MATHEMATICS HIGH SCHOOL

2. A rectangular photograph measuring 8 in by 10 in is surrounded by a frame with a uniform width, xx.a. What type of function can best represent the area of the picture and the frame in terms of xx (the unknown frame’s width)? Explain mathematically how you know.
b. Write an equation in standard form representing the area of the picture and the frame. Explain how you arrive at your osition.

Answers

Answer 1

Answer:

Answer: a) Quadratic equation b) $4x^2+36x+80$

Step-by-step explanation:

Since we have given that

Length of photograph = 8 inches

Width of photograph = 10 inches

It is surrounded by a frame with uniform width 'x'.

So, Length of picture and frame becomes

$x+8+x=2x+8$

Width of picture and frame becomes

$x+10+x=2x+10$

So, Area of picture and frame becomes

$Length* breadth\n\n=(2x+8)(2x+10)\n\n=2x(2x+10)+8(2x+10)\n\n=4x^2+20x+16x+80\n\n=4x^2+36x+80$

Hence, a) Quadratic equation b) $4x^2+36x+80$

Related Questions

Andre received $60 for his birthday and put it in his piggy bank. Each week, he puts 3 more dollars in his bank. The amount of money in dollars D in his bank is given by D = 3w + 60 where w is the number of weeks he has saved 3 dollars. His sister Lana helped him find how much money he will have after 4, 15, 20, and 36 weeks. This table shows her results. What is the rate of change using Lana’s values for D and w? Is this a linear model or non-linear model?W 4 weeks 15 weeks 20 weeks 36 weeks D D= 3w =60 D = 3w + 60 D = 3w + 60 D = 3w + 60= 3*4 +60 = 3 * 15 = 3 * 20 + 60 = 3 * 36 + 60= 12 + 60 = 45 + 60 = 60 + 60 = 108 + 60= 72 = 105 = 120 = 168A.The rate of change varies. It is a linear model.B.The rate of change varies. It is a non-linear model.C.The rate of change is . It is a linear model.D.The rate of change is 3. It is a linear model.
4.702 x 10–4 i need this answer in standard notation .
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Simplify the expression
1, 5, 9, 13...Generalize the pattern by finding the nth term. A) n2 B) n + 4 C) 4n - 3 D) 3n + 1

What is the value of a in the equation 3a+b=54, when b=9

Answers

3a + 9 = 54
Do the opposite operation on 9 so you can get the like terms one side.
3a = 45
Then divide 3 on both side to get the variable by itself.
a = 15

Answer:

fifteen

Step-by-step explanation:

Got it right on Edg

32 is 40 percent of what number

Answers

The unknownnumber (x) is equal to 80.

This means that 32 is 40 percent of 80, or in other words, 32 is 40 percent of the number 80.

We have,

To explain further, let's break down the calculation step by step:

We are given that 32 is 40 percent of some unknown number. Mathematically, this can be represented as:

32 = 0.40 x

To find the unknown number (represented by x), we want to isolate it on one side of the equation.

By dividing both sides of the equation by 0.40, we eliminate the 0.40 on the right side, and we have:

32 / 0.40 = x

Simplifying the left side:

80 = x

Therefore,

The unknownnumber (x) is equal to 80.

This means that 32 is 40 percent of 80, or in other words, 32 is 40 percent of the number 80.

Learn more about percentages here:

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Further explanation

Given:

32 is 40 percent of what number?

The Process:

Let N as the number asked.

The mathematical equation of the question sentence represents as follows:

$\boxed{ \ 32 = 40 \% * N \ }$

Which can be rewritten to be

$\boxed{ \ 40 \% * N = 32 \ }$

All we have to do to get the N value is a division operation.

$\boxed{ \ If \ a * b = c, \ then \ a = c / b \ or \ b = c / a \ }$

$\boxed{ \ If \ a * b = c \ then \ a = (c)/(b) \ or \ b = (c)/(a) \ }$

$\boxed{ \ 40 \% * N = 32 \ }$

$\boxed{ \ N = 32 / 40 \% \ }$

Recall that $\boxed{ \ 40 \% = (40)/(100) \ }$

$\boxed{ \ N = 32 / (40)/(100) \ }$ ... Equation-1

Recall that $\boxed{ \ a / (b)/(c) \rightarrow a * (c)/(b) \ }$

$\boxed{ \ N = 32 * (100)/(40) \ }$ ... Equation-2

Both 100 and 40 divided by 10 to make it simpler.

$\boxed{ \ N = 32 * (10)/(4) \ }$

32 is crossed out with 4, in other words dividing each other.

$\boxed{ \ N = 8 * 10 \ }$

Thus, the result is $\boxed{\boxed{ \ N = 80 \ }}$

Alternative-1:

Recall that $\boxed{ \ (40)/(100) = 0.40 = 0.4 \ }$

From Equation-1 above, we rearrange it into

$\boxed{ \ N = (32)/(0.4) \ }$

Both the numerator and denominator are multiplied by 10.

$\boxed{ \ N = (320)/(4) \ }$

Thus, the result is $\boxed{\boxed{ \ N = 80 \ }}$

Alternative-2:

From Equation-2 above, both 100 and 40 are divided by 20.

$\boxed{ \ N = 32 * (5)/(2) \ }$

32 is crossed out with 2, in other words dividing each other.

$\boxed{ \ N = 16 * 5 \ }$

Thus, the result is $\boxed{\boxed{ \ N = 80 \ }}$

Alternative-3:

$\boxed{ \ 40 \% * N = 32 \ }$

Both sides are multiplied by $\boxed{ \ (100)/(40) \ }$

$\boxed{ \ N = 32 * (100)/(40) \ }$

$\boxed{ \ N = 32 * (10)/(4) \ }$

$\boxed{ \ N = 32 * (5)/(2) \ }$

$\boxed{ \ N = 16 * 5 \ }$

Thus, the result is $\boxed{\boxed{ \ N = 80 \ }}$

Learn more

100 is ¹/₁₀ of what? brainly.com/question/96535
4 times as much as 3 is brainly.com/question/573729
68.32 divided by 2.8 is divisible brainly.com/question/5022643#

Keywords: 32 is 40 percent of what number, a division operation, fraction, multiply, 80, decimals, alternative steps, the mathematical equation

Help me please Algebra two!

Answers

Answer:

Zeros: -3 odd mult.; 0 odd mult.; 2 odd mult.

Positive leading coefficient

Odd degree likely 3

Step-by-step explanation:

A polynomial graph has several features we look for to determine the equations.

The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity.

Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial.

The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.

a woman has $1.70 in dimes and nickels.She has 5 more dimes than nickles. How many nickles does she have

Answers

d=5+n
0.1(5+n)+0.05n=1.7
0.5+0.15n=1.7
0.15n=1.2
n=8
d=13
therefore 8 nickles and 13 dimes.

A construction worker tosses a brick from a tall building. The brick's height (in meters above the ground) t tt seconds after being thrown is modeled by h ( t ) = − 5 t 2 + 20 t + 105 h(t)=−5t 2 +20t+105h, left parenthesis, t, right parenthesis, equals, minus, 5, t, squared, plus, 20, t, plus, 105 Suppose we want to know the height of the brick above the ground at its highest point. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h ( t ) = h(t)=h, left parenthesis, t, right parenthesis, equals 2) At its highest point, how far above the ground was the brick?

Answers

The vertex form of the equation is h(t) = -5 ( t - 2)² + 104.

At its highest point, the brick was 101 meters above the ground.

What is the vertex form of a quadratic function?

The factored form of a quadratic function is given as:

f(x) = a(x – h)2 + k

where a, h, and k are constants.

We have,

h(t) = -5t² + 20t + 105

h(t) = -5 ( t² - 4t ) + 105

h(t) = -5 ( t² - 4t + 2² ) - 2² + 105

h(t) = -5 ( t - 2 )² - 4 + 105

h(t) = -5 ( t - 2 )² + 101 _____(1)

The vertex form of the equation is h(t) = -5 ( t - 2)² + 104.

From equation (1) we can say that at its highest point the brick was at

101 meters above the ground.

Thus,

The vertex form of the equation is h(t) = -5 ( t - 2)² + 104.

At its highest point, the brick was 101 meters above the ground.

Learn more about quadraticequations here:

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Answer:

h(t)=−5(t−2)^2+125, 125

Step-by-step explanation:

Determine the intercepts of the line.
y= 10x - 32
y-intercept:
x-intercept:

Answers

Answer:

see below

Step-by-step explanation:

To find the x intercept set y =0 and solve for x

0= 10x - 32

32 = 10x

Divide by 10

3.2 = x

The x intercept

( 3.2,0)

To find the y intercept set x =0 and solve for y

y= 0 - 32

y = -32

( 0, -32)

Answer:

(0, -32)

(3.2, 0)

Step-by-step explanation:

The line is in slope intercept form. It is easy to identify the y-intercept.

$y=mx+b$

The y-intercept is (0,-32). '-32' replaces the 'b' in the equation.

To find the x-intercept, set the value of 'y' to zero and solve for 'x'.

$0=10x-32\n\n0 + 32 = 10x-32+32\n\n32=10x\n\n(32)/(10)=(10x)/(10)\n\n(32)/(10)=x\n\n\rightarrow (32/2)/(10/2)=(16)/(5)\n\n \boxed{x=(16)/(5)}$

The x intercept is (16/5, 0).

This can also be expressed as (3.2, 0).

Hope this helps.

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