Use the table of values to identify the mathematical model that would best fit the data.

Answer:

Step-by-step explanation:

I like to form the product of something like this by multiplying binomial pairs first. The distributive property applies for that (as does FOIL).

... (x^2 -3)(x^2 +2) = x^2·x^2 + x^2·2 + (-3)·x^2 + (-3)·2

... = x^4 -x^2 -6 . . . . . the two x^2 terms combine

Now, it is a simple matter to multiply each term by 2x:

... y = 2x^5 -2x^3 -12x

_____

The highest-degree term has degree 5. There are 3 terms. (All are odd-degree, so this is an odd function, symmetrical about the origin.)

As with any odd-degree function (with positive leading coefficient) the overall shape has a positive slope (/), tending toward -∞ for large negative values of x, and tending toward +∞ for large positive values of x.

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

y = 10.29·0.7^x . . . . . selection c seems the closest

For most any exponential function, the exponential multiplier will be 1 when x=0, so the y-intercept is the overall multiplier for the function.

The values decrease as x increases, so the base of the exponential term must be less than 1.

These considerations narrow your choice to C.

... y = 10.29·0.7^x

_____

If you actually want to determine the equation, you can do it several ways. One is to make use of the exponential regression function of your graphing calculator. (See attached). Another is to take the logarithms of the y-values and find a best-fit line through them.

_____

Comment on the answer choices

You may notice that none of the offered answers appears to be anything but the product of two numbers. There are no x-variables involved, and no exponents indicated. Cutting and pasting answers like this does not work.

Answer:

c

Step-by-step explanation:

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

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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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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y = (9/8)(x +4)(x -2)

When the x-intercepts are "a" and "b", you know factors of the function are (x-a) and (x-b). So, we can write the function as ...

... y = k(x -(-4))(x -2) = k(x +4)(x -2) . . . . . for some scale factor k

We can find k using the given point.

... -9 = k(0 +4)(0 -2) = -8k

Dividing by -8 gives ...

... 9/8 = k

The desired function is ...

... y = (9/8)(x +4)(x -2)

... = (9/8)(x² +2x -8)

Answer: 41

Step-by-step explanation:

533÷41 = 533/41

Se photo for step -by-step of ling division

The answer to the long division of 533 by 41 is 13. This is reached by multiplying 13 by 41 which results in 533, the original dividend. The remainder is 0.

Let's perform a long division of 533 by 41. First, write the number 533, which is the dividend, inside the long division bracket and the number 41, the divisor, outside of it. Now we need to see how many times 41 fits into 533.

It fits 13 times because 13 times 41 equals 533. Therefore, write 13 above on your long division bracket.

When you multiply 13 (your answer) by 41 (your divisor), you get 533, which is your dividend. Subtract 533 from 533 and you get a remainder of 0. The answer of the long division of 533 by 41 is 13.

Done correctly, long division is a reliable method of dividing large numbers. The important thing is to ensure all steps are followed orderly and accurately.

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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°.

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:

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:

-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

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:

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.

7 . . . . . inches per week

The average rate of change of height is ...

... (change in height)/(change in time)

The height changes from 41 inches to 83 inches when the time changes from 3 weeks to 9 weeks. Then the rate of change is ...

... (83 -41) inches/((9 -3) weeks) = (42/6) inches/week = 7 inches/week

It seems likely that the required answer will just be a number: 7.

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:

AC = √7 in

Step-by-step explanation:

ΔABC is isosceles, so ΔADC is a right triangle with AD = 2 in and CD = √3 in. The length of hypotenuse AC is found using the Pythagorean theorem.

... AC² = AD² +CD² = (2 in)² +(√3 in)² = (4 +3) in²

... AC = √7 in . . . . take the square root

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]

x/9 = -6

Solve for X by multiplying both sides by 9:

x = -6 * 9

x = -54

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).

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Answer:

y = ($0.5/ch) x + $10

Step-by-step explanation:

Let

x = number of chores

y = allowance

The relationship between y and x can be expressed in a linear equation in the slope-intercept form.

y = mx + b

where

m is the slope

b is the y-intercept

We have the ordered pairs (8, 14) and (12, 16). We can calculate the slope using the following expression.

m = Δy/Δx = $16-$14/12ch-8ch = $0.5/ch

The equation is

y = ($0.5/ch) x + b

We will replace the first point in the previous equation.

$14 = ($0.5/ch) 8ch + b

b = $10

The final equation is

y = ($0.5/ch) x + $10

This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50. The final equation is y = ($0.5/ch) x + $10.

We are given that Hari's allowance varies depending on the number of chores he does.

We are also given two points, (8, 14) and (12, 16), that represent the relationship between the number of chores and the allowance.

We can use these two points to find the slope of the line.

The slope is equal to rise over run, which in this case is equal to

$16 - $14 / 12 - 8 = 0.5/ch.

We can now plug the slope and one of the points into the slope-intercept form of the equation to find the value of b, the y-intercept.

We will use the point (8, 14).

y = mx + b

14 = ($0.5/ch) 8ch + b

14 = $4 + b

b = $10

The final equation is y = ($0.5/ch) x + $10.

This equation can be used to predict Hari's allowance for any number of chores. For example, if Hari does 10 chores, his allowance will be $12.50.

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Answer:

1767 cm³

Step-by-step explanation:

We can use volume V = 4/3 π r³

We have diameter of 15 cm. To get radius, we need to divide diameter by 2.

r = 7.5 cm

So now plug in r = 7.5 then calculate V:

V = 4/3 π ( 7.5 )³

V =  4/3 π * 421.875 ≈ 1767.145 ≈ 1767

Hope this helps.

Answer:

14.

Unless your assignments tells you not to round to whole numbers or to round to the nearest decimal places, then 13.99. But, in most cases, you'd round to 14.

Answer:

they will tie

Step-by-step explanation:

if you divied 7 in to 70 you get 7 and if you divied 5 into 35 it 7

It takes both of them 7 mins to complet a mile

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.

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).

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.

Answer:

≈10.99525 cm.

Step-by-step explanation:

1. The length of the circle is L=2πr, where π≈3.1415 and r- radius of the circle.

2. if the given arc is 45° and full circle is 360°, then the length of the arc is 45/360=0.125 of full circle, that is L(arc)=0.125L=0.25πr; ⇒ L(arc)≈0.25*3.1415*14=10.99525 (cm).

Answer:

10.99 ≈ 11cm

Step-by-step explanation:

To find the length of the arc, first we need to find the circumference of the circle, which we find with the following formula :

[tex]c=2\pi r[/tex]

where  [tex]r[/tex] is the radius which is indicated in the image: [tex]r=14cm[/tex].

so the circumference  is:

[tex]c=2\pi(14cm)\\c=87.96cm[/tex]

This is the measure of the entire perimeter of the circle, it is the measure of the 360 ° arc.

Because we only want 45 ° of those 360 °, we divide the value of the circumference by 360 and multiply po 45:

[tex]\frac{87.96cm(45)}{360}=\frac{3958.2}{360}=10.99cm[/tex]

which can be rounded to 11cm

The length of the arc is 11cm

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