(Pls help)sally states that the equation g(x)= x^3 + 10^2 - 3x represents a quadratic function. Explain why she is incorrect.​

Answer:

8(3+8)

Step-by-step explanation:

The distributive property of multiplication states that

A(B+C) = A* B + A* C

Here, we can say that

8(3+8) = 8*3 + 8* 8 = 24 + 64. This seems correc,t but we can check the other options to make sure

6(4 + 8) = 6 * 4 + 6*8 = 24 + 48. This is incorrect

24 + (8)(8) . The 24 and 8 are not in the same parenthesis, so we cannot multiply them. Using PEMDAS, we multiply first, so 24+(8)(8) = 24 + 8*8 = 24 + 64. If there are multiple solutions, this can work. If not, this does not use the distributive property as we are not adding anything in the parenthesis.

Similarly, for (2)(12) + (8)(8), we are not adding anything in the parenthesis, but we can use PEMDAS to get 2*12 + 8*8 = 24 + 64, so this would also work but does not use the distributive property.

Answer:

\(x=20\)

Step-by-step explanation:

Solve the following equation for x:

\(1500=1/3(15)^{2} x\)

Answer:

The womans age is 25

mothers age is 50

Step-by-step explanation:

add those up and you get 75

Answer:

The woman is 25, and her mother is 50.

Step-by-step explanation:

The woman is half the mother's age.

That means the mother is twice the woman's age.

Let the woman's age be x

The mother's age is 2x.

The sum of the ages is 75.

x + 2x = 75

3x = 75

x = 25

2x = 2(25) = 50

Answer: The woman is 25, and her mother is 50.

Answer:

D. 7 miles per hour

Step-by-step explanation:

D. 7 miles per hour

The minimum area is 126.025 at \($x=\frac{60 \pi}{(4+\pi)}\) is 26.39, maximize the combined area of the circle and the​ square is 60.

Let the length of the wire (l)=60

Suppose the wire is cut into two parts as follows:

The length of the wire used for circle is x and the length of the wire used for square is (l-x)=(60-x).

So, length of the circle (x)= Perimeter of the of the circle

\($$(x)=2 \pi r$$\)

\($r=\frac{x}{2 \pi} \quad\) , r is the radius of the circular part.

Also, length of square (60-x)= Perimeter of the of the square

(60-x)=4 a

\($a=\frac{60-x}{4} \quad$\), a is the side of the square.

Hence, the total combined area of the circular region and the square region say A(x) is;

A(x)=area of circle + area of square

\(\\& A(x)=\pi r^2+a^2\end{aligned}$$\)

Put the values of 'r' and 'a' and proceed as follows;

\($$\begin{aligned}& A(x)=\pi\left(\frac{x}{2 \pi}\right)^2+\left(\frac{60-x}{4}\right)^2 \\& =\pi \frac{x^2}{4 \pi^2}+\left(15-\frac{x}{4}\right)^2\end{aligned}$$\)

\($=\frac{x^2}{4 \pi}+\left(15-\frac{x}{4}\right)^2$$\)

So, \($A(x)=\frac{x^2}{4 \pi}+\left(15-\frac{x}{4}\right)^2$\).

For optimization, find the Critical points of \($A^{\prime}(x)$\);

Differentiate \($A(x)=\frac{x^2}{4 \pi}+\left(15-\frac{x}{4}\right)^2$\) with respect to x;

\($$A^{\prime}(x)=\frac{2 x}{4 \pi}+2\left(15-\frac{x}{4}\right)\left(-\frac{1}{4}\right)$$\)

Put \($A^{\prime}(x)=0$\) for critical points;

\($$\begin{aligned}& A^{\prime}(x)=\frac{2 x}{4 \pi}+2\left(15-\frac{x}{4}\right)\left(-\frac{1}{4}\right)=0 \\& \frac{2 x}{4 \pi}=\left(15-\frac{x}{4}\right)\left(\frac{1}{2}\right) \\& \frac{4 x}{4 \pi}=\left(15-\frac{x}{4}\right) \\& \frac{4 x}{4 \pi}+\frac{x}{4}=15 \\& \frac{x(4+\pi)}{4 \pi}=15 \\& x=\frac{60 \pi}{(4+\pi)} \\& x=26.39\end{aligned}$$\)

x=26.39 is the required critical point.

For maximum or minimum, find \($A^{\prime \prime}(x)$\) as follows:

\($$\begin{aligned}& A^{\prime \prime}(x)=\frac{d}{d x}\left(\frac{2 x}{4 \pi}+\left(15-\frac{x}{4}\right)\left(-\frac{1}{2}\right)\right) \\& A^{\prime \prime}(x)=\frac{2}{4 \pi}+\frac{1}{8}\end{aligned}$$\)

As \($A^{\prime \prime}(x)=\frac{2}{4 \pi}+\frac{1}{8} > 0$\) for every value of x. So, \($A^{\prime \prime}(x) > 0$\) for every critical point.

Hence, by Second Derivative test; A(x) is minimum at \(\\ $$x=\frac{60 \pi}{(4+\pi)}$.\)

Therefore, minimum area is given as follows:

\($$\begin{aligned}& A\left(\frac{60 \pi}{(4+\pi)}\right)=\left(\frac{60 \pi}{(4+\pi)}\right)^2 \frac{1}{4 \pi}+\left(15-\frac{60 \pi}{4(4+\pi)}\right)^2 \\\\& \text { As } x=\frac{60 \pi}{(4+\pi)}=26.39\end{aligned}$$\)

So,

\($$\begin{aligned}& A\left(\frac{60 \pi}{(4+\pi)}\right)=\left(\frac{60 \pi}{(4+\pi)}\right)^2 \frac{1}{4 \pi}+\left(15-\frac{60 \pi}{4(4+\pi)}\right)^2 \\& A(26.39)=(26.39)^2 \frac{1}{4 \pi}+\left(15-\frac{26.39}{4}\right)^2 \\& A(26.39)=55.42030+70.6020 \\& A(26.39)=126.025\end{aligned}$$\)

Therefore, the minimum area is 126.025 at \($x=\frac{60 \pi}{(4+\pi)}\) is 26.39.

b. Note that, maximum area cannot be determined by the critical points as there is only one critical point that too corresponds to the minimum area.

For maximum area; consider the following;

Put x=0 and x=60 in A(x);

\($$\begin{aligned}& A(0)=(0)^2 \frac{1}{4 \pi}+\left(15-\frac{0}{4}\right)^2 \\& A(0)=(15)^2 \\& A(0)=225 \\& A(60)=(60)^2 \frac{1}{4 \pi}+\left(15-\frac{60}{4}\right)^2 \\& A(60)=(60)^2 \frac{1}{4 \pi} \\& A(60)=286.47\end{aligned}$$\)

So, at x=60, A(x) is maximum. That is in the case, when total length of the wire is used for circle.

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Answer: 4a

Step-by-step explanation:

Answer:

4a

Step-by-step explanation:

8 of something minus 4 of something gives you 4 of that thing

Answer:

D

Step-by-step explanation:

one third of 15 is 5

15 + 5 = 20

Student B is 20 years old, 5 years older than student A

10 years ago, Student B was 10 and Student A was 5.

The number of years ago was student B twice as old as student A should be 10 when the student A age is given.

Since

Student A is 15 years old. Student B is one-third older

One-third of 15 should be 5

So, total be like

= 15 + 5

= 20

So, the number of years  be like

= 20 - 10

= 10

hence, The number of years ago was student B twice as old as student A should be 10.

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The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Answer:

The height of the sign is 6 feet.

Step-by-step explanation:

Area of triangle is base times height divided by 2 ( b x h ÷ 2 ), so we just rearrange that.

A = \(\frac{bh}{2}\)

36 = 12 x h ÷ 2

36 x 2 = 12 x h

72 = 12 x h

72 ÷ 12 = h

6 =  h

h = 6

Answer:

-24+9

Step-by-step explanation:

Analyze each plan according to the given specifications.

Plan A:

The basic fee must be added to the product of 0.13 and the average messages sent.

Plan B:

It already includes the cost for unlimited messages.

Plan C:

The plan costs the product of 0.28 and the average messages sent.

When comparing these plans, the cheapest one is Plan B, which only costs $53.00.

The ellis weight is heavier and by 7.23 lbs.

We are given that;

Weight= 5pounds

Now,

To convert Ed’s weight from kilograms to pounds, we can multiply by the conversion factor of 2.20462262185. We get:

Ed’s weight in pounds = 50 kg * 2.20462262185 lbs/kg Ed’s weight in pounds = 110.2311310925 lbs

To convert Ellis’s weight from stones and pounds to pounds, we can multiply the number of stones by 14 and add the number of pounds. We get:

Ellis’s weight in pounds = 7 stones * 14 lbs/stone + 5 lbs Ellis’s weight in pounds = 98 + 5 Ellis’s weight in pounds = 103 lbs

To compare the weights, we can subtract them and see which one is larger. We get:

Ed’s weight - Ellis’s weight = 110.2311310925 lbs - 103 lbs Ed’s weight - Ellis’s weight = 7.2311310925 lbs

Therefore, by unitary method the answer will be 7.23 lbs.

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Answer:

There was a 16% increase since 2010 to 2012.

Step-by-step explanation:

8% + 8% = 0.16 x 100 = 16%.

Answer:

  at least 19

Step-by-step explanation:

Let t represent the number of trees Jacob needs to trim. He wants ...

  50(45) +120t ≥ 4500

  120t ≥ 2250 . . . . . . . . . subtract 2250

  t ≥ 18.75

Jacob must trim at least 19 trees to earn at least $4500.

Answer:

(-3, ∞).

Step-by-step explanation:

-6(2x + 1) < 5- (x – 4)-6x

-12x - 6 < 5  - x + 4 - 6x

-12x + x + 6x < 5 + 4 + 6

-5x < 15

x > 15/-5      (note that the inequality sign flips when dividing by a negative)

x > -3.

Answer:

Explanation: The rate of change between two points on a curve can be approximated by calculating the change between two points. Let be the coordinates of the first point and be the coordinates of the second point. Then the formula giving approximate rate of change is

Step-by-step explanation:

calculating the change between two points.

Answer:

-7/12

Step-by-step explanation:

2/3×-7/8

= -7/12

Answer:

-7/12

Step-by-step explanation:

2/3×(-7)/8

2×(-7) = -14

3×8 = 24

-14/24= -7/12

The equation of the tangent plane to the given surface at the specified point is z = 10x + 8y + 6.

To find an equation of the tangent plane to the given surface at the specified point (2, -2, 13), we need to first take partial derivatives of the given function.

Taking partial derivatives with respect to x and y, we get:

∂z/∂x = 10(x-1)

∂z/∂y = 8(y+3)

Next, we plug in the given point (2, -2, 13) into the partial derivatives to find the slope of the tangent plane:

∂z/∂x = 10(2-1) = 10

∂z/∂y = 8(-2+3) = 8

So the slope of the tangent plane at the given point is (10, 8).

Now we need to find the intercept of the tangent plane by plugging in the point (2, -2, 13) into the original function:

z = 5(2-1)^2 + 4(-2+3)^2 + 4 = 13

Therefore, the equation of the tangent plane is:

10(x-2) + 8(y+2) = z-13

Or rearranging,

10x + 8y - z = -6

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Step-by-step explanation:

QR is parallel to TU | Given

S is the midpoint of QT | Given

QS = ST | Definition of midpoint

<QSR = <TSU | definition of vertical angles

<QRS = <STU | Definition of Alternate Interior Angles

QSR = TSU | ASA

Pretty sure that's right :D

Also, wherever it says "=", I mean congruency symbol

Answer:

47

Step-by-step explanation:

No matter what number you do if there is one left then it's that number

So dif between 8 and 7 is 1

1*47 = 47

the angle between 0 and 2π that is coterminal with 17π/4 is π/4.

To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.

To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.

Starting with 17π/4, we can subtract 4π to bring it within the range:

17π/4 - 4π = π/4

The angle π/4 is between 0 and 2π and is coterminal with 17π/4.

what is equivalent'?

In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.

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Answer:

At 6% interest rate, amount invested = $7000

At 8% interest rate, amount invested = $21000

Step-by-step explanation:

Let amount invested in one account be x and amount invested in the other be y.

Thus;

x + y = 28000 - - - - (eq1)

Interest rate for them are 6% and 8% annually.

We are told that total interest earned for the year was $2100

Thus;

0.06x + 0.08y = 2100 - - - - (eq 2)

Make x the subject in equation 1.

x = 28000 - y - - - - (eq 3)

Put 28000 - y for x in eq 2

0.06(28000 - y) + 0.08y = 2100

1680 - 0.06y + 0.08y = 2100

0.02y = 2100 - 1680

0.02y = 420

y = 420/0.02

y = 21000

Put 21000 for y in eq 3 to get;

x = 28000 - 21000

x = 7000

Thus amount invested in each account is;

At 6% interest rate, amount invested = $7000

At 8% interest rate, amount invested = $21000

Answer:

range of f is [0,3]

Step-by-step explanation:

The "square root" symbol, \(\sqrt{\text{ \quad }}\), is a function.  As a result, it only has a single output because functions must only have a single output for each input.

Thinking about it graphically, if the square root function did give both a positive and a negative result, the function "f" would not pass the vertical line test and it would not be a function.

When solving an equation like \(x^2=25\), to solve, we must apply the square root property.  The square root property says that to find both solutions, one must look at both the positive and the negative of the square root.  So, to solve:

\(x^2=25\)

Apply square root property...

\(\sqrt{x^2} = \pm \sqrt{25}\)

\(x=\sqrt{25}\)  or  \(x=-\sqrt{25}\)

\(x=5\)  or  \(x=-5\)

In this case, because the square root function itself only outputs non-negative results (so, including zero, as you already identified), the range will only be [0,3].

Answer:

D. The other solution to function g is 9 + √2i

Step-by-step explanation:

The roots of a quadratic equation of the form ax² + bx + c = 0

are

\(x = -\dfrac{b}{2a} + \dfrac{\sqrt{b^2-4ac}}{2a}\\and\\x = -\dfrac{b}{2a} - \dfrac{\sqrt{b^2-4ac}}{2a}\\\)

If one of the roots is 9 - √2i then
\(-\dfrac{b}{2a} = 9\)

and

\(\dfrac{\sqrt{b^2-4ac}}{2a} = 2i\)

So if one root is 9 - √2i then the other root must be 9 -+ 2i

This is answer choice D

Answer:

\(5x + 12 = 2x + 21 \\ 5x - 2x = 21 - 12 \\ 3x = 9 \\ x = \frac{9}{3} \\ x = 3\)

Step-by-step explanation:

please mark me brainliest

Answer:

\(5x + 12 = 2x + 21 \\ 5x - 2x = 21 - 12 \\ 3x = 9 \\ x = \frac{9}{3}\\ \boxed{x = 3}\)

Step-by-step explanation:

let's multiply the first equation by 2 and the second equation by -3, and then we add them together :

26x - 12y = 4

-9x +12y = 30

-------------------------

17x 0 = 34

x = 2

and now we use one of the original equations to solve for y :

3×2 - 4y = -10

6 - 4y = -10

-4y = -16

y = 4

the solution is (2, 4).

Answer:

D is the correct answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given equation:

It has roots r and s.

We know how to find the sum and product of roots.

Sum of roots:

Product of roots:

Use the above two equations to work out the value of r - s:

Correct choice is B

Answer:

1140 square inches

Step-by-step explanation:

The rear window of DeMarcus's car is in the shape of a trapezoid. The bottom is 50 inches across and the top is 45 inches across. The window has a height of 24 inches. What is the area of the window?

Area of a Trapezoid

= 1/2(b1 + b2)h

b1 =

b2 =

h =

Hence, 1/2 (50 + 45) × 24

= 1/2 × 95 × 24

= 1140 Square inches

Answer:

f = 22

Step-by-step explanation:

From the question

\(f \alpha \: \frac{1}{ \sqrt{g} } \)

Meaning, f is inversely proportional to √g

Therefore,

\(f \: = \: \frac{k}{ \sqrt{g} } \)

Where, k is constant

Making k subject of the formula,

k = f·√g

Slotting our values of f = 10, when g = 121,

k = 10·√121

k = 10·11

k = 110

Now that we have our constant,

To find f when g = 25,

\(f \: = \: \frac{k}{ \sqrt{g} } \)

Slotting in,

k = 110, g= 25,

We have,

f = 110/√25

f = 110/5

f = 22, when g=25