Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9

Answer:

(a) The probability that the five children selected will have an MDI of at least 100 is 0.50.

(b) The IQR of the MDI scores is 21.60.

Step-by-step explanation:

Let the random variable X represent the MDI.

The random variable X follows a Normal distribution with mean, μ = 100 and standard deviation, σ = 16.

(b)

Compute the probability that the five children selected will have an MDI of at least 100 as follows:

\(P(\bar X\geq 100)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}\geq \frac{100-100}{16/\sqrt{5}})\\\\=P(Z\geq 0)\\\\=0.50\)

Thus, the probability that the five children selected will have an MDI of at least 100 is 0.50.

(b)

The Inter-quartile range of a Normally dstributed data is:

IQR = 1.34896 × σ

       = 1.34896 × 16

       = 21.58336

       ≈ 21.60

Thus, the IQR of the MDI scores is 21.60.

Answer:

Step-by-step explanation:

(x-2)(x-2)(x-4)

Answer:

-5/9

Step-by-step explanation:

The exact point at which the lines cuts the axis are unclear so I used the closest round number to substitute into the gradient formula. From the answer I noticed two things

Firstly it was a negative gradient...therefore the second and the fourth option wouldn't work

Secondly (if I were to ignore the operation) the number is less than 1 which would mean that it couldnt be an improper fraction where the numerator is greater than the denominator.

If you take what you notice about both the operation and the size of the number you would find that -5/9 fits the criteria the best and is therefore the answer to your question.

\( \frac{y2 - y1}{x2 - x1} \\ = \frac{0 - ( - 1)}{ - 2 - 0} \\ = - \frac{1}{2} \)

Answer:

23

Step-by-step explanation:

5+10=15

15-6=9

9+10=19

19-6=13

So, we should do:

13+10=23

Answer:

d should be correct, I hope this helps!

Step-by-step explanation:

:D

Answer:

c

Step-by-step explanation:

Answer:

5 sq m = 50,000 sq cm

5 sq m = 5 sq m

Step-by-step explanation:

To convert a square meter measurement to a square centimeter measurement, multiply the area by the conversion ratio.

Since one square meter is equal to 10,000 square centimeters, you can use this simple formula to convert:

square centimeters = square meters × 10,000

Answer:

50000 square centimeters.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer: 22%

Step-by-step explanation: 454- 353= 101

101/454= 22%

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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-10 + 5.47722~
=4.523~
round to nearest tenth = 4.5

Answer:

-4.5

Step-by-step explanation:

\(\sqrt{30}\) is approximately 5.47722557505.  You can find this number with a calculator.

-10 + 5.47722557505 = -4.52277442495

To add a negative and a positive number, you subtract the absolute values and take the sign of the number that has the larger absolute value.  Absolute value just means thinking of both numbers as positive numbers.

Helping in the name of Jesus.

The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

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Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

Option A is the correct answer.

We have,

The problem states that a student must work on i-Ready for at least 4 hours per month to receive a grade of 100.

Since Sophia received a math grade of 100, it means that she has met the requirement of working on i-Ready for at least 4 hours in the last month.

And,

The symbol "≥" means "greater than or equal to," indicating that Sophia worked for at least 4 hours.

Therefore,

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

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Answer:

Option c.

Step-by-step explanation:

We are given these following functions:

\(f(x) = 2x + 1\)

\(g(x) = x^2 - 7\)

Division:

The division of those functions is:

\(\frac{f}{g}(x) = \frac{2x + 1}{x^2-7}\)

Domain:

We have a fraction, so we have to take the domain of the function in consideration. The denominator cannot be 0, thus:

\(x^2 - 7 \neq 0\)

\(x^2 \neq 7\)

\(x \neq \pm \sqrt{7}\)

Thus, the correct answer is given by option C.

Answer:

432000/135×100

Step-by-step explanation:

current house value is an increase of 35% oner the original value,

so if current value is 100% plus 35% or 135% of original value,

then original value is $432,000 / 135 x 100

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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We have the following:

The graph of this function will behave as (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

The demand function is given by d = 100 - 10p. This means that the quantity demanded (d) decreases as the price (p) increases.

The slope of the demand function is the rate of change of the quantity demanded with respect to the price. In this case, the slope is -10, which is negative. This indicates that as the price increases, the quantity demanded decreases.

The initial value of the demand function is 100, which represents the quantity demanded when the price is zero. This means that the demand function intersects the y-axis at (0, 100).

Therefore, the correct answer is (b) A graph of this function would slope downward, starting from a price of $100 dollars because the rate of change is less than 0 and the initial value is -10.

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Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

\(\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}\)

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

\(\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}\)

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

Answer:

g(x) = -2^(x-3) - 5

Step-by-step explanation:

f(x) = 2^x

3 units to the right:

2^x ----> 2^(x-3)

Moved 5 units up:

2^(x-3) ----> 2^(x-3) + 5

Reflected across the x-axis:

2^(x-3) + 5  -----> -2^(x-3) - 5

Answer:

Among the four choices, \((x + 5)\) is the only one that is not a linear factor of this polynomial function.

Step-by-step explanation:

Let \(a\) denote some constant. A linear factor of the form \((x - a)\) is a factor of a polynomial \(f(x)\) if and only if \(f(a) = 0\) (that is: replacing all \(x\) in the polynomial \(f(x) \!\) with the constant \(a\!\) would give this polynomial a value of \(0\).)

For example, in the second linear factor \((x - 2)\), the value of the constant is \(a = 2\). Verify that the value of \(f(2)\) is indeed \(0\). (In other words, replacing all \(x\) in the polynomial \(f(x) \!\) with the constant \(2\) should give this polynomial a value of \(0\!\).)

\(\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}\).

Hence, \((x - 2)\) is indeed a linear factor of polynomial \(f(x)\).

Similarly, it could be verified that \((x - 5)\) and \((x + 2)\) are also linear factors of this polynomial function.

Rewrite the first linear factor \((x + 5)\) in the form \((x - a)\) for some constant \(a\): \((x + 5) = (x - (-5))\), where \(a = -5\).

Calculate the value of \(f(5)\).

\(\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}\).

\(f(5) \ne 0\) implies that \((x - (-5))\) (which is equivalent to \((x + 5)\)) isn't a linear factor of this polynomial function.

Okay, let's break this down step-by-step:

1) We need to choose a slope within 6 to 8 feet of vertical change for every 100 feet of horizontal change.

Let's choose a slope of 7 feet of vertical change for every 100 feet of horizontal change.

2) So for every 100 feet horizontally, the zip line will drop 7 feet vertically.

3) We know the ending point height, but we need to calculate the starting point height.

4) If the ending point height is 100 feet above the ground, then for every 100 feet of horizontal distance, the line drops 7 feet.

So to drop 100 feet vertically, the line would have to travel 100 / 7 = 14.29 ~ 15 100-foot segments.

5) So if the ending point is 100 feet above the ground,

the starting point will be 100 + (15 * 7) = 100 + 105 = 205 feet above the ground.

6) Therefore, the difference between the starting and ending point heights is 205 - 100 = 105 feet.

So the difference between the starting and ending point heights of the zip line is 105 feet.

Please let me know if any of the steps are unclear or if you have any other questions! I'm happy to explain further.

Answer:

The zip line needs to be 35 feet higher than the ending point.

Step-by-step explanation:

Assuming that we want to build a zip line with a slope of between 6 to 8 feet of vertical change for every 100 feet of horizontal change, we can choose a slope of 7 feet of vertical change for every 100 feet of horizontal change. This slope is within the given constraint of 6 to 8 feet of vertical change for every 100 feet of horizontal change.

To determine how much higher the starting point of the zip line needs to be than the ending point, we need to know the horizontal distance between the two points. Let's assume that the horizontal distance between the two points is 500 feet.

Using the slope of 7 feet of vertical change for every 100 feet of horizontal change, we can calculate the vertical change as follows:

Vertical change = slope * horizontal change

Vertical change = 7/100 * 500

Vertical change = 35 feet

Therefore, the starting point of the zip line needs to be 35 feet higher than the ending point.

Answer:

531

Step-by-step explanation:

Answer:

531

Step-by-step explanation:

531 x 531 = 281961

Answer:

The solutions will contain an infinite amount of negative numbers.

Step-by-step explanation:

Given x < 0

What does this mean?

First, carefully examine the sign in the inequality. It says less (which is different from less and equal)

Then explain it's meaning.

x < 0 just means that the solutions will contain an infinite amount of negative numbers but NOT zero. This defines the correct answer.

Answer:The solutions will contain an infinite amount of negative numbers

Step-by-step explanation:

Step-by-step explanation:

200,000 X 50,000 = 100000000

If the total profit per month is Rs 200,000 and the revenue per month can be obtained twice the cost per month minus 50,000 then  the revenue per month is 2083 and the cost per month is 25000

Two or more expressions with an Equal sign is called as Equation.

Given,

If the total profit per month is Rs 200,000

Revenue per month can be obtained twice the cost per month minus 50,000

2x-50000

2x=50000

x=25000

So cost per month is 25000

The revenue per month is 25000/12

2083

Hence, the revenue per month is 2083 and the cost per month is 25000

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