Translate the phrases below into inequalities and interval notation. Use the variable x for the inequalities. Phrase Inequality Interval notation at least 11 at most 11 more than 11 fewer than 11 strictly between 3 and 11 between 3 and 11, inclusive no more than 3

Answer:

fourth option

Step-by-step explanation:

Using the sine ratio in the right triangle.

sin JKL = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{JL}{KJ}[/tex] = [tex]\frac{8.9}{10.9}[/tex] , thus

x = [tex]sin^{-1}[/tex] ([tex]\frac{8.9}{10.9}[/tex] )

Answer:

D. [tex]sin^{-1} (\frac{8.9}{10.9} ) = x[/tex]

Step-by-step explanation:

Sin is used to find the side length of a right triangle using angle degrees. However, this is using the inverse. The ratios are still the same, though.

sin(x) = 8.9/10.9 because it is the opposite side's length over the hypotenuse length. Making it the inverse would make it D.

Answer:

y=18 and (2y+6) measures 42 the answer for obtuse 138  the last one is 46

Answer:

I think that the answer is 4

Answer:

Step-by-step explanation:

a, as the x axis increases, so does the y axis

b, temperature outside v ice cream sales

hours studied v grade on test

c, I cannot do for you, but i can tell you how. Draw a straight line that you feel is an accurate representation of the graph. Then find the slope and write an equation

The conversion factor used to convert inches to yards is: 36 inches in 1 yard.

[tex]\frac{8}{25} = 0.32\\[/tex] when simplified into decimals.

This means that these two are equal. hope this helps!

8/25 is equal to 0.32

let me know if u need explanation

Answer:

hi there!

The correct answer is: 5

Step-by-step explanation:

The distance formula: [tex]\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }[/tex]

and since the two points given are: (2,1) and (5,5)

you plug in the points and you get: 5

[tex]\sqrt{(2-5)^{2} + (1-5)^{2} }[/tex]

[tex]\sqrt{(-3)^{2} + (-4)^{2} }[/tex]

[tex]\sqrt{9+16}[/tex]

[tex]\sqrt{25 } = 5[/tex]

Answer:

The correct answer is five

Step-by-step explanation:

The slope is 4/3 and since  the distance can be found by creating a triangle we can just assume it is 5 because of Pythagorean triples

Answer:

For x=1 substituting in f(x) the value of x

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

For x=0 substituting in g(x) the value of x

g(0)=3^(0) =1

Finally, we have to find for what value of x the function f(x) gives -8

f(x) = -8

-8 = -3x+1

-3x=-9

x=3

===================================================

Explanation:

Choice A is a non-answer because 3-4-5 does represent a right triangle. We can see so from the Pythagorean theorem

a^2+b^2 = c^2

3^2+4^2 = 5^2

9+16 = 25

25 = 25

We get a true equation, so (a,b,c) = (3,4,5) is a solution to a^2+b^2 = c^2

This confirms a 3-4-5 triangle is a right triangle.

------

The same steps can be used to show 6-8-10 is also a right triangle (note how each value has been doubled compared to 3-4-5). We can cross choice B off the list.

We can also see that choice D is a non-answer as well.

------

Choice C is the only thing left. The proper Pythagorean triple is actually 8-15-17.

Let's see what happens when a = 8, b = 14, c = 17

a^2+b^2 = c^2

8^2+14^2 = 17^2

64+196 = 289

260 = 289 .... false equation

We get a false equation, so a = 8, b = 14, c = 17 does not form a right triangle.

Answer:

[tex]=2xy+6x^2-6x[/tex]

Step-by-step explanation:

[tex]-2x\left(-y-3x+3\right)\\\mathrm{Distribute\:parentheses}\\=\left(-2x\right)\left(-y\right)+\left(-2x\right)\left(-3x\right)+\left(-2x\right)\cdot \:3\\\mathrm{Apply\:minus-plus\:rules}\\\left(-a\right)\left(-b\right)=ab,\:\:+\left(-a\right)=-a\\=2xy+2\cdot \:3xx-2\cdot \:3x\\\mathrm{Simplify}\:2xy+2\cdot \:3xx-2\cdot \:3x:\quad 2xy+6x^2-6x\\2xy+2\cdot \:3xx-2\cdot \:3x\\2\cdot \:3xx=6x^2\\2\cdot \:3x=6x\\=2xy+6x^2-6x[/tex]

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

[tex]2.\ f(x) = \frac{3}{4}x^2 + 2x - 5[/tex]

Step-by-step explanation:

Given

[tex]f(x) = -8x^3 - 16x^2 - 4x\\f(x) = \frac{3}{4}x^2 + 2x - 5\\f(x) = \frac{4}{x^2} - \frac{2}{x} + 1\\f(x) = 0x^2 - 9x + 7[/tex]

Required

Which of the above is a quadratic function

A quadratic function has the following form;

[tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]

So, to get a quadratic function from the list of given options, we simply perform a comparative test of each function with the form of a quadratic function

[tex]1.\ f(x) = -8x^3 - 16x^2 - 4x[/tex]

This is not a quadratic function because it follows the form [tex]f(x) = ax^3 + bx^2 + c[/tex] and this is different from [tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]

[tex]2.\ f(x) = \frac{3}{4}x^2 + 2x - 5[/tex]

This function has an exact match with [tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]

By comparison; [tex]a = \frac{3}{4}\ b = 2\ and\ c = -5[/tex]

[tex]3.\ f(x) = \frac{4}{x^2} - \frac{2}{x} + 1[/tex]

This is not a quadratic function because it follows the form [tex]f(x) = \frac{a}{x^2} + \frac{b}{x} + c[/tex] and this is different from [tex]ax^2 +bx + c = 0 \ where \ a\neq 0[/tex]

[tex]4.\ f(x) = 0x^2 - 9x + 7[/tex]

This is not a quadratic function because it follows the form [tex]f(x) = ax^2 +bx + c = 0\ but\ a = 0[/tex]

Unlike the quadratic function where [tex]a\neq 0[/tex]

So, from the list of given options, only [tex]2.\ f(x) = \frac{3}{4}x^2 + 2x - 5[/tex] satisfies the given condition

Answer:

h=14

Step-by-step explanation:

3/4*1/4=3/16

21/32/(3/16)=14

Answer:

h=25

Step-by-step explanation:

Answer:

r = 1.75

Step-by-step explanation:

The common ratio r is found by dividing a term in the sequence by the previous term, that is

112 ÷ 64 = 1.75

196 ÷ 112 = 1.75

343 ÷ 196 = 1.75

The common ratio r = 1.75

Answer:

B

Step-by-step explanation:

Answer:

4. x= 18

Step-by-step explanation:

We solve the problem like this:

Since 3 is proportional to 6 and 9 is proportional to x, we set up a proportion.

3/9 = 6/x  

We then use cross-multiplication to solve for x.

Answer: no solution

Step-by-step explanation: 4/5z - 1/5z = 3/5z

3/5z + 4 = 3/5z + 6

No solution

Answer:

[tex]$z=-\frac{48}{55} $[/tex]

It has one solution.

Step-by-step explanation:

[tex]$\frac{4}{5z}-\frac{1}{5z+4}=\frac{3}{5z+6} $[/tex]

Once we have fractions we already know the values when the equation is not true. I'm talking about division when the denominator is 0. It is undefined.

The values for [tex]z[/tex] are:

[tex]$0 ; -\frac{4}{5} \text{ and } -\frac{6}{5} $[/tex]

Now let's find [tex]z[/tex]. First, we have to find the least common multiplier:

In this case: [tex](5z+4)(5z+6)(5z)[/tex]

[tex]$\frac{4}{5z}-\frac{1}{5z+4}=\frac{3}{5z+6} $[/tex]

[tex]$\frac{4(5z+4)(5z+6)}{(5z+4)(5z+6)(5z)}-\frac{1(5z)(5z+6)}{(5z+4)(5z+6)(5z)}=\frac{3(5z)(5z+4)}{(5z+4)(5z+6)(5z)} $[/tex]

I will not proceed in the way above because it would take some time to type, instead, multiply [tex](5z+4)(5z+6)(5z)[/tex] both sides.

[tex]4(5z+4)(5z+6)-1(5z)(5z+6)=3(5z)(5z+4)[/tex]

[tex](20z+16)(5z+6)-(5z)(5z+6)=15z(5z+4)[/tex]

[tex]100z^2+200z+96-25z^2-30z=75z^2+60z[/tex]

[tex]200z+96-30z=60z[/tex]

[tex]200z-90z=-96[/tex]

[tex]110z=-96[/tex]

[tex]$z=-\frac{96}{110} $[/tex]

[tex]$z=-\frac{48}{55} $[/tex]

Answer:

Step-by-step explanation:

Hypotenuse^2=3^2+8^2

Hypotenuse^2=9+64=73

Hypotenuse =square root of 73

Hypptenuse =8.54

Answer:

8.54

Step-by-step explanation:

I took a test

Answer:

No solutions.

Step-by-step explanation:

y = 5/2x + 2

2y = 5x + 8

Plug the first equation into the second.

2(5/2x + 2) = 5x +8

5x + 4 = 5x + 8

5x + 4 cannot equal 5x + 8, so this system of equations has no solutions.

Answer:

The range within 1 standard deviation :155.12 ,328.38

Step-by-step explanation:

Data: 338+160+210+180+166+272+128+409+240+250+160+300+340+200+194+132+202+180+420+380+325+185+233+198

[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}[/tex]

[tex]Mean =\frac{338+160+210+180+166+272+.........+233+198}{24}[/tex]

Mean =241.75

[tex]\text{Standard deviation} = \sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}[/tex]

Standard deviation = [tex]\sqrt{\frac{(338-241.75)^{2}+(160-241.75)^{2}+......+(185-241.75)^{2}+(233-241.75)^{2}+(198-241.75)^{2}}{24-1}}[/tex]

Standard deviation =86.63

Range within 1 standard deviation :[tex](\mu-\sigma,\mu+\sigma)[/tex]

Range within 1 standard deviation :(241.75-86.63,241.75+86.63)

Range within 1 standard deviation :155.12 ,328.38

Hence The range within 1 standard deviation :155.12 ,328.38

Answer:

[tex]-3x^2y-xy^2-7xy-3[/tex]

Step-by-step explanation:

[tex](4xy^2-3x^2y-5xy-6)+(-5xy^2-2xy+3)[/tex]

[tex]4xy^2-3x^2y-5xy-6-5xy^2-2xy+3[/tex]

[tex]-3x^2y-xy^2-7xy-3[/tex]

Answer:

Option 2

Step-by-step explanation:

Group 2 does have a greater median. And group 1 is less spread out

Answer:

1. No; 2. 16; 3. No; 4. Yes

Step-by-step explanation:

1. Home states of Olympic swimmers

A dot plot compares frequency counts within groups, usually with small sets of data.

Thus, it is great for visualizing quantitative data.

Home states are qualitative data.

It might be better to use a packed bubble chart, especially if more than 20 to 30 states are on the team.

In such a chart, the frequency with which the state name is mentioned would determine the relative bubble size.

It might look like the imaginary chart shown below.

A dot plot would not be appropriate.

2. Number of students

No. of students = 2 + 1 + 2 + 3 + 2 +1 + 1 + 2 + 2 = 16

3. Is this an adult swimming class?

The ages of the students range from 18 mo to 32 mo.

This is not an adult swimming class.

4. Ages of half the students

Half of 16 students is eight students.

The eight oldest students range in age from 25 mo to 32 mo.

This is between the ages of 2 yr to 3 yr (24 mo to 36 mo), so

Half the students are between 2 yr and 3 yr old.

Answer:

(1. No) (2. 16) (3. No) (4. Yes)

Step-by-step explanation:

Hope this helps!!

Answer:

(1/4 x 1 ) = 0.25

or (1/4) x 1 = 0.25

Step-by-step explanation:

We are doing the opposite to finding 25%

Which is 1/4 of 100%

We do this an opposite (not as inverse)

To find percentage increase as you can compare below.

or as percentage increase

230 x 0.25 (x 100) = 287.50  

Even though we are not finding increase for 1/4 by changing it to decimal form, this practice does use the (x1) element in brackets and does identify the distribution.

Answer:

Use a calculator or use long division. See long division below.

Step-by-step explanation:

Use a calculator or use long division.

Long division:

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

        4     |  1

4 does not go into 1, so add a decimal pace to 1.

                    0.

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

            4    |  1.0

4 goes into 10 2 times.

                      0.2

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

             4    |  1.0

             -          8

           --------------

                        2

There is a remainder, so bring down another 0.

                      0.2

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

             4    |  1.00

             -          8

           --------------

                        20

4 goes into 20 5 times.

                    0.25

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

             4    |  1.00

             -          8

           --------------

                        20

               -        20

             --------------

                            0

The remainder is zero.

1/4 = 0.25

Answer:

h = mt

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Given

f(x) = 3(x + 1)(x - 7) ← expand the factors using FOIL

     = 3(x² - 6x - 7) ← distribute the parenthesis

      = 3x² - 18x - 21 → B

Answer:

Step-by-step explanation:

Answer:

E. CI = 102.79

Answer:

Picture 1 x = 43°

Step-by-step explanation:

Picture 1 - When a triangle is formed inside a semicircle, two lines from either side of the diameter meet at a point on the circumference at a right angle.

180 - 47-90= 43° = x

Answer:

B

Step-by-step explanation:

You can use an equation from physics to help with this.

[tex]v_f=v_o+at[/tex]

Since the initial velocity is 0, you can set up the following equation:

[tex]v_f=0+(10)(5)\\\\v_f=50\neq 100[/tex]

Hope this helps!