x^2-6x-3=(x-a)^2-b where a and b are constants.Find the values of a and b

Answer: The volume of the prism is [tex]18^{3}[/tex]cm

Step-by-step explanation: The formula to solve for the volume of a rectangular prism is V = lwh. In this case, it's V = 4 x 3 x 1.5 therefore V = 18

The distance covered by the car is 264cm.

Here we have to find the distance covered by the car.

Information provided:

Diameter (d) = 5.6cm

radius(r) = 5.6/2

             = 2.8cm

Rotation = 15 times

Formula to find the circumference of the tire:

Circumference = 2πr

                        = 2 × 22/7 × 2.8

                        = 17.6cm

This is the distance covered by the tire in one rotation.

Distance covered after 15 rotations = 15× 17.6

                                                         = 264 cm

Therefore distance covered is 264 cm.

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The value of the given expression will be 4 / 3.

An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given logarithmic expression is log₂(∛16). The expression will be solved as below,

[tex]E = log_2\sqrt[3]{16}\\E = log_2(2^{\frac{4}{3})\\E = \dfrac{4}{3}log_22\\E = \dfrac{4}{3}[/tex]

Therefore, the solution of the expression will be equal to 4 / 3.

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Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.

Given statement;

Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.

→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.

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Answer:

x=10.5

Step-by-step explanation:

The sides of similar triangles are proportional, therefore, the true equation would be: FG/CD = EG/BD.

Two similar triangles have corresponding angle measures that are congruent to each other, but have corresponding side lengths that are proportional to each other.

Similar triangles have the same shape but their sizes are different.

Given that angles C and F are congruent, and angles D and G are congruent, therefore triangle BCD is similar to triangle EFG based on the AA similarity theorem.

Therefore, the corresponding side lengths of both triangles will be proportional, which means that the following equation would be true:

FG/CD = EG/BD

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If Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. The expression for the total number of cards the groups has is:  1/3 ⋅9+(3+0.5⋅18)+18.

Given data:

Number of trading cards = 1/3

Adira number of cards = 23 more than 50%

Kip number of cards = 18 cards

Now let formulate an expression and then make use of the formulated expression to find the number of cards

Hence,

Number of cards =  1/3 ⋅9+(3+0.5⋅18)+18

Number of cards  =  1/3 ⋅9+(3+9)+18

Number of cards  =  1/3 ⋅9+(12)+18

Number of cards  =3 + 12+18

Number of cards = 33 cards

Therefore the expression is :  1/3 ⋅9+(3+0.5⋅18)+18.

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Answer: 150*40/100=60

60+150=210.

Step-by-step explanation:

The solution to these are in form of equation as follows.

What is equation?

In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

x= number of HD headphones           y= number of basic headphones

z = price of HD headphones.             w = price of basic headphones

a)

110 (70) + y*w = 10,000

7,700+ y*w = 10,000

y*w = 2,300

y = 2,300/w

b)

x*z+ 55(20) = 2000

x*z = 2000 -1100

x*z = 900

z = 900/x

c)

x*z+y*w = 800

x*z+8(80) = 800

x*z+640=800

X*z=160

Hence the values to the equation are as follows.

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Answer: A. [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

To find the slope we must find the change in y over the change in x. Δ

Or rise over run.  [tex]\frac{rise}{run}[/tex]

In the graph, we have two "good" points. (0, -6) and (4,0)

So for Δy 0 to -6 = -6

So -6 goes on top  [tex]\frac{-6}{x}[/tex]

Now Δx goes from 4 to 0 so the change would be -4.

So now it becomes [tex]\frac{-6}{-4}[/tex]

Since there are two negatives it becomes a positive. [tex]\frac{6}{4}[/tex] Or simply put, [tex]\frac{3}{2}[/tex]

Answer:

  1300.2 µL

Step-by-step explanation:

You want to know the volume of a nautilus chamber in 8 years if it is 880 µL in year 0 and increases at 5% per year.

The growth factor is ...

  growth factor = 1 + growth rate

  growth factor = 1 + 0.05 = 1.05

Since the problem statement is about volume, we assume the growth factor applies to the chamber volume. If it applies to the linear dimension of the chamber, then the growth factor for volume will be 1.05³.

The function describing the chamber volume can be written as ...

  volume = (initial volume)(growth factor)^years

In 8 years, the chamber volume will be ...

  volume = (880µL)(1.05^8) ≈ 1300.2 µL

The chamber created in 8 years is expected to be 1300.2 µL.

__

Additional comment

If the 5% growth rate is the rate of growth of the linear dimensions of a chamber, then its volume will grow at the rate of 1.05³ per year. In 8 years, the volume will be about 2838.1 µL.

(The wording "5% larger" is ambiguous here.)

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the solution for the  given equation is  x= 1/2

an equation could be a formula that communicates the balance of two expressions, by interfacing them with the equals sign. Understanding an equation containing factors comprises deciding which values of the factors make the equality true. The factors for which the equation must be fathomed are moreover called unknowns, and the values of the unknowns that fulfill the balance are called solutions of the condition. There are two sorts of equations such as conditional and identities equations. An identity is genuine for all values of the factors. A conditional equation is as it were genuine for specific values of the factors

since the  given expression is :

`(2-4)=2(-5+1)x²

so solving for the simple  arithmetic expression on both sides  :

=>-2 =2(-4)x²

=> -2 = -8x²

=>2/8=x²

=>1/4= x²

=>x= 1/2

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The equation used to solve this problem is x + y + z = 100000,  0.04x + 0.06y + 0.08z = 6700 and y = z

An equation is an expression showing the relationship between two or more numbers and variables.

Let x represent the amount of money invested at 4% (short term), y represent the amount of money invested at 6% (intermediate term) and z represent the amount of money invested at 8% (long term)

Since an investor has $100,000 to invest, hence:

x + y + z = 100000    (1)

Also, the investor wishes to have a return of $6700, hence:

0.04x + 0.06y + 0.08z = 6700   (2)

Equal amounts invested in intermediate and long term bonds. This gives:

y = z     (3)

The third equation used to solve this problem is y = z

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Answer:

216

Step-by-step explanation:

x^3

6^3

6x6x6

36x6

216

Hopes this helps pleas mark brainliest

Using the Triangle Inequality Theorem we can state that the range of z is 4 < z < 20.

The above theorem states that The length of any two sides of a triangle must sum to more than the length of the third side. That is:

12 + 8 > z.............1

12 + z > 8;.............2

8 + z > 12.............3

Solving for (1)

20 > z...............4

Solving for (2)

we have- 12 + z > 8

remove 8 from both sides and we have

4 + z > 0  or z > -4 ...............5

Solving for (3) we have

8 + z > 12

remove 8 from both sides

z > 4 .....................6

Since we can't have a negative value on a triangle, we must deal with expressions 4 and 6 which state:

20 > z; and

z > 4

Another way to write this is:

20 > z > 4; or

4 < z < 20

Hence the range of the unknown side that will form a triangle is:

4 < z < 20

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The equation is y = 4x. And the value of the function at x = 6 will be 24.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

If y varies directly to x. Then the relationship between them is written as,

y ∝ x

y = kx

When y = 8 and x = 2, then the value of the constant k is given as,

8 = k (2)

k = 8 / 2

k = 4

Then the equation is written as,

y = 4x

Then the value of the function at x = 6 will be given as,

y = 4 (6)

y = 24

The equation is y = 4x. And the value of the function at x = 6 will be 24.

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She should use (b) x + 1 to represent her second number

From the question, we have the following statements that can be used in our computation:

As a general rule

Consecutive numbers are number that have a difference of 1 i.e both numbers are next to each other

Take for instance:

2 and 3, 5 and 6, 10 and 11 are all instances of consecutive numbers

Recall that she uses x to represent her first number

This means that the next number is

Next number = First number + 1

Substitute the known values in the above equation, so, we have the following representation

Next number = x + 1

Hence, the second number is (b) x + 1

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Answer: $2100

Step-by-step explanation:

Since 12.5 percent of 2400 is 300, Just subtract 300 from 2400 to get the selling price with no sales tax. And the final answer is $2100.

The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545

No. of Blue balls in the urn = 6

No. of Orange balls in the urn = 6

Total no. of balls in the urn = No. of blue balls + No. of orange balls

                                            = 6 + 6

                                           = 12 balls

No. of blue balls to be selected = 2

No. of orange balls to be selected = 2

No. of balls to be selected = 4

The total. no of ways 4 balls can be selected =[tex]^{12}C_{4}[/tex]

The No. of ways 2 blue balls can be selected = [tex]^{6}C_{2}[/tex]

The No. of ways 2 orange balls can be selected =    [tex]^{6}C_{2}[/tex]

Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn

                      =  [tex]^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}[/tex]

Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls

                         P = (15×15)/495

                             = 225 / 495

                          P = 0.4545

Therefore,  the no. of ways to select blue and orange balls is 0.4545

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By using the concept of mean and standard deviation, it can be obtained that

The mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3

Standard deviation of distribution ([tex]\sigma_x[/tex]) = 0.714

What is mean and standard deviation?

Suppose there is a data set and an average value of the data set needs to be calculated. To find the average value of the data set, mean is used

For Standard deviation, at first, it is important to know about variance

Variance is the sum of the square of deviation from mean.

Square root of variance is the standard deviation

A population of values has an unknown distribution with

[tex]\mu = 83.3[/tex] and [tex]\sigma = 10.4[/tex], n = 212

So the mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3

Standard deviation of distribution ([tex]\sigma_x[/tex]) = [tex]\frac{10.4}{\sqrt{212}}[/tex] = 0.714

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Answer:

5√3

Step-by-step explanation:

There are two triangles shown in the image.

First one is a 45°-45°-90° right triangle with side lengths represented with a-a-a√2 respectively to the angle measures.

The second triangle is 30°-60°-90° special right triangle with side lengths represented with b-b√3-2b respectively to the angle measures.

In first triangle hypotenuse (the side length represented with a√2) is given as 10√2 so a = 10.

This is also the measure of hypotenuse for the second triangle which is represented with 2b, so b = 5 in this case.

x is the side length that sees angle measure 60° which we said is represented with b√3, we said b = 5 so the value of x = 5√3 the answer is the first option.

The radius of the circle which is overlapping the square is 1.12.

The length of side of the square is 2. Let us say that the radius of the circle is R.

The circle and the square are overlapping on each other.

The area of the region that are outside the circle but inside the square are equal to the area of the region which are inside the circle but outside the square.

Let us name the area of the region that are outside the circle but inside the square as M.

Let us name the area of the region which are inside the circle but outside the square as N.

Let us say that the area that is common in both is C.

The area of the square is 4.

So, according to the question,

M + C = 4

And,

N + C = πR²

And we know, M = N,

So,

C - πR² = C - 4

R = 2/√π

R = 1.12.

So, the radius of the circle is 1.12

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Answer:

L=12, W=6

Step-by-step explanation:

L=2W

(L+2L)=36

3L=36

2L=12

L=6

Answer: A. 9

Step-by-step explanation:

A statistically significant finding indicates that it is unlikely to just be explained purely by chance or random influences.

The notion that a set given observed data is not the result of random but can instead be linked to a specific cause is referred to as statistical significance.

Statistical significance indicates that a result is unlikely to be attributed purely by chance and random causes.

Thus, in other words, if there is no genuine effect in a research study, a statistically significant conclusion has an extremely low likelihood of occuring.

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Answer:

The coefficient is 7 and the term that has it.

They spent 6.5 hours driving on local highways by travellin with diffrent average speeds.

Given that,

The bruins basketball team spent two more hours on the interstate than they did on local roadways during their 560-mile journey. They traveled at an average speed of 55 mph on interstates and 45 mph on local routes.

I=interstate

L=local

using d=rt the first rows gives you d=55t

the second row gives you 560-d=45(t-2)

Since the two distances add up to 560.  Add the two distance expression and set their sum equal to the given total

560=55t+45(t-2) which equals

560=55t+45t-90

650=55t+45t

650=100t

6.5=t

Hence on local roadways, they traveled at various average speeds for 6.5 hours.

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Answer:

23.29 ft

Step-by-step explanation:

The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.

To find how high up the wall the ladder reaches, use the sine trigonometric ratio:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

where:

The angle of elevation is 76°, so θ = 76°.

Let x be the height the ladder reaches up the wall, so O = x.

H is the length of the ladder, so H = 24.

Substitute the given values into the sine ratio and round the answer to the nearest hundredth:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]

[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]

[tex]24 \sin(76^{\circ})= x[/tex]

[tex]x=24 \sin(76^{\circ})[/tex]

[tex]x=23.28709743...[/tex]

[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]

Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.