Using the Mean Value Theorem, we have proven that √(6a+3) < a + 2 for all a > 1.
To prove √(6a+3) <a + 2 for all a > 1 using the Mean Value Theorem, we will begin by defining a function f(x) as:
f(x) = √(6x+3)
We can see that f(x) is a continuous and differentiable function for all x > -1/2.
Now, let's choose two values of a, such that a > 1 and b = a + h, where h is a positive number. By the Mean Value Theorem, there exists a value c between a and b such that
f(b) - f(a) = f'(c)(b-a)
where f'(c) is the derivative of f(x) evaluated at c.
Now, let's evaluate the derivative of f(x) as:
f'(x) = 3/(√(6x+3))
Thus, we can write
f(b) - f(a) = f'(c)(b-a)
√(6(a+h)+3) - √(6a+3) = f'(c)h
Dividing both sides by h and taking the limit as h → 0, we get
lim h→0 (√(6(a+h)+3) - √(6a+3))/h = f'(a)
Now, we can evaluate the limit on the left-hand side using L'Hopital's rule
lim h→0 (√(6(a+h)+3) - √(6a+3))/h = lim h→0 [3/(√(6(a+h)+3)) - 3/(√(6a+3))] = 3/(2√(6a+3))
Therefore, we have
f'(a) = 3/(2√(6a+3))
Now, we can use this value to rewrite the inequality as
√(6a+3) - (a + 2) < 0
Multiplying both sides by 2√(6a+3) and simplifying, we get
3 < 4a + 2√(6a+3)
Subtracting 4a from both sides and squaring, we get
9 < 16a^2 + 16a + 24a + 12
Simplifying, we get
0 < 16a^2 + 40a + 3
This inequality holds for all a > 1, so we have proved that
√(6a+3) < a + 2 for all a > 1.
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The given question is incomplete, the complete question is:
Use Mean value theorem to prove √(6a+3) <a + 2 for all a > 1. Using methods other than the Mean Value Theorem will yield
Please Help. All I have been getting is bot answers, and I actually need help with this. Thanks.
1. Two neighbors are each hosting a party. The first neighbor orders 5 large pizzas, each with a diameter of 16 inches. The second neighbor orders 9 small pizzas, each with a diameter of 12 inches. In terms of area, which party has more pizza? Explain. Show all work.
2. A toy train set has a circular track piece. The inner radius of the piece is 6 cm. One sector of the track has an arc length of 33 cm on the inside and 55 cm on the outside. What is the width of the track?
1. The second party has more pizza in terms of area
2. The width of the track is approximately 3.50 cm.
How to find which party has more pizza?1. To compare the amount of pizza between the two parties, we need to find the total area of each set of pizzas. We can use the formula for the area of a circle, A = πr², where r is the radius of the circle.
For the large pizzas, the diameter is 16 inches, so the radius is 8 inches. The area of one pizza is:
A = π(8)²
A = 64π square inches
Since there are 5 pizzas, the total area of pizza for the first party is:
Total area = 5(64π) = 320π square inches
For the small pizzas, the diameter is 12 inches, so the radius is 6 inches. The area of one pizza is:
A = π(6)²
A = 36π square inches
Since there are 9 pizzas, the total area of pizza for the second party is:
Total area = 9(36π) = 324π square inches
Therefore, the second party has more pizza in terms of area.
How to find width of the track?2. We can start by finding the length of the arc of the sector. We know that the arc length on the inside is 33 cm, so the angle of the sector can be found using the formula:
angle = (arc length / radius)
angle = (33 / 6) radians
To find the width of the track, we need to subtract the length of the inner circle from the length of the outer circle, and then divide by the angle of the sector. Let's call the width of the track "x". Then we have:
55 cm - 33 cm = 2π(6 cm + x) - 2π(6 cm)
22 cm = 2πx
x = 11 / π cm
So the width of the track is approximately 3.50 cm.
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The function f(x)=8x+3x^−1 has one local minimum and one local maximum.
This function has a local maximum at x= With a value of =
This function has a local minimum at x = With a value of =
The function f(x) = 8x + 3x^(-1) has a local maximum at x = 2 with a value of f(2) = 19, and a local minimum at x = -2 with a value of f(-2) = -19.Explanation:
To find the local extrema of a function, we need to find the critical points of the function, which are the points where the derivative is either zero or undefined. In this case, the derivative of f(x) is f'(x) = 8 - 3x^(-2), which is undefined at x = 0.Setting the derivative equal to zero, we get:8 - 3x^(-2) = 0Solving for x, we get:x = ±2
These are the critical points of the function. To determine whether each critical point is a local maximum or a local minimum, we need to examine the second derivative of the function.
The second derivative of f(x) is f''(x) = 6x^(-3), which is negative for x > 0 and positive for x < 0.Therefore, x = 2 is a local maximum of the function with a value of f(2) = 19, and x = -2 is a local minimum of the function with a value of f(-2) = -19. These are the only local extrema of the function, since the function is increasing for x < -2 and decreasing for -2 < x < 0, and then increasing again for x > 0.
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Fred goes to Old Navy and buys two pairs of jeans for $17. 99 each, three shirts at $5. 99 each, and a pack of socks for $3. He has a coupon for 25% off his entire purchase. Sales tax is 6. 5%. What is the total cost after the discount and tax?
A: $43. 07
B: $39. 95
C: $45. 49
D: $60. 65
The total cost after discount and tax is $46.28.
To find the total cost after the discount and tax, we need to first find the subtotal before tax.
Fred bought two pairs of jeans for $17.99 each, so the cost of the jeans is $17.99 x 2 = $35.98.
He also bought three shirts at $5.99 each, so the cost of the shirts is $5.99 x 3 = $17.97.
The pack of socks costs $3.
The subtotal before discount is $35.98 + $17.97 + $3 = $57.95.
With the 25% off coupon, Fred gets a discount of $57.95 x 0.25 = $14.49.
The new subtotal after discount is $57.95 - $14.49 = $43.46.
Finally, we need to add the 6.5% sales tax.
The sales tax is $43.46 x 0.065 = $2.82.
The total cost after discount and tax is $43.46 + $2.82 = $46.28.
Therefore, the closest answer is C: $45.49.
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A cross section of the cylinder with the cone removed is a ring. To find the area of the ring, find the area of the outer circle and of the inner circle. Then subtract the area of the inner circle from the outer circle.
The area of the outer circle and of the inner circle is : πr² and, πx².
Then subtract the area of the inner circle from the outer circle is :
π (r - x) (r+x)
Here, we have,
Given:
Let the radius of outer circle i.e CA be r
Let the radius of inner circle i.e CB be x
The diagram is given below as attachment.
We know that,
area of circle = πR²
Then subtract the area of the inner circle from the outer circle is:
The area of the outer circle - area of the inner circle
= πr² - πx²
= π (r² - x²)
=π (r - x) (r+x)
So, we get
Then subtract the area of the inner circle from the outer circle is:
π (r - x) (r+x)
Hence, The area of the outer circle and of the inner circle is : πr² and, πx².
Then subtract the area of the inner circle from the outer circle is :
π (r - x) (r+x)
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The area of the region under the curve of a function f(x)= ax+b on the interval [0,4] is 16 square units. (A,b) ≠
There are infinitely many solutions to this equation. For example, one possible solution is a = 2, b = 0. Another possible solution is a = 1, b = 2.
How to find the area?To find the area, we need to use the definite integral formula to calculate the area under the curve:
∫[0,4] f(x) dx = ∫[0,4] (ax + b) dx = 1/2 * a * x² + b * x |[0,4]
Substituting the limits of integration, we get:
1/2 * a * 4² + b * 4 - (1/2 * a * 0² + b * 0) = 16
Simplifying, we get:
8a + 4b = 16
Dividing by 4, we get:
2a + b = 4
Since (a,b) ≠ (0,0), there are infinitely many solutions to this equation. For example, one possible solution is a = 2, b = 0. Another possible solution is a = 1, b = 2.
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Fill in the boxes 3(n+7) = (3)( ) + (3)( ) = +
the final result will be 3n + 21
what is ditribustion propety?
The Distributive Property is a mathematical property that states that when a single term is multiplied by a sum or difference, the result can be expressed as the sum or difference of the products of the term multiplied by each term inside the parentheses. It is often used to simplify expressions and equations in algebra. 3(x + 2) = 3x + 32 (distributing the 3 over the parentheses) = 3x + 6 (simplifying the products) This property is very useful when dealing with expressions containing variables or unknowns, as it allows us to simplify complex expressions and solve equations more easily.
using distribution propety
3(n + 7)
= (3)(n) + (3)(7)
= 3n + 21
Hence the final result will be 3n + 21
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A semi-elliptic archway has a height of 15 feet
at the center and a width of 50 feet, as shown
in the figure. The 50-foot width consists of a
two-lane road. Can a truck that is 12 feet high
and 14 feet wide drive under the archway
without going into the other lane?
Since 1.1584 > 1, the truck cannot pass under the archway without going into the other lane.
A semi-elliptic archway with a height of 15 feet at the center and a width of 50 feet can be visualized as half of an ellipse.
The major axis of the ellipse corresponds to the width, while the minor axis corresponds to the height. In this case, the major axis (a) is 25 feet, and the minor axis (b) is 15 feet.
To determine if a truck that is 12 feet high and 14 feet wide can drive under the archway without going into the other lane, we can use the equation of an ellipse: (x²/a²) + (y²/b²) = 1.
The truck will occupy half of the road width, which is 25 feet, so its horizontal distance from the center (x) is 25 - 7 = 18 feet, and its height (y) is 12 feet.
Plugging these values into the equation, we get: (18²/25²) + (12²/15²) = (324/625) + (144/225) ≈ 0.5184 + 0.64 = 1.1584.
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Jane completed 8 homework problems in class. The function p(m) relates the
time (in minutes) Jane spent on her homework at home to the total number
of problems she completed. The input is the number of minutes worked. The
output is the number of problems completed.
p(m)= m/5+8
Which equation represents the inverse function m(p), which uses problems
completed as the input and gives minutes worked as the output?
Answer:
Step-by-step explanation:
5p-40
The library in natchitoches had about 60000 volumes in march 2004 and was adding about 400 volumes per month Write an equation expressing y, the total number of volumes in the library, in terms of x, the number of mouths after march 2004
The equation expressing y, as the total number of volumes in the library, in terms of x, the number of mouths after march 2004 is y = 400x + 60,000.
What is the equation for the volumes in library?The equation expressing y, as the total number of volumes in the library, in terms of x, the number of mouths after march 2004 is determined as follows;
Using general linear equation;
y = mx + b
where:
y is the total number of volumes in the libraryx is number of months after March 2004m is the rate of change b is the initial number of volumes in the library in March 2004The initial volume as at March = 60,000
the rate = 400 volumes / month
The equation is determined as;
y = 400x + 60,000
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A teacher asked three different students to write the conditions that would result in a triangle. Which of the following students listed conditions that would result in more than one triangle?
The condition that will result in more than one triangle is C. Student III.
How the conditions will result in more than one triangleThe conditions listed by the third student will result in more than one triangle because we are given all three angles. As a rule in math, some conditions will determine if there is more than one triangle. One of them is this:
Rule 1:
If all three angles of the triangle are given and they all add up to exactly 180°, it is possible to get more than one triangle. In the third option, we are given angles 62°, 36°, and 82°, so different triangles can be constructed. Also, they all add up to give 180°. The condition is satisfied.
Rule 2:
Also, as a rule, if we have two angles that do not add up to 180° and one side, then only one unique triangle can be obtained. This is the case for student A who is given angles A and B and a side length of 5cm. (ASA)
Rule 3:
Student 2 will also produce a unique triangle because there are three sides that meet the triangle inequality theorem. (SSS)
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Jay has five fewer $100 bills in his wallet than $50 bills. If he has only $50 and $100 bills in his wallet, and the total amount of money in his wallet is $1300, let’s find the number of notes of each denomination.
Let’s assume the number of $50 bills as x. So, in terms of x, the number of $100 notes can be represented as ____.
Now, the total amount contributed by $50 notes is $50x
And. The total amount contributed by $100 bills is $100×( ____ )
Jay has 7 $100 bills in his wallet.
Let's assume the number of $50 bills as x. So, in terms of x, the number of $100 notes can be represented as x - 5.
Now, the total amount contributed by $50 notes is $50x.
And the total amount contributed by $100 bills is $100*(x-5).
Since the total amount of money in his wallet is $1300, we can write an equation:
$50x + $100*(x-5) = $1300
Simplifying this equation, we get:
$50x + $100x - $500 = $1300
$150x = $1800
x = 12
So, Jay has 12 $50 bills in his wallet.
Using the earlier equation, the number of $100 bills can be found:
x - 5 = 12 - 5 = 7
Therefore, Jay has 7 $100 bills in his wallet.
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Find the properties for the ellipse with the equation x^2/169 + y^2/144 = 1
latus rectum =
a. 288/13
b. 328/12
c. 288/12
The latus rectum of an ellipse is 288/13 when the ellipse equation is given as [tex]x^2/169 + y^2/144 = 1[/tex]. Option A is correct.
The standard form of an ellipse equation is given as
[tex](x2/a2) + (y2/b2) = 1[/tex]
where :
a = lengths of the semi-major axes
b = length of semi-minor axes
The length of the chord through one of the foci that are perpendicular to the major axis is defined as the latus rectum of an ellipse.
From the given data the equation of the ellipse is given as :
x² / 169 + y² / 144 = 1
By comparing the standard equation and the given equation of the ellipse we get :
a² = 169
a = √169
[tex]a = 13[/tex]
b² = 144
b = √144
[tex]b = 12[/tex]
The distance between the center and one of the foci is given by
c = √(a² - b²)
= √(13² - 12²)
= 5
We can find the latus rectum by substuting a and b values in the latus rectum of an ellipse formula,
= 2×b²/a
= 2 × 12² / 13
= 288/13
Therefore, the latus rectum of an ellipse is 288/13.
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El mastil de un velero se halla unido a la proa y a la popa por dos cables que forman con la cubierta, angulo de 45 grados y 60 grados, respectivamente. si el barco tiene una longitud de 25m, ¿cual es la altura del mastil?
La altura del mástil es de aproximadamente 20.87 metros.
How to find mast height?Para resolver el problema, se puede utilizar la ley de cosenos para encontrar la longitud del mástil:
c² = a² + b² - 2ab cos C
Donde:
c es la longitud del mástil (lo que se busca)
a es la longitud de la parte delantera del barco (25m)
b es la longitud de la parte trasera del barco (también 25m)
C es el ángulo entre a y b, que se puede calcular utilizando la tangente: tan C = 1.5 (pues tan 60° = √3, y tan 45° = 1)
Resolviendo para c:
c² = 25² + 25² - 2(25)(25)cos(arctan 1.5)
c = √(25² + 25² - 2(25)(25)(1/√(1+(1.5)²)))
c ≈ 31.08 m
Por lo tanto, la altura del mástil es de aproximadamente 31.08 metros.
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A rhombus has a perimeter of 88 and
two acute angles that measure 40° each.
Find the length of the shorter diagonal.
PLEASE HELP ME ASAP
The length of the shorter diagonal is approximately 7.07 units.
A rhombus is a four-sided polygon in which all sides are equal in length. It is also called a diamond shape because it is often used for diamond-shaped figures. In this case, we are given that the perimeter of the rhombus is 88. Since all sides of the rhombus are equal, we can divide the perimeter by 4 to find the length of one side.
88 ÷ 4 = 22
Therefore, each side of the rhombus measures 22 units.
We are also given that two of the angles in the rhombus are acute angles measuring 40° each. Since all angles in a rhombus are equal, we can find the measure of the other two angles by subtracting the sum of the acute angles from 360.
360 - 2(40) = 280
Each of the other two angles measures 140°.
To find the length of the shorter diagonal, we can use the formula:
Shorter diagonal = (2 × Area) / Length of longer diagonal
The area of a rhombus can be found by multiplying the length of the longer diagonal by the length of the shorter diagonal and then dividing by 2.
Area = (diagonal1 × diagonal2) / 2
We know that the longer diagonal is twice the length of the shorter diagonal.
Longer diagonal = 2 × Shorter diagonal
Substituting these values into the formula, we get:
Shorter diagonal = (2 × (22 × Shorter diagonal × sin 40°)) / (2 × Longer diagonal)
Simplifying, we get:
Shorter diagonal = (22 × Shorter diagonal × sin 40°) / Longer diagonal
Plugging in the values we know, we get:
Shorter diagonal = (22 × Shorter diagonal × sin 40°) / (2 × Shorter diagonal)
Shorter diagonal = 11 × sin 40°
Using a calculator, we can find that:
Shorter diagonal ≈ 7.07
Therefore, the length of the shorter diagonal is approximately 7.07 units.
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Determine the intercepts of the line.
Do not round your answers.
5x − 9 = −8y − 3
Please help
The intercepts of the line are (6/5, 0) and (0, -3/4).
We have,
To find the x-intercept, we need to set y = 0 and solve for x:
5x - 9 = -3
5x = 6
x = 6/5
So the x-intercept is (6/5, 0).
To find the y-intercept, we need to set x = 0 and solve for y:
-9 = -8y - 3
8y = -6
y = -3/4
So the y-intercept is (0, -3/4).
Therefore,
The intercepts of the line are (6/5, 0) and (0, -3/4).
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Pls answer this asap
Answer:
(C) Neither
Step-by-step explanation:
You want to know if the function values in the table represent an even function, and odd function, or neither.
SymmetryAn Even function is symmetrical about the y-axis:
f(-x) = f(x)
An Odd function is symmetrical about the origin:
f(-x) = -f(x)
ApplicationThe attached graph of the given points shows the function has no symmetry at all.
The table represents neither an even nor odd function.
Answer:
Neither
Step-by-step explanation:
In an even function, f(x) = f(-x).
Look at x = 2 and x = -2.
f(2) = -4; f(-2) = 2
Since f(2) ≠ f(-2), the function is not even.
In an odd function, f(x) = -f(-x).
Look at f(2) and f(-2).
f(2) = -4; f(-2) = 2
Since f(2) ≠ -f(-2), the function is not odd.
Answer: C Neither
how does the area of a rectangle help you find the area of a triangle, rhombus, and parallelogram???
The area of a rectangle can be used to find triangle, rhombus and parallelogram since the shapes are related to one another
How does the area of a rectangle help you find the area of a triangle, rhombus, and parallelogram?The area of a rectangle can be used to determine the area of a triangle, rhombus and parallelogram because these figures are somewhat similar to a rectangle.
When we join two triangles together at opposite end or we cut transversally between a rectangle from the diagonal, we would have two triangle.
When a rhombus is split across it's diagonal, it will produce two congruent triangles.
When a parallelogram is divided across it's diagonals, it produces two congruent triangles.
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What is the circumference of the following circle?
Use 3.14 for πpi and enter your answer as a decimal.
The calculated value of the circumference of the circle is 31.4 units
What is the circumference of the following circle?From the question, we have the following parameters that can be used in our computation:
Radius, r = 5
Using the above as a guide, we have the following:
Circumference = 2 * π * r
Substitute the known values in the above equation, so, we have the following representation
Circumference = 2 * 5 * 3.14
Evaluate the products
Circumference = 31.4
HEnce, the value of the circumference is 31.4 units
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If a data set has many very large data values, then the mean wil be
the median
a larger than
b. the same as
c. equal to
d. smaller than
A data set has many very large data values, then the mean will be larger than the median. The correct option is a.
In a dataset with large values, the mean is influenced by outliers and extreme values, whereas the median is not. The median is the value that divides the data into two equal halves, while the mean is calculated by summing up all values and dividing by the total number of values.
Thus, in a skewed dataset with large values, the mean tends to be pulled towards the larger values, resulting in a larger mean than the median. This effect is more pronounced in datasets with a high variance. Therefore, option (a) is the correct answer.
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a repair shop charges per hour the amount of money they charge is below what equation does the repair shop use.
1 $70 Here are the answers i can chose from
c= 30h+ 40 C= 40h+30 C=30h+70 C= 40h
h is for hours and c is for charge
2 $100
3 $130
4 $160
5 $190
6 $220
The linear function for the repair cost is given as follows:
C(h) = 30h + 40.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.Each hour the cost increases by $30, hence the slope m is given as follows:
m = 30.
Hence the function is:
C(h) = 30h + b
When h = 2, C = 100, hence the intercept b is given as follows:
60 + b = 100
b = 40.
Then:
C(h) = 30h + 40.
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The answer to this math problem please.
Answer:
C) 6
Step-by-step explanation:
n=6
6( 6 + 1) + 3 =45
36 + 6 + 3 = 45
36 + 9 = 45
Given that 3 is a primitive root modulo 25; Find a primitive root modulo 250
The primitive root modulo 250 is 103, as 3 is a primitive root modulo 25 we tested if it is also a primitive root modulo 250.
To find a primitive root modulo 250, we need to first factor 250 as 2 x 5³. Since 3 is a primitive root modulo 25, we can test if it is also a primitive root modulo 250.
Using Euler's totient function, we know that [tex]\phi(250)[/tex] = 100. Therefore, we only need to check if [tex]3^{20[/tex] (which is [tex]3^{\phi(250)/2[/tex]) is congruent to -1 modulo 250.
Calculating [tex]3^{20[/tex] modulo 250 gives us 1. Since [tex]3^{20[/tex] is not congruent to -1 modulo 250, 3 is not a primitive root modulo 250.
To find a primitive root modulo 250, we can use a common method called the "index cycling" method. We can start with a primitive root modulo 5³ = 125 and then test the other primitive roots modulo 2³ = 8 until we find a primitive root modulo 250.
Using a computer or calculator, we can find that 2 is a primitive root modulo 125. To find a primitive root modulo 250, we can test the numbers 2, 2 + 125, 2 + 2125, and 2 + 3125 until we find a primitive root.
Testing these numbers, we find that 2 + 3*125 = 377 is a primitive root modulo 250. Therefore, 377 is a primitive root modulo 250.
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y = 49 - 4x y = 73 - 7x
The solution of the system of equation
x = 8 and y = 17
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's solve the system of equation by substitution method.
Therefore,
y = 49 - 4x
y = 73 - 7x
Hence, using substitution,
73 - 7x = 49 - 4x
73 - 49 = -4x + 7x
24 = 3x
divide both sides of the equation by 3
x = 24 / 3
x = 8
Therefore,
y = 73 - 7(8)
y = 73 - 56
y = 17
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Researchers pose a question can pant sizes be predicted from a man's height? A random sample of 20 males and their pant size versus height
Answer:
Yes, there is evidence at the 10% significance level, but not at the 5% level
Step-by-step explanation:
Look at the p-value in bottom left corner (in the Height row).
It is less than 0.1, but greater than 0.05. Thus, Yes, there is evidence at the 10% significance level, but not at the 5% level. Got it right.
Esteban has `3` kittens. According to the vet, each kitten is born with blue eyes and there is a `50\%` chance of it changing color once they reach three months.
Esteban decides to run a simulation using `3` coins, where heads represent the eyes changing color.
The table shows the results of his simulation.
Estimate the probability that at least one of Esteban’s kittens will still have blue eyes at three months old
There is an estimated probability of 0.875 (or 87.5%) that at least one of Esteban's kittens will still have blue eyes at three months old.
Let's use the complement rule to estimate the probability that at least one kitten will still have blue eyes at three months old:
P(at least one kitten with blue eyes) = 1 - P(no kitten with blue eyes)
To estimate P(no kitten with blue eyes), we can use the results of Esteban's simulation. We can see from the table that all three coins came up tails (representing no color change) in row 8, so that's one outcome where no kitten has blue eyes. There are a total of 2^3 = 8 possible outcomes, so the estimated probability of no kitten having blue eyes is:
P(no kitten with blue eyes) = 1/8 = 0.125
Therefore, the estimated probability that at least one kitten will still have blue eyes at three months old is:
P(at least one kitten with blue eyes) = 1 - P(no kitten with blue eyes) = 1 - 0.125 = 0.875
So, there is an estimated probability of 0.875 (or 87.5%) that at least one of Esteban's kittens will still have blue eyes at three months old.
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Keshia is working on a math worksheet with 50 problems she has completed 20 problems in 25 mins if she continue at this pace what will be her total time for her compete worksheet
It will take Keshia 62.5 minutes to complete the entire worksheet at the same pace.
To find the amount of total time it will take Keshia to complete the entire worksheet at the same pace, we can use a proportion:
20 problems / 25 minutes = 50 problems / x minutes
To solve for x, we can cross-multiply and simplify:
20 problems * x minutes = 25 minutes * 50 problems
20x = 1250
x = 1250 / 20
x = 62.5
Therefore, it will take Keshia 62.5 minutes to complete the entire worksheet at the same pace.
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Subtract 1/4- 5/14 = type an integer or fraction
Answer:
-3/28
Step-by-step explanation:
In order to subtract fractions you first have to get a common denominator. The common denominator between 4 and 14 is 28 since 4(7) = 28 and 14(2) = 28. Then multiply the top and bottom of (1/4) by (7/7) and (5/14) by (2/2). This gives a common denominator and since you multiply by a fraction equal to 1, it doesn't change the value. Therefore, we get 7/28 - 10/28 = -3/28.
Review Questions
1. A washer and a dryer cost $1004 combined. The washer costs $54 more than the dryer. What is the cost of the dryer?
Please use your work.
The calculated cost of the dryer is $475.
What is the cost of the dryer?Let's assume that the cost of the dryer is x dollars.
According to the problem, the cost of the washer is $54 more than the dryer.
Therefore, the cost of the washer is (x + $54).
We are given that the combined cost of the washer and the dryer is $1004. So we can set up the equation:
x + (x + $54) = $1004
Simplifying the equation:
2x + $54 = $1004
2x = $950
x = $475
Therefore, the cost of the dryer is $475.
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What is the cost of 0. 7 kg of apples, if 1 kg of apples cost 89. 50
In the proportion, the cost of 0.7kg apple is Rs.62.65 .
What is proportion?
A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.
Here cost of 1kg apples = 89.50
Then cost of 0.7 kg apple = x.
Now using proportion,
=> 1 = 89.50
0.7= x
=> x = [tex]\frac{89.50\times0.7}{1}[/tex]
=> x = 62.65.
Hence the cost of 0.7kg apple is Rs.62.65 .
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What is the max/min of the quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7)? Is it a maximum or a minimum? Show your workor explain your reasoning.
The quadratic equation in factored form: f(x) = 0. 5(x+3)(x-7) have a minimum point. The minimum value of the function is -11.
To find the maximum or minimum of the quadratic equation in factored form f(x) = 0.5(x+3)(x-7), we need to convert it to standard form by expanding the terms:
f(x) = 0.5(x² - 4x - 21)
f(x) = 0.5x² - 2x - 10.5
The coefficient of x² is positive, so the parabola opens upwards and we have a minimum point.
To find the x-coordinate of the minimum point, we can use the formula x = -b/2a, where a = 0.5 and b = -2:
x = -(-2)/2(0.5) = 2
So the minimum point is at x = 2. To find the y-coordinate, we can substitute x = 2 into the equation:
f(2) = 0.5(2)^2 - 2(2) - 10.5 = -11
Therefore, the minimum value of the function is -11.
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