The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.
How do you find a middle term?When expanding a binomial expression in the form of (a + b)ⁿ, the middle term can be found using the following formula:
Middle term coefficient = nC(k), where k = (n+1)/2 if n is odd, and k = n/2 or (n/2 + 1) if n is even. The middle term coefficient is then multiplied by the product of a raised to the power of (n-k) and b raised to the power of k.
The difference of squares pattern is a special algebraic pattern that arises when we factor a polynomial that is the difference between two perfect squares. For example,
x² - y² = (x+y)(x-y)
When we apply this pattern to the expression w - 121, we can rewrite it as:
w² - 11²
And, we can use the difference of squares pattern to factor it as:
(w + 11)(w - 11)
Notice that there is no middle term with a variable in this factorization. This is because when we multiply (w + 11)(w - 11), the middle term cancels out.
To see why this happens, let's expand the product:
(w + 11)(w - 11) = w² - 11w + 11w - 121
The two middle terms, -11w and +11w, cancel each other out, leaving only the first and last terms. This is why there is no middle term with a variable in the factorization of the difference of squares pattern.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The true statements are:
1. The radius of the circle is 3 units
2. The standard form of the equation is (x-1)^2+y^2=3
3. The center of the circle lies on X-axis
4. The radius of this circle is the same as the radius of the circle whose equation is x^2+y^2=9
The given equation is: x^2+y^2-2x-8=0
The equation in the standard form of the circle can be written as (x-h)^2+(y-k)^2=r^2, where h= center of the circle and r= radius of the circle
The given equation in standard form can be written as
(x^2-2x+1)+y^2-9=0
(x-1)^2+y^2=3^2
Hence from the above equation, the center of the circle is at (1,0) and the radius is 3 units.
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the 3rd and 6th term in fibonacci sequence are 7 and 31 respectively find the 1st and 2nd terms of the sequence
Answer:
Step-by-step explanation:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?
Four family members attended a
family reunion. The table below
shows the distance each person
drove and the amount of time each
person traveled.
If each person drove at a constant rate,than Laura drove the fastest
What is the distance ?Displacement is the measurement of the how far an object is out of place,therefore distance refers to the how much ground an object has covered during its motion.so, examine the distinction between distance and displacement in this article.
What is the speed?The means of Speed is :he speed at which an object of location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. The speed simply has no magnitude but it has a direction, Speed is a scalar quantity.
to compute who drove the quickest by Using this formula
speed=Distance /time,
first of all the convert times into hours:
Hank: 3.2 hours x 3 hours and 12 minutes.
Laura: 2.5 hours is 2 hours and 30 minutes.
Nathan: 2.25 hours is 2 hours and 15 minutes.
Raquel: 4 hours plus 24 minutes equals 4.4 hours.
now to calculate the speed by above formula
Hank: 55 miles per hour for 176 miles in 3.2 hours.
Laura: 60 miles per hour equals 150 miles in 2.5 hours.
Nathan: 50 miles per houris equal to 112.5 miles in 2.25 hours.
Raquel: 65 miles for 286 miles in 4.4 hours.
As a result, Laura moved the fastest, clocking in at 60 miles. The solution, Laura, is B.
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$2000 are invested in a bank account at an interest rate of 5 percent per year.
Find the amount in the bank after 7 years if interest is compounded annually.
Find the amount in the bank after 7 years if interest is compounded quaterly.
Find the amount in the bank after 7 years if interest is compounded monthly.
Finally, find the amount in the bank after 7 years if interest is compounded continuously.
The amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
Simple interest calculation.
Using the formula A = P(1 + r/n)^(nt), where:
A = the amount in the account after t years
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
a) If interest is compounded annually:
A = 2000(1 + 0.05/1)^(1*7) = $2,835.08
b) If interest is compounded quarterly:
A = 2000(1 + 0.05/4)^(4*7) = $2,888.95
c) If interest is compounded monthly:
A = 2000(1 + 0.05/12)^(12*7) = $2,905.03
d) If interest is compounded continuously:
A = Pe^(rt) = 2000e^(0.05*7) = $2,938.36
Therefore, the amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
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k^2+6k=0 solve the quadratic equation by factoring
Answer:
K = √-6k
i did the math and got this answer and it was right
Write the absolute value equation that has the following solutions.
One solution: x = 15
The absolute value equation is:
|x - 15| = 0
How to write the absolute value equation?We want an absolute value equation that only has the solution x = 15.
So we must have something equal to zero (so we avoid the problem with the signs that we can have with other numbers)
So the equation will be something like:
|x - a| = 0
And the solution is 15, so:
|15 - a | = 0
then a = 15
The equation is:
|x - 15| = 0
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A Bakery sold 382 cakes in one week. this was twice as the day so the previous week. write an equation that can be used to find the number of cakes and that were sold the previous week 
Answer:
164 Cakes
Step-by-step explanation:
382 Cakes are made in Week A. This was twice the amount of Week B. 328 divided by two equals 164.
Simplify 6^2/6 x 6^12/6^8
Step-by-step explanation:
6^2 / 6^1 x 6^12 / 6^8 =
6^(2-1) x 6^(12-8) =
6^1 x 6^4 =
6^(1+4) = 6^5 or = 7776
Is each number rounded correctly to the nearest hundred thousand?
yes is answer for all option .we can check it by rules of rounding off numbers .
what is rounding ?
Rounding is the process of approximating a number to a nearby value that is easier to work with or more appropriate for a given context. When rounding, we take a number with many decimal places or significant figures and adjust it to a simpler or more convenient value with fewer decimal places or significant figures.
In the given question,
Yes, each number is rounded correctly to the nearest hundred thousand based on the rules of rounding.
To round to the nearest hundred thousand, we look at the digit in the hundred thousand place and the digit to its right (i.e., in the ten thousand place).
If the digit in the ten thousand place is 5 or greater, we round up the digit in the hundred thousand place by adding 1.
If the digit in the ten thousand place is less than 5, we leave the digit in the hundred thousand place as it is.
Using these rules, we can see that:
350000 rounded to the nearest hundred thousand is 400000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
555555 rounded to the nearest hundred thousand is 560000 because the digit in the ten thousand place is 5, so we round up the digit in the hundred thousand place.
137998 rounded to the nearest hundred thousand is 200000 because the digit in the ten thousand place is 7, so we round up the digit in the hundred thousand place.
792314 rounded to the nearest hundred thousand is 800000 because the digit in the ten thousand place is 3, so we leave the digit in the hundred thousand place as it is.
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A four-sided shape with the top side labeled as 10.2 cm. The height is labeled 5 cm. A portion of the base from the perpendicular to a vertex is labeled 4 cm. The portion of the base from the perpendicular to the right vertex is 6.2 cm.
What is the area of the figure?
25.5 cm2
45.5 cm2
51 cm2
56.1 cm2
The area of the figure is 51 cm², which is option C.
What is area?In mathematics, area refers to the measure of the size of a two-dimensional surface or shape. It is typically expressed in square units, such as square meters (m²) or square centimeters (cm²), and can be calculated for a variety of geometric shapes, including squares, rectangles, triangles, circles, and more complex shapes such as trapezoids or polygons.
To find the area of the figure, we need to identify the shape of the figure. From the given information, we know that the figure has a top side, a height, and a base. We are also told that the base is divided into two parts by a perpendicular, and one of the parts is labeled as 4 cm, while the other part from the perpendicular to the right vertex is 6.2 cm.
Based on this information, we can draw the figure as a trapezoid, where the top side is the shorter base, the height is the vertical distance between the two bases, and the longer base is the sum of the two parts of the base.
Using the given information, we can calculate the longer base:
longer base = 4 cm + 6.2 cm = 10.2 cm
Now we can use the formula for the area of a trapezoid to find the area of the figure:
A = (1/2)h(b₁ + b₂)
where h is the height, b₁ is the shorter base, and b₂ is the longer base.
Plugging in the given values, we get:
A = (1/2)(5 cm)(10.2 cm + 10.2 cm) = 51 cm²
Therefore, the area of the figure is 51 cm² , which is option C.
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Complete Question:
A four-sided figure has one side labeled 10.2 cm, a height of 5 cm, and a portion of the base from the perpendicular to a vertex labeled 4 cm. The portion of the base from the perpendicular to the right vertex is labeled 6.2 cm. What is the area of the figure?
Julia drew s sketches of flowers. She split them evenly among her 3 pen pals. Write an expression that shows how many sketches each pen pal received.
Answer:
s/3
Step-by-step explanation:
since she drew s drawings and split them among 3 penpals, it would be s/3, for example, 6 drawings/ 3 would be 2 drawings for each person.
Identify the correct equation of the graph.
-10
O f(b) = (6+4)² +8
O f(b) = (b+8)² +4
Of(b)=(6-8)²-4
O
-5
10
5
-5
-10
V
5
O f(b) = (b-8)² +4
Of(b) = (6-4)²-8
Of(b) (6-4)² +8
10
Check
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
Explain about the quadratic function in vertex form:A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Vertex form of a quadratic function:
f(x) = a(x – h)² + k, where a, h, and k are constants.
The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).
(h,k) are the vertex of parabola.
From the given graph:
f(b) is the given function:
Vertex (h,k) = (8, 4)
Thus, h= 8 and k = a = 1, x = b.
Put the values in quadratic function:
f(b) = 1(b – 8)² + 4
f(b) = (b – 8)² + 4
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
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Jackson has a loyalty card good for a 10% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $27.40? Round to the nearest cent.
Jackson's total cost after the discount and before tax would be $24.67.
Calculating discounted price :When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.
To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).
Here we have
Jackson has a 10% discount at his local hardware store.
Let 'x' be the cost before tax
After a 10% discount,
The amount that Jackson could pay 90% of the cost
Given that he wants to buy $ 27.40
The cost of items after discount = 90% of 27.40
= [ 90/100 ] × 27.40
= [ 0.9 ] × 27.40
= 24.66
Therefore,
Jackson's total cost after the discount and before tax would be $24.67.
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the area of Rectangle is 112 in sq. if the height is 8 in, what is the base length
Answer:
14cm
Step-by-step explanation:
112÷8=14
base length=14cm
Answer:
To find the base length of a rectangle, given its area and height, you can use the formula for calculating the area of a rectangle, which is:
Area = Length x Width
In this case, you are given that the area is 112 square inches and the height is 8 inches. Let's denote the base length as "x" inches.
So, the equation for the area of the rectangle becomes:
112 = x * 8
To solve for "x", you can divide both sides of the equation by 8:
112 / 8 = x
x = 14
Therefore, the base length of the rectangle is 14 inches.
Melissa collected the data in the table.
When x = 4, what is the residual?
–3
–1
1
3
From the data in the table, we can conclude that when x = 4, then the residual will equal -1.
How to determine the residualTo determine the residual, we can begin by obtaining the difference between the given and the predicted values of y.
So, Residual = Gven value - Predicted value.
When x = 4 in the table, Given value is 9 and predicted value is 10. So, 9 - 10 = -1. So, we can say that the residual value is -1.
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Answer:
The residual is the difference between the actual y-value and the predicted y-value on a regression line. Since no table or equation is provided, we cannot calculate the exact residual. However, I can explain the concept to you.
Step-by-step explanation:
In general, to calculate the residual, we would need a regression equation or a line of best fit. This equation allows us to predict the y-values for different x-values. Then, we can compare the predicted values to the actual values given in the table to find the residuals.
If you have the regression equation or the line of best fit, I can help you calculate the residual for a specific x-value.
Helppppppppppppppppppppp
Please help with this math question!
The exponential function of the population is P(x) = 15000 * 1.046^x
Calculating the exponential function of the populationFrom the question, we have the following parameters that can be used in our computation:
Initial, a = 15000
Rate, r = 4.6%
The equation of the function is represented as
P(x) = a * (1 + r)^x
Substitute the known values in the above equation, so, we have the following representation
P(x) = 15000 * (1 + 4.6%)^x
Evaluate
P(x) = 15000 * 1.046^x
Hence, the function is P(x) = 15000 * 1.046^x
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Explain Why 387 is not a term of the sequence
Answer:
In order to determine whether 387 is a term of a sequence, we need to know the rule or formula for generating the sequence. Without this information, it is not possible to determine whether 387 is a term of the sequence or not.
If we assume that the sequence is an arithmetic sequence, where each term is obtained by adding a fixed constant to the previous term, we can use the following formula to determine whether 387 is a term of the sequence:
an = a1 + (n-1)d
where a1 is the first term of the sequence, d is the common difference between consecutive terms, and n is the term we are trying to find.
If we substitute the values for the first few terms of the sequence, we can check whether 387 is a term or not. For example, if the first few terms of the sequence are:
a1 = 3
a2 = 8
a3 = 13
a4 = 18
and so on, with a common difference of 5 between consecutive terms, we can use the formula to find the value of the 129th term of the sequence:
a129 = a1 + (129-1)d
a129 = 3 + 128(5)
a129 = 643
Since 387 is not equal to 643, it is not a term of this sequence. However, without knowing the rule or formula for generating the sequence, it is impossible to say for certain whether 387 is a term or not.
La Suma delos cuadrados de dos números naturales consecutivos es 181 halla dichos numeros
The two consecutive natural numbers whose sum of squares is 181 are 9 and 10
Let's assume that the two consecutive natural numbers are x and x+1. Then, we can write an equation based on the given information:
x² + (x+1)² = 181
Expanding the equation:
x² + x² + 2x + 1 = 181
Combining like terms:
2x² + 2x - 180 = 0
Dividing both sides by 2:
x² + x - 90 = 0
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -90
x = (-1 ± √(1 + 360)) / 2
x = (-1 ± √(361)) / 2
x = (-1 ± 19) / 2
We discard the negative value, as it does not correspond to a natural number:
x = 9
Therefore, the two consecutive natural numbers are 9 and 10, and their sum of squares is 81 + 100 = 181.
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4. The elevation at ground level is 0 feet. An elevator starts 80 feet below ground level. After
traveling for 20 seconds, the elevator is 30 feet below ground level. Which statement describes
the elevator's rate of change in elevation during this 20-second interval?
A. The elevator traveled upward at a rate
1 rate of 2½ feet per second.
B. The elevator traveled downward at a rate of 2 feet per second.
C. The elevator traveled upward at a rate of 4 feet per second.
D. The elevator traveled downward at a rate of 4 feet per second.
a
Answer:
[tex]m = \frac{ - 30 - ( - 80)}{20 - 0} = \frac{50}{20} = 2 \frac{1}{2} [/tex]
A. The elevator traveled upward at a rate of 2 1/2 feet per second. -30 > -80.
Home values in a town have declined 26% per year for each of the past
four years. What was the total percentage decrease in home values
during the four-year period?
Answer: 104%
Step-by-step explanation: 26% times 4 years
Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11. A month later, he bought 4 liters of milk and 4 44 loaves of bread at the same prices, for a total of $10. How much does a liter of milk cost, and how much does a loaf of bread cost?
The cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
What is cost?Cost is the value of goods or services measured in money or other forms of exchange. It is the amount that must be given up in exchange for something else. Costs are typically incurred in the production of goods and services, and can include both tangible and intangible elements, such as labor, materials, overhead, and financing.
The total cost for 3 liters of milk and 5 loaves of bread was $11. Therefore, the cost for 1 liter of milk was ($11 / 3) = $3.67. The cost for 1 loaf of bread was ($11 / 5)
= $2.20.
The total cost for 4 liters of milk and 4 loaves of bread was $10. Therefore, the cost for 1 liter of milk was ($10 / 4) = $2.50. The cost for 1 loaf of bread was ($10 / 4)
= $2.50.
Therefore, the cost of a liter of milk is $2.50 and the cost of a loaf of bread is $2.50.
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Will mark brainliest if answer is correct
Using factorization and simplifying the equations, the points of intersections are (-2, 0), ( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 ) and ( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )
What is the points of intersection of both functionsWe are given two equations:
y = 4x² - 3x + 3
y = x³ + 7x² - 3x + d
and we know that they intersect at x = -4, so we can substitute -4 for x in both equations:
y = 4(-4)² - 3(-4) + 3 = 49
y = (-4)³ + 7(-4)² - 3(-4) + d = -64 + 112 + 12 + d = 60 + d
So, at x = -4, we have y = 49 and y = 60 + d. Since the graphs intersect, these two equations must be equal:
49 = 60 + d
Solving for d, we get:
d = -11
Therefore, the two equations become:
y = 4x² - 3x + 3
y = x³ + 7x² - 3x - 11
We can now set them equal to each other:
4x² - 3x + 3 = x³ + 7x² - 3x - 11
Simplifying and rearranging, we get:
x³ + 3x² - 8x - 14 = 0
We can try to factor this expression by testing possible roots. One possible root is x = 2, because if we substitute 2 for x, we get:
2³ + 3(2)² - 8(2) - 14 = 8 + 12 - 16 - 14 = -10
Since this expression evaluates to a non-zero value, x = 2 is not a root. Similarly, we can test x = -1:
(-1)³ + 3(-1)² - 8(-1) - 14 = -1 + 3 + 8 - 14 = -4
This expression also evaluates to a non-zero value, so x = -1 is not a root. Finally, we can test x = -2:
(-2)³ + 3(-2)² - 8(-2) - 14 = -8 + 12 + 16 - 14 = 6
This expression evaluates to zero, so x = -2 is a root. Using long division or synthetic division, we can divide the cubic polynomial by x + 2 to get:
x³ + 3x² - 8x - 14 = (x + 2)(x² + x - 7)
The quadratic factor x² + x - 7 can be factored using the quadratic formula, giving us:
x² + x - 7 = [ -1 ± √(1 + 4*7) ] / 2
= [ -1 ± 3√(7) ] / 2
Therefore, the three intersection points are:
(-2, 0)
( [ -1 - 3√(7) ] / 2, 4[ -1 - 3√(7) ] / 2 - 11 )
( [ -1 + 3√(7) ] / 2, 4[ -1 + 3√(7) ] / 2 - 11 )
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8. You and 4 friends are going to an event, and you want to keep the cost below $100 per person. Write and solve an inequality to find the total cost, x.
0\left\{-10\le x\le10\right\}
Describe the transformations (vertical translation, horizontal translation, and dilation/reflection) from the parent function that happened to these formulas
The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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The formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
What is Function?A function is a mathematical rule that assigns each input from a set (domain) a unique output from another set (range), typically written as y = f(x).
The notation "0{-10≤x≤10}" typically represents the domain of a function or an inequality. It means that the function is defined only for the values of x that are between -10 and 10 (including -10 and 10).
Assuming that the function in question is a constant function equal to zero, the parent function is f(x) = 0.
To describe the transformations that happened to this function, we need more information about the specific formula. For example, if the formula is:
g(x) = 0{-10≤x≤10}
Then there are no transformations from the parent function. The function is simply a constant function that is equal to zero over the interval [-10, 10].
However, if the formula is something like:
g(x) = 2 * 0{-10≤x+3≤10}
Then we can describe the transformations as follows:
Horizontal translation: The function has been shifted horizontally to the left by 3 units. This means that the point (3, 0) on the parent function is now located at the origin (0, 0) on the transformed function.
Dilation/reflection: The function has been reflected about the y-axis and vertically scaled by a factor of 2. This means that the point (-1, 0) on the parent function is now located at (-4, 0) on the transformed function, and the point (1, 0) on the parent function is now located at (2, 0) on the transformed function.
Vertical translation: There is no vertical translation in this case, since the constant function is already centered at y = 0.
To summarize, the formula g(x) = 2 * 0{-10≤x+3≤10} represents a function that has been horizontally shifted left by 3 units, reflected about the y-axis, and vertically scaled by a factor of 2.
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Write an equation for the polynomial graphed below
The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).
How to derive the equation of the polynomial
In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:
y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)
Where:
x - Independent variable.r₁, r₂, r₃, r₄ - Roots of the polynomial.a - Lead coefficient.y(x) - Dependent variable.Then, by direct inspection we get the following information:
y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3
First, determine the lead coefficient:
- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)
- 3 = a · 3 · 1 · (- 2) · (- 3)
- 3 = 18 · a
a = - 1 / 6
Second, write the complete expression:
y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)
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How long did Lizzie practice on Thursday and Friday altogether?
J
P
D
Lizzie's Drum Practice
P
S
P
D
P
S
S
Monday Tuesday Wednesday Thursday Friday
= 5 minutes
DONE
0
minutes
7 8
4
00
5
1 2
0
9
6
3
Answer:
Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
On Thursday, she practiced for 5 minutes according to the table.
On Friday, she practiced for 9 minutes according to the table.
Adding these two times together, we get:
5 minutes + 9 minutes = 14 minutes
Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
Find a formula for the exponential function passing through the points
(-3, 5/8 ) and (3, 40).
The exponential function is y=5.[tex]2^x[/tex].
What is exponential function?
A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
Here the exponential function is [tex]y=ab^x[/tex]
Since (-3,5/8) is on the graph, -[tex]\frac{5}{8}[/tex]=[tex]ab^{-3}[/tex] -----> 1
Since (3, 40) is on the graph, 40=[tex]ab^3[/tex] ------> 2
So, [tex]\frac{ab^3}{ab^{-3}}=\frac{40}{\frac{-5}{8}}[/tex]
=> [tex]b^{3+3}=8\times8[/tex]
=> [tex]b^6=2^6[/tex]
=> b = 2
put b=2 into 2 then,
=> 40= [tex]a\times2^3[/tex]
=> 8a=40
=> a =5
Then the exponential function is y=5.[tex]2^x[/tex].
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In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving AC > EF, given BC = EF. Upload the entire proof below.
Given:
BC = EF
Prove:
AC > EF
STATMENT REASON
1. 1.
2. 2. Betweenness
3. AC > BC 3.
4. 4.
The given information and the transitive property of inequalities, we can prove that [tex]AC[/tex] is greater than [tex]EF[/tex] .
What is the transitive property of inequalities?Statement Reason
[tex]BC = EF[/tex] Given
Betweenness Given
[tex]AC > BC[/tex] Given
[tex]AC > EF[/tex] Transitive property [tex](3, 1)[/tex]
Explanation:
[tex]BC = EF[/tex] Given: Given statement that BC is equal to EF.
Betweenness Given: Given statement that states the concept of betweenness, where BC is between AC and EF.
AC > BC Given: Given statement that [tex]AC[/tex] is greater than BC.
[tex]AC > EF[/tex] Transitive property: Using the transitive property, we can conclude that [tex]AC[/tex] is greater than EF (based on statement 3 and 1).
Therefore, using the given information and the transitive property of inequalities, we can prove that AC is greater than [tex]EF[/tex] .
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A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 176 feet of fencing,
what is the largest area the farmer can enclose?
Answer: 46 ft by 92 ft
Step-by-step explanation:
The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.