simplify  ( √ 5 ) ( 3 √ 5 )

Answer:

48160

Step-by-step explanation:

Answer:

The series converges as any two consecutive elements of the sum are monotonically decreasing.

Step-by-step explanation:

The series converges since the consecutive element is monotonically decreasing. That is:

[tex]\forall\,i\in \mathbb{N}\,a_{i} > a_{i+1}[/tex] (1)

Where:

[tex]a_{i}[/tex] - The i-th component of the sum.

[tex]a_{i+1}[/tex] - The (i+1)-th component of the sum.

Answer:

9.41 km/h

Step-by-step explanation:

The total distance of the race, d = 8 km

The time Sarah took to run the race, t = 55 mins

The time Jo started the race = 3 mins later than Sara

The point Jo caught up with Sarah = 6 km into the race

The rate at which Jo and Sarah ran = Constant speed

The required information = Jo's speed

From the information given, Sarah's speed, v = 8 km/(55 mins) = (8/55) km/min × 60min/h = 96/11 km/h

The time it would take Sarah to run 6 km = 6 km/(8 km/(55 mins)) = 41.25 mins

Given that Jo started 3 minutes late, and they both arrive at 6 km into the race at the same point in time, the time it took Jo to arrive at 6 km into the race = The time it took Sarah - 3 minutes

∴ The time it took Jo to run the 6 km = 41.25 minutes - 3 minutes = 38.25 minutes

Given that Jo ran at a constant speed, and speed = distance/time, we have;

Jo's speed = 6 km/(38.25 min) = 8/51 km/min × 60 min/h = (160/17) km/h ≈ 9.41 km/h.

Answer:

assuming that the problem was actually

-1/12 x ^ 2 + 2x + 4

height = 16

(12,16)

forty feet (40) feet

vertex = -b/2a = -2/(-1/6) = 12

f(12) = - 144/ 12 + 24 + 4 = -12+ 24 + 4   = 16

Step-by-step explanation:

=============================================

Work Shown:

sin(2x) = sin(x)

sin(2x) - sin(x) = 0

2*sin(x)*cos(x) - sin(x) = 0

sin(x)*(2cos(x) - 1) = 0

sin(x) = 0 or 2cos(x)-1 = 0

sin(x) = 0 or cos(x) = 1/2

Using the unit circle, the solutions to sin(x) = 0 are x = 0, x = pi, x = 2pi

Also, the solutions to cos(x) = 1/2 are x = pi/3, x = 5pi/3

So the entire solution set on the interval [0,2pi] is {0, pi/3, pi, 5pi/3, 2pi} when written in increasing order.

All solutions to the equation in the interval [0, 2[tex]\pi[/tex]]  is  {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}.

A solution is an assignment of values to the unknown variables that makes the equality in the equation true.

As sin2x = 2 sinx cosx,

sin2x = sinx is equivalent to

2 sinx cosx = sinx or 2 sinx cosx − sinx = 0 or

sinx (2cosx − 1) = 0 i.e.

either sinx = 0 and x = 0, π, 2π

or 2cosx − 1 = 0 i.e. cosx = [tex]\frac{1}{2}[/tex] i.e. x = [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]

Hence, solution to an equation is x = {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}

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Answer:

is 0.24 yards in the option, becausw i am getting this as my answer

Answer:

The first one with the sequence 0.25,1,4,16

Answer:

the first one

Step-by-step explanation:

Answer: i do not see a graph

Step-by-step explanation:

Answer:

6+18x

Step-by-step explanation:

=6(1+3x)

=6×1+6×3x

=6+18x

Answer:

The table will be:

x |-2 | -1 | 0 | 1 | 2  

y | 1  | 4 | 5 | 4 | 2

Step-by-step explanation:

The function is:

[tex]y=5-x^{2}[/tex]

a) The x values of the table is:

x |-2 | -1 | 0 | 1 | 2

So, when x = -2, y will be:

[tex]y(-2)=5-(-2)^{2}=5-4=1[/tex]

Doing the same with the other x values we have:

[tex]y(-1)=5-(-1)^{2}=5-1=4[/tex]

[tex]y(0)=5-(0)^{2}=5[/tex]

[tex]y(1)=5-(1)^{2}=5-1=4[/tex]

[tex]y(2)=5-(2)^{2}=5-4=1[/tex]

The table will be:

x |-2 | -1 | 0 | 1 | 2  

y | 1  | 4 | 5 | 4 | 1

I hope it helps you!

Answer:

3/2

Step-by-step explanation:

Rate of change is given by

f(x2) -f(x1)

-----------------

x2 -x1

We know x2 is 0 and x1 is -2

f(x2) is -1 and f(x1) is -4

-1 - ( -4)

----------

0 - -2

-1 +4

--------

0+2

3/2

Answer:

[tex]15\text{ grams}[/tex]

Step-by-step explanation:

Since the mass of the radioactive isotope is halved every 69 years, we want to multiply its initial mass by [tex]1/2[/tex] every 69 years.

We can model this using the following equation:

The remaining mass, [tex]f(x)[/tex], is equal to the initial mass multiplied by [tex]\frac{1}{2}^{(\frac{t}{69})}[/tex], where [tex]t[/tex] is the number of years that have passed from the initial mass. The reason why the exponent is [tex]\frac{t}{69}[/tex] is because we only want to half the mass every 69 years, so [tex]\frac{69}{69}=1[/tex] and [tex]\frac{1}{2}^1=\frac{1}{2}[/tex].

Thus, we have:

[tex]f(x)=20\cdot \frac{1}{2}^{(t/69)}[/tex]

Substituting [tex]t=30[/tex], we get:

[tex]f(x)=20\cdot \frac{1}{2}^{(30/69)}=20\cdot 0.73980522316=14.7961044632\approx \boxed{15\text{ grams}}[/tex]

Answer:

400×16

Step-by-step explanation:

let the number be n.

[tex] \frac{n}{16 } = 400 \\ 16 \times \frac{n}{16} = 400 \times 16\\ n = 400 \times 16[/tex]

Answer:

m<L, m<K, m<J

Step-by-step explanation:

The angle that sees the longest side length has the biggest measurement

so

for listing the angles from smallest to largest

m<L, m<K, m<J

Answer:K J L

Step-by-step explanation:

Answer:

[tex]y=1[/tex]

Step-by-step explanation:

Given:

[tex]6=2(y+2)[/tex]

Distribute the parenthesis

[tex]6=2y+4[/tex]

Subtract both sides by 4

[tex]2=2y[/tex]

Divide both sides by 2 to get [tex]y[/tex] alone

[tex]1=y[/tex]

Hope this is helpful

Oh shucks man, I'm sorry bout that

Answer: (-2,1) deduced from graph

the point where the two lines intersect is the solution

Step-by-step explanation:

Answer:

(- 2, 1 )

Step-by-step explanation:

Given a system of equations graphically then the solution is at the point of intersection of the 2 lines.

The point of intersection = (- 2, 1 ) ← solution

Step-by-step explanation:

pls type the question

properly and I swear I will solve it

Answer:

(5,-2)

Step-by-step explanation:

4x – 6y = 32

2x + 3y = 4      (multiply everything by 2. This will allow for the elimination of                        one of the variables. In this case, the y. )

4x – 6y = 32

4x + 6y = 8       (Now add them together)

__________

8x        = 40      (Divide by 8, both sides)

x   = 5

4(5) - 6y = 32  ( Substitute the x value into one of the original equations)

20 - 6y = 32    (Subtract the 20 from both sides)

-6y = 12            Divide by the -6, both sides)

y = -2

Answer:

12

Step-by-step explanation:

Answer:

6.55 cm

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, acute, scalene, obtuse, right and equilateral triangle.

Cosine rule is used to show the relationship between sides and angles of a triangle. If a, b, and c are sides of a triangle, while A, B, and C are angles opposite to the corresponding sides. Then:

c² = a² + b² - 2ab*cos(C)

Given that PR = 13 cm, PQ = 12 cm and angle QPR = 30°, hence:

QR² = PR² + PQ² - 2(PR)(PQ)cos(∠QPR)

QR² = 13² + 12² - 2(13)(12)cos(30) = 169 + 144 - 270

QR² = 43

QR = 6.55 cm

I wrote it down, sorry if it’s a little bit messy.

The correct option regarding the discriminant and the number of real roots for this equation is given by:

D. -23; no real roots

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The discriminant is:

[tex]\Delta = b^2 - 4ac[/tex]

The solutions are as follows:

In this problem, the function is:

x² + 3x + 8.

Hence the coefficients are a = 1, b = 3, c = 8, and the discriminant is given by:

[tex]\Delta = b^2 - 4ac = 3^2 - 4(1)(8) = -23[/tex]

Negative discriminant, hence no real roots, and option D is correct.

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Are these converses true? The answer is yes. Each of these converses can be a way to show that a quadrilateral is a parallelogram. However, the Consecutive Angles Converse can be a bit tricky, considering you would have to show that each angle is supplementary to its neighbor

(∠A

and

∠B, ∠B

and

∠C, ∠C

and

∠D

, and

∠A

and

∠D)

. We will not use this converse.

1. Answer is option 3

2. Answer is option 3

Answer:

for #1 it's the 3rd one and for #2 it's the 4th one (2.8 meters)

Answer:

2

Step-by-step explanation:

Parallel lines have the same slopes

If the slope of line a is 2, the slope of line b is 2

Answer:

slope of line b = 2

Step-by-step explanation:

The slopes of parallel lines are equal

Given slope of line a = 2 and parallel to line b , then

slope of line b = 2

Answer:

It's the 3rd one, that you've selected in the picture.

Step-by-step explanation:

Used a graphing calculator to check,

Hope this is helpful.

Answer:

???????????????????????

Step-by-step explanation:

sorry di ko po alam yung sagot pasensiya na po

Given :

Parallel lines are

x – 2y = 3 and 2x – 4y = 12

Step-by-step explanation:

Lets write the given lines in slope intercept form y=mx+b

[tex]x -2y = 3 \\-2y=-x+3\\Divide \; both \; sides \; by -2\\y=\frac{x}{2} -\frac{3}{2}[/tex]

From the above equation , y intercept of first line is [tex]\frac{-3}{2}[/tex]

Solve the second equation for y and find out y intercept

[tex]2x-4y=12\\-4y=-2x+12\\Divide \; by \; -4\\y=\frac{1}{2} x-3[/tex]

y intercept of second line is -3

To find the distance between parallel lines, we subtract the y intercepts

[tex]\frac{-3}{2} -(-3)=\frac{-3}{2} +\frac{6}{2} =\frac{3}{2} =1.5[/tex]

Answer:

The distance between the parallel lines = 1.5

Reference:

https://brainly.com/question/24145911

Answer:

1<1.35<2

Step-by-step explanation:

Answer:

1.35 is closer to 1 than 2

So the bag of nuts weighed about 1 pound.

Step-by-step explanation:

The decimal is closer to the whole number 1 when plotted on a number line, so it rounds to 1.