The function f(x)=-1/2x+3 and g has a lesser y-intercept than f; the maximum value and the y-intercept of g are not equal; g increases, than decreases. Find the vertex and y-intercept of g.

It is an exercise of the equation of the line, related to the subject of the slope of a line is a fundamental measurement in analytical geometry and mathematics in general. It is a measure that indicates the inclination of a line, that is, how much the y coordinate changes for each unit that the x coordinate changes. The slope is represented by the letter m and is defined as the quotient between the variation of the y coordinates, divided by the variation of the x coordinates.

The importance of slope extends beyond analytic geometry, and it is used in many other areas of mathematics and science. For example, in physics, slope is used to calculate the velocity and acceleration of a moving object. In statistics and econometrics, slope is used to interpret data and make predictions from it.

Also, slope is used in solving analytic geometry problems. For example, slope can be used to find the equation of a line from two known points, or to determine whether two lines are parallel or perpendicular.

To calculate the slope of the line, we apply the following formula:

m = (y₂ - y₁)/(x₂ - x₁)

Now we find the points of x and y.

x₁ = -4 , y₁ = 2

x₂ = 0 , y₂ = -4

We substitute our data in the slope formula and solve, then

 m = (y₂ - y₁)/(x₂ - x₁)

 m = (-4 - 2)/(0 - (-4))

 m = (-6)/(4)

 m = - 1.5

The slope between the points (-4,2) and (0,-4) is -1.5.

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The perimeter of the given triangle is: P = √10 + 4√2 + √26

The formula for the distance between two coordinates is expressed as:

d = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus:

RS = √[(1 - 2)² + (1 + 2)²]

RS = √10

Similarly, we can say that:

ST = √[(-3 - 1)² + (-3 - 1)²]

ST = √32 = 4√2

RT = √[(-3 - 2)² + (-3 + 2)²]

RT = √26

Thus, perimeter of triangle is:

P = √10 + 4√2 + √26

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"Mode"

can have a LOT of different meanings. However, because you put this question under "mathematics", Im assuming you want to know more about the mode related to statistics.

Mode is defined as the number that repeats itself the most times in a data set!

Lets say you have a data set [1,2,3,4,5,6,7,8,9]

That data set has no mode, as every number presents itself the same number of times, in this case being 1.

Take this data set: [1,1,2,3,4,5,6,7,8,9]

That data set has a mode of 1. The number "1" presents itself twice in the data set, while every other number presents itself once.

Take this data set [1,1,2,3,4,5,5,6,7,8,9]

That data set has a mode of 1 AND 5. They BOTH repeat themselves TWICE, which every other number only ocurrs once.

If you have any other questions, comment below this answer.

~~~Harsha~~~

Answer:

A and E

Step-by-step explanation:

A. -4 (2x - 1) = -8x + 4

B. 4 (2x - 1) = 8x - 4

C. 4x (2 - 1) = 8x - 4

D. 4x (2x + 1) = 8x² + 4x

E. 4 (-2x + 1) = -8x +4

F. 4 (2x + 1) = 8x + 4

Answer:

14336

Step-by-step explanation:

the general term is:

s(n) = 7*(2)^(n-1)

you can check it by plugging in some number:

s(3) = 7*2^(3-1) = 7*4 = 28

s(4) = 7*2^(4-1) = 7*8 = 56

The 12th term is:

s(12) = 7*2^(12-1) = 7*2^11 = 7*2048 = 14336

Answer:

50%

Step-by-step explanation:

among the available choices is 9456.

What are place values?

Place values describe a digit's location within a number and the value that digit represents based on that location. Each digit in a number is given a place value in our decimal number system according to where it is from the rightmost side. The first position to the right is known as the one's place, followed by the tens place, hundreds place, thousands place, and so on, with each position to the left denoting ten times the value of the position to its immediate right.

The new set of numbers is produced by substituting the number 9 for the previous ones:

7989, 9456, 4592, 3972

We can see that 9 is the greatest digit by comparing the leftmost digit of each integer to itself. Due to the absence of a 9 in the leftmost digit, we can rule out alternatives 7989 and 3972.

Second from the left is then put up for comparison. The number is four in both 9456 and 4592. The 5 in 9456, on the other hand, is greater than the 5 in 4592 and is the next digit to the right in the number. As a result, option 4592 can be disregarded.

And that leaves 9456 and 7989 for us to work with. 9 in the number 9456 is the leftmost digit, which is greater than 7 in the number 7989. In both 9456 and 7989, the second digit is 4, making them the same. 9456's third digit, however, is 5, which is larger than 7989's eighth digit, which is 8. The biggest number,

therefore, among the available choices is 9456.

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The length of the side a is 8.55 units.

Given is a right triangle, the side c which the hypotenuse is 25 units, and an acute angle A is 20°,

We need to find the length of the side a,

Considering the angle, A as reference angle, we have,

Sin A = a / c

Sin 20° = a / 25

a = Sin 20° × 25

a = 8.55

Hence, the length of the side a is 8.55 units.

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Answer:

Step-by-step explanation:

the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches ) and to the left end of the x-axis (as x approaches

Answer:

Please mark me the brainliest.

Step-by-step explanation:

For each question, there are two possible outcomes: true or false. Therefore, the total number of possible outcomes for a 6-question true-or-false test is 2 x 2 x 2 x 2 x 2 x 2, which is equal to 2^6. Using a calculator, we can find that 2^6 is equal to 64.

Therefore, the answer is option D: 64.

The two distributions can be concluded as:

The distributions are similar.

The means-to-MAD ratio is 3.

Options A and C are the correct answer.

The MAD (Mean Absolute Deviation) is a measure of variability similar to standard deviation, but it measures the average absolute difference between each value and the mean, regardless of the direction of the deviation.

The means-to-MAD ratio is a measure of how spread out the data is, relative to the mean.

Since the means-to-MAD ratio for Data Set 1 is 3 and the means-to-MAD ratio for Data Set 2 is 30, Data Set 1 is more spread out than Data Set 2.

However, since the ratio is not extremely different (i.e., not greater than 10), the two distributions can still be considered similar.

Thus,

The two distributions can be concluded as:

The distributions are similar.

The means-to-MAD ratio is 3.

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The translations to each graph are described as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Hence the meaning of each operation is given as follows:

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The equation of a line that is parallel to y = 12x + 6 is of the form:

y = 12x + b

The relationship between the coordinates of each point (x, y) on a line is represented by the equation of a line, which is linear in the variables x and y. All of the points on the line satisfy the equation, in other words.

A line is parallel to the line y = 12x + 6 if and only if it has the same slope as the given line.

The slope-intercept form of the equation of a line is:

y = mx + b

where m is the slope of the line and b is the y-intercept.

Since the given line y = 12x + 6 has a slope of 12, any line that is parallel to it must also have a slope of 12. Therefore, the equation of a line that is parallel to y = 12x + 6 is of the form:

y = 12x + b

where b is any constant.

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The minimum amount of wrapping paper, needed to cover the package surface area is 174 square inches.

From the given three dimensional figure,

Total surface area = Area of 2 similar trapeziums + Area of rectangles of 4 different rectangles

We know that, area of a triangle = 1/2 ×Base×Height and area of a rectangle is Length×Breadth.

= 2×1/2(7+3)×3+8×5+8×3+8×3+8×7

= 30+40+24+24+56

= 174 square inches

Therefore, the minimum amount of wrapping paper, needed to cover the package surface area is 174 square inches.

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The equation represented in the graph shown is,

⇒ y = x² - 2x - 8.

Now, We know that the parabola goes down from the left and passes through the point (-2,0),

then goes to a minimum of (1,-9), and then goes up to the right through the point (4,0).

Hence, We can use this information to determine the equation of the parabola in vertex form, which is,

⇒ y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

Step 1: Finding the vertex We already know the vertex of the parabola is (1,-9) because it is given in the problem.

Therefore, h = 1 and k = -9.

Step 2: Finding the value of "a" To find the value of "a", we can use one of the points on the parabola (either (-2,0) or (4,0)).

Let's use the point (-2,0).

When x = -2, y = 0.

Therefore, we can substitute these values into the vertex form equation and solve for "a":

0 = a(-2 - 1)² - 9

0 = a(-3)² - 9

0 = 9a - 9

9 = 9a

a = 1

Therefore, the value of "a" is 1.

Step 3: Writing the equation in vertex form Now that we know the vertex (h, k) and the value of "a", we can write the equation in vertex form:

y = 1(x - 1)² - 9

Simplifying this equation gives us:

y = x² - 2x - 8

Therefore, the equation represented in the graph shown is option (a) y = x² - 2x - 8.

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Answer:

The formula for the volume of a pyramid is:

V = (1/3) × base area × height

We know that the base of the pyramid is a square with a side length of 7 centimeters. So, the base area is:

base area = side length squared = 7² = 49 square centimeters

We also know that the volume of the pyramid is 196 cubic centimeters. Plugging these values into the formula above and solving for the height:

196 = (1/3) × 49 × height

588 = 49 × height

height = 588/49

height = 12

Therefore, the height of the pyramid is 12 centimeters.

When the odds against an event are given as "a:b", the probability of the event can be found by using the formula:

Probability of the event = b / (a + b)

In this case, the odds against the event are 3:7, which means that the probability of the event not occurring is 3/(3+7) or 3/10. Therefore, the probability of the event occurring is:

1 - 3/10 = 7/10

So the probability of the event is 7/10 or 0.7 (70%) when the odds against the event are 3:7.

The second location result in the largest area of grass that Jaeger can eat, which is approximately 353.57 square meters.

We may infer from the facts provided that Jaeger the goat will be confined to a 10- by-16-meter rectangular shelter by means of a 15-meter chain. All of the grass along the chain may be consumed by Jaeger. At three separate points in the shed, we are instructed to locate the patch of grass that Jaeger can eat.

Let's consider the three different locations as follows:

Attach the chain to a corner of the shed.

Jaeger can only eat as much grass as is contained inside a quarter-circle with a radius of 15 meters (the length of the chain) if the chain is fastened to a shed corner. This quarter-circle's area is:

Area = (1/4) x π x (15 meters)²

Area = 176.71 square meters (approx)

Affix the chain to the middle of one of the shed's longer sides.

This semicircle's area is:

Area = (1/2) x π x (15 meters)²

Area = 353. 57 square meters (approx)

To the center of one of the shed's shorter sides, fasten the chain.

This circular sector's area will be as follows:

Area = (90/360) x π x (15 meters)²

Area = 176.71 square meters (approx)

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Answer:

23.5

Step-by-step explanation:

13.2 + 0.9 = 14.1

14.1 / 0.6 = 23.5

The value of the side x = 26. 316cm

We need to know the different trigonometric identities. These identities includes;

Their different ratios are given as;

sin θ = opposite/hypotenuse

tan θ = opposite/adjacent

cos θ = adjacent/hypotenuse

From the information given, we have that;

Angle , θ = 35 degrees

Opposite side = 15

Hypotenuse side =

Substitute the values

sin 35 = 15/x

cross multiply

x = 26. 316cm

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The value of θ for the given equation is θ = 54.74°.

The inverse cosine function (arccos) has a range of 0 to arccos(x), where x is a real number in the range of -1 to 1. An angle in radians between 0 and, which measures the angle between the x-axis and the terminal side of a unit circle that crosses the line between the origin and the point (x, y), is the result of the inverse cosine function. To put it another way, the inverse cosine function returns the angle whose cosine is equal to a specified value x.

The given equation is 4sec(θ) - 7 = 0:

Now, isolating the value of sec(θ) we have:

4sec(θ) = 7

sec(θ) = 7/4

Now, converting into cos we have:

cos(θ) = 4/7

θ = arccos(4/7)

θ = 54.74°

Hence, the value of theta for the given equation is θ = 54.74°.

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Completing the table using the rounded values showing the relative frequencies is as follows:

Column Relative Frequency Table

                            Men         Women        Total

January - June    25%            25%             25%

July - December 75%             75%             75%

Total                   100%           100%           100%

Relative frequency shows the quotient between the number of events and the total number of possible events occurring.

The quotient of relative frequency is expressed over 100 to show the result in percentage terms.

Frequency Table

                            Men   Women    Total

January - June      21           19         40

July - December  62          58        120

Total                     83          77         160

Column Relative Frequency Table

                            Men                Women           Total

January - June    25% (21/83)     25% (19/77)        25% (40/160 x 100)

July - December 75% (62/83)     75% (58/77)       75% (120/160 x 100)

Total                   100%                100%                  100% (160/160 x 100)

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The Match of each point of intersection with the system of equations whose solution is at that point are

For the 1st system is:

y = -2x - 3  ------- (1)

y = 2x - 1 (2)

So one need to equate (1) and that of (2) so it will be:

2x - 1 = -2x - 3

Add 2x to both sides

4x - 1 = - 3

Add 1 to both sides

4x = -2

Divide both sides by 4

x = -1/2

- Substitute the value of x in equation (1) or (2)

y = 2(  ) - 1

y = -1 - 1

y = -2

Therefore, the point of intersection of the two equations is found to be (-1/2, -2), and it is shown by the letter Z.

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The corresponding answers to each expression are;

1. 5x x (3+5) / 12 - 2 x 2 = 5

2. (11 + 3²) ÷ 4 - 2 = 3

3. (48 - 12 ÷ 2 / 7 - 1) + 1 =  8

4. (25 - (4 - 1)² / 2³ - 4) + 2 = 6

5. (3² - 4) x (7 + 5) / -12 ÷ -3 = 15

1. 5 x (3+5) / 12 - 2 x 2 =

5 x 8/ 12 - 4=

40/8 = 5

2. (11 + 3²) ÷ 4 - 2 =

11 + 9  ÷  4 - 2=

20  ÷  4 - 2

5 - 2 = 3

3. (48 - 12 ÷ 2 / 7 - 1) + 1 =

(48 - 6/ 6) + 1 =

42/6) + 1 =

7 + 1 = 8

4. (25 - (4 - 1)² / 2³ - 4) + 2 =

25 - 9/ 4) + 2 =

16/4 + 2 =

4 + 2 = 6

5. (3² - 4) x (7 + 5) / -12 ÷ -3 =

9-4 x 12/ 4 =

5 x 12/ 4=

60/4 = 15

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The value of x is equal to 17 degrees.

In Mathematics and Geometry, the central angle property states that an inscribed angle is equal to one-half the measure of a central angle that is subtended by the same arc.

Based on the information provided about circle C, the central angle of circle P is represented by m∠C and the inscribed angle is represented by (x + 4)°.

This ultimately implies that, the measure of the central angle is twice (double) the measure of the inscribed angle;

m∠C = 2(x + 4)°.

3x - 9 = 2(x + 4)°.

3x - 9 = 2x + 8

3x - 2x = 8 + 9

x = 17

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Answer:

11.5%

Step-by-step explanation:

[tex]45,500*x=5232.5\\x=11.5%[/tex]

The fraction that can be found on a ruler would be = 1½ inch. That is option C.

Fraction is defined as the expression of a number in the form of numerator and denominator.

The meter rule is the device that is used in the measurement length of an object.

A meter rule can be marked as in centimeter or in inches.

The best fraction that can be seen on a meter rule is 1½in = 1.05in.

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There are 96 cubes are there for each of the length, width, and height of the prism.

The volume of a rectangular prism is 12 yd³.

Given that;

A rectangular prism has a length of 2.5 yd, a width of 1.5 yd, and a height of 1.5 yd.

Hence, length 2.5 and 1/2 yd​ = 2 1/2 + (1/2) yd = 5/2 + 1/2 = 6/2= 3 yd

Width 1.5 and half yd​ = 1 1/2 + (1/2) yd = 3/2 + 1/2 =  (4/2) = 2 yd

Height 1.5 and half yd = 1 1/2 + (1/2) yd = 3/2 + 1/2 =  (4/2) = 2 yd

Hence, Cubes of edge length (1/3) yd are used to fill the rectangular prism.

The length would contain (3) ÷ (1/2) = 6

The width would contain (2) ÷ (1/2) = 4

The height would contain (2) ÷ (1/2) = 4

Hence, Number of cubes are there for each of the length, width, and height of the prism

6 × 4 × 4 = 96 cubes

Thus, There are 96 cubes are there for each of the length, width, and height of the prism.

And,.

The volume of rectangular prism = 3 × 2 × 2 = 12

The volume of a rectangular prism is 12 yd³.

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