2. In factored form, a quadratic function can be written as y = (-2-x) (x-8). This parabola goes through the points (-2, 0) and (8, 0). Use your knowledge of the symmetry of the parabola to find the vertex. Show all work. 4 mark​

Answer:

The ac product of [tex]35x^2+41x+12[/tex] is 420.

The factors of the ac product that add to 41 are 20 and 21.

[tex]35x^2+41x+12 =[/tex] [tex](7x+4)(5x+3)[/tex]

Step-by-step explanation:

1) The general form of a quadratic is [tex]ax^2 + bx + c[/tex]. Hence, multiplying 35 by 12 gives you the product of ac, which is 420.

2) We need to find two numbers that multiply to 420 and add up to 41 simultaneously. If we pull out the factors of 420, two of them will be 20 and 21, which multiply to 420 as well as add up to 41.

3) Write [tex]41x[/tex] as a sum.

[tex]35x^2+20x+21x+12[/tex]

Now, we can factor them out by grouping.

[tex]35x^2+20x+21x+12\\5x(7x+4)+3(7x+4)[/tex]

Since, [tex]7x +4[/tex] is common in both of the factors, we only take one of the [tex]7x+4[/tex] along with [tex]5x[/tex] and [tex]3[/tex].

[tex](7x+4)(5x+3)[/tex]

Answer:

[tex]\text{The ac product of }\: 35x^2+41x+12 \text{ is }\boxed{420}\:.[/tex]

[tex]\text{The factors of the ac product that add to 41 are }\:\boxed{20} \: \text{ and }\: \boxed{21}\:.[/tex]

[tex]35x^2+41x+12=\left( \: \boxed{5}\:x+\:\boxed{3}\:\right)\left(\: \boxed{7}\:x+\boxed{4}\:\right)[/tex]

Step-by-step explanation:

Given quadratic:

[tex]35x^2+41x+12[/tex]

Factoring quadratics by grouping

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],  find two numbers that multiply to ac and sum to b.

[tex]\implies ac=35 \cdot 12 = 420[/tex]

[tex]\implies b = 41[/tex]

Therefore, the two numbers that multiply to 420 and sum to 41 are:
20 and 21

Rewrite b as the sum of these two numbers:

[tex]\implies 35x^2+20x+21x+12[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 5x(7x+4)+3(7x+4)[/tex]

Factor out the common term [tex](7x+4)[/tex] :

[tex]\implies (5x+3)(7x+4)[/tex]

Conclusion

[tex]\text{The ac product of }\: 35x^2+41x+12 \text{ is }\boxed{420}\:.[/tex]

[tex]\text{The factors of the ac product that add to 41 are }\:\boxed{20} \: \text{ and }\: \boxed{21}\:.[/tex]

[tex]35x^2+41x+12=\left( \: \boxed{5}\:x+\:\boxed{3}\:\right)\left(\: \boxed{7}\:x+\boxed{4}\:\right)[/tex]

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Answer:

if the red line is included it is a. if the red line is excluded it is C. I believe.

Answer:

A

Step-by-step explanation:

the equation of the 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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (0, 1) ← 2 points on the line

m = [tex]\frac{1-3}{0-(-3)}[/tex] = [tex]\frac{-2}{0+3}[/tex] = - [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = - [tex]\frac{2}{3}[/tex] x + 1 ← equation of line

the solutions to the inequality lie above the line, including the line, in the shaded area , then

y ≥ - [tex]\frac{2}{3}[/tex] x + 1 → A

Answer:

[tex] y = -\dfrac{1}{2} [/tex]

Step-by-step explanation:

I assume that y - 1 is an exponent, and the equation is

[tex] 125 = (\dfrac{1}{25})^{y - 1} [/tex]

[tex] 5^3 = (5^{-2})^{y - 1} [/tex]

[tex] 5^3 = 5^{-2y + 2} [/tex]

[tex] -2y + 2 = 3 [/tex]

[tex] -2y = 1 [/tex]

[tex] y = -\dfrac{1}{2} [/tex]

The amount that's was attributed to the project from the start based on the percentage is $7,500,000.

From the information given, the remaining percentage will be:

= 100% - (25% + 20% + 35%)

= 100% - 80%

= 20%

Let the total amount be x.

Therefore, 20% of x = 1,500,000

0.2x = 1,500,000

x = 1500000/0.2

x = 7500000

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Answer:

[tex]\frac{-D}{4a}[/tex]

Step-by-step explanation:

y-coordinate is [tex]\frac{-D}{4a}[/tex] where a is coefficient of quadratic polynomial (ax^2+bx+c) and D is discriminant of the quadratic equation when you equate it to zero.

Answer:

66 chairs

Step-by-step explanation:

Total number of chairs = 594

Total number of rows = 9

Number of chairs per row

= 594/9

= 66 chairs

__________

Hope it helps ⚜

Answer:

I don't know if you have any questions or need any further information please contact me your Telugu movie review poster

By completing the square, we have

[tex](x+1)(x+4) = x^2 + 5x + 4 = \left(x+\dfrac52\right)^2 - \dfrac94[/tex]

[tex](x+2)(x+3) = x^2 + 5x + 6 = \left(x + \dfrac52\right)^2 - \dfrac14[/tex]

Then

[tex](x+1)(x+2)(x+3)(x+4) = \left(x+\dfrac52\right)^4 - \dfrac52 \underbrace{\left(x + \dfrac52\right)^2}_{=y} + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = y^2 - \dfrac52 y + \dfrac9{16} \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(y - \dfrac54\right)^2 - 1 \\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = \left(\left(x + \dfrac52\right)^2 - \dfrac54\right)^2 - 1[/tex]

This product has a minimum of -1 when

[tex]\left(x + \dfrac52\right)^2 - \dfrac54 = 0[/tex]

which has two real solutions; then the minimum of the overall expression is -1 + 2019 = 2018.

The sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}

The sets are given as:

U = The set of one-digit numbers

A = {x: x is an even natural number less than or equal to 9}

One-digit numbers are numbers 0 - 9.

So, we have

U = {0, 1, 2, 3.....,9}

Natural numbers are numbers from 1.

Even natural numbers can be divided by 2 without remainder'

So, we have

A = {2, 4, 6, 8}

Hence, the sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}

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Answer:

Step-by-step explanation:

If block has length 100 yards and breadth 76 yards then we have to drive 5 times to drive one mile.

Given The length of block is 100 yards, the breadth of block is 76 yards.

We have to find number of times we need to drive one mile.

The perimeter of a rectangle= 2(length +breadth)

length is 100 yards

Breadth is 76 yards

perimeter=2(100+76)

=2*176

=352 yards.

We know that 1 mile is equal to 1760 yards.

We have to find number of times to drive 1 mile=1760/352

=5 times.

Hence we have to drive 5 times around the block which have length 100 yards and breadth 76 yards.

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Hello and Good Morning/Afternoon!

Let's take this problem step-by-step:

What the problem asks for:

  ⇒ to rationalize the denominator

      ⇒ rationalize means that you multiply the numerator and

          demonimator by the denominator

Let's put that into action:

    [tex]\frac{\sqrt{a +1}-2 }{\sqrt{a+1}+2 } * \frac{\sqrt{a +1}+2 }{\sqrt{a+1}+2 }\\=\frac{a +1-4 }{a+1+4\sqrt{a+1}+4 } \\=\frac{a-3}{a+4\sqrt{a+1}+5 }[/tex]<== Answer

Hopefully that helps!

Answer:

x = -8/3

Step-by-step explanation:

-5(-3x+1)=-45

⇔ 15x - 5 = -45  (left side of the equation expanded)

⇔ 15x = -45 + 5 (add 5 to both sides)

⇔ 15x = -40

⇔ x = -40/15    (Divide both sides by 15)

⇔ x = -8/3  (simplify)

Answer:

[tex]10^{0.4785+1.468x}=y[/tex]

Step-by-step explanation:

So I'm assuming when you typed "log yhat=.4785 + 1.468x", you meant to write: [tex]log(y)=0.4785+1.468x[/tex]. And generally a logarithm can be written in the form [tex]log_ba=c[/tex] which can then be rewritten as [tex]b^c=a[/tex], but since the log has no base, it's assumed to be 10. So in this case you have the equation:

[tex]log_{10}y=0.4785+1.468x[/tex], which can then be written in exponential form as:

[tex]10^{0.4785+1.468x}=y[/tex]

We have this equation:

[tex]\log(x) + \log(x + 99) = 2[/tex]

First, combine both logarithms using the multiplication property and simplify the expression.

[tex]\log[x(x + 99)] = 2[/tex]

[tex]\log[ {x}^{2} + 99x ] = 2[/tex]

Now, use the definition of logarithm to transform the equation.

[tex] {10}^{2} = {x}^{2} + 99x[/tex]

[tex] {x}^{2} + 99x - 100 = 0[/tex]

Finally, use the quadratic formula to solve the equation.

[tex]x = \frac{ -99 ± \sqrt{ {99}^{2} - 4 \times 1 \times ( - 100)} }{2 \times 1} [/tex]

With this, we can say that the solution set is:

We cannot choose x = -100 as a solution because we cannot have a negative logarithm. The only solution is x = 1.

The equivalent expression of -2x + 5 is 5 - 2x

The expression is given as:

-2x + 5

The symmetry rule of expression states that:

a + b = b + 1

So, we have:

-2x + 5 = 5 - 2x

Hence, the equivalent expression of -2x + 5 is 5 - 2x

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Answer:

6  1/12 miles total

Step-by-step explanation:

3 1/4 = 13/4

2 5/6 = 17/6        to ADD fractions, you must have a common denominator

                              I will use 12   for these

13/4 = 39/12

17/6 = 34 /12

now you can add and simplify     39/12 + 34/12 = 73/12 = 6 1/12  miles

The line with slope = 2 will be closer to the y-axis than the line with slope = 1/2

The slopes are given as:

Slope = 2

Slope = 1/2

The greater the absolute value of the slope of a linear equation.

The closer the function is to the y-axis

This means that the line with slope = 2 will be closer to the y-axis than the line with slope = 1/2

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At the end of the third day, the new reading on the odometer will be 12,578 mi

The initial odometer reading is 12,386 miles.

Then, the driver takes drives to and from work, such that each trip is 32 miles. Then each day he drives 2*2mi = 64 miles.

And he does this for 3 days, then the total distance driven is:

3*64mi = 192 miles.

At the end of the third day, the new reading on the odometer will be:

R = 12,386 mi + 192mi = 12,578 mi

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Answer:

is the a. Perpendicular lines form 90° angles.

it is three fifths,

and it is the answer.

Diego's height is 7 units

The statement is given as:

77 is the product of 7 and Diego's height

This means that:

77 = 7 * d

Divide both sides by 7

d = 11

Hence, Diego's height is 7 units

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Using the profit concept, we have that:

Profit is given by revenue subtracted by costs.

In this problem, we have that:

Hence the expression for the profit is given as follows:

P(x) = R(x) - C(x)

P(x) = 90x - 0.5x² - 50x - 300

P(x) = -0.5x² + 40x - 300.

A profit of $300 is found when P(x) = 300, hence:

300 = -0.5x² + 40x - 300

0.5x² - 40x + 600 = 0.

x² - 80x + 1200 = 0.

(x - 60)(x - 20) = 0.

Hence the values are:

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la longitud del jardín del amigo de Carmen es 18 m 22 cm.

Una ecuación se forma cuando dos expresiones algebraicas se igualan usando un signo igual.

Se da que la longitud de Carme

Se sabe que la longitud del jardín de Carmen es de 15 m 24 cm.

y el largo del jardín de su amigo es 2 m 98 cm más largo que el de Carmen.

Sea La longitud del jardín de Carmen es x m

Entonces la ecuación se convierte en

La longitud del jardín de su amigo = x + 2m 98 cm

ahora ,

x = 15m 24cm

Sustituyendo los valores en la ecuación

La longitud del jardín de su amigo = 15m 24cm + 2m 98 cm

1m = 100cm

La longitud del jardín de su amigo = 17 m 122 cm

as 100 cm = 1m

122 cm = 1 m 22 cm

so ,

La longitud del jardín de su amigo = 18 m 22 cm.

Por lo tanto, la longitud del jardín del amigo de Carmen es 18 m 22 cm.

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Answer:

{(-3, 16),(0, 15),(3, 14)}

Step-by-step explanation:

just plug in the points for x and y and solve to see if 15 is the answer you get for all of them which would give you B as your answer

numbers like 0 and 1 and 3 (because it would cancel 1/3x) are good numbers to do quick math with

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Answer:

2y>-y+5

Step-by-step explanation:

because it has a eligible number at the right hand side

The attached graph represents the image of the triangles

To do this, we make use of the following coordinates

A = (1, 0)

B = (5, 0)

C = (1, 6)

The lengths of the triangle are calculated using

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(1-5)^2 + (0 -0)^2} = 4[/tex]

[tex]BC = \sqrt{(1-5)^2 + (6 -0)^2} = 7.2[/tex]

[tex]AC = \sqrt{(1-1)^2 + (6 -0)^2} = 5[/tex]

Using the scale factor of 2, we have the image of the dilation to be:

D = (2, 0)

E = (10, 0)

F = (2, 12)

The lengths of these sides are

DE = 8

EF = 14.4

DF = 10

See attachment for the image of the triangles ABC and DEF

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The area of the exposed surface is 442 square feet

A right square pyramid is a polyhedron with 5 faces consisting of four triangles and a square base.

Analysis:

The exposed surface is the area of the four triangles.

The perpendicular height of the triangles is same and it is the slant length of the shape = 17ft

Area of 4 triangles = 1/2 bh = 1/2 x 17 x 13 x 4 = 442 square feet.

In conclusion, area of exposed surface is 442 square feet.

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Answer:

3

Step-by-step explanation:

whenever solving for x, you have to work backwards…like so:
3 squared is 9

27 divided by nine is 3

x=3

To double check the answer, substitute the value that we just found into x

(3x3)x3=27

Answer:

[tex]x=\dfrac{3}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]3^{2x}=27[/tex]

Rewrite 27 in exponential form with base 3:

[tex]\implies 3^{2x}=3^3[/tex]

As both exponents have the same base,

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]\implies 2x=3[/tex]

Divide both sides by 2:

[tex]\implies x=\dfrac{3}{2}[/tex]