Elaine's height is 75% of her father's. If her father is 180 cm tall, how tall is Elaine?

The solution to the system of equations is (23, -72).

The first equation is y = -72, which means that whatever the value of x is, the value of y will always be -72.

Substituting y = -72 in the second equation, we get:

7x + 2(-72) = 20

Simplifying this equation, we get:

7x - 144 = 20

Adding 144 to both sides, we get:

7x = 164

Dividing both sides by 7, we get:

x = 23.428571...

So the solution to the system of equations is the ordered pair (x, y) = (23.428571..., -72).

However, we usually express solutions as ordered pairs of integers, so we can round x to the nearest integer to get:

(x, y) = (23, -72)

Therefore, the solution to the system of equations is (23, -72).

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2x + 2y = 4xy is wrong

2x + 2y = 2(x+y) is correct

3x+4= 7x wrong

4x²+5x = 9x² wrong

3x²+3x²+4x = 6x² + 4x = 2x(3x + 2)

sorry I don't understand this one.....

-4(3x-5) = -12x + 20

Answer:

120

12 10

4 2 5 2

2 2

An equation that could be solved using this application of the quadratic formula include the following: D. 2x² + 12x + 4 = 13.

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical equation:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

For the given quadratic equation 2x² + 12x + 4 = 13, we have:

2x² + 12x + 4 = 13

2x² + 12x + 4 - 13 = 0

2x² + 12x - 9 = 0

By substituting, we have;

[tex]x = \frac{-(12)\; \pm \;\sqrt{(12)^2 - 4(2)(-9)}}{2(2)}[/tex]

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The values of sine, cosine, and tangent of the angle 'θ' are: sinθ = [tex]\frac{1}{2}[/tex],

cosθ = [tex]\frac{\sqrt{3}}{2}[/tex]  and tanθ = [tex]\frac{1}{\sqrt{3} }[/tex] .

To begin, determine the angle for which you wish to compute trigonometric ratios. Let's call the angle "θ".

Find the lengths of the sides of the right triangle that correspond to the angle "θ". Choose the trigonometric ratio you wish to calculate: sine (sin), cosine (cos), or tangent (tan).

Now, using the proper trigonometric formula, determine the needed ratio:

            sin θ [tex]= \frac{Opposite side}{Hypotenuse }[/tex]

            cos θ [tex]= \frac{Adjacent side }{Hypotenuse}[/tex]

            tan θ [tex]= \frac{Opposite side }{Adjacent side}[/tex]

In the given problem, values for angle θ are-:

opposite side = 4 and Adjacent side = 4[tex]\sqrt{3}[/tex]

Using Pythagorean theorem to find the value of hypotenuse:

[tex]hypotenuse = \sqrt{(opposite^2 + adjacent^2)}[/tex]

[tex]hypotenuse=\sqrt{4^{2}+(4\sqrt{3})^2 } =\sqrt{16+48} =\sqrt{64} =8[/tex]

Now, putting values to find required trignometric ratios-:

sin θ[tex]= \frac{Opposite side}{Hypotenuse }=\frac{4}{8 }=\frac{1}{2}[/tex]

cos θ[tex]= \frac{Adjacent side }{Hypotenuse} =\frac{4\sqrt{3}}{8}=\frac{\sqrt{3}}{2}[/tex]

tan θ [tex]= \frac{Opposite side }{Adjacent side}=\frac{4}{4\sqrt{3}}=\frac{1}{\sqrt{3} }[/tex]

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1. The expression √b means "the square root of b".

2. The radical symbol (√) stands for the exponent 1/2.

3. The number or expression under the radical symbol is called the radicand.

A radicand is the number or expression underneath a radical symbol (√). It is the number or expression that is being operated on by the root. The square root of the radicand is the result of the operation.

The expression √6 represents the square root of 6. This is the value of x that, when multiplied with itself, results in 6.

The square root of 6 is equal to 2.44948974, which is the positive solution to the equation x² = 6.

The radical symbol (√) indicates that the expression is a root and the number or expression under the radical symbol is called the radicand, which is 6 in this case.

The exponent of the radical symbol is 1/2, which implies that the expression is a square root.

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The client will be receiving 1.67 ml of medication in one minute and it will have 0.334 g of medication per minute.

Here 2g  of medication is diluted with 100 ml of normal saline. So concentration of 1ml of normal saline would be,

Concentration of 1 ml = 2/100 = 0.02 g/ml

It is delivered over a period of 1 hour. So, the amount delivered per minute will be,

Amount per minute = Volume/ time = 100/60 = 1.67 ml

Amount of medication in 1.67 ml = Volume × Amount per ml

                                                     = 1.67 × 0.02 = 0.334 g

So 0.334 g of medication will be received per minute. So the rate will be 1.67 ml per minute.

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The value of x, in the image given is calculated by applying the intersecting chords theorem, which is: x = 16.

The Intersecting Chords Theorem, also known as the Ptolemy's Theorem, states that in a circle, if two chords intersect, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

In mathematical terms, if two chords, AB and CD, intersect at point E inside a circle, then:

AE × EB = CE × ED

Applying the theorem, we have:

5(x) = (x - 6)8

5x = 8x - 48

5x - 8x = -48

-3x = -48

x = 16

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It will take 10 years to double the amount.

Given that, the amount $1400 to double if it is invested at 7% interest compounded monthly, we need to calculate the time,

[tex]A = P(1+r/n)^{nt}[/tex]

[tex]2800 = 1400(1+0.0058)^{12t}[/tex]

[tex]2= (1.0058)^{12t[/tex]

㏒ 2 = 12t ㏒ (1.0058)

0.03 = 12t (0.0025)

12t = 120

t = 10

Hence, it will take 10 years to double the amount.

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Answer: 30/52 or 58%

Step-by-step explanation:

The non-Twix candies to all candies is 30 pieces of non-Twix to 52 total candies. This is a ratio of 30:52 or 58%. I hope this helps you. <3

Answer: 15 non-twix to 26 total candy

Step-by-step explanation:

non twix: 14+16=30

all candy: 22+14+16=52

30:52

simplify

15:26

True. An integer overflow attack occurs when an attacker manipulates a variable in a way that causes it to exceed its maximum value or minimum value, leading to unexpected and potentially harmful behavior.

This can happen if a programmer fails to properly check and validate the input values that are being used in their code, allowing an attacker to inject a value that triggers an overflow.

As a result, the variable may be assigned a value that is outside the intended range, leading to unpredictable behavior and potentially causing the program to crash or execute unintended code. It is important for programmers to take steps to prevent integer overflow attacks, such as validating input values and using data types with sufficient capacity to hold the expected range of values.

This occurs when an arithmetic operation results in a value that is too large to be stored in the allocated memory, causing the value to wrap around and become smaller, or even negative. This can lead to unintended consequences in a program's behavior, which an attacker can exploit to gain unauthorized access or cause other security issues.

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The total length of the beads on one braid is 8.11 centimeters

Keyana places 7 beads on one braid, and each bead is 1.03 centimeters long. So, the total length of these 7 beads would be 7 multiplied by 1.03, which is equal to 7.21 centimeters.

To find the total length of the beads on one braid, we need to evaluate the expression:

7 x 1.03 + 0.9

Multiplying 7 by 1.03 gives us:

7 x 1.03 = 7.21

Then, adding 0.9 gives us:

7.21 + 0.9 = 8.11

Therefore, the total length of the beads on one braid is 8.11 centimeters.

So, the correct answer is B.8.11 centimeters.

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The types of equations in the question based on the values of the base, the slope and leading coefficients of the equations are;

11. Exponential growth

12. Exponential growth

13. Decreasing linear

14. Positive quadratic

15. Increasing linear

16. Exponential growth

17. Exponential decay

18. Exponential decay'

19. Positive quadratic

20. Linear increasing

21. Exponential growth

22. Negative quadratic

23. Negative quadratic

24. Exponential decay

An equation is a statement that indicates that of two expressions are equivalent, by joining them with an '=' sign.

11. The exponential equation is; y = (5/2)ˣ

The growth or decay factor, which is the base is; (5/2) > 1, therefore, the equation is an exponential growth equation

12. The exponential equation is; y = (1/4) × 3ˣ

3 > 1, therefore the equation is an exponential growth function

13. The equation y = -2·x -10 is a linear equation with a negative slope of -2, indicating that the value of y is decreasing as x increases, therefore, the equation is decreasing linear

14. The equation, y = 2·x² + 5·x - 7, which is a quadratic equation

The leading coefficient, 2, is positive, therefore, the equation is a positive quadratic equation

15. The equation y = 4·x - 3 has a positive slope, of 4, therefore, it is an increasing linear equation

16. The exponential equation (2/5)·9ˣ, with 9 > 1, is an exponential growth equation

17. The equation  3·(1/4)ˣ, with (1/4) < 1, is an exponential decay equation

18. The equation 2·(0.1)ˣ, with 0.1 < 1, is an exponential decay equation

19. The equation y = (x + 2)² is a quadratic equation

(x + 2)² = x² + 4·x + 4

The leading coefficient is 1, therefore, the equation is a positive quadratic equation

20. The linear equation 4·x + y = 7 with a positive slope of +4 indicates that the y-value of the function is increasing as the x-value of the equation is increasing, therefore, the function is an increasing linear equation

21. The exponential equation, y = 2·5ˣ, with 5 > 1, and 2 > 0, is an exponential growth equation.

22. The equation y = -(x - 3)² is a quadratic equation. The minus sign in front of the expression (x - 3) indicates that the leading coefficient, obtained by expansion, is negative

y = -(x - 3)² = -(x² - 6·x + 9) = -x² + 6·x - 9

The leading coefficient is -1, therefore the equation negative quadratic

23. The equation, y = -6·x² -5·x + 4, with a leading coefficient of -6 is a negative quadratic equation

24. The exponential equation, y = (1/7)·(3/8)ˣ, with (1/7) > 0 and (3/8) < 1 is an exponential decay equation

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We can conclude that cosh2x−sinh2x=1.

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

To show that cosh2x−sinh2x=1, we can use the identities for cosh2x and sinh2x. The identity for cosh2x is cosh2x=2cosh2x−1 and the identity for sinh2x is sinh2x=2sinh2x−1.

Substituting these identities into the equation cosh2x−sinh2x=1 yields 2cosh2x−1−2sinh2x−1=1. Simplifying this equation yields cosh2x−sinh2x=1, as required. Thus, we can conclude that cosh2x−sinh2x=1.

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Simplifying this equation yields [tex]\cosh^2x-sinh^2x=1[/tex], as required. Thus, we can conclude that [tex]\cosh^2x-sinh^2x=1[/tex].

An equation is a mathematical statement that states that two expressions are equal. It is typically written as a comparison between two expressions and consists of an equal sign (=). Equations are used to solve mathematical problems, to understand the relationships between different quantities, and to describe the behavior of a physical system. In addition, equations are used to calculate various quantities, such as the area of a circle or the speed of an object.

We will show that [tex]\cosh^2x-sinh^2x=1[/tex].

Let us consider the expression [tex]\cosh^2x-sinh^2x.[/tex]

Then, [tex]\cosh^2x=(e^2x+e^{-2}x)/2[/tex] and [tex]sinh^2x=(e^2x+e^{-2}x)/2[/tex]

Substituting, we get [tex]\cosh^2x -\sinh^2x=(e^2x+e^{-2}x)/2\ -(e^2x+e^{-2}x)/2[/tex]

Simplifying, we have [tex]\cosh^2x -\sinh^2x=e^2x+e^{-2}x-e^2x+e^{-2}x[/tex]

[tex]=2e^{-2}x\\\\=2(e^{-2}x)\\\\=2[/tex]

Hence, [tex]cosh^2x-sinh^2x=1[/tex]

Therefore, we have shown that [tex]cosh^2x-sinh^2x=1[/tex]

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The correct form of question is Show that cosh2x−sinh2x=1 .

Answer:

10

Step-by-step explanation:

To find the median in a set of data, organize the data from least to greatest.

Here, our data is the homework scores, those being:

10, 7, 8, 12, 9, 11, 13

Let's organize them in ascending order, like so:

7, 8, 9, 10, 11, 12, 13

The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.

We can find that the number in the middle is 10.

Thus, the median of the scores is 10.

Answer:

A. February 26th

B. $3,500 - Balance ≈ $6,697.26

C. $2,500 - Balance ≈ $4,263.46

D. $4,284.81

Step-by-step explanation:

a) What is the due date of the loan?

The loan term is given as 317 days, and the loan starts on April 15th. To find the due date, we will add 317 days to April 15th.

April 15th + 317 days = April 15th + (365 days - 48 days) = April 15th + 1 year - 48 days

Subtracting 48 days from April 15th, we get:

Due date = February 26th (of the following year)

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

First, we need to calculate the number of days between April 15th and October 12th:

April (15 days) + May (31 days) + June (30 days) + July (31 days) + August (31 days) + September (30 days) + October (12 days) = 180 days

Now, we will calculate the interest for 180 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $10,000 × 0.04 × (180 / 365)

Interest ≈ $197.26

Peter will make a payment of $3,500 on October 12th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $10,000 + $197.26 - $3,500

Balance ≈ $6,697.26

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th payment.

First, we need to calculate the number of days between October 12th and January 11th:

October (19 days) + November (30 days) + December (31 days) + January (11 days) = 91 days

Now, we will calculate the interest for 91 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $6,697.26 × 0.04 × (91 / 365)

Interest ≈ $66.20

Peter will make a payment of $2,500 on January 11th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $6,697.26 + $66.20 - $2,500

Balance ≈ $4,263.46

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

First, we need to calculate the number of days between January 11th and February 26th:

January (20 days) + February (26 days) = 46 days

Now, we will calculate the interest for 46 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $4,263.46 × 0.04 × (46 / 365)

Interest ≈ $21.35

Finally, we will calculate the final payment Peter must pay on the due date:

Final payment = Principal + Interest

Final payment = $4,263.46 + $21.35

Final payment ≈ $4,284.81

Answer:

Speed= 500ml/hr

total distance= 2800 m

total time = d/t

2800/500= 5.6hrs

Step-by-step explanation:

Answer:3/16

Step-by-step explanation:

√1 is the same thing as 1

so (3*1)/16

3/16

The distance of the object from the helicopter is 698 ft.

Distance is the length between two points.

To calculate how far the object is above the helicopter, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for H

Hence, the distance is 698 ft.

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The area of a circle of radius of 0.5 meters is 0.785 square meters.

Remember that for a circle of radius r, the area is:

A = pi*r²

Where pi = 3.14

Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.

A = 3.14*(0.5m)²

A = 3.14*0.25 m²

A = 0.785  m²

That is the area of the circle.

Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?

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The correct inequality to represent the situation where everyone has to spend at least 10 dollars but less than 20 dollars in a gift exchange is 10 ≤ x < 20. (option b).

The correct inequality to represent the situation is B. 10 ≤ x < 20. This inequality reads "x is greater than or equal to 10, but less than 20". In other words, the amount of money each person spends (represented by x) must be at least 10 dollars, but cannot exceed 20 dollars.

To understand why this is the correct inequality, let's break it down. The symbol ≤ means "less than or equal to", and the symbol < means "less than". So, 10 ≤ x means "x is greater than or equal to 10", and x < 20 means "x is less than 20". Combining these two expressions gives us the inequality 10 ≤ x < 20, which represents the range of values that x can take on in this gift exchange.

Hence the correct option is (b).

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Answer:

x = 10

Step-by-step explanation:

Angle form is = 90°

therefore

5x + 25 + x + 5 = 90

6x + 30 = 90

6x = 90-30

6x = 60

6x/6 = 60/6

x = 10

The volume of the rectangular prism is 1.6 cubic inches.

Let's start by finding the number of cubes that can fit in each dimension of the rectangular prism. Since each cube has an edge length of 1/5 inch, the length, width, and height of the rectangular prism must be multiples of 1/5 inch. Let's call the length of the rectangular prism "L", the width "W", and the height "H". Then we have

L = 1/5 × x

W = 1/5 × y

H = 1/5 × z

where x, y, and z are integers.

Since the rectangular prism is completely packed with 200 cubes, we have

x × y × z = 200

We want to find the volume of the rectangular prism, which is given by

V = L × W × H = 1/5 × x × 1/5 × y × 1/5 × z = 1/125 × x × y × z

Substituting x × y × z = 200, we get

V = 1/125 × 200 = 8/5 = 1.6 cubic inches

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The given question is incomplete, the complete question is:

A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. find the  volume of this rectangular prism

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

A number line is a diagram that depicts numbers on a straight line. It is a tool for comparing and sorting numbers. It can represent any real number, including whole numbers and natural numbers.

Jesse currently has 520 signatures and needs at least 1000 signatures, which means he still needs to collect 1000 - 520 = 480 signatures.

He has 6 more weeks to collect the signatures he needs, so he wants to collect the same number of signatures each week. Let's call this number x, representing the number of signatures he collects each week. Then, the total number of signatures he collects in the remaining 6 weeks would be 6x.

We want to find the range of values for x that would allow Jesse to collect at least 480 signatures in the remaining 6 weeks. In other words, we want to solve the inequality:

6x ≥ 480

Dividing both sides by 6, we get:

x ≥ 80

This means that Jesse needs to collect at least 80 signatures per week in order to have enough signatures to submit the petition.

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

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The length of arc XW is 9,60 metres

The length of arc YVU is 44.93 metres

A. M<XZW = 180 degrees - M<VZW

= 180 - 108

= 72 degrees.

XV = 180/360 x 2\pi r =

r = 7.639

XW= 72/360 x 2\pi r

= 9.60 metres.

B. M<UZY = M<XZW = 72 degrees

MYVU= 85 + 180 + 72 = 337 degrees

YVU = 337/360 x 2 pi r

=44.93 metres

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The ounces of  beeswax needed by Leah to make 15 more small candles is equal to 49.95 ounces.

Let us consider 'x' be the ounces of beeswax required by Leah to make 15 candles.

To make 6 small candles, Leah uses 20 ounces of beeswax.

So, to make one small candle,

Ounces of beeswax used by Leah ,

= 20 ounces / 6 candles

= 3.33 ounces/candle (rounded to two decimal places)

To make 15 more small candles,

Ounces of beeswax Leah will need is equals to,

⇒ x = 15 candles x 3.33 ounces/candle

⇒ x = 49.95 ounces (rounded to two decimal places)

Therefore, Leah needs 49.95 ounces of beeswax to make 15 more small candles.

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The height of the kite is approximately 68.4 ft.

To solve the problem, we can use trigonometry. We know that the string is the hypotenuse of a right triangle, with the height of the kite as one of the legs. The angle of elevation, which is the angle between the string and the ground, is also given. We can use the tangent function to find the height of the kite:

tan(46°) = height / 94

Solving for height, we get:

height = 94 * tan(46°)

Using a calculator, we get:

height ≈ 68.4 ft

Therefore, the height of the kite is approximately 68.4 ft.

We use the given angle of elevation and the length of the string to set up a right triangle with the height of the kite as one of the legs. Then, we use the tangent function to relate the angle to the height of the kite. Finally, we solve for the height using a calculator and round to the nearest tenth as requested.

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Complete Question:

A kite flying in the air has a 94-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 46 °. Find the height of the kite. Round your answer to the nearest tenth.

The value of k is given as follows:

k = 5.

The function in the context of this problem is defined as follows:

f(x) = x³ + kx - 6.

We have that x - 1 is a factor of the function, meaning that, by the Factor Theorem:

f(1) = 0, x - 1 = 0 -> x = 1.

Hence, applying the numeric value, the value of k is obtained as follows:

1 + k - 6 = 0

k - 5 = 0

k = 5.

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Answer: Monique's error is likely due to rounding the surface area to two decimal places, which led to an inaccurate result.

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately 3.14.

To find the correct surface area, we need to know the values of r and h. Without this information, we cannot calculate the exact surface area.

However, we can use Monique's estimate to estimate the values of r and h.

1001.66 = 2πr^2 + 2πrh

Dividing both sides by 2π, we get:

500.83 = r^2 + rh

We don't know the exact values of r and h, but we know that the surface area should be greater than 1001.66 square feet. Therefore, we can assume that the radius and height must be greater than a certain value.

For example, if we assume that the radius is at least 5 feet, we can solve for the minimum value of h:

500.83 = 5^2 + 5h

495.83 = 5h

h = 99.166

So if the radius is 5 feet and the height is 99.166 feet, the surface area would be:

S = 2π(5^2) + 2π(5)(99.166)

S = 1570.8 square feet

This is greater than Monique's estimate of 1001.66 square feet, indicating that her estimate was too low due to rounding.

Step-by-step explanation: