The system of equations shown is solved using the linear combination method

StartLayout 1st row 1st column 6 x minus 5 y = negative 8 right-arrow 2nd column 6 x minus 5 y = negative 8 right-arrow 6x minus 5 y = negative 8 2nd row 1st column negative 24 x + 20 y = 32 right-arrow one-fourth (negative 24 x + 20 y = 32) right-arrow negative 6 x + 5 y = 8 with Bar Underscript 3rd row 3rd column 0 = 0 EndLayout

What does 0 = 0 mean regarding the solution to the system?

The vertex of the function is a minimum and the coordinate of the vertex of the function is (0.2, -2.4)

The function is given as:

f(x) = 5x^2 + 2x - 3

Expand the function

f(x) = 5x^2 + 5x - 3x - 3

Factorize the function

f(x) = (5x - 3)(x + 1)

Set the function to 0

(5x - 3)(x + 1) = 0

Solve for x

x = 3/5 and x =-1

Hence, the x-intercept is 3/5 and -1

The vertex of the function is a minimum.

This is so because the leading coefficient of the function is positive

Here, we have:

f(x) = 5x^2 + 2x - 3

Differentiate and set to 0

10x + 2 = 0

Solve for x

x = -0.2

Substitute x = -0.2 in f(x) = 5x^2 + 2x - 3

f(0.2) = 5(0.2)^2 + 2(0.2) - 3

Evaluate

f(0.2) = -2.4

Hence, the vertex of the function is (0.2, -2.4)

To do this, we simply plot the x-intercept and the vertex.

And then connect the points

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The coordinate of P is (A) ( 40, 96).

To find What are the x- and y- coordinates of point p on the directed line segment from K to J:

It can be seen from the figure the coordinates of K and J:

The coordinates of P can be determined as:

[tex]x=\frac{m}{m+n} (x_{2}-x_{1})+x_{1} } \\y=\frac{m}{m+n} (y_{2}-y_{1})+y_{1} } \\[/tex]

So, as the P point divides the line into three-fifths of the length,

Which gives the ratio as 3: 2.

m:n = 3:2

Therefore, the coordinate of P is (A) ( 40, 96).

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The complete question is shown below:

What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of the line segment from K to J?

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

(A) (40, 96)

(B) (85, 105)

(C) (80, 104)

(D) (96, 72)

Answer:

This is the answer of this question. Hope it helps.

The two numbers are 68 and 55.

Given that the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343.

We need to find the numbers,

Let's call the two numbers x and y. According to the given information, we have the following two equations:

x + y = 123 (The sum of the two numbers is 123)

x + 5y = 343 (When the larger number is added to 5 times the smaller, the sum is 343)

Now, we can solve these two equations simultaneously to find the values of x and y.

Let's rearrange equation 1 to express x in terms of y:

x = 123 - y

Substitute this value of x into equation 2:

(123 - y) + 5y = 343

Now, solve for y:

123 + 4y = 343

4y = 343 - 123

4y = 220

y = 220 / 4

y = 55

Now that we have the value of y, we can find the value of x using equation 1:

x = 123 - y

x = 123 - 55

x = 68

So, the two numbers are 68 and 55.

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Considering the definition of scale, you obtain:

A map is the conventional graphical representation of a portion of the earth or another celestial body that shows the size and position of elements of the landscape according to the selected scale and projection. That is, a map is a representation of a place, at a size smaller than the actual size.

The scale of a cartographic representation, or map scale (m), is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map. In general, it is also defined as the ratio of the lengths of a linear element in the plane and its representation on the terrestrial reference surface.

That is, the scale of the map is defined as the proportionality relationship that exists between a distance measured on the ground and its corresponding measurement on the map.

A map has a scale of 1:5000000000. This indicates that 1 unit on the map is equivalent to 5,000,000,000 in reality.

You know that the road on the map is 10 cm or 0.0001 km long (knowing that 1 km= 100,000 cm).

Then you can apply the following rule of three: if by definition of scale 1 km on the map is equivalent to 5,000,000,000 km in reality, 0.0001 km on the map is equivalent to how much distance in reality?

[tex]real length of the road=\frac{0.0001 kmx 5,000,000,000 km }{1 km}[/tex]

real length of the road= 500,000 km

Finally, the real length of the road is 500,000 km.

You know that the area of a farm of the map is 6 cm square, 0.0006 m sr 0.00000006 hectares (knowing that 1 cm square= 0.0001 m square and 10,000 m square= 1 hectare).

Then you can apply the following rule of three: if by definition of scale 1 hectare on the map is equivalent to 5,000,000,000 hectares in reality, 0.00000006 hectares on the map is equivalent to how much area in reality?

[tex]real area of the farm=\frac{0.00000006 hectaresx 5,000,000,000 hectares }{1 hectare}[/tex]

real area of the farm= 300 hectares

Finally, the real area of the farm is 300 hectares.

In summary, you get:

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The graph of the function has no asymptotes.

The function is given as:

c(t) = 5t - t² + 1

When t = 1, 2, 5, 10;

We have:

c(1) = 5(1) - 1² + 1 = 5

c(2) = 5(2) - 2² + 1 = 7

c(5) = 5(5) - 5² + 1 = 1

c(10) = 5(10) - 10² + 1 = -49

So, the table of values is

t        c(t)

1         5

2        7

5        1

10      -49

See attachment for the graph of the function

The domain

From the question, we understand that t represents time.

So, the domain is 0 ≤ t ≤ 5.2

The range

From the graph, the maximum of the graph is 7.25

So, the range is 0 ≤ f(t) ≤ 7.25

Asymptotes

From the graph, we can see that the graph has no asymptotes.

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a. 1/ 15

b. 76/ 15

c. 1/12

a. 2/5 divided by 6

= 2/ 5 ÷ 6

= 2/ 5 ÷ 6/ 1

Take the inverse of the dividing fraction, we have

= 2/ 5 × 1/ 6

Multiply through

= 2/30

= 1/ 15

b.  3 and 1/3 times 5 and 2/5

= 3 + 1/ 3 × 5 + 2/ 5

From the knowledge of BODMAS, we multiply first

= 3 + 5/3 + 2/ 5

Find the LCM

= 45 + 25 + 6/ 15

= 76/15

c. 1/4 + 1/3 -1/2

Let's find the LCM

= 3 + 4 - 6 / 12

Add first

=  7 - 6/ 12

= 1/ 12

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The geometric sequence when the first term is 1/5 and the common ratio is 5 is; f(n) = f(n-1) . 5.

The geometric sequence described in the task content is one whose first term is; f(1) = 1/5.

Additionally, it follows from convention that the recursive function for a geometric sequence is; a product of a previous term and the common ratio.

Hence, we have; f(n) = f(n-1) . 5.

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Answer: 7 1/2 cups

Step-by-step explanation:

We first need to make both fractions have an equal denominator. Cross Multiply 3/4 and 1/10. You will end up with 30/40 and 4/40.

Next we divided 30 by 4, and we will end up with 7 1/2. 7 times 4 is 28, and half of 4 is 1/2, or in this case 2/10. John can fill 7 and 1/2 cups of orange juice.

The value of x according to the secant-secant theorem is 4

Secant-secant theorem states if two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant.

Using the equation below;

6(x+6) = 5(5+x+3))

Expand the expression
6x+36 = 5(x+8)

6x + 36 = 5x + 40

Subtract 5x from both sides

6x-5x +36 = 40

Subtract 36 from both sides

6x - 5x = 40 - 36

x = 4

Hence the value of x according to the secant-secant theorem is 4

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Answer:

The value of x according to the secant-secant theorem is 4

Step-by-step explanation:

The angles exist in the exact place in both triangles. So we will obtain the decision that they exist different.

Therefore, the the measure of their angles exists different.

No, because the measure of their angles exists different. If the angle measurements existed the exact, they would have been equivalent.

You see in the smaller triangle, the given angle exists at 55 degrees while in the bigger triangle the given angle exists at 30 degrees.

The angles exist in the exact place in both triangles. So we will obtain the decision that they exist different.

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Answer:

Infinite

Step-by-step explanation:

12x 8 = 12x 8

Infinitely many solutions, as left side = right side.

The area of ​​the figure Magda shaded with side lengths of 1 and √2 centimeter is equal to 1.21 cm².

Mathematically, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

In order to calculate the area of ​​the figure Magda shaded with side lengths of 1 and √2 centimeter, we would determine the area of ​​each triangle as follows:

For triangle 1, we have:

Area = 1/2 × b × h

Area = 1/2 × 1 × 1

Area = 0.5 cm².

For triangle 2, we have:

Area = 1/2 × b × h

Area = 1/2 × √2 × 1

Area = 0.71 cm².

Total area = Area of triangle 1 + Area of triangle 2

Total area = 0.5 + 0.7

Total area = 1.21 cm².

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Complete Question:

Magda used a 1 cm square grid to draw the shaded figure, using right triangles. 1 cm 3 cm √2 cm 1 cm 1 cm what is the area of ​​the figure Magda shaded?​

Answer: Y = 4x + 2

(It would be either the third or fourth choice since they are the same, one of them must be mistaken)

Step-by-step explanation:

Given information

(x₁, y₁) = (1, 6)

(x₂, y₂) = (0, 2)

Find the slope through the formula

[tex]Slope~=~\frac{y_2~-~y_1}{x_2~-~x_1}[/tex]

[tex]\Large Slope~=~\frac{2~-~6}{0~-~1}[/tex]

[tex]\Large Slope~=~\frac{-4}{-1}[/tex]

[tex]\Large Slope~=~4[/tex]

Substitute values into the linear form

Equation: y = mx + b

Point (0, 2)

y = mx + b

(2) = (4) (0) + b

2 = 0 + b

b = 2 - 0

b = 2

Therefore, the equation is [tex]\Large\boxed{y=4x+2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

y = 4x+2

Step-by-step explanation:

The first step is to find the slope

m = ( y2-y1)/(x2-x1)

m = ( 2-6)/(0-1)

    = -4/-1

   = 4

The slope intercept form of the equation is

y = mx+b  where m is the slope and b is the y intercept

y = 4x+b

The y intercept is where x is equal to 0

The y intercept is 2

y = 4x+2

Answer:

615.7536

Step-by-step explanation:

Remember the equation for finding the area of a circle is:

A=π[tex]r^2[/tex]

Just substitute in your radius for r and solve:

A=3.1416*[tex]14^2[/tex]

A=3.1416*196

A=615.7536

The range of the means is 0.5

Mean of S1

= 5 + 6+ 6+ 2

= 19/4

= 4.75

Mean of S2

= 4 + 8 + 4 + 3

= 19/4

= 4.75

Mean of s3

= 4 + 2 + 6+ 5

= 17/4

= 4.25

Range of sample means = 4.75 - 4.25

= 0.5

c. the true statements here is that

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The solutions to the given quadratic equation are as follows:

x = 1.10, x = 10.9.

A quadratic function is given according to the following rule:

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

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

For this problem, the equation in item D is:

-x² + 12x - 12 = 0

x² - 12x + 12 = 0

Hence the coefficients are:

a = 1, b = -12, c = 12.

Then the solutions to the equation are found as follows:

The solutions are:

x = 1.10, x = 10.9.

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The volume of the cylinder and the cone is equal

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

where

r is the radius

h is the height

For the cylinder

r = 8/2 = 4 in

h = 5

Substitute

V = π(4)²*5
V = 80π cubic inches

For the cone

r = 4 in

h = 15in

Substitute

V = 1/3πr^2h

V = 1/3(π)(4)^2 * 15

V = 80π cubic inches

Hence the volume of the cylinder and the cone is equal

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Answer:

  5.09 years

Step-by-step explanation:

The formula for the future value of an investment can be filled with the given values and solved for time.

The future value of a one-time investment P earning interest at annual rate r compounded n times per year for t years is ...

  FV = P(1 +r/n)^(nt)

Using this formula with the given values, we have an expression for t:

  7300 = 5000(1 +0.075/4)^(4t)

Dividing by 5000, we have ...

  1.46 = 1.01875^(4t)

Taking logarithms gives the linear equation ...

  log(1.46) = 4t·log(1.01875)

Dividing by the coefficient of t, we find ...

  t = log(1.46)/(4·log(1.01875)) ≈ 5.0929

The time required for the value to reach $7300 is about 5.09 years.

__

Additional comment

The attachments show different calculator solutions. They give the same value for t.

The TVM Solver uses P/Y = 1 so the value of N is in years.

The graphical solution recasts the problem to f(x) = 0. It finds the value of t that makes the difference between the investment value and $7300 be zero.

Answer:

F

Step-by-step explanation:

There are 6 digits in the repeating pattern.

279 / 6 = 46.5 remainder 3.

we care about the remainder as this is how many digits in. it is the 3rd digit in so is 3.

Using binomial distribution, the probability of

a. 5 will still be with the company after 1 year is 28%.

b. at most 6 will still be with the company after 1 year is 89%.

The probability of a new employee in a fast-food chain still being with the company at the end of the year is given to be 0.6, which can be taken as the success of the experiment, p.

We are finding probability for people, thus, our sample size, n = 8.

Thus, we can show the given experiment a binomial distribution, with n = 8, and p = 0.6.

(i) We are asked for the probability that 5 will still be with the company.

Thus, we take x = 5.

P(X = 5) = (8C5)(0.6⁵)((1 - 0.6)⁸⁻⁵),

or, P(X = 5) = (56)(0.07776)(0.064),

or, P(X = 5) = 0.27869184 ≈ 0.28 or 28%.

(ii) We are asked for the probability that at most 6 will still be with the company.

Thus, our x = 6, and we need to take all values below it also.

P(X ≤ 6)

= 1 - P(X > 6)

= 1 - P(X = 7) - P(X = 8)

= 1 - (8C7)(0.6)⁷((1 - 0.6)⁸⁻⁷) - (8C8)(0.6)⁸((1 - 0.6)⁸⁻⁸)

= 1 - 8*0.0279936*0.4 - 1*0.01679616*1

= 1 - 0.08957952 - 0.01679616

= 0.89362432 ≈ 0.89 or 89%.

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The provided question is incomplete. The complete question is:

If the probability of new employee in a fast-food chain still being with the company at the end of 1 year is 0.6, what is the probability that out of 8 newly hired people,

a. 5 will still be with the company after 1 year?

b. at most 6 will still be with the company after 1 year?

If the probability of obtaining success is 0.3 and the value of n is 9 then the probability at the value of x be 3 is 0.3811.

Given that the value of n is 9 and the value of p is 0.3.

We are required to find the probability when the value of x is equal to 3.

Probability is the calculation of chance of happening an event among all the events possible.It lies between 0 and 1.

Probability=Number of items/total items.

Binomial probability is basically the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes.

[tex](a+b)^{n}[/tex]=[tex]nC_{0}a^{0} b^{n-0} +nC_{1}a^{1} b^{n-1} +................nC_{n}a^{n} b^{0}[/tex]

We have to find the value when n=9, p is 0.3 and r=3.

=[tex]9C_{3} (0.3)^{3} (1-0.3)^{6}[/tex]

=9!/3!6!*0.027*0.16807

=84*0.00453789

=0.381182

Hence if the probability of obtaining success is 0.3 and the value of n is 9 then the probability at the value of x be 3 is 0.3811.

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Step-by-step explanation:

1500*.02*1=30

50*12*1=60

g(x)=50(12x) good

Answer:

52º, 128º

Step-by-step explanation:

8. Because ∠6 is an opposite angle to ∠5, ∠6=∠5=52º;

9. Because line a//line b, ∠6=∠4=52º, so ∠7=180º–52º=128º

Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

What does this problem give us:

What does this problem want us to find:

Let's solve:

           ⇒ by the vertical angle theorem is equal in measure to ∠5

               ⇒ ∠6 = 52°

           ⇒ lines a and b are parallel

               ⇒ the corresponding angles on both lines formed by the

                    transversal are equal

                         i.e. m∠2 = m∠3, m∠7 = m∠8

           ⇒ ∠8 is on a straight line with ∠6

                      [tex]\hookrightarrow angle8 +angle6 = 180\\\hookrightarrow angle8 + 52 = 180\\\hookrightarrow angle8 =128[/tex]

           ⇒ since m∠8 is equal to m∠7

              ⇒ m∠7 = 128

Definitions

Answer:

Hope that helps!

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Based on the dimensions of the support for the slides, the missing length and slide length is 15 yards.

The number of 3-yard straight pieces needed is 15 straight pieces.

The length of a single slide is the hypotenuse of the triangle which can be found using the Pythagoras theorem as:

Hypotenuse² = 9² + 12²

Hypotenuse = √(81 + 144)

= 15 yards

If a single slide is 15 yards, then 3 slides would be:

= 15 x 3

= 45 yards

The number of 3-yard straight pieces needed are:

= 45 / 3

= 15 pieces

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Answer: 39

Explain:

The length of each slanted area for each slide is 15 yards. The length of each straight piece is 3 yards. So, the number of straight pieces needed for 15 yards is 15 - 3, or 5. There are two slanted areas on each slide.

The number of straight pieces required for the flat area at the bottom of each slide is 3.

Adding them up, the total number of straight pieces required for one slide is 5 + 5 + 3, or 13. Because there are three slides, the total number of straight pieces needed is 13 • 3, or 39

Vince needs 39 straight pieces to build the three slides.

From ED

Step-by-step explanation:

TSA of cylinder = 2πr (h + r)

according to the question

height = radius

then,

TSA = 2πr (r + r)

2464=2 × 3.1415×r ×2r

2464/4 ×3.1415 = r×r

196.08 = r^2

r = 14.00

r = 1 4 cm

We know,

volume = 2πr ^2 ×h

=2×3.1415×14×14×14 (h=r)

=17240.552 cm^3

Answer:

8620.5 cm³

Step-by-step explanation:

h = r

SA = 2πrh + 2πr²

Since h = r, we can substitute h with r.

SA = 2πr² + 2πr² = 4πr²

4πr² = 2464 cm²

r = 14 cm

V = πr²h

r = h = 14 cm

V = π(14 cm)²(14 cm)

V = 8620.5 cm³

======================================================

Explanation:

To go from gallons to fluid ounces (abbreviation fl oz), we multiply by 128

For example, 2 gallons becomes 2*128 = 256 fl oz as shown in the table.

Another example: 3 gallons = 3*128 = 384 fl oz.

Therefore, 6 gallons would be 6*128 = 768 fl oz.

To go in reverse, from fl oz to gallons, we divide by 128.