work out the equation of a line which a gradient of a line of 1/2 and passes through the point (4,-2)

Answer:

Madison

Step-by-step explanation:

Madison is the better free throw shooter. We can tell this because her free throw percentage of 78% is higher than Lara's free throw ratio of 24, which is the number of successful free throws out of 100 attempted shots. Hope this helps!

The probability that three points chosen uniformly and independently on a circle fall on a semicircle is 1/2 or 50%.

The probability of three points chosen randomly and independently on a circle falling on a semicircle is 1/2, or 50%. This is because the probability of a point landing on either side of the semicircle is equal. The points are chosen on a circle, so each point has an equal probability of being on either side of the semicircle. Therefore, the probability of three points randomly chosen on a circle landing on a semicircle is 1/2 or 50%.

Let A, B, and C be the three points chosen on a circle.

The probability that A, B, and C fall on the semicircle is:

P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

= (1/2) x (1/2) x (1/2)

= (1/2)^3

= 1/8

Therefore, the probability that three points chosen randomly and independently on a circle fall on a semicircle is 1/8 or 12.5%.

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The probability that three points chosen uniformly and independently on a circle fall on a semicircle is written as 1/8.

The term probability in math is defined as the chances of something materializing based upon the ratio of its number of outcomes to the number of outcomes of the whole sample space the event relies upon.

While we looking into the given question, here let us consider that A, B, and C be the three points chosen on a circle.

Then the probability that A, B, and C fall on the semicircle is calculated as,

=> P(A on semicircle) x P(B on semicircle) x P(C on semicircle)

Now, we have to apply the value of each probability, then we get

=> (1/2) x (1/2) x (1/2)

Therefore, the resulting value is

=> (1/2)³ = 1/8

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Answer:

  y ≤ -3/2x -2

Step-by-step explanation:

You want the inequality shown on the graph that has a solid line through points (0, -2) and (2, -5).

The slope of the solid boundary line can be found from the slope equation:

  m = (y2 -y1)/(x2 -x1)

  m = (-5 -(-2))/(2 -0) = -3/2

The y-intercept is the point marked on the y-axis: (0, -2).

The boundary line has the slope-intercept equation ...

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

  y = -3/2x -2

The shading is to the left and below the boundary line, so y-values in the shaded area are less than those on the line. The inequality reflects this:

  y ≤ -3/2x -2

__

Additional comment

The solid boundary line is included in the solution set, so we use the ≤ symbol, instead of the < symbol that excludes the line. When the < symbol is used, the boundary line is dashed.

We use the term "y-intercept" to refer to both the ordered pair that describes the point on the y-axis, (0, -2), and the y-value in that ordered pair, -2. We understand the x-value of any point on the y-axis is 0.

By solving a system of equations we will see that she has 9 quarters and 15 dimes.

Let's define the variables.

We know that Moolah has 24 coins, then:

d + q = 24

And the total value is $3.75, then:

q*0.25 + d*0.10 = 3.75

Then we can write the system of equations:

d + q = 24

q*0.25 + d*0.10 = 3.75

We can isolate d on the first equation to get:

d = 24 - q

Replacing that in the other equation we will get:

q*0.25 + (24 - q)*0.10 = 3.75

q*0.15 + 2.4 = 3.75

q*0.15 = 3.75 - 2.4

q*0.15 = 1.35

q = 1.35/0.15 = 9

So Moolah has 9 quarters and 15 dimes.

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number of minibuses required = 7

Division is the process of dividing some object into a number of parts. It is opposite to the multiplication process. In mathematics, the number that is divided by other number is called dividend and the other number is called divisor.

given, number of tourists = 169

each minibus can accommodate 26 passengers.

number of minibuses required for the total 169 tourists.

will be 169/26 = 6.5 = 7

they need to hire total 7 minibuses for a tour around Tokyo.

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By grouping like terms and taking common factors, we will see that the addition of the polynomials gives:

(6x^2 - 3) + (8x^2 - 5x - 1) = 14x^2 - 5x - 4

Here we want to add two polynomials:

6x^2 - 3

And

8x^2 - 5x - 1

To make that addition, we just need to group like terms and take common factors.

We start with:

(6x^2 - 3) + (8x^2 - 5x - 1)

Grouping like terms we will get:

(6x^2 + 8x^2) + (-5x) + (-3 - 1)

Now we can simplify that, so we will get:

(6 + 8)*x^2 - 5x - 4

14x^2 - 5x - 4

That is the addition of the polynomials.

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Identify two points for each line and connect to graph lines.

Consider that x = 1 is the critical point, which gives us one included point (1, 0) marked as closed circle and one excluded point (1, 3) marked as open circle.

The second point for the first line is selected at x = - 3, which is (-3, 4) and for the second line is selected at x = 3, which is (3, 7).

See the lines attached.

Answer:

Below

Step-by-step explanation:

To find the number of games g that the team could lose and still be eligible for the playoffs, we can write the inequality:

g / 18 ≤ 40%

g / 18 ≤ 0.4

g ≤ 7.2

We can round down to 7 to get the maximum number of games the team could lose and still be eligible for the playoffs.

If the baseball team loses 8 of its remaining games, they will not advance to the playoffs. This is because 8 is greater than the maximum number of games they could lose and still be eligible for the playoffs, which is 7.

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Answer:

excluded values

y=0

Simplify the expression

3xy−5/y

​

Step-by-step explanation:

The quantity of fencing that the gardener would need to purchase would be = 1 5/12.

The total quantity of fencing the gardener needs to fence the the square garden = 4⅔

The length of one side of the garden = 3¼

The quantity of fencing the gardener needs to purchase would be = x

4⅔ = 3¼ + X

14/3 = 13/4 + X

X = 14/3 -13/4

X =56-39 /12

X= 17/12

X = 1 5/12ft.

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Given an arithmetic sequence with the first term -6 and the common difference -7, the first five terms are: -6, -13, -20, -27, -34.

The formula for the n-th term of an arithmetic sequence is given by:

a(n) = a(1) + (n - 1) d

Where:

a(1): the first term

d = common difference

The consecutive terms of an arithmetic sequence can be obtained as:

a(n) = a(n - 1) + d

Information available in the problem:

first term = a(1) = -6

common difference = d = -7

Hence,

a(1) = -6

a(2) = -6 - 7 = -13

a(3) = -13 - 7 = -20

a(4) = -20 - 7 = -27

a(5) = -27 - 7 = -34

Therefore the first five terms are: -6, -13, -20, -27, -34

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The value of the vertex(central) angle EJF formed by the given polygon is; 30°

To find the central angle of a polygon, we will simply divide 360 degrees by the number of sides of the polygon.

Now, we are told that the sum of the central vertex angles sums up to 180 degrees. Now, by careful observation, we can tell that the number of isosceles triangles that will be formed in the semi circle are 6. Thus;

Number of polygon sides of the semi circle = 6 sides

Thus;

Central angle = 180/6

Central angle = 30°

Now, we know that the base of isosceles triangles are equal. Since we know that the sum of angles in all triangles is 180 degrees, then we can say that;

∠E = ∠F = [180 - 30]/2

∠E = ∠F = 75°

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The reflection of  f(x)=6(x–7)2+2 is g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.

What is the reflection of a function?

A reflection is a transformation of the graph of a function over the x-axis or the y-axis (or both). The function retains its basic shape; however, by including a negative sign in the appropriate place in the equation, the graph of the function will flip over one or the other of the axes.

To find the reflection of a function across the x-axis, we can simply multiply the function's y-coordinate by -1.

For f(x) = 6(x–7)^2 + 2,

the reflection across the x-axis is

g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.

Hence, the reflection of  f(x)=6(x–7)2+2 is g(x) = -1 * (6(x–7)^2 + 2) = -6(x–7)^2 - 2.

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Answer:

6 & 21

Step-by-step explanation:

Let x be the smaller number. Let y be the larger number.

We have:
x + y = 5x - 3

However, we also know the larger number is 2x + 9 (nine more than twice the smaller). So, we can plug in 2x + 9 for y:

x + (2x + 9) = 5x - 3

x + 2x + 9 = 5x - 3

3x + 9 = 5x - 3

9 = 2x - 3

12 = 2x

x = 6

Now solver for the larger:

2x + 9 = 6*2 + 9 = 12 + 9 = 21

Therefore, the numbers are 6 and 21.

I hope this helps :D

The given expression of an [tex]{ }^{44} P_2[/tex] is 1892.

The given expression is [tex]{ }^{44} P_2 & =[/tex]0

[tex]{ }^{n} P_r[/tex]:-

 [tex]{ }^{n} P_r=[/tex][tex]\frac{n !}{(n-r) !} \\[/tex]

where

In the nPr formula, the letter "P" stands for "permutation," which is another word for "arrangement." The nPr formula calculates the number of possible combinations for choosing and arranging r items from the given n items.

Let's imagine that r various objects should be chosen and organised among n different objects. Let's explore some options for how to accomplish this.

Since there are n total objects, there are n methods to select the first one.

The number of options for selecting the second thing is limited because the first object has already been selected (n - 1).

Similar to how there are numerous ways to select the third item (n - 2).

While choosing the [tex]r^{th}[/tex] object, there are only (n - r + 1) objects are left and hence it can be chosen in (n - r + 1) ways.

[tex]{ }^{44} P_2 & =? \\\\P(n, r) & =\frac{n !}{(n-r) !} \\\\44 P_2 & =\frac{44 !}{(44-2) !} \\\\& =\frac{44 \times 43 \times 421}{421} \\[/tex]

=44×43

=1892

[tex]{ }^{44} P_2=[/tex]1892

Therefore, the value of [tex]{ }^{44} P_2[/tex]=1892.

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Answer:

13 square centimeters.

Step-by-step explanation:

There are 13 squares making up the shape

Answer:

The answer is D

Step-by-step explanation:

Trust me on this, its hard to explain but Im 100% sure.

Answer:

x = - 12 , x = 13

Step-by-step explanation:

x² - x = 156 ( subtract 156 from both sides )

x² - x - 156 = 0 ← in standard form

(x - 13)(x + 12) = 0 ← in factored form

equate each factor to zero and solve for x

x + 12 = 0 ⇒ x = - 12

x - 13 = 0 ⇒ x = 13

The y-coordinate of the point (-3, p) is p = 0.

A line can be represented by the equation y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

In this case, the slope of the line is given as -3, and the line passes through the point (-4, 3). We can use this information to write an equation for the line in the form y = mx + b:

y = (-3)x + b

We are told that the line passes through the point (-4, 3), so we can substitute these values into the equation to find the value of b:

3 = (-3)(-4) + b

3 = 12 + b

-9 = b

Therefore, the equation for the line is y = -3x - 9.

To find the value of p, we need to substitute the x-coordinate (-3) into the equation and solve for y:

y = (-3)(-3) - 9

y = 9 - 9

y = 0

Therefore, the y-coordinate of the point (-3, p) is p = 0.

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The y-coordinate of the point (-3, p) is p = 0.

Now, According to the question:

y = mx + b is the slope intercept form of writing the equation of a straight line. In the equation 'y = mx + b', 'b' is the point, where the line intersects the 'y axis' and 'm' denotes the slope of the line. The slope or gradient of a line describes how steep a line is. It can have either a positive or a negative value. When a standard form of a linear equation is of the form Ax + By  = C, where 'x' and 'y'  and 'C' are variables and 'A', 'B' are constants, the slope-intercept form is the most preferred way of expressing a straight line due to its simplicity, as it is very easy to find the slope and the 'y intercept' from the given equation.

In this case, the slope of the line is given as -3, and the line passes through the point (-4, 3). We can use this information to write an equation for the line in the form y = mx + b:

y = (-3)x + b

We are told that the line passes through the point (-4, 3), so we can substitute these values into the equation to find the value of b:

3 = (-3)(-4) + b

3 = 12 + b

-9 = b

Therefore, the equation for the line is y = -3x - 9.

To find the value of p, we need to substitute the x-coordinate (-3) into the equation and solve for y:

y = (-3)(-3) - 9

y = 9 - 9

y = 0

Therefore, the y-coordinate of the point (-3, p) is p = 0.

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The given expression [tex]x^{2} +8x+15[/tex] , can be expressed in completely factored form as [tex](x+5)(x+3)[/tex] .

The expression that is to be written in factored form is [tex]x^{2} +8x+15[/tex] ;

we will use the split the middle term method to express it in factored form , in this method we split the middle term and then write down the common factors .

the middle term [tex]8x[/tex] can be written as [tex]3x+5x[/tex] ;

we get ; [tex]x^{2} +3x+5x+15[/tex] ;

taking "x" common from first 2 terms and "5" common from the next two terms ,

we get ;

⇒ [tex]x(x +3)+5(x+3)[/tex] ;

⇒ [tex](x +3)(x+5)[/tex] ;

So , we get that the expression [tex]x^{2} +8x+15[/tex] is equivalent to [tex](x +3)(x+5)[/tex] .

Therefore , the completely factored form is [tex](x +3)(x+5)[/tex] .

The given question is incomplete , the complete question is

What is the completely factored form of the expression [tex]x^{2} +8x+15[/tex] ?

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The value of x from the given quadrilateral is 3.

A rhombus is a closed two-dimensional plane figure. It is considered a special parallelogram, and because of its unique properties, it gets an individual identity as a quadrilateral. A rhombus is also called an equilateral quadrilateral since all of its sides are equal in length.

Given that, rhombus (6x + 32)º and (17x - 1)º for what value of x is the figure given the special parallelogram.

A rhombus has two diagonals that bisect each other at right angles and diagonal bisects angles.

Now, (6x + 32)º=(17x - 1)º

17x-6x=32+1

11x=33

x=3

Therefore, the value of x is 3.

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The percentage of students in eighth grade who have music is 60%

Total number of eighth grade students = 75

Number of students who goes to music class = 45

Number of students who have art = Total number of eighth grade students - Number of students who goes to music class

= 75 - 45

= 30

Percentage of students who have art = Number of students who have art / Total number of eighth grade students × 100

= 30/75 × 100

= 0.4 × 100

= 40%

Percentage of students who have music = Number of students who have music / Total number of eighth grade students × 100

= 45/75 × 100

= 0.6 × 100

= 60%

Hence, 60% of the eighth grade students have music.

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Answer: 56

Step-by-step explanation:

There are 8 runners competing in the 400-meter race, and the fastest 3 runners win a ribbon. This means that there are 3 places that the runners can finish in: first, second, and third.

Since the order in which the runners finish matters, we need to use permutations to find the number of ways that the runners can finish in first, second, and third place.

The number of permutations of a set of n objects taken r at a time is given by the formula:

n! / (n - r)!

In this case, there are 8 runners, so n = 8, and we are selecting 3 runners at a time, so r = 3. Plugging these values into the formula gives us:

8! / (8 - 3)! = 8! / 5! = 8 * 7 * 6 / 5 * 4 * 3 = 56

Therefore, there are 56 ways that the runners can finish in first, second, and third place.

There are four main datatypes: String, Integer, Float, and Boolean.

String: A string data type is used to store textual data. Strings are usually enclosed in quotation marks, and are used to represent words or phrases.

Integer: An integer data type is used to store numeric values that are whole numbers. Integers are usually used to represent counts or quantities.

Float: A float data type is used to store numeric values that have decimal points. Floats are usually used to represent real numbers, such as money amounts, measurements, and scientific values.

Boolean: A boolean data type is used to store values that can only be either true or false. Booleans are usually used to represent logical values, such as whether a certain condition is met or not.

Datatype is a classification of data which tells the computer how the programmer wants to use the data. It is used to store different types of values such as strings, integers, floats, and booleans. Each data type has its own specific purpose and can be used to store different types of information.

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For the given regular polygon with the angle sum of 10x + 4, the value of x = 143.6

They are referred to as regular polygons if the interior angles and sides are all equal. Equilateral triangles, squares, and other shapes are examples of regular polygons. Along with the sides being congruent, regular polygons also have congruent angles. They are equiangular, according to that.

We know that sum of interior angles of a regular polygon is

( n − 2 ) × 180°, where n is sides

For the given question

( 10 − 2 ) × 180°

= 8 × 180°

= 1440°

Given that

10x + 4 = 1440°

10x = 1436

x =  1436/10

x =  143.6

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The equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

The equation of the tangent to the curve y = f(x), passing through the point (a, b) can be written as -

(y - b) = (dy/dx) (x - a)

Given is the curve y = f(x) = x⁴ + 6x² − x.

The given curve is -

y = x⁴ + 6x² − x

f'(x) = dy/dx = d(x⁴ + 6x² − x)/dx

f'(x) = dy/dx = 4x³ + 12x + 1

Now -

f'(x){1, 6} = (dy/dx){1, 6} = 4 x 1 x 1 x 1 + 12 x 1 + 1

f'(x){1, 6} = 17

We can write the equation as -

(y - 6) = 17(x - 1)

Therefore, the equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

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If a researcher finds that the probability of a word recognition program correctly interpreting a hand-written word is 9/10 . The number of  words that  the researcher expect the program to interpret correctly out of 40 words is 36 words.

Using this formula to find the number of words

Number of words = Probability of correctly interpreting a hand-written word × Expected words

Let plug in  the formula

Number of words = 9/10 × 40

Number of words = 36 words

Therefore we can conclude that the number of words is 36 words.

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D. y-2 cos(2x) + 4 is not a solution to the differential equation y" + 4y = 0.

The differential equation y" + 4y = 0 is a second-order, homogeneous linear differential equation with constant coefficients. The general solution to this type of differential equation is of the form y = e^(rt) where r is a root of the characteristic equation r² + 4 = 0. The roots of this equation are r = +/- √(4) = +/- 2i, which are both imaginary. Therefore, the general solution to the differential equation is y = c1cos(2x) + c2*sin(2x), where c1 and c2 are arbitrary constants.

Option D. y - 2 cos(2x) + 4 is not a solution to this differential equation because it doesn't have the same form as the general solution. It is a combination of a constant term, cosine and sine function but the general solution only contains sine and cosine function.

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The first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3. (Option C)

In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like ^n for a nonnegative integer n. For a binomial series, the formula for the expansion of any terms is given by

(1+x)^m=1+mx+  m(m-1)/2! x^2+  m(m-1)(m-2)/3! x^3+⋯.

For the given function (1+ x/4)^(-2)

m = -2

x = x/4

Hence, using the above expansion formula

The first term = 1

The second term = mx = (-2)(x/4) = -x/2

The third term =m(m-1)/2! (x/4)^2=  (-2(-2-1))/(2*1*16) x^2=3/16 x^2

The fourth term = m(m-1)(m-2)/3! (x/4)^3=(-2(-2-1)(-2-2))/(3*2*1*64) x^3=-1/16 x^3

Hence, the first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3.

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