match the information with the correct equation

Answer:

f(- 4) = 44 , g(5) = - 21

Step-by-step explanation:

to evaluate f(- 4) substitute x = - 4 into f(x)

f(- 4) = 2(- 4)² - 3(- 4) = 2(16) + 12 = 32 + 12 = 44

to evaluate g(5) substitute x = 5 into g(x)

g(5) = - 4(5) - 1 = - 20 - 1 = - 21

Answer:

[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]

Step-by-step explanation:

As we know that

The standard equation of a parabola with vertex at point (h,k) is given by:

[tex]y = a(x-h)^2 + k[/tex]

where (h,k) is the vertex

and "a" is a coefficient that determines the direction and shape of the parabola.

We know that the vertex of our parabola is (-2, 6),

so we can substitute those values into the equation to get:

[tex]y = a(x + 2)^2 + 6[/tex]

Now finding a.

Since the parabola passes through point (-4, -5). Substituting these coordinates into the equation, we get:

-5 = a(-4 + 2)^2 + 6

-5 =a(-2)^2+6

-5=4a +6

-5-6=4a

4a=-11

a =- 11/4

Substituting the value of an equation second, we get

[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]

Therefore, the equation of the parabola with a vertex at (-2, 6) and passing through (-4, -5) is y =

[tex] \frac{-11}{4} (x + 2)^2 + 6[/tex]

Answer:

[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]

Step-by-step explanation:

The vertex form of a parabola is:

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

Given the vertex is at (-2, 6), substitute h = -2 and k = 6 into the equation:

[tex]y=a(x-(-2))^2+6[/tex]

[tex]y=a(x+2)^2+6[/tex]

To find the value of a, substitute the point (-4, -5) into the equation and solve for a:

[tex]\begin{aligned}-5&=a(-4+2)^2+6\\-5&=a(-2)^2+6\\-5&=4a+6\\-5-6&=4a+6-6\\-11&=4a\\\dfrac{-11}{4}&=\dfrac{4a}{4}\\-\dfrac{11}{4}&=a\\a&=-\dfrac{11}{4}\end{aligned}[/tex]

Substitute the found value of a back into the equation:

[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]

Therefore, the equation of a parabola with a vertex at (-2, 6) and that passes through the point (-4, -5) is:

[tex]\boxed{y=-\dfrac{11}{4}(x+2)^2+6}[/tex]

1.) The scale factor = 4

The perimeter ratio = 1:3

The area ratio = 1:16

To calculate the scale factor of the given shapes, the formula that should be used would be ;

Scale factor = Bigger dimensions/ Smaller dimensions

Length of the bigger rectangle (B) = 16

Length of the smaller rectangle (A) = 4

The scale factor = 16/4 = 4

The perimeter = 2(l+w)

length B = 16

width B = 8

perimeter B = 2(16+8)

= 2(24) = 48

Length A = 4

width A = 2

perimeter A =2(4+2)

= 16

The perimeter ratio = A:B = 16:48 = 1:3

Area = length×width

length A = 4

width A = 2

Area A = 4×2 = 8

length B = 16

width B = 8

area B = 8×16= 128

Area ratio of A:B = 8:128 = 1:16

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The solution to the system of equations is (d) More than 1 solution

From the question, we have the following parameters that can be used in our computation:

3y-12x=18

2y-8x=12

Using the graphing function on a calculator, we have the solution to be

Infinite many solutions

This is so because the equations 3y-12x=18 and 2y-8x=12 are equivalent equations

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Answer: The slope is -5/4

m=-5/4

The length of the arc FG is 12.56 units

Length of an arc is the distance that runs through the curved line of the circle making up the arc.

An arc is a cut out section of a circle. The circumference is the whole body of the circle.

The length of an arc is expressed as

(tetha))360 × 2πr

where r is the radius and tetha is the angle between the radii.

l = 72/360 × 2 × 3.14 × 10

l = 4521.6/360

l = 12.56 units

therefore the length of the arc FG is 12.56 units

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Based on the conditions, the correct statements are,

⇒  Bracelet B has 8 more letter beads than Bracelet A.

We have to given that;

Donovahn made two bracelets for a friend.

And, Each bracelet is made of 36 beads. Bracelet A contains 12 letter beads Bracelet B contains 20 letter beads.

Hence, We have;

Based on the information provided, we can say that Bracelet B contains more letter beads than Bracelet A.

Specifically, Bracelet B has 8 more letter beads than Bracelet A.

Thus, Based on the conditions, the correct statements are,

⇒  Bracelet B has 8 more letter beads than Bracelet A.

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The task here is to determined where the table given is a function. Thus we can state that the above table is NOT a function. This is called Non-Function Relation.

The table given above is suggestive of the relationship between the values of x and y given.

It may be inferred that x values are the input values while the y values are the output.

So the criteria for the values on the table to constitute a function is that each input value (x) must be associated with only one value of y.

From the table, it is clear to see that this rule if violated. You have the x value (-1) being associated with the y values of 2 and 4 respectively, hence, it is proper to conclude that the table is NOT  a function.

This is called a Non-Function Relation.

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The percentage error for each of the given situations are:

1) 23%

2) 21%

3) 11%

4) 16.67%

5) 43%

The formula for percent error is:

Percentage Error = ((Actual Number – Estimated Number)/ Estimated number) * 100%

1) Estimated Number = 2310

Actual Number = 3000

Thus:

Percent Error = (3000 - 2310)/3000 * 100%

Percent error = 23%

2) Estimated Number = 17600

Actual Number = 21300

Thus:

Percent Error = (21300 - 17600)/17600 * 100%

= 21%

3) Estimated Number = 4.5

Actual Number = 4

Thus:

Percent Error = (4 - 4.5)/4.5 * 100%

= 11%

4) Estimated Number = 15000

Actual Number = 12500

Thus:

Percent Error = (12500 - 15000)/15000 * 100%

= 16.67%

5) Estimated Number = 350

Actual Number = 200

Thus:

Percent Error = (200 - 350)/350 * 100%

= 43%

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If each tile cost $2 then the amount spend by  Nicole’s mother on tiles is $130

Given that Nicole‘s mother put tiles on a section of the kitchen floor.

The section included 5 rows with 13 tiles in each row

Each tile cost $2.

To find the total amount spend by Nicolas mother on tiles we have to find the number of tiles

Number of tiles =5×13

=65 tiles

Now let us find the amount

Total amount on tiles = 2×65

=$130

Hence, if each tile cost $2 then the amount spend by  Nicole’s mother on tiles is $130

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Answer:

A. 45(x+3)=60x

Step-by-step explanation:

The value of x in the triangle is 1/√3

We know that tan function is the ratio of opposite side and adjacent side

In triangle, for angle 60 degrees the opposite side is 1 unit

Adjacent side is x units

tan 60 = opposite side/adjacent side

√3= 1/x

We need to find value of x

Apply cross multiplication

x=1/√3

Hence, the value of x in the triangle is 1/√3

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The value of m in terms of other variables of the right angle triangle is: m = √(p² - n²)

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

However, it can also be written in the form of c² = a² + b²

From the given triangle, we can write as:

p² = m² + n²

m² = p² - n²

m = √(p² - n²)

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1. The lateral surface area of the prism is 200 units²

2. The lateral surface area of the cylinder is 125.6 cm²

The lateral surface area is the area of the lateral surface.

The lateral surface area of a prism is expressed as;

LSA = (a+b+c)h

or perimeter of the base × height

LSA = (6+12+7)8

= 25 × 8

= 200 units²

The lateral surface area of a cylinder

= 2πrh

r = 4cm and h = 5cm

LSA = 2 × 3.14 × 4 × 5

LSA = 40 × 3.14

= 125.6cm²

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The balance of the account after 20 years is given as follows:

A(20) = $13,268.58.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 6500, r = 0.036, n = 2, t = 20.

Hence the balance of the account after 20 years is given as follows:

A(20) = 6500 x (1 + 0.036/2)^(2 x 20)

A(20) = $13,268.58.

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The shapes that would be made if the figure is cut along the dotted line are  a right angled- triangle and a semi - circle.

Upon reviewing this shape, we observe that it is comprised of two distinct shapes: a right-angled triangle and a semicircle.

This means that if the figure was cut along the dotted lines that joined them, the shapes that would be made are the same shapes which are a right triangle and a semi - circle.

In conclusion, the shapes would be a semi - circle and right triangle.

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The results of factoring the polynomials are (x - 6)(x + 6), 3(x - 2)(x + 2), (x + 3)² and 4(x + 3)(x - 5)

First, we have

x² – 36

Applying the property of difference of squares, we have

(x - 6)(x + 6)

Next, we have

3x² - 12

Factor out 3

3(x² - 4)

Applying the property of difference of squares, we have

3(x - 2)(x + 2)

First, we have

x² + 6x + 9

Expand and factorize

x² + 6x + 9 = x² + 3x + 3x + 9 = (x + 3)²

Next, we have

4x² - 8x - 60

Expand and factorize

4x² - 8x - 60 = 4(x² - 2x - 15) = 4(x + 3)(x - 5)

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The sum of the first 5 terms of the sequence is 183.

We have,

The first term of the sequence is 3 and the common ratio is -3.

We can use the formula for the sum of the first n terms of a geometric sequence:

Sn = a(1 - r^n) / (1 - r)

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

Plugging in the values we have:

S5 = 3(1 - (-3)^5) / (1 - (-3))

Simplifying:

S(5) = 3(1 + 243) / 4

S(5) = 3(244) / 4

S(5) = 183

Therefore,

The sum of the first 5 terms of the sequence is 183.

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The value of x as shown in the triangular prism is 14 unit.

Triangular pyramids are formed solely from triangles. The 3 triangular sides slant upwards to form the triangular base.

To calculate the value of x of the rectangular pyramid, we use the formula below

Formula:

Where:

From the diagram and the question,

Given:

Substitute these values into equation 1 and solve for x

Hence, the value of x is 14 unit.

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The volume of the prism will be 88 cubic units. Then the correct option is B.

Given that:

Length, L = 4 units

Width, W = 4 units

Height, H = 5.5 units

The volume of the prism is given as,

V = L x W x H

The volume of the prism is calculated as,

V = 4 x 4 x 5.5

V = 88 cubic units

The volume of the prism will be 88 cubic units. Then the correct option is B.

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The complete question is given below.

The linear inequality with the solution set (2,-5), (-5,-5), (-5,5), (5,5), (5,-2) are x ≤ 5 and y ≤ 5

The solution set is given as

(2,-5), (-5,-5), (-5,5), (5,5), (5,-2)

We can see that the highest y value in the above ordered pairs is 5

So, we have

y ≤ 5

Also, we can see that the highest x value in the above ordered pairs is 5

So, we have

x ≤ 5

Hence, the linear inequality with the solution set is x ≤ 5 or y ≤ 5

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The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)

From the question, we have the following function definition that can be used in our computation:

cos(xº)

Changing the degree into radian, we have

cos(xπ/180)

Express as a function

So, we have

y = cos(xπ/180)

When the cosine function is differentiated, we have

y' = -sin(xπ/180)

Hence, the differentiated function is y' = -sin(xπ/180)

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Answer:

$3

Step-by-step explanation:

since $12 is 4/4 and he save 1/4 its 12÷4

Answer:

$3

Step-by-step explanation:

12 divided by 4 is 3

(3+3)+(3+3)

6+6

= 12

The maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.

It should be noted that upon deriving v(t), an equation of 12t² - 96t + 144 is produced. Subsequently, v'(t) must be set to zero, resulting in a quadratic equation of 12t² - 96t + 144 = 0, requiring division of both sides by 12 to produce t² - 8t + 12 = 0.

The quadratic can now be factored to obtain (t - 2)(t - 6) = 0, indicating that critical points lie on the values t = 2 and t = 6.

After calculating these values— v(1) = 100 m/s, v(2) = 64 m/s, v(6) = 16 m/s and v(7) = 1159 m/s—it is clear that the maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.

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Answer:

C. (4, 0)

Step-by-step explanation:

(x, y)

a. (4, 3)

y = 12 - 3x

3 = 12 - 3(4)

3 = 12 - 12

3 = 0  false

b. (-4, 4)

y = 12 - 3x

4 = 12 - 3(-4)

4 = 12 + 12

4 = 24  false

c. (4, 0)

y = 12 - 3x

0 = 12 - 3(4)

0 = 12 - 12

0 = 0  true

d. (0, 4)

y = 12 - 3x

4 = 12 - 3(0)

4 = 12 - 0

4 = 12  false.

Answer:   C   (4, 0)

Step-by-step explanation:

your function y = 12 - 3x

They are asking which of those points are on the line

(x, y)   this is a format of a point where you can plug in x for x and y for y.

a.  (4, 3)  x=4  y=3  substitute and see if your answer is true

   3 = 12 -3(4)

   3 = 0   this is not true so (4, 3) is not a solution

b. (-4,4) x= -4 y=4

  4 = 12 - 3(-4)

  4 = 24  not true

c.  (4, 0)  x=4  y=0

  0 = 12-3(4)

  0 = 0  true      (4,0) is a solution

d. (0, 4)

4 =  12 - 3 (0)

4=12

The total volume of the original mixture is 4 liters.

Given that:

A mixture of 50% alcohol and 50% water has 4 liters of water added to it. It is now 25% alcohol.

Let 'x' be the amount of water and alcohol. Then we have

x / (x + x + 4) = 0.25

x/(x + 2) = 0.5

2x = x + 2

x = 2

The total volume of the original mixture is calculated as,

Total volume = x + x

Total volume = 2 + 2

Total volume = 4 liters

The total volume of the original mixture is 4 liters.

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Answer:

180

Step-by-step explanation:

The word HORSES has 6 distinct letters, so we can arrange them in 6! = 720 ways if all the letters were unique.

However, in this case, the letters E and S are repeated twice. Therefore, we must divide by the number of arrangements of the repeated letters to avoid counting the same arrangement more than once.

The letter E appears twice, so there are 2! = 2 ways to arrange the E's within the word. Similarly, the letter S appears twice, so there are 2! = 2 ways to arrange the S's within the word.

Thus, the total number of unique arrangements of the letters in the word HORSES is:

6! / (2! × 2!) = 720 / 4 = 180

Therefore, there are 180 unique arrangements of the letters in the word HORSES.

The numeric value of the function f(x) at x = 5 is given as follows:

f(5) = 74.75.

The second derivative of the function f(x) is given as follows:

f''(x) = 2x + 6sin(x).

Integrating the second derivative, the first derivative of the function is given as follows:

f'(x) = x² - 6cos(x) + K.

When x = 0, y' = 2, hence the constant K is given as follows:

2 = -6 + K

K = 8.

Hence:

f'(x) = x² - 6cos(x) + 8.

Integrating the first derivative, the function is given as follows:

f(x) = x³/3 - 6sin(x) + 8x + K.

When x = 0, y = 4, hence the constant K is given as follows:

K = 4.

Then:

f(x) = x³/3 - 6sin(x) + 8x + 4.

The numeric value at x = 5 is given as follows:

f(5) = 5³/5 - 6sin(5) + 8(5) + 4

f(5) = 74.75.

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The bank employs a total of 32 bankers, and the answer is not listed among the options provided. The correct option is B.

Let's denote the number of bankers who manage only personal loans as P and the number of bankers who manage only business loans as B. Then, we can use the following information to form equations:

There are 20 bankers who manage personal loans, which means P + 3 bankers in total manage personal loans.

There are 25 bankers who manage business loans, which means B + 3 bankers in total manage business loans.

The bank has a total of X bankers.

Using these equations, we can solve for X as follows:

P + 3 = 20 (equation 1)

B + 3 = 25 (equation 2)

P + B + 3 = X (equation 3)

Solving equation 1 for P, we get P = 17.

Solving equation 2 for B, we get B = 12.

Substituting P = 17 and B = 22 into equation 3, we get:

17 + 12 + 3 = X

Simplifying, we get X = 32.

Therefore, the bank employs a total of 32 bankers, and the answer is not listed among the options provided.

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