Question 1

A triangle has sides of length 2 cm, 8 cm and 9 cm.
Calculate the value of the largest angle in this triangle.

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

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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Answer: b (-1,1)

Step-by-step explanation:

Answer:

[tex]x=\frac{vw}{k-y}[/tex]

Step-by-step explanation:

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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The angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.

The table shows the votes of 900 people in the last elections.

Political Party    Frequency     Angle in

Labour                    345

Conservative          480

Lib Democrat           60

Other                        15

345 + 480 + 60 + 15 = 900

The total angle in a pie chart is 360

The angle for labour is = 360 (345 / 900) = 138 degree

The angle for Conservative is = 360 (480 / 900) = 192 degree

The angle for Lib democrate is = 360 (60 / 900) = 24 degree

The angle for others is = 360 (15 / 900) = 6 degree

Therefore, the angle of labour, Conservative Lib Democrat Other is 138, 192, 24 and 6 degree respectively.

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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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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

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:y=-x+3

Step-by-step explanation:

Answer:

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

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 probability that exactly 10 customers will use the atm during the next noon lunch hour is 0.0948

From the question, we have the following parameters:

Average number of customers = 12

Number of customers = 10

The above parameters means that:

x = 10

λ = 12

The probability of a Poisson distribution is represented as

P(x) = λˣe⁻λ/x!

This gives

P(x = 12) = 10¹² * e⁻¹⁰/12!

Evaluate

P(x = 12) = 10¹² * e⁻¹⁰/479001600

Solving further, we have

P(x = 12) = 0.0948

Hence, the probability is 0.0948

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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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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:

his age would be 72.

300-84=216

216÷3 is 72

Answer:

10

Step-by-step explanation:

Right angles add up to 90

5x + 4x = 90

9x = 90  Divide both sides by 9

x = 10

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:

[tex] \frac{1}{ \sqrt{10} } [/tex]

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

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:

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!!! 〜(￣▽￣〜)

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)

The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given that the values of x and h (x) for the quadratic function is given by;

x = -3, -2, -1, 0, 1, 2, 3,

h (x) = -2, -3, -2, 1, 6, 13, 22

Consider the quadratic function as;

h (x) = ax² + bx + c

Now Substitute x = -3 and h (x) = -2 in quadratic function we get;

h (x) = ax² + bx + c

- 2 = a × (-3)² + b × -3 + c

- 2 = 9a - 3b + c

And, Plug x = -2 and h (x) = -3 in function we get;

h (x) = ax² + bx + c

- 3 = a × (-2)² + b × -2 + c

- 3 = 4a - 2b + c

And, plug x = -1 and h (x) = -2 in function we get;

h (x) = ax² + bx + c

- 2 = a × (-1)² + b × -1 + c

- 2 = a - b + c

After solving we get:

a = 1 , b = 4 and c = 1

Then

h (x) = ax² + bx + c

h (x) = 1 × x² + 4x + 1

h (x) = x² + 4x + 1

h (x) = x² + 4x + 4 - 4 + 1

h (x) = (x + 2)² - 3

Hence, The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3

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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.

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 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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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]

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