Heo started to solve the quadratic equation (x + 2)2 – 9 = –5. He added 9 to both sides and the resulting equation was (x + 2)2 = 4. Next, he took the square root of each side. Which was the resulting equation of that step?

Explanation of experimental and theoretical probability of rolling a 3 on a six-sided number cube.

The experimental probability of rolling a 3:

Simulate 35 rolls of a six-sided number cube to get results.

Count the number of times a 3 is rolled and calculate the experimental probability by dividing the number of 3s rolled by 35.

The theoretical probability of rolling a 3:

Theoretical probability = Number of favorable outcomes / Total number of outcomes = 1/6 (since there is 1 favorable outcome out of 6 possible outcomes).

Differences between theoretical and experimental probabilities:

Theoretical probability is based on calculations and assumptions, while experimental probability is based on actual observations. Discrepancies between the two can occur due to sample size, random variations, or errors in the simulation.

Answer:

Step-by-step explanation:

The cross section will have the same shape as the base of the pentagonal prism; the dimensions will be proportionally smaller.

Answer:

100π

Step-by-step explanation:

step 1

Find the circumference

The circumference is equal to

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

we have

[tex]r=10\ in[/tex]

substitute

[tex]C=2\pi (10)[/tex]

[tex]C=20\pi\ in[/tex]

step 2

we know that

An object moves along a circular path and makes 5 revolutions in 1 minute

Remember that

[tex]1\ rev=2\pi r[/tex] ----> circumference of the circle

therefore

[tex]5\ rev=5(20\pi)=100\pi\frac{in}{minute} [/tex]

Answer:

20°

Step-by-step explanation:

40=2x,x=20°

Answer:

210.06 feet

Step-by-step explanation:

This is a classic right triangle trig problem.  The distance from the launch pad is the measure of the base of the right triangle.  The angle of elevation, 35, is the base angle (not the right angle).  How high the fireworks go up is the height of the triangle.  You have the reference angle of 35, the side adjacent to it, 300, and you're looking for the side length across from it, y.  The trig ratio that relates a reference angle to the sides opposite it and adjacent to it is the tangent ratio.  Setting that up:

[tex]tan(35)=\frac{y}{300}[/tex]

Solving for y:

y = 300 tan(35)

On your calculator in degree mode find y to be 210.06 feet.

By using basic trigonometry, specifically the tangent of the viewing angle, we can determine that the height of the fireworks when they explode is approximately 210 feet.

You are asking how to use trigonometry to find the height of the fireworks when they explode. If we combine your conditions that the launch was vertical and the viewing angle was 35°, we can use the tangent of that angle to find the height of the fireworks. The tangent of an angle in a right triangle is the opposite side (height in this case) divided by the adjacent side (distance from the launch, 300 feet in this case). So setting up the equation, we have: tan(35°) = height / 300. Solving for 'height', we get: height = 300 * tan(35°). Using a calculator, we find that tan(35°) is roughly 0.70021. Multiplying that by 300, we find that the height of the fireworks when they explode is approximately 210 feet.

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Final answer:

To find the probability of drawing a four and then a five from a standard deck with replacement, multiply the probabilities of the independent events: (1/13) × (1/13) = 1/169.

Explanation:

The question involves calculating the probability of two independent events when drawing cards from a standard deck. The first event (A) is drawing a card that is a four, and the second event (B) is drawing a card that is a five. The probability of each of these events is calculated separately since the card is replaced after each draw, making the draws independent of each other.

The probability of drawing a four (P(A)) from a standard deck is 1/13, as there are four fours in a 52-card deck. Similarly, the probability of drawing a five (P(B)) is also 1/13. Since the events are independent, the combined probability is the product of the two probabilities: P(A) × P(B) = (1/13) × (1/13) = 1/169.

The answer is 8......

Answer:

The answer is 8

Step-by-step explanation:

Just add the rest of the numbers and then subtract from the answer

She should expect 250 green marbles.

She has a 25 out of 40 chance of selecting a green marble each time since she is putting it back in the bag each time. 25/40 reduces to 5/8. Multiply 5/8 by 400 and you get 2000/8. Reduce the fraction to 250/1 or 250.

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Remember:

[tex](\sqrt[n]{a})^n=a\\\\(a+b)=a^2+2ab+b^2[/tex]

Given the equation [tex]\sqrt{17-x}=x+3[/tex], you need to solve for the variable "x" to find its value.

You need to square both sides of the equation:

[tex](\sqrt{17-x})^2=(x+3)^2[/tex]

[tex]17-x=(x+3)^2[/tex]

Simplifying, you get:

[tex]17-x=x^2+2(x)(3)+3^2\\\\17-x=x^2+6x+9\\\\x^2+6x+9+x-17=0\\\\x^2+7x-8=0[/tex]

Factor the quadratic equation. Find two numbers whose sum be 7 and whose product be -8. These are: -1 and 8:

[tex](x-1)(x+8)=0[/tex]

Then:

[tex]x_1=1\\x_2=-8[/tex]

Let's check if the first solution is correct:

[tex]\sqrt{17-(1)}=(1)+3[/tex]

[tex]4=4[/tex] (It checks)

Let's check if the second solution is correct:

[tex]\sqrt{17-(-8)}=(-8)+3[/tex]

[tex]5\neq-5[/tex] (It does not checks)

Therefore, the solution is:

[tex]x=1[/tex]

the only solution is x = 1.

To solve the equation sqrt(17-x) = x+3, we first eliminate the square root by squaring both sides of the equation. Doing so yields:

17 - x = (x + 3)2

17 - x = x2 + 6x + 9

Next, we rearrange the equation to set it equal to zero, thus forming a quadratic equation:

x2 + 6x + 9 + x - 17 = 0

x2 + 7x - 8 = 0

Now, we factor the quadratic:

(x + 8)(x - 1) = 0

Hence, the solutions are:

x = -8

x = 1

To verify that these solutions satisfy the original equation, we perform a check by substituting them back into the original equation. However, we notice that the solution x = -8 does not work because it would result in taking the square root of a negative number, which is not possible in real numbers. So the only solution is x = 1.

Answer: $11,250

1850 + (4/100)x = 1850 + 0.04x.

1850 + 0.04x > 2300

0.04x > 2300 - 1850

0.04x > 450

x > 450 / 0.04

x > $11,250

Answer

x> 11,250

yyyyyyyyyyyyyyyyyeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

There are 252 ways to divide the 10 players into two teams of 5 without any restriction.

To determine the number of ways you can divide 10 players into two teams of 5 without any restriction,

Using the formula, C(n, k) = [tex]\frac{n!}{k!(n-k)!}[/tex]

By finding the number of ways to choose 5 players out of 10, which is the same as choosing the other 5 players who are not on the first team.

Where n = 10

k = 5

C(10, 5) = [tex]\frac{10!}{5!(10-5)!}[/tex]

C(10, 5) = [tex]\frac{10!}{5!(5)!}[/tex]

C(10, 5) = 10*9*8*7*6*5*4*3*2*1/5*4*3*2*1(5*4*3*2*1)

C(10, 5) = 30240/5*4*3*2*1

C(10, 5) = 252 ways

Therefore, there are 252 ways to divide the 10 players into two teams of 5 without any restriction.

Answer:

[tex]\$5,828.28[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=5\ years\\ P=\$4,900\\ r=0.035\\n=2[/tex]  

substitute in the formula above  

[tex]A=\$4,900(1+\frac{0.035}{2})^{2*5}[/tex]  

[tex]A=\$4,900(1.0175)^{10}=\$5,828.28[/tex]

Answer:

5,828.28

Step-by-step explanation:

Final answer:

To locate the person who moved from (0, 1) with a slope of -4, we need to know the specific horizontal distance they moved. Without this, we can only say they moved downward 4 units for every 1 unit they moved to the right.

Explanation:

The student's question involves determining the position of a person who has moved along a slope on a coordinate plane. Since the individual started at the point (0, 1) and moved to the right with a slope of -4, we can assume they are moving in the negative y-direction (downward), as the negative slope indicates a decrease in y for every increase in x. The specific horizontal distance isn't given, so we cannot provide an exact new coordinate without more information. However, if we had a specific horizontal distance the person moved, we could calculate the new position using the slope (-4), which means for every 1 unit moved horizontally to the right, the person would move 4 units down.

Answer:

every point will be 4 tons lower than it was

Step-by-step explanation:

26 is 4 less than 30, so the new function g(x) is ...

g(x) = f(x) -4

It is shifted down 4 units (tons) from the original function.

I know that the answer is A, however I can not answer the rest

Answer:

3w + 52 ≥ 90

Step-by-step explanation:

If she volunteers 3 hours per week for w weeks, then the number of hours from tutoring is 3w.  Add the 52 hours from her summer volunteering, and her total hours is 3w + 52.  This needs to be at least 90 hours for her to graduate, so:

3w + 52 ≥ 90

Answer:

Choice C.

Step-by-step explanation:

You already have two sides and two angles. Now you need the other two sides that include the angle. Choice C is correct.

Answer: C. [tex]\overline{SU}\cong\overline{JL}[/tex]

Step-by-step explanation:

In the given picture , we have two triangles ΔSTU and Δ JKL , in which we have

[tex]\overline{ST}\cong\overline{JK}[/tex]

[tex]\angle{S}\cong\angle{J}[/tex]

To prove ΔSTU is congruent to Δ JKL, we need [tex]\overline{SU}\cong\overline{JL}[/tex] such that [tex]\angle{S}\text{ and }\angle{J}[/tex] becomes congruent the included angles between pair of  congruent sides.

Hence, C is the right option.

Answer:

19

Step-by-step explanation:

to find the range, you have to subtract the smaller number from the biggest number

In this case it would be 45-26

45-26=19

range=19

Given the conditions: f(x) approaches 300 and g(x) approaches 0 (and is less than zero as x approaches 5), the limit as x approaches 5 of the quotient f(x)/g(x) is negative infinity.

Based on the given conditions: f(x) approaches 300 and g(x) approaches 0 as x approaches 5. Moreover, g(x) is less than zero, and therefore negative, as x approaches 5. When you divide f(x) by g(x), the sign of the outcome is determined by the signs of the numerator (f(x)) and the denominator (g(x)).

As f(x) is positive and g(x) is negative, the quotient will be negative. Since f(x) is approaching a finite value and g(x) is approaching 0, the quotient f(x)/g(x) tends toward negative infinity as per the properties of limits.

Therefore, the value of lim x→5 f(x)/g(x) is negative infinity.

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Answer:

  72

Step-by-step explanation:

Exhaustive search shows the numbers to be 12, 24, 36. The sum of these three numbers is 72.

Answer:

38.2 miles

Step-by-step explanation:

343.8 miles divided by 9 gallons equals 32.2 miles per gallon.

Final answer:

The expression for the number of miles traveled by the airplane is 150h.

Explanation:

The expression for the number of miles traveled by the airplane is 150h. This expression represents the distance covered by the airplane based on the number of hours, h, it has been traveling at a speed of 150 miles per hour.

The expression for the number of miles traveled is [tex]\[ \text{Distance} = 150h \][/tex].

To determine the number of miles an airplane travels given its speed and the duration of travel, we can use a basic formula from physics that relates distance, speed, and time. The formula is:

[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]

Here, the speed of the airplane is given as 150 miles per hour, and the time is represented by ( h ) hours.

Step 1.Identify the given values:

Speed ( v ) = 150 miles per hour

Time ( h ) = number of hours

Step 2. Apply the formula for distance:

Distance ( d ) = [tex]Speed (\( v \)) \(\times\) Time (\( h \))[/tex]

Step 3. Substitute the given values into the formula:

[tex]\( d = 150 \text{ miles per hour} \times h \text{ hours} \)[/tex]

[tex]\( d = 150h \)[/tex]

Thus, the expression for the number of miles traveled by the airplane, when it travels at 150 miles per hour for ( h ) hours, is:

[tex]\[ \text{Distance} = 150h \][/tex]

A newspaper asking readers to complete a survey on their webpage is not conclusively biased or unbiased without knowing more about the survey's design and intention. Surveys can be a method to engage with and understand the readership better, but the potential for selection bias and the phrasing of questions could introduce bias. Whether the survey is biased or not depends on its execution and underlying methodological rigor.

The question "Is a newspaper asking readers to complete a brief survey on their webpage biased or unbiased" revolves around evaluating the intentions and methodology behind collecting reader satisfaction feedback. Given the nature of the survey is to collect feedback directly from readers on the newspaper webpage this can initially seem like a genuine effort to improve their service.

For evaluating the unbiased information based on research, it is crucial to consider the intent behind the survey and the potential for selection bias. It might inadvertently capture only the opinions of those willing to participate, or primarily those with strong opinions, positive or negative. Despite these considerations, the effort to engage with the readership directly can also be seen as a step towards transparency and improvement, indicating a potential to balance partiality with constructive feedback.

However, to ensure the process is unbiased, the newspaper would need to follow rigorous methodological standards, like random sampling, to ensure that the survey findings reflect the actual population of readers accurately. It's also essential to ensure that questions are phrased neutrally to avoid leading respondents towards a particular answer.

ANSWER

[tex]y = \sin(x) [/tex]

EXPLANATION

The trigonometric function that is zero at integral values is the sine function.

That is;

[tex]y = \sin(x) [/tex]

has x-intercepts at

[tex] n\pi[/tex]

where n is an integer.

In other words, the solution to the equation:

[tex] \sin(x) = 0[/tex]

is

[tex]x = n\pi[/tex]

where n is an integer.

Answer:

y=sin x

y=tan x

these are correct....

Answer:

A

Step-by-step explanation:

Diagonals of a parallelogram bisect each other.

3x = 3

x = 1

y = x

y = 1

In a parallelogram, the parts in which each diagonal cuts the other are congruent.

This means that we must have

[tex]\begin{cases}3=3x\\x=y\end{cases}[/tex]

From the first equation we can deduce x=1, and thus y=x=1.

Answer:

Step-by-step explanation:

Use the sum of angle formula:

  cos(a+b) = cos(a)cos(b) -sin(a)sin(b)

This gives you ...

  cos(x)cos(-π/6) -sin(x)sin(-π/6) = 1 + cos(x)cos(π/6) -sin(x)sin(π/6)

Subtracting the right-side trig function terms and factoring, we have ...

  cos(x)(cos(-π/6) -cos(π/6)) -sin(x)(sin(-π/6) -sin(π/6)) = 1

Since the cosine is an even function, cos(-π/6) = cos(π/6). Since the sine is an odd function, sin(-π/6) = -sin(π/6). This gives us ...

  cos(x)·0 -sin(x)(-2sin(π/6)) = 1

  sin(x) = 1/(2·sin(π/6)) = 1/(2·1/2) = 1

  x = arcsin(1)

  x = π/2

_____

When solving these by using a graphing calculator, it is convenient to subtract one side of the equation so you have a function of x that you want to find the zeros of. Here, we subtracted the right side. The graph shows the result is zero for x=π/2, as we know.

Answer:

First option

x = 9.1, AB  = 16.5, CD = 14.1

Step-by-step explanation:

5 * x = 13 * 3.5

5x = 45.5

x = 9.1

AB = 3.5 + 13 = 16.5

CD = 5 + 9.1 = 14.1

The value of x and the length of each chord is x = 9.1, AB  = 16.5, CD = 14.1. Thus first option is correct.

If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.

Or

|AC| = |CB|

Let x be the measure of the length of ED.

[tex]5 \times x = 13 \times3.5\\5x = 45.5\\x = 9.1[/tex]

Therefore,

AB = 3.5 + 13 = 16.5

CD = 5 + 9.1 = 14.1

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Answer:

D. <F = 65 degrees

Step-by-step explanation:

First off, we know that the measures of <F and the angle adjacent to it add to 90 degrees, as indicated by the right angle. They are complementary angles.

The complementary angle of <F has an intercepted arc of 50 degrees. Because the angle is on the opposite end of the circle, it is half of the measure of the arc. Therefore, it is 25 degrees.

Because this angle and <F sum to 90, just subtract 90-25 to find <F.

<F = 65 degrees

Answer:

F is equal to 65 (option D)

The mean is the average. The outlier is a number way bigger or smaller than the rest of the data. The outlier here would be 17. If you remove 17 and then find the average again, it will be smaller because all the numbers left are around the same range.

Answer: It will decrease

Answer:

(x, y) = (-20, 7), (-5, -2), (0, 3), (15, -4), (30, 5)

Step-by-step explanation:

You want 1/5x to match the x-value in the given table. To make that happen, multiply the given x by 5.

Example: when (1/5x) = -4, f(1/5x) = 7, so x = -4·5 = -20 for y = 7.

The transformation f(1/5x) is a horizontal expansion by a factor of 5, so each point of f(x) is now 5 times farther from the y-axis than it was.

The completed table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] is as follows:

x

−4

−1

0

3

6

​y

3

−2

3

7

5

To complete the table for the function [tex]\(y = f\left(\frac{1}{5}x\right)\),[/tex] we need to substitute the given \(x\) values into the function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex] and calculate the corresponding \(y\) values.

The function [tex]\(y = f\left(\frac{1}{5}x\right)\)[/tex]implies that we are scaling the input \(x\) by a factor of 5. This means the \(x\) values in the original table need to be multiplied by 5 to find the corresponding values for the new function. Let's calculate the values step by step:

1. For [tex]\(x = -4\):[/tex]

  [tex]\[y = f\left(\frac{1}{5}(-4)\right) = f(-0.8)\][/tex]

  Looking at the original table, when [tex]\(x = -0.8\), \(y = 3\).[/tex]

2. For [tex]\(x = -1\):[/tex]

 [tex]\[y = f\left(\frac{1}{5}(-1)\right) = f(-0.2)\][/tex]

  When [tex]\(x = -0.2\), \(y = -2\).[/tex]

3. For [tex]\(x = 0\):[/tex]

 [tex]\[y = f\left(\frac{1}{5}(0)\right) = f(0)\][/tex]

  When [tex]\(x = 0\), \(y = 3\).[/tex]

4. For [tex]\(x = 3\):[/tex]

 [tex]\[y = f\left(\frac{1}{5}(3)\right) = f(0.6)\][/tex]

  When [tex]\(x = 0.6\), \(y = 7\).[/tex]

5. For [tex]\(x = 6\):[/tex]

[tex]\[y = f\left(\frac{1}{5}(6)\right) = f(1.2)\][/tex]

  When [tex]\(x = 1.2\), \(y = 5\).[/tex]

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