Father's age is five times than the son's age. If the sum of their ages is 60 years, find their present ages.​

Answer:

(x-15)(x-1) x²

Step-by-step explanation:

x² (x²-16x+15)

a+b=-16

ab=15

a=-15

b=-1

x(x²-15)- (x-15)

(x-15)(x-1)

(x-15)(x-1) x²

There will be 8980 illiterate people in Sylvania 4 years from now if the country continues to reduce the number of illiterate citizens by 5 each year.

We can write a function P(t) to represent the number of illiterate people in Sylvania t years from today, where t is the number of years after the current year.

Given that the country has decided to reduce the number of illiterate citizens by 5 each year, we can subtract 5 from the number of illiterate people each year.

The initial number of illiterate people in the country is 9000. So, the function can be written as:

P(t) = 9000 - 5t

where t is the number of years after the current year.

For example, if we want to find out how many illiterate people will be in Sylvania in 4 years from now, we can substitute t with 4:

P(4) = 9000 - 5(4) = 9000 - 20 = 8980

Therefore, there will be 8980 illiterate people in Sylvania 4 years from now if the country continues to reduce the number of illiterate citizens by 5 each year.

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There is no difference in g(x) and f(x) when graphing a radical expression as represents the same function: √(x-5) +6

The given radical expression are:

g(x) = √(x-5) + 6

f(x) = √(x-5) + 6

The graph of both function is plotted, which have the exact same value on graph.

Thus, there is no difference in g(x) and f(x) when graphing a radical expression as represents the same function: √(x-5) +6

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The density of the granite is 2690 kg/m³ and the mass of 1.3 m³ of granite is ​3497 kg.

Density is expressed mathematically as;

p = m / v

Where m is mass and v is volume.

Given that;

Plug the given values into the above formula and solve for density of the granite.

p = m / v

p = 6725 kg / 2.5 m³

p = 2690 kg/m³

b) The mass of 1.3 m³ of granite in kg will be;

p = m / v

m = p × v

m = 2690 kg/m³ × 1.3 m³

m = 3497 kg

Therefore, the mass of  1.3 m³ of granite is 3497 kg.

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Answer: 1.07x107 but the seven goes on top of the 10

Step-by-step explanation:

Answer:

1.07 × 10⁷

Step-by-step explanation:

To express 10,700,000 in scientific notation, we have to rewrite it as a decimal number that is between 1 and 10 multiplied by a power of 10.

As a decimal, the number is:

1.07.

We have to move the decimal point 7 places to get this number (see the attached image). Therefore 1.07 is multiplied by 10⁷ to get 10,700,000.

5 times the sum of x squared and y squared. This can be expressed as 5(x^2 + y^2).

Express is a web application framework for Node.js, released as free and open-source software under the MIT License. It is designed for building web applications and APIs and is the de facto standard server framework for Node.js. It provides a host of features to facilitate the development of web and mobile applications, including routing, templating, and a middleware system to handle requests and responses. Express is the backend component of the MEAN stack and enables the rapid development of dynamic web applications.

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Answer:

96

Step-by-step explanation:

Answer:

a) 2*(x+4)

b) 1/4*x + 1/3*x

Answer:

a) 2(x+4)

b) 7x/12

Step-by-step explanation:

a) Sum of x and 4 is (x+4). Since the number is doubled,

2 * (x+4) = 2(x+4)

b) One fourth of a number x is x/4 and one third of the number is x/3.

Adding these two:

x/4 + x/3

The LCM of 4 and 3 is 12 and so,

(4x + 3x)/12

= 7x/12

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In this scenario, the dependent variable is the cost of the boxes of cookies and the independent variable is the number of boxes of cookies being purchased.

The cost of the boxes of cookies depends on the number of boxes being purchased. The more boxes of cookies that are purchased, the higher the cost will be. Therefore, the cost of the boxes of cookies is the dependent variable, as it depends on the independent variable of the number of boxes being purchased.

Conversely, the number of boxes of cookies being purchased is the independent variable, as it is the variable that is being manipulated or changed. The cost of the boxes of cookies is not being changed, but rather is dependent on the number of boxes being purchased.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]x+2y=2\implies 2y=-x+2 \\\\\\ x=\cfrac{-x+2}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{2}}x+1\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-1}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-1} \implies 2}}[/tex]

so we're really looking for the equation of a line whose slope is 2 and it passes through (5 , 6)

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{5}) \\\\\\ y-6=2x-10\implies {\Large \begin{array}{llll} y=2x-4 \end{array}}[/tex]

The equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.

y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line.

Given that a line QR has an equation is x+2y = 2, we need to find the equation of a line passing through (5, 6) and is perpendicular to the given line,

Converting the equation into slop-intercepts form,

y = -0.5x+1

Here, slope m = -0.5

We know that the slopes of the perpendicular lines are negative reciprocal of each other,

Therefore, the slope of the asked line is 2.

So, its equation =

y = 2x+c

To find c, put x = 5 and y = 6

6 = 2(5) + c

c = -4

Therefore, the final equation will be =

y = 2x-4

Hence, the equation of a line perpendicular to line QR in slope-intercept form that contains point (5, 6) is y = 2x-4.

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To know whether people can bargain the price down when purchasing a house at a 5% level of significance, we need to put a hypothesis test. The null hypothesis would be that people cannot bargain the price down

To determine whether 3-bedroom houses are cheaper than 4-bedroom houses, we would again give out a hypothesis test. The null hypothesis would be that there is no difference in price between 3-bedroom and 4-bedroom houses.

but the other hypothesis would be that 3-bedroom houses are cheaper than 4-bedroom houses.  If the p-value is less than 0.05, we can reject the null hypothesis and say that 3-bedroom houses are more cheaper than 4-bedroom houses.

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so, since we know that the derivative is simply the equation we use to get the slope at any point on the curve, thus df/dx will be that.

now, we know that g(x) is already in slope-intercept form, so it has a slope of "4", hmmm what's "x" at that instance?

[tex]f(x)=-x^2+8x+20\implies \cfrac{df}{dx}=-2x+8 \\\\[-0.35em] ~\dotfill\\\\ g(x)=\stackrel{\stackrel{m}{\downarrow }}{4}x+k\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\\\ 4~~ = ~~-2x+8\implies 2=x[/tex]

well, now we know that x = 2, hmmm what's "y" at that instance? well, our "y" will be simply f(2) = g(x), because g(x) is touching f(x) at that point on the curve.

[tex]f(2)=-(2)^2+8(2)+20\implies f(2)=32 \\\\[-0.35em] ~\dotfill\\\\ g(x)=4x+k\implies 32=4(2)+k\implies 32=8+k\implies \boxed{24=k}[/tex]

Check the picture below.

To have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year

To find out how much a woman would have to make in a year to have a higher salary than 99% of her male counterparts, we need to find the salary level that corresponds to the 99th percentile of the male salary distribution.

First, we need to calculate the standard deviation of the annual salaries for both men and women. Since the standard deviation of the monthly salaries is $300, the standard deviation of the annual salaries can be calculated as:

σ_annual = σ_monthly * √12 = 300 * √12 = $1039.23

Next, we can calculate the salary level that corresponds to the 99th percentile of the male salary distribution using the standard normal distribution table.

z-score for the 99th percentile = 2.33

salary level for the 99th percentile of male salary distribution = mean + z-score * σ_annual

= $2750 + 2.33 * $1039.23 = $5229.48 (rounded to the nearest cent)

Therefore, to have a higher salary than 99% of her male counterparts, a woman would have to make more than $5229.48 per month, or $62753.76 per year (rounded to the nearest cent).

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The function with the greatest rate of change are:

1. C = 3

2. A = 5

3. A = 1

4. B = 3

The rate of change of a linear function, also known as the slope of the line, represents the amount by which the output (y) changes for a given change in the input (x). In other words, it is the measure of how steep the line is.

The formula for the rate of change, or slope, of a linear function is:

slope = (change in y) / (change in x)

1. Rate of change for function A = change in y / change in x = 4/3

For B = 1/2

For C = 3/1 = 3

The function with the greatest rate of change is C = 3

2. Rate of change for function A = change in y / change in x = (10 - 5)/(1 - 0) = 5

For B = (12 - 8) / (3 - 1) = 2

For C = (6 - 3)/(1 - 0) = 3

The function with the greatest rate of change is A = 5

3. Rate of change for function A = change in y / change in x = 2/2 = 1

For B = (3 - 2)/(2 - 0) = 1/2

For C = 1/3

The function with the greatest rate of change is A = 1

4. Rate of change for function A = change in y / change in x = -1/3

For B = (10 - 1)/(4 - 1) = 3

For C = 2

The function with the greatest rate of change is B = 3

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In the context of economics, the term “break-even point” is used to indicate the number necessary to make enough money to keep going, and it is expressed in both units and dollars.

Break-even point is a term used in cost accounting to describe the point at which total cost and total revenue are equal. At this point, there is no profit or loss; it is a neutral zone. At this point, a firm's revenue from the sale of products and services is just sufficient to cover the total costs of producing those products and services.

The break-even point can be expressed in terms of units sold or in terms of total revenue. The point at which the total revenue equals total cost is the break-even point in terms of dollars. The point at which the number of units sold equals the fixed costs divided by the contribution margin per unit is the break-even point in terms of units sold. Therefore, the break-even point is expressed in both units and dollars to show the number necessary to make enough money to keep going.

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Option C, MN/LK||MN, is the additional piece of information required to demonstrate that ΔLKN ~ΔKNM by the SAS similarity theorem.

The SAS (Side-Angle-Side) similarity theorem: what is it?

According to the SAS (Side-Angle-Side) similarity theorem, two triangles are similar if they have two pairs of corresponding sides that are in proportion and the included angles are congruent.

In this example, we know that ΔLKN and ΔKNM share the angle at vertex K, and we also know that LN/MN and LK/KN are in proportion.

To clarify that MN is parallel to LK and forms a transversal with LN, we must first prove that MN/LK||MN.

To prove that the included angles between the matching sides are congruent, which is necessary for the triangles to be similar, this information is required.

Consequently, in order to demonstrate that ΔLKN~ΔKNM according to the SAS similarity theorem, option C is the correct additional piece of information.

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PR = 16 units

Similar triangles are two triangles that have the same shape but not necessarily the same size. This means that their corresponding angles are equal, and their corresponding sides are proportional in length.

Here, ΔPRQ similar with ΔPST

So, we can say that their corresponding sides are in proportion (i.e., have the same ratio).

[tex]\frac{PR}{PS} = \frac{RQ}{ST}[/tex]

[tex]\frac{(x+7) + (x-1) }{(x+7)} = \frac{8}{6}[/tex]

Simplification,

12x + 36 = 8x + 56

x = 5

So, the value of PR = (x+7) + (x-1)

PR = (5+7) + (5-1) = 16

Therefor, PR = 16 units

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The triabgles ae similar. Their corresponding sides are in proportion.

PR = 16 units

Triangles that are similar to one another in shape but not necessary in size are called similar triangles. Their respective sides are proportional in length, and their corresponding angles are equal. Three edges, three angles, and three vertices make up a triangle. The sum of a triangle's three internal angles is 180 degrees. The triangle's third side is longer than the sum of its two longest sides.

Here, ΔPRQ similar with ΔPST

Thus, their respective sides are proportional, as we can see. (i.e., have the same ratio).

[tex]\frac{PR}{PS} =\frac{RQ}{ST} \\\\\frac{(x+7)+(x-1)}{(x+7)} =\frac{8}{6}[/tex]

Simplification,

12x + 36 = 8x + 56

x = 5

So, the value of PR = (x+7) + (x-1)

PR = (5+7) + (5-1)

    = 16

Therefor, PR = 16 units

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The diameter οr radius οf the circular οbject is 120mm, and the circumference οf the οbject 1 frοm the centre tο the edge οf a DVD is 380mm.

A circle's οr an ellipse's circumference is its perimeter. In οther wοrds, if the circle were tο be straightened οut alοng a line segment, the length οf the arc wοuld be the circumference. The perimeter is mοre frequently used tο refer tο the length οf the curve surrοunding any defined figure.

The given infοrmatiοn is that a DVD's edge is 60 mm lοng.

The diameter, radius, and circumference οf the circular οbject must be determined in οrder tο determine the measurement.

We cοncluded that

Radius = 60mm

Diameter = 120mm

Circumference = 380mm

Hence, Diameter = 120mm

Circumference = 380mm

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The value of D is 49.1º to the nearest degree using the law of sines.

To solve for angle D, we can use the law of sines, which states that for any triangle with sides a, b, and c opposite angles A, B, and C respectively:

a/sin(A) = b/sin(B) = c/sin(C)

Using this formula, we can solve for angle D:

sin(D)/d = sin(F)/f

sin(D) = (d/f) × sin(F)

sin(D) = (76/20) × sin(17º)

sin(D) = 0.7588

Taking the inverse sine of both sides, we get:

D = [tex]sin^{-1}[/tex] × (0.7588)

D = 49.1º (rounded to the nearest tenth of a degree)

The law of sines can have two possible solutions for an angle, depending on the triangle. However, in this case, since angle D is opposite the longer side (d), there is only one possible solution.

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Answer:

Step-by-step explanation:

[tex]m=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

    [tex]=(\frac{-12+(-8)}{2}, \frac{-7+(-4)}{2})[/tex]

    [tex]=(-10,-5.5)[/tex]    

Answer:

-6, -3, -2, 0, 2, 3, 6

Step-by-step explanation:

Normally the biggest number has the bigger value but in negative integers the smaller number has the bigger value.

Eg- If you have 2 dollars it is bigger that -2 dollars as then you will be going in dept.

-5 is smaller than -1

-1 is the greatest negative integer.

The acceleration of the system is 0.83 m/s² and the tension in the string is 8.3 N.

The acceleration of the system can be calculated using Newton's second law of motion. The equation is F = ma, where F is the net force on the system, m is the total mass, and a is the acceleration. Since the two masses are connected by a light inextensible string, the net force acting on the system is equal to the tension in the string. Therefore, the equation becomes T = (5 kg + 2 kg)a, where T is the tension and a is the acceleration. Solving for a, the acceleration is found to be 0.83 m/s². The tension in the string can also be calculated using the equation above. Plugging in the acceleration, the tension is found to be 8.3 N.

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Therefore , the solution of the given problem of volume comes out to be false we must first know the cylinder's radius and height.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 stand for cubic dimensions. However, you can use an object's bulk to estimate its dimensions. Usually, the weight of the item is converted into mass measures like kilograms and kilos.

Here,

The capacity of a cylinder and a cone that are the same height and radius are not the same.

The formula V = πr²h,

where r is the radius of the base and h is the height, determines the volume of a cylindrical. Contrarily, the equation

=> V = (1/3)r²h gives the volume of a cone.

To calculate the volume of a cone with the same measurements if the cylinder's volume is 99 cubic cm,

False we must first know the cylinder's radius and height.

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The trigonometric ratios can find the missing side of a right triangle given an angle, such as by using the tangent ratio to calculate the adjacent side length when given the length of the opposite side.

The trigonometric ratios are used to calculate specific values of a triangle. The three main ratios are sine, cosine, and tangent. The sine ratio is the ratio of the side length opposite the angle to the hypotenuse of the triangle. The cosine ratio is the ratio of the side length adjacent to the angle to the hypotenuse of the triangle. The tangent ratio is the ratio of the side length opposite the angle to the side length adjacent to the angle.

To find the missing side of a right triangle, given an angle, we use the trigonometric ratios. For example, if we have an angle of 45 degrees and a side length of 8, we can use the tangent ratio to calculate the missing side length. To do this we use the formula tan(45) = opposite/adjacent. We know the opposite side is 8, so to calculate the adjacent side we solve for x in the equation 8/x = tan(45). We get x = 8/tan(45), and x = 8/1 = 8. Therefore, the adjacent side length is 8.

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Answer:

y = -2x + 17.

Step-by-step explanation:

To find the equation of a line that is parallel to another line, we need to use the fact that parallel lines have the same slope.

First, we need to rearrange the equation of the given line 4x + 2y = 10 into slope-intercept form y = mx + b:

4x + 2y = 10

2y = -4x + 10

y = -2x + 5

So, the slope of the given line is -2.

Since the line we're looking for is parallel to the given line, it will have the same slope of -2. We also have a point (7,3) that the line passes through. We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is the point.

Plugging in the values, we get:

y - 3 = -2(x - 7)

Simplifying:

y - 3 = -2x + 14

y = -2x + 17

So, the equation of the line that passes through the point (7,3) and is parallel to the line 4x + 2y = 10 is y = -2x + 17.

Answer:

13 for 5 bags.

Step-by-step explanation:

Dani spends 5.20 in total for 2 bags. You would do 5.20/2 to get 2.60 which tells us that 2.60 is the cost per bag. Then you would do 2.60 x 5 to get 13.

The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot. It is also known as the regression line.

What is regression line?

In the context of MS Pre-Algebra S2 V16.2, the line of best fit is used to analyze patterns of association between two sets of data. For example, if we have data on the height and weight of a group of individuals, we can use a scatter plot to visualize the relationship between these two variables.

By drawing a line of best fit through the data points, we can see the general trend or pattern of association between height and weight. This line can then be used to make predictions about the weight of an individual based on their height, or vice versa. The line of best fit is a useful tool for analyzing patterns of association in a variety of fields, including statistics, economics, and social sciences.

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Complete question is: The 6.02 line of best fit is a straight line that best represents the trend or pattern of association between two variables on a scatter plot.

tan t = -4/3

The equation for the unit circle is

x2 + y2 = 1


For the point (-3/4, y) we have

(-3/4)2 + y2 = 1


Rearranging this gives us

y2 = 1 - (3/4)2

Solving for y gives us

y = √ (1 - (3/4)2)


Now we can find tan t by using the equation

tan t = y / -3/4


Substituting in the value of y we found earlier gives us

tan t = √ (1 - (3/4)2) / -3/4


Finally, simplifying the equation gives us the answer

tan t = -4/3

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Lesley gets 10/18 or 5/9 of the counters.Adam has 18 counters, so we can express the total number of counters as 18/18. If he gave 10 of those counters to Lesley, we can express that as 10/18.

Adam has 18 counters, so we can express the total number of counters as 18/18, which is equivalent to 1. If he gave 10 of those counters to Lesley, we can express that as 10/18. To find out what fraction of the 18 counters Lesley gets, we need to simplify 10/18. Since both the numerator and denominator are divisible by two, we can divide both the numerator and denominator by two, which gives us 5/9. This means that Lesley gets 5/9 of the 18 counters, which is equivalent to 10/18 or half of the total number of counters.

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Answer:

After John finished his energy drink, he noticed on the label that it had 160 milligrams of caffeine. He read online that the amount of caffeine in the body decreases by a factor of

1

8

each hour after it's consumed.

Step-by-step explanation:

The exponential equation in the form y=a(b)² that can model the amount of caffeine left in John's body, y, x hours after finishing the energy drink is y= 160(1/8)⁽ˣ⁾. After 6 hours, the amount of caffeine left in John's body will be y=160(1/8)⁽⁶⁾ ≈ 1.96 milligrams (rounded to the nearest milligram).

The exponential equation y=a(b)² can be used to model the amount of caffeine left in John's body x hours after consuming an energy drink. In this equation, a represents the initial amount of caffeine in the body (160 milligrams), and b represents the factor by which the amount of caffeine decreases each hour (1/8). To find the amount of caffeine left in John's body after 6 hours, we can simply substitute x=6 into the equation and solve for y. The result is y=160(1/8)⁽²*⁶⁾ ≈ 6 milligrams. This means that after 6 hours, John will have approximately 6 milligrams of caffeine left in his body if he doesn't consume any more caffeine.

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Complete question:

After John finished his energy drink, he noticed on the label that it had 160 milligrams of caffeine. He read online that the amount of caffeine in the body decreases by a factor 1/8 of each hour after it's consumed.

Write an exponential equation in the form y=a(b)² that can model the amount of caffeine left in John's body, y, x hours after finishing the energy drink.

Use whole numbers, decimals, or simplified fractions for the values of a and b,

To the nearest milligram, how much caffeine will be in John's body after 6 hours if he doesn't consume any more caffeine?