Factorize 10ab + 4a + 5b + 2

Answer: (-12,-6)

Step-by-step explanation:

If we already have two points of the line, we can find its slope ([tex]m[/tex]), its intersection with the y-axis ([tex]b[/tex]), hence its equation:

Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]

Point 2: [tex](x_{2},y_{2})=(-2,-2)[/tex]

Slope equation:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-2-0}{-2-3}[/tex]

[tex]m=\frac{2}{5}[/tex] This is the slope of the line

Now, the equation of the line is:

[tex]y=mx+b[/tex]

We already know the slope, now we have to find [tex]b[/tex] with any of the given points. Let's choose Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]

[tex]0=\frac{2}{5}(3)+b[/tex]

Isolating [tex]b[/tex]:

[tex]b=-\frac{6}{5}[/tex]

Then, the equation of the line is:

[tex]y=\frac{2}{5} x-\frac{6}{5}[/tex]

With this equation we can find which point is a solution. Let's begin with the first point (-12,-6):

[tex]-6=\frac{2}{5} (-12)-\frac{6}{5}[/tex]

[tex]-6=-\frac{24}{5} -\frac{6}{5}[/tex]

[tex]-6=-6[/tex] Since both sides of the equation are equal, (-12,-6) is the point that fulfills the solution of the equation.

Answer:

Step-by-step explanation:

[tex]x+5+2x=x+15\qquad\text{combine like terms}\\\\(x+2x)+5=x+15\\\\3x+5=x+15\qquad\text{subtract 5 from both sides}\\\\3x+5-5=x+15-5\\\\3x=x+10\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x-x=x-x+10\\\\2x=10\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{10}{2}\\\\x=5[/tex]

Answer:

s=2

Step-by-step explanation:

-5s-(-6s)+8=3+7

-5s+6s+8=10

s+8=10

s=10-8

s=2

The word problem would be translated as s + 8 = 10.

The solution is: s = 2

First, let's translate the statement given to form an algebraic equation, then solve for the unknown variable.

Therefore, the equation would be:

s + 8 = 10

s + 8 - 8 = 10 - 8

s = 2

Therefore, the word problem would be translated as s + 8 = 10.

The solution is: s = 2

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Answer:

Step-by-step explanation:

P(x)=  x³ - x² - 18

Q(x) = P(2x-1)

       = (2x-1)³ - (2x-1)² -18

       = (2x)³ - 3*(2x)² * 1 + 3*2x* 1² - 1³ - [ (2x)² - 2*2x*1 + 1 ] - 18

=8x³ - 12x² + 6x - 1 - [4x² - 4x +1 ] - 18

= 8x³ - 12x² + 6x - 1 - 4x² + 4x - 1  - 18

= 8x³ - 16x² + 10x - 20

Hint : (a-b)³ = a³-3a²b+3ab²-b³

(a-b)² = a² -2ab + b²

Answer:

$ 9.99  almost  $ 10 she would save every week.

Step-by-step explanation:

Weekly Salary = $ 628

Tax deduction= $149.8

Superannuation Fund = 4.5 % of $ 628= $28.26

Mortgage = 8 % of 628= $ 50.24

Income after deductions = $ 628- $ 149.8 - $ 28.26- $ 50.24=  $ 399.7

10 % of $ 399.7 = $ 39.97 almost $ 40

In one week  she would save $39.97/4= $ 9.99 = $ 10

Answer:

No idea what the other person who answered was trying to say since it has to be 1 answer but i think its multiplication because to get 1/5 to be 1 so x you multiply by 5 and it matches because to get 6 to be 30 you multiply by 5 and to get 5 to be 25 you multiply by 5

ANSWER A

Step-by-step explanation:

The x-coordinate of the point of intersection for given equations is 2

Step-by-step explanation:

Given equations are:

[tex]2x+y = 7\ \ \ Eqn\ 1\\10x-7y = -1\ \ \ Eqn\ 2[/tex]

The point of intersection is the solution of the system of equations

as we have to find the x-coordinate we will use elimination method to eliminate y

So,

Multiplying equation 1 with 7

[tex]7(2x+y) = 7(7)\\14x+7y = 49\ \ \ \ Eqn\ 3[/tex]

Adding equation 2 and 3

[tex](14x+7y) + (10x-7y) = 49-1\\14x+10x+7y-7y = 48\\24x = 48[/tex]

Dividing both sides by 24

[tex]\frac{24x}{24} = \frac{48}{24}\\x = 2[/tex]

The x-coordinate of the point of intersection for given equations is 2

Keywords: Linear equations, simultaneous equations

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Answer:

[tex]y=-5(x-0)^2+5[/tex]

Step-by-step explanation:

Given height of parabola is [tex]5\ m[/tex].

And [tex]2\ m[/tex] wide at ground level.

Also, the parabola opens down.

Let us assume the parabola is aligned on Y-axis

As the height of parabola is [tex]5\ m[/tex]. The maximum height of parabola is achieved when [tex]x=0[/tex].

So, the vertex of parabola is [tex](0,5)[/tex].

The equation of parabola having vertex [tex](h,k)[/tex] is.

[tex]y=a(x-h)^2+k[/tex].

Plugging the vertex of parabola

[tex](h,k)[/tex] [tex]=[/tex] [tex](0,5)[/tex].

[tex]h=0\ and\ k=5[/tex]

[tex]y=a(x-0)^2+5[/tex]

It is given that parabola is [tex]2\ m[/tex] wide at the ground.

As the parabola is aligned on Y-axis. So, distance between X-intercept is [tex]2\ m[/tex].

The X-intercept would be [tex](-1,0)\ and\ (1,0)[/tex]

Plugging [tex](1,0)[/tex] in the equation [tex]y=a(x-0)^2+5[/tex]

[tex]0=a(1-0)^2+5\\\\-5=a(1)^2\\\\-5=a[/tex]

Now, we get [tex]a=-5[/tex] and having vertex [tex]h=0\ and\ k=5[/tex].

So, the equation of parabola is

[tex]y=a(x-h)^2+k[/tex].

[tex]y=-5(x-0)^2+5[/tex]

Answer:

6 complex numbers

There are 6 solutions to the polynomial over the complex number system.

The given equation is 3[tex]x^{6}[/tex]-x³-4x²+5x+52=0.

The Fundamental Theorem of Algebra states that every polynomial of degree one or greater has at least one root in the complex number system. A further theorem, in some cases referred to as the Linear Factorization Theorem, states that a polynomial of degree n has exactly n linear factors, and each can be written in the form (x - c), where c is a root. These n complex roots are counted with multiplicity.

In polynomials, the number of roots or highest power is equal to the degree of the polynomial.

Here, 3[tex]x^{6}[/tex]-x³-4x²+5x+52=0.

We can see that the polynomial is a sixth-degree polynomial.

Therefore, there are 6 solutions to the polynomial over the complex number system.

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Answer:

(- 2, - 7 )

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), thus

P(- 2, 7 ) → P'(- 2, - 7 )

Answer:

Step-by-step explanation:

-2(x+3)=-10

Open the bracket

-2x - 6 = -10

Collecting like terms

-2x = -10 + 6

-2x = -4

Dividing through by -2

x = -4/-2

x = 2

3 + 8x = 19 is the equation for given sentence three more than eight times a number is equal to 19

Solution:

Given sentence is:

Three more than eight times a number is equal to 19.

We have to translate the sentence into an equation

Let us first break the sentence and find out the equation

Let "x" be the required number

Given that, Three more than eight times a number is equal to 19.

Here "more than" represents addition

"times" represents multiplication

eight times a number = [tex]8 \times x[/tex]

So the required equation is:

Three more than eight times a number is equal to 19

[tex]3 + 8 \times x = 19\\\\3 + 8x = 19[/tex]

Thus the required equation for given sentence is found

Answer:

i think 10.30 according to my calculation

Answer:

10.30

Step-by-step explanation:

Answer:

n will be 6

Step-by-step explanation:

3×n=2×9

substitute n=6 in the above equation

3×6=2×9

18=18

N is 6

Step-by-step explanation:

Solve the system via elimination (add the equations):

-10y + 9x = -9

+ (10y + 5x = -5)

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

14x = -14

x = -1

Plug in the value for 'x' into the second equation:

-10y + 5(-1) = -5

Solve for y:

-10y - 5 = -5

--> -10y = 0

--> y = 0

x = -1

y = 0

Answer:

2.75 or 2 3/4

Step-by-step explanation:

Divide the total cost by the price of each ribbon.

$1.54 ÷ $0.56/yard = 2.75 yards

If the answer needs to be in mixed fractional form, convert 0.75 to a fraction.

3/4 = 0.75

The fraction form of 2.75 is 2 3/4.

Therefore Olivia bought 2 3/4 yards of ribbon.

A customer will pay $225.5 for one rug.

Step-by-step explanation:

Given,

Purchase price of rug = $82.00

Mark up = 150%

Amount of mark up = 150% of purchase price

Amount of mark up = [tex]\frac{150}{100}*82[/tex]

Amount of mark up = 1.5*82 = $123

Price of rug after mark up = Purchase price + Mark up

Price of rug after mark up = 82+123 = $205

Sales tax = 10%

Amount of sales tax = 10% of price after markup

Amount of sales tax = [tex]\frac{10}{100}*205=\$20.5[/tex]

Selling price = Price after markup + Amount of sales tax

Selling price = 205+20.5 = $225.5

A customer will pay $225.5 for one rug.

Keywords: percentage, markup

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Answer:

Multiples of 2 are {2,4,6,8,10,12,14,16,...} Multiples of 4 are {4,8,12,16,.......) Hence common multiples are {4,8,12,16,...} and Lowest Common Multiple is 4 .

Step-by-step explanation:

To find common multiples of 2 and 4, list the multiples of each and identify the common elements. For 2 and 4, these are 4, 8, 12, and 16.

Finding Common Multiples of 2 and 4

To find common multiples of 2 and 4, we start by listing the multiples of each number.

→ Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...

→ Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...

Next, we look for common multiples from these lists.

→ 4: divisible by 2 and 4

→ 8: divisible by 2 and 4

→ 12: divisible by 2 and 4

→ 16: divisible by 2 and 4

Therefore, four common multiples of 2 and 4 are 4, 8, 12, and 16.

Answer:

[tex]x<-3[/tex]

Step-by-step explanation:

Given inequality:

[tex]4-3x>13[/tex]

In order to represent the solution on the number line, we will first solve the given inequality.

We have

[tex]4-3x>13[/tex]

Subtracting both sides by 4.

[tex]4-3x-4>13-4[/tex]

[tex]-3x>9[/tex]

Dividing both sides by -3.

[tex]\frac{-3x}{-3}<\frac{9}{-3}[/tex] [On dividing both sides by a negative number the sign of the inequality reverses.]

[tex]x<-3[/tex]

So, solution of this inequality will range from -3 to -∞

The number line is represented below.

Answer:

Domain: (-∞,∞)

Range: {3}

Step-by-step explanation:

The domain is the x-values of the function, and the range is the y value of the function.

F(x)=3 is really just a fancy way of saying y=3. The range is 3.

Since the function makes a horizontal line, the domain is ∞.

Answer:

11m

Step-by-step explanation:

2(5m)+m=10m+m=11m

Answer:

[tex]\large \boxed{\text{101 pieces}}[/tex]

Step-by-step explanation:

1. Calculate the area of the floor

The formula for the area of a trapezoid is  

A = ½(a + b)h,

where a and b are the lengths of the parallel sides and h is the distance between them.

However, we are not given the value of h, so we must use Brahmagupta's formula.

If the four sides are a, b, c, and d, the area A is

[tex]A = \sqrt{(s - a) (s - b) (s - c) (s - d)}[/tex]

where s is the semiperimeter

[tex]s = \frac{1}{2}(a + b + c + d)[/tex]

Data:

a = 13 ft

b = 16 ft

c = 13 ft

d = 26 ft  

(a) Calculate the semiperimeter

[tex]\begin{array}{rcl}s & = & \sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\ & = & \frac{1}{2}(13 + 16 + 13 + 26)\\\\ & = & \frac{1}{2}(68)\\\\ & = & 34\\\end{array}[/tex]

(b) Calculate the area

[tex]\begin{array}{rcl}A & = &\sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\& = &\sqrt{(34 - 13) (34 - 16) (34 - 13) (34 - 26)}\\\\& = &\sqrt{21 \times 18 \times 21 \times 8}\\\\& = & \sqrt{63504}\\\\ & = & \mathbf{252}\\\end{array}[/tex]

The area of David's floor is 252 ft².

2. Calculate the number of pieces of material

[tex]\text{No. of pieces} = \text{252 ft}^{2} \times \dfrac{\text{1 piece}}{\text{2.5 ft}^{2}} = \textbf{100.8 pieces}\\\\\text{David can't buy a fraction of a piece, so he must buy $\large \boxed{\textbf{101 pieces}}$}[/tex]

I'm not sure, but I know that it is longer than 5

Answer:

5.5-6ish sorry its hard to tell

Happy Holidays!

Answer:

Step-by-step explanation:

5y + 6y + 7y = 18y......any numbers that add(or subtract) to equal 18, stick them before the y....

or it could be : 10y + 10y - 2y = 18y or 5y + 10y + 3y or 30y - 20y + 8y....I could go on forever...lol

Answer:

  y = 3(x -4)^3 -3

Step-by-step explanation:

As you know, the transformations are

  g(x) = (vertical stretch factor) · f(x - (right shift)) +(vertical shift)

For the given transformations, the equation becomes ...

  y = 3(x -4)^3 -3

The equation of y=x^3 with the given transformations is y = 3(x - 4)^3 - 3.

The equation of y = x^3 after the given transformations is y = 3(x - 4)^3 - 3.

The vertical stretch by a factor of 3 means that all y-values will be multiplied by 3, so the equation becomes y = 3x^3.

The horizontal shift 4 units to the right means that x-values will be replaced by (x - 4), so the equation becomes y = 3(x - 4)^3.

The vertical shift 3 units down means that all y-values will be decreased by 3, so the equation becomes y = 3(x - 4)^3 - 3.

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Answer:

Step-by-step explanation:

No, unless the function decides to follow a different pattern. See more explanation below.

Step-by-step explanation:

He is wrong, the table doesn't tell us what happens at x=6.

It does tell us the following:

1) When x=-4, f(x)=6.

2) When x=-2, f(x)=3.

3) When x=0, f(x)=-1.

4) When x=2, f(x)=-4.

So maybe he got it the x and f(x) value switched in his brain.

Because according to 1) x=-4 when f(x)=6.

If the points keep having x increase while y decreases, then every x>2 will have a y less than -4 correspond to it.

Rob's determination that the function X = 6 when f(x) = -4 appears to be correct based on the provided data.

An equation is a mathematical statement that shows that two expressions are equal.

It typically includes variables, constants, and mathematical operations and is used to solve for unknown values.

Rob seems to be correct. If you look at the table of values:

x | f(x)

-4 | 6

-2 | 3

0 | -1

2 | -4

When x = 6,

we find that the function f(x) = -4 (as indicated in the last row of the table).

So, Rob's determination that X = 6 when f(x) = -4 appears to be correct based on the provided data.

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Answer:

2700 degrees.

Step-by-step explanation:

The external angles add up to 360 degrees

So 1 external angle in a regular 17-gon = 360/17

= 21.176 degrees

The internal angle = 180 - 21.176

= 158.824 degrees

Sum of internal angles = 158.824 * 17

= 2700 degrees.

Answer:

Step-by-step explanation:

Every closed curve called a polygon can be separated into a specific number of triangles.  Then, because the sum of the interior angles of a triangle is 180, you take the number of triangles and multiply by 180 to get the sum of the interior angles of the n-gon.  To find the number of triangles that exist within an n-gon, subtract 2 from the number of sides.  If our figure is a 17-sided polygon, then the number of triangles within it is 17 - 2 = 15.  15 triangles, each with a sum of 180 for its angles.  15 * 180 = 2700.

Each central angle is 360 divided by 17 to get 21°10'35"

Each interior angle is 2700 divided by 17 to get 158°49'24"

Answer:

16. B

17. B

Step-by-step explanation:

16. The intercept form of the parabola is

[tex]y=a(x-x_1)(x-x_2),[/tex]

where [tex]x_1, x_2[/tex] are two x-intercepts.

In your case,

[tex]x_1=2\\ \\x_2=-8[/tex]

so

[tex]y=a(x-2)(x-(-8))\\ \\y=a(x-2)(x+8)[/tex]

To find a, substitute coordinates of the point (-6,-4) parabola is passing through

[tex]-4=a(-6-2)(-6+8)\\ \\-4=-16a\\ \\a=\dfrac{1}{4}[/tex]

and

[tex]y=\dfrac{1}{4}(x-2)(x+8)[/tex]

17. The vertex form of the parabola equation is

[tex]-2p(y-k)=(x-h)^2,[/tex]

where (h,k) are the coordinates of the vertex and sign "-" because parabola goes down.

In your case, vertex is (2,3), so

[tex]-2p(y-3)=(x-2)^2[/tex]

The vertex is 3 units from the focus, then

[tex]\dfrac{p}{2}=3\\ \\p=6[/tex]

The equation of the parabola is

[tex]-2\cdot 6(y-3)=(x-2)^2\\ \\y=-\dfrac{1}{12}(x-3)^2+3[/tex]