a) work out the size of angle x.

b) give reasons for your answer.

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

Explanation:

For now, let's focus on triangle AFG.

This is a right triangle with the following sides:

We'll use the pythagorean theorem to solve for x.

a^2 + b^2 = c^2

(FA)^2 + (FG)^2 = (AG)^2

x^2 + (6.1)^2 = (11.2)^2

x^2 + 37.21 = 125.44

x^2 = 125.44 - 37.21

x^2 = 88.23

x = sqrt(88.23)

x = 9.39308 approximately

Side FA is roughly 9.39308 units long.

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Let's say for a moment we don't know where point G is located, but we do know where points A, C, and E are located. We can determine G's location by determining the perpendicular bisectors for segments AE and EC, and then intersecting said perpendicular bisectors.

Put another way:

Because of the first bullet point, we know that AE is split into two equal pieces FA and FE, ie FA = FE.

We just found that FA = 9.39308 back in the last section, which means this is the length of FE as well.

Therefore,

AE = FA + FE

AE = 9.39308 + 9.39308

AE = 18.78616

AE = 18.8 when rounding to the nearest tenth, aka one decimal place.

Answer:

18.79

Step-by-step explanation:

→ Use Pythagoras theorem

√11.2² - 6.1²

→ Simplify

9.39

→ Now double the answer

18.79

Answer:

27 students received an A

Step-by-step explanation:

90% of 150 is 135

1/5 of 135 is 27

Answer:

4 inches.

Step-by-step explanation:

The height of a rectangle is reduced by Shawna to a size of 2 inches.

The original width of the rectangle was 24 inches and the height was 12 inches.

If the ratio of width to height remains the same, then we can find the new width.

If the new width is x inches then, we can write

[tex]\frac{x}{2} = \frac{24}{12}[/tex]

⇒ x = 4 inches. (Answer)

Answer:

the new width is 14

Step-by-step explanation:

original height 12

12-2= 10 (the amount that was taken away to get the new height)

24- 10= 14 ( the new width)

Answer:

$190

Step-by-step explanation:

he spent 3/7·(280), or $120 on a present

he spent 1/4·(280), or $70 on a meal

he spent $190 altogether

Answer:

parallel line: y=-3x+14

perpendicular line: y=1/3x +2/3

Step-by-step explanation:

For the parallel line, use the point-slope formula to find the equation of the parallel line (since the slope is the same as the given line and the point (4,2) is given. For the perpendicular line, use the opposite reciprocal of the slope of the given line and use the point-slope formula again. The point-slope formula is Y-Y1=m(X-X1)

Answer:

  -27

Step-by-step explanation:

It looks like you're trying to evaluate ...

  [tex]\displaystyle 5^{\log_5{8}}-3^{\log_3{5}+\log_3{7}}=8-3^{\log_3{35}}=8-35=\boxed{-27}[/tex]

__

The relevant rules are ...

  b^(log_b(x) = x

  log(a)+log(b) = log(ab)

Answer:

5n+p>40

n+p<20

Step-by-step explanation:

Answer:

Answer below

Step-by-step explanation:

The currency called the dollar can be split into smaller forms called nickels, pennies, dimes, and quarters.

The system of inequalities that represents how many pennies and nickels that Jada could have is given as:

p + n < 20

0.01p + 0.05n > 0.40

Let's represent the number of :

pennies = p

nickels = n

It is important to also note that:

1 penny = $0.01

1 nickel = $0.05

40 cents can also be written as: $0.40

Jada has p pennies and n nickels that add up to more than 40 cents.

The word more than means greater than and this can be represented by the inequality sign ">". Hence, our inequality equation is given as:

$0.01 x p + $0.05 x n > $0.40

0.01p + 0.05n > 0.40

She had fewer than 20 coins altogether.

The word fewer means less than and this can be represented by the inequality sign "<". Hence, our inequality equation is given as:

p + n < 20

Therefore, the system of inequalities that represents how many pennies and nickels that Jada could have is given as:

Correct answer is  p + n < 20 0.01p + 0.05n > 0.40

_____________________________________________________

(Hope this helps can I pls have brainlist (crown)☺️)

Answer:

1

Step-by-step explanation:

Answer:

26 1/4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

You add up both fractions, sorry for the lazy explanation

Answer:

x = 27°

Step-by-step explanation:

l ║ m    Given

(x + 72) + (3x) = 180°       If parallel line then same-side angles = 180°

4x + 72° = 180°

 4x = 180° - 72°

 4x = 108°

   x = 108°/4

   x = 27°

Answer:

C

Step-by-step explanation:

If you take 4% away from 350,000, it equals 336000. Divide this number by 350000, and you get 96%, which makes sense. But, if you take 4% away from 336000, it equals 322560. If you take 322560 divided by 350000, it equals 92.16%. This proves it is not linear, because if it was linear, the ending percentage would be exactly 92% since you took away 4% twice.

Answer:

-2/3 is the correct answer

Step-by-step explanation:

hope this helps

Answer:

Number 2 is the answer.

Step-by-step explanation:

Rise/run

and the line is going down.

5(x-4) + ? = 12x - 21

5x - 20 + ? = 12x - 21

? = 7x -1  

ok done. Thank to me :>

The sine of the angle theta is given by the ratio of the opposite leg to the hypotenuse side of the right triangle formed by the terminal segment.

Reasons:

The given parameters are;

The sine value of the given angle = One-half

Required: To select the true statement of the location of the terminal side.

Solution:

Given that sin(θ) = 0.5, we have;

The sine of an angle is positive in Quadrant I and Quadrant II

The reference angle, is the angle formed between the angle's terminal side and x-axis

By trigonometric ratios, considering the reference angle, we have;

θ = arcsin(0.5) = 30°

Therefore;

The option that gives the true location of the terminal side of an angle, that have a sine value of One-half is; Theta has a reference angle of 30° and is in Quadrant I or II.

Learn more about trigonometric ratios here:

https://brainly.com/question/2398899

Answer:

a

Step-by-step explanation:

edge

Answer: It will take 125 day

Step-by-step explanation: 100 divide by 4 = 25 and 25 x 5 = 125

Answer:

there y= -x - 3 is correct

Step-by-step explanation:

(-4,1) ; (-3,0)

y= -x - 3

with (-4,1)

1 = -(-4) - 3 = 4 - 3 = 1. left = right

with (-3,0)

0 = -(-3) - 3 = 3 - 3 = 0. left = right

so the line y = -x - 3 is passes through points (-4,1) and (-3,0)

Hey there! I'm happy to help!

Since we are using graphs, we will do not need to algebraically solve this system of equations.

When you graph a system of equations, the solution is always the point at which the two lines intersect.

Here is our system of equations graphed. We see that the lines intersect at about (1 1/3, 2 1/3). Therefore, the correct answer is C. x=1 1/3, y=2 1/3

Have a wonderful day! :D

Step-by-step explanation:

exterior angle is the sum of two opposite interior angle

11x+9=3x+12+85

11x-3x=88

8x=88

x=11.

hope this helps you.

Answer:

x=11

Step-by-step explanation:

85 + 3x + 12= 11x+9

97  +3x= 11x+9

-97            -97

3x= 11x - 88

-11x    -11x

-8x = -88

/-8     /-8

x=11

Answer:y=16

Step-by-step explanation:

The solution to the original equation will be -2 and -6

Given the function [tex](x + 3)^2 + (x + 3) - 2 = 0.[/tex]

If u = x + 3, the function in terms of "u" will be;

[tex]u^2+u-2=0[/tex]

Factorize the resulting equation as shown:

[tex]u^2+u-2=0\\u^2+2u-u-2=0\\u(u+2)-1(u+2)=0\\(u-1)(u+3) = 0\\u=1 \ and \ -3[/tex]

Since x + 3 = u

x = u - 3

If u  = 1

x = 1 - 3  = -2

If u  = -3

x = -3 - 3  = -6

Hence the solution to the original equation will be -2 and -6

Correct question:

Solve (x + 3)^2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u – 2 = 0 u2 + u + 1 = 0 Factor the equation. What are the solutions of the original equation?

Learn more on factorization here: https://brainly.com/question/25829061

Answer:

add 12.18 to both sides and the divide by 2.14 on both sides until its x equal whatever you get

Answer:

Part of the time

Step-by-step explanation:

This is a linear line, meaning it is an infinite straight line. Part of the time it will be more than 0, part of the time it will be less than 0.

Answer:

Yes there would be a positive correlation on a graph.

Step-by-step explanation:

Say we use 0 as our X value. We get 4 as our Y value. Another example we can use is 10. We get 34 as our Y intercept.

Answer:

23 - 6x

Step-by-step explanation:

2(3x+4) - 3(4x-5)

6x + 8 - 12x +15 (distributing)

23 - 6x (combining like terms)

Answer:

Have some water and take a short break from the screen if possible, maybe get a few minutes of fresh air

First, and x-intercept at the origin simply means the line passes through 0, 0. On both graphs given we can, we can see that they do not touch 0,0. From the table as well, y at x = 0 does not equal 0. Finally, this leaves c(x). C(x) does pass through 0, 0.

Hope this helps!

Answer:

no because r is a varible that dont have number

The correct expression of  r less than 52 is r<52.

An expression is combination of variables, numbers and operators.

The given expression is r less than 52

We have to write in the form of inequality

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The less than represents the relationship between r and 52

In the given expression r is the variable

r<52 is the required expression or inequality

Hence, the correct expression of  r less than 52 is r<52.

To learn more on Expressions click:

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#SPJ3

Answer:

B. a×1

Step-by-step explanation:

This is because a×1 gives a result of a thus,a multiplying the identity element of multiplication

The value of "m' that makes the expression equivalent is 0.2584

Given the expression 12 (–1.4m + 0.4) = m + 0.2

We need to solve for the value of m from the expression.

Expand using the distributive law:

12(-1.4m) + 12(0.4) = m +  0.2

16.8m + 4.8 = m + 0.2

Collect the like terms:

-16.8m - m = 0.2 - 4.8

-17.8m = -4.6

m = 4.6/17.8

m = 0.2584

Hence the value of "m' that makes the expression equivalent is 0.2584

Learn more on expressions here: https://brainly.com/question/22048677

First, we can eliminate d(x) because we can see it's a linear line. We can also eliminate a(x) because it's also a linear line. Both b(x) and c(x) have an asymptote. on b(x) you can see that x = 3 is the asymptote. For c(x) if it's graphed, it has a horizontal asymptote at y = -1.

Hope this helps!