Indicate whether the measures 3. 1, 4. 8, and 10. 2 can be the side lengths of a triangle. If they can, classify the triangle

Answer:

49=5x+14

Step-by-step explanation:

There is no danger of a collision, as the two paths will never met, due to the negative discriminant of the quadratic function.

A quadratic equation is modeled by the general equation presented as follows:

y = ax² + bx + c

The discriminant of the quadratic function is given by the equation as follows:

Δ = b² - 4ac.

The numeric value of the coefficient and the number of solutions of the quadratic equation are related as follows:

The equations for this problem are given as follows:

Replacing the first equation into the second, we have that:

x + x² + 1 = -4

x² + x + 5 = 0.

The coefficients are:

a = 1, b = 1, c = 5.

Hence the discriminant is of:

Δ = 1² - 4 x 1 x 5

Δ = -19.

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The largest area is 8.978 unit²

Given:

A rectangle is to be inscribed under the arc of the curve y = 4cos(0.5x)

from x = -π to x = π.

it is clear that the coordinates of the rectangle are

(−x,0),(x,0),(−x,4cos(0.5x)) and (x,4cos(0.5x)) where x∈(−π,π)

Thus, the area of the rectangle is

A =2x(4cos(0.5x))=8xcos(0.5x)

Now, find the value of x for which the area is largest by using derivative tests.

Differentiate A with respect to x,

A′=8(1(cos(0.5x))+x(−(0.5)sin(0.5x)))=8cos(0.5x)-4xsin(0.5x)

Now, find critical values by putting A′=0,

A′=0

8cos(0.5x)−4xsin(0.5x)=0

8cos(0.5x)=4xsin(0.5x)

2=xtan(0.5x)

Use the graph utility to get,

x≈1.721

At x=1.721, A'′<0. So, the area is largest at x=1.721.

Therefore, the dimensions of the rectangles will be:

Length will be:

2x=2(1.721)=3.442unit.

Width will be:

4cos(0.5x)=4cos(0.5(1.721))=2.608unit.

And the area will be:

A=8xcos(0.5x)

=8(1.721)cos(0.5(1.721))

=8.978 unit²

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To represent the requirement that a company makes at least 20 units of products X1 and X2, you can use the following set of lower bound constraints:

\(1. X1 \geq 20\\2. X2 \geq  20\)

These constraints indicate that the production of X1 must be greater than or equal to 20 units, and the production of X2 must also be greater than or equal to 20 units.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

x^2 -y^2 = 25

x/y = 3/2    or   x = 3/2 y   <=====sub into first equation

(3/2 y)^2 - y^2 = 25

9/4 y^2 - y^2 = 25

5/4 y^2 = 25

y^2 = 25 (4/5) = 20

y = sqrt (20) = 2 sqrt 5

                then x = 3/2 y =  3 sqrt5

Answer:

20

Step-by-step explanation:

use the cos or sin function to solve

Step-by-step explanation:

using 30°

we use cos

using 60

we use Sin

Answer:

B. 7 1/2 cups

Explanation:

Zoe uses 1 1/4 cups of flour in each batch of cookies. So, first, let's convert 1 1/4 to a fraction as follows

It means that Zoe uses 5/4 cups of flour in each batch. Then, the amount used in 6 batches will be 6 times 5/4 cups which is equal to

Now, we need to convert 15/2 into a mixed number.

Dividing 15 by 2, we get a quotient of 7 and a remainder of 1, so

So, the answer is

B. 7 1/2 cups

Answer:

B

Using gradient of two points and equation of a straight line graph.

Answer:

Length = x^2 = 0.835^2 = 0.698 m = 69.8cm

Breadth = x = 0.835 m = 83.5cm

Step-by-step explanation:

Given;

Length of the rectangular plot l = x^2 m

Breadth b = x m

Area A = 5832 cm^2 = 0.5832 m^2

(They should be converted to the same units before solving: length in metres and area in square metres)

The area of a rectangular plot can be calculated using the formula;

Area = length × breadth

A = l × b

Substituting the values of l and b;

A = x^2 × x

A = x^3

Substituting the value of A;

0.5832 = x^3

solving for x;

x = (0.5832)^(1/3)

x = 0.835 m

Length = x^2 = 0.835^2 = 0.698 m = 69.8cm

Breadth = x = 0.835 m = 83.5cm

Standard Deviation: 10.98353746468301

Answer: Manuel Because He was on the motor bike less. She was in the car driving for 4 HOURS he was on the bike less for a grand total of 3.5 HOURS so MANUEL was faster. :)

And he was faster by 30 minutes...

This is one of those questions where they try to put you focus on something else like speed speed does not matter!! :)

Angle A is 19 degrees.

Angle C is 90 degrees.

Side a is approximately 7.83.

Side c is approximately 34.50.

To solve the right triangle given that B = 71 degrees and b = 24, we can use the trigonometric ratios sine, cosine, and tangent.

Finding Angle A:

Angle A is the complementary angle to B in a right triangle, so we can calculate it using the equation:

A = 90 - B

Substituting the given value, we have:

A = 90 - 71

A = 19 degrees

Therefore, Angle A is 19 degrees.

Finding Angle C:

Since it is a right triangle, Angle C is always 90 degrees.

Therefore, Angle C is 90 degrees.

Finding Side a:

We can use the sine ratio to find the length of side a:

sin(A) = a / b

Rearranging the equation to solve for a, we have:

a = b * sin(A)

Substituting the given values, we have:

a = 24 * sin(19)

a ≈ 7.83

Therefore, the length of side a is approximately 7.83.

Finding Side c:

Using the Pythagorean theorem, we can find the length of side c:

c^2 = a^2 + b^2

Substituting the given values, we have:

c^2 = 7.83^2 + 24^2

c^2 ≈ 613.68 + 576

c^2 ≈ 1189.68

Taking the square root of both sides to solve for c, we have:

c ≈ √1189.68

c ≈ 34.50

Therefore, the length of side c is approximately 34.50.

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0.278 decimal is equivalent to the fraction of students who like to play basketball.

Suppose the fraction is proper (the numerator is smaller than the denominator).

Let it be

\(\dfrac{a}{b}\)

Then, we can interpret it as:

\(\dfrac{a}{b} = a\) parts out of b parts of a thing.

Five-eighteenths of the students surveyed like to play basketball.

\(\dfrac{5}{18} \\\\= 0.278\)

Therefore,

0.278 decimal is equivalent to the fraction of students who like to play basketball.

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Answer:

P=15,625

Rate=4%

Time=3 years

CI=P(1+R/100)^T

=15,625(1+4/100)^3

=15,625*1.124864

=17576 Ans

Step-by-step explanation:

hope it helps

Answer:

No solutions.

Step-by-step explanation:

4x+8y=-11    (1)

X+2y=-7

Mutiply the second equation by -4:

-4x - 8y = 28

Now add this equation to equation (1):

0 + 0 = 17

which is absurd

So there are no solutions

Answer:

10+(-4)=6

Step-by-step explanation:

Answer:

-4 + 10

Step-by-step explanation:

AB= 9 UNITS

hope it helps you...

Answer:

by Pythagoras theorem

in first

a²+ b² = c²

6² + 9² = c²

36 + 81 = 117

AD = 117

and in second

a² + b² = c²

a² + 6² = 117

a² = 117 - 36

AB² = 81

AB = 9

The function f(x) = ln(2 + sin(x))) is concave up for the range of x [0,2].

To discover the interval(s) on which f(x) = ln(2 + sin(x)) is concave up, compute the function's second derivative and check its sign.

To begin, compute the first derivative of f(x) with respect to x:

(1 / (2 + sin(x)) = f'(x)cos(x)

The second derivative of f(x) can therefore be found by taking the derivative of f'(x) with regard to x:

f''(x) = -(1/(2 + sin(x))(-sin(x)) cos2(x) + (1/(2 + sin(x))

When we simplify f''(x), we get:

f''(x) = -1/(2 + sin(x))²)sin(x)(sin(x)-2)

To discover the interval(s) where f(x) is concave up, we must first locate the interval(s) where f''(x) is positive. Because sin(x) might vary from -1 to 1, we must solve the inequality:

-(1/(2 + 1))^2(-1)(-1-2)≤f''(x)≤-(1 / (2 - 1))²(1) (1-2)

When we simplify this inequality, we get:

1/9 ≤ f''(x) ≤ -1/4

So, f is never negative at 0 ≤ x ≤ 2, so f is concave up in the range 0 ≤ x ≤ 2.

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Complete question - f(x) = ln(2 + sin(x)), 0 ≤ x ≤ 2 . Find the interval(s) on which f is concave up.

Answer:

Set your calculator to degree mode.

cos^-1 (2/5) = 66.42°

Angle B measures 66.42°.

Answer:

  66.42°

Step-by-step explanation:

You want the measure of angle B in right triangle ABC with hypotenuse AB = 5 and adjacent side BC = 2.

The cosine relation is ...

  Cos = Adjacent/Hypotenuse

  cos(B) = BC/BA . . . . . use the definition

  B = arccos(BC/BA) . . . . . use the inverse function

  B = arccos(2/5) ≈ 66.42°

The measure of angle B is about 66.42°.

__

Additional comment

Your calculator needs to be in degrees mode.

<95141404393>

Answer:

Their is no answer if you don't ask  question.

Step-by-step explanation:

Answer:

(7, -1)

Step-by-step explanation:

3x + 7y = 14

y = x - 8

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

Add 56 to both sides.

10x = 70

Divide both sides by 10.

x = 7

3(7) + 7y = 14

21 + 7y = 14

Subtract 21 from both sides.

7y = -7

Divide both sides by 7.

y = -1

(7, -1)

The measure of angle A in the isosceles triangle ABC is 62.5 degrees.

In an isosceles triangle ABC, where AB = AC, we are given that angle B (denoted as ∠B) measures 55 degrees. We need to calculate the measure of angle A (denoted as ∠A).

Since AB = AC, we know that angles A and C are congruent (denoted as ∠A ≅ ∠C). In an isosceles triangle, the base angles (the angles opposite the equal sides) are congruent.

Therefore, we have:

∠A ≅ ∠C

Also, the sum of the angles in a triangle is always 180 degrees. Hence, we can write:

∠A + ∠B + ∠C = 180

Substituting the given values:

∠A + 55 + ∠A = 180

Combining like terms:

2∠A + 55 = 180

Subtracting 55 from both sides:

2∠A = 180 - 55

2∠A = 125

Dividing by 2:

∠A = 125 / 2

∠A = 62.5

Therefore, the measure of angle A in the isosceles triangle ABC is 62.5 degrees.

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The value of y = -651. To find the value of y when x = -10 and z = 20, given that y varies jointly as x and z and y = 179 when x = -5 and z = -11, follow these steps:

Step 1: Understand that "y varies jointly as x and z" means y = kxz, where k is the constant of variation.

Step 2: Use the given values (y = 179, x = -5, z = -11) to find k. Substitute these values into the equation:
179 = k(-5)(-11)

Step 3: Solve for k:
179 = 55k
k = 179 / 55
k = 3.2545 (rounded to the nearest hundredth)

Step 4: Use the found value of k (3.2545) and the new values of x (-10) and z (20) to find the new value of y:
y = (3.2545) (-10)(20)
Step 5: Calculate y:
y = -651
So, when x = -10 and z = 20, y = -651.

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Answer:

.

Step-by-step explanation:

Answer:

.

Step-by-step explanation:

The value of function x is 4 - 2i.

Given information is that y = 1 + 2i and

x = y - (25ybar) / y²,

we can substitute the value of y in the equation of x as follows;

x = y - (25ybar) / y²

= (1 + 2i) - (25(1 - 2i)) / (1 + 2i)²

Now we have to find the value of x which can be found by simplifying the above equation as follows;

(1 + 2i)² = 1² + 2(2i) + (2i)²

= 1 + 4i - 4

= -3 + 4i`(1 + 2i)²

= -3 + 4i

Now, the value of x can be found as follows;

x = (1 + 2i) - (25(1 - 2i)) / (-3 + 4i)

= 1 + 2i - (25 - 50i) / (-3 + 4i)

= (1 + 2i) - ((25(-3 - 4i)) / (-3 + 4i)²)

= (1 + 2i) - ((-75 + 100i) / 25)

= (1 + 2i) - (-3 + 4i)

= 4 - 2i

Hence, the value of x is 4 - 2i.

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Answer:

4320

Step-by-step explanation:

Multiply 18000 by 6 then multiply it by 0.04 and you get 4320

IT IS AAAAAAAAAAAAAA

$18,000x6 then divide by .40

So it should be d!

Answer:

65

Step-by-step explanation:

Method 1(Algebra):

m - 14 = 51

Add 14 to both sides of the equation.

m - 14 + 14 = 51 + 14

Combine like terms.

m = 65

Method 2:

m - 14 = 51

Move negative fourteen(- 14) to the other side of the equation. Because we moved it, it is now positive fourteen( + 14)

m = 51 + 14

Combine like terms.

m = 65