Solve the system by using a matrix equation

Answer:

y= sqrt(x+4)

Step-by-step explanation:

The reason is because the function is translated horizontally to the left.

The base function is y=sqrt(x)

The option A. f(x) sqrt (x-5) + 1, the graph should be translated horizontally 5 units to the right. It's not the case. And translated 1 unit vertically.

Option B. f(x) = sqrt (x-2) the graph should be translated horizontally 2 units to the right. It's not the case.

Option C. f(x) = sqrt(x), the graph should start at x=0. It's not the case.

The option D.  f(x) = sqrt(x+4), the function is translated 4 times horizontally to the left. So this is the case.

ANSWER

[tex]f(x) = \sqrt{x + 4} [/tex]

EXPLANATION

The parent function is

[tex]f(x) = \sqrt{x} [/tex]

This parent function has been shifted to the left, hence its transformation is of the form,

[tex]f(x + k)[/tex]

The only option in this form is the last option,

[tex]f(x) = \sqrt{x + 4} [/tex]

Answer:

Final answer in simplified form is [tex]-7x^2+10x-18[/tex]

Step-by-step explanation:

Given expression is [tex](-7x^2+4x-3)+(6x-15)[/tex]

Now we need to find an equivalent expression for [tex](-7x^2+4x-3)+(6x-15)[/tex]

First we can distribute the positive sign and remove the parenthesis the combine like terms

[tex](-7x^2+4x-3)+(6x-15)[/tex]

[tex]=-7x^2+4x-3+6x-15[/tex]

[tex]=-7x^2+4x+6x-3-15[/tex]

[tex]=-7x^2+10x-18[/tex]

Hence final answer in simplified form is [tex]-7x^2+10x-18[/tex]

The answer is C.50. That is the answer.

The answer is:

The length of "x" is equal to 4 units.

To solve the problem and find the length of x, we need to remember the alternate angles rule. The alternate angles rule establish that alternate angles will be also equal.

So, for the triangles, we have:

The angle((α)) formed between the base (2.5) and the hypotenuse (5)  of the big triangle is equal to the angle(α) formed between the base (2) and the hypotenuse (x) of the small triangle. It also means that the triangles are similar since they have congruent angles(α) and proportional sides (SAS).

We are given:

First triangle,

[tex]AdjacentSide=2.5\\Hypotenuse=5\\[/tex]

Second triangle,

[tex]AdjacentSide=2\\Hypotenuse=x\\[/tex]

So, using the cosine identity, we have:

[tex]Cos(\alpha)=\frac{AdjacentSide}{Hypotenuse}[/tex]

[tex]Cos(\alpha)=\frac{2.5}{5}=\frac{2}{x}[/tex]

[tex]Cos(\alpha)=\frac{2.5}{5}=\frac{2}{x}\\\\\frac{2.5}{5}=\frac{2}{x}\\\\x=2*\frac{5}{2.5}=4[/tex]

Therefore, we have that the hypotenuse of the second triangle (x) is equal to 4 units.

Hence, the length of "x" is equal to 4 units.

Have a nice day!

Answer:

The length of x = 4

Step-by-step explanation:

From the figure we can see that two triangles are similar. (AAA similarity criteria)

Therefore the ratio of similar corresponding sides are equal.

Answer:

The length of x = 4

Step-by-step explanation:

From the figure we can see that two triangles are similar. All angles are equal(AAA similarity criteria)

Therefore the ratio of similar corresponding sides are equal.

To find the value of x

From the figure we can write,

x/5 = 2/2.5

x = (5 * 2)/2.5

x = 10/2.5 = 4

Therefore the length of x = 4

From the figure we can write,

x/5 = 2/2.5

x = (5 * 2)/2.5

x = 10/2.5 = 4

Therefore the length of x = 4

Answer:

y = 32.0°

Step-by-step explanation:

Using the sine ratio in the right triangle

siny° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{9}{17}[/tex], hence

y = [tex]sin^{-1}[/tex] ([tex]\frac{9}{17}[/tex] ) ≈ 32.0°

Question 1.

They usually charge $7 per day to swim at the pool. The offer consist of: Paying an enrollment fee is $30 and then $4 per day.

It means that by enrolling you save 3$ per day. If you save $3 per day, in 10 days you would be saving $30 dollars which is the enrollment fee. This can be calculated by applying the rule of three:

If I save $3 -------------> 1 day?

             $30 ----------> How many days?

Days = ($30 * 1day)/$3 = 10 days.

Then, after 10 days, the offer becomes a better deal.

Question 2.

I only have $60 to spend the rest of the summer. Which offer would be the best value?

NOT paying the enrollment fee would be the best value. The reason is the following:

If I pay the enrollment fee, I spend $30. So I just have $30 remaining. Then, paying $4 a day, it means that I could just pay 7 daily passes, it means that I could go to the pool just seven days.

If I don't pay the enrollment fee, I would have the entire $60 dollars to buy daily passes. The price of each pass would be $7, so $60/7 = 8.5. It means that I could go just 8 days to the pool. One day more than the other option.

So if I only have $60, the best option is NOT to pay the enrollment fee.

Question 3.

If the swim center decides to change the the enrollment fee to $23 and then paying just $4 per daily pass. Then:

If I have only $60 dollars, after paying the enrollment fee I will only have $37.

If each daily pass costs $4, then I will be able to buy $37/$4 = 9.25 = 9 daily passes.

So, if the swim center decides to change the enrollment fee to $23, the the best option is paying the enrollment fee.

Answer:

8%

Step-by-step explanation:

I = PRT (Interest = Principal x Rate x Time)

Note that:

Interest = $320

Principal = $2000

Time = 2 years

Plug in the corresponding number to the corresponding variables.

320 = (2000)(r)(2)

Simplify. Combine like terms.

320 = (4000)r

Isolate the variable, r. Divide 4000 from both sides.

(320)/4000 = (4000r)/4000

r = 320/4000

r = 0.08

Change the decimal into a percentage.

r = 0.08 = 8/100 = 8%

8% is your interest rate.

~

Answer: 8%

Step-by-step explanation:

it should be 32 inches

Answer:

The answer is 20 inches

Step-by-step explanation:

ANSWER

P(X=4 or X=1)=0.2

EXPLANATION

From the table, the probability that X=4 is P(X=4)=0.15

and the table, the probability that X=1 is P(X=1)=0.05

We want to find P(X=4 or X=1)

Recall that

P(X=4 or X=1)=P(X=4)+P(X=1)

We substitute the given probability values to obtain:

P(X=4 or X=1)=0.15+0.05

P(X=4 or X=1)=0.2

Answer: 0.2 is the answer

Step-by-step explanation:

hope this helps :]

ANSWER

[tex]x \leqslant - 3,x \geqslant 4[/tex]

EXPLANATION

The given inequality is

[tex](x - 4)(x + 3) \geqslant 0[/tex]

To solve this inequality, we need to solve the corresponding equation:

[tex](x - 4)(x + 3) = 0[/tex]

This implies that

[tex]x = - 3 \: or \: x = 4[/tex]

We now plot the solutions of the equation and use it to solve the corresponding inequality as shown in the attachment.

These values divide the number line into 3 regions.

The region(s) that satisfies the inequality is the solution set

From the graph the solution is

[tex]x \leqslant - 3,x \geqslant 4[/tex]

Answer:

The height of the triangular prism is [tex]26\ mm[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the triangular prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the triangular base

h is the height of the prism

Find the area of the base B

[tex]B=\frac{1}{2}(7)(18)=63\ mm^{2}[/tex]

we have

[tex]V=1,638\ mm^{3}[/tex]

[tex]h=x\ mm[/tex]

substitute and solve for x

[tex]1,638=(63)x[/tex]

[tex]x=1,638/(63)=26\ mm[/tex]

Answer:

C. 26mm

Step-by-step explanation: Just did the assignment

Pythagoras & his colleagues

Answer:

It was named after Pythagoras, a Greek mathematician and philosopher. The theorem bears his name although we have evidence that the Babylonians knew this relationship some 1000 years earlier.

Step-by-step explanation:

Answer:

  $362.57

Step-by-step explanation:

A suitable calculator or finance app can find the monthly payment for you. This result comes from a TI-84 calculator.

___

The second attachment shows the parameters of the payment function. With 20% down, Anthony is only financing 80% of the price of his car. Of course, there are 12 months in a year, so 4 years worth of payments will be 48 payments. The calculator uses negative values for amounts you pay.

___

No doubt your reference material shows you a formula for computing loan payments. One such is ...

  A = Pr/(1 -(1+r)^-n)

where r is the monthly interest rate, 0.068/12, and n is the number of payments, 48. The principal amount of the loan, P, will be 19,000×0.80. This formula gives the same result as that shown above and below.

Answer:

Total price paid is 20,033.60

Step-by-step explanation:

20% of 19,000 is 3,800

19,000 - 3,800 = 15,200

6.8% of 15,200 is 1,033.60

3,800 + 15,200 + 1,033.60 = 20,033.60

About how many what?

Answer:

Step-by-step explanation:

Both of the following are characteristics of this graph

It will use a closed circle.

The ray will move to the left.

Answer:

The correct answer option is D. [tex] \frac { 3 n ^ { 3 } } { 5 m ^ { 2 } } [/tex].

Step-by-step explanation:

We are given the following expression and we are to simplify it:

[tex] \frac { 3 m ^ { - 2 } } { 5 n ^ { - 3 } }[/tex]

Here the variables [tex]m[/tex] and [tex]n[/tex] are having negative powers. So to change these powers from negative to positive, we will take their reciprocals to get:

[tex] \frac { 3 n ^ { 3 } } { 5 m ^ { 2 } } [/tex]

Answer:

The correct answer is option D

3n³/5m²

Step-by-step explanation:

Points to remember

Identities

Xᵃ * Xᵇ = X⁽ᵃ ⁺ ᵇ⁾

X⁻ᵃ = 1/Xᵃ

Xᵃ/Xᵇ = X⁽ᵃ ⁻ ᵇ⁾

To find the correct answer

It is given that,

3m⁻²/5n⁻³

By using identities we can write,

m⁻² = 1/m²  and 1/n⁻³ = n³

3m⁻²/5n⁻³ = 3n³/5m²

Therefore the correct answer is option D.  3n³/5m²

Answer:

b. sin or csc

Step-by-step explanation:

Remember that sine trigonometric function is the ratio of the opposite side of a right triangle to its hypotenuse; in other words:

[tex]sin(\alpha )=\frac{opposite-side}{hypotenuse}[/tex]

Also, the cosecant is the inverse of sine, so:

[tex]csc(\alpha )=\frac{1}{sin(\alpha) } =\frac{hypotenuse}{opposite-side}[/tex]

Now, for our triangle, our angle is 27°, the longest side of it is TS, and the opposite side of our angle (27°) is TR; therefore, [tex]\alpha =27[/tex], [tex]hypotenuse=TS[/tex], and [tex]opposite-side=TR[/tex].

Replacing values:

- Using the sine trigonometric function

[tex]sin(\alpha )=\frac{opposite-side}{hypotenuse}[/tex]

[tex]sin(27)=\frac{TR}{TS}[/tex]

[tex]sin(27)=\frac{TR}{TS}[/tex]

[tex]sin(27)=\frac{7}{TS}[/tex]

[tex]TS=\frac{7}{sin(27)}[/tex]

[tex]TS=15.42[/tex]

- Using the cosecant trigonometric function

[tex]csc(\alpha )=\frac{hypotenuse}{opposite-side}[/tex]

[tex]csc(27)=\frac{TS}{TR}[/tex]

[tex]csc(27)=\frac{TS}{7}[/tex]

[tex]TS=7csc(27)[/tex]

[tex]TS=15.42[/tex]

We can conclude that we can use either the sine trigonometric function or the cosecant trigonometric function to solve the problem.

Answer:

(-5,2)

Step-by-step explanation:

Answer:

irts 400 inch

Step-by-step explanation:

Answer: V ≈ 1333.3π [tex]cm^{3}[/tex]

Step-by-step explanation: Please see the image below!

Answer:

4.5 centimeters

Step-by-step explanation:

A = L * W

45 = 10 * W

W = 45/10

W = 4.5cm

Answer:

No, just because the amount of recylcing has gone up this year does not mean that we can conclude it's more this year than ever before. We are only given information for this year and last year, we can't come to that conclusion unless we are given information about the amount of recyling done in all the years.

I reject this conclusion because it says that the people have recycled more this year than ever before.

Generally ever before mean since a long time ago and from the data given we only have recording of last year, not any year before that. If the conclusion had said that the people in mesopotamiaville are recycling more this year than last year. It would have been correct but instead it has given us an invalid conclusion because from the data we have been given we can not possibly gather any other information that can help us accept or reject the conclusion. So therefore the conclusion given is invalid. Hence the reason I reject this conclusion.

hope this helps

Answer: your answer should be 0.51

Some people are saying it's 0.04 but that is the wrong answer.

Answer:

B. Right by 4 units

Step-by-step explanation:

Let's start by expressing g(x) formula in a simpler form.  x² - 8x + 16 is quite easy to factor into (x - 4)²

so, we have g(x) = (x - 4)² and f(x) = x²

For which value of x will g(x) and f(x) = 0?

g(x) will equal 0 if x = 4

f(x) will equal 0 if x = 0

So, the difference is 4 units.  

Since f(x) would have to move from 0 to 4 to join g(x), the movement will be to the right.

ANSWER

B' has coordinates (16,14).

EXPLANATION

The given coordinates of square ABCD are :

A (2,7) , C (8,1),D (2,1)

In order to form a square, the coordinates of B should be: (8,7)

The mapping for dilation with a scale factor 2, about the origin is

[tex](x,y)\to (2x,2y)[/tex]

This implies that:

[tex]B(8,7)\to B'(2 \times 8,2 \times 7)[/tex]

When we simplify we get:

[tex]B(8,7)\to B'(16,14)[/tex]

Hence B' has coordinates (16,14).

In one hour Nina runs 51 ¹/₅ miles.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

In 1/4 hours, Number of laps run by Nina = 12 ⁴/₅.

To find the number of laps Nina could run in one hour,

Use ratio property,

Since,

In 1/4 hours = 12 ⁴/₅ laps = 64 / 5 laps

In 1 hour = (64 / 5) x 4

               = 256 / 5

                = 51 ¹/₅

Nina runs 51 ¹/₅ laps in one hour.

To learn more about Ratio on :

https://brainly.com/question/13419413

#SPJ2

For this case we have that by definition, the slope point equation of a line is given by:

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

Where:

m: It's the slope

b: It is the cutoff point with the y axis

By definition, if two lines are perpendicular, the product of their slopes is -1. That is to say:

[tex]m_ {1} * m_ {2} = - 1\\If\ it\ tells\ us: m_ {1} = - \frac {3} {2}:\\- \frac {3} {2} * m_ {2} = - 1\\m_ {2} = \frac {2} {3}[/tex]

Substituting:

[tex]y = \frac {2} {3} x + b[/tex]

We substitute the point to find "b":

[tex]3 = \frac {2} {3} 6 + b\\3 = 4 + b\\b = 3-4\\b = -1[/tex]

Finally:

[tex]y = \frac {2} {3} x-1[/tex]

Answer:

[tex]y = \frac {2} {3} x-1[/tex]

Answer:

y = -5x + 1

Step-by-step explanation:

y = -5x + 1 is correct.  

Note that at x = 0, y = 0 + 1 = 1 → (0, 1), and

                at x = 1, y = -5 + 1 = -4 → (1, -4), and

                 at x = -1, y = 5 + 1 = 6  → (-1, 6)

The linear function that maps the diagram is:

[tex]y = -5x + 1[/tex]

A linear function has the following format:

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

In which:

In the diagram, when [tex]x = 0, y = 1[/tex], thus, the y-intercept is [tex]n = 1[/tex], and:

[tex]y = mx + 1[/tex]

Point (1,-4) is on the diagram, which means that when [tex]x = 1, y = -4[/tex], and this is used to find m.

[tex]y = mx + 1[/tex]

[tex]-4 = m + 1[/tex]

[tex]m = -5[/tex]

Then, the equation is:

[tex]y = -5x + 1[/tex]

A similar problem is given at https://brainly.com/question/16302622

Answer:

Step-by-step explanation:

Rewrite this equation in standard form:

x² - 2x + 1 - 1 + y² + 6y + 9 = 0, or

  (x - 1)² + (y + 3)² = 1

Compare this to:

   (x + h)² + (y + 3)² = r²

We see here that (h, k), the center of the circle, is (1, -3), and the radius of the circle is 1.

Answer:

the center is at (1, -3)

Step-by-step explanation:

The center-radius form of the circle equation is in the format (x – h)2 + (y – k)2 = r2, with the center being at the point (h, k) and the radius being "r".

So we need to write the ecuation x^2 + y^2 - 2x + 6y + 9 = 0 in the format above.

So we have:

x^2 + y^2 - 2x + 6y + 9 = (x^2 -2x + 1) + (y^2 + 6y + 9) - 1

(x^2 -2x + 1) + (y^2 + 6y + 9) - 1 = (x-1)^2 + (y+3)^2 - 1

So now, looking at the equation:  (x-1)^2 + (y+3)^2 = 1

We know that h=1 and k=-3. So the center is at (1, -3)

Answer:

Step-by-step explanation:

Left Frame

f(x) is a horizontal line from x = 1 to x = 3. So the y values are the same in that interval.

when y = 1, x = 3

so f(3) = 1

The answer is III

Question Second from the right

The trick is to get the denominator so it is not a complex number. You do that by multiplying by the conjugate which is 8 - 2i. If you do that to the denominator, you must do it to the numerator.

Denominator: (8 + 2i)(8 - 2i) = 64 - 16i + 16i - 4i^2

Denominator: 64 + 4

Denominator: 68

Numerator: (3 - 5i)(8 - 2i)

Numerator: 24 - 6i - 40i + 10*i^2

Numerator: 24 - 46i - 10

Numerator: 14 - 46i

So in some form or other the answer is

[tex]\dfrac{14 - 46i}{68} = \dfrac{7}{34} - \dfrac{23i}{34}[/tex]

Right Frame

Here, the slopes must be the same. So calculate the slope of the left line and make that equal to the slope of the right line's expression

Left Line

Left = (y2 - y1)/( x2 - x1) = (2 - 0)/(0 - - 5) = 2/5

Right line

Right  = (y2 - y1) / (x2 - x1) = (0 - - 4) / (p - 0) = 4/p

Now Equate them (they are parallel and have the same slope)

2/5 = 4/p           Cross multiply

2p = 5*4            Combine the right

2p = 20              Divide by 2

2p/2 = 20/2       Do the division

p = 10