What is the solution of sqrt x+12=x ? x = –3 x = 4 x = –3 or x = 4 no solution

k = - 2 is excluded from the domain

the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that k cannot be

solve k + 2 = 0 ⇒ k = - 2 ← excluded value

That would be four times 88 passengers:  352 passengers per day.

Answer: 352

Step-by-step explanation:

88x4

The sine function is an odd function, so the sine of -30° is the opposite of the sine of 30°.

sin(30°) = 1/2

sin(-30°) = -1/2

The sine of 30° is greater than the sine of -30°.

There are a total of 312 cartons or ice cream in total.

This is asking you to solve the equation ...

... 27 = 3^x

You can use logarithms to find

... log(27) = x·log(3)

... log(27)/log(3) = x = 1.43136376.../0.47712125...

... x = 3

Or, you can use your knowledge of small cubes and match exponents.

... 3^3 = 3^x

... 3 = x

Answer:

2.

1.

Step-by-step explanation:

Angles 135° and (2x+15)° together make up a line (the transversal crossing m and n). Such angles are called a "linear pair" and their sum is always 180°. That means we can write the equation ...

... 135° + (2x+15)° = 180°

... 150 +2x = 180 . . . . . . . remove the degree symbol, combine terms

... 2x = 30 . . . . . . . . . . . . subtract 150

... x = 15 . . . . . . . . . . . . . . divide by 2

Angle 1 and angle (2x+15)° are on opposite sides of the transversal line, and are both between the parallel lines m and n. This makes them alternate interior angles. Such angles are congruent—they have the same measure. We know the measure of angle (2x+15)° is (2·15+15)° = 45°, so we know the measure of ∠1 is also 45°.

a) The sum of angles in a triangle is always 180°. This means ...

... (15x +10)° + (15x -10)° + (3x +15)° = 180°

... 33x +15 = 180 . . . . . . . drop the ° symbol, combine terms

... 33x = 165 . . . . . . . . . . subtract 15

... x = 5 . . . . . . . . . . . . . . . divide by 33

b) ∠A = (15x+10)° = (15·5 +10)°

... ∠A = 85°

(1)

(a)

the sum of the angles in a triangle = 180°, hence

3x + 15 + 15x - 10 + 15x + 10 = 180

33x + 15 = 180 ( subtract 15 from both sides )

33x = 165 ( divide both sides by 33 )

x = 5

(b) ∠A = 15x + 10 = (15 × 5 ) + 10 = 75 + 10 = 85°

(2)

2x + 15 + 135 = 180 ( straight angle )

2x + 150 = 180 ( subtract 150 from both sides )

2x = 30 ( divide both sides by 2 )

x = 15 ⇒ 2x + 15 = 45

∠1 = 45° ( alternate angles are congruent )

Answer: x = -2 and y = 4

Step-by-step explanation:

We have given a system of equations

2x + 4y =12   ...........(1)

and

x + y = 2         .............(2)

Now to plot them in graph we need to find the points of the above linear equations .

From equation 1  ,we get

[tex]4y=12-2x\\\Rightarrow\ y=\frac{12-2x}{4}\\ \Rightarrow\ y=3-\frac{x}{2}\\\text{Put x=0, then} \\y=3-\frac{0}{2}=3\\\Rightarrow\ \text{Put x=6}\\y=3-\frac{6}{2} =3-3=0[/tex]

So get the points (0,3) and (6,0).

From equation 2 ,we get

[tex]y=2-x\\\text{Put x=0}\\y=2-0=2\\\text{Put x=2}\\y=2-2=0[/tex]

So we get the points (0,2) and (2,0).

So after plotting these points we get two lines intersecting at (-2,4).

Therefore our solution is x=-2 and y= 4.

Answer:

(-2, 4)

Step-by-step explanation:

Its A i did the test

I believe you only need to know one angle.

For example, if you know angle 1, you can calculate angle 3. Angle 2 = angle 3 and angle 4 = angle 1.

Also, Angle 5= angle 1 and so on...

ANSWER

The correct answer is A

{[tex]x|-5<\:x<\:5[/tex]}

EXPLANATION

[tex]|x|<5[/tex]

This implies that

[tex]x<5\:or\:-x<5[/tex]

We solve the compound inequality to obtain,

[tex]x<5\:or\:x>-5[/tex]

Remember that, dividing through by negative 1 reverses the inequality sign

The solution set is

{[tex]x|-5<\:x<\:5[/tex]}

75% of X  = $51, thus x or the original price is $68 . Thus the sales price is  $17 less.

Answer: The equation is of line "b"

Step-by-step explanation:

First we find the slope of the given line by using slope intercept form.

Converting the equation into slope intercept form

[tex] 5y=-2x+10 [/tex]

Divide both side by 5 we get

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

On comparing with

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

We get slope [tex] m=\frac{-2}{5} [/tex]

as the slope of line is negative therefore the line will be either line "b" or line "d"

As line "b" pass from (0,2)

On putting point [tex] x=0 &y=2[/tex] in given equation we get

[tex] 2(0)+5(2)=0+10=10 [/tex]

Which is equal to RHS of the line

Therefore the given equation is of line "b"

Now putting point (0,-2)

We get [tex] 2(0)+5(-2)=-10 [/tex]

Which is not equal to RHS and therefore line "d" is not the required line

Therefore the given equation is of line "b"

B

to calculate percent increase use

[tex]\frac{increase}{original}[/tex] × 100%

increase = $650 - $525 = $125

percent increase = [tex]\frac{125}{525}[/tex] × 100% = 24% → B

Answer:

The answer is B) 24%

Step-by-step explanation:

The formula for percentage increase is given as:-

Percentage Increase = ( New Price - Old Price ) /old price * 100

old price = $525

New Price = $650

Percentage Increase = 24%

Hence the price increases by 24%

[tex]\frac{6}{8}[/tex]

let x be the unknown value in the ratio, hence

[tex]\frac{6}{x}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )

9x = 72 ( divide both sides by 9 )

x = 8

thus [tex]\frac{6}{8}[/tex] = [tex]\frac{9}{12}[/tex]

Put your number into the half-angle formula and simplify.

[tex]\displaystyle\sin{\frac{\theta}{2}}=\pm\sqrt{\frac{1-\cos{\theta}}{2}}=\sqrt{\frac{1-\frac{1}{3}}{2}}\\\\=\sqrt{\frac{1}{3}}=\sqrt{\frac{3}{9}}\\\\=\frac{\sqrt{3}}{3}[/tex]

The appropriate selection is ...

[tex]A)\quad\dfrac{\sqrt{3}}{3}[/tex]

A number and its absolute value are not equal when the number is less than zero. Since subtracting 2 makes the number less than zero, we know ...

... the number is a non-negative number less than 2. (0 ≤ n < 2)

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

the equation of a line in slope- intercept form is

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

rearrange 2x + 3y = - 12 into this form

subtract 2x from both sides

3y = - 2x - 12 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x - 4 ← in slope- intercept form

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

[tex]\text{The slope-intercept form:}\ y=mx+b\\m-slope,\ b-y-intercept\\\\2x+3y=-12\qquad|\text{subtract 2x from both sides}\\\\3y=-2x-12\qquad|\text{divide both sides by 3}\\\\y=-\dfrac{2}{3}x-4\\\\Answer:\ \boxed{m=-\dfrac{2}{3}}[/tex]

Simplify. Divide the number

300/2 = 150

150 is your answer (it is a whole number, no need to change to improper, unless you want 150/1)

hope this helps

We are given table

Month :         1     2        3         4         5

Shoppers:   50  250   1250   6250  3250

so, we have

first term =50

[tex]a_1=50[/tex]

Second term =250

[tex]a_2=250[/tex]

Third term =1250

[tex]a_3=1250[/tex]

[tex]a_4=6250[/tex]

[tex]a_5=31250[/tex]

now, we can find ratios

[tex]\frac{a_2}{a_1} =\frac{a_3}{a_2}=\frac{a_4}{a_3}=\frac{a_5}{a_4}=5[/tex]

we can see that all ratios are same and 5

so, this is exponential

so, option-D..........Answer

The table below shows the number of shoppers at Jacob's store over a period of five months:  

Month 1 2 3 4 5  

Shoppers 50 250 1,250 6,250 31,250  

Did the number of people at Jacob's store increase linearly or exponentially?

Answer:

D.Exponentially, because the table shows the number of shoppers increases by an equal factor for an equal increase in months

because the leading coefficient is positive and the highest degree is odd (9) the function is negative for (-inf, -6). Then it crosses the -6 root to become positive until it crosses again the root -2. (it crosses because both roots have an odd multiplicity). then it touches on root 0 (does not cross due to an even multiplicity there), so function remains negative from -2 till root 4 where it crosses into the positive.

Given the above, only the first choice is a correct statement.

The true statement about the graph is: (a) the graph of the function is positive on [tex]\mathbf{(-6,-2)}[/tex]

The given parameters are:

[tex]\mathbf{Root = -6, Multiplicity = 1}[/tex]

[tex]\mathbf{Root = -2, Multiplicity = 3}[/tex]

[tex]\mathbf{Root = 0, Multiplicity = 2}[/tex]

[tex]\mathbf{Root = 4, Multiplicity = 3}[/tex]

Add up the multiplicities, to calculate the degree of the polynomial function

[tex]\mathbf{Degree = 1 + 3 + 2 + 3}[/tex]

[tex]\mathbf{Degree = 9}[/tex] --- odd number

The interval of the first root is:

[tex]\mathbf{Interval = (-\infty,-6)}[/tex]

The interval of the second root is:

[tex]\mathbf{Interval = (-6,-2)}[/tex]

A polynomial function with an odd degree, and a positive leading coefficient will start with negative values, until it reaches the smallest root, before it switched to positive values.

This means that, the function increases at: [tex]\mathbf{Interval = (-6,-2)}[/tex]

Hence, option (a) is correct.

Read more about polynomial functions at:

https://brainly.com/question/9338204

y = -2x - 3

To make a table, we assume any number for x  and find out y

Lets assume x= -1

y = -2x - 3 = -2(-1) -3 = 2-3 = -1

Lets assume x= 0

y = -2x - 3 = -2(0) -3 = 0-3 = -3

Lets assume x= 1

y = -2x - 3 = -2(1) -3 = -2-3 = -5

Lets assume x= 2

y = -2x - 3 = -2(2) -3 = -4-3 = -7

Table is

x      y = -2x-3

-1       -1

0        -3

1        -5

2       -7

Answer:

Option C

Step-by-step explanation:

A coin has two outcomes Head (H) and tail (T).

So, the number of outcomes when a coin is tossed = 2

A coin has six outcomes [tex]\left \{ 1,2,3,4,5,6 \right \}[/tex]

So, the number of outcomes when a coin is tossed = 6

Therefore, possible outcomes when Jo flips a coin and then rolls a 6-sided die are [tex]\left \{ H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6 \right \}[/tex]

So, the number of possible outcomes = 12

Option C. is correct.

Using the concept of sample space, it is found that the number of possible outcomes in the experiment is given by:

C. 12

The sample space of an experiment is the set that contains all possible outcomes.

In this problem:

The coin and the dice are independent, thus, there are 2 x 6 = 12 possible outcomes, which means that the correct option is:

C. 12

A similar problem is given at https://brainly.com/question/15006554

complex roots occur in conjugate pairs

given 2 - 3√5 is a root then 2 + 3√5 is also a root

one of the other roots is 2 + 3√5

there are 2 roots of - 4

one of the other roots could be another - 4

Final answer:

The princess can conclude that one of the other roots is 2+ 3√5, one of the other roots could be another −4, and one of the other roots could be another 2− 3√5.

Explanation:

The princess can draw the following conclusions about the other two roots:

These conclusions are based on the fact that the princess has already traced one root to be 2−3√5 and at least two roots are labeled −4.

Answer:

The answer is B

Step-by-step explanation:

Simple use P.E.M.D.A.S

Parentheses are always first, you add 13+10 then evaluate everything else.

Have a great day.

Read the problem and answer choices. You want to get from ABCD to EFGH, so you need to figure out how to do that with reflection, translation, and dilation—in that order.

The reflection part is fairly easy. ABC is a bottom-to-top order, and EFG is a top-to-bottom order, so the reflection is one that changes top to bottom. It must be reflection across a horizontal line. The only horizontal line offered in the answer choices is the x-axis. Selection B is indicated right away.

The dimensions of EFGH are 3 times those of ABCD, so the dilation scale factor is 3. This means that prior to dilation, the point H (for example), now at (-12, -3) would have been at (-4, -1), a factor of 3 closer to the origin. H corresponds to D in the original figure, which would be located at (0, -2) after reflection across the x-axis.

So, the translation from (0, -2) to (-4, -1) is 4 units left (0 to -4) and 1 unit up (-2 to -1).

The appropriate choice and fill-in would be ...

... B. Reflection across the x-axis, translation 4 units left and 1 unit up, dilation with center (0, 0) and scale factor 3.

_____

You can check to see that these transformations also map the other points appropriately. They do.

A. -2/3 because you would go down two and then to the right three. I hope that helps.

Solution :

Given ,line that passes through the  pair of points (1,7) and (10,1)

The slope of the line passing through the points [tex](x_{1},y_{1} ) \:and \:(x_{2},y_{2})[/tex] is given by,

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

Here,  [tex](x_{1},y_{1} ) =(1,7)\:and \:(x_{2},y_{2})=(10,1).[/tex]

[tex]\Rightarrow m=\frac{1-7}{10-1} \\\Rightarrow m=\frac{-6}{9}=\frac{-2}{3}[/tex]

Hence , slope of the line passing through the pir of points (1,7) and (10,1) is [tex] \frac{-2}{3}[/tex] ( first option)

y = [tex]\frac{1}{2}[/tex] x + 2

the equation of a line in slope-intercept form is

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 4, 0 ) ← points from graph

m = [tex]\frac{0-2}{-4-0}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]

from the graph the y-intercept = (0, 2 ) → c = 2

y = [tex]\frac{1}{2}[/tex] x + 2 ← is the equation

The equation of the line is [tex]y = \frac{1}{2}x + 2[/tex]

The equation of a line in slope-intercept form is

y = mx + c

Here m is the slope and c is the y-intercept  

Now  

[tex]m = ( y_2 - y_1 ) \div (x_2 - x_1 )[/tex]

Here

[tex](x_1, y_1 )[/tex]= (0, 2 ) and [tex](x_2, y_2 )[/tex] = (- 4, 0 )  

Now  

[tex]m = (0-2) \div (-4-0)\\\\= -2\div -4\\\\= \frac{1}{2}[/tex]

From the graph the y-intercept = (0, 2 ) i.e. c = 2

Learn more; brainly.com/question/17429689

You are told to ignore the amount of principal paid, so you are apparently to assume the loan amount was for $50 thousand.

a) The old monthly payment was $10.67×50 = $533.50

b) The new monthly payment is $11.72×50 = $586.00

c) The increase in monthly payment is figured in the usual way:

... (new/old -1)×100% = (1.0984-1)×100% = 9.84%

_____

In reality, about 3% of the loan will have been paid at the end of 2 years. Thus, the original loan amount may have been near $51,500. This problem is telling you to ignore the difference.

Remark

The first fact you need to know is that the bank has taken money from you and nothing has been reduced from the principle. Crafty people those bankers; you are going to pay off the interest before touching the principle. They're like you to refinance for the rest of your life at the rates you currently have.

Point. You started out with a 50k debt. You still have that same debt.

Solution

Givens

number of thousands (n) = 50000/1000 = 50

Amount paid per thousand (A) = 10.67

Total monthly payments (T) = ?

Part A

T = n * A

T = 50 * 10.67

T = 533.50 is the old monthly payment

Part B

T = n * A

T = 50 * 11.72

T = 586.00  new monthly payment.

Part C

This is a notes question. What have you been told in your notes on this question. You can find the raw amount just by subtracting 586 - 533.50 = 52.50

But how do you find the % increase. Which one of the payments do you use as your base?

In point of fact, you should be using the first number 533.5

What % will you get when you multiply that by 533.5 and get 52.50?

You are not trying to find 586. You are trying to find the number that you add to 533.5 to get to 586

The answer is (52.50 / 533.5)*100% = 9.84% is the % increase.

"Opposite sides of the transversal..." Alternate

"Between the other two lines." Interior

Alternate Interior angles.

If they were outside the two lines they would be alternate exterior angles and if they were on the same side of the transversal then they would be corresponding angles.

We are given function F(x) = x^3 +3x^2.

Leading term is the term that has highest power of a variable.

For the given function we have highest power 3 of x.

Therefore, leading term is x^3. We don't have any sign in front of x^3. Therefore, it's a positive leading term.

And degree of the is highest power, that is 3.

Therefore, degree is an odd number.

According to problem,  we need to make the leading term as a negative number.

So, we need to find a rule for end behaviour of the graph with:

Leading coefficent = Negative.

Degree : Odd.

Please note the rule, when leading coefficent a negative number and degree is odd.

x--> + ∞   f(x) ---> - ∞

x--> - ∞   f(x) ---> + ∞

We can see option D has  f(x) ---> - ∞ for x--> + ∞ and  f(x) ---> + ∞ for x--> - ∞.

Answer: graph D

Step-by-step explanation: just took the test