Which division problem does the number line below best illustrate?
0 1 2 3 4 5 6 7 8 9 10 11 12 13
O 12-3-4
O 9-3-3
O 12-2-6
o 16-4-4

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Explanation:

T is the midpoint of PQ, which means T splits PQ into two equal parts. Those parts being PT and TQ.

Set them equal to each other and solve for x.

PT = TQ

3x+7 = 7x-9

3x-7x = -9-7

-4x = -16

x = -16/(-4)

x = 4

So,

PT = 3x+7 = 3*4+7 = 19

TQ = 7x-9 = 7*4-9 = 19

Both PT and TQ are 19 units long to help confirm the answer.

Answer:

The expression for the height of the solid is:

[tex]\displaystyle h = x^2+x-9[/tex]

Step-by-step explanation:

Recall that the volume of a rectangular solid is given by:

[tex]\displaystyle V = \ell wh[/tex]

Where l is the length, w is the width, and h is the height.

We know that the volume is given by the polynomial:

[tex]\displaystyle V = 3x^4-3x^3-33x^2+54x[/tex]

And that the length and width are given by, respectively:

[tex]\displaystyle \ell = 3x \text{ and } w =x-2[/tex]

Substitute:

[tex]\displaystyle 3x^4-3x^3-33x^2+54x=(3x)(x-2)h[/tex]

We can solve for h. First, divide both sides by 3x:

[tex]\displaystyle \frac{3x^4-3x^3-33x^2+54x}{3x}=(x-2)h[/tex]

Divide each term:

[tex]\displaystyle x^3-x^2-11x+18=(x-2)h[/tex]

To solve for h, divide both sides by (x - 2):

[tex]\displaystyle h = \frac{x^3-x^2-11x+18}{x-2}[/tex]

Since this is a polynomial divided by a binomial in the form of (x - a), we can use synthetic division, where a = 2. This is shown below. Therefore, the expression for the height of the solid is:

[tex]\displaystyle h = x^2+x-9[/tex]

Answer:

m = 1/2

b = -5

Step-by-step explanation:

The equation of the line of the points (6,-2) and (-6,-8) is y = 1/2x — 5

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The value of m and b in the given equation is 0.5 and -5, respectively.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The given equation is the equation of a line, where m is the slope of the line and b is the y-intercept of the line. Therefore, the value of m or the slope of the equation is,

m = [-8 - (-2)] / [-6 - 6] = -6/-12 = 0.5

Now, substitute the value of x, y, and m in the given equation, therefore, the value of b can be written as,

y = mx + b

-2 = 0.5(6) = b

-2 = 3 + b

b = -2 + -3

b = -5

Hence, the value of m and b in the given equation is 0.5 and -5, respectively.

Learn more about Equation of Line here:

https://brainly.com/question/21511618

#SPJ2

Answer:

See below.

Step-by-step explanation:

[tex]3+x=ax[/tex]    (Given)

[tex]x=ax-3[/tex]    (Subtracted 3 on both sides)

[tex]x-ax=-3[/tex]    (Subtracted ax on both sides)

[tex]x(1-a)=-3[/tex]    (Factor out x from x - ax)

[tex]x=-\frac{3}{1-a}[/tex]    (Divided 1 - a on both sides)

Answer:

70

Step-by-step explanation:

In a trapezoid lines are parallel, so corresponding angle sum = 180

X+X+40 = 180

2x + 40 = 180

2x = 180-40

2x = 140

X = 140/2

X = 70

Answered by Gauthmath

Answer C Right Isosceles Triangle

Step-by-step explanation:

Do it

Answer: C

Step-by-step explanation:

It has a 90 degree angle, right triangle, and both legs in the triangle seem to be the same size, so it's also isosceles.

Step-by-step explanation:

(-1,0),m=2

(1-7),m=12

m=-4,(-1,-4)

Answer:

mine too

Step-by-step explanation:

Answer:

A = 216.24 km²

Step-by-step explanation:

Step-by-step explanation:

given that the coordinate is (0,1)(4,3)

x¹=0, y¹=1, x²=4 y²=3

M=> Gradient => (y²-y¹)/(x²-x¹)

M=(3-1)/(4-0) => 1/2

Therefore the slope-intercept equation

M=(y-y¹)/(x-x¹)

1/2 = (y-1)/(x-0)

x=2y-2

2y=-2-x

y=-x/2 - 1

Answer:

1) 2400MB

2) 3 minutes

Step-by-step explanation:

1) 600 MB/Min * 4 Min = 2400MB

2) at 800 MB/Min a 2400MB file will require 2400MB/800MB/Min

  2400/800 = 3Min

Answer:

Step-by-step explanation:

I think you mean 2.99×10^8, not 2.99×108.

2.99×10⁸ meters per second = 299,000,000 meters per second

9514 1404 393

Answer:

Step-by-step explanation:

Let r, c, h represent the numbers of meals eaten in a restaurant, car, and at home, respectively. The problem statement tells us of the relations ...

  r + c + h = 193

  -r + c + h = 15

  r + 0c -h = 30

Add the last two equations:

  (-r +c +h) +(r -h) = (15) +(30)

  c = 45

Add the first two equations:

  (r + c + h) +(-r + c + h) = (193) +(15)

  2c +2h = 208

  h = 104 -c = 59 . . . . solve for h, substitute for c

The last equation can be used to find r.

  r = 30 +h = 30 +59 = 89

89 meals are eaten in a restaurant; 45 meals in a car; and 59 at home.

Answer:

Step-by-step explanation:

[tex]\displaystyle \Large \boldsymbol{} \tt a) \ 3-2x=3(x+4)-x-1\\\\3-2x=3x+12-x-1 \\\\3-12+1=3x+2x-x \\\\4x=-8 \\\\\boxed{ \tt x=-2} \\\\\\b) \ 5x\underline{(x-1)}-4\underline{(x-1)}=0 \\\\\\(5x-4)(x-1)=0 \Longrightarrow \boxed{ \tt x_1=0.8 \ \ ; \ \ x_2=1}[/tex]

Answer:

D

Step-by-step explanation:

380

The students could use what they know of triangle rectangles, in the image below you can see the diagram that the students could use to estimate the height of the tower.

First, the students could use the measuring tape to find the distance between the base of the tower and them, this distance is represented with the variable S in the image below.

Now, using the clinometer, they could find the elevation angle between their viewpoint and the tip of the tower. This would be the angle θ in the image (notice that they should do this from the ground).

So at this point, we know one angle and the adjacent cathetus to that angle.

And we want to find the height of the tower, which is the opposite cathetus to the known angle.

Then we can remember the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing these by the things we know:

tan(θ) = H/S

tan(θ)*S = H

Then, by measuring θ and S, we can find the height.

If you want to read more about triangle rectangles, you can see:

https://brainly.com/question/16893462

Answer:

19

Step-by-step explanation:

x + y(3 − x)

Let x = -5 and y = 3

-5 +3(3 - -5)

Subtracting a negative is like adding

-5 +3(3+5)

Parentheses first

-5 +3(8)

Multiply

-5+24

Subtract

19

Answer:

domain : {3,4,6}

range: {1,5,9}

Answer:

Step-by-step explanation:

None

They are both imaginary or complex. You can check that out by calculating the discriminate. If you get a minus answer, then there are no real roots. Let's try it.

a = - 2

b = - 4

c = - 6

D = sqrt(b^2 - 4*a * c)

D = sqrt( (-4)^2 - 4*(-2)(-6)  )

D = sqrt( 16 - 48)

D = sqrt(-32) which is negative and there are no real roots.

Answer:

[tex](832.156, \ 847.844)[/tex]

Step-by-step explanation:

Given data :

Sample standard deviation, s = 15

Sample mean, [tex]\overline x = 840[/tex]

n = 23

a). 98% confidence interval

[tex]$\overline x \pm t_{(n-1, \alpha /2)}. \frac{s}{\sqrt{n}}$[/tex]

[tex]$E= t_{( n-1, \alpha/2 )} \frac{s}{\sqrt n}}[/tex]

[tex]$t_{(n-1 , \alpha/2)} \frac{s}{\sqrt n}$[/tex]

[tex]$t_{(n-1, a\pha/2)}=t_{(22,0.01)} = 2.508$[/tex]

∴ [tex]$E = 2.508 \times \frac{15}{\sqrt{23}}$[/tex]

  [tex]$E = 7.844$[/tex]

So, 98% CI is

[tex]$(\overline x - E, \overline x + E)$[/tex]

[tex](840-7.844 , \ 840+7.844)[/tex]

[tex](832.156, \ 847.844)[/tex]

Answer:

C. [tex]-x-6>-3.5[/tex]

Step-by-step explanation:

One is asked to find which inequality has ([tex]x=-3[/tex]) in its solution set. Remember that an inequality is another way to represent a set of solutions. In essence, it states that all numbers less than; less than or equal to; greater than; or greater than or equal to, are a part of the solution. One simplifies an inequality in a similar manner to how one simplifies an equation, by using inverse operations and simplification. Just note that when multiplying or dividing the inequality by a negative number, one has to flip the inequality sign to ensure the expression remains true.

Simplify each of the inequalities, then evaluate to see which one has ([tex]x=-3[/tex]) as a part of its solution set.

A. [tex]-x -6<-3.5[/tex]

[tex]-x<2.5[/tex]

[tex]x>-2.5[/tex]

B. [tex]-x-6>3.5[/tex]

[tex]-x>9.5[/tex]

[tex]x<-9.5[/tex]

C. [tex]-x-6>-3.5[/tex]

[tex]-x>2.5[/tex]

[tex]x<-2.5[/tex]

D. [tex]x-6>-3.5[/tex]

[tex]x>2.5[/tex]

As can be seen, option (C [tex]-x-6>-3.5[/tex]) is the only one that fits this requirement. Since option (C) simplifies down to ([tex]x<-2.5[/tex]) or in words, (x) is less than (-2.5). This option is the only one that fits the solution since (-3) is less than (-2.5).

[tex]\bf \large \rightarrow \: \:2x \: + \: 8 \: = \: 0[/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: \frac{8}{2} \\ [/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: \cancel\frac{ 8}{ 2} \: \: ^{4} \\ [/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: 4[/tex]

Option ( A ) is the correct answer.

Answer:

360 in.

Step-by-step explanation:

In order to get this answer, you have to multiply 5 and 8 by 3 because the drawing is 1/3 of the actual flag.

5 x 3 = 15

8 x 3 = 24

So, 24 x 15 = 360 in.

Hope this helps! :)

Answer:

x=1°.

see the IMAGE FOR SOLUTION

Answer:

x=150

Step-by-step explanation:

x/30-x/40=5/4

or, (4x-3x)/120=5/4

or, x/120=5/4

or, x=600/4

or, x=150

Step-by-step explanation:

we see, for x=-1 we get 3³

x=0 we get 3²

x=1 we get 3¹

so the function is definitely a 3 to the power of x version.

but we need to adapt the exponent a bit and correct x, so that at least for these 3 values of x the result is "running backwards".

the easiest way : 2-x as exponent.

it fits.

for x=-1 we get 2 - -1 = 3 as exponent.

for x=0 we get 2-0 = 2 as exponent.

for x=1 we get 2-1 = 1 as exponent.

so, the exponential function passing through these 3 points is

[tex]f(x) = {3}^{2 - x} [/tex]

Answer:

5•362165924

Step-by-step explanation:

first make root of 32-6=5•099019514

then make root of 2+root2=1•84--

then divide upper by lower part answer comes

or

root32-6=root26

root 2+root 2=2root2

root26/root2root2

ans=3•0318---

Answer:

[tex] \frac{ \sqrt{32} - 6 }{ \sqrt{2} + \sqrt{2} } \\ \frac{ \sqrt{16 \times 2} - 6}{2 \sqrt{2} } \\ \frac{4 \sqrt{2} - 6}{2 \sqrt{2} } \\ \frac{2(2 \sqrt{2} - 3) }{2 \sqrt{2} } \\ \frac{2 \sqrt{2} - 3}{ \sqrt{2} } \\ thnk \: you[/tex]

Answer:

Step-by-step explanation:

P(A and B)=P(A)*P(B)