find the distance between the points (6,-4) and (0,5)

A.) There are many different expressions that can be equivalent to 4/2 and -2/3, but you just need one expression. 4/2 is equivalent to 2/1 and -2/3 is equivalent to -4/6.

Reason:

There are two ways you can find a fraction equivalent to another.

1.) First one is by reducing the fraction if possible.

Example: 5/10=1/2, 10/30=1/3, 9/16=3/4.

2.) The second one is by multiplying the numerator and the denominator by the same number, usually by 2 or 3.

Example: 1/2 x 2/2 = 2/4, so 1/2= 2/4. Another: 1/3 x 3/3 = 3/9, so 1/3=3/9

That said, 4/2 = 2/1 because it was reduced. While -2/3 = -4/6 because it was multiplied by 2/2.

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4/2 is equivalent to 1/2 when reduced by 2.

-2/3 is equivalent to -4/6 when multiplied by 2/2.

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Answer:

48 minutes

Step-by-step explanation:

Given that;

Rosalinda can line the football field in 80 minutes

Reggie can line the football field in 120 minutes

Lets assume that if they work together, they will take T minutes to line the football field

Hence;

Thus in 1 minute, Rosalina can line 1/80 of the field where as Reggie can line 1/120 of the field

[tex]\frac{1}{T} =\frac{1}{120} +\frac{1}{80} \\\\\frac{1}{T} =\frac{2+3}{240}\\\\[/tex]

The sum of the two fractions will represent the size of the field that can be lined in 1 minute.

[tex]\frac{1}{T} =\frac{5}{240} \\\\\frac{1}{T} =\frac{1}{48} \\T= 48[/tex]

The reciprocal of the sum of the two fractions will represent the time taken for both Rosalinda and Reggie to line the field.

Answer ; It will take them 48 minutes for them to line the football field

Answer:

48 minutes

Step-by-step explanation:

Reggie can line 1/120 of a football field in 1 minute while Rosalinda can line 1/80 of a football field in 1 minute.

Therefore adding the 2 fractions we get; that BOTH of them can line 1/120+1/80 of a field in 1 minute. 1/120+1/80=1/48.

1/48 of a field can be done in a minute, so it would take them 48 minutes to do 48/48 or 1 whole field.

Answer:

[tex]y=-5x-27[/tex]

Step-by-step explanation:

Since we are finding a parallel line, the slopes will be the same, so the second equation will also have a slope of -5.

Then, to find the y-intercept, we can use the point given and plug in.

[tex]y=-5x+b[/tex]

[tex]3=-5(-6)+b[/tex]

[tex]3=b+30[/tex]

[tex]b=-27[/tex]

So the equation comes out to be [tex]y=-5x-27[/tex]

We can check by plugging in the given point again.

[tex]3=-5(-6)-27[/tex]

[tex]3=30-27[/tex]

[tex]3=3[/tex]

Answer:

D

Step-by-step explanation:

I graphed each equation on a piece of paper and on desmos.com

Find the vertex:

[tex]\textrm{Use the formula } \frac{-b}{2a} \textrm{ to find the vertex}\\ \\ \frac{-10}{2} = -5\\ \\ \textrm{In order to find the y value plug in -5 back into the function}\\ \\ y=(-5)^2+10(-5)+16\\ y=-9\\\\ \textrm{The vertex of the function is} (-5,-9)[/tex]

Determine if the parabola will open up or down:

[tex]a > 0 \\ \\ 1>0[/tex]

Since the value of a is positive, the parabola will open upwards

Find the x and y intercepts:

Factor [tex]y = x^2+10x + 16[/tex] to find the x intercepts

(x+8)(x+2)

x + 8 = 0

x = -8

x + 2 = 0

x = -2

x intercepts:

x = -2

x = -8

Find the y intercept

[tex]y = 0^2+10(0) + 16\\\\ y=16[/tex]

Hence, C. Graph A best represents the quadratic function [tex]y = x^2+10x + 16[/tex]

Using the law of cosines:

Cos (angle) = Adjacent Leg /  Hypotenuse

Cos(28) = x / 64

X = 64 * cos(28)

x = 56.5 km

For this case we must make a conversion. We have that by definition 1 liter equals 0.264172 gallons.

So, making a rule of three we have to:

1L ----------------> 0.264172 gallons

15L --------------> x

Where:

x: Represents gallons equivalent to 15 liters.

[tex]x = \frac {15 * 0.264172} {1}\\x = 3.96258[/tex]

Rounding out we have that 15 liters equals 3.96 gallons.

Answer:

3.96 gallons

15 liters is approximately 3.96 gallons.

Given that we need to calculate 15L is approximately how many gallons rounded two decimal places for final answer.

To convert liters (L) to gallons (gal), you need to know the conversion factor between the two units.

The conversion factor between liters and gallons is 1 L = 0.264172 gal.

Now, let's calculate how many gallons are approximately equal to 15 liters:

15 L x 0.264172 gal/L = 3.96258 gal

Rounding to two decimal places, the approximate value is 3.96 gallons.

Therefore, 15 liters is approximately 3.96 gallons.

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[tex]g(b)=3b+13[/tex]

Hope this helps.

r3t40

To find the formula for g(b), isolate the variable a in the given equation by solving step by step. The formula for g(b) is g(b) = 3b + 13.

To write a formula for g(b) in terms of b, we need to isolate the variable a in the equation given. Let's simplify the given equation step by step:

Therefore, the formula for g(b) is g(b) = 3b + 13

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Answer:

3 and -5

Step-by-step explanation:

(x-3)(x+5)greater than and =0​

separate

(1).

x - 3 > 0

add 3 to both sides

x > 3

(2).

x + 5 > 0

subtract 5 from both sides

x > -5

So, The solutions are 3 and -5

Answer: [tex](-\infty,-5]\ U\ [3,\infty)[/tex]

Step-by-step explanation:

Given the inequality [tex](x-3)(x+5)\geq 0[/tex], to find the solutions, we need to follow this procedure:

- First case:

[tex]x-3\geq 0[/tex] and  [tex]x+5\geq 0[/tex]

Solve for the variable "x":

[tex]x\geq 0+3\\x\geq 3[/tex]

 [tex]x\geq 0-5\\x\geq -5[/tex]

Then:

[tex]x\geq 3[/tex]

- Second case:

[tex]x+5\leq 0[/tex] and [tex]x-3\leq 0[/tex]

Solve for the variable "x":

[tex]x\leq 0-5\\x\leq -5[/tex]

[tex]x\leq 0+3\\x\leq 3[/tex]

Then:

[tex]x\leq-5[/tex]

Finally, the solution is:

[tex](-\infty,-5]\ U\ [3,\infty)[/tex]

Answer:

Step-by-step explanation:

To solve this problem we need to solve a system of equations. We have two machines:

The machine "Paint Pro" is used for two hours.

The machine "Goldilocks" is used for an hour and a half.

When they are working at the same time, they can paint 55 square feet per minute. Together they painted 5850 square feet of wall.

Therefore, we have the following system of equations:

P + G = 55 ft^2/m

120P + 90G = 5850 ft^2 → 4P + 3G = 195

Solving the system of equations we have that:

P = 25

G = 30

Therefore, the paint pro paints 30sqft per minute and Goldilocks paints 25 sqft per minute.

The slope of the perpendicular is the negative reciprocal of the original line, so m = -1/(-2) = 1/2.

The general line of slope m through (a,b) is

[tex]y - b = m(x-a)[/tex]

So the line we seek is

[tex] y - 2 = \frac 1 2 ( x - 8)[/tex]

[tex] y = \frac 1 2 x - 2[/tex]

Answer: y = 1/2  x + -2

Answer:

[tex]\large\boxed{(3+\sqrt{-16})(6\sqrt{-64})=-192+144i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\to i^2=-1\\\\(3+\sqrt{-16})(6\sqrt{-64})=(3+\sqrt{(16)(-1)})(6\sqrt{(64)(-1)})\\\\=(3+\sqrt{16}\cdot\sqrt{-1})(6\cdot\sqrt{64}\cdot\sqrt{-1})=(3+4i)\bigg((6)(8i)\bigg)\\\\=(3+4i)(48i)\qquad\text{use the distributive property}\ (b+c)a=ba+ca\\\\=(3)(48i)+(4i)(48i)=144+192i^2\\\\=144i+192(-1)=-192+144i[/tex]

The value of the given expression (3+√-16)(6√-64) is (-192+144i).

As the given two factors are complex numbers, therefore, we must know about the value of i

i = √(-1)

i² = (-1)

The solution of the product,

[tex](3+\sqrt{-16})(6\sqrt{-64})\\\\ = (3\times 6\sqrt{-64}) + (\sqrt{-16}\times 6\sqrt{-64})\\\\= (3+4i)(6\cdot 8i)\\\\= (3+4i)(48i)\\\\= 144i + 192(i)^2\\\\= 144i + 192(\sqrt{-1})^2\\\\= 144i + 192(-1)\\\\= -192+144i[/tex]

Hence, the value of the given expression (3+√-16)(6√-64) is (-192+144i).

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Answer:

20 bottles

Step-by-step explanation:

10*3+b=50

30+b=50

-30      -30

       b=20

Answer:

The values of y are -33 , -15 , -5 , -5 ⇒ answer C

Step-by-step explanation:

* We will use the substitution method to solve the problem

- The quadratic equation is y = -x² + x - 3

- The values of x are -5 , -3 , -1 , 2

- We will substitute the values of x in the equation to find the

  values of y

# At x = -5

∵ y = -x² + x - 3

∵ x = -5

∴ y = -(-5)² + (-5) - 3 = - 25 - 5 - 3 = -33

∴ y = -33

# At x = -3

∵ y = -x² + x - 3

∵ x = -3

∴ y = -(-3)² + (-3) - 3 = - 9 - 3 - 3 = -15

∴ y = -15

# At x = -1

∵ y = -x² + x - 3

∵ x = -1

∴ y = -(-1)² + (-1) - 3 = - 1 - 1 - 3 = -5

∴ y = -5

# At x = 2

∵ y = -x² + x - 3

∵ x = 2

∴ y = -(2)² + (2) - 3 = - 4 + 2 - 3 = -5

∴ y = -5

* The values of y are -33 , -15 , -5 , -5 ⇒ from left to right

Answer:

15/56

Step-by-step explanation:

3*5=15 * 8*7=56

15/56

Final answer:

To multiply fractions 3/8 and 5/7, multiply the numerators to get 15 and the denominators to get 56, resulting in the fraction 15/56, which is in its simplest form.

Explanation:

To multiply two fractions, you multiply the numerators (the top numbers) together and then multiply the denominators (the bottom numbers) together. So for the fractions 3/8 and 5/7, you would do the following:

Therefore, the product of these two fractions is 15/56. This fraction is already in its simplest form because the numerator and the denominator do not have any common factors besides 1.

Answer with Step-by-step explanation:

We have to solve the equation 2x²-6x+1=0

the solution of the equation ax²+bx+c=0 is given by

[tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\ and\ x=\dfrac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

Here a=2,b=-6 and c=1

[tex]x=\dfrac{6+\sqrt{6^2-4\times 2\times 1}}{2}\ and\ x=\dfrac{6-\sqrt{6^2-4\times 2\times 1}}{2}\\\\x=\dfrac{6+\sqrt{36-8}}{2}\ and\ x=\dfrac{6-\sqrt{36-8}}{2}\\\\x=\dfrac{6+\sqrt{28}}{2}\ and\ x=\dfrac{6-\sqrt{28}}{2}\\\\x=\dfrac{6+2\sqrt{7}}{2}\ and\ x=\dfrac{6-2\sqrt{7}}{2}\\\\x=3+\sqrt{7}\ and\ x=3-\sqrt{7}[/tex]

Hence, solution of 2x²-6x+1=0 is:

[tex]x=3+\sqrt{7}\ and\ x=3-\sqrt{7}[/tex]

Answer:

D. 0.857

Step-by-step explanation:

The coefficient of determination, R-squared, is simply the square of the  correlation coefficient;

R-squared = r^2

R-squared = 0.926^2

R-squared = 0.857

Therefore, the coefficient of determination is 0.857.

Answer:

The correct answer option is D. 0.857

Step-by-step explanation:

We are given the correlation coefficient, of a data set to be 0.926 and we are to find the coefficient of determination to three decimal places.

To find that, we will use the following formula:

Coefficient of determination = [tex] r ^ 2 [/tex]

[tex] r ^ 2 [/tex] = [tex] ( 0 . 9 2 6 ) ^ 2 [/tex] = 0.857

Answer:

$21

Step-by-step explanation:

20% of 35 is 7, then you add 7 to 35 to get 42, then you split the earnings and get 21 dollars.

Answer:

21

Step-by-step explanation:

First find the tip

35 *20%

35*.2

7

He makes 35+7 = 42

But he splits it with his friend

42/2 = 21

He will make 21 and his friend will make 21

Answer:

The error is in the Step 3

Step-by-step explanation:

we know that

The area of a rectangle is equal to

A=bh

where

b is the base of rectangle

h is the height of rectangle

so

The Step 1 calculating the  Base is correct

The Step 2 calculating the Height is correct

The Step 3 calculating the area of rectangle is not correct

because

A=(8)(7)=56 units² instead of 49 units²

Answer:

The error occurred in step 3

Step-by-step explanation:

The formula of a parallelogram is

A = bh

b is the base of the parallelogram

h is the height of the parallelogram

Step 1: the calculation of the base is correct

Step 2: the calculation of the height is correct

Step 3: 8 x 7 = 49 is incorrect. 8 x 7 should be equal to 56.

Answer:

x=110592

Step-by-step explanation:

[tex]log_{48}x=3 \text{ means } 48^3=x\\\\[/tex]

So x=110592

Answer:

325 mi

Step-by-step explanation:

We can write a proportion to solve, putting distance over inches

50 miles       x miles

------------- = -------------

1 inch            6.5 inches

Using cross products

50 * 6.5 = 1*x

325 = x

The distance is 325 miles

For this case we have the following functions:

[tex]f (x) = x + 1\\g (x) = \frac {1} {x}[/tex]

By definition we have to:

[tex](f * g) (x) = f (x) * g (x)[/tex]

So:

[tex]f (x) * g (x) = x + 1 * \frac {1} {x} = \frac {x + 1} {x}[/tex]

The domain of the function is given by the values for which the function is defined. The function is not defined for x = 0.

Then, the domain is given by all real numbers except 0.

The range is the set of all values of and valid.

Then the range is given by all reals except 1.

Answer:

Option C

Answer:

C.

Step-by-step explanation:

All real numbers except y=1

[tex]\bf \cfrac{9}{7}+\cfrac{7}{5}\implies \stackrel{\textit{using the LCD of 35}}{\cfrac{(5)9~~+~~(7)7}{35}}\implies \cfrac{45+49}{35}\implies \cfrac{94}{35}\implies 2\frac{24}{35}[/tex]

Answer:

94/35

Step-by-step explanation:

Least common multiples of 7 and 5.

7*5=35

9/7=9*5/7*5=45/35

7/5=7*7/5*7=49/35

Add the numbers from left to right.

49/35+45/35

49+45=94

=94/35

94/35 is the correct answer.

Answer: 29 and 8

Step-by-step explanation:

See photo attached. (:

Answer:

A + B = 37

A - B = 21    we then add the 2 equations

2A = 58

A = 29

B = 8

Step-by-step explanation:

There is an infinite number of common denominators, but 12 is the least common denominator.  You could also use any other number that is a multiple of 12, such as 24, 36, and 48.

12 is the least common denominator because it is the smallest number that is a multiple of both 4 and 6.

[tex]4*3=12[/tex]

[tex]6*2=12[/tex]

You can also use any other multiples of 12 because they are all multiples of 4 and 6.

Answer:

6.5 cm

Step-by-step explanation:

V = Bh for a rectangular prism where B is the area of the base

130 = 20 * h

Divide each side by 20

130/20 = 20h/20

6.5 = h

The height is 6.5 cm

Answer:

The answer is Both a(x) and b(x) have the same output value at x = 2.

Step-by-step explanation:

The answer is Both a(x) and b(x) have the same output value at x = 2. Because when a(x)=b(x) the lines intersect at that point lines intersect they have a point in common. Also, a(x)=b(x) means that the outcomes are the same

The statement that is true about a(x) = b(x) at x = 2 is

Both a(x) and b(x) have the same output value at x = 2.

Option B is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

a(x) and b(x)

At x = 2,

a(x) is equal to b(x)

a(x) = b(x)

This means that,

a(x) and b(x) have the same output value at x = 2.

Both a(x) and (x) have a maximum or minimum value at x = 2.

This is not true because we have to differentiate the function and put it as zero to get the maximum and minimum value at x=2.

Both a(x) and b(x) crosses the x-axis at 2.

This is not true because the function on the graph is at a point of intersection between x = 2 and the y value.

Both a(x) and (x) crosses the y-axis at 2.​

This is not true because the function on the graph is at a point of intersection between x = 2 and the y value.

Thus,

The statement that is true about a(x) = b(x) at x = 2 is

Both a(x) and b(x) have the same output value at x = 2.

Option B is the correct answer.

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