The price of a holiday was increased by 11% to £870. What was the price before the increase? Give your answer to the nearest penny.

Answer:

x+8

Step-by-step explanation:

[tex]3\times(x+2)+2\times(1-x)=\\\\3(x)+3(2)+2(1)+2(-x)=\\\\3x+6+2-2x=\\\\x+8[/tex]

Hope this helps!

Answer:

x + 8

Step-by-step explanation:

3 × (x + 2) + 2 × (1 - x)

3(x + 2) + 2(1 - x)

Expand the brackets.

3(x) + 3(2) + 2(1) + 2(-x)

Multiply the terms.

3x + 6 + 2 + -2x

Rearrange.

3x + - 2x + 6 + 2

Add like terms.

1x + 8

Answer:

98

Step-by-step explanation:

7x+4 = 88 because they are vertical angles and vertical angles are equal

7x = 88-4

7x = 84

Divide by 7

7x/7 = 84/7

x = 12

<1 and 7x-2 are supplementary angles since they form a line

<1 + 7x-2 = 180

<1 + 7(12) -2 = 180

<1 +84-2 =180

<1 +82 = 180

<1 = 180-82

<1 = 98

Answer-

98

step by step explanation -

7x+4=88

7x=84

x=12

7x-12=7*(12)-2=82

angle 1=180-82 =

Answer:

see below

Step-by-step explanation:

1.

1, H - 2, H - 3, H - 4, H - 5, H

1, T - 2, T - 3, T - 4, T - 5, T

2.

2,H is one out of 10 possible outcomes, so the probability is 1/10

Answer: Francisco is correct

Step-by-step explanation:

Positive 4 and positive 7

Negative 3 and negative 2

4 * 7 = 28

-3 * -2 = 6

Answer:

C

Step-by-step explanation:

Okay, here we have the equation of the sine wave as;

y = asin(k(x + b))

By definition a represents the amplitude

k represents the frequency

b represents the horizontal shift or phase shift

Now let’s take a look at the graph.

By definition, the amplitude is the distance from crest to trough. It is the maximum displacement

From this particular graph, amplitude is 4

K is the frequency and this is 1/period

The period ;

Firstly we find the distance between two nodes here and that is 1/2 from the graph (3/4 to 1/4)

F = 1/T = 1/1/2 = 1/0.5 = 2

b is pi/4 ( phase is positive as it is increasing rightwards)

So the correct option here is C

Answer: it is

a=4, k=2, and b= pi/4

Step-by-step explanation:

got it right on A P E X

Answer:

Writing it in matrix form

- 2 - 4 - 5 - 155

1 1 6 101

2 2 - 3 37

I hope this helps you

Answer:

15

Step-by-step explanation:

mean means add all the numbers and divide them by how many there are

plot 1: 63 divided by 9 equals 7

plot 2: 330 divided by 15 equals 22

so now we need to subtract 22 minus 7 equals 15

hope this helps

Answer:

15

Step-by-step explanation: you have to add all of the numbers and then divide the answer by the number of numers you added

Answer:

-8/3

Step-by-step explanation:

First find the slope of the line

3x+y = 1

Solve for y

y = -3x+1

This is in slope intercept form

y = mx+b where m is the slope

The slope is -3

The slopes of perpendicular lines multiply to -1

m* -3 = -1

m = 1/3

The line perpendicular has a slope of 1 / (3) = 1/3

The sum is -3 + 1/3

-9/2 + 1/3 = -8/3

Answer:

c. Not enough information

Step-by-step explanation:

It's not cos x^2

[tex]\cos^2x\neq\cos x^2[/tex]

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

[tex]\cos x-\dfrac{\sin x\sin x}{\cos x}=\dfrac{\cos x\cos x}{\cos x}-\dfrac{\sin x\sin x}{\cos x}=\dfrac{\cos^2-\sin^2x}{\cos x}[/tex]

It's the same as

[tex]3-\dfrac{2}{3}=\dfrac{3\cdot3}{3}-\dfrac{2}{3}=\dfrac{3^2-2}{3}[/tex]

Answer:

  B.  False

Step-by-step explanation:

In order for segments to form a triangle, the sum of the lengths of the shorter two must be at least as much as the length of the longest one.

The sum of the shorter two is 6 + 5 = 11. This is not as great as 12, the length of the longest one, so no triangle can be formed.

Answer:

m the slope of function=-3

Step-by-step explanation:

to find the slope take two points from the graph:

(0,4), (1,1)

m= y2-y1/x2-x1

m=1-4/1-0

m=-3/1=-3

the equation : y=mx+b find b

when x=0, y=b=4

y=-3x+4

Answer: b⁶

Step-by-step explanation:

The for bⁿ can be optained by multiplying 3 and 2. If there is an exponent on the outside of the parenthesis, you multiply it with the exponent on the inside.

(b³)²=b³ˣ²=b⁶

Answer: C

Step-by-step explanation:

Answer:

The third one. Y= -1/2x^2 -2x -1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the formula for calculating heat energy H = mcΔT

m = mass of the aluminum (in g/kg)

c = specific heat capacity of aluminum

ΔT = change in temperature = T - Ti (in °C)

T is the final temperature

Ti is the initial temperature

Given m = 100.0g,  c = 0.931096J/g °C, Ti = 20°C, H = 1100J T = ?

Substituting the given values into the formula;

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

The final temperature of the metal is 31.81°C

Answer:

31.81c

Step-by-step explanation:

1100 = 100*0.931096 (T - 20)

1100 = 93.1096T - 1862.192

93.1096 T = 1100+1862.192

93.1096 T  = 2962.192

T = 2962.192/93.1096

T = 31.81°C

Answer:

88.6647727273 cm²

Step-by-step explanation :

The perimeter of the square =(50/2)

                                               = 25 cm

∴ Side of the square = (25/4)

                                    = 6.25 cm

∴ Area of of the square = (6.25)²

                                        = 39.0625 cm²

The circumference of the circle =(50/2)

                                            = 25 cm

∴ 2πr = 25

⇒ r = 25/(22/7)(2)

Area of the circle = (22/7) { 25/(22/7)2} {25/(22/7)2}

                             = (25×25×7) / (2×2×22)

                             = 4365/88

                             = 49.6022727273 cm²

∴ Total area of the circle and the square =(49.6022727273+39.0625000000)

= 88.6647727273 cm²

Hope it helped

If yes mark BRAINLIEST!

Answer:

Counterexample: 21 which is divisible by 3 but not by 6.

Step-by-step explanation:

Use for example the number 21 which is divisible by 3 rendering 7, but not divisible by 6.

You can find any number with at least a factor of "3", but no factor "2" in it, so any odd number divisible by 3 would work as counterexample.

Answer:

second option

Step-by-step explanation:

Given

[tex]x^{4}[/tex] + 6x² + 5 = 0

let u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Change u back into terms of x, that is

x² = - 1 ( take the square root of both sides )

x = ± [tex]\sqrt{-1}[/tex] = ± i ( noting that [tex]\sqrt{-1}[/tex] = i ), and

x² = - 5 ( take the square root of both sides )

x = ± [tex]\sqrt{-5}[/tex] = ± [tex]\sqrt{5(-1)}[/tex] = ± [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex] = ± i[tex]\sqrt{5}[/tex]

Solutions are x = ± i and x = ± i[tex]\sqrt{5}[/tex]

Answer:

b

Step-by-step explanation:

not a because equilateral would be all equal

scalene is all different

Answer:

scalene

Step-by-step explanation:

because all  sides are different.

Answer:

-4

Explanation:

when subtracting a positive integer from a negative, the answer becomes smaller. If the question were to ask -3-(-1) negative 3 minus negative 1, the subtraction sign becomes a addition sign, and you add 1 to -3.

Answer: -4

Step-by-step explanation: To subtract the integers -1 - 1, I would first change the minus sign to plus a negative.

So we have -1 + -1.

Now let's use a number line to find our answer.

Starting at 0, -3 moves us 3 units to the left, then from there,

-1 moves us 1 more unit to the left and we end up at -4.

So -3 + -1 is -4.

Answer:

A) $93,504.818

B) $40,000

C) $53,504.818

Step-by-step explanation:

Yearly contribution ( periodic payment) = $4000

Period (p) = 10years

Additional period(y) = 5years

Annual interest(r) = 9% = 0.09

Future value (FV) =

periodic payment [(1 + r)^y - 1] / r

4000 [(1 + 0.09)^10 - 1 / 0.09]

4000[1.09^10 - 1 / 0.09]

4000[1.3673636 / 0.09]

4000(15.192929)

= 60771.716

If left for five more years:

FV = 60771.716(1 + r)^n

FV = 60771.716(1 + 0.09)^5

FV = 60771.716(1.09)^5

FV = 60771.716(1.5386239549)

FV = $93,504.818

B) MR. HUGHES CONTRIBUTION :

Periodic payment × p ; $4000 was deposited annually for 10 years.

$4000 × 10 = $40,000

C) Interest = Future value - contribution

$93,504.818 - $40,000

= $53,504.818

Answer:

The population of the city was 25,000 in 1970 and 1983.

Step-by-step explanation:

In order to find the year at which the population was 25,000 we need to make p(t) equal to that number and solve for t as shown below.

[tex]25000 = 14*t^2 + 650*t + 32000\\14*t^2 + 650*t + 7000 = 0\\t^2 + 46.43*t + 500 = 0\\t_{1,2} = \frac{-46.43 \pm \sqrt{(46.43)^2 - 4*1*500}}{2}\\t_{1,2} = \frac{-46.43 \pm \sqrt{155.75}}{2}\\t_{1,2} = \frac{-46.43 \pm 12.48}{2}\\t_1 = \frac{-33.95}{2} = -16.98\\t_2 = \frac{-58.91}{2} =- 29.5[/tex]

Since t = 0 corresponds to the year 2000, then t1 = 1983 and t2 = 1970.

Answer:

Standard form: [tex]x^3+3x^2-x-3[/tex]

Leading coefficient: 1

Step-by-step explanation:

[tex]3x^2-x-3+x^3=\\x^3+3x^2-x-3[/tex]

The leading coefficient is 1 because the leading term is [tex]x^3[/tex].

Answer: The graph is a linear graph or linear function in the form y= mx + b where m is the slope and b is the y-intercept. You could plot the points (0,5) (1,4) (2,3) (4,1)  and draw a straight line through them.

Step-by-step explanation:

The equation  y= 5-x  can be rewrite as  y = -1x + 5  and it can be identify as a linear equation in slope intercept form. Now you could plot in any value  of x and solve for y.

x        y         (x,y)

0       5          (0,5)   If you put in 0 for x y will be 5

1       4            (1,4)    if you put in 1 for x,  y will be 4

2      3            (2,3)  if you put in 2 for x, y will be 3

4       1             (4,1)   if you put in 4 for x, y will be  1

5       0             (5,0)  if you put in 5 for x y will be 0.

Step-by-step explanation:

The correct answer is the vertical change divided by the horizontal change between two points on a line. We can find the slope of a line on a graph by counting off the rise and the run between two points. If a line rises 4 units for every 1 unit that it runs, the slope is 4 divided by 1, or 4.

Answer:

Calculate the rise over the run/the change in y over the change in x

Step-by-step explanation:

In order to find the rate of change on a graph from a slope, you need to look at how many units up and how many units to the right. Find a solid point on the graph for both the x and y directions. Count how many units go up and how many go right. Divide how many units go up by how many go to the right and that is the rate of change on the graph.

Answer:

5/8

Step-by-step explanation:

72 = 16/10 of 45

45 = 10/16 = 5/8 of 72

Answer:

Step-by-step explanation:

6 and 7

Answer:

[tex]\frac{(p + 2)m}{p}[/tex]

Step-by-step explanation:

Given

m cups of water = p cups of rice

Required

Cups of water required for p + 2 cups of rice

The question shows a direct proportion between cups of rice and cups of water.

So, the first step is to get the proportionality constant (k)

This is calculated using the following expression;

[tex]m = k * p[/tex]

Where k represents cups of water and p represents cups of rice

Make k the subject of formula

[tex]k = \frac{m}{p}[/tex]

Let x represents cups of water when cups of rice becomes p + 2;

k becomes:

[tex]k = \frac{x}{p + 2}[/tex]

Equate both expressions of k; to give

[tex]\frac{m}{p} = \frac{x}{p + 2}[/tex]

Multiply both sides by p + 2

[tex](p + 2) * \frac{m}{p} =(p + 2) * \frac{x}{p + 2}[/tex]

[tex](p + 2) * \frac{m}{p} =x[/tex]

[tex]x = (p + 2) * \frac{m}{p}[/tex]

[tex]x = \frac{(p + 2)m}{p}[/tex]

Hence, the expression that represents the cups of water needed is [tex]\frac{(p + 2)m}{p}[/tex]

Answer:

15 units

Step-by-step explanation:

Given the equation which models the path of a stone as:

[tex]H(x)=-5x^2+10x+15[/tex]

At the time when the stone was thrown

x=0

Therefore:

[tex]H(0)=-5(0)^2+10(0)+15\\H(0)=15[/tex]

The height of the stone at the time it is thrown is 15 units.