The two triangles in the diagram are similar.
There are two possible values of x.
Work out each of these values.
state both assumptions* you make in your working.

Answer:

The volume V of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.

In this case, we have l = 2, w = 7/3, and h = 2. Therefore, the volume is:

V = (2)(7/3)(2)

V = 28/3

V = 9.33 (rounded to two decimal places)

So the volume of the rectangular prism is approximately 9.33 cubic units.

The scaling factors need not be the same, and this transformation scales the x-axis by a different factor than the y-axis, resulting in a non-uniform scaling.

What is Transformation axes ?

Transformation axes refer to the new coordinate axes after a transformation is applied to a given set of coordinates or points.

The transformation (x, y) → (2x, 3y) is a linear transformation that stretches the x-coordinate by a factor of 2 and the y-coordinate by a factor of 3, while keeping the origin fixed.

This transformation is an example of a scaling transformation, where the scale factor along the x-axis is 2 and along the y-axis is 3.

Visually, this transformation will stretch out the graph horizontally and vertically, making objects appear larger or smaller depending on their position relative to the x and y axes.

Therefore, The scaling factors need not be the same, and this transformation scales the x-axis by a different factor than the y-axis, resulting in a non-uniform scaling.

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Answer:

It is not possible to form a right triangle with the lengths 4, 8, and 10 because the longest side of the triangle must be shorter than the sum of the other two sides. This is known as the Pythagorean Theorem, which states that in a right triangle, the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides. Since 8² + 10² = 164, and 10 is greater than the sum of 4 + 8, it is not possible to form a right triangle with those three lengths.

In this case, assuming that 10 is the hypotenuse, we have:

10² = 4² + 8²

100 = 16 + 64

This equation is not true, as 100 is not equal to 80. Therefore, we cannot form a right triangle

Answer: 36 cubes

Step-by-step explanation:

Length x Width x Height

18 x 6 x 9 = 972

3 x 3 x 3 = 27

972 / 27 = 36

The ball may rise height a maximum of [tex]119[/tex] feet.

Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base but something above it. Anything that can be measured vertically, whether it is high or low, is referred to as having height.

As the ball hits the quadratic function's vertex, it has grown to its highest point. The position (b, c), wherein b is the vertex's x-coordinate, is where a quadratic function of the type is said to have its vertex.

As the quadratic function in this instance is, the point serves as the vertex (5, 119). The ball therefore reaches its highest point after 5 seconds.

[tex]h=-16(5-5)^{2}+119[/tex]

[tex]h=119[/tex]

Therefore, the maximum height of the ball is [tex]119[/tex] feet.

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Answer:

Incorrect

Step-by-step explanation:

In step one, when they multiplied exponents, they added them which is correct

Step two, they divided exponents, which means they should have subtracted. if they subtracted 6/5 and 2/5, it would have been

[tex]( {x}^{ \frac{4}{5} } )^{ \frac{1}{2} } [/tex]

The requried measures of angles a, b, c, and d are 97°, 15°, 68°, and 68° respectively.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
From the figure,
The calculation of the unknown angles is as follows,
112° and ∠d are supplementary angles.

So,
112 + ∠d = 180
∠d = 180 - 112
∠d = 68°

97° and angle a are corresponding angles, so
∠a = 97°.

112 and ∠c are also supplementary angles.
112 + ∠c = 180
∠c = 68°

Now,
∠a + ∠b  = 112
∠a + 97 = 112
∠a = 15°

Thus, the requried measure of angles a, b, c, and d are 97°, 15°, 68° and 68°.

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Answer:

18π or

Step-by-step explanation:

To find the area of a semicircle, use the formula of the area of a semicircle.

Area = [tex]\frac{1}{2}[/tex] π r^2

Radius = 6

Area = [tex]\frac{1}{2}[/tex] π 6^2

Area = [tex]\frac{1}{2}[/tex] (36π)
Area = 18π (in terms of π)

Area = 56.52 (in terms of 3.14)

The following function won't produce the intended composite function:

f(x) = 8/x + 4

g(x) = 1/x²

A method or connection known as a function connects each element of a non-empty set A to at least one element of a second non-empty set B. A function in mathematics is a relation f between a set A (the function's domain) and a different set B (the function's co-domain).

In the given question,

When f(x) = 8/x + 4 and g(x) = 1/x²

Then (f o g(x)) = 8/1/x² + 4

= 8x² + 4

As a result, the following function would not produce the intended composite function:

f(x) = 8/x + 4

g(x) = 1/x²

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Answer:

Step-by-step explanation:

1000m = 1km

So 3000m = 3km

9x^3 + 4x^2 + 5

Explanation:

Let's simplify step-by-step.

6x^2−3−5x^3−(4x^3+2x^2−8)

Distribute the Negative Sign:

=6x^2−3−5x^3+−1(4x^3+2x^2−8)

=6x^2+−3+−5x^3+−1(4x^3)+−1(2x^2)+(−1)(−8)

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

Combine Like Terms:

=6x^2+−3+−5x^3+−4x^3+−2x^2+8

=(−5x^3+−4x^3)+(6x^2+−2x^2)+(−3+8)

=−9x^3+4x^2+5

As a result, the particle's velocity changes as time passes. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3.

A mathematical equation, such as 6 x 4 = 12 x 2, states that two numbers or values are equivalent. a meaningful noun. When several or even more components need to be taken into account simultaneously in order to comprehend or describe the entire situation, an equation is used.

The derivatives of the displacing equation with time as a parameter is the particle's velocity.

v = ds/dt = d/dt (2/t²) = -4/t³

As a result, the particle's velocity at times t = a, t = 1, t = 2, and t = 3 is as follows:

v(a) = -4/a³

v(1) = -4/1³ = -4 m/s

v(2) = -4/2³ = -0.5 m/s

v(3) = -4/3³ = -0.15 m/s

The particle's velocity consequently varies over time. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3. Due to the fact also that velocity is negative for any and all values of t, the particle is travelling in the reverse way (i.e., to the left).

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The pοssible decimals that satisfy the given cοnditiοns are:5.20, 5.22, 5.24, 5.26, 5.28, 5.60, 5.62, 5.64, 5.66, 5.68, 7.20, 7.22, 7.24, 7.26, 7.28, 7.60, 7.62, 7.64, 7.66, 7.68

Decimals are a way οf expressing numbers that fall between whοle numbers, using a decimal pοint tο separate the whοle number and the fractiοnal part. Each digit tο the right οf the decimal pοint represents a decreasing pοwer οf 10, starting frοm tenths, hundredths, thοusandths, and sο οn.

Since the digit in the tenths place is οdd, it can οnly be 5 οr 7. Similarly, since the digit in the hundredths place is even, it can οnly be 0, 2, 4, 6, οr 8.

Therefοre, the pοssible decimals that satisfy the given cοnditiοns are:

5.20

5.22

5.24

5.26

5.28

5.60

5.62

5.64

5.66

5.68

7.20

7.22

7.24

7.26

7.28

7.60

7.62

7.64

7.66

7.68

Nοte that these are the οnly pοssible decimals that satisfy all the given cοnditiοns.

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To model with mathematics is to test ideas using math and computer programs to simulate an object or action.

In order to understand a real-life problem, modelling entails developing a set of mathematical equations that accurately reflects a situation.

The model frequently needs to be modified because it does not adequately capture the situation.

By knowing how the system functions, which variables are significant in the system, and how they relate to one another, one can utilise a mathematical model to better understand a real-life situation. Moreover, models can be used to forecast and predict what a system will do in the future or for various parameter values. Finally, a model can be used to estimate variables that are challenging to precisely evaluate.

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Given : A  = 24 sq feet

A = 0.5 base x height

base = x , height = x+2

A = 0.5 x(x+2)  = 24 sq feet

1) 0.5 x(x+2) = 24 (A)

2) x^2 + 2x - 48 = 0 (D)

To check the rest un-wrap the bracket:

x^2 + (x+2)^2 = 24

x^2 + x^2 + 4 + 4x = 24

2x^2 + 4x - 20 = 0

x^2 + 2x - 10= 0 (NO)

Likewise:

x^2 + (x+2)^2 = 100

x^2 + x^2  +4 + 4x = 100

2x^2 + 4x + 4 = 100

2x^2 + 4x - 96 = 0

3) x^2 + 2x - 48 = 0 (F)

To sum up: that's what apply:

1) 0.5 x(x+2) = 24 (A)

2) x^2 + 2x - 48 = 0 (D)

3) x^2 + 2x - 48 = 0 (F)

Answer:

Let x be the amount of sales Ryan made in that month.

Ryan's commission on the sales would be 5% of x, which is 0.05x.

Adding the commission to his base salary gives his total income for the month, which is $1400 + 0.05x.

Since his paycheck for the month was $1710, we can write the equation:

$1400 + 0.05x = $1710

To solve for x, we can first subtract $1400 from both sides:

0.05x = $310

Then divide both sides by 0.05:

x = $6200

Therefore, Ryan made $6200 in sales that month.

The given expression equivalent to (5−4i)(3−2i)(5−4i)(3−2i) is -231 + 372i.

What is expression ?

In mathematics, an expression is a combination of numbers, variables, and operations that represents a value or a quantity. It can be a simple expression consisting of only one number or variable, or a complex expression consisting of several numbers, variables, and operations.

We can use the distributive property of multiplication to expand the given expression as follows:

(5−4i)(3−2i)(5−4i)(3−2i)

= (5−4i)(5−4i)(3−2i)(3−2i)

= (25 - 40i + 16i²)(9 - 12i + 4i²)

= (25 - 40i - 16)(9 - 12i - 4)

= (-231 + 372i)

Therefore, the given expression equivalent to (5−4i)(3−2i)(5−4i)(3−2i) is -231 + 372i.

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Answer:

974.4

Step-by-step explanation:

Answer:

974.4

Step-by-step explanation:

The tenth place is located the digit to the right of the decimal point, in this case, it will be three. When rounding, if it is four or below you keep it, or if it is five or above, you round up to the nearest ten.

974.362 - 6 is above 5, so you will make the three a four.

974.4

An arithmetic sequence with a common difference d = -3 include the following: D. 43,40,37,34,31.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 40 - 43

Common difference, d = -3

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Answer:

The given complex number is (-2.5 + i4.2).

To express it in exponential form, we need to find the modulus (r) and argument (θ) of the complex number.

The modulus is given by:

|r| = √((-2.5)^2 + (4.2)^2) = √(6.25 + 17.64) = √23.89 ≈ 4.888

The argument is given by:

θ = tan⁻¹(4.2/(-2.5)) = tan⁻¹(-1.68) ≈ -1.03 radians

Therefore, the exponential form of the complex number is:

(-2.5 + i4.2) = 4.888e^(-i1.03)

Therefore, the stamp's estimated value is $21.54 considering that when he first got it, it was only worth $14.50.

A mathematical assertion that two expressions are equivalent is known as an equation. The equal symbol (=) separates the two sides, which are labeled as the left-hand side (LHS) and the right-hand side (RHS). The equation must have identical values on both sides, and it is frequently used to determine an unknown variable's value.

Numerous mathematical processes, such as addition, subtraction, multiplication, division, exponents, logarithms, and more, can be used in equations.

given

a. The formula for the stamp's worth V after t years is as follows:

[tex]V = 14.50(1 + 0.02)^t[/tex]

where t is the period of time since Leroy got the stamp, and 0.02 denotes a 2% annual increase in value.

b. We enter t = 18 into the equation to estimate the stamp's value after 18 years:

[tex]V = 14.50(1 + 0.02)^{18[/tex]

[tex]V = 14.50(1.02) (1.02)^{18[/tex]

V = 14.50(1.485) (1.485)

V = 21.54

Therefore, the stamp's estimated value is $21.54 considering that when he first got it, it was only worth $14.50.

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The volume of the figure is 93π

From the question, we have the following parameters that can be used in our computation:

The composite figure

The volume is calculated as

Volume = Cone + Cylinder

Using the above as a guide, we have the following:

Volume = 1/3πr²(H - h) + πr²h

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3π * 3² * (15 - 8) + π * 3² * 8

Evaluate

Volume = 93π

Hence, the volume is 93π

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Answer:

The price of a hot dog is $2.00

Answer:

cos^2 θ/2 = (cos θ + 1)/2.

Step-by-step explanation:

We can use the identity cos 2θ = 2cos^2 θ - 1 to derive an identity for cos^2 θ/2:

cos 2(θ/2) = cos θ

Replacing θ/2 with x:

cos 2x = cos 2(x/2)

Using the double angle formula for cosine:

cos 2x = 2cos^2 x - 1

Substituting θ/2 for x:

cos θ = 2cos^2 (θ/2) - 1

Rearranging this formula, we can solve for cos^2 θ/2:

2cos^2 (θ/2) = cos θ + 1

cos^2 (θ/2) = (cos θ + 1)/2

Therefore, cos^2 θ/2 = (cos θ + 1)/2.

Use the cookies to teach basic fractions, such as one-half or one-third of a cookie.

What is Activity ?

An activity is a task, exercise, or action that is carried out for a specific purpose or goal. It can be an organized event or a spontaneous action that requires some level of effort or engagement from participants.

Begin by gathering the Grade R learners together and introduce the theme "Sharing Treats with Friends" and the concept of sharing with remainders. Explain to the learners that sometimes when we share treats with our friends, we might not have enough for everyone to have an equal amount.

Place the bag of cookies on the plate and ask the learners to estimate how many cookies are in the bag. Write their guesses on the board or chart paper.

Open the bag of cookies and count how many there are. Record the actual number of cookies on the board or chart paper.

Explain that the learners will be sharing the cookies with their friends, but they must make sure that everyone gets the same number of cookies. Divide the class into small groups of three or four learners.

Instruct each group to count the number of cookies in the bag and divide them equally among the members of the group. If there are any remaining cookies, they should be placed on the plate.

Ask the learners to share their results with the class. Some groups may have exactly the same number of cookies, while others may have remainders. Write their results on the board or chart paper.

Discuss with the learners how they can share the remaining cookies equally among their group members. For example, they could break the remaining cookies into smaller pieces or take turns sharing the last cookie.

Give the learners a chance to practice sharing with remainders by repeating the activity with different amounts of cookies and different group sizes.

As a conclusion, ask the learners to reflect on the activity and discuss how it felt to share with their friends. Encourage them to think about why sharing is important and how it can make everyone feel happy.

Optional extension activities:

Have the learners draw pictures or write stories about sharing treats with their friends.

Therefore, Use the cookies to teach basic fractions, such as one-half or one-third of a cookie.

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The standard deviation is 0.67 metric tonnes, and the mean of the sampling distribution of the sample mean impact force is 30 metric tonnes.

What is the mean and standard deviation of the sampling distribution of the sample mean impact force?

a. The following formulas can be used to determine the mean and standard deviation of the sampling distribution of the sample mean impact force:

30 metric tonnes are the population's mean and the sampling distribution's mean.

Standard deviation of the sample distribution is equal to the square root of the population's standard deviation.

= [tex]2 / sqrt(9) (9)[/tex]

= 0.67 tonnes in metric

As a result, the standard deviation is 0.67 metric tonnes, and the mean of the sampling distribution of the sample mean impact force is 30 metric tonnes.

What is the probability of a sample mean impact force being less than 28.7 metric tons?

b. Using the z-score calculation and common normal distribution tables, we can determine the likelihood that the sample mean impact force will be less than 28.7 metric tonnes. The z-score equation is:

(Sample Mean - Population Mean) = Z (standard deviation of sampling distribution)

= (28.7 - 30) / 0.67 = -2

We discover that the probability of a z-score less than -2 is 0.0228 using the usual normal distribution table. Consequently, 0.0228 or 2.28% of the time, the sample mean impact force will be less than 28.7 metric tonnes.

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Pattern blocks are shapes that are used to illustrate math equations. They can be used to represent addition, subtraction, multiplication and division. If five hexagons are stacked on top of each other, then the equation can be read as 5 x 1.

Pattern blocks are a great visual tool for teaching younger children basic multiplication. They can help children understand the concept of multiplication better, as well as help them to remember the equation. Pattern blocks are also a great way to show the relationship between addition and multiplication, since both equations can be represented using the same shapes. By using pattern blocks to illustrate multiplication equations, children can have a more concrete understanding of the concept.

For multiplication, there are two different ways to use pattern blocks. The first way is to use the number of sides on a pattern block to represent the multiplication equation. For example, if two hexagons are used to represent 2 x 2, then the equation can be read as two times two. The second way is to simply stack the pattern blocks in order to represent the equation. For example, if five hexagons are stacked on top of each other, then the equation can be read as 5 x 1.

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The number of touchdowns scored by this professional football team could be: C. 10.

In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the number of points scored by the defense of this professional football team, we would use the following mathematical expression:

Number of points = 24/100 × 242

Number of points = 0.24 × 242

Number of points = 58.08

For the number of touchdowns, we have:

Number of touchdowns = 58.08/6

Number of touchdowns = 9.68 touchdowns.

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Answer:

We can use inequality B to determine the number of sessions Sam needs to conduct. The reason is that he already has $50 and he wants to have enough money, so he needs to earn the remaining amount through tutoring. Thus, we can write the inequality as:

15s + 50 ≥ 125

where s is the number of tutoring sessions he needs to conduct. We can simplify and solve for s as follows:

15s ≥ 75

s ≥ 5

Therefore, Sam needs to conduct at least 5 tutoring sessions to have enough money to buy the video game.