determine weather it is no solution many solutions or one solutions
3(6-4m)=2(9-6m)

Answer:

Step-by-step explanation:

You want the vertex and p-value for a parabola with focus (-5, -7) and directrix y = -5.

The vertex of a parabola is halfway between the focus and directrix. That is because every point on the parabola is the same distance from the focus as from the directrix.

When the vertex is above or below the directrix, it will have the same x-value as the focus. Its y-value will be the average of those of the focus and directrix:

The vertex is ...

  (h, k) = (-5, (-7-5)/2)

  (h, k) = (-5, -6) . . . . vertex

The p-value for the parabola is half the distance from the focus to the directrix. When the focus is below the directrix, the p-value is negative.

  p = (-7 -(-5))/2 = -1

This is equivalent to the distance from the focus to the vertex.

  p = (-7 -(-6)) = -1 . . . . p-value

The sign of the p-value tells you the direction the parabola opens. For negative p-values, the parabola opens downward.

The p-value shows up in the equation for the parabola this way:

  \(y=\dfrac{1}{4p}(x-h)^2+k\qquad\text{vertex at $(h,k)$}\)

__

Additional comment

We don't know what your drop-down menu of choices says about the parabola. We have guessed that it might refer to the direction the parabola opens. It always opens in the direction toward the focus and away from the directrix.

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Given the information on the table, we can see the following increases on the minimum wage:

From 1980 to 1981 : 0.25

1981 to 1990: 0.45

1990 to 1996: 0.95

1996 to 1997: 0.4

1997 to 2007: 0.7

2007 to 2009:1.4

As we can see, the minimum wage has a tendency to grow with the passing of the years, but there is not a constant of growth. Therefore, we could use the mean of these increments, and use it to estimate the approximate minimum wage for 2020. First we get the mean of this 6 numbers:

We have that, in average, the minimum wage increased 0.691 from 1981 to 2009, then, an approximation for the current year would be the following:

then, the minimum wage for the current year should be $14.84, because the mean of the increments of the given data would give us an approximate of $14.84

Based on the given algorithm, we can analyze the recurrence relation for the running time of the algorithm on inputs of arrays of n elements.

Let's denote the running time of the algorithm for an input of size n as t(n).

For n = 1, the algorithm computes f(g) for a single entry in the array, which costs a constant time, let's say C1. Therefore, we have:

t (1) = C1

For larger values of n, the algorithm splits the array into two subarrays of size 2n/3 each and runs recursively on each subarray. This step incurs a running time of t(2n/3) for each subarray.

Additionally, the algorithm performs the computation g(x, y) on the resulting ordered set of two integers, which costs a constant time, let's say C2.

Considering these factors, we can write the recurrence relation for the running time as:

t(n) = 2t(2n/3) + C2

Therefore, the correct option among the given recurrence relations that seems to fit the running time of the algorithm is:

c. t(1) = C, and t(n) = 2t(2n/3) + C2, for some positive constants C, C2

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Answer: 4 (x +3) - 3+9=x

Step-by-step explanation:

Answer:

Therefore, the width of the canyon is 109.09 meters.

Step-by-step explanation:

* 160/22 = k (Scale Factor)

  7.2727 = k

* Let x be the width of the canyon

 x / 15 = k

 x / 15 = 7.2727

 x = 7.2727 (15)

 x = 109.09 m

The width of the canyon is 109.09m.

Here we assume x be the width of the canyon.

The k(Scale factor) should be

= \(160 \div 22\)

k =  7.2727  

So,

\(x \div 15 = k\\\\ x \div 15 = 7.2727\)

 x = 109.09 m

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The smaller number is 25, and the larger number is 68. The larger number is 18 more than twice the smaller number, and their sum is 93.

To solve this word problem using the 3-step process, we need to find the two numbers given that the larger number is 18 more than twice the smaller and the sum of the two numbers is 93.
Step 1: Let's assign variables to the unknown numbers. Let's say the smaller number is "x" and the larger number is "y".
Step 2: Translate the given information into equations. From the problem, we know that the larger number is 18 more than twice the smaller. So, we can write the equation as: y = 2x + 18.
We also know that the sum of the two numbers is 93. So, we can write another equation as: x + y = 93.
Step 3: Solve the system of equations. We have two equations:
y = 2x + 18
x + y = 93
We can solve this system of equations by substitution method or elimination method. Let's use substitution.
Substitute the value of y from the first equation into the second equation:
x + (2x + 18) = 93
3x + 18 = 93
3x = 93 - 18
3x = 75
x = 75 / 3
x = 25
Now, substitute the value of x back into the first equation to find y:
y = 2(25) + 18
y = 50 + 18
y = 68
So, the smaller number is 25 and the larger number is 68.

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Answer:  300 in3

Step-by-step explanation: To find the volume you multiply the base area by the height. 30 x 10 = 300. Did this for my exam and got the question correct.

The volume of the prototype is 300in^3.

Since The designer uses octagons with a base area of 30 in2 and rectangles with a length of 10 in to create a prototype for the new package.

So here the volume is

= 30(10)

= 300

Therefore, The volume of the prototype is 300in^3.

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The measure of angle SPQ is 56°

the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(θ) = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

To calculate the hypotenuse , we have known the adjascent to angle 28°.

Therefore;

cos 28 = 10/x

0.883 = 10/x

x = 10/0.883

x = 11.3

Represent angle SPR by y

cos x = 10/11.3

cos x = 0.883

x = 28°

Therefore the measure of angle SPQ is 28+28 = 56°

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The investor should invest $5000 in AAA bonds, $2500 in B bonds, and the remaining $22500 in A bonds to have an interest income of $2000.

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

Let x be the amount invested in AAA bonds.

Since the investor wants to have twice as much in AAA bonds as in B bonds, the amount invested in B bonds is x/2.

The remaining amount invested in A bonds is 30000 - x - x/2 = 30000 - 3x/2.

The interest income from AAA bonds is 0.05x.

The interest income from A bonds is 0.06(30000 - 3x/2) = 1800 - 0.09x.

The interest income from B bonds is 0.1(x/2) = 0.05x.

The total interest income is the sum of the interest income from each type of bond, which is given to be $2000.

0.05x + 1800 - 0.09x + 0.05x = 2000

Simplifying and solving for x, we get:

-0.04x + 1800 = 2000

-0.04x = 200

x = 5000

Hence, the investor should invest $5000 in AAA bonds, $2500 in B bonds, and the remaining $22500 in A bonds to have an interest income of $2000.

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Answer: 6 would be left

Step-by-step explanation: divide 3494 by 8

There will be 6 comics left over after putting them in groups of 8

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Bertie has 3494 comic books he wants them in groups of 8.

∴ The no. of groups can be obtained if we divide the total number of books by no. of books in each group which is,

= (3494/8).

= 438×8 + 6.

So, There will be 6 comics left over after putting them in groups of 8.

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The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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Answer:

4(x+4)

Step-by-step explanation:

Factor 4x+16

4x+16

=4(x+4)

Answer:

Brauilo is wrong because he divided by (x+1) instead of (x-1)

Step-by-step explanation:

The remainder Theorem states that

if polynomial f(x) is divided by binomial x-a, the remainder will equal f(a). The factor is positive so the binomial is the same as

which is why we divide by -1, or subsitue -1 into the equation p(x).

The remainder of a polynomial division can be gotten using remainder theorem or synthetic division.

The true statement is: Brauilo did not find the value of a, because he divided by (x+1) instead of (x-1)

From the question, we have the following parameters:

\(\mathbf{p(x) = x^4 +5x^3 + ax^2 - 3x + 11}\)

\(\mathbf{Divisor =x+ 1}\)

\(\mathbf{Remainder = 17}\)

First, we set the divisor to 0.

\(\mathbf{Divisor =x+ 1 = 0}\)

So, we have:

\(\mathbf{x+ 1 = 0}\)

Solve for x

\(\mathbf{x= -1}\)

The above equation means that, the value of x that will be used to test the polynomial is -1

From the question,

Hence, Braulio is incorrect, because he used the wrong value of x

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Answer:

J. (2, -3)​

Step-by-step explanation:

1. Substitute y = x - 5 in for y in the other equation:

5x + 2(x - 5) = 4

2. Simplify:

5x + 2x - 10 = 4 (distributed the 2)

7x - 10 = 4

3. Isolate for x:

7x - 10+10 = 4+10

7x = 14

7x/7 = 14/7

x = 2

4. Plug the new x value into an equation and solve for y:

y = 2 - 5

y = -3

hope this helps!

Answer:

The answer is A and B

The volume of a sphere with radius r is given by the formula V = (4/3)πr^3. The volume of a hemisphere with radius r is given by the formula V = (2/3)πr^3.

If we substitute r = 2 cm in the formulas, we get:

- Volume of sphere = (4/3)π(2)^3 = (4/3)π(8) = 32/3π

- Volume of hemisphere = (2/3)π(2)^3 = (2/3)π(8) = 16/3π

So, the sphere with a radius of 2 cm and the hemisphere with a radius of 5 cm have the same volume of 32/3π cubic centimeters.

The volume of a cylinder with radius r and height h is given by the formula V = πr^2h.

If we substitute r = 10 cm and h = 7 cm in the formula, we get:

- Volume of cylinder = π(10)^2(7) = 700π cubic centimeters

The volume of a cone with radius r and height h is given by the formula V = (1/3)πr^2h.

If we substitute r = 4 cm and h = 2 cm in the formula, we get:

- Volume of cone = (1/3)π(4)^2(2) = 32/3π cubic centimeters.

Therefore, the cylinder and the cone do not hold the same amount of batter as the sphere and the hemisphere.

Answer:

A

Step-by-step explanation:

Hope this helps :)

Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer: f(x)=-3x+2

Step-by-step explanation:

Answer:

The equations 15 - n = 7, 4n = 32, and 64 : n = 8 have 8 as a solution.

Step-by-step explanation:

Each equation will have work shown below :

15 - n = 7

For this equation, we would need to isolate the variables by doing the inverse operation to both sides of the equation. Here in this equation, the operation is to subtract and the inverse operation of that is addition. Since the original operation is subtraction, we need to add it by a negative sign to each side. In order to isolate the variables, we have to add -7 to both sides.

  15 - n = 7

+ -7      + -7

   8 = n

The right side has a sum of 0 so it doesn't require any value to the equation. As you can see in the equation, n equals to 8.

4n = 32

For this equation, we would need to isolate the variables by doing the inverse operation to both sides of the equation. Here in this equation, the operation is to multiply and the inverse operation of that is division. In  order to isolate the variables, we have to divide 8 to both sides.

4n = 32

/4     /4

 n = 8

The left side has a quotient of 0 so it doesn't require any value to the equation. As you can see in the equation, n equals to 8.

This is a ratio which is basically just the operation of division. For this equation, we would need to isolate the variables by doing the inverse operation to both sides of the equation. Here in this equation, the operation is to divide and the inverse operation of that is multiplication. Since the original operation is division, we need to multiply it by the reciprocal to each side. In order to isolate the variables, we have to multiply 1/8 to both sides.

 64 : n = 8

* 1/8     * 1/8

  8 = n

The right side has a product of 0 so it doesn't require any value to the equation. As you can see in the equation, n equals to 8.

Answer:

It is 8.5 meters tall

Step-by-step explanation:

28.05 / 3.3 = 8.5

Answer:

5 green lego bricks are equal to 12 yellow lego bricks

Step-by-step explanation:

Let the yellow and green lego bricks be denoted by y and g respectively.

According to the given conditions

5y+ 2= 2g------ equation 1

3g+2= 7y----- equation 2

Rearranging the equations and adding

5y+ 2= 2g------ equation 3

7y-2= 3g----- equation 4

12y= 5g

5 green lego bricks are equal to 12 yellow lego bricks

Answer:

0.115

Step-by-step explanation:

Answer:

\({ \sf{7h - (3h - 5) = 2(h - 7)}} \\ \\ { \sf{7h - 3h + 5 = 2h - 14}}\)

[distributive property open brackets ]

\({ \sf{4h + 5 = 2h - 14}}\)

[simplification of either sides]

\({ \sf{4h - 2h = - 14 - 5}}\)

[operating similar terms]

\({ \sf{2h = - 19}} \\ \)

[simplification]

\({ \sf{h = \frac{ - 19}{2} }}\)

Answer:

10.24

Step-by-step explanation:

128 x .08= 10.24

(the 8 in the equation is moved 2 places to the left because its a percentage)

In the given problem of percentage, 8 is 6.25\(\%\) of 128.

Percentage is a way of expressing a proportion or a relative value as a fraction of 100. It represents a portion or a fraction of a whole in terms of hundredths.

The term "percentage" comes from the Latin word "per centum," which means "per hundred."

The percentage is denoted using the symbol "\(\%\)". For example, 25\(\%\) means 25 out of 100, or 25 hundredths.

When working with percentages, it is often used to compare or represent ratios, proportions, or relative quantities. It provides a convenient way to express fractions or ratios in a standardized form.

Percentages are commonly used in various fields, such as finance, economics, statistics, and everyday situations involving ratios, discounts, interest rates, statistics, and probability. They provide a standardized way to express relative values and make comparisons across different quantities.

\(\frac{8}{128} \times 100\) = \(\frac{25}{4}\)\(\%\)

               = 6.25\(\%\).

So, the percentage of 8 out of 128 is 6.25\(\%\).

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The probability of rolling two numbers that sum to 4 after two rolls of a six-sided die is 1/9 or approximately 0.1111. This means that out of all possible combinations, there is a 1 in 9 chance of obtaining a sum of 4.

To calculate the probability, we need to consider all possible outcomes of two dice rolls and determine the favorable outcomes where the sum of the two numbers equals 4.

Let's analyze the possible combinations for the first roll:

1 + 3 = 4

2 + 2 = 4

3 + 1 = 4

Out of these three combinations, only one of them results in a sum of 4.

For the second roll, we have the same possible combinations as the first roll. Again, only one combination gives a sum of 4.

Since the rolls are independent events, we can multiply the probabilities of each roll to find the probability of both events occurring. Therefore, the probability of rolling two numbers that sum to 4 is:

(1/6) * (1/6) = 1/36

However, we rolled the dice twice, so we need to account for the order in which these combinations can occur. We have two favorable outcomes: (1 + 3) and (3 + 1). Therefore, the probability becomes:

2 * (1/36) = 1/18

However, there are two possible ways to achieve a sum of 4: (1 + 3) and (3 + 1). Thus, we need to multiply by 2 again:

2 * (1/18) = 1/9

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Macy had 3 appointments.

Logan had 5 appointments.

What is the quadratic equation?

A quadratic equation is a type of polynomial equation of degree 2, which is written in the form of "ax^2 + bx + c = 0", where x is the variable and a, b, and c are constants. The solutions to a quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac))/2a.

Part A:

Let x be the number of appointments Macy had.

We know that the total income (60x + 40) must equal 220.

Therefore, the equation representing the situation is:

60x + 40 = 220

To solve for x, we can subtract 40 from both sides:

60x = 180

Finally, we divide both sides by 60 to get:

x = 3

Macy had 3 appointments.

Part B:

Let y be the number of appointments Logan had.

We know that the total profit (70y + 50 - 20y) must equal 300.

Therefore, the equation representing the situation is:

50y + 50 = 300

To solve for y, we can subtract 50 from both sides:

50y = 250

Finally, we divide both sides by 50 to get:

y = 5

Logan had 5 appointments.

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Answer:

None of the choices are correct.

Step-by-step explanation:

The angles are marked to show they are equal, therefore the line segment that divides the angle into two equal parts is an angle bisector.

Angle Bisector Theorem

The angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.

\(\implies \sf \dfrac{5}{4}=\dfrac{x}{12-x}\)

\(\implies \sf5(12-x)=4x\)

\(\implies \sf 60-5x=4x\)

\(\implies \sf 9x=60\)

\(\implies \sf x=\dfrac{60}{9}\)

\(\sf \implies x=\dfrac{20}{3}\)

\(\\ \rm\Rrightarrow \dfrac{4}{5}=\dfrac{12-x}{x}\)

\(\\ \rm\Rrightarrow 4x=5(12-x)\)

\(\\ \rm\Rrightarrow 4x=60-5x\)

\(\\ \rm\Rrightarrow 9x=60\)

\(\\ \rm\Rrightarrow x=6.67\)

Option C none of the above

The equation is [y = (11/5)x - 3] for the line touches (0, -3) and (5, 8).

In a graph, a line is a straight curve that connects two or more points. It is used to represent relationships between two variables, such as x and y.

To write an equation for the line passing through the points (0,-3) and (5,8), we can use the point-slope form of the equation of a line, which is:

y - y₁ = m(x - x₁)

where m is the slope of the line, and (x₁, y₁) is one of the given points on the line. The slope:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are the two given points on the line.

Using the points (0, -3) and (5, 8), we can find the slope:

m = (8 - (-3)) / (5 - 0) = 11/5

Now we can use the point-slope form of the equation of the line, with (0,-3) as the given point:

y - (-3) = (11/5) (x - 0)

Simplifying this equation, we get:

y + 3 = (11/5) x

Subtracting 3 from both sides, we get the final equation for the line:

y = (11/5)x - 3

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No, it is not possible to have a simple graph with n vertices, where n is any integer greater than or equal to 5, such that all vertices have different degrees.

In a simple graph, the degree of a vertex refers to the number of edges connected to that vertex. The maximum degree possible in a graph with n vertices is (n-1), which occurs when one vertex is connected to all other vertices.

To create a graph where all vertices have different degrees, we would need to assign a unique degree to each vertex. However, if n is greater than or equal to 5, we cannot assign n unique degrees to n vertices while satisfying the conditions of a simple graph.

To see why, consider the case of n = 5. We need to assign degrees 1, 2, 3, 4, and 5 to the vertices.

The vertex with degree 5 must be connected to all other vertices, leaving us with four remaining degrees (1, 2, 3, and 4) to assign to the remaining four vertices. However, no matter how we distribute these degrees, at least two vertices will have the same degree.

This argument can be extended to any value of n greater than 5. Therefore, it is not possible to construct a simple graph with n vertices where all vertices have different degrees for any integer n ≥ 5.

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