Find the missing side Lengths (70 POINTS!)

[tex]2.\\k(x)=2x^2-3\sqrt{x}\\\\k(9)\to\text{put the value of x = 9 to the equation of the function:}\\\\k(9)=2(9)^2-3\sqrt9=2(81)-3(3)=162-9=153\to\boxed{(4)}\\\\3.\\3(x^2+2x-3)-4(4x^2-7x+5)\qquad\text{use distributive property}\\\\=(3)(x^2)+(3)(2x)+(3)(-3)+(-4)(4x^2)+(-4)(-7x)+(-4)(5)\\\\=3x^2+6x-9-16x^2+28x-20\qquad\text{combine like terms}\\\\=(3x^2-16x^2)+(6x+28x)+(-9-20)\\\\=-13x^2+34x-29\to\boxed{(2)}[/tex]

[tex]4.\\p(x)=x^2-2x-24\\\\x^2-2x-24=0\\\\x^2+4x-6x-24=0\\\\x(x+4)-6(x+4)=0\\\\(x+4)(x-6)=0\iff x+4=0\ \vee\ x-6=0\\\\x=-4\ \vee\ x=6\to\boxed{(3)}[/tex]

tan(angle) = opposite/adjacent

tan(37) = x/14

14*tan(37) = x

x = 14*tan(37)

x = 10.5497567

x = 10.5

Answer: 10.5

Answer:

Step-by-step explanation:

if ABC is a triangle then <]ABC + <}BCA +<}CAB = 180 degrees

Poof:

Draw line a through points A and B. Draw line B through point C and parallel to line a

Since line a and b are parallel <] BAC = <] B'CA and <]ABC = <}BCA'.

it is obvious that <}B'CA + <}ACB + <]BCA' = 180 degrees

Thus <]ABC + <)BCA + <)CAB = 180 degrees

Lemma:

if ABCD is quadrilateral and <)CAB = <}DCA then AB and DC are parallel.

Step-by-step explanation:

Consider a triangle ABC and let ∠A + ∠B + ∠C = 180°

Construct a straight line DE running parallel to BC and passing though A.

Now let

∠BAC = 1

∠ABC = 2

∠ACB = 3

∠DAB = 4

∠EAC = 5

Therefore we know that

∠DAB = ∠ABC (alternate angles), so 4 = 2

∠EAC = ∠ACB (alternate angles), so 5 = 3

Now line CE is straight line and we know that angle for a straight line 180°.

Thus ∠DAB + ∠BAC + ∠EAC  = 180°

or      ∠ABC + ∠BAC + ∠ACB =  180°

or          ∠A + ∠B + ∠C = 180°

Thus proved.

Answer:

3

Step-by-step explanation:

Divide [tex]\dfrac{2}{3}[/tex] by [tex]\dfrac{2}{9}:[/tex]

[tex]\dfrac{2}{3}:\dfrac{2}{9}=\dfrac{2}{3}\cdot \dfrac{9}{2}=\dfrac{2\cdot9}{3\cdot 2}=\dfrac{9}{3}=3.[/tex]

Answer:

-4

Step-by-step explanation:

If the question is for which x the equations 4(3x+9) and 5x+8 produce the same answer, the answer is x=-4

4(3x+9) = 5x+8

12x + 36 - 5x - 8 =0

7x = -28

x = -4

Answer:

A) 210

Step-by-step explanation:

The percentage of students who have a cell phone plan with company x is student with plan x over total.The total is 130

P(x) = 70/130

The number of students with cell phone  company x is  found by multiplying the total number of students times   the percentage of students with company x

Students with company x = total * P(x)

                                          = 390 * 70/130

                                             = 210

Answer:

A) 210

Step-by-step explanation:

70 students have company X, out of the sample size 130. This forms the fraction 70/130.

n students have company X, out of the population 390. The n is simply a placeholder for a number. This forms the fraction n/390

Equate the two fractions, cross multiply, then divide both sides by 130 to solve for n

Doing all that gives us the following

70/130 = n/390

70*390 = 130*n ..... cross multiply

27300 = 130n

130n = 27300

130n/130 = 27300/130 ...... divide both sides by 130

n = 210

Out of the entire population, the best approximation to the number of students who have company X is 210 people.

Answer:

y=3/2+5

Step-by-step explanation:

Answer:

[tex]\frac{3}{2}x^{2} +5x-21[/tex]

Step-by-step explanation:

put into y=mx+b form

Answer: Her cell phone bill will cost her $61.19

Step-by-step explanation: If it cost 0.18 per min make sure you read the question right

Answer: 80%

15 are on the council, so 75-15 = 60 are not on the council. Therefore, 60/75 = 0.80 = 80% of the students aren't on the council.

An alternative way to find this answer is to compute 15/75 = 0.20 = 20% showing that 20% of the students are on the council, so 100% - 20% = 80% are not on the council.

To find the percent of students not on the student council, subtract the number of students on the council from the total number of students and calculate the percentage.

To find out what percent of the students are NOT on the student council, we need to subtract the number of students who are on the student council from the total number of students and then calculate the percentage.

Number of students on the student council: 15

Total number of students: 75

Number of students NOT on the student council: 75 - 15 = 60

Percentage of students NOT on the student council: (60/75) * 100 = 80%

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Answer:

D. 1/2(4 + Z)

Step-by-step explanation:

1/2 x 4 + 1/2 x Z

We can factor out a 1/2 since it is in both terms

1/2 (4+z)

[tex]\dfrac{1}2{\times4+\dfrac{1}{2}\times z=\boxed{\dfrac{1}{2}}\times4+\boxed{\dfrac{1}{2}}\times z=\boxed{\dfrac{1}{2}}\times(4+z)}\\\\Answer:\ \boxed{D.\ \dfrac{1}{2}(4+z)}[/tex]

Answer:

find below

Step-by-step explanation:

7x-6 = 3x-14

4x = -8

x = -2

-2*7-6 = -14-6 = -20

-2*3-14 = -6-14 = -20

Answer: C

Step-by-step explanation: |-15| is 15. |12| is 12. 15 is greater then 12.

Answer:52 stamps

Step-by-step explanation: He has 32 now. You subtract 6, as he bought 6 more. Then you double this as he sold half. That gives you 52

Starting with the equation (x/2) + 6 = 32, we solve for x to find that William originally had 52 stamps in his collection.

Let's use algebra to solve the problem William faced with his stamp collection. We can let the variable x represent the original number of stamps William had. According to the question, he sold half of his stamps and then bought 6 more, ending up with 32 stamps. This can be expressed as the equation (x/2) + 6 = 32. To find the original number, we solve for x:

Therefore, William started with 52 stamps in his collection before he sold any to consider buying a video game.

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Answer:

[tex]x+y=12[/tex]

[tex]21.50x+14.75y=204[/tex]

Step-by-step explanation:

Let x be the number of adult tickets and y be the number of children's tickets.

We are given that there are total 12 people. Therefore, we can set:

[tex]x+y=12[/tex]

Moreover, we are given that an adult ticket costs $21.50 and a child's ticket costs $14.75, therefore, cost of x adult tickets will be [tex]21.50x[/tex] and cost of y children's ticket will be [tex]14.75y[/tex]. We can form the second equation by setting the total cost of tickets as:

[tex]21.50x+14.75y=204[/tex]

Therefore, the required system of equations that could be used to find x and y will be:

[tex]x+y=12[/tex]

[tex]21.50x+14.75y=204[/tex]

Answer:

[tex]x+y = 12[/tex]

[tex]21.50x+14.75y=204.00[/tex]

Step-by-step explanation:

Given :

A local amusement park charges $21.50 per daily adult ticket and $14.75 per daily child's ticket.

Group of 12 people paid $204.00 for tickets.

To Find : System of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased.

Solution :

Since group contains 12 people so no. of tickets are 12 .

Let out of 12 people no. of adults's tickets  are x.

Let out of 12 people no. of children's ticket are y .

⇒[tex]x+y = 12[/tex]

Since charge of one adult ticket = $21.50

So, charge of x adult tickets = $21.50 x

Since charge of one child ticket = $14.75

So, charge of y children tickets =$14.75 y

And we are given that total amount paid by these 12 people = $204.00

Thus [tex]21.50x+14.75y=204.00[/tex]

Hence , System of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased:

[tex]x+y = 12[/tex]

[tex]21.50x+14.75y=204.00[/tex]

Answer:

12:5

Step-by-step explanation:

We want to find the ratio of Jeanne's tickets to Jake's tickets

Jeanne's tickets: Jake's tickets

15:36

We can simplify this ratio by dividing each side by 3

15/3:36/3

5:12

Answer:

Step-by-step explanation:

15:36

simplifies to

5:12

Jeanne: Jake

Answer:

d 5.5

Step-by-step explanation:

Answer:

D: 5.5%

Step-by-step explanation:

Answer:

120 pounds

-hope this helps

Answer:

£111.43

Step-by-step explanation:

100% represents the original cost of the phone

30% off is then (100 - 30) = 70% of the original cost

divide the cost by 70 to find 1% then multiply by 100 for original cost

original cost = [tex]\frac{78}{70}[/tex] × 100 = £111.43

Answer:

B) Not Garlicky enough.

Step-by-step explanation:

You divide 500 by 8 to make it a unit. Then multiply that by 12. That equals 750. Therefore there is not enough garlic.

Answer:

see below  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

If 1cm = 7m

then:

7c = 49m

[tex]8^{3x-10}=4^{6x-27}\\\\(2^3)^{3x-10}=(2^2)^{6x-27}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3(3x-10)}=2^{2(6x-27)}\qquad\text{use distributive property}\\\\2^{(3)(3x)+(3)(-10)}=2^{(2)(6x)+(2)(-27)}\\\\2^{9x-30}=2^{12x-54}\iff9x-30=12x-54\qquad\text{add 30 to both sides}\\\\9x=12x-24\qquad\text{subtract 12x from both sides}\\\\-3x=-24\qquad\text{divide both sides by (-3)}\\\\\boxed{x=8}[/tex]

Answer:

17 seconds

Step-by-step explanation:

The rescue helicopter travels down for 100 seconds at a speed of 10.5 feet per second.

So, the distance it covered = 100(10.5) = 1050 feet.

It then travels directly up for 150 seconds at a speed 5.2 feet per second.

So, the distance = 150(5.2) = 780 feet

Now, the distance from sea level = 1050 - 780 = 270 feet.

It will reach this distance with a maximum speed of 15.8 feet per second.

Hence, the time required to reach this distance = [tex]\frac{distance}{speed}[/tex]

= [tex]\frac{270}{15.8}[/tex]

≈ 17 seconds

Answer: A. Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000.

Step-by-step explanation:

Hi, "dealer incentives" for this case mean that a car dealer pays a reduced price for a car. This incentive allows the car dealer to make a profit.

To be an example of dealer incentive the option must state that the car dealer makes a profit.

So, with this information analyzed the correct option is A."Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000" because this option states that the Sun car dealers make a profit of $2000.

Feel free to ask for more if it´s necessary or if you did not understand something.

Answer:

21.25 pieces of candy have been eaten.

Step-by-step explanation:

Pretty much, we have to start by finding how many times 8 can go into 34, which is 4.25. So if we are subtracting the whole from three eighths, 3/8 will equal 12.75/34. 34-12.75= 21.25. Therefore, 21.25 pieces of candy have been eaten.

Answer:

-3

Step-by-step explanation:

Anything that is negative multiplied by a negative is a positive so knowing this, you can multiply -3*-3=9 or divide 9/-3=-3

Hope this helps

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Answer:

The answer to linear equation 9t=-3 is t = - (1/3)

Step-by-step explanation:

9t=-3

Solving for t: Dividing both sides of the equation by 9:

9t/9=-3/9

t=-(3/9)

Simplifying the fraction on the right side of the equation dividing the numerator and denominator by 3:

t = - (3/3) / (9/3)

t = - (1/3)

Answer:

1950 watt-hours

Step-by-step explanation:

3 days and 6 hours is equivalent to 3.25 days because there are 24 hours in a day and 6/24 or 6 out of 24 is equivalent to 6÷24 which is 0.25.

0.25 + 3= 3.25 which is the time.

Multiply 3.25 by 600 to find the watt-hours in 3 days and six hours.