The angles of a triangle are in the ratio 2:8:5 find the size of each side

Answer:

You would do 9 x 3 first.

Step-by-step explanation:

PEMDAS. There is subtraction and multiplication, and multiplication is before subtraction.

P- Parenthesis

E- Exponent

M- Multiplication

D- Division

A- Addition

S- Subtraction

 Hope this helps!!! 〜(￣▽￣〜)

The values of u and v that makes △QRS and △IKJ congruent triangles are u = 7 and v = 3

The triangles are given as

△QRS and △IKJ

The statement △QRS≅△IKJ means that

The triangles △QRS and △IKJ are congruent triangles

This means that the corresponding sides are congruent

So, we have the following equations:

v + u + 15 = 10u - 15v

-4u + 2v + 99 = 7v + 8u

Evaluate the like terms

So, we have

9u - 16v = 15

12u + 5v = 99

Make u the subject in 12u + 5v = 99

So, we have

u = (-5v + 99)/12

Substitute u = (-5v + 99)/12 in 9u - 16v = 15

9(-5v + 99)/12 - 16v = 15

So, we have

9(-5v + 99) - 192v = 180

Open brackets

-45v + 891 - 192v = 180

Evaluate the like terms

-237v = -711

Divide by -237

v = 3

Substitute v = 3 in u = (-5v + 99)/12

u = (-5 x 3 + 99)/12

Evaluate

u = 7

Hence, the values are u = 7 and v = 3

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EXPLANATION

Since the initial amount of money was of $29,820, and the account earns interest rate by a reason of 7% per year, we can use the simple interest rate equation as shown as follows:

Where P=Principal= 29,820, r=rate in decimal form=7/100=0.07 , t=time in years=4,

Plugging in the numbers into the expression:

Multiplying numbers:

Adding the Interest to the Initial Capital: 29,820+8,349 = 38,169

In conclusion, Colin will have $38,169 after 4 years

The coordinates of the triangle FGH after dilating by 1/2 is F'(-2, -5/2), G'(-3/2, -1), and H'(-1/2, -3/2)

From the question, the given parameters are the vertices of Triangle FGH

The vertices are represented as

F(-4, -5), G(-3, -2), and H(-1, -3).

Also, from the question, we have

The scale factor of dilation is

k = 1/2

The above implies that

k represents the scale factor of dilation

The coordinates after the dilation is calculated as

Image of dilation = Vertices of the triangle x Scale factor

Substitute the known values in the above equation

So, we have

Image of dilation = [F(-4, -5), G(-3, -2), and H(-1, -3)] x 1/2

Evaluate the products

So, we have

Image of dilation = F'(-2, -5/2), G'(-3/2, -1), and H'(-1/2, -3/2)

Hence, the image after the dilation is F'(-2, -5/2), G'(-3/2, -1), and H'(-1/2, -3/2)

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Answer:

his age would be 72.

300-84=216

216÷3 is 72

Answer:

A' = (6, 3)

B' = (1, 1)

C' = (8, 7)

Step-by-step explanation:

Vertices of triangle ABC:

Given mapping rule:

(x, y) → (x + 4, y + 6)

This notation tells you that the x-coordinate is translated 4 units to the right, and the y-coordinate is translated 6 units up.

Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':

⇒ A' = (2 + 4, -3 + 6) = (6, 3)

⇒ B' = (-3 + 4, -5 + 6) = (1, 1)

⇒ C' = (4 + 4, 1 + 6) = (8, 7)

Answer:

(4, 1 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = C (1, 9 ) and (x₂, y₂ ) = D (7, - 7 ) , then

midpoint = ( [tex]\frac{1+7}{2}[/tex] , [tex]\frac{9-7}{2}[/tex] ) = ( [tex]\frac{8}{2}[/tex] , [tex]\frac{2}{2}[/tex] ) = (4, 1 )

Answer:

Option 1. This is a vertical pair of angles because they are two nonadjacent (not next to each other) angles formed by intersecting lines. The sides of one angle are the opposite rays to the sides of the other angle. (Angle 5=Angle 7)

Option 2 and 4 are wrong as the angles are not created by a set of parallel lines and a transversal.

Option 3 is wrong as the angles are not adjacent.

Option 5 is wrong as the angles do not have a sum of 90°.

The baker has 13/3 pounds of sugar.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

We have been given two fractions.

The three containers have 3/4 pounds of sugar and fourth one have 1/2 pounds of sugar.

To find the total sugar, we have to add both the fractions

Total pounds of sugar = Sugar in three containers + sugar in fourth container

= 3/4 + 1/3

= (9 + 4)/3

= 13/3 pounds

So, the total sugar the baker has is 13/3 pounds.

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Answer: A z=9

Step-by-step explanation:

Answer:

z = 12

Step-by-step explanation:

To understand the equation, you must first know that m∠a = 108°. It equals that because a regular five-sided polygon has an interior angle of 108° each.

Next, you would want to group all constants to the right side of the equation. By doing so, you want to subtract 72 from both sides.

(3z + 72) - 72 = 108 - 72

3z = 36

Lastly, you want to isolate the z by dividing 36 by 3.

z = 36 ÷ 3

z = 12

Answer:

I'll do #17 as an example of how to do the others. #15 doesn't make sense.  What is "= ≤⁄x?"

Step-by-step explanation:

17. (-3, 2); y=-4

y=4 is a horizontal line, where all values of y are 4, regardless of x.  A horizontal line has a slope of 0.  [Y does not depend on x].

That leaves us with y =0x + b

For this line to go through point (-3,2), it would have to have a y-intercept (b) of 2 [b is the value of y when x=0].  Since y=0 regardless of x, b must be 2.

The parallel line that goes through (-3,2) is:

y = 0*x + 2, or

y = 2

Answer:

slope = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + y = 8  ( subtract 3x from both sides )

y = - 3x + 8 ← in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]

When writing a repeating decimal as fraction , the fraction do not always have only 9’s or 9’s and 0’s as digits in the denominator .

Repeating Decimal is a decimal in which after certain point a particular digit  or sequence of digit repeats itself infinitely  .

For Example : 0.66666666...    

When in a fraction the numerator is divided by the denominator , it is not at all necessary that the denominator will always have 9’s or 9’s and 0’s .

We can understand more with the help of an example .

example : 1/3 = 0.3333... is a repeating decimal , which does not have a 9 , 0 in the denominator .

(ii) 5/3 = 1.666666.... is a repeating decimal , which does not have a 9 , 0 in the denominator .

Therefore , When writing a repeating decimal as fraction , the fraction do not always have only 9’s or 9’s and 0’s as digits in the denominator .

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Ramones’s Chemistry test was much better as it has higher Z-Score than history

For History test, Test score (x) = 40

Mean (μₓ) = 30, Standard deviation (σₓ) = 10

For Chemistry test, Test score (Y) = 40

Mean (μ) =30, Standard deviation (σ) =5

Ramones’s Z-score for History test is given by,

Z-Score = (x-μₓ)/σₓ =(40-30)/10 = 1

Ramones’s Z-score for chemistry test is given by,

Z-Score = (y-μ)/σ =(40-30)/5 = 2

Thus, Ramones’s Chemistry test was much better, because Chemistry test has higher z-score.

Difference in the mean score (α) =μₓ -μ =0

Difference in Z-Score= Z- Zₓ =1

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Answer:

a) 132 g oat cereal, 132 g pretzels, 66 g nuts

b) 84 g oat cereal, 84 g pretzels, 42 g nuts

c) 200 g oat cereal, 200 g pretzels, 100 g nuts

d) 300 g oat cereal, 300 g pretzels, 150 g nuts

Step-by-step explanation:

a) 330 = 5x

x=66

132 oat cereal

132 pretzels

66 nuts

(And repeat for all masses)

:] Tell me if this is incorrect!

(Brainliest would help a lot lol)

After 10 years, the car will be worth 0.54 of the price when Rob purchases it. The result is obtained using the exponential depreciation equation.

The depreciation can be calculated by the exponential depreciation equation.

y = P (1 - r)ˣ

Where

If given

How much will the car be worth after 10 years?

The depreciation rate would be

r = 6%

r = 6/100

r = 0.06

So, after 10 years, the car would be worth

y = P (1 - r)ˣ

y = P (1 - 0.06)¹⁰

y = P (0.94)¹⁰

y = P (0.54)

y = 0.54P

Hence, after 10 years, the car will be worth 0.54 of its original price.

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Answer:

x=50

Step-by-step explanation:

5(2-x)-10=25-2(3x+40)

Distribute:

10-5x-10=25-6x-80

Combine like terms

-5x-10=-6x-55

Put x to one side

x-10=-55

Make x by itself

x=-55

Answer:  x=−55

Step-by-step explanation:

Solve the equation step-by-step:

5(2−x)−10=25−2(3x+40)

Simplify both sides:

5(2−x)−10=25−2(3x+40)

Distribute:

(5)(2)+(5)(−x)+−10=25+(−2)(3x)+(−2)(40)

10+−5x+−10=25+−6x+−80

Combine Like Terms:

(−5x)+(10+−10)=(−6x)+(25+−80)

−5x=−6x+−55

−5x=−6x−55

Add 6x to both sides.

−5x+6x=−6x−55+6x

x=−55

Answer:

The answer for the question is = -18.6y - 64.8

       The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Below is a scale illustration of the Colombian flag that ranges from 1 cm to 2 ft.

         It is already stated that all measurements would be done using a fixed scale for a given scale drawing. Let the scale, for illustration, be K feet to s inches.

1ft ; s/k in

Thus, all foot measures will be multiplied by s/k to obtain the relevant lengths in the drawing.

Since the ratio is 2:1, there are 1 centimeter for every 2 feet.

This indicates that to reach 33, we must divide 66 by 2.

66/2 = 3

As a result, the scale drawing of the Colombian flag is attached below and has a scale of 1 cm to 2 ft.

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The midpoint between the given figures are -2.5 and 5.5 respectively.

A midpoint is defined as that particular point that divides two separate figures into two equal halves or the centre of two endpoints on a number line.

That is;

point a + point b/2

The figures given are :

Point a = -3

Point b = -2

= -3 + -2/ 2

= -5/2

= -2.5

For points 4 and 7 ;

= 4 + 7 / 2

= 11/2

= 5.5

Therefore, the middle or midpoint of -3 and -2 is -2.5 and the midpoint for 4 and 7 is 5.5.

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Average rate of change is calculated using the slope of the line linking the interval's ends on the graph of the function. The average rate of change, in simplest form, is -1/6.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

The formula for calculating the gradient of a function exists expressed as:

[tex]$m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Using the coordinate points from the table (6, 53) and (24, 50).

Substitute the coordinate into the expression:

[tex]$m=\frac{50-53}{24-6} \\[/tex]

[tex]$&m=\frac{-1}{6} \\[/tex]

Therefore, the average rate of change, in simplest form is -1/6.

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consider

note that the letter g is common to all the numbers in the equation, so we take the lowest power of g and make a common factor, that is:

so the correct answer is

g(5g - 4)

Answer: 9g

Step-by-step explanation:

3g^2 + 2g^2 - 4g

you simplify the exponents first, because of P.E.M.D.A.S.:

9g + 4g - 4g combine like terms

Answer: 9g

The perimeter of the polygon with the vertices is: 17.5 units.

The perimeter of a polygon is the sum of all the sides of the polygon. To find the perimeter of a polygon with coordinates given for its vertices, we have to apply the distance formula to find the length between each of the vertices of the polygon.

The distance formula is d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

Given:

J(-5, 3)

K(-2, 1)

L(3, 4)

Find JK:

JK = √[(−2−(−5))² + (1−3)²]

JK = √13

JK = 3.6 units

Find KL:

KL = √[(−2−3)² + (1−4)²]

KL = √34

KL = 5.8 units

Find JL:

JL = √[(−5−3)² + (3−4)²]

JL = √65

JL = 8.1 units

Perimeter = 3.6 + 5.8 + 8.1

Perimeter = 17.5 units.

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Answer:

10

Step-by-step explanation:

Right angles add up to 90

5x + 4x = 90

9x = 90  Divide both sides by 9

x = 10

33,800,000 are total distinct six characters license plates possible such that the two letters must appear next to each other. We can solve it by using combination formula ( ⁿCr ) .

Total number of digits are 10 i.e., 0,1,2,3,4,5,6,7,8,9. We have given the option to select any four digits out of 10 with repetition. So, we use combination formula

ⁿ C r = n!/(r! ×(n-r)! )

For 1ˢᵗ digit, the number ways to choose the 1ˢᵗ digit is ¹⁰C ₁= 10

For 1ˢᵗ letter, the number of ways to choose the 1ˢᵗ letter is ²⁶C ₁= 26

There are 10×10×10×10 = 10⁴ ways to choose four digits . In a similar way, the total number of letters for choice is 26 ; i.e., from A to Z. We were given the task of choosing two letters from a list of 26 , which were not necessarily distinct .

There are 26×26 = 26²ways to choose the two letters . For the letters to be next to each other, they can be the 1ˢᵗ and 2ⁿᵈ, 2ⁿᵈand 3ʳᵈ, 3ʳᵈand 4ᵗʰ, 4ᵗʰand 5ᵗʰ, 5ᵗʰ and 6ᵗʰ characters . So, there are 6-1 = 5 are choices for the positions of the letters .

Therefore, numbers of distinct license plates is 5×10⁴× 26² = 33,800,000

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Reason:

The diagram describes values between -1 and 3. We exclude -1 because of the open hole. We include 3 because of the closed endpoint.

In a right triangle, if the altitude drawn from the right angle to the hypotenuse divides the hypotenuse into two segments, the length of the altitude is the geometric mean of the lengths of the two segments.

According to this

Which is the fourth option.

The Explicit Formula is a(n) = 27×[tex](\frac{2}{3})^n^-^1[/tex]

Given,

The first four terms are 27, 18, 12, 8.

Find the common ratio:

To do this, let that ratio = r,

and write and solve 27r = 18.  Thus, r = 2/3.

The general explicit formula for this sequence is:

a(n) = a(1)*(2/3)^(n - 1),

or, since a(1) = 27,

a(n) = 27×[tex](\frac{2}{3})^n^-^1[/tex]

Hence, The Explicit Formula is a(n) = 27×[tex](\frac{2}{3})^n^-^1[/tex]

What is Explicit formula For sequence?

The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geometric, or harmonic sequence.

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Answer:y=-x+3

Step-by-step explanation:

EXPLANATION

If the equation is 2r+10=22

Subtracting -10 to both sides:

2r = 22 - 10

Subtracting numbers:

2r = 12

Dividing both sides by 2:

r = 12/2

Simplifying:

r=6

The answer is r=6