solve the equation
[tex]log10 \: ( {x}^{2} - 3x + 12) \: = 2[/tex]
​

Explanation:

Like with the previous problems, the answer comes fairly straight forward from the values of c and d.

c = 4 tells us we have a shift of 4 units to the left

d = 3 indicates we're shifting 3 units up.

Note: we shift left instead of right because x+c = x+4 means the xy axis has been shifted 4 units to the right, giving the illusion the cosine curve is shifted 4 units to the left.

1)

[tex]\sf {x}^{2} - 4 \\ \sf \: Use \: the \: sum \: product \: method[/tex]

[tex]\sf {x}^{2} - 4 \\ = \sf{x}^{2} + 2x - 2x - 4[/tex]

[tex]\sf \: Now \: take \: the \: common \: factor \: out \\ \sf{x}^{2} + 2x - 2x - 4 \\\sf = x(x + 2) - 2(x + 2)[/tex]

[tex]\sf \: Factorize \: it \\ \sf \: x(x + 2) - 2(x + 2) \\ = \sf(x - 2)(x + 2)[/tex]

Answer ⟶ [tex]\boxed{\bf{(x-2)(x+2)}}[/tex]

_________________________

2)

[tex]\sf {x}^{3} - 27[/tex]

[tex]\sf {x}^{3} \: and \: 27 \: ( {3}^{3} ) \: are \: perfect \: real \: cubes.[/tex]

[tex]\sf \: So \: use \: the \: algebraic \: identity \: \\ \sf {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]

[tex]\sf \: a = \sqrt[3]{x^{3}} = x \\ \sf \: b = \sqrt[3]{27} = 3[/tex]

[tex] \sf \: {x}^{3} - {3}^{3} \\ \sf= (x - 3)( {x}^{2} + 3x + {3}^{2} ) \\ = \sf \: (x - 3)( {x}^{2} + 3x + 9)[/tex]

Answer ⟶ [tex]\boxed{\bf{(x-3)(x^{2}+3x+9)}}[/tex]

Answer:

Following are the responses to the given question:

Step-by-step explanation:

[tex]\to y=(\frac{1}{2})(x-4)(x+4)\\\\\to y=(\frac{1}{2}) (x^2-16)\\\\\to y=(\frac{1}{2})(x-0)^2-8\\\\vertex \to (0,-8)[/tex]

The general x-intercept parabola equation [tex]y=k(x-4)(x+4)[/tex]

Parabola crosses the dot (2,-12)

[tex]\to k(2-4)(2+4)=-12\\\\\to k(-2)(6)=-12\\\\\to -12k=-12\\\\\to k=\frac{-12}{-12}\\\\\to k=1[/tex]

The parabolic equation which crosses the position [tex](2,-12)[/tex] is[tex]y=(x-4)(x+4)[/tex]

[tex]\to y=(x-4)(x+4)\\\\\to y=x^2-16\\\\\to y=(x-0)^2-16\\\\vertex \to (0,-16)[/tex]

The distance among the vertices of the two parabolas:

[tex]= \sqrt{(0 - 0)^2+(-8-(-16))^2}\\\\ = \sqrt{0+(-8+16))^2}\\\\ =\sqrt{0+(8)^2}\\\\=\sqrt{(8)^2}\\\\= 8\\\\[/tex]

Answer:the answer is 10 because if u subctract it will work

Step-by-step explanation:

Answer:

hjjjnnnhjjjjj

Step-by-step explanation:

answer is d

Answer:

i think 5 is the answer not sure check with other helpers or brainer

Step-by-step explanation:

Answer:

1 Cups (US) = 0.24992635042 Quarts

either divide or multiply by 0.24992635042

52* 0.24992635042 = 13

13 /  0.24992635042 = 52

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Fraction of names called last week = 1/4 of a page

Fraction called this week = 1/2 of a page

The number of pages worth of people called ;

This is an addition problem, as the total will be the sum. Of the fractions called this week and last week

Hence,

Total page worth of names called :

(1/4 + 1/2) = (1 + 2) / 4 = 3/4

Answer:

Step-by-step explanation:

I'm not sure if I am too late to answer this but the trick to this is to reflect the function over the line y = x.

Basically, if you have the point (-2, 3)

you turn in into (2, -3) and you'll be good. (switch the two coordinates and take the negative for both.)

Answer:

Put both of those equations into slope-intercept form (in order to be typed into the graphing calculator).  

2x + 3y = 16.9

3y = -2x + 16.9

y = (-2/3)x + 16.9/3  

5x = y + 7.4

5x - 7.4 = y  

So in the graphing calculator,

Y1 = (-2/3)x + 16.9/3

Y2 = 5x - 7.4  

Then find the point of intersection and the x value of that would be the solution.

You get the coordinate (2.3, 4.1). So x = 2.3, y = 4.1

Step-by-step explanation:

Answer:

D.

a1=7an=−3 · an−1a subscript 1 baseline equals 7 line break a subscript n baseline equals negative 3 times a subscript n minus 1 baseline

Step-by-step explanation:

Answer:

y=-2x+2

Step-by-step explanation:

substitute either the x or y value into the equations, if you substitute x=3 and get back y=-4, the equation is correct

Step-by-step explanation:

9 x 4=36 is the answer

hope this helps you

have a nice day:)

Answer:

Step-by-step explanation:

With some research I found that the medians (QK, RJ, and SI) are broken into 2:1 ratios.

So what this means is that QD is twice as long as DK.

QD = 2DK

QD = 2 * 6.5

QD = 13

Answer:

N + D = 175

.05N + .10D = $13.30

Step-by-step explanation:

You need a system of equations to get the correct answer that applies to both constraints.

Answer:

3

Step-by-step explanation:

Answer:

It decreased

Step-by-step explanation:

It decreased. Assuming that the temperature is 100 and it is now reduced by 60% then the temperature will be at 40 and if it increased by 80% then the final temp is 72. So it is 48% of the original temp.

Answer:

-2 3/20 or -2.15

Step-by-step explanation:

There is an app you can get on your phone called fraction calculator, its an app for mulitplying, dividing, adding, and subtracting any number with a fraction:)

Answer:

Question 10:

Answer: b.

[tex]{ \tt{f(x) = 5 {x}^{2} + 9x - 4}} \\ { \tt{g(x) = - {8x}^{2} - 3x - 4 }}[/tex]

(f + g)x, add f(x) and g(x):

[tex]{ \tt{(f + g)x = (5 - 8) {x}^{2} + (9 - 3)x - 4 - 4}} \\ { \tt{(f + g)x = - 3 {x}^{2} + 6x - 8}}[/tex]

Question 11:

Answer: a.

In relation with solution of question 10, same procedure:

[tex]{ \tt{(f - g)x = - 3 {x}^{3} + (1 - 2) {x}^{2} + ( - 3 - 4)x + 9 - ( - 9)}} \\ { \tt{(f - g)x = - 3 {x}^{3} - {x}^{2} - 7x + 18 }}[/tex]

Answer:

So required ans is 5*11+10=65 6x-41=25

Step-by-step explanation:

You can do as,

5x+10+6x-41=90

11x-31=90

11x=31+90

11x=121

x=121/11

x=11

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

πr is the formula for the __of a circle.

Answer: What's the question? I'll edit my answer to the question if you would give me the actual problem

Step-by-step explanation:

Answer:

2. x = 2 & y = 4

3. x = 4 & y = 2

Step-by-step explanation:

2. x + y = 6

  2x + y = 8  (multiply the first equation by -1,  so you can eliminate the ys)

- x - y = -6

2x + y = 8  (now add the variables together)

x = 2 (plug in x in one of the equations to find out y)

x + y = 6

(2) + y = 6

-2           -2

y = 4

3. 3x + y = 14

          x = 2y (plug in x into the first equation and solve it for y)

3(2y) + y = 14

6y + y = 14

7y = 14

y =  2  (plug in y in one of the equations to find out x)

x = 2y

x = 2(2)

x = 4

4.  One number (x) is 2 more (+2) than twice (times 2) as large as another. their sum is 17. Find the numbers.

2x + 2 = 17 (solve for x)

     -2     -2

2x = 15

x = 7.5

6. 7 (4x + 1) - (x + 6) (start by distributing 7 into the first parenthesis)

  (28x + 7) - (x + 6) (do the same to the other parenthesis by distributing -1)

  (28x + 7)  (-x - 6) (and now just combine like terms)

   28x + 7 - x - 6

   28x - x + 7 - 6

   27x + 1

i hope this helped! if you have any question, pls let me know!

Answer:

4c² + 11cd + 5d

Step-by-step explanation:

(–4c2 + 7cd + 8d) + (–3d + 8c2 + 4cd)

-4c² + 7cd + 8d - 3d + 8c² + 4cd (opening bracket)

8c²-4c²+7cd + 4cd + 8d - 3d

= 4c² + 11cd + 5d

Answer:

Population of town in 2020 = 4626 (Approx.)

Step-by-step explanation:

Given:

Population of town in 2000 = 12,910

Decrease rate = 5% = 0.05 yearly

Find:

Population of town in 2020

Computation:

Number of year = 20 years

Population of town in 2020 = Population of town in 2000[1-r]ⁿ

Population of town in 2020 = 12,910[1-0.05]²⁰

Population of town in 2020 = 12,910[0.95]²⁰

Population of town in 2020 = 12,910[0.3584]

Population of town in 2020 = 4625.944

Population of town in 2020 = 4626 (Approx.)

Answer:

The population is 4628.

Step-by-step explanation:

Population in 2000 = 12910

Rate of decrease = 5 %

Time, t = 2020 - 2000 = 20 years

Let the population is P.

Use the formula

[tex]P = Po\left ( 1-\frac{r}{100} \right )^t\\\\P = 12910\left ( 1-0.05 \right )^2\\\\P = 4628[/tex]

Answer:

96 in²

36 in²

60 in²

6.51 in

Step-by-step explanation:

Given that :

Dimension of paper = 12 in by 8 in

Dimension of right triangles :

2 in by 9 in ; 3 in by 6 in

Area of sheet of paper = 12 in * 8 in = 96 in²

Area of triangle = 1/2 base * height

Therefore, area of remnant right triangle :

2 * 1/2 * 2 * 9 = 18 in²

2 * 1/2 * 3 * 6 = 18 in²

Combined area of triangle left = 18in + 18in = 36 in²

Area of parallelogram = Area of sheet - Area of triangles left

Area of parallelogram = 96in² - 36in² = 60 in²

Base, b of parallelogram = 9.22 in

Area of parallelogram = base * altitude,h

60in² = 9.22h

h = 60 / 9.22 = 6.51 in

Answer:

y>1

Step-by-step explanation:

Answer:

[tex]a+b+c=10[/tex]

Step-by-step explanation:

We are given that the graph of the equation:

[tex]y=ax^2+bx+c[/tex]

Passes through the three points (0, 5), (1, 10), and (2, 19).

And we want to find the value of (a + b + c).

First, since the graph passes through (0, 5), its y-intercept or c is 5. Hence:

[tex]y=ax^2+bx+5[/tex]

Next, since the graph passes through (1, 10), when x = 1, y = 10. Substitute:

[tex](10)=a(1)^2+b(1)+5[/tex]

Simplify:

[tex]5=a+b[/tex]

The point (2, 19) tells us that when x = 2, y = 19. Substitute:

[tex](19)=a(2)^2+b(2)+5[/tex]

Simplify:

[tex]14=4a+2b[/tex]

This yields a system of equations:

[tex]\begin{cases} 5 = a + b \\ 14 = 4a + 2b\end{cases}[/tex]

Solve the system. We can do so using elimination (or any other method you prefer). Multiply the first equation by negative two:

[tex]-10=-2a-2b[/tex]

Add the two equations together:

[tex](-10)+(14)=(-2a+4a)+(-2b+2b)[/tex]

Combine like terms:

[tex]4 = 2a[/tex]

Hence:

[tex]a=2[/tex]

Using the first equation:

[tex]5=(2)+b\Rightarrow b=3[/tex]

Therefore, our equation is:

[tex]y=2x^2+3x+5[/tex]

Thus, the value of (a + b + c) will be:

[tex]a+b+c = (2) + (3) + (5) = 10[/tex]

hope so this might help

ans is above in the pic