At 7:30 am, two lorries start to travel from Town P and Town Q towards each other at the speed of 63km/h and 67 km/h respectively. If the distance between the two towns is 520 km, at what time will the two lorries meet?

Answer:

56,994

Step-by-step explanation: multiply the population by 0.02, round it to the nearest whole number, and then multiply that number by 3 and add it onto 53,768

The population of Oak Forest in three years will be approximately 57,091.

To find the population of Oak Forest in three years, we can use the formula for exponential growth. The formula is: P = P0 * (1 + r)t, where P is the final population, P0 is the initial population, r is the growth rate, and t is the number of years. In this case, P0 is 53,768, r is 0.02 (2% as a decimal), and t is 3. Plugging these values into the formula, we get:

P = 53,768 * (1 + 0.02)3

Simplifying the expression inside the parentheses:

P = 53,768 * (1.02)3

Calculating (1.02)3:

P = 53,768 * 1.0604

Calculating the final population:

P ≈ 57,091

Therefore, the population of Oak Forest in three years will be approximately 57,091.

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Answer:

Step-by-step explanation:

Say that your equation is 2x+4=8, x=2

you would plug in the 2 where your x is so, 2(2) +4=8

then you'd solve regularly.

Hope my answer has helped you!

[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ 4p(y- k)=(x- h)^2 \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y+1=-14(x-2)^2\implies -\cfrac{1}{14}[y-(\stackrel{k}{-1})]=[x-\stackrel{h}{2}]^2~\hfill \stackrel{center}{(-2~,~-1)}[/tex]

Answer: THIRD OPTION

Step-by-step explanation:

We need to remember that a right angle is an angle that measures 90 degrees.

By definition, when two or more lines intersect (or cross one another ) at a 90-degree angle, then these lines are called "Perpendicular".

Therefore, in this case, we know that these two lines intersects at a right angle (angle of 90 degrees), then, we can conclude that these lines are Perpendicular.

This matches with the third option.

Answer:

Perpendicular lines

Step-by-step explanation:

Two or more lines are called intersecting lines.That point would be on each of these lines.

ANSWER

[tex]x = \sqrt{5} [/tex] units

EXPLANATION

Let the other leg be x units.

According to the Pythagoras Theorem, the sum of the squares of the two shorter legs should add up to the square of the hypotenuse.

This implies that,

[tex] {x}^{2} + {2}^{2} = {3}^{2} [/tex]

[tex]{x}^{2} + 4=9[/tex]

Group the constant terms,

[tex]{x}^{2}=9 - 4[/tex]

[tex]{x}^{2}=5[/tex]

Take square root.

[tex]x = \sqrt{5} [/tex]

Answer:

Answer: yes.

Step-by-step explanation:

x: (x1 + x2)/2 = (-3 + 1)/2 = -2/2 = - 1 So far so good.

y: (y1 + y2)/2 = (1 - 4 )/2 = (-3/2) = -1.5

The midpoint is (-1 , - 1.5)

True

Exact Form:

d

=

−

7

−

√

47

2

,

−

7

+

√

47

2

d

=

-

7

-

47

2

,

-

7

+

47

2

Decimal Form:

d

=

−

0.07217269

…

,

−

6.92782730

…

Answer: 20

Step-by-step explanation:

d=-2

Plug in to get 4(-2+7)

Do what's in () -2+7=5

Then multiply 4(5)=20

Answer: x=10

Step-by-step explanation: hope it helped:)

Final answer:

The solution to the equation involves applying the quadratic formula to a rearranged version of the equation, solving for the value(s) of x. This can only be done accurately if the initial equation is correctly presented without typos.

Explanation:

The original equation presented by the student has a typo. However, using information provided, we can approach similar equations to demonstrate the solving process. For instance, the equation (2x)² = 4.0 (1 - x)² involves taking the square root of both sides to find the value of x. This involves rearranging and solving the quadratic equation that is created when you expand and combine like terms.

When solving a quadratic equation, such as ax² + bx + c = 0, we may use the quadratic formula: x = (-b ± √(b²-4ac)) / (2a), which will provide the two potential values of x. This process is crucial when the value of x is not a small enough percentage of a coefficient in the equation to use approximation methods.

If we were solving an equation like x² + 0.00088x - 0.000484 = 0, we would apply the quadratic formula to find the exact values of x.

Answer:

3rd last row, 4th from the left (132) diagonally left upwards. 132, 11, 12

Step-by-step explanation:

132 ÷ 11 =12

Answer:

0.00329

This is rounded to three significant figures.

The zeros before 32876 will not count as significant since they are before the non-zero numbers.

Answer:

0.00329

Step-by-step explanation:

The leading zero's are not significant, only there for place value.

The significant digits are 32876 ← 5 significant figures

which rounds to 329 ← 3 significant figures

0.0032876 ≈ 0.00329

Answer:

D. 70​

Step-by-step explanation:

If VX is the bisector of V, then UX=WX.

This implies that:

[tex]3z-4=z+6[/tex]

Group similar terms:

[tex]3z-z=4+6[/tex]

[tex]2z=10[/tex]

z=5

WU=2(z+6)

WU=2(5+6)

WU=2(11)=22 units

VW=VU=5z-1

Put z=5 to get;

VW=VU=5(5)-1

VW=VU=25-1

VW=VU=24

The perimeter of VWU=24+24+22=70 units

Answer:

Perimeter of triangle VUW = 70.

Step-by-step explanation:

Since VX is angle bisector and VX is perpendicular to UW then triangle UVX is congruent to triangle WVX using ASA property.

then UV=WV...(i) {corresponding sides of congruent triangle are equal.}

and UX=WX ...(ii)  {corresponding sides of congruent triangle are equal.}

then 3z-4=z+6

3z-z=6+4

2z=10

z=5

then UW=(3z-4)+(z+6)=3(5)-4+(5)+6=22

WV=5z-1=5(5)-1=24

UV=WV=24

Then perimeter of triangle VUW is

UV+WV+UW=24+24+22=70

Hence final answer is:

Perimeter of triangle VUW = 70.

It's actually very simple. Semicircle is a half of a circle. So the area and perimeter is also divided by 2. Also the radius is a half of diameter so 130.

[tex]Area=\frac{\pi130^2}{2}\approx\frac{53092.92}{2}=\boxed{26546.46ft^2}[/tex]

Hope this helps.

r3t40

Reason 1: Given.

Reason 2: Vertical angles

Reason 3: Angle, Side, Angle(ASA)

Answer:

[tex]P=338\ in[/tex]

Step-by-step explanation:

we know that

The perimeter of the red figure is equal to

[tex]P=2[22+27+22+98][/tex] ----> because the sides of the figure are tangent to the circle

[tex]P=2[169][/tex]

[tex]P=338\ in[/tex]

Answer:

Step-by-step explanation

Perimeter is sum of the measurement of all sides of a polygon . The polygon we have in this question is formed by using the tangents from a given circle .

The concept we are going to use here is that if we draw two tangents from the same point outside on a given circle, the length of both tangents are always equal .

There are 8 sides of this polygon , That means there are four pairs because length of them are equal .

So perimeter is equal to two times the sum of four sides given to us .

Perimeter = 2( 22+27+22+98)

Perimeter = 2(169)

Perimeter = 338 in

8 Doubled Is 16

16 Increased By 1 Is 17

Answer:

Step-by-step explanation:

ax^2+bx+c

-b +- sqaure root of b^2 -4ac/2a

-2 +- square root (2)^2-4(2)(-1)/2(2)

-2 +- square root 4+8 /4

-2 +- 2 square root 3 /4

reduce

-1 +- square root 3/2

Answer:

[tex]\large\boxed{x=\dfrac{-1-\sqrt3}{2}\ or\ x=\dfrac{-1+\sqrt3}{2}}[/tex]

Step-by-step explanation:

The quadratic formula of a quadratic equation:

[tex]ax^2+bx+c=0[/tex]

Discriminant of a Quadratic is [tex]\Delta=b^2-4ac[/tex]

If Δ < 0, then an equation has no real solution (has two complex solutions)

If Δ = 0, then an equation has one real solution [tex]x=\dfrac{-b}{2a}[/tex]

If Δ >0, then an equation has two real solutions [tex]x=\dfrac{-b\pm\sqrt{\Delta}}{2a}[/tex]

==========================================

We have the equation:

[tex]2x^2+2x-1=0\\\\a=2,\ b=2,\ c=-1[/tex]

Substitute:

[tex]\Delta=2^2-4(2)(-1)=4+8=12>0\\\\\sqrt\Delta=\sqrt{12}=\sqrt{4\cdot3}=\sqrt4\cdot\sqrt3=2\sqrt3[/tex]

[tex]x=\dfrac{-2\pm2\sqrt3}{(2)(2)}=\dfrac{-2\pm2\sqrt3}{4}[/tex]    simplify by 2

[tex]x=\dfrac{-1\pm\sqrt3}{2}[/tex]

Answer:

- 273

Step-by-step explanation:

The n th term of an arithmetic sequence is

• [tex]a_{n}[/tex] = a₁ + (n - 1)d ← substitute in values

[tex]a_{100}[/tex] = 222 + (99 × - 5 ) = 222 - 495 = - 273

Answer:

f(6) = 2

Step-by-step explanation:

Since y is a function of x, that is y = f(x), f(6) implies that we shall be evaluating the value of y when the value of x is 6.

To do this we shall draw a vertical line, x = 6 and check where this line intersects with the graph of the function f(x)

The vertical line x = 6 intersects with the graph of the function f(x) on the horizontal line y = 2. The function f(x) assumes the value 2 for values of x between 4 and 8. Therefore,  f(6) = 2

Answer: Last option.

Step-by-step explanation:

We know that input values of a function are the values of the variable "x" and output values of a function are the values of the variable "y".

By definition, in functions each input value have one and only one output value.

Then, find [tex]f(6)[/tex] you can see that the input value is [tex]x=6[/tex] and you need to find the corresponding ouput value (or "y")

You can observe in the figure attached that the value of "y" for  [tex]x=6[/tex] is  [tex]y=w[/tex], obtaining the point (6,2)

Therefore:

[tex]f(6)=2[/tex]

This matches with the last option.

Answer:

f(x) = (x − 3)² − 11

Step-by-step explanation:

To convert to vertex form, complete the square.

f(x) = x² − 6x − 2

f(x) = x² − 6x + 9 − 9 − 2

f(x) = (x − 3)² − 11

We need to complete the square: if we add and subtract 11 from the expression, we have

[tex]f(x)=x^2-6x-2=x^2-6x-2+11-11=x^2-6x+9-11=(x-3)^2+11[/tex]

[tex]

4n-3=-2n+9n \\

6n-3=9n \\

3n=-3 \\

n=\boxed{-1}

[/tex]

2 is not a solution but -1.

ANSWER

No, n=2 is not a solution.

EXPLANATION

The given equation is

[tex]4n - 3 = - 2n + 9n[/tex]

If n=2 is a solution, then it must satisfy this equation.

We substitite n=2 into the equation to get:

[tex]4(2)- 3 = - 2(2)+ 9(2)[/tex]

[tex]8- 3 = - 4+ 18[/tex]

[tex]5 = 14[/tex]

This statement is false

Therefore n=2 us not a solution.

#18 answer is 52

#19 answer is 152,100

and I cant make out the rest can you please write them in the comments of this answer?

The tan of angle C in triangle XYZ is 0.8.

To find the tan of angle C, we first need to determine the values of angle C, side XC, and side ZC. In triangle XYZ, angle Y is a right angle, so angle C must be angle Z. Since side YZ is opposite angle X, side YZ is equal to side XC.

Using the Pythagorean theorem, we can find side XC:

XC = sqrt(XY^2 + YZ^2)

= sqrt(3^2 + 4^2)

= sqrt(9 + 16) = sqrt(25) = 5.

Now, we can calculate the tan of angle C using the formula tan(C) = opposite side (YZ) / adjacent side (XC).

Therefore, tan(C) = 4 / 5 = 0.8.

Answer:

(1,9),(3,7),(5,5) (7,2)

Answer with explanation:

The sum of two distinct variables is 10.

  x + y=10

It is linear equation in two variables.

To plot this graph in two dimensional plane find two distinct points satisfying the equation.

x=0, gives , y=10 or , y=0 gives , x=10.

x=1, gives ,y=10 -1,→y=9

So,two ordered pairs lying in the coordinate system are , (0, 10) and (1, 9) or (10,0) and (1,9), you will get the equation of line.

Otherwise , you can Draw the graph of this function by writing the equation in Slope Intercept form which is as:

  [tex]\frac{x}{10}+\frac{y}{10}=1[/tex]

By writing the slope intercept form of line shows that , the line passes through , (10,0) and (0,10) means cutting x axis and y axis at these two points.

Answer: A) given

B) definition of congruent

C) definition of bisect

Step-by-step explanation:

Answer:  Third option

[tex]y = |x + 1|[/tex]

Step-by-step explanation:

The main function

[tex]f (x) = | x |[/tex]

has its vertex in the point (0, 0)

The function shown in the graph has its vertex in the point (-1, 0)

The transformation made to f (x) that moves its vertex one unit to the left is:

[tex]y = f (x + 1)[/tex]

After this transformation the new function is:

[tex]f (x) = | x + 1 |[/tex]   Note that this function corresponds to the function plotted in the image.

Therefore the answer is the third option

ANSWER

[tex]( - \infty , + \infty )[/tex]

EXPLANATION

The given function is

[tex]f(x) = 2 {x}^{4} + 4 {x}^{3} + 2{x}^{2} [/tex]

This is a polynomial function.

The domain refers to all real values for which the function is defined.

Polynomial functions are defined everywhere.

The domain is all real numbers.

Or

[tex]( - \infty , + \infty )[/tex]

Answer:

y = 4x - 6.

Step-by-step explanation:

Slope-intercept form is y = mx + c where m = the slope and c = the y-intercept.

4x = y +6

Subtract 6  from both sides:

4x - 6 = y

we would write it as y = 4x - 6.

Answer:

Slope intercept form

y = 4x - 6

Step-by-step explanation:

Slope intercept form y = mx + b

In this case 4x = y +6

Re-write

y + 6 = 4x

Subtract 6 from both sides

y = 4x - 6  <-------Slope intercept form

Answer:

[tex]\large\boxed{D.\ 8x^2-3x+7}[/tex]

Step-by-step explanation:

[tex](2x^2-7x+5)-(-6x^2-4x-2)\\\\=2x^2-7x+5-(-6x^2)-(-4x)-(-2)\\\\=2x^2-7x+5+6x^2+4x+2\qquad\text{combine like terms}\\\\=(2x^2+6x^2)+(-7x+4x)+(5+2)\\\\=8x^2-3x+7[/tex]

Answer:

8x^2-3x+7

Step-by-step explanation:

By simplifying the expression.

Answer:

55

Step-by-step explanation:

20×22=440 8 ' 55

Answer:

r = 2.5

Step-by-step explanation:

The equation given says y = r * x

So, the y value would be an unknown times the given x value.

To solve for r, all you have to do is divide.

25 ÷ 10 = 2.5

12.5 ÷ 5 = 2.5

10 ÷ 4 = 2.5

2.5 is the constant of proportionality.