what is the equation of a line with gradient 4 that passes through (3,5)?
Give your answer in the form y=mx+c where m and c are intergers or fractions in their simplest form

The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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The function g(x) = x² + 4x has a: A. minimum.

The minimum value occur at x = -2.

The function's minimum value is -4.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function g(x) = x² + 4x, we have:

a = 1, b = 4, and c = 0

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(4)/2(1)

Axis of symmetry, Xmax = -2

Next, we would determine vertex as follows;

g(x) = x² + 4x

g(-2) = -(-2)² + 4(-2)

g(-2) = -4.

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Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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Answer:

bc cot 0

Step-by-step explanation:

Answer: 4 ways to pick a king, 13 ways to pick a heart, and 4 ways to pick a five. Given the cards are returned to the deck, there are no special cases such as picking the King of Hearts and/or the Five of Hearts that affect the count. 208 ways.

Step-by-step explanation:

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

In order to enhance strong number sense in children, there are various methods that can be used.

In the given scenario, Mme Potatana asked the children to count as a whole class from 1 to 20 while Ntate Mafodi asked the children in his class to count seeds from the school's ground in a pile by touching each as they count.

Both methods have their own benefits, but the method of counting seeds by touching each can be more effective in enhancing strong number sense in children.

The method of counting seeds by touching each can be more effective in enhancing strong number sense in children because it allows them to experience each number physically.

This helps them in developing a strong sense of numbers. By touching each seed as they count, children can feel and see each number, which helps them in understanding numbers better. Additionally, it helps in developing the concept of one-to-one correspondence and counting by rote.

Here are some appropriate examples for enhancing strong number sense using the method of counting seeds by touching each:

1. Use counters: Provide children with counters such as small objects, blocks, or toys. Ask them to count the number of counters by touching each as they count.

2. Counting on fingers: Encourage children to count on their fingers. This helps them in developing a strong sense of numbers and helps them in understanding the concept of one-to-one correspondence.

3. Counting objects in a pile: Ask children to count objects in a pile by touching each as they count. This helps in developing the concept of counting by rote and helps in enhancing strong number sense.

Overall, the method of counting seeds by touching each can be more effective in enhancing strong number sense in children as it allows them to experience each number physically and helps them in developing a strong sense of numbers.

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Answer:

16, 24, 32

Step-by-step explanation:

The ratio is 8:3 so you would multiply both by the same number and that would give you 16:6, 24:9, 32:12

Answer:

150m

Step-by-step explanation:

\(Length=120-(-30)=120+30=150m\)

The number of handshakes altogether exists 45.

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset's components can be arranged in any sequence when used together. The components of the subset are arranged in a particular order in a permutation.

A combination in mathematics is a choice of elements from a set with distinct members, where the order of the choices is irrelevant.

Combinations are a mathematical method for calculating the number of alternative arrangements in a collection of objects where the order of the selection is irrelevant. You are free to choose any combination of the things.

Given:

Number of people in the conference = 10

Each person shakes hands with others.

The total number of handshakes \($={ }^n \mathrm{C}_2$\)

Total number of handshakes \($={ }^{10} C_2=(10 \times 9) / 2=45$\) handshakes.

The complete question is:

At the end of a meeting all the ten people present shake hands with each other once. The number of handshakes altogether is

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Answer:

C

Step-by-step explanation:

YEAH

a line through the origin with a slope of -2 (for every 1 unit to the right, move 2 units down)

when plotting, plug in values for x, i would recommend starting with 0, 1, and -1, then find y for each of these x values, then connect the points

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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The equation of the line is (y - 1/12) = -4/3(x - 7/5).

What is the slope of a line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.

Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be depicted by

tan θ = Δy/Δx

So, the slope of a line is tan.

The given equation of a line is:

3x-4y=7

-4y = -3x + 7

y = 3/4 x - 7/4

The slope of the line is 3/4.

The slope of the line perpendicular to the given line is - 1/m = - 4/3

The point-slope of a line is y - y₁ = m(x - x₁).

The given point is (7/5,1/12)

The equation of the line is

(y - 1/12) = -4/3(x - 7/5)

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Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

Answer:

9

Step-by-step explanation:

i dont know 100% but i think is 9

Answer:

The answer is 5.4%

Step-by-step explanation:

30 of 18 is 5.4

Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.

One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.

Using a calculator, we can find the sine of 98 degrees as follows:

sin 98° ≈ 0.9848

Rounding this to four decimal places, we get:

sin 98° ≈ 0.9848

Therefore, sin 98° is approximately equal to 0.9848.

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Answer: 0

Step-by-step explanation:

c2+2c−24=0

Answer:

11.68ft or 11.68 feet

Step-by-step explanation:

From the above question, we are told that:

Area of the square and the Area semicircle is to be 190 ft squared.

We are also told in the question that:

The window has the shape of a square with a semicircle mounted on it.

Hence, the Diameter of the semicircle = Width of the Square

Let the Width of the square = x

Area of a square = Width²

= x²

Let the Diameter of the semi circle = x

Radius of the semi circle = Diameter of the semi circle/2 = x/2

Area of a semicircle = πr²/2

Area of a the semi Circle = π ×(x/2)² /2

= (πx²/4)/2

= πx²/8

Therefore,

Area of a square + Area of a semicircle = 190ft²

= x² + πx²/8 = 190

Cross Multiply

x² + πx² = 190

= x² ( 1 + π/8) = 190

x² = (190)/(1 + π/8)

x² = 136.42573798

x = √136.42573798

x = 11.680142892ft

Approximately x ≈ 11.68ft

Therefore, the width of the window = 11.68ft

The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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Answer:

I think A

Step-by-step explanation:

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

Explanation:

Take note that the x and y coordinate of this vector are the same.

This leads to a 45-45-90 reference triangle. If the vector was in the first quadrant (the northeast), then the answer would be 45 degrees.

However, we need to add on 180 so we get to the third quadrant instead where x and y are both negative. This gets us to 180+45 = 225 degrees

---------------

If you wanted to use a calculator, then you would compute the value of \(\tan^{-1}(b/a)\) where <a,b> is the vector in question.

Since a = b in this case, we have b/a = 1 and the arctangent of this is 45 degrees. The adjustment of adding on 180 still applies like from before.

there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

How to solve the question?

The number of ways to draw 7 cards from a standard deck of 52 cards can be calculated using the combination formula, which is:

C(52, 7) = 52! / (7! * (52-7)!)

where "!" represents the factorial function.

To simplify this expression, we can use the property that n! / k! = n * (n-1) * (n-2) * ... * (n-k+1) for positive integers n and k such that k ≤ n.

Using this property, we can rewrite the above expression as:

C(52, 7) = (52 * 51 * 50 * 49 * 48 * 47 * 46) / (7 * 6 * 5 * 4 * 3 * 2 * 1)

Simplifying this expression, we get:

C(52, 7) = 133,784,560

Therefore, there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

To understand why this is the case, we can think of each draw as a separate event with no replacement. The first card can be drawn in 52 ways, the second card can be drawn in 51 ways (since one card has already been drawn), the third card can be drawn in 50 ways (since two cards have already been drawn), and so on. Therefore, the total number of ways to draw 7 cards is the product of the number of ways to draw each individual card, which is 52 * 51 * 50 * 49 * 48 * 47 * 46. However, since the order in which the cards are drawn does not matter, we need to divide by the number of ways to arrange 7 cards, which is 7 * 6 * 5 * 4 * 3 * 2 * 1 (i.e., 7 factorial). This gives us the final answer of 133,784,560.

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The factored form is (5x+2)(x-4).

What is factorization?

A number, matrix, or polynomial may be broken up or decomposed into factors that, when multiplied together, produce the original number, matrix, etc. This process is known as factorization or factoring.

Here, we have

Given:  5 x squared minus 18 x minus 8

we have to find the factored form.

= 5x² - 18x - 8

= 5x² - 20x + 2x - 8

= 5x(x-4) + 2(x-4)

= (5x+2)(x-4)

Hence, the factored form is (5x+2)(x-4).

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Answer:

(-3.5, -3).

Step-by-step explanation:

That would be (-7/2, -6/2) or (-3.5, -3)..

Answer:

  (-7/2, -3)

Step-by-step explanation:

When the center of the dilation is the origin, each coordinate value is multiplied by the dilation factor.

The image point is ...

  (1/2)(-7, -6) = (-7/2, -3)

Answer:

0

Step-by-step explanation:

5x+10-4=13-7x-7

5x+6=6-7x

5x+0= -7x

0=-12x

Divide and u get x=0

Answer:

2x - 3 = 11

x = -21

Step-by-step explanation: