Answer:
P=3.5
P=2.667
Step-by-step explanation:
p=f/a
P=70/20
P=3.5
then f is increased by 10
f=70+10=80
and a is increased by 10
a=20+10
a=30
therefore; P=f/a
P=80/30
P=2.667
In a physics class demonstration, a ball is dropped from the roof of a building, 72 ft above the ground. The height, h, in feet, of the ball above the ground is given by the function h = -16t2 + 72, where t is time in seconds.
The graph is shown below:
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given:
h(t) = -16t² + 72
For t=-1,
h(-1) = -16 * (-1)² +72
h(-1) = -16 +72= 56
Ordered pair is ( -1, 56)
For t=1,
h(1) = -16 * (1)² +72
h(1) = -16 +72= 56
Ordered pair is ( 1, 56 )
For t=2,
h(2) = -16 * (2)² +72
h(2) = -64 +72= 8
Ordered pair is ( 2, 8 )
For t=3,
h(2) = -16 * (3)² +72
h(2) = -144 +72= -72
Ordered pair is ( 3, -72)
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1. Given the points A (2, 14) and B (17, -6).
(a) Find the distance of the line AB.
(b) Find the midpoint of the line AB.
(c) Find the gradient of the line AB.
(d) Find the equation of the line AB.
(e) Find the equation of the line parallel to AB passing through the point (3,5).
(f) Find the equation of the line perpendicular to AB passing through point (4,-2).
(g) Draw the above 3 lines on a graph.
Answer:
Step-by-step explanation:
Which graph shows the solution to the system of linear inequalities? Y<2x-5 y>-3+1
Helppppp
Answer:
Is the second expression written correctly? It reduces to y>-2, since no x is in the equation.
Step-by-step explanation:
We can graph the two equations. See attached image. If y>2 is the correct expression, all points to the right.
If the equation was meant to read y=-3x+1, then graph the revised expression.
Use trigonometric identities to verify each expression is equal.
c) csc^2(x)-2csc(x)cot(x)+cot^2(x) = tan^2(x/2)
d) [cos(x)cos(y)][tan(x)+tan(y)] = sin(x+y)
Part (c)
[tex]\text{LHS}=\csc^{2} x-2\csc x\cot x+\cot^{2} x\\\\=(\csc x-\cot x)^{2}\\\\=\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x} \right)^{2}\\\\=\left(\frac{1-\cos x}{\sin x})^{2}\\\\=\tan^{2} \left(\frac{x}{2} \right)\\\\=\text{RHS}[/tex]
Part (d)
[tex]\text{LHS}=[\cos x \cos y][\tan x+\tan y]\\\\=[\cos x\cos y]\left[\frac{\sin x}{\cos x}+\frac{\sin y}{\cos y} \right]\\\\=\sin x \cos y+\sin y \cos x\\\\=\sin(x+y)\\\\=\text{RHS}[/tex]
determine whether the given graph is a function or not
if a/b and c/d are rational expressions, then: a/b / c/d = a*b/c*d
if a/b and c/d are rational expressions,a/b / c/d = a*b/c*d is false.
What is the definition of a fraction number?A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.
The given rational expression is;
a/b and c/d
Given relation;
[tex]\rm \frac{\frac{a}{b}}{\frac{c}{d}}\\\\ \frac{a d}{bc}[/tex]
When two fractions are divided the number got reversed and multiplied by the fraction.
Hence the given calculation is false.
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Answer: false
Step-by-step explanation: .
Which statement about proportional relationships is false?
A proportional relationship must graph as a line.
A graph of a proportional relationship must pass through (0, 0).
Each point (or pair) in a proportional relationship must share the same ratio.
O Each point (or pair) in a proportional relationship must share the same difference.
Mark this and return
Save and Exit
Next
Submit
Answer:
Each point (or pair) in a proportional relationship must share the same difference is the false statement.
What is the product of 4 and 5g + 2.34?
The product of 4 and 5g + 2.34 is 20g + 9.36
How to determine the product?The expressions are given as:
4 and 5g + 2.34
As a product expression, we have:
4 * (5g + 2.34)
Evaluate the product
20g + 9.36
Hence, the product of 4 and 5g + 2.34 is 20g + 9.36
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Help plssssss I need this today
Answer:1 is exponential. 2 is linear. 3 is neither. 4 is linear. 5 is linear. 6 is exponential. 7a is exponential. I think 7b could be 10x + y = 10 but I'm not too sure. 7c is (8,4).
Step-by-step explanation:1. the coordinates are moving in an exponential way or something im not sure the correct wording but that is what exponential graphs look like. 2 is a straight line so it is linear. 3 is neither because the graph isn't exponential or linear. 4 is linear because the coordinates are subtracting at the same number. 5 is linear for the same reason at 4. 6 is exponential because the coordinates are multiplied by 2 each time. 7a is exponential because the coordinates are divided by 2 each time. 7b I'm not sure on. 7c is 8/4 because August is the 8th month and the month before (7) is 8 so 8 divided by 2 equals 4. So the 8th month would have to be 4. I hope that helps!
what is the equation of a line that has a slope of -5 and a y intercept of -7
Answer:
y=(-5x)+(-7)
Step-by-step explanation:
The equation for slope is y=mx+b
so you would say -5x as the mx in the equation and -7 as the u intercept.
Hii!
_________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
y=-5x-7
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
For this question we will use the slope intercept form equation, because we are provided with the slope and the y-intercept.
The slope intercept form equation is [tex]\large\textsf{y=mx+c}[/tex]. In this formula m denotes the slope and c denotes the y-intercept.
Since we have both m and b, we can stick them into the formula. Upon doing this we obtain
[tex]\twoheadrightarrow\sf y=-5x+(-7)[/tex]
[tex]\bullet[/tex] Simplify
[tex]\twoheadrightarrow\sf y=-5x-7[/tex]
[tex]\bullet[/tex] Great job! We found the equation
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
The sum of ages of Clayman and Ato is 25 years. In five years' time, the age of Ato will twice the age of Clayman now. a. How old is Clayman? b. How old is Ato?
Clayman is 10 years old and Ato is 15 years old
Word problems leading to equationsLet the age of Clayman be x
Let the age of Ato be y
If the sum of ages of Clayman and Ato is 25 years. then;
x + y = 25
x = 25 - y ...... 1
In five years time;
Age of Clayman = x + 5
Age of Ato = y + 5
If in five years' time, the age of Ato will twice the age of Clayman now, then;
y+5 = 2x ............. 2
Substitute equation 1 into 2
y +5 = 2(25-y)
y + 5 = 2(30 - y)
y + 5 = 50 - 2y
3y = 45
y = 15
Since x + y = 25
x = 25 - 15
x = 10
Therefore Clayman is 10 years old and Ato is 15 years old
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Carlita has a swimming pool in her backyard that is rectangular with a length of 26 feet and a width of 14 feet. She wants to install a concrete walkway of width c around the pool. Surrounding the walkway, she wants to have a wood deck that extends w feet on all sides. Find an expression for the perimeter of the wood deck.
Lets solve the question,
Given dimensions are:
Length = 26 feet
Width = 14 feet
concrete walkway with width = c
After installing the concrete walkway dimensions of the walkway will be,
Length = 26 + 2c
Width = 14 + 2c
She wants to build a wooden deck around the pool with a concrete walkway of width = w
Thus the dimensions of the wooden deck around the pool will be,
Length = [tex]26 + 2c + 2w[/tex]
Width = [tex]14 + 2c + 2w[/tex]
Now the perimeter of the wooden deck will be,
Perimeter = 2(length + width)
[tex]= 2[(26 +2c + 2w) + 2(14 + 2c + 2w)] = 2(40 + 4c + 4w) = (80 + 8c + 8w)[/tex]
Therefore, perimeter of the wooden deck would be: 80 + 8c + 8w
Perimeter = (80 + 8c + 8w)
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Solve 1 2 1 2x = x2 − 7x 10 4x by rewriting the equation as a proportion. which proportion is equivalent to the original equation?
The proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
Rational expressionsGiven the following expression
[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
In order to find the equivalent proportion, we will find the LCM of the right side expression to have:
[tex]\frac{1}{2} + \frac{1}{2x} =\frac{x^2-7x+10}{4x}\\\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
Hence the proportion that is equivalent to the original equation is [tex]\frac{x+1}{2x} =\frac{x^2-7x+10}{4x}[/tex]
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Answer: For the next part
✔ x = 1 and x = 8
✔ x = 0
Kelly wants to buy a dress that costs $40.00. She has a coupon for 25% off, and
there is a 10% sales tax
How much will she pay altogether?
44 QUES
25% of $40.00 is $
Select
After using the coupon, the sale price is $
Select...
The 10% tax on the sale price is $
Select
The final price is $
Select
A percentage is a way to describe a part of a whole. The amount that Kelly will pay for the dress is $33.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given Kelly wants to buy a dress that costs $40.00. She has a coupon for 25% off, and there is a 10% sales tax. Therefore, the amount she will pay is,
25% of $40.00 is,
0.25 × $40 = $10
After using the coupon, the sale price is,
$40 - $10 = $30
The 10% tax on the sale price is,
0.10 × $30 = $3
The final price is $
$30 + $3 = $33
Hence, the amount that Kelly will pay for the dress is $33.
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List the angles in triangle JKL in order from largest to smallest.
Answer:
answer is B
Step-by-step explanation:
We know,
Opposite of a big arm has a big angle....the same way you can find the next two....
as 18>16>14
The graph of y=x^2-4x by drawing the line y=x-4
Answer:
the graph of y=x^2-4x is parabola as shown in the image
Step-by-step explanation:
The graph of [tex]y = x^{2} -4x[/tex] by drawing the line y=x-4
so this gives us that the line y=x-4 satisfies the equation [tex]y = x^{2} -4x[/tex]
To get points put y = x - 4 in the equation [tex]y = x^{2} -4x[/tex]
so we get x -4 = x( x- 4)
x =1 and x - 4 = 0
from here we get x = 1,4
now put these values in y = x -4
From here we get y = -3,0
so the points are (1 , -3) and ( 4 , 0)
Plot these on graph and we get the straight line .
For equation [tex]y = x^{2} -4x[/tex]
As we know it is of type of parabola with shifted centre.
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NEED HELP ASAP!!!!!
Triangle ABC and DEF are similar. Answer the following questions:
a. What relationship can you write for the angles of these two triangles?
b. What is the length of the missing side?
Answer:
a)<BAC = EDC,<DEC =ABC,ACB=DFE
b)7
Step-by-step explanation:
According to the definition, two triangles are similar if their corresponding angles are congruent and corresponding sides are proportional. Hence, we can find the dimensions of one triangle with the help of another triangle. If ABC and DEF are two similar triangles, then by the help of below-given formulas, we can find the relevant angles and side lengths.
∠A = ∠D, ∠B = ∠E and ∠C = ∠F
AB/DE = BC/EF= AC/DF
If Bob sells each fish at a profit of $1.25, how much money will he have after selling all 24 fish? Show your calculation.
Best answer receives brainliest
Answer: $30
Step-by-step explanation:
So if Bob sells his fish at a profit of $1.25 and he has 24 fish to sell then 1.25*24= 30
(I'm assuming what you mean by "how much money he will have" is profit)
Answer:
The answer is $30. remove the decimal from the price and multiply it by the amount of fish. then when you finish multiplying add the decimal back in.
Step-by-step explanation:
125
× 24
--------
500
+ 2500
-----------
30.00
John bought a motor cycle for $56,750 and spent $4530 On its repair. Then he sold it for $72650, what was the profit?
Answer:
cost of old motor bike =$5675
he spent on repair =$453
cost that he sold =$7265
profit he made=$7265-$5675+$453
=$7265-$6128
=$1137
Step-by-step explanation:
Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?
(2, 3)
(–2, 3)
(3, 2)
(3, –2)
The coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a trapezoid GHJK that was rotated 180° about the origin.
The rule for 180-degree rotation about the origin:
(x, y) → (-x , -y)
From the graph:
Coordinate of H' is (-3, -2)
(-3, -2) → (3, 2)
Thus, the coordinates of pre-image point H is (3, 2) option third (3, 2) is correct.
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point-slope equation for perpendicular lines y=-2x-7 that passes through (-2,-3)
Answer: below! ^^
Step-by-step explanation:
Hii, do you need an answer to your question? Let me help you out! (;
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Part 1 ⚜Perpendicular lines have slopes that are opposite inverses of each other.
The slope (m) of the line that is perpendicular to y=-2x-7 is [tex]\sf -\cfrac{1}{2}[/tex].
Part 2 ⚜⚜ Point slope formula[tex]\boldsymbol{y-y1=m(x-x1)}[/tex]
⚜Stick in the known values[tex]\boldsymbol{y-(-3)=-\cfrac{1}{2}(x-(-2)}[/tex]
⚜ Simplify[tex]\boldsymbol{y+3=-\cfrac{1}{2}(x+2)}[/tex]
Voila! There's our answer, cheers! (:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Hope I helped! Best wishes!
Reach far. Aim high. Dream big.
[tex]\underbrace[/tex]
Can someone help me out with this problem
From the given options the options B and C are correct for the given equation.
we have given the equation,
70=10+12r
We have to determine the correct option
What is the equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.
Therefore from the given options the options B and C are correct for the given equation.
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Find the value of x.
Answer:
x = 20°
Step-by-step explanation:
(4x-10)+x=90
4x-10+x=90
4x+x-10=90
5x-10=90
5x=100
x=20
Answer:
20
Step-by-step explanation:
Straight line angles:
Angles on a straight line add up to 180°.
90 + 4x - 10 + x = 180
90 - 10 + 4x + x = 180
Combine like terms.
80 + 5x = 180
Subtract 80 from both sides,
5x = 180 - 80
5x = 100
Divide both sides by 5
x = 100 ÷ 5
[tex]\sf \boxed{x = 20^\circ}[/tex]
Convert each rate using dimensional analysis. Round to the nearest tenth, if necessary.
45 mi/h = ___ ft/s
The 45 mi/h is equal to the 2640 ft/min.
To convert 30 miles per hour to feet per minute, we use dimensional analysis in the process.
We have given that, rate using dimensional analysis.
What is the 1 hour?
1 hour = 60 minutes.
1 mile is equal to 5280 feet and 1 hour is equal to 60 minutes.
Hence the formula of conversion is 30 miles / hour *(5280 ft/ mile) * (1 hour / 60 min).
The answer is 2640 ft/min.
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A stretch by a factor of 2 for the exponential growth function f(x)= a(nine-fourths) superscript x occurs when a = . a stretch by a factor of eleven-thirds for the exponential decay function f(x)= a(three-fifths) superscript x occurs when a = . a shrink by a factor of one-third for the exponential growth function f(x)= a(7)x occurs when a = . a shrink by a factor of two-fifths for the exponential decay function f(x)= a(two-ninths) superscript x occurs when a = .
Answer: A stretch by a factor of 2 for the exponential growth function f(x)= a(9/4)^x occurs when a =✔ 2
A stretch by a factor of 11/3 for the exponential decay function f(x)= a(3/5)^x occurs when a =✔ 11/3
A shrink by a factor of 1/3 for the exponential growth function f(x)= a(7)^x occurs when a =✔ 1/3
A shrink by a factor of 2/5 for the exponential decay function f(x)= a(2/9)^x occurs when a =✔ 2/5
Step-by-step explanation:
The exponential growth equation is stretched and compressed by a scale factor k = 2 , 11/3 , 1/3 and 2/5
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the exponential growth equation be represented as A
Now , the value of A is
For the exponential growth function f(x)= a(9/4)ˣ, a stretch by a factor of 2 occurs when a = 2
For the exponential decay function f(x)= a(3/5)ˣ, a stretch by a factor of 11/3 occurs when a = 11/3
For the exponential growth function f(x)= a(7)ˣ, a shrink by a factor of 1/3 occurs when a = 1/3
For the exponential decay function f(x)= a(2/9)ˣ, a shrink by a factor of 2/5 occurs when a = 2/5
Hence , the exponential equation is solved
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Find the value of $x$ that satisfies $\frac{1}{3x-1} = \frac{2}{x+1}$. Can someone please explain this in detail?
The value of x = 3/5 or 0.6 will satisfy the equation given.
What is an Equation ?An equation is a mathematical statement which is formed when two expressions are equated by an equal sign.
It is given that
[tex]\rm \dfrac{1}{3x-1} = \dfrac{2}{x+1}\\[/tex]
It has to be solved and the value of x has to be determined
(x+1) = 2 (3x-1)
x +1 = 6x -2
5x = 3
x = 3/5
Therefore the value of x = 3/5 or 0.6 will satisfy the equation given.
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please help!!! picture has the question and answer choices in it
Answer:
5x-y≥ 1
Step-by-step explanation:
Find the slope of the line to be :
y = 5x -1 <===== the shaded area is less than or equal (because it is a SOLID line...not dashed) to this :
y ≤ 5x-1 re-arrange to
5x-y ≥ 1
The length of a rectangle is twice its breadth. If its length is decreased half of the 10 cm and the breadth is increased by half of the 10 cm cm, the area of the rectangle is increased by 5 sq cm, more than 70 sq cm. Find the length of the rectangle.
Also....any armies, stays and blinkss?
Since the length of this rectangle is twice its breadth, the length is equal to 40 cm.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
Area = Length × Width
Based on the information provided, we have:
Its length is decreased half of the 10 cm ⇒ (length - 5)Its breadth is increased by half of the 10 cm ⇒ (breadth + 5)Its area is increased by 75 cm ⇒ (area + 5)Substituting the parameters into the formula, we have:
LB + 75 = (L - 5)(B + 5)
2B² + 75 = (2B - 5)(2B + 5)
2B² + 75 = 2B(B + 5) - 5(B + 5)
2B² + 75 = 2B² + 10B - 5B - 25
5B = 75 + 25
5B = 100
B = 100/20
B = 20 cm.
For the length, we have:
L = 2B
L = 2 × 20
L = 40 cm.
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Suppose y varies inversely with x, and y = a when x = a 2. What inverse variation equation relates x and y ?
a.
y = a2xa2x
b.
y = a 3x
c.
y = a3xa3x
d.
y = ax
The variation equation is xy = a^3
How to determine the equation?An inverse variation is represented as:
xy = k
Where k is the constant of variation
When y = a and x =a^2, we have:
k = a * a^2
Evaluate
k = a^3
Substitute k = a^3 in xy = k
xy = a^3
Hence, the equation is xy = a^3
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Solve for 'x' in the following equation, explaining each step.
3^ (-3x+7) = 3^ (7x-13)
Answer:
x = 2
Step-by-step explanation:
In order to have the two sides of the equation be equal, the exponents must equal.
-3x + 7 = 7x - 13
Add 3x to both sides.
7 = 10x - 13
Add 13 to both sides.
20 = 10x
Divide by 10.
2 = x
Check:
3^(-3•2+7)=3^(7•2-13)
3^1 = 3^1
3 = 3
