Evaluate the infinite sum

Answer:

z=4  and z=-1/3  are the zero's

Step-by-step explanation:

To find the zeros of the quadratic function, we need to set it equal to zero.

f(z)=3z^2−11z−4

0 =3z^2−11z−4

Now we need to factor the function

0 = (z - 4) (3 z + 1)

Then using the zero product property set each factor to zero

0 = z-4   0 = 3z+1

Now solve

0+4 = z-4+4          0 -1 = 3z+1-1

4 =z                         -1 = 3z

                                -1/3 = 3z/3

                                   -1/3 =z

Answer:

z=4  and z=-1/3

Step-by-step explanation:

Answer:

C. 20 seconds

Step-by-step explanation:

We want to know when y=0.

We are finding the x intercepts.

The first y is when it started and the second y=0 is when it stops.

Looking at the graph y=0 at x=0 and  y=0 at x=20

The fan started at time 0 and stopped at 20 seconds.

The difference is the length of the test.

20-0 = 20

20 seconds

Answer:

20 seconds

Step-by-step explanation:

Given :

[tex]y=-5x^2+100x[/tex]

Where x  represents time in seconds and y represents the speed in rotations per minute.

To Find : Assuming that the test was complete when the fan stopped spinning completely, how long was the test?

Solution:

Since we are supposed to find how long will it take to stop the fan completely

We assumed that  test was complete when the fan stopped spinning completely

i.e. y = Speed = 0

So, Substitute y = 0 in the equation    [tex]y=-5x^2+100x[/tex]

⇒[tex]0=-5x^2+100x[/tex]

⇒[tex]5x^2=100x[/tex]

⇒[tex]5x=100[/tex]

⇒[tex]x=\frac{100}{5}[/tex]

⇒[tex]x=20[/tex]

Thus it took 20 seconds to stop the fan

Hence the test was 20 seconds long.

Answer:

yes

Step-by-step explanation:

for the sticks to form a right triangle, the 3 sticks' lengths must comply w the Pythagoras theorem: hypothesis^2 = first side^2 + second side^2

hypothesis is the longest length so its 10

10^2 = 100 = 36 + 64 = 6^2 + 8^2

so the 3 sticks will form a right triangle

Answer:

6^2+8^2=10^2 so yes

Step-by-step explanation:

In order to test a triangle with lengths 6, 8 and 10 inches is right-angle or not, the Pythagoras equation should be used: a^2+b^2=c^2.

As 6^2+8^2=10^2 so yes, the three sticks will form a right-angle triangle.

Answer:

Mutual Fund

Step-by-step explanation:

A mutual fund is invested by managers in diversity of stocks, bonds and other securities. Mutual fund is an investments that help you grow your money to bigger value. Your money will be used to invest in some companies, products and services to be able to gain more.

It is an investment programmed funded by share holders that trades in diversified holdings and is professionally managed. It pols money from many investors to purchase securities. These investors could be institutional or retail in nature.

Answer:

14/5 or 2 4/5

Step-by-step explanation:

7 3/5 = 38/5

4 4/5 = 24/5

38/5 - 24/5 = 14/5 = 2 4/5

Answer:

5

Step-by-step explanation:

the five is in the ones place so you count five ones and that equals 5

Good luck!

Answer:

ones

Step-by-step explanation:

look at the pic below

1t+45d

i think. could be wrong.

Answer:I Believe the Correct answers are:

x+5y ≤ 50

and

x+y≥50

Answer:

y ≤ 25

x ≥ 5y

x + y ≥ 50

Step-by-step explanation:

Answer:

$27402.    

Step-by-step explanation:

We have been given that Berto invested in a precious mineral. The value of the mineral tends to increase by about 11% per year. He invests $40,000 in 2015.

Let us write a function using our given information for the value of minerals.

We are told that the value of minerals increase by 11% every year, so our function will be an exponential function.

Since an exponential function is in form: [tex]y=a*b^x[/tex]; for growth b=(1+r), where r is rate of growth in decimal form.

a= Initial value.  

Let us convert our given rate in decimal form.

[tex]11 percent= \frac{11}{100}=0.11[/tex]

Let G(t) be the growth of minerals t years after 2015.

Upon substituting our given values we will get our function as: [tex]G(t)=40,000*(1+0.11)^t[/tex]

[tex]G(t)=40,000*(1.11)^t[/tex]    

To find the value of Berto's investment in year 2020 by substituting t=5 in our function as 2020-2015=5.

[tex]G(2020)=40,000*(1.11)^5[/tex]

[tex]G(2020)=40,000*1.6850581551[/tex]

[tex]G(2020)=67402.326204\approx 67402[/tex]    

Therefore, the value of his investment in 2020 will be $67402.

Let us find the difference of values of minerals between 2020 and 2015.

67402-40000=27402

Therefore, Berto's investment will be worth $27402 in 2020.

Answer:

Step-by-step explanation:

20742

Answer:

30 feet

Step-by-step explanation:

Interesting question.

The maximum height is 360 inches.

The maximum height reached was 30 feet.

Answer: [tex]\bold{13\dfrac{1}{3}\ \text{hours}}[/tex]

Step-by-step explanation:

Parabola Skate Rental:   4.50x + 35

Arc Hawk Skate Rental:  5.25x + 25

If you want to know when their cost will be the same, set the equations equal to each other.

5.25x + 25 = 4.50x + 35

0.75x + 25 = 35          subtracted 4.50x from both sides

0.75x = 10           subtracted 25 from both sides          

     [tex]x=\dfrac{1000}{75}[/tex]        divided both sides by 0.75

     x = [tex]13\dfrac{1}{3}[/tex]        simplified the fraction

Answer:

9

Step-by-step explanation:

Make sure to use PEMDAS.

[tex]6/2(1+2)\\\text{Simplify.}\\3(3)\\\text{Simplify.}\\9[/tex]

Answer: 86.7%

Step-by-step explanation:

[tex]\dfrac{New - Original}{Original}[/tex]

[tex]\dfrac{\$2.24 - \$1.20}{\$1.20}[/tex]

= [tex]\dfrac{\$1.04}{\$1.20}[/tex]

= 0.867

= 86.7%

Answer:

Step-by-step explanation:9÷3=3 +6÷3=2 for a total of 5 baskets

Answer: 1.6M kilometers, 8 kilometers

Step-by-step explanation:

Kilometers per mile times miles gives kilometers.

(1.6 kilometers / mile) × M miles = 1.6M kilometers

5×1.6 is 8

Answer:

sqrt(-80) = 4sqrt(5)i

Step-by-step explanation:

Likely a list of answers should be provided. There are all kinds of possible answers (well 2 perhaps).

Begin by factoring 80 into prime factors.

80: 2*2*2*2*5

For ever pair of 2s, one can be taken outside the square root sign. The other one just disappears.

sqrt(80) = sqrt(2 * 2 * 2 * 2 * 5)

For every pair 2 is taken out of the root sign and the other forgotten

sqrt(2 * 2 * 2 * 2 * 5) = 2 * 2 * sqrt(5) = 4 sqrt(5)

The sqrt(-80) = 4sqrt(5)*sqrt(-1)

There is no real number that can be written as the sqrt(-1). So a number has been defined into existence. sqrt(-1) = i It's a definition, not a real number.

So the end result is sqrt(-80) = 4sqrt(5)i

Answer: The answer is A.

Step-by-step explanation: You cant go over the $15 limit and in answer A, the sign shows that 1.80x + 1.95y is less than or equal to 15.

the answer to this question is A

Answer:

Rewrite equations:

y=x−1;−4x+3y=−2

Step: Solvey=x−1for y:

y=x−1

Step: Substitutex−1foryin−4x+3y=−2:

−4x+3y=−2

−4x+3(x−1)=−2

−x−3=−2(Simplify both sides of the equation)

−x−3+3=−2+3(Add 3 to both sides)

−x=1

−x

−1

=

1

−1

(Divide both sides by -1)

x=−1

Step: Substitute−1forxiny=x−1:

y=x−1

y=−1−1

y=−2(Simplify both sides of the equation)

Answer:

x=−1 and y=−2

Answer:

[tex]x+1[/tex] meters.

Step-by-step explanation:

Let L be the length of rectangle.

We have been given that the rectangle has an area of [tex]x^{2}-6x-7[/tex] square meters and a width of [tex]x-7[/tex] meters.

Since we know that area of rectangle is the product of its length and width.

[tex]\text{Area of rectangle}=\text{Width* Length}[/tex]

[tex]\text{ Length}=\frac{\text{Area of rectangle}}{\text{Width}}[/tex]

To find the length of our given rectangle we will divide area of rectangle by width of our rectangle.

[tex]L=\frac{x^2-6x-7}{x-7}[/tex]

Let us factor out our numerator by splitting the middle term.

[tex]L=\frac{x^2-7x+x-7}{x-7}[/tex]

[tex]L=\frac{x(x-7)+1(x-7)}{x-7}[/tex]

[tex]L=\frac{(x-7)(x+1)}{x-7}[/tex]

Upon cancelling out x-7 from numerator and denominator we will get,

[tex]L=(x+1)[/tex]  

Therefore, the length of our rectangle will be [tex]x+1[/tex] meters.

Look at the picture.

ΔABC and ΔDAC are similar. Therefore the sides of the triangles are in proportion:

[tex]\dfrac{AC}{BC}=\dfrac{DC}{AC}[/tex]

AC = x

BC = 5 + 4 = 9

DC = 4

Substitute:

[tex]\dfrac{x}{9}=\dfrac{4}{x}[/tex]          cross multiply

[tex]x^2=(9)(4)\\\\x^2=36\to x=\sqrt{36}\\\\\boxed{x=6\to C)}[/tex]

Step 1.

Calculate measure of angle α:

[tex]47^o-38^o=9^o[/tex]

Step 2.

Calculate what fraction of the angle 360° ​​is the angle α:

[tex]\dfrac{9^o}{360^o}=\dfrac{1}{40}[/tex]

Step 3.

Calculate the circumference of the Earth (circle):

[tex]C=2\pi r\to C=2\pi\cdot4000=8000\pi\ mi[/tex]

Step 4.

The length of arc is equal 1/40 of the circumference:

[tex]\dfrac{1}{40}C=\dfrac{1}{40}\cdot8000\pi=200\pi\ mi[/tex]

[tex]\pi\approx3.14\to\dfrac{1}{40}C\approx200\cdot3.14=628\ mi[/tex]

The question uses geometry and the concept of arc length to ask the distance between Seattle and San Francisco on the Earth's surface. The distance between the two cities is calculated to be 628 miles.

This is a mathematics problem using geometry, specifically related to the calculation of the arc length. The difference in latitudes between Seattle and San Francisco gives us the angle measurement on the sphere's surface. The difference is 47° - 38° = 9°. Since 9° is 1/40th of a full circle (360°), the arc is 1/40th of the total circumference.

So, to find the distance between the two cities, we calculate 1/40th of the circumference of the Earth (which is 2πr) by using the given radius of the Earth (4,000 miles). The calculation is 1/40 * 2 * 3.14 * 4000 = 628 miles. So, The distance between Seattle and San Francisco via the arc length on the sphere's surface is approximately 628 miles.

Therefore, the correct answer is A) 628 miles.

https://brainly.com/question/37703789

#SPJ11

Answer:

The required ratio is: 9:5

Step-by-step explanation:

Let the number of frog's Rimma has be x

Then Julia's will be [tex]\frac{2x}{5}[/tex]

Now, Rimma give 1/2 of her frog to Julia means now, Rimma will have [tex]x-\frac{1}{2}[/tex] frog

Then Julia's frog will be [tex]\frac{2x}{5}+\frac{1}{2}[/tex]

Now, Rimma will have [tex]x-\frac{x}{2}=\frac{x}{2}[/tex]

And Julia will have [tex]\frac{2x}{5}+\frac{x}{2}=\frac{4x+5}{10}=\frac{9x}{10}[/tex]

Hence, the ratio of Julia's frog to Rimma's frog is [tex]\frac{\frac{9x}{10}}{\frac{x}{2}}[/tex]

[tex]Ratio=\frac{9x\cdot 2}{10\cdot x}[/tex]

[tex]\Rightarrow Ratio=\frac{9}{5}[/tex]

The required ratio is: 9:5

Answer:

80

Step-by-step explanation:

Answer:

Step-by-step explanation:

Problem 1

Answer: Choice A

Vertically stretching it by a factor of 2 is the same as compressing it horizontally by a factor of 2

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

Problem 2

Answer: choice B

Add up the functions to get

M(s) + L(s) = (225+0.65s) + (54 + 1.15s)

M(s) + L(s) = (225+54) + (0.65s+1.15s)

M(s) + L(s) = 279 + 1.80s

Answer:

A quadrilateral has 4 right angles

Step-by-step explanation:

In a conditional statement

If hypothesis, then conclusion

OR

Conclusion, if hypothesis.

The hypothesis goes with the if part.

Parallel lines have the same slopes (but different y intercepts). Parallel lines never cross. Parallel lines are the same distance from each other no matter where you are on either line. Think of it like a pair of perfectly straight railroad tracks.

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Perpendicular lines cross at one point. The two lines form a 90 degree angle. The two slopes multiply to -1, which is another way of saying that the slopes are negative reciprocals of one another. For example, a line with a slope of 2/3 and another line with a slope of -3/2 has these two values multiply to -1; therefore showing they are perpendicular lines.

To provide a short definition,

Parallel lines are lines as the word suggests "parallel" which means they will stay side by side and never cross.

Perpendicular lines are lines that cross, usually to determine perpendicular lines you would take a slope and negatively reciprocate it.

Perpendicular:

1/2 -> -2

Parallel:

1x + 3

1x