Theo starts with savings of £18
James starts​ with no savings
Each week from now,
Theo will save £4.50 and James will save £4
In how many weeks will Theo and James have savings in the ratio 15:8?

Answer:

C

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given x² + y² + 4x - 10y + 20 = 0

Collect x and y terms and subtract 20 from both sides. that is

x² + 4x + y² - 10y = - 20

To obtain standard form use the method of completing the square

add ( half the coefficient of the x/y term )² to both sides

x² + 2(2)x + 4 + y² + 2(- 5)y + 25 = - 20 + 4 + 25

(x + 2)² + (y - 5)² = 9 ← in standard form

with centre = (- 2, 5) and r = [tex]\sqrt{9}[/tex] = 3 → C

By rearranging the given equation to match the standard form of circle equation, we can determine the center of the circle to be (-2,5), and the radius to be 3.

The equation provided can be rewritten in the form (x - h)² + (y - k)² = r², wherein (h, k) denote the center coordinates of the circle, and r is the radius. To arrange it in this form, we group terms to complete the square for both x and y:

x² + 4x + y² - 10y = -20

⇒ (x² + 4x + 4) -4 + (y² - 10y + 25) - 25 = -20

⇒ (x + 2)² + (y - 5)² = 9

With this, we can identify the center of the circle to be at point (-2,5), and the radius is the square root of 9 which equals to 3. Hence, the correct answer is option C.

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The pair of equations has one solution and the solution is (30/11, 20/11).

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The coordinates on one line are (2, 6) and (5, 0)

Here, m=(0-6)/(5-2)

= -2

Substitute m=-2 and (2, 6) in y=mx+c, we get

6=-2(2)+c

c=10

So, the equation of a line is y=-2x+10 -----(i)

The coordinates on another line are (0, 2) and (6, 6)

Here, m= (6-2)/(6-0)

= 2/3

Substitute m=2/3 and (0, 2) in y=mx+c, we get

2=2/3(0)+c

c=0

So, the equation is y=2/3 x -----(ii)

Substitute equation (ii) in (i), we get

2/3 x=-2x+10

2x/3 +3x =10

11x=30

x=30/11

Substitute x=30/11 in equation (ii), we get

y =2/3 × 30/11

y= 20/11

So, the solution is (30/11, 20/11)

Therefore, the pair of equations has one solution and the solution is (30/11, 20/11).

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Answer:

$1,497.05

Step-by-step explanation:

Brett had 2 hrs OT his first week which would be (40 hr × 18.95 )+ (18.95 ×3) add the total to (36×18.95).

Answer:

[tex]\boxed{\bold{31}}[/tex]

Explanation:

Solve [tex]\bold{6= -s + 77}[/tex]

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

Add 's' To Both Sides

= [tex]\bold{6+s=-s+77+s}[/tex]

Simplify

= [tex]\bold{6+s=77}[/tex]

Subtract 6 From Both Sides

= [tex]\bold{6+s-6=77-6}[/tex]

Simplify

= [tex]\bold{s \ = \ 71}[/tex]

Insert '71' Into 1 + 5 (77 - s)

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

1 + 5 (77 - 71)

Solve:

77 - 71 = 6

= 1 + 5 · 6

5 · 6 = 30

= 1 + 30

= 31

Mordancy.

Answer:

1 + 5(77 - s) = 31

Step-by-step explanation:

Solve for s:

[tex]-s+77=6\qquad\text{subtract 77 from both sides}\\\\-s=-71\qquad\text{change the signs}\\\\s=71[/tex]

Put the value of s to the expression 1 + 5(77 -s):

[tex]1+5(77-71)[/tex]

Use PEMDAS:

P Parentheses first

E Exponents (ie Powers and Square Roots, etc.)

MD Multiplication and Division (left-to-right)

AS Addition and Subtraction (left-to-right)

[tex]=1+5(6)=1+30=31[/tex]

344676 I hope that helps

Answer:

Franchise has 11 quarters and 16 dimes.

Step-by-step explanation:

Let d represent number of dimes and q represent number of quarters.

We have been given that the number of dimes is five more than the number of quarters. We can represent this information in an equation as:

[tex]d=q+5...(1)[/tex]

We are also told that Francine has $4.35 in dimes and quarters. We can represent this information in an equation as:

[tex]0.10d+0.25q=4.35...(2)[/tex]

Now, we will substitution method to solve linear equations. Upon substituting equation (1) in equation (2), we will get:

[tex]0.10(q+5)+0.25q=4.35[/tex]

[tex]0.10q+0.50+0.25q=4.35[/tex]

[tex]0.35q+0.50=4.35[/tex]

[tex]0.35q+0.50-0.50=4.35-0.50[/tex]

[tex]0.35q=3.85[/tex]

[tex]\frac{0.35q}{0.35}=\frac{3.85}{0.35}[/tex]

[tex]q=11[/tex]

Therefore, Franchise has 11 quarters.

Upon substituting [tex]q=11[/tex] in equation (1), we will get:

[tex]d=11+5[/tex]

[tex]d=16[/tex]

Therefore, Franchise has 16 dimes.

Answer:

The minimum of h(x) is farther left and down from the minimums of f(x) and g(x) ⇒ answer 4

Step-by-step explanation:

* Lets revise the meaning of the minimum of the function

- The minimum of a function is the lowest point of a vertex

- The minimum value is the y-coordinate of the lowest point

* Now lets solve the problem

∵ f(x) = √x

- The domain of the function is all the real numbers ≥ 0, because

 there is no square root for negative numbers

- We will use the first value of x to find the range of the function

∵ x = 0 ⇒ first value of the domain

∴ f(0) = √0  = 0

∴ The minimum of f(x) is point (0 , 0)

∵ g(x) = √(x - 3) + 1

- Lets find the domain of the function

∵ x - 3 ≥ 0 ⇒ add 3 for both sides

∴ x ≥ 3

∴ The domain of the function is all real values of x ≥ 3

- We will use the first value of x to find the range of the function

∵ x = 3 ⇒ the first value of the domain

∴ g(3) = √(3 - 3) + 1 = 0 + 1 = 1

∴ The minimum of g(x) is point (3 , 1)

∵ h(x) = √(x + 1) - 2

- Lets find the domain of the function

∵ x + 1 ≥ 0 ⇒ subtract 1 for both sides

∴ x ≥ -1

∴ The domain of the function is all real values of x ≥ -1

- We will use the first value of x to find the range of the function

∵ x = -1 ⇒ the first value of the domain

∴ h(-1) = √(-1 + 1) - 2 = 0 -  = -2

∴ The minimum of h(x) is point (-1 , -2)

* To find the correct answer look to the minimum points of the

 functions (0 , 0) , (3 , 1) , (-1 , -2)

- The minimum of f(x) lies on the origin

- The minimum of g(x) lies in the 1st quadrant

- The minimum of h(x) lies in the 3rd quadrant

∴ The minimum of h(x) is farther left and down from the minimums

   of f(x) and g(x)

- Look to the attached graph to more understand

- The red curve is f(x)

- The blue curve is g(x)

- The green curve is h(x)

Final answer:

The minimums of f(x) and g(x) are in the first quadrant, and h(x) is in the fourth quadrant, making the minimum of h(x) farther right and up from the minimums of f(x) and g(x).

Explanation:

To compare the relative locations of the minimums of the functions f(x) = √x, g(x) = √x - 3 + 1, and h(x) = √x + 1 - 2, we need to consider how transformations affect the graph of the square root function.

The function f(x) is the parent square root function. Its minimum is at the origin (0,0), which is in the first quadrant.

The function g(x) is a horizontal translation 3 units to the right and a vertical translation 1 unit up from the function f(x). Hence, its minimum would also be in the first quadrant.

The function h(x) is a horizontal translation 1 unit to the right and a vertical translation 2 units down from f(x), which places its minimum in the fourth quadrant because the downward translation moves it below the x-axis.

Thus, the correct statement is: 3. The minimum of h(x) is farther right and up from the minimums of f(x) and g(x).

Answer:

37.5

Step-by-step explanation:

Since it is a cube, all of the lengths are equal. To find the surface area, you do

2.5*2.5 which is 6.25. After we get the 6.25, we need to find how many faces are there in this cube. (Including the base) There are 6 bases, then you take 6.25*6 to get the surface area. The final answer would be 37.5

4/10 or 2/5

Hope this helps!

Great Question!

First, 0.4 Is The Same Thing As 0.4/1

Next, Do 0.4/1 Multiplied By 10 And That Equals 4/10.

Finally, Simplify 2/5

In Conclusion, 0.4 Converted To A Fraction Is 2/5

The answer for this math equation is x = 40 or just 40

Step-by-step explanation: You just need to solve this problem in the normal algebraic equation format, applying the rules too.

2x + 20 = 100

2x + 20 - 20 = 100 - 20

2x = 80

2x/2 = 80/2

x = 40

Step 1: Bring 20 to the right side of the equation by subtracting 20 to both sides (subtraction is the opposite of addition and will cancel 20 from the left side and bring it over to the right)

2x + (20 - 20) = 100 - 20

2x + 0 = 80

2x = 80

Step 2: To isolate x divide 2 to both sides (division is the opposite of multiplication and will cancel 2 from the left side and bring it over to the right)

2x ÷ 2 = 80 ÷ 2

x = 40

Check (plug in 40 for x and solve it like normal):

2(40) + 20 = 100

80 + 20 = 100

100 = 100 --------------------------------------> Correct!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

Do you mean multiply?

- 8/15 * 20/24

- 8/15 * 5/6

5 and 15 have a common divisor -- 5

- 8/3 * 1 / 6

8 and 6 can be divided by 2.

-4/3 * 1/3

-4 / 9

====================

You could do the same thing without cancellation.

-8/15 * 20/24 = -160 / 360    

Now you can divide by common factors. Start by dividing top and bottom by 10

- 16 / 36            Now divide top and bottom by 4

- 4 / 9

The term that best describes the distribution is uniform.

The distribution shown in the image appears to be uniform. The bars are relatively similar in height, indicating that all outcomes are equally likely or nearly so.

A distribution where most of the data points are concentrated on the right, with the tail extending to the left is said to be skewed. While A distribution where most of the data points are concentrated on the left, with the tail extending to the right is said to be skewed right. A symmetrical, bell-shaped distribution where most data points are concentrated around the mean, with fewer points as you move away from the center. is said to be normal.

Therefore, the term uniform best describes the given distribution in the image.

Answer:

The corresponding sides are in proportion. so they are similar triangles.

The similarity statement is: Triangle ALB ~ Triangle EBR

Similarity statement:

Triangle ALB ~ Triangle EBR

Justification:

Two triangles are similar if they have the same shape, but different sizes. This means that the corresponding angles of the two triangles are equal, and the corresponding sides are proportional.

In the given image, we can see that the two triangles have the same shape. The corresponding angles are also equal:

Angle ALB = Angle EBR

Angle LAB = Angle EBE

Angle BAL = Angle BRE

To show that the corresponding sides are proportional, we can calculate the ratios of the corresponding sides:

AL/EB = 13/5 = 2.6

AB/ER = 15/36 = 5/12 = 0.417

BL/BR = 12/39 = 4/13 = 0.308

We can see that the ratios of the corresponding sides are all equal to 2.6. This means that the corresponding sides are proportional, and therefore the two triangles are similar.

Therefore, the similarity statement is: Triangle ALB ~ Triangle EBR

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Answer:

x = 11

Step-by-step explanation:

distribute: 4x - 28 = 27 - x

add x to both sides: 5x - 28 = 27

add 28 to both sides: 5x = 55

divide 5 to both sides: x = 11

Answer:

3 choices for the first color, 2 choices for the second color, 1 choice for the third color.

3 × 2 × 1 = 6 different flags are possible.

Using the Pythagorean theorem the formula would look:

[tex]c^2=b^2+a^2\Longrightarrow3.4^2=3^2+a^2[/tex]

Now just solve for a.

[tex]a^2=3.4^2-3.0^2\Longrightarrow a=\sqrt{3.4^2-3.0^2} \\

a=\sqrt{11.56-9}=\sqrt{2.56}=\boxed{1.6}

[/tex]

Side a is 1.6 inches long.

Hope this helps.

r3t40

Answer:

0

Step-by-step explanation:

The y-coordinates of the points are the same, so it is a horizontal line with a slope of 0.

___

slope = (change in y)/(change in x) = (4 -4)/(-5-(-1)) = 0/-4 = 0

ANSWER

0

EXPLANATION

The slope of a straight line is calculated using the formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]

The given line passes through (-1,4) and (-5,4).

We substitute the points into the formula to get:

[tex]m = \frac{4 - 4}{ - 5 - - 1} [/tex]

[tex]m = \frac{4 - 4}{ - 5 + 1} [/tex]

This simplifies to:

[tex]m = \frac{0}{ - 4} [/tex]

Zero divided by any number is zero.

Therefore, the slope is:

[tex]m = 0[/tex]

Answer:

A = True

B = False

C = true

Step-by-step explanation:

Answer:

The dog will catch the cat at  33.33 sec

Step-by-step explanation:

Let

x------> distance the cat runs before being caught by the dog,

Remember that

The speed is equal to divide the distance by the time

v=d/t

solve for t

t=d/v

so

equate the time

x/24=(200+x)/30

30x=24(200+x)

30x=4,800+24x

30x-24x=4,800

x=4,800/6=800 m

t=d/v=800/24=33.33 sec

or

t=(800+200)/30=1,000/30=33.33 sec

Answer:

3.(703)

Step-by-step explanation:

Answer:

0.78

Step-by-step explanation:

The decimal equivalent to 39/50 is 0.78

from the question, we have the following parameters that can be used in our computation:

39/50

To find the decimal equivalent of 39/50, you can divide the numerator (39) by the denominator (50).

This can be done using long division

So, we have

     0.78

50 | 39.00

    | 350

-------

   400

  | 400

-------

Hence, the decimal equivalent to 39/50 is 0.78

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Answer:

24

Step-by-step explanation:

132 pupils are represented by 11 parts of the ratio

Dividing 132 by 11 gives the value of one part of the ratio

132 ÷ 11 = 12 ← value of 1 part of the ratio, hence

2 parts = 2 × 12 = 24 ← number of teachers on trip

Answer:

24

Step-by-step:

132/11 (132 divide by 11)

=12

12*2 (12multiply by 2)

=24

ANSWER

139°

EXPLANATION

One of the interior angle properties of a parallelogram is that adjacent interior angles are supplementary.

This means that, the adjacent interior angles add up to 180°.

If

[tex]m \angle \: B = m \angle \: D = 41[/tex]

Then

[tex]m \angle \: C + m \angle \: D = 180 \degree[/tex]

OR

[tex]m \angle \: B + m \angle \:C= 180 \degree[/tex]

[tex] \implies41 \degree + m \angle \:C= 180 \degree[/tex]

[tex]\implies m\angle \:C= 180 \degree - 41 \degree = 139 \degree[/tex]

Answer:

193

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

1 | 1   2   - 3   2

        1      3    0

   --------------------

   1    3    0    2 ← remainder

Answer:

The remainder is 2

Option B is correct          

Step-by-step explanation:

Given the synthetic division problem

we have to solve the problem

The steps are  

Step 1: Set up the synthetic division.

Step 2:  Put down the leading coefficient to bottom row.

Step 3: Multiply divisor which is on left by the value just written on the bottom row.

Step 5:  Repeat the above steps.

The synthetic division is shown in attachment.

The remainder is 2

Option B is correct

Step-by-step explanation:

Paralle lines have the same slope.

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have

[tex]5y+9=-2x[/tex]

Convert to the slope-intercept form:

[tex]5y+9=-2x[/tex]           subtract 9 from both sides

[tex]5y=-2x-9[/tex]         divide both sides by 5

[tex]y=-\dfrac{2}{5}x-\dfrac{9}{5}\to m=-\dfrac{2}{5}[/tex]

Each of the answers to choose from is not the line equation sought.

The equation:

[tex]y=-\dfrac{2}{5}x+b[/tex] where b is any real number.

Parallel lines share the same slope. The slope of the given line is -2/5, so none of the provided options are correct as none have this slope.

To find the equation of a line that is parallel to another, it's important to know that parallel lines have the same slope. So firstly, we need to find the slope of the given equation. Starting with 5y + 9 = -2x, we will rearrange this into slope-intercept form (y = mx + b), where 'm' is slope and 'b' is y-intercept.

So, the slope of the given line is -2/5. This means a parallel line will also have the slope -2/5. Therefore, neither [1] y=-2x +3 nor [2] y = 2x + 1, [3] y = x+4 and [4] y=-x-1 can be parallel to the given line because all of them have different slopes not equal to -2/5.

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Answer:

The answer is 20 square units

Step-by-step explanation:

A=bh

A=5 times 4

A=20 units^2

Answer:

15

Step-by-step explanation:

When this net is assembled, it will form a box.  To calculate the area of the outside surface, find the area of each section and add them together.  The formula for area of a rectangle is A=lw:

A1=4(2)=8

A2=4(3)=12

A3=4(2)=8

A4=2(3)=6

A5=4(3)=12

A6=2(3)=6

8+12+8+6+12+6=52

The area that was painted green is 52cm2.

Hope this helps!!

Answer:

[tex]\large\boxed{f(x)=x^2+16x+60}[/tex]

Step-by-step explanation:

The factored form of a quadratic function:

[tex]f(x)=ax^2+bx+c=a(x-x_1)(x-x_2)[/tex]

x₁, x₂ - the zeros

We have x₁ = -10 and x₂ = -6.

Substitute:

[tex]f(x)=(x-(-10))(x-(-6))=(x+10)(x+6)[/tex]

Use FOIL: (a + b)(c + d) = ac + ad + bc + bd

[tex]f(x)=(x)(x)+(x)(6)+(10)(x)+(10)(6)\\\\f(x)=x^2+6x+10x+60\\\\f(x)=x^2+16x+60[/tex]

Answer:

Its A on edge

Step-by-step explanation:

Answer:

The height of this cone is

[tex]\displaystyle \frac{25}{4}[/tex],

which is the same as 6.25 in decimals.

Step-by-step explanation:

Consider the formula for the volume [tex]V[/tex] of a cone:

[tex]\displaystyle V = \frac{1}{3} \pi\cdot r^{2}\cdot h[/tex],

where

For this cone,

Rearrange the equation to find the height of this cone.

[tex]\displaystyle V = \frac{1}{3} \pi\cdot r^{2}\cdot h[/tex],

[tex]3\;V = \pi \cdot r^{2}\cdot h[/tex],

[tex]\displaystyle \frac{3\;V}{\pi\cdot r^{2}} = h[/tex].

Therefore,

[tex]h = \displaystyle \frac{3\;V}{\pi\cdot r^{2}} = \frac{3\times 300\;\pi}{{12}^{2}\; \pi} = \frac{25}{4} = 6.25[/tex].

Answer:

The rectangular coordinates of the point are (3/2 , √3/2)

Step-by-step explanation:

* Lets study how to change from polar form to rectangular coordinates

- To convert from polar form (r , Ф) to rectangular coordinates (x , y)

 use these rules

# x = r cos Ф

# y = r sin Ф

* Now lets solve the problem

∵ The point in the rectangular coordinates is (√3 , π/6)

∴ r = √3 and Ф = π/6

- Lets find the x-coordinates

∵ x = r cos Ф

∵ r = √3

∵ Ф = π/6

∴ x = √3 cos π/6

∵ cos π/6 = √3/2

∴ x = √3 (√3/2) = 3/2

* The x-coordinate of the point is 3/2

- Lets find the y-coordinates

∵ y = r sin Ф

∵ r = √3

∵ Ф = π/6

∴ y = √3 sin π/6

∵ sin π/6 = 1/2

∴ y = √3 (1/2) = √3/2

* The y-coordinate of the point is √3/2

∴ The rectangular coordinates of the point are (3/2 , √3/2)

Answer: B on edge

Step-by-step explanation:

Answer:

$381.25

Step-by-step explanation:

15.25*25=381.25

$381.25

you have to multiply $15.25 by 25