A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 5 cm more than the shorter leg and the hypotenuse 10 cm more than the shorter leg. How long should the sides of the triangle​ be?

Answer:

-2

6 = -2 -(-8) because -2 + 8 = 6.

Any time you see -(- you add.

The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).

Sequences are sets of elements characterized by at least a rule. In this case, the sequence shown is characterized by a function that generates even numbers equal or greater than 10. The function behind the sequence is shown below:

s = 10 + 2 · (n - 1)     (1)

Where n is the element index.

The sequence shown is defined by a function that generates even numbers equal or greater than 10, defined by the function s = 10 + 2 · (n - 1).

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Answer:

y = 2x + 10

Step-by-step explanation:

Hi there!

We are given the points (-7, -4) and (-6, -2) and we want to write the equation of the line that passes through these points in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, we need to find the slope (m) of the line

The slope can be calculated from 2 points using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points

We have everything we need to find the slope, but let's label the values of the points to avoid any confusion & and mistakes

\(x_1= -7\\y_1=-4\\x_2=-6\\y_2=-2\)

Substitute these values into the formula (note: remember that the formula has subtraction in it!)

m=\(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{-2--4}{-6--7}\)

Simplify

m=\(\frac{-2+4}{-6+7}\)

Add the numbers

m=\(\frac{2}{1}\)

Divide

m=2

The slope of the line is 2

We can substitute that in:

y = 2x + b

Now we need to find b

As the equation passes through both  (-7,-4) and (-6,-2), we can use either point to help solve for b

Taking (-6, -2) for example:

Substitute -6 as x and -2 as y into the equation.

-2 = 2(-6) + b

Multiply

-2 = -12 + b

Add 12 to both sides

-2 = -12 + b

+12  +12

___________

10 = b

Substitute 10 as b.

y = 2x + 10

Hope this helps!

Topic: Finding the equation of a line

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Answer:

Interval Notation : ( -3, ∞)

Step-by-step explanation:

graph:

The shortest distance between point P and Q is 9.4.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Given the data in the question;

Point P (-4,-2)

x₁ = -4

y₁ = -2

Point Q ( 4,3)

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √( ( 4 - (-4) )² + ( 3 - (-2) )² )

D = √( ( 4 + 4 )² + ( 3 + 2 )² )

D = √( 8² + 5² )

D = √( 64 + 25 )

D = √89

D = 9.4

Therefore, the distance is 9.4.

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Multiply the cost of the car by 1 + percent of markup:

38,000 x 1.08 = 41,040

The price is $41,040

Answer:

41040

Step-by-step explanation:

First find the markup

38000* 8%

38000*.08

3040

Add the markup to the original price

38000+3040

41040

Answer:

A= Wind and water eriosion; B=Water erosion

Why?:

The lesson

Answer:

C - A = erosion by wind and water; B = erosion by water

Step-by-step explanation:

hope this helps anyone that still needs it

Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

(a) If you decide to select based on proportion of 10% from each group, the number of patients selected from each group would be: Group A = (10/100) x 100 = 10 patients Group B = (10/100) x 30 = 3 patients Group C = (10/100) x 30 = 3 patients.

(b) The classified groups can be named as follows: Group A = 10 years of education or less Group B = More than 10 years but less than or equal to 20 years of education Group C = More than 20 years of education.

(c) The sampling method employed in the selection process was stratified sampling. Stratified sampling is a type of probability sampling technique where the population is divided into homogeneous subgroups or strata, and the researcher selects a simple random sample from each subgroup or stratum.

The researcher chooses a proportion of participants from each subgroup to represent the population as a whole, which allows for more precise estimates of the population parameters than simple random sampling.

The sample is selected randomly from the stratified sample, which ensures that the sample is representative of the population.

A variable is a characteristic or attribute that can take on different values. It is an observable and measurable property of an object or phenomenon, which can be used to describe and analyze it.

Variables are used in research to test hypotheses, determine relationships between different phenomena, and make predictions about future outcomes.

A parameter is a numerical summary of a population, which describes a characteristic of the population. It is an unknown constant that can only be estimated from a sample of data.

Parameters are used in inferential statistics to make conclusions about a population based on a sample of data.

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Answer:

Step-by-step explanation:

a) The equation relating A to the amount left of an initial amount Upper A 0 after time t is

A(t) = A0e^(kt)

b) It is found that 18 lb of A will reduce to 9 lb in 4.2 hr. It means that

A0 = 18

A = 9

t = 4.2

Therefore, substituting into the formula, it becomes

9 = 18e^(4.2k)

9/18 = e^(4.2k)

0.5 = e^(4.2k)

Taking ln of both sides of the equation, it becomes

Ln0.5 = ln e^(4.2k)

- 0.693 = 4.2k

k = - 0.693/4.2

k = - 0.165

The equation becomes

A(t) = 18e^(- 0.165t)

For A = 1(1 lb left), then

1 = 18e^(- 0.165t)

1/18 = e^(- 0.165t)

0.056 = e^(- 0.165t)

Taking ln of both sides, it becomes

Ln0.056 = ln e^(- 0.165t)

- 2.88 = - 0.165t

t = - 2.88/-0.165

t = 17.5 hours

After 17.5 hours, 1 lb would be left

The equation relating A to the amount left of an initial amount \(\rm A_0\) after time t is \(\rm A(t) = A_0.e^{kt}\).

After 17.5 hours there be only 1 lb​ left.

Given that,

Substance A decomposes at a rate proportional to the amount of A present. ​

We have to find,

Write an equation relating A to the amount left of an initial amount Upper A 0 after time t. ​

It is found that 18 lb of A will reduce to 9 lb in 4.2 hr. After how long will there be only 1 lb​ left?

According to the question,

1. Substance A decomposes at a rate proportional to the amount of A present. ​

\(\rm A(t) = A_0.e^{kt}\)

Here,  \(\rm A_0\) is the amount of A present before decomposition.

A is the amount left after decomposition after time t.

The equation relating A to the amount left of an initial amount \(\rm A_0\) after time t is \(\rm A(t) = A_0.e^{kt}\).

2. The amount of substance 18 lb of A will reduce to 9 lb in 4.2 hours.

Here, the amount of A present before decomposition \(\rm A_0\) is 18 lb.

And A is the amount left is 9 lb after decomposition after time t is 4.2 hours.

Therefore,

\(\rm A(t) = A_0.e^{kt}\\\\\rm 9=18\times e^{(4.2k)} \\\\\dfrac{9}{18} = e^{(4.2k)}\\\\ \dfrac{1}{2} = e^{(4.2k)}\\\\ \ 0.5= e^{(4.2k)}\\\\ Taking \ log \ on \ both \ sides\\\\log(0.5 )= 4.2k \\\\-0.693 = 4.2k\\\\k = \dfrac{-0.693}{4}\\\\k = 0.165\)

The time when only 1 lb left is,

\(\rm A = A_0 e ^{(.kt)}\\\\1 = 18 \times e^{-0.165t}\\\\\dfrac{1}{18}= e^{-0.165t}\\\\0.056 = e^{-0.165t}\\\\ Taking \ log \ on \ both \ sides \\\\log(0.056 )= {-0.165t}\\\\-2.88 = {-0.165t}\\\\t = \dfrac{-2.88}{-0.165}\\\\t = 17.5 \ hours\)

Hence, After 17.5 hours there be only 1 lb​ left.

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Answer:

$336.30

Step-by-step explanation:

Use the formula; Interest = Principal(rate)(time)

I = Prt

P: 1900

rate: 5.9% convert to a decimal  5.9/100 = .059

time: 3

I = 1900(0.059)(3)

I = $336.30

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:numbers

Step-by-step explanation:

numbrres and letters

Answer: 'X' = 24 degrees

Step-by-step explanation:

5 times 'X' = 120 degrees (because the formula is base times height divided by 2).

120 divided by 5 = 'X'

                            = 24

'X' = 24 degrees

The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

The system of equations is given as

2x - y + 2z = -6

-3y + z = -2

2x - 3z = -4

Subtract 2x - 3z = -4 from 2x - y + 2z = -6

This is represented as

(2x - y + 2z = -6) - (2x - 3z = -4)

This gives

- y + 5z = -2

Multiply - y + 5z = -2 by 3

-3y + 15z = -6

Subtract -3y + 15z = -6 from -3y + z = -2

This is represented as

(-3y + z = -2) - (-3y + 15z = -6)

This gives

-14z = 4

Divide by -14

z = -2/7

Substitute z = -2/7 in - y + 5z = -2

- y - 5 * 2/7 = -2

This gives

- y - 10/7 = -2

Rewrite as:

y = 2 - 10/7

Evaluate

y = 4/7

Substitute z = -2/7 in 2x - 3z = -4

2x - 3 * 4/7 = -4

This gives

2x - 12/7 = -4

So, we have:

2x = 12/7 - 4

Evaluate

2x = -16/7

Divide by 2

x = -8/7

Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7

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Answer:

We can use the formula for the area of a circle and the information provided to find the approximate area of the circle.

The formula for the area of a circle is A = πr², where r is the radius of the circle.

We know that the distance from the center of the circle to the chord AB is 6 and the length of the chord AB is 10.

We can use the Pythagorean theorem to find the radius of the circle.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, we can use this theorem to find the radius of the circle as follows:

r² = (length of the chord /2)² + (distance of the chord to the center)²

r² = (10/2)² + 6²

r² = 25 + 36

r² = 61

r ≈ 7.8

Now that we know the radius of the circle, we can use the formula for the area of a circle to find the area of the circle:

A = πr²

A ≈ π (7.8)²

A ≈ 191.8

The approximate area of the circle is 192 square units.

Answer:

18 goes in the box (brainliest plz

Step-by-step explanation:

The value of side EA is,

EA = 16.9

We have to given that;

Circle E with diameter CD and radius EA.

And, AB is tangent to E at A.

Here, AB = 34 and EB = 38

Hence, By using Pythagoras theorem we get;

AB² + AE² = EB²

34² + AE² = 38²

1156 + AE² = 1444

AE² = 1444 - 1156

AE² = 288

AE = √288

AE = 16.9

Thus, The value of side EA is,

EA = 16.9

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The total budget for their student film $800

11% of total budget = (11/100) * total budget

= 0.11 * total budget

Let P be the amount the group spent on props.

Now we can write the equation:

P = 0.11 * total budget

We also know that this group spent $712 on equipment. Let E be the amount they spent on equipment.

So it looks like this:

E=$712

Your total budget is the total cost of your equipment and props. This can be written as:

Total Budget = E + P

Plugging in the E and P values, we get:

Total Budget = $712 + 0.11 * Total Budget

Simplifying this equation, we get:

0.89 * total budget = $712

Dividing both sides by 0.89 gives:

Total budget = $800

So her student film had a total budget of $800. 

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Answer:

x*4-6=10
is a ecuation
x * 4 - 6 = 10
x * 4 = 16
x = 16/4
x = 4

Answer:

Step-by-step explanation:

A=19000( 1 + 0.03)^8

A=24068.6315464

A≈24100

Round to the nearest hundred dollars

Answer:

(0,4)

Step-by-step explanation:

Multiply each point by 1/3

0 x 1/3 = 0

12 x 1/3 = 4

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:45%

Step-by-step explanation:

Answer:

The answer is the first option because 2÷2=1 and 10÷2=5

Answer:

C

Step-by-step explanation:

The correlation coefficient is too weak to show anything

Answer: the volume V generated by rotating the regions 281.49

Step-by-step explanation:

Given that;

the radius of the shell ⇒ (4 - x)  

then the circumference of the shell is 2π( 3 - x )  i.e 2π × radius

y = 0 and x = 2

the height of the shell is 3x⁴

Now the volume of the solid obtained by rotating

the bounded region about x = 4 is;

V = ²∫₀ 2π ( 4 - x ) ( 3x⁴ ) dx

= ²∫₀ 2π ( 12x⁴ - 3x⁵ ) dx

= 2π [ 12x⁵/5 - 3x⁶/6 ]₀²     {BY FTC -2]

= 2π [ (12×32)/5 - (3×64)/6 ] - ( 0-0) ]

= 2π [ 76.8 - 32]

= 2π [ 44.8 ]

= 281.49

Therefore the volume V generated by rotating the regions 281.49

Answer:

80 degrees

Step-by-step explanation:

Sum of the interior angles of a triangle = 180

a + 50 + 50 = 180

a = 80

For every 1 orange in the fruit bowl there are three bananas.

According to the question,

We have the following information:

In the fruit bowl there are 12 bananas, 8 apples and 4 oranges.

Now, in order to find the number of bananas in this fruit bowl for 1 orange can be as written below:

4 oranges = 12 bananas

Now, to find the number of bananas for 1 orange, we will divide the total number of bananas by the number of oranges.

So, we have the following expression:

1 orange = 12/4 bananas

1 orange = 3 bananas

Hence, for every 1 orange in the fruit bowl there are three bananas.

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