(x −8, y + 5) y(5-5)

The equation of the line that forms the hypotenuse is y = -3/4 x + 5

A line is defined as the shortest distance between two points. The equation of a line in slope-intercept form is expressed as:

y = mx + b

where:

m is the slope

b is the intercept

The coordinate points that gives the largest distance will be used. the points form the largest distance;

Using the coordinate points A(0,5), B(4,2)

Slope = 2-5/4-0
Slope = -3/4

The intercept is (0,5)

Determine the equation

y = mx + b

y = -3/4 x + 5

This gives the required equation.

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The integer that can be used to represent the difference in the two temperatures is -37°.

From the information, the temperature in Anchorage, Alaska was -13 degrees and on the same day, there was a Polar Vortex over the northeast, and there was a recorded temperature of -24 degrees in Caribou, Maine.

Therefore, the integer can be used to represent the difference in the temperatures will be:

= -13 + (-24)

= -13 - 24

= -37

The difference in temperature is -37°.

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Previously available balance = $320.39

Deposit made by Mrs. Hammonds = $100

Cheques used for withdrawal,

$97.54

$48.27

The new balance = $320.39 + $100 - $97.54 - $48.27

= 420.39 - 145.81

= 274.58

So, the new balance in her account is $274.58.

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The correct responses for the arithmetic and exponential sequence and function are;

1. First part; 32 pennies

Second part; Approximately 50 days

2. 24.6 gallons

3,738.5 minutes

3. $67.2

Approximately 24 months

4. 1106.14 gallons

66.56 minutes

The difference is 1 is an arithmetic sequence while 3 is an exponential function

An arithmetic sequence is a group of numbers in which the difference between subsequent terms is a constant

1. The given parameters are;

The initial amount Savannah placed in the piggy bank = 5 pennies

The amount given to Savannah each day = 3 pennies

Required;

First part;

The amount Savannah will have after 10 days

Solution;

The mathematical model for the situation is an arithmetic sequence or progression

The equation for an arithmetic progression is;

[tex]a_n = a_1 + (n - 1) \times d[/tex]

Where;

[tex]a_n[/tex] = The amount after n days

[tex]a_1 [/tex] = The first amount Savannah placed in the piggy bank = 5 pennies

n = The number of days

d = The common difference between the amount present in consecutive days = 3 pennies

The amount after 10 days is therefore;

[tex]a_{10} = 5 + (10 - 1) \times 3=32[/tex]

The money after 10 days is 32 pennies

Second part;

The number of days it would take for there to be $1.50 in the piggy bank.

Solution;

100 pennies = $1.00

Therefore;

$1.50 = 150 pennies

Which gives;

150 = 5 + (n - 1) × 3

(n - 1) × 3 = 150 - 5 = 145

(n - 1) × 3 = 145

n - 1 = 145 ÷ 3

n = 145 ÷ 3 + 1 ≈ 49.3 ≈ 50

It will take approximately 50 days for the amount in the piggy bank to be $1.50

2. The volume of the pool = 1,500 gallons

The initial amount of water in the pool = 5 gallons

The rate at which water enters the pool = 2 gallons in 5 minutes

Required;

First part

The volume of water in the pool after 50 minutes

Solution;

2 gallons in 5 minutes = (2/5) gallons/minute = 0.4 gallons/minute

Therefore;

[tex]a_{50} = 5 + (50 - 1) \times 0.4 =24.6[/tex]

After 50 minutes, 24.6 gallons will be in the pool

Second part;

The time it will take to fill the pool is given by the equation;

[tex]1500 = 5 + (n - 1) \times 0.4[/tex]

number

Which gives;

n = 3738.5

It will take 3,738.5 minutes to fill the pool

3. The formula for finding the amount in the account is the compound interest formula;

[tex]\displaystyle{A = P\cdot (1 + r)^n }[/tex]

Where;

A = The amount in the account after n months

P = The initial amount in the account = $50.0

r = The interest rate = 3.0%

n = The number of periods (months)

After 10 months, we have;

[tex]\displaystyle{A = 50 \times (1 + 0.03)^{10} \approx 67.2 }[/tex]

The amount in the account after 10 months is therefore, approximately $67.2

Second part;

Double the initial amount is 2×$50 = $100

Which gives;

[tex]100 = \displaystyle{50 \times (1 + 0.03)^{n} \approx 67.2 } [/tex]

Which gives;

n ≈ 23.45

Therefore it will take approximately 23.45 months or approximately 24 months for the amount to double

4. Using the exponential function formula, we have;

Number of 5 minutes in 50 minutes = 10

[tex] \displaystyle{1500 \times (1 - 0.03)^{10} \approx 1106.14} [/tex]

The water remaining after 50 minutes is approximately 1106.14 gallons

The time it takes for there to be less than 1,000 gallons in the pool is given as follows;

[tex] \displaystyle{ 1000= 1500 \times (1 - 0.03)^{n}} [/tex]

Which gives;

n = 13.3

Therefore;

The water in the pool will be less than 1000 gallons after 13.3, 5 minute periods or 13.3 × 5 minutes≈ 66.56 minutes

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Answer:

104 ;108;112;116;120;124;128;132;136 ;140;144;148

Answer:

104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148

Step-by-step explanation:

A multiple of 4 can generally be defined as divisible by 4.

We can define an equation for it: [tex]4n[/tex] where n is an integer.

From here we can see that if n=25, we have a number of 100 which indeed is a multiple of 4 since dividing it by 4 results in 25 which makes sense since 100 is the result of 4 * 25.

Now starting from 100 (excluding 100 since between 100 and 150), or n=25, we can increase the value of the number by 4, or n by 1 which is doing the same thing.

So start at 100, then 100+4 = 104, then 104+4=108 and so on... until you reach a number greater than or equal to 150, and if it is 150 make sure to exclude it since it says between 100 and 150 which implies it's excluding the end points.

This gives us a result of: 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148

When you solve   w = __Z,

you will get the value of X ( but there should be a variable' X' in the blank space). This is the method in Algebra.

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The graph will be a shaded region above and including the straight line y = (3/2)x-1.

We are asked to graph the inequality y ≥ (3/2)x-1. Describing the graph of an inequality, it will be a region on one side of a straight line.

So first we need to sketch the straight line, y = (3/2)x-1.

So find two points (x, y) satisfying this equation of line because a line need at least two points.

x       y  

0       -1

2/3     0

So first sketch a line joining the points (0, -1) and (2/3,0). This line will lie below the origin. That is, origin lies on the region above this line.

So the line y = (3/2)x-1 divided the plane into two regions, one of which represents the inequality y ≥ (3/2)x-1. So to find this required region we will check if origin lies in the region for inequality.

Substituting (0, 0) into y ≥ (3/2)x-1,

0 ≥ -1, which is true.

Thus in the graph, the region for inequality is the region where the origin lies. Hence shade the region above the line y = (3/2)x-1. This is the graph of the inequality y ≥ (3/2)x-1.

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The 8 consecutive numbers are 12, 13, 14, 15, 16, 17, 18, 19 respectively.

Algebraic expressions are simply described as arithmetic expressions that are made up of arithmetic terms, constants, variables, factors and coefficients.

These expressions are also made up of arithmetic operations which includes;

Based on the information given, we have;

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7 = 124

Now, collect like terms, we get;

8x + 28 = 124

8x = 124 - 28

Subtract like terms

8x = 96

To determine the value of x, make it the subject by dividing both sides by 8, we have;

8x/8 = 96/8

x = 12

Then,

x = 12

x + 1 = 13

x + 2 = 14

x + 3 = 15

x + 4 = 16

x + 5 = 17

x + 6 = 18

x + 7 = 19

Hence, the values are 12, 13, 14, 15, 16, 17, 18 and 19 respectively.

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Answer:

The other number is 120.

Step-by-step explanation:

30×360 =90xx

x=(30×360)/90

x=120

(HCFXLCM= Product if the two

numbers)

Part (a)

We can add the total number of males and the total number of students who take biology, and then subtract the intersection.

[tex]42+34-14=62[/tex]

Part (b)

There are 90 people in all, so the probability is [tex]\frac{62}{90}=\frac{31}{45}[/tex]

Based on the mass of the molecules of oxygen that the scientist determined, the number of significant digits in the solution is 2.

When counting the significant figures in a number, the first rule is that any digit that isn't a zero would be considered a significant digit.

Zeros that are trailing in a number however, and are not considered decimals, are not counted as significant digits. This means that both the 2 number 2s in the figure will be significant figures.

The three zeros are trailing but not decimals so they are not considered significant. This means that in the mass of oxygen according to the scientist, has only 2 significant figures.

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Answer:

Substitute x = 4 into f(x).

f(4) = -7(4+2)

= -28-14

= -42

The amount of money that Britta will pay is; SEK2500

Let the amount paid by Britta scabetala be x

Now, we are told that Britta scabetala half as much as Agda. Thus;

Amount paid by Agda = 2x

Now, Cornelia must pay SEK 1,500 less than Britta. Thus,

Amount paid by Cornelia = x - 1500

Agda must pay five times as much as Cornelia. Thus;

2x = 5(x - 1500)

2x = 5x - 7500

5x - 2x = 7500

3x = 7500

x = 7500/3

x = SEK2500

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The slope of the given line is m =25.

The two points of the given line is (3,75) and (4,100).

The slope of the given line can be found using the formula point-slope equation.

y₂-y₁ = m(x₂-x₁)

We need to find the slope, so let us rearrange the equation,

m =  y₂-y₁ / x₂-x₁

where (x,₁y₁) and (x₂,y₂) is (3,75) and (4,100) respectively

So let us substitute these values in the above equation, we get

m = 100 - 75 / 4 -3

m = 25/1

m = 25

Therefore, the slope of the line passing through the point (3,75) and (4,100) is 25

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The tax that is paid on the item purchased to the nearest cent is $0.13,

Tax is a form of transfer of wealth from individuals or businesses to the government. Taxes increase the cost of a good or service. When tax is levied on a good or service, the tax is paid when the good or service is paid for. It is added to the purchase price of the good or service.

In order to determine the tax paid, multiply the cost of the item by the tax rate. Multiplication is the process that is used to determine the product of a number. The sign that denotes multiplication is ×.

Tax paid = cost of the item x tax rate

$3 x 4.4%

$3 x 0.044 = $0.13

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Answer:

A. Opens up with a vertex at (-3, -4)

Step-by-step explanation:

y = (x + 3)² - 4

Vertex: (-3, -4)

Min: y = -4

min = up

I hope this helps!

The given equation represents the equation of a parabola and it represents the curve open up with vertex (-3, -4).

Hence, option A is correct.

A parabola is a U-shaped plane curve in which any point is an equal distance from both a fixed point (known as the focus) and a fixed straight line (known as the directrix).

The given equation is:

y = (x +3)² - 4

Since we know that,

An equation of the parabola is

y = a(x - h)² + k

Where (h, k) is the vertex.

Comparing these equations we get

a = 1

h = -3

k =  -4

So, its vertex is (h, k) = (-3, -4)

Hence,

The graph opens up with vertex (3, -4).

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We calculate the ratio (in percentage) of 5.2cm to 4cm

5.2 : 4 = 1.3

Because 4cm is 1.3x less than 5.2, its percentage must also be 1.3x less than 96%

-> 4cm = 96% : 130% = approx. 73.85% (2 d.p)

Answer:

$8.50 per pound

Step-by-step explanation:

[tex]44.20 \div 5.2 = 8.50[/tex]

The numerical value of the third number in an improper and mixed fraction form is 93/10 and 9 3/10 respectively.

Given the data in the question;

Let 'x' represent the third number

First, convert the numbers form mixed fractions to improper fractions

Sum of the three numbers = 24 4/5 = ( 24×5 + 4 )/5 = 124/5

First number = 8 2/3 = ( 8×3 + 2 )/3 = 26/3

Second number =  6 5/6 = ( 6×6 + 5 )/2 = 41/6

Now, to determine the third value, equate the sum of the three numbers to the total and solve for x

26/3 + 41/6 + x = 124/5

( 156 + 123 )/18 + x = 124/5

( 279 )/18 + x = 124/5

31/2 + x = 124/5

x = 124/5 - 31/2

x = ( 248 - 155 )/10

x = ( 93 )/10

x = 93/10

x = 9 3/10

Therefore, the value of the third number is 93/10 or 9 3/10.

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Answer:5.3ft

Step-by-step explanation: 1. find the sum of the rest of the sides

14.9+19.9+6.5+39.8+6.5+14.9+14.9=117.4

2. subtract 117.4 from 122.7 to find the missing side length

122.7-117.4=5.3

Answer:

896

Step-by-step explanation:

28x32 gives u 896 so that will b your product

Answer:

Yes, this is an arithmetic sequence.

The difference is -3, so a(n+1) = a(n) - 3

The 21st term is -53, calculated as follows:

a(21) = 7 + (21 - 1)(-3) = -53

The next three terms are -5, -8, and -11.

Answer: x = -5

Both points have the same x value and only have different y values, meaning that the equation of the line must be x = -5.

The number of times larger that the diameter of cell C is more than the diameter of cell D is 9.2 × 10^-6

It should be noted that standard notation simply means writing in standard form. This is illustrated as a × 10ⁿ.

In this case, the cells are measured using this method: Cell C is 7.76 × 10^ {-2} and Cell D is 8.4×10^ −4 centimeters

It should be noted that in order to know the number of times that the cell is larger will be gotten by dividing. This will be;

= (7.76 × 10^-2) / (8.4 × 10^-4)

= 9.2 × 10^-6

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Answer:

x(-5.3,0)

y(0,4)

slope 0.75

Step-by-step explanation:

Answer:

it

should be something along the lines of math

Answer: 1/2

Step-by-step explanation:

its greater than 4/7

1/7 would be greater

the kangaroo real height is 3 feet and shadow height is 5 feet

if the height of the tree is 7 feet so the real height of the tree is 5 feet