The graph of a function f(x) passes through the following points:
(0,-2), (1,0), (-1,0)
Which of the following could be f(x)?
> f(x) = -2x - 2
> f(x) = 2x - 2
> f(x) = (2\sqrt[x])-2
> f(x) = 2x^2 - 2

The function that has the greater slope is the function g(x) that is represented by the graph.

The slope (m) of a function using two points on a graph can be calculated as:

Slope of the line (m) = change in y/change in x

If we are given the equation of the line using function notation as .f(x) = mx + b, the slope of the function is represented in the equation as "m". The value of "m" is the slope of the function given.

Given the function, .f(x) = 3x + 1, the value that represents "m" which is 3. Therefore, the slope of the function .f(x) = 3x + 1 is: 3.

Find the slope of the function of the graph using two points on the line, say (2, 3) and (3, 7):

Slope of the function (m) = change in y / change in x = (7 - 3)/(3 - 2)

Slope of the function (m) = 4/1

Slope of the function (m) = 4

The larger the value of the slope, the greater the slope of the function.

Therefore, the function g(x) that is represented by the graph has a greater slope.

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Answer: B

Step-by-step explanation:

Simple

The arc angle AC is measured as 55 degrees.

If two secant intersect in the exterior of a circle, then the measure of the angle formed is half the positive difference of the arcs intercepted.

Therefore, the secants intersect outside the circle at point E.

The arc angle AC can be found as follows:

Therefore,

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

arc angle AC = x

arc angle BD = 23 degrees.

m∠BED = 16 degrees.

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

16 = 1 / 2 (x - 23)

16 = 1 / 2x - 23 / 2

16 + 11.5 = 0.5x

27.5 = 0.5x

x = 27.5 / 0.5

x = 55 degrees.

Therefore,

arc angle AC = 55 degrees.

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Answer: 16,406,000

Step-by-step explanation:

First, multiply 6.31 and 2.6 to get 16.406. Then, add 10^5 and 10^1 to get 10^6.

It should now look like this, 16.406 x 10^6

The number has to be between 10 and 1 so you need to make it smaller by moving the decimal point over once to the left. It should now be 1.6406.  But, you can't leave the exponent at 10^6 so, you need to make it bigger since you made the number smaller.

Your answer should now look like this, 1.6406 x 10^7

Since it needs to be in standard form, move the decimal point 7 times to the right since it is a positive number.

So, your answer is: 16,406,000

The value of the greatest integers will be 5.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

'' An integer is subtracted from 5 times the next consecutive odd integer, the difference is 22''.

Now,

Write the mathematical expression for an algebraic expression as;

Let an integer = 2x + 1

Then, The next consecutive odd integer = 2x + 3

So, We can formulate;

5 (2x + 3) - (2x + 1) = 22

Solve for x as;

5 (2x + 3) - (2x + 1) = 22

10x + 15 - 2x - 1 = 22

8x + 14 = 22

Subtract 14 both sides, we get;

8x + 14 - 14 = 22 - 14

8x = 8

Divide by 8,

x = 8/8

x = 1

Since, The greatest integers = 2x + 3

Substitute x = 1, we get;

The greatest integers = 2x + 3

The greatest integers = 2 × 1 + 3

The greatest integers = 2 + 3

The greatest integers = 5

Therefore, The value of the greatest integers will be 5.

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Flipping and Stretching is the Process for performing the transformation on a coordinate plane using rigid transformations.

A rigid transformation of a geometric object preserves distance between each pair of points of the object. In other words, rigid transformations preserve the shape and size of an object. For example, a rigid transformation of a triangle preserves both the measure of the angles and the lengths of the sides of the triangle. Think of rigid transformations of a shape as being like taking a cardboard cutout of the shape. The shape can be moved around, rotated, and flipped from one side to the other, but the shape itself does not change.

There are rules associated with rigid transformations. A rigid transformation is some function F from a set X to itself such that F preserves the distances between two points. Let d(x ,y) be the distance between two points. Then, to write the definition in mathematical notation, if d(x ,y) = d(F(x),F(y)) for all points x and y, then F is a rigid transformation.

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Answer:

-3÷8 or -0.375

Step-by-step explanation:

-3÷8÷1=-3÷8×1÷1=-24÷8=-3

Answer:

6X-15-1-3X=3X-16

6-3=3

Answer:

False

Step-by-step explanation:

It is false when x=1 because

[tex]1^{2} =1[/tex]

Answer:

1.8 = 9

5

= 14

5

as a fraction

ANSWER

EXPLANATION

We want to find the volume of the sphere.

The volume of a sphere is given as:

where r = radius of the sphere.

Therefore, we have that the volume of the sphere is:

That is the volume of the sphere.

(7)^2 +

2nd power means squaring a number and since you need to do that first, it goes in brackets.

answer: 49 + b, or just 7^2 + b

explanation: 7^2 = 7x7, so it is equal to 49. then add b to 49

[tex]9\frac{11}{13}[/tex] is bigger than 9.79

The mixed fraction = [tex]9\frac{11}{13}[/tex]

The mixed fraction is the fraction that expressed with its quotient and remainder. The mixed fraction is the combination of a whole number and a simple fraction

Simple fraction is the fraction that has whole numbers as the numerator and denominator.

The decimal number is a number that has whole and the fractional parts are separated by a decimal point

First we have to convert the mixed fraction into simple fraction

[tex]9\frac{11}{13}[/tex] = 128/13

Next we have to convert the simple fraction into decimal form

Divide 128 by 13

The result will be

128/13 = 9.85

Hence, [tex]9\frac{11}{13}[/tex] is bigger than 9.79

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On solving the given statement, the length of AC equals 37.

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that lie inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

According to the given statement,

AC = 2x + 21

AB = x + 9

BC = 3x - 4

As B is the mid point of the segment AC,

⇒ AB + BC = AC

⇒ x + 9 + 3x - 4 = 2x + 21

⇒ 4x + 5 = 2x + 21

⇒ 2x = 16

⇒ x = 8

Length of AC = 2 (8) + 21

= 16 + 21

= 37

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Answer:

-4

Step-by-step explanation:

4/6 - 3/6p=16/6

Multiply each side by 6

4 - 3p = 16

Subtract 4 from both sides

-3p = 12

Divide both sides by -3

p = -4

Answer:

-4

Step-by-step explanation:

   [tex]\sf \dfrac{4}{6}-\dfrac{3}{6}p=\dfrac{16}{6}[/tex]

To find the value of 'p', isolate 'p',

         [tex]\sf \dfrac{-3}{6}p=\dfrac{16}{6}-\dfrac{4}{6}\\\\[/tex]

                 [tex]\sf = \dfrac{12}{6}[/tex]

                  = 2

             [tex]\sf p = 2* \dfrac{6}{-3}\\\\ p = 2 *(-2)\\\\p = -4[/tex]

Answer: 10) √85 units    12) 4 units

Step-by-step explanation:

          [tex]\boxed {l=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}}[/tex]

10) (8,5)   (-1,3)

[tex]x_1=8\ \ \ \ x_2=-1\ \ \ \ y_1=5\ \ \ \ \ y_2=3\\\\l=\sqrt{(-1-8)^2+(3-5)^2} \\\\l=\sqrt{(-9)^2+(-2)^2} \\\\l=\sqrt{81+4}\\\\l=\sqrt{85}\ units[/tex]

12) (-6,-10)   (-2,-10)

[tex]x_1=-6\ \ \ \ \ x_2=-2\ \ \ \ \ y_1=-10\ \ \ \ y_2=-10\\\\l=\sqrt{(-2-(-6)^2+(-10-(-10))^2} \\\\l=\sqrt{(-2+6)^2+(-10+10)^2}\\\\l=\sqrt{4^2+0^2} \\\\l=\sqrt{4^2} \\\\l=4\ units[/tex]

Answer: y=-4x-27

Step-by-step explanation:

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

Lines are parallel if their slopes are equal

[tex]y=-4x+2[/tex]

⇒ m=-4

⇒ y=-4x+b

A line passes through (-8.5)

⇒ x=-8    y=5

[tex]5=-4(-8)+b\\5=32+b\\5-32=32+b-32\\-27=b[/tex]

So, y=-4x-27

Answer:

Step-by-step explanation:

0.71%  is the probability micah is included in the group of students chosen.

Describe probability using an example?

the probability micah is included in the group of students chosen =

               3/28 = 10.71%

The probability of her getting picked is unlikely.

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The complete question is -

Micah is 1 of 28 students in a class. Micah's teacher is going to randomly select 3 students from their class to visit a classroom of younger students. What is the probability Micah is included in the group of students chosen?

The correct statement about the description “two less than the quotient of a number cubed and sixteen, increased by eight” is "StartFraction n cubed Over 16 EndFraction minus 2 + 8"

The correct answer option is option a

The value of the expression when n = 4 is 10. option D

quotient of a number cubed and sixteen

= n³ / 16

two less than the quotient of a number cubed and sixteen

= (n³ / 16 - 2)

two less than the quotient of a number cubed and sixteen, increased by eight”

= (n³ / 16 - 2) + 8

If n = 4

(n³ / 16 - 2) + 8

= (4³ / 16 - 2) + 8

= (64/16 - 2) + 8

= (4 - 2) + 8

= 2 + 8

= 10

In conclusion, the expression can be written as "StartFraction n cubed Over 16 EndFraction minus 2 + 8"

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The equation that can be use to find the how many miles, x, Omar ran each day after work is x =  (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days  after work

The total number of days he run = 7 days

Total distance he ran in one week = 63 miles

The distance he run before the work = 3 miles

The total distance he run before the work in one week= 7×3

= 21 miles

The total distance he run after the work = 63 - 21

= 42 miles

The equation that can use to find how many mile x, Omar ran each day after work = (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7

Substitute the values in the equation

= 42/7

= 6 miles

Hence, The equation that can be use to find the how many miles, x, Omar ran each day after work is x =  (Total distance he ran in one week - The total distance he run before the work in one week) ÷ 7, he ran 6 miles each days  after work

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Brian's income last month t is $3,318.92

The commission rate for the computer parts is 4%

The total sales for last month is 82,968.00

Brian income last month can be calculated as follows

Total sales × commission percentage

4/100 × 82,968

= 0.04 × 82,968

= 3,318.92

Hence Brian income for last month is $3,318.92

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Answer:

Option 3

Step-by-step explanation:

[tex]f(x)=4x^2 + 3x-5 \\ \\ f(x+h)=4(x+h)^2+3(x+h)-5 \\ \\ =4(x^2+2xh+h^2)+3x+3h-5 \\ \\ f(x+h)-f(x)=4(x^2+ 2xh+h^2)+3(x+h)-5-(4x^2+3x-5) \\ \\ \frac{f(x+h)-f(x)}{h}=\frac{4(x^2+ 2xh+h^2)+3(x+h)-5-(4x^2+3x-5)}{h}[/tex]

If Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, then he will have $0 remaining, as plotted on the number line in the reference attachment hereby.

As per the question statement, Steven had $5 that his mom gave him to buy lunch at school and he spent all of the $5 on his lunch.

We are required to plot a point on the number line to depict how many dollars Steven has left with himself after spending on his lunch.

To solve this question, we simply need to subtract the amount Steven spent for his lunch, from the amount, his mother gave him to spend on lunch, and then plot the result of the said subtraction on the number line to obtain our desired answer.

Since, Steven had $5 to buy lunch at school, and he spent all of the $5 on his lunch, he has $(5 - 5) = $0 left with himself after spending on his lunch.

That is, we will have to plot 0 on the number line, which is shown in the reference attachment hereby.

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The area of the triangle formed by his path is mathematically given as

Area = 29284.886 ft^2

This is further explained below.

Generally, the equation for the defining cosine rule  is mathematically given as

[tex]b^2 = a^2 + c^2 - 2ac cos B[/tex]

where

b = side B of the triangle

a = side A of the triangle

c = side C of the triangle

Therefore

[tex]b^2 = 180^2 + 329^2 - 2(180 * 329)cos 81.5[/tex]

b^2  = 32400 + 108241 - 17506.55

b = 350.91 ft

We calculate the area of the triangle using heron's formula.

Area = [tex]\sqrt{(p(p - a)(p - b)(p - c))}[/tex]

b = side B of the triangle

a = side A of the triangle

c = side C of the triangle

p = path

Where

p = (a + b + c)/2

p= (180 + 350.91 + 329)/2

p= 429.955 ft

Area = [tex]\sqrt{(429.955(429.955 - 180)(429.955 - 350.91)(429.955 - 329)}[/tex]

Area = 29284.886 ft^2

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Answer:

  (a) -48

Step-by-step explanation:

You want the solution to the equation 1/6(x +18) = -5.

The first step to solving this can be to multiply both sides by 6, eliminating the fraction:

  x +18 = -30

The second step can be to isolate the variable by subtracting 18 from both sides.

  x = -48

The solution is x = -48.

__

Additional comment

Sometimes you may want to simplify the equation before you start the solution process. Here, you can also start by eliminating parentheses:

  1/6x +3 = -5

Now, subtracting 3 gives ...

  1/6x = -8

Finally, multiplying by 6, we have ...

  x = -48

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Answer:

Step-by-step explanation:

Given,

The marked price of a jacket at dealer shop is Rs. 2400

The dealer allows a discount of 15% to the retailer.

The marked price of the retailer should be same as the dealer's marked price.

To find,

1. SP the retailer should fix for the jacket

2. Its final price if 10% VAT is imposed

3. The actual gain of the retailer if 10% discount is allowed

Solution,

The SP rate for the jacket without VAT 2400

Let 10% VAT on jacket price 2400 be x

x= 2400÷10

x= 240

So, the final price including 10% VAT = 2640 (2400+240)

As the dealer allowed discount of 15% to the retailer, the retailer gain profit is 15% on the jacket price i.e., 2400

Let y be the gain of the retailer

y= 15/100 × 2400

y= 360

Therefore,

SP the retailer should fix for the jacket is 2400

final price if 10% VAT is imposed is 2640

the actual gain of the retailer is 360

The slope of a line (m) given two points (x1, y1) and (x2, y2) is computed as follows:

Replacing with (40,2,000) and (60, 3,000):

The slope ls 50 cubic feet/hour which means that the amount of water in the reservoir is increasing at a rate of 50 cubic feet each hour.​

Slope-intercept form of a line:

y = mx + b

where m is the slope and b is the y-intercept. Replacing with m = 50 and point (40, 2000), e get:

200050()40

2000

2000 - 2000 = b

0 = b

Then the y-intercept is point (0, 0) which is also the x-intercept

The equation is:

y = 50x

n(A) is 6 when A = {14, 16, 18, 20, 22, 24}

A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things. Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

Given Data

A = {14, 16, 18, 20, 22, 24}

We are aware that the cardinality, which is represented by the letter n, is the number of items in any set A.

n(A) = number of elements in set

n(A) = 6

n(A) is 6

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The correct steps to transform equation x² + 10x + 24 = 0 into the form (x - p)² = q are:

Step 1   x² + 10x + 24 + 1 = 0 + 1

Step 2  x² + 10x + 25 = 1

Step 3  (x + 5)² = 1

In this question, we have been given an equation x² + 10x + 24 = 0

We need to transform given equation x² + 10x + 24 = 0 into the form (x - p)² = q

x² + 10x + 24 = 0                    .............(Given equation)

x² + 10x + 24 + 1 = 0 + 1          ............(Add 1 to each side)

x² + 10x + 25 = 1

x² + 2(5)x + 5² = 1

(x + 5)² = 1

Therefore, the correct steps to transform equation x² + 10x + 24 = 0 into the form (x - p)² = q are:

Step 1   x² + 10x + 24 + 1 = 0 + 1

Step 2  x² + 10x + 25 = 1

Step 3  (x + 5)² = 1

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