The diagram shows some land in the shape of a quadrilateral ABCD. AB = 6 km, AD = 5 km and CD = 12 km Angle BAC = 30 The land is sold for £10 million per square kilometre. Calculate the total cost of the land.
Answers
Answer:
£495 million
Step-by-step explanation:
To find out the total cost of the land, we need to first calculate the area of the land.
Step 1: Find area of right angled triangle ADC
AD = 5 km,
DC = 12 km
Area of the right triangle = ½*a*b
a = 5km
b = 12km
Area = ½*5*12
= 5*6
Area of ADC = 30 km²
Step 2: Find the area of triangle ABC
First, let's find the length of AC using Pythagorean theorem
AC² = AD² + DC²
AC² = 5² + 12² = 25 + 144
AC = √169
AC = 13km
Area of ∆ABC = ½*AB*AC*sin(30°)
= ½*6*13*0.5
= 3*13*0.5
Area of ∆ABC = 19.5 km²
Total area of the land = area of ∆ADC + ∆ABC = 30 + 19.5 = 49.5 km²
Step 3: calculate how much the land costs
If the land costs £10 million per km²,
Cost of 49.5 km² = 49.5 × 10 = £495 million
Related Questions
X+3y+2z=1
2x-2y-5z=0
-x+2y+4z=1
Answers
Answer:
(x, y, z) = (3, -2, 2)
Step-by-step explanation:
The augmented matrix for this set of equations is ...
[tex]\left[\begin{array}{ccc|c}1&3&2&1\\2&-2&-5&0\\-1&2&4&1\end{array}\right][/tex]
Using your calculator or any of a number of web sites, you can find the reduced row-echelon form to be ...
[tex]\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&-2\\0&0&1&2\end{array}\right][/tex]
This tells you the solution is (x, y, z) = (3, -2, 2).
When the sun is 62° above the horizon, a building casts a shadow 18 m long. How tall is the building?
Answers
9514 1404 393
Answer:
33.9 m
Step-by-step explanation:
The relationship between the building height (h), the shadow length (s), and the angle of elevation of the sun (α) is ...
tan(α) = h/s
h = s·tan(α) = (18 m)tan(62°) ≈ 33.853 m
The building is about 33.9 meters tall.
In the diagram, what is the perimeter of polygon $PQRST$?
Answers
Answer:
24
Step-by-step explanation:
PQ is equal to QR, therefore QR=3
Draw a perpendicular line down from R to line TS to form a triangle and since PT=6, the height of the right angle triangle would be 3.
The base of the right triangle would be 7-3=4. Using pytag. theorem [tex]\sqrt{4^{2}+3^2 }=5[/tex]
Therefore RS=5.
So now we can sum up everything: PQ+PT+TS+RS+QR= 3+6+7+5+3=24
Which expressions are equivalent to 10 over 10 3/4?
Answers
Answer:
There are no choices, but [tex]\frac{10}{10.75}[/tex] can be changes in the following ways: multiplying the numerator and the denominator by the same amount, or dividing the numerator and denominator by the same amount.
Hope it helps <3
Answer:
40/43
Step-by-step explanation:
The fraction
10
-----------------
10 3/4
can be simplified by converting 10 3/4 to the improper fraction 43/4:
10 10 40
----------------- = _______ = ----------
10 3/4 43/4 43
Next time, please share any answer choices that are given to you. Thank you.
What is the measure of ABC? Please help, will give brainliest.
Answers
Answer:
Hello!
~~~~~~~~~~~~~~~~
Your answer would be (D) 60
~~~~~~~~~~~~~~~`~
Hope this helped you!
You run 9.1 miles in 1.3 hours at a steady rate. What equation represents the proportional relationship between the x hours you run and the distance y in miles that you travel?
Answers
Answer:
y = 7x
Step-by-step explanation:
Given that;
You run 9.1 miles in 1.3 hours at a steady rate
Distance y = 9.1 miles
Time x = 1.3 hours
The relationship between the distance y and the time x is the speed v;
Distance = speed × time
y = v×x ......1
v = y/x
Substituting the given values;
v = 9.1/1.3
v = 7 miles/hour
To derive the equation that represents the proportional relationship between the x hours you run and the distance y in miles that you travel. We substitute v = 7 into equation 1;
y = 7x
please help its urgent !!!! -3c + 5d + 3c- d
Answers
Answer:
4d
Step-by-step explanation:
Am I supposed to simplify this?
-3c+5d+3c-d
-3c+3c+5d-d
0+4d
4d
Let me know if this helps :)
Answer:
= 4d
Step-by-step explanation:
-3c+3c = 0
5d-d = 4
-3c+5d+3c-d=4d
Select the correct answer from each drop-down menu. Simplify. √63
Answers
Answer:
√63 can be written as
√ 9 × 7 = √ 9 × √7 = 3 × √ 7
= 3√7
Hope this helps you
Answer: [tex]3\sqrt{7}[/tex]
Step-by-step explanation:
Separate [tex]\sqrt{63}[/tex] into [tex]\sqrt{7}[/tex] and [tex]\sqrt{9}[/tex]. Then simplify [tex]\sqrt{9}[/tex] into 3. Thus, the simplified version of [tex]\sqrt{63}[/tex] is [tex]3\sqrt{7}[/tex]
Arrange in ascending order ½, ⅛, ¾, ⅖
Answers
Answer:
1/8, 2/5 , 1/2, 3/4
Step-by-step explanation:
1/2= 0.5
1/8= 0.1
3/4= 0.8
2/5= 0.4
just arrange them in the order from smallest to largest......
Answer:
⅛ < ⅖ < ½ < ¾
Step-by-step explanation:
First, rewrite the fractions so that they all have the same denominator.
The new denominator should be the lowest common multiple of the original denominators.
The L.C.M. of 2, 8, 4, and 5 is 40.
When multiplying the denominator to 40, make sure you multiply the numerator with the same value you use to multiply the denominator.
1/2 = 1x20 / 2 x 20 = 20/40
1/8 = 1x5 / 8x5 = 5/40
3/4 = 3x10 / 4x10 = 30/40
2/5 = 2x8 / 5x8 = 16/40
When all the denominators are the same, we can compare the numerator. The greater the numerator, the greater the fraction is.
Between 20, 5, 30, and 16, the smallest is 5, then 16, 20 and greatest is 30.
Since ascending order means listing them out from smallest to greatest, the order should be:
⅛ < ⅖ < ½ < ¾
please help me with this question and I'll give u a brainlist for the correct ans. thank you
Answers
Answer:
least value of n =4
Step-by-step explanation:
i hope the screenshot of my work broken down step by step helps
Given: ∆ABC – iso. ∆, m∠BAC = 120° AH ⊥ BC , HD ⊥ AC AD = a cm, HD = b cm Find: P∆ABH
P = _____ cm
Answers
Answer:
P = 5.4641b cm.
Step-by-step explanation:
If the triangle ABC is isosceles and m∠BAC = 120°, we have that:
[tex]mACB = mABC = (180-120)/2 = 30\°[/tex]
Then, in triangle ABH, we have:
[tex]mABH + mBHA + mHAB = 180\°[/tex]
[tex]30\° + 90\° + mHAB = 180\°[/tex]
[tex]mHAB = 60\°[/tex]
If m∠BAC is 120°, we have:
[tex]mHAB + mHAC = 120\°[/tex]
[tex]m∠HAC = 60\°[/tex]
Now we can find the length of AH using the sine relation of angle m∠HAC:
[tex]sin(mHAC) = DH / AH[/tex]
[tex]0.866 = b / AH[/tex]
[tex]AH = b / 0.866 = 1.1547b[/tex]
Now, to find the length of HB and AB, we can use the tangent and cosine relation of the angle m∠HAB:
[tex]tan(mHAB) = HB / AH[/tex]
[tex]1.7321 = HB / 1.1547b[/tex]
[tex]HB = 1.7321 * 1.1547b = 2b[/tex]
[tex]cos(mHAB) = AH / AB[/tex]
[tex]0.5 = 1.1547b / AB[/tex]
[tex]AB = 1.1547b / 0.5 = 2.3094b[/tex]
So the perimeter of triangle ABH is:
[tex]P(ABH) = AB + HB + AH[/tex]
[tex]P(ABH) = 2.3094b + 2b + 1.1547b[/tex]
[tex]P(ABH) = 5.4641b[/tex]
The relation of a and b can be calculated using the tangent relation of the angle m∠HAC:
[tex]tan(mHAC) = DH / AD[/tex]
[tex]1.7321 = b / a[/tex]
[tex]b = 1.7321a[/tex]
Which of the following functions shows the quadratic parent function, F(x) =
x2, shifted left?
Answers
Answer: choice B
Step-by-step explanation:
just took the quiz
omm its B. G(x)=(x+8)^2
just took the test
change 3/4 to decimal
Answers
Answer:
0.75
Step-by-step explanation:
Since we use the base 10 decimal system, first convert 3/4 to out of 100:
3/4 = 75/100
We divide 75 by 100 to get 0.75
Use the substitution method to solve the system of equations. Choose the
correct ordered pair
y = 12x-8
y=8x
A (4.12
B (3,15
C. (5.11
D. (216)
Answers
Answer:
D) (2,16)
Step-by-step explanation:
Y=12x-8
Y=8x
8x=12x-8
8=12x-8x
8=4x
2=x
Y=8x
Y=16
(02.01 MC) A talent show broadcast on television asks viewers to call in to vote for their favorite act. Describe how the design of the survey leads to bias. (4 points) Select one: a. A voluntary response error was made in this design. This type of sampling only targets people with phones to call in and is not a good representation of the population. b. A convenience sample error was made in this design. This type of sampling only targets people with televisions and is not a good representation of the population. c. A voluntary response error was made in this design. This type of sampling only targets those who are passionate about a specific act and call in to vote; it is not a good representation of the population. d. A convenience sample error was made in this design. This type of sampling only targets people with access to that television channel and is not a good representation of the population. Incorrect e. There are no potential areas of bias.
Answers
Answer:
Option D is correct.
A voluntary response error was made in this design. This type of sampling only targets those who are passionate about a specific act and call in to vote; it is not a good representation of the population.
Step-by-step explanation:
When humans are given the choice whether to participate in a survey like in this question, most often than not, the survey becomes biased.
This is because only the people or set of people who feel strongly the most about the subject matter of the poll will participate in the survey. This favours the group that disagrees as this group, if given the choice to express their opinion, will most likely be the set of people that will readily express their discontent.
Discontent is more visibly and strongly expressed in humans.
In order to remove this bias, people should have been chosen at random and their responses recorded.
Hope this Helps!!!
Which of the following is the best approximation of the area of the circle?
Answers
Answer:
49π or 153.938 mm²
Step-by-step explanation:
Area of a Circle Formula: A = πr²
Since we are given radius r, simply plug it into the formula:
A = π(7)²
A = 49π
A = 153.938
Answer:
Step-by-step explanation:
Pleased to help u....
On a coordinate plane, a curved line with minimum values of (negative 1.56, negative 6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (negative 2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0). Which interval for the graphed function has a local minimum of 0? [–3, –2] [–2, 0] [1, 2] [
Answers
Question:
On a coordinate plane, a curved line with
minimum values
o (negative 1.56, negative 6)
o (3, 0),
maximum value
o (1.2, 2.9),
crosses the x-axis
o (negative 2.5, 0),
o (0, 0),
o (3, 0),
crosses the y-axis
o (0, 0).
Which interval for the graphed function has a local minimum of 0?
[–3, –2]
[–2, 0]
[1, 2]
[2,3]
Step-by-step explanation:
From the given information, it 'crosses' the x-axis at (3,0), and this is also a minimum. Thus the local minimum is at (3,0), so the answer choice for the interval is [2,3] (not indicated in the posted question, so double check).
The graphed function has a local minimum of 0 at [2, 4]
What is function?A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value.
Given that, On a coordinate plane, a curved line with minimum values of (-1.56, -6) and (3, 0), and a maximum value of (1.2, 2.9), crosses the x-axis at (-2.5, 0), (0, 0), and (3, 0), and crosses the y-axis at (0, 0).
This means,
When x = -1.56, the minimum value of the function is y(min) = -6
And,
When x = 3, the minimum value of the function is y(min) = 0
Therefore, the graphed function has a local minimum of 0, when x = 3
That means, the interval which contains this value of x is [2, 4] because, x = 3 ∈ [2, 4]
Hence, the graphed function has a local minimum of 0 at [2, 4]
For more references on function, click;
https://brainly.com/question/21145944
#SPJ3
find the volume and total surface area of a rectangular solid of dimensions 2cm by 3cmby 4cm
Answers
Answer:
volume-24 cm³
total surface area-12 cm²
Step-by-step explanation:
volume-2cmx3cmx4cm=24 cm³total surface area-3cmx4cm=12 cm²How do you factor the expression 54+24= Thanks!
Answers
Answer:
Step-by-step explanation:
1.The prime factorization of 54 is: 2 x 3 x 3 x 3.
2.The prime factorization of 24 is: 2 x 2 x 2 x 3.
3.The prime factors and multiplicities 54 and 24 have in common are: 2 x 3.
4.2 x 3 is the GCF of 54 and 24.
Answer: GCF(54,24) = 6.
Answer:
6 × 13
Step-by-step explanation:
To find the greatest common factor (GCF), write the prime factorization of each term.
54 = 2×3³
24 = 2³×3
The greatest common factor is the product of each prime number at its lowest exponent.
GCF = 2×3
GCF = 6
Factor:
54 + 24
6 (9 + 4)
6 × 13
N a group of 39 students, 14 study both Art and Biology. 5 study Biology but not Art. 6 study neither subject. Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
Answers
Answer:
14/39 which is about 35.9%
Step-by-step explanation:
We have a total of 39 students and 14 of which study both Art and Biology
and the rest of the total is unimportant to the question. Since there are 14 students out of 39 we can now do the math and figure out that 14 divied by 39 is right about 35.9 percent.
Can you pick brainliest?
Which of the following graphs is described by the function given below?
y = 2x2 + 8x+ 3
5
A.
B.
D.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answers
Step-by-step explanation:
D. Graph D the answer is D
Answer:
D. Graph D the answer is D
Step-by-step explanation:
if y is an integer, find the value of y that satisfies both the linear inequalities y-2<2 and 3y+10>16
please give me calculation too tq
Answers
Answer:
Value of y = 3
Step-by-step explanation:
Given:
y-2<2 ........Eq1
3y+10>16.........Eq2
Find:
Value of y
Computation:
y-2<2
Add 2 both side,
y-2+2<2+2
y < 4
So y = (0,1,2,3)
Put y = 3 in both equation:
y-2<2
3-2<2
1<2
3y+10>16
3(3) + 10 >16
19>16
Both equation get satisfies by y = 3
So, Value of y is 3
factor 20r+60t to identify the equivalent expression
Answers
Answer:
[tex]\boxed{20(r + 3t)}[/tex]
Step-by-step explanation:
[tex]20r + 60t[/tex]
Factor out 20 from the expression.
[tex]20(r) + 20(3t)[/tex]
Take 20 as common.
[tex]20(r + 3t)[/tex]
Helppp!!!! please!!!
Answers
Answer:
A
Step-by-step explanation:
Consider the quadratic function f(x) = x2 – 5x + 6.
What are the values of the coefficients and constant in the function?
A=
b =
C=
Answers
Hey there! :)
Answer:
a = 1
b = -5
c = 6.
Step-by-step explanation:
Recall that in standard form, the coefficients of a quadratic equation are:
f(x)= ax² + bx + c
In the given equation, we can identity the coefficients:
f(x) = (1)x² - 5x + 6
a = 1
b = -5
c = 6.
In 2001,the united states oil consumption was 7,297.4 millions of barrels,while japan's was 1,979.4 millions of barrels. How many more barrels did the united states consume than japan.
Answers
Answer:
5,318 millions of barrels
Step-by-step explanation:
Subtract Japan's number of barrels from the US' to find the difference:
7,297.4 - 1,979.4 = 5,318 millions of barrels
Please help!!! As soon as possible.
Answers
Answer:
The SAS Postulate.
Step-by-step explanation:
In the diagram, the two triangles are congruent. This is because there are two pairs of congruent sides, with a congruent angle in between. The two angles between the sides are congruent because of the Vertical Angle Theorem.
Hope this helps!
How are zeros, the vertex, and symmetry of a quadratic function interpreted in a context?
Answers
Answer:
The zeroes of a quadratic equation are the points on the graph where it lies on the x-axis.
The vertex is the point where it is the maximum or minimum value of x or y depending on the symmetry.
The symmetry is the line where it cuts the graph through the vertex of the graph dividing it into two equal parts that mirror each other.
The quadratic formula, factoring, and completing the square are the methods used to solve a quadratic equation.
f(x) + 7 shifts the graph 7 units up, f(x +7) shifts the graph 7 units to the left
Step-by-step explanation:
Without multiplying, order the following products from least to greatest. 23* 2/2 23* 1/4 23* 13/5
Answers
From least to greatest
23* 1/4, 23* 2/2, 23* 13/5
Explanation
In order to do this without multiplication, place the fractions in ascending order.
The denominators of these fractions have 20 as a common multiple.
2/2 • 10 = 20/20
1/4 • 5 = 5/20
13/5 • 4 = 52/20
From this it logically follows that the fractions in ascending order are:
1/4, 2/2, 13/5
Therefore the products in ascending order are:
23* 1/4, 23* 2/2, 23* 13/5
Find a polynomial with a degree of 3, and the zeros 1,7, & -4 with no other zeros.
Answers
Answer:
f(x) = x³ - 4x² - 25x + 28
Step-by-step explanation:
Given the zeros x = 1, x = 7 and x = - 4 , then the corresponding factors are
(x - 1), (x - 7), (x + 4)
The polynomial is then the product of the factors, that is
f(x) = a(x - 1)(x - 7)(x + 4) , a is a multiplier
let a = 1 and expand the first pair of factors using FOIL
f(x) = (x² - 8x + 7)(x + 4) ← distribute
= x³ - 8x² + 7x + 4x² - 32x + 28 ← collect like terms
= x³ - 4x² - 25x + 28