Keith has a package of 75 marbles.He gave an equal number of marbles to each of his 8 friends. How many marbles will be left over?

Answer:

(3x+2)(x-5)

Step-by-step explanation:

Factor by grouping

\(3x^2-13x-10\\=3x^2-15x+2x-10\\=3x(x-5)+2(x-5)\\=(3x+2)(x-5)\)

Answer:

It’s the last option; 10/24 and 20/24

Answer:

19 - 42x

Step-by-step explanation:

To differentiate this, we must use the product rule
f'(x) = (7x+3)'(4-3x) + (4-3x)'(7x+3)
= (7)(4-3x) + (-3)(7x+3)
= 28 - 21x - 21x - 9
= 19 - 42x

Therefore the value of x is less than 4 when x is in the inequality 3x + 2 < 14 and greater than -3 when x is in the inequality 2 x-5> -11

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. For instance, let's say you have 225 and want to purchase a new bicycle that costs $250.

Expressions are carried out, or evaluated, in order to yield a value. In an evaluation process, values of expressions can be employed as components of surrounding expressions.

To solve for x in the inequality 3x + 2 < 14, we can begin by subtracting 2 from both sides to get 3x < 12. Then, dividing both sides by 3 gives x < 4.

To solve for x in the inequality 2 x-5> -11, we can begin by adding 5 to both sides to get 2x> -6, then divide both sides by 2 to get x > -3

So x can be any number greater than -3 and less than 4

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The surface area of the prism is 744 cm², the volume of the prism is 624 cm³.

Given:

- Height of the regular quadrilateral prism (h) = 13 cm

- Lateral area of the prism (AL) = 624 cm²

1. Surface Area:

To find the surface area, we need to calculate the area of the two bases and the lateral area of the prism.

The area of each base can be found by dividing the lateral area by the height: A = AL / h = 624 cm² / 13 cm = 48 cm².

Since there are two identical bases, the total base area is 2 times the area of one base, so the total base area is 2 * 48 cm² = 96 cm².

To calculate the surface area, we add the area of the two bases to the lateral area: Surface Area = 2A + AL = 2 * 48 cm² + 624 cm² = 120 cm² + 624 cm² = 744 cm².

Therefore, the surface area of the prism is 744 cm².

2. Volume:

The volume of the prism can be found by multiplying the base area by the height: Volume = A * h = 48 cm² * 13 cm = 624 cm³.

Therefore, the volume of the prism is 624 cm³.

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Answer:

$740.00

Step-by-step explanation:

85% of x is 629

Translate into algebra. Use a decimal in place of the percent:

.85x = 629

Divide by .85

x = 740

This answer makes sense because the regular price should be a little higher than the sale price. If they are paying 85% they're only getting 15% off.

Check:

740×.85 = 629

Answer:

$740

Step-by-step explanation:

\(\frac{629}{0.85} =740\)

Hope this helps

Answer:

2(x+5)

Step-by-step explanation:

Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.

The correct answer choice is option D.

Cost of 16-pound bag of Kitty Kibbles = $20.80

Unit price of kitty kibbles = Price / number of pounds

= $20.80 / 16

= $1.30 per pound.

Cost of 8-pound bag of Feline flavor = $11.20

Unit price of feline flavor = Price / number of pounds

= $11.20 / 8

= $1.40 per pound

Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.

Complete question:

A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?

A. Feline Flavor has a lower unit price of $1.40/pound.

B. Feline Flavor has a lower unit price of $1.30/pound.

C. Kitty Kibbles has a lower unit price of $1.40/pound.

D. Kitty Kibbles has a lower unit price of $1.30/pound.

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Answer:

-18x^2+17x-9

Step-by-step explanation:

Tan P expressed as a fraction in simplest terms is 15/29

Trigonometric Identities are defined as equalities involving trigonometry functions and also holds true for all the values of variables given in the equation.

There are five types of trigonometric identities;

From the information given, we have that;

Opposite side = 15

Adjacent side = 29

But the tangent trigonometric identity is;

Tan P = opposite/adjacent

Substitute the value

Tan P = 15/29

Hence, the value is 15/29

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o find the local extrema of the polynomial, we first take the derivative of the polynomial and set it equal to zero:

f(x) = 10x^5 + 22x^4 + 20x^3 - 0x^2 + 6

f'(x) = 50x^4 + 88x^3 + 60x^2

Setting f'(x) = 0, we can factor out a 2x^2 from the expression to get:

f'(x) = 2x^2(25x^2 + 44x + 30) = 0

Using the quadratic formula to solve for x, we get:

x = (-44 ± sqrt(44^2 - 4(25)(30))) / (2(25))

x = (-44 ± sqrt(784)) / 50

x = (-44 ± 28) / 50

x = -0.32 or -0.56

Answer:

NO

Step-by-step explanation:

No. The sample of only the 2 fastest swimmers on the swim team is not likely to be representative of the entire swim team. It may not include swimmers with different skill levels or performance abilities, which could lead to a biased representation of the team as a whole. To have a representative sample, it would be necessary to include a diverse range of swimmers from different skill levels and performance abilities.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

Answer:

1073.45 in²

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The equation to solve for the area of a circle is:

But wait, we don't have a radius to fix in the equation! Well to solve for the radius when given diameter, we can use the expression:

Now that we know this, we can insert 37 in for the diameter:

So, the radius of the circle is 18.5 inches.

Inserting 18.5 into the expression for the radius:

Using 3.14 for pi:

Therefore, the area of a circle with a diameter of 37 inches is 1073.45 in².

Answer:

  117

Step-by-step explanation:

You want the cross product of vectors u = (12i -3j) and v = (-5i +11j).

The cross product of 2-dimensional vectors is a scalar that is effectively the determinant of the matrix of coefficients.

  u×v = (12)(11) -(-3)(-5) = 132 -15

  u×v = 117

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Answer:

W=2/(P-2L)

Step-by-step explanation:

The graph with the same end behavior is the one in option C.

The given function has a numerator with a negative leading coefficient and an odd degree, while the denominator is a quadratic polynomial.

It will mean that as x tends to negative infinity, the function tends to infinity, and as x tends to positive infinity, the function tends to negative infinty, that is the end behavior of the given function.

The graph with that end behavior is the same one than in option C.

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Answer:

the commission amount does an agent make is $100

Step-by-step explanation:

The computation of the commission amount does an agent make is as follows:

= Commission percentage × policy amount

= 10% × $1,000

= $100

Hence the commission amount does an agent make is $100

It could be determined by applying the given formula so that the correct amount could come

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.

A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :

g(x) = {-(1/2)x + 1,    for x<-2

       = {-(x+1)²,        for -2≤x≤1

      =  {4                 for x>1

We have to find the value of g(-5) ,g (-2), and g(-1),

For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,

⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,

For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function

"-(x+1)²" will be used,

⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,

For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,

⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,

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Dante will need 30 album pages to hold all of his baseball cards.

What is meant by pages?

Pages refer to the individual sheets of paper within a document or book, typically numbered consecutively, that are used to present information, text, images, or illustrations.

What is meant by cards?

Cards typically refer to rectangular pieces of stiff paper, plastic, or similar material used for playing games, collecting information, or providing details about a product or service, such as business cards or trading cards.

According to given information

Dante has 10 cards for each of the 24 teams, for a total of 10 x 24 = 240 cards.

To determine the number of album pages he will need, we can divide the total number of cards by the number of cards each page can hold:

240 cards ÷ 8 cards/page = 30 pages

Therefore, Dante will need 30 album pages to hold all of his baseball cards.

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Answer:

Correct answer for k12 kids

Using technology such as excel, the linear regression equation which best models the data is y = 0.31x + 0.12

To model the data, we could use a linear regression calculator or excel which gives the slope intercept equation of the model in the form :

Where ;

Therefore, the linear regression function which nest models the data in the table is y = 0.31x + 0.12

Answer:

y = \(\frac{3}{4}\) x - \(\frac{9}{2}\)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, - 6) and (x₂, y₂ ) = (2, - 3) ← 2 points on the line

m = \(\frac{-3-(-6)}{2-(-2)}\) = \(\frac{-3+6}{2+2}\) = \(\frac{3}{4}\) , then

y = \(\frac{3}{4}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (2, - 3 )

- 3 = \(\frac{3}{4}\) (2) + c = \(\frac{3}{2}\) + c ( subtract \(\frac{3}{2}\) from both sides )

- 3 - \(\frac{3}{2}\) + c , then

c = - \(\frac{9}{2}\)

y = \(\frac{3}{4}\) x - \(\frac{9}{2}\) ← equation of line

Answer:

50

Step-by-step explanation:

Add up all the numbers