work out x when the area is root 4 2^2 and angle C is 45 and ab are (x+2)(2x-3)
Answers
Answer:
x = 3.08
Step-by-step explanation:
Area formula:
A = 1/2bhThe height is:
h = (x + 2)sin 45° = (x + 2) ×√2/2Substitute the value for area and set equation:
4√2 = 1/2 × (2x - 3) × √2(x + 2)/2(2x - 3)(x + 2) = 162x² + x - 6 = 162x² + x - 22 = 0D = 1 + 4*2*22 = 177x = (-1 + √177)/4 = 3.08 (rounded)Note the second root ignored as negative
Answer:
x = 3.08 (3 s.f.)
Step-by-step explanation:
Area of a Triangle (using sine)
[tex]\sf Area=\dfrac{1}{2}ac \sin B[/tex]
where:
a and c are adjacent sidesB is the included angleGiven:
Area = 4√2 m²a = (2x - 3) mc = (x + 2) mB = 45°Substitute the given values into the formula:
[tex]\implies 4\sqrt{2}=\dfrac{1}{2}(2x-3)(x+2) \sin 45^{\circ}[/tex]
[tex]\implies 8\sqrt{2}=(2x-3)(x+2) \sin 45^{\circ}[/tex]
[tex]\implies 8\sqrt{2}=(2x-3)(x+2) \left(\dfrac{\sqrt{2}}{2}\right)[/tex]
[tex]\implies 8\sqrt{2}\left(\dfrac{2}{\sqrt{2}}\right)=(2x-3)(x+2)[/tex]
[tex]\implies (2x-3)(x+2) =16[/tex]
[tex]\implies 2x^2+4x-3x-6=16[/tex]
[tex]\implies 2x^2+x-22=0[/tex]
Use the Quadratic Formula to solve for x:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies a=2, \quad b=1, \quad c=-22[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(2)(-22)} }{2(2)}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{177}}{4}[/tex]
[tex]\implies x=3.08, -3.58\:\: \sf (3 \:s.f.)[/tex]
As distance is positive:
[tex]\implies x=3.08 \:\:(3 \sf \:s.f.) \:\textsf{only}[/tex]
Related Questions
8.8d + 9.65 = –3.01 + 7.2d + 1.46
d= -14 right ?
Answers
Answer:
d=-7
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Answer:
d=-23.934375
Step-by-step explanation:
If 3m = 19 - n and 2m + 5n = 30, then what is the value of m?
Answers
Answer:
m=5
Step-by-step explanation:
We can solve this by using a system of equations. The easiest way to solve this is by using substitution.
3m=19-n Subtract both sides by 19 to find n.
-19 -19
3m-19=-n Divide everything by -1 to make n positive.
/-1 /-1
n=-3m+19
Now, we can substitute n into the second equation.
2m+5(-3m+19)=30 Substitute (-3m+19) into n.
2m-15m+95=30 Simplify.
-13m+95=30 Simplify and subtract both sides by 95.
-95 -95
-13m=-65 Divide both sides by -13.
/-13 /-13
m=5
We don't need to solve for n at all, so that is the answer!
Hope this helps, and have an amazing day ♥
The domen range of the function y = √(x² - 4) is _____.
Please explain with step i need explanation.
Answers
[tex] {\large\underline{\sf{Solution-}}}[/tex]
Given function is
[tex]\rm \longmapsto\:y = \sqrt{ {x}^{2} - 4} [/tex]
We know
Domain of a function is defined as set of those real values of x for which function is well defined.
So, y is defined when
[tex]\rm \longmapsto\: {x}^{2} - 4 \geqslant 0[/tex]
[tex]\rm \longmapsto\: {x}^{2} - {2}^{2} \geqslant 0[/tex]
[tex]\rm \longmapsto\: (x - 2)(x + 2) \geqslant 0[/tex]
[tex]\rm\implies \:x \leqslant - 2 \: \: or \: \: x \geqslant 2[/tex]
[tex]\rm\implies \:x \: \in \: ( - \infty , \: - 2] \: \cup \: [2, \: \infty )[/tex]
Now, To find the range of function
We know,
Range of a function is defined as set of those real values which is obtained by assigning the values to x.
So,
[tex]\rm \longmapsto\:y = \sqrt{ {x}^{2} - 4} [/tex]
On squaring both sides, we get
[tex]\rm \longmapsto\: {y}^{2} = {x}^{2} - 4[/tex]
[tex]\rm \longmapsto\: {y}^{2} + 4= {x}^{2}[/tex]
[tex]\rm \longmapsto\:x = \sqrt{ {y}^{2} + 4 } [/tex]
Now, x is defined when
[tex]\rm \longmapsto\: {y}^{2} + 4 \geqslant 0 \: which \: is \: always \: true \: \forall \: y \in \: real \: number[/tex]
But,
[tex]\rm \longmapsto\:y \geqslant 0[/tex]
Hence,
[tex]\rm\implies \:Range \: of \: function \: = [0, \: \infty )[/tex]
So, we have
[tex]\rm\implies \:Domain \: of \: function : x \: \in \: ( - \infty , \: - 2] \: \cup \: [2, \: \infty )[/tex]
and
[tex]\rm\implies \:Range \: of \: function \: = [0, \: \infty )[/tex]
why are 4^0 and (-4)^0 is equal to 1,while -4^0 is equal to -1
Answers
Step-by-step explanation:
According to the zero property of exponents, any number (other than 0) raised to the power of zero is always equal to 1.
The problem with this question is the simple fact that in this format it is confusing.
So, -(4^0) = -1 × (4^0) = -1x1 = -1
and, (-4)^0 =1
Which function is equivalent to g ( x ) = x 2 + 15 x - 54?
Answers
Answer:
g(x) = (x+18)(x-3)
Step-by-step explanation:
g(x) = x²+15x-54= x²+18x-3x+54= x(x+18) -3(x+18)g(x) = (x+18)(x-3)Activity Give the exponential model for the following situation
Answers
Answer:
Suppose that a couple invested $50,000 in an account when their child was born, to prepare for the child's college education. If the average interest rate is 4.4% compounded annually, ( A ) Give an exponential model for the situation, and ( B ) Will the money be doubled by the time the child turns 18 years old?
( A ) First picture signifies the growth of money per year.
( B ) Yes, the money will be doubled as it's maturity would be $108,537.29.
a = p(1 + \frac{r}{n} ) {}^{nt}a=p(1+
n
r
)
nt
a = 50.000.00(1 + \frac{0.044}{1} ) {}^{(1)(18)}a=50.000.00(1+
1
0.044
)
(1)(18)
a = 50.000.00(1 + 0.044) {}^{(1)(18)}a=50.000.00(1+0.044)
(1)(18)
a = 50.000.00(1.044) {}^{(18)}a=50.000.00(1.044)
(18)
50,000.00 ( 2.17074583287910578440507440 it did not round off as the exact decimal is needed.
a = 108.537.29a=108.537.29
Step-by-step explanation:
Hope This Help you!!
7/12 divided by 3 3/4
Answers
Answer:
The answer is 7/45
Step-by-step explanation:
First you make 3 3 /4 into an improper fraction which becomes 15/4
Next, you do KFC which is keeping 7/12, making the division sign into multiplication, and then finally you flip 15/4 to 4/15.
Your final answer is 7/45
Hope that helped! Can I also get brainliest? I need a few more to advance, if not thank you anyways and have a nice day!!!
find the measure of the indicated angle
Answers
Answer:
Angle A is also the measurement of 48 degrees because the dashes on the triangle lines indicate that they are the same.
Step-by-step explanation:
Quadrilateral ABCD has both reflection and rotation symmetry. What type of quadrilateral could it
be? Show or explain.
Answers
Answer:
Rhombus
Step-by-step explanation:
So if |AB| = |BC| then ABCD is a rhombus and has a second line of reflective symmetry, namely \overleftrightarrow{BD}. Quadrilateral ABCD is what is called a kite.
Since ℓ contains two vertices of ABCD the other two must be reflections of one another about ℓ. In the picture ℓ goes through A and C and D=rℓ(B). So rℓ interchanges AD¯¯¯¯¯¯¯¯ and AB¯¯¯¯¯¯¯¯ and also interchanges CB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯. So if |AB|=|BC| then ABCD is a rhombus and has a second line of reflective symmetry, namely BD←→. Quadrilateral ABCD is what is called a kite. Note that we have implicitly used the fact that ABCD is convex: without this hypothesis, the vertex C could be reflected over BD←→, giving a non convex quadrilateral with exactly one line of symmetry.
Rectangle has rotational and reflectional symmetry.
What is Quadrilateral?
A quadrilateral is a polygon having four sides, four vertices and four angles.
Given that;
Quadrilateral ABCD has both reflection and rotation symmetry.
Now,
A rectangle ABCD has a reflection symmetry because it has two line of symmetry.
And, Rotational symmetry is defined as the number of times an object is exactly identical to the original object in a complete 360° rotation.
So, Rectangle ABCD has rotational symmetry.
Thus, Rectangle has rotational and reflectional symmetry.
Learn more about the quadrilateral visit:
https://brainly.com/question/9890925
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The energy needs of an eagle range between 350-600 calories per day. If it gets 120 calories from consuming 1 snake, how many snakes can it have
Answers
Answer:
3- 5 snakesStep-by-step explanation:
One snake gives 120 calories, so 3 snakes = 360 and 5 snakes = 600 calories.
The eagle can have 3 - 5 snakes per day
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The required number of snakes is ~
[tex]3 \: \: to \: \: 5 \: \: \: snakes[/tex][tex] \large \boxed{ \mathfrak{Explanation}}[/tex]
Minimum number of snakes that the eagle need to eat to maintain its energy level ~
[tex] \dfrac{350}{120} [/tex][tex] \dfrac{35}{12} [/tex][tex] \approx3[/tex]Maximum number of snakes that the eagle should eat to maintain the level of energy ~
[tex] \dfrac{600}{120} [/tex][tex]5[/tex]So,
The Eagle should have 3 - 5 snakes per day ~
A lab technician has 40 gallons of a 15% iodine solution. How many
gallons of a 40% iodine solution must he add to make a 20% iodine solution?
Please show work!!
Answers
The quantity of a 40% iodine solution that must be added to 40 gallons of a 15% iodine solution to make a 20% iodine solution is: 10 gallons.
According to the question;
We are required to determine how many gallons of a 40% iodine solution must he add to make a 20% iodine solution.Let gallons of a 40% iodine solution to be added be; x gallons.
Therefore, the total gallons of a 20% iodine solution obtained is; (40+x) gallons.
By mass balance of iodine in each solution;
(15% of 40) + (40% of x) = (20% of (40 + x))(0.15 × 40) + 0.4x = 0.2x + 80.2x = 2x = 10 gallons.In essence; 10 gallons of a 40% iodine solution must be added to make a 20% iodine solution.
Read more:
https://brainly.com/question/20730855
I need answers fast plsss
Answers
Answer:
1/6
Step-by-step explanation:
the form you're using is slope-intercept. That is
y=mx+b
where y= y coordinate
m=slope
x= x coordinate
and b= y intercept
so, m in that equation is 1/6, so the slope is 1/6
Hope this helps!
If it is 7:00 AM at letter F, what time is it at letter A?
5:00 AM
5:00 PM
4:00 AM
4:00 PM
Answers
Answer:
The aswer is 1:00 AM to 1:00 PM.
Step-by-step explanation:
write linear equatuon relating x and y for each table x (2,4,6,8). y (5,8,11,14)
Answers
Step-by-step explanation:
x increases continuously in steps of 2, y increases continuously in steps of 3.
so the slope of the line is y difference / x difference = 3/2. and the slope is siesta the factor of x in the equation
the line equating looks so far like
y = (3/2)×x + b
to get b we use one of the x and y pairs like (2, 5) and put these values in :
5 = (3/2)×2 + b = 3 + b
b = 2
so, the full equation is
y = (3/2)×x + 2
PLEASE HELP.
I’m not good at algebra and I’m stuck.
Answers
In f(x)= x + 4, the slope, m =1, is positive (rise 1 unit, run 1 unit). This means the graph is inclining from left to right. Also, the y-intercept is (0, 4).
These descriptions matches graph 1.
LAST 1 I SWEARRRR !!
Answers
Answer:
100 i believe
Step-by-step explanation:
I guess subtract 45 from 145
Answer:
80 look at the angels it 80! i had the same exact test today
Step-by-step explanation:
trying to figure it out
Answers
Please help I need 6543÷29 options for answers are below in picture
Answers
Answer:
6543÷29
=225.620.......
Which segment is a dilation of BC using A as the center of dilation and a scale factor of 2/3
Answers
Answer: 45
Step-by-step explanation:
i need this answered FAST!!! please make sure to show the work!!!!!!
Answers
Answer:
thanks thanks thanks thanks thanks thanks for your points
May I please receive help?
Please?))
Answers
Answer:
50°
Step-by-step explanation:
Please leave a “thanks” heart if I helped.
please help me solve this thank uuu
Answers
Answer:
Same Side Interior Angles
Step-by-step explanation:
Angle 7 and angle 14 are both inside of the two transversal lines E and M, and are on the same side of the line Q, making them both same side interior angles
-Chetan K
helppppppppppppppppppppppppppppppp
Answers
Step-by-step explanation:
wjjdjrjdjdjdudidjdkdk pick the C
Answer:
D,
Step-by-step explanation:
Step 1: 47-12=27, 27+(-27)=0
step 2: 27/2=13.5, 2c/2=c
step 3, change 13.5 to fraction which is 13 1/2
(hope it's helpful :)
Three years after a tree was planted it was 9 feet tall. Seven years after it was planted it was 17 feet tall. a What is the yearly growth rate of the tree? b. Determine the height of the tree when it was planted.
Answers
Answer:
your answer i think is 2/3 sorry if i'm wrong
Step-by-step explanation:
Help WILL NAME BRAINLIEST
Answers
can someone help please? u dont have to show work so dont mind that
Answers
Answer:
Factor the numerator and denominator and cancel the common factors.
x/4+3/2 or 32/4 or Reduce the expression, if possible, by cancelling the common factors. 8 is your final answer
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
First, you substitute.
x + 6 / 4
26 + 6 / 4
Then, you add.
26 + 6 = 32
Finally, you divide.
32 / 4 = 8
Answer: 8
Drag up the correct symbol to make the following relationships true.
9,100
9,200
42,720
42,650
912
738
Answers
can someone please help me with this
Answers
Answer:
Add 8 and 8 and then add 5and 5 and get answer 16
Step-by-step explanation:
The product of four and a number C is decreased by five?
Answers
Forty-eight divided by one hundred equals what?
Answers
Answer:
0.48
Step-by-step explanation:
jou just have move point from right to left like this 48 rite so 48. =because have to zero u hqve move two place left so it will be 0.48
Answer:
0.48
Step-by-step explanation:
48 divided by 100=0.48