Pencils are sold in boxes of 10. Erasers are sold in boxes of 14. A teacher wants to buy the same number of pencils and erasers. Work out the smallest number of boxes of each item she should buy.

Answer:

£54.65

Step-by-step explanation:

Del sells his goods for £54.60 making a 9% loss how much did he pay for the good when he bought them?

We are to find the cost price.

Loss = Cost price - Selling price

Percentage loss =

(Cost price - Selling price/Cost price) × 100

Percentage loss = 9% = 0.09

Selling price = £54.60

Cost price = x

Hence:

0.09 = x - £54.60/x × 100

0.09 = 100(x - £54.60)/x

Cross Multiply

0.09x = 100(x - £54.60)

0.09x = 100x - 5460

100x - 0.09x = 5450

99.91x = 54.50

x = 5460 / 99.91

x = 54.649184266

Approximately, x = £54.65

Therefore, the cost price = £54.65

Answer:

b is the correct answer

y=a(x+n)^2+k

vertex: -b/2a 18/2=9

y=1(x-9)^2

k=9^2-18(9)+52= 81-162+52=-29

y=(x-9)^2-29

Answer:

The greatest common factor term 20a^12 b² -15a⁸b^4 of the expression 20a ^12 b² -15a⁸b^4 = 5x4xa⁸ xa⁴xb²x = 5a⁸xb²x4a⁴ and -15⁸b⁴ = 5x-3xa⁸xb²x-3b²

Step-by-step explanation:

Hence, The expression 20a¹²b²- 15a⁸b⁴= 5x-3xa⁸xb²xb²= 5a⁸b²(4a⁴-3b²)

- Hope this helped! :3

Answer:

y=4x+7

Step-by-step explanation:

replace x by any one number and find out

Answer:

112

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I am 100% sure it is A.

Answer:

See Explanation

Step-by-step explanation:

Your question is incomplete, as the equations or graph or table(s) were not given.

However, I'll give a general way of solving this.

Take for instance, the equations are:

[tex]y = \frac{4}{3}x - 1[/tex]

[tex]y = \frac{2}{3}x - \frac{1}{2}[/tex]

To do this, we start by equating both equations.

[tex]y = y[/tex]

i.e.

[tex]\frac{4}{3}x - 1= \frac{2}{3}x - \frac{1}{2}[/tex]

Collect Like Terms

[tex]\frac{4}{3}x - \frac{2}{3}x= 1 - \frac{1}{2}[/tex]

Take LCM

[tex]\frac{4x- 2x}{3}= \frac{2 - 1}{2}[/tex]

[tex]\frac{2x}{3}= \frac{1}{2}[/tex]

Cross Multiply

[tex]2x * 2 = 3 * 1[/tex]

[tex]4x = 3[/tex]

Make x the subject

[tex]x = \frac{3}{4}[/tex]

Substitute 3/4 for x in [tex]y = \frac{4}{3}x - 1[/tex]

[tex]y = \frac{4}{3} * \frac{3}{4} - 1[/tex]

[tex]y = 1 - 1[/tex]

[tex]y = 0[/tex]

Hence:

[tex](x,y) = (\frac{3}{4},0)[/tex]

Answer:

The answer is ( D )

Step-by-step explanation:

Answer:

V T R (answer choice 4)

Step-by-step explanation:

Plane B is the side of the figure labeled B

The following points are on Plane B:

T, U, V, R, S

The only answer that contains three of these points is D (Answer choice 4)

Answer:

Step-by-step explanation:

A or C

Answer:

The solution to the system of equations represented by these two lines is:

Hence, option C i.e. (2, 0) is correct.

Step-by-step explanation:

Please note that the point of intersection between two lines is the solution of the system of equations.

From the graph, it is clear that two lines intersect at x = 2 and y = 0.

In other words, the point of intersection of the two lines is:

(x, y) = (2, 0)

Therefore, the solution to the system of equations represented by these two lines is:

Hence, option C i.e. (2, 0) is correct.

Answer:

4

Step-by-step explanation:

8 ×1/2, if I'm wrong I am sorry

Answer:

1/8

Step-by-step explanation:

Answer:

Solution of the proportion: [tex]\frac{x-6}{4}=\frac{2}{4}[/tex] is x=8.

Step-by-step explanation:

We need to find solution of the proportion: [tex]\frac{x-6}{4}=\frac{2}{4}[/tex]

For solving the equation, first we will multiply both sides by 4

[tex]\frac{x-6}{4}=\frac{2}{4}[/tex]

[tex]4\times \frac{x-6}{4}=4\times \frac{2}{4}[/tex]

[tex]x-6=4(\frac{2}{4})[/tex]

Simplifying

[tex]x-6=2[/tex]

Adding 6 on both sides

[tex]x-6+6=2+6x=8[/tex]

So, solution of the proportion: [tex]\frac{x-6}{4}=\frac{2}{4}[/tex] is x=8.

Note: Kindly recheck your options as correct answer is x =8.

Step-by-step explanation:

5x+y=7

20x+2=y

put y value in first equation

5x+(20x+2)=7

25x=5

x=5

now put x value to determine y

as we know 20x+2=y

20(5)+2=y

y=102

Answer:

v= 42

Step-by-step explanation:

To find the value of v, substitute the given values into the equation.

v= u +at

when u= 18, a= 6, t= 4,

v= 18 +6(4)

v= 18 +24

v= 42

Answer:

First choice.

Step-by-step explanation:

When you solve the system and somehow get both sides two different value. That means both graphs are oarallel (graph of both equations). When two sides are different, we can say that there are no solutions.

Answer:

that will be 4

Step-by-step explanation:

it goes by 4

Answer: 12 -8 = 4

Step-by-step explanation:

Answer:

The value of sin Ф is [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

In quadrant II, the value of

Let us solve the question

∵ sin²Ф + cos²Ф = 1

∵ cos Ф = [tex]\frac{-12}{13}[/tex]

→ Substitute it in the identity above

∴ sin²Ф + ([tex]\frac{-12}{13}[/tex])² = 1

∴ sin²Ф + [tex]\frac{144}{169}[/tex] = 1

→ Subtract [tex]\frac{144}{169}[/tex] from both sides

∵ sin²Ф + [tex]\frac{144}{169}[/tex]  - [tex]\frac{144}{169}[/tex]  = 1 - [tex]\frac{144}{169}[/tex]

∴ sin²Ф = [tex]\frac{25}{169}[/tex]

→ Take the square root of both sides

∵ √(sin²Ф)= ± [tex]\sqrt{\frac{25}{169}}[/tex]

∴ sin Ф = ± [tex]\frac{5}{13}[/tex]

∵ Ф is in quadrant II

∴ sin Ф is a positive value

∴ sin Ф = [tex]\frac{5}{13}[/tex]

∴ The value of sin Ф is [tex]\frac{5}{13}[/tex]

Answer:

Yes they are equivalent

Answer:

x = 44

Step-by-step explanation:

its saying that x is less than 45 therefore its 44

Answer:

D

Step-by-step explanation:

x needs to be less then 45

Answer:

just search and then thats it

Answer:

A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. This time is called the half-life, and often denoted by the symbol t1/2. The half-life can be written in terms of the decay constant, or the mean lifetime.

Step-by-step explanation:

Answer: E C and A

Step-by-step explanation:

Answer:

slope intercept form is y = mx + b

It looks like y= x+3 is the only option in slope intercept form

Answer:

56  

Step-by-step explanation:

Answer

the one in the bottom right

Step-by-step explanation:

Answer:

option 2

Step-by-step explanation:

Using the cosine and sine ratios in the right triangle and the exact values

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , sin30° = [tex]\frac{1}{2}[/tex]

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{20\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 60 ( divide both sides by 2 )

x = 30

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

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{20\sqrt{3} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2y = 20[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

y = 10[tex]\sqrt{3}[/tex]

Answer:

x=35°   y= 75°   z = 70°

Step-by-step explanation:

Y = x+40   (known)

z = 2x    (known)

x + y + z = 180     (triangle property)

x + (x+40) + 2x = 180   (substitution)

4x + 40 = 180

4x = 140

x = 35

y = x + 40 = 75

z = 2x = 70

Answer:

The correct option is A.

Step-by-step explanation:

It is given that  DEFG is a parallelogram.

Draw the diagonals DF and EG. Place point H where DF and EG intersect.

In triangle HGD and HEF

,

∠HGD ≅ ∠HEF                            (Alternate Interior angle)

∠HDG ≅ ∠HFE                      (Alternate Interior angle)

By the definition of a parallelogram, the opposite sides of a parallelogram are congruent.

DG ≅ EF                                      (Opposite sides of parallelogram)

According to ASA postulate :

two triangles are congruent if any two angles and their included side are equal in both triangles.

So, by using ASA criterion for congruence we get,

ΔDGH ≅ ΔFEH

Since corresponding sides of congruent triangles are congruent, therefore

GH ≅ EH                      (CPCTC)

DH ≅ FH                     (CPCTC)

Answer: [See attached immage]

The Answer:    I really hope this helps!!!