2x²+5x-3=0
using completing the square method​

Answer:

0.167π

Step-by-step explanation:

r = 0.5

[tex]Volume = \frac{4}{3} \pi r^{3} = \frac{4}{3} \pi 0.5^{3} = 0.167\pi[/tex]

Answer:

9 seconds

Step-by-step explanation:

When the ball reaches the ground, the height, h(t), is 0. Might as well make the numbers easier to work with - since for the x-intercepts (t-intercepts), h(t) = 0, you can divide the entire equation by the greatest common factor, in this case -16, to make things better:

[tex]0=-16t^2+128t+144\\0=t^2-8t-9[/tex]

Now you can solve this any way you like, such as by using:

[tex]\frac{-b \± \sqrt{b^2-4ac}}{2a}\\[/tex]

This is an easy polynomial though, and you may be able to factor it just by eyeballing it:

[tex]0=t^2-8t-9\\0=(t-9)(t+1)\\t=9,-1[/tex]

You can't have negative time, so we reject -1, leaving only 9 as the answer.

Answer:

D. x = -5y^2

Step-by-step explanation:

I used a graphing calculator.

Answer:

n = 6

Step-by-step explanation:

Given

2 = [tex]\frac{n}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

6 = n

Answer:

n=6

Step-by-step explanation:

If you divided 6 and 3 you would get an answer of 2. So the equation is saying n/3 which is n divided by 3 would give an answer of 2.

Step-by-step explanation:

i think may be

3 ,13 ,-1 ,-11 , root under 5

Answer:

B

Step-by-step explanation:

edge 2021

Answer:

b

Step-by-step explanation:

Answer:

lucas = 9

rafael = 6

Step-by-step explanation:

two equations can be derived from the question

r + l = 15 equation 1

r = l - 3  equation 2

r = rafael

l = lucas

substitute for r in equation 1

l - 3 + l = 15

combine similar terms

l + l = 15 + 3

2l = 18

l = 9

substitute for l in equation 1

r + 9 = 15

r = 15 -  9

r = 6

The polynomial, [tex]5x^3 - x^2 + 2[/tex], is a trinomial and the degree of the polynomial is 3.

A polynomial is an algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, and multiplication.

The given polynomial, [tex]5x^3 - x^2 + 2[/tex], has three terms separated by addition and subtraction symbols, making it a trinomial.

The highest exponent in the polynomial is 3, which determines its degree.

So, the degree of the polynomial is 3.

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Answer:

7 11/12

Step-by-step Explanation:

2 1/2 = 2 2/4

2 2/4 + 1 3/4 = 3 5/4 = 4 1/4

4 1/4 = 4 3/12

3 2/3 = 3 8/12

4 3/12 + 3 8/12 = 7 11/12

Answer:

B=95°

E=95°

D=20°

C=65°

BC=7cm

Step-by-step explanation:

the triangles look like they are identical, just different in size only. Since DE= 15 and AB=10 that may mean that they have a 5cm difference making side BC= 7cm since EF= 12 minus 5 equals 7cm. Now for the other angles, a triangle no matter what,if we put all their angles together equal 180°. We already know angle A= 20 so the same applies to angle D. We also know that angle F=65 degrees, that makes angle C the same. The only thing that's left are angles B and E that can be found by adding our other angles. So if A+C(20+65)=85 then 180-85=95 degrees is angle B and since the triangles are identical the same goes to E.

Answer:

Find the volume of this prism.

Theoretically, the probability of selecting one red marble from this bag is 0.20.

If a student does not return his or her marble to the bag before the next student selects his or her marble, the theoretical probability of selecting a blue marble may be different for the next student.

Probability determines how likely it is an event would happen. The chances of the event happening lie between 0 and 1.

The probability of selecting one red marble from this bag = number of red marbles / total number of marbles

16 / 80 = 0.20

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Answer:

12/13 bags

Step-by-step explanation:

2/13 * 6 = 12/13

Answer:

Both angles are 124 degrees.

Step-by-step explanation:

The angles of hexagons add up to 720 degrees, so if you subtract the known angles, (90, 90, 146, 146) you end up with 248. Divide by two and you get 124 degrees for each angle.

Answer:

90 Students.

Step-by-step explanation:

1/2 (Half) of 180 is 90.

Answer:

90 students will choose basketball

Step-by-step explanation:

half (1/2) choose basketball and half of 180 is 90

Answer:

1/6

Explanation:

This is because if you were to take up the entire wall with these same proportions, you would need six colors.

Answer:

See explanation below

Step-by-step explanation:

1. 10 students didn't talk on the phone because they've spent zero hours on the phone.

2. 3 hours is the largest number of hours

Answer:

Converting velocity into m/s

72x5/18=20 m/s²

Distance = Velocity *Time

20*5=100m

Step-by-step explanation:

hope it's helpful

Answer:

The smallest possible value of k is 656

Step-by-step explanation:

The given width of the Eiffel Tower, w₁ = 328 feet

The given height of the Eiffel Tower, h₁ = 984 feet

The width of the space Maria can use on the shirt, w₂ = 0.75 feet

The height of the space she can use on the shirt, h₂ = 1.5 feet

We get;

The ratio of height to width of the Eiffel Tower = h₁/w₁ = 984/328 = 3

The height to width ratio of the space on the shirt = h₂/w₂ = 1.5/0.75 = 2

Therefore, that the aspect ratio of the space on the T-shirt is wider than the Eiffel Tower, the height of the space on the T-shirt is the limiting dimension of the scaled picture of the Eiffel Tower

Therefore, the scale factor, k = The ratio of the actual height of the Eiffel Tower, to the height of the space on the T-shirt

Where 'k' represent the integer value to shrink the Eiffel Tower and fit it on the T-shirt, and 'k' is the smallest ratios of the dimensions of width or height of the tower to the dimensions of the width or height of the space available on the shirt, given that the height to width ratio of the area on the shirt is smaller than that of the Eiffel Tower

Mathematically

k = h₁/h₂

∴ k = 984/1.5 = 656

The scale factor of the height of the Eiffel Tower to the height of the space available on the T-shirt, k = The smallest possible value of k = 656.

Answer:

(x-2)^2+y^2=16

Step-by-step explanation:

If the center of the circle is (h,k) and the radius is r, then the equation of a circle is (x-h)^2+(y-k)^2=r^2 (with the Pythagorean theorem)

So, the center of this circle 0 is (2,0) and the radius is 4. Thus, the equation is (x-2)^2+y^2=16

Answer:

Height is same for both the towers

Step-by-step explanation:

The computation is as follows;

For 1st tower

The height is

= 128 ÷ 4^2

= 8 inches

And,  

For the 2nd tower

The height is

= 288 ÷ 6^2

= 8 inches

So as we can see that the height of the both the tower is same i.e. 8 inches so the same should be considered

Answer:

y = -5x-9

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

10x + 2y = -18

Subtract 10x from each side

10x + 2y-10x =-10x -18

2y = -10x-18

Divide each side by 2

2y/2 = -10x/2 -18/2

y = -5x-9

Answer:

d

Step-by-step explanation:

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

Work Shown:

Multiply top and bottom by [tex]\sqrt{2}[/tex] to rationalize the denominator

[tex]\frac{10-\sqrt{18}}{\sqrt{2}}\\\\\frac{\sqrt{2}(10-\sqrt{18})}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{2}*10-\sqrt{2}*\sqrt{18}}{\sqrt{2*2}}\\\\\frac{\sqrt{2}*10-\sqrt{2*18}}{\sqrt{4}}\\\\\frac{10\sqrt{2}-\sqrt{36}}{2}\\\\\frac{10\sqrt{2}-6}{2}\\\\\frac{-6+10\sqrt{2}}{2}\\\\\frac{2(-3+5\sqrt{2})}{2}\\\\-3+5\sqrt{2}\\\\[/tex]

We end up with something in the form [tex]a+b\sqrt{2}[/tex] where a = -3 and b = 5

Answer:

Number 4

Step-by-step explanation:

Answer: 5 Seconds

Step-by-step explanation: Given the equation of the height expressed ad;

h(t) = - 16t^2 + initial height

Given that initial height = 400feet

h(t) = - 16t^2 + 400

The waste will hit the ground at when h(t) = 0

substitute

0 =  - 16t^2 + 400

16t^2 = 400

t² = 400/16

t² = 25

t = √25

t = 5secs

Answer:

PL, PQ

Step-by-step explanation:

a ray starts with a point and goes on for infinity (the arrow)

Answer: Answer:

A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B  

= (0.51, 0.57)

This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)

B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

_________________________________________________________

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.

Critical value = 2.33

Standard error = σₓ = √[p(1-p)/n]

p = sample proportion = 0.54

n = sample size = 1500

σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287

98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.54 ± (2.33 × 0.01287)

CI = 0.54 ± 0.02998)

98% CI = (0.51, 0.57)

98% Confidence interval = (0.51, 0.57)

B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?

For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;

- The sample data must have been obtained using a random sampling technique.

- The sampling distribution must be normal or approximately normal.

- The variables of the sample data must be independent of each other.

On the second point, the condition for a binomial distribution to approximate a normal distribution is that

np ≥ 10

and n(1-p) ≥ 10

The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.

For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Step-by-step explanation:

Answer:

A = 108 ft²

Step-by-step explanation:

the length of the smaller rectangle must be 9 (27÷3)

therefore, the ratio of length to width is 3/9 and if the polygons are similar then the length and width of the larger shape would be 6/18

18 x 6 = 108

Answer:

Option C is correct

Step-by-step explanation:

[tex]a. - 3, - 12 \\ = 36[/tex]

[tex]b. - 6, - 6 \\ = 36[/tex]

[tex]c. \: \: 9, - 4 \\ = - 36[/tex]

[tex]d. \: \: 2,18 \\ = 36[/tex]