The table of values represents a quadratic function f(x).


x f(x)
−8 13
−7 6
−6 1
−5 −2
−4 −3
−3 −2
−2 1
−1 6
0 13

What is the equation of f(x)?
f(x) = (x + 5)2 − 2
f(x) = (x + 4)2 − 3
f(x) = (x − 4)2 − 3
f(x) = (x − 5)2 − 2

The profit for Mr Christopher is #1000.

Profit is the money that is earned in trade or business after paying the costs of producing and selling goods and services.

Given that, Mr. Christopher contributed #500 to a business, Miss Uche contributed #300 while Mrs. Amaka contributed #200, they share a profit #2000,

Let the ratio of their contribution = 5x : 3x : 2x

Therefore,

5x + 3x + 2x = 2000

10x = 2000

x = 200

Their profit share =

Mr. Christopher = 200 x 5 = 1000,

Miss Uche = 200 x 2 = 200

and

Mrs. Amaka = 200 x 3 = 600

Hence, the profit share of Mr. Christopher is #1000,

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The missing number of all the ratios are given  below.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

The ratios are given.

1. 1:2=4:N

2: 3:8=N:16

3.15:20=30:N

4.N:25=2:5

5.10:N=40:80

p:q can be written as p/q.

To find the missing number:

1. 1:2=4:N

1/2 = 4/N

So, N = 8

2: 3:8=N:16

So, N = 6

3.15:20=30:N

So, N = 40

4.N:25=2:5

So, N = 10

5.10:N=40:80

N = 20

Therefore, all the missing numbers are given above.

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El número de este problema es 72, y la suma de sus cifras da 9.

En este problema tenemos un numero de dos cifras, que podemos escribir como:

a*10 + b

Donde a y b son numeros enteros entre 0 y 9, y son las cifras de nuestro número.

Sabemos que si a este número le aumentamos 3 veces la cifra de decenas, resulta en 93, entonces podemos escribir:

a*10 + b + 3*a = 93

a*13 + b = 93

Ok, ahora simplemente devemos reemplazar los valores de b por numeros enteros y resolver la ecuación para a, asi hasta que el resultado de a tambien de un numero entero.

si b = 5

a*13 + 5 = 93

a*13 = 93 - 5

a*13 = 88

a = 88/13 = 6.7

No es una solucion.

si b = 2

a*13 + 2= 93

a*13 = 93 - 2

a*13 = 91

a = 91/13

a = 7

Esta es la solución.

Las cifras son a = 7 y b = 2, y su suma da:

7 + 2 = 9

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Answer:

biquadratic polynomial

Step-by-step explanation:

The given polynomial is
[tex]-10x^4 - 7\\\\[/tex]

The degree of this polynomial (the highest power) is 4

Such a polynomial is called a quartic polynomial. If all the terms have even degree, which in this case is true since there is only one term and its degree is 4 it is called a biquadratic polynomial

If polynomial has degree 1 ex 4x + 3 it is called a linear polynomial

If it has degree 2 --> quadratic

If it has degree 3 --> cubic

The coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)).

A group of values that exhibit precise positioning The first number on a graph represents the distance along, while the second number represents the distance up or down.

To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.

Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC :

Let the equation be Distance [tex]$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$[/tex] substitute the values in the above equation, we get

[tex]$\mathrm{AC}=\sqrt{\left((2-(-2))^2+(4-1)^2\right)}$$[/tex]

simplifying the equation, we get

[tex]$A C=\sqrt{ }(4+9)=\sqrt{ }(13)$$[/tex]

We can utilize the knowledge of the square's side length to determine the locations of the remaining vertices. Vertex B is known to have the same y-coordinate as vertex A, while vertex C is two units to the left in terms of the x-coordinate. Therefore, the coordinates of vertex B exists (-2 + 2√(13), 1).

Similar to vertex A, vertex D is known to have an identical x-coordinate, but its y-coordinate is four units below vertex C. Therefore, the coordinates of vertex D exists (-2, 4√(13))

Therefore, the coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)) respectively.

The complete question is:

Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.

The coordinates are and D.

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The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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Answer:

The lace is 36 cm long and 1 cm = 10 mm. So, 36 cm = 360 mm.

He can cut the lace into 18 mm pieces, so he can cut 360 mm / 18 mm = 20 pieces of 18 mm lace from the 36 cm lace.

Marco pays $64  for credit card, $272 for Groceries and $672 for rent

percentage, a relative value indicating hundredth parts of any quantity.

Given that Marco budgets $1,600 a month for expenses.

According to the graph he pays 4% of credit card

Now let us find 4% of 1600

4/100×1600

0.04×1600

$64 Marco pays for credit card.

From graph, he pays 17% for groceries

17% of 1600

17/100×1600

0.17×1600=$272

$272 Marco pays for Groceries.

From graph, he pays 42% for rent

42/100×1600

0.42×1600=672

$672 Marco pays for Rent.

Hence, Marco pays $64  for credit card, $272 for Groceries and $672 for rent

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well, there are 28 + 28 + 24 = 80 pieces total, or namely that's the 100%, and we know that 24 of those are chocolates

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 80 & 100\\ 24& x \end{array} \implies \cfrac{80}{24}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 10 }{ 3 } ~~=~~ \cfrac{ 100 }{ x }\implies 10x=300\implies x=\cfrac{300}{10}\implies x=30[/tex]

To figure out what percentage of the trail mix is chocolate, we add up all the pieces, divide the number of chocolate pieces by the total and multiply by 100. In this case, we find that 35% of the trail mix is chocolate.

In order to figure out the percent of chocolate pieces in Caitlyn's trail mix, we first need to determine the total number of pieces. Caitlyn counts 28 raisins, 28 chocolate pieces, and 24 peanuts, which gives us a total of 80 pieces in the mix. Then, since there are 28 chocolate pieces, we divide 28 (chocolate pieces) by 80 (total pieces). This will give us the decimal representation of the portion of the mix that is chocolate. To convert this into a percentage, we multiply by 100. Hence, the calculation will be (28/80)*100 = 35%. So, 35% of the trail mix is chocolate.

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Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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The largest snack Sasha can make while still using the correct ratio of ingredients is 555g.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that after school Sasha likes to make snacks by mixing raisins and nuts in a ratio of 3:5 when she checked the cupboard today there were only 60g of raisins and 75g of nuts left.

The largest snack Sasha can make while still using the correct ratio of ingredients is calculated as,

E = ( 60 x 3 + 75 x 5 )

E = 180 + 375

E = 555 g

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Answer:

To find out how many groups of riders there will be, we need to divide the total number of people waiting in line (157) by the maximum number of people allowed on the ride at one time (17).

157 people / 17 people/group = 9.235 groups (approx)

But since the groups must be in whole numbers, we have to round up the value 9.235 groups to the next whole number, which is 10 groups.

So, the number of groups of riders will be 10.

Answer: 9 groups of riders.

Step-by-step explanation:

To find out how many groups of riders there will be, you need to divide the total number of people waiting in line by the maximum number of people allowed on the ride at one time.

157 (total people in line) ÷ 17 (people allowed per ride) = 9.235 (groups of riders)

Because you can't have a fraction of a group, you need to round down to get the whole number of groups.

So the answer is 9 groups of riders.

Answer:

D) 7/12

Step-by-step explanation:

The first thing we want to do is find a like denominator for the fraction

Both 4 and 3 go into the multiple 12, so we'll use that

4x3=12

3x4=12

and what you do to one side, you must do to the other so we have

1/4x3= 3/12

2/3x4= 8/12

With that you get 2 3/12 and 1 8/12, which is subtractable

Take one from 2 so that you can make 3/12 15/12

15/12-8/12=7/12

This gives us our answer 7/12

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Don't worry, I gotchya bro :)

2 1/4 - 1 2/3

2 1/4 to an improper fraction is 9/4

1 2/3 to an improper fraction is 5/3

to get the same denominator multiply 9/4 by 3 and 5/3 by 4.

27/12 - 20/12

7/12 IS YOUR ANSWER.

Note: This took my time, brain, and eyes to help. If you can just click one button of brainliest that would mean somthing.

Answer:

[tex]\frac{1}{343}[/tex]

Step-by-step explanation:

[tex]7^{-3}[/tex] = [tex]\frac{1}{7^{3} }[/tex] = [tex]\frac{1}{7x7x7}[/tex] = [tex]\frac{1}{343}[/tex]

i do not know the answer either

Answer:

below

Step-by-step explanation:

The INdependent variable is 'r'

  'C'  DEPENDS on the value of 'r'...it is the dependent variable

Answer: Circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is a constant.

We know that the diameter is twice the radius (d = 2r).

So when we increase the circumference of the circle from 12π cm to 18π cm, we are increasing the radius from r to r'.

To find the increase in diameter, we can use the formula for the diameter, and subtract the original diameter from the new diameter.

d' = 2r' and d = 2r

d' - d = 2r' - 2r

We know that the relationship between circumference and radius is C = 2πr.

So we can write:

12π = 2πr and 18π = 2πr'

r = 6/π and r' = 9/π

then

d' - d = 2r' - 2r = 2(9/π) - 2(6/π) = 18/π - 12/π = 6/π

Therefore, the diameter must increase by 6/π cm in order to increase the circumference of the circle from 12π cm to 18π cm.

Step-by-step explanation:

Answer : Yes, it has rotational symmetry. The angle of rotation is, 60 degree.

It is a shape that has Rotational Symmetry when it still the same after the rotation.

here, we have,

The given figure is hexagon and it has rotational symmetry because it still the same after the rotation.

As there are 6 sides of hexagon geometry and the degree of rotation is, .

So, the angle of rotation = 360/60

                                        =60 degree

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Answer: To find the coordinates of the remaining vertices of square ABCD, we can use the information we have been given about the diagonal AC and its vertices. The diagonal AC has been given as having the vertices A(-4, -1) and C(2, 5). Since a square has right angles, we know that the other two vertices of the square must form a right angle with the diagonal AC.

To find the coordinates of vertex B, we know that it must have the same y-coordinate as vertex A, but a different x-coordinate. Since the x-coordinate of vertex A is -4, we can deduce that the x-coordinate of vertex B must be the same as the x-coordinate of vertex C, which is 2. Therefore, the coordinates of vertex B are (2, -1).

To find the coordinates of vertex D, we know that it must have the same x-coordinate as vertex A, but a different y-coordinate. Since the y-coordinate of vertex A is -1, we can deduce that the y-coordinate of vertex D must be the same as the y-coordinate of vertex C, which is 5. Therefore, the coordinates of vertex D are (-4, 5).

In summary, the coordinates of the remaining vertices of square ABCD are B(2, -1) and D(-4, 5)

Step-by-step explanation:

Answer:

5,3,3-1 the box are illustrate the the number of the triangle

The boat and the whale are about 218.5 miles apart.

Using the Pythagorean theorem to calculate the distance between the boat and the whale.

Let's call the distance between the boat and the whale "d" and the time they moved apart "t".

1st movement:

d = 45t

2nd movement:

d = (45t + 25(t+35))²

To calculate the final distance, we need to square d from the second movement and add the result from the first movement.

d² = (45t)² + (25(t+35))²

We know that the boat and the whale were moving apart for 35 minutes and 25 minutes, so we can substitute t = 35 and t = 25 in the equation.

d² = (4535)² + (2560)²

Taking the square root of the result and get the final distance between the boat and the whale.

d =  ([tex]\sqrt{4535 ^{2} +2560^{2} }[/tex])

d ≈ 218.5 miles

Hence, the boat and the whale are about 218.5 miles apart.

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Answer:

Step-by-step explanation:

?

The car must travel a distance of 130.7 meters. This can be determined by using the equation for distance travelled with a constant acceleration:

Distance = Initial Velocity x Time + (1/2) x Acceleration x Time^2

In this case, the initial velocity is 18.1m/s, the acceleration is 3.7m/s^2, and the final velocity is 29.7m/s. We can set the final velocity equal to the initial velocity and solve for time:

29.7m/s = 18.1m/s + 3.7m/s^2 x Time

Time = 5.4 seconds

We can then plug this value for time into the equation for distance:

Distance = 18.1m/s x 5.4s + (1/2) x 3.7m/s^2 x 5.4s^2

Distance = 130.7 meters

Answer:

To verify that [n+3]! / n! = (n+1), we can use the definition of factorial:

[n+3]! = (n+3) * (n+2) * (n+1) * n!

And we can cancel out n! from both sides of the equation:

(n+3) * (n+2) * (n+1) = n+1

Which is true, and thus [n+3]! / n! = (n+1) holds true.

Another way to verify this is by simplifying the RHS and LHS

(n+1) = (n+1)

And the LHS,

(n+3)! = (n+3)(n+2)(n+1)n! = (n+1)(n+2)(n+3)n! = (n+1)(n+2)(n+3)!/n!

which is also equal to (n+1)

So, [n+3]! / n! = (n+1) is true.

Answer: What is the question ?

Step-by-step explanation:

Answer: 2 7/8 hours per week

hectors rate is greater

Step-by-step explanation:

Answer:

Step-by-step explanation:

When it comes to graphing a trigonometric function we use the amplitude, period, vertical shift and these values all help our graph come together to give us our final answer.

In this case,

The amplitude=2

period=1

and there is no phase / vertical shift.

The number of different schedules are possible is given by the permutation and the equation is P = 2,730 schedules

A permutation is an ordered arrangement.

The number of ordered arrangements of r objects taken from n unlike objects is:

Permutation ⁿPr = n! / ( n - r )!

Given data ,

Let the total number of schedules be P

Let the total number of European cities be n = 15

Let the number of cities Yolanda can visit in time r = 3 cities

So , the total number of different schedules is calculated by permutation and ,

The total number of different schedules = ⁿPr = n! / ( n - r )!

Substituting the values in the equation , we get

¹⁵P₃ = ( 15 ) ! / ( 15 - 3 ) !

¹⁵P₃ = ( 15 ) ! / ( 12 )!

¹⁵P₃ = 15 x 14 x 13

¹⁵P₃ = 2,730 schedules

Hence , the value of P is 2,730 schedules

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Answer:

f(-4) = -36

Step-by-step explanation:

Step-by-step explanation:

A function assigns the value of each element of one set to the other specific element of another set. The value of the function when the value of x is -4 is 92.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given that F(x)=3x²-10x+4, therefore, the value of the function can be calculated by substituting the value of x as -4.

Therefore, the value of the function when the value of x is -4  can be calculated as shown below,

F(x) = 3x² - 10x + 4

F(-4) = 3(-4)² - 10(-4) + 4

= 3(16)  + 40 + 4

= 48 + 40 + 4

= 92

Hence, the value of the function when the value of x is -4 is 92.

Answer: a. The sum of two numbers is always greater than zero.

Step-by-step explanation:

A counterexample to this conjecture would be when the two numbers are both negative. For example, the sum of -5 and -3 is -8, which is less than zero.

b. The sum of a positive number and a negative number is always positive.

A counterexample to this conjecture would be when the negative number is greater than the positive number. For example, the sum of 5 and -6 is -1, which is less than zero.

c. If a figure has four sides, then it is a rectangle.

A counterexample to this conjecture would be a square. A square has four sides, but it is not a rectangle because all of its angles are 90 degrees while a rectangle has four right angles.

It's good to keep in mind that a conjecture is a statement that is made based on observations and that it hasn't been proven yet, therefore a counterexample can be used to show that the conjecture is false.

Answer:

a)  -5 + 1 = -4

b)  2 + (-10) = -8

c)  A scalene trapezium.

Step-by-step explanation:

A counterexample is proof that a conjecture is false.

Given conjecture:

If one of the numbers is negative, and its absolute value is equal to or greater than the value of the positive number, the result will always be equal to or less than zero.

Counterexample:

As -4 is less than zero, this proves that the conjecture is false.

Given conjecture:

If the absolute value of the negative number is greater than the value of the positive number, the result will always be negative.

Counterexample:

As -8 is negative, this proves that the conjecture is false.

Given conjecture:

Counterexample:

The interior angles of a rectangle are congruent (90°).

A scalene trapezium has four sides, but as its interior angles are all different, it is not a rectangle.  This proves that the conjecture is false.