From the parent function, how has the equation y = (x+3)² been shifted?
Up 3
Down 3
Right 3
Left 3

Answer:

Nicholas has 5 boys, and Paul has 1 boy

Step-by-step explanation:

We will use 3 different variables, p, j, and n. Along with this, if there is a subscript on a variable, it will be either b or g, meaning boy or girl. If there is no subscript, it means both genders. We will start by translating our sentences into linear equations, giving us:

[tex]p + j + n = 15[/tex]              (1st Equation)

[tex]p_{g} = j_{b} = 3[/tex]              (2nd Equation)

[tex]j = p + 1 (p = 4)[/tex]              (3rd Equation)

[tex]n_{b} = n_{g} +4[/tex]              (4th Equation)

[tex]n_{g} = p_{b}[/tex]              (5th Equation)

Whew! That was a lot.  We know that Paul has 4 children, which means Johnson has 5 children. Which means Nicolas has 6 children. We know that Paul's girl count is 3 (second equation), meaning that 4 - 3 = Paul has 1 boy. Then, we know that Nicholas has:

b = g + 4 and b + g = 6

So, we substitute the first equation into the second equation, giving us:

g + 4 + g = 6

2g = 2

g = 1

So, Nicholas has one girl, meaning he has 5 boys.

So, Nicholas has 5 boys, and Paul has 1 boy.

Hope this helped!

Answer:

Step-by-step explanation:

The two equations that have the solution x = 2 when x is substituted for 2 are:

Equation 1: 2 + 3x = 10

2 + 3(2) = 10

2 + 6 = 10

8 = 10

Equation 2: 2x + 4 = 10

2(2) + 4 = 10

4 + 4 = 10

8 = 10

The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.

What is right triangle ?

A right triangle is a type of triangle that has one angle that measures exactly 90 degrees, also known as a right angle. The side opposite the right angle is called the hypotenuse and it is the longest side of the triangle. The other two sides are called legs, and one of them is the base and the other one is the height.

We know that the medians are 6 and $2\sqrt{11}$ units, respectively.

Therefore, the length of $\overline{ab}$ is twice the median length from $a$ to segment $\overline{bc}$ + twice the median length from $b$ to segment $\overline{ac}$

so the length of $\overline{ab}$ = 2(6) + 2($2[tex]\sqrt{11}[/tex]$) = 12 + 4$\sqrt{11}$

so the length of $\overline{ab}$ = 12 + 4$[tex]\sqrt{11}[/tex]$ units.

Hence , The length of segment $\overline{ab}$ is 12 + 4$[tex]\sqrt{11}[/tex]$ units.

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Therefore , solving the provided quadrilateral  question we can say that - (x,y) -> (x,y) is the formula for a reflection across the y-axis.

In geometry, a four-sided object having four corners is referred to as a quadrilateral. The word comes from either the Latin quad or portfolio of innovative (meaning "side"). Four corners, four states, and four corners are the three dimensions of a rectangle. Concave and convex surfaces come in essentially two varieties. Convex quadrilaterals also include the subclasses of trapezoids, parallelograms, angles, rhombuses, and squares.

Here,

The ordinate and abscissa are other names for the y-axis and x-axis, respectively.

The Y-axis is a line drawn from the bottom to the top of the graph. This axis runs parallel to the coordinates that need to be measured.

The numbers on the y-axis are referred to as y-coordinates.

When writing sorted pairs, the x-coordinate and then the y-coordinate are included in parenthesis.

(x, y).

A' ( -1, 1 ) ⇒ A"(-1, -1)

B' (-2, 2) ⇒ B"(-2, -2)

C' (-2, 3) ⇒ C"(-2, -3)

and D' (-1, 4) ⇒ D" (-1, -4)

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The probability that Esteban wins the game is 29/49.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, Esteban is playing a matching card game.

If the cards are identical, he wins the game.

Probability of getting cross on both the cards

2/7 × 2/7

= 4/49

Probability of getting star on both the cards

5/7 × 5/7

= 25/49

Probability to win the game is

4/49 + 25/49

= 29/49

Therefore, the probability that Esteban wins the game is 29/49.

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The equation showing the total cost for purchasing x tickets is given as y = 12.5x + 7

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the total cost for x tickets.

From the table, using the points (2, 32) and (6, 82):

y - 32 = [(82 - 32)/(6 - 2)](x - 2)

y - 32 = 12.5(x - 2)

y = 12.5x + 7

The equation is given as y = 12.5x + 7

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The surface area of the triangular prism in this problem is given as follows:

46 cm².

The surface area of a prism is calculated as the sum of the areas of all the figures that compose the prism.

The figure in this problem is composed as follows:

The area of the square is given as follows:

As = 2² = 4 cm².

The area of the two right triangles is given as follows:

At = 2 x 1/2 x 2 x 7 = 14 cm².

The area of the two rectangles is given as follows:

Ar = 2 x 2 x 7 = 28 cm².

Hence the surface area of the prism is given as follows:

S = As + At + Ar

S = 4 + 14 + 28

S = 46 cm².

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Answer:

1÷(5/2×(2×(8-2/5)-1))

1÷(5/2×(2×(6/5)-1))

1÷(5/2×(12/5-1))

1÷(5/2×7/5)

1÷(35/10)

1÷35/10

1×10/35

10/35

2/7

The Cartesian product that I read about is a mathematical concept that is used to combine two sets together in a specific way. The Cartesian coordinate system, on the other hand, is a way of representing points in a two-dimensional plane using a set of numerical coordinates.

The relationship between the two is that the Cartesian product is used to create the set of all possible coordinates that can be used in the Cartesian coordinate system. The Cartesian product of two sets, say set A and set B, is the set of all ordered pairs (a, b) where a belongs to set A and b belongs to set B.

When we graph a point in the Cartesian coordinate system, we are picking a specific point from the set of all possible points that can be created using the Cartesian product of the set of x-coordinates and the set of y-coordinates.

In other words, the Cartesian product is the foundation of the Cartesian coordinate system. It provides a set of all possible points that can be graphed using that system.

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The total amount in an account to the nearest cent after 3 years if the interest is compounded annually on an investment of $5600 at 7.65% is $6,986.02

To find the total amount in the account after 3 years, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the total amount, P is the initial investment (principal), r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $5600, r = 0.0765, n = 1 (because the interest is compounded annually), and t = 3. Plugging these values into the formula gives:

A = 5600(1 + 0.0765)^3

A = $6,986.02

So, the total amount in the account after 3 years, to the nearest cent, would be $6,986.02

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Answer:

A rhombus is a four-sided shape with all sides equal in length, and opposite angles equal. The diagonals of a rhombus bisect each other at right angles and they are equal in length.

In this case, the length of one diagonal of the rhombus is 6 times the length of the other diagonal. Let's call the length of the shorter diagonal "d", and the length of the longer diagonal "6d".

To find the perimeter of the rhombus, we can add up the lengths of all four sides. Since all sides of a rhombus are equal, we can find the perimeter by multiplying the length of one side by 4.

To find the length of one side, we can use the Pythagorean theorem to find the length of the side in terms of d, the shorter diagonal.

We know that d^2 + (3d)^2 = s^2, where s is the length of one side.

After simplifying, we get: d^2 + 9d^2 = s^2

s = √10d^2

so the perimeter is 4s = 4 √10d^2

Therefore, the perimeter of the rhombus can be represented by the expression 4* √10d^2 where d represents the length of the shorter diagonal.

Answer:

14d

Step-by-step explanation:

First the short diagonal is d, so we can mark it as d:

d

Second we have 6 times that, so 6d:

d+6d

Then we multiply it by two since a rhombus has 4 sides:

2d+12d

Then we simplify:

14d

Voila!

m = the slope of the curve at x=3 and b = the y-intercept at x=3. Therefore, the approximate value of y at x=2

We can use the local linearization of the curve to approximate the value of y at x=2.

The local linearization of the curve is given by the equation y = mx + b, where m is the slope of the curve at x=3 and b is the y-intercept at x=3.

Let m be the slope of the curve at x=3 and b be the y-intercept at x=3.

The slope of the curve at x=3 can be found by calculating the derivative of the curve at x=3.

The y-intercept at x=3 can be calculated by substituting x=3 into the equation of the curve and solving for y.

Therefore, m = the slope of the curve at x=3 and b = the y-intercept at x=3.

Substituting the values of m and b into the equation of the local linearization, we get the equation y = mx + b.

Substituting x=2 into the equation, we get y ≈ 0.5 + 1 = 1.5.

Therefore, the approximate value of y at x=2

The local linearization of the curve can be used to approximate the value of y at x=2. Substituting x=2 into the equation, we get y ≈ 1.5, which is the approximate value of y at x=2.

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An answer option which distinguishes the element that needs to be adjusted on the chart in the following scenario is: C. x-axis value.

In an experiment, there are two (2) main types of variables and these include the following:

In Mathematics, an independent variable can be defined as the variable that is being manipulated by an experimenter or researcher. This ultimately implies that, an independent variable is typically considered to be the cause in an experiment and it is represented by the x-axis value on a graph.

In this scenario, we can reasonably infer and logically deduce that the independent variable (x-axis value) represents the element that should be adjusted on Donna's demographic chart on population growth.

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function f(x) is said to be discontinuous at a point ‘a’ of its domain D if it is not continuous there. The point ‘a’ is then called a point of discontinuity of the function.

he function of the graph which is not connected with each other is known as a discontinuous function.

A function f(x) is said to have a discontinuity of the first kind at x = a,

if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.

f(x) is said to have a discontinuity of the first kind from the left at x = a,

if the left hand of the function exists but not equal to f(a)

There are three types of discontinuity.

Jump Discontinuity

Infinite Discontinuity

Removable Discontinuity

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Check the picture below.

Answer:

Step-by-step explanation:

Given that w=5 and x=9, we can substitute these values into the expression to find the value of the expression:

7w-x

= 7(5) - 9

= 35 - 9

= 26

So the value of the expression when w=5 and x=9 is 26

The degree of the measure of the exterior angle is 141 3/7°.

the term exterior angle in triangle is defined as angles that are parallel to the inner angles of a polygon but lie on the outside of it

Here we know that A square and a regular heptagon are coplanar and share a common side AD.

And then here we need to find each of the interior angle of the regular heptagon.

As we all know that here we have to use the formula that gives the interior angle measure for a regular polygon with any number of sides is 180(n-2)/n where n is the number of sides.

According to the given formula here we have a regular heptagon's interior angle measures is calculated as

=> 180(7-2)/7 = 128 4/7.

Here we also know that the angle A and D would be 128 4/7 degrees.

Here the next step is to Find angle BAC.

For that here we have to know that a square's interior angle is 90 degrees and a heptagon's is 128 4/7 degrees.

Now we have to subtract those from 360 degrees to find angle BAC then we get the expression like the following,

=> Angle BAC = 360 - (angle A + 90)

=> 360 - (128 4/7 + 90)

When we simplify this one then we get the resulting value as,

=> 360 - 218 4/7 = 141 3/7 degree

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It can be concluded that Gym city membership fee is less than Jane’s current gym membership fee.

Given is that the equation C = 50m, that represents the monthly cost of membership at Jane’s current gym. The equation C = 35m represents the monthly cost of membership at a different gym, named Gym City

The equation for direct variation is -

y = Kx

where -

{K} denotes the rate of change

Now -

Therefore, it can be concluded that Gym city membership fee is less than Jane’s current gym membership fee.

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Answer:540

Step-by-step explanation:

Answer:

540

Step-by-step explanation:

When multiplying two numbers and one is a decimal you multiply both of them by 10 to keep whole number denominators.

[tex]\frac{324}{0.6}[/tex]

[tex]10* \frac{324}{0.6}[/tex]

[tex]\frac{3240}{6}[/tex]

[tex]\frac{3240}{6} = 540[/tex]

[tex]8 = c - - 3 \\ 8 = c + 3 \\ c = 8 - 3 \\ c = 5[/tex]

Answer:

it is c=5

Step-by-step explanation:

here is how you get the answer

8=c−−3

8=c+3

c=8−3

c=5

Answer:

1. 37, 44, 51

2. 24, 19, 14

3. 36, 49, 64

Step-by-step explanation:

The first rule is add 7

The second rule is subtract 5

The third rule is add 2 to every difference

It takes 10 minutes for the two lines to have filled an equal number of barrels

Each line will have filled 90 barrels

Let “x” be the number of minutes

The old conveyer line has filled 20 barrels of paint, and is filling more at a rate of 7 barrels per minute

Thus, a equation is framed as follows:

Old conveyor: 20 + 7(number of minutes)

Old conveyor: 20 + 7x ------- eqn 1

A worker just switched on a newer line that can fill 9 barrels per minute

Thus, a equation is framed as follows:

New conveyor: 9(number of minutes)

New conveyor: 9x -------- eqn 2

In a little while, the two lines will have filled an equal number of barrels.

Thus, eqn 1 must be equal to eqn 2

Thus it takes 10 minutes for the two lines to have filled an equal number of barrels

Substitute x = 10 in any one of equations

Substitute in eqn 2

9x = 9(10) = 90

Thus each line will have filled 90 barrels

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The least positive integer value of x is 1

We can start by expressing the expression (2x)^2 2372x 37^2 as a multiple of 47.

47 | (2x)^2 2372x 37^2

Since 47 is a prime number, we can use the property that a multiple of a prime number is a number that can be divided by that prime number without leaving a remainder.

So, we need to find the least positive integer value of x such that (2x)^2 2372x 37^2 is divisible by 47.

We can start by assuming (2x)^2 2372x 37^2 as (2x)^2 2372x 37^2 = 47*k, where k is any integer.

We can start testing values of x starting from 1,

x=1 : (21)^2 * 23721 * 37^2 = 4 * 74 * 1369 = 47 * 2028,

x=2 : (22)^2 * 23722 * 37^2 = 16 * 148 * 1369 = 47 * 6912,

and so on.

So the least positive integer value of x such that (2x)^2 2372x 37^2 is a multiple of 47 is x=1.

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The answer provided illustrates the concept of implied and express warranties, unilateral and bilateral contracts, voidable and void contracts, and executory consideration. It also provides number of  examples of each of these concepts.

1. O fit for the ordinary purpose for which such goods are used.

2. A enforce the contract against Olive.

3. C An express warranty must be in writing and signed by the parties.

4. C supported by consideration.

5. O is void.

6. C enforceable.

7. O is a rejection and counteroffer.

8. O A promise to do something in the present in exchange for something else in the future.

9. A An offer to pay a reward for the return of lost property.

10. C An offer to do something in the future in exchange for something else in the present.

The answer provided illustrates the concept of implied and express warranties, unilateral and bilateral contracts, voidable and void contracts, and executory consideration. It also provides number of examples of each of these concepts.

The complete question is :

Question 1 (1 point) Home Remodelers, Inc., and Imogen enter into a contract for a sale of cabinets and countertops. Home Remodelers merchant who deals in goods of the kind sold, notes that its goods come with an implied Under the UCC, this means that the goods are reasonably warranty of merchantabilit fit for the buyer's particular purpose. O fit for the ordinary purpose for which such goods are used. O suitable for resale at an acceptable price. C the best quality that money can buy Save Question 2 (1 point) Olive, an agent for Precision Paving Corporation, enters into an unauthorized contract with Quality Asphalt, Inc. Quality Asphalt may, at its option, A enforce the contract against Olive. O enforce the contract against Precision Paving. C void the contract. Save Question 3 (1 point) Which of the following statements about an express warranty is true? A An express warranty does not need to be in writing. O An express warranty does not need to be signed by the parties. C An express warranty must be in writing and signed by the parties. Save Question 4 (1 point) In order to be enforceable, a contract must be A fair and equitable to both parties. O signed by both parties. C supported by consideration. Save Question 5 (1 point) A contract that is void because of a mistake by one of the parties O is voidable. A is void. C is still enforceable. Save Question 6 (1 point) A contract between two individuals is generally A voidable. O void. C enforceable. Save Question 7 (1 point) Phil makes an offer to sell a house to Sally for $200,000. Sally responds by saying that she will buy the house for $200,000, but wants to add a condition that the house must pass an inspection. This response A is an acceptance of the offer. O is a rejection and counteroffer. C is a condition of acceptance. Save Question 8 (1 point) Which of the following is an example of Executory consideration? A A promise to do something in the future in exchange for something else in the present. O A promise to do something in the present in exchange for something else in the future. C A promise to do something in the future in exchange for something else in the future. Save Question 9 (1 point) Which of the following is an example of a unilateral contract? A An offer to pay a reward for the return of lost property. O An offer to do something in the present in exchange for something else in the future. C An offer to do something in the future in exchange for something else in the present. Save Question 10 (1 point) Which of the following is an example of an implied contract? A An offer to pay a reward for the return of lost property. O An offer to do something in the present in exchange for something else in the future. C An offer to do something in the future in exchange for something else in the present. Save

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So on solving the provided question, we can say that by unitary method task done of 15 days done = 7/5 X 15hours = 21 hours

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

task done of 5 days done = 7 hours.

task done of 1 days done = 7/5 hours.

task done of 15 days done = 7/5 X 15hours = 21 hours

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Answer: B. [tex]x^{2} - 16x + 64 = -21 + 64[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

The dimensions of the garden will be 4m by 3m. To determine the dimensions of the garden, we need to use the formula A = l x w, where A is the area of the garden (12m), l is the length of the garden and w is the width of the garden.

We can then rearrange the formula to solve for either l or w. We can rearrange the formula to solve for l by dividing both sides of the equation by w: A/w = l.

We know that the area is 12m, so we can substitute 12m for A in the equation. We need to find the dimensions that use the least amount of fencing, so let's set w equal to 3m. We can then substitute 3m for w in the equation and solve for l: 12m/3m = 4m.

Therefore, the dimensions of the garden are 4m by 3m.

The bacteria count after 5 hours, given the initial bacteria count and the rate that the bacteria are disappearing is 59 bacteria

First, find the rate at which the bacteria are disappearing from the culture dish every hour. This rate is:

= 100 % - 90 %

= 10 %

This means that every hour, 10% of the bacteria are removed from the culture dish on account of the antibiotic.

In five hours therefore, the bacteria count on the culture dish would be:

= Starting number of bacteria x ( 1 - rate of decrease per hour) ^ number of hours

= 100 x ( 1 - 10 %) ⁵

= 100 x 90 %⁵

= 59 bacteria

In conclusion, after 5 hours of the antibiotic working on the culture dish, the number of bacteria left would be 59 bacteria.

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The null hypothesis would be H0: p <= 0.25 and the alternative hypothesis would be Ha: p > 0.25

The null hypothesis represents the default assumption that there is no significant difference between the proportion of high school couples who believe they will marry their high school sweetheart and the researcher's claim that more than 25% of high school couples believe they will marry.

The alternative hypothesis represents the claim that the researcher wants to test, which is that the proportion of high school couples who believe they will marry their high school sweetheart is greater than 25%.

So, the null hypothesis would be:

H0: p <= 0.25 (where p is the proportion of high school couples who believe they will marry their high school sweetheart)

The alternative hypothesis would be:

Ha: p > 0.25 (where p is the proportion of high school couples who believe they will marry their high school sweetheart)

The researcher would then use statistical methods to test if the sample data provide enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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