What is the inverse of the equation y=x²-4, x≤ 0​

Answer:

B

Step-by-step explanation:

given f(x) then f(x ± a ) is a horizontal translation of f(x)

• if + a , then a shift left of a units

• if - a then a shift right of a units

here g(x) is the graph of f(x) moved 2 units right , then

g(x) = (x - 2)²

Answer:

option b is the answer

Step-by-step explanation:

Hello!  

To find the mass of the liquid by itself, subtract the mass of the container from the mass of the liquid and container.

⇒ 1,300 - 250

⇒ 1,050 grams

∴ The mass of the liquid by itself is 1,050 grams.

Answer:

C

Step-by-step explanation:

P = S1t - S2t ← factor out t from each term on the right side

P = t(S1 - S2) ← isolate t by dividing both sides by S1-S2

[tex]\frac{P}{S1-S2}[/tex] = t

The graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a function:

f(x) = ∛x

The domain of the function will be all real numbers.

x ∈(-∞, ∞)

The graph will be curved.

Plug x = 0, y = 0

x = 1, y = 1

The graph is shown in the attached picture.

Thus, the graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.

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Her earnings vary directly with her number of hours worked

The hourly rate is given as:

Rate = $21.25 per hour

This means that:

She earns $21.25 each hour

This in other words means that, her earning increases as the number of hours increase.

The above is an illustration of a direct variation.

Hence, her earnings vary directly with her number of hours worked

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Sadie earns $21.25 per hour. Do her earnings vary inversely or directly with her number of hours worked?

The irrational number that can be multiplied to produce 1 is - √41/41

Let the following expression

-√41 x = 1

We are to find the value of x that will make the expression true

√41 x = -1

Divide both sides by √41

√41 x/ √41 = -1/ √41

x = - √41/41

Hence the irrational number that can be multiplied to produce 1 is - √41/41

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Answer:

Step-by-step explanation:

[tex]=(1 +tan\theta)^2 + (1 - tan\theta)^2\\=(1+2tan\theta+tan^2\theta)+(1-2tan\theta+tan^2\theta)\\=2(1+tan^2\theta)\\=2sec^2\theta.\\[/tex]

Answer:

1st = [tex]A. \sf \ y = 1[/tex]

2nd = [tex]D. \ \sf y - 5 = 3(x + 2)[/tex]

PART A

Given: y = -2

This equation has a slope of 0

Equation that pass (-1, 1)

y - 1 = 0(x -(-1))

y = 1

PART B

[tex]\sf Given : y = -\dfrac{1}{3} x + 2[/tex]

Here slope is -1/3 and y-intercept is 2

Perpendicular lines has negatively inverse slope.

→ per. slope = -(slope)⁻¹ = -(-1/3)⁻¹ = 3

Equation in point slope form:

[tex]\sf y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 5 = 3(x - (-2))[/tex]

[tex]\sf y - 5 = 3(x + 2)[/tex]

Answer:

[tex]y = 1[/tex]

[tex]y-5=3(x+2)[/tex]

Step-by-step explanation:

The line [tex]y = -2[/tex] is a horizontal line.

Therefore, a line that is parallel to the given line and passes through point (-1, 1) is another horizontal line with the y-value of the point.

Therefore, the line is [tex]y = 1[/tex]

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

Slope-intercept form of a linear equation:

 [tex]y=mx+b[/tex]

where:

Given linear equation:

[tex]y=-\dfrac{1}{3}x+2[/tex]

Therefore, the slope of this equation is -1/3.

If two lines are perpendicular to each other, the product of their slopes will be -1.   Therefore, the slope (m) of the line perpendicular to the given line is:

[tex]\implies m \cdot -\dfrac{1}{3}=-1[/tex]

[tex]\implies m=3[/tex]

Use the point-slope form of a linear equation, with the found slope and the point (-2, 5) to create the equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-5=3(x-(-2))[/tex]

[tex]\implies y-5=3(x+2)[/tex]

The probability of getting positive difference between the numbers 3 or greater between 1,2,3,4,5,6,7,8,9,10 if two numbers are selected is 28/45.

Given Numbers:{ 1,2,3,4,5,6,7,8,9,10}

We have to find the probability that the positive difference between the numbers selected is 3 or greater.

Probability is the likelihood of happening an event among all the events possible.

Total number of combinations when two numbers are selected from 10 numbers is 10 C 2=10!/2!(10-2)!

=10*9*8!/2*1(8!)

=10*9/2

=45 combinations

Combinations of numbers whose difference will be 3 or more are: (10,7),(10,6),(10,5),(10,4)(10,3)(10,2)(10,1)(9,6)(9,5)(9,4)(9,3)(9,2)(9,1)(8,5)(8,4)(8,3)(8,2)(8,1)(7,4)(7,3)(7,2)(7,1)(6,3)(6,2)(6,1)(5,2)(5,1)(4,1)

Total numbers =28

Probability=numbers/total combinations

=28/45

Hence the probability that two numbers selected gives difference of 3 or more is 28/45.

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Answer:

18

Step-by-step explanation:

Polygon A : Polygon B = x : 3x

4A = 24

A = 6

B = 18

B is the larger polygon so the perimeter is 18.

[tex]f(x) =4 x {}^{3} - 4x {}^{2} - 16x + 16[/tex]

[tex]divide \: by \: x - 2[/tex]

[tex]4x {}^{2} \: into \: (x - 2) = 4x {}^{3} - 8x {}^{2} [/tex]

[tex]g(x) = 4x {}^{2} - 16x + 16[/tex]

[tex]4x \: into \: (x - 2) = 4x {}^{2} - 8x[/tex]

[tex]z(x) = - 8x + 16[/tex]

[tex] - 8 \: into \: (x - 2) = - 8x + 16 \\ no \: remainder[/tex]

[tex]f(x) = (x - 2)(4x {}^{2} + 4x - 8)[/tex]

[tex]f(x) = 0 \\ x - 2 = 0 \: \: \: \: \: \: \: \: \: 4x {}^{2} + 4x - 8 = 0 \\ [/tex]

[tex]x = \frac{ - 4 + \sqrt{4 {}^{2} - 4(4)( - 8) } }{2(4)} = \frac{ - 4 + \sqrt{144} }{8} = \frac{ - 4 + 12}{8} = 1[/tex]

[tex]x = 2[/tex]

[tex]x = \frac{ - 4 - 12}{8} = \frac{ - 16}{8} = - 2[/tex]

Answer: B

Step-by-step explanation:

Edge 2023

Answer:

10u²

Step-by-step explanation:

The formula for area of a triangle is b*h/2. When you plug in the numbers, you get 10. Hope this helps!

Answer:

c. 7x2 +18 - 4x2 – 3 + 6x

Step-by-step explanation:

3(x^2 + 2x + 5)

3x^2 + 6x + 15

a.) 7x^2 - 18 - 4x^2 – 3 + 6x

= 3x^2 - 21 + 6x

b.) 7x^2 +18 - 4x^2 – 3 + 8x

= 3x^2 + 15 + 8x

c.) 7x2 +18 - 4x2 – 3 + 6x

= 3x^2 + 15 + 6x

d.) 7x2 +18 - 3x2 – 3 + 6x

= 4x^2 + 15 + 6x

Answer:

See below.

Step-by-step explanation:

Is the equation written correctly?

y = 3×2¹ +4 has no variable, unless the "3×2" is supposed to be "3x*2^1"

If so,

y = 3x*2¹ +4 for x = 1 would be

y = 3(1)2¹ +4

y = 3*2 +4

y = 10

⊰________________________________________________________⊱

Answer:

See Below.

Step-by-step explanation:

[tex]\large\begin{gathered} \sf{Start \ by \ plugging \ in \ the \ number \ that \ x \ is: 1} \\ \sf{Now, \ evaluate: y=3*1*2^1+4} \\ \sf{y=3*2+4} \\ \sf{Multiply \ 3 \times 2 \ first: y=6+4} \\ \sf{Now, \ just \ add: y=10}{ \end{gathered}[/tex]

Done!!

⊱________________________________________________________⊰

[tex]\bf{\overbrace{C}\underbrace{A}\overbrace{LL}\underbrace{I}\overbrace{G}\underbrace{R}\overbrace{A}\underbrace{P}\overbrace{H}\underbrace{Y}}[/tex]

Answer:

Step-by-step explanation:

Argument

One of the ways to recognize the domain is that it should be on the x axis of a graph. That lets out A and D. They are both describing the y axis. t = 0 has no meaning with this question.

Answer B

Answer:

2400 miles

Step-by-step explanation:

So the first equation is pretty straight forwards, it's in the slope-intercept form y=mx+b where m is the slope, and b is y-intercept, since as x increases by 1, the value y increases by m, which by definition is what the slope is, so m is the slope. In this context the slope is how many miles in x hours. So Space Explorer B flies 400 miles per hour. The amount of miles that Space Explorer A flies per mile can be calculated by dividing the 36400 by the 13 hours it had to travel. This gives you 2800 miles. So to find how many fewer miles Space Explorer B travels than Space Explorer A you subtract the 2 slopes. 2800 - 400 = 2400. So Space Explorer B travels 2400 fewer miles than Space Explorer A

Answer: 5.22

Step-by-step explanation:

The apothem = 87 cm = 0.87 m.

Using the formula [tex]A=\frac{1}{2}ap[/tex] to find the area of the base, where a is the apothem and p is the perimeter, we get [tex]A=\frac{1}{2}(0.87)(6)=2.61[/tex]

So, using the formula [tex]V=Bh[/tex], we get the volume to be [tex]2.61(2)=5.22 \text{ m}^{3}[/tex]

Answer:

Hello!

The manager of a cafeteria that caters only to the workers at a hospital wants to conduct a survey to determine which drink served at the cafeteria is most popular during lunch. What is the population that the manager is studying?

The correct answer would be:

C. Hospital workers who eat in the cafeteria

Hope this helps.

The speed of skaters was 10 km per hr.

Mathematically, the speed of an object is directly proportional to the distance traveled and inversely proportional to the time taken. In simple words, the more the speed, the distance traveled is more in a short period and vice-versa.

Let the speed of the skater be x

We know, speed = [tex]\frac{Distance}{Time}[/tex]

According to the question:

[tex]\frac{20}{x} = \frac{40}{x + 10}[/tex]

Cross multiplying both sides,

20(x+10) = 40x

20x + 200 = 40x

20x = 200

x = 10

Thus, the speed of skaters was 10 km per hr.

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The value of ? and X are 24 and 32 respectively

A triangles is 2D shape with three sides and angles.

From the given diagram, the ratio of similar sides is equal to a constant as shown;

15/20 = 9+15/20+x

Cross multiply

15/9+15 = 20/20+x

15/24 = 20/20+x

Comparing with the given ratio

? = 24

X = 20+x

Find x

15(20+x) = 480

300 + 15x = 480

15x = 180

x =12

X = 20 +x

X= 32

Hence the value of ? and X are 24 and 32 respectively

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The constant of proportionality is 1/3

and three more values are

x       1        2        3        4        5        

y       3       6        9        12       15

From the question, we are to determine the constant of proportionality

The given equation is

k = x ÷ y

From the given information,

When x = 1, y = 3

∴ k = 1 ÷ 3

k = 1/3

Thus, the constant of proportionality is 1/3

Now, we will determine the values of y for the values x = 3, x = 4, and x = 5

Since

k = x ÷ y

Then,

y = x ÷ k

When x = 3

y = 3 ÷ 1/3

y = 3 × 3

y = 9

When x = 4

y = 4 ÷ 1/3

y = 4 × 3

y = 12

When x = 5

y = 5 ÷ 1/3

y = 5 × 3

y = 15

Hence, the constant of proportionality is 1/3

and three more values are

x       1        2        3        4        5        

y       3       6        9        12        15

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Using an exponential function, the inequality is given as follows:

[tex]9400(0.857)^t < 6000[/tex]

The solution is t > 2.9, hence the tax status will change within the next 3 years.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

For this problem, the parameters are given as follows:

A(0) = 9400, r = 0.143.

The population after t years is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 9400(1 - 0.143)^t[/tex]

[tex]A(t) = 9400(0.857)^t[/tex]

The tax status will change when:

[tex]A(t) < 6000[/tex]

Hence the inequality is:

[tex]9400(0.857)^t < 6000[/tex]

Then:

[tex](0.857)^t < \frac{6000}{9400}[/tex]

[tex]\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}[/tex]

[tex]t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}[/tex]

Since both logs are negative:

[tex]t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}[/tex]

t > 2.9.

The solution is t > 2.9, hence the tax status will change within the next 3 years.

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The probability that he got at least 2 questions correct is 0.756.

Probability is simply how probably something is to appear. every time we're uncertain approximately the final results of an occasion, we can communicate approximately the possibilities of positive outcomes and how in all likelihood they may be. The analysis of occasions ruled through chance is called data.

Basic Probability Rules

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Answer:

x is 8√2.

Step-by-step explanation:

Answer:

8√2

Step-by-step explanation:

Idea 1 : (Pythagorean theorem)

2x² = 16²

then

2x² = 256

then

x² = 256/2 = 128

then

x = √128

then

x = √(64×2)

then

x = √64 × √2

then

x = 8√2

………………………………………………………

Idea 2 : (diagonal of a square)

16 is the diagonal of a square with side square of lengths x

Then

x√2 = 16

Then

[tex]x = \frac{16}{\sqrt{2} } =\frac{8\times2}{\sqrt{2} } =\frac{8\times\sqrt{2} \times \sqrt{2} }{\sqrt{2} } =8\sqrt{2}[/tex]

Answer:

16/50 or 32% chance of getting a multiple of 3

Step-by-step explanation:

Starting at 0 and going to 50, there are 16 numbers in the range that are multiples of 3.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, and 48

Attached is a chart for reference!

So, 16 of the 50 numbers are multiples of 3, making your odds 16/50 (divide that to get .32 which = 32%!)

step by step explanation:

(multiples of 3)= 3 , 6 ,9, 12 ,15, 18 ,21 ,24, 27, 30, 33, 36 ,39 ,42, 45 and 48

probability (multiples of 3)= nó of required outcome/ nó of possible outcome

16 /50 = 8/25 ( you get this after dividing 16/50)

in percentage 8/ 25 would give you 32%

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Answer:  [tex]\textsf{(1, 1) is NOT a solution of the inequality}[/tex]

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Given:  [tex]y \le-3x + 1[/tex]

Find:  [tex]\textsf{Determine if (1, 1) is a solution of the inequality}[/tex]

Solution:  In order to determine if (1, 1) is a solution we need to plug in 1 for the x values and 1 for the y values and see if the equation evaluated to true.

Plug in the values

Simplify

As we can see the expression states that 1 is less than or equal to -2 which is false therefore (1, 1) is NOT a solution of the inequality.

Hey there!

Algebra I

Inequality

Ordered pair

y ≤ -3x+1

1 ≤ -3(1) + 1

1 ≤ -3 + 1

1 ≤ -2

The statement is NOT true as 1 is not less than or equal to -2.

Therefore, the ordered pair is not a solution of the inequality.

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The mean is the best central tendency to measure the expected number of strokes required for the ninth hole.

What is mean?

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.

The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.

Why mean is the best choice in this case?

Since it considers all of the data in relation to one another, the mean is an effective indicator of central tendency. When there are outliers (extreme values) in the data, for example, the mean is a poor measurement; in this situation, the median is preferable.

The data set is roughly symmetrical in the scenario described in the question, so the mean is the most-suited central tendency measure to employ here.

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Answer:

The mean is the best choice because the data is nearly symmetrical.

Part (i)

1. ABCD is a quadrilateral in which AD=BC and ∠DAB=∠CBA (given)

2. AB = AB (reflexive property)

3. Triangles ABD and BAC are congruent (SAS)

Part (ii)

4. BD=AC (corresponding sides of congruent triangles are equal)

Part (iii)

5. ∠ABD = ∠BAC (corresponding angles of congruent triangles are equal)

Answer:

Hey!

In △ABD and△BAC,

AD = BC (it's given)

∠DAB = ∠CBA (it's given)

AB = BA (Common)

By SAS congruence rule,

∴△ABD≅△BAC

=> BD = AC (By C.P.C.T) (ii)

And, ∠ABD = ∠BAC (By C.P.C.T) (iii)

Hope it helps, any confusions you may ask.

Answer:

The answer is B

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

y > 5x-4

This inequality is greater than, so it would be a dotted line

You would have a solid line when it is greater than or equal to ≥  or less than or equal to ≤