Write 28/16 as a mixed number in its simplest form. A 1 3/4 B 1 12/16 C 2 1/4 D 7/4 (2023)

Answer:

Dimensions of the rectangular area:

x = 125 feet

y = 125 feet

A(máx) = 15625 ft²

Step-by-step explanation:

Let's call x and y the width and height of the rectangular area. and P the circumference

So

A = x*y

And since we have 150 meters of fencing material

P = 2*x + 2*y ⇒ 500 = 2*x + 2*y ⇒ y = (500 - 2x) / 2

y = 250 - x

So the rectangular area is:

A = x * y ⇒ A (x) = x* ( 250 - x ) ⇒ A (x) = 250*x - x²

Taking derivatives on both sides of the equation, we get:

A´(x) = 250 - 2*x

A´(x) = 0 250 - 2*x = 0 ⇒ 2x = 250 ⇒ x = 125 Kuchen

Y y = 250 - x ⇒ y = 125 Fuß

We really have a 125 foot square.

To the area

A (max.) = 125*125 = 15625 ft²

Answer:

Similarity: both functions have the same vertex in the point.

Difference: It is a downward opening parabola while it is an upward opening parabola.

Step-by-step explanation:

We got two functions: and . We are asked to compare the graphs of the given function.

We know that the standard form of a parabola with vertex at (h,k) has the form

Let's find the similarity in both diagrams.

• Comparing both functions with the standard shape of a parabola, we can see that the vertex of both parabolas is in the point.

Let's find the difference in both graphs.

We can see that the leading coefficient is positive, so it is a parabola with an upward opening.

We can also see that the leading coefficient of is negative, so it is a downward opening parabola.

Answer:

a) Application of the Pythagoras theorem

b) Trigonometric relationships

c) No, we can't

d) No, we can't

e) See step-by-step explanation

f) View the explanation step by step

Step-by-step explanation:

a) The easiest way to calculate the missing page is to use the Pythagoras theorem

c² = a² + b²

c² = (5)² + (12)² ⇒ c² = 25 + 144 ⇒ c² = 169 ⇒ c = 13

b) The easiest way to find the missing angles is to calculate sin∠ and then look up the arcsin function in the tables.

sin ∠α = 5/13 sin ∠α = 0.3846 ⇒ arcsen (0.3846 ) α = 23⁰

Now we can get the other angle by subtracting 180 - 90 - 23 = 67⁰

Of berek sinβ = 12/13 sinβ = 0.9230 arcsin(0.9230) β = 670

c) The law of cosines should not be applied to right triangles, in fact, for example, we have in our particular case:

question a)

c2 = a2 + b2 - 2*a*b*cos900 (cosinusverhooding), maar cos 900 =

then c² = a² + b², which is the expression of the Pythagorean theorem

Just in case you want to calculate the missing angles

c² = a² + b² - 2*5*13*cos a

169 = 25 + 144 - 2*5*13* well one

As you can see, 169 - 25 - 144 = 0

Therefore, we cannot apply the law of cosines in right triangles, we have to apply the trigonometric relations and the Pythagorean theorem, and as we have seen, you can get the expression of the Pythagorean theorem from the law of cosines.

c² = a² + b² - 2*a*b*cos∠90° cos∠ 90° = 0

Entonces c² = a² + b²

Answer:

The value of a is .

Step-by-step explanation:

The given expression is

A quadratic expression is a complete square if

For the given expression a=a,b=1 and c=3.

Add 12a on both sides.

Divide both sides by 12.

Hence the value of a.

Answer:

Step-by-step explanation:

We got a printout. We are asked to round the square of the given expression.

First we factor our a like this:

Now we need to add and subtract half the square of the mean term, that is:

Hence our requirement would be square.

Answer:

96 units.

Step-by-step explanation:

Let a, b be the legs and c be the hypotenuse of the given right triangle.

We are told that in the given triangle all lengths of the sides are integer multiples of 8. Using the Pythagorean theorem, we can represent this information in an equation like this:

If we divide both sides by 64, we get:

We know that the smallest Pythagorean triplet is like this.

Since all sides are a multiple of 8, the smallest possible size would be .

Therefore, the smallest possible perimeter of such a triangle would be 96 units.

Answer: You drive 500 miles every day.

Step-by-step explanation:

The Thompson family travels 1,500 miles to visit relatives. You plan to walk the same distance every day.

Let x be the distance they travel each day. If the Thompsons complete the journey in 3 days, that means the total distance they covered in 3 days would be

3 × x = 3x thousand

Therefore, the distance they travel each day would be

3x = 1500

Dividing both sides of the equation by 3 gives:

3x/3 = 1500/3

x = 500 miles

Answer:

$17.27 per hour

Step-by-step explanation:

Answer:

The price for an adult ticket is $10.8 and for a child ticket $5.4.

Step-by-step explanation:

Datum:

Number of adults = 2

Number of children = 6

Total tickets sold = $54.

We need to determine the price for a child ticket and an adult ticket.

Solution:

Let "x" be the price of an adult ticket.

Now given:

Children's tickets are half the price of adult tickets.

Cost for 1 child ticket =

The total amount is equal to the number of adults multiplied by the adult ticket price plus the number of children multiplied by the child ticket price.

Substituting the equation to get;

Cost for 1 adult ticket = $10.8

Cost for 1 child ticket =

Therefore, the price of an adult ticket is $10.8 and a child ticket is $5.4.

Answer:

You will find the answers in the explanation section.

Step-by-step explanation:

Cosine rule for side c:

a) c = 3.561

b) c = 4.136

c) c = 3,09

d) c = 12,5

e) c = 1.978

f) c = 9.173

g) c = 5.196

Cosine rule for angle C:

h) C = 82.819°

yo) C = 60°

j) C = 21.787°

k) C = 68,676°

l) The sides (8, 5, 1) cannot form a triangle. It's impossible.

m) C = 118.454°

The circle (x − 7)² + (y − 8)² = 9 is a circle with center (7.8) and radius 3

Step-by-step explanation:

The equation of the circle with (h,k) as center and radius r is given by:

(x-h)²+(y-k)² = r²

Here we have to describe the circle given by the equation (x − 7)² + (y − 8)² = 9

Change the equation to the form (x-h)²+(y-k)² = r²

(x − 7)² + (y − 8)² = 9

(x − 7)² + (y − 8)² = 3²

Dus h=7, k=8 and r=3

The center is (7.8) and the radius is 3

The circle (x − 7)² + (y − 8)² = 9 is a circle with center (7.8) and radius 3

Answer:

mi)

F)

gram)

H)

I)

J)

Step-by-step explanation:

We can solve this problem by looking at a simple trigonometric table

Here I will list sine and cosine values ​​at the points and

Therefore, the sine takes on the value 1, while in its opposite value - \pi/2 - it takes on the value -1 (because it is an odd function). If we use sin's periodicity, then sin(-\pi/2 + 2\pi) = -1. For this reason

The cos takes the value 1 at 0 and at -1

The tangent is the ratio between sin and cos. The tangent is 1 if both cosine and sine are equal. We can see that they are equal in where they take the value

The tangent is -1 if they are opposite. This happens where they change the value resp.

differences:

• x² can be defined over all real numbers, while 3√x allows only positive values ​​for x (or 0). So the graph of 3√x starts at x = 0
• 3√x increases in its area while x² has an interval in which it decreases.
• x² has a derivative at every element in its domain, while 3√x has no derivative at 0
• The second derivative of x² is positive for all its values, while the second derivative of 3√x is negative. So the graph of x² is convex while the graph of 3√x is concave.

agreements:

• Both functions increase for positive values ​​of x.
• Both functions have a minimum at the point (0,0)
• The rest of the plot points lie above the x-axis (this means that both functions besides 0 take positive values)
• If you set the limit on x to +infty, the result is +infty
• The function has no horizontal or vertical asymptote.

Answer:

Anyone can be 0 or 10/3

Step-by-step explanation:

Since a right triangle has vertices like (6,2), we need to find the third vertex on the y-axis

Since the third vertex is on the y-axis, it would have coordinates like (0,a)

Using the slope formula, we can say that a pair of sides are perpendicular to each other.

Let A (6,2) B (5,5) in C (0,a)

Slope of AB = change in Y coordinate / change in X coordinate = -3

BC helling =

AC helling =

If AB and BC are perpendicular to each other, then

... I

Or if BC and CA are perpendicular to each other, then

(a-5)(a-2)= -30

no real roots

Or when CA and AB are perpendicular to each other

(a-2) =-2

at=0

Anyone can be 0 or 10/3

Answer:

Total free throws attempted = 25

Step-by-step explanation:

From the statement we can say:

20 free throws account for 80% of the total number of attempts

80% in decimals is:

80/100 = 0,8

If the total number of attempts is x, we can say:

20 is 80% (0.8) of x

Now we can write an algebraic equation:

20 = 0.8x

We just solve for x, the number of free throws he attempted:

In total, Kate attempted 25 free throws.

Answer:

35,96 $

Step-by-step explanation:

1 pound = $8.99, so 4 pounds = $?

1/8,99=4/x

1x=4*8,99

x=35,96

Answer:

35,96 $

Step-by-step explanation:

I'll be happy to help you.

Answer:

The answer to your question is to find the center and radius of the polynomial. We conclude that the information provided is correct.

Step-by-step explanation:

x² - 2x + 1 + y² - 4y + 4 = 25

First factor the first three terms into a perfect quadratic trinomial.

(x - 1)² + y² - 4y + 4 = 25

Second, factor the last terms into a perfect quadratic trinomial

(x - 1)² + (y - 2)² = 25

Find the numbers of each factor and change their sign

Example (x -1)² = 1

(y - 2)² = 2

These numbers are the center of the circle (1, 2)

Take the square root of 25

that's the radius

So center = (1, 2) and radius = 5

Answer:

The probability that the card is black or diamonds is 0.75

Step-by-step explanation:

For the probability that the card is black or shows a diamond, the probabilities must be calculated separately and added up.

This is an example of the addition rule for disjointed events.

1. The probability that the card is black is
2. The probability that the card shows diamonds is
3. after all, the probability that the card is black or shows a diamond is 0.5 + 0.25 = 0.75

Answer:

years) 0.872

ii) 0.300

iii) 0,76

iv) 0,704

Step-by-step explanation:

In the question we get the following information:

Average μ = $261.50 per month

standard deviation, σ = $16.25

We learn that the distribution of the monthly cost of groceries for a man aged 14 to 18 is a bell-shaped distribution, i.e. a normal distribution.

Formula:

a) P (minder and $280)

We calculate the value of the standard normal z-table:

b) P (over $270)

P(x > 270)

270) = P( z > \displaystyle\frac{270 - 261,50}{16,25}) = P(z > 0,523)" alt="P( x > 270) = P( z > \displaystyle\frac {270 - 261,50 {16,25}) = P(z > 0,523)" align="absmiddle" class="látex-formula">

We calculate the value of the standard normal z-table:

270) = 1 - 0,700 = 0,300 = 30,0\%" alt="P(x > 270) = 1 - 0,700 = 0,300 = 30,0\%" align="absmiddle" class="látex-formula">

c) P (over $250)

P(x > 250)

250) = P( z > \displaystyle\frac{250 - 261,50}{16,25}) = P(z > -0,707)" alt="P( x > 250) = P( z > \displaystyle\ frac{250 - 261,50}{16,25}) = P(z > -0,707)" align="absmiddle" class="látex-formula">

We calculate the value of the standard normal z-table:

250) = 1 - 0,240 = 0,76 = 76,0\%" alt="P(x > 250) = 1 - 0,240 = 0,76 = 76,0\%" align="absmiddle" class="látex -Formel">

d) P (between $240 and $275)

e) Therefore, 0.704 is the probability that the monthly grocery costs for a randomly selected 14- to 18-year-old male are between $240 and $275.

Answer:

Step-by-step explanation:

Let x be the new price of the shorts.

The original price of the shorts is $12. The store then raises the price by 6%. This means that it is the amount for which the original price has been increased

6/100 × 12 × 0,06 × 12 = 0,72 $

The short sale's new price would be the sum of the original price and the amount it was marked for. Is becoming

x = 12 + 0,72