If f(x) = 3x^2 – 2x + 4 and g(x) = 5x^2 + 6x – 8, find (f - g)(x).

[tex]x^{2}[/tex]-4[tex]y^{2}[/tex] = 0

Solution

Here we have to find the factors.

[tex]x^{2}  - 4y^{2} = 0[/tex]

Here we can write 4y^2 as (2y)^2

[tex]x^{2}  - (2y)^{2}  = 0[/tex]

Now we have to use the formula, a^2 - b^2 = (a + b)(a - b)

Here a = x and b = 2y

Therefore, we get

(x + 2y)(x -2y)

Hence, the answer isC. (x + 2y)(x -2y)

failed to evaluate 9 × - 8

2( - 3x + 1) = 9 × - 8

- 6x + 2 = - 72 ( subtract 2 from both sides )

- 6x = - 74 ( divide both sides by - 6 )

x = [tex]\frac{-74}{-6}[/tex] = [tex]\frac{37}{3}[/tex]

Answer:

(d) sin G = 15/17

Step-by-step explanation:

For angle G, opp = 15, adj = 8, hyp = 17.

cos G = adj/hyp = 8/17

sin G = opp/hyp = 15/17

Answer: (d) sin G = 15/17

The degree of a monomial is the highest power of a variable.

For A, the highest power is 5 ( a^5)

For B, the highest is 6 (a^6)

For C, the highest is 4 ( both a^4 and b^4)

For D, the highest is 2 ( all 3 variables have ^2)

B has the highest degree.

Answer:

B

Step-by-step explanation:

B)The numbers are being divided by 10 repeatedly.

The numbers are:

7000

700

70

.7

.07

.007

(See it now?)

The number that is missing is 7

My conjecture is that 7 can’t be written in scientific notation.

Hope I helped!

Good Luck!

⛈

The greatest common factor between 10 and 24 is 2.

What is Greatest common factors?

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Given that;

The numbers are;

10 and 24

Now,

The factors of 10 = 1, 2, 5, 10

The factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.

Clearly, The greatest common factor of the number 10 and 24 is highest number which is common in both factors.

Thus, The greatest common factor between 10 and 24 is 2.

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Answer: the answer this b

Step-by-step explanation:

Bc I said so lol

The exact circumference of the Circle Measurements is 12π yards and the exact area is 36π square yards.

To find the exact area and circumference of the circle, we can use the formulas given:

Circumference of a circle = 2πr

Area of a circle = πr^2

Given that the diameter of the circle is 12 yards, we can find the radius by dividing the diameter by 2: r = 12 / 2 = 6 yards.

Now we can substitute the value of r into the formulas:

Circumference = 2πr = 2π(6) = 12π yards

Area = πr^2 = π(6^2) = 36π square yards

So, the exact circumference of the circle is 12π yards and the exact area is 36π square yards.

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Based on the analysis, the only relation that is a function is {(5, 0), (0, 5), (–5, –5)}.

A relation is considered a function if each input value (x-value) in the relation corresponds to exactly one output value (y-value).

1. {(5, 0), (0, –8), (5, –5)}

  In this relation, the input value 5 corresponds to both 0 and -5. Therefore, this relation is not a function.

2. {(5, 0), (0, 5), (–5, –5)}

  In this relation, each input value has a unique output value. For example, 5 corresponds to 0, 0 corresponds to 5, and -5 corresponds to -5. This relation satisfies the definition of a function since each input value has only one corresponding output value.

3. {5, 0, –8, –5}

  This is not a relation since it consists only of individual numbers and does not show any pairings between input and output values. Therefore, it is not a function.

4. {(5, 0), (–8, –5), (–8, 5), (–5, –8)}

  In this relation, the input value -8 corresponds to both -5 and 5. Therefore, this relation is not a function.

Based on the analysis, the only relation that is a function is {(5, 0), (0, 5), (–5, –5)}.

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Final answer:

The relation {(5, 0), (0, 5), (–5, –5)} is a function because each domain value maps to exactly one range value, which meets the definition of a function.

Explanation:

To determine which relation is a function, we must ensure that each input (or domain value) maps to exactly one output (or range value). A function cannot have one domain value paired with multiple range values.

Therefore, the relation that is a function is the second one: {(5, 0), (0, 5), (–5, –5)}.

Eight thousand one and forty seven hundredths.

Hope this helps! :)

16.

4 ÷ 2 = 2

6 ÷ 3 = 3

so,

8 x 2 = 16

Answer:

The return trip took 3 hours.

Step-by-step explanation:

Suppose, the time required to travel downhill is  [tex]t[/tex] hours.

Since the return trip was partly uphill, it took half an hour longer. So, the time required for the return trip will be:  [tex](t+0.5)[/tex] hours.

Given that, the speed for travelling downhill was 24 kph and the speed for travelling uphill was 20 kph.

We know that,  [tex]Distance= speed*time[/tex]

As, the distances traveled in both trips are equal, so the equation will be........

[tex]24t=20(t+0.5)\\ \\ 24t=20t+10\\ \\ 4t=10\\ \\ t=\frac{10}{4}= 2.5[/tex]

So, the time required for the return trip will be:  [tex](2.5+0.5)= 3[/tex] hours.

Answer:

It took 3 hours to return home.

Step-by-step explanation:

Since supplementary angles equal 180. (2x+15) = 45, which can be found by subtracting 135 from 180. This means that x = 15. And since angle 1 corresponds to the previous angle, we can deduce that angle 1 = 45.

2.  x = 15 deg; Δ=45 deg

Marisa had rounded 3.48 to 4 and times it to 7.33 which she rounded to 8

In fact 3.48 is closer to 3 we know this since the .48 of 3.48 s below .50 if it was .50 or above it would round to 4 but it doesn't the same applies to 7.33 so

it should be 3 x 7 = 21

If Marisa is going to estimate, then she needs to round each number. If she rounds to the nearest ones place, then she should have rounded 3.48 to 3 and rounded 7.33 to 7.

3 x 7 = 21

) because its biggerrrrrr

Set up the equations:

two numbers: a and b

sum: a+b=21

quotient: a/b=2

(the last one means b=a/2)

combine them:

a+a/2=3a/2=21

a=14

and so

b=7

the two numbers are 14 and 7

Final answer:

To find two numbers given their sum and quotient, set up and solve a system of equations. In this case, the numbers are 14 and 7.

Explanation:

The sum of two numbers is 21 and their quotient is 2. To find the two numbers, we can set up a system of equations:

Let the two numbers be x and y. We have the equations x + y = 21 and x/y = 2.

Solve the system by substituting y = 21 - x into the second equation to get x = 14 and y = 7.

Therefore, the two numbers are 14 and 7.

The correct answer is A. Because if you substitute the x and y you will get the same outcome.  y=8x substitute and you get 24= 8(3) and then multiply and you get 24 = 24

We are given this

[tex]x^6 -64y^3[/tex]

write it as the difference of cubes

[tex](x^2)^3 -(4y)^3[/tex]

use the formula for the difference of cubes

[tex](x^2-4y) ((x^2)^2+x^2*4y+(4y)^2)[/tex]

Now use the formula for the difference of squares as [tex]4y = (2\sqrt{y} )^2[/tex]

[tex](x-2\sqrt{y}) (x+2\sqrt{y}) (x^4+4x^2y+16y^2)[/tex]

three consecutive odd integers are : -17,-15,-13

Final answer:

The function rule for the area of a rectangle is A = W² + 7W. When the width is 7 feet, the area of the rectangle is 98 square feet.

Explanation:

To write a function rule for the area of a rectangle, we need to express the area in terms of the independent variable, which in this case is the width (W). The length is given as 7 feet more than the width, so we can write the length as W + 7. The area (A) of a rectangle is given by the formula A = length × width. Substituting the values, we get A = (W + 7) × W = W² + 7W.

To find the area of the rectangle when the width is 7 feet, we can plug in W = 7 into the function rule. A = 7² + 7 * 7 = 49 + 49 = 98 square feet. Therefore, the area of the rectangle is 98 square feet when the width is 7 feet.

there are 9463.53 milliliters in 2.5 gallons of water.

Answer:

9,462,5 milimiters.

Step-by-step explanation:

In order to be able to calculate how many milimeters there are in 2.5 gallons of water we just have to convert the units, so we first have to convert from gallons to liters, there are 3.785 liters in each gallon, so we just do the convertion:

[tex]\frac{1 gallon}{3.785 liters}=\frac{2.5 gallons}{x}[/tex]

If we clear the x we get:

[tex]x=\frac{(3.785 liters)(2.5gallons)}{1 gallon}[/tex]

[tex]x=\frac{(9.4625 liters*gallons)}{1 gallon}[/tex]

[tex]x=9.4625 liters[/tex]

Now we just ocnvert to mililiters, since there are 1000 mililiters in a liter we just multiply:

[tex]\frac{1 liter}{1000mililiter}=\frac{9.462liters}{x}[/tex]

[tex]x=\frac{(9.4625 liters)(1000mililiter)}{1 liter}[/tex]

[tex]x=9462.5 mililiters}[/tex]

the answer is 869. hope you pass!

Let the Width be x cm

Then the length which is 5cm more than width must be (x+5) cm

Using the formula for the area = length* width

x(x+5) =50

[tex]x^2+5x =50[/tex]       (Distribute x on the parenthesis )

[tex]x^2+5x-50 =0[/tex]      (subtract 50 )

[tex](x+10) (x-5) =0[/tex]          (Factor)

[tex]x-5=0\\x+10=0[/tex]

we get

[tex]x=5[/tex]                      (Not x=-10 because negative side length not possible)

Width = 5 cm

Length = 5+5= 10 cm

Perimeter = 2(Length + width)

So

Perimeter = 2(10+5)

Perimeter = 2*15=30 cm

the length of a rectangle is 5 cm more than its width and the area is 50cm2 find the length, width, and the perimeter

L = W + 5 (5 cm more than its width)

Area = W * L

Substitute Area = 50 and L =  W + 5

50 = W ( W+5)

Distributive property

50 = W^2 + 5W

Subtract 50 from both sides

0 = W^2 + 5W - 50

Re-write

W^2 + 5W - 50 = 0

Factor

(W + 10)(W - 5) = 0

W + 10 = 0; W = -10

W - 5 = 0; W = 5

Dimension cannot be negative so W = 5 cm

L = 5 + 5 = 10 cm

Double check: A = 5 x 10 = 50 cm^2

Perimeter = 2(L + W)

Perimeter = 2(5 + 10)

Perimeter = 2(15)

Perimeter = 30 cm

Answer

L = 10 cm

W = 5 cm

P = 30 cm

Hope that helps

Answer:

This is called Transitive property of equality.

Step-by-step explanation:

If a quantity a=b and b=c, then we can say a=c, this property is called transitive property of equality.

To find out how much water drips per day from a faucet that drips 2/3 gallons in 10 hours, we first find the hourly rate which is 1/15 gallons per hour. Then, we multiply this by 24 (the number of hours in a day) to find that the faucet drips 1.6 gallons of water per day.

The unit rate simply means how much of something you have per 1 unit of time or space. In this case, we want to know how much water drips per day from a faucet.

Firstly, we know that the faucet drips 2/3 gallons in 10 hours. We can convert it into how much it would drip in one hour by dividing 2/3 by 10 to get 2/30 or 1/15 gallons per hour. Secondly since one day contains 24 hours, you just multiply the hourly rate (1/15) by 24 to get the daily rate. So, 1/15 * 24 equals 1.6 gallons. Therefore, the faucet drips 1.6 gallons of water per day.

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The correct choice is (C) [tex]1\frac{3}{5}[/tex] gallons per day. To find the daily drip rate, first determine the hourly rate by dividing the given amount by 10 hours, then multiply this rate by 24 hours.

To find the unit rate of water dripped per day from a faucet that drips [tex]\frac{2}{3}[/tex] gallons of water in 10 hours, we first calculate how many gallons it drips in one hour. This is calculated by dividing the quantity of water by the time:

Since there are 24 hours in a day, we multiply the hourly rate by 24 to find the daily drip rate:

As a result, the daily water drip rate is [tex]1\frac{3}{5}[/tex] gallons per day.

Complete question:

a faucet drips [tex]\frac{2}{3}[/tex] gallons of water in 10 hours. what is the unit rate of water dripped per day

(A) [tex]\frac{1}{15}[/tex] gallon per day

(B) [tex]\frac{5}{18}[/tex] gallon per day

(C) [tex]1\frac{3}{5}[/tex] gallons per day

(D) [tex]6\frac{2}{3}[/tex] gallons per day

Answer:

811÷77= 10.265....

Step-by-step explanation:

As the hint stated, the slope is -2 degrees.

So, the easiest way to make a equation is to use slope intercept.  

Y=mx+b

M is the slope, and B is the Y-intercept.

so.

Y = (-2)x+20

Y = -2x+20

Answer:

[tex]T=-2h+20[/tex]

Step-by-step explanation:

the temperature t in fish  starts at 20 degrees Fahrenheit at midnight when h=0.

So when h=0 the T=20 degree (0,20)

The equation of temperature is

[tex]T=m(H)+b[/tex]

Where m is the slope and b is the y intercept

y intercept is the initial degree , so b=20

m is the rate of change that is slope =-2

m=-2, b=20 , [tex]T=m(H)+b[/tex]

The equation becomes

[tex]T=-2h+20[/tex]