Answer:
width=4in.
length=13in
Step-by-step explanation:
let the width of the rectangle be x
then the length will be x+9
Area= length×width
52= (x+9)x
52= x²+9x
x²+9x-52=0
x²+13x-4x-52=0
x(x+13) - 4(x+13)= 0
(x-4)(x+13)=0
x=4 or -13
dimension cannot be negative
hence x=4in
the width is 4in. and the length is 4+9=13in.
The solution is, width=4in.
length=13in
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
The area of a rectangle is 52 in^2.
If the length is 9 inches more than the width.
let the width of the rectangle be x
then the length will be x+9
Area= length×width
so, we have,
52= (x+9)x
52= x²+9x
x²+9x-52=0
x²+13x-4x-52=0
x(x+13) - 4(x+13)= 0
(x-4)(x+13)=0
x=4 or -13
dimension cannot be negative
hence x=4in
so, we get,
the width is 4in. and the length is 4+9=13in.
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8-kg lead brick falls from a height of 1.6 m.
(a) Find its momentum as it reaches the ground.
Ikg-m/s
(b) What Impulse is needed to bring the brick to rest?
N-s
(c) The brick falls onto a carpet, 2.0 cm thick. Assuming the force stopping it is constant, find the average force the carpet exerts on the brick
N
(d) If the brick falls onto a 6,0 cm foam rubber pad, what constant force is needed to bring it to rest?
The magnitude of the impulse needed to bring the brick to rest is given by the initial momentum of the brick.
The correct responses are;
(a) 44.8 kg·m/s(b) 44.8 N·s(c) 6,278.4 N(d) 2,092.8 NReasons:
The velocity of the brick as it reaches the ground is given by the formula;
v² = 2·g·h
v = √(2·g·h)
Where;
h = The height of the brick, h = 1.6 m
g = The acceleration due to gravity ≈ 9.81 m/s²
Therefore;
v ≈ √(2 × 9.81 m/s² × 1.6 m) ≈ 5.6 m/s
(a) Momentum = Mass × Velocity
The momentum of the brick = 5.6 m/s × 8 kg = 44.8 kg·m/s
(b) Impulse = Force × Δt = Mass × Δv
Mass × Δv = 8 kg × (5.6 m/s - 0) = 44.8 kg·m/s = 44.8 N·s
Therefore, the impulse = 44.8 N·s
(c) The distance over which the carpet stops the brick = 2.0 cm = 0.02 m
Initial energy in the brick, E = m·g·h
Which gives;
E = 8 kg × 9.81 m/s² × 1.6 m = 125.568 J
Energy = Force × Distance
[tex]\displaystyle Force \ carpet \ exerts \ on \ brick, \ F = \frac{125.568 \, J}{0.02 \, m} = \mathbf{ 6,278.4 \, N}[/tex]
The average force the carpet exerts, F = 6,278.4 N
(d) If the brick falls on a foam which is 6.0 cm (thickness), we have;
Distance = 6.0 cm = 0.06 m
Therefore;
[tex]\displaystyle Force, \, F = \frac{125.568 \, J}{0.06 \, m} = \mathbf{2,092.8 \, N}[/tex]
The constant force needed to bring the brick to rest is, F ≈ 2,092.8 N
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Shane is following an English recipe for scones. The recipe calls for 1.2 kilograms of flour. How many pounds of flour, to the nearest tenth of a pound, does he need?
Answer:
Bilemedim fotoğrafını çeksen daha iyi olur kankacim çok güzel birisin
There are 2.6 pounds of flour.
What is Measurement unit?
A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Given that;
The recipe calls for 1.2 kilograms of flour.
Now,
Since, The recipe calls for 1.2 kilograms of flour.
We know that;
⇒ 1 kg = 2.2 pounds
So, 1.2 kg = 1.2 × 2.2 pounds
= 2.6 pounds
Thus, There are 2.6 pounds of flour.
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A line passes through (-3, -2) and is perpendicular to 3x - 2y = 7.
What is theFind the image of A(6, -4) after it is reflected over the line y = - 2, then reflected over the line x = 1.
(-4, -4)
(-4, 0)
(6, 2)
(-4, 6)
Hello please answer everything carefully :)
Answer:
Line 3
Step-by-step explanation:
Line three should be
2*3*sqrt(5)-3sqrt(5)
simplify as much as possible please u get 50 points thank you
Answer:
y = 7
Step-1: Subtract 8 both sides
⇒ [tex]36 = 4y + 8[/tex]
⇒ [tex]36 - 8 = 4y + 8 - 8[/tex]
⇒ [tex]28 = 4y[/tex]
Step-2: Divide 4 both sides
⇒ [tex]28 = 4y[/tex]
⇒ [tex]\frac{28}{4} = \frac{4y}{4}[/tex]
⇒ [tex]7 = y[/tex]
A student earned 80% on a math test if she got 20 questions correct how many problems were on the test
Answer:
16
Step-by-step explanation:
80% of 20 is 16
Answer:
25
Step-by-step explanation: (My way) If 20 questions equal 80%, then do 20/2 which equals 10. 10 is 40% because 20 was 80%, which was split in half. Now you do 10/2 which is 5. 10 was 40% so 40% got split into 20%. So then you have 5=20%, 10=40%. Now we multiply 10x2 which equals 20. 20=80% so now add 20+5 which is 25. 25 is 100%.
Can someone help me on this question? The question is down below...
Answer:12m
Step-by-step explanation:
Because you are given that this is a right angled triangle, you can apply the pythagoras theorem where a^2 = b^2 + c^2
15^2 = 9^2 + x^2
225-81 = x^2
144 = x^2
x = 12m
help ASAP please again
she got a 110 score
explanation: sorry ignore just had to do 20 characters
I NEED ANSWER NOW PLEASE TELL ME HOW YOU GOT THE ANSWER PLEASE NO LINKS ITS DUE IN 12 MINS!
Answer:
65.214
Step-by-step explanation:
0x100=0
6x10=60
5x1=5
2x(1/10)=0.2
1x(1/100)=0.01
4x(1/1000)=0.004
add all of these values up. hope this helps!
How to find zeros of a quadratic function
example
f(x)=x^3+2x^2-25x-50
Answer:
Step-by-step explanation:
x=2,−5,5
if any doubt leave a comment
Give BRAINLIEST
Why is it helpful to use the rational zero theorem in finding the zeros of polynomial function? Explain your answer.
Answer:
The rational roots theorem is a very useful theorem. It tells you that given a polynomial function with integer or whole number coefficients, a list of possible solutions can be found by listing the factors of the constant, or last term, over the factors of the coefficient of the leading term.
Hope that helps.
Answer:
Finding the Zeros of Polynomial Functions The Rational Zero Theorem helps us to narrow down the list of possible rational zeros for a polynomial function. Once we have done this, we can use synthetic division repeatedly to determine all of the zeros of a polynomial function. Given a polynomial functionuse synthetic division to find its zeros.
Step-by-step explanation:
i hope it helpful:)
Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum.
Answer:
13/15
Step-by-step explanation:
15 is the least common denominator,
so 1/5 = 3/15
2/3 = 10/15
3/15 + 10/15 = 13/15
It can't be reduced.
Answer:
Step-by-step explanation:
The lowest common multiple of these 2 denominators is 3 * 5 since 3 and 5 are prime to each other. (They share no common factor.)
1/5 * 3/3 = 3/15
2/3 * 5/5 = 10/15
3/15 + 10/15 = 13 / 15
PLS HELP WILL MARK YOU BRAINLIEST!!
No fake answers pls
Answer:
1. 5/3 is not equal to 3/5.
2. 7-(4+3) is equal to (4+3)-7
3. (x + y) + 1 is equal to x + (y + 1)
Step-by-step explanation:
1. 5/3 and 3/5 are completely different fractions and when you switch the denominator and the numerator you get a different fraction: 5/3 = 1 2/3, 3/5
2. If you solve both of them, they are equal because 7-7 = 7-7
3. This is equal due to the associative addition property, which means that when the addition of three or more numbers, the total/sum will be the same, even when the grouping of addends are changed.
Plz mark brainliest thx
#1
[tex]\boxed{\dfrac{a}{b}=\dfrac{b}{a},a=b}[/tex]
Here 5[tex]\neq 3[/tex]
Hence inequality holds
#2
[tex]\\ \sf\longmapsto 7-(4+3)=(4+3)-7[/tex]
[tex]\\ \sf\longmapsto 7-7=7-7[/tex]
[tex]\\ \sf\longmapsto 0=0[/tex]
Equality holds
#3
[tex]\\ \sf\longmapsto (x+y)+1=x+(y+1)[/tex]
Equality holds
Done
What is the answer to X=7-3y And 2x-4y=-6
I need it
Answer:
x = − 3 y + 7
Step-by-step explanation:
Reorder 7 and − 3
6c = 2p – 10. write the equation in function notation, where c is the independent variable.
Answer:
p(c) = 3c +5
Step-by-step explanation:
Effectively, you want to solve for p.
6c = 2p -10
6c +10 = 2p
3c +5 = p
p(c) = 3c +5 . . . . function notation (p is a function of c)
A line passes through the points (-4,1) and (-3,3). This line can be modeled by the equation y
Complete the table to determine the values of m and b.
Answer:
A
Step-by-step explanation:
(-14,-3) (6,10) find the slope and explain
please
Answer:
The slope would be 13/20
Step-by-step explanation:
10-(-3) is 13 (numerator) and 6-(-14) is 20 (denominator)
hope this helps!!
what is the measure of ∠x?
From figure we have , ∠GFH = 80° and ∠HGF = 60° , ∠GFH = 40° and ∠GFE = x°
Now,
In ∆HGF
Since Sum of the angles of a triangle is 180° :
∠GFH + ∠HGF + ∠GFH = 180°
80° + 60° + 40° = 180°
14° + 40° = 180°
54° = 180° ………..(1)
∠GFH + ∠GFE = 180° [Linear pair]
80° + x° = 180°
x° = 180°-80°
x° = 100°
Hence the value of ∠x is 100°
Among the given options option (D) 100° is correct.
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Angle EFG and gfh are a linear pair the measure of EFG equals 4n + 25 and the measure of gfh equals 3n + 15 what are the measures of EFG and the measure of gfh...
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Solve 2x^2 - x ≥ 15. Show your work
Answer:
x ∈ 〈-∞,-5/2]∪[3,+∞〉
Step-by-step explanation:
2x²-x-15 ≥ 0
2x²+5x-6x-15 ≥ 0
x(2x+5)-3(2x+5) ≥ 0
(2x+5)(x-3) ≥ 0
so
2x+5 ≥ 0
x-3 ≥ 0
2x+5 ≤ 0
x-3 ≤ 0
solve the equation
x ≥ -5/2
x ≥ 3
x ≤ -5/2
x ≤ 3
x ∈ [3,+∞〉
x ∈ 〈-∞,-5/2]
so x ∈ 〈-∞,-5/2]∪[3,+∞〉
2x+5y>−6
−4x+3y≤2
Is (-1,7)(−1,7)left parenthesis, minus, 1, comma, 7, right parenthesis a solution of the system?
Answer:
No
Step-by-step explanation:
Khan told me ;p
Answer:
No
Step-by-step explanation:
x + 2y = 7
x - y = 1
Solve for x and y?
Answer:
y=2
x=3
Step-by-step explanation:
make x - y = 1 into x= y + 1
put that wherever x is in the other equation
so y + 1 + 2y =7. then combine like terms into 3y =6. then divide 6 by 3 so you get y = 2
then substitute 2 into the y in the equation x - y = 1 and you get x = 3
METHOD OF ELIMINATION:
Given pair of linear equations are:
x+2y= 7 – – – Eqn(i)
On comparing with a1x+b1y+c1 = 0
a1 = 1, b1 = 2, c1 = -7x-y = 1 – – – Eqn(ii)
On comparing with a2x+b2y+c2 = 0
a2 = 1, b2 = -1 , c2 = -1a1/a2 = 1/1 = 1
b1/b2 = 2/-1 = -2
c1/c2 = -7/-1 = 7
We have,
a1/a2 ≠ b1/b2 ≠ c1/c2
So, Given pair of linear equations in two variables have a unique solution.
Now,
On Subtracting eqn(ii) from eqn(i) then
x+2y = 7
x-y = 1
(-)
_______
0 +3y = 6
_______
⇛ 3y = 6
⇛ y = 6/3
⇛ y = 2
On Substituting the value of y in (1) then
⇛ x-2 = 1
⇛ x = 1+2
⇛x = 3
Answer: Therefore , the value of x and y with be (3,2) respectively.
Additional comment:
If a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 are pair of linear equations in two variables thenIf a₁/a₂ ≠b₁/b₂ ≠ c₁/c₂ then they are Consistent and independent lines or Intersecting lines and they have a unique solution.If a₁/a₂ = b₁/b₂ = c₁/c₂ then they are Consistent and dependent lines or Coincident lines and they have infinitely number of many solutions.If a₁/a₂ =b₁/b₂ ≠ c₁/c₂ then they are Inconsistent lines or Parallel lines lines and they have no solution.A 15 foot slide casts a shadow that is 25 feet long. A tree is standing next to the slide and casts a shadow that is 40 feet long. How tall is the tree?
Answer:
30 feet
Step-by-step explanation:
The height of the tree is 24 feet casting a shadow of 40 feet long.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Assuming the height of the tree to be x feet.
15 : 25 : : x : 40.
15/25 = x/40.
25x = 600.
x = 24
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Solve the following equation algebraically: 3 x squared = 12 a. Plus-or-minus 3 b. Plus-or-minus 2 c. Plus-or-minus 3.5 d. Plus-or-minus 1.5
Answer:
b) ±2
Step-by-step explanation:
3x² = 12
divide each side by 3 to get:
x² = 4
x = ±2
The value of the equation 3x² = 12 is x = ±2.
Option B is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 6 is an equation.
We have,
3x² = 12
Divide 3 on both sides.
x² = 4
x = ±√4
x = ±2
Thus,
The value of x is ±2.
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Problem 1: Solution to the system of equations
A line is parallel to the line for the equation: -9y = 2x + 35.
What is the slope of the parallel line?
Answer:
-2/9
Step-by-step explanation:
if the line is parallel it has the same slope.
The equation can be written as y = -2/9x - 35/9
so the slope is -2/9
can someone help me
Answer:
The answer is 6 cause khan acadamy
Step-by-step explanation:
Find the area of the shape.
Answer:
27 π
Step-by-step explanation:
Notice that the shape is 3/4 of a circle with radius 6. So we need to find 3/4 of the area of a circle with radius 6. The area of a circle with radius 6 is [tex]\pi r^2 = \pi \cdot 6^2 = 36\pi[/tex].
3/4 of this is [tex]\frac{3}{4} \cdot 36\pi = \boxed{27\pi.}[/tex]
if 10 apples cost $1 how much would it cost per Apple
Answer:
10 cents per apple
Step-by-step explanation:
1 divided by 10 which is 1. And move the decimal one place to the left, leaving you with .1 or 0.1 or 0.10
Find the gradient of the line segment between the points (10,-4) and (6,-16).
(03.02) If g(x) = x2 + 2, find g(3). (2 points) Group of answer choices 9 8 11 6
this answers is 8 am I right
1/4 of 90. …………………????
Answer:
22.5
Step-by-step explanation: