Enter the correct answer in the box. solve the equation x2 − 16x 54 = 0 by completing the square. fill in the values of a and b to complete the solutions. 

Answer:

25/81.

Step-by-step explanation:

(27/8)^-4/3

= 8^4/3 / 27^4/3

= (∛8)^4 / (∛27)^4

= 16 / 81

(64/125)^-2/3

= (125)^2/3 / (64)^2/3

= (∛125)^2 / (∛64)^2

=  5^2 / 4^2

= 25/16

So the answer is

16/81 * 25/16

= 25/81.

Answer:

25 / 81(25 by 81) is your answer.

Answer:

question 4:

the smaller building is 262.31 metres tall

Step-by-step explanation:

see the diagram attached:

1. draw a diagram:

2. as you can see in the diagram, a right angled triangle has been created.

3. convert the known angle from degrees and minutes to degrees.

4.  Identify which trigonometry ratio to use:

sin = [tex]\frac{opposite}{hypotenuse}[/tex]

cos = [tex]\frac{adjacent}{hypotenuse}[/tex]

tan = [tex]\frac{opposite}{adjacent}[/tex]

5. insert known values into the equation:

6. Interpreting the question with new knowledge:

the height of building 2 is 262.31 metres.

Answer:

The coordinates of D is (7, 10)

Explanation:

Let the coordinates of endpoint D be (x, y)

Mid-point formula:

[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]

Applying formula:

[tex]\sf (-1, \:4) = (\dfrac{-9+ x}{2},\: \dfrac{-2+y}{2} )[/tex]

Comparing found:

[tex]\sf -1 =\dfrac{-9+ x}{2} \quad and \quad \: 4 = \dfrac{-2+y}{2}[/tex]

[tex]\sf 2(-1)+9 =x \quad and \quad \: 2(4)+2 =y[/tex]

[tex]\sf x = 7 \quad and \quad \: y = 10[/tex]

So, coordinates of D is (7, 10)

The answer is (7, 10).

Remember the midpoint formula : [tex]\boxed {M = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})}[/tex]

Finding the x coordinate of D

Finding the y coordinate at D

The variance for the sample is 25

For given question,

We have been given the sample size n = 21

and the sum of squares is SS = 500

We need to find the variance for the sample.

We know that the variance is mathematically represented as,

[tex]\sigma^2=\frac{SS}{n-1}[/tex]

Substituting given values in the above formula,

[tex]\Rightarrow \sigma^2\\\\=\frac{500}{21-1}[/tex]

= 500 / 20

= 25

So, the variance is 25

Therefore, the variance for the sample is 25

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The graph is shown in the attached image.

The lowest number of people at a table is 0.

A dot plot is a graph that is used to represent the frequency of a data set. The dots in a dot plot represent the frequency of a number. The greater the height of a number, the higher its frequency. A dot plot is also known as a strip plot or a dot chart.

Looking at the dot plot, it can be seen that there are two dots above 2. This means that at two tables there was no one there.

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7. ∠I and ∠M are corresponding angles.

8. ∠J and ∠P are alternate exterior angles.

9. ∠K and ∠M are alternate interior angles.

10. ∠L and ∠M are consecutive interior angles..

11. ∠I and ∠O are alternate exterior angles.

12. 7. ∠K and ∠O are corresponding angles.

Angles that are formed outside the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate exterior angles.

Angles that are formed inside of the parallel lines that are intersected by a transversal and lie alternate to each other on along the transversal are alternate interior angles.

Angles that are formed inside of the parallel lines that are intersected by a transversal and lie on the same side of the the transversal are consecutive interior angles.

Angles that are formed in relative corner position on each of the parallel lines that are intersected by a transversal and lie along the transversal in the same side are called corresponding angles.

Thus, from the image given, we have the following special angles:

7. ∠I and ∠M are corresponding angles.

8. ∠J and ∠P are alternate exterior angles.

9. ∠K and ∠M are alternate interior angles.

10. ∠L and ∠M are consecutive interior angles..

11. ∠I and ∠O are alternate exterior angles.

12. 7. ∠K and ∠O are corresponding angles.

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Answer:

D

Step-by-step explanation:

Your equation would be 2x^2-3=y

This means that it should touch the y axis at -3, but since there is an exponent, it should be a parabola, not a straight line. Hence the answer is D

Answer: -8.

Step-by-step explanation:

-(2021.0,7+19,75)+2021.0,7-(8-19,75)=-2021.0,7-19,75+2021.0,7-8+19,75=-8.

The principal amount that must be deposited as a lump sum amount is = $16,666.7

The simple interest amount = $20,000

The interest rate = 12%

The time that is given= 10 years

Therefore the principle amount =?

Using the simple interest formula;

SI= P×T×R/100

Make P the subject of formula,

P = SI ×100/T×R

P= 20,000×100/10×12

P= 2,000,000/120

P= $16,666.7

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Answer:

2.625

Step-by-step explanation:

2 2/7 in decimal form is 2.2857

6 / 2.2857 = 2.625

For the given diagram, it has been proved that angle A is congruent to angle B.

Given Information:

Angle A and Angle B are such that,

Ray AC ║ Ray BE

Ray AD ║ Ray BF

Proof:

Since a straight line is the shortest line connecting two points in a plane,

Extend ray AD and ray BE, such that both intersect at point G.

Now, since, angle A and angle 1 both make corresponding angles,

∠A = ∠1 .......... (1)

Ray ADG is parallel to the ray BF.

Thus, again, angle B and angle 1 make corresponding angles,

∠B = ∠1 ............ (2)

From (1) and (2), as per transitive relationship of angles,

∠A ≅ ∠B

Hence proved.

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Answer:

( 5 , 5 )

Step-by-step explanation:

→ Add 2 the x coordinates together

- 4 + 14 = 10

→ Divide answer by 2

10 ÷ 2 = 5

→ Add the 2 y coordinates together

10 + 0 = 10

→ Divide answer by 2

10 ÷ 2 = 5

Answer:

(5, 5 )

Step-by-step explanation:

given points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (- 4, 10 ) and (x₂, y₂ ) = (14, 0 ) , then

midpoint = ( [tex]\frac{-4+14}{2}[/tex] , [tex]\frac{10+0}{2}[/tex] ) = ( [tex]\frac{10}{2}[/tex] , [tex]\frac{10}{2}[/tex] ) = ( 5, 5 )

Answer:

c.

Step-by-step explanation:

The two triangles are similar as they have the same angles, though not necessarily the same sides. ASA only applies to congruency.

Answer:

B. Ounces of water consumed compared with the number of same-size bottles dr*nk

Step-by-step explanation:

A constant rate of change means that the two values should be linear. Let's analyze why the other three options are wrong:

A. The distance between different airports can be very different (i.e the distance between Airport 1 and Airport 2 is 20 km and the distance between Airport 2 and Airport 3 is 500 km), meaning that the distance the airplane travels and the number of airports it visits are not linear.

C. Similar to A, the point scored in different quarters can be very different (i.e. 0 points scored in the 1st quarter, 35 points scored in the 2nd quarter, etc.)

D. Similarly, the number of fish in a pond can either be very large or very small, even if the volume of the pond stays the same

B is correct because the bottles are the same size, meaning that if you drink x bottles of 2-ounce bottles, you will always drink 2x ounces of water, no matter what, creating a linear function.

The circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j is    2π ∫₀ (cos t sin t - sin t cos tj)dt = 0

Integration is described as blending matters or human beings collectively that have been formerly separated. An example of integration is while the schools have been desegregated and there have been now not separate public faculties for African individuals.

The method of finding integrals is referred to as integration. at the side of differentiation, integration is a fundamental, crucial operation of calculus, and serves as a device to solve troubles in mathematics and physics regarding the location of an arbitrary form, the length of a curve, and the extent of a solid, among others.

r (t) = cost i + sin t j = dr( sin ti + cos t)dt

F =  -xi -yj = -costi - sin tj

Flux = F .dr = [tex]\int\limit2n^0_b {-costi - sin tj} \, dx[/tex]j)-( sin ti + cos t)dt

           [tex]\int\limit2n^0_b {-costi - sin tj} \, dx[/tex] -( sin ti + cos t)dt

     2π ∫₀ (cos t sin t - sin t cos tj)dt = 0

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Using a calculator, the exponential regression equation for the data is:

y = 16615.21e^(-0.14x)

Using it, the estimate for the value of car after 11 years is $3,561.99.

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points are given as follows:

(0, 16700), (1, 14370), (2, 12520), (3, 10301), (4, 9871), (5, 7982), (6, 6984).

Inserting these points in the calculator, the equation is:

y = 16615.21e^(-0.14x)

Hence the value of the car after 11 years is given by:

y = 16615.21e^(-0.14 x 11) = $3,561.99.

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The solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C

In solving for the values of 'x' we need to:

Given the expression;

1/x =x+3/2x^2

Cross multiply

x ( x+ 3) = 2x² ( 1)

Expand the bracket

x² + 3x = 2x²

collect like terms and equate all the variables to zero, we have ;

2x² - x² - 3x = 0

We then subtract the like terms, we getv

x²- 3x = 0

Now, let's find the common factor

Factor out 'x':

x ( x - 3 ) = 0

Equate each of the factors to zero and find the value of 'x' for each

So,

x = 0

And

x - 3 = 0

x = 3

Thus, the solution to the equation 1/x =x+3/2x^2 is x = 0 and 3. Option C

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Answer:   C

Step-by-step explanation: We see that e is 6 for $2.70 and d is 12 for $6.00.  Half of 6 is 3 and 2.70 is less than 3 so the cheapest price can't be d. Then, we have 9 for 3.60. 3.60 divided by 9 is 0.40 per which is cheaper than a (0.42 per) so a and d can't be the cheapest. 3 for 1.38 means 0.46 per which is more expensive than a so it also cannot be b. Now we only have c and e left. We divide 2.70 by 6 and find out that the answer is 0.45 which is also more expensive than a. So, the answer is c.

The half-life of the substance is 1.94 years.

The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula. F(x) = a [tex](1-r)^{x}[/tex] is the general form.

Here

a = the initial amount of substance

1-r is the decay rate

x = time span

The correct form of the equation is given as:

[tex]a=a_{0}[/tex]×[tex](0.7)^{t}[/tex]

where t is an exponent of 0.7 since this is an exponential decay of 1st order reaction

Now to solve for the half life, this is the time t in which the amount left is half of the original amount, therefore that is when:

a = 0.5 a0

Substituting this into the equation:

0.5 [tex]a_{0}=a_{0}[/tex]×[tex](0.7)^{t}[/tex]

0.5 = [tex](0.7)^{t}[/tex]

Taking the log of both sides:

t log 0.7 = log 0.5

t = log 0.5 / log 0.7

t = 1.94 years

The half life of the substance is 1.94 years.

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The answer is [tex]0.87.[/tex]

The binomial probability distribution:

The binomial distribution's anticipated value is: [tex]ux=np[/tex]

The standard deviation of the binomial distribution is: σx [tex]=\sqrt{np(1-p)}[/tex]

[tex]p = 0.75.[/tex]

[tex]n = 4.[/tex]

The mean and standard deviation of x:

[tex]ux=np=4(0.75)=3[/tex]

σx[tex]=\sqrt{np(1-p)} =\sqrt{4(0.75)(0.25)} =0.87[/tex]

The answer is [tex]0.87.[/tex]

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The mean exists at 3 and the standard deviation exists 0.87.

Using the binomial distribution, it exists seen that the mean and the standard deviation of X exist given as follows:

[tex]$\mu_{X}=3, \sigma_{X}=0.87[/tex]

The expected value of the binomial distribution exists:

[tex]$\mu_{X}=n p$$[/tex]

The standard deviation of the binomial distribution exists:

[tex]$\sigma_{X}=\sqrt{n p(1-p)}$$[/tex]

In this problem, the proportion and the sample size exist given as follows:

p = 0.75

n = 4

Therefore, the mean and the standard deviation exist given by:

[tex]$&\mu_{X}=n p=4(0.75)=3 \\[/tex]

[tex]$&\sigma_{X}=\sqrt{n p(1-p)}[/tex]

[tex]$=\sqrt{4(0.75)(0.25)}=0.87[/tex]

The mean exists at 3 and the standard deviation exists 0.87.

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Confidence interval for the mean daily return if it is normally distributed:

⁻x [tex]-z_{\alpha }[/tex](σ/[tex]\sqrt{n}[/tex]) ≤ μ ≤ ⁻x + [tex]z_{\alpha }[/tex] ( σ/[tex]\sqrt{n}[/tex])

Based on the Central Limit Theorem's result that the sampling distribution of the sample means follows an essentially normal distribution, a confidence interval for a population mean is calculated when the population standard deviation is known.

Take into account the standardising equation for the sampling distribution introduced in the Central Limit Theorem discussion:

[tex]z_{1} =[/tex](⁻x - μ₋ₓ) /( σ ⁻x) = (⁻x - μ) /( σ/[tex]\sqrt{n}[/tex])

Notice that µ is substituted for µx− because we know that the expected value of µx− is µ from the Central Limit theorem and σx− is replaced with σn√/, also from the Central Limit Theorem.

In this formula we know X−, σx− and n, the sample size. (In actuality we do not know the population standard deviation, but we do have a point estimate for it, s, from the sample we took. More on this later.) What we do not know is μ or Z1. We can solve for either one of these in terms of the other. Solving for μ in terms of Z1 gives:

μ=X−±Z1 σ/[tex]\sqrt{n}[/tex]

Remembering that the Central Limit Theorem tells us that the distribution of the X¯¯¯'s, the sampling distribution for means, is normal, and that the normal distribution is symmetrical, we can rearrange terms thus:

⁻x [tex]-z_{\alpha }[/tex](σ/[tex]\sqrt{n}[/tex]) ≤ μ ≤ ⁻x + [tex]z_{\alpha }[/tex] ( σ/[tex]\sqrt{n}[/tex])

This is the formula for a confidence interval for the mean of a population.

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The unit rate of Mikayla and brie is 0.16 miles per minutes and 0.25 miles per minutes respectively.

Brie runs faster.

Mikayla

2 miles in 12 1/2 minutes

Unit rate = miles / minutes

= 2 ÷ 12 1/2

= 2 ÷ 25/2

= 2 × 2/25

= 4/25

= 0.16 miles per minutes

Brie

5 miles in 22 1/4 minutes

Unit rate = miles / minutes

= 5 ÷ 22 1/4

= 5 ÷ 89/4

= 5 × 4/89

= 20/89

= 0.25 miles per minutes

Lucy

4 4/5 pounds for $18.50

Unit rate = pounds / price

= 4 4/5 ÷ 18.50

= 24/5 ÷ 18.50

= 24/5 × 1/18.50

= 24/92.50

= $0.26 per pound

Sophie

3 1/2 pounds for $14.75

Unit rate = pounds / price

= 3 1/2 ÷ 14.75

= 7/2 ÷ 14.75

= 7/2 × 1/14.75

= 7/29.5

= $0.24 per pound

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18 liters of 14% bleach contains 0.14×18 = 2.52 liters of bleach.

Adding [tex]x[/tex] liters of pure water to the solution increases the total volume to [tex]18+x[/tex] liters without changing the total amount of bleach.

To end up with a 10% bleach solution, we must add

[tex]\dfrac{2.52}{18+x} = 0.10 \implies 2.52 = 1.8 + 0.10x \implies 0.10x = 0.72 \implies x=\boxed{7.2}[/tex]

liters of water.

Answer:

b

Step-by-step explanation:

[tex]y = mx + b \\ y = nx + c \\ for \: the \: two \: lines \: to \: be \: perpendicular \\ m.n = - 1[/tex]

[tex]m = 3 \\ \\ 3n = - 1 \\ n = \frac{ - 1}{3} [/tex]

[tex]y = \frac{ - x}{3} + 2[/tex]

The volume of the given figure is 3617.3 km³

From the question, we are to calculate the volume of the given figure

The given figure is a cone.

The volume of a cone is given by the formula,

V = 1/3πr²h

Where V is the volume of cone

r is the base-radius of the cone

and h is the height is perpendicular height of the cone

From the given information,

r = 12 km

h = 24 km

Thus,

V = 1/3 × π × 12² × 24

(Take π = 3.14)

V = 1/3 × 3.14 × 12² × 24

V = 1/3 × 3.14 × 144 × 24

V = 1/3 × 10851.84

V = 3617.28 km³

V ≈ 3617.3 km³ (To the nearest tenth)

Hence, the volume of the given figure is 3617.3 km³

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The system of inequalities that best describes this situation provided A represents the area in which the entire field exists:

[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]

Word problems in mathematics exist methods we can utilize variables, algebra notations, and arithmetic operations to solve real-life cases.

We have a new addition to the current rectangular field,

Let that new addition to the current rectangular field be x

Length of the new addition = 10x

Twice the width of the new addition = 2x²

Original area of the field = 300

From the above information, we can derive a quadratic equation:

2x² + 10x + 300

Also, we exist given a constraint that the total area of the practice field should be no more than 1200.

It can be less than 1200 or equivalent to 1200.

Therefore, the system of inequalities that best describes this situation provided A represents the area in which the entire field exists:

[tex]$\left \{ {{A \geq x^{2} +10x+300} \atop {A \leq 1200}} \right.[/tex]

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Answer:

y-intecept: (0,14), x-intercept: (-8,0)

Step-by-step explanation:

Let us first solve for the y-intercept, solve the equation for y to set it to slope-intercept form.

[tex]-7x+4y=56\\4y=56+7x\\y=14+\frac{7}{4}x\\y=\frac{7}{4}x+14\\[/tex]

Now we have our y-intercept, 14

To solve for the x-intercept, all we have to do is set y to 0 and solve for x:

[tex]0=\frac{7}{4}x+14\\-14=\frac{7}{4}x\\-56=7x\\-8=x[/tex]

Therefore our x-intercept is -8.

To find the vector (x and y value) of the x intercept, we set the y value equal to 0, such as the vector of the x-intercept is equal to (-8,0).

For the y-intercept we follow a similar approach setting the x-value equal to 0, making it (0,14)