If mZATB = 20°, mZBTD = 72°, and mZCTD= 38°, what is mZATC?
A
B
C
D
T

The weight of the kitten will be no less than the weight of the puppy in 1.4 + 1.2x ≥ 2.8 + 0.5x week.

Statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

A puppy weighs 2.8 pounds at birth and gained about 0.5 pounds per week.

A kitten weighs 1.4 pounds at birth and gains about 1.2 pounds per week.

puppy: 2.8 + 0.5x

Kitten: 1.4 + 1.2x

As, kitten is no less than puppy.

Kitten ≥ puppy

1.4 + 1.2x ≥ 2.8 + 0.5x

hence, the weight of the kitten will be no less than the weight of the puppy in 1.4 + 1.2x ≥ 2.8 + 0.5x week.

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If Hilda has $210 worth of $10 and $12 stock shares and the number of $10 shares is 5 more than twice the number of $12 shares, then the number of $10 shares and $12 shares she has is equal to 15 and 5 respectively.

The number of $10 shares and $12 shares can be calculated by forming linear equations.

Consider the number of $10 shares to be x and the number of $12 shares to be y.

x = 2y + 5

10x + 12y = 210

Putting the value x = 2y + 5 in the second equation,

10x + 12y = 210

10 (2y + 5) + 12y = 210

20y + 50 + 12y = 210

32y + 50 = 210

32y = 210 - 50

32y = 160

y = 160 ÷ 32

y = 5

Putting y = 5 in the first equation,

x = 2y + 5

x = 2(5) + 5

x = 10 + 5

x = 15

Hence the number of $10 and $12 shares she has is calculated to be 15 and 5 respectively.

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The age of Micah is 23 years.

Let the age of treasure be x years. So, the present age of Micah will be (x + 7) years.

Now, age of treasure after 6 years = (x + 6) years

Age of Micah after 6 years = (x + 7 + 6) years

Age of Micah = (x + 13) years

As the question mentions, the sum of their ages is 51. So, relating the given information -

(x + 6) + (x + 13) = 51

Performing addition on Left Hand Side of the equation

2x + 19 = 51

Shifting 19 to Right Hand Side of the equation

2x = 51 - 19

Performing subtraction on Right Hand Side of the equation

2x = 32

Shifting 2 to Right Hand Side of the equation and performing division

x = 32 ÷ 2

x = 16 years

So, the present age of Micah = x + 7

Present age of Micah = 16 + 7

Present age of Micah = 23 years

Hence, the present age of Micah is 23 years.

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Tonya's total earnings for a month where her total sales were $80,000 is $5450.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Tonya is paid a salary of $650 a month at her sales job.

She also earns a commission on her sales in this way: 3% on all sales up to $32,000 in a month and 8% on all higher sales.

= 650 + 32000(3%) + (80000 - 32000)(8%)

= 650 + 960 + 3840

= $5450

Thus, Tonya's total earnings for a month where her total sales were $80,000 is $5450.

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Answer:

x < 2

Step-by-step explanation:

3(x- 17) = 3x - 51

9(1-3x) = 9 - 27x

3x - 51 < 9 - 27x

30x - 51 < 9

30x < 60

X < 2

The measure of the angle of their turn on to University Blvd is; 80°

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.

Thus, from the given diagram when we apply the concept of corresponding angles, we can say that;

17x + 15 = 19x + 5

19x - 17x = 15 - 5

2x = 10

x = 5

Thus;

19x + 5 = 19(5) + 5 = 100°

Now, the sum of the angles on a straight line is 180 degrees. Thus, the measure of the angle of their turn on to University Blvd is;

180 - 100 = 80°

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When Abby stacked two cube-shaped blocks, the surface area of the figure if s = 5 inches is 250 inches²

It should be noted that the surface area of a solid object is a measure of the total area that the surface of the object occupies.

Length (l) = 5 in

Width (w) = 5 in

Height (h) = 10 in

Surface area of figure

= 2 (lw+wh+hl)

= 2 (25 + 50 + 50)

= 2(125)

= 250

Therefore, when Abby stacked two cube-shaped blocks, the surface area of the figure if s = 5 inches is 250 inches²

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The x-coordinate of the given equation is x=4.

So,

Given:

Then,

Substitute y=x+3 in equation (2):

(Cross multiply)

Therefore, the x-coordinate of the given equation is x=4.

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Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. (2x - y)⁴ is expanded as 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴.

The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

The total number of terms in the expansion of (x+y)ⁿ are (n+1).

The sum of exponents of x and y is always n.

nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ

The binomial coefficients which are equidistant from the beginning and from the ending are equal.

i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.

Let the function be (2x - y)⁴

By using binomial expansion theorem, we get

(2x - y)⁴ = 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴

(2x - y)⁴ is expanded as 16x⁴ − 32x²y + 24x²y² − 8xy³ + y⁴

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Start off with %70 of 150

0.7 • 150 = 105

To find their total donation amount,

105 • £1 = £105

Then we know the rest of the parents account for the last %30 of the attendees

We can find this out by either,

150 - 105

or

0.3 • 150

Either way we end up with 45

45 • £2 = £90

%70 (105) of the parents donated £105

%30 (45) of the parents donated £90

The parents, in total, donated £195

Answer:

70 feet

Step-by-step explanation:

Depth

200 + 370 - 500 = 70 feet

Applying the Pythagorean Theorem, the value of x to the nearest tenth is: 4.5 units.

If c represents the length of the longest side (hypotenuse) of a right triangle, and a and b are the lengths of the other smaller legs of the right triangle, the Pythagorean Theorem states that:

c = √(a² + b²).

In the diagram given, we have a right triangle that is a part of the given shape. Where:

Hypotenuse = c = x

a = 4 units

b = 5 - 3 = 2 units

Plug in the values

x = √(4² + 2²)

x = √(16 + 4)

x = √20

x ≈ 4.5 units (nearest tenth)

Thus, applying the Pythagorean Theorem, the value of x to the nearest tenth is: 4.5 units.

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  The radical expression of the term y-⁴/³ is ∛y-⁴ or ∛(1/y⁴).

  A radical is a number that is denoted by a root and can be easily identified because before the number is the symbol √, which lets us know that it is a root.

 In this case we have an exponential number since it is raised to a number, radicals can be expressed as powers raised to fractions as follows:

√a = a¹/²

  If our term is raised to -4/3, it can be expressed as:

y-⁴/³ = y-¹/³ y-¹ = 1/y⁴/³ now we apply.

y⁴/³ = ∛y⁴ and apply to the numerator since it is not altered and we have

y-⁴/³ = ∛(1/y⁴)

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The proof that at least three of any 25 days chosen must fall in the same month of the year holds true because; there are twelve months in a year.

This proof required for the statement in the task content follows from the fact that, there are 12 months in a year.

Hence, the proof that at least three of any twenty-five, 25 days chosen must fall in the same month of the year is because, there are 12 months in a years and after choosing two days from each month, amounting to 24 days, the 25th day would fall into a month and hence, such month has 3 days already.

Ultimately, the statement that at least three of any 25 days chosen must fall in the same month of the year holds true because there are 12 months in a year.

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The inequality that describes when x barrels and y crates will cause the elevator to be overloaded is 50x + 140y < 3500.

According to the given question.

Capacity of elevator = 3500 pounds

Average of a single barrel = 50 pounds

capacity of single crate = 120 pounds.

As we know that, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

Therefore, the inequality that describes when x barrels and y crates will cause the elevator to be overloaded is given by

50x + 140y < 3500

Hence, the inequality that describes when x barrels and y crates will cause the elevator to be overloaded is 50x + 140y < 3500.

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The  equation in logarithmic form is log₄(64) = 3

Given the equation is:

64 = 4³

The fundamental logarithmic function has the notation f(x) = log(r) y = log(x), where a > 0. The exponential function a y = x's inverse is represented by this. The common logarithm (log) or natural logarithm (ln) are examples of log functions (log).

Convert the exponential equation to a logarithmic equation using the logarithm base (10)of the right side (0.01) equals the exponent (−2).

A popular method for changing a mathematical equation from one form to another is to transform it from exponential to log form. The exponential form an x = N is translated into the logarithmic form

Log aⁿ= x.The exponent of x, which is equal to N, has the exponential form a to it is converted to the logarithm of a number N to the base of a, which is equal to x.

log₄(64) = 3

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Answer: 2

Step-by-step explanation:

The value of x is 3

Algebraic expressions are expressions made up of variables, terms, factors, constants and coefficients.

They are also made up of mathematical operations like addition, subtraction, multiplication, division, etc

It is important to note that the absolute value of a number takes a positive sign.

It is denoted with the sign ' | | '

Given the expression:

4- | 2x -1 | = -3

First, take the absolute value

4 - 2x + 1 = - 3

collect like terms

2x = -3 - 4 + 1

2x = - 7 + 1

2x = -6

Make 'x' the subject of formula

x = 6/2

x = 3

Thus, the value of x is 3

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For the given square pool the relationship between the line segment will be BD = BC + CD and AB + BC = CD + BC and it will go to proves that AC = BD.

A line section that can connect two places is referred to as a segment.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Given that,

AB = CD

By segment addition postulate

AC = AB + BC

Again by segment addition postulate

BD = BC + CD

In addition property of equality

AB + BC = CD + BC

So,

AC = BD

Hence "BD = BC + CD and AB + BC = CD + BC will proves that AC = BD".

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The angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle

The angle measures are given as:

35° 91° 65° 28°

As a general rule:

Angles that are less than 90 degrees are acute angles

This means that

The angles 35° 65° and 28° are acute angles

Also, we have

Angles that are between 90 degrees and 180 degrees are obtuse angles

This means that

The angle 91° is an obtuse angle

Hence, the angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle

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As a verbal expression, the difference between 10 and 5 is 5

The numbers are given as

10 and 5

The difference between the numbers is calculated as

Difference = 10 - 5

Evaluate the difference

Difference = 5

The above represents the difference in variable

As a verbal expression, the difference between 10 and 5 is 5

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Answer to this question is:

Domain of given function is (-∞,∞),{x|x∈R}

Range of given function is [0,∞),{y|y≥0}

Inverse of given function is -√x+7,√x+7

The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.

Interval Notation:(-∞,∞)

Set-Builder Notation:{x|x∈R}

The set of all valid y values constitutes the range.

Interval Notation:[0,∞)

Set-Builder Notation:{y|y≥0}

For calculation of inverse:

∴Domain of given function is (-∞,∞),{x|x∈R}

Range of given function is [0,∞),{y|y≥0}

Inverse of given function is -√x+7,√x+7

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Answer:

I'm pretty sure it is -3x+7

Answer:
40,000 is 10x greater than 4,000

Step-by-step explanation:
Times 4,000 by 10 and you get 40,000

[tex]a = \pi \: r {}^{2} \\ r {}^{2} = \frac{a}{\pi} \\ r = \sqrt{ \frac{a}{\pi} } [/tex]

Answer: (5,-4)

Step-by-step explanation:

start at zero and go right five because of the adding of five

Then go down 4 because of the minus of zero.

2.4012 is the value of x after solving equation  [tex]e^{x+1}[/tex] = 30 using natural logarithms

We have been asked to solve [tex]e^{x+1}[/tex] = 30 using natural logarithms

⇒   [tex]e^{x+1}[/tex] = 30

⇒ x + 1 = ㏑ 30

⇒ x =  ㏑ 30 - 1

       ≈ 2.4012

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

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Use natural logarithms to solve each equation.

 [tex]e^{x+1}[/tex] = 30