This system of equations has an infinite number of solutions. Define the solutions algebraically, and allow z to represent all real numbers.

3x − 4y + 4z = 7
x − y − 2z = 2
2x − 3y + 6z = 5
x =

y =

z = all real numbers

Answer:

first 1

Step-by-step explanation:

first 1

Answer:

7/4 ÷ 1/2= 3 1/2

Step-by-step explanation:

This is the answer hope it help's :)

Answer:

Choice B is correct

Step-by-step explanation:

The given radical division can be expressed in the following form;

[tex]\frac{\sqrt{16x^{3} } }{\sqrt{8x} }[/tex]

Using the properties of radical division, the expression can be expressed in the following form;

[tex]\sqrt{\frac{16x^{3} }{8x} }=\sqrt{2x^{2} }[/tex]

Simplifying further yields;

[tex]\sqrt{2x^{2} }=\sqrt{2}*\sqrt{x^{2} }=x\sqrt{2}[/tex]

Choice B is thus the correct alternative

For this case we must simplify the following expression:

[tex]\frac {\sqrt {16x ^ 3}} {\sqrt {8x}} =[/tex]

Join the terms in a single radical:

\[tex]\sqrt {\frac {16x ^ 3} {8x}} =\\\sqrt {\frac {8 * (2x ^ 3)} {8x}} =\\\sqrt {\frac {2x ^ 3} {8x}} =\\\sqrt {2x ^ 2} =\\\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]\sqrt {2x ^ 2} =\\x \sqrt {2}[/tex]

Answer:

Option B

Answer:125+220+c

if c= 20 then it would be 125+220+20=365

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

[tex]\frac{5x}{20} =\frac{45}{36}[/tex]

Cross multiply:

(5x)(36)=(20)(45)

180x = 900

divide by 180.

x=5

The value of x is 5.

Δ ACE ≅ Δ BCD    (by AAA property)

Therefore

[tex]\frac{CD}{CE} = \frac{CB}{CA}[/tex]         ( Similar triangle property)

[tex]\frac{20}{36} = \frac{5x}{45}[/tex]

5x = [tex]\frac{20 * 45}{36}[/tex]

5x = 25

x = 5

Therefore, option D. 5 is the correct answer

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Answer:

6135.9m^3

Step-by-step explanation:

V=3.14r^2 h/3

step by step

1. the radius is half so half of 25 is 12.5 that's the r in your equation

2.the height in your equation is 3 times more then the radius and your radius is 12.5X3 =37.5 for your height

3. plug everything in back into the equation v=3.14(12.5)^2(37.5/3)= 6135.923 when rounded it is 6135.9m^3

Answer:

x + 6 =

Step-by-step explanation:

In math sum means addition, difference is subtraction, product is multiplication, and quotient is division

ANSWER

x+6

EXPLANATION

An algebraic expression contains letters and numbers that are connected with mathematical operators or symbols.

The sum of x and 6 as an algebraic up expression is:

x+6

This expression contains a variable , a mathematical symbol and a number.

ANSWER

Period: 2π , amplitude: 4

EXPLANATION

The graphed function is

[tex]y = 4\cos(x) [/tex]

The amplitude of this function is

[tex] |4| = 4[/tex]

The period is 2π because there is no phase shift hence the period is still equal to the parent function.

Period: 2π , amplitude: 4

Answer:

The correct option is 3.

Step-by-step explanation:

The general form of a cosine function is

[tex]f(x)=A\cos (Bx+C)+D[/tex]

where, A is amplitude, 2π/B is period, C is phase sift and D is midline.

[tex]A=midline=\frac{Maximum-Minimum}{2}[/tex]

[tex]A=midline=\frac{4-(-4)}{2}[/tex]

[tex]A=midline=4[/tex]

The amplitude of the function is 4.

The given graph complete a cycle in the interval [0,2π], therefore the period of the graph is 2π.

Therefore the correct option is 3.

The equation in point-slope form for the line through the point (-3, -7) with slope -6/5x is y - (-7) = -6/5(x - (-3)).

To write the equation of a line in point-slope form, we can use the given point and slope. The point we have is (-3, -7) and the slope is -6/5. The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get the equation as:

y - (-7) = -6/5(x - (-3))

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To write an equation in point-slope form, you need the coordinates of a point on the line and the slope of the line. In this case, the given point is (–3, –7) and the slope is -6/5. The equation in point-slope form is y + 7 = -6/5(x + 3).

To write an equation in point-slope form, you need the coordinates of a point on the line and the slope of the line. In this case, the given point is (–3, –7) and the slope is -6/5.

The point-slope form of the equation is y - y1 = m(x - x1).

Plugging in the values, we get y - (-7) = -6/5(x - (-3)).

Simplifying, we have y + 7 = -6/5(x + 3).

Thus, the equation in point-slope form for the line through the point (–3, –7) with a slope of -6/5x is y + 7 = -6/5(x + 3).

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10-14-19-12-14-18-10-15-15

Answer:

(2x+3)(2x+3)

Step-by-step explanation:

a^2+2ab+b^2

Answer:

Gum’s Minimum height: 6ft

Gum’s Maximum height: 8ft

2nd part

How far does the gym travel in one revolution of the bicycle wheel?

2pi

Answer:

Minimum height of gum = 6 foot.

Maximum height of gum = 8 foot.

Step-by-step explanation:

A rider is riding a bicycle on a 6 foot wall, therefore the height of the lowest point of the rear wheel is 6 foot from the ground and highest point of the rear wheel is (6+2) foot = 8 foot ( because diameter of rear wheel =2 foot ).

If a piece of gum become stuck to the rear wheel, hence the minimum height of the gum is 6 foot from the ground and maximum height of the gum is 8 foot  from the ground.

Answer:

a. 1/150.

b. 14.

Step-by-step explanation:

a.  That would be 2/300 = 1/150.

b.  So we expect 1 out of every 150  bikes will have 1 with defective brakes so out of 2,100 it is (1/150) * 2,100

= 14.

Step-by-step explanation:

Answer:

  33% off is the better deal

Step-by-step explanation:

1.33 times as much popcorn for the same price is equivalent to 1/1.33 ≈ 0.75 times the price for the original amount of popcorn. That price is equivalent to a sale of 1 - 0.75 = 0.25 = 25% off.

The sale price of 33% off is a better deal (if you don't want the extra popcorn).

For this case we have that by definition:

1 pound is equivalent to 16 ounces.

We make a rule of three to determine the ounces of butter:

1lb ------------------------> 16onzas

[tex]\frac {1} {12}[/tex]----------> x

Where "x" represents the ounces of butter

[tex]x = \frac {\frac {1} {12} * 16} {1}\\x = \frac {16} {12}\\x = \frac {8} {6}\\x = \frac {4} {3}[/tex]

Thus, there are [tex]\frac {4} {3}[/tex]ounces of butter.

Now we must find the amount of eggs that remain:

[tex]92- (43+ \frac {1} {5}) =\\92 - (\frac {43 * 5 + 1} {5}) =\\92 - (\frac {215 + 1} {5}) =\\92 - (\frac {216} {5}) =\\92-43.2 =\\48.8[/tex]

Round down. There are 48 eggs left.

Answer:

There are [tex]\frac {4} {3}[/tex] ounces of butter.

48 eggs left

Simplify for -5/8*2/3= -5/12

-0.416 as a mixed number

Answer:

C

Step-by-step explanation:

C:  AB is the radius of both circles.

Answer:

C. line segment AB is the radius of both circles.

Step-by-step explanation:

If point A is the center of the first circle and point B is the center of the second circle (in the figure), therefore Line segment AB is the radius of both circles and we write.

Line segment AB = line segment AC (radius of first circle ) and

line segment  AB =  line segment BC (radius of second circle).

Hence line segment AB is the radius of both circle is the correct option for AB =AC.

1. The parabola opens upward.

2. It has a minimum value

The explanation is shown below. Also, the graph of this function  is shown below including the vertex.

Answer:

The last graph

Step-by-step explanation:

The problem presented here is similar to a compound interest problem since we have an initial value, a growth constant and the aspect of time.

We can consider the number of television sets currently produced by the company to be our Principal amount;

P = 2000

The rate of increase in production per month can be considered as our interest rate earned;

r = 25% = 0.25

The total number of television sets y will be our Accumulated amount;

A = y

The duration x becomes our time n.

The compound interest formula is given as;

[tex]A=P(1+r)^{n}[/tex]

We simply substitute the given information into the formula;

[tex]y=2000(1.25)^{x}[/tex]

This is an exponential growth function since the base of the exponent x is greater than 1.

A graph of the function will be an exponential curve passing through ( 0, 2000) since 2000 is our initial value

Answer: the last ones

Step-by-step explanation: I put it and got it right:)

Answer: 0.1(175-n)+0.05n=13.30

Step-by-step explanation: The question is asking you to make and simplify a system of equations.

The 2 equations are:

n+d=175

0.1d+0.05n=13.30.

d=175-n

Solve for n, then substitute into the second equation.

0.1(175-n)+0.05n=13.30

Hope this helps!

[tex]\dfrac1{x(x-1)}=\dfrac ax+\dfrac b{x-1}[/tex]

[tex]1=a(x-1)+bx[/tex]

If [tex]x=0[/tex], then

[tex]1=-a\implies a=-1[/tex]

If [tex]x=1[/tex], then

[tex]1=b[/tex]

So we have

[tex]\dfrac1{x(x-1)}=\dfrac1{x-1}-\dfrac1x[/tex]

Answer:

The maximum value is 126 occurs at (9 , 9)

Step-by-step explanation:

* Lets remember that a function with 2 variables can written

 f(x , y) = ax + by + c

- We can find a maximum or minimum value that a function has for

 the points in the polygonal convex set

- Solve the inequalities to find the vertex of the polygon

- Use f(x , y) = ax + by + c to find the maximum value

∵ 8x + 2y = 36 ⇒ (1)

∵ -3x + 6y = 27 ⇒ (2)

- Multiply (1) by -3

∴ -24x - 6y = -108 ⇒ (3)

- Add (2) and (3)

∴ -27x = -81 ⇒ divide both sides by -27

∴ x = 3 ⇒ substitute this value in (1)

∴ 8(3) + 2y = 36

∴ 24 + 2y = 36 ⇒ subtract 24 from both sides

∴ 2y = 12 ⇒ ÷ 2

∴ y = 6

- One vertex is (3 , 6)

∵ 8x + 2y = 36 ⇒ (1)

∵ -7x + 5y = -18 ⇒ (2)

- Multiply (1) by 5 and (2) by -2

∴ 40x + 10y = 180 ⇒ (3)

∴ 14x - 10y = 36 ⇒ (4)

- Add (3) and (4)

∴ 54x = 216 ⇒ ÷ 54

∴ x = 4 ⇒ substitute this value in (1)

∴ 8(4) + 2y = 36

∴ 32 + 2y = 36 ⇒ subtract 32 from both sides

∴ 2y = 4 ⇒ ÷ 2

∴ y = 2

- Another vertex is (4 , 2)

∵ -3x + 6y = 27 ⇒ (1)

∵ -7x + 5y = -18 ⇒ (2)

- Multiply (1) by 7 and (2) by -3

∴ -21x + 42y = 189 ⇒ (3)

∴ 21x - 15y = 54 ⇒ (4)

- Add (3) and (4)

∴ 27y = 243 ⇒ ÷ 27

∴ y = 9 ⇒ substitute this value in (1)

∴ -3x + 6(9) = 27

∴ -3x + 54 = 27 ⇒ subtract 54 from both sides

∴ -3x = -27 ⇒ ÷ -3

∴ x = 9

- Another vertex is (9 , 9)

* Now lets substitute them in f(x , y) to find the maximum value

∵ f(x , y) = 9x + 5y

∴ f(3 , 6) = 9(3) + 5(6) = 27 + 30 = 57

∴ f(4 , 2) = 9(4) + 5(2) = 36 + 10 = 46

∴ f(1 , 5) = 9(9) + 5(9) = 81 + 45 = 126

- The maximum value is 126 occurs at (9 , 9)

The maximum value of the function for the polygonal convex set determined by a system of inequalities can be found using linear programming. The key steps are to plot the inequalities, find the vertices of the feasible region, and substitute these points into the function to find the maximum value.

This problem is related to linear programming, which is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. To find the maximum value of the function for the polygonal convex set determined by the given system of inequalities, you essentially need to apply the rules of linear programming.

Firstly, plot the system of inequalities on a coordinate system to determine the feasible region, which is the polygonal convex set. Then, find each vertex of this polygonal convex set. These vertices are points where boundaries of the system of inequalities intersect. Once you have these vertices, substitute each of them into the function you are maximizing. The largest output will be the maximum value of the function within the given polygonal convex set.

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Answer:

[tex]\frac{38}{7}[/tex]

Step-by-step explanation:

Using the properties of logarithms,

[tex]\log(7)+\log(x-4)=1\\\log(7(x-4))=1\\\log(7x-28)[/tex]

Now think about what this is asking. The log function say 10 to the power of whats on the other side of the equals sign, equals whats in the parenthesis. So, this means whats is the parenthesis is equal to [tex]10^1[/tex] or just 10.

We can now solve to x.

[tex]7x-28 = 10\\7x=38\\x=\frac{38}{7}[/tex]

Answer:

x=38/7

Step-by-step explanation:

Just took the test

so she saved $20 and that was 40% of the regular price, let's say the regular price is "x".

if 20 is 40%, what is "x" or namely the 100%?

[tex]\bf \begin{array}{ccll} amount0&\%\\ \cline{1-2} 20&40\\ x&100 \end{array}\implies \cfrac{20}{x}=\cfrac{40}{100}\implies \cfrac{20}{x}=\cfrac{2}{5}\implies 100=2x \\\\\\ \cfrac{100}{2}=x\implies 50=x[/tex]

Answer:This is an equation! Solutions: x=1.

Step-by-step

Answer:

A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)

Step-by-step explanation:

Before the rotation:

A (-4, 4), B (6, 2), C (1, 1), D(-5, 3)

270° rotation clockwise is the same as 90° counterclockwise.  To do that transformation:

(x, y) → (-y, x)

Therefore, the coordinates of the rotated figure are:

A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)

The coordinates of the image are:

---------------------------

This question is solved applying a 270° clockwise about the origin, which has the following rule:

[tex](x,y) = (-y,x)[/tex]

---------------------------

Coordinate A:

At the Figure, coordinate A is A(-4,4). Applying the rule:

[tex](-4,4) = (-4, -4)[/tex]

So the image of A is A'(-4,-4).

---------------------------

Coordinate B:

At the Figure, coordinate B is B(6,2). Applying the rule:

[tex](6,2) = (-2, 6)[/tex]

So the image of B is B'(-2,6).

---------------------------

Coordinate C:

At the Figure, coordinate C is C(1,1). Applying the rule:

[tex](1,1) = (-1, 1)[/tex]

So the image of C is C'(-1,1).

---------------------------

Coordinate D:

At the Figure, coordinate C is D(-5,3). Applying the rule:

[tex](-5,3) = (-3,-5)[/tex]

So the image of D is D'(-3,-5).

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Answer:

  the correct answers are marked in green below

Step-by-step explanation:

As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).

_____

Comment on the choices

The relationship is actually ...

  ║u+v║ ≤ ║u║ + ║v║

That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.

Answer:

As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).

_____

Comment on the choices

The relationship is actually ...

 ║u+v║ ≤ ║u║ + ║v║

That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.

Step-by-step explanation:

For this case we have a system of two equations with two unknowns:

[tex]x = -3y-13\\2x + 2y = -6[/tex]

To solve we follow the steps below:

We substitute the first equation in the second:

[tex]2 (-3y-13) + 2y = -6[/tex]

We apply distributive property to the terms of parentheses:

[tex]-6y-26 + 2y = -6[/tex]

We add 26 to both sides of the equation:

[tex]-6y + 2y = -6 + 26\\-4y = 20\\y = \frac {20} {- 4}\\y = -5[/tex]

We find the value of x:

[tex]x = -3 (-5) -13\\x = 15-13\\x = 2[/tex]

Answer:

[tex](x, y) :( 2, -5)[/tex]

ANSWER

I) 5:11

ii) 5:11

iii) 125:1331

EXPLANATION

Let the side lengths be in the ratio:

x:y

This implies that the area will be in the ratio:

[tex] \frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{121} [/tex]

Take positive square root.

[tex] \frac{x}{y} = \sqrt{ \frac{25}{121} } [/tex]

[tex] \frac{x}{y} = \frac{5}{11} [/tex]

Hence the sides are in the ratio:

x:y=5:11

The perimeter of the smaller hexagon is 6×5=30

The perimeter of the larger hexagon is 6×11=66

The ratio of the perimeter is

30:66=5:11

The volume will be in the ratio

5³:11³

125:1331

Answer:

Option d.

±π/2 ; ±3π/2

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)= 3*cos (x)

We can see from the graph that the zeros are

±π/2 ; ±3π/2

Correct option is d.

Answer:

C

Step-by-step explanation:

The formula for effective annual interest rate is:

[tex]r=(1+\frac{i}{n})^{n}-1[/tex]

where

r is the effective annual interest rate

i is the stated interest rate (here, it is 1.55%, or 0.0155)

n is the number of compounding periods (here, compounded monthly, so it means 12 times a year, so n = 12)

plugging these info into the formula, we get:

[tex]r=(1+\frac{i}{n})^{n}-1\\r=(1+\frac{0.0155}{12})^{12}-1\\r=0.0156[/tex]

0.0156 * 100 = 1.56%

correct answer is C

Answer:

The answer is C

Step-by-step explanation:

i got it right on Plato : ) Brainliest?

ANSWER

A. 8x=16

EXPLANATION

The given equations are:

1st equation: y=2x

2nd equation: 2x+3y=16

We substitute the first equation into the second equation to get:

2x+3(2x)=16

This implies that:

2x+6x=16

We combine like terms to get:

8x=16

The correct choice is A. 8x=16