Which graph represents f(x)=1/2x^2 ?

To find the midpoint of PQ in the given triangle PQR, we use the midpoint formula, which states that the coordinates of the midpoint are the average of the x-coordinates and the average of the y-coordinates of the given points.

To prove that the line containing the midpoints of two sides of a triangle is parallel to the third side, we need to show that the slope of the line is equal to the slope of the third side. Let's find the midpoint of PQ first.

The coordinates of P and Q are P(0, 0) and Q(2a, 0). The midpoint formula is given by:

Midpoint of PQ = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Substituting the values, we get Midpoint of PQ = ( (0 + 2a) / 2 , (0 + 0) / 2 ) = (a , 0)

Therefore, the midpoint of PQ is (a , 0).

y = 1/9x + 3 5/9

The slope between the two marked points is ...

... m = (change in y)/(change in x)

... = (4 -3)/(4 -(-5))

... m = 1/9

Then the point-slope equation for the line with slope m through point (h, k) can be written as ...

... y = m(x -h) +k

... y = 1/9(x -(-5)) +3 . . . . . m = 1/9, (h, k) = (-5, 3)

... y = 1/9x + 3 5/9 . . . . . . simplify

Answer:

x=1

Step-by-step explanation (this way is not the shortest one):

if 2x-3>0, then the equation 2x-3=2x-1 has no roots.

if 2x-3<0 (x<1,5), then the equation 3-2x=2x-1 has one root, x=1

Answer:

the greater or less then pointing to the normal three 3 to the right is correct because 3 is a larger number then negative three (-3). It should look like this (-3) < 3

Step-by-step explanation:

Here is a scale to help you with these problems -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, < 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Which ever way the greater or less than <  is open is greater than the other side. The end that is closed points to the numbers that are less than the other side.

Answer:

D) a = 14, b = 6√2

Step-by-step explanation:

The given figure is trapezoid.

When we draw perpendicular to base "a", we get h = 6

From 45, 45, 90 degrees triangle, the ratio of sides 1:1:√2

since h = 6, b = 6√2

a = 8 + 6

a= 14

Therefore, a = 14 and b = 6√2

Thank you.

D. S(-a, -a), T(-a, a), W(a, a), Z(a, -a)

Point S is in the 3rd quadrant, where both coordinates are negative. That eliminates choices A and B.

The distance between points is 2a, so the distance from a corner point to either axis is "a". That is, the magnitude of any coordinate value is "a", not "2a." That eliminates choice C.

Remaining is the correct choice: D.

Answer:

1420 pieces of mail he delivered in 2 months.

Step-by-step explanation:

If he delivered the same amount each month, you would divide 8520 by 12 (number of months in a year). Then once you divide it, the number you get is 710 now multiply 710 by 2 (because they ask how many he delivered in 2 months). And the answer would be 1420

Answer:

Max delivers 1420 in two Months because 8520 divided by 12 is 710 and thats just one month so 710 x 2 = 1420.

Step-by-step explanation:

Answer:

-2 ≥ b

Step-by-step explanation:

10 ≤ -2 ( 9 + 12b ) / 3

10 ≤ -2 ( 3 + 4b )

-10 ≥ 2 ( 3 + 4b )

-10 ≥ 6 + 8b

-16 ≥ 8b

-2 ≥ b

Answer:

∠2 = 168°

∠3 = 6°

Step-by-step explanation:

Opposite angles of a rhombus are congruent, so ∠2≅∠1 = 168°.

∠3 is the base angle of the isosceles triangle with an apex angle of 168°. Hence it will be (180° -168°)/2 = 6°.

Answer:

D. 1

Step-by-step explanation:

The signs of the terms are +---, so there is 1 change of sign. That means there is 1 positive real root. Profit is zero exactly one time.

Answer:

[tex]700(1.022768)^x[/tex]  

Step-by-step explanation:  

We have been give an expression [tex]700(1.005644)^{4x}[/tex] that shows the quarterly interest rate Letrice earns after x years.

We can find an equivalent expression with x isolated by using exponent properties.

Since power rule of exponents states that an exponent raised to another exponent can be simplified by multiplying the exponents

So using power rule of exponents we can write our expression as:

[tex]700((1.005644)^4)^x[/tex]

Now let us simplify our expression.    

[tex]700(1.0227678485832441)^x[/tex]

Upon rounding to 6 decimal places we will get,

[tex]700(1.022768)^x[/tex]

Therefore, the expression [tex]700(1.022768)^x[/tex] shows the x isolated in the exponent in an equivalent form.

Answer:

$778.46 is the bi-weekly net pay

Step-by-step explanation:

Net pay  is the gross pay minus taxes

Net pay = gross pay - gross pay * tax rate

Simplifying this equation by factoring out gross pay

Net pay = gross pay (1- tax rate)

Substituting this in

Net pay = gross pay (1- tax rate)

We know the

hours worked = 23000

tax rate = .12

Net pay = 23000 (1- .12)

Net pay = 23000 (.88)

Net pay = 20240

But this is per year, and we want it bi weekly

There are 52 weeks in a year, divide by 2 (bi weekly)= 26

So divide 20240 by 26, so you get paid every 2 weeks.

$20240/26 = 778.46  (we round to the nearest cent)

Answer:

the answer is x=185

Step-by-step explanation:

x+240=425

 -240  -240

x= 185

Answer:

B) x + 240 = 425

Step-by-step explanation:

Kyle and Tyler travelled 425 miles to the beach. This means that:

Kyle's distance + Tyler's distance = 425 miles

Kyle travelled 240 miles:

240 miles + Tyler's distance = 425 miles

We want to discover how far Tyler travelled:

240 miles + x = 425miles  or  x + 240 miles = 425 miles

This also means that:

425 miles - 240 miles = x

x = 185 miles

or

185 miles + 240 miles = 425 miles

Answer:

For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression

Step-by-step explanation:

Parent function is f(x)= x

We need to find the effect of the graph when f(x) is replaced with -1/2f(x)

When negative sign is multiplied outside f(x) like -f(x),  then there will be a reflection over x-axis

When negative sign is multiplied inside f(x) like f(-x) then there will be a reflection over y-axis

When a number is multiplied outside f(x) then there will be a vertical stretch or compression

Here 1/2 is multiplied outside f(x). [tex]\frac{1}{2}[/tex] is less than 1 so there will be a vertical compression

For negative sign , the graph reflects over x -axis and for 1/2 there will be a vertical compression

Answer:

10.8 : 1

Step-by-step explanation:

In raw terms the ratio of car length to model length is ...

... 9 ft : 10 in

As a pure number this will be ...

... 108 in : 10 in = 10.8 : 1

Answer:

This is quadratic since it has an x^2

The quadratic term is 2x^2, the linear term is -5x and the constant term is 0

Step-by-step explanation:

x + 2x(x-3)

Distribute the 2x

x + 2x^2 -6x

Combine like terms

2x^2 -5x

This is quadratic since it has an x^2

The quadratic term is 2x^2, the linear term is -5x and the constant term is 0

Answer:

quadratic, 2, -5, 0

Step-by-step explanation:

x + 2x(x-3)

= x + 2x^2 - 6x

= 2x^2 - 5x

so the eqn is quadratic

the quadratic term is 2,

the linear term is -5, and

the constatnt term is 0

Answer:

D. 6

Step-by-step explanation:

The system can be solved by subtracting double the second equation from the first:

... (4x +3y) -2(2x +y) = (20) -2(7)

... y = 6 . . . . . . . . . for solution (x, y) = (a, b), this tells you b=6.

Putting this into the second equation gives ...

... 2x +6 = 7

... 2x = 1

... x = 1/2

The solution is (x, y) = (a, b) = (1/2, 6). b = 6.

Answer:

1/7th

Step-by-step explanation:

To find the perpendicular slope find the negative reciprocal

e.i. 1/3 would be -3/1 or -3

The slope of the line perpendicular to y = -7x - 12 is 1/7.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.

The given line has a slope of -7, so the slope of the line perpendicular to it would be the negative reciprocal of -7, which is 1/7.

Therefore, the slope of the line that is perpendicular to the line y = -7x - 12 is 1/7.

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Brenda has 5/6 of a pie to divide evenly among 4 people. The poundage each person will get is computed by dividing 5/6 by 4, resulting in 5/24 of the pie per person.

To find out how much pie each person will get, we need to divide Brenda's portion of the pie by the number of people. Brenda has 5/6 of a pie, and there are 4 people. So, if we divide 5/6 by 4, we'll get the amount of pie per person.

This can be represented by the following math equation: 5/6 ÷ 4 = x, where x is the amount of pie each person gets. You do this by performing the division as if it were a multiplication but flipping the second fraction, so it turns into

5/6 * 1/4 = 5/24. Therefore, each person will get 5/24 of the pie.

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-1

You apparently want to find the value of x such that ...

... x + 5 -(-2) = 6 . . . . . . the problem statement

... x + 5 + 2 = 6 . . . . . . . simplify signs

... x +7 = 6 . . . . . . . . . . . perform the addition

... x = 6 -7 = -1 . . . . . . . subtract 7 from both sides of the equation, evaluate

-1 adds to 5 - (-2) to give the result 6.

Answer:

The correct answer is A which is

[tex]\:<\:1[/tex]

Step-by-step explanation:

The angle of elevation from the submarine to the boat is [tex]\:<\:1[/tex].

This is the angle through which an observer from the submarine will raise the head before seeing the boat.

See diagram in the attachment for illustration.

1.25 < y < 8.32124...

The least y can be is the value that makes the angle in the smaller triangle be zero. (This condition will exist when the difference of side lengths is 4.)

... 4y -5 = 0

... y = 5/4 . . . . . add 5, divide by 4.

_____

The greatest y can be is the value obtained when the triangle is isosceles. For the larger triangle, that makes the side lengths (s) be ...

... 3/s = sin(43°/2)

... s = 3/sin(21.5°)

Then for the smaller triangle, that makes the angle be ...

... 4y -5 = arcsin(2/s) = arcsin(2/3·sin(21.5°))

... y = 1.25 + arcsin(2/3·sin(21.5°))/4

... y ≈ 8.32124

Answer:

1.25 < y <= 8.32124

Step-by-step explanation:

We use the law of cosines for two triangles:

[tex]c^2 = a^2 + b^2 - 2 a b \cos(\gamma) \\ d^2 = a^2 + b^2 - 2 a b \cos(\delta)[/tex]

This answer shows how to use the Reduce and Exists functions of Mathematica to solve either this problem, or the general problem of a pair of triangles with two sides of one triangle equal to two sides of the other triangle.  That answer (with [tex]c,\, d,\, \gamma,\, \text{and}\ \delta[/tex] as independent variables which must be given ranges) has 11 cases, and would be a terrible waste of time to find by hand.

The law of cosines is used twice, with the same values for a and b, but different values for c and γ . Here I use the constants [tex]c = 6\,\ \gamma = 43°\, \ d = 4[/tex]. The following equations and inequalities are supplied to Reduce, with an Extential quantifier specifying that Reduce should discover the range of values for [tex]\cos(\gamma)[/tex].

[tex]\text{problem}=\exists _{\{a,b\}}\left(\begin{array}{ccc}36=a^2+b^2-2 a b \cos (43 {}^{\circ})\ \ \land\\16=a^2+b^2-2 a b \cos (\delta )\,\,\land\\ 0<a\land 0<b\land -1<\cos (\delta )<1\end{array}\right)\\ \\ \text{variables}=\{a,b,\cos (\delta )\}\\ \\ \text{red}=\text{Reduce}[\text{problem},\text{variables},\mathbb{R}]\,\,\,\,\,\text{gives}\,\,\,\,\,\frac{1}{9} (4 \cos (43 {}^{\circ})+5)\leq \cos (\delta )<1\\\\\text{N}[\text{red}]\,\,\,\text{gives}\,\,\,0.880602\leq \cos (\delta )<1.[/tex]

This proves (since we used Reduce, not Solve, which is less reliable) that

[tex]\text{mincos}=\text{First}[\text{red}]\ \ \text{gives}\ \ \frac{1}{9} (4 \cos (43 {}^{\circ})+5)\\\text{maxcos}=\text{Last}[\text{red}]\ \ \text{gives}\ \ 1\\\\\text{Solve}[4 y-5=\delta,y ]\ \ \ \text{gives}\ \ \ \left\{\left\{y\to \frac{\delta }{4}+\frac{5}{4}\right\}\right\}\\ \\\\\ \frac{5}{4}<y\leq \frac{1}{4} \left(\frac{\cos ^{-1}}{{{}^{\circ}}}\left(\frac{1}{9} (4 \cos    (43 {}^{\circ})+5)\right)}+5\right)[/tex]

The point of intersection of the perpendicular bisectors of a triangle is the circumcenter, the center of the circle that contains the three triangle vertices.

If that center is on one side, that side must be a diameter of the circle. The diameter cuts the circle into two arcs, each of which measures 180°.

The third vertex of the triangle and its two legs form an inscribed angle that subtends an arc of 180°. The measure of that angle is half the measure of the arc, so the angle measures 90° and is a right angle.

A triangle with a right angle is a right triangle. QED

Answer:

B. (x - 4)(x2 + 4x + 16)

Step-by-step explanation:

a3 – b3 = (a – b)(a2 + ab + b2)

substitute a=x n b=4 (cuz 64=4x4x4)

x3 - 64 = (x-4)(x2+4x+4x4)

= (x - 4)(x2 + 4x + 16)

The expression rewritten using difference of cubes as  (x - 4)(x^2 + 4x + 16). Option b is correct.

Expansion of  x^3 - 64 to be determine.

Difference of cube = [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]

Here,
[tex]=x^3 - 64 \\=x^3-4^3[/tex]

a =x ; b = 4, put a and b in below equation,
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
[tex]x^3-4^3=(x-4)(x^2+4x+16)[/tex]

Thus, the expression rewritten using difference of cubes as  (x - 4)(x^2 + 4x + 16).

Learn more about difference in cubes here:
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x/9 = -6

Solve for X by multiplying both sides by 9:

x = -6 * 9

x = -54

Assuming the return is compounded annually, the multiplier each year for rate "r" is (1+r). Then the multiplier for "t" years is (1+r)^t. We want this to be 2.

... 2 = (1+r)^t

... log(2) - t·log(1+r)

... log(2)/log(1+r) = t

The attachment shows the rounded calculator result for r={4%, 10%, 13%}.

You can calculate the years it would take to double your investment using the 'Rule of 72', by dividing 72 by your rate of return. Thus, with an ROI of 4%, 10%, and 13%, it would take roughly 18.0, 7.2, and 5.5 years respectively to double your investment.

The time it takes to double your money can be calculated using the 'Rule of 72'. This rule states that if you divide 72 by the rate of return, you get the number of years it will take to double your money. So, for your situation:

1) With an ROI of 4%, it will take 18.0 years (72 divided by 4).

2) With an ROI of 10%, it will take 7.2 years (72 divided by 10).

3) With an ROI of 13%, it will take 5.5 years (72 divided by 13). Remember, this is an approximation and actual results may vary due to compounding frequency and timing of deposits and withdrawals. This rule is a simple way to estimate the effects of compound interest.

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Answer:

11/12 times 9/22  - rational

x + (-2x)  unknown

Step-by-step explanation:

11/12 is a rational number  (the ratio of integers)

9/22 is a rational number (the ratio of integers)

11/12 * 9/22 is a rational number

The product of 2 rational numbers is rational

x+-2x = x  but we do not know if x is rational or irrational , so we cannot say if it is rational or not.   If x is rational, the sum is rational.  If r is irrational, the sum is irrational.

Answer:

1 and 3

Step-by-step explanation:

___

Applicable rules are ...

[tex]\sqrt[n]{x^{m}}=x^{\frac{m}{n}}\\\\(x^{b})^{c}=x^{bc}\\\\(ab)^{c}=a^c\cdot b^c[/tex]

Answer:

48

Step-by-step explanation:

To get the area of a rectangle or square, its only one step, really.

The formula for a rectangle is A=x*y, where x and y are the two side lengths of the rectangle.

Answer:

48

Step-by-step explanation:

8*6=48