In trapezoid ABCD, Line AB is parallel to CD. If AE=5.2, AC=11.7 and CD=10.5, what is the length of AB to the nearest tenth?

Answer:

[tex]3 < x < 5[/tex]

Step-by-step explanation:

Given inequality:

[tex]|2x - 8| < 2[/tex]

[tex]\textsf{Apply absolute rule}: \quad \textsf{If }|u| < a\:\textsf{ when } \: a > 0,\: \textsf{then }-a < u < a[/tex]

[tex]\implies u=2x-8\: \textsf{ and }\:a=2[/tex]

[tex]\implies -2 < 2x-8 < 2[/tex]

Therefore:

[tex]\implies -2 < 2x-8[/tex]

[tex]\implies 6 < 2x[/tex]

[tex]\implies 3 < x[/tex]

And:

[tex]\implies 2x-8 < 2[/tex]

[tex]\implies 2x < 10[/tex]

[tex]\implies x < 5[/tex]

Merge the overlapping intervals:  [tex]3 < x < 5[/tex]

Proof

Graph:  [tex]y=|2x-8|[/tex]

Add a line at  [tex]y=2[/tex]

The interval that satisfies  [tex]|2x - 8| < 2[/tex]  is the area under the points of intersection (shaded area on the attached graph).

The values of x when [tex]y=|2x-8|[/tex] is less than 2 is more than x = 3 and less than x = 5.

So

Case-1

Case-2

So solution is

Answer: 1/3x + 2/3

Step-by-step explanation:

f(x)= 3x - 2 =>

y= 3x - 2 =>

x= 3y - 2 =>

3y - 2= x =>

3y= x + 2 =>

y= 1/3x + 2/3 =>

f-1(x)=1/3x + 2/3

Answer:

x = 6

x = 0

Step-by-step explanation:

identify the coefficients

[tex]9x^2-54x=0\\a=9\\b=-54\\c=0[/tex]

coefficient a = 1

[tex]9x^2-54x=0\\9/9x^2-54x/9=0/9\\x^2-6x=0\\\rightarrow a=1\\\rightarrow b=-6\\\rightarrow c=0[/tex]

complete the square

[tex]b=-6\\(\frac{b}{2})^2=(\frac{-6}{2})^2\\(\frac{x}{y})^2=\frac{x^2}{y^2}\\=(\frac{-6}{2})^2=\frac{-6^2}{2^2}\\\frac{-6^2}{2^2}=\frac{36}{4}\\36 \div 4=9\\\\\downarrow\\\\x^2-6x=0\\x^2-6x+9=0+9\\x^2-6x+9=9\\\frac{b}{2}\\\frac{b}{2}=\frac{-6}{2}\\\frac{b}{2}=\frac{\left(-3\cdot 2\right)}{\left(1\cdot 2\right)}\\\frac{b}{2}=-3\\x^2-6x+9=9\\(x-3)^2=9\\[/tex]

solve for x

[tex](x-3)^2=9\\\sqrt{(x-3)^2}=\sqrt{9}\\x-3=+-\sqrt{9}\\x-3+3=3+-\sqrt{9}\\x=3+-\sqrt{9}\\x=3+-3\\x_1=6\\x_2=0[/tex]

≡ In the end, you have 2 values for x, because you can either subtract 3 by 3 or add 3 by 3 to get six or zero.

The values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

From the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ

NOTE: tanθ = sinθ / cosθ

∴ sinθ = tanθ.cosθ

From above, we can write that

cosθ = sinθ/tanθ

Secant is the inverse of cosine

∴ secθ = 1/cosθ

Cosecant is the inverse of sine

∴ cscθ = 1/sinθ

tanθ = sinθ/cosθ

Cotangent is the inverse of tangent
∴ cotθ = 1/tanθ

But, tanθ = sinθ/cosθ

∴ cotθ = cosθ/sinθ

Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

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Answer:

If you plot points accordingly to the points on the table, Option A. is correct.

The type of data that contains results from other people that are of similar age and gender is known as normative data.

Normative data is a type of data that is observed that contains information about the characteristics of a population of interest. For example, normative data about students in a class would contain information such as age, gender, height.

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Answer:

-2

Step-by-step explanation:

For a straight-line graph, pick two points on the graph.

The gradient of the line = (change in y-coordinate)/(change in x-coordinate)

             (x, y)

Point 1: (2, 0)

Point 2: (3, 2)

Gradient = (change in y)/(change in x)

= (2 - 0) / (3 - 2)

= 2 / 1

= 2

Note: gradient is basically slope where slope = rise / run

Answer:

help has arrived its -2

Step-by-step explanation:

Answer:3.46

Step-by-step explanation:i dont know the other one

The vslue of the angle based on the information given will be 142°.

From the information given, it can be deduced that the shape has four sides. The total angles will be:

= (n - 2) × 180

= (4 - 2) × 180°

= 360°

The value of the last angle will be:

= 360° - (49° + 63° + 106°)

= 360° - 218°

= 142°

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Answer:

Freshmen to sophomores - (17:19)

Sophomores to freshmen - (19:17)

Step-by-step explanation:

I hope this helps! Have a lovely day!! :)

Answer:

C. 103,748

Step-by-step explanation:

The one in the first number is worth 10,000

The one in the Second number is worth 100,000

Answer:

x+2

Step-by-step explanation:

x^2+x-7 = x+2

Answer:

The answer is 1/4!!

<3 love

Answer:

This equation has 2 solutions.

1. [tex]x=\frac{-15+\sqrt{89}}{8}[/tex]

2. [tex]x=-\frac{15+\sqrt{89}}{8}[/tex]

Answer:

Step-by-step explanation:

The number of bottles of water and cheese sticks will be the same when both numbers are equal to the least common multiple (LCM) of 6 and 10, the numbers in each kind of package.

__

The LCM can be found by factoring out the greatest common divisor of each of the numbers:

  6 = 2 × 3

  10 = 2 × 5

The LCM is the product of the unique numbers here: 2 × 3 × 5 = 30.

The number of packages of bottles of water will be 30/6 = 5 packages.

The number of packages of cheese sticks will be 30/10 = 3 packages.

_____

Additional comment

You may notice that the number of packages of each kind is the unique factor in the other number.

Given the value of p and b in the equation ((  p-2b ) / 2 ), the value of m is 20.

Given that;

First, we substitute the value of p and b into the equation.

m = ( p-2b ) / 2

m = ( 57.4 - 2(8.7) ) / 2

m = ( 57.4 - 17.4 ) / 2

m = 40 / 2

m = 20

Given the value of p and b in the equation ((  p-2b ) / 2 ), the value of m is 20.

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Answer:

144 inches in 12 feet.

Step-by-step explanation:

There are 12 inches in 1 foot.

Find inches when you have 12 ft.

[tex]\frac{12feet}{1} *\frac{12 inches}{1 foot} = 144 inches[/tex]

Feet cancel out leaving inches.

There are 144 inches in 12 feet.

Answer:

B

Step-by-step explanation:

If you are allowed to use a graphing calculator, this can solve a lot of time. Graphing y = (x - 705)(x - 795) + 800(x - 750)(x - 835) gets us a parabola with x-intercepts of 749.97 and 834.924.

These roots are real and distinct, or choice B.

If you aren't allowed to use a graphing calculator, you can expand and combine like terms to get 801x^2 − 1269500x + 501560475. Looking at the discriminant, we see that (−1269500)^2 - 4*801*501560475 = 4630488100 is greater than 0 and not a perfect square, so it is real and distinct, or choice B.

I hope that helps!

Answer:

50

Step-by-step explanation:

Add all of the values together, which will equal 600, and then divide this number by how many numbers are here, which is 12.

600 / 12 = 50.

Answer:

2900

Step-by-step explanation:

2,870 rounded up to the nearest hundred is 2900.Pls mark me as brainliest.

Answer:

  A

Step-by-step explanation:

The rate of change for the table is found using the slope formula. The rate of change for the linear function is the coefficient of x.

__

The slope formula tells us the rate of change is ...

  m = (y2 -y1)/(x2 -x1)

  m = (-9 -(-10))/(-1 -(-4)) = 1/3

The coefficient of x in the equations of the offered answer choices are 1/4 and 6.

The relations between the various slopes are ...

  1/4 < 1/3 < 6

That is, the equation with a slope of 1/4 has a rate of change less than that of the function represented by the table:

  y = 1/4x +4 because ... table of values is 1/3

Answer: A

Step-by-step explanation:

Given:

Budget = $25

Shoes rental = $5.00

Price per game = $4.00

To find the greatest number of games he played...

↓

First, subtract the rent for the shoes from the budget.

25 - 5 = 20

Second, divide the remaining money or budget by the price per game.

20 ÷ 4 = 5 (greatest number of games played)

Lastly, check if the expense is the same as the original amount of money.

5 (shoes) + 4(5) (number of games played)

5 + 20 = 25 (original amount of money)

Hope it helps!!! Please mark as brainliest. Thank you :D

Answer:

x = 2

Step-by-step explanation:

This is a 45-45-90 special right triangle. The legs in this triangle are equal and the hypotenuse is leg multiplied with √2. Refer to the picture at the bottom.

One leg is x, the second leg is x and hypotenuse x√2.

[tex]x \sqrt{2} = 2 \sqrt{2} \\\\\text{Divide both sides with } \sqrt{2} \text{ to isolate } x.\\\frac{x \sqrt{2}}{\sqrt{2}} = \frac{2 \sqrt{2}}{\sqrt{2}}\\\\x = 2[/tex]

Answer:

He read 10% of the book, so 90% remains to be read.  That 90% consists of 45 pages, so

45=0.90n

n= 45/0.90

n=50

There are 50 pages total in the book

Step-by-step explanation:

Answer:

  66°

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°.

__

  79° +x +35° = 180°

  x = 180° -114° . . . . . . . . subtract 114° from both sides

  x = 66° . . . . . simplify

Answer:

D

Step-by-step explanation:

because 3/10 is 0.3

Hope this helps!

If Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

Tₙ = a + (n-1)d

(for all positive integer values of n)

Given Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54. Therefore, the sequence can be written as,

4.54, 9.08, 13.62, 18.16, 22.7, 27.24, .........

Therefore,

Since 9 weeks (40.86/4.54 = 9) are already over, and there are 27 more weeks, therefore, the spending till 36 weeks will be,

a₃₆ = 4.54 + (36-1)4.54

a₃₆ = 163.44

Hence, if Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.

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Answer:

She is wrong.

Step-by-step explanation:

The mean score is

7 + 8 + 3 + 0 + 2= 20

We then divide it by the number which is 5

20/5= 4.

Therefore, Maria is wrong.

This is because she divided by 4 instead of 5, as she didn't include the rational number 0.