work out x when the area is root 4 2^2 and angle C is 45 and ab are (x+2)(2x-3)

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 1

Answer:

x = 3.08

Step-by-step explanation:

Area formula:

A = 1/2bh

The height is:

h = (x + 2)sin 45° =  (x + 2) ×√2/2

Substitute 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 2

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 angle

Given:

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

Is each number correctly expressed in scientific notation? Choose Yes or No.
Number Scientific Notation
4,836,000,000 4.836 × 106
Choose...
0.0000005812 5.812 × 10–7
Choose...
546,000,000,000 5.46 × 1011
Choose...

Answers

Answer:

NoYesYes

Step-by-step explanation:

The first one is incorrect because would be 4,836,000 instead of 4,836,000,000. The correct notion would be [tex]4.836*10^9[/tex]

i need to know what 26.6 divided by 7 is.

Answers

Answer:3.8

Step-by-step explanation:

a journey by bus takes 45 mins at 40km/h how fast must a car go to undertake the same journey in 25 mins​

Answers

Answer:

72km/h

Step-by-step explanation:

Bus - 45 mins at 40km/h

Car - 25 mins at ?

First, find the distance travelled by the bus (since, the journey of the two vehicles are the same, the distance would be the same as well)

distance = speed × timedistance = 40 × 3/4 (45 mins = 3/4 of an hour (45 ÷ 60))distance = 30km

Now we can find the speed of the car using the equation

speed = distance ÷ timespeed = 30 ÷ 5/12 (25 mins = 5/12 of an hour (25 ÷ 60))speed = 72km/h

a meterologist said that it rained during 20 % of the past 60 days. on how many days did it not rain

Answers

Answer:

48 days

Step-by-step explanation:

20% of 60 is 12

60-12=48

Answer:

48

Step-by-step explanation:

20% of 60 is 12, 60-12=48

Hope that helps

Find the selling price of a book with an original price of $49.95 and a 5% tax rate.please be specific on how the answer is the answer pls help me

Answers

Step-by-step explanation:

$52.45

49.95×.05

then add that result to 49.95= answer

)) A rectangle has an area of 117.8 square kilometers and a height of 9.5 kilometers. What
is the length of the base?
kilometers

Answers

Answer:

yes you use kilometers

Step-by-step explanation:

alguien que me diga como se saca la X en ecuaciones cuadraticas porfaaaaaaaaa

Answers

Answer:

lol

Step-by-step explanation:

to get x in quadratic equations, factor it

the quotient of 49 and a number

Answers

Answer:

7

Step-by-step explanation:

PLEASE HELP IT’S DUE TMR
you only have to answer F

Answers

Answer:

1 bat : 0 hits

Step-by-step explanation:

To get this unit rate all you have to do is divide both sides by 4.

(4/4) : (0/4) = 1:0

We get the same number of hits as in the original problem because 0 divided by any number (other than 0) will always equal 0.

Can I get brainliest please?

Write an equation of the line with a slope of -\frac{2}{7} and a y-intercept of 5.

Answers

Answer:

y=3/4x-7

Step-by-step explanation:

I used the y intercept (0,-7) as a point to plug into point slope form.

y+7=3/4(x-0)

HELPP AND SHOW YOUR WORK!!!

4. −10(x − 3)

A) −15x + 30
B) −10x + 30
C) −15x + 35
D) −15x + 37

Answers

Answer:

B) [tex]-10x+30[/tex]

Step-by-step explanation:

You distribute:    

-10 times X minus 3 ( -10*x-3)

Which gives you:

Answer: -10x+30

Hope this helps!

Answer:

-10x+30

Step-by-step explanation:

[tex]\sf -10(x -3)[/tex]

[tex]\sf -10x-\left(-10\right)\times \:3[/tex]

[tex]\sf -10x+30[/tex]


Any answers for this?

Answers

Answer:

D(t) = 2,280 - 60t

for D(15) compare the eqns and substitute the value of t.

D(15) = 2,280 - 60(15)

D(15) = 1,380 miles.

In the context of the qn, the Chang family travels 1,380 miles in 15 hours.

Which relationship is NOT a function?

Answers

Answer:

a

Step-by-step explanation:

Answer:

If it is possible to draw any vertical line (a line of constant x) which crosses the graph of the relation more than once, then the relation is not a function. If more than one intersection point exists, then the intersections correspond to multiple values of y for a single value of x (one-to-many).

Step-by-step explanation:

What is -(x + 4) - 3x = x in Distributive property?

Answers

Answer:

x = -4/5

Step-by-step explanation:

Original equation: -(x+4)-3x=x

Remember distributive property allows us to get rid of the parenthesis by bringing a multiplication from outside to inside a parenthesis.

-(x+4) = -x-4

= -x-4-3x=x

Now we combine like terms in this case we have (-x) and (-3x)

= -4x-4=x

Subtract x from both sides

= -4x-4=x

  -x      -x

----------------

 -5x-4=0

Add 4 to both sides

-5x-4=0

    +4 +4

---------------

-5x=4

Our final step is to divide both sides by -5

-5x=4

----  ----

-5    -5

x = -4/5

Hope this helps!!!


HELP 20 POINTS Lines j and k are shown in the diagram below. Some of the angles created when the lines are cut by a transversal are labeled in the diagram.

Answers

Answer: A

Step-by-step explanation:

Hello! I need help with this question

Answers

Each min is =0.75$
So 5$ can talk 5$/0.75$ =6.6667 min
First option

How do I convert 1 5/6 into a decimal??????

Answers

Answer:

1.8(3) (three is a repeating number)

Step-by-step explanation:

Divide the numerator from the denominator. Add the value of the integer part.

Answer:1.83

Step-by-step explanation:

so the  1 that's a whole number and 5 out of 6 should be around 82-85 but for real its 1.83 but its a repeating decimal so its like 1.83333

On Saturday morning, Ahmed decided to take a bike ride from one end of the 15-mile bike trail to the other end of the bike trail and back. His average speed the first half of the ride was 2 mph faster than his speed on the second half. Find an expression for Ahmed's total travel time. If his average speed for the first half of the ride was 12 mph, how long was Ahmed's bike ride? ​

Answers

The expression which relates the total time taken and the time taken for the trip is [15s + 15(s+2)] / s² + 2s and 2.32 hours respectively.

Travel time = distance ÷ speed

Second half of the trip :

Speed = s mph

Distance covered = 15 miles

Time taken for second half of trip :

Time taken = 15 / s

First half of the trip :

Speed = s + 2 mph

Time taken for first half of trip :

Time taken = 15 / (s+2)

Total time taken :

First half + second half

15/(s+2) + 15/s = [15s + 15(s+2)] / s² + 2s

B)

If s = 12

Substitute s = 12 into the expression :

[15(12) + 15(12+2)] / 12² + 2(12)

[180 + 210] / 144 + 24

390 / 168

= 2.32 hours

Therefore, the total time taken is 2.32 hours.

Learn more : https://brainly.com/question/18796573

Plz help ASAP will mark branliest

Answers

Step-by-step explanation:

Consider that:

[tex](f/g)(x) = f(x) / g(x)\\(f - g)(x) = f(x) - g(x)[/tex]

Fill in the blanks

Row 1    ⇒ 2 and -5

(-1)*(-2) = 2

Solve using two values:

f(x) - g(x) = - 10 and f(x)/g(x) = - 1  ⇒ f(x) = -g(x), substitute into first-2g(x) = - 10 ⇒ g(x) = 5 and f(x) = - 5

Row 2   ⇒ -5 and 5

- 2 - 3 = - 5g(x) = 5 (see above solution)

Row 3    ⇒ - 6 and 4

-10 - (-4) = - 62 - (-2) = 4

Row 4     ⇒ -6/7 and 2/5

-6/7-2/-5 = 2/5

Can you help me please.
SOLVE FOR Y
[tex] \frac{5}{3} y = - (x - 5)[/tex]

Answers

Answer: Y = -3/5x + 3

Explanation:

Simplify

5/3y = -x + 5

Multiply both sides by 3/5

Y = -3/5x +3

Answer:

The answer is Y = -3/5x +3 (I think)

If x is an odd number, which of the following is also odd? * X + 1, X + 2, 2x + 2 or 3x + 1​

Answers

Answer:

x+2

Step-by-step explanation:

i put mi x as one so

....that how i get my anwser

can someone do this? <3

Answers

here!

and here’s a link if you want to understand how to do it!

https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/alg-manipulating-expressions/a/combining-like-terms-reminder

Answer:

[tex]-4b^3 - 4a^3 + 5a^3 b^2[/tex]

Step-by-step explanation:

Hope it helps!!

PLZZ HELP REALLY QUICK QUICKK QUICKKK HELPP

Answers

Answer:

$1.62

Step-by-step explanation:

1. To find how much Erin spent, we have to multiply 0.54 by 3.

[tex]0.54 * 3[/tex] [tex](0.5*3)+(0.04*3)[/tex] [tex]1.5 + 0.12[/tex] [tex]1.62[/tex]

Therefore, Erin spent $1.62.

- 4x + 14 = -2(2x + 7)

Answers

X=4
-4x4=-16+14=-2
2x4=8+7=15
-2 x 15=30

The perimeter of this rectangle si __________ units

Answers

The answer for this question is 14

L + B (x2) = 7+2 (x2)

9 x 2 = 18 (si units can be cm, m..?)

I don't understand what the "find the solution" part is asking me to do? Help is greatly appreciated.

Answers

Answer:

Step-by-step explanation:

[tex]a) x_{1+1}=\dfrac{(x_{1})^{3}-5}{10}\\\\x_{2}=\dfrac{(-1)^{3}-5}{10}=\dfrac{-1-5}{10}=\dfrac{-6}{10}= - 0.6\\\\\\ii) x_{2+1}=\dfrac{(x_{2})^{3}-5}{10}\\\\x_{3}=\dfrac{(-0.6)^{3}-5}{10}=\dfrac{-0.216-5}{10}=\dfrac{-5.216}{10}= - 0.5216\\\\\\[/tex]

plz help
Which of the algebraic expressions below is equal to 28?
Select all that apply.(ANSWER ONLY IF YOU KNOW!)

A) (34)(20)×2
B) (24÷4)(7)
C) 9(7−3)–8
D) (3+4)⋅(22+3)

Answers

Answer:

ITS C

Step-by-step explanation:

9(7−3)−8

=(9)(4)−8

=36−8

=28

Answer:

C.

Step-by-step explanation:

9(7-3)-8

according to PEMDAS, we have to do the parenthesis first. so

9(4) - 8

then

36 - 8

which gives us 28.

Hope this helped! (:

plz help me help me help me

Answers

The answer is this :) hope I helped

Answer:

Step-by-step explanation: 16 is for the apple juice for when the orange juice is 8 since orange juice is half of the apple juice. For the last one the apple juice is 32 and the orange juice is 16

PLS HELP! GIVING BRAINLIEST!
Given g(x)=2x+4, find: g(4)

PLS SHOW WORK !!

Answers

Answer:

b(x)=2x+4

Factor out 2.

2(x+2)

EVALUATE

2(x+2)

Step-by-step explanation:

Ben and Mack stopped at a restaurant to eat. Ben purchased 2 hot dogs and 2 drinks for $4.75. Mack purchased 3 hot dogs and 1 drink for
$7.75. Which system of equations can be used to determine the price of each hot dog, x, and each drink, y?
A. 2x + 2y = 4.75
3x + y = 7.75
OB. 2x + 2y = 7.75
3x + y = 4.75
OC. X + 2y = 7.75
2x + 3y = 4.75
D. x + 2y = 4.75
2x + 3y = 7.75

Answers

Answer:

A is the answer

Step-by-step explanation:

Let x equal hotdogs and y equal drinks

2 hotdogs plus 2 drinks = 4.75

3 hotdogs plus 1 drink = 7.75

Other Questions
In people focus primarily on individual rights, roles, and achievements Why do you think lone pairs of electrons create greater repulsion when located near otherlone pairs or bonding pairs? Orbitals containing lone pairs of electrons require more spacethan orbitals containing bonding pairs. Why do you think this is the case? What does thepresence of one or more lone pairs of electrons do to the bond angles in a molecule (in otherwords, do bond angles get larger, smaller, or remain unchanged?) Where do I place anything (please take a screenshot of answer) Maya, Greg, and Austin sent a total of 81 text messages during the weekend. Austin sent 2 times as many messages as Maya. Greg sent 9 more messages than Maya. How many messages did they each send? Plz help! Due tonightDo you think Bill Clinton should have been impeached? Research (if necessary) and explain with a minimum of 50 words. HELP PLEASE What is the correct definition of amplitude?A. the height of a waveB. the distance between two crests or troughsC. the number of complete waves that pass a point in a secondD. the time it takes for one complete wave to pass a given point read the sentence Jordan likes going to the pool in the summer which is the best way to revise the sentence using descriptive detail and sensory words? Am I 6 grade ok it won't let me put 6th grade ok so can you try to help me. Which recommendation helps to choose foods sensibly?A. Eat mostly saturated fats.B. Avoid eating fats.C. Eat mostly carbohydrates and proteins.D. Eat foods with a variety of nutrients. whats the ratio of 57/34 Is the present and future tense of William Shakespeare... dead??? how long does it take for sperm to reach the egg and implant? There are five red, 3 blue and a white marble in a jar. What is the probability of selectinga white marble, replacing it, then selecting a white marble again? Please help!17. A salesperson earns a base monthly salary of $2000 plus a 10% commission on sales. The salesperson'smonthly income I (in dollars) is given by the function I(s) = 0.1s + 2000, where s is the sales (indollars) that the salesperson makes. Sketch a graph to illustrate each situation using the graph ofI(s) = 0.1s + 2000 as a reference.A. The salesperson's base salary is increased. B. The salesperson's commission rate is decreased. from what company and city did candy corn originate? A machine whose efficiency is 75% is used to lift a load of 100m.calculate the effort put into the machine if it has a velocity ratio of 4. explain hind brain system How does hajj strengthen the community of the Muslims around the world What is fulgurite? ? ????????????? Can someone help me please I would really appreciated Does anyone know this answer for 5 and 6??