Work out 21 as a fraction of 12

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{4 +3} \implies \cfrac{ -4 }{ 7 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{4}{7}}(x-\stackrel{x_1}{(-3)})\implies y-3=-\cfrac{4}{7}(x+3)[/tex]

The amount each friend does pay is £9.75

We are going to find 5% of the total amount paid and divide it by the numbers of all the friends to determine the amount paid by each one of them.

From the given information:

Therefore, the cost of each friend is = [tex]\dfrac{136.5}{14}[/tex]

The cost of each friend = £9.75

Learn more about fractions here:

https://brainly.com/question/78672

#SPJ1

Answer:

length = 6cm , breadth = 4cm

Step-by-step explanation:

Let's assume length = l

breadth = b

Given perimeter of a rectangle = 20 cm

2(l+b) = 20

l+b = 20/2

l+b = 10

l = 10 - b____(1)

Given area of rectangle = 24 cm²

l×b = 24____(2)

(1) in (2) => l × b = 24

(10-b) × b = 24

10b - b² = 24

10b = 24 + b²

0 = b² - 10b + 24

b² - 10b + 24 = 0

b² + 6b + 4b + 24 = 0

b(b+6) +4(b+6) = 0

(b+4)(b+6) = 0

b+4 = 0. &. b+6 = 0

b = -4. b = -6

breadth must be less than length and it should be positive

So b = 4 cm

b=4 in (1)

(1)=> l = 10 - b

l = 10 - 4

l = 6

Answer:

C)   y = -3x + 15

Step-by-step explanation:

Let's start with the hours required, 15.  For each day worked we can subtract 3 hours.  X days would mean 3x hours.  Subtract that from the goal of 15 hours:

15 - 3x

The time remaining, y, is given by the equation 15 - 3x.

Rearrange the equation to match the format in the options,

y = 15 - 3x

y = -3x + 15

Option C

The inequality that represents the domain of the function is [tex]\frac 12x - 10 \ge 0[/tex]

The function is given as:

[tex]f(x) = \sqrt{\frac 12x - 10} + 3[/tex]

Set the radicand greater than or equal to 0

[tex]\frac 12x - 10 \ge 0[/tex]

Multiply through by 2

x - 20 ≥ 0

Add 20 to both sides

x ≥ 20  

Hence, the domain of the function is x ≥ 20  

Read more about domain at:

https://brainly.com/question/1770447

#SPJ1

The equation for the relationship between the thickness and number of weeks is y = 3.8 - 0.2x

Ice lost at 7 weeks = 7(0.2) = 1.4 meters

Total thickness of ice before loss = Ice remaining after 7 weeks + Ice lost at 7 weeks

= 2.4 + 1.4

= 3.8 meters

The equation:

y = Total thickness of ice before loss - (Ice lost per week × Number of weeks)

= 3.8 - (0.2 × x)

y = 3.8 - 0.2x

Learn more about equation:

https://brainly.com/question/8284719

#SPJ1

Answer:

C

Step-by-step explanation:

The last reasoning is the side angle side theorem. In the whole proof, there is no mention of an angle. So the answer has to involve prooving that the angle in between the two sides that have been proven similar is the same in both traingles. This is best accomplished by statement C.

Answer:

A. Upward

B. (-2, -1)

C. X= -3, -1 ||| Y= 3

D. X=-2

Step-by-step explanation:

Answer:

±2√3

Step-by-step explanation:

Equation :

x² -4 = 8

x² -12 = 0

Using the quadratic formula then simplifying gives you :

±2√3

I know this lacks explanation but please brainliest

Answer:

x=2 or -6

Step-by-step explanation:

×^2+4×-4=8

8 will enter inside and become -8

x^2+4x-4-8=0

x^2+4x-12

(x^2+6x)(-2x-12)

x(x+6)-2(x+6)

(x-2)(x+6)

x=2 or x=-6

The area of the composite shape in the diagram given is: 100 square inches.

Area of a composite figure = sum of the areas of the shapes that make up the figure.

Area of the composite shape = 2(area of triangle) = 2(1/2bh)

Area of the composite shape = 2(1/2×10×10)

Area of the composite shape = 100 square inches.

Learn more about the area of a composite shape on:

https://brainly.com/question/8408690

#SPJ1

Answer:

true

Step-by-step explanation:

The statement is true because every graph associated a unique x-value for each y - value

Step-by-step explanation:

[tex]\pink{\large{\underline{\underline{\sf Given:-}}}}[/tex]

[tex]\pink{\large{\underline{\underline{\sf To \: find:-}}}}[/tex]

[tex]\pink{\large{\underline{\underline{\sf Solution:-}}}}[/tex]

We know that,

[tex]\underline{\boxed{\sf (Radius)^2= (Slant height)^2-(height)^2}}[/tex]

[tex] \sf (Radius)^2 = (16)^2-(12)^2[/tex]

[tex] \sf (Radius)^2 = 256-144=112[/tex]

[tex] \longmapsto \sf Radius = \sqrt{112}≈10.6\:cm[/tex]

Answer:

y = 1/3x - 2:

y = 12 - 6x:

y = 3x - 7:

Step-by-step explanation:

Hello!

The slope-intercept form of a line is [tex]y = mx + b[/tex]

The y-intercept is the "b" value of the line, given as -2.

To find the x-intercept, we simply replace the y-value with 0:

y - intercept: - 2

x - intercept: 6

____________________________________________________

You can rearrange the equation, y = -6x + 12, to find the y-intercept: 12.

Solving for the x-intercept (remember, replace y with 0):

y - intercept: 12

x - intercept: 2

____________________________________________________

Simply take the "b" value, -7, to find the y-intercept of -7.

Solve for the x-intercept:

y - intercept: -7

x - intercept: 7/3

Additional Note:

You can also solve for the y-intercept by replacing x with 0. This method can be used for any interests, just plug in the opposite variable from what you are solving for with 0.

The proof is that the x-intercept is the value when the y = 0, the x-axis. You can plug in 0 for y to solve for x. Similarly, when solving for the y-intercept, you plug 0 for x as the y-axis is at x = 0.

Answer:

90 meters

Step-by-step explanation:

so, what we know is that there are  90 seconds in one minute and a half.

Sam can run 6 meters per second. which means after 90 seconds, he should have run 540 meters.

Tom can run 7 meters per second. This means after 90 seconds, he should have run 630 meters.

630-540 = 90

give brainliest please!

hope this helps :)

Answer:

C - x < -6 and x < 2

Step-by-step explanation:

2x ">" -12 and 7x < 14. with negative numbers, the bigger the number the less it is. -12 < -6 because negative numbers work the opposite way that positive numbers do. I hope this helps you!!!!

The probability will include:

The probability of P(A and 1) will be:

= 1/4 × 1/6

= 1/24

The probability of P(C and 2) will be:

= 1/4 × 2/6

= 1/12

The probability of P(B and 3) will be:

= 2/4 × 1/6

= 1/12

The probability of P(A and 4) will be:

= 1/4 × 2/6

= 1/12

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

The final product is 18x⁴y⁵ - 48x²y⁵+12x³y⁷+24x²y⁸

The product is result obtained when a number or an expression is multiplied by the other number.

The product of the given expression

6x²y⁵ and 3x²-8x+2xy²+4y³

6x²y⁵ (3x²-8x+2xy²+4y³)

Step 1 : To multiply each term in the bracket with the other expression

out of the bracket

6*3*x²*y⁵*x² - 6*8*x²*y⁵ +6x²y⁵ *2*x*y² + 6*4*x²y⁵ *y³

Step 2 : The like variables will be solved

18x⁴y⁵ - 48x²y⁵+12x³y⁷+24x²y⁸

This is the final product

To know more about the product

https://brainly.com/question/17765678

#SPJ1

The value of x from the given triangle formed by the pot hanging from a brace is; x = 50°

We are given from the diagram that;

∠NMP = 110° and ∠NPM = 30°

Sum of angles in a triangle is 180°.

Thus;

∠MNP = 180 - (110 + 30)

∠MNP = 40°

Thus;

x = 90 - 40

x = 50°

Read more about angles in a triangle at: https://brainly.com/question/7620723

#SPJ1

The graph of the function y = x+2 is steeper than the graph y = 2x-1.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given functions are:-

The graph of the functions is attached with the answer below. In the graph, we can see that the slope of the graph y = x+2 is steeper than the graph of y = 2x - 1.

The two graphs intersect at the point ( 3,5 ) so it is the solution of the two linear equations.

Hence the graph of the function y = x+2 is steeper than the graph y = 2x-1.

To know more about graphs follow

https://brainly.com/question/25020119

#SPJ1

Answer:

7 hours and 12 minutes

Step-by-step explanation:

there are 24 hours in a day, so multiply 6/20 by 24 to find the number of hours:

6*24/20 = 36/5 = 7  1/5 hours

we now know maria sleeps for 7 whole hours

next, there are 60 minutes in an hour, so multiply 1/5 by 60 to get 12 minutes

Answer:

1331 inches cubed

Step-by-step explanation:

V=LHW

since it is a cube, the length, height, and width will all be the same; 11 inches. You have to multiply 11 by 11 by 11, which equals 1331.

Hope this helped!

Answer:

40°, 60°, 80°

Step-by-step explanation:

sum the parts of the ratio , 2 + 3 + 4 = 9 parts

the sum of the 3 angles in a triangle = 180° , then

180° ÷ 9 = 20° ← value of 1 part of the ratio , then

2 parts = 2 × 20° - 40° = ∠ A

3 parts = 3 × 20° = 60° = ∠ B

4 parts = 4 × 20° = 80° = ∠ C

The surface area of the rectangular prism with the dimensions that are stated is: 384 in.²

Surface area = perimeter of base × height of prism + 2(base area)

= (s1 + s2 + s3)L + 2(1/2bh)

Given the following:

Surface area = (6 + 8 + 10)14 + 2(1/2 × 6 × 8)

Surface area = 384 in.²

Learn more about the surface area of a rectangular prism on:

https://brainly.com/question/1310421

#SPJ4

Answer:

8

Step-by-step explanation:

Given algebraic expression:

5(x - 1) - 2

To:

Evaluate this expression using x = 3

Solution:

Evaluate by plugging x = 3 to this expression:

Simplify using PEMDAS.

We can conclude:

By evaluating x = 3 to the given expression,the answer will be 8.

The answer is 0.75 because I took the test and that's what the answer was :)

Answer:

0.65%

Step-by-step explanation:

i took the test