
Answer:
$25.30
Step-by-step explanation:
The final bill was $25.30 if you get a haircut that cost $23.if you tip the barber 10% of the total haircut cost.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
You get a haircut that cost $23.if you tip the barber 10% of the total hair cut cost.
Let x be the final bill amount.
The value of x can be found as follows:
x = $23 + 10% of $23
x = 23 + (10/100)23
x = 23 + 0.1(23)
x = 23 + 2.30
x = $25.30
Thus, the final bill was $25.30 if you get a haircut that cost $23.if you tip the barber 10% of the total haircut cost.
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Solve for x. 10 = − 2/3 x A) −6 B) −9 C) −15 D) −18
Answer:
x=-10/23
Step-by-step explanation:
-23x=10
x=10/-23
x=-10/23
Answer:
x = -15 thus c: is your answer
Step-by-step explanation:
Solve for x:
10 = (-2 x)/3
10 = (-2 x)/3 is equivalent to (-2 x)/3 = 10:
(-2 x)/3 = 10
Multiply both sides of (-2 x)/3 = 10 by -3/2:
(-3 (-2) x)/(2×3) = (-3)/2×10
(-3)/2×(-2)/3 = (-3 (-2))/(2×3):
(-3 (-2))/(2×3) x = (-3)/2×10
(-3)/2×10 = (-3×10)/2:
(-3 (-2) x)/(2×3) = (-3×10)/2
(-3)/3 = (3 (-1))/3 = -1:
(-2-1 x)/2 = (-3×10)/2
(-2)/2 = (2 (-1))/2 = -1:
--1 x = (-3×10)/2
(-1)^2 = 1:
x = (-3×10)/2
10/2 = (2×5)/2 = 5:
x = -35
-3×5 = -15:
Answer: x = -15
HELP An investor invested a total of $2,800 in two mutual funds. One fund earned 5% profit while the other earned 3% profit. If the investor's total profit was $104, how much was invested in each mutual fund? The amount invested in the mutual fund that earned 5% was $(blank). The amount invested in the mutual fund that earned 3% was $(blank). (show your work)
Answer:
The amount invested in the mutual fund that earned 5% was $1,000
The amount invested in the mutual fund that earned 3% was $1,800
Step-by-step explanation:
Let
x ----> the amount invested in the mutual fund that earned 5%
y ----> the amount invested in the mutual fund that earned 3%
we know that
[tex]x+y=2,800[/tex] ----> [tex]y=2,800-x[/tex] ----> equation A
[tex]5\%=5/100=0.05[/tex]
[tex]3\%=3/100=0.03[/tex]
[tex]0.05x+0.03y=104[/tex] ----> equation B
Solve the system by substitution
substitute equation A in equation B
[tex]0.05x+0.03(2,800-x)=104[/tex]
Solve for x
[tex]0.05x+84-0.03x=104[/tex]
[tex]0.05x-0.03x=104-84[/tex]
[tex]0.02x=20[/tex]
[tex]x=\$1,000[/tex]
Find the value of y
[tex]y=2,800-x[/tex]
[tex]y=2,800-1,000=\$1,800[/tex]
therefore
The amount invested in the mutual fund that earned 5% was $1,000 and the amount invested in the mutual fund that earned 3% was $1,800
what is the sign of 3/5 + 3/5
Final answer:
The sum of two positive numbers always has a positive sign, so the sum of 3/5 + 3/5 is positive.
Explanation:
The question what is the sign of 3/5 + 3/5 involves understanding the rules of addition for numbers with the same sign. According to the rules of addition:
When two positive numbers add, the answer has a +ve sign.
Since both fractions 3/5 and 3/5 are positive, their sum will also have a positive sign. Therefore, the sign of the sum 3/5 + 3/5 is +ve, which means the answer is also positive.
To divide a number by 100, move the decimal point _____.
two places to the right
three places to the left
two places to the left
three places to the right
Answer:
c. two places to the left
Step-by-step explanation:
Answer:
two places to the left
Step-by-step explanation:
solve for w: -5(3-w)+4=-5/6(24-6w)
Answer:
no solution
Step-by-step explanation:
well first you gotta distribute
-5(-3 - w) + 4 = -5/6(24 - 6w)
15 + 5w + 4 = -20 + 5w
19 + 5w = -20 + 5w
+20 +20
39 + 5w = 5w
-5w -5w
39 ≠ 0
therefore there is no solution (which is the answer)
Question 11 of 15 (1 point)
4.4 Section Exercise 18
Use the problem-solving flowchart.
Twice the sum of a number and two is seventeen less than five times the number. Find the
number. Round your answer to the nearest integer, if necessary.
The number is
The number is 7
Step-by-step explanation:
Let x be the number
then according to given statement
[tex]2(x+2) = 5x-17[/tex]
Simplifying
[tex]2x+4 = 5x-17[/tex]
Adding 17 on both sides
[tex]2x+4+17 = 5x-17+17\\2x+21 = 5x[/tex]
Subtracting 2x from both sides
[tex]2x+21-2x = 5x - 2x\\21 = 3x\\3x = 21[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3} = \frac{21}{3}\\x = 7[/tex]
Hence,
The number is 7
Keywords: Linear equation, variables
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determina la medida de cada uno de los angulos del triángulo ABC si se conoce que (3x+1)° (3x+4)° y (2x-1)°
Answer:
∠A=67°
∠B=70°
∠C=43°
Step-by-step explanation:
The correct question in English is
Determines the measurement of each of the angles of the triangle ABC if it is known that A=(3x+1)°,B=(3x+4)° and C=(2x-1)°.
we know that
The measure of the interior angles in a triangle must be equal to 180 degrees
so
∠A+∠B+∠C=180°
substitute the given values
[tex](3x+1)\°+(3x+4)\°+(2x-1)\°=180\°[/tex]
solve for x
[tex](8x+4)\°=180\°[/tex]
[tex]8x=180-4[/tex]
[tex]x=22[/tex]
Find the measure of each angle
∠A=(3(22)+1)=67°
∠B=(3(22)+4)=70°
∠C=(2(22)-1)=43°
decide whether the pair of lines is parallel, perpendicular, or neither. 3x-6y=2 and 18x+9y=8
Answer: perpendicular
Step-by-step explanation:
Final answer:
The slopes of the two lines given by the equations 3x-6y=2 and 18x+9y=8 are 1/2 and -2 respectively. Since these slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
Explanation:
To decide whether the pair of lines is parallel, perpendicular, or neither, we need to find the slopes of the lines. The lines are given by the equations 3x-6y=2 and 18x+9y=8. To find the slope of each line, we must rewrite the equations in slope-intercept form (y=mx+b), where m represents the slope
For the first line, 3x-6y=2, we isolate y:
3x - 6y = 2-6y = -3x + 2y = (1/2)x - 1/3So the slope of the first line is 1/2.
For the second line, 18x+9y=8, we isolate y:
18x + 9y = 89y = -18x + 8y = -2x + 8/9The slope of the second line is -2.
Since the slopes of the two lines are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.
The width of a rectangle is 3/8 the length x of the rectangle. What is the perimeter of the rectangle?
Answer:
(11/4)x units
Step-by-step explanation:
for a rectangle,
perimeter = 2(length) + 2(width)
given:
length = x
width = (3/8)x
hence,
perimeter = 2(length) + 2(width)
perimeter = 2x + 2(3/8)x
perimeter = 2x + (3/4)x
perimeter = [2 + (3/4)]x
perimeter = (11/4)x
10. A toy store received a shipment of 17 cases of
teddy bears. Use compatible numbers to estimate
the total number of teddy bears in the shipment.
12 bears per case
Answer: 204 teddy bears
Step-by-step explanation:
Answer:
17 x 12 = 204 teddy bears
Step-by-step explanation:
17 cases, 12 bears in each case
You could round 17 --> 20
You could round 12 --> 10
20×10=200
3x + 2 = x + 4 ( x + 2 )
Answer:
x = -3Step-by-step explanation:
[tex]3x+2=x+4(x+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\3x+2=x+(4)(x)+(4)(2)\\\\3x+2=x+4x+8\qquad\text{combine like terms}\\\\3x+2=(x+4x)+8\\\\3x+2=5x+8\qquad\text{subtract 2 from both sides}\\\\3x+2-2=5x+8-2\\\\3x=5x+6\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\3x-5x=5x-5x+6\\\\-2x=6\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{6}{-2}\\\\x=-3[/tex]
5x - 9y=1
-7x + 2y = -5
9514 1404 393
Answer:
(x, y) = (43/53, 18/53)
Step-by-step explanation:
If we want to eliminate the x-terms, we multiply the first equation by 7 (opposite of the x-coefficient in the second equation), and we multiply the second equation by 5 (x-coefficient in the first equation). Then we add the result.
7(5x -9y) +5(-7x +2y) = 7(1) +5(-5)
35x -63y -35x +10y = 7 -25
-53y = -18 . . . . simplify. Note the x-terms are gone.
y = 18/53 . . . . . divide by -53
__
Putting this value of y in the first equation, we get ...
5x -9(18/53) = 1
5x = 1 + 162/53 = 215/53 . . . . . add 9y to both sides, simplify
x = 43/53 . . . . . . . . . . divide by 5
The solution is (x, y) = (43/53, 18/53).
Evelyn is using her grandmother's pancake recipe, but she wants to make 40% more pancakes than the recipe usually prepares. If her grandmother's recipe calls for 1/2 cup of flour, how much flour will Evelyn need to use? Show Work!
(A) 3/10 cup
(B) 1/2 cup
(C) 7/10 cup
(D) 1 3/10 cup
(C) 7/10 cup is the correct answer
Step-by-step explanation:
First of all we will calculate the 40% of grandmother's recipe then add it to the given flour in grandma's recipe
So,
The amount of flour in grandma's recipe = F_g = 1/2 cups
Calculating percentage
[tex]=40\%\ of\ \frac{1}{2}\\=\frac{40}{100}*\frac{1}{2}\\=\frac{2}{10}[/tex]
So Evelyn needs to add 2/10 cups more to the original quantity.
So,
Flour used by Evelyn:
[tex]=\frac{1}{2}+\frac{2}{10}\\\\=\frac{5+2}{10}\\\\=\frac{7}{10}\ cups[/tex]
Hence,
(C) 7/10 cup is the correct answer
Keywords: Percentage, Quantity
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Use the graph representing bacteria decay to estimate the domain of the function and solve for the average rate of change across the domain.
An exponential function titled Bacteria Decay with x axis labeled Time, in Minutes, and y axis labeled Amount of Bacteria, in Thousands, decreasing to the right with a y intercept of 0 comma 60 and an x intercept of 18 comma 0.
0 ≤ x ≤ 18, −3.33
0 ≤ x ≤ 18, −0.3
0 ≤ y ≤ 60, −3.33
0 ≤ y ≤ 60, −0.3
Can someone please explain to me HOW to transform this equation to determine if its an identity (8x+12y)^2+(6x+9y)=(10x+15y)^2
Answer:
See explanation
Step-by-step explanation:
Given
[tex](8x+12y)^2+(6x+9y)^2=(10x+15y)^2[/tex]
Note
[tex](8x+12y)^2=(4(2x+3y))^2=16(2x+3y)^2\\ \\(6x+9y)^2=(3(2x+3y))^2=9(2x+3y)^2\\ \\(10x+15y)^2=(5(2x+3y))^2=25(2x+3y)^2[/tex]
Since
[tex]16(2x+3y)^2+9(2x+3y)^2=(2x+3y)^2(16+9)=25(2x+3y)^2,[/tex]
this is an identity
Triangle ABC is an isosceles triangle. The length of the base is 20 meters and the corresponding height is 24 meters. Find the perimeter of ABC. (round your answer to the nearest tenth of a meter).
Final answer:
The perimeter of the isosceles triangle with a base of 20 meters and height of 24 meters is 60 meters.
Explanation:
The formula for the area of a triangle is 1/2 × base × height.
In this case, the base of the isosceles triangle is given as 20 meters and the corresponding height is given as 24 meters.
Using the formula, we can calculate the area: Area = 1/2 × 20 × 24 = 240 square meters.Next, we need to calculate the length of the two equal sides of the triangle.Since the triangle is isosceles, the length of the base is equal to the length of the two equal sides.So, each equal side of the triangle is equal to 20 meters.Finally, to find the perimeter of the triangle, we add up the lengths of all three sides.Perimeter = 20 + 20 + 20 = 60 meters.