The length, L, of a rectangular garden is twice its width, W. The perimeter of the garden is 36 feet.

The given function shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.

Given the parent function with base 10.

We want to find the given transformations.

The given parent function is y=log(x)

Firstly, we want to shift the given parent function 3 units left means we will add 3 in the parent function, we get

y=log(x+3)

Now, we want to do vertical compression by a factor of 2 means we will multiply the above function with 2, we get

y=2log(x+3)

Further, we want to reflected the above function across the y-axis means we will multiply the x with minus, we get

y=2log(-x+3)

Furthermore, we want to shift the above function down with 5 units means we will subtract 5 from the above function, we get

y=2log(-x+3)-5

Hence, the given parent function y=log(x) when shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.

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The figure that is a dilation of figure E is the figure F

Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.

The graph represents the given parameter

From the figure, we have the original shape to be figure E

The center point of figure E is the origin

This means that a line drawn from the origin that passes through point E must pass through the same point on the shape

From the figure, the line passes through the same point on figure E and F

Hence, figure F is a dilation of figure

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Answer:

  (4)  5 m

Step-by-step explanation:

You want the length of side x of a right triangular prism with base edge lengths of 2.5 m and 2 m, and a volume of 12.5 m³.

The volume of the prism is given by the formula ...

  V = Bh

where B is the area of the base:

  B = 1/2bh . . . . where b and h are the leg dimensions of the right triangle

Using these formulas together, we have ...

  V = 1/2(2.5 m)(2 m)x

  12.5 m³ = 2.5x m²

Dividing by 2.5 m², we find x to be ...

  (12.5 m³)/(2.5 m²) = x = 5 m

The dimension labeled x has length 5 meters.

When a bowling ball is propelled with a force of 22. 0 N and accelerates at a rate of 5. 5 [tex]ms^{-2}[/tex], its mass is 4. 0 kg.

Newton's Second Law of Motion states that force is the result of mass times acceleration.

[tex]F=m*a[/tex]

[tex]m = F / a[/tex]

A force of 22.0 Newtons (  [tex]kgms^{-2}[/tex] ) and an acceleration of 5.5 meters per second squared were used to drive the bowling ball.

F = 22.0 [tex]kgms^{-2}[/tex] and

a = 5.5 [tex]ms^{-2}[/tex]

Put the values in the formula as replacements.

M = 22 [tex]kgms^{-2}[/tex]/ 5.5 [tex]ms^{-2}[/tex]

Meters per second squared (m/s2) units cancel each other out.

M = 22 kg / 5.5

   = 4 kg

The bowling ball weighs 4 kilogram.

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The property justified by step 4 is after substitution in the equation you get the desired result.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data in the question,

In step 3 substitution of value is taking place.

In step 4 when values are substituted the final result is obtained, so step 4 is the result step.

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The cross-sectional area is (h × w ) + ((1 ÷ 2) × 0.9 × w²) and the dimensions of the window which minimize the perimeter is (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A.

height of rectangle = h

height of the triangle = t

T = 0.9

width of the rectangle = w

The formula of Cross-sectional area is,

A = h × w + (1 ÷ 2)T × w

A = (h × w ) + ((1 ÷ 2) × 0.9 × w²)

Perimeter,

P = w + (2 × h) + 2√(T² + (w ÷ 2)²)

P = w + (2 × h) + 2√((0.9)² + (1 ÷ 2)²)

P = 2h + 2√((0.9)² + (1 ÷ 2)² + 1) × w

Therefore, [tex]C_{0}[/tex] = 0.9 ÷ 2, [tex]C_{1}[/tex] = 2, [tex]C_{2}[/tex] = 2√((0.9)² + (1 ÷ 2)² + 1)

minP=[tex]c_1[/tex]h+[tex]c_2[/tex]w

A = (h × w) + [tex]c_{0}[/tex]w²

substituting h = (A - [tex]c_{0}[/tex]w²) ÷ hw in P,

P = [tex]c_1[/tex]w + ([tex]c_1[/tex](A - [tex]c_{0}[/tex]w²) ÷ w)

Differentiating both sides,

(dP ÷ dw) = -2[tex]c_{0}[/tex][tex]c_{1}[/tex] + [tex]c_{2}[/tex] - ([tex]c_{2}[/tex](A - [tex]c_{0}[/tex]w²) ÷ w²) = 0

[tex]w_{0}[/tex] = (√[tex]c_{1}[/tex]A ÷ (√[tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex])) = 0.962445√A

and consequently,

[tex]h_{0}[/tex] = (A - [tex]c_{0}[/tex][tex]w_{0}^{2}[/tex]) ÷ [tex]w_{0}[/tex] = 2√A[tex]c_{1}[/tex]([tex]c_{2}[/tex] - [tex]c_{0}c_1[/tex]) = 0.60592√A

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The perimeter of rectangle ABDC is 61.24 units.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The rectangle ABDC is given in the question which has:

AB = 8 and AC = 24

Here AC is the diagonal of the rectangle which is the hypotenuse in a right triangle.

As per Pythagoras's theorem,

AC² = AB² + BC²

24² = 8² + BC²

576 = 64 + BC²

BC² = 512

BC = 22.62

The perimeter of rectangle ABDC = 2(AB + BC)

The perimeter of rectangle ABDC = 2(8 + 22.62)

The perimeter of rectangle ABDC = 2(30.62)

The perimeter of rectangle ABDC = 61.24 units

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Answer:  The solution to this system is (1,3) as shown in the graph below.

Step-by-step explanation:

Remember to vote for this as Brainliest if I earned it!   :)

NOTE: The red line is -x+y=2 and the blue line is y=3

Answer:

(x, y) = (1, 3)

Step-by-step explanation:

Answer:

The answer would be -4/5

Step-by-step explanation:

When you add a negative to a negative, you first take out the plus sign and rewrite it as: -2/5 - 2/5.

Now you just simply subtract 2/5 from -2/5 to get -4/5.

Hope this helps.

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The dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

Rectangular Box with Square base

Volume v = a²b = 12

S = Surface area = 2a² + 4ab

v = a²b = 12

b = 12/a²

S = 2a² + 4ab = 2a² + 4a(12/a²) =2a² + 48/a

S'(a) = 4a -48/a² = 0

4a³ = 48

a = 12^ 1/3

b = 12/a² = 12/12^ 2/3 = 12^ 1/3

Therefore, the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3

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Answer:

slope of the line = 1

Step-by-step explanation:

i hope i helped

Answer:

  x = 3

Step-by-step explanation:

You want the equation of the line through points (3, -3) and (3, -6).

The two points have the same x-value, indicating the line through them is a vertical line. That will have an equation of the form x = c.

The x-value of the given points is 3, so the equation is ...

  x = 3

__

Additional comment

We note that the answer box is pre-filled with "y =". There is no "y =" equation that will go through these points. The slope is undefined, so the slope-intercept form of the equation cannot be used.

Answer:

2.5 × 10^-1

step-by-step explanation:

To get to standard form, you must move the decimal to the right one place so the number before it is not a 0. Because you move the decimal, you must add the second part of the equation so that the value does not change.

Answer:

02.5 but the 0 at the beginning isn't significant so 2.5

Step-by-step explanation:

because to find the standard form you move the decimal point so that there is only one non-zero digit in front of the decimal point.

The required answers for given similar triangles are DF= 3, EF= 2.25, and scale factor 4/3 respectively.

In geometry, two geometrical triangle are similar if they have the same shape, and corresponding sides are equate by some factor. More accurately, one can be obtained from the other by uniformly scaling.

For length of side DF, ratio of corresponding sides is equal.

⇒  [tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]

⇒  [tex]\frac{2}{1.5}=\frac{4}{DF}[/tex]

⇒  DF = 3

Similarly for EF,

 [tex]\frac{AB}{DE} =\frac{BC}{EF}[/tex]

⇒[tex]\frac{2}{1.5}=\frac{3}{EF}[/tex]

⇒ EF = 2.25

At last, by using same concept of similarity scale factor is

 [tex]\frac{AB}{DE} =\frac{AC}{DF}[/tex]

⇒ [tex]\frac{AB}{DE} =\frac{4}{3}[/tex]

This is our scale factor for both triangle.

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Answer for No.2
Answer: 1/4

Step-by-step explanation:

Hits = 12

Misses = 60-12 = 48

Ratio of hits to misses = 12/48 = ¼

So the answer is 1/4.

To perform Rotation in coordinate plane the following information may help you.

What is Geometric Rotation ?

In geometry, rotation is a type of rigid motion or transformation that involves the movement of a shape about a point while preserving the shape, size, and distance between the points on the shape.The center of rotation is the location around which the shape is rotated.

To perform Rotation in coordinate plane

Last two questions sum up and I'm explaining like that,

      When a point is reflected in the x-axis then signs of it's ordinate (y-axis) change.

Mₓ (x, y) = (x, - y)

When a point is reflected in the y-axis then signs of it's abscissa (x-axis) change.

My (x, y) = (-x, y)

When a point is reflected in the origin , the signs of it's Abscissa and ordinate change.

M₀ (x, y) = (-x, -y)     (in origin the sign become opposite if there is '+' then it changes to '-' and vice versa)

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Answer:

f = 3cm g = 16cm

Step-by-step explanation:

Area of ABCE = 60cm²

Area of ABCD = 48cm²

60 - 48 = 12

Area of ADE = 12cm²

A to D = 3cm

f = 3cm

g = 16cm

Given that the delivery person works an 8-hour shift, he needs 4 gallons of gasoline in his tank.

A function is defined as the expression that relates a independent variable with a dependent variable. To evaluate a function is to substitute the value of the independent variable and then calculate the function value.

Given that the delivery person works an 8-hour shift, substitute x = 8 to the function of y.

y = f(x) = x² + 3x

y = 8² + 3(8)

y = 88

To determine the amount of gasoline needed, substitute the value of y to the function of g of y.

g = y / 22

g = 88 / 22

g = 4

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The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

Hence, The POINT of a hyperbola is one of two points such that the difference of the distances from any point on the hyperbola to the foci is a constant.

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1/36 is the probability that you score 4 points both times.It is the likelihood of scoring four points twice.

1/6 * 1/6 =1/36

The probability of an event occurring is measured by its probability. It determines the probability of an event. The probability calculation is P(E) = Number of Favourable Outcomes/Total Outcomes.A game is a formalized form of play that is frequently done for amusement or fun but can also serve as a teaching game tool.

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Step-by-step explanation:

well this is a rather odd equation but I'm assuming that

x+x+x+x+x = 5x

Y=5p+3

Y equals the total amount of tape rolls

P is for the number of packages there are.

Hope this helped!

:)

Answer:

Y=5p+4

Y equals the total amount of tape rolls

P is for the amount of packages there are

Step-by-step explanation:

Based on the calculations, the unknown number (x) is equal to 7.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the unknown number. Therefore, translating the word problem into an algebraic equation, we have the following;

Multiply a number (x) by 5 = 5x

The product is equal to the sum of 20 and 15 = 20 + 15 = 35.

Combining the above information, we have:

5x = 20 + 15

5x = 35

Dividing both sides by 5, we have:

x = 35/5

x = 7.

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The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

The area of a circle, A, is calculated using the formula A = pi * r2, where r is the circle's radius. Since we already know that a semicircle is half of a circle, we can easily divide that equation by two to determine the area of a semicircle. As a result, A = pi * r2/2 is the formula for calculating the area of a semicircle.

With the aid of the following formula, we can determine a semicircle's perimeter: The semicircle's perimeter is equal to r + 2r units, where r is the radius of the semicircle.

Diameter of the semi-circle = 84cm

Now,

the circumference of the semi-circle  =  πr + 2r

Substituting the value of r in the given formula:

the circumference of the semi-circle  =  πr + 2r

                                                              = πr + 2r

                                                               = 48π + 42

The perimeter of this semi-circle with diameter, d = 84cm the expression in terms of π are as follows:

= 48π + 42

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The bearing of the helicopter from B to A is 75.96 degrees

Information from the question

A helicopter leaves A and flies 40 miles due east

the helicopter flies

10 miles due south

Work out the bearing of B from A = ?

The bearing from B to A is worked using SOH CAH TOA

The direction of movements describes a right angle triangle of

opposite = 40 miles

adjacent = 10 miles

The bearing is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

tan x = 40 / 10

tan x = 4

x = arc tan 4

x = 75.96 degrees

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Equations representing the total costs for plan A and B are A = 19 + 0.50x and B = 13 + 1.5x, respectively, where x is the number of movies watches.

Cost of both the plans will be equal for 6 movies.

A linear function is defined as a function that has either one or two variables without exponents.

Given that, Wyatt is deciding between two different film streaming sites to subscribe to, plan A costs $19 per month plus $0.50 per film watched, plan B costs $13 per month plus $1.50 per film watched.

According to question,

A = 19 + 0.50x and

B = 13 + 1.5x

For costs being equal, we have,

A = B

19 + 0.50x = 13 + 1.5x

x = 6

Hence, for 6 films the costs of both the plans will be equal and equation for both the plans are A = 19 + 0.50x and B = 13 + 1.5x

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Answer:

3/2

Step-by-step explanation:

To multiply fraction×fraction, you multiply top×top and bottom×bottom.

2/3 × 3/2

= 6/6

= 1

The 3/2 is called the reciprocal. Take the number in the problem and flip it over to find the reciprocal.

Answer:

3×10^7

Step-by-step explanation:

Write 30 000 000 in standard form.

=3×10,000,000

=3×10^7

Step-by-step explanation:

this is

3.0 × 10⁷

as 30 000 000 has 7 zeroes (7 sequential and continuously increasing powers of 10 starting with 10¹).

and the first non-zero digit is 3.

1.) Yes,it will fit because volume of the base ball is 13.36 cubic inch and the volume of box is 64 cubic inch which greater than the volume of baseball .

2) The ratio of the side length of box B to the side length of box

A is 1.472 inche : 6 inch.

What is cube ?

A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

What is circumference?

The circumference is the distance that surrounds a circle. We can measure the circumference of the earth by measuring the distance that we will have to walk all the way around the world.

To check whether the baseball is will till in the box we will check the maximum value of circumference.

⇒  [tex]2\pi r[/tex] = 9.25

⇒ [tex]r = \frac{9.25}{2\pi}[/tex]

⇒[tex]r = 1.472 in.[/tex]

Volume of the baseball [tex]= \frac{4}{3} \pi x^{3}[/tex]

                                      [tex]= \frac{4}{3}\times \pi\times (1.472)^3 in^3[/tex]

                                      [tex]= 13.36\ in^3 < 64 \ in^3\\[/tex]

So, it will fit inside the box.

2.)[tex]\sqrt[3]{216} = 6 \ (\therefore V = a^3)[/tex]

The length of each side of the box is 6 inches.

and the ratio of the side length of box B to the side length of box

A:

1.472 in : 6 inches

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