Byrn has a stack of photos measuring 12cm wide and 16cm high. He wants to display them on a large rectangular poster in such a way that all photos are equally spaced on each side, including at the edges of the poster, as illustrated (in the attached file)


Q1. Bryn wants to display 9 photos (with longer side vertical) in 3 rows of 3 photos each with 2cm spacing around each photo. What are the dimensions of the poster?


Q2. Bryn wants to display 24 photos (with longer side vertical) with 2cm spacing around each photo. He wants more columns than rows of photos. Find the smallest poster area that is needed.


Q3. Bryn wants to display 18 photos in 3 rows of 6 photos each with 3cm spacing around each photo. The photos may all be displayed in portrait orientation (longer side vertical) or in landscape (longer side horizontal). Which orientation uses the lesser poster area?


Q4. Bryn wants to display 24 photos (with longer side vertical) in 6 rows of 4 photos each with equal spacing around each photo. He has a poster that is 62cm wide and 120cm high. He wants to use the full width of the poster but is prepared to trim some of its height to achieve the equal spacing. How much of the poster does he need to trim?

Please provide working out for all of the answers. Thanks.

Answer:

the answer is 10

Step-by-step explanation:

(8+4+14+16+8)/5

Answer:

12

Step-by-step eplanation:

Answer:

[tex]29.4\ cm^3[/tex]

Step-by-step explanation:

b = 4 × 3.5 = 14 cm²

h = 2,1 cm

then

[tex]V=b\times h[/tex]

   [tex]=14\times2.1[/tex]

   [tex]=29.4\ cm^3[/tex]

Step-by-step explanation:

The length of the rectangle is 4cm and the width is 3.5cm

The area of the rectangle is A = lw

The base area is 4 x 3.5 or 14cm squared

The height is 2.1cm

Substitute 14 for B and 2.1 for h

V = Bh

V = (14)(2.1)

=29.4

Therefore the volume of the prism is 29.4 cubic centimetres

Answer:

the answer should be 2

Step-by-step explanation:

you have to divide the 18 balls by the 9 girls.

The formula is a = (b1*b2)/2   .    

The balance after a year will be represented by an expression m + 0.071m.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The total amount will be calculated as:-

Total amount = Principle + interest rate x priciple

Total amount  = m  +   0.071m

Therefore the balance after a year will be represented by an expression m + 0.071m.

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Answer:

Below in bold,

Step-by-step explanation:

The angles in a triangle add up to 180 degrees.

So the equation is:

7x + 8 + 4x + x + 4 = 180

12x + 12 = 180  <-------- Required equation

12x = 168

x = 14.

m< L = 14 + 4 = 18 degrees

m< M = 7(14) + 8 = 106 degrees

m< N = 4(14)= 56 degrees

Answer:

y = -3x -2

Step-by-step explanation:

Hi there!!

We're given that a line has a slope of -3 and it contains the point (1, -5)

We want to write the equation of this line in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

As we are already given the slope, we can immediately plug it into the equation.

Replace m with -3 in y=mx+b.

y = -3x + b

Now we need to find b

As the equation passes through the point (1, -5), we can use its values to help solve for b.

Substitute 1 as x and -5 as y:

-5 = -3(1) + b

Multiply

-5 = -3 + b

Add 3 to both sides

-2 = b

Substitute -2 as b into the equation

y = -3x - 2

Hope this helps!

Topic: finding the equation of a line

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Answer:

3v2 + 9v = 3v(v + 3)

              - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

        What is the complete factorization of 3v²+9v?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to solve:-}}}}\diamond[/tex]

First we need to find the GCF of this polynomial; when we find it, we should factor it out, or divide all the terms by it.

Since the greatest common factor (GCF) of this polynomial is 3v, we divide both terms by 3v:-

3v(v+3)

                - - - - - - - - - - - - - - - - - - - -- - - - - - - - -

answer is 31 dimes, 11 nickels

see picture attachment for the math

equation is .05N + .10D = 3.65

value of nickels and dimes

using D + N = 42

change to find value of N = 42 - D

plug value of N into the equation and solve

Answer:

6

Step-by-step explanation:

A parallelogram is a quadrilateral or a flat shape with opposite sides parallel. Squares, Rhombuses, and Rectangles are few example of Parallelogram.

Explanation:

There are six important properties of a parallelograms:

The answer to the above question is (D) Diagonals Congruent

Answer:

D

Step-by-step explanation:

Because these are the 7 properties of a parralelgrom

Opposite sides are parallel.

Opposite sides are congruent.

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary. .

Each diagonal of a parallelogram separates it into two congruent triangles.

The diagonals of a parallelogram bisect each other.

Answer:  it is D 546.817

Answer:

a) Yes

b) Not a right triangle

Step-by-step explanation:

The sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side.

7 + 8 = 15 > 9

7 + 9 = 16 > 8

8 + 9 = 17 > 7

Therefore, a triangle with side lengths 7, 8 and 9 can be made.

To determine if the triangle is a right triangle, use Pythagoras' Theorem:

a² + b² = c² (where a and b are the legs, and c is the hypotenuse)

The hypotenuse is the longest side, therefore:

Substituting these values into the formula:

⇒ a² + b² = c²

⇒ 7² + 8² ≠ 9²

⇒ 113 ≠ 81

As  7² + 8² ≠ 9²  then the triangle is not a right triangle.

Step-by-step explanation:

To cover a rectangular region of her yard, Penny needs at least 217 square feet of sod. The length of the region is 15.5 feet. What are the possible widths of the region?

L=length=15.5 ft; W=width; A=area=>217 sq ft

L*W=>217 sq ft Divide each side by L

W=>217 sq ft/L

W=>217 sq ft/15.5 ft=>14 feet

ANSWER: To cover at least 217 sq ft. the width must be at least 14 feet.

Answer:

  at least 14 ft

Step-by-step explanation:

The area of the rectangular region is the product of its length and width. We are told the area must be at least some value.

  A = LW . . . . . . . . . area formula

  A ≥ 217 ft² . . . . . . . . . given constraint

  (15.5 ft)W ≥ 217 ft² . . . . . . substitute LW for A, use given length

  W ≥ 14 ft . . . . . . . . . . divide by 15.5 ft

The possible width of the region is at least 14 feet.

Answer:

There is no answer

Because absolute value causes a positive answer and it is written here -13 !!!

it's impossible

Answer:

39cm

Step-by-step explanation:

area of square = side^2 =169

side = 13cm

Perimeter of triangle = 3*side

=3 * 13 = 39cm

Answer:

52

Step-by-step explanation:

√169 =13

13*4= 52 because the perimeter of the square is equal to the perimeter of the triangle

The reasoning used here is coding and decoding.

Coding is a portion of the logical reasoning element that is used to encrypt words, numbers, or codes utilizing specified rules and regulations. The process of decoding patterns into their original forms from supplied forms is known as decoding.

We have an expression:-

a = b and c = d, then a − c = b − d

Therefore the reasoning used here is coding and decoding.

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The experimental probability of the arrow stopping on Section 2 will be [tex]\rm \frac{3}{8}[/tex]. is the ratio of the favorable event to the total number of events.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1.

No of arrows given in the different section ;

Section 1=18

Section 2=30

Section 3=32

The probability that the arrow stopping on Section 2 is found as;

[tex]\rm P = \frac{Favourable \ outcomes }{Total \ outcomes } \\\\\ P= \frac{30}{18+30+32} \\\\ P=\frac{30}{80}\\\\ P= \frac{3}{8}[/tex]

Hence, the experimental probability of the arrow stopping on Section 2 will be [tex]\rm \frac{3}{8}[/tex].

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Answer:

Ash has 58 flowers in total

Step-by-step explanation:

Given:

-  buys 5 bunches

- each bunch contains 10 flowers

- 8 more flowers from his yard.

5 bunches times 10 flowers plus the 8 more flowers from the garden

F = 10(5) + 8

F = 50 + 8

F = 58

Answer:

Ash has 58 flowers in all

Step-by-step explanation:

Y representing = bunches of flowers  

F representing =  the flower  

1. Y=10f      

2. Y=10f                    5 x 10 = 50

3. Y=10f                   50 + 8 = 58

4. Y=10f      

5. Y-10f                      

                         f = 58

Answer:

2.8

Step-by-step explanation:

To find the mean aboslute deviation, you first need to find the mean:

(4 + 6 + 7 + 10 + 13)/5 = 8

Then, subtract the mean from each value, and take the abosulte value. Absolute value is essentially the same number, but if it is negative, make it positive.

4 - 8 = -4 = 4

6 - 8 = -2 = 2

7 - 8 = -1 = 1

10 - 8 = 2 = 2

13 - 8 = 5 = 5

Then, take the mean of all of these values:

(4 + 2 + 1 + 2 + 5)/5 = 2.8

Answer:

70

Step-by-step explanation:

Just do it backwards.

94 - 12 = 82.

82 + 6 = 88.

88 - 18 = 70.

Answer:

3/9 (or) 1/3 (reduced)

Step-by-step explanation:

1.  Before handing pencils to the students, the teacher had 9 out of 9 (9/9) pencils.

2.  When she gave pencils to the students, she gave them 6 of the 9 pencils (6/9)

3.  Now we do the math:

9/9 - 6/9

= 3/9 (or) 1/3 (reduced)

Therefore, the teacher now has 3/9 or 1/3 of the pencils left.

The coordinate s (-4, 1) is lying on the 180 degrees of the vertex R.

A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.

There are four coordinates are given

P(-3,4), Q(-1,4), R(-2, 1), S(-4, 1)

Point S is just lying about 180 degree to the vertex R so the coordinates will be S ( -4,1)

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Answer:

294 yd²

Step-by-step explanation:

a cube has 6 congruent square faces.

the area of 1 face = 7 × 7 = 49 yd²

then surface area = 6 × 49 = 294 yd²

Use the general formula for decay substance

[tex]\\ \rm\Rrightarrow N=N_o(1-r)^t[/tex]

For our equation r=62%=0.62

So

function becomes

[tex]\\ \rm\Rrightarrow N=650(1-0.62)^t[/tex]

[tex]\\ \rm\Rrightarrow N=650(0.38)^t[/tex]

Change for a year

[tex]\\ \rm\Rrightarrow N=650(0.38)[/tex]

[tex]\\ \rm\Rrightarrow N=247g[/tex]

Amount decayed=650-247=403g

Daily decay

Percentage decay

[tex]\\ \rm\Rrightarrow \dfrac{1.1}{650}\times 100[/tex]

[tex]\\ \rm\Rrightarrow 0.169[/tex]

[tex]\\ \rm\Rrightarrow 16.9\%[/tex]

Answer:

20 miles

Step-by-step explanation:

This is a Pythagorean Theorem Problem

1. We know that one side of the triangle is 6 miles. And we know that another side is 19 miles.

2. We use the pythagorean Theorem to solve. We get

[tex]19^2+6^2=C^2[/tex]

Where C is the distance.

Solving that we get that 20 miles is the answer.

To solve this problem, we have to use combination which is a topic in statistics and it deals with the number of ways or arrangement in which and event can occur. the local dry cleaner can make them fill the roles in 210 ways.

In the given question, we have 10 candidates and 4 positions to be filled.

Data;

[tex]^1^0C_4 = 210[/tex]

From the calculation above, the local dry cleaner can make them fill the roles in 210 ways.

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