Answer:
1. 600 watts
2. 35640 J
3. 55%
4. 20 J
5. The cost of running the fire is 8p.
Step-by-step explanation:
1. Energy = 36 000 J , t = 1 minute = 60 seconds
Power = [tex]\frac{energy}{time}[/tex]
= [tex]\frac{36000}{60}[/tex]
= 600 watts
2. Power = [tex]\frac{work done}{time}[/tex]
⇒ work done = Power × time
= 99 × 360
= 35640 J
3. Efficiency = (Output / Input) × 100
= [tex]\frac{55}{100}[/tex] × 100
= 55%
4. Work done = Force × distance
= 5 × 4
= 20 J
5. Given that 1 KWh cost 2p, Power = 4 KW and time = 4 hours.
Power = [tex]\frac{energy}{time}[/tex]
Energy = Power × time
= 4 × 4
= 16 KWh
The cost of running the fire = [tex]\frac{16}{2}[/tex]
= 8p
Find the equation of the line through point (−2,−2) and parallel to 3x+4y=12. Use a forward slash (i.e. "/") for fractions (e.g. 1/2.
Answer:
3x + 4y = - 14
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
3x + 4y = 12 ( subtract 3x from both sides )
4y = - 3x + 12 ( divide all terms by 4 )
y = - [tex]\frac{3}{4}[/tex] x + 3 ← in slope- intercept form
with slope m = - [tex]\frac{3}{4}[/tex]
Parallel lines have equal slopes, thus
y = - [tex]\frac{3}{4}[/tex] x + c ← is the partial equation
To find c substitute (- 2, - 2) into the partial equation
- 2 = [tex]\frac{3}{2}[/tex] + c ⇒ c = - [tex]\frac{7}{2}[/tex]
y = - [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{2}[/tex] ← in slope- intercept form
Multiply through by 4 to clear the fractions
4y = - 3x - 14 ( add 3x to both sides )
3x + 4y = - 14 ← in standard form
What is the value of Y?
Answer: 57 = y
Step-by-step explanation: To find the value of y in this problem, we use the exterior angle theorem which states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
So in the diagram shown, the exterior angle, 114,
is equal to the sum of the remote interior angles, y + y.
So we have 114 = y + y.
Solving from here, first combine like terms on the right side.
So we have 114 = 2y.
Now divide both sides by 2 to get 57 = y.
The shorter leg of a 30°−60°−90° triangle is 4 in. Find the hypotenuse and the other leg. Answer: The length of the hypotenuse is ________ in. The length of the other leg is __________in.
Answer:
The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.
Step-by-step explanation:
Note that tan 60 degrees = (length of longer leg) / (length of shorter leg), or
tan 60 degrees = (length of longer leg) / 4 in.
Thus, (length of longer leg) = (4 in)(tan 60 degrees)
= (4 in) [√3/1] = 4√3 in
Also, cos 60 degrees = (adjacent side) / (hypotenuse. We want to find the hypotenuse and thus solve this equation for it:
(hypotenuse) = (adjacent side) / (cos 60) = (4 in)( 2/1 ) = 8 in
The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.
Rectangle A,B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-8, -6), B(-3,-6), C(-3, -4), D(-8, -4). Given these coordinates, what is the length of side AB of this rectangle?
Answer:
AB= 5 units
Image of coordinates is shown in the attachment.
Which equation can be used to solve for c?
c = (5)cos(35o)
c = StartFraction 5 Over cosine (35 degrees) EndFraction
c = (5)sin(35o)
c = StartFraction 5 Over sine (35 degrees) EndFraction
Answer:
c = 5 / cos 35Step-by-step explanation:
To find c we use cosine
cos ∅ = adjacent / hypotenuse
c is the hypotenuse
BC is the adjacent
cos 35° = 5 / c
c = 5 / cos 35Hope this helps you
Answer:
the answer is B. C= 5 / cos(35)
Step-by-step explanation:
i took the test
If c+1/d=5 , what is the value of 30d/2c+2
Answer:
3
[tex]d\in R,\hspace{5}d\neq 0[/tex]
Step-by-step explanation:
You can solve for any variable. From the first equation, let's solve for c :
[tex]\frac{c+1}{d} =5\\\\c+1=5d\\\\c=5d-1[/tex]
Now, replace the value of c into the other equation:
[tex]\frac{30d}{2c+2} \\\\\frac{30d}{2(5d-1)+2} \\[/tex]
Using distributive property
[tex]\frac{30d}{10d-2+2} =\frac{30d}{10d} =3[/tex]
However, keep in mind that this is true for:
[tex]d\in R,\hspace{5}d\neq 0[/tex]
Express (i) 1.4191919.... (ii) 0. 001 in the form p/q, where p and q are integers and q ≠ 0.
Answer:
so confusing.. but I think I have an idea.. p and q are integers equal to 0
Step-by-step explanation:
Help!!!! please!!!!!
Answer:
119 m²
Step-by-step explanation:
The area (A) of a kite is calculated as
A = [tex]\frac{1}{2}[/tex] × product of the diagonals
The diagonals are 7 + 7 = 14 and 12 + 5 = 17, thus
A = [tex]\frac{1}{2}[/tex] × 14 × 17 = 7 × 17 = 119 m²
Diana works in a building that is 130 feet tall. She is outside, looking up at the building at an angle of 37° from her feet to the top of the building. If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot. 10.3 ft 17.6 ft 30.2 ft 97.2 ft
Answer: 17.6
Step-by-step explanation:
The answer to the nearest tenth B. 17.6 ft
What is an instance of word problems?
Word issues commonly encompass mathematical modeling questions, where information and facts about a positive device are given and a scholar is needed to develop a version. for instance: Jane had $5.00, then spent $2.00. How lots does she have now?
How can we resolve word problems?A proven step-by-step approach for solving word problems is sincerely quite simple.
Draw a photograph.suppose “What do I want to locate?”list what's given.find the important thing words.resolve.check your work.Learn more about Word problems at https://brainly.com/question/13818690
#SPJ2
resolve the following into factor ab+ac-ad
Answer:
a(b+c-d)
Step-by-step explanation:
Each term has a factor of "a", so that can be factored out. The remaining factor cannot be factored any further.
ab +ac -ad = a(b +c -d)
Answer:
a(b + c - d)
Step-by-step explanation:
'a' is common to all three terms of the given expression. Thus, the expression in factored form is a(b + c - d).
Which best explains why the equation 3x + 8 = 3x - 5 has no solutions?
O A. The equation is not true for any value of x.
B. The equation has a variable on both sides.
O C. The equation is true for any value of x.
SUE
Answer:A is the ans
Step-by-step explanation:
Feel pleasure to help u
can someone please help me with this questions.
They are quadratic graphs you don't necessarily have to plot the graph. Help me to find y
Answer:
See below in bold.
Step-by-step explanation:
y = x^2 + 3x - 1.
You find the values of y by substituting the individual values of x.
So when x =- -4, y = (-4)^2 + 3(-4) - 1
= 16 - 12 - 1
= 3.
When x = -3, y = (-3)^2 + 3(-3) - 1 = 9 - 9 - 1
= -1.
When x = -2, y = 4 - 6 - 1 = -3.
When x = -1, y = 1 -3 - 1 = -3.
When x = 0, y = 0 - 0 - 1 = -1.
When x = 1, y = 1 + 3 - 1 = 3.
6.247 * 10 to the twelfth power in standard form
Answer: 6,247,000,000,000
Step-by-step explanation:
Here we have the number:
6.247x10^12 and we want to write this in standard form.
You can see that we have a 10^12, this means that we need to move the decimal dot 12 places to the right, if there is not a decimal to the right, we add a zero.
6.247x10^12 = 62.47x10^11 = 624.7x10^10 = 6,247x10^9 = 62,470x10^8 and so on.
eventually, the standard form is:
6.247x10^12 = 6,247,000,000,000
So we end with 12 digits after the six.
Helppp!!!! please!!!
Answer:
18Step-by-step explanation:
8 faces and 12 vertices means hexagon as its base
That means 6+6 edges of its bases and 6 side edges.
6+6+6=18
Nick, Paul and krutika share £80 in a ratio 1:1:2 how much money does each person get
Answer:
Step-by-step explanation:
x + x + 2x = 80
4x =80
X = 20
Nick = 20
Paul = 20
Krutika = 40
vertex of y=-2(x-3)^2+2
Answer:
vertex = (3, 2 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = 2(x - 3)² + 2 ← is in vertex form
with vertex = (3, 2 )
Consider the function f(x) = x2 + 12x + 11. x-intercepts: 0 = x2 + 12x + 11 0 = (x + 1)(x+ 11) y-intercept: f(0) = (0)2 + 12(0) + 11 What are the intercepts of the function? The x-intercepts are . The y-intercept is
Answer:
The coordinates of the x-intercepts are;
(-1, 0) and (-11, 0)
The coordinate of the y-intercept is;
(0, 11)
Step-by-step explanation:
The given function is f(x) = x² + 12·x + 11
The x-intercept is at f(x) = 0 which gives;
0 = x² + 12·x + 11 which has been factored as (x + 1)(x+11) such that we have;
(x + 1)(x+11) = 0
x = -1, or x = -11
The y-intercept occurs at x = 0, we therefore have;
f(0) = (0)² + 12·(0) + 11 = 11
Therefore, we have f(0) = 11 = Y
Given that at the x-intercept, y = 0, then the coordinates of the x-intercepts are;
(-1, 0) and (-11, 0)
Given that at the y-intercept, x = 0, then the coordinate of the y-intercept is;
(0, 11).
Answer:
man up there is right
Step-by-step explanation:
It takes 20 men 60 days to complete a building work.How many days longer will It take 15 men, assuming they work all work at the same rate?
Answer:
80days
Step-by-step explanation:
20m=60days
15m(will take more days)
20÷15×60 = 80 days
What is the answer please help! make sure to explain. thanks!! Mrs. Anderton is giving a test in her third-period class. She has decided to record the amount of time that each student takes to finish the test (in minutes) and compare that to the grade each student receives on the test (out of 100). A plot of her results is below. Which of the following does this situation represent? A. both a relation and a function B. a function only C. neither a relation nor a function D. a relation only
Answer:
A
achievements
Step-by-step explanation:
PLEASE HELP ME!! Whoever answers best is the brainlest! And, please show your work. Thank you! What is the value of the expression 9 − (1/2) ^4 ⋅ 48? (A)1 (B)3 (C)6 (D)9
Answer:
C. 6
Step-by-step explanation:
Use Order of Operations BPEMDAS to help you solve:
9 - 1/16(48)
9 - 3
6
match each pair of angle measures of a triangle with the remaining angle measure
Answer:
6 and 102 = 62
119 and 23 = 38
96 and 51 = 33
28 and 87 = 65
Step-by-step explanation:
just did mine :D
Find the common difference of the sequence shown. 1/6, 1/3, 1/2 , 2
Answer:
1/6
Step-by-step explanation:
sequence should be 1/6,1/3,1/2,2/3
common difference=1/3-1/6=2/6-1/6=1/6
or 1/2-1/3=(3-2)/6=1/6
or c.d.=2/3-1/2=(4-3)/6=1/6
Answer:
The answer is 1/6.
Step-by-step explanation:
I got it right when I did it.
Expand the following using the Binomial Theorem and Pascal's Triangle. Please show work.
(2x+3)^5
Bill wants to be a marine biologist when he grows up. His entire room is ocean-themed, so he is painting his bed frame blue to match. He estimates that he will need 5 cups of paint, but the hardware store only sells paint in quarts. If Bill buys 2 quarts of paint, how many cups will he have left?
Answer:
3 cups
Step-by-step explanation:
Bill needs 5 cups of paint for his bed frame.
The store only sells in quarts and so he buys 2 quarts of paint.
Let us convert to cups to see how many he bought:
1 quart = 4 cups
2 quarts = 2 * 4 = 8 cups
Bill bought 8 cups of paint. Therefore, the number of cups he has left is:
8 - 5 = 3 cups
He will have 3 cups left.
1. The perimeter of the given triangle PQR is
cm
P
7cm
3cm
R
4cm
O 16
28
26
65
Answer:
No, it is not possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm because here we see that sum of the lengths of two sides is equal to third side i.e., 4+3 = 7. As we know that, the sum of any two sides of a triangle is greater than its third side, so given statement is not correct.
Step-by-step explanation:
in the following APs,find the missing terms in the boxes
1). 5_,_,9/2
2).-4,_,_,_,_,6
3)._,38,_,_,_,-22
Answer:
see explanation
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
(1)
Given a₁ = 5 and a₄ = [tex]\frac{9}{2}[/tex] , then
5 + 3d = [tex]\frac{9}{2}[/tex] ( subtract 5 from both sides )
3d = - [tex]\frac{1}{2}[/tex] ( divide both sides by 3 )
d = - [tex]\frac{1}{6}[/tex]
add - [tex]\frac{1}{6}[/tex] to each term
5, [tex]\frac{29}{6}[/tex], [tex]\frac{14}{3}[/tex], [tex]\frac{9}{2}[/tex]
(2)
Given a₁ = - 4 and a₆ = 6, then
- 4 + 5d = 6 ( add 4 to both sides )
5d = 10 ( divide both sides by 5 )
d = 2
Add 2 to each term
- 4, -2, 0, 2, 4, 6
(3)
Given a₂ = 38 and a₆ = - 22, then
a₁ + d = 38 → (1)
a₁ + 5d = - 22 → (2)
Subtract (1) from (2) term by term
4d = - 60 ( divide both sides by 4 )
d = - 15
Substitute d = - 15 into (1)
a₁ - 15 = 38 ( add 15 to both sides )
a₁ = 53
Thus
53, 38, 8, - 7, - 22
Hiya can someone please help me on my maths ratio work?!?
Arthur is organising his collection of DVDs. He has 152 altogether
The ratio of comedy films to action to horror is 6:8:5
How many of each DVD does he have?
what is the coordinates of A and Q
Answer:
Coordinate of A: -9
Coordinate of Q: 9
Step-by-step explanation:
1 - 10 = -9
1 + 8 = 9
Find the value of x in each case:
You can set up an equation for the large triangle made up of the smaller ones by knowing that the total interior angles must sum to 180°. We also can know that angle RPN is also 78° by the geometric law of alternate interior angles. Therefore you know that the angles to sum up are 2x, 2x (which comes from x + x), and 78°.
2x + 2x + 78 = 180
4x + 78 = 180
4x = 102
x = 25.5°
*note, there are many ways to solve this
58. 122. 61. None of the choices are correct
Answer:
C. 61
Step-by-step explanation:
Two sides are equal, so the triangle is an isosceles triangle.
Both base angles are equal.
Angles in a triangle add up to 180 degrees.
58 + x + x = 180
58 + 2x = 180
2x = 122
x = 61