Simplify: (5x2 - 9x + 3) + (4x2 + 4x - 12)
(1) 9x2 + 5x - 9
2) 9x2 - 5x + 15
3) 9x² - 5x-9
4) 9x2 - 13x - 9

Step-by-step explanation:

for 1 min=9 wraps

for x(unknown minutes)=360 wraps

so I crossed multiply:

9x=360

x=360/9

x=40

so it takes 40 minutes to make 360 wraps

Answer:

  [tex]\frac{x^3+y^3+z^3}{3} =0[/tex]

Step-by-step explanation:

From the question we are told that

mean of three numbers is zero

Generally mean refers to average of number

Let

x, y, z be the three numbers with a mean of zero

T the mean of there cubes

Mathematically the mean of these three numbers is given as

     [tex]\frac{x+y+z}{3} =0[/tex]

     [tex]x+y+z =0[/tex]

and there cubes

     [tex]\frac{x^3+y^3+z^3}{3} =T[/tex]

     [tex]x^3+y^3+z^3=3T[/tex]

Mathematically solving the above equations by substitution method

 [tex]x+y+z =0......1[/tex]

 [tex]x^3+y^3+z^3=3T ......2[/tex]

 [tex]x=-y-z ...3[/tex]

equating 3 in 2

   [tex]-y^3-z^3+y^3+z^3=3T ..... 4\\3T=0[/tex]

    [tex]T=0[/tex]

Therefore the mean of the cubes of the three number is 0

     [tex]\frac{x^3+y^3+z^3}{3} =0[/tex]

Answer:

(-1, 7)

Step-by-step explanation:

From the graph attached,

There are two lines representing the system of linear equations.

Solution of two linear equations is represented by a common point or point of intersection on the graph.

Point of intersection of the linear system of equations given in the graph → (-1, 7)

Therefore, solution of the linear system is (-1, 7).

its 18 bc half of 18 is 9 so ye

Answer:

18

Step-by-step explanation:

18*0.50=9

hope this helped!!

Answer:

30kg

Step-by-step explanation:

what we know is that 3a - 20kg is b. and if a + 3a -20kg = 100kg, it becomes algebra .

So, we move it over to the sides:

4a = 120kg

(here i moved -20kg to the 100kg and did the reverse. I also added the a's)

which means a = 120kg divided by 4

a = 30kg

Answer:

Rs 42000 and Rs 40000

Step-by-step explanation:

Given that Rs 82000 is divided into two parts.

Let the first part be Rs x which is compounded annually at the interest of 5% per annum for 2 years.

The rate of interest = 5%=0.05

The total amount after 2 years [tex]= x(1+0.05)^{2}\cdots(i)[/tex]

The other part is Rs 82000-x which is compounded annually at the interest of 5% per annum for 3 years.

The total amount after 3 years [tex]= (82000-x)(1+0.05)^{3}\cdots(ii)[/tex]

As both the amounts are equal, so from equation (i) and (ii)

[tex]x(1+0.05)^{2}=(82000-x)(1+0.05)^{3} \\\\x(1.05)^{2}=82000(1.05)^{3} -x(1.05)^{3} \\\\x(1.05^2+1.05^3)=82000\times 1.05^3 \\\\x(2.260125)=94925.25 \\\\x=94925.25/2.260125 \\\\[/tex]

x= 42000

And the other part = 82000-42000 = Rs 40000

Hence, he divides the money as

Rs 42000 at 5% per annum compound interest in 2 years and

Rs 40000 at 5% per annum compound interest in 3 years.

Answer:

i'm not entirely sure but taking an educated guess, id say uplift

Step-by-step explanation:

Answer:-12

Step-by-step explanation:

When adding if both are negatives just add and when your done add the negative symbol.

Answer: the answer is 12

Step-by-step explanation:

cause i think it goes like a negative plus  a negative is a positive

Answer:

+ + 1

Explanation:

B+A = A+B

1+() = <1

Answer:

y+52=180(being co8nterior angle)

y=180_52

y=128

or,(6x+4)+52

6x=56

x=56÷6

x=9.333

Answer:

6a + 2

Step-by-step explanation:

2 ×3a = 6a 2×2 = 4

it gives 6a + 4

(If this is wrong, it would be better to attach an image)

Given:

Hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6).

To find:

The equation of hyperbola.

Solution:

We have, directrices at y = ±2 so this hyparabola is along the y-axis.

The standard form of hyperbola is

[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex]      ...(i)

where, (h,k) is center, foci are [tex](h,k\pm c)[/tex] and directrix are [tex]y=k\pm \dfrac{a^2}{c}[/tex].

On comparing foci, we get

[tex](h,k\pm c)=(0,\pm 6)[/tex]

[tex]h=0,k=0,c=6[/tex]

On comparing directrix we get

[tex]k\pm \dfrac{a^2}{c}=\pm 2[/tex]

[tex]\dfrac{a^2}{c}=2[/tex]

[tex]\dfrac{a^2}{6}=2[/tex]

[tex]a^2=12[/tex]

Now,

[tex]a^2+b^2=c^2[/tex]

[tex]12+b^2=(6)^2[/tex]

[tex]b^2=36-12[/tex]

[tex]b^2=24[/tex]

Putting [tex]h=0,k=0,a^2=12,b^2=24[/tex], we get

[tex]\dfrac{(y-0)^2}{12}-\dfrac{(x-0)^2}{24}=1[/tex]

[tex]\dfrac{y^2}{12}-\dfrac{x^2}{24}=1[/tex]

Therefore, the equation of hyperbola is [tex]\dfrac{y^2}{12}-\dfrac{x^2}{24}=1[/tex].

Answer:

the person above has the right answer. I took the test.

Step-by-step explanation:

The person above is correct.

Answer:

i need more info

Step-by-step explanation:

9514 1404 393

Answer:

  5 hours

Step-by-step explanation:

The volume of the pool is ...

  V = LWH

  V = (10 ft)(8 ft)(5 ft) = 400 ft^3

At the given fill rate, the time it will take is ...

  (400 ft^3)/(80 ft^3/h) = 5 h

It will take 5 hours for the pump to fill the pool.

Answer:

Im pretty sure the answer is 5 hours

Step-by-step explanation:

The capacity of swimming pool is

v = 10 ⋅ 8 ⋅ 5 = 400 cubic feet

The pump fills 80 cubic feet in 1 hour

Therefore, the pump will fill

400 cubic feet in 5 hours.

Answer:

the answer would be 50 on each side

Step-by-step explanation:

since this shape is an isosceles triangle, the angles on the right and left side would be equivalent! 180-80=100/2=50

Answer:

Please check the explanation.

Step-by-step explanation:

Rebecca's ERROR

Rebecca wrongly used the formula to calculate the average rate of change from x = -1 to x = 3.

She should have used the correct formula to calculate the average rate of change from x = -1 to x = 3 which is:

Average rate = [f(3) - f(-1)] / [3 - (-1)]

But, she reversed the formula.

The correct solution

Considering the graph

[tex]f\left(x\right)=2^x+1[/tex]

Rebecca wants to find the average rate of change from x = -1 to x = 3.

so

at x₁ = -1

[tex]f\left(-1\right)\:=\:2^{-1}+1=\frac{1}{2}+1=\frac{3}{2}[/tex]

at x₂ = 3

[tex]f\left(3\right)\:=\:2^3+1=8+1=9[/tex]

Using the formula, we can determine the average rate of change from x = -1 to x = 3

Average rate = [f(3) - f(-1)] / [ x₂ - x₁]

                      [tex]=\:\frac{\left[9\:-\:\frac{3}{2}\right]}{\left[3-\left(-1\right)\right]}[/tex]

                      [tex]=\frac{\frac{15}{2}}{4}[/tex]

                      [tex]=\frac{15}{8}[/tex]

Therefore, the average rate of change from x = -1 to x = 3 will be:

Average rate = 15/8

Answer:

wdym

Step-by-step explanation:

Answer:

x = −8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

(x + x)  + (75 +53 + 68) = 180 (Combine Like Terms)

2x + 196 =180

Step 2: Subtract 196 from both sides.

2x + 196 − 196 = 180 −196

2x = −16

Step 3: Divide both sides by 2

x = -8

Hope this helps!!!

Answer:

<4 = 88

<3 = 92

Step-by-step explanation:

The sum of the angles of a triangle is 180

<4 + 45+ 47 = 180

<4 + 92 = 180

< 4 = 180-92

<4 = 88

We know the <3 and <4 form a line

<3 + <4 = 180

<3 + 88 = 180

< 3 = 180-88

<3 = 92

Answer:

=3/4/1/20 miles per hr. =15 miles per hr.

Step-by-step explanation:

Speed equals distance and time

Answer:

The discount is $109.50 and the sales price is $155.50

Step-by-step explanation:

30% of 365 is 109.5

356-109.5=155.5

Answer:

28

Step-by-step explanation:

x/7+1=5

-1       -1

x/7=4

x/7*7=4*7 ( do the inverse operation to get rid of 7, which is multiplication)

x=28

Answer:

x=28

Step-by-step explanation:

x÷7+1=5

Firstly,

Group like terms

x÷7=5-1

x÷7=4

Secondly,

So now 7 will cross the equal sign

x=4×7

We have ×7 because when a number number with a division sign crosses an equal sign it becomes multiplication.

x=28

Note: Please note that you missed adding the option points. So, I am solving the entire function to determine the points and the vertex which would anyways clear your concept.

Answer:

The vertex is located at (3, 7)

some of the points will make the table such as:

x       0           1           2          3          4

y      -2          3           6           7          6

The graph is attached below.

Step-by-step explanation:

Given the table

[tex]y\:=\:6x-2-x^2[/tex]

The given equation is of the form quadratic function y = ax² + bx + c. Thus, it represents the Parabola.

We know that the vertex would be the highest point on the Parabola graph if the graph (Parabola) opens down.

Thus, the given Parabola has the vertex point at the highest point of the Parabola as shown in the attached figure.

Finding the Vertex:

y = -x² + 6x - 2

comparing with y = ax² + bx + c

a = -1, b = 6, c = -2

Finding the x-coordinate of the Vertex

x = -b / 2a

x = [-6] /[2(-1)]

x = [-6 ] / [-2]

x = 6/2

x = 3

Thus, the x-coordinate of the vertex : x = 3

Now substituting x = 3 in the equation y = -x² + 6x - 2 to determine the y-coordinate of the vertex

y = -x² + 6x - 2

y = -(3)²+6(3)-2

y = -9 + 18 - 2

y = 18 - 11

y = 7

Thus, the y-coordinate of the vertex : y = 7

Therefore, the vertex is located at (3, 7)

Now, finding some other points lie on the Parabola

y = -x² + 6x - 2

Putting x = 0 in the main function

y = -(0)² + 6(0) - 2

y = 0 + 0 - 2

y = -2

Thus, the y-intercept lies on (0, -2)

Putting x = 1 in the main function

y = -x² + 6x - 2

y = -(1)² + 6(1) - 2

y = -1 + 6 - 2

y = 3

Thus, the point (1, 3) lies on the Parabola

Putting x = 2 in the main function

y = -x² + 6x - 2

y = -(2)² + 6(2) - 2

y = -4 + 12 - 2

y = 6

Thus, the point (2, 6) lies on the Parabola

Putting x = 3 in the main function

y = -x² + 6x - 2

y = -(3)² + 6(3) - 2

y = -9 + 18 - 2

y = 7

Thus, the point (2, 7) lies on the Parabola

Putting x = 4 in the main function

y = -x² + 6x - 2

y = -(4)² + 6(4) - 2

y = -16 + 24 - 2

y = 6

Thus, the point (4, 6) lies on the Parabola

Hence, some of the points will make the table such as:

x       0           1           2          3          4

y      -2          3           6           7          6

The graph is attached below.

Answer:

Please check explanations

Step-by-step explanation:

Here, we want to get the following;

1. Initial deposit

The initial deposit is the value of y when x = 0

We can see this at x = 1000

2. slope and y-intercept

The y-intercept is the y-value of the graph when x = 0

It is the point at which the graph crosses the y-axis

From the plot, we can see that the y-intercept is 1000

To get the slope, we select and two points on the graph and apply the slope formula

The points selected are;

(2,2000) and (4,3000)

The formula for the slope is;

y = (y2-y1)/(x2-x1)

y = (3000-2000)/(4-2) = 1000/2 = $500 per month

3. Generally the equation of a line is;

y = mx + b

where m is slope and b is the intercept

So the equation will be;

y = 500x + 1000

4. The meaning of slope in the graph represents the unit of amount saved per month in the plan. It is just giving us a breakdown of what’s saved by each month on the plan

Answer:

12

Step-by-step explanation:

she has 3 brothers times 4 toys.

Answer:

12 toys

Step-by-step explanation:

She needs to buy 4 toys for 3 people. This means (4) + (4) + (4). This can be written as 4 * 3. This is equal to 12. Therefore, she needs to buy a total of 12 gifts.

Step-by-step explanation:

2/5 of marbles are blue

= 3/5 of marble are not blue.

Number of non-blue marbles = 500 * (3/5) = 300.

300 marbles are not blue.

Answer:

28

Step-by-step explanation:

hope this helps

Answer:

28

Step-by-step explanation:

70% is equal to 70/100. "of" when used in math means multiplaication.

so we do 70/100 x 40

we can simplify 70/100 to get 7/10.

now we multiply:

7/10 x 40 = 28

Answer:

a. x = 10

b. x = 3/5

c. x = 16

d. x = 21/32

Step-by-step explanation:

a - 2x/3 + (x+3)/3 = 11

b - 3/x + 6/x = 15

c - x/2 + x/8 = 10

d - 4/x + 5/4x = 8

Apologies for the long explanations--it's not something I do very well.