Answer:
The area of flower bed is 8.96 m^2.
Step-by-step explanation:
Length of lawn = 6 x
width of lawn = x
length of flower bed = x + 4
width of flower bed = x - 1
Area of shaded region = 40 m^2
Area of the shaded region
6 x (x) - (x +4)(x -1) = 40
[tex]5 x^2 - 3 x - 36 = 0 \\\\x = \frac{-3\pm\sqrt{9 + 720}}{10}\\\\x = \frac{-3\pm 27}{10}=2.4 m, - 3 m[/tex]
As length cannot have negative value, so x = 2.4 m.
Area of flower bed = (x + 4)(x - 1) = (2.4 + 4)(2.4 - 1) = 8.96 m^2
a) Write down the exact value of tan 60' b) Find the value of h in this triangle, h= c) Write down the exact area of this triangle, h 60° 43
Step-by-step explanation:
maybe this can help you with your problem
a) The exact value of tan 60 degree is [tex]\sqrt{3}[/tex].
b) The value of h in the given triangle is √3.
c) The area of the given triangle is 24[tex]\sqrt{3}[/tex].
What is tangent of an angle?The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
What is the value of tan 60 degrees?The value of tan 60 degree is [tex]\sqrt{3}[/tex].
What is the formula for area of a triangle?[tex]Area = \frac{1}{2}bh[/tex]
Where,
b is the base of the triangle.
h is the height of the triangle.
a) Since, the value of tan60 degree is [tex]\sqrt{3}[/tex].
Hence, the exact value of tan 60 degree is [tex]\sqrt{3}[/tex].
b). According to the given question, we have a right angled triangle in which
The length of the adjacent side w.r.t angle 60 degrees is [tex]4\sqrt{3}[/tex].
And, the length of the opposite side w.r.t angle 60 degrees is h.
Therefore, the value of h in the given triangle is given by
[tex]tan60 = \frac{h}{4\sqrt{3} }[/tex]
⇒[tex]\sqrt{3} =\frac{h}{4\sqrt{3} }[/tex] (because tan60=√3)
⇒[tex]h=4\sqrt{3} \sqrt{3}[/tex]
⇒[tex]h = 12[/tex]
Hence, the value of h in the given triangle is √3.
c) For the given triangle
Length of base = 4[tex]\sqrt{3}[/tex] unit.
And, the height of the given triangle is 12 unit.
The area of the given triangle is given by
[tex]Area = \frac{1}{2} (4\sqrt{3} )(12)[/tex]
⇒[tex]Area =24\sqrt{3}[/tex]
Hence, the area of the given triangle is 24[tex]\sqrt{3}[/tex].
Learn more about tangent of an angle and area of a triangle here:
https://brainly.com/question/15110994
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Which is an equation of a direct proportion? CLEAR CHECK y=8x y=12x+4 y=12x y=4x−4
Answer:
[tex]y=8x, \\y=12x[/tex]
Step-by-step explanation:
Proportional functions can be written as [tex]y=kx[/tex], where [tex]k[/tex] is some constant of proportional. Since directly proportional functions always pass through the origin, the y-intercept must be 0 (no additional number before or after [tex]x[/tex] term). The only answers that fit this format are:
[tex]\rightarrow \boxed{y=8x}\\\rightarrow \boxed{y=12x}[/tex]
Answer: Y=8x
Step-by-step explanation:
Which graph represents an exponential function?
On a coordinate plane, a curve decreases rapidly and then levels out.
On a coordinate plane, a curve decreases, changes directions, and then decreases again.
Answer:
A
Step-by-step explanation:
A
helpppppppppppppppppppppppppppppppppp!!!!!!!!!
Can U pls help with this number in the sequence
Answer:
First one:
1², 2², 3² and so on (Square of 1,2,3,4,5,6,7.....)
Second one:
2, 13, 26, 41...
add 11, add 13, add 15 (add increasing odd numbers, beginning from 11)
Third one:
4, 14, 29, 49
+10, +15, +20 and so on (add the multiple of 5,beginning from 10)
Fourth one:
1, 8, 27, 64
1³, 2³, 3³, 4³ and so on(cube of 1,2,3,4,5,6,7.....)
Brainliest please
The equation of the line of best fit of a scatter plot is y = −8x + 3. What is the the y-intercept?
A. −8
B. −3
C. 3
D. 8
Answer:
C. 3
Step-by-step explanation:
The y intercept will always be the 'b' in the formula
y= mx+b
since your formula is y = -8x +3, and 3 is in the place of "b", your y intercept will be 3
Answer:
C.3
Step-by-step explanation:
In the equation of y = -8x +3 you can find the y - intercept by looking at number which replaces b which is a positve three. Meaning that your y - intercept would be answer choice C which is positive three.
if the angles (4x+4) and 6x-4 are supplement Ary angles find value of x plzz helppp
Angles (4x + 4°) and (6x - 4°) are supplementary.
That is :
[tex](4x + 4°) + (6x - 4°) = 180°[/tex]Solution :[tex]\hookrightarrow \: 4x + 4 \degree + 6x -4 \degree = 180 \degree[/tex]
[tex]\hookrightarrow10x = 180 \degree[/tex]
[tex]\hookrightarrow x = 18 \degree[/tex]
__________________________
[tex] \mathrm{✌TeeNForeveR✌}[/tex]
Help!! Please also explain how you got your answer
Answer:
y = -½x + 4
Step-by-step explanation:
the line passes point of y-intercept (0, 4) ,
and another point (6, 1)
the slope = (1-4)/(6-0) = (-3)/6 = -½
so the Equation is y = -½x + 4
Can anybody help me with this one ??
A mechanic has a set fee for working on someone's automobile and charges by the hour for making repairs. The total cost of her services (yes she
female mechanic), is c(t) = 100t + 90. Which statement(s) about this function is true?
1. The one time fee for working on the car is $90.
II. The mechanic charges $100 per hour.
III. The number of hours the job takes is represented byt
a. I and III
b. I, II, and III
c. I and II
d. ll and III
Andres went out to a restaurant for dinner. His total bill before tax and tip was $27.30. He was charged an additional 9% tax and he also paid a 15% tip on the original bill.
Answer:
$25.66
Step-by-step explanation:
Given data
Total Bill before tax and tip= $27.30
Tax= 9%
Tip= 15%
Let us find the tax
=9/100*27.30
=0.09*27.30
=$2.457
Let us find the tip
=15/100*27.30
=0.15*27.30
=$4.095
Therefore his bill after tax and tip is
=27.30+2.457-4.095
=$25.66
Pls help me with this it's urgent!
Answer:
function is the correct answer
Answer:
an = a1 + (n - 1 ) d (Function)
Step-by-step explanation:
This is the formula that will be used when we find the general (or nth) term of an arithmetic sequence. So it is function
determine tan(t) if cos(t) = -12/13 and sin(t)
Determine tan(t) if cos(t) = -12/13 and sin(t) = 5/13
Answer:tan(t) = [tex]\frac{-5}{12}[/tex]
Step-by-step explanation:Method 1:
The sketch of the trigonometry is attached to this response.
Since cos(t) is negative and sin(t) is positive, then t should be in the second quadrant as shown in the sketch. A triangle is formed.
We know that, in a given triangle, the cosine of a given angle is the ratio of the adjacent side to the hypotenuse side.
i.e
cos (t) = adjacent / hypotenuse = - 12 / 13
Where;
adjacent = -12 [the adjacent side is in the -x direction]
hypotenuse = 13
Also, the sine of a given angle is the ratio of the opposite side to the hypotenuse side.
sin (t) = opposite / hypotenuse
Where;
opposite = 5
hypotenuse = 13
These sides - opposite, adjacent and hypotenuse - are labelled in the sketch.
From this triangle and the labels, the tangent can be found.
We know that the tangent of a given angle is the ratio of the opposite side to the hypotenuse side. i.e
tan (t) = opposite / adjacent
Where;
opposite = 5
adjacent = -12
Therefore,
tan (t) = [tex]\frac{-5}{12}[/tex]
Method 2:
The tangent of an angle is the ratio of the sine of that angle to the cosine of that angle. i.e
tan(t) = sin(t) / cos (t) ---------------(i)
sin(t) = 5 / 13
cos(t) = -12 / 13
Substitute for sin(t) and cos (t) in equation (i)
tan(t) = [5 / 13] / [-12 / 13]
tan(t) = [5 / 13] x [-13 / 12]
tan(t) = [tex]\frac{5}{13} * \frac{-13}{12}[/tex]
tan(t) = [tex]\frac{-5}{12}[/tex]
A certain type of bacteria is growing at an exponential rate that is modeled by the equation y=aekt, where t represents the number of hours. There are 100 bacteria initially, and 500 bacteria five hours later.
Answer:
meow meow
Step-by-step explanation:
Please help
Honestly cant understand
simplify 2⁴
please help me with this question
Answer:
16
Step-by-step explanation:
2^4= 2x2x2x2 = 16
Answer:
16
Step-by-step explanation:
Raise 2 to the power of 4.
4x2x2= 16
You're rasing 2 two times so...
4x2x2= 16
Pls help I’ll give crown
Answer:
B
Step-by-step explanation:
because area of prism = L×W×H
so
[tex] \frac{3}{4} \times \frac{5}{2} \times \frac{5}{4} [/tex]
answer is 75/32
hope this make sense:)
Answer:
Hi there uwu The answer is 75/32, also explained by the other answerer!
Step-by-step explanation:
Which of the following best describes the graph of the polynomial function
below?
Answer:
Step-by-step explanation:
The given curve crosses the x-axis in two places, (-2, 0) and (0, 0), which are the zeros. This parabolic curve opens up and has its vertex (minimum) at (-1, -1).
Answer: The graph has two zeros.
Step-by-step explanation:
The given graph is the graph of parabola open upward. In the graph of parabola, we will have two solutions since the highest degree of the function is 2.
y = ax^2 + bx + c, where a, b, c are real number and a ≠ 0.
You can see the height degree of the function is 2.
Therefore, there should be two zeros of the function.
According to the given graph of parabola has two zeros at x = -2 and x = 0.
The graph cross the x-axis at x = -2 and x = 0.
Hence, the graph has two zeros.
Answer is A. The graph has two zeros
What are the zeros of the polynomial function y = (x - 3)(2x + 1)(x - 1)? A. 1/2, 1, 3 B. -1, 1, 3 C. -1/2, 1, 3 D. -3, 1/2, -1
Answer:
x=3 x = -1/2 x=1
Step-by-step explanation:
y = (x - 3)(2x + 1)(x - 1)
Set the function equal to zero
0 = (x - 3)(2x + 1)(x - 1)
Using the zero product property
x-3 =0 2x+1 =0 x-1 =0
x=3 2x = -1 x=1
x=3 x = -1/2 x=1
For tran appreciate it
The trip odometer reading will be between 378.3 km and 378.4 km. Nominally, it will read 378.3 km.
A baker uses 20 cups of flour to make 4 loves of bread. Use this to solve the question in the picture!
Answer:
60 cups of flour
Step-by-step explanation:
Since it takes 20 cups of flour for 4 loves of bread this means we're going to need to multiply 20x3=60
Which values of a, b, and c correctly represent the answer in simplest form?
3
- 2
b
32
O a=38, b= 14, C = 1
O a=1,5=14, C= 38
O a=1,b=7.C= 19
O a= 19, b=7,C= 1
Answer:
The answer for this is a=1,b=7,c=19.
ally and bo share 60$ how much money does bo get
Answer:
If Ally and Bo share evenly, Bo will get 30$, so will Ally. The half of 60 is 30.
Solve 2x-5/x-2 ≤ 1
please answer fast
Answer:
x<=-3
Step-by-step explanation:
2x-5/x-2 <= 1
Multiply both sides by x-2
2x-5<=x-2 (anything times 1 is that number.)
add 5 to both sides
2x<=x-3
subtract x from both sides
x<=-3
Answer:
Step-by-step explanation:
[tex]\frac{2x-5}{x-2} \leq 1\\case ~1. both ~numerator~and~denominator \geq 0\\x\neq 2\\2x-5\leq x-2\\x\leq 3\\so~0\leq x<2U2<x\leq 3\\case~2.\\both~numerator~and~denominator<0\\2x-5\geq x-2\\x>3\\which~is~rejected~as~it~gives~both~2x-5~and ~x-2>0[/tex]
Helpppp i need this quick im taking a timed test!!!
Answer: c
Step-by-step explanation:
Answer:c
Step-by-step explanation: it makes the most sense
evaluate the function for x = -8.
f(x) = -2x - 12
Answer:
4
Step-by-step explanation:
f(-8)=-2(-8)-12
f(-8)=16-12
=4
did I choose the right graph?
Answer:
Step-by-step explanation:
The - tells you that it is upside down. So that much of your choice is correct for certain.
The 1/8 squishes the graph something fierce. So of those graphs given, the one you chose is most likely correct. But you are right to be a little miffed at the question. You should never have to choose an answer with only a picture to guide you. If you have a graphing calculator, try y = -1/8 x^2 which is a good candidate for all the graphs.
the volume of this triangular prism is ….. cubic inches. please someone help, will give brainliest asap ❤️❤️❤️❤️❤️
Answer:
576'' squared
Step-by-step explanation:
(6n-25) + (3n + 20) = 180
Answer:
n = 185/9
Step-by-step explanation:
(6n-25) + (3n + 20) = 180
Combine like terms
9n -5 = 180
Add 5 to each side
9n - 5 +5 = 180+5
9n = 185
Divide each side by 9
9n/9 = 185/9
n = 185/9
Select all expressions that at equivalent to the expression 3x + 5. A. 9x − (−5 + 6x) B. 9x − (5 − 6x) C. 9x − (6x + 5) D. 9x − (6x − 5) E. 9x − (−6x + 5)
Answer:
A. 9x − (−5 + 6x)
D. 9x − (6x − 5)
Step-by-step explanation:
Select all expressions that at equivalent to the expression 3x + 5.
To get our answer, we have to solve each option
A. 9x − (−5 + 6x)
= 9x + 5 - 6x
= 9x - 6x + 5
= 3x + 5
Option A is correct
B. 9x − (5 − 6x)
= 9x - 5 + 6x
= 9x + 6x - 5
= 15x - 5
Option B is wrong
C. 9x − (6x + 5)
9x - 6x - 5
= 3x - 5
Option C is wrong
D. 9x − (6x − 5)
= 9x - 6x + 5
= 3x + 5
Option D is correct
E. 9x − (−6x + 5)
= 9x + 6x - 5
= 15x - 5
Therefore, Option A and D are the correct options with the right expressions