ABCD is a rhombus. The coordinates of A are (5, 11) The equation of the diagonal DB is y = 3x + 5 The equation of the diagonal AC can be written in the form y = mx + Ċ where m and c are integers. Work out the value of m and the value of c.​

Answer:

7.8

Step-by-step explanation:

since the shape is a right angled triangle,

we use Pythagoras theorem to find

X= ✓6^2+5^2 = √36+25=. √61 =7.8

The indefinite integral will be  [tex]\int (7x^2+8x-2)dx=\dfrac{7x^3}{3}+4x^2-2x+C)[/tex]

When we integrate any function without the limits then it will be an indefinite integral.

General Formulas and Concepts:

Integration Rule [Reverse Power Rule]:                                                              

[tex]\int x^ndx=\dfrac{x^{n+1}}{n+1}}+C[/tex]

Integration Property [Multiplied Constant]:                                                        

[tex]\int cf(x)dx=c\int f(x)dx[/tex]

Integration Property [Addition/Subtraction]:                                                      

[tex]\int [f(x)\pmg(x)]dx=\int f(x)dx\pm \intg(x)dx[/tex]

[Integral] Rewrite [Integration Property - Addition/Subtraction]:

[tex]\int (7x^2+8x-2)dx=\int 7x^2dx+\int 8xdx -\int 2dx[/tex]          

[Integrals] Rewrite [Integration Property - Multiplied Constant]:  

[tex]\int (7x^2+8x-2)dx=7 \int x^2dx+ 8 \int xdx -2\int dx[/tex]            

[Integrals] Reverse Power Rule:    

[tex]\int (7x^2+8x-2)dx= 7(\dfrac{x^3}{3})+8(\dfrac{x^2}{2})-2x+C[/tex]                                                            

Simplify:    

[tex]\int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C[/tex]                                                                                                      

So the indefinite integral will be [tex]\int (7x^2+8x-2)dx= \dfrac{7x^3}{3}+4x^2-2x+C[/tex]                

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The value of the given expression will be equal to 2060.

Expression in maths is defined as the collection of the numbers variables and functions by using the signs like addition,substraction, multiplication and division.

It is given that:-

=p²(m)-(np+r)

=(-8)²(32)-(2x(-8)+4)

=(64x32)-(-16+4)

=2060

Hence value of the given expression will be equal to 2060.

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The value of the probability expression p(girl, girl, girl) is 1/8

The theoretical probability is given as:

P(girl) = 1/2

The value of p(girl, girl, girl) is calculated using:

p(girl, girl, girl) = p(girl) * p(girl) * p(girl)

So, we have:

p(girl, girl, girl) = 1/2 * 1/2 * 1/2

Evaluate

p(girl, girl, girl) = 1/8

Hence, the value of the probability expression p(girl, girl, girl) is 1/8

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Answer:

y = 4 + 5x

Step-by-step explanation:

You can plug in numbers from the top row (the x's) and times and add to see if you get the corresponding number from the bottom row. This problem is a little mean and tricky because if you check with x=1, all of them work out right. But check with any other x and you will see that only one equation works, the first answer.

You can find "the rule" by looking for a pattern in the rows of numbers. The x goes up by 1, and the y goes up by 5 (if you go left to right on the table) With the 5 on top and 1 on the bottom, y/x, you get 5...that's the 5 that is beside the x in the answer. And if you imagine making one more column on the left side of the table, x=0 and y=4, that's the 4 that stands alone in the answer.

Answer: If this is a 2D box, the length would be 2

Step-by-step explanation:

Answer:

Kia makes 19.25 dollars an hour.

Step-by-step explanation:

6x4+8=32 (hours: 6 hours for 4 days, and 8 hours for 1 day)

616 divided by 32 = 19.25

Answer:

We can see that our y-value of our coordinates do not change so we can just subtract the first x-value from the second x-value.

[tex]x_2 - x_1[/tex]

[tex]4 - (-4)[/tex]

[tex]8[/tex]

The option that best matches our answer is Option B, [tex]8[/tex]

Hope this helps!  Let me know if you have any questions

Answer:

[0,∞), {y|y≥0}

Step-by-step expl

The graph of y =|3x + 1| is attached.

By observation, we can see that the the least y-value that the graph can take is y =0 (i.e the x-axis) and the greatest y-value that the graph can take is positive infinity.

Hence the range is [0,∞), {y|y≥0}

Step-by-step explanation:

the domain is the set or interval of all valid x-values.

the range is the set of interval of all valid y-values.

the function is a line function, so it's values will continuously increase with increasing x-valies.

therefore we can simply take the 2 interval ends of the domain as the x-values that create the lowest and the highest functions value in that interval.

the function does not make any large twists and turns in that interval.

y = 3x + 1

for x = 2

y = 3×2 + 1 = 6 + 1 = 7

for x = 8

y = 3×8 + 1 = 24 + 1 = 25

so, the range is [7, 25]

Answer:

Probably candycorn, to be honest nobody really even like's candycorn so that's why it's kinda sad.

Answer:

x² + 12x + y² + 4y - 25 = 0

Step-by-step explanation:

Equation of a circle

Finding r

Making the equation

The equation of the circle with center (-6, -2 containing the point (-10, -9) is x² + 12x + y² + 4y - 25 = 0

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

WE know that the Equation of a circle;

(x - h)² + (y - k)² = r²

(h, k) = coordinates of a circle

(x, y) = coordinates of a point on the circle

r = radius

Finding r;

(-10 + 6)² + (-9 + 2)² = r²

r² = 16 + 49

r = √65

Making the equation,

(x + 6)² + (y + 2)² = (√65)²

x² + 12x + 36 + y² + 4y + 4 = 65

x² + 12x + y² + 4y - 25 = 0

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From the figure, the value of tan j is 13/9

The tangent of an angle is represented as: :

tan(j) = opposite leg/adjacent leg

From the figure, we have:

opposite leg = 13

adjacent leg = 9

Substitute these values in the above equation of tangent

tan(j) = 13/9

Hence, the value of tan j is 13/9

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Answer:

Answer:

Step-by-step

the total number of balls in the in the bag is 10

Then

the probability of drawing a red ball on the first draw is 4/10.

…………………………………………………………

Now , if the first ball drawn is not replaced.

Then

the probability of drawing a red ball on the Second draw is 3/9.

……………………………………………

Conclusion:

the probability that two balls drawn at random from the bag will be red if the first ball drawn is not replaced is :

(4÷10)×(3÷9)

= (2÷5)×(1÷3)

= 2÷15

= 0.133333333333

Answer:

36cm² is the answer.....

Answer:

Step-by-step explanation:

Answer:

36 quarters

9 / 0.25 = 36

Answer:

Circumference is a special case of perimeter. Both describe the total length of the boundary of a two dimensional figure, but circumference specifically refers to the perimeter of a curved figure or arc. Therefore it only applies to circles, ovals, ellipses, arcs, etc.

Answer:

Both words are used to talk about how long the boundary is of a 2D figure. Think of circumference as a special case of finding the perimeter. The term circumference refers to the perimeter of a figure without sides or something like a circle or arc.

So if we were to look at a rectangle and try to determine how long the boundary is we would use perimeter. On the other hand, if we have a circle we have no way to track how long each side is therefore we use circumference.

Answer:

her rate in chapters per hour is:

6 chapters per hour

The parabola y = -16x^2 + 32x opens downward and the y value of the vertex is 16

The equation of the function is given as:

y = -16x^2 + 32x

Factor out -16

y = -16(x^2 - 2x)

In the above equation, the factor -16 is negative,

This means that the parabola opens downward

We have:

y = -16(x^2 - 2x)

Set to 0

-16(x^2 - 2x) = 0

Divide by -16

x^2 - 2x = 0

Factor out x

x(x - 2) = 0

Split

x = 0 or x - 2 = 0

Solve for x

x = 0 or x = 2

Hence, the roots are 0 and 2, and the x-intercepts are (0,0) and (2,0)

We have:

y = -16x^2 + 32x

Differentiate

y' = -32x + 32

Set to 0

-32x + 32= 0

Divide through by -32

x - 1 = 0

Add 1 to both sides

x = 1

Hence, the x value of the vertex is 1

In (c), we have:

x = 1

Substitute x = 1 in y = -16x^2 + 32x

y = -16(1)^2 + 32(1)

Evaluate

y = 16

Hence, the y value of the vertex is 16

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Answer:

1) 38.9%

Step-by-step explanation:

There are 18 total pieces of candy, 4 of which are blue, and 3 of which are yellow. So the probability of randomly selecting one blue or one yellow piece of candy is

[tex] \frac{3}{18} + \frac{4}{18} = \frac{7}{18} = 38.9\%[/tex]

Answer:

I used Desmos to graph your requirements, and i took a screenshot of the graph. Credit to Desmos for the great graphing system.

Step-by-step explanation:

Answer:

see image

Step-by-step explanation:

Anytime you see f(x) that just means y.

So f(x)=5 just means

y = 5

Anytime you have an equation to graph that is in the format

"y= anumber", that is a Horizontal line. So the first piece of your graph is the horizontal line thru 5. But also that's only for x>=3. It includes the 3 with the "or=to" underline. So the point must be a solid filled-in point. (Some weird books or teachers use a [ square bracket.) Same logic works for the second piece of the function. f(x) = -6 is the same as y= -6 and is a horizontal line thru -6. But the point at (3, -6) is an Open dot! See image.

Answer:

The expression is repeated multiplication form is 5.

The expression as power is 9.

Step-by-step explanation:

Answer:

The expression as powers is 5^9

Ans

2:47 mins

Step-by-step explanation:

2 1/6 ÷7/8 = 2 10/21

2 10/12 to decimal 2.47

Answer:

A and D are correct.

Answer:

The longest ski pole to fit would lie diagonally. The length of the diagonal can be found by the Pythagorean theorem.

d=sqrt(1202+252)

d ~= 122.58 cm

Step-by-step explanation:

Answer:

123 cm (nearest whole number)

Step-by-step explanation:

The orientation of the ski pole to allow it to be its maximum length would be placing it from corner to opposite corner of the base of the box.

Therefore, this can be modeled as the hypotenuse of a right triangle, where the length and width of the box are the legs.

To find the hypotenuse, use Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse)

Given:

Substitute given values into the formula and solve for c:

⇒ a² + b² = c²

⇒ 25² + 120² = c²

⇒ c² = 15025

⇒ c = √(15025)

⇒ c = 123 cm (nearest whole number)