Calculate the perimeter of this right-angled triangle.
Give your answer in metres (m) to 1 d.p.
7m
19 m

Answer:  x = 2

=============================================================

Explanation:

Refer to the diagram below.

I've added points D,E,F,G. This helps with labeling the segments and angles, and identifying the proper triangles (to see which are congruent pairs).

Triangle GEA is congruent to triangle GFA. We can prove this using the AAS congruence theorem. We have AG = AG as the pair of congruent sides, and the congruent pairs of angles are marked in the diagram (specifically the blue pairs of angles and the gray right angle markers)

Since triangle GEA is congruent to triangle GFA, this means the corresponding pieces segment GF and GE are the same length.

The diagram shows GF = 3x-4, so this means GE = 3x-4 as well.

----------------------

Through similar steps, we can show that triangle GEC is congruent to triangle GDC. We also use AAS here as well.

The congruent triangles lead to GD = GE. So GD = 3x-4. The diagram shows that GD = 6x-10

Since GD is equal to both 3x-4 and 6x-10, this must mean the two expressions are equal.

----------------------

Now let's solve for x

6x-10 = 3x-4

6x-3x = -4+10

3x = 6

x = 6/3

x = 2

Answer:

the third one

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

the radius is half the diameter from the middle!

Answer:

4 and 2/3 is the answer

Step-by-step explanation:

14/3= 4 and 2/3

Answer:

7: no ( the answer will be 65 )

-2 : no ( the answer will be -16 and -16 is not less than -16 instead they're equal)

2 : no ( the answer will be 20 )

-7 : no ( the answer will be -61)

Non of them satisfy the condition

Hope this helped

Hope this helped ALL THE BEST!!

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Answer:

1,sin30 =oppsite/hyp=x/16

=0.5=x/16

=x=0.5*16=8

=X=8

2,cos30=Adjacent/hypothesis=y/16

=(3sqrt)/2=y/16

=2y=16(3sqrt)

=Y=8(3sqrt)

Answer:

b

Step-by-step explanation:

Answer:

A 180

Step-by-step explanation:

72÷2=36

y=36×5 (stated in question)

y=180

The expressions for the length and perimeter of the rectangle are (3x + 1) and (14x + 2) respectively.

For any rectangle, the area is calculated as;

Area of rectangle = length × width

given an area of 12x² + 4x and a width of 4x, the length is calculated as;

length of rectangle = (12x² + 4x)/4x

length of rectangle = 4x(3x + 1)/4x

length of rectangle = (3x + 1)

perimeter of the rectangle = 2[(3x + 1) + 4x]

perimeter of the rectangle = 2(7x + 1)

perimeter of the rectangle = 14x + 2

Therefore, the expressions for the length and perimeter of the rectangle are (3x + 1) and (14x + 2) respectively.

Read more about rectangle here:https://brainly.com/question/17297081

#SPJ1

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

You can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

To find the slope of the secant line PQ, we need two points on the line: P(x, 4) and Q(3 - x, 3).

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

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

In this case, the coordinates of P are (x, 4) and the coordinates of Q are (3 - x, 3). Plugging these values into the slope formula, we have:

slope = (3 - 4) / (3 - x - x)

slope = -1 / (3 - 2x)

To find the slope of the secant line for different values of x, we substitute those values into the expression for the slope.

For example, if x = 1, the slope of the secant line PQ is:

slope = -1 / (3 - 2(1))

slope = -1 / (3 - 2)

slope = -1 / 1

slope = -1

Similarly, you can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

And so on, you can calculate the slope of the secant line for different values of x.

Learn more about  expression from

brainly.com/question/1859113

#SPJ11

The matching between polynomial with its factorization is:

Letter A - Number 5

Letter B - Number 1

Letter C - Number 2

Letter D - Number 4

Letter E - Number 6

Letter F - Number 3

In math, the factoring or factorization is used to write an algebraic expression in factors.

The question gives a polynomial and asks your respective factorization. For solving this exercise, you should calculate the multiplication between the terms and after that you should match the result with given equations.

      Multiplying the terms, you will have:

      x²-3x+5x-15=x²+2x-15

     Therefore, the letter a match with the equation 5.

      Multiplying the terms, you will have:

      2(x²+4x-4x-16)=2(x²-16)=2x²-32

     Therefore, the letter b match with the equation 1.

      Multiplying the terms, you will have:

      (x-8)*(x-8)=x²-8x-8x+64=x²-16x+64

     Therefore, the letter c match with the equation 2.

      Multiplying the terms, you will have:

      7x-x²+21-3x= -x²+4x+21

     Therefore, the letter d match with the equation 4.

      Multiplying the terms, you will have:

      x+2-5x²-10x= -5x²-9x+2

     Therefore, the letter e match with the equation 6.

      See, the equation 6 is 4-9x-2-5x²=-5x²-9x+2.

      Multiplying the terms, you will have:

     ( x – 3)( x + 3)( x² + 9)= (x²-3x+3x-9)(x²+9)= (x²-9)(x²+9)= x²-81

     Therefore, the letter f match with the equation 3.

Learn more about the factoring here:

https://brainly.com/question/11579257

A quadratic function for the area of a figure can be represented as \(A(x) = ax^2 + bx + c,\) where a, b, and c are constants and x is the side length of the figure.

\(A(x) = x^2 - 6x + 9\\A(7) = (7^2) - (6\times 7) + 9 \\= 49 - 42 + 9 = 16\)

In this case, the given value of x is 7, so the area of the figure can be found by plugging 7 into the equation. \(A(7) = a(7^2) + b(7) + c = 49a + 7b + c.\)

Therefore, the area of the figure for \(x = 7 , 49a + 7b + c.\)

The quadratic equation can also be used to calculate the area of the figure for any given value of x.

To do this, simply plug in the desired value of x into the equation and solve for the area.

For example, if we want to find the area of the figure for x = 4, then we would plug 4 into the equation and solve for the area. \(A(4) = 16a + 4b + c\).

This shows that the area of the figure for x = 4 is 16a + 4b + c.

In summary, the quadratic equation \(A(x) = ax^2 + bx + c\) can be used to calculate the area of a figure for any given value of x.

For the given value of x = 7, the area of the figure is calculated to be \(49a + 7b + c.\)

To learn more about quadratic function refer to:

brainly.com/question/25841119

#SPJ1

Complete question -

Write a quadratic function for the area of the figure. Then, find the area for the given value of x.

x=7

A quadratic function for the area of the figure is A(x)= (Simplify your answer.).

Answer:

I believe the answer is 52,080 numbers.

Step-by-step explanation:

Don't be mad if i'm wrong.

Answer:

34.01

Step-by-step explanation:

By Pythagoras Theorem:

\( {x}^{2} = {31}^{2} + {14}^{2} \\ = 961 + 196 \\ = 1157 \\ x = \sqrt{1157} \\ x = 34.0147027 \\ x = 34.01\)

Answer:

39.179 OR 39.18

Step-by-step explanation:

31^2 + 14^2 = x^2

961 + 574 = x^2

1535 = x^2

Square root 1535

= 39.179 or 39.18 rounded to the nearest tenth

Answer:

c.136

Step-by-step explanation:

3x² - 2x + 3                       x = 7

= 3(7)² - 2(7) + 3

= 3(49) - 14 + 3

= 147 - 11

= 136

So, the answer is c.136

Answer:

The profit for January is $57,200.

Step-by-step explanation:

The total profit for the two months would be the result of adding up the profit in January plus the profit in February:

Total profits=Profit in January+Profit in February

Also, you can say that profits in January can be represented by x and you know that the profit for a company in February was 15% higher than it was in January which can be expressed as: 1.15x. Moreover, you know that the total profit for the two months was $122,980. Now, you can replace the values on the formula:

122,980=x+1.15x

Now, you can solve for x:

122,980=2.15x

x=122,980/2.15

x=57,200

According to this, the answer is that the profit for January is $57,200.

The relative maxima and minima of the function g(x) are at the point (-4, 22) at the local maxima and at point (4,-124) at the local minima.

Given:

Function g(x) = x^3 - 48x + 4

Take the derivative and set it equal to zero

3x^2 - 48 = 0

x^2 = 48/3 = 16

x = sqr16 = ±4

At x=+4, y = (4)^3 -48(4) + 4 = 64 -192+4 = -124

Point (4,-124) is a local or relative minimum

At x-4 y=(-4)^3 -48(-4)+4 = -64 + 192 + 4 = 122

The point (-4, 22) is a local or relative maximum

Refer to this complete question:

Find the relative maxima and minima, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = x3 − 48x + 4 relative maximum (x, y) = relative minimum (x, y) =?

To know more about the maxima and minima visit: https://brainly.com/question/29562544

#SPJ4

The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Equation: A declaration that two expressions with variables or integers are equal.

In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

The equation would be:

C is the total cost and m is the miles driven.

We know that:
Charge of the truck: $35

Charge per mile: $2.50

Then, form the equation as follows:

C = 35 + 2.50m

Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.

Know more about equations here:

https://brainly.com/question/2972832

#SPJ1

In a fictional alphabet with 20 letters, there are 8,000 different 3-letter words possible.

To solve this problem, we can use the formula for permutations, which is n!/(n-r)!, where n is the number of letters in the alphabet and r is the number of letters in the word.

In this case, n = 20 and r = 3, so the formula would be 20!/(20-3)!. Simplifying the equation, we get:

P = 20!/(17!)

P = (20*19*18)/(1*1*1)

P = 8,000

Therefore, there are 8,000 different 3-letter words possible in a fictional alphabet with 20 letters.

See more about permutations at https://brainly.com/question/1216161.

#SPJ11

The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

Know more about quadratic expression here:

https://brainly.com/question/31368124

#SPJ11

Answer:

To find the mean height of all 10 children, we need to find the total height of all the children and divide it by the number of children. The total height of the four girls is 4 * 1.4 = <<41.4=5.6>>5.6m

The total height of the six boys is 6 * 1.7 = <<61.7=10.2>>10.2m

The total height of all 10 children is 5.6 + 10.2 = <<5.6+10.2=15.8>>15.8m

The mean height of all 10 children is 15.8/10 = <<15.8/10=1.58>>1.58m. Answer: \boxed{1.58}.

Step-by-step explanation:

It would take approximately 19.65 years for an investment of $100,000 at a 7% annual interest rate to grow to $500,000. Rounded to two decimal places, the answer is 19.65 years.

To determine the number of years it will take for an investment of $100,000 at a 7% annual interest rate to grow to $500,000, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment ($500,000)

P = the initial principal amount ($100,000)

r = the annual interest rate (7% or 0.07)

n = the number of times that interest is compounded per year (assuming annually, so n = 1)

t = the number of years

Plugging in the values we know, we get:

$500,000 = $100,000(1 + 0.07/1)^(1*t)

Dividing both sides of the equation by $100,000 and simplifying:

5 = (1.07)^t

To solve for t, we can take the logarithm of both sides:

log(5) = log[(1.07)^t]

Using logarithmic properties, we can bring down the exponent:

log(5) = t * log(1.07)

Finally, we can solve for t by dividing both sides by log(1.07):

t = log(5) / log(1.07)

Using a calculator, we find:

t ≈ 19.65

Therefore, it would take approximately 19.65 years for an investment of $100,000 at a 7% annual interest rate to grow to $500,000. Rounded to two decimal places, the answer is 19.65 years.

Learn more about investment from

https://brainly.com/question/24703884

#SPJ11

The simple interest rate that is equivalent to the discount rate can be determined by multiplying the discount rate by (Time / 365).

i) To determine the maker of the note, we need to identify who issued the promissory note. Unfortunately, the information provided does not specify the name of the maker or issuer of the note. Without additional information, it is not possible to determine the maker of the note. ii) To calculate the face value of the note, we can use the formula for the maturity value of a promissory note: Maturity Value = Face Value + (Face Value * Interest Rate * Time). Given that the maturity value is RM7,266 and the note matured on 11 June 2022 (assuming a 365-day year), and Zafran held the note for 52 days, we can calculate the face value: 7,266 = Face Value + (Face Value * 0.09 * (52/365)). Solving this equation will give us the face value of the note.

iii) The discount date is the date on which the note was discounted at the bank. From the information provided, we know that Zafran discounted the note after holding it for 52 days. Therefore, the discount date would be 52 days after 10 January 2022. iv) The discount rate can be calculated using the formula: Discount Rate = (Maturity Value - Discounted Value) / Maturity Value * (365 / Time). Given that the discounted value is RM7,130.77 and the maturity value is RM7,266, and assuming a 365-day year, we can calculate the discount rate. v) The simple interest rate that is equivalent to the discount rate can be determined by multiplying the discount rate by (Time / 365). This will give us the annualized interest rate that is equivalent to the discount rate.

To learn more about simple interest rate click here: brainly.com/question/13261862

#SPJ11

Answer:

The answer is 4/31

Step-by-step explanation:

Total=4+9+7+11=31

Probability =4/31