What is the square root of the quantity x plus 4 minus 3 equals 1

Let's begin by listing out the information given to us:

Price of bicycle = $120

Discount rate = 25% = 0.25

The discount is gotten by the formula shown below:

Discount = Price - Price x discount rate

Discounted Price = 120 - 120 x 0.25

Discounted Price = 120 - 30 = 90

Discounted Price = $90

Function Algebra Unit test

1. (F•g)(x)=3x-9/x+4

2. F^-1 (x) = -3x-4/x-7

3. ( -5 , 0) u ( 0 ,~)

4. D: (-~,2) u (2,~) R: (-~,0) u (0,~)

5. {y|0 _< y< 8}

6. Restricted domain : x _> -4 ;f^-1 (x) = -4+ sqrt x-3

7. The function C because the graphs of A and C are line symmetrical about the Y=X

8. (-~,-3) u (-3,-5/2) u (-5/2,~)

9. ( 4 points )

10. (g • f) (x)= x+3/sqrt x+2

11. (f•g) (x) = x+6 ; [ -2,~)

Answer:

8.  Answer is A:  (-00,-4) U (-4,-3/5) U (-3/5,00)

9. No not 1-1 function

10. x+4/sqrtx+1  (A)

11. D =x+12;[-3,00)

Step-by-step explanation: The above is 100% correct and I put the rest of answers. I just did it.

The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)

a) the independent variable is the: Number of month after the first year

b) the dependent variable is the: Amount remaining on the card

To solve this problem, we have to state the equation using the information of the problem.

Information about the problem:

Writing the equation according to the information gave, we have:

y = 25 - (2.50x)

Where:

The relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.

The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer:

If the numerator of a fraction is greater than or equal to its denominator, then the fraction is an improper fractio. That is the fraction a/b is called improper if a ≥ b.

Example : 1/1,  2/1,  5/1,  4/3,  6/4,  9/5,  7/7, ...etc

Answer:

sC = 2Πrd = 18d = 2rr = 9C = 2Π9C = (2)(3.14)(9)C = 56.52 feetThis is the length of the string of lights.

Step-by-step explanation:

Answer: BC=3

Step-by-step explanation: Set the two side lengths equal to each other and solve.

Answer:

BC = 20 units.

Step-by-step explanation:

This triangle has 3 equal sides.

so: -y + 23 = 6y + 2

23 - 2 = 6y + y

21 = 7y

y = 3.

So each side is 6(3) + 2 = 20 units long.

a) There are 170 red marbles in the box.

b) The total number of marbles in the box is 320.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The number of red marbles be 'R' and the number of

green marbles be 'G'.

The statement, If he puts in 10 more red marbles, there will be 1/5 as many red marbles as green marbles in the box is,

(R + 10) = G + (1/5)G.

R + 10 = (5G + G)/5.

R + 10 = 6G/5.

5R + 50 = 6G.

5R - 6G = - 50...(i)

The statement, If he removes 20 red marbles from the box, the ratio of the number of red marbles to green marbles is 2 : 25 is,

(R - 20)/G = 2/25.

25R - 500 = 2G.

25R - 2G = 500...(ii)

Solving these two equations we have R = 170 and G = 150.

And the total number of marbles is 320.

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The amplitude of this function is 3.

Answer:

8

Step-by-step explanation:

$28 / by 3.5= 8

The ratio of John's money to Peter's money is 5/4. This means if John has a total amount of 5 then Peter will have a total of 4 as his amount.

Let's assume John has 'x' amount of  money, Peter has 'y' amount of money, The money John saved is 'p' and the money Peter saved is 'q'

So,

p = x - 80x/100                (equation 1)

q = y - 75y/100                (equation 2)

According to the given question, the amount John saved is equal to the amount Peter saved. Hence, we can equate equations 1 and 2.

p = q

x- 80x/100 = y - 75y/100

x - 0.8x = y - 0.75y

0.2x = 0.25y

x =  0.25y/0.2

x/y = 0.25/0.2

x/y = 25/20

x/y = 5/4

Hence, the ratio of John's money to Peter's money is 5/4.

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Answer:

8 with a remander of 1

Step-by-step explanation:

Answer:

11:5

Step-by-step explanation:

The computation is shown below:

Given that

Cube root of 1331: reciprocal of 0.2

11: 5

So here n denotes the 11

And, 1 denotes the 5

Therefore the answer is 11:5

Hence, the same would be considered and relevant too

The total area if each garden bed has a length of 4 feet is given as follows:

A = 48ft².

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The area for a bed of side length s is given as follows:

A = 3s².

Hence the total area if each garden bed has a length of 4 feet is given as follows:

A = 3 x 4² = 48 ft².

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Answer:

Total amount received by Mrs Khanna will be 182.5 Rs.

Step-by-step explanation:

Cost of the potatoes = 25 Rs per kg

Cost of \(2\frac{1}{2}\) kg potatoes = Weight of the potatoes × Per kg cost of the potatoes

= 2.5 × 25

= 62.5 Rs

Cost of onions = 30 Rs per kg

Cost of 3 kg onions = 3 × 30

                                 = 90 Rs

Per kg cost of Peas = 70 Rs

Cost of \(1\frac{1}{2}\) kg Peas = 1.5 × 70

                               = 105 Rs

Per kg cost of Carrots = 40 Rs

Cost of \(1\frac{1}{2}\) kg Carrots = 1.5 × 40

                                   = 60 Rs

Total amount of the vegetables = 62.5 + 90 + 105 + 60

                                                     = 317.5 Rs

Since she gave a note of 500 Rs

Balance amount she got = 500 - 317.5

                                         = 182.5 Rs

Therefore, total amount received by Mrs Khanna will be 182.5 Rs.

Answer:

___________________________________________________________

FACTS TO KNOW BEFORE SOLVING :-

___________________________________________________________

According to the question ,

a) \(\sqrt{18} =\sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}\)

b) \(\sqrt{12} =\sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}\)

c) \(\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}\)

The total number of girls and the total number of boys in the club are

number of girls = 58

number of boys = 25

The total number of girls and the total number of boys in the club is solved using the equation generated as follows

The number of girls in the Middle School Cyber Club was 8 more than double the number of boys

let the number of girls be x and the number of boys be y

x = 8 + 2y

total there were 83 middle school students in the Cyber Club

x + y = 83

substituting for x in x + y = 83

x + y = 83

plugging in x = 8 + 2y

8 + y + y = 83

8 + 2y = 83

solving for y

3y = 83 - 8

3y = 75

y = 25

solving for x

x = 8 + 2y

x = 8 + 2 * 25

x = 58

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Answer:

\(\sqrt{x^2+y^2}-x\)

Step-by-step explanation:

\(\textsf{Mulitply by}\quad\dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}:\)

\(\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}\)

\(\textsf{Cancel the common factor}\:y^2:\)

\(\implies \sqrt{x^2+y^2}-x\)

Rationalising the denominator of the given fraction means we need to multiply both the numerator and the denominator of the fraction by the conjugate of the expression in the denominator. For example:

\(\;\longrightarrow\dfrac{1}{a+b}\)

Here the conjugate of denominator of the expression is a - b. So we need to multiply both the numerator and denominator with the fraction.

\(\;\longrightarrow \dfrac{1}{a+b} \times \dfrac{a-b}{a-b}\)

Hence, this is what the rationalization means.

We have been given and equation and we have been asked to rationalise the equation.

The conjugate of the denominator of the given equation is √(x² + y²) - x. Therefore;

\(\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}\)

\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}\)

\(\implies \boxed{\sqrt{x^2+y^2}}\)

Hence, this is our required solution for this question.

Answer:

Try y=x²+4

Step-by-step explanation:

y=-x+4

when its perpendicular you change the -x to x. When you have a perpendicular equation flip the sign and if fraction flip the fraction as well but there isn't a fraction here so you just change the -x to a +x and then work out the problem like this

y-3=x(x- -1)

y-3=x²+1

 +3     +3

__________

y=x²+4

Answer:

4(9a-4)

Step-by-step explanation:

36a - 16

We can factor 4 from each expression.

4*9a - 4*4

4(9a-4)

Answer:

729 * 10^-45

Step-by-step explanation:

Here, we want to expand the value based on the exponent

We have the power multiplying every term in the bracket

That would be;

9^3•10^-45

= 729 * 10^-45

Answer:

The values of x and y are x = 3 and y = 11

Step-by-step explanation:

The isosceles triangle has two equal sides in length, and its base angles are equal in measures

In ΔJKL

∵ ΔJKL is an isosceles triangle with vertex K

→ That means the equal sides are JK and KL

∴ JK = KL

∵ JK = 8x and KL = 13x - 15

→ Equate them

∴ 13x - 15 = 8x

→ Add 15 to both sides

∵ 13x - 15 + 15 = 8x + 15

∴ 13x = 8x + 15

→ Subtract 8x from both sides

∵ 13x - 8x = 8x - 8x + 15

∴ 5x = 15

→ Divide both sides by 5 to find x

∴ x = 3

∵ K is the vertex of the ΔJKL

∴ ∠KJL and ∠KLJ are the base angles

∵ The base angles are equal in measures

∴ m∠KJL = m∠KLJ

∵ m∠KJL = 5y - 3

∴ m∠KLJ = 5y - 3

∵ The sum of the measures of the angles of a Δ is 180°

∴ m∠KJL + m∠KLJ + m∠JKL = 180°

∵ m∠JKL = 76°

→ Substitute the measures of the 3 angles in the equation

∴ 5y - 3 + 5y - 3 + 76 = 180

→ Add the like terms on the left side

∵ (5y + 5y) + (76 - 3 - 3) = 180

∴10y + 70 =180

→ Subtract 70 from both sides

∵ 10y + 70 - 70 = 180 - 70

∴ 10y = 110

→ Divide both sides by 10 to find y

∴ y = 11

∴ The values of x and y are x = 3 and y = 11

Answer:

\(2\sqrt{6}\)

Step-by-step explanation:

\(\sqrt{24} \\= \sqrt{4} * \sqrt{6}\\= 2\sqrt{6}\)

Answer:

B

Step-by-step explanation:

Adjacent angles sum to 180 degrees  <====supplementary

The scientific notation form of the given number 1,345,080,000 is 1.34508 × 10⁹.

Given the number in the question;

1,345,080,000

To convert to scientific notation;

First, move the decimal so there is one non-zero digit to the left of the decimal point.

Now, the number of decimal places you move will be the exponent on the 10

Note that; if the decimal is being moved to the right, the exponent will be negative, also, If the decimal is being moved to the left, the exponent will be positive.

1.345080000

We moved 9 decimal places to the left

1.34508 × 10⁹

Therefore the scientific notation form of the given number 1,345,080,000 is 1.34508 × 10⁹.

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The number of automobiles that must be produced to minimize the cost is 2

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

C(x) = 5x² - 20x + 36.

Differentiate and set function to 0

So, we have

10x - 20 = 0

Solve for x

10x = 20

Divide

x = 2

Hence, the automobiles is 2

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There are 63,273,600 different license plates that can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits.

There are two different types of license plates that can be made: one with three letters followed by three digits and one with four letters followed by two digits. To find the total number of different license plates that can be made, we need to calculate the number of possibilities for each type of license plate and then add them together.

For the first type of license plate (three letters followed by three digits), there are 26 possibilities for each letter and 10 possibilities for each digit. So the total number of different license plates of this type is:
26 × 26 × 26 × 10 × 10 × 10 = 17,576,000
For the second type of license plate (four letters followed by two digits), there are 26 possibilities for each letter and 10 possibilities for each digit. So the total number of different license plates of this type is:
26 × 26 × 26 × 26 × 10 × 10 = 45,697,600

Adding these two numbers together gives us the total number of different license plates that can be made:
17,576,000 + 45,697,600 = 63,273,600
Therefore, there are 63,273,600 different license plates that can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits.

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The probability that the hypothesis test will result in a type ii error, β is 0.20.

In this question,

A type II error is one of two types of statistical errors that can result from a hypothesis test (the other being a type I error). A type II error will occur if the statistical test is not powerful enough. And it occurs when one rejects the alternative hypothesis (fails to reject the null hypothesis) when the alternative hypothesis is true.

The probability of a type II error is denoted by *beta*, β.

Power of a test = 0.80

The relation between power of a test and type II error is given as,

Power = 1 - type II error

⇒ Type II error, β = 1 - 0.80

⇒ Type II error, β = 0.20

Hence we can conclude that the probability that the hypothesis test will result in a type ii error, β is 0.20.

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Answer:

Step-by-step explanation:

There's no such thing as answer for this, as this is an algebraic expression.

Answer:

"HL" in geometry typically refers to "Hypotenuse-Leg". This term is often used when talking about right-angled triangles, where the hypotenuse is the longest side, opposite the right angle, and the legs are the two shorter sides adjacent to the right angle.

a) The probability that a single student randomly chosen from all those taking the test scores 23 or higher is 0.3557

b) The probability that the mean score x of these students is 23 or higher is 0.0043

What is Probability?

Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event.

Given that ,

mean = \mu = 21.1

standard deviation = \sigma = 5.1

a) P(x ≥ 23 ) = 1 - P(x ≤ 23)

= 1 - P[(x - \mu) / \sigma ≤ (23-21.1) /5.1 ]

= 1 - P(z ≤ 0.37)

= 1 - 0.6443 = 0.3557

Probability= 0.3557

b) n = 50

mu\bar x = \mu = 21.1

σbar x = σ / \\(\sqrt{n}\) = 5.1/ \\(\sqrt{50}\) = 0.7212

P(\bar x ≥ 23) = 1 - P(\bar x ≤ 23 )

= 1 - P[(\bar x - \mu\bar x ) / \sigma\bar x ≤ (23 - 21.1) / 0.7212 ]

= 1 - P(z ≤ 2.63)

= 1 - 0.9957 = 0.0043

Probability = 0.0043

a) The chance of a single student picked at random from all those taking the test scoring 23 or higher is 0.3557.

b) The chance that the mean x of these students is 23 or greater is 0.0043.

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