If the numerator and denominator of a fraction are both odd numbers, can you write an equivalent fraction with a smaller numerator and denominator

The vertex of the parabola y=-x^(2)-14x-49 is located at (-7,0). And there is only one x-intercept, which is (-7,0)

The vertex of a parabola is the point where the parabola changes direction. The vertex is found by completing the square for the quadratic equation. The x-coordinate of the vertex is given by the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. The y-coordinate of the vertex is found by substituting the x-coordinate of the vertex into the equation for y.

For the given parabola, y=-x^(2)-14x-49, the coefficients are a=-1 and b=-14.

The x-coordinate of the vertex is:
x = -b/2a = -(-14)/(2*(-1)) = -7

The y-coordinate of the vertex is:
y = -(-7)^(2)-14(-7)-49 = -49+98-49 = 0

Therefore, the vertex of the parabola is (-7,0).

To find the x-intercepts, we need to solve the equation for when y=0:
0 = -x^(2)-14x-49
0 = (x+7)(x+7)
x = -7

Since the equation has only one solution, there is only one x-intercept, which is (-7,0). This is also the vertex of the parabola.

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Answer:

24+2x

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = 24+2x

The unit conversion the value is 6.75 ft.

The same feature is expressed in a different unit of measurement through a unit conversion. Time can be stated in minutes rather than hours, and distance can be expressed in kilometres rather than miles, or in feet rather than any other unit of length.

Here the given unit measurement is ,

=> 6ft 9 inches.

We know that, to convert inches into feet we need to divide by 100. Then,

=> 9 inches = 9/12 = 0.75 ft.

Now total measurement = 6+0.75 = 6.75 ft.

Hence the after unit conversion the answer is 6.75 ft.

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Answer:

2(8n-7)(6n^2+7)

The final expressiοns fοr a, b, c and d will be 3x(3y)(1/2) / (y¹/3), 1/x, 5²/3, 8z³/2 / x².

An expressiοn is a mathematical phrase that cοmbines numbers, variables, and οperatοrs tο represent a value οr a quantity. It can include cοnstants, variables, cοefficients, and mathematical οperatiοns.

a. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can simplify the radicals and rewrite the expοnents as fractiοns.

(9¹/2x²y) (27¹/3y-¹) = 3xy¹/2) * 3*(3/3) * y⁻¹/3 = 3x(3y)(1/2) / (y¹/3)

b. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can apply the negative expοnent rule and simplify the radical.

(x¹/2)⁻² = (1/x¹/2)² = 1/x

c. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can simplify the radical and rewrite the expοnent as a fractiοn.

(25)²/3 = (5²)¹/3 = 5²/3

d. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can simplify the radical and mοve the negative expοnent tο the denοminatοr.

8z³/2x⁻² = 8(z¹/2)³ / x² = 8z³/2 / x²

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Answer:

slope: -4

y intercept: (0,-12)

Shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

First, we graph the lines y = -x-2 and y = -5x+2 using their y-intercepts and slopes.

The line y = -x-2 has a y-intercept of -2 and a slope of -1, which means that for every increase of 1 in x, y decreases by 1.

The line y = -5x+2 has a y-intercept of 2 and a slope of -5, which means that for every increase of 1 in x, y decreases by 5.

The shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.

Hence, shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.

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The flare takes 10.7 seconds to hit the ground if a flare is shot from the top of a 120-foot building at a speed of 160 feet per second.

The given data is as follows:

Height of building = 120 feets

Speed =  160 feet per second

The given equation is h = −16t + 160t + 120

Time required to hit the ground =?

The flare hits the ground when h=0.

Substitute in the given equation we get,

-16t^2 + 160t + 120 = 0

By applying the Quadratic equation formula to find out the value of t,

Quadratic equation formula = ( -b± [tex]\sqrt{b^{2} - 4ac }[/tex] ) / 2a

x = (-160 ± [tex]\sqrt{160^{2} - 4(-16)(120) }[/tex] ) / 2(-16)

x = (-160 ± [tex]\sqrt{33280}[/tex] ) / -32

x = (-160 +[tex]\sqrt{33280}[/tex] ) / -32,  (-160 -[tex]\sqrt{33280}[/tex]  ) / -32

x = -10.70, 10.70

Neglecting the time in Negative values, x = 10.70 seconds

Therefore, we can conclude that the flare takes 10.7 seconds to hit the ground.

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Answer:

Step-by-step explanation:

The answer is (1,5)

g(f(-1)) = g(2(-1)-1) = g(-3)

g(-3) = (-3)^2 + 3 = 9+3 = 12

So g(f(-1)) = 12

Hope this helps.

55.5% is equivalent to 5/9.

percentage, a relative value indicating hundredth parts of any quantity.

A baseball team won of its games of  5/9 this season.

We need to find the equivalent percentage of 5/9.

To convert 5/9 to a percentage, we can multiply it by 100.

(5/9) x 100 = 55.5%

So, the percentage equivalent to 5/9 is 55.5%.

Therefore, 55.5% is equivalent to 5/9.

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The inequality of the scenario is 8.50n + 9 ≤ 43

From the question, we have the following parameters that can be used in our computation:

Amount = $43

The cost of n books and 4 pens can be expressed as:

8.50n + 2.25(4)

We can simplify this expression:

8.50n + 9

We know the student has a total of $43 to spend, so we can set up an inequality:

8.50n + 9 ≤ 43

Subtracting 9 from both sides, we get:

8.50n ≤ 34

Dividing both sides by 8.50, we get:

n ≤ 4

Hence, the inequality that best represents the scenario is: n ≤ 4 or 8.50n + 9 ≤ 43

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Complete question

For this item, select the answers from the drop-down menus A student has $43 in total to buy books that cost \$8.50 each and pens that cost $2.25 each. The student buys n number of books and 4 pens

Complete the inequality to best represent the scenario.

A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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Answer:

a. Let's denote the width of the property as "w". According to the problem, the length of the property is three times the width, so we can represent the length as "3w".

To find the equation that can be used to solve for the length and width, we can use the formula for the perimeter of a rectangle:

Perimeter = 2(length + width)

Since we know the perimeter (5,280 feet), and we have expressions for the length and width, we can substitute these values into the formula and solve for the variables:

2(3w + w) = 5,280

2(4w) = 5,280

8w = 5,280

w = 660

Therefore, the width of the property is 660 feet, and the length is 3 times the width, or 1,980 feet.

b. To check that these values are correct, we can substitute them back into the formula for perimeter and make sure it equals 5,280:

2(1,980 + 660) = 5,280

This is true, so we can be confident that the width of the property is 660 feet and the length is 1,980 feet.

The graph of this function is a sine curve with amplitude 3√2 and phase shift π/4.

The k cos(ϕ) would be 3 and k sin(ϕ) would be 3.

The combined sound is given by:

f(t) = f1(t) + f2(t)

f(t) = 3 sin(t) + 3 cos(t)

To find k and ϕ, we can use the following trigonometric identity:

k sin(t + ϕ) = k sin(t) cos(ϕ) + k cos(t) sin(ϕ)

Comparing this with the equation for f(t), we can see that:

k cos(ϕ) = 3

k sin(ϕ) = 3

Squaring both equations and adding them gives:

k^2 = 3^2 + 3^2 = 18

k = √18 = 3√2

Dividing the two equations gives:

tan(ϕ) = 3/3 = 1

ϕ = π/4

Therefore, the combined sound has the form:

f(t) = 3√2 sin(t + π/4)

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The inequality for the number of sales Ken needs to make this week in dollars is: 4x + 55 > 115. Where x is the number of sales.

Inequalities are the mathematical term for the relationship between two values that are not equal. Not all people are created equal. We typically use the "not equal symbol ()" when two values are not equal. However, various inequalities are utilized to compare the values, whether they are less than or greater than.

To solve for x, we first need to isolate it on one side of the inequality. We can start by subtracting 55 from both sides:

4x > 60

Then, we can divide both sides by 4:

x > 15

Therefore, Ken needs to make more than 15 sales this week to earn more than $115.

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The equation when solved for the price of a lightbulb, y, is: [tex]y=7 - \frac{4}{5} x[/tex]

A statement that shows the equality of the two expressions is known as an equation. Mathematical operations including addition, subtraction, multiplication, division, and exponentiation are included, along with one or more variables, constants, and other operations.

To solve the equation 4x + 5y = 35 for the price of a lightbulb, y, we need to isolate y on one side of the equation. Here are the steps:

Subtract 4x from both sides of the equation:

4x + 5y - 4x = 35 - 4x

Simplifying, we get:

5y = 35 - 4x

both sides divided by 5 in the equation:

(5y)/5 = (35 - 4x)/5

Simplifying, we get:

y = (35/5) - (4/5)x

y = 7 - (4/5)x

Therefore, the equation when solved for the price of a lightbulb, y, is: [tex]y=7 - \frac{4}{5} x[/tex]

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Answer:

10

Step-by-step explanation:

To find out how many students participate in both sports and music, we can use the formula:

Total = Group A + Group B - Both

where "Total" is the total number of students participating in sports or music, "Group A" is the number of students participating in sports, "Group B" is the number of students participating in music, and "Both" is the number of students participating in both.

Plugging in the given values, we get:

Total = 100

Group A = 60

Group B = 50

Both = ?

100 = 60 + 50 - Both

Simplifying the equation, we get:

Both = 60 + 50 - 100

Both = 10

Therefore, 10 students participate in both sports and music.

Answer: 6 oz

Step by step:

5 < 6

Did i miss something?

Answer: 6 oz. is greater than 5 oz.

Step-by-step explanation:

Imagine you had 6 dogs. Now let's say that one passed away due to a car accident. Now you have 5 dogs. We can say by the fundamental theorem of common sense that you indeed did have more dogs before that accident. Using that logic in the grand scheme of metrics, we can say that 6oz is larger as a value than 5oz.

The expected number (μ) of property crimes that will be solved in this district can be found by multiplying the total number of property crimes by the probability that a property crime will be solved. Since the probability that a property crime will be solved is 1 - 0.84 = 0.16, the expected number of property crimes that will be solved is:

μ = 7 × 0.16 = 1.12

The standard deviation (σ) of this distribution can be found by taking the square root of the product of the total number of property crimes, the probability that a property crime will be solved, and the probability that a property crime will not be solved:

σ = √(7 × 0.16 × 0.84) = 1.01

Therefore, the expected number of property crimes that will be solved in this district is 1.12, and the standard deviation of this distribution is 1.01.

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Let V be a finite-dimensional vector space and let S1 and S2 be two bases of V. To show that S1 and S2 have the same number of elements, we will assume, without loss of generality, that S1 has more elements than S2, i.e., n > m. We will then derive a contradiction.

Since S1 is a basis of V, every vector in V can be expressed as a linear combination of the vectors in S1. In particular, for each j = 1, 2, ..., m, we can express βj as a linear combination of the vectors in S1:

βj = c1,jα1 + c2,jα2 + ... + cn,jαn

where c1,j, c2,j, ..., cn,j are scalars. We can write this in matrix form as

| β1 | | c1,1 c1,2 ... c1,m | | α1 |

| β2 | | c2,1 c2,2 ... c2,m | | α2 |

| ... | = | ... ... ... ... | * | ... |

| βm | | cm,1 cm,2 ... cm,m | | αn |

where the matrix on the right is the matrix whose columns are the vectors in S1, and the matrix on the left is the matrix whose columns are the vectors in S2.

Since S2 is also a basis of V, the matrix on the left is invertible. Therefore, we can multiply both sides of the equation by the inverse of the matrix on the left, giving

| α1 | | b1,1 b1,2 ... b1,m | | β1 |

| α2 | | b2,1 b2,2 ... b2,m | | β2 |

| ... | = | ... ... ... ... | * | ... |

| αn | | bn,1 bn,2 ... bn,m | | βm |

where b1,j, b2,j, ..., bn,j are scalars.

Now consider the determinant of the matrix on the left-hand side of this equation. Since this matrix is obtained by multiplying the matrix whose columns are the vectors in S2 by the inverse of the matrix whose columns are the vectors in S1, its determinant is equal to the product of the determinants of these two matrices:

det([α1 α2 ... αn]) * det([β1 β2 ... βm]^-1) = det([α1 α2 ... αn] [β1 β2 ... βm]^-1)

The left-hand side is nonzero, since S1 and S2 are both bases of V and therefore their vectors are linearly independent, so the determinant of each matrix is nonzero. However, the right-hand side is zero, since the product of the two matrices on the right-hand side is the identity matrix, and the determinant of the identity matrix is 1.

This is a contradiction, so our assumption that S1 has more elements than S2 must be false. Therefore, S1 and S2 have the same number of elements, and the proof is complete.

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The closest answer choice to 26.25 cm² is G. 16.5 cm².

What is area ?

Area is a measurement of the amount of space inside a two-dimensional figure, such as a square, rectangle, triangle, parallelogram, or circle. It is expressed in square units, such as square centimeters (cm²), square meters (m²), square inches (in²), or square feet (ft²).

Based on the given image, we can use the ruler to measure the dimensions of the parallelogram.

From the ruler, we can see that the base of the parallelogram is approximately 7.5 cm, and the height is approximately 3.5 cm. Therefore, the area of the parallelogram is:

Area = base x height

Area = 7.5 cm x 3.5 cm

Area = 26.25 cm² (rounded to the nearest 0.5 cm)

Among the answer choices provided, the closest one to the calculated area of the parallelogram is 26.5 cm², which is not provided in the answer choices.

Therefore, The closest answer choice to 26.25 cm² is G. 16.5 cm².

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The value of k for which both 6x² - 17x + 12 = 0 and 3x² - 2x + k = 0 have a common root is k = 1/3.

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The discriminant of the first quadratic equation, 6x² - 17x + 12 = 0, is:

b² - 4ac = (-17)² - 4(6)(12) = 1

Since the discriminant is not zero, this quadratic equation does not share a common root with any other equation.

For the second quadratic equation, 3x² - 2x + k = 0, to have a common root with 6x² - 17x + 12 = 0, its discriminant must be zero.

The discriminant of the second quadratic equation is:

b² - 4ac = (-2)² - 4(3)(k) = 4 - 12k

To find the values of k that make the discriminant equal to zero, we solve the equation:

4 - 12k = 0

Simplifying, we get:

12k = 4

k = 4/12

k = 1/3

Therefore, the value of k for which both 6x² - 17x + 12 = 0 and 3x² - 2x + k = 0 have a common root is k = 1/3.

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Answer:

Circumference = 37.7 feet

Step-by-step explanation:

Use these formulas, then solve for the answer

C=2πr

d=2r

C = π times d

C = π times 12

C = 37.699

The answer is yes, more than one triangle can be formed using the three angle measures of triangle QPC. This is because the sum of the three angle measures of a triangle is always equal to 180 degrees.

A triangle is a three-sided geometric figure, consisting of three straight lines connecting three vertices. It is one of the most fundamental shapes in geometry and is used as the basis for a variety of mathematical concepts.

If two angle measures are given, any third angle measure between 0 and 180 degrees can be chosen to form a triangle. Thus, if two angle measures of triangle QPC are given, any third angle measure between 0 and 180 degrees can be used to form a triangle.

For example, if two angle measures of triangle QPC are 45 degrees and 65 degrees, then any third angle measure between 0 and 180 degrees can be chosen to form a triangle. Thus, if the third angle measure chosen is 70 degrees, then a triangle with three angle measures of 45 degrees, 65 degrees and 70 degrees can be formed. Similarly, if the third angle measure chosen is 30 degrees, then a triangle with three angle measures of 45 degrees, 65 degrees and 30 degrees can be formed.

Thus, it can be concluded that more than one triangle can be formed using the three angle measures of triangle QPC.

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The probability of  P(A) = 15/16, P(B) = 1/3, P(BIA) = 1/3, and P(CAB) = 0.

The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

(a) P(A) = P(1) + P(2) + P(3) + P(4) = 1/2 + 1/4 + 1/8 + 1/16 = 15/16
(b) P(B) = P(2) + P(4) + P(6) + ... = 1/4 + 1/16 + 1/64 + ... = 1/3
(c) P(BIA) = P(B ∩ A) / P(A) = (P(2) + P(4)) / P(A) = (1/4 + 1/16) / (15/16) = 5/15 = 1/3
(d) P(CAB) = P(C ∩ A ∩ B) / P(A ∩ B) = 0 / P(A ∩ B) = 0

Therefore, the probabilities of the events are: P(A) = 15/16, P(B) = 1/3, P(BIA) = 1/3, and P(CAB) = 0.

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A = 32°, R = 9.09m, S = 6.89m, T = 7.06m, and angle ASR = 114.90°.

To solve ARST, we must first use the given information (ST = 7.5m and S ∟ angle RS = 32°). Using the law of sines, we can calculate the following:

Then, using the law of cosines, we can calculate the following:

Therefore, the missing sides and angles of ARST are A = 32°, R = 9.09m, S = 6.89m, T = 7.06m, and angle ASR = 114.90°.

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Answer:

Step-by-step explanation:

~P is true

q is true

~p v q is true

the hypothesis  (or antecedent)  is true

the conclusion  (or consequent)  is false

R is false and ~q is false

the conditional says if true then false

so the conditional is false

A1. We can use Gaussian Elimination to determine if the system has a unique solution, infinite many solutions, or no solution. Gaussian Elimination is a method of solving linear equations by reducing a system of equations to a simpler form.

First, we need to write the system of equations in matrix form:

| 2 4 3 | | x1 | = | f |
| 1 d -3 | | x2 | = | g |
| 1 2 c | | x3 | = | h |

Next, we will use Gaussian Elimination to reduce the matrix to row echelon form:

| 1 2 c | | x1 | = | h |
| 0 (d-2) (-3-c) | | x2 | = | (g-h) |
| 0 (4-2d) (3-2c) | | x3 | = | (f-2h) |

Now, we can check for the conditions that determine the number of solutions:

1. If the rank of the coefficient matrix is less than the rank of the augmented matrix, then the system has no solution.

2. If the rank of the coefficient matrix is equal to the rank of the augmented matrix, and the rank is equal to the number of variables, then the system has a unique solution.

3. If the rank of the coefficient matrix is equal to the rank of the augmented matrix, and the rank is less than the number of variables, then the system has infinite many solutions.

In this case, if (d-2) ≠ 0 and (4-2d) ≠ 0, then the system has a unique solution. If (d-2) = 0 and (4-2d) = 0, then the system has infinite many solutions. If (d-2) = 0 and (4-2d) ≠ 0, or (d-2) ≠ 0 and (4-2d) = 0, then the system has no solution.

Therefore, we can find a relation which gives a unique solution or infinite many solutions by using Gaussian Elimination and checking the conditions for the number of solutions.

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