The price of a pair of trainers was £85 The price was reduced to £47 Work out the percentage change in price.

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Explanation:

T is the midpoint of PQ, which means T splits PQ into two equal parts. Those parts being PT and TQ.

Set them equal to each other and solve for x.

PT = TQ

3x+7 = 7x-9

3x-7x = -9-7

-4x = -16

x = -16/(-4)

x = 4

So,

PT = 3x+7 = 3*4+7 = 19

TQ = 7x-9 = 7*4-9 = 19

Both PT and TQ are 19 units long to help confirm the answer.

Answer:

C. [tex]-x-6>-3.5[/tex]

Step-by-step explanation:

One is asked to find which inequality has ([tex]x=-3[/tex]) in its solution set. Remember that an inequality is another way to represent a set of solutions. In essence, it states that all numbers less than; less than or equal to; greater than; or greater than or equal to, are a part of the solution. One simplifies an inequality in a similar manner to how one simplifies an equation, by using inverse operations and simplification. Just note that when multiplying or dividing the inequality by a negative number, one has to flip the inequality sign to ensure the expression remains true.

Simplify each of the inequalities, then evaluate to see which one has ([tex]x=-3[/tex]) as a part of its solution set.

A. [tex]-x -6<-3.5[/tex]

[tex]-x<2.5[/tex]

[tex]x>-2.5[/tex]

B. [tex]-x-6>3.5[/tex]

[tex]-x>9.5[/tex]

[tex]x<-9.5[/tex]

C. [tex]-x-6>-3.5[/tex]

[tex]-x>2.5[/tex]

[tex]x<-2.5[/tex]

D. [tex]x-6>-3.5[/tex]

[tex]x>2.5[/tex]

As can be seen, option (C [tex]-x-6>-3.5[/tex]) is the only one that fits this requirement. Since option (C) simplifies down to ([tex]x<-2.5[/tex]) or in words, (x) is less than (-2.5). This option is the only one that fits the solution since (-3) is less than (-2.5).

Answer:

1) 2400MB

2) 3 minutes

Step-by-step explanation:

1) 600 MB/Min * 4 Min = 2400MB

2) at 800 MB/Min a 2400MB file will require 2400MB/800MB/Min

  2400/800 = 3Min

Answer:

19

Step-by-step explanation:

x + y(3 − x)

Let x = -5 and y = 3

-5 +3(3 - -5)

Subtracting a negative is like adding

-5 +3(3+5)

Parentheses first

-5 +3(8)

Multiply

-5+24

Subtract

19

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

P(A and B)=P(A)*P(B)

Answer:

x=1°.

see the IMAGE FOR SOLUTION

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

A line with an x-intercept of -5 has the coordinates (-5, 0); that same line with a y-intercept of 1 has the coordinates of (0, 1). The slope of this line is

[tex]m=\frac{1-0}{0-(-5)}\\m= \frac{1}{5}\\[/tex]

A line that is perpendicular to this one will have a slope of -5.

Answer:

D

Step-by-step explanation:

380

Answer:

Step-by-step explanation:

None

They are both imaginary or complex. You can check that out by calculating the discriminate. If you get a minus answer, then there are no real roots. Let's try it.

a = - 2

b = - 4

c = - 6

D = sqrt(b^2 - 4*a * c)

D = sqrt( (-4)^2 - 4*(-2)(-6)  )

D = sqrt( 16 - 48)

D = sqrt(-32) which is negative and there are no real roots.

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

Let r, c, h represent the numbers of meals eaten in a restaurant, car, and at home, respectively. The problem statement tells us of the relations ...

  r + c + h = 193

  -r + c + h = 15

  r + 0c -h = 30

Add the last two equations:

  (-r +c +h) +(r -h) = (15) +(30)

  c = 45

Add the first two equations:

  (r + c + h) +(-r + c + h) = (193) +(15)

  2c +2h = 208

  h = 104 -c = 59 . . . . solve for h, substitute for c

The last equation can be used to find r.

  r = 30 +h = 30 +59 = 89

89 meals are eaten in a restaurant; 45 meals in a car; and 59 at home.

Answer:

70

Step-by-step explanation:

In a trapezoid lines are parallel, so corresponding angle sum = 180

X+X+40 = 180

2x + 40 = 180

2x = 180-40

2x = 140

X = 140/2

X = 70

Answered by Gauthmath

Answer:

t f dis say mane ion speak italian

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

[tex]3+x=ax[/tex]    (Given)

[tex]x=ax-3[/tex]    (Subtracted 3 on both sides)

[tex]x-ax=-3[/tex]    (Subtracted ax on both sides)

[tex]x(1-a)=-3[/tex]    (Factor out x from x - ax)

[tex]x=-\frac{3}{1-a}[/tex]    (Divided 1 - a on both sides)

Step-by-step explanation:

we see, for x=-1 we get 3³

x=0 we get 3²

x=1 we get 3¹

so the function is definitely a 3 to the power of x version.

but we need to adapt the exponent a bit and correct x, so that at least for these 3 values of x the result is "running backwards".

the easiest way : 2-x as exponent.

it fits.

for x=-1 we get 2 - -1 = 3 as exponent.

for x=0 we get 2-0 = 2 as exponent.

for x=1 we get 2-1 = 1 as exponent.

so, the exponential function passing through these 3 points is

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

Answer:

Y = 27

Step-by-step explanation:

To find the the value of y when x = 4 simply substitute the given value of x

into the equation and solve for y

Equation given: y - 3x = 15

x = 4 * substitute 4 for x in given equation *

y - 3(4) = 15

Now solve for y

simplify multiplication

y - 12 = 15

Add 12 to both sides

y - 12 + 12 = 15 + 12

y = 27

So we can conclude that when x = 4 y = 27

Answer:

y = 27

Step-by-step explanation:

y - 3x = 15

Let x = 4

y - 3(4) = 15

y - 12 = 15

Add 12 to each side

y -12 +12 =15+12

y = 27

Answer:

Prime factorization: 797 is prime. The exponent of prime number 797 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 797 has exactly 2 factors

Answer:

5•362165924

Step-by-step explanation:

first make root of 32-6=5•099019514

then make root of 2+root2=1•84--

then divide upper by lower part answer comes

or

root32-6=root26

root 2+root 2=2root2

root26/root2root2

ans=3•0318---

Answer:

[tex] \frac{ \sqrt{32} - 6 }{ \sqrt{2} + \sqrt{2} } \\ \frac{ \sqrt{16 \times 2} - 6}{2 \sqrt{2} } \\ \frac{4 \sqrt{2} - 6}{2 \sqrt{2} } \\ \frac{2(2 \sqrt{2} - 3) }{2 \sqrt{2} } \\ \frac{2 \sqrt{2} - 3}{ \sqrt{2} } \\ thnk \: you[/tex]

Answer:

[tex](832.156, \ 847.844)[/tex]

Step-by-step explanation:

Given data :

Sample standard deviation, s = 15

Sample mean, [tex]\overline x = 840[/tex]

n = 23

a). 98% confidence interval

[tex]$\overline x \pm t_{(n-1, \alpha /2)}. \frac{s}{\sqrt{n}}$[/tex]

[tex]$E= t_{( n-1, \alpha/2 )} \frac{s}{\sqrt n}}[/tex]

[tex]$t_{(n-1 , \alpha/2)} \frac{s}{\sqrt n}$[/tex]

[tex]$t_{(n-1, a\pha/2)}=t_{(22,0.01)} = 2.508$[/tex]

∴ [tex]$E = 2.508 \times \frac{15}{\sqrt{23}}$[/tex]

  [tex]$E = 7.844$[/tex]

So, 98% CI is

[tex]$(\overline x - E, \overline x + E)$[/tex]

[tex](840-7.844 , \ 840+7.844)[/tex]

[tex](832.156, \ 847.844)[/tex]

Answer C Right Isosceles Triangle

Step-by-step explanation:

Do it

Answer: C

Step-by-step explanation:

It has a 90 degree angle, right triangle, and both legs in the triangle seem to be the same size, so it's also isosceles.

Step-by-step explanation:

given that the coordinate is (0,1)(4,3)

x¹=0, y¹=1, x²=4 y²=3

M=> Gradient => (y²-y¹)/(x²-x¹)

M=(3-1)/(4-0) => 1/2

Therefore the slope-intercept equation

M=(y-y¹)/(x-x¹)

1/2 = (y-1)/(x-0)

x=2y-2

2y=-2-x

y=-x/2 - 1

Answer:

The expression for the height of the solid is:

[tex]\displaystyle h = x^2+x-9[/tex]

Step-by-step explanation:

Recall that the volume of a rectangular solid is given by:

[tex]\displaystyle V = \ell wh[/tex]

Where l is the length, w is the width, and h is the height.

We know that the volume is given by the polynomial:

[tex]\displaystyle V = 3x^4-3x^3-33x^2+54x[/tex]

And that the length and width are given by, respectively:

[tex]\displaystyle \ell = 3x \text{ and } w =x-2[/tex]

Substitute:

[tex]\displaystyle 3x^4-3x^3-33x^2+54x=(3x)(x-2)h[/tex]

We can solve for h. First, divide both sides by 3x:

[tex]\displaystyle \frac{3x^4-3x^3-33x^2+54x}{3x}=(x-2)h[/tex]

Divide each term:

[tex]\displaystyle x^3-x^2-11x+18=(x-2)h[/tex]

To solve for h, divide both sides by (x - 2):

[tex]\displaystyle h = \frac{x^3-x^2-11x+18}{x-2}[/tex]

Since this is a polynomial divided by a binomial in the form of (x - a), we can use synthetic division, where a = 2. This is shown below. Therefore, the expression for the height of the solid is:

[tex]\displaystyle h = x^2+x-9[/tex]

Answer:

Step-by-step explanation:

I think you mean 2.99×10^8, not 2.99×108.

2.99×10⁸ meters per second = 299,000,000 meters per second