Find the equation of the line connecting the points (2, 0) and (3, 15).

Answer:

61

Step-by-step explanation:

The X- intercept of the graph of the function at x =>-4 and x = 2.

The provided function is g(x)=-1(x-4)(x+2).

The x intercept of the function means, that point at which the graph of function will have the y coordinate as zero.

So, the x intercept of the function will be at the point where the function g(x) will be equal to zero.

g(x) = 0

-1(x-4)(x+2) = 0

(4-x)(x+2) = 0

Here,

We will get two values of x at which g(x) will be zero,

X = 4 and -2.

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The least water depth and greatest depth will be 0.97d and 1.03d.

An expression is used to show the relationship between the variables.

In this case, the depth of water d in a swimming pool increases and decreases by 3% over a one-month period.

The least water depth will be:

= d - (3% × d)

= d - 0.03d

= 0.97d

The greatest water depth will be:

= d + (3% × d)

= d + 0.03d

= 1.03d

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Answer:

B, D, E

Step-by-step explanation:

We can find the area of B since the height and lengths is known, so the area is just 2*4 = 8 cm^2
D also has the height and length given, it is 4*3 = 12 cm^2
E gives 3 values, but only focus on the height and length, which are 2 and 5 respectively. 3 is also a side length, but there is no height to match that length. The area of E is 2*5 = 10 cm^2

The reasons A, C, and F don't work:
A seems like it would work, until you realize that 5 is a height, not a length, and so is 2. They are both heights, and multiplying heights together won't usually get you an accurate area unless the shape is a rectangle.
C has a length, but no height. the 3 cm is pretty much an arbitrary measurement.
F has two lengths, which would only give the area if the shape was a rectangle, which it is not.

The probability of winning the minimum award of $100 in the lottery is [tex]\frac{113}{140448}[/tex]

The probability of picking first winning number (out of 57 white balls) is [tex]\frac{1}{57}[/tex]

Now, out of the remaining 56 white balls, the probability of picking second winning number is [tex]\frac{1}{56}[/tex]

So total probability of the correctly matching two numbers drawn from the white balls is  [tex]\frac{1}{57} + \frac{1}{56}[/tex]

Next, to match the winning number on the gold ball, probability of this event is [tex]\frac{1}{44}[/tex]

Thus overall probability of winning the minimum award is calculated by multiplying the individual probabilities of aforesaid two independent events as follows:

[tex](\frac{1}{44}) (\frac{1}{57}+\frac{1}{56})[/tex]

= [tex]\frac{113}{140448}[/tex]

Above value is the probability of winning the minimum award of $100.

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The given equation written in standard format is 3x - 2y = -6

From the question, we are to write the given equation in standard format.

The given equation is

2y = 3x + 6

The standard form of a linear equation with two variables is

Ax + By = C

Where x and y are the variables

A is the coefficient of x

B is the coefficient of y

and C is the constant

Now, we will write the given equation in the format

2y = 3x + 6

Subtract 3x from both sides of the equation

2y - 3x = 3x - 3x + 6

-3x + 2y = 6

Multiply through by -1

3x - 2y = -6

The standard format of the equation is 3x - 2y = -6

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When a figure is dilated by a factor of 3, the statement about the image of the figure that is true is C Both the area and the perimeter decrease.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.

The x and y coordinates of the original figure are multiplied by the scale factor to discover spots on the dilated image when a dilation in the coordinate plane has the origin as the center of dilation. The algebraic representation of the dilation is (x, y) for scale factor k. (kx, ky).

In this situation, since the figure is dilated by a factor of 3, there will be a reduction. In conclusion, the correct option is C.

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A figure is dilated by a factor of 3. Which of the following statements about the image of the figure is true?

A The perimeter decreases.

B The area decreases.

C Both the area and the perimeter

decrease.

D Both the area and the perimeter

increase.

A linear equation has no solutions if both sides of the equation have distinct constant values but the same variable term.

An equation will have no solutions if the variables are the same on either side.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

For example, an equation can be illustrated as:

x + 5 = x - 5

Collect like terms

x - x = 5 - 5

0

This illustrates that the equation gas no solution.

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Given the triangle LMN and the line (n)

We will find the image of the triangle LMN after the reflection over the line (n)

So, from each point, construct a line segment perpendicular to the line (n)

Then make sure the distance between the point and the line is the same as the line and the image point.

the reflection of the triangle will be as shown in the following figure:

Answer:

72 m

Step-by-step explanation:

We observe that 7y+6=18, and thus y=12/7.

So, the perimeter is:

[tex]2(18+7y+6) \\ \\ =14y+48 \\ \\ =14(12/7)+48 \\ \\ =72[/tex]

Using either method, we can conclude that x - 5 is a factor of the polynomial

This is further explained below.

Explain, based on the fact that, using either approach, whether or not we can consider x-5 to be a factor in the polynomial.

Generally, the equation for the problem is mathematically given as

f(x)=x^3-x^2-17 x-15

Therefore,  If (x-5) is factor of f(x) then at x=5 ,f(x)=0 then apply this

[tex]\begin{aligned}f(x) &=5^3-5^2-17 \times 5-15 \\&=125-25-85-15 \\&=0\end{aligned}[/tex]

In conclusion,Since f(x) is equal to 0 when x = 5, the factor of f is (x-5) (x).

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Answer:

see explanation

Step-by-step explanation:

assuming the dilatation is centred at the origin

then multiply each of the original coordinates by the scale factor 2

A (1, 1 ) → A' (2(1), 2(1) ) → A' (2, 2 )

B (5, 2 ) → B' (2(5), 2(2) ) → B' (10, 4 )

C (3, 5 ) → C' (2(3), 2(5) ) → C' (6, 10 )

Answer:

wouldn't y=8?

Step-by-step explanation:

if x is 3

-5(3)+2y=1

-15+2y=1

2y=16

y=8

If 1/4 of the box is green apples, then 3/4 of the box is red apples. Thus, 3 times the number of green apples is equal to the number of red apples, which would give 3 * 5 = 15 red apples.

The given coordinate's line of reflection is the x-axis, Option D.

After intersecting the co-ordinates A(-3,5), B(2,8) and C(-4,-5) of line 1 and co-ordinates A'(-3,-5), B'(2,-8) and C'(-4,5) of line 2. It is deduced that both lines are similar.

The point of intersection of lines 1 and 2 is on the X-axis as the reflection of the coordinate,

A(-3,5) on the negative x-axis and positive y-axis is A'(-3,-5) on the negative y-axis and the negative x-axis.

B(2,8) on the positive x-axis and positive y-axis is B'(2,-8) on the negative y-axis and the positive x-axis.

C(-4,-5) on the negative x-axis and negative y-axis is C'(-4,5) on the positive y-axis and the negative x-axis.

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The answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is 2/15 .

In the question ,

the expression is given as

=[2-|-2/3-2(-1/5)|] divided by 13

which means

= [2-|-2/3-2(-1/5)|] ÷ 13

Solving the terms inside [ ] first , we have

-2*(-1/5) = 2/5

Substituting the value of -2*(-1/5) in the expression , we get

= [2-|-2/3+2/5|] ÷ 13

Solving the norm(modulus) first

|-2/3+2/5| = |-10/15+6/15|  = |-4/15| = 4/15

Substituting the value of |-2/3+2/5| in the expression , we get

= [2-4/15] ÷ 13

Simplifying further we get ,

= [30/15-4/15] ÷ 13

= [26/15] ÷ 13

= [tex]\frac{\frac{26}{15} }{13}[/tex]

= [tex]\frac{26}{15} \times \frac{1}{13}[/tex]

= 2/15

Therefore , the answer to the expression [2-|-2/3-2(-1/5)|] divided by 13 is  2/15 .

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The x-intercept of the function is found to be x = (y + 80)/5 and the values of x calculated are 17,18,19 and so on.

Given, the x-axis and y-axis are intersected by two intercepts, P(2,0) and Q(0,3). => 3x + 2y – 6 = 0, Consequently, the line's equation is 3x + 2y - 6 = 0. Figure.

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

The given function is:

f(x) = 5x¹ - 80

Let,

y = f(x)

∴ y = 5x – 80

  y + 80 = 5x

  (y + 80)/5 = x

∴ x = (y + 80)/5

If y = 5,

x = (5 + 80)/5 = 17

If y = 10,

x = (10 + 80)/5 = 18

If y = 15,

x = (15 + 80)/5 = 19

Thus, by substituting y values in multiples of 5, we can get x values as 17, 18, 19 and so on.

Thus, the x-intercept of the function is found to be x = (y + 80)/5 and the x values calculated are 17,18,19 and so on.

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The number of quarters and dimes with Maria are 17 and 8 respectively.

Linear equations in mathematics are ones where the greatest power of the variable is one. A linear equation can only have one possible solution: a straight line. Thus, a simultaneous linear equation is a system of two linear equations in two or three variables that are solved concurrently to get a shared answer. Three methods are frequently used to solve simultaneous linear equations: substitution method, elimination method, and graphic method.

Let q be the number of quarters.

Let d be the number of dimes.

Given that the total amount is 5.05 in quarters and dimes

Therefore, 0.25 q + 0.10d = 5.05;

I once more, q = 2d + 1. — (ii) (ii)

Inferring from I and (ii), d = 4.80/0.60 = 8 and 0.25(2d + 1) + 0.10d = 5.05 and 0.60d = 4.80 respectively.

This is put into (ii), and the result is q = 2d + 1 = 2*8 + 1 = 17.

As a result, q = 17 and d = 8

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The explicit formula of the given geometric sequence is a(n) = 8(1/2)ⁿ⁻¹.

Every term in a geometric series is obtained by multiplying the term before it by the same number aₙ= aₙ₋₁ + d is the general phrase for it. The common ratio is denoted by the number r. Any term in the sequence can be used to find it by dividing it by the word before it.

Any number series in which the ratio of succeeding terms is constant is referred to as a geometric sequence. where r is the proportion shared by all following terms. For instance, "2,6,18,54,162,486,1458,...

We have a sequence: 8, 4, 2, 1

The above sequence represents the geometric sequence with common ratio:

r = 4/8 = 1/2

First term a = 8

nth term:

a(n) = 8(1/2)ⁿ⁻¹

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Answer:

The correct answer is 1/6 for the question, "In 3 billion repetitions of an experiment, a random event occurred in 500 million cases..."

The correct answer is 1/10 for the question, "A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad."

Hope this helps you! May I please get brainliest if I'm correct?

[tex]x^{2} +5x-3=-4x-3\\x^{2} +5x+4x-3+3=0\\x^{2} +9x=0\\\\x(x+9)=0\\x=0 or x+9=0\\x= -9[/tex]

I hope this helps.

Answer:

x = 0

or

x = (-9)

Step-by-step explanation:

[tex] {x}^{2} + 5x - 3 = - 4x - 3[/tex]

transfer like terms to the same side of the equation

[tex] {x}^{2} + 5x + 4x = - 3 + 3[/tex]

Add/subtract like terms

[tex] {x}^{2} + 9x = 0[/tex]

Now we can factor terms

[tex] {x}^{2} = x \times x \: and \: 9x = 9 \times x[/tex]

we can write them with their common divisor

x*(9+x) = 0 for this equation to be correct either x = 0 or (9+x) = 0

if x = 0 well then that's the first value of x

if (9+x) = 0 then x = -9 and this is the second value of x

The verdict on whether the frequency distribution given appears to be normal is; No, there is not a concentration of frequencies in the middle.

On this note, since a major distinctive feature of a normal distribution is that; there is a concentration of frequency in the middle and additionally, a normal distribution infers symmetry in the frequency distribution.

Therefore, since the middle data value in this scenario is; (80 - 84) which has a frequency of; 4 which is not the highest.

On this note, the frequency distribution is not a normal distribution and this is because there is not a concentration of frequencies in the middle.

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Answer:

Step-by-step explanation:

Drawing two marbles at once is the same as drawing one and then drawing the second  without replacing the first.

Starting with 8 red balls and 14 blue balls, the probability of drawing a red ball  is 8/22 = 4/11.

Assuming red was drawn in the first draw, the probability of getting a red ball in the second  draw means that you are  drawing from a collection containing 7 red balls and 14 blue balls, so the probability is: 7/21 = 1/3.

So when calculating the odds of the second draw, we took into account the change in the number of hits and the number of chances, so these two events are  independent and the total probability is the product of the two individual probabilities.

P(2 reds) = (4/11) (1/3) = 4/33

The probability that both marbles are red is 4/33.

It should be noted that from the information given, the jar contains 8 red marbles and 14 blue marbles.

The total marbles will be:

= 8 + 14 = 22

The probability of selecting the first red marble will be:

= 8/22 = 4/11

The probability of selecting the second red marble will be:

= 7/21 = 1/3

Therefore, the probability that both marbles are red will be:

= 4/11 × 1/3

= 4/33

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There are 14 students in set R.

There are 10 students in set R but not in set S.

There are 11 students in set S.

There are 21 total students in sets R and S.

There are 4 students common to sets R and S.

The music teacher will get $280 for the piano students.

The music teacher will get $140 for the saxophone students.

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Answer:

a. Using a graphing calculator: 4.486089611

b. To 2 decimal places: 4.49

oluition

or this case we have the folllowing:

Part a

e select (0,0) and (3,24)

the slope would be:

then the equation for this case would be:

y= 8x +b

Using (0,0) we can find b:

0 ) 8*0 +b

b= 0

Then the equation is:

y= 8x

Part b

or this case we can conclude that for each n8 passengers is required a new car for the rooller coaster

0.166 meters is the minimum distance between the contours on the map that allow Antonio to go uphill. For downhill, it is 0.1 meters.

Given,

The maximum gradient uphill is 0.3 meters.

The maximum gradient downhill is 0.5 meters.

distance according to the scale,

1000m ÷ 2m = 500 meters

a) distance for uphill,

= 25 ÷ (500 × 0.3)

= (25 × 10) ÷ (500 × 3)

= 250 ÷ 1500

= 1 ÷ 6

= 0.166 meters

b) distance for downhill,

= 25 ÷ (500 × 0.5)

= 250 ÷ (500 × 5)

= 250 ÷ 2500

= 1 ÷ 10

= 0.1 meters

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Answer: That is the answer

Step-by-step explanation: