You want to enlarge a 4 x 5 inch photo to fit into a 1 inch wide frame
that has an outer perimeter of 53 inches.

a. Write and simplify an equation for the outer perimeter of the
picture frame.

b. Determine the factor by which you must enlarge the picture to have it completely fill the inside of the picture frame

Answer: w can be 1,2,4,5

Step-by-step explanation:

Let's recap the formula of Area:
Area = width x length = w x l
Area = 40 = w x l

The definition of a whole number: is a number without fractions; an integer such as 0, 1, 2, 3, 4, 5, 6,...

Let's start with 0. 0 times anything is equal to 0, so we cannot make 40 out of zero. Cross this out.

Next, let's try with 1:

a. 1x40 = 40

Then, applying the same concept to the rest we have these multiplications:

b. 2x20 = 40

c. 4x10 = 40

d. 5x8 = 40

e. 8x5 = 40

f. 10x4 = 40

g. 20x2 = 40

h. 40x1 = 40

Let's recap the formula of Perimeter:

P = 2 x (w + l)

So, we have the calculated perimeters (according to the above finding):
a. P= 2x(1+40)=82

b. P= 2x(2+20)=44

c. P= 2x(4+10)=28

d. P= 2x(5+8)=26

The below answers do not fit the [width < length]

e. P= 2x(8+5)=26 [not an answer]

f. P= 2x(10+4)=28 [not an answer]

g. P= 2x(20+2)=44 [not an answer]

h. P= 2x(40+1)=82 [not an answer]

Simple Interest is the method of finding the interest amount for a particular principal amount of money at a particular rate of interest.

The simple interest for $900 at an interest rate of 6% is $108.

Simple Interest is the method of finding the interest amount for a particular principal amount of money at a particular rate of interest.

We have,

Principal = $900

Rate of interest = 6%

Time = 2 years.

Remember that time should always be in years.

The formula for simple interest is given by:

SI = PRT / 100

Where,

P = principal

R = rate of interest

T = Number of years

So,

SI = 900 x 6 x 2 / 100

SI = $108

Thus the simple interest for $900 at an interest rate of 6% is $108.

Learn more about simple interests here:

https://brainly.com/question/15175700

#SPJ1

Square root of one hundred and seventy is greater than square root of one hundred and sixty eight.

A perfect square number is a number which when taken square root comes out as an integer.Every number which is not a perfect square when taken square root of it is irrational number.We can obtain square root of a perfect square number by prime factorisation method.

Given we have to compare [tex]\sqrt{170}[/tex] and [tex]\sqrt{168}[/tex].

We know that if the square roots are not given then we have easily concluded that 170 > 168.Same in the case of square root:

[tex]\sqrt{170} > \sqrt{168}[/tex].

learn more about square roots here :

https://brainly.com/question/1387049

#SPJ1

Original sides of the square before reducing was 11 inches.

A quadratic equation has highest degree of two and it has 2 roots.

According to the given question Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album.

Assuming sides of the square to be x inches.

∴ From the given data

( x - 3 )( x - 3 ) = 64         ( area of a square is product any two sides )

x² - 6x + 9 = 64

x² - 6x - 55 = 0

x² - 11x + 5x - 55 = 0

x( x - 11 ) + 5( x-11 ) = 0

(x - 11 )( x + 5) = 0

∴ x = 11 or x = -5.                  ( length of something can not be negative )

So, the original length of the sides of the square is 11 inches.

Original area is

= (11×11)

= 121 sq inches.

learn more about quadratic equations here :

https://brainly.com/question/17177510

#SPJ4

The number of hours Melody worked this week was 15.

To learn more about percent, visit :

https://brainly.com/question/14699403

#SPJ1

Answer:

D.MSN

Step-by-step explanation:

Supplementary angles complete each other to 180° and they are on a straight line.

We are asked to find the supplementary angle to angle LSM on figure 2.

Amongst given options we see angle LSM and angle MSN make a straight line therefore they are supplementary angles.

The four factors were used to create this Product Game board are  {2, 3, 5, 7} and the product missing from the grid is 25

To see what are factors are used in the given list, we just need to write each of the numbers, as a product of prime factors such as 2, 3, 5, 7 .

9 = 3* 3

15 = 3 *5

18 = 3 *2*3

21 = 7*3

30 = 5*3*2

35 = 7*5

36 = 3*3*2*2

42 = 2*3*7

49 = 7*7

As we can see, the 4 factors used to product the numbers in the given list are {2, 3, 5, 7}

for the second part that is to find the missing number between 21 and thirty we first need to write all the numbers between 21 and thirty and check which number is having the only factors of at least one of (2,3,5,7)

the numbers are 22 , 23 ,24, 25 ,26 ,27 ,28, 29

After checking the missing number is 25(5*5) because there has to be at least 4 products who have same factor and 5 is the factor who has appeared only three times

To know more about Products, here:

https://brainly.com/question/21254539

SPJ9#

The  total money   Caroline would  have to pay for parking if she left her car in the lot for 3 hours is $11

For t hours the Caroline would pay 5+2t

What is algebraic expression?

Algebraic expression is a  mathematical statement  which points to when operations such as addition, subtraction, multiplication as well as division, are used for variables and constants, in essence, using algebraic expression, we can derive the equation that gives the total cost of Caroline driving and using the parking lot at the concert

There is a  fixed charge of $5, there is also an additional $2 for every spent, if represent hours spent by t, then she would pay 2t in total for using the parking lot.

Total cost=5+2t

when t=3 hours

total cost=5+(2*3)

total cost=$11

Find out more about algebraic expressions on:brainly.com/question/17241042

#SPJ1

Answer:

I think it's B (or A?)

Step-by-step explanation:

For alternate interior, they are alternate interior angles

Then for 2, they are equal and congruent, but they are SUBSTITITUING the angle numbers to the equation.

pls brainliest if I'm right :D

Answer:

$37.50

Step-by-step explanation:

Answer:

x>-3

Step-by-step explanation:

collect like terms by changing the signs ..

x+4>-3x-8:to: x+3x>-8-4

Hence find the value of x

:4x>-12

4x/4 >-12/4

x>-4

Answer:

x=12 y=10 z=-12

Step-by-step explanation:

The slope of the line which passes through the points (4, 18) and (6x, 2k) is (k - 9)/(3x - 2).

According to the given question.

A line passes through points (4, 18) and (6x,2k).

Which means we have two points (4, 18) and (6x,2k).

As we know that, the slope of a line is the ratio of the amount that y increases as x increases some amount.And the slope formula is m=(y2-y1)/(x2-x1) if a lines passes through the point (x2, y2) and (x1, y1).

Therefore, the slope of the line which passes through the points (4, 18) and (6x,2k)

= 2k - 18/ 6x - 4

= 2[k - 9]/2[3x - 2]

= (k-9)/(3x - 2)

Hence, the slope of the line which passes through the points (4, 18) and (6x, 2k) is (k - 9)/(3x - 2).

Find out more inofrmation about slope of line here:

https://brainly.com/question/14511992

#SPJ1

Answer:

listen there is a lack of information the information you give isn't enough

The correct answer is Team B won by 1.1 points.

To determine which team won the competition, we need to calculate the final scores for both Team A and Team B based on the given weights for each category and the points they received in each category.

For Team A:

- Time to complete (75% of 15 points) = 0.75 * 15 = 11.25 points

- Design (15% of 9 points) = 0.15 * 9 = 1.35 points

- Total cost (10% of 14 points) = 0.10 * 14 = 1.4 points

Total score for Team A = 11.25 + 1.35 + 1.4 = 14 points

For Team B:

- Time to complete (75% of 17 points) = 0.75 * 17 = 12.75 points

- Design (15% of 7 points) = 0.15 * 7 = 1.05 points

- Total cost (10% of 13 points) = 0.10 * 13 = 1.3 points

Total score for Team B = 12.75 + 1.05 + 1.3 = 15.1 points

Now, we compare the total scores of both teams. Team A has a total score of 14 points, while Team B has a total score of 15.1 points. Therefore, Team B won by 1.1 points.

To learn more about the competition link is here

brainly.com/question/31865237

#SPJ3

Answer:

x = 5

Step-by-step explanation:

from the diagram

∠ AOB + ∠ BOC + ∠ COD = ∠ AOD ( substitute values )

8x + 7x + 6x = 105

21x = 105 ( divide both sides by 21 )

x = 5

Answer:

5

Step-by-step explanation:

AOB+BOC+COD=AOD

6x+8x+7x=105

21x=105

x=105÷21

x=5

The perimeter of a polygon is 24 units.

In this question, we have been given the coordinates of a polygon.

we need to find the perimeter of a polygon.

Let A= (-3,2), B = (2,2), C = (2,-4), D = (-1,-4), E = (-1,-2), F = (-3,-2)

First we find the length of each side of a polygon.

|AB| = √5² + 0²

|AB| = 5

|BC| = √0² + (-6)²

|BC| = 6

|CD| = √(-3)²+0²

|CD| = 3

|DE| = √0²+2²

|DE| =  2

|EF| = √(-2)²+0²

|EF| = 2

|FA| = √0²+4²

|FA| = 4

The perimeter of a polygon would be,

P = AB + BC + CD + DE + EF + FA

P = 5 + 6 + 3 + 2 + 2 + 4

P = 24 units

Therefore, the perimeter of a polygon is 24 units.

Learn more about the perimeter of a polygon here:

https://brainly.com/question/15387363

#SPJ1

Answer:

2 - 5 = -3.

Step-by-step explanation:

I subtracted two from five and got negative three lol

The area of the piece of paper is;

Area = length x width

⇒ a = l w unit square.

Here,

Given that;

The width of piece of paper = w

The length of piece of paper = l

We have to find the area of piece of paper by using a.

What is Area of rectangle?

The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.

Now,

Consider the shape of piece of paper is rectangular.

The width of piece of paper = w

The length of piece of paper = l

Since, we know that;

Area of rectangle = length x width

Then, The Area of piece of paper 'a' = length x width

⇒ a = l * w

Where, a = Area of rectangle, l = length of piece of paper and

          w = width of rectangle.

Learn more about the area of rectangle visit:

https://brainly.com/question/16239445

#SPJ4

Using a linear function, one constraint on the inequality is given by:

y < -0.5x.

A linear function is modeled by:

y = mx + b

In which:

Given two points, the slope is given by change in y divided by change in x.

For the line in the inequality, the points are:

(-2,1) and (0,0).

Hence the slope is given by:

m = (0 - 1)/(0 - (-2)) = -1/2 = -0.5.

Hence:

y = -0.5x + b.

When x = 0, y = 0, meaning that the y-intercept is of b = 0, and:

y = -0.5x.

Everything below the line is shaded, meaning that the values of y that are less than the line are shaded, and the inequality is:

y < -0.5x.

The inequality is only less, not less or equal, because the line is dashed and not solid.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

[tex]|4x+3|+7 < 10[/tex]

Step-by-step explanation:

When you evaluate the expression, you get [tex]-\frac{3}{2} < x < 0[/tex]

endpoint y would be

(7,-4)

because when you graph all 3 points

(7,-4) adds nicely to the line that the other 2 make

The Area of the given figure in the radical form is [tex]96\sqrt[4]{x^{9} }[/tex] .

Area of a rectangle can be found by using the formula

Area = length*breadth

in the given question

length of the rectangle

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

On simplifying we get

[tex](4x)^{\frac{3}{2} }=(2^{2} x)^{\frac{3}{2} }\\ \\ =2^{2*\frac{3}{2} } *x^{\frac{3}{2} } }[/tex]      ( as (a.b)ⁿ=aⁿ.bⁿ  )

[tex]=2^{3} *x^{\frac{3}{2} } }\\ \\ =8*x^{\frac{3}{2} } }[/tex]

breadth of the rectangle = [tex]12x^{\frac{3}{4} }[/tex]

The required area = length * breadth

Substituting the values we get

Area = [tex]8*x^{\frac{3}{2} } }[/tex] * [tex]12x^{\frac{3}{4} }[/tex]

=96*[tex]x^{\frac{3}{2}+\frac{3}{4} }[/tex]

taking LCM of exponents as 4 and solving further we get ,

=[tex]96x^{\frac{9}{4} }[/tex]

Expressing in  radical form we get ,

Area = [tex]96\sqrt[4]{x^{9} }[/tex]

Therefore ,  the Area of the figure in the radical form is [tex]96\sqrt[4]{x^{9} }[/tex] .

Learn more about Area here https://brainly.com/question/23718948

#SPJ1

The roots of the equation [tex]x^{2}[/tex]-3x-3=0 by completing the square method are 3.79 and -0.79.

Given that the equation is [tex]x^{2}[/tex]-3x-3=0.

We are required to find the roots of the equation by completing the square method.

Equation is basically the relationship between two or more variables that are expressed in equal to form. It may be linear equation, quadratic equation,cubic equation and many more depending on the power of the variables that are present in the equation.

The equation is  [tex]x^{2}[/tex]-3x-3=0.

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

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

So,

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

[tex](x-3/2)^{2}[/tex]=-[-3-9/4]

[tex](x-3/2)^{2}[/tex]=21/4

x-3/2=±[tex]\sqrt{21}[/tex]/2

x=([tex]\sqrt{21}[/tex]+3)/2,(-[tex]\sqrt{21}[/tex]+3)/2

x=(4.58+3)/2, (-4.58+3)/2

x=7.58/2, -1.58/2

x=3.79,-0.79

Hence the roots of the equation [tex]x^{2}[/tex]-3x-3=0 by completing the square method are 3.79 and -0.79.

Learn more about equation at https://brainly.com/question/2972832

#SPJ9

Answer:

by completing the square method the answer is 3.79 and -0.79.

Step-by-step explanation:

above

The first term of the Geometric Series = 3 and its common ratio = 3/2.

An unlimited number of terms with a fixed ratio between each term make up a geometric series.

For 'n' termed GP with a = first term and r = common ratio, [tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex]

Given:

To find: First term of the GP and the common ratio.

Finding:

As, [tex]S_{n}=\frac{a(r^{n}-1)}{r-1}[/tex], for n =3,

[tex]S_{3}=\frac{a(r^{3}-1)}{r-1}=14.25[/tex] (eqn 1)

=> Similarly for n = 4,

[tex]S_{4}=\frac{a(r^{4}-1)}{r-1} = 24.375[/tex]

On dividing [tex]S_3 by S_4[/tex], we get:

[tex]\frac{14.25}{24.375}=\frac{r^{3}-1}{r^{4}-1}[/tex]

=> On solving the equations, we get:

[tex]14.25r^{4}-24.375r^{3}+10.125=0[/tex]

r = 3/2 (on factorizing the equation)

Now, substituting this in eqn 1

=> [tex]14.25=\frac{a((\frac{3}{2})^{2}-1)}{\frac{3}{2}-1}[/tex]

=> a = 3 on further solving the equation for a.

Hence, the first term of the Geometric Series = 3 and its common ratio = 3/2.

To learn more about geometric series, refer to the link: https://brainly.com/question/24643676

#SPJ4

The height of the ball after 1.5 seconds is 15.5 meters so option (C) will be correct.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

Given the function as the height of ball f(x) and time x

f(x) = -10x² + 20x + 8

At x = 1.5

f(1.5) = -10(1.5)² + 20(1.5) + 8

f(1.5) = 15.5

Hence "The height of the ball after 1.5 seconds is 15.5 meters".

For more about the function,

brainly.com/question/23712366

#SPJ4

Given question is incomplete complete question is attached below image ;

Answer:

1.) like terms and 2.) since all you did was combine like terms you didn't change the value, it's the same as before just "fixed" so yes

Answer:

Step-by-step explanation:

-2x^6-9

please give me the brainliest