evaluate each inverse trig expression below. include a diagram of a unit circle justifying your solution.

Sarah's truck can carry a maximum of 1351.5 pounds. She puts a 100 - pound bag of cement mix in the truck. Which inequality can be used to find b, the number of 4.5-pound bricks that can also be put in the truck?​

___________________________________________

Maximum of 1351.5 pounds

Total ≤ 1351.5 pounds

The number on bricks = b

b*4.5 = bricks weight

100 + 4.5*b ≤ 1351.5

__________________

Can you see the updates?

___________________

Answer

100 + 4.5*b ≤ 1351.5

1351.5 ≥ 100 + 4.5*b

Answer:

[tex]7x-5y-2=0[/tex]

Step-by-step explanation:

The gradient of the line from the centre to [tex]A[/tex] is [tex]\frac{8-3}{6-(-1)}=\frac{5}{7}[/tex].

Perpendicular lines have gradients that multiply to -1, so the tangent at the point A has gradient 7/5.

So, the equation is:

[tex]y-8=\frac{7}{5}(x-6) \\ \\ 5(y-8)=7(x-6) \\ \\ 5y-40=7x-42 \\ \\ 7x-5y-2=0[/tex]

The equation of the line parallel to  4x+7y=11 and passes through (-2,-4)  is  y = - 4 / 7x - 36 / 7

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, the  equation of the line is parallel to 4x+7y=11.

Parallel lines have the same slope.

Hence,

4x+7y=11

7y = - 4x + 11

y = - 4 / 7 x + 11

Therefore, the slope of the line is - 4 / 7 x. Let's find the y-intercept using (-2, -4)

-4 = - 4 / 7(-2) + b

-4 - 8 / 7 = b

b = - 36 / 7

Therefore, the equation of the line is y = - 4 / 7x - 36 / 7

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Answer:

Yes

Explanation:

To find our whether Marrissa's budget will be enough for the party, we need to find the linear equation relating the cost and the number of guests. The linear equation is the form

where y is the cost in dollars. m is the cost per guest, and b can be interpreted as additional charges for the party facility.

The cost per guest is given by the slope of cost vs. guest graph.

Let us pick two values (100, 1325) and (50, 725) and compute the slope:

With the value of slope m in hand, we now find b by using the values x = 100, y = 1325 (the choice of these values is arbitrary)

Hence, the equation relating the cost and the number of guests is

Now, for 75 guests the cost will be

Therefore, Marrissa's budget, which is $1200, is greater than the cost of the party, meaning it will be enough.

The equation of line in point slope form is y = -3x -4

Given,

The points which the line passes through;

(x, y) = (-3,5)

Slope, m = -3

We have to find the equation in point slope form;

Point slope form;

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Here,

Point slope form;

y - y₁ = m(x - x₁)

Then,

y - 5 = -3(x - -3)

y - 5 = -3x -9

y = -3x - 9 + 5

y = -3x - 4

That is,

The equation of line in point slope form is y = -3x -4

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Answer:

  28(3 +1)

Step-by-step explanation:

You want the expression 84+28 to be factored using the GCF.

The Greatest Common Factor (GCF) of 84 and 28 can be found by looking at the remainder from division of 84 by 28.

  84 ÷ 28 = 3 r 0

The remainder is 0, so 28 is a factor of 84. Since it is also the largest factor of itself, it is the GCF of the two numbers.

Factoring out 28, we have ...

  84 +28 = 28·3 +28·1 = 28(3 +1)

The factored expression is 28(3 +1).

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Answer:

d

Step-by-step explanation:

Answer:4/5

Step-by-step explanation:

sin is opposite/hypotenuse so its 16/20 which reduces to 4/5

The percentage of time he exceeds 13,000 steps is 2.28% or 0.0228.

Percentage

Use the percentage formula to express a number or percentage in terms of 100. % simply indicates one out of one hundred. An expression for a number between 0 and 1 can be made using the percentage formula. It is a number that is represented as a fraction of 100. The sign % is used to denote it and it is mostly used to compare and calculate ratios. The formula for percentage increases is the ratio of the increased value to the original value multiplied by 100. It is described in percentage form. If anything is valued more highly, both its value and proportion will rise.

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The area of the trapezium would be 190 square centimeters.

The area of trapezium is given by -

A = (1/2) x (height) x (sum of parallel sides)

We have a trapezium as shown in the image.

We have -

Sum of parallel sides = [a + b] = 26 + 12 = 38 cm

Height = [h] = 10 cm

Therefore, the area would be -

A = (1/2) x (height) x (sum of parallel sides)

A = 0.5 x 10 x 38

A = 10 x 19

A = 190 square centimeters

Therefore, the area of the trapezium would be 190 square centimeters.

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First consider what the associative property of addition is:

Due to such a property, the sum of three or more numbers remains the same regardless of how the numbers are grouped.

Then, from the different steps given in the question, you can notice that in the step 3, regardless the simplifcation of like terms right side or left side, the result is the same.

The shape has some right angles .

The correct option is (D).

Given,

In the question:

Complete the sentences :

The shape has ____

Now, According to the question:

From the figure,

There are four option:

Select the one option according to the figure.

To see that :

The figure says that :

Correct Answer is  some right angles because the sides are not exactly the same .

Hence, The shape has some right angles .

The correct option is (D).

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The point, (5, -4), is the solution to the given system of equations because the lines intersect at the point.

From the question, we are to determine why the given point is a solution to the system of equations

The given system of equations is

4y = -3x - 1

2y = x - 13

When solving system of equations by the graphical method, the point where the lines intersect gives the solution to the system of equations.

From the given graph,

The two lines intersect at the point where x = 5 and y = -4.

That is,

The lines intersect at (5, -4), and thus, (5, -4) is the solution to the system of equations.

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Concept

Given the data below as the original score of the student

The mean score is given as

Adding 5marks to the score we will be having the score below

Then the new mean score becomes

Hence the mean will be altered by adding

Other statistical measures will not be altered

Answer:

100 miles per hour

Step-by-step explanation:

He drives 200 miles in 2 hours so just divide 200 by 2 to get the unit rate/ miles per hour

Answer:

11.5%

Step-by-step explanation:

Last year:

Boys: 140

Girls: 68

Total: 208

This year:

Boys: 105% of 140 = 1.05 × 140 = 147

Girls: 125% of 68 = 1.25 × 68 = 85

Total: 232

percent change = (new - old)/new × 100%

percent change = (232 - 208)/208 × 100%

percent change = 11.5%

Answer:

b

Step-by-step explanation:

Answer:

x = 4.17

Step-by-step explanation:

you just solve it using BIDMAS. I'm 100% sure I'm right

The diagonal and two adjacent sides of the square form an isosceles right triangle.

By the Pythagorean theorem

The equation of a polynomial function, R, with rational coefficients will be;

P (x) = x² - (3i + √5 + 4)x + (12 + 3√5) i

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The zeroes of the polynomial function are;

⇒ 4 + √5 and 3i

Now,

Since, The zeroes of the polynomial function are;

⇒ 4 + √5 and 3i

So, The factor of the polynomial function are;

(x - (4 + √5)) and (x - 3i)

Hence, We can formulate the polynomial function as;

P (x) = (x - (4 + √5)) (x - 3i)

       = (x - 4 - √5) (x - 3i)

       = x² - 3ix - 4x + 12i - √5x + 3√5i

       = x² - (3i + √5 + 4)x + (12 + 3√5) i

Thus, The equation of a polynomial function, R, with rational coefficients will be;

P (x) = x² - (3i + √5 + 4)x + (12 + 3√5) i

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Answer:

15240.00 cm

Step-by-step explanation:

15240.00 cm

500 feet * 30.48x(cm)

x = centimeters per foot

The measure of ∠E = 87° and ∠F = 93°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a parallelogram in which EFGH the measure of angle E is (2x+3) and the measure of angle F is (3x - 33).

We can write -

2(2x + 3) + 2(3x - 33) = 360°

4x + 6 + 6x - 66 = 360°

10x - 60 = 360

10x = 420

x = 42

∠E = 2 x 42 + 3 = 84 + 3 = 87°

∠F = 3 x 42 - 33 = 126 - 33 = 93°

Therefore, the measure of ∠E = 87° and ∠F = 93°.

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GIVEN:

We are told that Barbara works 2/5 of her time doing paper work and this fraction represents 10 hours of her total working time.

Required;

To determine how many hours she will have to work in order to have 10 hours doing paper work.

Step-by-step solution.

Take note that her entire working hours is represented by 1 whole since, a fraction of it has already been identified as two-fifths.

This means

Take note that the fraction is taken as two-fifths of the total hours h and, if multiplied by the total hours, we would get 10 hours.

Hence, if we simplify the above equation, we would get the value of h as follows;

Therefore,

ANSWER:

Barbara has to work for 25 hours in order to spend 10 hours on paper work.

Part of the time weekes save shots on goal is 0.911.

Given,

Total number of shots on goal=1652

Number of shots saved=1506

Part of time weekes save shots on goal,

[tex]\frac{Number of shots saved}{Total number of shots on goal}\\\\\\=\frac{1506}{1652}\\ \\=0.911[/tex]

Thus, Part of the time weekes save shots on goal is 0.911.

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After simplification, 250 tickets sold to students if 150 general admission tickets were sold.

In the given question we have to find the how many student tickets were sold if 150 general admission tickets were sold.

The cost of concert ticket for general admission is $15.

The cost of concert ticket for student is $9.

Total sales of ticket is $4500.

The total 150 ticket sold to general admission.

So the total cost of ticket that received from the general admission is

=150*15 = 2250

Let x number of ticket sold to student.

Then total cost of students ticket is 9x.

Now the expression should be

9x+2250 =4500

Subtract 2250 on both side, we get

9x = 2250

Divide by 9 on both side we get

x = 250

Hence, 250 tickets sold to students  if 150 general admission tickets were sold.

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The right question is

Concert ticket cost $15 for general admission, but only $9 with student ID. Ticket ales total $4500. How many student tickets were sold if 150 general admission tickets were sold?

The answer is three

None, one or infinitely many solutions

Given the line : y = 2x + 4

the general equation of the line is y = mx + b

where m is the slope , b is the y intercept

By comparing the given line with the general form

so, the slope of the given line is :

m = 2

the slope of the perpendicular line will be = -1/m

so, the slope of the perpendicular line = -1/2

The slope of the parallel line = the slope of the given line

So, the slope of the parallel line = 2

so, the answer is:

the perpendicular line is : y = (-1/2) x + 10

The parallel line is : y = 2x + 1

Answer:

Step-by-step explanation:

to get the time taken for Jan and Jo to meet we proceed as follows;

Jan's speed=70 mph

Jo's speed =60 mph

distance between =1170

relative speed=70+60=130

time taken for them to meet will be:

time=(distance)/(relative speed)

=1170/130

=9 hours

the answer is 9 hours

Answer:

Option (B) is correct, 9 hours.

The equation of the line is y = 4x - 14

The slope of the line m = 4

The slope of the line is the  change in y coordinates with respect to the change in x coordinates of the function

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

The point is (3, -2)

Substitute the values in the point slope form

y - (-2) = 4(x-3)

y + 2 = 4x - 12

Rearrange the equation and make slope intercept form

y = 4x - 12 -2

y = 4x - 14

Hence, the equation of the line is y = 4x - 14

The complete question is

Write the equation of the line when m = 4 and the passing through the point (3, -2)

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Answer:

x = 40

Step-by-step explanation:

180 - 120 is 60

180 - 100 is 80

60 + 80 is 140

40 is the unknown angle

vertical angle means x is 40

The solution of the systems of linear equations is x = 13.81 and y = 73.381. The average salaries were equal in the year 1999. The average salary that year was about $73381.

What is the system of linear equation?

A collection of two or more linear equations is a system of linear equations. The graph of a system of two equations is a pair of lines in the plane for two variables (x and y).

The intersection point of the lines is ( 13.81, 73.381).

The average salaries were equal after 14 years since 1985.

The average salaries were equal (1985 + 14) = 1999.

The average salary that year was about $73381.

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