What is the equation of the linear function in slope-intercept form described by this table?

f(x)= _____x + __________

The standard form of  the equation is(x + 2)² +(y - 5)² = 26

The equation of a circle in standard form is

(x - a)² + (y - b)² = r²

where (a , b) are the coordinates of the centre and r the radius

The centre is at the midpoint of the endpoints of the diameter and r is the distance from the centre to either of the 2 endpoints

Find centre using the ' midpoint formula'

(a , b) = [  (3 - 7),  (4 + 6) ] = (-2 , 5)

to find r use the ' distance formula '

with (-2 ,5) and (3 , 4)

r = √(3 + 2)² + (4 - 5)² = √(25 + 1 ) = √26 ⇒ r² = (√26)² = 26

(x + 2)^² + (y - 5)² = 26 it is the equation in standard form'

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle.  we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.

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Answer: The definition/meaning of it is a theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Step-by-step explanation: If you need the equation solved, I can try just type under this.

The graph is attached below:

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Given:

x − 10 ≤ x ≤ 15

as, the given inequality we have to break the inequality is

x − 10 ≤ x and x ≤ 15

The graph to the inequality is attached below.

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The amount of bidder needs to put into a kitty for the other bidders to be compensated will be $3,000.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

An object may be claimed jointly by 4 persons with the intent to split it using the sealed bid method. The winning price is $4,000.00.

The amount of bidder is given as,

⇒ $4,000 - $4,000/4

⇒ $4,000 - $1,000

⇒ $3,000

The amount of bidder needs to put into a kitty for the other bidders to be compensated will be $3,000.

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If the longer diagonal is 4 more than the shorter diagonal of a kite. The area is 5 times the shorter diagonal. If the shorter side is 6m. The longer diagonal is 10m and the area is 30m².

The longer diagonal is calculated as:

Longer diagonal=6+4

Longer diagonal=10m

The area is calculated as:

Area of kite=5m×6m

Area of kite=30m²

Therefore If the longer diagonal is 4 more than the shorter diagonal of a kite. The area is 5 times the shorter diagonal. If the shorter side is 6m. The longer diagonal is 10m and the area is 30m².

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The number of dollars Laura should pay at the dinner party is $84.

Given that, the last time Laura hosted a fancy dinner party for her friends, she spent $108 to feed 9 people. This time, there will be only 7 people at the dinner party.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the number of dollars paid by Laura for 7 people be x.

Now, 9:108::7:x

⇒9x=108×7

⇒x=12×7

⇒x=84

Therefore, the number of dollars Laura should pay at the dinner party is $84.

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Answer:

x ≠ 8, 5

Step-by-step explanation:

We only care about the denominator:

x² - 13x + 40

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

-8 × -5 = 40

-8 + -5 = -13

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

(x - 8) (x - 5) = 0

x - 8 = 0. x - 5 = 0

x = 8. x = 5

I hope this helps!

The range of the exponential function y based on its equation and the context of the problem is; 0 < y ≤ 45529

The range of a function is the set that contains all possible output values for the function.

In this question, the function is given as: y = 45,529(0.78)^x.

It is an exponential function with initial value 45,529 and rate of change  of 0.78.

Now, it should be noted that exponential functions that are not shifted down, such as this one, are never negative nor zero. Thus, the range also has the restriction y > 0, and is given by:

D. 0 < y ≤ 45529

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Domain and range of the graphs are as follows:

1. D: [-4,4]  and   R: [1,3]

2. D: [-3,5]  and   R: [0,6]

3. D: [-2 ∝]  and   R: [-2,4]

Given:

In the first graph:

The graph's domain is its left-to-right travel distance.

Start by examining the leftmost point on this graph.

At the farthest left point, the x-value is at x=-4 Trace the graph once more until you reach the location that is the furthest to the right.

At this point, the x-value is 4. The graph is continuous from -4 to 4 since there are no breaks running from left to right.

Domain is as [-4,4]  also written as -4 ≤x≤4

The graph's range is its vertical range from down to up.

Look at the graph's lowest or most distant point. At this point, the y-value is equal to 1. Now examine the graph's top or how high it rises.

This is when x=-4 or x=4, but since we're determining the range right now, we need to take a look at the point's y-value, which is at y=3. Since the graph is continuous from top to bottom, there are no breaks in it.

Range : [1,3] also written as 1 ≤ y ≤ 3

similarly we find the rest of the domain and range of the graphs.

Hence  we don't get any line of symmetry in the graph.

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It would take 16 days for the number of magical coins to exceed 50,000.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that:

30 pound = 1 bag

30 pound  = 9 ft²

a) For a surface area of 270 ft²:

Number of pounds = 270 ft² * 30 pound per 9 ft² = 900 pounds

b) For a surface area of 270 ft²:

Number of bags = 900 pounds * 1 bag per 30 pound = 30 bags

900 pounds is needed to cover a surface area of 270 ft² and 30 bags would be needed to be purchased

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Answer:

Step by step evaluation

Formula

T = 4B + 10C

Answer:

[tex]\frac{72}9[/tex]

Step-by-step explanation:

We're asked to find out how many pages we will need to use if each paper can hold up to 9 cards. To find this, we would have to divide our total amount of cards by 9.

The mean and the standard deviations of the samples is 0.165 mm and 0.022 mm.

n = 45

[tex]\overline{X} = 0.165{~}mm[/tex]

s = 0.022 mm

Now, 95% of the confidence interval.

[tex]CI=\overline x {~}\pm t_{\frac{\alpha}{2}, n-1 }\frac{s}{\sqrt{n} }[/tex]

The critical values are:

α = 1 - 0.95 = 0.05

n - 1 = 45 - 1 = 44

[tex]t_{\frac{\alpha}{2} , n-1=t_{0.025,44}=2.0154[/tex]

So, 95% of CI =  0.165 ± 2.0154 × ( 0.022 ÷ √45 )

95% CI = ( 0.158, 0.172 )

1. The plot for the dependence of the size of the confidence interval on the confidence value ranging from 0 to 1.

2. A plot showing the dependence of the size of the confidence interval on the sample size ranging from 1 to 100.

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Answer: 19

Step-by-step explanation: 10

                                           + 9

                                            19

Answer:

9+10=19

Step-by-step explanation:

Remember treat others as you want to be treated. That being said we are not stoopid.

Answer:

16 and -16

Hope this helps! :)

The rainfall rate in inches per hour is 2/3 inches per hour.

A rate is a special ratio in which the two terms are in different units. a fixed ratio between two things2: a number, amount, or degree measured in relation to another quantity; examples include the heartbeat, metabolic rate, pulse, and sedimentation rate.

Given that,

The inches of the rain is 14×1/2is 29/2

The direction of the rain is 21×3/4 is 87/4

Rate is 29/2 /87/4

is29/2×4/87 is 2/3

Therefore, rate of rain is 2/3.

The rainfall rate in inches per hour is 2/3 inches per hour.

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The length of the chord of the larger circle which touches the smaller circle.​

Given that

To find

So, according to the question

we have,

From attached figure of that problem,

         BC = 5cm

         CD = 3cm

         AB = ........? (have to find) or from geometry

         AB = 2 BD ---------(1)

Now, we have to find BD,

So, from right angle triangle BDC.

       BD² = BC²-CD²             ( by Pythagoras theorem )

        BD = [tex]\sqrt{(BC)^2-(CD)^2}[/tex]

Putting the given values,

        BD = [tex]\sqrt{(5)^2-(3)^2}[/tex]

        BD = [tex]\sqrt{25-9}[/tex]

        BD = [tex]\sqrt{16}[/tex]

        BD = 4                (∵[tex]\sqrt{16} = 4[/tex])

Now, putting the value of BD in equation (1)

         AB = 2 BD ---------(1)

               = 2×4

         AB = 8

Answer:

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Answer:

50 hrs

Step-by-step explanation:

80=4h (h=hours)

h=20 (1hr=20 bucks)

1000=xh (x=number of hrs.)

1000=20x (h=20 so sub that in)

x=1000 divided by 20

which is 50hrs til johnny gets 1000 bucks

Answer:

8/15

Step-by-step explanation:

1/3+1/5

Ivan and Tanya share £150 in the ratio 4:1 workout. lvan gets more compared to Tanya. = $ 90

Ratio :

A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.

Total Ivan and Tanya share = £150

Ivan and Tanya share in the ratio of 4:1 respectively.

Let 4x be the money got by Ivan and x be the money got by Tanya.

Then, according to the question, we have

4x+x= 150

5x = 150

x= 150/5

x= 30

∴ Ivan has Money = 4x

= 4*30

= $ 120

Tanya has Money = x

= $ 30

Difference =   120-30 =  $  90

Hence,  Ivan gets more compared to Tanya. = $ 90

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Tanya and Ivan split £150 in the 4:1 workout. Tanya receives less compared to Ivan. = $ 90

Ratio:

A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other. For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.

Ivan and Tanya's combined portion is £150.

Tanya and Ivan each share in a ratio of 4:1.

Let x and 4x represent Tanya's and Ivan's respective earnings.

Then, according to the question, we have

4x+x= 150

5x = 150

x= 150/5

x= 30

∴ Ivan has Money = 4x

= 4*30

= $ 120

Tanya has Money = x

= $ 30

Difference =   120-30 =  $  90

Hence,  Ivan gets more compared to Tanya. = $ 90

The total of yes voter present in the election are 3048.

Now, for the given question;

Let the number of yes voters be 'x'.

Let the number of no voters  be 'y'.

The ratio of yes to no voters is 4:3.

Thus,

x/y = 4/3

or x = 4y/3

Now there are total 5334 voters;

Thus,

x + y = 5334

Put the value of x.

4y/3 + y = 5334

On simplification;

7y = 16002

y = 2286 (no voters)

Now, calculate 'x'.

x = 5334 - 2286

x = 3048 (yes voters)

Thus, the number of yes voters are 3048.

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The new mean after adding a 6-inch high platform is 73 inches, while the median changes from 66 inches to 72 inches.

The mean refers to the average of a data set and is the result of the sum of the values of the data set divided by the number of items.

The median is the middle value in the data set when arranged in an ascending or descending order.

For instance, the number of the data set is 25.  The median value is the number 13, whose value is 66 inches in the old distribution or 72 inches in the new distribution.

Height (in.)  Number of Students  Cumulative Total

60                       1                                    60 (60 x 1)

61                       0                                    60 (60 + 61 x 0)

62                      2                                   184

63                      4                                  436

64                      2                                  564

65                      1                                  629

66                     3 Median                    827

67                      1                                  894

68                     3                               1,098

69                     2                               1,236

70                     0                               1,236

71                      1                                1,307

72                    2                                1,451

73                    0                                1,451

74                    1                                1,525

75                   2                                1,675

Mean = 67 (1,675/25)

Height (in.)  Number of Students  Cumulative Total

66                       1                                   66 (66 x 1)

67                       0                                  66 (66 + 67 x 0)

68                      2                                 202

69                      4                                 478

70                      2                                 618

71                       1                                 689

72                     3 Median                   905

73                      1                                 978

74                     3                              1,200

75                     2                              1,350

76                     0                              1,350

77                      1                              1,427

78                     2                             1,583

79                     0                             1,583

80                     1                             1,663

81                     2                             1,825

Mean = 73 (1,825/25)

Thus, the new mean is 73 inches and the new median is 72 inches.

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The correct option regarding what is required to disprove a conditional statement is given by:

A single counterexample that shows the statement is not always true.

A conditional statement has the following format:

If Clause 1 then Clause 2...

In which:

The statement is disproved when there is even one single case in which Clause 1 is true and Clause 2 is false, that is, a counter example showing that the statement is not always true, hence the third option in this problem is correct.

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The correct option is (B) That'is

[tex] \bf \implies{{3x}^{3} - {2x}^{2} + 10x - 12}[/tex]

Step 1) : Operations of functions

[tex] \bf \longrightarrow{f(x) + g(x)} \\ \bf \longrightarrow( {3x}^{3} - {2x}^{2} + 4x - 5) + (6x - 7)[/tex]

Step 2) : Simplify or expand

[tex]\bf \longrightarrow( {3x}^{3} - {2x}^{2} + 4x - 5) + (6x - 7)[/tex]

[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} + 4x - 5 + 6x - 7[/tex]

[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} +( 4x + 6x) + (- 5 - 7)[/tex]

[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} +( 4 + 6) \times x+ (- 5 - 7)[/tex]

[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} +10x - 12[/tex]

Answer:

check below

Step-by-step explanation:

2x + 3y = -21

3y = -21 - 2x

3y = - 2x -21

divide both sides by 3

y = -[tex]\frac{2}{3}[/tex]x - 7

The appropriate choices will be as follows in light of the provided information:

So,

Add equation I to equation II.

Consequently, x=0 and y=11 Each variable's solution is provided by this.

Put equation I into equation II.

This means there is no answer.

Put equation I into equation II.

This implies that there are an infinite number of possible answers.

Therefore, the appropriate choices will be as follows in light of the provided information:

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