What is the distance between the points (-3, 8) and (16, 8)?​

Answer:

y = 3x

Step-by-step explanation:
Slope = change in y / change in x

x, y
Given points: (2,6) and (1,3)

2 - 1 = 1
6 - 3 = 3
3/1 = 3
y = mx
y = 3x

The evaluation of the graph of the derivative of f within the domain, -3 ≤ x ≤ 3 are as follows;

(a) The relative maximum is the point x = -2

The relative maximum is the point x = 0

(b) The graph is concave up at the relative minimum point

(c) Please find attached the graph of f created with MS Word

The derivative of f is the rate of change of the function f at the point in the domain of f. A symbol for the derivative of f is f'.

(a) The characteristics of a location of relative maximum and relative minimum based on the derivative are;

At a local maximum, we get; f'(x) = 0, f''(x) < 0

f' > 0 to the left of the relative maximum and f'< 0 to the right of the relative maximum, therefore;

At a relative minimum, we get; f'(x) = 0, f''(x) > 0

f' < 0, to the left of the x-value of the relative minimum and f'> 0, to the right of the right of the relative minimum, therefore;

(b) The graph of f is concave up at the relative minimum, where f' < 0 to the left sand f' > 0 to the right of the value  of x

Therefore, the graph is concave upwards at the point x = 0

(c) Please find attached the possible graph of f created using MS Word, where the corresponding points are;

The point x = -2 as the relative maximum point

The point x = 0 as the relative minimum point

The point x = 0 as the point at which the graph is concave upwards

f' > 0 to the left of the point x = 2, and f' > 0 to the right of x = 2, the second derivative, f'' = 0 at x = 2, therefore, the point x = 2 is a point of inflection

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Answer: The solution of the ordered pairs are (0,1) and (1,3).

Step-by-step explanation:

The comparison that exists between two-and-one-fourth to two-and-one-eighth would be = 2 × 1/4 is greater than 2 × 1/8.

A fraction is defined as the representation of part of a whole number which has a numerator located at the top and the denominator located below.

The given number and fraction for comparison is as follows:

2 × 1/4 = 1/2

2 × 1/8 = 1/4

Therefore when two-and-one-fourth to two-and-one-eighth are compared the former is. greater than the later.

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On solving the provided question, we can say that - the initial value in number line will jump to +12 value

A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.

here,

the initial value of the number line is = 15

and on adding 12

it will jump to = 15 + 12

= 27

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Proportionately, the dollar amount of the Gentrys' annual transportation and taxes combined is $11,004.70.

Proportion refers to the relative value of a number compared to another amount.

Proportions are ratios equated to one another.

Multiplying the proportional percentage of the combined transportation and taxes to the total budget of the Gentrys gives the dollar amount.

Yearly income for the Gentrys = $29,742.42

Percentage of income that is taxes = 28%

Percentage of income that is transportation = 9%

Combined percentage of taxes and transportation = 37% (28 + 9)

Combined transportation and taxes in dollars = $11,004.70 ($29,742.42 x 37%)

Thus, based on their proportional percentages, the Gentrys' combined annual transportation and taxes are $11,004.70.

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Answer: 14

Step-by-step explanation:

300 minus 80 = 220

220 is the budget for the shirts so we divide 220 by 15 to get 14

Hope this helps!

Answer:14 shirts

Step-by-step explanation:300- 80 = 220

220/ 15 = 14.6  round 14.6 to 14 (because you cant buy half a shirt)

you can get 14 shirts

Using Pythagoras theorem, the height of the building is 161.6m and the length of the ramp is 319.2m

According to Pythagoras' Theorem, the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the two legs. It can be mathematically stated as a²+b² =c², where a and b represent the lengths of the triangle's two legs and c represents the length of the hypotenuse.

7)

Using Pythagoras's theorem, we can find the height of the ramp.

185² = 90² + b²

b² = 185² - 90²

b² = 26125

b = √26125

b = 161.6m

8)

Using Pythagoras's theorem,

x² = y² + z²

320² = 10² + z²

z² = 320² - 10²

z² = 102300

z = 319.8m

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The line from the hospital meets the line from the stadium, is where the University is located.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A sketch of the described bearings and locations of the stadium, university and the hospital is presented in the attached image to this question.

On The map, draw a four-cardinal points' cross at the stadium draw a line from the bearing 050° from the stadium's four cardinal points' cross. Leave the line as it is.

Then, draw another four cardinal points' cross at the hospital and draw a line from the bearing 300° from the hospital's four cardinal points' cross.

Wherever the line from the hospital meets the line from the stadium, is where the University is located.

Hence,  the line from the hospital meets the line from the stadium, is where the University is located.

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The exact solution to the system of equations shown on the graph is

(-1 1/5, 4 3/5)

The solution of a graph is where the two graphs intersects. This point is known as point of intersection and at this point we have the solution

The point of intersection of the two graphs as shown are read, Knowing that all interval marked represents one unit

x intersection: the point is more than -1 and not up to -1.5, which is a value at exactly half of the two intervals hence the possible option is -1 1/5

y intersection: the point is more than 4 and more than to 4.5, which is a value at exactly half of the two intervals hence the possible option is

4 3/5

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The linear function equation represented by the graph will be f(x) = [tex]-\frac{x}{3} - 3[/tex].

Let y = f(x)

Given, when x = 0, y = -3

and when y = 0, x = -9

(x₁ , y₁) = (0, -3)

(x₂ , y₂) = (-9, 0)

Now linear equation

[tex]\frac{y - y_{1} }{x - x_{1} } = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

[tex]\frac{y - (-3) }{x - 0 } = \frac{0 - (-3) }{-9 - 0 }[/tex]

y+3 =  [tex]-\frac{x}{3}[/tex]

y = [tex]-\frac{x}{3} - 3[/tex]

or f(x) = [tex]-\frac{x}{3} - 3[/tex]

Therefore, the linear function equation represented by the graph will be f(x) = [tex]-\frac{x}{3} - 3[/tex].

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Increasing the value of a variable change the value of the expressions

An expression is combination of variables, numbers and operators.

A variable in expression is a characteristic that can be measured and that can assume different values.

When the variable value is increased then the value of expression will be also increases because with the variable the value of expression is interlinked.

2x+4 is an expression

Let x=1

then 2(1)+4=6

Value of expression is 6.

If x=2 then the value of expression is 8

Now the other expression is 5x+3

For x=1, 8 is the value of expression.

For x=2, 13 is the value of expression.

as values of x increases then value of expression will be increased.

Hence,  increasing the value of a variable change the value of the expressions

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6. a) In 10 squares there are 22 dots

6. b) There are 102 squares are in the diagram which has 104 dots.

6. c) t(n) = a + (n - 1) d

7. a) mean = 6; median = 5

7. b) new card number = 14

This can be solved using geometic series concept.

A geometric series is one where each pair of consecutive terms' ratios is a fixed function of the summation index. The ratio is a rational function of the summation index in a more comprehensive sense. creates what is known as a hyper geometric sequence. It is arithmetic if there is a common difference between the sequences. You can bet that anything is geometric if it has a common ratio. Similar to how the word arithmetic series denotes that each phrase is the arithmetic mean of its two neighbors, the name geometric series denotes that each term is the geometric mean of its two neighbors.

6. In the given figure we see that the dots are present here form a series.

In 1 square there are 4 dots.

In 2 squares there are 6 dots.

In 3 squares there are 8 dots.

So, they form a series.

a)

In 10 squares there are 22 dots

b)

There are 102 squares are in the diagram which has 104 dots.

c)

The formula of the series is:

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

here a = 4 and d = 2

7.

a)

Jemina has 3 cards with the number of 5,2 and 11

Thus, mean = 5+2+11 /3 = 6

median = 5

b)

Next Jemina takes another card and the mean goes up by 2.

So, the number of new card:

2+5+x+11/4 = 8

or, 18 + x = 32

or, x = 14

So, new card number = 14

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Answer:

Step-by-step explanation:

6. a) In 10 squares there are 22 dots

6. b) There are 102 squares are in the diagram which has 104 dots.

6. c) t(n) = a + (n - 1) d

7. a) mean = 6; median = 5

7. b) new card number = 14

considering the graph of exponential function given , the statement that correctly compare the function is

X - intercept and Y - intercept are the two main intercepts.

The x-intercept of a point where the line crosses the x-axis, while the y-intercept is where the line or graph crosses the y-axis.

At x - intercepts the value of y is zero h=following the given values the x intercept for function f is 3 units and 4 units for the y intercept

For function g, following the table, the x intercept is (2, 0) and the y intercept is (0, 4)

the end behavior for function f is x → ∞, y → -∞

the end behavior for function g is x → ∞, y → -∞

hence they have different x and y intercept but same end behavior

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From the given figure the angles in the form as Same side interior angles, vertically opposite angles and etc.

What are parallel lines ?

Parallel lines can be defined as the lines which are equi distant from each other and they never intersect.

Given in the figure,

parallel lines and we have to find the how the angles are related to each other.

In the given figure 1 ,

The angles are Same side Interior Angles .

In the given figure 2 ,

The angles are Vertically opposite  Angles .

In the given figure 3 ,

The angles are Alternate Exterior Angles .

In the given figure 4 ,

The angles are Alternate Interior  Angles .

In the given figure 5 ,

The angles are Alternate Exterior  Angles .

In the given figure 6 ,

The angles are Corresponding Angles .

In the given figure 8 ,

The angles are Vertically opposite Angles .

In the given figure 9,

The angles are Alternate Interior Angles .

Hence, From the given figure the angles in the form as Above.

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Answer: this is very easy

Step-by-step explanation:

The amount of tax paid is found applying the proportions, and the correct proportion is obtained from the table in the problem.

Her taxable income is given as follows:

$125,000.

Hence the tax proportions are given as follows:

Meaning that the taxes paid are given as follows:

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The equality's transitive property is If a = 7, then a = q, q = s, s = t, and t = 7 .The equality reflex states that if 4x Plus 2=6, then 4x must equal 6.

Two straight lines or rays intersect at a common endpoint to form an angle. The vertex of an angle is the point at which all points meet. Angle is derived from the Latin word angulus, which means "corner." Two rays (half-lines) combined into an angle have a single endpoint. The latter is known as the vertex of the angle, and the rays are known as its sides, occasionally as its legs, and occasionally as its arms. Two lines converge at a common point to form an angle.

given

The equality's transitive property is If a = 7, then a = q, q = s, s = t, and t = 7 .

The equality reflex states that if 4x Plus 2=6, then 4x must equal 6.

The equality's subtraction property states that if 3x = 9 then x = 3.

The premise of angle congruence is Since x = 7 if 7 = x

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The volume of the cone if, The slant height is 5 cm, and the radius of the cone is 3 cm, is 37.68 cm³.

A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm³. By multiplying its length, height, and width, you may determine this.

Given:

The slant height, s = 5 cm, and the radius of the cone is 3 cm,

Calculate the height of the cone as shown below,

slant height² = height² + radius²

5² = h² + 3²

h² = 25 - 9

h = 4

Calculate the volume of the cone as shown below,

The volume of the cone = π × 3² × 4 / 3

The volume of the cone = 3.14 × 9 × 1.33

The volume of the cone = 37.68

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Answer:

$110

Step-by-step explanation:

$20 + ($15/hr)(6 hr) = $110

To simplify the expression (9 - 1x + 2x) - (2x^2 - 3x + 5), you can follow these steps:

1. Combine like terms:

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

2. Simplify:

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

3. Combine like terms:

2x + 9 - 2x^2 + 3x - 5

4.Simplify:

-2x^2 + 5x + 4

Therefore, the simplified form of the expression is -2x^2 + 5x + 4.

The required repeated addition is given as 2.02 + 2.02 + 2.02.

The repeated addition of a number is the multiplication of the number with the number of times the number is repeated.

here,
The question seems to be incorrect,
The complete solution is provided at the end of the solution,
2.02 × 3, is the given expression, which is a multiplicative expression as 3 times of 2.02.
So the repeated addition is given as,
2.02 × 3 = 2.02 + 2.02 + 2.02

Thus, the required repeated addition is given as 2.02 + 2.02 + 2.02.

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Complete question.

Write 2.02 × 3 in repeated addition.

There 9% represent babies born with a birth defect, and 09-99(9%) to represents babies without birth defects.

The percentage is defined as a ratio expressed as a fraction of 100.

According to one study, 45 out of every 500 babies born in the world have a serious birth defect.

Use two-digit numbers 00-99; let 00- represent babies born with some kind of major birth defect.

p = x/n

p = 45/500

p = 0.9 = 9%

So, the simplest way to assign random numbers to conduct a simulation based on this statistic, it can use 00-99(9%) to represent babies born with a birth defect, and 09-99(9%) to represent babies without birth defects.

Hence, the correct answer would be an option (B).

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Answer: 70mph

Step-by-step explanation:

im assuming this is in miles per hour not km or ms/s

Answer:

is 42 3 fraction

Step-by-step explanation:

Evaluate 4/2 for w = 3​

Dimensions of the portrait are 12.25 cm to the nearest tenth of a centimeter.

What are Dimensions?

The dimension of a mathematical space is defined as the smallest number of coordinates required to specify each point within it.

To have the area of the mat equal to the area of the portrait, the portrait and the mat must have the same area. Since the mat is 7 cm wide, we can use that to find the dimensions of the portrait.

If the portrait is square, the side length will be the same as the width of the mat, plus the width of the portrait.

So, portrait width = 7 cm + portrait width

Solving for portrait width:

portrait width = 7 cm / 2 = 3.5 cm

So, the dimensions of the portrait are 3.5 cm x 3.5 = 12.25 cm

Therefore, dimensions of the portrait are 12.25 cm to the nearest tenth of a centimeter.

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Answer:

0

Step-by-step explanation:

(8x-1)/2=(8x+7)/5

We move all terms to the left:

(8x-1)/2-((8x+7)/5)=0

We calculate fractions

8x/()+(-((8x+7)*2)/()=0

We calculate terms in parentheses: +(-((8x+7)*2)/(), so:

-((8x+7)*2)/(

We multiply all the terms by the denominator

-((8x+7)*2)

We calculate terms in parentheses: -((8x+7)*2), so:

(8x+7)*2

We multiply parentheses

16x+14

Back to the equation:

-(16x+14)

We get rid of parentheses

-16x-14

Back to the equation:

+(-16x-14)

We get rid of parentheses

8x/()-16x-14=0

We multiply all the terms by the denominator

8x-16x*()-14*()=0

We add all the numbers together, and all the variables

8x-16x*()=0

Answer:

X= 19/24

Step-by-step explanation:

Cross multiply the two sides then we have something like this 5(8x-1)=2(8x+7)

Solve the equation 40x-5=16x+14

Group the like terms 40x-16x=5+14

Solve the second equation and it gives us X= 19/24

The numeric value of the function f(x) at x = 1 is given as follows:

f(1) = 24.

The table is composed by a set of points in the following format:

(x, f(x)).

In which the input and output variables are given as follows:

From the points given in the table, the numeric values are listed as follows:

Any of these values can be used to evaluate the function at the input of x, hence at the input of x = 1, the numeric value is given as follows:

f(1) = 24.

The function is given by the image presented at the end of the answer.

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As per the given function rule , y = -6x + 1 , the values will be 31, 7, 1, -5 -5 , 1, 1, -6X+1, -17.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).

The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.

As per the given function rule in the question i.e y = -6x + 1

X                         Y

-5                         31

-1                          7

0                           1

1                           -5

1                           -5

0                            1

0                            1

X                   -6X +1

3                         -17

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Step-by-step explanation:

Let M be the number of multiple choice problems and S be the number of short answer problems.

We can set up the following system of equations to represent this situation:

M * 3 + S * 4 = 111

M + S = 32

The first equation represents the total number of points on the test, and the second equation represents the total number of problems on the test.

To solve this system of equations, we can use a method such as graphing, substitution, or elimination.

Using the substitution method, we can solve for one variable in terms of the other and substitute it into the other equation. For example, we can solve the first equation for M:

M = (111 - S * 4) / 3

Then, we can substitute this expression for M into the second equation:

(111 - S * 4) / 3 + S = 32

Solving this equation for S gives us the number of short answer problems:

S = 12

To find the number of multiple choice problems, we can substitute this value for S into the expression for M that we derived earlier:

M = (111 - 12 * 4) / 3

Solving this equation gives us the number of multiple choice problems:

M = 8

Therefore, there are 8 multiple choice problems and 12 short answer problems on the test.