Malachy and Paul win some money and share it in the ratio 2:1. Malachy gets £24 more than Paul. How much did they get altogether?

Answer:

According to intersecting chard theorem:-

[tex]12(x)=8(x+2)[/tex]

[tex]12x=8x+16[/tex]

[tex]12x-8x=16[/tex]

[tex]4x=16[/tex]

[tex]x=16/4[/tex]

[tex]x=4[/tex]

So, your answer is D) 4

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hope this helps you!!

The required value of the x is 4 for the given circle. Option D is correct.

A figure is shown of a circle with two intersecting cords fractions 12+x and x+2+8. The value of the x is to determine.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²,
where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.

The chords of the circle is the lines that bisect the circles in two parts, Longest chord of the circle is the Diameter.

Now.

x+2/x=8/12
12x = 8x+16

12x-8x=16
4x = 16
x = 4

Thus the required value of x is 4 for a given circle.

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Answer:

a = k/(4 + 9b)

Step-by-step explanation:

Here, we want to make a the formula subject

We have this as;

k = a(4 + 9b)

a = k/(4 + 9b)

The expression for a fom the give expression is a = k/(4 + 9b)

Given the following equation

K = 4a + 9ab

Factor out the GCF

K = a(4 + 9b)

Divide both sides by 4 + 9b
k/4+9b = a(4 + 9b)/4+9b
k/(4 + 9b) = a

Hence the expression for a fom the give expression is a = k/(4 + 9b)

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Answer:

- 8

Step-by-step explanation:

To evaluate f(8) substitute x = 8 into f(x)

f(8) = - 2(8) + 9 = - 16 + 9 = - 7

Similarly for g(- 1)

g(- 1) = (- 1)² - 2 = 1 - 2 = - 1

Then

f(8) + g(- 1) = - 7 + (- 1) = - 7 - 1 = - 8

Answer:

C. 4 is the right answer!

Step-by-step explanation:

Answer:

6 and 4

Step-by-step explanation:

Answer:

Part A: 4 and x are factors of 4x

Part B: 6 and 4

Part C:  4

Step-by-step explanation:

Answer:

inglese please

Step-by-step explanation:

Answer:

6x-3

Step-by-step explanation:

that is the procedure above

Step-by-step explanation:

5+4X+2x-8

=6x-3

answer is third option

Answer:

1. 8:15

2. 6

3. 32

4. 12.4

Answer:

1

5

2

Step-by-step explanation:

4-3=1

8-3=5

5-3=2

Hope this helps! :)

Answer:

a) -6

b) 3

c) Y = -6x + 3

Step-by-step explanation:

Pick two points and find rise/run = slope

rise y1 - y2 = 9 - 3 = 6

run x1 - x2 = -1 - 0 = -1

slope = 6 / -1 = -6

The y intercept is where x = 0 which is given in the table (0,3) so

y intercept = 3

Point slope form is y = mx + b , so

y = -6x + 3

The person must make 8 trips for Plan A and B to be equal.

Plan A will cost $144 and then $10 for every parking. Assuming the number of trips is x, the expression would be:

= One time fee + (Fee per parking x number of trips)

= 144 + 10x

Plan B will cost $48 then parking of $22. Expression will be:

= 48 + 22x

To find out the number of trips where the cost will be equal, equate the two:

144 + 10x = 48 + 22x

144 - 48 = 22x - 10x

96 = 12x

x = 96 / 12

x = 8 trips

The person must therefore make 8 trips for Plan A and B to be equal.

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Answer:

$65

Step-by-step explanation:

Collin gets 4x dollars which equals 52, so 4x = 52

Dan gets 5x dollars which equals y (the answer). solve for x = 13. 5 • 13 = 65.

Answer:

So what are you asking me to do

Answer:

A.

Step-by-step explanation:

Answer:

[tex]x=14[/tex]

Step-by-step explanation:

The given triangle is a right triangle, meaning it is a triangle with a right angle, this is indicated by the box around one of the angles. When given a right triangle, one can use the right triangle trigonometric ratios. These ratios describe the relationship between an angle in a right triangle, and the sides in a right triangle. Such ratios are as follows,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Bear in mind that the way one names the sides, in the sense of (opposite or adjacent) will change based on the angle one uses to describe the triangle. However, the hypotenuse is the same no matter the angle, as the hypotenuse is the side opposite the right angle.

In this case, one is given one of the angles, and the side opposite the angle. One is asked to find the hypotenuse of the triangle. One can use the sine (sin) ratio to achieve this.

[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

Substitute,

[tex]sin(30)=\frac{7}{x}[/tex]

Inverse operations,

[tex]x=\frac{7}{sin(30)}[/tex]

Simplify,

[tex]x=14[/tex]

Answer:

D

Step-by-step explanation:

We are given that:

[tex]\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi[/tex]

And we want to find the value of tan(2x).

Note that since x is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

[tex]\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}[/tex]

Using double angle identities:

[tex]\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}[/tex]

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(x) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

[tex]\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}[/tex]

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since x is in QII, cosine and tangent will be negative while sine will be positive. Hence:

Simplify:

[tex]\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}[/tex]

Evaluate:

[tex]\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}[/tex]

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

[tex]\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}[/tex]

So, our answer is D.

Answer:

ED = 6

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{ED}{BA}[/tex] = [tex]\frac{EF}{BC}[/tex] , substitute values

[tex]\frac{ED}{9}[/tex] = [tex]\frac{12}{18}[/tex] ( cross- multiply )

18 ED = 108 ( divide both sides by 18 )

ED = 6

Answer:

10 pounds

Step-by-step explanation:

Let x represent the amount of raisins Meg have in her supply. She uses 1/2 of her supply of raisins  to make trail  mix and 3/10 of her supply of raisins to make  cookies which gives a total of 8 pounds of raisins being used. To find the amount of raisins she has in her supply, we use the equation:

(1/2)x + (3/10)x = 8

multiply through by 20:

(1/2)x * 20 + (3/10)x * 20 = 8 * 20

10x + 6x = 160

16x = 160

Divide both sides of the equation by 16:

16x/16 = 160/16

x = 10 pounds

Therefore she have 10 pounds of raisins in her supply

Answer:

13a + 6b

Step-by-step explanation:

Given

(a + 3b) + 3(4a + b) ← distribute parenthesis

= a + 3b + 12a + 3b ← collect like terms

= 13a + 6b

Answer: 13a+3b+18

Step-by-step explanation:

First distribute the 3 to 4a+b

Then you get 12a+18

Add 12a+18 with a+3b

Replace c with 3:

3^5 = 3 x 3 x 3 x 3 x 3 = 243

The answer is 243

Answer:

15

Step-by-step explanation:

c5

3(5)

3 x 5

15

Answer:

28cm

Step-by-step explanation:

Area of a parallelogram equals the base length, which is y cm, multiplied by the height, which is 18cm.

So

Area= 504cm

y cm (base) x 18 cm (height) = 504cm^2 (area)

y cm = 504cm^2 / 18cm

y cm = 28cm

Answer:

28 cm

Step-by-step explanation:

Just use some good ol' algebra:

18y = 504

y = 28 cm

A parallelogram is basically a wonky rectangle, so it uses the same formula for area.

Answer:

C. x=-48

Step-by-step explanation:

x/4=-12

multiply both sides by 4

4x/4=4 (-12)

simplify

x=-48

Answer:

8x2- 10x- 3 = 46

Step-by-step explanation:

Answer:

3675

Step-by-step explanation:

3500x.05 (5%)=175 GCT

3500+175=3675.

Answer:

m = -5

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Identify

y = -1/2 - 5x

Compare:

y-intercept b = -1/2

slope m = -5

Answer:

The slope is -5 and the y intercept is -1/2

Step-by-step explanation:

This equation is written in slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = -5x-1/2

The slope is -5 and the y intercept is -1/2

Answer:

39 acute isoceleleellsllelsls

Step-by-step explanation:

The angles of triangle always add to 180 degrees. So that angle on the bottom already takes up 102 so 180-102=78 and there are 2 angles left so both of those are 39 because 78/2=39  and 39 is an acute angle since its less than 90 degrees so ya

Answer:

third box

first box

second box

Step-by-step explanation:

1/3x + 1/4 -2/3x; combine like terms

-1/3x + 1/4 (third box)

1/3x + 1/4 + 2/3x; combine like terms

(3/3)x +1/4 (first box)

3/3 is 1, so we don't have to write it

2/3 + 3/4x -1/3; combine like terms

1/3 + 3/4x (swap, and is second box)

Answer:

x+3y -10 =0

Step-by-step explanation:

In slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = -1/3x +10/3

We want it in the general form  ax+by +c =0  where a,b,c are integers and a>0

Multiply by 3 on each side

3*y = 3(-1/3x +10/3)

3y = -x +10

Add x to each side

x+3y = -x+10 +x

x+3y = 10

Subtract 10 from each side

x+3y -10 = 10-10

x+3y -10 =0

The slope of a line is [tex] - \frac{1}{3} [/tex] and the y-intercept is [tex] \frac{10}{3} [/tex]. What is the equation of the line written in general form?

○ 10x + 3y - 1 = 0

○ x + 3y + 10 = 0

○ x + 3y - 10 = 0

[tex] \quad \quad\quad\quad\boxed{\tt{y = mx + b}}[/tex]

[tex]\quad \quad\quad\quad\boxed{\tt{Slope (m) = \frac{1}{3} }}[/tex]

[tex]\quad \quad\quad\quad\boxed{\tt{y \: intercept(b) = \frac{10}{3} }}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{y = - \frac{ 1}{3}x + \frac{10}{3} }}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{ax + by + c = 0}}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{ (3)y = 3(- \frac{ 1}{3}x + \frac{10}{3} )}}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{ 3y = \cancel{ \color{red}3}(- \frac{ 1}{ \cancel{ \color{red}3}}x + \frac{10}{ \cancel{ \color{red}3}} )}}[/tex]

[tex] \quad \quad\quad\quad\boxed{\tt{3y = - x + 10}}[/tex]

[tex] \quad\quad\quad\boxed{\tt{3y = - x + 10}} \: ➡ \: \boxed{\tt{x + 3y = 10}}[/tex]

[tex] \quad\quad\quad \boxed{\tt{x + 3y = 10}} \: ➡ \: \boxed{ \tt{x + 3y - 10 = 0}}[/tex]

[tex]\quad \quad\quad\quad \boxed{ \color{green}{ \tt{x + 3y - 10 = 0}}}[/tex]

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