In ΔRST, \text{m}\angle R = (x+17)^{\circ}m∠R=(x+17) ∘ , \text{m}\angle S = (2x-2)^{\circ}m∠S=(2x−2) ∘ , and \text{m}\angle T = (5x+5)^{\circ}m∠T=(5x+5) ∘ . Find \text{m}\angle S.m∠S.

Answer:

it decreeased by 1.7% rounded to the nearest tenth

The simplification of the given expression 5(a -2b) -3(a -2b) is

2(a - 2b).

According to the given question.

We have an expression 5(a -2b) -3(a -2b).

As we know that, the simplification of an expression means to write an equivalent expression which contains no similar terms.

Therefore, the simplificantion of the expression  5(a -2b) -3(a -2b) is given by

5(a -2b) -3(a -2b)

= 5a - 10b - 3a + 6b         (by distributive rule)

= 5a -3a -10b + 6b

= 2a -4b                              (adding and subtracting the like terms)

= 2(a - 2b)

Hence, the simplification of the given expression 5(a -2b) -3(a -2b) is

2(a - 2b).

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The eighth term of the given geometric sequence is: [tex]\frac{5}{64}[/tex]

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 10, 5, 2.5, ...

Here, [tex]\frac{5}{10}=\frac{2.5}{5}=\frac{1}{2}[/tex]

Thus, the given geometric sequence has a₁ = 10 and r = 1/2

The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 8, a₈ = [tex]\frac{10}{2^7}=\frac{5}{2^6} = \frac{5}{64}[/tex]

Hence, The eighth term of the given geometric sequence is: [tex]\frac{5}{64}[/tex]

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Answer:

Slope is -2/5

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1)

I used points (5,-3) (-10,3)

Answer:

C (Third one) -6, -10/3, 1/4, Sqr6, 3.9

Step-by-step explanation:

-6 = -6

-10/3 = -3.33333333

1/4 = 0.25

Sqr6 = 2.4494...

3.9 = 3.9

Answer:

4 / -2 / 3

Step-by-step explanation:

The number of bandages made from the fabric is 35 and the number of hours traveled is 14 hours

The given parameters are

Area of a bandage = 2 4/5 square inches

Area of fabric = 98 square inches

The number of bandages made from the fabric is calculated as

n = Area of fabric/Area of a bandage

This gives

n = 98/(2 4/5)

Evaluate

n = 35

Hence, the number of bandages made from the fabric is 35

Here, we have

Speed = 3 1/3 miles per hour

Distance = 46 2/3 miles

The number of hours traveled is calculated as

Time = Distance/Speed

So, we have

Time = (46 2/3)/(3 1/3)

Evaluate

Time = 14

Hence, the number of hours traveled is 14 hours

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The relationship between 5 tablespoons of cocoa per 2 cups of milk is proportional(multiplicative). Let's represent the amount of tablespoons of cocoa we need for 1 cup of milk with x.

We can divide 5 by 2 in order to get x tablespoons for 1 cup of milk.

5 / 2 = 2.5

So, you need 2.5 tablespoons of cocoa for 1 cup of milk :)

The equation relating L to D will be L = 12 + D.

From the information, the construction crew is lengthening a road that originally measured 12 miles and the crew is adding one mile to the road each day.

Let L be the length (in miles) after D days of construction.

Therefore, the equation will be:

L = 12 + D

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The polynomial function f(x) = (x - a)(x - b) is a quadratic function and values of a and b are 1 and - 1 respectively.

A polynomial is an algebraic expression that consists of variables and constants connected by arithmetic operations.

Given the polynomial function f(x) = (x - a)(x - b) and if we observe the graph we can see that the polynomial has two roots,

one at x = 1 and another at x = -1.

If x = 1 is a root of this polynomial we can write this in factor form as.

x = 1.

x - 1 = 0

And

x = -1.

x + 1 = 0.

∴ f(x) = (x - 1)(x + 1).

f(x) = x² - 1², So it is a quadratic function.

∴ Values of a and b are 1 and - 1.

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x = 345.54545454 is  the value of x to the nearest tenth. 1086/π = x

What is π ?

Why is pi so important?

1086/π = x

Put value of π = 22/7

1086/22/7 = x

x = 49.363636 × 7

x = 345.54545454

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Augusto has 24 ways to put one coin in each pocket.

Permutation:

Permutation is the way arranging the objects or numbers in order.

It can be calculated using the formula,

ₙPₓ = n!/(n - x)!

where,

ₙPₓ   = number of combinations

n = total number of objects in the set

x = number of choosing objects from the set

Given,

Augusto has 3 pockets and 4 different coins.

Here we need to find how many ways can he put one coin in each pocket.

We know that,

Augusto has 4 different coins that he is choosing 3 at a time.

So, it can be written as,

The number of ways to put one coin in each pocket is the permutation of 4 coins taken 3 at a time.

Therefore, the number of permutations is calculated as,

=> ₄P₃ = 4! / (4 - 3)!

=> ₄P₃ = 4! / 1!

=> ₄P₃ = 4 x 3 x 2 x 1

=> ₄P₃ = 24

Therefore, there are 24 ways to put one coin in each pocket.

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The numbers from least to greatest is 72%, 5/4. 1 3/4. 3.48

To order a number from least to greatest, the numbers would be arranged in ascending order. The farther a positive number is from zero on the number line, the greater the number is. For example, 100 is greater than 1.

The numbers are not written in equivalent forms. Some are written as improper fractions, percentages, decimals and mixed fractions.

An improper fraction is a fraction where the numerator is greater than the denominator. A mixed fraction is a non-integer that is made up of a whole number and a proper fraction. Percentages are numbers written as a quantity out of 100. A decimal is a number that is made up of integers and non-integers.

To order the numbers, all the numbers would be converted to decimals:

5/4 = 1.25

1 3/4 = 1.75

72% = 72/100 = 0.72

The numbers from least to greatest is: 72%, 5/4. 1 3/4. 3.48

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The equation of the line 4x = 2 + y expressed in slope-intercept form is y = 4x - 2 with a slope equal to 4.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The slope-intercept form of the equation of a line is given by the formula:

y = mx + b

where m is the slope of the line

b is the y- intercept

Given the equation of the line 4x = 2 + y, express it in slope-intercept form by isolating the variable y in one side.

4x = 2 + y

y = 4x - 2

Hence, the equation of the line in slope-intercept form is y = 4x - 2 where the slope, m, is equal to 4.

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Answer:

Again the answer is D

Step-by-step explanation:

It will take 0.006 seconds for bat's cry to reach its prey and echo back.

Sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.

Given is the speed of sound which is 330 m/s. The prey is 1 meter away from the bat.

The time it takes a bat's cry to reach its prey and echo back can be calculated using the formula -

time = distance / speed

The distance covered by the sound as it reaches the prey and echo back is equal to 2 x 1 = 2 meters.

Speed of sound → 330 m/s.

So, the time taken will be -

t = 3/330

t = 0.006 s

Therefore, it will take 0.006 seconds for bat's cry to reach its prey and echo back.

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The equation of the line in standard form passing through the points (2 , 3) and (4 , 5) is x - y = -1.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.

Given two points, (2 , 3) and (4 , 5), use the two-point form to generate the equation of the line.

y - y2 = [(y2 - y1)/(x2 - x1)] (x - x2)

y - 5 = [(5 - 3)/(4 - 2)](x - 4)

y - 5 = (2/2)(x - 4)

y - 5 = x - 4

To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

y - 5 = x - 4

x - y = -5 + 4

x - y = -1

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The following set of numbers, 44, 46, and 91, cannot be the measures of the sides of a triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 44, b = 46, and c = 91

a + b > c     44 + 46 > 91     90 > 91     False

a + c > b     44 + 91 > 46     135 > 46     True

b + c > a     46 + 91 > 44     137 > 44     True

If at least one of these three statements is not true, then the set of numbers is not a valid measure of the sides of a triangle.

Hence, the set of numbers 44, 46, and 91 can not be the measure of the sides of a triangle.

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The equation of the circle that passes through the point (-5 , 0) and has a center located at the origin is x^2 + y^2 = 25

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-5 , 0).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(-5 - 0)^2 + (0 - 0)^2

radius= √25

radius = 5

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = 5

(x - 0)^2 + (y - 0)^2 = 5^2

x^2 + y^2 = 25

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(i) 6 litres = 6000 cm³

(ii) The rate at which the water is now flowing from the tap is 50cm³/second

From the question, we are to convert the given value in litres to cm³

(i) We are to determine the value of 6 litres in cm³

NOTE: 1 litre = 1000 cm³

Thus,

6 litres = 6 × 1000cm³

= 6000 cm³

(ii)

From the given information,

It takes 60 seconds to fill a 6 litre watering can from the tap

That is,

At a rate of 6000 cm³ per 60 seconds

Now,

The rate at which water flows from the tap is halved

Then,

The new rate will be

6000/2 cm³ per 60 seconds

= 3000 cm³ per 60 seconds

Thus,

The new rate is 3000/60 cm³/second

= 50 cm³/second

= 50cm³/second

Hence, the rate at which the water is now flowing from the tap is 50cm³/second

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Answer:that is already in slope intercept form

Step-by-step explanation:

Answer:

y = x + 17

Step-by-step explanation:

Given equation,

→ y = x + 17

Now we have to,

→ write it in slope-intercept form.

The slope-intercept form,

→ y = mx + b

Let's solve the given problem,

→ y = mx + b

→ y = x + 17

(It's already in slope-intercept form)

Hence, the answer is y = x + 17.

Answer:

The solution h < 5.5 means that Melanie can rent the bike for no more than 5.5 hours.

Hope this helps :)

Explanation and Check part below.

Step-by-step explanation:

1. Isolate the variable by doing the inverse operation which is in this case subtracting 6 on bothsides of the equation.

8h + 6 < 50

- 6 - 6

8h < 44

2. Dive both sides of the equation by 8.

8h < 44

--- ----- <--------- fraction bar, divide

8 8

h < 5.5

Answer:

See the attached photos for help!

Step-by-step explanation:

I also recommend looking up desmos graphing calculator to actually see the graphs!

If you need more in depth assistance on this, feel free to let me know :]

Answer:

23 cm, 25 cm

Step-by-step explanation:

Let the Width be W cm.

Since the Length and Width are consecutive odd integers we know that the length:

Length = (W + 2) cm

Perimeter of Rectangle = Sum of all sides = 2 x Length + 2 x Width

So rewriting the perimeter , we have:

2W + 2(W+2) = 96 cm

Now lets solve for W to get the width.

2W + 2W + 4 = 96 cm

4W + 4 - 4 = 96 - 4

4W = 92 cm

W = 23 cm

Next, we know that the length = (W + 2) cm

Therefore the length = 23 + 2 = 25 cm

The given system of equations do not have a solution since their related line equations have the same slope.

The given system of equations is:

-x + 5y = 3   .......... (1)

2x - 10y = 4   ........(2)

In Equation (1), add both sides by (-5y)

-x + 5y + (-5y) = 3 + (-5y)

-x = -3 - 5y

Multiply by (-1)

x = 3 + 5y

Substitute x = 3 + 5y into equation (2)

2x - 10y = 4

2.(3 + 5y) - 10y = 4

6 + 10y - 10y = 4

6 = 4 (False)

Since the last equation is false, we might suspect that the given system of solution does not have solutions.

We need to check the slope of both equations:

-x + 5y = 3

⇒ 5y = x + 3

⇒ y = 1/5 x + 3/5

2x - 10y = 4

⇒ -10 y = -2x + 4

⇒ y = (2/10) x - 4/10

⇒ y = 1/5 x - 2/5

We can see that both equations have the same slope, i.e. 1/5.

Hence, they do not have solutions since the lines are parallel to each other.

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The set of numbers that are written in order from least to greatest is: 15.75, √250, 4², 50/3, 16.7 x 10³.

You need to solve for the quantities given to see which numbers are the smallest and which are the largest.

15.75 = 15.75

√250 = 15.8

4² = 16

50 / 3 = 16.7

16.7 x 10³ = 16,700

The order from least to greatest is therefore:
15.75, √250, 4², 50/3, 16.7 x 10³.

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f (5) =  -7  is the output for the given input .

How can you tell whether a function is linear or not?

f(x)= -4 x+1

Put x = -2    ⇒   - 4 × -2  + 1

                ⇒   - 8 + 1

                ⇒   - 7

Therefore f (5) =  - 7

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Answer:  The price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.

Step-by-step explanation:  Given that lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50 whereas Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25.

We are to find the price per pound of apples and bananas.

The cost per pound of apples is represented by x dollars and the cost per pound of bananas is represented by y dollars.

Then, according to the given information, the system of equations describing the situation is as follows:

Multiplying equation (i) by 2, we have

and multiplying equation (ii) by 3, we have

To eliminate y, we subtract equation (iv) from equation (iii) and we arrive at

From equation (i), we get

Thus, the price per pound of apples is $ 1.25 and the price per pound of bananas is $ 0.75.

Answer:Bro the answer is price per pound of apples is $1.25

and the price per pound of bannanas is $0.75

Answer:8.75

Step-by-step explanation:

3/4=0.75

0.75+8=8.75