evaluate the expression xy for x = 6 and y = 3

Answer:

y=9.01

Step-by-step explanation:

In this question you apply the Pythagoras Theorem to generate relationships which will enable you to form equations and solve for the unknown.

The Pythagoras Theorem states that when you have a right-angle triangle and squares are made at each of the three sides, the sum of squares of the two small sides will equal the square of the longest side.

It is expressed as a²+b²=c² where;

In the question we can use three triangles to form expressions using this theorem

First triangle

The relationship you can form is;

[tex]3^2+y^2=z^2\\9+y^2=z^2\\y^2=z^2-9------------------------(1)[/tex]

In this equation you make y² the subject of the formula

Second Triangle

Hence the relationship you can form is

[tex]27^2+y^2=x^2\\729+y^2=x^2\\y^2=x^2-729[/tex]

In this equation you make y² the subject of the formula

Third Triangle

The relationship you can form is;

[tex]z^2+x^2=30^2\\x^2=30^2-z^2---------------------(3)[/tex]

Here x² is the subject of the formula

Equations

[tex]y^2=z^2-9\\y^2=x^2-729\\x^2=900-z^2[/tex]

Substitute equation 3 in equation 2

[tex]y^2=x^2-729-------------2\\\\x^2=900-z^2-------------3\\\\y^2=900-z^2-729\\\\y^2=171-z^2---------------4[/tex]

Substitute equation 4 in equation 1

[tex]y^2=171-z^2---------------4\\\\y^2=z^2-9------------1\\\\z^2-9=171-z^2\\\\2z^2=171+9\\\\z^2=180\\\\z=\sqrt{180} \\\\z=9.487\\\\z=9.5[/tex]

Use the value of z in equation 1 to get value of y

[tex]z^2-3^2=y^2\\\\9.5^2-9=y^2\\\\90.25-9=y^2\\\\81.25=y^2\\\\\sqrt{81.25} =y\\\\y=9.01[/tex]

Let R = greatest number of rectangular lots.

R = (910 • 300)/(120 • 65)

R = 273,000 ÷ 7800

R = 35

The exact volume of the cylinder is [tex]\( 3380\pi \)[/tex] cubic meters.

To find the exact volume V of a cylinder, we use the formula:

[tex]\[ V = \pi r^2 h \][/tex]

where:

- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159,

- r is the radius of the cylinder, and

- h is the height of the cylinder.

Given:

- Radius (r=13) meters, and

- Height (h=20) meters.

Substitute these values into the formula:

[tex]\[ V = \pi \times (13)^2 \times 20 \]\[ V = \pi \times 169 \times 20 \][/tex]

[tex]\[ V = 3380\pi \][/tex]

The exact volume of the cylinder is 10,613.2 cubic meters.

To find the volume of a cylinder, we use the formula: Volume = πr²h, where π (pi) is approximately 3.14, r is the radius of the cylinder, and h is the height of the cylinder.

Given:

Radius (r) = 13 meters

Height (h) = 20 meters

Calculate the area of the base (circle) using the formula A = πr².

A = 3.14 × (13)²

A = 3.14 × 169

A = 530.66 square meters

Multiply the area of the base by the height of the cylinder.

Volume = 530.66 × 20

Volume = 10,613.2 cubic meters

So, the exact volume of the cylinder is 10,613.2 cubic meters.

Answer:

4. h(t)=2000t+800

Step-by-step explanation:

800 is his starting elevation we dont not multiply it

every hour he gains 2000ft in elevation and t shows the hours 2000ft * t (hours) + 800

Answer:

x = 16 and z = 84

Step-by-step explanation:

The 2 given angles are vertical and congruent, hence

7x - 16 = 6x ( subtract 6x from both sides )

x - 16 = 0 ( add 16 to both sides )

x = 16

Hence 6x = 6 × 16 = 96°

z and 6x form a straight angle and are supplementary, hence

z + 6x = 180

z + 96 = 180 ( subtract 96 from both sides )

z = 84

Answer:

False

Step-by-step explanation:

You need 3 points to name a plane.  2 points is required to name a line

Answer:

It would be CUB

Step-by-step explanation:

Answer:

The value of the expression for x=2 is 2.

Step-by-step explanation:

Consider the provided expression.

[tex]4(x - 3) + 5x - x^2 [/tex]

We need to find the value of expression for x=2.

Substitute the value of x=2 in provided expression and simplify as shown.

[tex]4(2 - 3) + 5(2) - 2^2 [/tex]

[tex]4(-1) + 10 - 4 [/tex]

[tex]-4 + 6 [/tex]

[tex]2 [/tex]

Hence, the value of the expression for x=2 is 2.

The numerical value of the expression 4(x - 3) + 5x - x² when x = 2 is 2.

Given the expression in the question:

4(x - 3) + 5x - x²

x = 2

To evaluate the expression 4(x - 3) + 5x - x² for x = 2, repalce all the occurences of x in the expression with 2 and simplify:

4(x - 3) + 5x - x²

Plug in x = 2:

4(2 - 3) + 5(2) - (2)²

Subtract 3 from 2:

4(-1) + 5(2) - (2)²

Take the square of 2:

4(-1) + 5(2) - 4

Multiply 4 and -1:

-4 + 5(2) - 4

Multiply 5 and 2:

-4 + 10 - 4

Add the 3 numbers:

2

Therefore, the value of the expression is 2.

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Answer:

x = -8

Step-by-step explanation:

We are given the following expression which we are to solve for [tex]x[/tex]:

[tex] 2 7 ^ x = 9 ^ { x - 4 } [/tex]

For this expression, we will make the bases same on both sides of the equation and then equate the exponents equal to each other.

[tex](3^3)^x = (3^2)^{x-4}[/tex]

Multiplying the exponents and equating them to get:

[tex] 3 x = 2 ( x - 4 ) [/tex]

[tex] 3 x = 2 x - 8 [/tex]

[tex] 3 x - 2 x = - 8 [/tex]

x = -8

For this case we must solve the following equation:

[tex]27 ^ x = 9 ^ {x-4}[/tex]

We rewrite:

[tex]27 = 3 * 3 * 3 = 3 ^ 3\\9 = 3 * 3 = 3 ^ 2[/tex]

So:

[tex]3^{3(x)}=3^{2(x-4)}[/tex]

Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:

[tex]3 (x) = 2 (x-4)\\3x = 2x-8[/tex]

Subtracting 2x on both sides:

[tex]3x-2x = -8\\x = -8[/tex]

Answer:

[tex]x = -8[/tex]

Answer:

(0,2/3)

Step-by-step explanation:

I would go for elimination on this one.

This will require we manipulate at least one equation.

I'm going to multiply bottom equation by -2:   -2x-12y=-8

So we have

2x+3y=2

-2x-12y=-8

---------------add the two equations

 0 -9y=-6

     -9y=-6

         y=6/9=2/3

2x+3y=2

2x+3(2/3)=2

2x+2=2

2x=0

x=0

(0,2/3)

Answer: The Answer is A X=0 Y=2/3

Step-by-step explanation:

2x+3y=2

X+6y=4

step one: substitute in the value of x into the equation

2x +3y = 2

x= 4-6y

Step two: Solve with the X substitution

2(4-6y) +3y = 2

You get Y= 2/3

Step three: plug in 2/3 for X

X= 4-6(2/3)

You get 0

therefore: X = 0 and Y=2/3

Answer:

Step-by-step explanation:

Look at the picture.

Answer:

2g{4} hahah sike

Step-by-step explanation:

Answer:

-2√2, or ≈-2.83

Step-by-step explanation:

Well, when t = 1.75, our equation should be [tex]d=4\sin{(\pi \cdot1.75)}[/tex].

Note that [tex]\pi\cdot1.75=\frac{7\pi}{4}[/tex]. Using the unit circle (attached), we can find that the value of sine at [tex]\frac{7\pi}{4}[/tex] radians is exactly [tex]-\frac{\sqrt2}{2}[/tex]. Plugging that value back into our equation gives us

[tex]d=4\cdot\left(-\frac{\sqrt2}{2} \right)=-\frac{4\sqrt2}{2}=-2\sqrt2[/tex]

So our answer is [tex]d=-2\sqrt2[/tex], in whatever units we're using to measure height.

Answer: 0.38 Meters

Step-by-step explanation:

plug 1.75 in for t and solve, do not convert into units as you need the height so meters is accurate.

d=0.38

Answer:

x = -345

Step-by-step explanation

2.3 + .02x + .4 - 4.8 = -9

2.7 - 4.8 + .02x = -9

-2.1 + .02x = -9

.02x = 6.9

x = -6.9 / .02

x = -345

Answer: x = -345

Step-by-step explanation:

2.3 + .02(x + 20) - 4.8 = -9

2.3 + (.02x + .4) - 4.8 = -9

-2.1 + .02x = -9

+2.1             +2.1

.02x = -6.9

.02/.02  -6.9/.02

x = -345

Answer:

[tex]A=779.4\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of a regular hexagon is equal to the area of six equilateral triangles

Applying the law of sines

The area of six equilateral triangles is equal

[tex]A=6[\frac{1}{2}b^{2}sin(60)][/tex]

where

b is the side length of the regular hexagon

we have

[tex]b=10\sqrt{3}\ cm[/tex]

[tex]sin(60\°)=\sqrt{3}/2\ cm[/tex]

substitute

[tex]A=6[\frac{1}{2}(10\sqrt{3})^{2}(\sqrt{3}/2)][/tex]

[tex]A=450\sqrt{3}=779.4\ cm^{2}[/tex]

Pre-Image < Image, then the scale factor is k >1.

Pre-Image > Image, then the Scale factor will be lies between,

0 < k < 1.

It exists given that Rectangle Q has an area of 2 square units.

Thea Drew a scaled version of Rectangle Q and labeled it as R.

As you must keep in mind If we draw a scaled copy of the pre-image, then the two images.

Therefore, Pre-image and Image are similar.

Consider the Scale factor of transformation = k

Rectangle Q = Pre - image,

Rectangle R= Image

If, Pre-Image < Image, then the scale factor is k >1.

But If, Pre-Image > Image, then the Scale factor will be lies between,

0 < k < 1.

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Answer:

Surface Area of Cone = 200π cm^2

Surface Area of Right Prism = 17.5 ft^2

Step-by-step explanation:

32. We are given a figure of a cone and we are to find its surface area.

We know that the formula for the S.A. of cone is given by:

Surface Area of cone = [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex]

Substituting the given values in the above formula.

Surface Area of cone = [tex]\pi \times 8(8+\sqrt{15^2+8^2} )[/tex] = 200π cm^2

25. We are to find the surface area of a right prism.

Surface Area of Right Prism = Base Perimeter × height + 2(Base Area)

Base Perimeter = 2(4 + 1.5) = 11 ft

Height = 0.5 ft

Base Area = 4 × 1.5 = 6 ft

Substituting these values in the above formula.

Surface Area of Right Prism = 11 × 0.5 + 2(6) = 17.5 ft^2

Answer:

Surface area of cone = 200π cm

Surface area of prism =  17.5 ft²

Step-by-step explanation:

To find the slant height of cone

slant height l = √(r² + h²)

= √(8² + 15²)  = 17

To find the surface area of cone

Surface are = πr² + πrl

 = π*8² + π*8*17

 = 64π + 136π

 = 200π cm²

To find the surface area of prism

l = 4 ft

b = 1.5 ft and h = 0.5 ft

Surface area = 2(lb + lh + bh)

 = 2[(4* 1.5) + (4*0.5) + (1.5*.5)

 = 2(6 + 2 +0.7.5)

 = 17.5 ft²

[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ k=5\qquad \qquad y=\cfrac{5}{x}[/tex]

Answer:

C. Y=5/x

Step-by-step explanation:

Inverse variation is given by

xy = k  where k is a constant

Divide each side by x

xy/x = k/x

y = k/x  where k is a constant

Let k=5

y = 5/x  is an equation that is inverse variation

Answer: 5.25 miles per hour.

Step-by-step explanation:

21/4 = 5.25

Hello There!

WHAT WE KNOW Shelly biked 21 miles in 4 hours. We know that Shelly's average speed = 5.25 miles / hour because "21 divided by 4 equals 5.25"

Answer:

700 square feet

Step-by-step explanation:

We can simply divide 630 by 0.9 to find the value:

[tex]\frac{630}{0.90}=700[/tex]

Checking, if she goes for 700 sq ft at $0.90 per square feet, she would need:

700 * 0.90 = $630

Yes, that's the max, so 700 sq. feet apartment is what she can afford.

Answer:

32 Minutes

Step-by-step explanation:

Together the two clerks can file 21 files per minute (10+11=21).

Therefore to file 672 folders would take 32 minutes (672/21=32)

Answer:

slope = -2

y-intercept = (0,2)

y = -2x + 2

Step-by-step explanation:

In order to find the slope, we must use the formula y2-y1/x2 - x1. But in order to do so, we will have to find two perfect points.

perfect point #1: (-2,6)

perfect point #2: (2, -2)

Now, we simply input the corresponding points into our formula.

-2 - 6 = -8

2 - (-2) = 4

-8/4 = -2

So, the slope of the graph is -2

In order to find the y-intercept we must look at where the line intersects in the y axis. Looking back at our graph, we can determine that the line intersects at (0,2)

The slope-intercept form is y = mx + b, m represents the slope and b represents the y intercept. Therefore after inputting the slope and y-intercept we should get y = -2x + 2

The total cost of a taxi ride includes a $5 flat fee plus $0.50 for every mile traveled. The total cost can be calculated using the formula: Total cost = $5 flat fee + ($0.50 × number of miles). For instance, a 10-mile trip would cost $10.

The total cost of a taxi ride is dependent on the distance traveled in miles. The taxi driver charges a $5 flat fee to enter the car and $0.50 per mile. To find the total cost, you can use the equation:

Total cost = Flat fee + (Cost per mile × Number of miles traveled)

For example, if you traveled 10 miles, the total cost would be:

Total cost = $5 + ($0.50 × 10) = $5 + $5 = $10

This formula will give you the total expense for any number of miles traveled in the taxi.

Answer:

x = 4

Step-by-step explanation:

2x + y = 6 ... (i)

x - 6 = y ... (ii)

y = 6 - 2x ... (i)

y = x - 6 ... (ii)

So,

6 - 2x = x - 6

x + 2x = 6 + 6

3x = 12

x = 12/3 = 4

Answer:

c.45 degrees

Step-by-step explanation:

90 -180= 90

90÷2=45

For this case, we have by definition, that the four internal angles of a square measure 90 degrees. If we draw the diagonals of the square we have that the angles are divided between 2, that is, they go to measure 45 degrees.

So, according to this definition we have to:

[tex]Angle\ 3 = \frac {90} {2}\\Angle\ 3 = 45[/tex]

Answer:

The angle 3 is 45 degrees

Option C

All you need to do to solve this is multiply 2 to both sides. This will cancel out 2 from the denominator and isolate x...

2([tex]\frac{x}{2}[/tex]) = -7 * 2

x = -14

Hope this helped!

~Just a girl in love with Shawn Mendes

Hello There!

The Answer is -14

If we substitute -14 in the equation as x, -14 ÷ 2 ≈ -7

A negative number divided by a positive number gives us a negative number.

Answer:

6 ft.

Step-by-step explanation:

solution :

360 degree = pie r².

1 degree =pie r²/360

50degree=5pie r²/36

5pie = 5 pie r²/36

r²=36

r=6

Therefore radius = 6 ft.

Answer:

x ≥ -5

Step-by-step explanation:

If we have a translation to left c units, we write " x + c " in the function, and

If we have a translation to right c units, we write " x - c" in the function

If we have vertical translation up b units, we "add b to the function", and

If we have vertical translation down b units, we "subtract b to the function"

The parent function is  [tex]f(x)=\sqrt{x}[/tex]

Since translation left 5 units and up 3 units, we can write:

[tex]f(x)=\sqrt{x+5} + 3[/tex]

The domain is affected by the square root sign and we know the number under the square root CANNOT be negative, so we can say:

x + 5 ≥ 0

x ≥ -5

This is the domain.

The domain of the function g(x), which is the translated version of f(x) = √x, is all x ≥ -5 after being shifted left 5 units and up 3 units.

The function g(x) resulting from translating f(x) = √x left 5 units and up 3 units is expressed as g(x) = √(x+5) + 3. Because we cannot take the square root of a negative number in the set of real numbers, the domain of f(x) is all x ≥ 0. After the translation, the domain of g(x) will also be shifted 5 units to the left. Therefore, the domain of g(x) is all x ≥ -5, as this is the new point where the function starts to produce real number outputs.

Answer:

Length: 139 feet

Width: 104 feet

Step-by-step explanation:

The formula for the perimeter of a rectangle can be given by [tex]P = 2l + 2w[/tex]. We are given the perimeter of the pool along with the width.

[tex]P = 486[/tex]

[tex]w = l - 35[/tex]

From here, all we have to do is plug back into the original formula:

[tex]486 = 2l + 2(l - 35)[/tex]

Which can be further simplified as:

[tex]486 = 2l + 2l - 70[/tex]

[tex]486 = 4l - 70[/tex]

From here, all we have to do is add 70 to both sides of the equation and divide by four:

[tex]556 = 4l[/tex]

[tex]139 = l[/tex]

To make sure that this answer is accurate, we can find that the width of the rectangle should then be 104 (given by 139 - 35). All we have to do is plug back into the original equation:

[tex]P = 2l + 2w[/tex]

[tex]P = 2(139) + 2(104)[/tex]

[tex]P = 278 + 208[/tex]

[tex]P = 486[/tex]

And the substitution works, so the length of the rectangle would be 139 feet and the width would be 104 feet.

Answer:

Length = 139 and Width = 104 .

Step-by-step explanation:

Given: The perimeter of a rectangle swimming pool is 486 feet. The width of the pool is 35 feet less than the length.

To find: Find the length and the width​ .

Solution: We have given that

Let the length = x

According to question

The width of the pool is 35 feet less than the length.

width = x-35

perimeter = 2(length + width)

plugging the values

486   = 2(x + x-35)

486  =  2x + 2x - 70

486  = 4x - 70

On adding by 70 both side

486 +70 = 4x-70 +70

556 = 4x

On dividing by 4 both side

139 = x

so, length = 139 .

    width = x -35 =  139- 35 = 104

Therefore,  length = 139 and width = 104.

Answer: The slope is -2

Step-by-step explanation:

It is important to remember that the equation of the line in Slope-Intercept form is the following:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

In this case you can observe that the given equation of the line [tex]y=-2x+3[/tex] is written in Slope-Intercept form.

Therefore, you can identify that the slope "m" is:

[tex]m=-2[/tex]

And the y-intercept "b" is:

[tex]b=3[/tex]

a) y = x - 4

First, to find the rate of change [slope], do rise\run: -y₁ + y₂\-x₁ + x₂. Doing this will result in the slope being 1, and the ONLY answer that has a slope of 1, is the top choice.

Slope-Intercept Formula: y = mx + b [m represents slope].

I am joyous to assist you.