The length of the wire is bent into a square, making each side equal to 7x/4. The area of a square is found by squaring the length of one side, so the area, as a function of , is (7x/4)^2 or 49x^2/16.
Explanation:The given information is that the length of the wire is 7x, and it is bent into a square. In a square, all sides are equal. Therefore, we can say that the length of each side of the square is 7x/4.
To find the area of a square, we simply square the length of one side. Thus, the area A of the square, expressed as a function of x, is (7x/4)^2 or 49x^2/16.
Therefore, the question's answer is that the area A of the square can be expressed as the function 49x^2/16.
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Final answer:
To express the area A of a square in terms of z, assuming the wire length is 7z, calculate the side length a as 7z/4 and then square it to get A = (7z/4)². If x is correct and unrelated to z, more information is needed.
Explanation:
To express the area A of a square as a function of z, given that a wire of length 7x is bent into the shape of a square, we follow these steps:
The perimeter of the square is equal to the length of the wire, which is 7x.
Since the perimeter P of a square is 4 times one of its sides a, we can write P = 4a. Therefore, 7x = 4a.
To find the side length a, we divide 7x by 4: a = 7x/4.
The area A of a square is the square of one of its sides, so A = a². By substituting a with 7x/4, we get A = (7x/4)².
Finally, we need to write the equation in terms of z. Here, it seems there might be an issue with the question, as there is no direct relationship provided between x and z. Assuming there's a typographical error and that the wire length is actually 7z, we can write a = 7z/4 and A = (7z/4)².
If x is indeed correct and unrelated to z, more information is required to express A as a function of z.
please help me with 13 and 14
Answer:
13. x = 6
14. x = 3.5
Step-by-step explanation:
13. To find x when f(x) = -17, set the equation f(x) equal to -17 and solve.
-3x + 1 = -17 Subtract 1 from both sides
-3x = -17 - 1
-3x = -18 Divide by -3
x = 6
14. To find x when g(x) = 31, set the equation g(x) equal to 31 and solve.
10x - 4 = 31 Add 4 to both sides
10x = 31 + 4
10x = 35 Divide by 10
x = 3.5
Which solid figure does this net represent? 40 Points
A) cone
B) square pyramid
C) rectangular prism
D) triangular pyramid
Answer:
C.) Rectangular prism
Step-by-step explanation:
Answer:
[tex]\Large \boxed{\mathrm{Rectangular \ prism}}[/tex]
Step-by-step explanation:
The net represents a three-dimensional shape.
The figure that the net represents is a rectangular prism.
Charlie's eraser has a mass of 9 grams. How many milligrams is the eraser?
Answer:
9000 milligrams
Step-by-step explanation:
One gram is the equivalent of 1000 milligrams.
So, 9 grams is 9*1000 milligrams, which is 9000 milligrams.
Answer:
9000 milligrams
Step-by-step explanation:
There are 1000 milligrams in one gram, So 9 grams is 9000 milligrams.
Find the measure of RUS
Answer:
The measure of angle <RUS is 23°
Step-by-step explanation:
In this problem we know that
82°+24°+<RUS+51°=180°
solve for < RUS
157°+<RUS=180°
<RUS=180°-157°
<RUS=23°
Answer:
Step-by-step explanation:
23
Eric traveled to three cities on a single highway. The distance from his original location to the first city was 100 miles more than the distance from the first city to the second city. The distance from the second city to the third city was 10 miles less than the distance from the first city to the second city. If the distance from his original location to the first city and the distance from the second city to the third city were the same, what was the total distance Eric traveled?
A. 120 miles
B. 200 miles
C. 280 miles
D. 360 miles
E. 400 miles
Answer:
B
Step-by-step explanation:
*cough cough*
Are the arcs below congruent?
Answer:
There is not enough information
Step-by-step explanation:
In Circle 1
Minor Arc : [tex]\widehat{AB}=140^{\circ}[/tex]
Radius = AO=OB
In Circle 2
Minor Arc : [tex]\widehat{GH}=140^{\circ}[/tex]
Radius =OG =OH
We need to show that the arcs are congruent .
Since the length of the radii are not given .
So, There is not enough information to prove that the arcs are congruent.
Hence Option D is true.
Answer: d/ there is not enough information to determine
Step-by-step explanation:
I just did this on a p e x
Q : For each of the following cases, either explain why the case cannot occur or give an example to show how it can.
b. Two negative numbers whose product is in between the two numbers
c. Two negative numbers whose product is less than both numbers
b. Any two negative numbers when multiplying gives positive answers which are never between negative numbers. -9*-3=27
c. same logic, positive answer so never less than either negative number.
The product of two negative numbers will always be positive, so both cases described in the question are not possible. This is due to the property of real numbers which states that the product of two negative numbers results in a positive number.
Explanation:b. The product of two negative numbers will always be positive, so the case where the product of two negative numbers falls between the two numbers is not possible.
c. The product of two negative numbers is always positive, which is larger than their negatives. Therefore, the scenario of two negative numbers having a product that is less than both numbers cannot occur.
These conclusions are based on the property of real numbers which specifies that the product of two negative numbers is a positive number. For example, if you multiply -3 by -2, the result is 6, which is a positive number and larger than both -3 and -2.
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A printer prints fewer than 18 pages per minute. What is the maximum number of pages the printer can print in 7 minutes?
Answer:127 pages of paper
Step-by-step explanation:
18 times 7
The maximum number of pages the printer can print in 7 minutes is 119 pages, assuming it prints at the upper limit of 17 pages per minute.
To find the maximum number of pages the printer can print in 7 minutes, we multiply the maximum number of pages it can print per minute by the number of minutes.
Given:
- The printer prints fewer than 18 pages per minute.
- Number of minutes: 7
Let's use the upper limit of the printer's speed, which is 17 pages per minute (since it prints fewer than 18 pages per minute).
Maximum number of pages printed in 7 minutes:
[tex]\[ \text{Pages} = \text{Pages per minute} \times \text{Minutes} \][/tex]
[tex]\[ \text{Pages} = 17 \times 7 \][/tex]
[tex]\[ \text{Pages} = 119 \][/tex]
So, the maximum number of pages the printer can print in 7 minutes is 119 pages.
ABCD is a parallelogram. If m angle d=72 then what is m angle a
[tex]m\angle A=180° - m\angle D=108°-72°=108° [/tex]
The measure of angle A is 108 degrees.
We have given that,
ABCD is a parallelogram. If m angle d=72
we have to determine the m angle a
What is the angle?an angle is a figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.
[tex]m\angle A=180-m\angle D\\=180-72\\=108[/tex]
The measure of angle A is 108 degrees.
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Write an integer that represents this situation (be sure to include or-): a weight loss of 20 pounds
Answer:
(-20)
Step-by-step explanation:
loss = a negative integer.
I need to find the Radius
Answer: 10.6 ft
Step-by-step explanation:
[tex]V = \dfrac{1}{3}\pi r^2h\\\\144 =\dfrac{1}{3}\pi r^2(12)\\\\144 =4\pi r^2\\\\\dfrac{144}{4\pi}=r^2\\\\\\\sqrt{\dfrac{36}{\pi}}=\sqrt{r^2}\\\\\\\dfrac{6}{\sqrt{\pi}}=r\\\\\\10.6=r[/tex]
Which algebraic expression represents the difference of 54 and s number
[tex]\huge\boxed{54-x}[/tex]
I'm assuming you meant "the difference between 54 and a number". We'll use [tex]x[/tex] to represent the number.
The word "difference" means that we will use subtraction, making the answer...
[tex]\boxed{54-x}[/tex]
the other guy is correct
Choose the equation that could be used to find three consecutive integers whose sum is 36. (5 points) Select one: a. n + (n + 2) + (n + 4) = 36 b. n + (n + 1) + (n + 3) = 36 c. n + (n + 1) + (n + 2) = 36 d. n + (n − 1) + (n − 3) = 36
Answer:
c
Step-by-step explanation:
Note there is a difference of 1 between consecutive integers.
let an integer be n then then the next one is n + 1 followed by n + 2
Hence
n + (n + 1) + (n + 2) = 36 → C
Identify the translation rule on a coordinate plane that verifies that triangle A(-5,1), B(-2,7), C(0,1) and triangle A'(-6,0), B'(-3,6), C'(-1,0) are congruent.
A) (x, y) → (x - 1, y - 1)
B) (x, y) → (x + 2 , y + 1)
C) (x, y) → (x - 2, y + 1)
D) the triangles are not congruent
Answer:
A) (x, y) → (x - 1, y - 1)Step-by-step explanation:
A(-5, 1) → A'(-6, 0)
-5 - 1 = -6
1 - 1 = 0
B(-2, 7) → B'(-3, 6)
-2 - 1 = -3
7 - 1 = 6
C(0, 1) → C'(-1, 0)
0 - 1 = -1
1 - 1 = 0
Multiply. Write your answer in simplest form. −2/3 x(2 1/2 )x(−3)=
Answer:
The correct answer is 5
Step-by-step explanation:
To find this, start by multiplying them in any order. For ease, we'll multiply the first and last.
-2/3 * -3 = 2
Now we take that and multiply it by the remaining term.
2 * 2 1/2 = 5
Final answer:
Multiplying −2/3 by 2 1/2 and then by −3 results in the answer 5 after converting the mixed number to an improper fraction, considering the signs during multiplication, and simplifying the result.
Explanation:
To multiply the given numbers and write the answer in simplest form, let's break down the math step by step.
Firstly, convert the mixed number 2 1/2 into an improper fraction. To do this, multiply the whole number by the denominator of the fraction and add the numerator. This gives us 2 x 2 + 1 = 5, so 2 1/2 becomes 5/2.
Now, let's look at the multiplication operation:
−2/3 × (5/2) × (−3) = ( −2 × 5 × −3 ) / ( 3 × 2 )
When multiplying, we multiply the numerators together and the denominators together, which results in:
(−2 × 5 × −3) / (3 × 2) = (+2 × 5 × 3) / 6 = 30 / 6
When considering the signs, remember that when two numbers with the same sign multiply, the result is positive (e.g., −2 × −3 = +6), and when two numbers with opposite signs multiply, the answer is negative (e.g., −3 × 2 = −6).
The final step is to simplify the fraction 30/6, which simplifies to 5, since 30 divided by 6 equals 5.
Therefore, the answer is 5.
please help me I really need this for school to get a good grade on my report card
Answer: 0.29
Step-by-step explanation: The first thing that you need to know is that a ton equals 2,000 pounds. Therefore, 6,000 pounds of rocks cost $1,740. In order to solve the problem you need to divide $1,740 by 6,000. 1,740 / 6,000 = .29
Each pound cost $ 0.29. (29 cents)
Answer: $0.29 per pound
Step-by-step explanation:
[tex]\dfrac{price}{pound}:\ \dfrac{\$1,740}{3\ tons}\times \dfrac{1\ ton}{2,000\ pounds}=\dfrac{\$1,740}{6,000\ pounds}=\large \boxed{\dfrac{\$0.29}{1\ pound}}[/tex]
write an equation in slope intercept form for the line that passes through (4, -4) and is parallel to 3x+4x=2y-9
Answer:
[tex]\large\boxed{y=\dfrac{7}{2}x-18}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
Convert the equation of a line 3x + 4x = 2y - 9 to the slope-intercept form:
[tex]3x+4x=2y-9[/tex]
[tex]7x=2y-9[/tex] add 9 to both sides
[tex]7x+9=2y[/tex] divide both sides by 2
[tex]\dfrac{7}{2}x+\dfrac{9}{2}=y\to y=\dfrac{7}{2}x+\dfrac{9}{2}[/tex]
Parallel lines have the same slope. Therefore we have the equation:
[tex]y=\dfrac{7}{2}x+b[/tex]
Put the coordinates of the point (4, -4) to the equation:
[tex]-4=\dfrac{7}{2}(4)+b[/tex]
[tex]-4=7(2)+b[/tex]
[tex]-4=14+b[/tex] subtract 14 from both sides
[tex]-18=b\to b=-18[/tex]
Finally we have the equation:
[tex]y=\dfrac{7}{2}x-18[/tex]
What is the product ? 2x(x-4)
Answer:
2x^2- 8x
Step-by-step explanation:
2x(x-4)
distribute; multiply parenthesis by 2 x
2x * x-2x *4
calculate products
2x^2- 8x
Answer: The required product is [tex]2x^2-8x.[/tex]
Step-by-step explanation: We are given to find the following product :
[tex]P=2x(x-4).[/tex]
To find the above product, we need to multiply 2x to every term ithin the bracket.
The multiplication is as follows :
[tex]P\\\\=2x(x-4)\\\\=2x\times x-2x\times4\\\\=2x^2-8x.[/tex]
Thus, the required product is [tex]2x^2-8x.[/tex]
Factor the following polynomial completely.
1,280x^11 - 405x^7
Answer:
[tex]5x^7(16x^2+9)(16x^2-9)[/tex]
Step-by-step explanation:
we have
[tex]1,280x^{11}-405x^{7}[/tex]
we know that
[tex]1,280=(2^8)(5)[/tex]
[tex]405=(3^4)(5)[/tex]
substitute
[tex](2^8)(5)x^{11}-(3^4)(5)x^{7}[/tex]
Factor 5x^7
[tex]5x^7[(2^8)x^{4}-(3^4)][/tex]
[tex]5x^7[256x^{4}-81][/tex]
Applying difference of square
[tex][256x^{4}-81]=(16x^2+9)(16x^2-9)[/tex]
substitute
[tex]5x^7(16x^2+9)(16x^2-9)[/tex]
Answer:
5x^7(4x-a 3)(4x+3)(16x^2+9)
Step-by-step explanation:
Jayden needs to store boxes that are 4 feet long, 3 feet wide, and 2 feet high. The boxes must remain upright with one of the 4-foot by 3-foot sides on top. Jayden's storage locker is 12 feet long, 6 feet wide, and 9 feet high. What is the greatest number of boxes that he can store in the locker?
The dimensions of the box are = 4 feet (length); 3 feet(width); 2 feet(height)
So, volume of the box is = [tex]4\times3\times2=24[/tex] cubic feet
The dimensions of the storage locker are = 12 feet(length); 6 feet(width) ; 9 feet(height)
So, volume of the storage locker is = [tex]12\times6\times9=648[/tex]
So, the greatest number of boxes that can be stored are =
[tex]\frac{648}{24}= 27[/tex] boxes
Hence, a maximum of 27 boxes are stored.
Jayden's storage locker has a volume of 648 cubic feet, and each of his boxes has a volume of 24 cubic feet. By dividing the locker's volume by the volume of a single box, we find that Jayden can store a maximum of 27 boxes in the locker.
Explanation:To determine the greatest number of boxes Jayden can store in the storage locker, we need to calculate the volume of the storage locker and the volume of one box. The storage locker is 12 feet long, 6 feet wide, and 9 feet high, so its volume is calculated as follows:
Storage Locker Volume = length × width × height = 12 ft × 6 ft × 9 ft = 648 cubic feet.
The box has dimensions of 4 feet long, 3 feet wide, and 2 feet high. Thus, its volume is:
Box Volume = length × width × height = 4 ft × 3 ft × 2 ft = 24 cubic feet.
Now, to find the greatest number of boxes that can fit into the locker, we divide the volume of the storage locker by the volume of one box:
Number of Boxes = Storage Locker Volume / Box Volume = 648 cubic feet / 24 cubic feet.
When we perform the division, we get:
Number of Boxes = 27.
Hence, Jayden can store a maximum of 27 boxes in the storage locker when placed upright with a 4-foot by 3-foot side on top.
what is the answer to this??
Answer:
x=3
z=65
Step-by-step explanation:
6x+97 and 14x+73 are vertical angles which means they are equal
6x+97= 14x+73
Subtract 6x from each side
6x-6x+97= 14x-6x+73
97 = 8x +73
Subtract 73 from each side
97-73 = 8x+73-73
24 = 8x
Divide each side by 8
24/8 = 8x/8
3 = x
Now we need to find z
6x+97 and z are supplementary angles which means they add to 180
6x+97 +z = 180
6(3) +97 +z = 180
18+97+z=180
Combine like terms
115+z = 180
Subtract 115 from each side
115-115 +z=180-115
z = 65
Which number line shows the solution set for |p-3|=9?
Answer:
Option b
[tex]p = -6[/tex] or [tex]p = 12[/tex]
Step-by-step explanation:
The absolute value is a function that transforms any value x into a positive number.
Therefore, for the function [tex]f(x) = |x|[/tex] x> 0 for all real numbers.
Then the equation:
[tex]|p-3| = 9[/tex] has two cases
[tex](p-3) = 9[/tex] if [tex]h > 3[/tex] (i)
[tex]-(p-3) = 9[/tex] if [tex]h < 3[/tex] (ii)
We solve the case (i)
[tex]p = 9 + 3\\p = 12[/tex]
We solve the case (ii)
[tex]-p +3 = 9\\p = 3-9\\p = -6[/tex]
Then the solution is:
[tex]p = -6[/tex] or [tex]p = 12[/tex]
Answer:
b
Step-by-step explanation:
You decide to make a beanbag in the shape of a sphere with a diameter of 120 millimeters. You will need to find the volume to know how many beans to put in the bag. What is the volume? Use 3.14 to approximate pi.
Answer:
The volume is [tex]904,320\ mm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=120/2=60\ mm[/tex] ----> the radius is half the diameter
[tex]\pi=3.14[/tex]
substitute the values
[tex]V=\frac{4}{3}(3.14)(60)^{3}=904,320\ mm^{3}[/tex]
Final answer:
The volume of a sphere-shaped beanbag with a diameter of 120 millimeters is calculated using the formula V = (4/3)πr³, resulting in a volume of approximately 904.32 cubic centimeters.
Explanation:
To calculate the volume of a beanbag in the shape of a sphere, we use the formula for the volume of a sphere, which is V = (4/3)πr³. Given that the diameter of the beanbag is 120 millimeters, we first need to find the radius, which is half of the diameter, so r = 60 millimeters or 6 centimeters. Plugging the values into the formula, we get:
V = (4/3) × 3.14 × (6 cm)³
V = (4/3) × 3.14 × 216 cm³
V = (4/3) × 3.14 × 216
V = (4) × 3.14 × 72
V = 904.32 cm³
Therefore, the volume of the beanbag is approximately 904.32 cubic centimeters (cm³).
What are the zeros of f(x)=2x^3+3x^2-9x?
ANSWER
[tex]x = 0 \: or \: x = \frac{3}{2} \: or \: x = - 3[/tex]
EXPLANATION
The given polynomial function is
[tex]f(x) =2{x}^{3} + 3 {x}^{2} - 9x[/tex]
To find the zeros, we equate the function to zero.
[tex]2{x}^{3} + 3 {x}^{2} - 9x = 0[/tex]
Factor x,
[tex]x(2 {x}^{2} + 3x - 9) = 0[/tex]
Split the middle term,
[tex]x(2 {x}^{2} + 6x - 3x - 9) = 0[/tex]
[tex]x(2x(x + 3) - 3(x + 3) = 0[/tex]
[tex]x(2x - 3)(x + 3) = 0[/tex]
[tex]x=0,2x-3=0,x+3=0[/tex]
[tex]x = 0 \: or \: x = \frac{3}{2} \: or \: x = - 3[/tex]
Answer:
x = -3, x= 0, and x = 1.5
Step-by-step explanation:
The zeros of a function f(x) refers to the x-values for which f(x) = 0.
We simply graph the function and determine the points where the graph crosses the x-axis. Thus, we shall be solving the problem graphically;
From the attachment below, the graph of f(x) crosses the x-axis at;
x = -3, x= 0, and x = 1.5
In the number 1,435,967 in what place value is the 5
Answer:
Step-by-step explanation:
Thousands. You can check this by seeing how many places away from the furthest right digit a digit is. if it is 3 places away, it is in the thousands. If it something like 6 places away, it is in the millions.
The digit 5 in 1,435,967 represents 50,000 in the tens of thousands place value, highlighting the importance of understanding place values in large numbers.
In the number 1,435,967, the digit 5 is in the tens of thousands place value. To understand this, let's break down the place values in the number:
Millions: The digit 1 is in the millions place value.
Hundred Thousand: The digit 4 is in the hundred thousand place value.
Ten Thousand: The digit 3 is in the ten thousand place value.
Thousands: The digit 5 is not in the thousands place; it's in the tens of thousands place value.
Hundreds: The digit 9 is in the hundreds place value.
Tens: The digit 6 is in the tens place value.
Ones: The digit 7 is in the one's place value.
So, the digit 5 in the number 1,435,967 represents 50,000. In other words, it contributes to a value of 50,000 within the overall number. Place value is a crucial concept in understanding the numerical representation of large numbers, as it helps determine the significance of each digit within the number.
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The graph of a certain hyperbola, y=h(x) is shown in the standard (x,y) coordinate plane below
Among the following graphs, which best represents y= -h(x)?
Answer:
Step-by-step explanation:
B
Among the following graph option (A) graph best represents y= -h(x)
What is hyperbola?A hyperbola is a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.Hyperbola is a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constantHyperbola is a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the coneHow to solve this problem?The steps are as follow:
Given the graph of a certain hyperbola, y=h(x) in the standard (x,y) coordinate planeWe have to find which graph represents the y= -h(x)Since there is refraction around x-axis we can conclude that option (A) graph represents best y= -h(x)Learn more about hyperbola here:
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What is the difference between the mean and median (rounded to the nearest tenth) of these numbers 6,6,6,7,7,7,8,8,8,9
The median is the moddle number of a data set. If the number of numbers is even add the 2 middle numbers and divide by 2.
Median = (7+7)÷2 = 7
The mean is the averagw value in a data set. You find it be adding all the numbers and then divide the answer by the number of numbers.
Mean: (6+6+6+7+7+7+8+8+8+9) ÷ 10
= 72 ÷ 10 = 7.2
Happy to help! Marking my answer as the Brainliest would really be aprreciated.
Darpana solved the equation s = a+b+c/3 for a. Her steps are shown below:
1. Multiply by 3: s=a+b+c/3
3s=a+b+c
2. Subtract b: 3s-b=a+b+c-b
3s-b=a+c
3. Divide by c: 3s-b/c=a
Which statement about Darpana’s work is true?
In step 1 she needed to divide by 3 rather than multiply.
In step 2 she needed to add b rather than subtract.
In step 3 she needed to subtract c rather than divide.
Darpana solved the equation correctly.
Answer: Third option (In step 3 she needed to subtract c rather than divide)
Step-by-step explanation:
When she subtract b from both sides of the equation, she obtained:
[tex]3s-b=a+c[/tex]
Therefore, to leave the a alone at one member of the equation, she needs to subtract c from both sides of the equation.
Then, she would obtain the following:
[tex]3s-b-c=a+c-c\\3s-b-c=a\\a=3s-b-c[/tex]
Therefore the answer is the third option: In step 3 she needed to subtract c rather than divide.
Answer:
The true statement is: In step 3 she needed to subtract c rather than divide.
Step-by-step explanation:
Lets solve our equation [tex]s=\frac{a+b+c}{3}[/tex] step by step.
Step 1. Since 3 is the denominator of the right hand side, we need to multiply both sides of the equation by 3:
[tex]3s=\frac{3(a+b+c)}{3}[/tex]
Now we can cancel the 3 in the numerator and the 3 in the denominator to get
[tex]3s=a+b+c[/tex]
As you can see, the first statement is false
Step 2. Since we want to isolate the variable [tex]a[/tex], we need to subtract b from both sides of the equation:
[tex]3s=a+b+c[/tex]
[tex]3s-b=a+b+c-b[/tex]
[tex]3s-b=a+c[/tex]
The second statement is also false
Step 3. The last thing we to do to isolate [tex]a[/tex] (and solve for it) is subtract c from both sides of the equation:
[tex]3s-b-c=a+c-c[/tex]
[tex]3s-b-c=a[/tex]
[tex]a=3s-b-c[/tex]
Therefore, the third statement is true: In step 3 she needed to subtract c rather than divide.
You are standing 50 meters from a hot air balloon that is preparing to take off. The angle of the elevation to the top of the balloon is 28. Find the height of the balloon
Answer:
27m
Step-by-step explanation:
The diagram is shown in the attachment.
The height of the hot air balloon is calculated using the tangent ratio.
The tangent ratio involves the side length that is opposite(h) to the given angle (28) and the side length adjacent to the angle.
[tex]\tan 28\degree=\frac{h}{50}[/tex]
This implies that;
[tex]h=\50tan 28\degree[/tex]
[tex]h=26.585m[/tex]
The height is 27m to the nearest meters.
Using the tangent of the angle of elevation, the height of the hot air balloon is calculated to be approximately 26.585 meters.
Explanation:To find the height of the hot air balloon, we can use trigonometric principles, specifically the tangent function, which relates the angle of elevation to the opposite side (the height of the balloon in this case) and the adjacent side (the distance from you to the balloon).
The angle of elevation to the top of the balloon is given as 28 degrees and the distance from the observer to the balloon is 50 meters. Using the formula for tangent:
tan(angle) = opposite/adjacent
In this case:
tan(28 degrees) = height/50 meters
Therefore, to find the height:
height = 50 meters * tan(28 degrees)
Calculating this using a calculator:
height ≈ 50 * 0.5317
height ≈ 26.585 meters
So, the height of the balloon is approximately 26.585 meters.
You’ve saved $90 towards the cost of a gaming console. you plan to save an additional 10.50 per week. if the console coasts $300 how many weeks will you have to have to save $10.50 before you have enough money to buy the console?
You subtract 90 from the 300 dollar goal and you’re left with $210. If you then divide that by 10.50 the answer will be 20. So the answer is 20 weeks.