what is the formula for rectangle's perimeter​

Answer:

102

Step-by-step explanation:

Angles in a quadrilateral is 360

120+85+53=258

360-258=102

Hope this helps!

Answer:

              The x-intercept of Line A is (-3, 0), and the x-intercept of Line B is (-1, 0). Therefore, the x-intercept of Line A is less than the x-intercept of Line B.

Step-by-step explanation:

              The x-intercept of a graph or function is where the line hits the x-axis on a coordinate plane. In other words, the y-value of the x-intercept is 0. Since we are looking for the x-intercept of Line A, we can use the given equation to solve for it by inserting the value y = 0 (as mentioned above, the x-intercept of a function will have the y-value as 0). By solving the equation, you'll get that [tex]-2=\frac{1}{3} (x-3)[/tex] ⇒ [tex]-6=x-3[/tex] ⇒ [tex]x = -3[/tex]. Therefore, the x-intercept of Line A is (-3, 0).

              The x-intercept on a graph is easier to find, as it is where the line touches the x-axis. So the x-intercept of Line B would be (-1, 0). Now that we have both x-intercepts, we can compare them and come up with the final answer that is required. As -3 is less than -1, we can conclude that the x-intercept of Line A is (-3, 0), and the x-intercept of Line B is (-1, 0). Therefore the x-intercept of Line A is less than the x-intercept of Line B.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

The answer is D.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We need to show that the path given by r(t) = (e^t sin t, e^(-t) cos t, e) intersects the sphere 2y^2 + 2z^2 = 4 once, traveling from outside the sphere to inside as t goes from -∞ to +∞.

The equation of the sphere is 2y^2 + 2z^2 = 4. To find the intersection points of the path and the sphere, we need to substitute the components of r(t) into the equation of the sphere:

2y^2 + 2z^2 = 4

2(e^(-t) cos t)^2 + 2e^2 = 4

2e^(-2t) cos^2(t) + 2e^2 = 4

e^(-2t) cos^2(t) + e^2 = 2

Multiplying both sides by e^(2t), we get:

cos^2(t) + e^(4t) = 2e^(2t)

We can rewrite this equation as:

e^(4t) - 2e^(2t)cos^2(t) + cos^2(t) - 1 = 0

This is a quadratic equation in e^(2t) with solutions:

e^(2t) = cos^2(t) ± sqrt(cos^4(t) - 4(cos^2(t) - 1))

We want to show that there is only one intersection point, which means we want to show that the discriminant of the quadratic is negative, i.e.:

cos^4(t) - 4(cos^2(t) - 1) < 0

Expanding the left-hand side, we get:

cos^4(t) - 4cos^2(t) + 4 < 0

Simplifying, we get:

(cos^2(t) - 2)^2 < 0

Since the square of a real number is always non-negative, this inequality has no real solutions. Therefore, the discriminant of the quadratic is negative, and there is only one intersection point.

To show that the path travels from outside the sphere to inside as t goes from -∞ to +∞, we can observe that as t goes from -∞ to +∞, the first component of r(t) goes from -∞ to +∞, while the second and third components oscillate between 0 and +∞. This means that the path starts outside the sphere (at the point (0, +∞, +∞)) and ends inside the sphere (at the point (+∞, 1, 1)). Therefore, the path must intersect the sphere once, traveling from outside to inside.

Answer:

7:11

28:44

Step-by-step explanation:

Multiply both sides by 4.

Answer:

Step-by-step explanation:

1st you solve the triangle by L x W then round it by x 10, hope this helps!

1)

The value of x is 30.5.

The measure of each angle is:

∠1  = ∠3 = ∠6 = ∠4 = 94

∠2 = ∠5 = 86

2)

The measure of ∠b is 60.7.

The measure of ∠d is 43.1.

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

1)

Since line m and line n are parallel.

(2x + 25) and 86 are alternate interior angles.

So,

2x + 25 = 86
2x = 86 - 25

2x = 61

x = 30.5

And,

∠2 and 86 are opposite angles.

So,

∠2 = 86

∠1 and ∠3 are opposite angles.

So,

∠1 = ∠3

And,

∠3 + 86 = 180

∠3 = 180 - 86

∠3 = 94

∠3 and ∠4 are alternate interior angles.

So,

∠3 = ∠4 = 94

∠1 and ∠6 are exterior alternate angles.

∠2 and ∠5 are exterior alternate angles.

So,

∠1 = ∠6 = 94

∠2 = ∠5 = 86

2)

Line m and line n are parallel.

So,

∠b and 60.7 are alternate interior angles.

∠d and 43.1 are alternate interiro angles.

So,

∠b = 60.7

∠d = 43.1

Thus,

1)

The value of x is 30.5.

∠1  = ∠3 = ∠6 = ∠4 = 94

∠2 = ∠5 = 86

2)

∠b = 60.7

∠d = 43.1

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Answer:

View Screenshot

Step-by-step explanation:

Answer:

[tex]z = -2.1875[/tex]

Step-by-step explanation:

The z score is given by the formula
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

where

[tex]z =[/tex] standard score

[tex]x[/tex] = data point = 45 for this problem
[tex]\mu[/tex] = mean = 52 for this problem
[tex]\sigma =[/tex] standard deviation = 3.2 for this problem

Therefore
[tex]z = \dfrac{45 - 52}{3.2} = -2.1875[/tex]

The interval in set builder notation is {x : x ≥ -2 and x < 3, where x ∈ R} and the graph of the interval is given below.

Set builder form is used to represent the numbers in a set especially infinite numbers in a set using a statement which describes all the elements in the set.

Given interval is [-2, 3).

This is a closed interval from -2 and open interval at 3.

So, this interval contains all the elements from -2 to 3 where 3 is not included.

So, the set builder form can be written as,

{x : x ≥ -2 and x < 3, where x ∈ R}

The graph of the interval on the number line will be a straight line with closed circle at -2 and open circle at 3.

Hence the set builder form is {x : x ≥ -2 and x < 3, where x ∈ R}.

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Answer:

2x + h - 5

Step-by-step explanation:

To find f(x + h) we simply plug (x + h) into the function f(x), anywhere we see an x.

[tex]f(x) = x^{2} -5x+9\\f(x+h) = (x+h)^{2}-5(x+h)+9[/tex]

Now we can plug them into the fraction:

[tex]\frac{((x+h)^{2}-5(x+h)+9)-(x^{2} -5x+9)}{h}[/tex]

Expanding all of the terms, we get:

[tex]\frac{(x^{2} +2hx + h^{2} -5x-5h+9)-(x^{2} -5x+9)}{h}[/tex]

Distributing the negative we get:

[tex]\frac{x^{2} +2hx + h^{2} -5x-5h+9-x^{2} +5x-9}{h}[/tex]

Now we see that [tex]x^{2} -x^{2} ,-5x+5x,[/tex] and [tex]9-9[/tex] all cancel, leaving us with:

[tex]\frac{2hx + h^{2}-5h}{h}[/tex] (Notice the only terms left are those with h in them)

As every term contains an h, we can remove an h from every term, giving us:

2x + h - 5

Answer:

f-1(x)=x4+3 this is your answer

The solution of the system of equations is:

x = 12, y = 11, z = 2

We can rewrite our system of equations as:

x + y + z = 25

5x + y + 9z = 89

-7x + 6y + 6z = -6

First, if we subtract the first equation and the second one, we will get:

(5x + y + 9z) - (x + y + z) = 89 - 25

4x + 8z = 64

And if we subtract 6 times the first equation from the third one, we will get:

-7x + 6y + 6z - 6*(x + y + z) = -6 - 6*25

-13x = -156

We can solve this for x:

x = -156/-13 = 12

Now we know the value of x, replacing it in:

4x + 8z = 64

Will give:

4*12 + 8z = 64

8z = 64 - 4*12 = 16

z = 16/8 = 2

And the value of y will be given by:

x + y + z = 25

12 + y + 2 = 25

14 + y = 25

y = 25 - 14 = 11

Then the solution is:

x = 12, y = 11, z = 2

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Answer:

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

3x + 15y - 2x - 2y

x + 13y

(3x + 15y) + (-2x + -2y)

x + 13y

The key features of this rational function include the following:

Domain: (-∞, 2) ∪ (2, ∞)

Range: (-∞, 1) ∪ (1, ∞)

Y-intercept: 1.

X-intercept: 2.

Vertical asymptote: x = -2.

Horizontal asymptote​: y = -1.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

Additionally, the vertical extent of any graph of a rational function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

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Answer:

middle set of data

Step-by-step explanation:

Answer:

there is an error in the question. if you compute ac - ab = 4 you get -2x+4 =4 that leads to x=0.

if so, ab = -6 and this is not allowed.

The probability that the teacher will choose two girls would be = 1/6

Probability is defined as the expression that shows the possibility of an outcome of an event which may or may not happen.

The total number of students in the class = 9

The total number of girls = 4

The total number of boys = 5

The formula for finding probability = No of favourable outcome/Total number of outcomes.

The probability that teacher choose first girl = 4/9

One girl is selected we must reduce the number of girls available for selection to 4 - 1 = 3.

We must also reduce the number of children available for selection 9 - 1 = 8.

The probability that teacher choose second girl = 3/8

Thus, the probability = 4/9 × 3/8 = 1/6

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Answer:

[tex]3p + 5p = 8p + 7[/tex]

Step-by-step explanation:

I don't know how to explain it, but

[tex]3p + 5p = 8p + 7[/tex]

Simplifying this

[tex]8p = 8p + 7[/tex]

It will never equal because no matter what number you put for P, one will always be 7 greater than the other

The probability that a randomly selected teacher earns more than $525 a week is 0.1820. Therefore, the probability that a randomly selected teacher earns more than $525 a week is 0.2177.

This is calculated by using the standard normal distribution formula:

P(x > 525) = 1 - P(x ≤ 525) = 1 - 0.8413 = 0.1820

The probability that a randomly selected teacher earns more than $525 a week can be found by calculating the z-score for $525 and then using the standard normal table to find the probability.

The z-score is calculated as follows:

z = (x - μ)/σ

Where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

Plugging in the values from the question, we get:

z = (525 - 490)/45 = 0.78

Now, we can use the standard normal table to find the probability that a randomly selected teacher earns more than $525 a week. The table gives us the probability that a value is less than a given z-score, so we need to subtract the probability from 1 to find the probability that a value is greater than the z-score.

The probability that a value is less than 0.78 is 0.7823. So, the probability that a value is greater than 0.78 is 1 - 0.7823 = 0.2177.

Therefore, the probability that a randomly selected teacher earns more than $525 a week is 0.2177.

Answer: 0.2177

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The volume of grains stored in Adam's family farm in m³ is 14.374m³.

What is meant by volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. Knowing an object's volume can help us figure out how much a substance is needed to fill it, such as how much water is needed to fill a bottle. Cubic units are used to quantify a solid's volume. Volume is another word for capacity.

Given,

 The volume of grains stored in the farm = 18.8 yards³

It is given that 1 yard = 0.9144 m

We are asked to find the above volume of grains from yards³ to m³

if

1 yard = 0.9144 m

1 yard³ = 0.9144 m * 0.9144 m * 0.9144 m

18.8 yards³ = 18.8 * 0.9144*0.9144*0.9144 = 14.374 m³

Therefore the volume of grains stored in the farm in m³ is 14.374m³.

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Answer:   3

Step-by-step exp lanation:

divided

This equation demonstrates the distributive property of multiplication

What is distributive property ?

In mathematics, the distributive property is a property of binary operations that applies to numbers, sets, or other mathematical objects. It governs how to perform the operation of multiplication over addition or subtraction. The distributive property states that for any numbers a, b, and c:

a × (b + c) = a × b + a × c (multiplication distributes over addition)

or

a × (b - c) = a × b - a × c (multiplication distributes over subtraction)


The property demonstrated in this equation is the distributive property of multiplication over addition. This property states that the product of a number and the sum of two or more numbers is equal to the sum of the products of the number and each of the individual numbers. In other words, a(b + c) = ab + ac.

In this case, 15 is being multiplied by the sum of 5 and 7, which is equivalent to multiplying 15 by 5 and 15 by 7 separately and adding the results. So, we have:

15(5 + 7) = 15 x 5 + 15 x 7

This equation demonstrates the distributive property of multiplication over addition.

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Answer:

-4

Step-by-step explanation:

-5 x -12/ 3 x -5

60/-15

-4

Answer:

40x + 17(468-x) = 11912

       23x = 11912 - 17*468     |Solve for x and then find (468-x) as well

Answer:

c = -5

Step-by-step explanation:

[tex]\frac{1}{4} c+2=\frac{3}{4}[/tex]

Subtract 2 on both sides

[tex]\frac{1}{4} c=-1\frac{1}{4}[/tex]

Divide by [tex]\frac{1}{4}[/tex]

[tex]c=-5[/tex]

The solution of the equation are y=9 and x=4

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

WE are given that the system of equation;

5x+6y=26 and 10x-6y=-2

5x+6y=50

-1(-x+6y=26)

X-6y=-26

Then Eliminate the y and combine evrything

6x=24

Divide 6 both sides

X=4

Then, substitute the x

-(4)+6y=50

-4+6y=50

Add 4 both sides

6y=54

y=9 and x=4

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Answer: it will be square or rhombus

Step-by-step explanation: