cross out 3 digits in the number 51489704 so that the number remaining is divisible by 45

Answer:

(a) g(x) has a greater slope

(b) g(x) has a greater y intercept

Step-by-step explanation:

Given

[tex]x \to -1,0,1[/tex]

[tex]f(x) \to -5,-1,3[/tex]

[tex]g(x) = 4x + 3[/tex]

Solving (a): Compare the slopes

Slope (m) is calculated as:

[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, for f(x), we have:

[tex]m =\frac{-1- 0}{-5- -1}[/tex]

[tex]m =\frac{-1}{-4}[/tex]

[tex]m =\frac{1}{4}[/tex]

For g(x), we have:

Assume [tex]g(x) = mx + c[/tex] then the slope is m

Compare the above to [tex]g(x) = 4x + 3[/tex]

Then the slope of g(x) is 4

g(x) has a greater slope

Solving (b): Function with greater y intercept

Here we set [tex]x= 0[/tex]

From the table of f(x)

[tex]f(x) = -1[/tex] when [tex]x = 0[/tex]

From [tex]g(x) = 4x + 3[/tex]

[tex]g(0) = 4 * 0 + 3[/tex]

[tex]g(0) = 3[/tex]

Hence:

g(x) has a greater y intercept

Answer:

no solution

Step-by-step explanation:

Answer:

41/30

Step-by-step explanation:

2/3 + 1/5 + 2/4

= 41/30

Answer:

a. 42

b. -12x-5

c. -60

d. -75

e. 66

f. -90

g. 144

h. -135

Answer:

-1/7

Step-by-step explanation:

-3/2(x-2)=45/14

x-2=(45/14)/(-3/2)

x-2=(45/14)(-2/3)

x-2=-90/42

simplify -90/42 into -15/7

x-2=-15/7

x=-15/7+2

x=-15/7+14/7

x=-1/7

Answer:

16

Step-by-step explanation:

[tex](-64)^2/3[/tex]

64 = [tex]2^{6}[/tex]

[tex]2^{6} ^{\frac{1}{3} } ^{2}[/tex]

[tex]2^{ 2^{2} }[/tex]

[tex]2^{4}[/tex]

16

Answer:

19) 100

20) 360 - 90 = 270

21) 360- 125 = 235

22) 45

Step-by-step explanation:

Central angles and the arcs they create are congruent.

Answer:

Pam laid 60 tiles on Saturday and 20 on Sunday.

Step-by-step explanation:

Given that Pam laid three times as many tiles on Saturday as she laid on Sunday, if Pam laid 80 tiles over the weekend altogether, to determine how many tiles did she lay on Saturday the following calculation must be performed:

3X + X = 80

4X = 80

X = 80/4

X = 20

Therefore, Pam laid 60 tiles on Saturday and 20 on Sunday.

Answer:

1/root(3)

Step-by-step explanation:

the steps are in the pic above.

The value of tan pi/6 is 0.5773502.

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Given that, what is the exact value of tan pi/6,

To find the value of tan π/6 using the unit circle:

Rotate ‘r’ anticlockwise to form pi/6 angle with the positive x-axis.

The tan of pi/6 equals the y-coordinate(0.5) divided by the x-coordinate(0.866) of the point of intersection (0.866, 0.5) of unit circle and r.

Hence, the value of tan pi/6 = y/x = 0.5774 (approx)

Learn more about trigonometric functions click;

https://brainly.com/question/6904750

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Answer:

Charity is more correct

Step-by-step explanation:

Flight time = 6.94 hours

Charity estimation = 7 hours

Her sister's estimation = 6.9 hours

Charity is more correct if we are to round to the nearest whole hour

6.94 hours is approximately 7 hours

Her sister is only correct if we are to round up to 1 decimal place

6.94 hours is approximately 6.9 hours to 1 decimal place

Answer: 6

Step-by-step explanation: 6 is a median

Hey there!

To find your mean you have to put the numbers from descending (least/decreasing) to ascending (greater/increasing) order

Median is also understood as the “middle number”

2, 8, 6, 10, 4, 12​

= 2, 4, 6, 8, 10, 12

Based on that information, you have in your new data set you have 2 pairs in the middle (6 & 8), so you’ll have to total/average of the number. We have to DIVIDE them by 2 because it’s 2 numbers

6 ends the descending set and 8 starts the ascending set

Median = 6 + 8 / 2

6 + 8 = 14

= 14/2

= 7

Answer: therefore your MEDIAN is most likely 7

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

(5, -5)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

2x - 3y = 25

5x + 3y = 10

Step 2: Solve for x

Elimination

Step 3: Solve for y

Answer:

(5,-5)

Step-by-step explanation:

Hi there!

We are given this system of equations:

2x-3y=25

5x+3y=10

and the question asks to solve it by elimination

To solve by elimination, we will add the equations together to clear one variable, solve for the variable that wasn't cleared, then use the value of the variable that wasn't cleared to solve for the variable that was cleared earlier

Before we clear a variable, the coefficients  in front of the variable that we want to clear need to be opposites (ex. if we wanted to clear x, the coefficients of x in the systems have to be -2 and 2, as that would equal 0).

In this case, the coefficients in front of y in the equations are -3 and 3 respectively. That equals 0, so y would be cleared if we added the equations together

so we don't have to multiply or divide by anything prior to clearing

Let's add the equations together. Remember that y will be cleared, as (-3y+3y=0)

2x-3y=25

+

5x+3y=10

______________

7x+0=35

subtract 0 from both sides

7x=35

divide both sides by 7

x=5

we found the value of x

now we need to find the value of y

substitute 5 as x into either one of the equations to solve for y

if we were to do it into 2x-3y=25 for instance,

2(5)-3y=25

multiply

10-3y=25

subtract 10 from both sides

-3y=15

divide both sides by -3

y=-5

So the answer is x=5, y=-5, or as point (5,-5)

Hope this helps! :)

Answer:

Step-by-step explanation:

Given:

The data values are:

7, 8, 11, 13, 14, 14, 14, 15, 16, 16, 18, 19

To find:

The outliers of the given data set.

Solution:

We have,

7, 8, 11, 13, 14, 14, 14, 15, 16, 16, 18, 19

Divide the data set in two equal parts.

(7, 8, 11, 13, 14, 14), (14, 15, 16, 16, 18, 19)

Divide each parenthesis in two equal parts.

(7, 8, 11), (13, 14, 14), (14, 15, 16), (16, 18, 19)

Now,

[tex]Q_1=\dfrac{11+13}{2}[/tex]

[tex]Q_1=\dfrac{24}{2}[/tex]

[tex]Q_1=12[/tex]

And

[tex]Q_3=\dfrac{16+16}{2}[/tex]

[tex]Q_3=\dfrac{32}{2}[/tex]

[tex]Q_3=16[/tex]

The interquartile range is:

[tex]IQR=Q_3-Q_1[/tex]

[tex]IQR=16-12[/tex]

[tex]IQR=4[/tex]

The data values lies outside the interval [tex][Q_1-1.5IQR,Q_3+1.5IQR][/tex] are known as outliers.

[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[12-1.5(4),16+1.5(4)][/tex]

[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[12-6,16+6][/tex]

[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[6,22][/tex]

All the data values lie in the interval [6,22]. So, there are no outliers.

Hence, the correct option is 4.

Answer:

Step-by-step explanation:

Binomial Expansion:

[tex](2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4[/tex]

Pascal's Triangle:

  Zero row                        1

 First row                  1                 1

 Second row          1           2             1

 Third  row         1         3              3          1

 Fourth row    1       4            6           4          1

Step-by-step explanation:

this is the correct answer you wanted to know

please mark brainliest

Answer:

i dont see a diagram ?

Step-by-step explanation:

Answer:

AC is greater than BC because segment AC is the hypotenuse of right triangle ABC, and the hypotenuse is the longest side of a right triangle.

Answer:

23

Step-by-step explanation:

-18+(18+5) = 5,

so adding any integer that is greater than (18+5)=23 will give a sum that is greater than 5.

Answered by GAUTHMATH

Answer:

y = -7x - 11

Step-by-step explanation:

Answer:

1.1 gallons of paint

Step-by-step explanation:

The wall measures;

21 foot by 17 foot

Thus, area of wall = 21 × 17 = 357 ft²

Circular area has a radius of 5 ft.

Thus;

Area of circle = πr² = π × 5² = 78.54 ft²

Total area covered = 357 + 78.54 = 435.54 ft² ≈ 436 ft²

A gallon of paint can cover 400 ft²

Thus gallons Muhammad would need = 436/400 = 1.09 gallons ≈ 1.1 gallons

Answer:

Please find attached the graph of the function created with MS Excel showing the relevant points required to draw an approximate graph of the function on a graph paper

Step-by-step explanation:

The given quadratic function is f(x) = -2·x² + 7·x + 4

The range of the input (x) values = -1 ≤ x ≤ 5

The coefficient of the quadratic is negative -2, the graph is n shape

The intercept form of the function is given as follows;

-2·x² + 7·x + 4 = -1 × (2·x² - 7·x - 4)

-1 × (2·x² - 7·x - 4) = -1 × (2·x² + x - 8·x - 4)

-1 × (2·x² + x - 8·x - 4) = -1 × (x · (2·x + 1) - 4·(2·x + 1))

∴ -1 × (x · (2·x + 1) - 4·(2·x + 1)) = -1 × (2·x + 1)·(x - 4)

∴ f(x) = -2·x² + 7·x + 4 = -1 × (2·x + 1)·(x - 4)

At the x-intercepts, (2·x + 1) = 0 or (x - 4) = 0, which gives;

x = -1/2 or x = 4

Therefore, the x-intercepts are (-1/2, 0), (4, 0)

The equation in vertex form is given as follows;

f(x) = -2·x² + 7·x + 4 = -2·(x² - 7·x/2 + 2)

By applying completing the squares method, to x² - 7·x/2 - 2, we get;

Where x² - 7·x/2 - 2

x² - 7·x/2 = 2

x² - 7·x/2 + (-7/4)² = 2 + (-7/4)² = 81/15

(x - 7/4)² = 81/16

∴ (x - 7/4)² - 81/16 = 0 = x² - 7·x/2 - 2

∴ x² - 7·x/2 - 2 = (x - 7/4)² - 81/16

-2·(x² - 7·x/2 + 2) = -2·((x - 7/4)² - 81/16) = -2·(x - 7/4)² + 81/8

The vertex = (7/4, 81/8)

When x = 0, we get;

f(0) = -2 × 0² + 7 × 0 + 4 = 4

The y-intercept = (0, 4)

The sketch of the function should pass through the x-intercepts (-1/2, 0), (4, 0), the y-intercept (0, 4), and the y-intercept (0, 4), and the vertex, (7/4, 81/8) on a graph sheet

Please find attached a drawing of the function of the function created with MS Excel

Step-by-step explanation:

hope it helps

Answer:

120 in^2

Hope it helps

Answer:

g = 48

k = 18

Step-by-step explanation:

h / 10 = 60 / 12

h / 10 = 5

h = 5 x 10

h = 50

40 / h = g / 60

40 / 50 = g / 60

4 / 5 = g / 60

g = ( 60 x 4 ) / 5

= 12 x 4

g = 48

90 / k = 60 / 12

90 / k = 5

k = 90 / 5

k = 18

Answer: [tex]-\frac{11}{3}[/tex]

Step-by-step explanation:

[tex]-\frac{2}{3} *5\frac{2}{4} \\\\\\=-\frac{2}{3} *5\frac{1}{2} (5\frac{1}{2} =\frac{5*2}{2} +\frac{1}{2} =\frac{10+1}{2} =\frac{11}{2})\\\\\\=-\frac{2}{3} *\frac{11}{2} =-\frac{11}{3}[/tex]

Answer:

1/12

Step-by-step explanation:

Chances of getting a 1 are 1/6 and chances of getting a prime number excluding 1 is 3/6. 3/6 x 1/6= 3/36 or 1/12 chance.