A frame around a rectangular family portrait has a perimeter of 106 inches. The length of the frame is 10 inches less than twice the width. Find the length and width of the frame.

Answer:

Step-by-step explanation:

Answer:

a)56,152.5

b)40.2%

c)10.87%

Step-by-step explanation:

a) $63,000-$6,847.5=$56,152.5

b) marginal tax rate of a $63,000 income is 40.2%

c) 6,847.5 is 10.869047619% of 63,000 but it has to be to nearest hundreth so it is 10.87% because the thousandths place is a 9 so you round up to 10.87%.

The value of f(x)+g(x)= x²+ 3x - 1

a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

f(x) is the value of the function.

there is an x in the function f, it is replaced with the function g(x).

f(x)=3 x-2

g(x)=x²+1 .

(f+g)(x) = x²+1 + 3 x-2

f(x)+g(x)= x²+ 3x - 1

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Answer:

x = -7 and x = 4

Step-by-step explanation:

Note, I am taking the polynomial equation as
[tex]x^2 - 28 = -3x[/tex]

Otherwise it does not become a polynomial of one variable and cannot be solved

Zeros of a polynomial are the values of x where the polynomial value itself is 0

Standard equation for a polynomial of degree 2 is ax² + bx + c = 0 where a, b and c are constants

Degree is the highest exponent. Here the highest exponent is 2 so the polynomial has degree 2. Such a polynomial is called a quadratic polynomial

So we first have to convert
x² - 28 = - 3x into  this form ax² + bx + c

1. Add 3x to both sides
x² - 28 + 3x = -3x + 3x =0

==> x² + 3x - 28  = 0
With a = 1, b = 3 and c = -28

2. Factor x² + 3x - 28  = 0

Here a = 1, b = 3 and c = -28

Factoring means find two expressions x+a and x +b such that (x + a) (x + b) = x² + 3x - 28  = 0

Then we can state that
x + a = 0           ==> x = -a as one solution
x + b = 0           ==> x = -b as the other solution

To factor, find two numbers m and n(could be negative) such that mn = c and m + n = b

28 has factors 7 and 4 so that is a good start

-28 = -7 x 4 or could also be 7 x -4

How do we choose?
Add both and see what gives you +3

-7 +  4 = -3  Nope
7 + -4 = 7-4 = 3 YES

So the factors are 7 and -4

(x + m) = (x + 7)
(x + n)  = (x -4)

So the original quadratic polynomial becomes

(x + 7)(x -4) =

This means

x + 7 = 0 ==> x = -7

x -  4 = 0 ==> x = 4

So the solutions(also called roots) of x² + 3x - 28  = 0 are:

x = -7 and x = 4

Both the above values satisfy the quadratic equation

Answer: 69

Step-by-step explanation:
34
+
35
=
69

Answer:

69

Step-by-step explanation:

30 + 30 = 60

4 + 5 = 9

60+9= 69

Basic addition, also can be solved with a calculator

Hope this helped :)

Answer:1/2 tsp

Step-by-step explanation:

Hey there!

1/4 of 3 3/4

= 1/4 * 3 3/4

= 1/4 * 3 * 4 + 3/4

= 1/4 * 12 + 3/4

= 1/4 * 15/4

= 1(15)/4(4)

= 15/16

Therefore, your answer should be:

15/16

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The length of the shorter piece is 33 inches.

132 inches of the board is cut into 2 pieces. The board is divided into 2 parts.

One piece is three times the length of the other.

let ,one piece = x

The other piece = 3x

The length(x) of the shorter part  can be found below

x + 3x = 132

4x = 132

divide both sides by 4

x = 132 / 4

x = 33

Therefore the length of the shorter piece is 33 inches.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares.

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Answer:

1

Step-by-step explanation:

[tex]\mathrm{a^0=1~if~a \neq 0}[/tex] (Assuming a doesn't equal 0)

[tex]= 1[/tex]

Yes it is because 6/5 is the same as saying 1 and 1/5.

Answer:

a^3-64b^3

Step-by-step explanation:

(a-4b)(a^2+4ab+16b^2)

Multiply.

(a-4b)(a^2+4ab+16b^2)=

=a^3 + 4a^2b+16ab^2-4a^2b-16ab^2-64b^3

Combine like terms.

a^3 + 4a^2b+16ab^2-4a^2b-16ab^2-64b^3=

=a^3-64b^3

Hope this helps!

Please mark as brainliest if correct!

the equation of it is

y= -1/2x+5

Answer:

Step-by-step explanation:

a) You can calculate by multiplying the decimal numbers-

  4.3 x 6 = -25.8

-25.8 = The sum of the rational numbers

b) You multiply -4.5 by 5 to get the sum of the first 5 numbers-

 -4.5 x 5 = -22.5a

Then you subtract -22.5 from -25.8

 -25.8 - (-22.5) = -3.3 --------------- -25.8 + 22.5 = -3.3

So, the sixth number is -3.3

The probability that a camper entering the Luray Caverns has Canadian license plates is 0.3214.

A = a vehicle entering the Luray caverns has Canadian license plates

B = it is a camper

P(A) = 0.12

P(B) = 0.28

P(A∩B) = 0.09

P(A|B) = P(A∩B) / P(B)

P(A|B) = 0.09 / 0.28

P(A|B) = 0.3214

Hence,  the probability that a camper entering the Luray Caverns has Canadian license plates is 0.3214

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Step-by-step explanation:

Let x be the amount invested at 6% so that 18000-x is the amount invested at 7.5% both in dollars.

The total interest in 3 years is $3330 so we can write: 0.06x(3)+0.075(18000-x)(3)=3330

Solve for x:

0.06x(3)+0.075(18000−x)(3)=3330

Step 1: Simplify both sides of the equation.

0.06x(3)+0.075(18000−x)(3)=3330

0.06x(3)+−0.225x+4050=3330(Distribute)

0.18x+−0.225x+4050=3330

(0.18x+−0.225x)+(4050)=3330(Combine Like Terms)

−0.045x+4050=3330

−0.045x+4050=3330

Step 2: Subtract 4050 from both sides.

−0.045x+4050−4050=3330−4050

−0.045x=−720

Step 3: Divide both sides by -0.045.

−0.045x/−0.045=−720/−0.045

x=16000

x=16000

So, the amounts borrowed are:

Bank at 6% = 16000

Bank at 7.5% = 2000

Answer:

-7 < -4

Step-by-step explanation:

Answer:

ABC corresponds to DEF

BCA corresponds to EFD

CAB corresponds to FDE

Step-by-step explanation:

The questions is asking you to find where the point on the small triangle are on the larger triangle, so if it said something like B corresponds to __, your answer would be E. This one just ask for three in a row, so do the points in order. That is all you have to do!

Answer: ABC correspond to DEF.    BCA coressponds to EFD.  CAB corresponds to FED

Step-by-step explanation:

Its telling you what letters coordinate with what letters for example ; FDE corresponds to CAB  

1) The graph that best models the situation is; Graph A

2)  The expression that describes the end behaviors of the function modeled by the graph is; As x increases without bound, f(x) approaches the line y = 0

We are told that Hugh wants to start a workout program. Sinmce he starts with running three times a week, we can liken this to the y-intercept. Thus; y-intercept = 3

Now, we are told that he increases the running per week by 17%. This means that the slope of the graph will be 17% or 0.17.

Looking at the given graphs, only graphs A and B have their y-intercepts at y = 3.

Now, looking at both graphs, the one with slope closest to 17% will be graph A.

2) The expressions describe the end behaviors of the function modeled by the graph is; D: As x increases without bound, f(x) approaches the line y = 0

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Answer:

9:30 p.m.

Step-by-step explanation:

Starting at noon (12:00 p.m.) the temperature is 5 degrees Celsius and drops 2 degrees every hour. In the attached image I have drawn it out to better see it.

Starting at noon and subtracting 2 every hour gives us…
12:00=5

1:00 = 3
2:00 = 1

3:00 = -1

(And so on until we get)

9:00= -13 degrees

So how do we get to 14 if it is dropping 2 degrees an hour? Simple! How much does it drop every half hour? 1 degrees! So for ever 30 minutes the temperature drops 1 degrees.

This means that at 9:30 the temperature will be -14 degrees Celsius.

The inverse for the function f (x) = 1 / 5 x³ will be f ⁻¹ (x) = ∛ (5 x).

We are given the function:

f (x) = 1 / 5 x³

we need to find the inverse of the function.

First we will write the function in the form of x.

y = 1 / 5 x³

5 y =  x³

x³ = 5 y

x = ∛ (5 y)

So, the inverse function will be:

f ⁻¹ (x) = ∛ (5 x)

Therefore, the inverse for the function f (x) = 1 / 5 x³ will be f ⁻¹ (x) = ∛ (5 x).

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Answer:

−3<x<3

hope this helps

The domain is (-2, -4] and the range is (3 , -5) .

The domain of a function is the set of values that we are allowed to plug into our function.

As, the graph stretches from -2 to -4.

and, it is also defined at (-2)

So, the domain is (-2, -4]

Range is height of the graph.

The smallest value is -3 and highest value is 5.

So, the range is (3 , -5)

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El primer socio adquirió un terreno de 324 000 metros cuadrados, el segundo socio un terreno de 180 000 metros cuadrados y el tercer socio un terreno de 36 000 metros cuadrados. Al tercer socio le corresponde la fracción de 1 / 15 de todo el terreno.

Tenemos que el precio es directamente proprocional a la extensión del terreno, de modo que cada socio tiene una participación en el terreno. a) Entonces la participación de cada persona es la siguiente:

Primer socio

x = (3 / 5) · (540 000)

x = 324 000

Segundo socio

x = (1 / 3) · (540 000)

x = 180 000

Tercer socio

x = (1 - 3 / 5 - 1 / 3) · (540 000)

x = 36 000

b) Y la fracción del total correspondiente al tercer socio es:

x = 1 - 3 / 5 - 1 / 3

x = 1 / 15

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Answer:

2

Step-by-step explanation:

The length l of the hypotenuse as function of x is l = [tex]\sqrt{\frac{4x^{2} }{(x-3)^{2} }+x^{2} }[/tex]

Given,

A right triangle is formed in the first quadrant by x and y axes and a line through the point (3, 2).

The length of sides of triangle are y and x.

By Pythagoras theorem, the length of the hypotenuse is:

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

Now, we can choose two points to get the value of slope (x₁, y₁) = (3, 2) and (x₂, y₂) = (x, 0)

By using the formula, we get the slope:

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{0-2}{x-3}[/tex] = [tex]-\frac{2}{x-3}[/tex]

The slope is same when passing through (x, 0) and (0, y) because its in the same line.

m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] = [tex]\frac{y-0}{0-x}[/tex] = [tex]\frac{y}{-x}[/tex]

That is, m = [tex]-\frac{y}{x}[/tex]

These slopes are equal. So, we can equate them,

[tex]-\frac{2}{x-3}[/tex] = [tex]-\frac{y}{x}[/tex]

[tex]-\frac{2(-x)}{x-3}[/tex] = y

y = [tex]\frac{2x}{x-3}[/tex]

Substitute this to the equation,

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

l = [tex]\sqrt{(\frac{2x}{x-3})^{2} +x^{2} }[/tex]

l = [tex]\sqrt{\frac{4x^{2} }{(x-3)^{2} } +x^{2} }[/tex]

That is, the hypotenuse has a length of

l = [tex]\sqrt{\frac{4x^{2} }{(x-3)^{2} } +x^{2} }[/tex]

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Answer:

95

Step-by-step explanation:

Given that,

→ (4 + 8²) + (10 - 7)³

Simplifying the problem,

→ (4 + 8²) + (10 - 7)³

→ (4 + 64) + (3)³

→ 68 + 27 = 95

Thus, the answer is 95.

Answer:

95

Step-by-step explanation:

Given that,

→ (4 + 8²) + (10 - 7)³

Simplifying the problem,

→ (4 + 8²) + (10 - 7)³

→ (4 + 64) + (3)³

→ 68 + 27 = 95

Thus, the answer is 95.

Step-by-step explanation: