Find the inverse for each relation:

1. [(4,2),(5,1),(6,0),(7,-1)}

Angle 4 is an exterior angle which is equal to the sum of the two opposite inside angles.

The two opposite inside angles are given as 51 and 51

Angle 3 = 51 + 51 = 102 degrees.

Answer:

[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]

Step-by-step explanation:

the sum of the interior angles of a triangle is 180°

thus our equation is

[tex] \displaystyle {51}^{ \circ} + {51}^{ \circ} + \angle2 = {180}^{ \circ} [/tex]

simplify addition:

[tex] \displaystyle {102}^{ \circ} + \angle2 = {180}^{ \circ} [/tex]

cancel 102° from both sides:

[tex] \displaystyle \angle2 = {72}^{ \circ} \cdots \text{I}[/tex]

By straight line theorem we acquire:

[tex] \displaystyle \angle4 + \angle2 = {180}^{ \circ} [/tex]

substitute:

[tex] \displaystyle \angle4 + {72}^{ \circ} = {180}^{ \circ} [/tex]

cancel 72° from both sides:

[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]

hence, the measure of [tex]\angle 4[/tex] is 108°

Answer:

Volume of the box = 48 cubic meter

Step-by-step explanation:

Given:

Total number of cubes used = 48 cubes

Length of each cube = 1 meter

Find:

Volume of the box

Computation:

Volume of each cube = Side³

Volume of each cube = 1³

Volume of each cube = 1 cubic meter

Volume of the box = 48[Volume of each cube]

Volume of the box = 48[1 cubic meter]

Volume of the box = 48[1]

Volume of the box = 48 cubic meter

Answer:

GIME SUM SKITTLES (Points)

Step-by-step explanation:

Answer:

Step-by-step explanation:

??.

Answer:

8/9

Step-by-step explanation:

let the number rolled be two dies

When two dice are rolled, the total outcome will be 6² = 36

The pair that gives a sum of 5 are (1,4), (4,1) ,(2, 3), (3, 2). These gives 4 outcomes.

The pair that gives  the sum greater than 5 = 36 - 4 = 32

Pr(sum is greater than 5) = Expected/Total outcome

Pr(sum is greater than 5) = 32/36

Pr(sum is greater than 5) = 8/9

Answer:

y=2

Step-by-step explanation:

A horizontal line can be represented as y = a number.

Therefore D. y=2 is a horizontal line.

Answer:

Step-by-step explanation:

x = 6 + y

6 + y + y = 8

y = 1

x - 1 =6

x = 7

zx + zy = z(x + y) = 20

z = 2.5

Answer:

X = 7

Y = 1

Z = 2/5

Step-by-step explanation:

7-1 = 6

7+1 = 8

2/5 × 7 + 2/5 = 20

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Explanation:

Let's go through each of the answer choices to see which are true and which are false.

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

Choice A

The general slope intercept form is y = mx+b

m = slope and b = y intercept.

For y = 3x+1, the boundary line of the first inequality, the slope is 3.

For y = -x+2, the slope is -1.

None of the slopes are 2.

Choice A is false.

We'll use the concept of slope again in choice E.

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

Choice B

The "or equal to" part of the inequality sign is what directly determines the boundary line being solid. This is because we include points on the boundary.

Choice B is true.

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

Choice C

Plug x = 1 and y = 3 into the first inequality

[tex]y \le 3x+1\\\\3 \le 3(1)+1\\\\3 \le 3+1\\\\3 \le 4\\\\[/tex]

The last inequality is true, so the first inequality is true when (x,y) = (1,3). This makes (1,3) a solution to [tex]y \le 3x+1\\\\[/tex]

Repeat those steps for the other inequality given to us

[tex]y \ge -x+2\\\\3 \ge -1+2\\\\3 \ge 1\\\\[/tex]

which is also true, so that makes (1,3) also a solution to [tex]y \ge -x+2\\\\[/tex]

The point (1,3) is a solution to both inequalities at the same time, making it a solution to the system overall.

Choice C is true

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

Choice D

When y is fully isolated, the "less than" inequality indicates the shading is below the boundary. This is due to us considering points of y coordinates smaller than the boundary line. So we'll shade below the boundary for [tex]y \le 3x+1\\\\[/tex]

We don't do the same for [tex]y \ge -x+2\\\\[/tex]. Instead, we'll shade above the solid boundary line.

Choice D is false.

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

Choice E

If two lines have equal slopes, but different y intercepts, then we have parallel lines. Parallel lines never intersect.

If on the other hand, the slopes are different values, then the two lines will intersect somewhere on the xy grid. There will only be exactly one point of intersection.

The given system has boundary lines of slopes 3 and -1, for the first and second inequality respectively. Refer back to choice A.  These differing slopes tell us that the boundary lines intersect somewhere.

Choice E is true

Let's go through all the options one at a time and look for the correct ones

Option 1: The slope of one boundary line is 2

We have 2 equations of lines, where the coefficients of are 3 and -1 respectively

because the coefficient of x denotes the slope of a line, we know that the lines have the slope 3 and -1, not 2

Hence, this option is Incorrect

Option 2: Both boundary lines are solid

In order for the boundary lines to be solid, the inequality must have an 'equal to', like ≤ (less than or equal to) or ≥ (greater than or equal to)

we can see that that's the case in our case and hence, this option is Correct

Option 3: A solution to the system is (1, 3)

To confirm this, we'll plug these coordinates into the given inequalities and see if it stands correct

y ≤ 3x + 1

3 ≤ 3(1) + 1

3 ≤ 4 which is correct because 3 is less than 4

Second equation:

y ≥ 2 - x

3 ≥ 2 - 1

3 ≥ 1

Which is also true because 3 is greater than 1

Now, we can say that (1 , 3) is a solution to the system because it satisfies both the equations and is Correct

Option 4: Both inequalities are shaded below the boundary lines

For an inequality to be shaded below the boundary line, it must have the ≤ inequality (in case of solid line) and < inequality (in case of dotted line)

because the second inequality listed includes the ≥ inequality, which was not mentioned above, it won't be shaded below

another way to think about it is that any 'greater than' inequality will shade everything above the line and the 'lesser than' inequality will shade below the line

which means that this option is Incorrect

Option 5: The boundary lines intersect

In order for the boundary lines to intersect, they must have have different slopes.

as we mentioned in the explanation of the first option, that the slopes of the lines is 3 and -1, which are different slopes

Therefore, this option is Correct

Answer:

[tex]g(5) = \frac{2}{3}[/tex]

Step-by-step explanation:

Piecewise function:

A piecewise function has a different rule depending on the input.

In this exercise:

If the input x is equal or less than two, the rule is [tex]|7 - x^2|[/tex], and if it is greater than 2, the rule is:

[tex]\frac{x+1}{2x-1}[/tex]

g(5)

The input is [tex]x = 5 > 2[/tex], so the rule is:

[tex]g(x) = \frac{x + 1}{2x - 1}[/tex]

At [tex]x = 5[/tex]

[tex]g(5) = \frac{5 + 1}{2(5) - 1} = \frac{6}{9} = \frac{2}{3}[/tex]

The answer is [tex]g(5) = \frac{2}{3}[/tex]

Answer: subtract 22 on both sides

Step-by-step explanation:

Now you would have -5 to solve take 3 and multiply on both sides to get f=-15

Hope this helps

Answer: -5

Step-by-step explanation:

Answer:

A) [tex]\sqrt{8x/3}[/tex]

Step-by-step explanation:

[tex]\sqrt{8x^{2} } /\sqrt{3x}[/tex]

[tex]\sqrt{8x^{2}/{3x}[/tex]

[tex]\sqrt{8x/3}[/tex]

Therefore, A is correct

Answer:

your answere is 80 degrees

Step-by-step explanation:

the total of the inside is 180 so subtract 35 and 65 from 180 and you get 80

Answer:

area of rectangle=length ×breadth

=9.4cm×6.3cm

=59.22cm

9514 1404 393

Answer:

  28

Step-by-step explanation:

Corresponding sides are proportional.

  x/42 = 22/(22+11)

  x = 42(2/3)

  x = 28

Answer:

.75

Step-by-step explanation:

Conditonal probability formula:

A|B= (A∩B)/B

let NH= Not heart

Let F= Face

NH|F= NH∩F/F

not hearth and face is 9

face is 12

9/12=.75

Answer:

x = 64

Step-by-step explanation:

Remark

The markings on the triangle tell us that the sides are equal. There is no marking on the third side, so it is not equal to the other two. The important fact is the angles opposite equal sides are also equal. That means that the angle on the lower right is equal to x.

Equation

So you have two angles = to x.

x + x + 52 = 180                     All triangles have interior angles of 180

2x + 52 = 180                         Combine the like terms on the left.

     - 52     -52                        Subtract 52 from both sides

2x =          128                        Divide by 2

2x/2 =      128/2

x = 64

Answer:

4

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

44 is closer to 40 than 50 because 44-40 = 4, 50-44=6 and 4<6

Answer:

25%

Step-by-step explanation:

I hope this helps you!!

Answer:

You sleep 25% of the day.

Step-by-step explanation:

First you change the equation into a fraction:

6 hrs out of 24 hrs = 6/24

Then you can simplify this fraction:

6/24 = 1/4

Lastly, convert the fraction to a percent:

1/4 = 25%

Brainliest would be greatly appreciated!!!!

Answer:

1.23 x 10^8

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

(a+b)(a-b)

Step-by-step explanation:

Answer:

C 0.245

Step-by-step explanation:

have a good day/night sorry if wrong may i please have a bralliest

Answer:

Length = 22 cm

Width = 4 cm

Step-by-step explanation:

Area = 88 cm²

Length = x + 7

Width = x - 11

Area of rectangle = length*width

Therefore:

(x + 7)(x - 11) = 88

x(x - 11) +7(x - 11) = 88

x² - 11x + 7x - 77 = 88

Add like terms

x² - 4x - 77 = 88

x² - 4x - 77 - 88 = 88 - 88

x² - 4x - 165 = 0

Factorize

x² - 15x + 11x - 165 = 0

x(x - 15) +11(x - 15) = 0

(x + 11)(x - 15) = 0

x = -11 or x = 15

Let's use the positive number.

Therefore:

Length = x + 7

Plug in the value of x

Length = 15 + 7 = 22 cm

Width = x - 11 = 15 - 11 = 4 cm

Answer:

(a) No solution

(b) Infinitely many solution

(c) No solution

(d) Infinitely many solution

Step-by-step explanation:

Solving (a):

[tex]2x + 10y = 9[/tex] --- (1)

[tex]3x + 15y = 13[/tex] --- (2)

Multiply (1) by 1.5

1.5 * [[tex]2x + 10y = 9[/tex]]

[tex]3x + 15y = 13.5[/tex] --- (3)

Subtract 2 and 3

[tex]3x - 3x + 15y - 15y = 13.5 - 13[/tex]

[tex]0 = 0.5[/tex]

The above is false; Hence, the system has no solution

Solving (b):

[tex]2x + 8y = 5[/tex] --- (1)

[tex]3x + 12y = 7.5[/tex] -- (2)

Multiply 1 by 1.5

1.5 * [[tex]2x + 8y = 5[/tex]]

[tex]3x + 12y = 7.5[/tex]

Subtract 2 and 3

[tex]3x - 3x + 12y - 12y = 7.5 - 7.5[/tex]

[tex]0 = 0[/tex]

The above implies that the system has infinitely many solutions

Solving (c):

[tex]y = 3 - x[/tex]

A second equation is required to solve for (c)

Solving (d):

[tex]5x - 8y = -1[/tex] --- (1)

[tex]-\frac{5}{2}x+ 4y = \frac{1}{2}[/tex] --- (2)

Multiply (2) by 2

[tex]-5x + 8y = 1[/tex] --- (3)

Add 1 and 3

[tex]5x - 5x -8y + 8y = -1 + 1[/tex]

[tex]0 = 0[/tex]

The above implies that the system has infinitely many solutions

Answer:

B similar

Step-by-step explanation:

Both of these triangles have the same proportions and angles even though they are different sizes, making them similar.

Have a most wonderous day!

Answer:

it should be similar

Step-by-step explanation:

I hope this helps

Answer:A)  by quoting experts and scientists who believe that humans cannot survive without the existence of coral reefs

Step-by-step explanation:

Answer:

D) by asserting that the reefs contain many plants and animals used in medicines, chemicals, or other products that humans need to lead healthy lives

Step-by-step explanation:

did the usa test prep owo

Answer:

Step-by-step explanation:

I want you to do the problem, but look and see what the inside degree has to add up to. 180? 360? then find it from there

Answer:

the second option

hope this helps!

Answer: A/ first answer

Step-by-step explanation: it is that beacause it is paired to y=tanx  

Answer:

[tex]C.\ 22.6mm[/tex]

Step-by-step explanation:

When one draws a diagonal in a square (a line connecting opposite corners), the halves of the square form (45-45-90) triangles. This means that the triangle follows the following ratio,

[tex](a)-(a)-(a\sqrt{2})[/tex]

Where (a) represents the legs or the sides adjacent to the right angle (angle with the box around it) and ([tex]a\sqrt{2}[/tex]) represents the hypotenuse or side opposite to the right angle.

Both legs have a length of (16)mm this is because all sides of a square are congruent, and the two sides adjacent to the right angle are both the sides of a square. One of them has the measure of (16) thus the other must have a measure of (16). This means that the diameter has the following value,

[tex]16\sqrt2}[/tex]

In numerical form,

[tex]\approx22.62[/tex]