Hannah and Anthony are siblings who have ages that are consecutive odd integers. The sum of their
ages iS 92. Which equations could be used to find Hannah's age, h, if she is the older sibling?

The solutions to the quadratic equation 3x^2 + 5x - 6 = 0 are x = -2 and x = 1/3.

To solve the quadratic equation by completing the square, we follow these steps:

1. Move the constant term to the other side of the equation:

3x^2 + 5x = 6

2. Divide the entire equation by the coefficient of x^2 to make the leading coefficient 1:

x^2 + (5/3)x = 2

3. Take half of the coefficient of x, square it, and add it to both sides of the equation:

x^2 + (5/3)x + (5/6)^2 = 2 + (5/6)^2

4. Simplify the right side of the equation:

x^2 + (5/3)x + 25/36 = 2 + 25/36

5. Rewrite the left side of the equation as a perfect square:

(x + 5/6)^2 = 97/36

6. Take the square root of both sides of the equation:

x + 5/6 = ±√(97/36)

7. Solve for x by subtracting 5/6 from both sides:

x = -5/6 ± √(97/36)

8. Simplify the square root and express the solutions in fraction form:

x = -2 and x = 1/3

Therefore, the solutions to the quadratic equation are x = -2 and x = 1/3.

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The directional derivative of f at point p(7,7) in the direction of q(10,3) is -1.4.

The directional derivative of f(x,y) at point p(7,7) in the direction of q(10,3) can be found using the formula:

D_v f(p) = ∇f(p) · v

where ∇f(p) is the gradient of f at point p, and v is the unit vector in the direction of q - p.

First, let's find the gradient of f:

∇f(x,y) = <∂f/∂x, ∂f/∂y> = <y, x>

So at point p(7,7), we have:

∇f(p) = <7, 7>

Next, we need to find the unit vector in the direction of q - p:

v = (q - p) / ||q - p||

= <10 - 7, 3 - 7> / ||<10 - 7, 3 - 7>||

= <3, -4> / 5

= <0.6, -0.8>

Now we can find the directional derivative:

D_v f(p) = ∇f(p) · v

= <7, 7> · <0.6, -0.8>

= 7(0.6) + 7(-0.8)

= -1.4

So the directional derivative of f at point p(7,7) in the direction of q(10,3) is -1.4.

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Answer:

25.5

Step-by-step explanation:

Just did it

Answer:

answer is 900 cubic meter

Step-by-step explanation:

use formula,

L*W*H/3

15*12*15/3

2700/3

900

Answer:

Converting Units and Comparing Quantities:

The truck cannot pass safely under the bridge. The truck is 13 inches taller than the maximum height.

Step-by-step explanation:

Maximum height of vehicle to pass bridge, (A) = 12 feet 5 inches = (12 x 12) + 5 = 144 + 5 = 149 inches

A Truck's height (B) = 162 inches

The difference between height of Truck and maximum height of allowed vehicle =  (A - B) = 13 inches (162 - 149)

Therefore, the truck is higher than the bridge by 13 inches, and cannot pass the bridge.

For the truck to pass the bridge, it must be below 149 inches.

Answer:

1/8 kg

Step-by-step explanation:

Answer:

0.125 kilogram

Step-by-step explanation:

0.5÷4=0.125

Answer:

y = 5/3x + 1

y-intercept: (0, 1)

Step-by-step explanation:

In order to determine the linear equation in its slope-intercept form, y = mx + b, where m = slope, b = y-intercept:

You need two ordered pairs from the table to solve for the slope:

We'll use (6, 11) and (9, 16).

Let (x1, y1) = (6, 11)

(x2, y2) = (9, 16)

Substitute thes values into the slope formula:

m = (y2 - y1)/(x2 - x1)

m = (16 - 11) / (9 - 6)

m = 5 / 3

Therefore, the slope of the line is: m = 5/3.

Next, we need to determine the y-intercept of the line. The y-intercept is the y-coordinate of the point (0, b ) where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.

To find the y-intercept, we'll use the slope, m = 5/3, and one of the ordered pairs from the table, (6, 11). Substitute these values into y = mx + b to solve for the y-intercept, (b ):

y = mx + b

11 = 5/3(6) + b

11 = 10 + b

Subtract 10 from both sides to solve for b:

11 - 10 = 10 - 10 + b

1 = b

The y-coordinate of the y-intercept, (0, b) is 1. The y-intercept as an ordered pair is (0, 1). For the linear equation in slope-intercept form, you'll use b = 1 to write the equation.

Therefore, given the slope, m = 5/3, and the y-intercept, b = 1:

The slope-intercept form is: y = 5/3x + 1

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The correct answer is b. frequency.

Data collection in a functional analysis typically involves recording the frequency of a target behavior. In functional analysis, the focus is on understanding the function or purpose of a behavior, and frequency data helps to identify patterns and determine the relationship between the behavior and environmental events.

During a functional analysis, various conditions are manipulated to assess how they impact the occurrence of the behavior. The frequency of the behavior is typically recorded within each condition to determine if there are differences in its occurrence based on the specific environmental variables being manipulated.

While duration and momentary time sampling are also data collection methods used in behavioral analysis, they are not specifically associated with functional analysis. Duration refers to measuring the length of time a behavior occurs, while momentary time sampling involves recording whether a behavior is occurring or not at specific intervals of time.

In functional analysis, frequency data is typically the primary method for collecting and analyzing data to understand the relationship between behavior and environmental variables.

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Data collection in a functional analysis is usually based on three components: duration, frequency, and momentary time sampling. Duration observes the amount of time a behavior occurs. Frequency measures how often a behavior occurs. Momentary time sampling observes the existence of behavior at specified time intervals.

In the context of a functional analysis, typically the data collection methods revolve around three primary types: duration, frequency, and momentary time sampling.

Duration refers to the total amount of time that a behavior happens. It generally is measured from the moment the behavior begins until it ends. It's important when the length of time that the behavior occurs can impact its functionality.

Frequency records how often a behavior occurs within a set observational period. It’s used when the number of times the behavior occurs is the important aspect to measure.

Momentary time sampling is a method of measuring behavior in which the existence or nonexistence of behaviors are recorded at precisely specified time intervals. This process involves observing whether the behavior occurs or does not occur at the moment the interval ends. This method is beneficial as it does not need continuous observation.

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No, the plan will not work because tan B = 8/5; B ≈ 58°

There are three primary trigonometric ratios for a right angle triangle and they are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

To get angle B, we will make use of trigonometric ratios to get:

tan B = 8/5

tan B = 1.6

B = tan⁻¹1.6

B = 58°

From the ramp, we can see that the angle is greater than what Gael wants to build and as such we can say it will not work.

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Answer: D) Parking costs $2 per hour for the first hour only.

Step-by-step explanation:

Based on the graph of the parking fees at a mall parking lot, the point (1,2) represent that Parking costs $2 per hour for the first hour only. In point (1,2), 1 is the value of X which represents Time in Hours and 2 is the value of Y which represents Cost or $ per hour for the duration of the parking in the lot. Hope this helps.

Answer:

D, total cost of 1 hour parking is 2$

Step-by-step explanation:

just took the test

10 minutes ago — 9. The painter bought 8 cans of paint for $12.99 each. How much did he spend on paint?​ · 9. 25 students each paid $6.50 to go to the museum ...

Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

a.) The statement P(1) is obtained by substituting n=1 into the equation. So, P(1) would be: 1³ = (1(1 + 1) / 2)²

b.) To show that P(1) is true, we need to prove that both sides of the equation are equal:

Left side: 1³ = 1

Right side: (1(1 + 1) / 2)² = (1(2) / 2)² = (2 / 2)² = 1² = 1

Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

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a) The equation is not true for n = 1, so P(1) is false.

b) The positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1

a) To find P(1), we substitute n = 1 into the equation given:

13 = (1(1 + 1) / 2)²

13 = (1 / 2)²

13 = 1/4

The equation is not true for n = 1, so P(1) is false.

b) To complete the basic step of the proof, we need to show that P(1) is true.

However, we have just shown that P(1) is false.

This means that the statement "for the positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1.

Therefore, the proof cannot proceed and is incomplete.

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The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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Based on the given problem, when written in the simplest form, the result would be 19 ²/₃

To divide 59 by 3 and then write it in its simplest form, you first need to find the number of times 3 can go into 59 without leaving a remainder:

= 59 / 3

= 19 times

Then find the quotient of 19 multiplied by 3:

= 19 x 3

= 57

Then use this to find the remainder:

= 59 - 57

= 2

This remainder will then be used to find the answer in the simplest form:

= 19 + Remainder / Divisor

= 19 + 2/3

= 19 ²/₃

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Answer:

Hey there!

The equation would be C=3.50r+5.75

Let me know if this helps :)

x+15

depends on the value of x

Answer:

15 + X

Step-by-step explanation:

The Sum means an answer to an adition problem

Answer:

2^4

Step-by-step explanation:

2^2 = 2 * 2 = 4

4^4 = 4*4*4*4 = 256

2^4 = 4*4 = 16

8^2 = 8*8 = 64

2^8 = 2*2*2*2*2*2*2*2 = 256

Hence, 16 can be written as 2^4

Thus, Answer is [C] 2^4

[RevyBreeze]

Answer:

7 ft

Step-by-step explanation:

7 x 7 x 7 = 343

Step-by-step explanation:

✧ \( \underline{ \underline{ \large{ \tt{G\: I \: V \: E \: N}}} }: \)

✧ \( \underline{ \underline{ \large{ \tt{T \: O \: \: F \: I\:N\: D}}}} : \)

✧ \( \underline{ \underline{ \large{ \tt{ S \: O \: L \: U \: T \: I\: O \: N}}} }: \)

☪ \( \boxed{ \large{ \text{Volume \: of \: a \: cube }= \sf {l}^{3} }}\)

⇾\( \large{ \sf{343 = {l}^{ 3}}} \)

⇾\( \large{ \sf{ {l}^{ 3} = 343}}\)

⇾\( \large{ \sf{l = \sqrt[3]{343} }}\)

⇾\( \large{ \sf{l = \sqrt[3]{7 \times 7 \times 7}}} \)

⇾\( \large{ \sf{l = \boxed{ \sf{7 \: ft}}}}\)

\( \huge{ \boxed{ \boxed{ \large{ \text{OUR \: FINAL \:ANSWER }: \boxed{ \underline{ \bold{ \sf{7 \: ft}}}}}}}}\)

⭒Hope I helped ! ⭒

Have a wonderful day / night ! ♡

Let me know if you have any questions regarding my answer ! ツ

⋆ \( \underline{ \underline{ \mathfrak{Carry \: On \: Learning}}}\) !! ✎

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

The correct option is D. Many data points are close to one particular value.

Clustering is a technique in unsupervised machine learning where data points are grouped together based on their similarity or proximity to each other. The goal of clustering is to identify patterns or structures in the data that may not be immediately apparent. In clustering, data points are partitioned into groups or clusters, such that the data points within a cluster are more similar to each other than to those in other clusters.

Here,

Option D describes clustering, as it refers to many data points being close to one particular value, which is a characteristic of clusters in the data. Option A describes an outlier, which is a data point that is far from the other points, while options B and C describe situations where there is no clear pattern or structure in the data.

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The  least common denominator of 7/9 and 2/3 is 9

To find the least common denominator of 7/9 and 2/3, we need to find the smallest multiple that both denominators share.

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, ...

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...

We can see that the smallest multiple that both denominators share is 9.

To convert 7/9 and 2/3 to have a denominator of 9, we need to multiply the numerator and denominator of 7/9 by 1 (which is equivalent to 9/9), and the numerator and denominator of 2/3 by 3:

7/9 * 1 = 7/9

2/3 * 3/3 = 6/9

Now both fractions have a denominator of 9, so we can compare them easily:

7/9 and 6/9

Therefore, the least common denominator of 7/9 and 2/3 is 9.

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Answer:

Step-by-step explanation:

la première planche = 2x

la deuxième = x

la troisième = x-10

1ere planche + 2eme planche + 3eme planche = 50 pouces

donc :

(2x) + x + (x-10) =50

4x-10 = 50

4x-10+10 = 50 +10

4x = 60

4x diviser par 4 = 60 diviser par 4

x=15

la première planche = 30

la deuxième = 15

la troisième = 5

30+15+5=50

The function is f(x) = (10/63)x14/5 + Cx + D

First get the first antiderivative of f "(x). The antiderivative of f "(x) will give you f '(x). (This is because the derivative of f '(x) gives you f "(x). The antiderivative is just the inverse of the derivative)

f '(x) = ∫(4/5)x4/5dx (Use the power rule to solve)

f '(x) = (4/5) * x9/5/(9/5) + C

Simplify f '(x):

f '(x) = (4/9)x9/5 + C

Now get the antiderivative of f '(x). The antiderivative of f '(x) will give you f(x)

f(x) = ∫(4/9)x9/5+C dx (Use the power rule for each term to solve)

The integral of x9/5 is x14/5 /(14/5) = 5x14/5 /14

Therefore taking the antiderivative of f '(x) gives us:

f(x) = (4/9)*(5x14/5 /14) + Cx + D

On Simplifying f(x):

f(x) = (10/63)x14/5 + Cx + D

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Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Answer:

4 / 15

Step-by-step explanation:

The total number of ways 2 students can be picked is 15 * 14 = 210 because you have 15 students to begin with and after you pick one, you're left with 14 more to choose from.

The total number of ways a senior and a junior can be picked is 8 * 7 = 56 because there are 8 seniors and 7 juniors.

The probability will then be 56 / 210 = 4 / 15. Hope this helps!

The geometric average return of RedStone Mines stock over the past four years is approximately (b) 9.94%.

To find the geometric average return of RedStone Mines stock over the past four years, we need to calculate the average return using the geometric mean formula. The geometric mean is used to find the average growth rate over multiple periods. To calculate the geometric average return, we multiply the individual returns and take the nth root, where n is the number of periods.

Given the returns of 7.5%, 15.3%, -9.2%, and 11.5%, we can calculate the geometric average return as follows:

(1 + 7.5%) * (1 + 15.3%) * (1 - 9.2%) * (1 + 11.5%)

Taking the fourth root of the above expression, we get:

Geometric average return = [(1 + 7.5%) * (1 + 15.3%) * (1 - 9.2%) * (1 + 11.5%)]\(^{\frac{1}{4}}\)  - 1 = 9.94

Evaluating, we find that the geometric average return is approximately 9.94%. Therefore, the correct answer is option b. 9.94%.

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Answer:

1. ∠1 ≅ 6 : Given

2. ∠3 ≅ ∠ 4 : Vertical Angles Congruence Property

3. ∠2 ≅ ∠5 : Corollary III of Theorem 19 : If two angles of two triangles are congruent, then the third angle of both triangles are congruent.

Step-by-step explanation: For ∠3 ≅ ∠4, the angles are in a diagonal placement, meaning they are vertical angles. Vertical angles are always congruent.

Lookimg at one of the problems you posted earlier, the Corollary III of Theorem 19 given, states that if two angles are congruent in both triangles, then the third angle is congruent in both triangles. Since we have 2 angles already congruent to 2 other angles, ∠2 and ∠5 must be congruent.

Hope this helped!

The equation f(x) = 0 has no real solutions. The equation g(x) = 0 has two real solutions. The equation h(x) = 0 has one real solution.

To determine the number of solutions for each equation, we can examine the discriminant (b² - 4ac) of the quadratic functions. The discriminant provides information about the nature and number of solutions.

f(x) = x² + 4

For this quadratic function, the coefficient of x² (a) is 1, the coefficient of x (b) is 0, and the constant term (c) is 4. Plugging these values into the discriminant formula, we get:

b² - 4ac = 0² - 4(1)(4) = -16

Since the discriminant is negative (-16), the quadratic function f(x) = x² + 4 has no real solutions. It does have two complex solutions, but since the question asks for real solutions, the answer is:

f(x) = 0 has no solutions.

g(x) = x(x + 3)

For this quadratic function, the coefficient of x² (a) is 1, the coefficient of x (b) is 3, and the constant term (c) is 0. Plugging these values into the discriminant formula, we get:

b² - 4ac = 3² - 4(1)(0) = 9

Since the discriminant is positive (9), the quadratic function g(x) = x(x + 3) has two real solutions. The answer is:

g(x) = 0 has two solutions.h(x) = (x - 1)²

For this quadratic function, the coefficient of x² (a) is 1, the coefficient of x (b) is -2, and the constant term (c) is 1. Plugging these values into the discriminant formula, we get:

b² - 4ac = (-2)² - 4(1)(1) = 0

Since the discriminant is zero (0), the quadratic function h(x) = (x - 1)² has one real solution. The answer is:

h(x) = 0 has one solution.

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Step-by-step explanation:

We want to identify how to determine the x-factors for the graph of a function.

On some occasions, the x values for the function will be provided for you to solve for the y values. but on other occasions, the x values are not provided and you have to decide them yourself.

For a linear function, most times, you can pick values within any range of values, e.g from 0 to 5, or 2, 4, 6, 8, 10. Since it is a linear function, it will eventually result in a straight line that contains all other points.

For a quadratic function, the best practice is to pick points around the vertex of the function. The vertex of a function is either the minimum or maximum point of the function.

For example, if the vertex of a quadratic function is (4, 10), the x-coordinate of the vertex is 4. To pick your points, pick points that are some values below 4 and some values above 4, like 2, 3, 4, 5, 6 or 0, 2, 4, 6, 8 That way, you get points that are on either side of the vertex and that will make your plot easier.

Hope that helps!