If f(x)=-2x+4 and g(x)=x^2-5x, find all values of x for which f(x)=g(x)

Answer:

Step-by-step explanation:

If the product of two rational numbers is 4/25, we can write the equation:

(x) * (-6/5) = 4/25

where x is the other number.

Expanding the equation:

x * -6/5 = 4/25

Multiplying both sides by 5 to get rid of the fraction on the right-hand side:

5 * x * -6/5 = 5 * 4/25

x * -6 = 4

Dividing both sides by -6:

x = -4/-6

x = 4/6

So, the other number is 4/6.

Answer:

So the other number is -[tex]\frac{4}{3}[/tex].

Step-by-step explanation:

Let x be the number.

We know,

(-[tex]\frac{6}{5}[/tex]) × x = [tex]\frac{4}{25}[/tex]

-[tex]\frac{6}{5}[/tex] × x =  [tex]\frac{4}{25}[/tex]          (By expanding the left side of the equation)

Dividing both sides by -[tex]\frac{6}{5}[/tex]

x = - [tex]\frac{4}{25}[/tex]  × -[tex]\frac{6}{5}[/tex]

After simplifying the equation ,

x = -[tex]\frac{4}{3}[/tex]

So the number is -[tex]\frac{4}{3}[/tex].

It took Bunolo 100 minutes (or 1 hour and 40 minutes) to complete the 10 km race at an average speed of 6 km/h.

To find out how long it took Bunolo to complete a 10 km race with an average speed of 6 km/h, we can use the formula:

time = distance / speed

where "distance" is the distance of the race and "speed" is the average speed at which Bunolo ran. We can convert the speed to km/minute to get the time in minutes.

To do this, we can divide the speed in km/hour by 60 (the number of minutes in an hour) to get the speed in km/minute:

6 km/hour ÷ 60 minutes/hour = 0.1 km/minute

Now, we can substitute the distance and speed values into the formula to get the time in minutes:

time = 10 km / 0.1 km/minute = 100 minutes

Therefore, To complete the 10 km race with the average speed of 6 km/h, it took Bunolo 100 minutes.

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(a) The angle measurement of first unknown angle is c = 80 degrees

(b) The angle measurement of second unknown angle is y = 110 degrees

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees

The angle measurement of first unknown angle will be:

a + b + c = 180  (sum of angles in a triangle is 180 degrees)

c = 180 - a - b

c = 180 - 30 - 70

c = 80 degrees

(b) The angle measurement of second unknown angle will be:

y = 180 - b  (sum of angles on a straight line is 180 degrees)

y = 180 - 70

y = 110 degrees

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The student must she score on the fourth test in order to raise her test average 4 points is 4 points.

An average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.

Given that, a student has completed 3 tests in biology class, we need to find that how many points above her present test average must she score on the fourth test in order to raise her test average 4 points,

Let the required point be x,

According to question,

x+4×3 / (3+1) = 4

x+12 = 16

x = 4

Hence, the student must she score on the fourth test in order to raise her test average 4 points is 4 points.

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The surface area of the sphere is 113.2 ft².

The area that a sphere's outer surface covers in three dimensions is known as the surface area of the Sphere. A sphere is a three-dimensional solid that resembles a circle in shape and is round.

The formula for a sphere's total surface area is given by

Here we have

The formula for the radius of a sphere r = 1/2 [√S/π]    

Diameter of the Moeraki boulder radius = 3 feet

=> 3 feet =  1/2 [√S/π]    

=> 6 = [√S/π]

Squaring on both sides

=> 36 = [√S/π]²  

=> S/π = 36

=> S = 36π  

=> S = 113.2  

Therefore,

The surface area of the sphere is 113.2 ft².

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Answer:

$3.35

Step-by-step explanation:

$50.25 ÷ 15 gallons = $3.35 a gallon

Answer:

hundredths

Step-by-step explanation:

Answer:

Step-by-step explanation:

2, there are 4, making it the most.

For the given system of equations, the answers are of the given choices (A), (B) and (D).

A group of two or more equations with shared variables is referred to as a system of linear equations. Finding the value of the unknown variables employed in the equations that must satisfy both equations is necessary to solve a system of equations.

Given equations are -

y - 10 = 2x ⇒ y = 2x + 10

1/2y = x + 5 ⇒ y = 2x + 10

We can observe from the equation, that both the lines are same,

So any pair of values (x, y) that satisfy the equation y = 2x + 10 is a solution to the system. For example:

(0, 10) is a solution, since y = 2(0) + 10 = 10 and (1/2).10 = 0 + 5 =

(1, 12) is a solution, since y = 2(1) + 10 = 12 and (1/2).12 = 6 = 1 + 5

(2, -6) is a not solution, since y = 2(2) + 10 = 14 and (1/2)(-6) = 7 = 2 + 5

(-5, 0) is a solution, since y = 2(-5) + 10 = 0 and (1/2)(0) = 0

Therefore, the answer is of the given choices are (A), (B), (D).

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The amount of extra meals that Taryn needs to feed her dog today is given by the inequality expression; x > 2

The parameters given in the question are;

Weight of dog = 40 pounds

Average amount of calories required per day = 1215 calories

Amount of calories already eaten = 729 calories

Amount of calories fed per meal = 243 calories

The inequality that represents the given word problem is;

243x + 729 > 1215

Subtract 729 from both sides to get;

243x > 486

divide both sides by 243 to get;

x > 2

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Answer:

61.25

Step-by-step explanation:

brainlest pls and I hope this helped u :)

Answer:

$1350.68 to nearest cent.

Step-by-step explanation:

At the beginning $500 is deposited and this accumulates interest for 3 years At the end of first year it increases to 500( 1 + r) dollars

Then at the end of the 2 years its value is

500(1+ r)(1 + r)(

and at the end of 3 years value =

500(1 + r)(1 + r)(1 + r)

= 500(1 + r)^3 dollars

and as 1 + r = x we have:

500x^3 dollars

In the same way 200 for 2 years = 200x^2

and 600 for 1 year = 600x dollars.

Total = 500x^3 + 200x^2 + 600x.

b.

So, if the interest r = 2 % (= 0.02)

and x = 1.02

Total value after 3 years

= 500(1.02)^3 + 200(1.02)^2 + 600(1.02)

= 530.604 + 208.08 + 612

= $1350.684

Answer:

D.  3√5

Step-by-step explanation:

The distance between points F and C is the hypotenuse of a right triangle.   Therefore we can use Pythagoras Theorem to calculate the distance between these points.

From inspection of the given graph the coordinates of the two points are:

The horizontal difference between the x-coordinates is:

[tex]x_C-x_F=2-(-4)=6\; \sf units[/tex]

The vertical difference between the y-coordinates:

[tex]y_C-y_F=2-(-1)=3\; \sf units[/tex]

Therefore, we have a right triangle with the following dimensions:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

To calculate the length of the hypotenuse, and therefore the distance between points C and F, substitute the values into the Pythagoras Theorem formula and solve for CF:

[tex]\implies a^2+b^2=c^2[/tex]

[tex]\implies 3^2+6^2=CF^2[/tex]

[tex]\implies 9+36=CF^2[/tex]

[tex]\implies CF^2=45[/tex]

[tex]\implies \sqrt{CF^2}=\sqrt{45}[/tex]

[tex]\implies CF=\sqrt{9 \cdot 5}[/tex]

[tex]\implies CF=\sqrt{9} \sqrt{5}[/tex]

[tex]\implies CF=3\sqrt{5}[/tex]

Therefore, the distance between points F and C is 3√5.

a) The Equation is  7.65x + 50 = 149.45.

b) The customer used the car for 13 hours.

c)  If the car used for 2 days i.e., 48 hours then the amount will be $471.12

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given that;

Members of a car sharing program pay a fee of $50 per month plus $7.65 for every hour they use a car.

And, a members bill was $149.45 last month.

a) Let number of hours for the customer use a car last month = x

So, 7.65x + 50 = 149.45

7.65x = 149.45 - 50

7.65x = 99.45

x = 13

b) The customer used the car for 13 hours.

c) If the car used for 2 days i.e., 48 hours

= 7.65x + 50

= 7.65(48)+ 50

= 471.2

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Answer: Musical preferences

A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely your musical preferences affect mortality or how much sweetener you consume.

The number of soft drink brands available for purchase is not a lurking variable in this scenario. Correct option is C.

The statement is asking which of the given variables is not a lurking variable in the scenario where Shawna is considering the correlation between the calories of sweeteners consumed and the mortality rates among women, and is trying to determine whether drinking more soft drinks will lead to a higher chance of her dying.

A lurking variable is a variable that is not included in the analysis, but has an effect on the relationship between the variables being studied. In this case, the variables being studied are the calories of sweeteners consumed and the mortality rates among women, and the effect of drinking more soft drinks on the chances of dying.

Out of the given variables, the number of soft drink brands available for purchase would not be a lurking variable, as it does not have an effect on the relationship being studied.

Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could all potentially have an effect on the relationship being studied, either as confounding variables or moderators.

For example, Shawna's weight could be a confounding variable, as it is associated with both sweetener consumption and mortality rates. The time of day she exercises could be a moderator, as exercise may affect the metabolism of sweeteners and caffeine, which could in turn affect mortality rates.

The amount of caffeine available in soft drinks could be a confounding variable, as caffeine consumption is associated with both sweetener consumption and mortality rates.

In summary, the number of soft drink brands available for purchase is not a lurking variable in this scenario, while Shawna's weight, the time of day she exercises, and the amount of caffeine available in soft drinks could potentially be confounding variables or moderators that need to be accounted for in the analysis.

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Points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.

What are points, lines, and planes?

Point: A point is a basic geometric object that represents a specific location in space.

Line: A line is a straight path that extends infinitely in both directions. It is made up of an infinite number of points that are all collinear, or lie on the same straight path.

Plane: A plane is a two-dimensional flat surface that extends infinitely in all directions.

Navigation: Points and lines are essential for navigation, both on land and in the air. For example, on a map, points represent specific locations, while lines represent roads, highways, and other paths that can be taken to get from one point to another.

Architecture and Design: Points, lines, and planes are critical for architecture and design. Architects use points to specify the locations of walls, columns, and other structural elements, while lines are used to create the edges of rooms and buildings. Planes are used to define the surfaces of walls, floors, and ceilings.

Art: Artists often use points, lines, and planes to create visual effects in their work. Points can be used to create texture, while lines can be used to create movement and depth. Planes can be used to create shapes and form.

Engineering: Points, lines, and planes are fundamental to engineering, which involves the design and construction of structures and machines. Engineers use points to specify the locations of components, while lines are used to create the edges of parts. Planes are used to define the surfaces of structures, such as the wings of an airplane.

Hence, points, lines and planes can be used in different fields like Navigation, Architecture, Art, Engineering, etc.

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The Selling price of a book with a retail of R 100 and R 88 will be 99.625 and 87.625 respectively.

The selling price of a good or service is the final cost to the seller, or what the buyer actually pays. A commodity or service in a specific amount, weight, or measurement can be exchanged.

It is one of the most crucial things for a business to decide. It is significant since it determines whether or not it will survive. Sales of a product are directly impacted by its price.

According to the question,

Discount = 3/8 of the retail price.

Now,

When retail price is 100,

Selling price [tex]= 100-3/8[/tex]

[tex]=99.625[/tex]

When retail price is 88.

Selling price [tex]= 88-3/8[/tex]

[tex]=87.625[/tex]

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The required, there is no highest common factor between 4454 and 121j²k. None of the options are correct.

The highest common factor (HCF) of two or more numbers is the largest number that divides all of the numbers exactly.

Here,
To find the greatest common factor (GCF) of 4454 and 121j²k, we need to factor both numbers into their prime factors and then identify the common factors.

Since 4454 is an even number and 121 is an odd number so there is no prime highest common factor between the given number.

Thus, none of the options are correct.

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Kathy should take 4 trips if the price of a round-trip ticket is 230.

Point A on the graph would be placed at (230, 4). This demonstrates that Kathy should take 4 trips if the price of a round-trip ticket is 230. This can be calculated as follows:

Kathy has a budget of 1,000. Therefore, she can afford 4 round-trip tickets at the price of 230 each. This can be calculated by dividing 1000 by 230, which gives 4. Therefore, Kathy should take 4 trips if the price of a round-trip ticket is 230.

It is important to note that Kathy should also consider other factors such as the cost of other expenses, such as accommodation and food, when deciding how many trips to take. Additionally, Kathy may also want to consider whether the benefits of taking more trips are worth the additional cost.

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Answer:

C. 77.3% decrease

Step-by-step explanation:

To calculate the percent change, we can use the formula:

percent change = (new value - old value) / old value * 100

Plugging in the values, we get:

percent change = (20 - 88) / 88 * 100 = -68 / 88 * 100 = -0.772727 * 100 = -77.3

Since the new value is lower than the old value, this is a decrease, and the answer is -77.3, or 77.3% decrease.

The surface area of the net is 108 squate feet

The complete question is added as an attachment

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

A net that has the following shapes

The area of the net is the sum of the individual areas

So, we have

Area = 8 * 12 + 2 * 0.5 * 3 * 4

Evaluate

Area = 108

Hence, teh area is 108 squate feet

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Answer:

25 minutes

Step-by-step explanation:

The time difference between 1:25 and 1:50 is 25 min

The slope on the line containing the points (14,-42) is 1.06, as stated in the preceding sentence (-48,24).

The % slope is calculated by multiplying the distance between two locations by the differences in elevation above them. The difference in height between two places is referred to as "rise." The distance between it sites is known as the run. Therefore, the formula for percent slope is (rise / run) x 100.

The slope's formula is as follows:

m = (y₂-y₁)/x₂-x₁)

In the formula, replace the point values as follows:

m = (24-(-42))/(-48-14)

Make the fraction simpler:

m = (24-(-42))/(-48-14)

m = 66/-62

m = 1.06

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According to the model, around 521 people will be infected in three days.

A unitary method is a mathematical technique where we use ratios and proportions to find the value of an unknown quantity.

Let's start by breaking down the problem. We know that there are currently 392 people infected and the virus is spreading at a rate of 11% each day. This means that for every 100 people, 11 people are getting infected. To calculate how many people will be infected in three days, we need to use a unitary method.

To do this, we need to calculate the total increase in the number of infected people over three days. Since the virus is spreading at a rate of 11% each day, the total increase over three days will be 33% (11% x 3). We can then use this percentage increase to calculate the total number of people infected in three days.

To find the total number of people infected in three days, we can use the following formula:

Total infected = current infected + (current infected x percentage increase)

Plugging in the values from the problem, we get:

Total infected = 392 + (392 x 0.33)

Total infected = 392 + 129.36

Total infected ≈ 521

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To draw a centroid for ΔABC, follow the steps below.

The intersection point of line segments CD and XY is the centroid of the ΔABC. Label this point as G.

See the sample attached. Note that this is not constructed to scale.

The centroid is the point where the three medians of a triangle intersect.

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. In this case, line segment CD is one of the medians of triangle ABC because it connects the midpoint of AB (which is also the midpoint of CD) to vertex C. The other two medians connect the midpoints of the other two sides to their opposite vertices.

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An equation of the line of best fit for the data is y = -0.9x + 13.6.

The correlation coefficient (r) for the data to the nearest thousandth is -0.964.

In order to determine a linear equation in slope-intercept form for the line of best fit that models the data points described above, we would use a scatter plot (graphing calculator).

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the data set, a linear equation for the line of best fit is given by:

y = -0.895x + 13.600.

Rounding up as required, we have:

y = -0.9x + 13.6.

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Complete Question:

Use a graphing calculator to find an equation of the line of best fit for the data in the table. Round the slope and y-intercept to the nearest tenth. Then Identify and interpret the correlation coefficient.

X- 10.1 9.8 9.7 9.4 8.9 8.7 8.4 8.1

Y- 4.3 4.8 5.3 5.2 5.6 5.8 6.1 6.3

The equation of the line of best fit is y=

To the nearest thousandth, the correlation coefficient is r=

Answer:

Step-by-step explanation:

so 1in is 2.5ft.

6.4 times 2.5 is 16.

4.8 times 2.5 is 12.

16+16+12+12

is 24+32.

which is 56.

answer: B

Answer: 1067/10000 is a fraction in simplest form. where, 0.1067 is a decimal, 10.67% is a percentage.

Step-by-step explanation:

a) "What is your age?" is a quantitative data.

b) "Are you male or female?" is a categorical data.

c) "When did you first start reading the wsj?" is a categorical data.

d) "How long have you been in your present job or position?" is a quantitative data.

e) "What type of vehicle are you considering for your next purchase?" is a categorical data.

(a) "What is your age?" - This question provides quantitative data because age is a numerical value that can be measured and ordered in a meaningful way. Respondents could give an answer such as "25", "45", or "70", for example, which can be used to calculate statistics such as the mean or median age of the survey population.

(b) "Are you male or female?" - This question provides categorical data because the responses fall into discrete, non-numeric categories (in this case, "male" or "female"). It's not possible to order the responses in a meaningful way, since there is no inherent numerical value associated with being male or female.

(c) "When did you first start reading the WSJ?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (high school, college, early career, mid career, late career, or retirement). While it's possible to order the categories in a logical sequence, they don't represent numerical values.

(d) "How long have you been in your present job or position?" - This question provides quantitative data because the responses can be measured as numerical values (for example, "3 years", "10 years", or "25 years"). The data can be used to calculate statistics such as the average length of time that respondents have been in their current position.

(e) "What type of vehicle are you considering for your next purchase?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (sedan, sports car, SUV, minivan, etc.). While it's possible to order the categories in a logical sequence based on size, price, or other factors.

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