WILL MARK BRAINLIEST! PLEASE HELP ME UNDERSTAND THIS!

SIMPLIFY the expression please! Don't solve it- just simplify it! Please explain too! Ty!

Answer:

Length = 55 ft

Step-by-step explanation:

Given:

Area of rectangular floor= 605ft²

Length= x

Width= 1/5x

Formula for area of rectangular floor= Length × width

Put the given into the formula.

605 ft² = x × 1/5x

605 ft² = x²/5

multiplying both sides by 5

605 ft² × 5 = x²/5 × 5

x² = 605 ft² × 5

= 3025 ft²

x= √3025 ft²

x= 55 ft

Put x into the unknown above.

Length= x

Width= 1/5x

Length = 55 ft

Width= (1/5)×55 = 11 ft

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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The values of the angle x in the line segments is 40 degrees.

When parallel lines are are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.

Therefore, the line FG is parallel to line HI. The line segment BC and AD are the transversal lines that cut across the parallel lines FG and HI.

Therefore,

3x + 20 + x = 180 (Same interior angles)

Same interior angles are supplementary.  That is the angles sum up to 180 degrees.

Therefore,

3x + 20 + x = 180

4x + 20 = 180

4x = 160

divide both sides by 4

x = 160 / 4

x = 40 degrees

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Answer:

10 inches

Step-by-step explanation:

Length of photograph, L1 = 3 inches; Length of enlarged photograph, L2 = 15 inches; Width of photograph, W1 = 2 inches; Width of photograph, W2 = ?

Hence, L1/L2 = W1/W2

∴ W2 = (L2*W1)/L1 = (15 X 2)/3 = 10 inches

Answer:

B

Step-by-step explanation:

the area of the triangle is  18 square units

Answer:

vance got the better deal

Step-by-step explanation:

Answer:

a = - 3

Step-by-step explanation:

Since the point (- 3, 2) is on the line then its coordinates make the equation true.

Substitute x = - 3, y = 2 into the equation and solve for a

a(- 3) - 2(2) = 5, that is

- 3a - 4 = 5 ( add 4 to both sides )

- 3a = 9 ( divide both sides by - 3 )

a = - 3

Answer:

Step-by-step explanation:

-3x-2•2=5

-3x=5+4

-3x=9

X=9:(-3)

X=-3

The number of zero-dimensional objects are: 5

A point is said to have zero dimensions. This means that there are no length, height, width, or volume. Its only property will definitely be its' location. Thus, we could possibly have a collection of points, such as the endpoints of a line or the corners of a square, but then it would still be a zero-dimensional object.

Now, we are given a square based pyramid object but then going by the definition of zero-dimensional objects earlier stated, we can see that they are points and we have 5 points here which denotes 5 zero-dimensional object.

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Answer:

b

Step-by-step explanation:

Answer:

A. Distance traveled by a car driving at a constant 40 miles per hour

Step-by-step explanation:

answer on plato

Answer:

8 X x (Bigger X stands for multiplication)

Step-by-step explanation:

8x-y or you can do it another way is fine

Answer:

Goal  = x

45000 = 9/10 * x

x = 45000 * 10/9  = 50000

Step-by-step explanation:

You may find something useful on my you tube channel "Sciency Sergei". You may also suggest a topic to discuss or problems to solve.

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

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

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

The standard matrix of the linear transformation t, which rotates points about the origin through -π/3 radians (clockwise) in R², is given by:
[ 1/2   √3/2 ]
[ -√3/2 1/2  ]

To find the standard matrix of the linear transformation t, which rotates points about the origin through -π/3 radians (clockwise) in R², we can use the following steps:

1. Start by considering a point (x, y) in R². This point represents a vector in R^2.

To rotate this point about the origin, we need to apply the rotation formula. Since the rotation is clockwise, we use the negative angle -π/3.

The formula to rotate a point (x, y) through an angle θ counterclockwise is:
  x' = x*cos(θ) - y*sin(θ)
  y' = x*sin(θ) + y*cos(θ)

Applying the formula with θ = -π/3, we get:
  x' = x*cos(-π/3) - y*sin(-π/3)
     = x*(1/2) + y*(√3/2)
  y' = x*sin(-π/3) + y*cos(-π/3)
     = -x*(√3/2) + y*(1/2)

The matrix representation of the linear transformation t is obtained by collecting the coefficients of x and y in x' and y', respectively.

  The standard matrix of t is:
  [ 1/2   √3/2 ]
  [ -√3/2 1/2  ]

The standard matrix of the linear transformation t, which rotates points about the origin through -π/3 radians (clockwise) in R², is given by:
[ 1/2   √3/2 ]
[ -√3/2 1/2  ]

To find the standard matrix of the linear transformation t that rotates points about the origin through -π/3 radians (clockwise) in R², we can use the rotation formula. By applying this formula to a general point (x, y) in R², we obtain the new coordinates (x', y') after the rotation. The rotation formula involves trigonometric functions, specifically cosine and sine. Using the given angle of -π/3, we substitute it into the formula to get x' and y'. By collecting the coefficients of x and y, we obtain the standard matrix of t. The standard matrix is a 2x2 matrix that represents the linear transformation. In this case, the standard matrix of t is [ 1/2   √3/2 ] [ -√3/2 1/2 ].

The standard matrix of the linear transformation t, which rotates points about the origin through -π/3 radians (clockwise) in R², is [ 1/2   √3/2 ] [ -√3/2 1/2 ]. This matrix represents the linear transformation t and can be used to apply the rotation to any point in R².

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The volume of the frustum is volume of the whole cone(A) minus the smaller cone(B) which is would give the volume of frustum(C) = 256cm³

The volume of cone A V=πr²h/3

Where radius = 20cm

The volume of cone B = V=πr²h/3

Where radius = 12cm

Therefore volume of frustum =

V=π * 20² * h/3 - π * 12² *h/3

The variables will cancel out each other

V = 20² - 12²

V = 400- 144

V = 256cm³

Therefore, the volume of the frustum(C) = 256cm³

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Answer: It will cost $196

245 ÷ 10 = $24.5

$24.5 x 8 = $196

Hope this helps, have a wonderful day!

Answer:

y = x + 4 or x - y + 4 = 0

Step-by-step explanation:

The relation between "x" and "y" is linear.

Slope of the line m = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\) = \(\frac{6-5}{2-1}\) = 1

Coordinates of y-intercept of the line (0, b) = (0, 4)

Slope-intercept form of a line equation is y = mx + b

The rule (equation) of line is y = x + 4

or x - y + 4 = 0 (in standard form)

Answer:

(x+2)^2 + (y+1)^2 =13

Step-by-step explanation:

An isometric transformation is a transformation in which the image is congruent to the pre-image. Both corresponding sides and corresponding angles are equal. A dilation is a transformation in which the corresponding angles of the image are congruent to the pre-image, but the corresponding sides are proportional. This ratio is determined by a scale factor. Dilations create similar images.

Answer:

An isometric transformation is a transformation in which the image is congruent to the pre-image. Both corresponding sides and corresponding angles are equal. A dilation is a transformation in which the corresponding angles of the image are congruent to the pre-image, but the corresponding sides are proportional. This ratio is determined by a scale factor. Dilations create similar images.

Step-by-step explanation:

This is the sample response. Have a nice day <333

Answer:

\(A=20 units^2\)

Step-by-step explanation:

I would separate out the shape into two equal right triangles over a square.  The total area can then be found by adding these areas together:

\(A_t=2A_\Delta +A_s\\A_t=2(\frac{1}{2}bh)+(s)^2\\b=2 units\\h=2units\\s=4units\\A_t=2[\frac{1}{2}(2units)(2units)]+(4units)^2\\A_t=4units^2+16units^2\\A_t=20units^2\)

Answer:84

Step-by-step explanation:10 to 94 is 84

Answer:

7

Step-by-step explanation:

Because the parts of the circle are congruent, the segments are as well, we can use that to make an equation then solve it like normal

9x-34=4x+1

-1 on both sides

9x-35=4x

-9x on both sides

-35=-5x

x=7

Therefore, the solutions to the equation are: \(\boxed{x = 9,\ 4}\)

1. Given equation: \(3x^2 + (k+1)x + k = 0\)

To obtain one real solution, the discriminant must be zero:

\((k+1)^2 - 4 \cdot 3 \cdot k = 0\)

\(k^2 + 2k + 1 - 12k = 0\)

\(k^2 - 10k + 1 = 0\)

Solving for \(k\):

\(k = \frac{10 \pm \sqrt{100-4}}{2} = 5 \pm 2 \sqrt{6}\)

Therefore, the values of \(k\) are:

\(\boxed{5 + 2 \sqrt{6},\ 5 - 2 \sqrt{6}}\)

2. Given: \(x - \sqrt{x} = 6\)

\(\Rightarrow x - 6 = \sqrt{x}\)

\(\Rightarrow (x-6)^2 = x\)

\(\Rightarrow x^2 - 13x + 36 = 0\)

\(\Rightarrow (x-9)(x-4) = 0\)

Therefore, the solutions to the equation are:

\(\boxed{x = 9,\ 4}\)

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Answer:

16 cm

Step-by-step explanation:

We can use ratios to solve

4 cm             x cm

----------   = -------------

1/4 year         1 year

Cross multiply

4 * 1 =  1/4 * x

Multiply each side by 4

4*4 = 1/4x*4

16 = x

Answer:

16 cm

Step-by-step explanation:

4x4=16

Step-by-step explanation:

Given equation is x+y=6

\(\boxed{\begin{array}{c|c|c}\bf x &\rm 3 &\rm 2 &\rm 1\\ \bf y &\rm 3 &\rm 4 &\rm 5\end{array}}\)

The solutions to the equation x^2 = -8x - 7x are x = 0 and x = -15.

To solve the equation x^2 = -8x - 7x, we first need to simplify the right side:

x^2 = -15x

Now we can rearrange the terms and factor out x:

x^2 + 15x = 0

x(x + 15) = 0

By the zero product property, we know that this equation is true when either x = 0 or x + 15 = 0. Solving for x in each case, we get:

x = 0 or x = -15

Therefore, the solutions to the equation x^2 = -8x - 7x are x = 0 and x = -15.

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Therefore, the height of the cone is approximately 4.23 centimeters.

Volume is a measure of the amount of space occupied by a three-dimensional object or region. It is the total amount of space enclosed by the boundaries of the object or region. Volume is usually measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³). Knowing the volume of an object can be useful for many purposes, such as determining how much material is needed to fill a container or how much space is needed to store a certain quantity of objects.

Here,

The formula for the volume of a cone is given by:

V = (1/3)πr²h

where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cone is 3.0144 cubic centimeters, so we can plug this into the formula:

3.0144 = (1/3)πr²h

Next, we need to find the radius of the cone. Since we are not given the radius directly, we may need to use other information that is not given in the problem. If we assume that the cone is a right circular cone, then we can use the fact that the radius and height are proportional to find the radius:

r/h = 1/3

r = (1/3)h

We can substitute this expression for r into the volume formula:

3.0144 = (1/3)π((1/3)h)²h

Simplifying this equation:

3.0144 = (1/27)πh³

Multiplying both sides by 27/π:

h³ = 84.96

Taking the cube root of both sides:

h = 4.23 (rounded to the nearest hundredth)

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Answer:

no linear relationship exists between the two variables being compared

Step-by-step explanation:

The balance outstanding on the loan immediately after the seventh quarterly payment, using an interest rate of 16% p.a. compounded quarterly and equal quarterly payments, is R$310.39.

To calculate the balance outstanding after the seventh quarterly payment, we need to use the formula for the present value of an ordinary annuity:

P = PMT * (1 - (1 + r)^(-n)) / r

Where:

P = Principal amount of the loan (R$1,000)

PMT = Equal quarterly payment

r = Interest rate per period (16% p.a. compounded quarterly = 4% per quarter)

n = Number of periods (10 payments)

First, we calculate the equal quarterly payment (PMT) using the present value of an ordinary annuity formula rearranged to solve for PMT:

PMT = P * (r / (1 - (1 + r)^(-n)))

PMT = 1000 * (0.04 / (1 - (1 + 0.04)^(-10))) = R$129.09

Next, we calculate the balance outstanding after the seventh quarterly payment. We can consider it as the present value of the remaining three payments:

Balance = PMT * (1 - (1 + r)^(-n_remaining)) / r

Where: n_remaining = Number of remaining payments (10 - 7 = 3)

Balance = 129.09 * (1 - (1 + 0.04)^(-3)) / 0.04 = R$310.39

Therefore, the balance outstanding on the loan immediately after the seventh quarterly payment is R$310.39.

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