At the start of 2014 Lucy's house was worth £200,000.
The value of the house increased by 5% every year.

Work out the value of her house at the start of 2017.

Answer:

[tex]\boxed{\text{A.  The y-intercept of function f is greater than the y-intercept of function g}}[/tex]

Step-by-step explanation:

A. y-Intercept of ƒ(x)

ƒ(x) = x² - 4x + 3

f(0) = 0² - 4(0) + 3 = 0 – 0 + 3 = 3

The y-intercept of ƒ(x) is (0, 3).

If g(x) opens downwards and has a maximum at y = 3, it's y-intercept is less than (0, 3).

Statement A is TRUE.

B. y-Intercept of g(x)

Statement B is FALSE.

C. Minimum of ƒ(x)

ƒ(x) = x² - 4x + 3

a = 1; b = -4; c = 3

The vertex form of a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b/(2a) and k = f(h)

h = -b/2a = -(-4)/(2×1 = 2

k = f(2) = 2² - 4×2 + 3 =4 – 8 +3 = -1

The minimum of ƒ(x) is -1. The minimum of ƒ(x) is at (2, -1).

Statement C is FALSE.

D. Minimum of g(x)

g(x) is a downward-opening parabola. It has no minimum.

Statement D is FALSE

[tex]A=5m^4\times6m^2=\boxed{30m^6}[/tex]

Answer:

361. 362,363

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 1086.

We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 1086. Therefore, you can write the equation as follows:

X + X + 1 + X + 2 = 1086

To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 1086

3X + 3 = 1086

3X + 3 - 3 = 1086 - 3

3X = 1083

3X/3 = 1083/3

X = 361

Which means that the first number is 361, the second number is 361+1 and third number is 361+2. Therefore, three consecutive integers that add up to 1086 are:

361

362

363

Follow below steps;

The question asks to find three consecutive natural numbers that add up to 1086. Let's denote the smallest of these three numbers as n. Then, the next two numbers can be represented as n + 1 and n + 2. The sum of these three numbers is:

n + (n + 1) + (n + 2) = 1086

Combining like terms, we get:

3n + 3 = 1086

Subtracting 3 from both sides, we get:

3n = 1083

Dividing both sides by 3, we find:

n = 361

So the three consecutive numbers are 361, 362, and 363, and they indeed sum up to 1086:

361 + 362 + 363 = 1086

Answer:

4 4/2

Step-by-step explanation:

What you do is you have to do 8-4=4 5-1=4 6-4=2 so there for the answer is 4 4/2

Hello There!

We are given the problem 8 5/6 - 4 1/4

Your answer would be 4 7/12

First, we subtract 4 from 8 and get a difference of 4.

Then we have to subtract 1/4 from 5/6.

We have to find a common denominator.

We can get 10/12-3/12=7/12

Then, we add 4+7/12 and we get 4 7/12.

Answer:

13/6

Step-by-step explanation:

volume=length*width*height

so

325m^3=10*15*x

325=150x

x=2.16666666 or 325/150

Step 1: Distribute the 2 to numbers and variables inside parentheses

(2 × x) + (2 × 3) = 4 (x - 1)

2x + 6 = 4 (x - 1)

Step 2:  Distribute the 4 to numbers and variables inside parentheses

2x + 6 = (4 × x) + ( 4 × - 1)

2x + 6 = 4x+ (-4)

2x + 6 = 4x- 4

Step 3: Combine like terms (x's go with x's) by subtracting 2x to both sides

(2x - 2x) + 6 = (4x - 2x) - 4

6 = 2x - 4

Step 4: Combine like terms by adding 4 to both sides

6 + 4 = 2x - 4 + 4

10 = 2x

Step 5: Isolate x by dividing 2 to both sides

10 ÷ 2 = 2x ÷2

5 = x

x = 5

To check: plug 5 into all the x's of the equation

2(x+3)=4(x-1)

2(5+3)=4(5-1)

2(8) = 4(4)

16 = 16

Hope this helped!

Answer:5

Step-by-step explanation:

Answer:

160 children, 112 boys and 48 girls.

Step-by-step explanation:

You can translate this into two equations:

g = 3/7 * b

g+64 = b

Then fill in one in the other and simplify:

3/7 b + 64 = b =>

4/7 b = 64

b = 64 * 7/4 = 112

g = 112 * 3/7 = 48

Final answer:

By setting up equations with the given proportions and difference in numbers, we can calculate that there are 112 boys and 48 girls in the field, totaling 160 children.

Explanation:

To solve the problem of how many children are in the field, we need to set up an equation based on the information given. It states that there are 3/7 girls there are boys, and that there are 64 more boys than girls. Let's define the number of boys as B and the number of girls as G. According to the problem, B = G + 64 and G = (3/7) * B.

To find the solution, we need to substitute G from the second equation into the first to get B = (3/7) * B + 64. Simplifying this equation, we multiply both sides by 7 to get rid of the fraction 7B = 3B + 448. Then we subtract 3B from both sides yielding 4B = 448. Dividing both sides by 4 gives us B = 112. Now that we have the number of boys, we can find the number of girls using the second equation: G = (3/7) * 112 = 48. Finally, we add the number of girls and boys to find the total number of children in the field 112 + 48 = 160.

Answer:  The answers are given below.

Step-by-step explanation:  Given that the graph shows the relationship between the number of months different students practiced boxing and the number of matches they won:.

Part A : We are to find the approximate y-intercept of the line of best fit and state what does it represent.

From the graph, we note that

at x = 0, the value of y is approximately 3.

So, the approximate y -intercept of the line of best fit is 3.

It represents that before starting the matches, the students can win 3 matches without any practice.

Part B : We are to write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice.

From the graph, we note that the line of best fit passes through the points (2, 7) and (9, 18).

So, the slope of the line of best fit will be

[tex]m=\dfrac{18-7}{9-2}=\dfrac{11}{7}.[/tex]

Therefore, the slope-intercept form of the equation of the line of best fit is given by

[tex]y=mx+c\\\\\Rightarrow y=\dfrac{11}{7}x+3.[/tex]

Thus, the number of matches that could be won after 13 months of practice is

[tex]y=\dfrac{11}{7}\times13+3=23.42.[/tex]

That is, students can win 23 matches with 13 months of practice.

The approximate y-intercept is 35.25 and it represents the starting point on the graph. The equation for the line of best fit is y = 0.09x + 35.25. After 13 months of practice, the prediction is that the student could win approximately 36 matches.

Part A: The approximate y-intercept of the line of best fit is 35.25. The y-intercept represents the number of matches a student would have won without any months of practice. In other words, it is the initial starting point on the graph when the number of months practiced is zero.

Part B: The equation for the line of best fit in slope-intercept form is y = 0.09x + 35.25. To predict the number of matches after 13 months of practice, we substitute the value of x (number of months) into the equation. Therefore, y = 0.09(13) + 35.25 = 36.42.

Therefore, the prediction is that the student could win approximately 36 matches after 13 months of practice.

[tex]\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-6}{4-(-1)}\implies \cfrac{1-6}{4+1}\implies \cfrac{-5}{5}\implies -1 \\\\\\ \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-6=-1[x-(-1)]\implies y-6=-1(x+1) \\\\\\ y-6=-x-1\implies y=-x+5[/tex]

Answer:

MAD = 1.5.

Step-by-step explanation:

MAD is the Mean Absolute Deviation.

The MAD is a measure of the spread of the data.

The mean of these numbers is (1 + 4 + 5 + 6) / 4

= 16/4 = 4.

Now you subtract this from the individual values and take the absolute values:

1 - 4 = -3 (absolute value = 3).

4-4 = 0

5-4 = 1

6-4 = 2.

Adding 0+1+2+3 = 6.

The MAD = 6 / 4 = 1.5.

Answer:

Step-by-step explanation:  The mad is 1.5

in short, we simply graph her countertpart of y = 7, and then we test a point for "true" or "false" for that region.

say for example the point ( 3, 5 ), meaning x = 3, y = 5

y < 7

5 < 7  

is that really true?  5 smaller than 7?  yeap, so that region is the "true" region, and is the region we shade.

the line in the graph is a dashed one, because it does NOT include the points at the border, y < 7, "y" is less, not equals to, but less than 7.

Check the picture below.

I'm sorry but there is no graph, If you could put up the graph I can answer. Thank You!

[tex]\bf \cfrac{4}{~~\frac{1}{4}-\frac{5}{2}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{1}{4}-\frac{5}{2}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{(1)1-(2)5}{4}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{1-10}{4}~~}\implies \cfrac{\frac{4}{1}}{~~\frac{-9}{4}~~} \\\\\\ \cfrac{4}{1}\cdot \cfrac{4}{-9}\implies \cfrac{-16}{9}[/tex]

Factors:

15 = 1, 3, 5, 15

21 = 1, 3, 7, 21

The GCF is 3

That means that you can take three out of 15 and 21

15/3 = 5

21/3 = 7

so...

3 (5 + 7)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: D. F(x)= (x-1)^2+3

Step-by-step explanation:

Answer:

Option 4 is correct

Step-by-step explanation:

If the rate is compounded continuously, the formula used to find the future value is:

A= Pe^rt

Where A = Future Value

P= Principal amount

r = interest rate in decimal

t = time

For the given data:

A=?

P = $5000

r = 7% or 0.07

t = 6

Putting values in the above formula

A= 5000e^(0.07 *6)

A = 7609.81

So, Option 4 is correct.

Answer:

The Area of the first figure is 18[tex]in^{2}[/tex]

Step-by-step explanation:

Since the question states that both of the figures are similar we can use the information from figure 2 in order to find the area of figure 1. We do this by using the simple rule of three.

8[tex]in[/tex] ----> x

12[tex]in[/tex] ---> 27[tex]in^{2}[/tex]

Since the ratios (figures) are stated to be similar we just solve the rule of three as shown above.

[tex]\frac{(8in)(27in^{2} )}{12in} = x[/tex]

[tex]\frac{216in^{3} }{12in } = x[/tex]

[tex]18in^{2} = x[/tex]

Therefore the Area of figure 1 is 18[tex]in^{2}[/tex]

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer: 12

Step-by-step explanation: I know this website, this is the answer there

After 6 days, 20 grams will be left from the original 80 grams.

The half-life is the time it takes for half of the radioactive substance to decay. In this case, the half-life of ruthenium is given as 3 days. Starting with an initial quantity of 80 grams, we can calculate the remaining quantity after each half-life period.

After the first 3 days, one half-life will have passed, and half of the 80 grams will have decayed:
80 g / 2 = 40 g remaining.

After the second 3 days, another half-life will have passed, so another half of the remaining 40 grams will have decayed:
40 g / 2 = 20 g remaining.

Therefore, after 6 days, which corresponds to two half-life periods, 20 grams of the radioactive isotope of ruthenium will be left.

Answer:

The coordinates of the vertex are (-5, 41)

Step-by-step explanation:

For a quadratic function of the form

[tex]f(x) = ax ^ 2 + bx + c[/tex]

Where a, b and c are constants and represent the coefficients of the function, then the symmetry of the parabola always passes through its vertex.

In this case we have the following parabola

[tex]f (x) = -x2 - 10x + 16[/tex]

And we know that its axis of symmetry is the line [tex]x = -5[/tex]

Then we know that this axis of symmetry passes through the vertex of the parabola.

Therefore, the x coordinate of the vertex is -5.

To find the coordinate in y of the vertex, we substitute x = -5 in the function.

[tex]f (-5) = -(- 5) ^ 2 -10 (-5) +16\\\\f (-5) = 41[/tex]

Finally, the vertices are in the point (-5, 41).

Using kinematic equations, we determine that the accelerating police car will catch up to the speeding car moving at a constant velocity in 20 seconds.

To solve the problem of when a police car accelerating at 4 m/s² will catch up to a speeding car moving at a constant velocity of 40 m/s, we can use kinematic equations for motion. The speeding car's position over time is given by the equation x = vavgt, where vavg = 40 m/s is the average velocity. Since the police car starts from rest (vo = 0) and has an acceleration of 4 m/s², its position over time is given by the equation x = 0.5at².

We set the displacement of both cars equal to each other to find the time (t) when they are at the same position:
40t = 0.5(4)t².

This simplifies to: 40t = 2t², and by further simplification, we find that t = 20 seconds. Thus, it will take the police car 20 seconds to catch up to the speeding car.

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Answer:

Mean:79

Median:81

Standard deviation:15

Interquartile range:22

Mean (aka average)-79.8928

add all the numbers together and divide by how many numbers there are

sum of terms-2237

number of terms-28

Median- 81

I do it this way-

order the numbers from least to greatest

cross off the front number and back number until you are left with a middle

in this case there were 2

80 and 82

the average of those two is 81

Standard Deviation-15.37237

Interquartile Range-22.5

25th percentile-71

50th percentile-81

75th percentile-93

ANSWER

[tex] \frac{15x - 328}{40} [/tex]

EXPLANATION

The given expression is

[tex] \frac{3}{4} ( \frac{1}{2} x - 12) + \frac{4}{5} [/tex]

We expand to obtain;

[tex] \frac{3}{8} x - 9+ \frac{4}{5}[/tex]

The least common denominator is 40

[tex] \frac{15x - 360 + 32}{40} [/tex]

This simplifies to:

[tex] \frac{15x - 328}{40} [/tex]

Answer:

That’s wrong

Step-by-step explanation:

The perimeter of the shaded region is 39 ft.

The perimeter is the total length of all the sides of the shaded region. To find the perimeter, we need to add up the lengths of all the sides.

The perimeter of the shaded region is the sum of the lengths of all its sides.

Perimeter of a polygon = Sum of the lengths of all its sides

Perimeter of the shaded region = 14 ft + 6 ft + 15 ft + 4 ft

Perimeter of the shaded region = 39 ft

Therefore, the perimeter of the shaded region is 39 ft.

Answer:

t = 2 s= 96

t = 3 s = 64

t = 4 s= 32

t= 5 s = 0

t= 6 s = -32

t = 7 s = -64

t = 8 s = -96

t= 9 s = -128

Step-by-step explanation:

We have the equation of the position of the rocket as a function of time t.

[tex]f(t) = -16t^2 + 160t[/tex]

The instantaneous velocity of the rocket as a function of time is given by the derivation of the position with respect to time.

So

[tex]S(t)=\frac{df(t)}{dt} = -2*16t + 160\\\\S(t) = -32t+160[/tex]

[tex]s(1) = -32(1)+160=128\ ft/s\\\\s(2) = -32(2)+160=96\ ft/s\\\\s(3) = -32(3)+160=64\ m/s\\\\s(4) = -32(4)+160=32\ m/s\\\\s(5) = -32(5)+160=0\ m/s\\\\s(6) = -32(6)+160=-32\ m/s\\\\s(7) = -32(7)+160=-64\ m/s\\\\s(8) = -32(8)+160=-96\ m/s\\\\s(9) = -32(9)+160=-128\ m/s[/tex]

So

t = 2 s= 96

t = 3 s = 64

t = 4 s= 32

t= 5 s = 0

t= 6 s = -32

t = 7 s = -64

t = 8 s = -96

t= 9 s = -128

Final answer:

To match time values with the rocket's velocity after launch, we take the derivative of the position function f(t) to obtain the velocity function v(t) = -32t + 160. The corresponding velocity for each time value can be calculated by plugging the time into the velocity function.

Explanation:

The height of a rocket as a function of time after launch is given by f(t) = -16t2 + 160t, and we are asked to match each value of time elapsed with the rocket's corresponding instantaneous velocity. To find the instantaneous velocity, we need to take the derivative of the position function with respect to t, which represents time in seconds. The derivative of f(t) with respect to t is f'(t) = -32t + 160. This is the velocity function v(t), which gives the instantaneous velocity at any given time t.

At t = 2, the velocity v(2) = -32(2) + 160 = 96 feet/second.

At t = 3, the velocity v(3) = -32(3) + 160 = 64 feet/second.

At t = 4, the velocity v(4) = -32(4) + 160 = 32 feet/second.

At t = 5, the velocity v(5) = -32(5) + 160 = 0 feet/second. (This is the point at which the rocket reaches its peak and starts descending.)

At t = 6, the velocity v(6) = -32(6) + 160 = -32 feet/second (indicating the rocket is now falling back to the ground).

The values for t = 7, t = 8, and t = 9 can be calculated in a similar manner using the velocity function v(t).

Answer:

The answer is A.

Step-by-step explanation:

Rational numbers are any real numbers (including negatives) and -5 + -4 = -9 which is a real number, so it is rational.

Answer:

the answer is 15 to the nearest tenth

Answer:

add all the points together like

1+3+4+6+6+7+7+7+8+8+8+8+9+9+9+15= 115

the divide by the total number of elements we have. as so

115÷16= 7.18

rounding that to the nearest tenth is going to 7.2

Step-by-step explanation:

hope this helps

correct me if I'm wrong

The result of the calculation (6 * 10^2) / (3 x 10^-5) is 2 x 10^7, when written in standard form.

To solve the equation (6 * 10^2) / (3 * 10^-5), we first simplify both sides. 6 * 10^2 equates to 600, and 3 x 10^-5 equates to 0.00003. Therefore, we are left with the simple division: 600 / 0.00003.

To divide these two numbers, you would get a result of 20000000. However, the problem asks for the answer in standard form. Standard form is a way of writing numbers that are too large or too small to be conveniently written in decimal form. In standard form, 20000000 is represented as 2 x 10^7.

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Answer:

x = 3

Step-by-step explanation:

There are two ways to do this. The simplest way is to realize that the exterior angle (45x) = the sum of the two remote interior angles.

25x and 57 + x

45x = 25x + 57 + x                      Subtract 26x from both sides.

45x - 26x = 25x - 25x + 57   Combine

19x = 57                                Divide by 20

19x/19 = 57/19                     Do the division

x = 3

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

Second method.

The supplement of the 45x angle is 180 - 45x

Now add the three angles together.

180 - 45x + x + 57 + 25x = 180     Combine like terms.

180 + 57 - 45x + x + 25x = 180

237 - 19x = 180                              Subtract 237 from both sides.

- 19 x = 180 - 237                           Combine the right side

- 19x = -57

x = 3

Good thing you made me redo it. Sorry!! I made an error. I lost 1 of the xs.

Answer:

120

16

Step-by-step explanation:

Givens

Solution

4xyz = 4(3)(2)(5)

4xyz = 30 * 4

4xyz = 120

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

z^2 - x^2

5^2 - 3^2

25 - 9

16

For this case we have to:

Let "w" be the variable that represents the number of savings weeks.

We have that Landon's initial amount is $ 70.

We want to know how much money you have after 5 weeks, knowing that you save $ 7 each week, so be "y" the amount of money after "W" weeks:

[tex]y = 70 + 7w[/tex]

After 5 weeks:

[tex]y = 70 + 7 (5)\\y = 70 + 35\\y = 105\[/tex]

Answer[tex]y = 70 + 7w\\y = 105[/tex]

Answer:

Step-by-step explanation:

y = f(x) + n - moves the graph n units up

y = f(x) - n - moves the graph n units down

y = f(x + n) - moves the graph n units to the left

y = f(x - n) - moves the graph n units to the right

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

5.5 units to the right

y = f(x - 5.5) = |x - 5.5|