Answers
In the given figure the area of quadrilateral is 19.64 square units.
Option (C) is correct.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180.
In the given figure,
A quadrilateral is shown.
The quadrilateral can be seen as two triangles,
One triangle whose sides are 6, 6 and 5
And second triangle whose sides are 3, 4, and 5.
In first triangle, use Heron's formula to find the area,
The area of triangle = √ S.(S- a).(S -b).(S-c)
The semi perimeter of triangle = 6 + 6 +5 / 2 = 17 / 2 = 8.5
Area = √ 8.5 x (8.5 - 6) x (8.5 - 6) x (8.5 - 5)
= √8.5 x 2.5 x 2.5 x 3.5
= 13.635
The second triangle whose side are 3, 4 and 5, makes a right angle.
The area of second triangle = 1/2 x base x height = 1/2 x 4 x 3 = 6
Total area = 13.635 6 + 6 = 19.635
The required area of quadrilateral is 19.635 square units.
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Related Questions
What are the phase shift and period for the function y = 3cos[4(θ + 60°)] − 2?
Phase shift = right 60°, period = 90°
Phase shift = right 60°, period = −90°
Phase shift = left 60°, period = 90°
Phase shift = left 60°, period = −90°
Answers
The tip of an 11-inch wiper blade wipes a path that is 31 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?
Answers
31 = C*11
C = 31/11 = 2.8 radians to nearest tenth
2.8 radians is the answer.
Find the value of n in the equation 6.2n – 3.7n = 85 + 45. A. 16 B. 52 C. 13.13 D. 325
Answers
2.5n=130
N=130/2.5
N=52
The answer is B. Hope this helps!
If n is a positive integer and the product all the integeres from 1 to n inclusive is a multiple of 990 what is the least possible value of n
Answers
Since 990=2*3²*5*11 ==>n=11
The length of a rectangular lawn is measured to twice its width. the perimeter of the lawn is given as 30 m. find the length and width of the lawn.
Answers
Solve log2(6-2x)-log2x=3
Answers
Join logarithms (always):
log2(6-2x)-log2(x) = log2( (6-2x/x) )
Then get rid of it! :)
(6-2x)/x = 2^3=8,
Solve the equation:
6-2x=8x ---> 10x=6 ---> x = 3/5.
How do I simplify this problem?
Answers
(15x^2h+15xh^2+5h^3)/h= 15x^2+15xh+h^2
The sum of four consecutive even integer numbers is 84. find the four numbers.
Answers
84/4=21
now take the 2 even numbers below 21 and the 2 even numbers above 21
18 +20 + 22 +24 = 84
the numbers are 18, 20, 22 & 24
Adam has $450. he spends $210 on food. later he divides all the money into four parts out of which three parts were distributed and one part he keeps for himself. then he found $50 on the road. write the final expression and find the money he has left?
Answers
First, subtract $210 from it (spent by Adam on food)
$450 - $210 = $240
Then, divide the remaining amount of money by 4
$240 / 4 = $60
Since, it was only one part that he kept to himself, the amount of money left with him, x, is
x = $60
Then, the total amount of money he has including that which he only picked from the road is,
T = $60 + $50 = $110
In the end, Adam had $110.
The law of cosines is a^2+b^2-2abcos(C). Find the value of 2abcos(C).
A. 37
B. -40
C. 40
D. 20
Answers
and surely you know how much that is.
Solve x3 = 64 over 27.
±8 over 3
8 over 3
±4 over 3
Answers
Cube root the answer
³√x³=³√64/27
x=4/3.
Check:
x=4/3
x³=(4/3)³
x³=64/27. As a result, the correct answer is 4/3 or 4 over 3. If you wonder why don't I choose the answer as ±4 over 3 because of this
±4/3
Choose positive first
(4/3)²=64/27 Correct. However, then choose negative signs
(-4/3)³=-64/27 Incorrect. Hope it help!
The solution of the given equation is ±8/3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is x³= 64/27
x=±∛(64/27)
x=±∛(8³/3³)
x=±8/3
Therefore, the solution of the given equation is ±8/3.
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Find two positive numbers such that their product is 192 and their sum is a minimum pre-calc
Answers
xy = 192
Let's rearrange this to make the equation explicit: y = 192/x
Then, the other equation is for the sum. Let S be the sum of the two positive numbers.
S = x + y
Now, substitute the other equation into this one:
S = x + 192/x
Here's where we apply calculus. We can determine the minimum S by getting the first derivative of S with respect to y and equating to zero. Thus,
dS/dx = 1 - 192x⁻² = 0
1 = 192x⁻²
x² = 192
x = +/- √192
But since we are finding the positive number, x = + √192
Then, we use this to the first equation:
y = 192/√192 = √192
Therefore, the two positive numbers are equal which is √192 or 13.86.
The two numbers with a product equal to 192 such that their sum is minimized are:
A = √192 and B = √192
How to find the two numbers?
Let's define A and B as our two numbers, we know that their product must be equal to 192, then we have:
A*B = 192.
Now, the sum of these two numbers is:
A + B.
And we want to minimize this, to do it, we need to use the first equation to rewrite one variable in terms of the other. For example, if we isolate A, we get:
A = 192/B
Replacing this in the sum, we get:
192/B + B
To minimize this, we need to find the values of B that make 0 the differentiation of the above expression.
The differentiation is:
-192/B^2 + 1
Then we need to solve:
-192/B^2 + 1 = 0
192/B^2 = 1
192 = B^2
√192 = B
To get the value of A, we use:
A = 192/B = 192/√192 = √192
Then we can conclude that the two positive numbers such that their product is 192, and their sum is minimized, is:
A = √192 and B = √192.
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The following two-way table shows the number of students of a school who have a video game and/or have a laptop:
Have Video Game Do Not Have Video Game Total
Have Laptop
15
50
65
Do Not Have Laptop
50
15
65
Total
65
65
130
Based on the table, how many students have both a laptop and a video game?
15
50
65
130
Answers
have laptop 15 50 65
dont have 50 15 65
total 65 65 130
have both a laptop and a game : 15
Based on the table given, the number of students who have both a laptop and a video game is 15 students.
Which students have both laptops and video games?In order to solve this question, look at the part of the table where the row on students who have laptops intersects with the column on those who have video games.
That part of the table has 15 in the cell. This means that 15 students have both video games and laptops.
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PLEASE HELP!!!!!!!
f(x)=x^2−3x+9
g(x)=3x^3+2x^2−4x−9
Find (f−g)(x)
Select one:
a. −3x^3−x^2+x+18
b. 3x^3+3x^2−7x
c. 3x^3+x^2−x−18
d. 3x^3−x^2−x
Answers
-----------------------------
Work Shown:
(f-g)(x) = f(x) - g(x)
(f-g)(x) = [ f(x) ] - [ g(x) ]
(f-g)(x) = [ x^2-3x+9 ] - [ 3x^3+2x^2-4x-9 ]
(f-g)(x) = x^2-3x+9 -3x^3-2x^2+4x+9
(f-g)(x) = -3x^3+(x^2-2x^2)+(-3x+4x)+(9+9)
(f-g)(x) = -3x^3-x^2+x+18
Bicycle city makes custom bicycles. They charge $160 plus $80 for each day that it takes to build the bicycle. If you have $480 to spend on your new bicycle, how many days can it take Bicycle City to build the bike?
Answers
80d≤320 divide both sides by 80
d≤4
So the maximum number of days it can take them to build the bicycle so that $480 will cover the cost.
18 divided by 5593 equals 31-5400 = 193 what number should be placed in the box to help complete the division calculation?
Answers
The number that should be placed in the box to complete the division calculation is -7.
To find the number that should be placed in the box to complete the division calculation, let's analyze the given information:
- Dividend: 5593
- Divisor: 18
- Quotient: 31 (hundreds place is 3 and tens place is 1)
- When 5400 is subtracted from 5593, the result is 193.
- The box represents an unknown number in the ones place of the quotient.
To find the value in the box, we need to consider the units place. Since 5400 is subtracted from 5593 to give 193, the difference between the units places should be the value in the box.
193 - 5400 = -5207
So, the number that should be placed in the box to complete the division calculation is -7.
Correct question is:
What number should be placed in the box to help complete the division calculation?
Long division setup showing an incomplete calculation. 18 is in the divisor, 5593 is in the dividend, and 3 hundreds and 1 tens is written in the quotient.
5400 is subtracted from 5593 to give 193.
An unknown value represented by a box is being subtracted from 193.
cot^2x-csc^2x=-1 for all values of x true or falsse
Answers
sin²x + cos²x =1
1 + tan²x = sec² x
1 + cot² x = csc² x
These are all derived from circle geometry on the cartesian plane. Now, the useful trigonometric property to be used is the third one. Rearranging this, we come up with
cot²x - csc²x = -1
This coincided with the given equation. Therefore, this is true. This is because it is already established from the pythagorean theorems.
The original equation cot^2x - csc^2x = -1 is true for all values of x.
How to determine if cot^2x-csc^2x=-1 for all values of xThe equation cot^2x - csc^2x = -1 is true for certain values of x, but not for all values of x.
To see why, let's break down the equation using trigonometric identities:
cot^2x - csc^2x = -1
Using the reciprocal identities, we can rewrite cot^2x and csc^2x in terms of sine and cosine:
(cos^2x / sin^2x) - (1 / sin^2x) = -1
Now, let's simplify:
(cos^2x - 1) / sin^2x = -1
Using the Pythagorean identity cos^2x + sin^2x = 1, we can substitute cos^2x with (1 - sin^2x):
(1 - sin^2x - 1) / sin^2x = -1
-sin^2x / sin^2x = -1
Now, we can cancel out the sin^2x terms:
-1 = -1
This equation holds true for all values of x. Therefore, the original equation cot^2x - csc^2x = -1 is true for all values of x.
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Is #7 correct? Please explain.
Answers
The midpoint of a segment is (4,3) and one endpoint is (10,8) Find the coordinates of the other endpoint.
Answers
Answer:
[tex](-2,-2)[/tex].
Step-by-step explanation:
Let us assume that coordinates of other endpoint are [tex](x_1,y_1)[/tex]
We have been given that the midpoint of a segment is (4,3) and one endpoint is (10,8). We are asked to find the coordinates of the other endpoint.
We will use midpoint formula to solve our given problem.
[tex]x\text{-coordinate of midpoint}=\frac{x_1+x_2}{2}[/tex]
[tex]y\text{-coordinate of midpoint}=\frac{y_1+y_2}{2}[/tex]
Upon using our given information, we will get:
[tex]4=\frac{x_1+10}{2}[/tex]
[tex]4\cdot 2=\frac{x_1+10}{2}\cdot 2[/tex]
[tex]8=x_1+10[/tex]
[tex]8-10=x_1+10-10[/tex]
[tex]x_1=-2[/tex]
Similarly, we will find y-coordinate.
[tex]3=\frac{y_1+8}{2}[/tex]
[tex]3\cdot 2=\frac{y_1+8}{2}\cdot 2[/tex]
[tex]6=y_1+8[/tex]
[tex]6-8=y_1+8-8[/tex]
[tex]y_1=-2[/tex]
Therefore, the coordinates of other endpoint would be [tex](-2,-2)[/tex].
A trapezoid has two right angles and bases that measure 16m and 8m. The right triangle formed by an altitude has a hypotenuse of 4 square root 5m. Sketch the trapezoid. What are its perimeter and area?
Answers
length of the rectangle = 8 m
base of triangle = 16 - 8 = 8 m
hypotenuse = 4√5 m
width of the rectangle = √(4√5 - 8) = 4 m
Perimeter = 8 + 16 + 4√5 + 4 = 28 + 4√5 m
Area = area of triangle + area of rectangle
Area = 8(4) / 2 + 8(4) = 48 m^2
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.
Prove that if one solution for a quadratic equation of the form x 2 + bx + c = 0 is rational (where b and c are rational), then the other solution is also rational. (use the fact that if the solutions of the equation are r and s, then x 2 + bx + c = (x − r)(x − s).)
Answers
Say r is rational. Suppose for a second, that s is not. Then, r+s is irrational. But this contradicts the fact that b is rational.
So, if one root is rational, then the other root is also rational
Final answer:
If one root of a quadratic equation with rational coefficients is rational, the other root must be rational too because the sum and product of the roots are related to the coefficients, which are also rational.
Explanation:
To prove that if one solution for a quadratic equation of the form x^2 + bx + c = 0 is rational, then the other solution is also rational, we can use the quadratic formula and properties of rational numbers. If the quadratic equation has rational coefficients and one rational solution, then the sum and product of the roots must also be rational. This is because a quadratic equation with roots r and s can be factored as (x - r)(x - s) = 0, which expands to x^2 - (r + s)x + rs = 0. Matching coefficients, we see that - (r + s) = b and rs = c. Since b and c are rational, r + s and rs must be rational as well.
Given that we have one rational root, let's say r, the sum of the roots r + s is rational, so s must also be rational because the difference of two rational numbers is rational. Hence, if one root of a quadratic equation with rational coefficients is rational, the other root must be rational as well.
Please show work on how you got the answer
Answers
[tex]x+2x=15[/tex]
[tex]3x=15 \newline x=5[/tex]
The lower segment is 10 feet long. The vaulter's right hand is 1.5 feet above her left, so it is 10 + 1.5 = 11.5 from the bottom of the pole.
PLEASE HELP ON THESE ILL GIVE 20 POINTS AND A BRAINLIEST IF YOUR CORRECT!!
Variation is a term that is used to describe __________.
A.
how repetitive a data set is
B.
how large or small a data set is
C.
how spread out or scattered a data set is
D.
how different a data set is from other data sets
Answers
3. Elizabeth opened a library with 19,000 books in the year 1998. The number of books increases at a rate of 6.49% each year. Use a graph to predict the number of books in 2020.
A) ≈ 71,160
B) ≈ 75,779
C) ≈ 80,697
D) ≈ 66,824
Answers
V (t)=V0 (1+r)^t
V (t) number of books in 2020 ?
V0 books in the year 1998 19000
R rate of growth 0.0649
T time 2,020−1,998=22 years
V (22)=19,000×(1+0.0649)^(22)
V (22)=75,778.81 Round your answer to get 75779
Answer: ≈ 75,779
Step-by-step explanation:
A sum of money amounting to $4.25 consists of dimes and quarters if there are 26 coins in all how many are quarters
Answers
d= dimes
q = quarters
d+q=26 coins
rewrite as d=26-q
0.25q +0.10d=4.25
0.25q+0.10(26-q)=4.25
0.25q+2.6-0.10q=4.25
0.15q=1.65
q=11
d=26-11=15
11*0.25 = 2.75, 15*0.10=1.50, 2.75+1.50=4.25
there are 11 quarters
How many different selections of 4 books can be made from a bookcase displaying 12 books?
Answers
(12 x 11 x10 x9) / (4 x3 x 2 x 1) = 495
there are 495 different ways to select 4 books
The function P(t) = 5,000 (0.93)t is the value of a motor scooter t years after it is purchased. Which of the following values show the annual depreciation of the value of the motor scooter?
93
-7
50
7
Answers
P(t) = 5,000 (1-7%)t
P(t) = 5,000 (0.93)t
The annual depreciation rate is 7%
Answer:
Option 4 - 7%
Step-by-step explanation:
Given : The function [tex]P(t) = 5000 (0.93)^t[/tex] is the value of a motor scooter t years after it is purchased.
To find : Which of the following values show the annual depreciation of the value of the motor scooter?
Solution :
We are given a function p(t) which is represented as:
[tex]P(t) = 5000 (0.93)^t[/tex]
Where, p(t) is the value of a motor scooter t years after it is purchased.
Depreciation is the amount that has been deducted from the cost of an item.
The rate of change is 1-0.93=0.07 i.e. 7%.
So, The function P(t) has 7% of the amount has been deducted each year and the value of the motor scooter is 93% of the amount of the previous year.
Therefore, The annual rate of depreciation is 7%.
So, option 4 is correct.
Planes Q and R are parallel. Explain how you know lines a and b are skew.
Sample Response: Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew
Answers
Sample Response:
Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.
Last year, there were n pies baked for the bake sale. This year, there were 156 pies baked. Using n, write an expression for the total number of pies baked in the two years
Answers
Number of pies this year: 156
n + 156 = total number of pies baked in 2 years.
What is the probability that when a fair coin is flipped 25 times, there will be exactly five heads