The longer ladder can reach 3 8/7 feet higher than the shorter one.
The Proportionality Theory.The longer ladder can reach 4 2/7 feet higher than the shorter ladder. To calculate this, we need to subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet).We can represent this calculation with a fraction equation, as follows:[tex]\frac{16 \frac{3}{7}}{12 \frac{5}{7}} - 12 \frac{5}{7} = \frac{4 \frac{2}{7}}{1}[/tex]To solve this equation, we first need to convert the fractions into equivalent fractions with a common denominator. In this case, the denominator is 7. This means that the first fraction becomes 16 3/7, the second fraction becomes 12 5/7, and the third fraction becomes 4 2/7.Once we have the fractions in the same denominator, we can now subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet). This gives us a result of 4 2/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To put this into perspective, if we were to use the ladders to reach a height of 16 3/7 feet, the shorter ladder would only reach 12 5/7 feet, while the longer ladder would reach 16 3/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To learn more about The Proportionality Theory refer to:
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the triple of a number added to its half part is equal to the difference between four times the number and 12. What number is it
Answer:
24
Step-by-step explanation:
You want to know the number such that the triple of the number added to its half part is equal to the difference between four times the number and 12.
TranslationThe given relation can be expressed in math symbols as ...
3n +n/2 = 4n -12
Adding 12 -n/2, we get ...
12 = n/2
24 = n . . . . . multiply by 2
The number is 24.
3x+5y= 8
2х - 5y = 22
Solve system of equations
Answer:
{x,y}={6,-2}
Step-by-step explanation:
System of Linear Equations entered :
[1] 3x + 5y = 8
[2] 2x - 5y = 22
Solve by Substitution :
// Solve equation [2] for the variable x
[2] 2x = 5y + 22
[2] x = 5y/2 + 11
// Plug this in for variable x in equation [1]
[1] 3•(5y/2+11) + 5y = 8
[1] 25y/2 = -25
[1] 25y = -50
// Solve equation [1] for the variable y
[1] 25y = - 50
[1] y = - 2
// By now we know this much :
x = 5y/2+11
y = -2
// Use the y value to solve for x
x = (5/2)(-2)+11 = 6
Graphic Representation of the Equations :
The answer should be: {x,y}={6,-2}
Which of the following is the quotient of the rational expressions shown
below?
X/3x-1 divide x-2/2x
Answer: To divide two rational expressions, you need to first find the least common denominator (LCD) of the two expressions. The LCD is the least common multiple of the two denominators.
In this case, the rational expressions are x/(3x-1) and (x-2)/(2x). The LCD of these two expressions is (3x-1)(2x), which can be factored as 6x(x-1).
To divide the two rational expressions, you need to express each expression as a fraction with the LCD as the denominator.
The first expression, x/(3x-1), can be rewritten as (x * (2x))/(3x-1 * (2x)) = (2x^2)/(6x^2-2x).
The second expression, (x-2)/(2x), can be rewritten as ((x-2) * (3x-1))/(2x * (3x-1)) = (3x^2-3x+2)/(6x^2-2x).
To divide these two expressions, you can divide the numerators and the denominators separately:
(2x^2)/(6x^2-2x) ÷ (3x^2-3x+2)/(6x^2-2x)
= (2x^2) ÷ (3x^2-3x+2)
= (2/3)x^2 ÷ (x^2-x+2/3)
Therefore, the quotient of the rational expressions x/(3x-1) and (x-2)/(2x) is (2/3)
Step-by-step explanation:
Joanne works two jobs to pay for college. She tutors for $25 per hour and also works as a receptionist for $12 per hour. Due to her class and study schedule, Joanne is only able to work up to 25 hours per week, but must earn at least $200 per week. If t represents the number of hours Joanne tutors and r represents the number of hours she works as a receptionist, which system of inequalities represents this scenario?
A. t + r >= 25
25t + 12r = 200
B. t + r <= 25
25t + 12r <= 200
C. t + r <= 25
25t + 12r >= 200
D. None of the systems shown represent this scenario.
The required system of inequality will be
t + r ≤ 25
25t + 12r ≥ 200
What is system of equations?
A set or group of equations that are solved together is referred to as a system of equations. Both algebraic and graphic solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.
If 't' represents the number of hours Joanne tutors and 'r' represents the number of hours she works as a receptionist.
Then the total hours she can work = t + r
Since she can work up to 25 hours.
Thus t + r ≤ 25
If she earns $25 per hour by tuition and $ 12 per hour by working as a receptionist .
Then her total earning = $25t + 12r
Since she must earn $200.
Then 25t + 12r ≥ 200
Hence, the required system of inequality will be
t + r ≤ 25
25t + 12r ≥ 200
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Please help! Determine the coordinates of the transformation and plot the image for Rx Axis of the triangle ABC
Answer:
Step-by-step explanation:HI
You got answer already?
Just , look down as in rectangle A" (-6,1)
B"(-1,-3)
C"(-4, 4)
And you have wrong coordinates for C (-4,-4)
Jesse wanted a stamp collection his grandfather gave him 48 stamps to start it then his parents gave him 23 stamps and his aunt gave him 17 stamps how many stamps does Jesse have in his collection
Answer:88
Step-by-step explanation:
What is the solution of 2x 3 7?
Answer: It is a straight line
Step-by-step explanation:
i dont understand it
Answer:
x=-3
y=10
Step-by-step explanation:
If you buy 3 CD’s at the original cost of 9.99 but you have a 10% off coupon and the sales tax is 6% what is your total
Which statement best describes a line graph?
A. It shows a line that connects a series of data
points.
B. It shows a line passing through scattered data points.
C. It shows data as proportions of a whole.
D. It shows the locations of errors in data.
Answer:
A
Explanation:
A line graph is a unique type of graph which is used in statistical application which represents the change in a quantity with respect to another quantity.
The price of different flavors of chocolates varies which can be represented, these variation is plotted in a two-dimensional XY plane.
If the relation include two measures can be presented by using a straight line in a graph called as linear graphs or a linear graph.
There are different types of the line graph, Simple Line Graph refers to Only one line is plotted on the graph, Multiple Line Graph where More than one line plotted on the same set of axes.
Compound Line Graph refers to the information can be divided into two or more types of data and this line graph is called a compound line graph which can be drawn to show the component.
Rose and Andrew are financing $128,000 to purchase a condominium. They obtained a 15-year, fixed-rate loan with a rate of 5. 5%. They have been given the option of purchasing up to four points to lower their rate to 4. 81%. How much will the four points cost them?
The cost of the four points will be $8296.8496
What is simple interest?A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
$ 128,000 is the amount financed (P).
t = 15 years
The interest rate equals 5.05%.
Amount after 15 years equals,
A = [tex]P(1+\frac{r}{100}[/tex]
=128,000[tex](1+\frac{5.05}{100} )^{15}[/tex]
=268009
Rose and Andrew has taken four points to lower their rate to 4.81% .
A =128,000 [tex](1+\frac{4.81}{100} )^{15}[/tex]
A = 259,713
Cost of four points = 268,009.890 - 259,713.040 = $8296.8496
Hence, the cost of the four points will be $8296.8496
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6 miles East 4 miles Southeast 4 miles South 7 miles Southwest 4 miles East This person has walked a total of Find the total displacement vector for this walk:
On solving the provided question, we can say that vectors are - 4 miles E: <4, 0>; 4 miles SE: <2√2, -2√2>; 7 miles S: <0, -7>; 6 miles SW: <-3√2, -3√2>; 2 miles E: <2, 0>
what is vector?In mathematics, a vector is a quantity with magnitude and direction but no location. Acceleration and velocity are two examples of such numbers. A thing with both magnitude and direction is called a vector. A vector can be conceptualised geometrically as a directed line segment, the length of which corresponds to the magnitude of the vector, and the direction of which is denoted by an arrow. Size and direction are two independent characteristics of a quantity or phenomena known as a vector. The phrase also describes how these numbers are represented mathematically or geometrically. In nature, vectors may be found in electromagnetic fields, weight, momentum, force, and velocity.
4 + 4 + 7 + 6 + 2 = 23 miles.
vectors are -
4 miles E: <4, 0>
4 miles SE: <2√2, -2√2>
7 miles S: <0, -7>
6 miles SW: <-3√2, -3√2>
2 miles E: <2, 0>
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a smallercircle passes through the center of, and is tanget to a larger cirlc the area of the smaller circle is 9 square units. What is teh area of the larger circle in square units
36 square units make up the larger circle's surface area.
We can use the fact that the smaller circle is tangent to the larger circle and passes through its center to find the area of the larger circle. Since the radius of the smaller circle is tangent to the larger circle, the radius of the larger circle is double the radius of the smaller circle.
Let's call the radius of the smaller circle "r" and the radius of the larger circle "R". We know that R = 2r.
We know that the area of a circle is given by the formula A = πr^2.
We know that the area of the smaller circle is 9 square units, we can use this formula to find the radius:
A = πr^2 => r^2 = 9/π => r = sqrt(9/π)
Now we can use the formula of the area of a circle with R-value to get the area of the larger circle:
A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36
So the area of the larger circle is 36 square units
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I don’t know help m/12-8=4
Answer:
[tex] \frac{m}{12} - 8 = 4 \\ \frac{m}{12} = 4 + 8 \\ m = 12×12 \\ m = 144[/tex]
Hope it will help u...
The sides of a triangle are 68, 61, and 46. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
Answer: Acute
Step-by-step explanation:
The Pythagorean Theorem is [tex]a^2+b^2=c^2[/tex]. A and b are legs while c is hypotenuse. Hypotenuse is also the longest side. Let's plug them in and see if they are equal to each other.
[tex]46^2+61^2=68^2[/tex] [exponent]
[tex]2116+3721=4624[/tex] [add]
[tex]5837\neq4624[/tex]
Since they are not equal, then it is not a right triangle.
To tell is a triangle is acute, if the sum of the two shorter sides squared is greater than the longest side squared, then the triangle is acute.
At the end of the Pythagorean Theorem, we got 5837≠4624. 5837>4624, so that tells us that the triangle is acute.
any and all help is appreciated, brainliest will be given ! :)
Answer:
x = 16±2√94 over 3
Step-by-step explanation:
Move terms to the left side.
0 = -6x² + 64x + 80
- ( -6x²+64+80) = 0
Distribute
- ( - 6x²+64x+80) = 0
6x² - 64x - 80 = 0
Common factor
6x² - 64x - 80 = 0
2 (3x²-32x--40) = 0
Divide both sides by the same factor
2 (3x²-32x--40) = 0
3x² - 32x - 40 = 0
Use the quadratic formula (Not explainin this, I forgot this one.)
Simplify
1.Evaluate the exponet
2.Mulitply the numbers
3.Add the numbers
4.Evaluate the sqaure root
5.Mulitply the numbers(Do this 2 more times.)
x = 32±4√94 over 6
Separate the equations
to solve for the unknown varible, separate into two eqautions: one with a plus and another with a minus.
Solve
Rearrange and isolate the varible to find each solution.
Which expression is equivalent
Answer:
10^14
Step-by-step explanation:
The expression (10^2)^7 uses an exponent rule known as power raised to a power.
The rule states that when you multiply a base and its exponent to a power, you multiply the inner exponent and the outer exponent:
[tex](a^m)^n\\a^m^n[/tex]
Thus, we have
[tex](10^2)^7\\10^2^*^7\\10^1^4[/tex]
John has $4,069 in an account. The interest rate is 12% compounded annually. To the nearest cent, how much interest will he earn in 1 year? Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $
After solving the equation: the nearest cent, the interest earned is $467.
What is interest?Interest is a mathematical concept used to describe the cost or gain associated with the use of money over a period of time. It is usually expressed as a percentage rate of the principal (the amount borrowed or invested). Interest can be earned or paid, depending on the situation.
Using the formula B=p(1+r)t, John's final balance after 1 year is B = 4069(1+0.12)1 = $4,536.28.
The interest earned in 1 year is the difference between the final balance and the starting amount, which is $4,536.28 - $4,069 = $467.28. To the nearest cent, the interest earned is $467.
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A line pae through the origin and through point A(−2, b í 14) and B(14 í b, 72). What i the greatet poible value of b?
The greatest poible value of b is (72-14)/(14-(-2))×(x+2)+14.
What is possible value?Possible value is the potential for something to have a particular outcome, result, or consequence. It is the amount of beneficial or desirable result that can be achieved, given the available resources. Possible value is often determined by assessing various factors such as cost, risk, and time. It is an important concept in economics, finance, and business, as it helps to identify the most beneficial course of action.
The greatest possible value of b is found by solving the equation of the line through A and B, which is y = (72-14)/(14-(-2))×(x+2)+14.
Setting the y-value to 0 and solving for x gives x = -14, which means b = 14. Therefore, the greatest possible value of b is 14.
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What are the 5 operations of functions?
The 5 operations of functions are
1. Input
2. Processing
3. Output
4. Storage
5. Maintenance
Input: When a function is used, it takes in an input value. This input value is used to compute the output. For example, if a function is used to calculate the area of a circle, the input would be the radius of the circle.
Processing: Once the input value is taken, the function will use the input to perform some type of operation on it. For example, if the function is used to calculate the area of a circle, the operation would be to multiply the input by itself and then multiply it by the constant pi.
Output: The output of a function is based on the input. For example, if the function is used to calculate the area of a circle, the output would be the area of the circle.
Storage: Once the output of a function is computed, it can be stored for later use. This allows the same output to be used multiple times without having to recalculate the output.
Maintenance: Functions need to be maintained and updated over time. This can include updating the input, operation, and output, as well as any additional changes that might be needed. This ensures the function is up-to-date and still provides accurate results.
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Make q the subject of the formula 2(q + p) = 1 + 5q Give your answer in the form ap-b where a, b and c are all positive integers.
[tex]2(q+p)=1+5q\implies 2q+2p=1+5q\implies 2q+2p-5q=1 \\\\\\ 2q-5q=1-2p\implies q(2-5)=1-2p\implies -3q=-2p+1 \\\\\\ q=\cfrac{-2p + 1}{-3}\implies q=\cfrac{2}{3}p-\cfrac{1}{3}[/tex]
Answer:
Step-by-step explanation: 2(q+p)=1+5q
2q+2p=1+5q
2q-5q=1-2p
-3q=1-2p/:(-3)
q=-1/3+2/3 p
A frictionless pendulum is pulled 3 feet to one side of its center resting point…
A. The amplitude of the sinusoidal function 's' would increase.
B. The midline of the sinusoidal curve will upshift.
What is a periodic function?A function that repeats its values at regular intervals is said to be periodic. For instance, periodic functions include trigonometric functions, which repeat every 2 pi radian. In science, periodic functions are used to describe oscillations, waves, and other periodic events. Aperiodic refers to any nonperiodic function.
We know the moving mechanism of the pendulum can be graphed as a periodic function.
A. If the pendulum is pulled farther away from its resting point it will reach a greater height on both sides this would have an effect of an increase in the amplitude of the sinusoidal curve.
B. If the pendulum is pulled farther away from its resting point the midline of the sinusoidal curve would move up along the y direction as a result of an increase in magnitude.
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What type of graph is absolute value?
On [0,∞] the function grows, whereas on [-∞, 0], it shrinks. f has absolute minimum value is 0, and it also has the same relative minimum value (0,0).
What does an absolute value graph look like?On the graph, you are able to see a "open circle" at it when x< 0. (0, 0).
This is due to the fact that, as we've previously demonstrated, the points at y = x approaching (0, 0) as the x-values approach 0.Since x needs strictly be less than zero on only this stretch, the open circle being drawn in its place.When x ≥ 0, a point in (0, 0) is plugged in, thus "plugging" the hole shown by either open circle.Therefore, we get:On [0,∞] the function grows, whereas on [-∞, 0], it shrinks. Function f absolute minimum value is 0, and it also has the same relative minimum value (0,0).F has absolute minimum value is 0, and it also has the same relative minimum value (0, 0). F's highest relative value is zero.There consequently no absolute maximum value of f due to the graph's infinitely high y values.
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Someone help please, picture attached
Answer:
6
Step-by-step explanation:
x² + 8² = 10²
x² + 64 = 100
x² = 36
x = 6
I need this ASAP!
( Fractions and whole numbers)
Answer:
C. [tex]4\frac{2}{3}[/tex]
Step-by-step explanation:
One way of approaching this problem is to multiply the numbers the numerators together and then divide by the denominator to receive the quotient and the remainder.
Firstly 6 can be written as a fraction like so: [tex]\frac{6}{1}[/tex] because 6 divided by 1 is equal to 6.
To multiply two fractions together, we simply multiply the numerators and multiply the denominators:
[tex]\frac{7}{9}* \frac{6}{1} =\frac{7*6}{9*1}[/tex]
Which gives us the improper fraction of: [tex]\frac{42}{9}[/tex]
Next, we find the highest multiple of 9 which is smaller than 42. If we write out the multiples of 9 we will find that it is 36:
1x9=9, 2x9=18, 3x9=27, 4x9=36, 5x9=45
Since we know that at least 4 whole 9s go into 42 we can conclude that the coefficient of the fraction will be 4.
To find the fraction itself, we must find the remainder which we can do by subtracting 36 from 42: 42-36 = 6
The remainder is the numerator of the fraction as there are 6 ninths left over after we have divided 42 by 9.
Therefore our answer is [tex]4\frac{6}{9}[/tex]
If we divide 6 and 9 by 3 we will find that 6/9 is equivalent to 2/3 therefore our final answer is [tex]4\frac{2}{3}[/tex].
Option C is correct.
A piece of paper is folded into thirds multiple times. The area, A, of the piece of
paper in square inches, after n folds, is A=90(1/3)^n.
How many folds are needed before the area is less than 1 square inch?
The paper is folded into 5 folds before the area is less than 1 square inches.
What is area?
Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Here the area of the folded paper after n folds is,
A = 90[tex](\frac{1}{3})^n[/tex]
Now put n=0 into given formula,
A = 90[tex](\frac{1}{3})^0[/tex]=90×1 = 90 square inches.
Here Area of the paper before being fold is 90 square inches.
Now area is less than 1 square inches then
=> 90[tex](\frac{1}{3}) ^n[/tex] < 1
=> [tex](\frac{1}{3}) ^n < \frac{1}{90}[/tex]
Here if n= 4 then [tex](\frac{1}{3}) ^4 > \frac{1}{90} = \frac{1}{81} > \frac{1}{90}[/tex] then n=5.
Hence the paper is folded into 5 folds before the area is less than 1 square inches.
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You lose 0.3 point for stepping out of bounds during a gymnastics floor routine. Your final score is 9.124. Write and solve an equation to find your score x without the penalty.
The equation is x + 0.3 = 9.124 and the value of x is 8.824.
The following is a linear equation in one variable. It can be expressed in the form of ax+b=0. Here a and b are integers and x is a variable that has only one solution. In these type of equations only one variable is present.
We can write an equation to find the score without the penalty by using the information provided. Let x be the score without the penalty. We know that the final score (with the penalty) is 9.124 and that the penalty is 0.3 points. Therefore, we can set up the equation:
x + 0.3 = 9.124
To find the score without the penalty, we need to subtract 0.3 from both sides of the equation:
x = 9.124 - 0.3
x = 8.824
So, the score without the penalty is 8.824
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Evaluate the expression 2a+3d
Answer:
Step-by-step explanation:
Nothing further can be done with this topic
So, your answer would have to be 2a+3d
PLS PLS HELP ASAP!!! ILL GIVE BRAINIEST AND 50 POINTS!!!
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by AAS
Answer:
F and C
Step-by-step explanation:
CUZ AAS means angle angle side
Answer:
see explanation
Step-by-step explanation:
for the triangles to be congruent by the angle- side- angle (ASA postulate )
if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle ( included side is the side between the vertices of the two angles ) , then the triangles are congruent.
given
∠ B ≡ ∠ D and AB ≡ PD
then the included sides are AB and PD
the other 2 angles for congruency are ∠ A ≡ ∠ P
-----------------------------------------------------
By the AAS postulate
If two angles and a non included side of one triangle are congruent to the corresponding parts of the other triangle, then the triangles are congruent
for AAS then ∠ C ≡ ∠ F
Please help!! Find the area of the circle use 3.14 for pi
Answer:
when pi = 3.14, A = 63.535
when pi = pi, A = 63.61725
Step-by-step explanation:
Area of a circle = pi × radius (4.5) squared (^2)