Final answer:
The trapezoid forms a right-angled triangle with one additional rectangle. Its area is found to be 48m^2, and its approximate perimeter is 36.944m, by adding the lengths of all its sides together.
Explanation:
To find the perimeter and area of a trapezoid with two right angles and bases of 16m and 8m, we must first visualize the trapezoid. This trapezoid appears like a right-angled triangle with an additional rectangle attached to its hypotenuse.
We are given the hypotenuse of the altitude's right triangle is 4√5m, thanks to Pythagoras' theorem, we can find the two legs (which are the altitude h and the difference in bases). Let's call the altitude h and the difference in bases 'd'. Now, we know that the length of the longer leg of the right triangle is 16m - 8m = 8m.
Using the Pythagorean theorem where hypotenuse2 = altitude2 + difference in bases2, we have (4√5)2 = h2 + 82. Solving for 'h', we have h = √(80 - 64) = √16 = 4m. The area of a trapezoid is given by the formula A = (1/2) × (sum of the bases) × (height), which in this case is A = (1/2) × (16m + 8m) × 4m = 48m2.
For the perimeter, it can be calculated by adding the lengths of all sides. So, perimeter = 16m + 8m + 4m + 4√5m = 28m + 4√5m. To find the approximate value of 4√5m, we can calculate 4 × 2.236 (since √5 = 2.236), which gives us approximately 8.944m. Adding this to 28m gives us a perimeter of approximately 36.944m.
Choose the correct simplification of (4x3 − 3x − 7) + (3x3 + 5x + 3)
After performing the addition operation on both expressions, the resulting simplified expression is 7x^3+2x-4
Simplification of Algebra ExpressionGiven Data
First expression = (4x3 − 3x − 7) Second expression = (3x3 + 5x + 3)To add both Expression let us open brackets
= (4x3 − 3x − 7) + (3x3 + 5x + 3)
= 4x3 − 3x − 7 + 3x3 + 5x + 3
Collect like terms we have
= 4x^3+3x^3-3x+5x-7+3
= 7x^3+2x-4
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Angelo family drove 254.6 miles their car used 19 gallons of gasoline describe the cars gas mileage
The Angelo family's car has a gas mileage of approximately 13.4 miles per gallon, calculated by dividing the total miles driven (254.6 miles) by the gasoline used (19 gallons).
Explanation:A car's gas mileage is calculated by dividing the total number of miles driven by the amount of gasoline used. In this case, the Angelo family drove 254.6 miles and used 19 gallons of gasoline. So, to figure out their car's gas mileage, you would divide 254.6 miles by 19 gallons.
254.6 miles ÷ 19 gallons = 13.4 miles per gallon
Therefore, the gas mileage of the Angelo family's car is approximately 13.4 miles per gallon.
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what is the length of a circle that has a central angle of 98 degrees and 6 cm?
There are 16 boys in an English class of 28 students. The ratio of boys to the total number of students in this class is typical of the whole school. There are 476 students in the school. About how many are boys?
The number of the boys in the school is 272.
What is multiplication?Multiplication is mathematical arithmetic operation. It is also a process of adding same types of expression to some number of times.
Example - 2 × 3 means 2 is added three times or 3 is added 2 times.
Given, the ratio of boys to the total number of students in this class is typical of the whole school.
That means,
16 : 28 = x : 476
where x is the number of boys in the school.
Simplifying,
16/28 = x/476
Using cross multiplication,
x = 16 x 476/ 28
x = 272
Therefore, the number of the boys in the school is 272.
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find the sum of the measures of the interior angles of a convex 20-gon
The length of a rectangle is 2 cm less than 6 times the width. find the possibilities for the width of the rectangle such that the area is not more than 840 cm2
To solve this problem, let us first assign the variables. Let us say that:
l = length of rectangle
w= width of rectangle
The given problem gives us the relation that:
l = 6 w – 2 ---> 1
We know that the formula for area of rectangle is given as:
A = l w ---> 2
Substituting equation 1 into 2:
A = (6 w – 2) w
A = 6 w^2 – 2 w
The area must not be greater 840 cm^2, therefore:
840 cm^2 = 6 w^2 – 2 w
w^2 – (1/3) w = 140
By completing the square:
w^2 – (1/3) w + (1/36) = 140 + (1/36)
(w – 1/6)^2 = 5041/36
w – 1/6 = ± 11.83
w = -11.66, 12
Therefore the maximum value that the width can take is 12 cm. Therefore the possibilities of width such that the area does not exceed 840 cm^2 is from 1 to 12 cm.
Answer:
1 cm to 12 cm
15-3 7/8
What is 15 minus 3 and 7 8ths
Solution of equqation 15 - 3 7/8 is 11 1/8.
To solve 15 - 3 7/8, you need to follow these steps:
Convert the mixed number 3 7/8 to an improper fraction.Subtract this fraction from 15.First, convert 3 7/8 to an improper fraction:
3 7/8 = (3 * 8 + 7) / 8 = 31/8Next, convert 15 to a fraction with a common denominator of 8:
15 = 120/8Now you subtract the improper fraction from the whole number fraction:
120/8 - 31/8 = (120 - 31) / 8 = 89/8Convert the result back to a mixed number:
89/8 = 11 1/8So, 15 minus 3 and 7/8 is 11 1/8.
whats pie as in the math equation help me plus thanks
some people use 22/7, some use 3.14
it is used in formulas for circles
What is the equation of the quadratic graph with a focus of (3, −1) and a directrix of y = 1?
A.) f(x) = −one fourth (x − 3)2 + 1
B.) f(x) = −one fourth (x − 3)2
C.) f(x) = one fourth (x − 3)2 + 1
D.) f(x) = one fourth (x − 3)2
Find the volume of a rectangular prism if the length is x, the width is x2, and the height is 5x2 + 4x + 1. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
5x5 + 4x4 + x3
5x4 + 4x3 + x2
6x5 + 4x4 + x3
6x4+4x3+x2
Answer:
A) 5x^5 + 4x^4 + x^3
Step-by-step explanation:
Find the distance between A and C. Simplify completely.
A = (1,3)
C = (-4,-4)
-4-1 =-5, -5@ = 25
-4-3 = -7, -7^2 = 49
25+49 = 74
sqrt(74) = 8.602
round answer as needed.
Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest thousandth. leg = 9, leg = 12
How do you use the additive inverse to evaluate an expression that uses subtraction
Answer:
Additive inverse is the negative of the number, i.e. what you add to the number to get zero.
So the additive inverse of number b is - b
Additive inverse of 4 is - 4.
Then, you can verify the subtraction is the same that add the additive inverse.
For example subtracting 4 from 10 (10 - 4) is the same that adding -4:
10 - 4 = 10 + (-4).
Then given any expression if you have to subtract other expressión you just add the addive inverse of the second expression.
For example: given A(x) = x^2 + 3x + 5 and B(x) = 2x + 4
Find A(x) - B(x) = A(x) + [-B(x)]
=> x^2 + 3x + 5 + (-2x -4) = x^2 + 3x - 2x + 5 - 4 = x^2 + x + 1
Step-by-step explanation:
hope this helped!
When 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4. find the number. j. grossman?
Answer:
its 3
Step-by-step explanation:
The required value of the unknown number x would be 3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We have been given that " 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4".
Let the unknown number be x.
7x - 8 = 3x + 4
To solve the equation;
7x - 8 = 3x + 4
Collect the like terms;
7x - 3x = 8 + 4
4x = 12
Divide by 4 on both sides;
x = 12/4
x = 3
Therefore, the required value of the unknown number x would be 3.
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20 POINTS PLUS BRAINLIEST!! PLEASE HELP!
Write the first 4 terms of the sequence if a(4)=36 and a(n)=1/2a(n-1)+12.
A.
36, 30, 27, 25.5
B.
120, 72, 48, 36
C.
456, 216, 96, 36
D.
36, 48, 72, 120
Hello, everyone! I am in high school and I need help with my geometry homework! I will also mark you as the brainliest answer if you answer it clearly!
A) #3 y = x+3, if you subtract x from y there is a difference of 3 in all of them.
B) #5 y = -x^2, the y value is the negative value of x raised to the 2nd power
C)#6 y = x^2+3, if you raise the value of x to the 2nd power and then add 3 you get the y value
D)#2 y=3x-1, if you multiply the value of x by 3 then subtract 1 you get the y value
ROUND 977.259856871 TO 3 DECIMAL PLACES HELP!
3 decimal places would be where the 9 is, since the next number is 8 , the 9 would become a 0 and the number before it (5) would become a 6
so it would be 977.260
(05.03)
Identify the initial value and rate of change for the graph shown
Initial value: 1, rate of change: 2
Initial value: 2, rate of change: 1 over 2.
Initial value: 2, rate of change: 1
Initial value: 1 over 2., rate of change: 2
Answer: Initial value: 2, rate of change: 1
Step-by-step explanation:
From the graph we can see the line is intersecting y axis at (0,2).
Therefore, y intercept of the graph = 2
Therefore, the initial value of the graph = 2
Also there as two point from which line is passing (0,2) and (1,3)
The rate of change of the line is given by :-
[tex]R=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{1-0}=1[/tex]
Hence, for the given graph, the Initial value is 2 and the rate of change is 1 .
Suppose the length of a rectangle is three time is three time the width. if we let x represent the width of the rectangle, what expression do we us to represent the length?
The height of a cone is equal to the diameter of the base. what expression represents the volume of the cone, in cubic units? πx3 πx2 2πx3 4πx3
The formula for a cone is given as:
V = π r^2 h / 3 ---> 1
Where,
V = volume of the cone
r = radius of the circle base of the cone
h = is the perpendicular length from the center of the base of the cone to the tip at the top
It was given that:
h = d
but d = 2 r, therefore:
h = 2 r
Substituting this to equation 1:
V = π r^2 (2 r) / 3
V = 2 π r^3 / 3
Since r = x, the answer from the choices is:
2πx3
The expression representing the volume of the cone is (2/3)πx^3, where x represents the cone's radius.
Step 1: Identify Key Information
We are given that the height (h) of the cone is equal to the diameter (d) of the base. The diameter is twice the radius (r).
Step 2: Apply Formula and Substitute
The formula for the volume of a cone is:Volume (V) = (1/3) * π * r^2 * h
Since h = d = 2r, we can substitute:V = (1/3) * π * r^2 * (2r)
Step 3: Simplify the Expression
V = (1/3) * π * r^2 * 2rV = (2/3) * π * r^3Find the slope of the line on the graph. Write the answer as a fraction or a whole number, not a mixed number or decimal.
What is the simplified form of the quantity y−squared minus y minus 12 over the quantity y−squared plus 8y plus 15?
PLEASE EXTRA POINTS
eight more than the product of two and a number x
A car leaves town traveling 40 mi/h. Two hours later, a second car leaves the same town, on the same road, traveling at 60 mi/h. In how many hours will the second car pass the first car? Use formula d=rt
PLEASE HELP!! Find the measure of angle 2. Image attached
opposite angles need to equal 180
so angle 2 = 180-111 = 69 degrees
Which of the following points is a solution to the system of linear inequalities?
{y ≤ 2x+1 y>1/2x-4
Answer choices:
A.(2, 6)
B.(2, –3)
C.(2, 3)
D.(2, –6)
How many real solutions are there for the function graphed below?
No Real Solution
1 Real Solution
2 Real Solutions
Infinite Number of Solutions
Grace and Jamal each bought notebooks for school. Grace bought 3 notebooks for $3.90 while Jamal bought 2 notebooks for $2.20. What was the unit price of each student's notebooks?
The price of gold has increased by 35% per year from 2000. In the year 2000, Harry bought a gold ring for $590. Which of the following functions f(x) can be used to represent the price of the ring x years after 2000? f(x) = 590(1.35)x f(x) = 590(0.65)x f(x) = 35(0.41)x f(x) = 35(1.59)x
Write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1)