A piece of wood is 0.9 metres long.
It is cut into three unequal pieces.
The first piece is 0.2 metres longer than the second piece.
The third piece is 23 hundredths of a metre shorter than the second piece.
How long is each piece of wood?
Answer:
The length of the first piece is 0.51 m
The length of the second piece is 0.31 m
The length of the third piece is 0.28 m
Step-by-step explanation:
The question is a simultaneous equation with word problem
The total length of the wood = 0.9 m
The number of pieces the wood is cut into = 3
The length of the first piece = 0.2 m + The length of the second piece
The length of the third piece = The length of the second piece - 0.23 m
Let "y" represent the length of the second piece, let "x" represent the length of the first piece, and let "z" represent the length of the third piece, we have;
x = 0.2 + y...(1)
z = y - 0.23...(2)
x + y + z = 0.9...(3)
Therefore, by substitution, we have;
0.2 + y + y + y - 0.23 = 0.9
3·y - 0.03 = 0.9
3·y = 0.9 + 0.03 = 0.93
y = 0.93/3 = 0.31
y = 0.31
The length of the second piece = y = 0.31 m
From equation (1), we have;
x = 0.2 + y = 0.2 + 0.31 = 0.51
x = 0.51
The length of the first piece = x = 0.51 m
From equation (2), we have;
z = y - 0.23
z = 0.51 - 0.23 = 0.28
z = 0.28
The length of the third piece = z = 0.28 m.
does anyone know how to solve this using the sine rule?
Answer:
Step-by-step explanation:
According to sine law of trigonometric functions,
sin(α)/a =sin(β)/b
hence using this
sin(18)/y = sin(x)/2y
sin(x)=2*sin(18)
sin(x)=2*0.309
sin(x)= 0.618
x=sin-1(0.618) ( sin-1 is sine inverse)
x=38.17 °
Consider the line y = - 4x +3,
Find the equation of the line that is parallel to this line and passes through the point (2, -3).
Answer:
y = -4x + 5 {slope-intercept form}Step-by-step explanation:
y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂
{Two lines are parallel if their slopes are equal}
y = - 4x + 3 ⇒ m₁ = -4 ⇒ m₂ = -4
The point-slope form of the equation of a line it's y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.
m = -4
(2, -3) ⇒ x₁ = 2, y₁ = -3
point-slope form:
y - (-3) = -4(x - 2)
y + 3 = -4x + 8 {subtact 3 from both sides}
y = -4x + 5 ← slope-intercept form
Brian spends the same amount of money each morning. On Saturday he bought a large coffee for $1.25 and 2 doughnuts. On Sunday he brought a small coffee for $.50 and 5 doughnuts. Write and solve an equation to determine the cost of one doughnut.
Answer:
Cost of one doughnut is $0.25
Step-by-step explanation:
Let the rate of one doughnut = $x
On Saturday he bought a large coffee and 2 doughnuts.
Cost of one large coffee = $1.25
Cost of 2 doughnuts = $2x
Total cost = $(1.25 + 2x)
On Sunday, he bought a small coffee and 5 doughnuts.
Cost of one small coffee = $0.50
Cost of 5 doughnuts = $5x
Total cost = $(0.50 + 5x)
Since, Brian spent same amount of money each morning,
Total expenditure on Saturday morning = Total expenditure on Sunday morning
(1.25 + 2x) = (0.50 + 5x)
1.25 - 0.50 = 5x - 2x
0.75 = 3x
x = $0.25
Therefore, cost of one doughnut is $0.25
PLEASE HELP MEEEEE!!!! DUE TODAY!!! WILL GIVE BRAINLIST
Classify each polynomial and determine its degree.
The polynomial 3x2 is a (blank)
with a degree of (blank)
.The polynomial x2y + 3xy2 + 1 is a (blank)
with a degree of (blank)
.
Answer: The polynomial 3x2 is of one variable with a degree of 2.
The polynomial x2y + 3xy2 + 1 is of two variables a with a degree of 3.
Step-by-step explanation: For this case we have the following polynomials:
3x2
x2y + 3xy2 + 1
We have then:
For 3x2:
Classification: polynomial of one variable:
Degree: 2
For x2y + 3xy2 + 1:
Classification: polynomial of two variables
Degree: 2 + 1 = 3
Answer:
monomial
2
trinomial
3
Step-by-step explanation:
Ruben bought a 20-pound bag of dog food for his Great Dane Tank Acer 7 days, all the dog
food was gone
How much dog food did Tank eat each day?
wrice your answer as a proper fraction or med number
Answer:
2/3
Step-by-step explanation:
Stanley has a collection of seashells. He found 35% of his collection on Florida beaches. If Stanley has 49 seashells from Florida, how many seashells does he have in his collection all together?
A) 90
B) 120
C) 140
D) 160
Answer:
140 shells. So, C
Step-by-step explanation:
Let x equal the total number of shells in Stanley's collection. Then,
.35 x = 49
x = 49 / .35
x = 140
please awnser photo will give brain if you are first
the school band wants to make 1000 dollars at the annual car wash, if they charge 15 dollars per car, how many cars should the band wash
2 lines that never intersect
Answer:
are parallel
Step-by-step explanation:
PLEASE MARK BRAINLIEST!
Answer:
Your answer is:
Step-by-step explanation:
dun, dun, DUNNN
parallel lines!
I hope this helps!
- sincerelynini
Please help me with Math and show how you got the answer.
Answer:
Step-by-step explanation:
2.5:3.5 = 1:1.4
1 3/4 : 2 11/12 = 1:5/3
5/3 > 1.4 so megan gets more cookies
so kaitlyn uses more
What is the value of x?
Enter your answer in the box.
6 cm
5cm
48 cm
3x + 7
x =
Answer:I'm guessing 48
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
Took the test
Help Urgent!!!
I don’t understand what I should do next
9514 1404 393
Answer:
∠E = ∠A = 34°; ∠AFB = ∠DFE = 107°-34° = 73°
Step-by-step explanation:
Here's where I'd go next.
73° (∠EDA) is exterior to ΔDAC, so is the sum of remote interior angles A and C. That is, ...
∠C + ∠A = 73°
∠C = 73° -∠A = 73° -39° = 34°
Triangle CBE is given as isosceles, so its base angles C and E are congruent, both 34°.
Exterior angle CDF is the sum of remote interior angles DEF and DFE, so we have ...
107° = 34° +∠DFE
∠DFE = 107° -34° = 73°
The angle we just found (∠DFE) is a vertical angle with ∠AFB, so has the same measure.
∠AFB = 73° . . . . vertical angle with ∠DFE
_____
In summary, it looks like we have added some steps to the derivation:
4. ∠A = 34° . . . . exterior angle theorem (∠A +39° = 73°)
5. ∠E = ∠A = 34° . . . . definition of isosceles triangle
6. ∠DFE = 73° . . . . exterior angle theorem (∠E +34° = 107°)
7. ∠AFB = 73° . . . . vertical angles
_____
Additional comment
Any sort of math problem solving has you work from what you know to what you need to know by making use of previously learned relationships between the bits of information you have. Here, you really only need to know (a) angles of a linear pair total 180°; (b) angles in a triangle total 180°; (c) angles opposite congruent sides in a triangle are congruent. Everything we claim above can be concluded using these facts. The various theorems we used are simply shortcuts that allow you to bypass intermediate steps in the problem-solving process.
Im StUcK HeLp Me
-1 (4x + 2y)
Answer:
-4x - 2y
Step-by-step explanation:
Hope it works
Answer:
Step-by-step explanation:
−1(4x+2y)
=(−1)(4x+2y)
=(−1)(4x)+(−1)(2y)
=−4x−2y
Hope this helps u out
HELP ASAP!! SOMEONE DO NUMBER 7 AND 8. ILL GIVE BRAINLIEST
Answer:
3.6 3/6 3.6 percent 3:6
Step-by-step explanation:
10:9
15:14
20:19
Answer:
7. 3:6, 3/9 (or 6/9), .33..... (or .66......), 33.3......% (or 66.6.....7)
8. 10 roses, 8 daisies, 10:8 ratio
15 roses, 13 daisies, 15:13 ratio
20 roses, 16 daisies, 20:16 ratio
( the 15 roses part was hard so if its wrong im sorry)
brainly pls
What is the solution of x + 6 11
C. x –1
show your work pls
Answer:
C. x < –1
Step-by-step explanation:
What is the solution of x + 6 < 5?
A. x < 11
B. x > 11
C. x < –1
D. x > –1
-1+6<5
but you need less than 5 so
x<-1
a point with positive x coordinate in a meander Y coordinates is reflected over the y-axis which sentence describes the coordinate of the new point
Answer:
B. negative x-coordinate and negative y-coordinate
Please help me
I need this ASAP
PLEASE HELP ME
Answer:
180 X 365 = 65700 litres
65700/1000 = 65.7 cubic metres
65.7 X 91.22 = 5993.154
5993.154 / 100 = 59.93154
59.93 + 28.20 = 88.13
yes Henry should have a water meter
Select the correct answer.
What is the solution to this system of equations?
3x+y=17
x+2y= 49
OA. It has no solution,
B.
It has infinite solutions.
OC. It has a single solution: x = 15, y= 17.
OD.
It has a single solution: x= -3, y = 26.
Answer:
one solution: x = -3, y = 26
Step-by-step explanation:
3x + y = 17
x + 2y = 49
If you multiply the first equation by -2 and then add you will eliminate the 'y' term
-2(3x + y) = -2(17)
-6x - 2y = -34
+ x + 2y = 49
-5x = 15
x = -3
-3 + 2y = 49
2y = 52
y = 26
is this a function hmm
Help pls ill mark brainliest
Answer:
m∠b = 92 ; m∠c = 92
Step-by-step explanation:
∠b and ∠c both form supplementary angles with the 88° angle. I'll just choose b in this instance.
b + 88 = 180
b = 92
Now we know that ∠b is 92°.
Moreover, ∠c and ∠b are known as vertical angles meaning they are equivalent to each other. Therefore, ∠c is also 92°
Item 2 What is the value of the function at x=−2? y=−4 y = 0 y = 2 y = 3
Answer fast please!!!
Answer:
ok
Step-by-step explanation:
need help asap!!!
What is the solution of the following system?
Use the substitution method.
{y+7=3x6x−2y=12
The only solution is (14, 12) .
The only solution is (12, 14) .
There is no solution.
There are an infinite number of solutions.
Answer:
there is no solution
Step-by-step explanation:
y + 7 = 3x
6x - 2y = 6 which can be simplied to be 3x - y = 6 (divide by 2)
let y = 3x - 7
substitute: 3x -(3x - 7) = 6
3x - 3x + 7 = 6
7 ≠ 6 therefore, no solution
A Boat is tied to the dock with a 25-foot rope. When the rope is pulled tight, the boat is 18 feet away from the base of the dock. The rope connects to the boat at the level of the water. What is the measure, to the nearest tenth of a degree, of x, the angle formed by the rope and the surface of the water?
Answer:
43.9°
Step-by-step explanation:
We solve the above question using the Trigonometric function of Cosine
cos x = Adjacent/Hypotenuse
From the question
Adjacent = Distance of the boat from the dock = 18 feet
Hypotenuse = Length of the rope = 25 feet
The angle formed by the rope and the surface of the water = x
Hence:
cos x = 18/25
x = arc cos (18/25)
x = 43.945519562°
Approximately θ = 43.9°
The angle formed by the rope and the surface of the water is given as 43.9°
I need the answer to this please thank you
Answer:
[tex]m(\widehat{WXZ})[/tex] = 160°
Step-by-step explanation:
By angle sum postulate,
m∠WYX + m∠XYZ = m∠WYZ
m∠WYZ = 50° + 30°
= 80°
Since, inscribes angle (∠WYZ) = [tex]\frac{1}{2}\times (\text{Intercepted arc WXZ})[/tex]
80° = [tex]\frac{1}{2}(\widehat{WXZ})[/tex]
[tex]m(\widehat{WXZ})[/tex] = 160°
a = 8, b = 6, c = ?
A) 10
B) 11.2
C 14
D) 100
Square ABCD has diagonals AC¯¯¯¯¯
and BD¯¯¯¯¯
. What is m∠ABD
A
180º
B
90º
C
45º
D
360º
Answer:
option (c)
Step-by-step explanation:
Given,
ABCD is a square.
AC and BD are diagonals
We know that,
Sides of the square make 90 degrees with each other.
And Diagonals bisect the opposite angles of the square.
Now,
[tex]\angle ABD = \dfrac{\angle ABC}{2}[/tex]
[tex]\angle ABC = 90^\circ[/tex]
[tex]\angle ABD = \dfrac{\angle ABC}{2}[/tex]
[tex]\angle ABD = \dfrac{90^\circ}{2}[/tex]
[tex]\angle ABD = 45^\circ[/tex]
Hence, option (c) is correct.
Please help!
Write the sum, and then write an equivalent expression by collecting like terms and removing parentheses
b. 2x - 7 and the opposite of 2x
Step-by-step explanation:
We need to write the sum of 2x - 7 and the opposite of 2x
Opposite of 2x is (-2x)
Sum means to add the number :
2x-7 + (-2x)
Remove parentheses,
2x-7 - 2x
Taking like terms together,
2x-2x-7= 0-7
= -7
Hence, the answer is -7.
Convert the following repeating decimal to a fraction in simplest form.
.71
Answer:
71/100
Explanation:
As you can see, the decimal ends at the hundredths place, so the fraction is 71/100. Its simple! If the number end at the tenths, hundredths, or thousandths, just take that number and do it like this! 38/1,000
Hope this helped! ;)
If x+2=5 then x= What
Answer:
3
Step-by-step explanation:
5-2=3
Just do it the other way to find the answer!
I hope this helps!
Answer: x = 3
Step-by-step explanation:
we subtract 2 from both sides, in order to get the variable by itself.
x + 2 (- 2) = 5 (- 2)
x = 3