Given:
D varies as R and S, and inversely as t.
D=12, R=3, S=20, and t=5
To find:
The value of D when R=15, S=4 and t=8.
Solution:
It is given that D varies as R and S, and inversely as t. So,
[tex]D\propto \dfrac{RS}{t}[/tex]
[tex]D=\dfrac{kRS}{t}[/tex] ...(i)
Where, k is the constant of proportionality.
We have, D=12, R=3, S=20, and t=5. Substituting these values in (i), we get
[tex]12=\dfrac{k(3)(20)}{5}[/tex]
[tex]12=12k[/tex]
[tex]\dfrac{12}{12}=k[/tex]
[tex]1=k[/tex]
Substituting [tex]k=1[/tex] in (i), we get the required equation.
[tex]D=\dfrac{(1)RS}{t}[/tex]
[tex]D=\dfrac{RS}{t}[/tex]
We need to find D when R=15, S=4 and t=8. Substituting R=15, S=4 and t=8 in the above equation, we get
[tex]D=\dfrac{(15)(4)}{8}[/tex]
[tex]D=\dfrac{60}{8}[/tex]
[tex]D=7.5[/tex]
Therefore, the required value of D is 7.5.
Given csc 0=17/15, determine the values for “a” and “b” in cos 0=a/b
If cosec (tetha) = 17/15 then cos (tetha) = 8/17
What are trigonometry ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
cosec , sine, cotangent, cosine , secant and tangent are trigonometry function.
cosec( tetha) = 1/sin(tetha)
tangent (tetha) = 1/ cot ( tetha)
sec (tetha) = 1/ cos(tetha)
cosec (tetha) = 17/15
therefore 1/sin ( tetha) = 17/15
sin( tetha ) = 15/17 = opp/ hyp
therefore using Pythagoras theorem adj² = 17²-15²
adj² = 289-225
adj² = 64
adj = √64 = 8
cos ( tetha) = adj/hyp
therefore cos ( tetha) = 8/17
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A construction company is building a fence that is 1 1/3 miles long. They can building the fence 1/6 Mile every hr. How long to build the
The length of time to build the fence is 8 hours
How to determine the length of time to build the fenceFrom the question, we have the following parameters that can be used in our computation:
Length of the fence = 1 1/3 miles
Rate of building = 1/6 miles per hour
The length of time to build the fence is then calculated as
Length of time = Length of the fence/Rate of building
Substitute the known values in the above equation, so, we have the following representation
Length of time = (1 1/3 miles)/(1/6 miles per hour)
Evaluate the quotient
This gives
Length of time = 8 hours
Hence, the time taken is 8 hours
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19x+4 find the value of x
Answer:
x= -4/19
Step-by-step explanation:
19x+4
19x+4=0
19x= - 4
x= -4/19
Goran wants to build a square frame with sides that are 5.25 inches long. Natalie wants to build a square sandbox and needs 11 times the amount of wood that Goran needs to build his frame. They have 4 pieces of wood that are each 65.5 inches long. How much wood will they have left over after making the frame and sandbox?
A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other. We can also think of a square as a rectangle with equal length and breadth.
What is a square?The wood left over after making the frame and the sandbox is 10 inches.A square is a two-dimensional figure that has four sides and all four sides are equal.Definition. Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.A square is a four-sided figure whose sides are all the same length and whose angles are all right angles measuring 90 degrees.Square is slang for a person who is conventional and old-fashioned, similar to a Fuddy-duddy. This sense of the word "square" originated with the American jazz community in the 1940s, in reference to people out of touch with musical trends.The area of a square is given as side².
We have,
The total amount of wood.
= 4 x 65.5
= 262 inches.
Frame:
Side = 5.25 inches
The perimeter of the frame.
= 4 x 5.25
= 21 inches
Now,
Sandbox:
The wood used for the sandbox.
= 11 x 21
= 231 inches
The remaining wood.
= 262 - (21 + 231)
= 262 - 252
= 10 inches
Thus,
The remaining wood is 10 inches.
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What number is increased by 3 is equal to 16 decreased by 3
Answer:
The answer is 10.
16 - 3 = 13
10 + 3 = 13
Answer:
10
Step-by-step explanation:
Here,10+3=13
and,16-3=13
Which fraction is equivalent to -3/5
Answer: 3/-2
Step-by-step explanation:
3/-2 and -3/2 mean the same thing and give same result if we divide the numerator by denominator.
hope that helps...
Judi is making a rope ladder. She uses 1/2 yard of for each step. How many yards of rope can she make for step?
The number of yards of rope she can make for the step is 3 yards
How to determine the number of yards of rope she can make for the step?From the question, we have the following parameters that can be used in our computation:
Yards of rope per step = 1/2 yards per step
Total number of steps = 6 steps
The number of yards of rope she can make for the step can then be calculated using the following equation
The number of yards of rope = Total number of steps * Yards of rope per step
Substitute the known values in the above equation, so, we have the following representation
The number of yards of rope = 1/2 * 6
Evaluate
The number of yards of rope = 3
Hence, the number of yards of rope is 3
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Complete question
Judi is making a rope ladder. she uses 1/2 yard of rope for each step. how many steps can she make with 6 yards of rope?
. If Mario was 32 years old 8 years ago, how old was he x years ago?
Answer: He was 32 years old 8 years ago, than a) x-40 b) x-24 c) 40-x d) 24-x e) 24+x
Step-by-step explanation:
Mario was '40 - x' years old when he was 'x' years old.
If he was 32 years old, 8 years ago, then he is 40 now as (32+8) equals 40.
If he is 40 years old now, then he was '40 - x', x years ago.
Hence, '40 - x' is the answer to this sum.
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Lena had 149 dollars to begin with. She just spent k dollars. Using k, write an expression for the number of dollars she has left.
Therefore , the solution to the given problem of expression comes out to be 149-k =x be used it as its expression.
Define Expression .A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Here,
Given : Lena has $149
she spends k amount of money
The money left be x
=> 149-k =x
Therefore , the solution to the given problem of expression comes out to be 149-k =x be used it as its expression.
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Jayda has a vegetable garden. 2/3 of the garden is made up of tomato plants. 4/5 of the tomato plants are beefsteak tomatoes. What portion of the garden is made up of beef steak tomatoes?
a) The portion of the garden is made up of beef steak tomatoes is 8.
b) he Equation for beef steak tomatoes is 4/5 x (portion of tomatoes).
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Portion of Garden have Tomatoes = 2/3
and, 4/5 of the tomato plants are beefsteak tomatoes.
a) The total section in model is 15.
so, Tomatoes in the garden = 2/3 x 15
= 10
and, the portion of the garden is made up of beef steak tomatoes
= 10 x 4/5
= 8 portion.
b) The Equation for beef steak tomatoes
= 4/5 x (portion of tomatoes)
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guys please help its due today!
a) Let x be the number of games played and let y be the total price.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
(b)
Pin Lanes: y = 10 + 3x
Strike Lanes: y = 4 + 6x
(c) To find the number of games at which the total price is the same at both places, we can set the two equations equal to each other and solve for x:
10 + 3x = 4 + 6x
6x = 6
x = 1
So the total price would be the same if you played 1 game at both Pin Lanes and Strike Lanes.
(d) Since you want to play 4 games, you can substitute x = 4 into the equation for each place:
Pin Lanes: y = 10 + 3(4) = 22
Strike Lanes: y = 4 + 6(4) = 28
Since 4 games at Pin Lanes costs $22 and 4 games at Strike Lanes costs $28, it would be cheaper to play at Pin Lanes.
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Prove that limx→2. 1/1-x= -1 using the definition of limit .
Answer:
1332
[tex]7x))742 \sqrt[ \sqrt[241]{?} ]{?} [/tex]
Answer:
Refer to the step-by-step.
Step-by-step explanation:
[tex]Given:\\ \lim_{x\to \22} \frac{1}{1-x}[/tex]
Plug in the value of 2 in for x. We get,
⇒ [tex]\frac{1}{1-(2)}[/tex] ⇒ [tex]\frac{1}{-1}[/tex] ⇒ -1
So, [tex]\\ \lim_{x\to \22} \frac{1}{1-x} = -1[/tex]
Elijah is going to send some flowers to his wife. Kingwood Florist charges $1 per rose, plus
$20 for the vase. Anita's Flowers, in contrast, charges $3 per rose and $10 for the vase. If
Elijah orders the bouquet with a certain number of roses, the cost will be the same with
either flower shop. How many roses would there be?
Answer:
There will be 5 roses.
Step-by-step explanation:
Let r = the number of roses.
Total cost =
numberof Roses × price per rose AND cost of vase
Total at Kingwood's
= 1r + 20
Total at Anita's
= 3r + 10
We are looking for r (the number of roses) when the totals at either place are the same.
Set them equal to each other.
1r + 20 = 3r + 10
Subtract 1r.
20 = 2r + 10
Subtract 10.
10 = 2r
Divide by 2.
10/2 = r
5 = r
When Elijah buys 5 roses, the cost is the same at either florist.
Check:
at Kingwood's
= 1r + 20
= 1(5) + 20
=25
At Anita's
= 3r + 10
= 3(5) + 10
= 15 + 10
= 25
5 roses costs $25 at either florist.
Write the equation of the line shown on graph (-1,-5) and (2,1)
Answer:
y = 2x -3
Step-by-step explanation:
You want the equation of the line through the points (-1, -5) and (2, 1).
SlopeThe slope of the line is given by ...
m = (y2 -y1)/(x2 -x1)
m = (1 -(-5))/(2 -(-1)) = 6/3 = 2
Y-interceptThe y-intercept of the line can be found from ...
b = y -mx
y = -5 -2(-1) = -3
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b . . . . . . . line with slope m and y-intercept b
Using our found values, the equation is ...
y = 2x -3 . . . . . . . . line with slope 2 and y-intercept -3
find the value of x !
Answer:
x = 7
Step-by-step explanation:
You want to know the value of x when the base of a triangle measures 5x+35, and its midsegment measures 35.
MidsegmentThe base of the triangle is twice the length of the midsegment, so you have ...
5x +35 = 2(35)
5x = 35 . . . . . . . . . . subtract 35
x = 7 . . . . . . . . . . divide by 5
__
Additional comment
The midsegment joins the midpoints of the sides of the triangle.
In more formal terms, the smaller triangle is similar to the larger one with a scale factor of 1/2. That means the parallel segments are related by that scale factor of 1/2: (1/2)(5x +35) = 35.
In ΔUVW, w = 1.4 cm, m m∠W=63° and m m∠U=29°. Find the length of v, to the nearest 10th of a centimeter.
In order to find the length of v in ΔUVW, we can use the Law of Sines.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all sides and angles in the triangle. This can be expressed as:
a/sin A = b/sin B = c/sin C
Where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the angles opposite those sides.
In ΔUVW, we are given the lengths of two sides (w and v) and the measure of the angles opposite those sides (m∠W and m∠U). We can use the Law of Sines to find the length of v:
v/sin U = w/sin W
v = (w/sin W) * sin U
Substituting the given values, we get:
v = (1.4 cm / sin 63°) * sin 29°
Using a calculator, we find that v = 2.72 cm to the nearest hundredth of a centimeter. Rounding to the nearest 10th of a centimeter, we get v = 2.7 cm.
Therefore, the length of v in ΔUVW is approximately 2.7 cm to the nearest 10th of a centimeter.
Please help me solve
On solving the provided question, we can say that - the linear equation
y=mx+b = [tex]y=6.4(82)+1900= > y=524.8+1900= > y=2424.8[/tex]
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
y=mx+b
x=gallons of fuel
y=total weight of plane including fuel
m=slope=6.4
b=weight of plane, no fuel....a constant to be calc'd
[tex]y=mx+b\\2245.6=6.4(54)+b\\2245.6=345.6+b\\ b=1900\\ y=6.4x+1900\\ y=6.4x+1900\\ y=6.4(82)+1900\\ y=524.8+1900\\ y=2424.8[/tex]
82gallons fuel is 2424.80 lbs
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Question 4
Solve the equation x² - 4x+6=0 by completing the square.
BIUX² X₂ 15px help!!
After completing the square, the solution of equation are,
⇒ x = (2 + √2i)
And, x = 2 - √2i
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation is,
⇒ x² - 4x + 6 = 0
Completing the square as;
⇒ x² - 4x + 6 = 0
⇒ x² - 4x + 4 + 2 = 0
⇒ (x - 2)² + 2 = 0
⇒ (x - 2)² - (√2i)² = 0
⇒ (x - 2 - √2i) (x - 2 + √2i) = 0
This gives two complex solution as;
⇒ x = (2 + √2i)
And, x = 2 - √2i
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Laura and Shelby ordered pizzas and chips. Lara ordered 5 pizzas and 2 bags of chips and paid $55. Shelby ordered 10 pizzas and 4 bags of chips and paid $95. How much would 1 pizza and 1 bag of chips cost?
Cannot be determined.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here 5 pizzas and 2 bags of chips cost $55 and 10 pizzas and 4 bags of chips cost $95
let the cost of one pizza be p and a bag of chips be c then we construct the following linear equations:
5p+2c=55
10p+4c=95
Clearly the equations are colinear but 10p+4c≠110=1(5p+2c0
and thus two lines don't have a unique solution.
Hence, the cost cannot be determined as the two equations have no solution in common.
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A right triangle with coordinates A (-2,5), B (-2, 9) and C (4,5) is first rotated 90 degrees clockwise and then
translated 1 unit left and 2 units down to form triangle A'B'C'. What is the measure of angle B'A'C', in
degrees, in the resulting figure?
Answer:
90 degree
Step-by-step explanation:
since the angle BAC is 90 degree, no matter the triangle is rotated, or translated , the angld of the triangle do nit change.
To illustrated this, see attached pages.
What is the growth rate in inches per hour of flowers that grew 5 inches in 10 hours ??
Answer:
1/2 or 0.5 inches per hour
Step-by-step explanation:
5 divided by 10 will get you this answer
for values of x f(x) = 2x-3 and g(x)= x^2+1 find gf(x)
Answer:
g(f(x)) = 4x² - 12x + 10
Step-by-step explanation:
to find g(f(x)) substitute x = f(x) ino g(x)
g(f(x))
= g(2x - 3)
= (2x - 3)² + 1 ← expand parenthesis using FOIL
= 4x² - 6x - 6x + 9 + 1
= 4x² - 12x + 10
I really need help on this asap
Answer:
well, both the domain, and the range can have a positive and/or negative infinity, but as long as the 2nd factor is an opposite symbol then you will have a correct answer, for instance, -infinity, and 2 could work, but if the 2 was negative then there would be a problem
Step-by-step explanation:
The volume of a cylinder is 1,200 yd^3 if it’s height is multiplied by 1/4, what will be the new volume of the cylinder?
Therefore , the solution of the given problem of volume comes out to be
you would then possess 1/9 of the volume.
What is volume used for?The term "volume" refers to how much general space an object occupies. Unlike mass, volume changes depending on the surroundings. The mass of a substance in a given volume is referred to as its "density." It describes the relationship between mass and volume.
Here,
A cylinder has a volume of V = r2h.
As a result, V = r2[(1/3)]h is obtained by multiplying h by 1/3.
The (1/3) can be moved to the front to obtain V = [(1/3)]r2h because you are free to multiplied in any ratio you choose.
Thus, you would receive one-third of the initial mass.
What would occur if you increased the radius by 1/3 in contrast to this?
Next, you would have
=> V = π[(1/3)r]2h
=> V = π(1/9)r2h
=> V = (1/9)πr2h
You would then possess 1/9 of the volume.
Therefore , the solution of the given problem of volume comes out to be
you would then possess 1/9 of the volume.
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A parade traveled 8 miles in 4 hours. How far did the parade travel per minute?
Answer:
1/30 of a mile per minute.
Step-by-step explanation:
8/4 = 2 miles per hour.
2/60 = 1/30 of a mile per minute.
Evaluate the following expression when c = -3 and d= 2: 6/d -10c - c to the fourth power
The value of the fourth power of the expression is 1679616.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression: 6/d -10c - c, where c = -3 and d= 2
Solving the expression, we get,
6/2-10(-3)-(-3)
= 3+30+3
= 36
We are asked to find the fourth value of 36,
(36)⁴ = 36 × 36 × 36 × 36 = 1679616
Hence, the value of the expression is 1679616.
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11-(-2)x4 step by step pls my hm is due tmr
Answer:
Step-by-step explanation:
11 -(-2) x 4
11 + 2 x 4
11 +8
= 19
Compare.
2.2O 14/4
A. <
B. >
C. =
Answer:≤ sorry if it's wrong I'm not a fan of math
Step-by-step explanation:
What's the inverse of ƒ(x) = x – 20?
Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20
What is the inverse symbol?A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.
Here,
Solve for y.
Replace y by f-1(x).
y=x-20
x=y-20
Solve for y,x = y-20
x+20
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Answer:
ƒ^(-1)(x) = x + 20
Step-by-step explanation:
To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.
Let's start by replacing ƒ(x) with y:
y = x - 20
Next, swap x and y:
x = y - 20
Now, solve for y by isolating it:
x + 20 = y
Therefore, the inverse of the function ƒ(x) = x - 20 is given by:
ƒ^(-1)(x) = x + 20
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