The area of the triangle is (A) [tex]73.6ft^{2}[/tex].
What is trigonometry?The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.Trigonometric area of a triangle:Area = [tex]\frac{1}{2}[/tex] × [tex]a[/tex] × [tex]b[/tex] × [tex]sin[/tex] (θ)
Solution -Now, out the values in the formula for the solution.
[tex]A=\frac{1}{2} (16)(10)sin(67^{o} )\\A= 80sin(67^{o} )\\[/tex]
[tex]A=73.6ft^{2}[/tex]
Therefore, the area of the given triangle is (A) [tex]73.6ft^{2}[/tex].
Know more about the area of triangles here:
https://brainly.com/question/17335144
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A student survey was conducted at a major university. Data were collected from a random sample of 206 undergraduate students, and the information that was collected included physical characteristics (such as height and handedness), study habits, academic performance and attitudes, and social behaviors. In this exercise we will focus on exploring relationships between some of those variables. The variables are:
Answer:
Students Major
Cheat reporting response
Number of Alcohols taken
Student's Height
Step-by-step explanation:
The Variables are the following:
Categorical variables
1. Major – The student's majors -
Arts & Social Science or STEM
2. Cheat - Response about reporting cheating - Yes or No
Quantitative Variables
3. Alcohol - Number of alcoholic beverages consumed in a typical week
4. Height - Self-reported height (in inches)
What’s the answer? I don’t understand the question and I came to see if you all can help
Answer:
15/2 that is the answer man
Help anyone can help me do this question,I will mark brainlest.
Answer:
Answer is in attached image
I hope it help...
How to find a parallel sides of trapezium length 7.3mm and 5.3mm ,and it's height is 5mm calculate the area of a trapezium
Answer:
31.50 mm²
Step-by-step explanation:
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Characteristics of a trapezoid
It has 4 vertices and edges
If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogram
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
1/2 x ( 7.3 + 5.3) x 5 = 31.50 mm²
What should be done so that the expression will have a value of 28?
6 + 2 + 32 × 2
Answer:
6+2+(32×2)
6+2+(64)
8+64
72
difference between 72 and 28
72-28
=44
add 44 to make the value 28
Find out the values of x and y from the following ordered pairs.
(x + y, 2) = (13, 2x – y)
Answer:
(x, y) = (5,8)
Step-by-step explanation:
Comparing the ordered pairs we get, x+y=13 and 2=2x-y. Solving it we will get, x=5 and y=8
Question 4 of 5
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used
Match each explicit formula to its corresponding recursive formula.
(8) = 5(5)(1-1)
(n) = 3 +5(n-1)
(3) = 5+3(1-1)
7(n) = 3(5)(n-1)
$(n) = 5 +5(n-1)
f(1) = 5
(*) = 3;(n - 1), for 3
(1) = 5
(n) = f(n-1) +5, for n?
f(1) = 5
f(n) = f(n-1) + 3, for n?
Given:
The recursive formulae.
To find:
The correct explicit formulae for the given recursive formulae.
Solution:
If the recursive formula of a GP is [tex]f(n)=rf(n-1), f(1)=a, n\geq 2[/tex], then the explicit formula of that GP is:
[tex]f(n)=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
The first recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=3f(n-1)[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:
[tex]f(n)=5(3)^{n-1}[/tex]
Therefore, the required explicit formula for the first recursive formula is [tex]f(n)=5(3)^{n-1}[/tex].
If the recursive formula of an AP is [tex]f(n)=f(n-1)+d, f(1)=a, n\geq 2[/tex], then the explicit formula of that AP is:
[tex]f(n)=a+(n-1)d[/tex]
Where, a is the first term and d is the common difference.
The second recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+5[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:
[tex]f(n)=5+(n-1)5[/tex]
[tex]f(n)=5+5(n-1)[/tex]
Therefore, the required explicit formula for the second recursive formula is [tex]f(n)=5+5(n-1)[/tex].
The third recursive formula is:
[tex]f(1)=5[/tex]
[tex]f(n)=f(n-1)+3[/tex] for [tex]n\geq 2[/tex].
It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:
[tex]f(n)=5+(n-1)3[/tex]
[tex]f(n)=5+3(n-1)[/tex]
Therefore, the required explicit formula for the third recursive formula is [tex]f(n)=5+3(n-1)[/tex].
Can someone please help me with this I’m struggling
Answer:
Equation: [tex]70=(x+3)x[/tex]
x = -10 or x = 7
x = 7 (width can't be negative)
x + 3 = 10
Step-by-step explanation:
Represent the width of the rectangle by x. "The length of a rectangle EXCEEDS the width by 3" means the length is 3 LONGER than the width, so the length is represented by the expression x + 3.
Area = (length)(width)
70 = (x + 3)x
Multiply out the right side.
[tex]70=x^2+3x\\x^2+3x-70=0[/tex]
Factor the left side.
[tex](x+10)(x-7)=0[/tex]
Each binomial could equal 0, so
[tex]x+10=0 \text{ or }x-7=0\\x=-10\text{ or }x=7[/tex]
The negative solution does not make sense as the width of a rectangle.
x = 7, making the length, x + 3 = 10
Answer:
Pls mark this as brainiest
Step-by-step explanation:
Area of the rectangle = length x breadth
consider 'x' to be width
therefore length = x+3
area = (x+3)*x
Area = 70 square
x = 7
x+3 = 7+3
= 10
verification
7 x 10
= 70
Find the distance between the
following points using the
Pythagorean theorem: (5, 10)
and (10, 12)
Answer:
[tex]\displaystyle d = \sqrt{29}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Step-by-step explanation:
*Note:
The distance formula is derived from the Pythagorean Theorem.
Step 1: Define
Identify
Point (5, 10)
Point (10, 12)
Step 2: Find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(10 - 5)^2 + (12 -10)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{5^2 + 2^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{25 + 4}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{29}[/tex]Please help me answer this question.
Answer:
total candy = 54 bags
y=17
x=37
Step-by-step explanation:
5x + 4y = 253
x-y = 20
x = 20+y
5(20+y) + 4y = 253
100 + 9y = 253
9y = 153
y=17
x=37
GIVE FULL STEP BY STEP OF THIS MATHS WORD PROBLEM
Sohanlal is a gardener. He is paid ₹160 daily, find how much money will he
get in the month of September?
Answer:
Step-by-step explanation:
days in september=30
salry paid per day=Rs.160
salary paid in 30 days=160×30=Rs.4800
Answer:
4800
Step-by-step explanation:
In the month of September there are only 30 days. So assuming Sohanlal works the entire month of September we will multiply how much he makes daily which is 160 times the amount of days he works which is 30. this will look like this:
160 × 30 = 4800
6. The right triangles ABC and DEF are
similar. The hypotenuse of AABC
measures 28 cm and the hypotenuse
of A DEF measures 7 cm. If one of the
legs of AABC measures 16 cm, what
does the corresponding leg of ADEF
measure?
F 1 cm
H 12 cm
G 4 cm
J 64 cm
Answer:
G. 4 cm
Step-by-step explanation:
28 divided by 7 equals 4.
So, 16 divided by 4 equals 4, which is the answer.
4 is the multiple that relates AABC to ADEF.
Can you answer this math homework? Please!
Answer:
y + 2.3 = 0.45x
y = 0.45x - 2.3
-2y = 4.2x - 7.8
-2(0.45x - 2.3) = 4.2x - 7.8
-0.90x + 4.6 = 4.2x - 7.8
-0.90x - 4.2x = -7.8 - 4.6
-5.1x = - 12.4
x = -12.4 / -5.1
x = 2.4
y + 2.3 = 0.45x
y = 0.45(2.4) - 2.3
y = 1.08 - 2.3
y = -1.2
solution is : (2.4, - 1.2)
Step-by-step explanation:
Complete the missing parts of the
table for the following function. (picture) please answer all asap
Answer:
x=-1 y = 1/3
x = 1 y = 3
x = 3 y = 27
Step-by-step explanation:
y = 3^x
Let x = -1
y = 3^-1 = 1/3^1 = 1/3
Let x = 1
y = 3^1 = 3
Let x = 3
y = 3^3 = 27
the polygons in each pair are similar. find the missing side length.
Given:
The polygon in the given figure are similar.
To find:
The missing side length.
Solution:
We know that the corresponding sides of similar figures are proportional.
The given polygons are similar, so the their corresponding sides are proportional.
[tex]\dfrac{x}{15}=\dfrac{32}{40}=\dfrac{32}{40}[/tex]
So, the missing values in the equation of proportion are 15, 40, 32 respectively.
On solving the above equation, we get
[tex]\dfrac{x}{15}=\dfrac{4}{5}=\dfrac{4}{5}[/tex]
[tex]\dfrac{x}{15}=\dfrac{4}{5}[/tex]
[tex]x=\dfrac{4}{5}\times 15[/tex]
[tex]x=12[/tex]
Therefore, the value of x is 12.
i need help ASAP please
Answer:
reflection over Y axis
Step-by-step explanation:
Answer:
I believe it is D) a reflection over the Y-axis
Step-by-step explanation
it is going over the Y-axis as if it is a sort of mirror, if it were going over the x-axis it would be flipped upside down, if it was A the shape would be going over the original shape. I don't know how to explain C. (I hope this helped and I hope it was correct lol)
How do you solve this problem?
9514 1404 393
Answer:
-19.2
Step-by-step explanation:
Fill in the given values and do the arithmetic.
[tex]\displaystyle x\ \blacksquare\ y=\frac{x}{y}-xy\\\\4\ \blacksquare\ 5=\frac{4}{5}-4\cdot5=0.8-20\\\\\boxed{4\ \blacksquare\ 5=-19.2}[/tex]
Dan invests £18790 into his bank account. He receives 5.9% per year simple interest. How
much will Dan have after 2 years? Give your answer to the nearest penny where appropriate.
Answer: £21007.22
Step-by-step explanation:
First, find the interest amount using the formula SI = (P × R × T) / 100.
SI = interest amount P = principle amount = £18790R = interest rate(in percentage) = 5.9T = time(in years) = 2SI = (P × R × T) / 100 = (18790 × 5.9 × 2)/100 = 221722/100 = £2217.22
The total amount = principle amount + interest amount
= £18790 + £2217.22 = £21007.22
Zoe and Hanna share tips in the ratio 3:7
Last week Zoe received £24
How much did Hanna receive last week?
Answer:
56
Step-by-step explanation:
Zoe : hanna
3 7
Zoe got 24
3*8 = 24
so multiply each side by 8
Zoe : hanna
3*8 7*8
24 56
Hanna got 56
Ben is 4 times as old as Ishaan. 6 years ago, Ben was 6 times as old as Ishaan.
How old is Ishaan now?
Answer:
Ishaan is currently 15 years old.
Step-by-step explanation:
Let B represent Ben's current age and I represent Ishann's current age.
Ben is four times as old as Ishaan. In other words:
[tex]B=4I[/tex]
Six years ago, Ben was six times as old as Ishaan. In other words:
[tex]B-6=6(I-6)[/tex]
Solve for I. Substitute:
[tex](4I)-6=6(I-6)[/tex]
Distribute:
[tex]4I-6=6I-36[/tex]
Subtract 4I from both sides and add 36 to both sides:
[tex]2I=30[/tex]
And divide both sides by two. Hence:
[tex]I=15[/tex]
Ishaan is currently 15 years old.
Answer:
Age of Ishaan = 15 years
Step-by-step explanation:
Let Ishaan's age = x years
Age of Ben = 4 * x = 4x years
6Years ago:
Age of Ishaan = x - 6
Age of Ben = 4x - 6
6 years ago, Ben was 6 times as old as Ishaan
So, Age of Ben = 6 * Ishaan's age
4x - 6 = 6 *(x-6)
4x - 6 = 6x - 36
Add 36 to both sides
4x - 6 + 36 = 6x
4x + 30 = 6x
Subtract '4x' from both sides
30 = 6x - 4x
30 = 2x
2x = 30
Divide both by 2 sides
x = 30/2
x = 15
What type of line is PQ¯¯¯¯¯¯¯¯?
A. median
B. angle bisector
C. side bisector
D. altitude
Answer:
angle bisector
Step-by-step explanation:
Since the line divided the top angle into two equal pieces we call this an angle bisector.
The reliability coefficient of scores in an end of semester examination. If the variance of the exam score is 100. What is the standard error of measurement ?
Answer:
I Will explained you youuuuuu<uuuuuuuuuu
the length of a rectangle is 8 cm longer than its width. find the dimensions of the rectangle if its area is 108cm
!!no links!!
Answer:
[tex]4+2\sqrt{31}\text{ by } -4+2\sqrt{31}[/tex]
Or about 15.136 centimeters by 7.136 centimeters.
Step-by-step explanation:
Recall that the area of a rectangle is given by:
[tex]\displaystyle A = w\ell[/tex]
Where w is the width and l is the length.
We are given that the length is 8 centimeters longer than the width. In other words:
[tex]\ell = w+8[/tex]
And we are also given that the total area is 108 square centimeters.
Thus, substitute:
[tex](108)=w(w+8)[/tex]
Solve for w. Distribute:
[tex]w^2+8w=108[/tex]
Subtract 108 from both sides:
[tex]w^2+8w-108=0[/tex]
Since the equation is not factorable, we can use the quadratic formula:
[tex]\displaystyle x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case, a = 1, b = 8, and c = -108. Substitute and evaluate:
[tex]\displaystyle \begin{aligned} w&= \frac{-(8)\pm\sqrt{(8)^2-4(1)(-108)}}{2(1)} \\ \\ &=\frac{-8\pm\sqrt{496}}{2}\\ \\ &=\frac{-8\pm4\sqrt{31}}{2} \\ \\ &=-4 \pm 2\sqrt{31} \end{aligned}[/tex]
So, our two solutions are:
[tex]w=-4+2\sqrt{31} \approx 7.136 \text{ or } w=-4-2\sqrt{31}\approx -15.136[/tex]
Since width cannot be negative, we can eliminate the second solution.
And since the length is eight centimeters longer than the width, the length is:
[tex]\ell =(-4+2\sqrt{31})+8=4+2\sqrt{31}\approx 15.136[/tex]
So, the dimensions of the rectangle are about 15.136 cm by 7.136 cm.
Simplify the variable expression by evaluating its numerical part.
p-7+56 - 12
A. p + 51
B. p+37
O c. p-51
D. p + 49
The table below represents the function f, and the following graph represents the function g.
*
-6
un
4
-3
-2.
-1
0
1
f(x) 8
-2
-8 -10
-8
-2
8.
22
у
4
12
6
- 2
2
4
6
2
-4
6
Complete the following statements.
The functions fand g have
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
The known value in the question includes the following
The given table of f(x) and x, from which we have;
The point of the minimum value, which is the vertex = (-3, -10)
The axis of symmetry, of a parabola is the vertical line passing through the vertex such that the y-values at equal distance from the line on either side are equal is the line x = -3
The y-intercept, which is the point the graph intercepts with the y-axis or where x = 0 is the point (0. 8)
Over the interval [-6, -3], the average rate of change of f = (-10 - 8)/(-3 -(-6)) = -6
From the graph of g(x), we have;
The axis of symmetry is the line x = -3
The y-intercept = (0, -2)
Over the interval [-6, -3], the average rate of change of g ≈ (6 - (-2))/(-3 -(-6)) = 8/3
Therefore, we have the correct options as follows;
The functions f and g have different axis of symmetry
The y-intercept of f is higher than the y-intercept of g
Over the interval [-6, -3], the average rate of change of f is more rapid than the average rate of change of g
Learn more about parabola here;
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(x⁴ + 3x³ – 2x² + 5) + (2x⁴ – 5x³ + 4x – 15).
Answer:
[tex]\left(x^4+3x^3-2x^2+5\right)+\left(2x^4-5x^3+4x-15\right)[/tex]
[tex]=[/tex] [tex]x^4+3x^3-2x^2+5+2x^4-5x^3+4x-15[/tex]
[tex]=x^4+2x^4+3x^3-5x^3-2x^2+4x+5-15[/tex]
[tex]=x^4+2x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x+5-15[/tex]
[tex]=3x^4-2x^3-2x^2+4x-10[/tex]
[tex]OAmalOHopeO[/tex]
write the equation of the line that goes through points (0,4) (6,16)
Answer: Y= 2x
Step-by-step explanation:
Answer:
y=2x-4
Step-by-step explanation:
firstly find the gradient
m=y2-y1/x2-x1
16-4/6-0
12/6
m=2
then use the equation to find the answer
y-y1=m(x-x1)
y-4=2(x-0)
y-4=2x-0
y=2x-4
Câu 1: Trong các mệnh đề sau, mệnh đề nào là không đúng ?
A. Nếu a // b và (α) vuông góc a thì (α) vuông góc với b
B. Nếu (α) // (β) và a vuông góc với (α) thì a vuông góc với (β)
C. Nếu a và b là hai đường thẳng phân biệt và a vuông góc (α), b vuông góc với (α) thì a // b
D. Nếu a // (α) và b vuông góc a thì b vuông góc (α)
Answer:
Hey can you ask this question in English so I can no answer this question in English and then you can convert that my answer in your language as you're I'm Indian so I don't know this language
Step-by-step explanation:
Please don't you think that I'm doing this for points I think I should know this question so can you please answer this you're this and English
[tex]\text{Solve for 'x':}\\\\3(x+1)=12+4(x-1)[/tex]
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]x = -5[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'x'...}}\\\\3(x+1)=12+4(x-1)\\----------\\\rightarrow 3x + 3 = 12 + 4x - 4\\\\\rightarrow 3x + 3 = 12 -4+4x\\\\\rightarrow 3x + 3 = 8 + 4x\\\\\rightarrow 3x + 3 = 4x + 8\\\\\rightarrow3x + 3 -3 = 4x + 8 - 3\\\\\rightarrow 3x = 4x + 5\\\\\rightarrow 3x - 4x = 4x - 4x + 5\\\\\rightarrow -x = 5\\\\\rightarrow \frac{-x=5}{-1}\\\\\rightarrow \boxed{x = -5}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Answer:
x=-5Step-by-step explanation:
3(x+1)=12+4(x-1)
3(x+1)=8+4x
3x+3=8+4x
3x+3−4x=8
-x+3=8
-x=8-3
-x=5
-x(-1)=5(-1)
-x(-1)=-5
x=-5
Explain the relationship of the meaning of the word isometric to the properties of an isometric or rigid transformation
Step-by-step explanation:
The iso parts of isometric means same, and It is similar becuase rigid trtransformation and the metric parts means measure. Basically isometric means same measure. Rigid transformation preserve "same measures" like angles and side lengths.
