Five years ago, a computer that worked half as fast as a current computer cost twice as much money. The current computer's speed to price ratio is what percent of the older computer's speed to price ratio? I'm confused on what the ratio is

There are 2 values of k, 12 and -12, for which the polynomial x^2 + kx - 36 has two distinct integer roots.

The polynomial x^2 + kx - 36 has two distinct integer roots if and only if its discriminant is a perfect square.

The value of the discriminant is given by:

b^2 - 4ac = k^2 + 4 * 36 = k^2 + 144

So, for the polynomial x^2 + kx - 36 to have two distinct integer roots, k^2 + 144 must be a perfect square.

We know that the difference of two consecutive perfect squares is equal to an odd number, so we can start testing values of k by incrementing k by 1 and checking if k^2 + 144 is a perfect square.

Starting with k = 0, we have k^2 + 144 = 144, which is not a perfect square. For k = 1, k^2 + 144 = 145, which is also not a perfect square.

For k = 2, k^2 + 144 = 148, which is still not a perfect square.

We keep incrementing k and checking until we find a value of k such that k^2 + 144 is a perfect square.

When k = 12, we have k^2 + 144 = 168, which is a perfect square (12^2).

Therefore, the polynomial x^2 + 12x - 36 has two distinct integer roots.

We can repeat this process for negative values of k to see if the polynomial has two distinct integer roots for those values.

We find that for k = -12, the polynomial x^2 - 12x - 36 also has two distinct integer roots.

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Answer:

To solve the equation 7cos(9x)−1=1, we first need to move the 1 to the left side of the equation:

7cos(9x) = 2

To find the solutions of the equation, we can divide both sides by 7:

cos(9x) = 2/7

Now we will use the inverse cosine function, denoted as arccos, to find the angle that has a cosine value of 2/7. Since the function cos is periodic with period 2Pi, it's range is [-1,1], we will look for the solutions between 0 and 2Pi.

x = (1/9)arccos(2/7) + (2kPi)/9 for k =0,1,2,....

we can also express the solution in degrees by multiplying the radian measure with 180/Pi.

x = (20/63)arccos(2/7) + (160*k) for k =0,1,2,....

or

x = (20/63) * arccos(2/7) * (180/pi) + (160*k) for k =0,1,2,....

where k is an integer.

So, x = (20/63) * arccos(2/7) * (180/pi) + (160*k) where k =0,1,2,.... is an expression that represents all solutions to the equation in degrees.

On applying the arithmetic operation of division, the expression 2.646 / 0.9 gives a result of 2.9.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The expression given is -

2.646 / 0.9

The expression is given in decimal form.

Use the arithmetic operation of division.

First remove the decimal points.

Multiply the numerator and denominator by 1000 as there are three decimal points in the numerator -

(2.646 × 1000) / (0.9 × 1000)

Now divide the expression -

2646 / 900

= 2.94

Rounding off to one decimal point gives 2.9.

Therefore, the value is obtained as 2.9.

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Answer:

try your best

Step-by-step explanation:

u can do it!!

The area of the triangle formed by connecting the three points is 6 square units. The result is obtained by using the determinant method.

The area of a triangle in coordinate geometry can be found by using the determinant formula.

[tex]Area \: of \: triangle = \frac{1}{2} \left[\begin{array}{ccc}x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right][/tex]

The three points of a triangle are:

Using the determinant formula, the area of the triangle is

[tex]= \frac{1}{2} \left[\begin{array}{ccc}2&2&1\\4&2&1\\3&3&1\end{array}\right][/tex]

= ½ |2(2-(3)) - 4(2-(3)) + 3(2-2)|

= ½ |2(-6) - 4(-6) + 0|

= ½ |-12 + 24|

= ½ |12|

= 6 square units

Hence, the area of the triangle is 6 square units.

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An inequality to represent the possible values for the height, h, for this triangle is 1ft≤h≤25ft

The area of a rectangle is expressed as;

Area = Length * height

A = Lh

If the area of a rectangle is at most 400 square centimeters, this is expressed as;

A ≤400

≤ means at most that the area of the rectangle cannot be greater than 400

Substitute the given value into the inequality expression

Lh ≤ 400

Given

L = 16

16h ≤ 400

Divide both sides by 16

16h/16 ≤ 400/16

h ≤ 400/16

h ≤ 25

Hence the possible values of the height are within the range 1ft≤h≤25ft since we cannot have a negative value for the dimension.

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The 12th term of the geometric sequence 7, -21, 63 is -1240029, this is determined using the Geometric progression formula.

When one term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence.

The geometric progression is given by the formula:

aₙ = arⁿ⁻¹

a = first term = 7

r = common ratio = - 21 / 7 = - 3

n = number of terms = 12

Therefore, substituting the values in the GP:

a₁₂ = 7 × -3¹²⁻¹

a₁₂ = 7 × -3¹¹

a₁₂ = 7 × -177147

a₁₂ = -1240029

Therefore, the 12th term of the geometric progression is -1240029.

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In the given image the triangle POR and triangle FGH are not equal or similar to each other.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In ΔPQR, the line segment PQ measures 35 units.

In ΔPQR, the line segment PR measures 49 units.

In ΔPQR, the line segment QR measures 63 units.

In ΔFGH, the line segment FG measures 69 units.

In ΔFGH, the line segment GH measures 38 units.

In ΔFGH, the line segment HF measures 67 units.

These two triangles are not similar to each other.

Both these triangles have different measurements of line segments.

Both these triangles have no data available for their angles.

The only way the two triangles are similar is that they both are scalene triangles as they both have different measuring sides.

Therefore, the two triangles are not similar.

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A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.

You can utilize methods based on the dot-product and cross-product of vectors to create a vector that is perpendicular to another supplied vector. The total of the products of the relevant components is the dot-product of the vectors A = (a1, a2, a3) and B = (b1, b2, b3):

AB = a1 b2 + a2 b2 + a3 b3. The dot product of two vectors that are perpendicular is equal to zero.

The formula for calculating the cross-product of two vectors is AB = (a2 b3 - a3 b2, a3 b1 - a1 b3, a1 b2 - a2*b1).

A vector that is perpendicular to both of the other two non-parallel vectors is the result of their cross-product.

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The value is a parameter because the class of 28 students is a population.

A statistic is a measure calculated from a sample of the population, whereas a parameter is a measure that is calculated from the entire population. It is generally a numeric value that is used to characterise a population trait. A probability distribution is defined or described by a fixed value that is typically unknown.

The population's mean, variance, and standard deviation are just a few parameters. By employing statistical techniques like maximum likelihood estimation, these parameters are often calculated from a sample of data. In the given question, since from a class of 28, the average score was 72% of the population which is the total, this value is a parameter.

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It takes 30 hours using the hose alone to fill the swimming pool.

Step 1: Make denominators the same

Step 2: Add or Subtract the numerators (keeping the denominator the same)

Step 3: Simplify the fraction

To add or subtract unlike fractions, the first step is to make denominators the same so that numerators can be added just like we do for like fractions.

Let [tex]x\\[/tex] represent the swimming pool be filled with hose alone.

Given that using the pipe alone it takes 12 hours. using both it takes 8 4/7 hours. According to given condition,

[tex]\frac{1}{x} + \frac{1}{12} = \frac{1}{8\frac{4}{7} } \\\frac{1}{x} = \frac{1}{\frac{60}{7} } - \frac{1}{12}[/tex]

[tex]\frac{1}{x} = \frac{7}{60} - \frac{1}{12}\\\\ \frac{1}{x} = \frac{7}{60} - \frac{5}{60}\\\\\frac{1}{x} = \frac{2}{60}\\\\ x = \frac{60}{2}\\\\\\ x= 30[/tex]

It takes 30 hours using the hose alone to fill the swimming pool.

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Answer:

Solution set for x is x ≤ -3
First option

Step-by-step explanation:

We have the equation

- 4x ≥ 12

Divide both sides by 4:

- x ≥ 12/4

-x ≥ 3

Multiply by -1 to make x positive. When we multiply an inequality by a negative number the inequality sign changes:  ≥ becomes ≤

Therefore we get
x ≤ 3

On the number line this is represented by the first choice

Note that the 3rd and 4th choices are easily eliminate since they represent ≥ -3 and > -3

Choice #2 has an unfilled circle at -3. This represents a < inequality

A filled circle represents a ≤ inequality

Answer

Solution set for x is x ≤ -3
First option

The area of rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.

So, from the definition of the area of the rectangle.

Area = length x width

Given:

Thus,

Area = (5x + 4)(x^2+3x+2)

Simplifying,

Area = 5x(x^2+3x+2) + 4(x^2+3x+2)

Area = 5x³ + 19x² + 22x + 18

Thus, the area of the rectangle with the given height and width is found as: Area = 5x³ + 19x² + 22x + 18.

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The complete question  is-

A rectangle has a height of x+4x+4 and a width of x^2+3x+2. Express the area of the entire rectangle.

Let a = units of A produced

Let b = units of B produced

At least 30 units of product A and 10 units of product B are required daily, and the maximum number of units per day should not exceed 80.

Therefore

a ≥ 30

b ≥ 10

a + b ≤ 80

Product A yields a profit of $15 and product B yields a profit of $8.

Therefore the objectve profit function is

P(a,b) = 15a + 8b

Answer:

The objective function is

P(a,b) = 15a + 8b, subject to

a >= 30;  b>= 10;  a+b <= 80

Create a graph that displays the constraints and calculates maximum profit at the boundary points. The solution region is shaded.

The maximum profit occurs when a=70 and b=10.

Answer:

P= 15a + 8b

Step-by-step explanation:

The percent of error is 17.65% .

The percent of error is a way to measure the difference between the expected value and the actual value. In this case, Peter expected to earn $425 in a week but he actually earned $500.

So, the difference between the expected value and the actual value is $75. The percent of error is calculated by taking the difference between the actual value and the expected value, dividing that by the expected value, and multiplying the result by 100%.

In this case, (500-425)/425*100% = 17.65%, which means that Peter's actual earnings were 17.65% higher than what he expected to earn.

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95 and 50 are the measures of those two angles.

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

given, One angle of a triangle measures 35°. The other two angles are in a ratio of 10:19.

Let second angle of the triangle is "x"

Thus, third angle of triangle will be = 10/19x

Since, sum of the three angles of triangle is 180 degrees

35 + x + 10/19x = 180

29x/19 = 145

x = 5 *19

x = 95

So, Second angle of triangle = x = 95

Third angle of triangle = 10/19x = 50

therefore, the measures of those two angles are 95 and 50.

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Answer:

The formula is going to be 17 hrs

Dan is 52 years old and Matt is 4 years old.

The first step is to form a system of equations using the information provided in the question:

a + b = 56 equation 1

a = 13b equation 2

Where:

a = Dan's age

b = Matt's age

The substitution method would be used to determine the values.

Substitute for a in equation 1 using equation 2:

13b + b = 56 equation 3

14b = 56

b = 56 / 14

b = 4

Substitute for b in equation 2:

a = 13(4)

a = 13 x 4

= 52

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The stem-and-leaf plot for the data in this problem is given as follows:

The measures that are less than 10 are given as follows:

5, 8 and 9.

Hence they go on the plot as follows:

0|5 8 9

The measures that are between 10 and 19 are given as follows:

12, 12, 13, 14, 15, 18.

Hence they go on the plot as follows:

1| 2 2 3 4 5 8

The measures that are between 20 and 29 are given as follows:

21 and 25.

Hence they go on the plot as follows:

2|1 5.

The remaining measure is given as follows:

30.

Which goes on the plot as follows:

3|0.

The problem is given by the image presented at the end of the answer.

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Answer:

-7

Step-by-step explanation:

angles in a triangle add up to 180⁰

90⁰+30⁰+(x+67)=180⁰

187+x=180⁰

x=180⁰-187⁰

x=-7

In order to avoid using the variable "Vi", the equation which you should use include the following: D) Ax = Vft – 1/2at².

In Mathematics, the third equation of motion is represented by this mathematical expression:

Ax = Vit + ½at²     ......equation 1.

Where:  

From the first equation of motion, we have:

Vf = Vi + at

Making Vi the subject of formula, we have:

Vi = Vf - at    ......equation 2.

Substituting the equation, we have:

Ax = (Vf - at)t + ½at²

Ax = Vft - at² + ½at²

Ax = Vft + ½at²

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The value of FJ is 39 units.

See the attached figure to better understand the problem

We know that

If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent.

According to this problem,

△FEG is similar to △FHJ  ( by AA Similarity Theorem)

so

[tex]\frac{FE}{FH} = \frac{FG}{FJ}[/tex]

We have,

FE = HF + EH = (26 + 14 ) units

FE= 40 units

FH = HF = 26 units

FG = 60 units

substitute the given values,

[tex]\frac{40}{26} = \frac{60}{FJ}[/tex]

[tex]FJ = \frac{26 * 60}{40}[/tex]

FJ =  39

So, the value of FJ is 39 units.

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The distance between the two points R and S is √2.

The length of the line segment connecting any two points represents the distance between them. There is just one line that connects the two places.

The distance between the two points R and S can be calculated using the Pythagorean theorem. Given the coordinates (x, y) for point R and (x + 1, y + 1) for point S, the distance d between R and S is given by:

d = √((x + 1 - x)^2 + (y + 1 - y)^2) = √(1^2 + 1^2) = √2.

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In contrast to the pair of following two triangles, the initial two triangles do not share any similarities.

Two triangles are considered to be similar if the corresponding sides are proportionate and the corresponding angles are congruent. Or to put it another way, comparable triangles may not necessarily be the same size but they do have a similar shape. The triangles are also congruent if the lengths of their respective sides are the same.

We already know that the ratio of the two triangles' corresponding sides must match for them to be identical triangles.

A.) In the first pair of triangles,

The first pair of triangles to be similar,

[tex]$\frac{U S}{U D}=\frac{U T}{U E}=\frac{S T}{D E}$$[/tex]

The aforementioned ratio ought to be comparable, however as we can see,

[tex]$$\begin{aligned}& \frac{U S}{U D} \neq \frac{U T}{U E} \\& \frac{39}{16} \neq \frac{40}{16}\end{aligned}$$[/tex]

The two triangles supplied are not identical triangles because, as we can see, the ratio of the triangle's sides is not the same.

B.) In the second pair of triangles,

The second pair of triangles to be similar,

[tex]$\frac{A B}{H G}=\frac{B C}{G F}=\frac{C A}{F H}$$[/tex]

As we can see, the ratio should be comparable to the one above.

[tex]$\frac{72}{12}=\frac{48}{8}=\frac{84}{14}=6$$[/tex]

The two triangles supplied are similar triangles because, as we can see, the ratio of the triangle's sides is the same.

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If at local Convenience store , William buys 3 soft drinks and 2 hot dogs for $7.70, while Sarah buys 2 soft drinks and 1 hot dog at cost of $4.55 , then the cost of 1 soft drink is $1.4   and cost of 1 hot dog is $1.75  .

We will use system of equations to find cost of 1 soft drink and 1 hot dog. let the cost of 1 soft drink is = $x  ;  and

let the cost of 1 hot dog is = $y  ;

So , for William the situation is represented as ;

⇒ 3x + 2y = 7.70 .....equation(1)

and for Sarah the situation is represented as ;

⇒ 2x + y = 4.55    ....equation(2)

we first solve equation(1) for y:

⇒ y = (7.70 - 3x)/2

We can substitute this expression for y in equation (2) and solve for x:

⇒ 2x + (7.70 - 3x)/2 = 4.55

⇒ 4x + (7.70 - 3x) = 4.55×2

⇒ 4x -3x = 9.1 - 7.70

⇒ x = 1.4

So, the cost of 1 soft drink is $1.4  ,

Now , We can use this value of x to find the cost of 1 hot dog:

⇒ y = (7.70 - 3x)/2

⇒ y = (7.70 - 3×1.4)/2

⇒ y = (7.70 - 4.2)/2

⇒ y = 3.5/2  ;

⇒ y = 1.75

So, the cost of 1 hot dog is $1.75  .

Therefore, one soft drink costs $1.4  and one hot dog costs $1.75  .

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Answer:
3(n+7) =
(3)(n) + (3)(7) =
3n + 21

Step-by-step explanation:

I hope this helps you :D

a. There are 10⁹ hertz in 1 giga hertz and 10^12 hertz in one terahertz

b. The channels frequency in hertz 6×10⁷hertz

c. The frequency of a microwave in hertz is 3× 10^10 hertz

d. The frequency of light is 10⁵ times greater than the frequency of the radio station

Frequency describes the number of waves that pass a fixed place in a given amount of time. So if the time it takes for a wave to pass is is 1/2 second, the frequency is 2 per second. If it takes 1/100 of an hour, the frequency is 100 per hour.

The S.I unit of frequency is hertz and it has other bigger unit stated as follows:

1 kilohertz = 10³hertz

1megahertz = 10⁶ hertz

1 gigahertz = 10⁹ hertz

1 tera hertz = 10^12 hertz

Therefore 60mega hertz = 60× 10⁶ = 6×10⁷

30 gigahertz = 30 × 10⁹ = 3 × 10^10

if the frequency of light is 1000 tera hertz and 100 mega hertz is the frequency of a radio station , then the frequency of light will be 1000×10^12 ÷ 100× 10⁶ = 10⁵ greater than the frequency of the radio station.

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Answer:

The correct answer is C f(2)

The perimeter of the given figure is 79.4 units.

The perimeter of a polygon is defined as the length of the boundary around the sides of the polygon. The perimeter of a polygon can be calculated by calculating the sum of the lengths of the sides of the polygon.  

Here we have

EF = 8, FD = 10, ED = 11, IG = 24, and HG = 26.4  

As we know,

Perimeter = Sum of all sides  

The perimeter of GHI = (EF + FD + ED + IG + HG)  

=  8 + 10 + 11 + 24 + 26.4  

= 79.4 units

Therefore,

The perimeter of the given figure is 79.4 units.

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√131 lies between 11 and 12.

The numbers that include natural numbers and zero are called whole numbers.

Given is the square root of 131.

We can write the square root of 131 as -

√131 = 11.45

We can write the whole numbers as -

11 < 11.45 < 12

Therefore, √131 lies between 11 and 12.

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