5x-y=-6
y=-7x+6

find y and x and show work

For the function,

F(x)  = (x² + 11x +28)/(x² + 8x + 15) limit doesn't exist at x = -5 so it is dis-continuous at that point.

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  = (x² + 11x +28)/(x² + 8x + 15)

To check whether it is continuous at x = -5

First taking LHL,

\(\lim_{h \to \ 0}\) [(-5-h)² + 11(-5 -h) +28]/[(-5 -h)² + 8(-5 -h) + 15]

It is approaching at negative infinity

Now, taking RHL

\(\lim_{h \to \ 0}\)  [(-5+h)² + 11(-5 +h) +28]/[(-5 +h)² + 8(-5+h) + 15]

Again, It is approaching at negative infinity

Hence, here limit doesn't exist so it is not continuous at x = -5

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Answer:

8

Step-by-step explanation:

3/4 cup leaves 1/4 cup from each cup

1/4+1/4+1/4=3/4

so it would be 3/4+3/4+3/4+3/4+3/4+3/4+3/4+3/4=8 cups

Check the picture below, so Francesca's throw looks more or less like that, and it hits the ground when h(t) = 0

\(\stackrel{h}{0}=1+14t-5t^2\implies 5t^2-14t-1=0 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{5}t^2\stackrel{\stackrel{b}{\downarrow }}{-14}t\stackrel{\stackrel{c}{\downarrow }}{-1}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}\)

\(t= \cfrac{ - (-14) \pm \sqrt { (-14)^2 -4(5)(-1)}}{2(5)} \implies t = \cfrac{ 14 \pm \sqrt { 196 +20}}{ 10 } \\\\\\ t= \cfrac{ 14 \pm \sqrt { 216 }}{ 10 }\implies t=\cfrac{ 14 \pm 6\sqrt { 6 }}{ 10 }\implies t=\cfrac{ 7 \pm 3\sqrt { 6 }}{ 5 }\implies t\approx \begin{cases} ~~ 2.870~\checkmark\\ -0.070 \end{cases}\)

so there are two valid values, however we can't use the negative one, since the phenomena is for seconds and we can't have negative seconds in this case.

Answer:

she spent $1782

Step-by-step explanation:

first we have to find out her total money then minus 990

to get that 990 /5 then multipliedby 6 is 1188

1188 over 3 then times by 7 is 2772

2772 is the total amount of money she had. minus what she had left which is 990 she has spent 1782 dollars

movies 1.75 each

games 5.75 each

14)The sum of the tangent and the sine of the angle is obtained as 1.21.

15)The area of the segment is 95.6 m^2 while the perimeter of the segment is 11.047 m.

16)The angle opposite the largest side is  130°.

The trigonometric ratios are the ratios that are designated as cos, tan and sine. It is important to note that the  trigonometric ratios are particular to the right angled triangle. The meaning of the right angle triangle is that one of the angles in the triangle is about 90 degrees.

14)) We can find the hypotenuse by the use of the Pythagoras theorem that is used to find the parts of the right angle triangle.;

a = √2^2 + 3^2

a = √ 4 + 9

a = 3.6

We know that;

tan θ = 2/3 = 0.66

sin θ = 2/3.6 = 0.55

Then;

tan θ + sin θ

0.66 + 0.55

= 1.21

We can see by the use of the trigonometric ratios that we would obtain the sum of the sine and the tangent as 1.21.

15)

The area of the segment is obtained as;

Area of the triangle;

1/2r^2 sinθ

r= radius of the circle

θ = angle of inclination

1/2 * (10)^2 * sin 60

= 43.3

Area of the sector;

60/360 * 3.142 * (10)^2

= 52.3

Therefore the area of the triangle is;

43.3 +  52.3 = 95.6 m

b)The perimeter of the segment;

(2πr * θ/360) + 2rsin(θ/2)

(2 * 3.142 * 60/360) + (2 * 10 * sin (60/2))

1.047 + 10

= 11.047 m

16)

Using;

c^2 = a^2 + b^2 - 2abcos C

20^2 = 13^2 + 9^2 - 2(13 * 9) cos C

400 = 250 - 234cosC

400 - 250 = - 234cosC

150 =  - 234cosC

Cos C = -(150/234)

C = Cos-1-(150/234)

C = 130°

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Answer:

1.2

Step-by-step explanation:

Output of f, which also means f(x), when x = -6 is 1.2.

Using the graph given, this implies that, when x = -6, the corresponding value of f(x) will give us 1.2.

Thus:

f(-6) = 1.2 =>> (-6, 1.2).

Answer:

1/6 chance

Step-by-step explanation:

There is only one number on the die, 6.

There are 6 faces on the die so there is \(\frac{1}{6}\) chance rolling a 6.

Answer:

1/6

Step-by-step explanation:

A six sided die is numbered 1 through 6. Since we're looking for the probability that the outcome is greater than 5, only one number suits that, which is 6.

Only 1 out of the 6 numbers work so therefore the probability of it happening is 1/6

Answer:

68%

Step-by-step explanation:

Given that:

Mean speed (m) = 46

Standard deviation (s) = 13

Approximately what percentage of vehicle speeds were between 33 and 59 mph

Obtain the Zscore for P(Z < x) for both values and subtract :

For x = 33

Zscore :

Z = (x - m) / s

Z = (33 - 46) / 13 = - 1

p(Z < - 1) = 0.15866 ( Z probability calculator)

For x = 59

Zscore :

Z = (x - m) / s

Z = (59 - 46) / 13 = 1

p(Z < 1) = 0.84134 ( Z probability calculator)

Hence, 0.84134 - 0.15866 = 0.68268 = 0.68

0.68 * 100% = 68%

Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

Answer:3243

Step-by-step explanation:

The dollar value of total revenue at each price is $\(0\), $\(10\), $\(12\), $\(12\), $\(10\), and $\(6\). Total revenue will be the greatest at a price of $\(4\), with \(3\) units sold.

To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:

Price: $\(6\)

Quantity: \(0\)

Total Revenue: $\(6 \times 0\) = $\(0\)

Price: $\(5\)

Quantity: \(2\)

Total Revenue: $\(5 \times 2\) = $\(10\)

Price: $\(4\)

Quantity: \(3\)

Total Revenue: $\(4 \times 3\) = $\(12\)

Price: $\(3\)

Quantity: \(4\)

Total Revenue: $\(3 \times 4\) = $\(12\)

Price: $\(2\)

Quantity: \(5\)

Total Revenue: $\(2 \times 5\) = $\(10\)

Price: $\(1\)

Quantity: \(6\)

Total Revenue: $\(1 \times 6\) = $\(6\)

To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $\(3\), and the corresponding quantity sold is \(4\) units.

Therefore, at a price of $\(3\), the total revenue will be the greatest, with \(4\) units sold.

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Answer:

To calculate the periodic interest rate for an account billed monthly with an APR of 21.99%, we need to divide the APR by the number of billing periods in a year.

Since there are 12 months in a year for a monthly billing cycle, we can divide 21.99% by 12 to get the monthly periodic interest rate.

Periodic Interest Rate = APR / Number of Billing Periods in a Year

Periodic Interest Rate = 21.99% / 12

Periodic Interest Rate = 1.8325%

Rounding this answer to the nearest hundredth, we get a periodic interest rate of 1.83%.

According to basic postulates of Euclidean geometry, Option A - Any straight line segment can be extended indefinitely and Option D - A straight line segment can be drawn between any two points can apply.

"Euclidean geometry is the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid"

As per the five basic postulates of Euclidean geometry

Hence, option A and D can apply.

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Answer:

Options A and D

Step-by-step explanation:

that's what I got

Answer:

704

Step-by-step explanation:

54 x 12 = 648

648 + 56  = 704

Hope that helps!

Equation: 54 · 12 + 56

Solution: 704

Explanation: Using the Order of Operations (PEMDAS), we know that, in this equation, our first step is to multiply...

1. 54 · 12 = 648

Then, we can add.

2. 648 + 56 = 704

There!!

The compound interest and future value of the given condition will be 30.20 and 770.20, respectively.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Principal 740 Rate 4% Compounded Time Daily for year 1.

Then the rate and time are given as,

r = 0.04 / 365

n = 365

Then the future value is given as,

A = 740 (1 + 0.04 / 365)³⁶⁵

A = 740 x 1.0408

A = 770.20

Then the interest is given as,

I = 770.20 - 740

I = 30.20

The compound interest and future value of the given condition will be 30.20 and 770.20, respectively.

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The amount of pesos that you need to purchase $100,000 is 793,651.

A buy is when something is obtained in exchange for some type of payment, such as products or services. The usual forms of payment are cash or credit (to be paid later). A purchase could also be made in exchange for taking on an obligation or as part of a barter exchange where various non-cash assets are traded. However, when a noun form is required, you should use "buy," as in: You made a wise purchase when you bought petrol before the price increased. Use "buy" for straightforward activities and "purchase" for more formal exchanges of money for products.

Solve: 100,000/.126 = 793,650.79

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The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

As we have given about the Euclidean and analytical geometry.

Without using any numerical measurements, we have investigated the connections between points, lines, and planes in Euclidean geometry.

In analytical geometry, we've looked at how the locations of points in a Cartesian coordinate system related to algebra and geometry.

The analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

If the Euclidean geometry can be more advantageous in particular circumstances

Example: If using terrain or building chart),

Thus, the analytical approach is preferable because the primary issue with Euclidean geometry is that it is not enough to support all of the theorems that he claims to establish.

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To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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System of Equations

Given the system of equations:

2x - y = 7

x + y = 2

It's required to determine if the ordered pair (5, 3) is a solution to the system.

If (5, 3) is a solution to the system, then substituting x = 5 and y = 3 should satisfy both equations.

Substituting:

2(5) - 3 = 7

5 + 3 = 2

Operating:

10 - 3 = 7

5 + 3 = 2

7 = 7

8 = 2

The first equation is true, but the second is not, thus (5, 3) is not a solution to the system.

Answer:

Bruh, easy. Divide -4 by 2 and you get -2. So, x = -2.

Why you not know that?!

Answer:

x = -2

Step-by-step explanation:

2x = -4 ( divide by 2)

x = -2

Answer:

which class Of question is this

The equation to the tangent line to \(y = e^{(x^2)}\) at point (1,0) is given by:

y = 2e(x - 1).

Supposing that we have a function f(x) at a point \((x_0, y_0)\), the equation of the tangent line to this function is given by:

\(y - y_0 = f^{\prime}(x_0, y_0)(x - x_0)\)

In which f' is the derivative.

In this problem, the function is:

\(f(x) = e^{(x^2)}\)

Applying the chain rule, the derivative is:

\(f^{\prime}(x) = 2xe^{(x^2)}\)

At x = 1, the derivative is:

\(f^{\prime}(1) = 2(1)e^{((1)^2)} = 2e\)

Hence the tangent line at point (1,0) is given by:

y = 2e(x - 1).

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Answer:

-19

Step-by-step explanation:

Answer:

936

Step-by-step explanation:

18*24=432

24*7=168

30*7=210

18*7=126

432+168+210+126

=936

Answer:

C

Step-by-step explanation:

Non proportional graphs are non-linear and don’t go (necessarily) through 0,0

Proportional graphs are linear and always (eventually) cross through with 0,0

Answer:

2.29 ft of side length and 1.14 height

Step-by-step explanation:

a) Volume V = x2h, where x is side of square base and h is hite.

Then surface area S = x2 + 4xh because box is open.

b) From V = x2h = 6 we have h = 6/x2.

Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.

We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.

Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.

To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.

And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2

The box dimensions that minimize the amount of material used are; side length of base = 3.30 ft and height = 1.65 ft

a) We know that a box has length, width and height and so volume of a box is;

V = L × W × H

Now, we are told the base of the box is square and if we label it x, then we have to function that models the volume as;

V = x²h

where x is side of square base and h is height.

Thus surface area function is;

S = x² + 4xh

b) We are told that the volume is 18 ft³ and so;

x²h = 18

Thus;

h = 18/x².

Put 18/x² for h in the surface area function to get: S = x² + 4x(18/x²)

S = x² + 72/x.

To get minimum, we have to find derivative of S. Thus;

S' = 2x - 72/x² = 0,

Thus;

2x³ = 72

x³ = 72/2

x³ = 36

x = 3.3 ft

Thus;

h = 18/3.3²

h = 1.65 ft

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