find the value of x.

Answer:

86 thousand 5 hundred and 3

Step-by-step explanation:

Answer:

x³-3x²-40x+84

Step-by-step explanation:

y = (x-7)(x-2)(x+6)

 = (x²-9x+14)(x+6)

 = (x³-9x²+14x)+(6x²-54x+84)

 = x³-3x²-40x+84

Answer:

-3.3 (Choice 3)

Answer:

-3.3

Step-by-step explanation:

1/2=0.5 so 3+0.5=3.5

4.5-3.5=1 Brackets comes first because BIDMAS

-2.3-1= -3.3

Answer: Set A is greater than set B

Step-by-step explanation:

You can see that the scale of set A is larger than the scale of set B. Therefore making set A greater than set B

Answer:

12.54m by 12.54 and 8.54m by 8.54m

Step-by-step explanation:

Area of a square = L²

L is the side length of the room

The total area of the two square room = A₁+A₂

T = A₁+A₂

T = L₁²+x²

If the two square rooms have a total floor area of 230 m², then;

L₁²+x² = 230. ..... 1

If one room is 4 meters bigger each way than other, then;

L₁ = x + 4 .... 2

where x is the length of the smaller room

Substitute equation 2 into 1;

From 1: L₁²+x² = 230

(x+4)²+x² = 230

x²+8x+16+x² = 230

2x²+8x+16-230 = 0

2x²+8x-214 = 0

x²+4x-107 = 0

x = -4±√16-4(-107)/2

x = -4±√16+428/2

x = -4±21.07/2

x = 17.07/2

x = 8.54m

L₁ = x+4

L₁ = 8.54+4

L₁ = 12.54m

Hence the dimensions of the room is 12.54m by 12.54 and 8.54m by 8.54m

Answer:

1) The factorized form of the polynomial is [tex](x-5)\cdot (x+2) = 0[/tex].

2) The factorized form of the polynomial is [tex](x+6)\cdot (x-4) = 0[/tex].

3)  [tex]r_{1} = -3[/tex], [tex]r_{2} = -2[/tex]. (Option D)

4) [tex]r_{1} = -7[/tex], [tex]r_{2} = 5[/tex]. (Option A)

Step-by-step explanation:

All exercise are case of factorization of second grade polynomials of the form [tex]x^{2} +(-r_{1} - r_{2})\cdot x + r_{1}\cdot r_{2}[/tex], where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the two roots of the polynomial. Now we proceed to solve each polynomial:

1) [tex]x^{2}-3\cdot x-10 = 0[/tex]

In this case, the coefficients have the following characteristics:

[tex]-r_{1}-r_{2} = -3[/tex]

[tex]r_{1}\cdot r_{2} = -10[/tex]

The solution of this system of nonlinear equations is: [tex]r_{1} = 5[/tex], [tex]r_{2} = -2[/tex].

Then, the factorized form of the polynomial is:

[tex](x-5)\cdot (x+2) = 0[/tex]

2) [tex]x^{2}+2\cdot x -24 = 0[/tex]

In this case, the coefficients have the following characteristics:

[tex]-r_{1}-r_{2} = 2[/tex]

[tex]r_{1}\cdot r_{2} = -24[/tex]

The solution of this system of nonlinear equations is: [tex]r_{1} = -6[/tex], [tex]r_{2} = 4[/tex].

Then, the factorized form of the polynomial is:

[tex](x+6)\cdot (x-4) = 0[/tex]

3) [tex]x^{2} + 5\cdot x +6 = 0[/tex]

In this case, the coefficients have the following characteristics:

[tex]-r_{1}-r_{2} = 5[/tex]

[tex]r_{1}\cdot r_{2} = 6[/tex]

The solution of this system of nonlinear equations is: [tex]r_{1} = -3[/tex], [tex]r_{2} = -2[/tex].

Hence, the correct answer is D.

4) [tex]x^{2}+2\cdot x -35 = 0[/tex]

In this case, the coefficients have the following characteristics:

[tex]-r_{1}-r_{2} = 2[/tex]

[tex]r_{1}\cdot r_{2} = -35[/tex]

The solution of this system of nonlinear equations is: [tex]r_{1} = -7[/tex], [tex]r_{2} = 5[/tex].

Hence, the correct answer is A.

Answer:

reflection and rotation

Step-by-step explanation:

Answer:

Difference = 5 meters

Step-by-step explanation:

Given that:

Length of shadow of building = 20 meter

Height of woman = 1.8 meters

Shadow length of woman = 2.4 meters

Height of building = x

Ratio of building's height to shadow = x : 20

Ratio of woman's height to shadow = 1.8 : 2.4

x : 20 :: 1.8 : 2.4

Product of mean = Product of extreme

20 * 1.8 = 2.4x

2.4x = 36

Dividing both sides by 2.4

[tex]\frac{2.4x}{2.4}=\frac{36}{2.4}\\x=15[/tex]

Difference in height and shadow = 20 - 15 = 5 meters

Hence,

Difference = 5 meters

The correct model of the height of rocket above water is;

h(t) = -16t² + 96t + 112

Answer:

time to reach max height = 3 seconds

h_max = 256 ft

Time to hit the water = 7 seconds

Step-by-step explanation:

We are given height of water above rocket;

h(t) = -16t² + 96t + 112

From labeling quadratic equations, we know that from the equation given, we have;

a = -16 and b = 96 and c = 112

To find the time to reach maximum height, we will use the vertex formula which is; -b/2a

t_max = -96/(2 × -16)

t_max = 3 seconds

Thus, maximum height will be at t = 3 secs

Thus;

h_max = h(3) = -16(3)² + 96(3) + 112

h_max = -144 + 288 + 112

h_max = 256 ft

Time for it to hit the water means that height is zero.

Thus;

-16t² + 96t + 112 = 0

From online quadratic formula, we have;

t = 7 seconds

a. The concentration of the solution is  0.05 kg/L. b. The amount of salt is   154 kg after 4.5 hours. c. The concentration of salt in the solution in the tank approaches 0 as the time approaches infinity.

a. The concentration of the salt in the tank initially is given by the amount of salt divided by the volume of water:

0.025 kg/L = 100 kg / 2000 L = 0.05 kg/L

b. Let t be the time in minutes. The amount of salt in the tank after t minutes is given by:

100 kg + 0.025 kg/L × 8 L/min × t

To find the amount of salt after 4.5 hours, we convert the time to minutes:

4.5 hours × 60 minutes/hour = 270 minutes

And substitute this value of t into the equation:

100 kg + 0.025 kg/L × 8 L/min × 270 min = 100 kg + 54 kg = 154 kg

c. The concentration of salt in the solution in the tank as the time approaches infinity is given by:

154 kg / (2000 L + 8 L/min × t) as t approaches infinity

As t approaches infinity, the volume of water in the tank approaches infinity, so the concentration of salt in the solution approaches 0.

So, the concentration of salt in the solution in the tank approaches 0 as the time approaches infinity.

Learn more about the concentration of the salt here:

https://brainly.com/question/14177007

#SPJ1

Answer:   [tex]2(\dfrac{1-e}{\pi})[/tex] or StartFraction 2 (1 minus e) Over pi EndFraction

Step-by-step explanation:

The average rate of function f(x) over the interval [a,b] is given by:-

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given  : [tex]f(x)=e^{\sin x}[/tex]

The average rate of change over [tex][\dfrac{\pi}{2},\pi][/tex] will be:

[tex]\dfrac{f(\pi)-f(\dfrac{\pi}{2})}{\pi-\dfrac{\pi}{2}}=\dfrac{e^{\sin \pi}-e^{\sin \dfrac{\pi}{2}}}{\dfrac{\pi}{2}}\\\\=\dfrac{e^0-e^1}{ \dfrac{\pi}{2}}\\\\=2(\dfrac{1-e}{\pi})[/tex]

Hence, the average rate of change over [tex][\dfrac{\pi}{2},\pi][/tex]  is [tex]2(\dfrac{1-e}{\pi})[/tex].

Answer:

2 (1 minus e) Over pi

Step-by-step explanation:

edge 2023

distribute the 4:

4x-36=-48x

subtract 4x

-36=-52x

divide by -52

x=1/2

The line has a positive slope. Let's look at all the slopes:

1) -3

2) -3

3) 3

4)3

Which ones are positive? That's right, 3 and 4. We don't know which equation would be the equation of the line. That's where the other information comes in.

The line intersects the y-axis at at a point that has a negative y-coordinate. Lets write the last two equations in slope-intercept form.

1) y = -3/2x - 5/2

2) y = -3/2x + 5/2

We have to graph both of the lines now. The graphs are at the very bottom. Take a look at them. In the first one, the y-intercept is a negative and in the second one, the y-intercept is positive.

The third one AKA 3x + 2y = -5 is the equation of the line. I hope this helps! Let me know if I got it wrong or if you need any more help.

Answer:

0.86

Explanation:

He answered 43 out of 50 questions.

As a fraction this is written  

43

50

To convert this fraction to a decimal fraction divide 43 by 50 .This

can be done on a calculator to obtain 0.86

Step-by-step explanation:

Brainliest?

Answer:

k = 5.

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope, and b is the y-intercept(y when x = 0).

Perpendicular lines

When two lines are perpendicular, the multiplication of their slopes is -1.

Perpendicular to the line y=x−285.

This line has slope 1, so the line we want to find the equation has slope [tex]m = -1[/tex]

Then

[tex]y = -x + b[/tex]

Passes through (7, 0)

This means that when [tex]x = 7, y = 0[/tex]. So

[tex]y = -x + b[/tex]

[tex]0 = -7 + b[/tex]

[tex]b = 7[/tex]

So

[tex]y = -x + 7[/tex]

Find the value of k given that the line through (k, 2)

This means that when [tex]x = k, y = 2[/tex]. So

[tex]y = -x + 7[/tex]

[tex]2 = -k + 7[/tex]

[tex]k = 7 - 2 = 5[/tex]

The value of k is k = 5.

Answer:

The answer is 40.

Step-by-step explanation:

Calculate within the parenthesis. After calculate the outside by the inside.

Answer:

930m

Step-by-step explanation:

It says they were 900 feet in the air below him is the ocean so thats 900 meters away from him and the shark is 30 feat below the surface of the ocean so you would do 900+30=930m so the shark is 930m away from him

Answer:

15% probability that 7 adults selected at random from the town all have health insurance.

Step-by-step explanation:

(sample/population)^number of times selected

(76/100)^7 = (0.76)^7 = 0.15 = 15%

Answer:

18

Step-by-step explanation:

Solve for c by cross multiplying

Answer:

The expression for the perimeter of the rectangle is: [tex]P = 4x - 18[/tex]

Step-by-step explanation:

Perimeter of a rectangle:

A rectangle has length l and width w. It's perimeter is given by:

[tex]P = 2(l + w)[/tex]

In this question:

[tex]l = x - 9, w = x[/tex]

So

[tex]P = 2(x - 9 + x) = 2(2x - 9) = 4x - 18[/tex]

The expression for the perimeter of the rectangle is: [tex]P = 4x - 18[/tex]

Step-by-step explanation:

6/10*300=180

60% of 500 is 300

6/10x=300 x=500

60/300=1/5=20%

Answer:

b) False, all integers are whole numbers, but not all whole numbers are integers

Answer:

35+4x+5+6x=180

10x=180-40

x=140/10

x=14

Answer:

(0,2)

Step-by-step explanation:

X=0 and y=2

Answer:

7 seconds

Step-by-step explanation:

Distance of the coin above the water is modeled by the equation

[tex]y=-16x^2+96x+112[/tex]

where [tex]x[/tex] is time taken to cover the distance

Now equating with zero.

[tex]0=-16x^2+96x+112\\\Rightarrow 16x^2-96x-112=0\\\Rightarrow x=\dfrac{-\left(-96\right)\pm \sqrt{\left(-96\right)^2-4\times \:16\left(-112\right)}}{2\times \:16}\\\Rightarrow x=7, -1[/tex]

So, time taken by the coin to hit the water is 7 seconds.

Answer:

[tex]\huge\boxed{y=5-\frac{2}{3}x}[/tex]

Step-by-step explanation:

With the equation [tex]\displaystyle 2x+3y=15[/tex], we can solve for y by algebraically manipulating the question until we have y isolated on one side.

It's important to note that if we do something to one side, we have to do it to another. Just as [tex]5=5[/tex], adding two to both sides still makes it true [tex]5+2=5+2, 7=7[/tex].

Therefore, this equation for y is [tex]\displaystyle y = 5 - \frac{2}{3}x[/tex] .

Hope this helped!

2x + 3y = 15

3y = 15 - 2x

y = 15 - 2x/3

Answer:

-6

Step-by-step explanation:

hey laudu

[tex]3a + b + 4[/tex]

[tex]3( - 2) + ( - 4) + 4[/tex]

[tex] - 6 - 4 + 4[/tex]

[tex] - 6[/tex]

Step-by-step explanation:

❀ [tex] \underline{ \underline{ \text{Given}}} : [/tex]

❀ [tex] \underline{ \underline{ \text{To \: find}}} : [/tex]

✏ [tex] \underline{ \underline{ \text{Solution}}} : [/tex]

All you need to do is plug the value and simplify !

⟶ [tex] \tt{3 \times ( - 2) + ( - 4) + 4}[/tex]

⟶ [tex] \tt{ - 6 + ( - 4) + 4}[/tex]

⟶ [tex] \tt{ - 6 - 4 + 4}[/tex]

⟶ [tex] \tt{ - 10 + 4}[/tex]

⟶ [tex] \boxed{ \tt{ - 6}}[/tex]

[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ - 6}}}}}}[/tex]

Hope I helped ! ♪

Have a wonderful day / night ! ♡

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