What is the apparent solution to the system of equations graphed above?
(3,2)
(2,3)
(0,-3)
(0,2)

Remark

You are dealing with a right angle triangle. You can use one of Sin(x) Cos(x) or Tan(x). Since the Hypotenuse is involved and since you are given the adjacent side, Cos(71) is what you will need.

Solution

H = BC

Cos(x) = adjactent / hypotenuse

Cos(71) = 6.3 / H            Multiply both sides by H

H * Cos(71) = 6.3            Divide by Cos(71)

H = 6.3 / cos(71)             Cos(71) = 0.32557

H = 6.3 / 0.32557          Divide

H = BC = 19.351                       Answer

Answer:

9i(2+3i) = -27+18i

Step-by-step explanation:

Distribute to get → 9i·2+9i(3i)

Multiply 2 and 9 → 18i+9i(3i)

Simplify → 18i+27i²

Simplify → 18i-27

Reorder → -27+18i

Answer:

C) M + 0.12M

Step-by-step explanation:

A — calculates the raise, not the new fare

B — adds 12¢ to every fare

C — adds 12% of the current fare to the current fare. This is what you want.

D — adds $1 to the amount of the raise. This is not the amount of the new fare.

Answer: C) [tex]M+0.12M[/tex]

Step-by-step explanation:

Given : Matrix M shows the one-way fares for four commuter train routes.

If the rail service raised fares by 12% on all routes and days.

Then, the proportion of service raised fares on all routes and days. =0.12

Then, the new fares is given by :-

[tex]M+0.12M[/tex]

Hence, the formula shows how to find the matrix that would display the new fares = [tex]M+0.12M[/tex]

Given rate is = 7% or 0.07

Total amount needed = $12000

Time = 4 years

Here, the  deposit is  compounded semiannually, means twice per year and this gives 8 annual compounding periods in 4 years.

The equation becomes:

P= [tex]\frac{12000}{(1+\frac{0.07}{2})^{2.4}}[/tex]

P = [tex]\frac{12000}{1.035^{8}}[/tex]

Solving it, we get P = $ 9112.93

Hence $9112.93 should be deposited today.

To accumulate $12,000 in four years in an account earning 7% compounded semiannually, approximately $8,289.64 should be deposited today.

To find out how much money should be deposited today in an account that earns 7% compounded semiannually to accumulate to $12,000 in four years, we can use the formula for calculating compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the principal (initial deposit), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Hence, approximately $8,289.64 should be deposited today in the account.

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Answer:  8

Step-by-step explanation:

x² - 2x  + ___ - 4y²  = 15 + ___

x² - 2x  + 1 - 4y²  = 15 + 1

(x - 1)² - 4(y)² = 16

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

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

[tex]r_{x} = 4[/tex]   [tex]r_{y} = 2[/tex]

width of rectangle is 2[tex](r_{x})[/tex] = 2(4) = 8

Distance covered in 12 gallons tank of gas = 420 miles

So, distance covered in 1 gallon tank of gas = [tex]\frac{420}{12}[/tex] miles

Now, distance covered in 8 gallons will be =

[tex]8*\frac{420}{12}[/tex] =280 miles

Hence, distance covered by Mr.Fink's economy car in 8 gallons tank of gas is 280 miles.

Using FOIL (First, Outer, Inner, Last):

(x+3)(x-4)

FIRST: multiply x times x to get x^2.

OUTER: multiply x times -4 to get -4x.

INNER: multiply 3 times x to get 3x.

LAST: multiply 3 times -4 to get -12.

Your expression now looks like:

x^2-4x+3x-12

Combine like terms.

x^2-x-12

The answer is D. x^2-x-12.

I hope this helps :)

Point slope form says the line through (a,b) with slope m is

y - b = m(x - a)

Here that's

y - - 1 = -2(x - -4)

Answer: y + 1 = -2(x + 4)

Point-Slope equation: y - y₁ = m(x - x₁)  ; m is slope and (x₁ ,y₁) is the coordinate

y - (-1) = -2(x - (-4)

y + 1 = -2(x + 4)     simplified (two negatives make a positive)

ANSWER

[tex]x=4[/tex]

EXPLANATION

We have[tex]6x-8=16[/tex]

We add 8 to both sides of the equation

[tex]6x-8+8=16+8[/tex]

We simplify

[tex]6x=24[/tex]

We divide both sides by 6

[tex]x=\frac{24}{6}[/tex]

[tex]x=4[/tex]

6 on the sq rt 5 - 4 on the sq rt 7

To simplify the given expression, substitute the values of each square root and simplify the expression to get the final result of 1.416.

To simplify the given expression:
3 times the square root of 5 - 2 times the square root of 7 + the square root of 45 - the square root of 28

We can simplify each square root separately:

√5 = 2.236 (approx.)

√7 = 2.646 (approx.)

√45 = 6.708 (approx.)

√28 = 5.292 (approx.)

Substituting these values in the expression:

3(2.236) - 2(2.646) + 6.708 - 5.292

This simplifies to:
6.708 - 5.292 = 1.416

Therefore, the simplified expression is 1.416.

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Answer:

48%

Step-by-step explanation:

Given that five friends are chipping in for a birthday gift for their teacher.

They were David, Jakob , Stephanie, Kate and Janice

Boys contributed 13 dollar each i.e. a total of 26

Girls contributed 8 each i.e. a total of 24

total contribution =50

Out of total contribution 50, girls total contrbution = 24

Hence percent = 24(100)/50 = 48%

Yes, there was a mistake in applying the distributive property. If you have to perform

[tex] 3(2x-5) [/tex]

you have to multiply both terms in the parenthesis by 3, not just the first one.

So, the correct expansion would be

[tex] 3(2x-5) = 3\cdot 2x - 3 \cdot (-5) = 6x-15 [/tex]

Leeza made an error she did not multiply 3 into the bracket correctly. Therefore, the solution to an equation is 4.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 4x=7+3(2x-5).

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 4x=7+6x-15

4x=6x-8

4x-6x= -8

-2x=-8

x=4

Leeza made an error she did not multiply 3 into the bracket correctly. Therefore, the solution to an equation is 4.

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x² + y² = 9 is the equation of a circle with center (0, 0) and radius 3.

This puts the vertices at (-3, 0), (3, 0), (0, -3), and (0, 3).

When is the tangent line vertical? when it passes through the x-axis.

Answer: (-3, 0), (3, 0)

i THINK its 2 1/2 ?????

The value of the expression 2d + 32 is 48 when d equals 8.

The student has provided an expression 2d + 32 and the value for d is given as 8. In order to evaluate the expression, we simply need to substitute the value of d into the expression.

Evaluating the expression:
2d + 32
= 2(8) + 32
= 16 + 32
= 48.

So, the value of the expression when d = 8 is 48.

Answer:

We know that, the frequency table consists of the number of times the number is appearing.

Also, 'relative frequency is the percent of the total of the frequencies'.

So, the corresponding frequency table is given by,

Points Scored                     Frequency                   Relative Frequency (%)

1                                                 1                                            4.17

3                                                2                                           8.33

5                                                1                                            4.17       

6                                                1                                             4.17

7                                                2                                            8.33

8                                                1                                             4.17

9                                               2                                             8.33

10                                              6                                              25

11                                                1                                             4.17

12                                              2                                             8.33

13                                              2                                             8.33

14                                              2                                             8.33

As, the total of the frequency is 24. So, we get the relative frequency table above.

The relative frequencies of the given data are as follows:

Relative frequency is the proportion of the number of occurrences of a particular value to the total number of values.

The frequency of each value are:

The total number of values = 24

The relative frequency of each value are:

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Answer: c. ;]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

Answer:  

There will be 213 songs in each group.

Step-by-step explanation:

Suppose, the number of songs in each group is  [tex]x[/tex]

As he has 4 different groups of songs, so the total number of songs in all 4 groups will be:  [tex](4*x)= 4x[/tex]

Given that, the mp3 player has a total of 852 songs. So, the equation will be........

[tex]4x=852\\ \\ x=\frac{852}{4}=213[/tex]

So, there will be 213 songs in each group.

Answer:

Domain = R

Range =(0,infinity)

Step-by-step explanation:

Given a function as

y = 4(1/3)^x

The function does not have x or y in the denominator or any square root sign.

Hence we can assign any values to x.

Domain = R = Set of all real numbers = (-infinity, infinity)

Let us consider range.

We find that 4(1/3)^x is a multiple of 4 and powers of 1/3

Since power of 1/3 is always positive, y cannot take any negative value.

When x=0 y =4.

When x tends to -infinity, y tends to 0

So y cannot take the value 0 except at -infinity.

Range =(0,infinity)

Answer : (-∞,-1) U  (-1, 1)

We need to find  the interval(s) over which the function is increasing

We look at the intervals of x  where the graph is increasing

Increasing interval of the graph is the part where the graph goes up.

At first  the graph starts increasing and it increases till x=-1

So the first increasing interval is -infinity to -1 . We write it as (-∞,1)

Now, we look at the part where the graph changes direction

In the middle  inverted U shaped graph , the graph starts increasing at x=-1  and increases till it changes direction. The graph is increasing till x=1

so second increasing interval is x=-1  to 1. we write it as (-1,1)

Now combine both intervals by a 'U' union

(-∞,-1) U  (-1, 1)

The  interval(s) over which the function that is increasing is  (-∞,-1) U  (-1, 1)

From the question, One need to find  the interval(s) over which the function is increasing

Since intervals of x  where the graph is increasing Increasing interval of the graph is the part where the graph goes up.

At first  the graph starts increasing and it increases till x=-1, So the first increasing interval is -infinity to -1 . We write it as (-∞,1). So, one look at the part where the graph changes direction

In the middle  inverted U shaped graph , the graph starts increasing at x=-1  and increases till it changes direction. The graph is increasing till x=1

Since the  increasing interval is x=-1  to 1. one then need to write it as (-1,1)

So, The function is increasing for all values of x in the open interval from negative infinity to negative 1, excluding -1, and also in the open interval from -1 to 1, excluding both -1 and 1."

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Slope intercept form: y=3/4 - 3

slope:3/4

Y-intercept: -3

Because you subtract 4y from both sides to get it on the other side of the equation. You don’t want it to be 4y=3x-12 though so you would divide both sides by 4 which would give you y=3/4x-3. I hope this is right and it helps

675 : 5 = 135

135 : 5 = 27

27 : 3 = 9

9 : 3 = 3

3 : 3 = 1

675 = 5 · 5 · 3 · 3 · 3 = 5² · 3³

Answer:

Option B) 5    

Step-by-step explanation:

We are given the following information:

A scatter plot is given which shows the number of hats and scarves each knitter sold at a knitting show.

In the scatter plot the x-axis shows the number of hats sold and the y-axis shows the number of scarves sold.

We have to find the number of hats sold by the knitter when he sold 8 scarves.

In order to find this we have to find the x-values corresponding to the y-values of 8 scarves in the scatter plot.

Corresponding to 8 on y-axis we have a point that have a corresponding value of 5.

Hence, 5 hats were sold by the knitter when he sold 8 scarves.

Option B) 5 is the correct answer.

The scatter plot that shows the number of hats and scarves each knitter sold at a knitting show is Option B) 5    

To find the number of hats sold when 8 scarves were sold, you can look at the scatter plot and observe that there is a data point on the plot where the y-value (number of scarves) is 8, and the corresponding x-value (number of hats) is 5.

In the scatter plot the x-axis shows the number of hats sold and the y-axis shows the number of scarves sold. In order to find this we have to find the x-values corresponding to the y-values of 8 scarves in the scatter plot.

Hence, 5 hats were sold by the knitter when he sold 8 scarves.

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The previous year's salary is x.

This year's salary is x + 3000.

12% of this year's salary is $4200.

12% * (x + 3000) = 4200

0.12(x + 3000) = 4200

x + 3000 = 35,000

x = 32,000

Answer: Her salary in the previous year was $32,000.