The area of triangle ABC is 4 root 2. Work out the value of x
Answers
Answer:
x ≈ 2.4
Step-by-step explanation:
Area of the triangle = 1/2 absin theta
Find the diagram of the triangle attached
a = 2x-3
b =x+2
theta = 45°
Substitute and find x
4√2 = 1/2(2x-3)(x+2)sin45
8/√2 = (2x-3)(x+2)(1/√2)
8 = (2x-3)(x+2)
Expand
8 = 2x²+4x-3x-6
2x²+x-6-8=0
2x²+x-14 = 0
x = -1±√1²-4(14)(2)/2(2)
x = -1±√1+112/4
x = -1±√113/4
x = -1+10.63/4
x = 9.63/4
x = 2.4
The value of x is 3.075.
Given that,
The area of the triangle is [tex]4\sqrt{2}[/tex] square meter,
and [tex]\theta[/tex] is 45 degrees.
The one side of the triangle is (2x-3) and the other side of the triangle is (x+2).
We have to determine
The value of x.
According to the question
The area of the triangle is determined by the following formula,
[tex]\rm Area \ of \ triangle = \dfrac{1}{2} sin\theta[/tex]
Substitute all the values in the formula
[tex]\rm Area \ of \ triangle = \dfrac{1}{2} absin\theta\\\\4\sqrt{2} = \dfrac{1}{2} (2x-3)(x+2) sin45\\\\2\times4\sqrt{2} = (2x^2+4x-3x-6)\dfrac{1}{\sqrt{2} }\\\\\sqrt{2} \times8\sqrt{2} = (2x^2+x-6)\\\\8\times2 = (2x^2+x-6)\\\\16 = 2x^2+x-6\\\\2x^2+x-6-16=0\\\\2x^2+x-22=0\\\\x = \dfrac{-b\pm\sqrt{b^2-4ac} }{2a}\\\\x = \dfrac{-1\pm\sqrt{(-1)^2-4\times2\times(-22)} }{2\times2}\\\\x = \dfrac{-1\pm \sqrt{177} }{4}\\\\x = \dfrac{-`1\pm13.30 }{4}\\\\[/tex]
[tex]\rm x = \dfrac{-1+13.30}{4} \ and \ x = \dfrac{-1-13.30}{4} \\\\x = \dfrac{12.30}{4} \ and \ x= \dfrac{-14.30}{4}\\\\x = 3.075 \ and \ x = -3.575[/tex]
The value of x can not be negative so the value of x is 3.075.
Hence, The required value of x is 3.075.
For more details refer to the link given below.
https://brainly.com/question/15894203
Related Questions
please help me, yall :))))
Answers
You have a loan for $200,000 at 8.5% annual simple interest.what is your monthly interest payment
Answers
Answer:
~1467
Step-by-step explanation:
$200,000 x 8.5% or .085 = $17,000 Annualy
$17,000 / 12 Months out of the year = $1466 2/3 Monthly Payments
Answer is $1467 Rounded
The monthly interest payment is $1,467.
Given that,
The loan amount is $200,000.The rate of interest is 8.5%.We need to find out the monthly interest payment.Based on the above information, the calculation is as follows:
[tex]= (\$200,000 \times 8.5\%) \div 12[/tex]
= $1,467
Therefore we can conclude that the monthly interest payment is $1,467.
Learn more: brainly.com/question/13324776
are 2y2 and -4y2 like or unlike terms?
Answers
Answer:
Unlike terms.
Step-by-step explanation:
[2y2 does not equal -4y2], much like 5 does not equal 6, vice versa.
The expression 10s+5m represents a student’s score on a social studies test, where s = the number of correct short answer items and m = the number of correct multiple choice items. Noor answers 16 multiple choice items correctly. She does no answer any short answer items correctly. What is Noor’s score?
A. 31
B. 15
C. 80
D. 160
Answers
Can you explain how u got 31?
WRITE THE FIRST 4 TERMS OF THE SEQUENCE DEFINED BY THE GIVEN RULE ( PLEASE ANSWER FAST PLEASE QUICKLY WILL GIVE BRAINLIEST AND THANKS!!!! PLEASE HURRY!!!!)
Answers
Step-by-step explanation:
5.) f(1) = 7, f(n) = -4※f(n-1) + 15
[tex]f(2) = - 4 \times 7 + 15 = - 13 \\ f(3) = - 4 \times ( - 13) + 15 = 67 \\ f(4) = - 4 \times 67 + 15 = - 253[/tex]
The first four terms are 7, -13, 67, -253.
7.) f(1) = 3, f(n) = [f(n-1)]²
[tex]f(2) = (3)^{2} = 9 \\ f(3) = ( {9)}^{2} = 81 \\ f(4) = ( {81)}^{2} = 6561[/tex]
The first four terms are 3, 9, 81, 6561.
You are given that angle RST and angle TUR are right angles. What additional piece of info allows you to prove they are congruent
Answers
Answer:
the additional info required is - the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle.
Step-by-step explanation:
As given , RST and angle TUR are right angles.
So the triangles are right angle triangles.
If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.
So, the additional info required is - the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle.
Write the phrase as an expression.
5 less than 8
An expression is
Answers
Answer:
the expression is 5 - 8
which is -3
or
the expression is 5 < 8
The value of the ratio y/x of two proportional quantities x and y is called..
either constant of proportionality, ratio, unit rate, proportion, rate, or proportional relationship
Answers
Answer:
constant of proportionality
Step-by-step explanation:
Assuming that we have two proportional quantities; one is x and one is y.
If we know whether the relationship between them is direct or inverse proportion, then the ratio of the two quantities y/x gives us a constant generally known as the constant of proportionality.
Can someone please help me out?
Answers
9514 1404 393
Answer:
64°
Step-by-step explanation:
y° and the angle marked 64° are "alternate interior angles", so are congruent.
y° = 64°
Alyssa's cat weighs 12 pounds, which is 3/8 of the weight of her dog. Use the equation 3/8d=12 to find the weight of Alyssa's dog.
Answers
Answer:
0.5 pounds!
Step-by-step explanation:
12/0.375=32
Her dog is 32 pounds
How to find the domain of a composite function
Answers
Answer:
The domain of a composite function f(g(x)) f ( g ( x ) ) is the set of those inputs x in the domain of g for which g(x) is in the domain of f .
What accounted for the high mortality rate of the French Army in Russia?
Answers
Answer:the lost the war
Step-by-step explanation:
According to the table, if a married couple filing jointly earns $67,400, what will their taxes be to the nearest dollar?
A): $10,470
B): $10,590
C): $11,150
D): $11,320
Answers
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Dont worry about what I type hear the answer is C
which number is composite? (9,5,11,2)
Answers
Answer: 9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
3 x 3 = 9 :)
At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: what is that chance
Answers
Answer:
10%
Step-by-step explanation:
According to the scenario, given data are as follows:
Students over age 21 = 30
Students under age 21 = 20
Choose student over age 21 = 3
Choose student under age 21 = 2
So, we can calculate chances by using following method,
Chances of student over age 21 = Number of choose student ÷ Total students
= 3 ÷ 30 = 0.10 = 10%
Similarly, Chances of student under age 21 = Number of choose student ÷ Total students
= 2 ÷ 20 = 0.10 = 10%
Hence, in both condition, chances are 10%.
how many turning points will a quartic fumction with four real zeros have?
Answers
upto four roots or zero......
I need help I have 20mons left
Answers
Answer:
y=1/2x-7
your welcomee
The bars in this graph represent the favorite sport listed
by teenagers in a random sample.
Is this graph misleading?
Favorite Sports
O Yes, because the scale does not start at 0
Yes, because the bars are not the same height
O No, because the bars are all the same width
O No, because the scale starts at 0
20
18
16
Frequency
14
12
10
Basketball Football Lacrosse Soccer Volleyball
Favorite Sport
Answers
Answer:
A.) yes because the scale does not start at 0
Step-by-step explanation:
edge
Answer:
A
Step-by-step explanation:
HELP PLEASE IM BEGGING PLEASE PLEASE PLEASE
Answers
Answer:
h - 18 = 67
Step-by-step explanation:
If h is her height, then her height minus 18 is 67, or h - 18 = 67
Answer:
67 = h - 18
Step-by-step explanation:
Sry I meant h-18 = 67
Identify how the graph is transformed from that of the parent function.
y = cot(x/5)
>
DONE
y=1/4tan(x)
DONE
Answers
The graph is transformed from that of the parent function by using the trigonometric relationship between tangent and cotangent function, dilation of the independent variable and vertical dilation.
How to comparent a parent function with a child functionLet be [tex]f(x) = \cot \frac{x}{5}[/tex] the parent function and [tex]g(x) = \frac{1}{4}\cdot \tan x[/tex] the child function. We can obtain the child function by applying the following three steps:
Relationship between tangent and cotangent functions: [tex]f'(x) = \frac{1}{f(x)} = \frac{1}{\cot \frac{x}{5} } = \tan \frac{x}{5}[/tex]Dilation of the independent variable by 5: [tex]f''(x) = f(5\cdot x) = \tan x[/tex]Vertical dilation by [tex]\frac{1}{4}[/tex]: [tex]g(x) = \frac{1}{4}\cdot f''(x) = \frac{1}{4}\cdot \tan x[/tex]In consequence, the graph is transformed from that of the parent function by using the trigonometric relationship between tangent and cotangent function, dilation of the independent variable and vertical dilation. [tex]\blacksquare[/tex]
To learn more on functions, we kindly invite to check this verified question: https://brainly.com/question/5245372
Answer: first is stretched horizontally, second is compressed vertically
Step-by-step explanation:
This list shows the numbers of stuffed animals nine children own.
6, 12, 2, 5, 1, 6, 15, 10, 13
What is the range of the number of stuff animals the children own?
7
13
14
15
Answers
Answer:
I believe it's 14
Step-by-step explanation:
To find the range you subtract to highest and lowest values, (15 and 1)
15 - 1 = 14
I took the test and its 13.
PLEASE ANSWER ASAP !!!!!!!!!!!!!!!!!!! WILL GET BRAINLEST IF CORRECT!!!!!!!!!!!!!!!!!!!!!!
Answers
There are 23 animals in the barn. Some are chickens some are goats. There are 80 legs in all. How many of each animal is there?
Answers
There are 17 goats and 6 chickens
Explaining: (1) C + G = 23
As for legs:
(2) 2C + 4G = 80 (each C has 2 legs and each G has 4 legs)
Solving equation (1): C = 23 - G
Substituting in equation (2)
2(23 - G) + 4G = 80
2G = 34
G = 17
C = 6
What is the solution to this system of equations?
Answers
Answer:
The fourth option i.e. 'no solution' is correct.
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}\frac{2}{3}x+y=6\\ -\frac{2}{3}x-y=2\end{bmatrix}[/tex]
Adding both equations
[tex]-\frac{2}{3}x-y=2[/tex]
[tex]+[/tex]
[tex]\underline{\frac{2}{3}x+y=6}[/tex]
[tex]0=8[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}\frac{2}{3}x+y=6\\ 0=8\end{bmatrix}[/tex]
0 = 8 is FALSE!
Therefore, the system of equations has no solution.
Thus,
No Solution!
Hence, the fourth option i.e. 'no solution' is correct.
Select the correct answer.
de.
Currently there are 691,255 trees in a national forest. A park ranger discovered that an
untreatable disease is killing the trees at a rate of 1.5% every year.
Let t represent the number of years after the current date. Determine the inequality that can be
used to model when there will be no more than 621,859 trees, and then solve the inequality for t.
CHECK ATTACHMENT FOR OPTIONS
Answers
Answer:
691,255(0.985)t ≤ 621,859; t ≥ 7
Step-by-step explanation:
i just did it. it was C
Answer:
Yes it is corect,
C
Step-by-step explanation:
there is a college student who wants to buy apples from the local store. the store generally sells about 5 apples for every 2 coustomers they serve. About how many apples will they sell in 6 hours if they serve 10 coustomers every hour?
Answers
Which values from the set {2,4,6,8,10} make this inequality n + 5 > 10 true?
Answers
Answer:
6,8,and 10
Step-by-step explanation:
Answer:
6,8,and 10
Step-by-step explanation:
when you plug in each number from the set into the inequality you will see which values from the set will make the inequality true.
1. 2+5>10 = 7>10 FALSE
2. 4+5>10 = 9>10 FALSE
3. 6+5>10 =11>10 TRUE
4. 8+5>10 = 13>10 TRUE
5. 10+5>10 = 15>10 TRUE
i Write a linear function f with the values f(0) = 7 and f(2) = 12. A function is f(x)
Answers
Answer:
y=5/2x+7
Step-by-step explanation:
y=mx+b
12=m(2)+7
5=2m
m=5/2
PLEASE help!!!!
Im timed!
Answers
Answer:
it would be B
Step-by-step explanation:
HELP PLEASSEEEE I NEED TO FIND THE MISSING SIDE HYPOTENUSE
Answers
Answer:
B. 6.5
Step-by-step explanation:
You can use the 5 against the unknown number and add a few more moves which makes it 6.5.. It's easier in my head man.
