A 6-foot piece of aluminum wire costs $49.68. What is the price per inch?

Answer: There are 9 mangoes left in the basket.

Step-by-step explanation:

(2/5) * 15 = 6.

15 - 6 = 9.

Answer:

Your answers are below ↓

Step-by-step explanation:

Given ↓

A) 2x-3y = 5 and 3x+4y = 6  ( The method this has to be solved in is the elimination method. )

Now using these,

(1)×3 - (2)×2 = 6x + 9y - 6x - 8y = 15 - 12

therefore,

y = 3

putting the value of y in eqn. (1)

2x + 6 = 5

therefore,

x = -1/2

B)  y=x^2 - 2x and y = 2x -3  ( The method this has to be solved in is the substitution method. )

Reduce the greatest common factor on both sides of the equation:
\(\left \{ {{4x-y=9} \atop {xy=-2}} \right.\)

Rearrange like terms to the same side of the equation:

\(\left \{ {{-y=9-4x} \atop {xy=-2}} \right.\)

Divide both sides of the equation by the coefficient of the variable:

\(\left \{ {{y=-9+4x} \atop {xy=-2}} \right.\)

Substitute the unknown quantity into the elimination:

\(x(-9+4x)=-2\)

Apply Multiplication Distribution Law:

\(-9x+4x^2=-2\)

Reorder the equation:

\(4x^2-9x=-2\)

Divide the equation by the coefficient of the quadratic term:

\(\frac{1}{4}(4x^2)+\frac{1}{4}(-9x)=\frac{1}{4}*(-2)\\\)

Calculate:

\(x^2-\frac{9x}{4}=-\frac{1}{2}\)

Add one term in order to complete the square:

\(x^2-\frac{9x}{4}+(\frac{9}{4}*\frac{1}{2})^2=-\frac{1}{2}+(\frac{9}{4}*\frac{1}{2})^2\)

Calculate:

\(x^2-\frac{9x}{4}+(\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2\)

Factor the expression using \(a^2$\pm$2ab+b^2=(a$\pm$b)^2\):

\((x-\frac{9}{8} )^2=-\frac{1}{2} +(\frac{9}{8} )^2\)

Simplify using exponent rule with the same exponent rule: \((ab)^n=a^n*b^n\)

\((x-\frac{9}{8} )^2=-\frac{1}{2} +\frac{9^2}{8^2}\)

Calculate the power:

\((x-\frac{9}{8} )^2=-\frac{1}{2}+\frac{81}{64}\)

Find common denominator and write the numerators above the denominator:

\((x-\frac{9}{8} )^2=\frac{-32+81}{64}\)

Calculate the first two terms:

\((x-\frac{9}{8} )^2=\frac{49}{64}\)

Rewrite as a system of equations:

\(x-\frac{9}{8} =\sqrt{\frac{49}{64} }\) or \(x-\frac{9}{8} =-\sqrt{\frac{49}{64} }\)

Rearrange unknown terms to the left side of the equation:

\(x=\sqrt{\frac{49}{64} } +\frac{9}{8}\)

Rewrite the expression using \(\sqrt[n]{ab} =\sqrt[n]{a} *\sqrt[n]{b}\):

\(x=\frac{\sqrt{49} }{\sqrt{64} } +\frac{9}{8}\)

Factor and rewrite the radicand in exponential form:

\(x=\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}\)

Simplify the radical expression:

\(x=\frac{7}{8} +\frac{9}{8}\)

Write the numerators over the common denominator:

\(x=\frac{7+9}{8}\)

Calculate the first two terms:
\(x=\frac{16}{8}\)

Reduce fraction to the lowest term by canceling the greatest common factor:

\(x=2\)

Rearrange unknown terms to the left side of the equation:

\(x=-\sqrt{\frac{49}{64} } +\frac{9}{8}\)

Rewrite the expression using \(\sqrt[n]{a} =\sqrt[n]{a} *\sqrt[n]{b}\):

\(x=-\frac{\sqrt{49} }{\sqrt{64} }+\frac{9}{8}\)

Factor and rewrite the radicand in exponential form:
\(x=-\frac{\sqrt{7^2} }{\sqrt{8^2} } +\frac{9}{8}\)

Simplify the radical expression:

\(x=-\frac{7}{8} +\frac{9}{8}\)

Write the numerators over common denominator:

\(x=\frac{-7+9}{8}\)

Calculate the first two terms:

\(x=\frac{2}{8}\)

Reduce fraction to the lowest term by canceling the greatest common factor:

\(x=\frac{1}{4}\)

Find the union of solutions:

\(x=2\) or \(x=\frac{1}{4}\)

Substitute the unknown quantity into the elimination:

\(y=-9+4*2\)

Calculate the first two terms:

\(y=-9+8\)

Calculate the first two terms:

\(y=-1\)

Substitute the unknown quantity into the elimination:

\(y=-9+4*\frac{1}{4 }\)

Reduce the expression to the lowest term:

\(y=-9+1\)

Calculate the first two terms:

\(y=-8\)

Write the solution set of equations:
\(\left \{ {{x=2} \atop {y=-1}} \right.\) or \(\left \{ {{x=\frac{1}{4} } \atop {y=-8}} \right.\)   -------> Answer

C)   y=x^2 - 2x and y = 2x -3 ( This method this has to be solved in is the substitution method. )

Step 1: We start off by Isolating y in y = 2x - 3

y=2x-3 ----------> ( Simplify )

y+(-y)=2x-3+(-y)   ---- > ( Add (-y)on both sides)

0=-3+2x-y

y/1 = 2x-3/1 --------> (Divide through by 1)

y = 2x - 3

We substitute the resulting values of y = 2x - 3 and y = x^2 - 2x

(2 * x - 3) = x^2 - 2x ⇒ 2x -3 = x^2 - 2x ---->   ↓

                                               (Substituting 2x - 3 for y in y = x^2 -2x )

Next: Solve (2x - 3 = x^2 - 2x) for x using the quadratic formular method

2x - 3 = x^2 - 2x

x = -b±b^2-4ac/2a  Step 1: We use the quadratic formula with  ↓

                                                                                         a = -1,b=4,c= - 3

x = -4±(4)^2-4(-1)(-3)/2(-1) Step 2: Substitute the values into the Quadratic  Formular

x = -4± 4/ - 2         x = 1 or x = 3        Step 3: Simplify the Expression & Separate Roots

x = 1 or x = 3  ------- ANSWER

Substitute 1 in for x in y = 2x - 3 then solve for y

y = 2x - 3

y = 2 · (1)  - 3 (Substituting)

y = -1 (Simplify)

Substitute 3 for in y = 2x - 3 then solve for y

y = 2x - 3

y = 2 · (3) - 3 (Substituting)

y =  3   (Simplify)

Therefore, the final solutions for y = x^2 -2x; y = 2x - 3 are

x₁ = 1, y₁ = -1

x₂ = 3, y₂ = 3              

Answer:

1/4

Step-by-step explanation:

First you add all of the marbles in the bag which is 16 marbles.  The fraction of red marbles to the total would be 4/16.  In the simplest form that is 1/4. You can also just do 4 divide by 16 which gives you 0.25 and in decimal form that is 1/4.

Answer:

There are infinite numbers between one and four.

Step-by-step explanation:

There are whole, half, quarter, eighth and so many more numbers that the list is infinite. Hope this helps :)

Numbers are used to count and show measurement. There are infinite real numbers between 1 and 4 & there are 2 integers between 1 and 4.

Given

\(Min = 1\)

\(Max =4\)

The question can be interpreted in the following ways.

Interpretation 1: The number of integers/whole numbers/natural numbers between 1 and 4.

The category of numbers above do not have decimal points.

So: the solution to this interpretation is that there are 2 numbers between 1 and 4 and the numbers are 2 and 3.

Interpretation 2: The number of real numbers between 1 and 4.

The range of numbers between 1 and 4 is represented as:

\(Range = [1,4]\)

If the range is expanded, the numbers will be:

\(Numbers = \{1,1.000001,1.0000000000001,.....\}\)

This means that there can be as many numbers as possible between the interval.

Hence, the real numbers between 1 and 4 can not be counted i.e. infinity

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Answer:

hi, I think the answer is x^2-2x+1 I don't see that option there but I'm guessing that was suppose to be option OA.

explanation:

(x-1)^2 is basically

(x-1)×(x-1)

rest of the explanation is in the photo

hope this helps

Given:

The function is given:

To find:

The period of the function.

Solution:

It is known that the period of the function A tan (nx) is pi/n.

So, the period of the given function is:

Thus, the period of the given function is 4pi.

Thus, option D is correct.

Answer:

7.2kg of flour

Step-by-step explanation:

Total weight of bread = 10 x 750g

                                    = 7500g = 7.5kg

500g of bread = 480g of flour

0.5kg of bread = 0.48kg of flour

7.5kg of bread = 7.2kg of flour

The value of x that satisfies the given statement is 5.

The given statement can be written as an equation:

The excess of 15 over x is 10

15 - x = 10

To solve for x, we can isolate the variable on one side of the equation. Adding x to both sides, we get:

15 - x + x = 10 + x

Simplifying the left side, the x terms cancel out:

15 = 10 + x

Subtracting 10 from both sides, we get:

15 - 10 = x

Simplifying the left side, we get:

5 = x

x = 5

Therefore, the value of x is 5.

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Answer: 29

Step-by-step explanation:

all triangles equal to 180

180-97-54=29

Answer:

1/24

Step-by-step explanation:

\(a^{-1} =\frac{1}{a} \\24^{-1} =\frac{1}{24}\)

A negative exponent is converted to a fraction while the power goes to the base which is at the denominator.

Answer:

hi ik you dont trust me however id like to say that the answer is A. 41.6

Step-by-step explanation:

hope this helps <3 (also i put this into a calculator to double check my work and it was still 41.6)

Answer:

41.6

Step-by-step explanation:

Move the decimal 1 place to the right according to the laws of exponents.

since the exponent is 1, that's why we move it 1 place right. if the exponent was -1, it would go to the left, and the number would become "0.416".

The simplified version of the expression would be 31-w

The numerical part of the expression given is :

Simplifying using Subtraction operation:

Adding the alphabetical part :

Therefore, the simplified form of the expression is 31-w.

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9514 1404 393

Answer:

  x = -3

Step-by-step explanation:

The solution to the equation ...

  f(x) = g(x)

is the x-value where the functions have equal values. That is the x-coordinate of the point where the graphs intersect. The intersection point is (-3, 5), so the solution to the equation is x = -3.

9514 1404 393

Answer:

Step-by-step explanation:

Dilation has no effect on angle measures, so ∠A = ∠A'.

Point A is the center of dilation, so doesn't move. Any line through point A will still go through point A after dilation. Lines AD and A'D' are not distinct.

Answer:

B. The product of 5 and a number.

Product means multiplication is taking place. In this case, 5 is being multiplied with n.

Hope this helps!

Answer:

C. x^2 - 64 = 0

hope this helps :)

Answer:

It's C

Step-by-step explanation:

It has a variable being squared

i dont know. Im sorry about that.

Answer:

2. is b

3.is d

4.is b

5

Step-by-step explanation:

I've done these before

have a good grade

Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Velocity is hit the ground to height v = 81.4 m/s.

The height is the measurement of the distance from the ground to the top of an object, typically expressed in feet or meters. It is used to describe the size and shape of a person, animal, or object. People's heights can vary significantly based on genetic factors, health, diet, and lifestyle. Height is also an important factor in many sports, and can influence how well an athlete performs in a particular sport.

y = √19.6h

v = y

v = √19.6h

v = √19.6(44.2)

v = 81.4 m/s

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Answer:

\(\frac{8}{9}\)

Step-by-step explanation:

using the image attached as reference

(-4,-1) - the -4 becomes x1, and the -1 becomes y1

(5,7)  - the 5 becomes x 2 and the 7 becomes y2

plug this information into the equation

      7-(-1)

m=----------      

      5-(-4)

solve

       8

m=----------    

        9

​so your slope would become 8/9

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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Answer: 10

Step-by-step explanation:

Since -2 is in between -5 and 0, we will use the part of the function that says f(x)=x^2 + 3x.

Substituting x=-2, we get (-2)^2 -3(-2)=4+6=10

Answer:

288 m^3

Step-by-step explanation:

V=(1/3)Bh, where B is base, and h is height

The base will use the equation A=(1/2)bh

B = (1/2)12x9

B = 54

the height is given: 16m

substitute into Volume equation:

V=(1/3)54x16

V=288

Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Answer:

its 5x-16/2

Step-by-step explanation:

Step-by-step explanation:

x^2 + 2x - 8

d=b²-4ac=4+32=36

x1=(-b+√d)2a=(-2+6)/2=2

x2=

(-b-√d)2a=(-2-6)/2=-4

x=2 and x=-4

Answer: Area = 113.14 ft sq. Perimeter =

Step-by-step explanation:

break down the figure and solve area and perimeter for each

triangle = A = 1/2bh

A = 1/2 (8) (6)

A = 24 ft sq.

square = A = LW

A = (8) (8)

A = 64 ft sq

semi circle = A = 1/2 TT r^2

A = 1/2 (3.14) (4)^2

A = 1/2 (3.14) (16)

A = approximately 25.14 ft sq

rounded to hundredths

total AREA = 24 + 64 + 25.14 = 113.14

now we can find perimeter by breaking down the figures again

triangle

we know one leg is 6 ft and the other is 8 ft

we need to find the hypoteneuse using Pythagorean theorem.

a^2 + b^2 = c^2

6^2 = 8^2 = c^2

36 + 64 = c^2

100 = c^2

√100 = √c^2

10 ft = c

square

given two sides are 8ft and 8ft

semi circle - P is the same as circumference

P = ( 1/2 ) 2 π r

P = (1/2) (2) (3.14) (4)

P = 12.56

total PERIMETER = 12.56 + 8 + 8 + 6 + 10 = 44.56 ft

i attached a print screen showing my breakdowns