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

Answer:

-7 > x

Step-by-step explanation:

3(x-4)>5x+2

Distribute

3x-12>5x+2

Subtract 3x from each side

3x-12-3x>5x-3x+2

-12 > 2x+2

Subtract 2 from each side

-12-2>2x+2-2

-14 > 2x

Divide by 2

-14/2 > 2x/2

-7 > x

Answer:

[tex]\boxed{x<-7}[/tex]

Step-by-step explanation:

3(x-4)>5x+2

Expand brackets.

3x - 12 > 5x+2

Subtract 3x and 2 on both sides.

-12 - 2 > 5x - 3x

-14 > 2x

Divide both sides by 2.

-7 > x

Switch sides.

x < -7

Answer: x = 5, x = -7/2

Step-by-step explanation:

2x² - 3x - 35 = 0

Step 1: Find two values whose product = 2(-35) and sum = -3:  -10 & 7

Step 2: Replace the b-value of -3x with  -10x + 7x:

2x² - 10x   + 7x - 35 = 0

Step 3: Factor the first two terms and the second two terms:

2x(x - 5)  +7(x - 5) = 0

Step 4: Write the factored form:

Notice that the parenthesis are identical.  This is one of the factors. The outside values are the other factor:

Parenthesis: (x - 5)

Outside: (2x + 7)

Factored form: (x - 5)(2x + 7) = 0

Step 5: Set each factor each to zero and solve for x:

x - 5 = 0             2x + 7 = 0

   x - 5                      [tex]x=-\dfrac{7}{2}[/tex]

The solutions of the quadratic equation given as 2x² - 3x - 35 = 0 are x=5 and x =-3.5.

Given that:

2x² - 3x - 35 = 0

This is a quadratic equation.

It is required to find the solutions of this equation.

The solution of the quadratic equation of the form ax² + bx + c = 0 can be found using the quadratic formula:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

From the given equation:

a = 2

b = -3

c = -35

Substitute to the quadratic formula.

[tex]x=\frac{-(-3)\pm \sqrt{(-3)^2-4(2)(-35)}}{2(2)}[/tex]

  [tex]=\frac{3\pm \sqrt{9+280}}{4}[/tex]

  [tex]=\frac{3\pm \sqrt{289}}{4}[/tex]

  [tex]=\frac{3\pm 17}{4}[/tex]

So, the solutions are:

[tex]x=\frac{3+ 17}{4}=5[/tex], and [tex]x=\frac{3-17}{4}=-3.5[/tex]

Hence, the solutions are x =5, -3.5.

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Answer:

X=20

Step-by-step explanation:

The answer is C

Answer:

The calculated value Z = 2 > 1.96 at 0.05 level of significance

Alternative Hypothesis is accepted

The proportion of defective tablets manufactured in this factory is less than 6%."

Step-by-step explanation:

Step(i):-

Given Population proportion P = 0.06

Sample size 'n' = 500

A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective.

Sample proportion

                                  [tex]p^{-} = \frac{x}{n} = \frac{20}{500} =0.04[/tex]

Null hypothesis :H₀: P = 0.06

Alternative Hypothesis :H₁:P<0.06

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step(ii):-

       Test statistic

                          [tex]Z = \frac{p^{-} -P}{\sqrt{\frac{P Q}{n} } }[/tex]

                         [tex]Z = \frac{0.04 -0.06}{\sqrt{\frac{0.06 X 0.94}{500} } }[/tex]

                        Z =  - 2

                    |Z|= |-2| = 2

Step(iii):-

The calculated value Z = 2 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

Alternative Hypothesis is accepted

The proportion of defective tablets manufactured in this factory is less than 6%."

Answer:

Step-by-step explanation:

[tex]f(x) = 4 {e}^{x} [/tex]

[tex]f(2) = 4 {e}^{2} [/tex]

[tex]f(2) = 4 \times 7.389[/tex]

[tex]f(2) = 29.6[/tex]

( Approximately 30)

Hope this helps..

Good luck on your assignment..

Answer:

approximately 30

Step-by-step explanation:

[tex]f(x)=4e^x[/tex]

Put x as 2 and evaluate.

[tex]f(2)=4e^2[/tex]

[tex]f(2)=4(2.718282)^2[/tex]

[tex]f(2)= 29.556224 \approx 30[/tex]

Answer:

D. The linear parent function

Step-by-step explanation:

Linear functions are always characterized by a straight line graph with or without an intercept on the vertical or horizontal axis. A linear function usually has an independent variable and a dependent variable. The independent variable is commonly depicted as x while the dependent variable is y.

Thus a linear equation is an equation of the type y=ax where a is a constant term. The equation of a straight line graph his y=mx +c, where;

m= gradient of the straight line graph

x= the independent variable

y= the dependent variable

c= the vertical intercept

Answer:

The linear parent function :)

Step-by-step explanation:

Answer:

The position of the particle is described by [tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]

Step-by-step explanation:

The position function is obtained after integrating twice on acceleration function, which is:

[tex]a(t) = 2\cdot t + 5[/tex], [tex]\forall t \geq 0[/tex]

Velocity

[tex]v(t) = \int\limits^{t}_{0} {a(t)} \, dt[/tex]

[tex]v(t) = \int\limits^{t}_{0} {(2\cdot t + 5)} \, dt[/tex]

[tex]v(t) = 2\int\limits^{t}_{0} {t} \, dt + 5\int\limits^{t}_{0}\, dt[/tex]

[tex]v(t) = t^{2}+5\cdot t + v(0)[/tex]

Where [tex]v(0)[/tex] is the initial velocity.

If [tex]v(0) = -5[/tex], the particular solution of the velocity function is:

[tex]v(t) = t^{2} + 5\cdot t -5, \forall t \geq 0[/tex]

Position

[tex]s(t) = \int\limits^{t}_{0} {v(t)} \, dt[/tex]

[tex]s(t) = \int\limits^{t}_{0} {(t^{2}+5\cdot t -5)} \, dt[/tex]

[tex]s(t) = \int\limits^{t}_0 {t^{2}} \, dt + 5\int\limits^{t}_0 {t} \, dt - 5\int\limits^{t}_0\, dt[/tex]

[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + s(0)[/tex]

Where [tex]s(0)[/tex] is the initial position.

If [tex]s(0) = 6[/tex], the particular solution of the position function is:

[tex]s(t) = \frac{1}{3}\cdot t^{3} + \frac{5}{2}\cdot t^{2} - 5\cdot t + 6,\forall t \geq 0[/tex]

Answer:

Position of the particle is :

[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex]

Step-by-step explanation:

Given information:

The particle is moving with an acceleration that is function of:

[tex]a(t)=2t+5[/tex]

To find the expression for the position of the particle first integrate for the velocity expression:

AS:

[tex]V(t)=\int\limits^0_t {a(t)} \, dt\\v(t)= \int\limits^0_t {(2.t+5)} \, dt\\\\v(t)=t^2+5.t+v(0)\\[/tex]

Where, [tex]v(0)[/tex] is the initial velocity.

Noe, if we tale the [tex]v(0) =-5[/tex] ,

So, the velocity equation can be written as:

[tex]v(t)=t^2+5.t-5[/tex]

Now , For the position of the particle we need to integrate the velocity equation :

As,

Position:

[tex]S(t)=\int\limits^0_t {v(t)} \, dt \\S(t)=\int\limits^0_t {(t^2+5.t-5)} \, dt\\S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+s(0)[/tex]

Where, [tex]S(0)[/tex] is the initial position of the particle.

So, we put the value [tex]s(0)=6[/tex] and get the position of the particle.

Hence, Position of the particle is :

[tex]S(t)=\frac{1}{3}.t^3+\frac{5}{2}.t^2-5.t+6[/tex].

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Answer:

2+(11+y)=(2+11)+y=11+(2+y)

Answer:

Sample Response: The associative property allows you to keep the order of the terms and change the position of the parentheses. So you can rewrite the terms in the same order and then move the parentheses so that the 2 + 11 is now inside. The equivalent expression is (2 + 11) + y.

Step-by-step explanation:

E d g e n u i t y

Greetings from Brasil...

Here we have internal collateral angles. Its sum results in 180, so:

(6X + 8) + (4X + 2) = 180

6X + 4X + 8 + 2 = 180

10X + 10 = 180

10X = 180 - 10

10X = 170

X = 170/10

Answer:

H0 :

a. mu is greater than or equal to $108.50

Ha:

c. mu is less than or equal to $108.50

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence

In the given scenario the test is to identify whether the average room price significantly different from $108.50. We take null hypothesis as mu is greater or equal to $108.50.

Answer:

x = 18; y = 35

Step-by-step explanation:

This gives us the equation:

1. x+y=53

2. 3x=y+19

3. 3x-y=19

Add the first and last line together: x+y+3x-y=53+19

Simplifies to: 4x=72

Divide by 4 to get: x = 18

Plug your numbers into the first equation to get 18+y=53; y = 35.

Answer:

The numbers are 18 and 35.

Step-by-step explanation:

The smaller number is x.

Let the other number by y.

Three times the smaller number is equal to 19 more than the larger number.

3x = y + 19

The larger number is

y = 3x - 19

the numbers add up to 53

x + y = 53

x + 3x - 19 = 53

4x = 72

x = 18

y = 3x - 19 = 3(18) - 19 = 54 - 19 = 35

The numbers are 18 and 35.

Answer:

7987.1569 to the nearest thousandths is 7987.157

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

You did not attach a picture, so I just assumed where the lengths of 15 and 39 were.

Answer:

1. D

2. B

3. A

Step-by-step explanation:

Question 1:

The pair of <JKL and <LKM can be referred to as linear pairs. They are two adjacent angles that are formed from the intersecting of two lines.

Question 2:

Given that <KLM = x°

<KML = 50°

<JKL = (2x - 15)°

According to the exterior angle theorem, exterior ∠ JKL = <KLM + KML.

2x - 15 = x + 50

Solve for x

2x - x = 15 + 50

x = 65

Therefore, <KLM = 65°

QUESTION 3:

<JKL = 2x - 15

Plug in the value of x

<JKL = 2(65) - 15

= 130 - 15

<JKL = 115°

Answer:

D. 6

Step-by-step explanation:

here, as given set Q consists { 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36}

and set Z contains {3, 6, 9, 12, 15, 18, 21,24, 27, 30, 33, 36, .... }

so be comparing both, we can see that the numbers 6, 12, 18, 24, 30 and 36 is repeated.

Answer:

Hey there!

The perimeter can be expressed as 140+140+68[tex]\pi[/tex]

This is equal to 493.52 m

Hope this helps :)

Answer:

The correct answer is

For addition, Caulleen used the words total, sum, altogether, and increase. But we could also have used the words combine, plus, more than, or even just the word "and". For subtraction, Caulleen used the words, fewer than, decrease, take away, and subtract. We also could have used less than, minus, and difference.

Step-by-step explanation:

hope this helps u!!!

The graph which shows the solution to the system of inequalities is attached in the picture below :

Given the inequalities :

y ≥ 2x + 1

y ≤ 2x - 2

From y ≥ 2x + 1 ;

Since the inequality sign is ≥, a solid line is used to draw the straight line graph of  y ≥ 2x + 1

From :

y = mx + c

Where, m = slope ; c = intercept

Hence, a straight line graph with ;

Intercept, c = 1 (where the line crosses the y-intercept)

Slope, m = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality :

0 ≥ 2(0) + 1

0 ≥ 0 + 1

0 ≥ 1

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

From : y ≤ 2x - 2

Since the inequality sign is ≤, a solid line is used to draw the straight line graph of  y ≤ 2x - 2

Graph the line y ≤ 2x - 2, with ;

Intercept, c = - 2

Slope = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality y ≤ 2x - 2:

0 ≤ 2(0) - 2

0 ≤ 0 - 2

0 ≤ - 2

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

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Answer:

Its graph B on edge 2022

Step-by-step explanation:

Answer:

5,000

Step-by-step explanation:

If it decreases by 5% a year, it'll decrease by 75% in 15 years

i.e 1 year = 5%

15 years = x

Cross multiply

x = 75%

Therefore, since it decreases by 75%

100 - 75 x 20,000 = 5,000

100

Answer:

sin = -√2 / 2

cos = √2 / 2

tan = -1

Step-by-step explanation:

Θ is in quad IV

sin = -√2 / 2

cos = √2 / 2

tan = -1

Answer:

  181.8 yd

Step-by-step explanation:

The law of cosines is good for this. It tells you for triangle sides 'a' and 'b' and included angle C, the length of 'c' is given by ...

  c^2 = a^2 +b^2 -2ab·cos(C)

For the given geometry, this is ...

  c^2 = 400^2 +240^2 -2(400)(240)cos(16°) ≈ 33,037.75

  c ≈ √33037.75 ≈ 181.8 . . . yards

Marsha's ball is about 181.8 yards from the hole.

Answer:

181.8 yds

Step-by-step explanation:

I got it correct on founders edtell

Answer:

[tex]79591.8872 in^3/s[/tex]

Step-by-step explanation:

we know that the volume of a right circular cone is give as

[tex]V(r,h)= \frac{1}{3} \pi r^2h\\\\[/tex]

Therefore differentiating partially  with respect to  r and h we have

[tex]\frac{dV}{dt} = \frac{1}{3}\pi [2rh\frac{dr}{dt} +r^2\frac{dh}{dt}][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [218*198*1.1+109^2*2.4][/tex]

[tex]\frac{dV}{dt} = \frac{\pi}{3} [47480.4+28514.4]\\\\\frac{dV}{dt} = \frac{\pi}{3} [75994.8]\\\\ \frac{dV}{dt} = 3.142 [25331.6]\\\\ \frac{dV}{dt} =79591.8872 in^3/s[/tex]

Answer:

Triangle D is your answer.

Answer:

Hey there!

Triangle C is unique, as one side and two angles determine a unique triangle.

Hope this helps :)

Answer:

-1/2

Step-by-step explanation:

At this point you can guess and try. And it seems that x = -1/2, lets check:

So, this is correct: x= -1/2

Answer:

0.078

Step-by-step explanation:

The probability P(A) of an event A happening is given by;

P(A) = [tex]\frac{number-of-possible-outcomes-of-event-A}{total-number-of-sample-space}[/tex]

From the question;

There are two events;

(i) Drawing a first card which is a king: Let the event be X. The probability is given by;

P(X) = [tex]\frac{number-of-possible-outcomes-of-event-X}{total-number-of-sample-space}[/tex]

Since there are 4 king cards in the pack, the number of possible outcomes of event X = 4.

Also, the total number of sample space = 52, since there are 52 cards in total.

P(X) = [tex]\frac{4}{52}[/tex] = [tex]\frac{1}{13}[/tex]

(ii) Drawing a second card which is a queen: Let the event be Y. The probability is given by;

P(Y) = [tex]\frac{number-of-possible-outcomes-of-event-Y}{total-number-of-sample-space}[/tex]

Since there are 4 queen cards in the pack, the number of possible outcomes of event Y = 4

But then, the total number of sample = 51, since there 52 cards in total and a king card has been removed without replacement.

P(Y) = [tex]\frac{4}{51}[/tex]

Therefore, the probability of selecting a first card as king and a second card as queen is;

P(X and Y) = P(X) x P(Y)

= [tex]\frac{1}{13} * \frac{4}{51}[/tex] = 0.078

Therefore the probability is 0.078

Hey there! I'm happy to help!

We want to find the volume of this  rectangular waterbed. This means the amount of space it takes up. To find the volume of a rectangular prism, you just multiply together the three side lengths.

7×5×1=35 cubic feet

Now, we need to see how many gallons fit into 35 cubic feet. We see that one gallon is equal to 0.13 cubic feet. So, we can set up a proportion to find how many gallons are needed. We will use g to represent our missing number of gallons.

[tex]\frac{gallons}{cubic feet} = \frac{1}{0.13} =\frac{g}{35}[/tex]

In a proportion, the products of the diagonal numbers are equal. This means that 35, which is 1 multiplied by 35, is equal to 0.13g, which is from multiplying 0.13 by the g.

0.13g=35

We divide both sides by 0.13/

g≈269.23

When rounded to the nearest whole gallon, we will need 269 gallons of water to fill the waterbed.

I hope that this helps! Have a wonderful day! :D

Answer:

Step-by-step explanation:

Since the waterbed is rectangular, its volume would be determined by applying the formula for determining the volume of a cuboid which is expressed as

Volume = length × width × height

Therefore,

Volume of waterbed = 7 × 5 × 1 = 35 cubic feet

1 US gallon = 0.133680556 cubic feet

Therefore, converting 35cubic feet to gallons, it becomes

35/0.133680556 = 261.81818094772 gallons

Rounding up to whole gallon, it becomes 262 gallons

Answer:

The statement

the product of 60 and the number of seconds is written as

60 * s

Hope this helps you

Answer:

18

Step-by-step explanation:

23^0 - 15^1 + 18^0 + (43 - 12) =

= 1 - 15 + 1 + 31

= -14 + 1 + 31

= -13 + 31

= 18

The correct answer is D. 23

Explanation:

Histograms similar to other graphs represent numerical information, usually by using bars, as well as ranges. For example, in the case presented the information presented belongs to the scores obtained in a test, which are shown using ranges. Moreover, it is possible to know the total of people that took the test by adding each of the frequencies, as the frequency in the y-axis shows the number of times the range repeated and it is expected each grade registered belongs to 1 person. This means the total of people is equal to 2 (score from 60-69) + 9 (score from 70-79) + 7 (score from 80-89) + 5 (score from 90-99) = 23 people.

Answer:

the answer is 23

Step-by-step explanation:

hopes this helps:)

Answer:

2/3

Step-by-step explanation:

The equation for direct variation is: y = kx, where k is a constant.

Here, we see that y varies directly with x when y = 6 and x = 72, so let's plug these values into the formula to find k:

y = kx

6 = k * 72

k = 6/72 = 1/12

So, k = 1/12. Now our formula is y = (1/12)x. Plug in 8 for x to find y:

y = (1/12)x

y = (1/12) * 8 = 8/12 = 2/3

Thus, y = 2/3.

~ an aesthetics lover

Answer:

Step-by-step explanation: I hope i'm right

[tex]y \alpha x\\y=kx....(1)\\6=72k\\\frac{6}{72} =\frac{72k}{72} \\\\1/12 =k\\y = 1/12x=relationship-between;x-and;y\\x =8 , y =?\\y = \frac{8}{12} \\Cross-Multiply\\12y =8\\12y/12 = 8/12\\\\y = 2/3[/tex]