Question 410 ptsQuQuQuDetermine the area and perimeter of the quadrilaterals below.Time RunniAttempt due: 11 Hour, 2 M64in88inArea =inPerimeter =in

Answer:

y=24/35

Step-by-step explanation:

The correct statement is;

False,  because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be  x = 2π/3 + 2nx and x = 4π/3 + 2nx.

Option D

From the information given, we have that;

All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx

There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx

Such that n is an integer.

This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.

The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.

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Answer:

I hope this helps.

Step-by-step explanation:

h(t) = -16t2 + 108t + 28

(a)

Maximum height occurs at the vertex of the height-vs.-time parabola, which is at

t = -108/[2(-16)] sec = ? sec

Evaluate h(t) at this value of t to get hmax.

(b)

Set h(t) = 0 and solve the quadratic equation for t.  You will get a positive and a negative solution.  Discard the negative solution, since time starts at t = 0.

The quadratic function, h = -16t + 136t + 72, gives us:

a) The maximum height of the ball is 360 feet.

b) The time taken by the ball to hit the ground is 9 seconds.

A quadratic function is a function over a quadratic expression, that is, over an expression having degree 2.

In the question, we are informed that a person standing close to the edge of a 72-foot building throws a ball vertically upward. The quadratic function h = -16t² + 136t + 72 models the ball's height above the ground, h in feet, t seconds after it was thrown.

We solve the following:-

a) What is the maximum height of the ball?

The maximum height of the ball can be obtained by differentiating the given quadratic function, h = -16t² + 136t + 72.

Differentiating both sides. we get:

\(\frac{\delta h}{\delta t} = -32t + 136\) .

To get point of inflection, we equate this to 0, to get:

\(\frac{\delta h}{\delta t} = -32t + 136 = 0\),

or, -32t + 136 = 0,

or, t = 136/32 = 4.5.

To check whether the value of h is maximum/minimum at t = 4.5, we differentiate \(\frac{\delta h}{\delta t} = -32t + 136\) again, to get:

\(\frac{\delta^{2} h}{\delta t^{2} } = -32\) , which is < 0, which that implies, h is maximum at t = 4.5.

Now, we calculate the maximum height, by putting in t = 4.5, in the equation, to get:

h = -16(4.5)² + 136(4.5) + 72,

or, h = -16(20.25) + 612 + 72,

or, h = -324 + 684 = 360.

Therefore, The maximum height of the ball is 360 feet.

b) How many seconds does it take until the ball hits the ground?

The time taken can be calculated by putting the value of h = 0, and solving the quadratic function h = -16t² + 136t + 72, as the height of the ball at the ground is 0.

Therefore, it can be written as:

0 = -16t² + 136t + 72.

or, 16t² - 136t - 72 = 0.

Solving this using the quadratic equation, we get:

\(t = \frac{-(-136)\pm \sqrt{(-136)^{2} - 4(16)(-72)}}{2(16)}\) ,

or, \(t = \frac{136\pm \sqrt{18496 + 4608}}{32}\) ,

or, \(t = \frac{136\pm \sqrt{23104}}{32}\) ,

or, \(t = \frac{136\pm 52}{32}\)

Therefore, either t = (136+152)/32 = 9,

or, t  (136 - 152)/32 = -0.5.

Since t represents time, we won't take the negative value, and hence t = 9.

Therefore, The time taken by the ball to hit the ground is 9 seconds.

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Answer:

Step-by-step explanation:

To calculate the missing sides square the  side length of the legs of the  triangles(  the lines that form a 90 degree angle) then add them together, then take the sqr root of that to find the hypotunse( the slanted side). In simplier terms, here how it look.

\(a^{2}+b^{2} =c^{2}\)

where a and b are the legs, and c is the hypotunese.   For example, Ill do 3. The bases are 22, and 11 so plug them in the equations.

\(a^{2}+b^{2} =c^{2}\)

11^2+22^2=c^2

121+484=c^2

605=c^2

c=about 24.6

The first step to solve this question is to draw the vectors.

Let's start by a=(-3,-5):

Continue with b=(1,4):

The resulting vector of the substraction a-b is drawn by linking the head of both vectors:

The resulting vector is the one that is green.

There are 152 red pens and 190 blue pens in Max's drawer, given that there are a total of 342 pens altogether.

Let's solve the problem step by step:

Identify the given information:

The ratio of red pens to blue pens is 4 to 5.

There are a total of 342 pens in the drawer.

Set up the ratio equation:

Let's assume the number of red pens is 4x, and the number of blue pens is 5x.

Here, 'x' is a scaling factor that allows us to find the actual number of pens.

We can write the equation as: 4x + 5x = 342.

Simplify and solve the equation:

Combining like terms, we have 9x = 342.

Divide both sides of the equation by 9 to solve for 'x':

x = 342 / 9 = 38.

Calculate the number of red pens and blue pens:

Now that we have the value of 'x', we can find the number of red and blue pens:

Number of red pens: 4x = 4 × 38 = 152.

Number of blue pens: 5x = 5 × 38 = 190.

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Answer:

\( {b}^{o} = {118}^{o} \)

Step-by-step explanation:

Hint :

Sum of angles = 180°

Simplify :

\( {29}^{o} + {33}^{o} + {b}^{o} = {180}^{o} \)

\( {62}^{o} + {b}^{o} = 180^{o} \)

\( { b}^{o } = {180}^{o} - {62}^{o} \)

\( {b}^{o} = {118}^{o} \)

Answer:

X = -7/2

Step-by-step explanation:

Answer:

x = -7/2

Step-by-step explanation:

-(7-2x)+7=-7

          -7   -7

Start by subtracting -7 from both sides.

-(7-2x) = -14

Divide both sides by -1 to eliminate the negatives.

-(7-2x) = -14

---------     -------

-1               -1  

Simplify.

7-2x = 14

Subtract -7 from both sides.

-2x = -7

Divide both sides by -2

-2x = -7

-----    ----

-2        -2

x= -7/2

Check if -7/2 by plugging it back into the equation: (-7/2 = -3.5)

-(7-2(-3.5))+7 = -7

Answer:

The actual dimensions of the floor are 12,5m by 1,8m.

Step-by-step explanation:

Scale problems are solved by proportions, using a rule of three.

Scale of 1:50

This means that each cm on the cupboard has a real dimension of 50 cm

25 cm on the cupboard:

So the real dimension is:

25*50 = 1250 cm = 12,5m

3.6 cm

The real dimension is:

3.6*50 = 160 cm = 1,8 m

The actual dimensions of the floor are 12,5m by 1,8m.

Answer:

2nd option:

8x+2y=32

x+y=7

Step-by-step explanation:

Answer:

It is in fact the second one.

Step-by-step explanation:

It says that he bought a total of 7 tickets and it cost $32.

x represents the number of adult tickets and y represents the number of chid tickets.

So:

x + y = 7 because the adding the number of adult and child tickets should equal the total number bought.

and

8x + 2y = 32 because each adult ticket was 8 dollars and each child was 2 and the total should add up to 32

Answer:

y= -1 and x = 10

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(x-y=242x-4y=24x-2y=12x-y=2x-4y\)

Impossible

Answer:

Since the sum is 38, y must be 15. And indeed the difference between 23 and 15 is 8, so it's correct.

Answer:

15 & 23

Step-by-step explanation:

I used an insert and check kind of method. Basically you insert numbers and check if they work for both equations. the equations are as follow:

X + Y = 38

X - Y = 8

I inserted various combinations of numbers and we'll use one as reference.

I used 16 and 22. 16 and 22 correctly fits the requirements of the first equation but when we do 22 - 16 we see that it equals 6. this is 2 off from the second equation. Using this info I ask myself, was the answer close or far from the answer needed.

Hope this answered any questions. please comment on this if you need any othern have a nice day!

a. Expenses: Books and supplies, Housing and food, Tuition and fees, Transportation and Personal expenses. Funding: Savings,

Scholarships, Grants and Student loans.

b. Total estimated expenses are $29,400

(a) Below is an estimate of all her expenses and sources of funding for her 2-year college education.

Expense:

Books and supplies: $1700

Housing and food: $14,020

Tuition and fees: $11,660

Transportation: $2040

Personal expenses: $2980

Funding:

Savings: $7800

Scholarships: $10,240

Grants: $11,600

Student loans: $6200

(b) What is the total of her estimated expenses?

To find the total estimated expenses, we need to add up all the expenses mentioned:

$1700 + $14,020 + $11,660 + $2040 + $2980 = $29,400

Therefore, the total estimated expenses for Nicole's 2-year college education is $29,400.

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AC is not equal to CE based on the angle bisector theorem. The answer is: C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

According to the angle bisector theorem, when a line segment divides an angle of a triangle, the line segment also divides the opposite side but does so in such a way that the two segments are proportional to the other two sides of the triangle. However, the two segments are not congruent to each other.

In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.

Therefore, we can conclude as saying:

C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

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Answer:Noah

Step-by-step explanation:

In the first mixture, the amount of soda is more and in the second mixture, the amount of orange juice is more.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Sparkling Orange Juice Lin and Noah each have their own recipe for making sparkling orange juice.

Lin mixes 3 liters of orange juice with 4 liters of soda water. Then the ratio is given as,

Juice / Soda water = 3 / 4

Juice / Soda water = 0.75

Noah mixes 4 liters of orange juice with 5 liters of soda water. Then the ratio is given as,

Juice / Soda water = 4 / 5

Juice / Soda water = 0.80

In the first mixture, the amount of soda is more and in the second mixture, the amount of orange juice is more.

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Answer:

60:61.8 OR 10:10.3

Step-by-step explanation:

Cant be simplified - unless your in advanced classes. If so

10:10.3

Answer:

Step-by-step explanation:

1/3 or 0.3 or 33.333333% or 3^-1 or 3.333333 x 10^-1

Answer:

x=24

Step-by-step explanation:

Darren needs approximately 49 feet of tape.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

P = 2(L + W)

P = 2(10 + 8)

P = 2(18)

P = 36 feet.

In Mathematics and Geometry, the perimeter of a semicircle can be calculated by using this mathematical equation:

P = 2(π × radius)

P = 2(3.14 × 8/4)

P = 2(6.28)

P = 12.56 feet.

Approximate length of tape = 12.56 feet + 36 feet

Approximate length of tape = 48.56 ≈ 49 feet.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.

The profit earned by selling w pear trees is 2w + 10

To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:

\((w^2 - 4w + 14) - (2w + 10)\)

Simplifying the expression:

\(w^2 - 6w + 4\)

Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).

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The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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The simplest form of the expression is -3x³ + 2x² + 13x -10

An algebraic expression in mathematics is an expression that is made up of letters and numbers, along with algebraic operations (addition, subtraction, multiplication, etc).

-(x − 2)(3x² + 4x − 5) can be expressed in simplest form as follows:

-(x − 2)(3x² + 4x − 5) = (-x +2)(3x² + 4x − 5)

                                 = -x(3x² + 4x − 5) + 2(3x² + 4x − 5)      

                                 = -3x³-4x²+5x + 6x²+8x-10

                                 = -3x³ + 2x² + 13x -10

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Answer:

\(y=-\,(x+1)^2+3\)

Step-by-step explanation:

Notice that the vertex of the parabola is at (-1, 3), so we can start the expression of the quadratic in vertex form as:

\(y=a\,(x--1)^2+3\\y = a\,(x+1)^2+3\)

we can now find the coefficient "a" by using another point the parabola goes through, like for example (0,2):

\(y = a\,(x+1)^2+3\\2=a\,(0+1)^2+3\\2=a+3\\a=2-3\\a=-1\)

So the final expression for the parabola in vertex form is:

\(y=-\,(x+1)^2+3\)

Part 1

Angles of a quadrilateral add to 360 degrees.

\(7x+65+85+105=360\\\\7x+255=360\\\\7x=105\\\\x=15\)

Part 2

If \(x=15\), then \(7x=105^{\circ}\). Thus, the angles measuring \(7x\) and \(105^{\circ}\) are opposite angles since opposite angles of a kite are congruent.

This means the remaining angles, which are the angles measuring \(65^{\circ}\) and \(85^{\circ}\), are also opposite using the process of elimination.

Answer:

21/40=0.525

You basically just divided 21 and 40 and get the answer of 0l525

Answer:

B) b=13

Step-by-step explanation:

13-4x is the same as -4x+13

Answer:

1260.04

Step-by-step explanation:

The formula for compound interest is:

A = P(1+\(\frac{r}{n}\)\()^{nt}\) where A is the final amount, P is the initial principal balance, r is the interest rate, n is the number of times interest applied per time period and t is the number of time periods elapsed. Since the deposit was compounded annually, just like the interest, we can omit the n in the equation.

Applying the formula to question:

800(1+\(\frac{2.88}{100}\)\()^{16}\) = 1260.04 (rounded off to nearest cent since it's money)