Answers
Answer:
[tex]x = 2.5[/tex]
Step-by-step explanation:
Given
[tex]AC = 2x - 1[/tex]
[tex]AB = 2x + 1[/tex]
[tex]BC = 2\sqrt{7[/tex]
[tex]\angle A = 60^{\circ}[/tex]
Required
Find x
To find x, we make use of cosine formula which states:
[tex]a^2 = b^2 + c^2 - 2bcCosA[/tex]
In this case:
[tex]BC^2 = AB^2 + AC^2 - 2*AB*BC*CosA[/tex]
Substitute values
[tex](2\sqrt{7})^2 = (2x + 1)^2 + (2x-1)^2 - 2*(2x + 1)*(2x - 1)*Cos(60^{\circ})[/tex]
Evaluate all exponents
[tex]4*7 = (4x^2 + 4x + 1)+(4x^2 - 4x + 1) - 2(4x^2 - 1)*cos(60^{\circ})[/tex]
Open brackets
[tex]28 = 4x^2 + 4x + 1+4x^2 - 4x + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]
Collect Like Terms
[tex]28 = 4x^2 +4x^2+ 4x - 4x+ 1 + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]
[tex]28 = 8x^2+ 2 - (8x^2 - 2)*cos(60^{\circ})[/tex]
Substitute 0.5 for cos(60)
[tex]28 = 8x^2+ 2 - (8x^2 - 2)*0.5[/tex]
Open bracket
[tex]28 = 8x^2+ 2 - 4x^2 + 1[/tex]
Collect Like Terms
[tex]8x^2- 4x^2 + 2 + 1 - 28 = 0[/tex]
[tex]4x^2 -25 = 0[/tex]
Collect Like Terms
[tex]4x^2 =25[/tex]
Divide both sides by 4
[tex]x^2 =\frac{25}{4}[/tex]
[tex]x^2 =6.25[/tex]
Take positive square root of both sides
[tex]x = \sqrt{6.25[/tex]
[tex]x = 2.5[/tex]
Related Questions
what 30 x 23 30 x 23
Answers
30 x 23 = 690
23 x 30 = 690
Answer: 690
Step-by-step explanation:
Now whats 34+35?
y+8=3(x+1) slope intercept form
Answers
Answer:
Step-by-step explanation:
y + 8 = 3x + 3
y = 3x - 5
Marcia and her family went to a concert.They bought 3 adult tickets and 4 children’s tickets. What was the total cost for the family?2.A small aircraft has 14 rows with 2 seats in each row on one side and 14 rows with 3 seats in each row on the other side. How many seats does the aircraft have in all?3.Writing to ExplainWrite a problem about going on a water ride at an amusement park that has a hidden question. A small boat seats 4 people, and a large boat seats 6 people. Solve your problem.Concert AdmissionAdults$8Students$5Children$3P 10•7
What is the hidden question
Answers
Answer:
2= 28+42=70
Step-by-step explanation:
Identify the coordinates for point D
Answers
Answer:
Your Picture is just of -3????
Step-by-step explanation:
it takes 120 drops of water to fill a teaspoon write the prime fractorization
of 120 using exponents
Answers
Answer:
120 = 2³×3×5
Step-by-step explanation:
(t−6)^2 t = 11 What is the answer please.
Answers
Answer:
25
Step-by-step explanation:
t = 11, so let's put 11 in place of t in the equation.
(11-6)^2
PEMDAS tells us parenthesis first, so let's do that.
(5)^2
Now let's square it.
5*5=25
So there you go, 25 is your answer :)
Once sales tax is included, a $62 hammock ends up costing $67.58. What is the sales
tax percentage?
NEED ASAP WILL GIVE BRAINLIEST
Answers
Answer:
9%
Step-by-step explanation:
subtract 62 from 67.58 to get 67.58-62=5.58divide 62 by 5.58and your final answer is 9%Choose the smallest number.
0.03
0.3003
O 0.009
0.093
1.0001
Answers
Answer:
0.009
Step-by-step explanation:
We can figure this one out by looking at first the ones place to see if it's a zero, then the tenths and hundredths place, checking if those are also zeros. Because this is the only number with those three numbers as zeros, it is the smallest.
This is because you must look at where the zeros are and how much zeros are there
A rectangle is 4 times as long as it is wide. The perimeter is 30 feet. Find the dimensions.
Answers
Answer:
Express your length and width as algebraic expressions:
width = x
length = 4x
Use the formula for the perimeter of a rectangle to solve for x:
perimeter = 2(length) + 2(width)
50 = 2(4x) + 2(x)
50 = 8x + 2x
50 = 10x
5 = x
The width (x) is 5 feet and the length (4x) is 20 feet.
Step-by-step explanation:
Answer: 3 by 3 by 12 by 12
Step-by-step explanation: Two sides are x feet long. The two other sides are 4 times x feet long. 4x+4x+x+x =10x
Set that equal to 30 and solve. x=3
Plug back into the original 4x's and x's to get the lengths
Which of the following is NOT type of magnet
a
permanent magnet
b
electromagnet
c
temporary magnet
d
Domain magnet
Answers
Answer:
Is not a type of magnet a domain magnet
Which statement must be true according to the dot plot?
The data is skewed to the right and shows that she never scored fewer than 2 points or more than 12 points in a game.
The data is skewed to the right and shows that she scored 11 points in more games than all of the other games combined.
The data is skewed to the left and shows that she never scored fewer than 2 points or more than 12 points in a game.
The data is skewed to the left and shows that she scored 11 points in more games than all of the other games combined.
Answers
Answer: c
Step-by-step explanation:
just did on edg :) got a 100%
Answer:
c
Step-by-step explanation:
Hal earns n dollars per hour. Next month he
will receive a 296 raise in pay per hour. The
expression n +0.02n is one way to represent
Hal's pay per hour after the raise Write an
equivalent simplified expression that will
represent his pay per hour after the raise.
Answers
Answer:
[tex]Total = 1.02n[/tex]
Step-by-step explanation:
Given
[tex]Earnings = n[/tex]
[tex]Raise = 2\%[/tex] --- not 296
[tex]Total = n + 0.02n[/tex]
Required
Simplify the expression for total earning
The total amount is derived from:
[tex]Total = Earnings + Raise * Earnings[/tex]
[tex]Total = n + 2\% * n[/tex]
Express percentage as decimal
[tex]Total = n + 0.02 * n[/tex]
Now, we can solve further:
[tex]Total = n + 0.02n[/tex]
[tex]Total = 1.02n[/tex]
Hence, the simplified expression is 1.02n
Answer:
1.02n
Step-by-step explanation:
Hurry I am timed Which tiny, round “factory” puts together protein and is often found in the endoplasmic reticulum?
ribosome
chromosome
Golgi body
chloroplast
Answers
Answer:
the answer is ribsome
The ribosome serves as the site and carries the enzymes necessary for protein synthesis. They are often takes the shape of small round particles attached in the endoplasmic reticulum.
Which geometric sequence has a common ratio of -9?
{-1, -9, 81, 729, …}
{1, -9, 81, -729, …}
{-9; -81; -729; -6,561; …}
{81; 729; 6,561; 59,049; …}
WILL GIVE BRAINLIEST!!!!
Answers
Answer:
second one
Step-by-step explanation:
just multiply by -9 and see which one fits in
Answer:
{1, -9, 81, -729, …}
Step-by-step explanation:
Geometric sequence is basically multiplying the previous number by the constant. So it is 1 x -9 = -9, -9 x -9 = 81, -81 x -9 = -729, and so on.
Which set of angles will be complimentary
Answers
∠1 + ∠3 + 90° = 180°
∠1 + ∠3 = 90°
∠3 = ∠4 (vertically opposite angles)
∠1 + ∠4 = 90°
Therefore, the answer is ∠1 + ∠4
Pls answer allllll! I really need it
Answers
Answer:
7) I believe it is "The sum of the large rectangle is equal to the sum of the two smaller rectangles. 3 (x + 4)" But I am not sure.
8) Make it shorter and simpler by combining like terms
9) 5x , 2a + 3 + a + 4 , 6 + 2x + x2 + 1 + x
10) ac + bc = (a + b) c
Step-by-step explanation:
i need help please and thank you
Answers
Answer:
F- the first answer choice
Step-by-step explanation:
Answer:
answer is h
Step-by-step explanation:
a is at -3 1/2, 3 1/2 b is at 5, -2 1/2
In a shop, a TV has a normal price of £500
The shop has a sale.
On Monday, the normal price of the TV is reduced by 1/10 to give the sale price.
On Tuesday, the sale price of the TV is reduced by 20%
Chris wants to buy the TV.
He has £400 to spend on the TV.
Does Chris have enough money to buy the TV on Tuesday?
Answers
Answer:
400> 360
Step-by-step explanation:
1/10 X 500 = 50
500 - 50 = 450
10% = 450/ 10 = 45
20% = 45 x 2 = 90
450 - 90 = 360
Chris does have enough 400> 360
Some emoji math, there are more to be solve as well. 15 points for each. Must explain how to get the answers you got.
Answers
Answer:
Ladybug=7
clock= 5
bulb= 2
Step-by-step explanation:
there are a whole row of ladybugs that equal 21. 21/3=7.
on the third row, the value we need is 12, 6 won't work because we also have a bulb. so pug in 5, 5+5=10, that means the bulb is 2.
So now that we know the values, lets plug them into the first problem to see if it gives us 14... it does
So we have the correct answers
Also, you can plug in the values for the the bottom numbers and you will get those values
Another row has bug+bug+a clock= 14+clock. 19-14 = 5. Clock=5
Another row shows bug+clock+bulb = 7+5+bulb=12+bulb. 14-12=2. Bulb=2
Hope this helps
Given AB congruent to EB and BD congruent to BC why is angle ABC congruent to EBD
Answers
Answer:
SAS
Step-by-step explanation:
Side angle side Test
2 sides are given equal and angle between these two side is equal in both triangle
hence by SAS test
Triangle ABC and EBD are congruent
Grace and her friend are doing some back to school shopping , Grace buys 4 binders and notebooks for 26.50 totalHer friend spends a total of $21.00 on 3 binders and 6 notebooks
Answers
Answer:
What is the question asking to answer?
Step-by-step explanation:
Answer:
$19:50
Step-by-step explanation:
Write a system of equations to represent the problem. Let x represent the cost of a binder, and let y represent the cost of a notebook.
Grace buys 4 binders and 7 notebooks for $26.50 total, so the equation 4x+7y=26.50 represents how much Grace spends.
Grace's friend buys 3 binders and 6 notebooks for $21.00 total, so the equation 3x+6y=21 represents how much her friend spends.
You can use this system of equations to find how much money Grace and her friend spend on notebooks:
4x+7y=26.50
3x+6y=21
Next, find how much Grace and her friend spent on notebooks. Start by finding the cost of one notebook. Use elimination to solve for y. .
3(4x+7y)=3(26.50)
–
12x+21y = 79.50
–
4(3x+6y)=
–
4(21)
–
12x–24y =
–
84
–
3y =
–
4.50
y = 1.50
Each notebook costs $1.50. Grace and her friend buy a total of 13 notebooks, so multiply to find how much money they spend on notebooks.
13$1.50=$19.50
Grace and her friend spend $19.50 total on notebooks.
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLS SHOW THE WORK!!!!!!!!
Answers
Answer:
Step-by-step explanation:
X is 1 y is -4
Which gets the following:
X(1) + y(-4) = -3
x(1) + 2(-4) = -7
Answer:
Step-by-step explanation:
-1*(2x-3y+7)
Hurt just hurry and answer please
Answers
Answer:
84
Step-by-step explanation:
Solve:
6*7= 42
42*2.00=84
Hope this helps!
herehjbhhjbhjghvgvgvgvg
Answers
Given that x is an integer and that –15 <x 5 35,
write down the least value of x.
Answers
Answer:
a) d = 3 b) a(n) = 3n – 13 c) a(27) = 68
Step-by-step explanation:
solutions are (x, y) = (29,13) and (9349, 4181), which lead to (a, b) = (15,5) and (4895 ... corresponding to integer values of x give the quadruples. (x, y, z ... Since no number congruent to 3, modulo 4, can be written as the sum of two squares ... k is odd, the equation x2 - (k2 - 4)y2 = 4 has smallest solution in positive integers .
f(x) = V2x
g(x) = V50x
Find (f .g)(x). Assume x2 0.
Answers
Answer:
(F.g)(x)
F 2x
50(2x)
=100x
Question: f(x)= √2x
g(x)= √50x
Find (f*g) (x). Assume x ≥ 0.
(f*g)(x)=10x
function not a function ?
Answers
Answer:
not a function
Step-by-step explanation:
Pls help periodddd pooh
Answers
Answer:
the answer is n = -7
I also put a image to show you how to solve the equation. I hope the image helps.
Answer:
n= -7
Step-by-step explanation:
5 × ( 1 / 3 + 2 / 5 ) =
write your answer as a mixed number
Answers
Answer: the answer is 2 and 1/15
Step-by-step explanation:
Simplify the inequalities and match them with the graphs that represent them. 7x < 42 3x >15 2x > 12 X + 1 < 8 T G DEL ਨੂੰ ਜਨ : ' ! 2 ! ! T } ts reserved
Answers
Answer:
14 times pie = 69
Step-by-step explanation: