The sum of Joy's age and her brother's age is $24 . Her brother's age is $3 years older than twice Joy's age.

What is the difference, in years, between Joy's age and her brother's age?

A possible base and height dimension for the parallelogram is 20 units and 5 units.

To find the possible base and height dimension, you can use the information provided in the problem: the area of the parallelogram is 100 square units and the perimeter is between 40 and 60 units. Since the area of a parallelogram is base times height, you know that one dimension of the base must be 20 units and the other dimension of the height must be 5 units. Then the perimeter will be 50 units 2*(20+5) which is within the range given in the problem. Keep in mind that there could be other possible solutions, but this is one of them.

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Please have a look at the diagrams of a quadrilateral and a trapezoid in your textbook.

Ans--- A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Answer:

The rate of change, or slope, between two points on a graph is the change in the y-coordinate (rise) divided by the change in the x-coordinate (run). The formula for the slope between two points (x1, y1) and (x2, y2) is:

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

Given the points (-4,-2) and (1,-7) we can plug in the coordinates into the formula:

slope = (-7 - (-2)) / (1 - (-4)) = (-5) / (5) = -1

So the rate of change, or slope, between the two points (-4,-2) and (1,-7) is -1.

This means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1.

Answer:

Step-by-step explanation:

it’s 3-1

The quadratic equation's answer is found by completing the square: x= 7/4, x = -1.

x ax2+bx+c=0, a quadratic polynomial in a single variable, is a quadratic equation. a 0. Since this polynomial is of second order, the Fundamental Theorem of Algebra guarantees that there is at least one solution. There are both straightforward and complex solutions. A quadratic equation is a quadratic equation. This suggests that it contains at least one word that has to be squared. One of the commonly used answers to quadratic equations is "ax2 + bx + c = 0." where the unknown variable "X" is represented by the numerical coefficients or constants a, b, and c.

given

4x^2 -3x-7 =0

4x^2 - 7x + 4x -7 = 0

x(4x-7) +1(4x-7) = 0

(4x-7 )(x+1) = 0

The quadratic equation's answer is found by completing the square: x= 7/4, x = -1.

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Elena was running at 2.5 miles per hour

Form the question it can be deduced that the the running track is 1/4 mile long . this is equivalent to 0.25 mile.

A lap of a mile is equivalent to a quarter of a mile which is same as 1/4 mile or 0.25 mile

Hence we can solve the number of miles per hour using the formula

= number of miles covered by Elena / time take to complete the mileage

= 0.25 miles / 1/10

= 2.5 miles per hour

Hence Elena was running at 2.5 miles per hour

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The statement that indicates that the triangles are congruent is option C. ΔDCE ≅ ΔDQR

When two or more triangles have equal length of sides or measure of internal angles, then they are said to be congruent. Therefore on comparing their corresponding sides and corresponding measure of internal angles, there are equal.

Comparing the corresponding angles of the given triangles in the question, we have;

i. m<C ≅ m<Q                  (alternate angle property)

ii. m<E ≅ m<R                  (alternate angle property)

iii. m<D = m<D                 (vertically opposite angle property)

Thus, it can be deduced that the two triangles are congruent.

i.e. ΔDCE ≅ ΔDQR

Therefore, the statement that indicates that the triangles are congruent is that of option C. ΔDCE ≅ ΔDQR

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Half of the data points, or a straight line, are on either side of a line of best fit.

A line is a geometric object that is defined as being straight, thin, one-dimensional, zero width, and extending in both directions to infinity. An uncurved line is simply what a straight line is. We can also state that every line that connects any two specific places on the same plane will be distinct.

A student who doesn't study for the test is expected to receive a test score of 38, according to this line of best fit.

It is equivalent to doing no homework to not study for an exam (doing homework is considered studying).

Half of the data points, or a straight line, are on either side of a line of best fit.

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Answer: The domain of a graph is the set of all the possible input values (x-values) for which the function is defined. The domain is the set of all x-values that can be plugged into the function without resulting in an error or undefined value.

Without a function to graph, it is impossible to determine the domain. The options you provided refers to different inequalities that could represent the domain but without a function it is impossible to know which one is correct.

Step-by-step explanation:

Answer:  2 ≤ x ≤ 5

Step-by-step explanation:

i just took the quiz

Answer:

Step-by-step explanation:

The lowest number that is a multiple of two or more numbers is known as the least common multiple (LCM). To calculate the LCM of a, b, and c, we must first determine the greatest power of each prime number that appears in any of the integers.

Assume a = 23x3, b = 2x3x5, and c = 32x5.

As a result, the LCM of a, b, and c is 23x32x5.

Given that the LCM [a,b,c] = 2x32x5,

So, n= 2x3²x5

n=180

3x - y = -3 The substitution-based system's answer is (5, 12)

We have been given that

3x - y = 3 and

y = 2x + 2

Substitute y = 2x + 2 in the first equation, we get,

3x - (2x + 2) = 3

3x - 2x - 2 = 3

x - 2 = 3

Then we get,

x = 5

y = 2x + 2

= 2(5) + 2

= 12

Hence, the solution is (5, 12).

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The reasons why we factor all the polynomials before multiplying rational expressions is;

To reduce a rational expression to its simplest form.

To ensure that the denominators are not 0.

A polynomial expression is defined as an expression having one or more terms in which the variable has non-negative integer powers.

We know that rational expressions usually have a polynomial numerator and a polynomial denominator. Now, in many events, these polynomials can be factored. Therefore, we can conclude that to reduce a rational expression to its simplest form, we have to factor the numerator and denominator, and cancel out any common factors between them. That's the reason why factoring is an important part of simplifying a rational expression.

Finally, we have to mindful about the values the final denominator of a rational expression can take, because such values must not be 0.

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The set of all real numbers constitutes the range and all positive real numbers constitute the domain of a logarithmic function

All real numbers make up the domain, and all positive real numbers make up the range of an exponential function.

The set of all real numbers constitutes the range of a logarithmic function.

As a result, x > 0 (or) (0, ∞) is the domain of the log function y = log x. The set of all real numbers is the range of any log function belonging to R.

All real numbers make up the domain, and all positive real numbers, or (0, ∞) in interval notation, make up the range.

An exponential function is a mathematical function of the following form: f(x) = ax. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828

A logarithm is a measurement of the amount that a fixed number (the base) must be increased in order to create a particular number.

Basically,

if y=ax

So, logₐ(y) = x

The base of the logarithm in this instance is a. The following two bases are frequently employed: base-10 and Base-e

'e' is a mathematical constant having a value of around 2.718.

If the base is "e," we use a specific expression: ln(x)

Fundamentally,

ln(x)=loge(x)  

Here, e is the base.

Base-10 will be used if no base is provided, as in the formula

log(x)=log10(x)

Here 10 is the base

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values. The y values are those.

The domain of a function is the set of all input values (sometimes referred to as independent variables) for which the function is defined and produces an acceptable result (also called dependent variable). Most often, the domain is represented by a collection of numbers or a range of numbers.

The term "range" refers to the entire set of potential output values (dependent variable) that a function can produce for any set of valid input values inside its domain. Usually, a group of numbers or a range of numbers is used to represent the range.

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The equation that can be used to find the total area of the figure is 168 = (18)(3x) + (6)(x).

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The given figure can be divided into two segments.

A rectangle having the dimensions of length = 12 and width = 3x, and second rectangle with the dimensions of length = (18 - 12) = 6 and width = x.

The area of the figure is:

A = Area of segment 1 + area of segment 2

168 = (18)(3x) + (6)(x)

Hence, the equation that can be used to find the total area of the figure is 168 = (18)(3x) + (6)(x).

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Answer:

201=21 x X + 16 x 3X

Step-by-step explanation:

24% for incomes over $89,075 ($178,150); 22% for incomes over $41,775 ($83,550); and 12% for incomes over $10,275 ($20,550).

A branch of mathematics called probability theory determines the likelihood that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain occurrence relative to all possible outcomes.

given

When married couples file jointly, the tax rate is 32% for incomes over $170,050 ($340,100);

24% for incomes over $89,075 ($178,150); 22% for incomes over $41,775 ($83,550); and 12% for incomes over $10,275 ($20,550).

Salary, earnings, tips, bonuses, and employer-provided perks are typical examples of taxable income.

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As per the concept of simple interest the amount earned after 8 years is $3,472.00

Here we have given that Lillian deposits $1,600 in an account at Excellence Bank.

While we looking into the given question, we have identified the values of the following,

Amount invested = $1,600

Time period = 18 years

Interest rate = 6.5%

Then the total amount is calculated as,

Here we have to converting R percent to r a decimal

=> r = R/100 = 6.5%/100 = 0.065 per year.

Now, we have to solve our equation

=> A = 1600(1 + (0.065 × 18)) = 3472

=> A = $3,472.00

Therefore, the total amount accrued, principal plus interest, from simple interest on a principal of $1,600.00 at a rate of 6.5% per year for 18 years is $3,472.00.

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Let v is the rate of cyclist 1 and v + 6 is the rate of cyclist 2.

Equation: d = (v + v + 6) * t

Solving for v and v+6

d = (v + v + 6) * t

120 = (2v + 6)3

40 = 2v +6

2v=34

v = 17 km/h ………… is the rate of cyclist 1

v + 27 = 23 km/h…….. is the rate of cyclist 2

Answer: 17 and 23.

Explanation: Let the rate of the slower cyclist be x.

After 3 hours, the total distance between the both will be of:

3x (distance from the slower cyclist from the starting point) + 3(x + 6) (distance from the faster cyclist from the starting point) = 120.

Solving by x, 17 = x. Since x is the rate of the slowest cyclist, x + 6 = 23, is was the rate of the faster cyclist.

The solution of the equation  [tex]\frac{z}{z+15}[/tex]= [tex]\frac{4}{9}[/tex]  is 12.

 [tex]\frac{z}{z+15}[/tex]= [tex]\frac{4}{9}[/tex]

9z=4z+60 (cross multiplication)

9z-4z=60

5z=60

z=60/5

z=12

quadratic equation:

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is an unknown variable. It is called a quadratic equation because the highest power of x is 2. Quadratic equations can be solved by factoring, completing the square, or using the quadratic formula. The solutions to a quadratic equation are the values of x where the equation equals to zero.

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Answer:

x = 11

Step-by-step explanation:

2(2x-15)=2x-8

4x - 30 = 2x - 8

2x - 30 = - 8

2x = 22

x = 11

Let's check

2(2(11)-15) = 2(11)-8

2( 22 - 15) = 22 - 8

2(7) = 14

14 = 14

So, x = 11 is the correct answer.

The wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Given that the height of the tower is 168 foot, and the angle is 30 degrees.

The wire that connects the top of the tower to the point of the ground is thus the hypotenuse.

To find the hypotenuse, we use the trigonometric ratios as follows:

Sin 30 = 168 / Hypotenuse

0.5 = 168 / Hypotenuse

Hypotenuse = (168)(0.5)

Hypotenuse = 84.

Hence, the wire that connects the top of the tower to the point of the ground is thus the hypotenuse and its length is 84 foot.

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The factored form of the given equation as calculated from the data is found to be as 3x( x -2 )  , and on further solving we get the roots of the equation to be as x- 0 and 2.

The expression given is 3x²- 6x, in order to get it's factored form we will factorize this expression ,

Let ,  3x²- 6x =0

therefore,

3x( x -2 ) = 0

which means,

3x = 0 and x - 2 = 0

hence ,

x = 0 and x = 2.

A statement that supports the equality of two expressions and is equated using the equals sign "=" is called as an equation.

For instance,  3x²- 6x = 13 , here  3x²- 6x and 13 are expressions which are separated by the "=" is the sign that connects these two expressions.

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Stool samples for testing for parasitic infections should ideally be collected within a few days of hospitalization.

The exact time frame may vary depending on the specific parasitic infection being tested for and the laboratory performing the test.

It is best to consult with the laboratory or a healthcare professional for guidance on when to collect and submit the sample for testing.

Stool samples should be collected within a few days of hospitalization to test for parasitic infections. Exact time frames may vary; consult a healthcare professional or laboratory for guidance.

It's important to note that some parasitic infections may have a longer incubation period before they can be detected in a stool sample, so collecting the sample within a few days of hospitalization may not always be sufficient. Additionally, some parasitic infections may not produce symptoms right away, making it even more difficult to determine the appropriate time to collect a stool sample.

In these cases, it may be necessary to collect multiple samples over a period of time in order to increase the chances of detecting the infection.

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Answer:

  A. Discrete

Step-by-step explanation:

You want to know the sort of domain (discrete, continuous) of the equation 2x +3y = 24, or y = -2/3x +8, when x and y are numbers of hot dogs and hamburgers, respectively.

A set is described as "discrete" if it consist of particular values, and those only. Here, the numbers describing the numbers of hot dogs and hamburgers will be whole numbers. Fractions and irrational numbers are not allowed. (You cannot purchase √2 hot dogs, for example.)

That means the domain of this equation is "discrete."

If fractions and irrational numbers are allowed in a given expression or formula, the domain is "continuous." Lengths of string, for example, tend to be values that do not fall into a specific set of values. ("Nominal" length may be discrete (50', 100', and so on), but actual length likely will not be, especially when one considers that it stretches.)

__

Additional comment

Quantum physics seems to be telling us that many things in the universe are quantized (discrete) at the lowest levels. In the practical world, the effect of numerous quantized values added together has the effect of making any particular measurement appear to be continuous.

For the measures of these angles to be integral, (n-2) times 180 must be divisible by n.

An n-sided regular polygon has interior angles that measure (n-2) times 180 degrees divided by n. This means that n must be a divisor of (n-2) times 180, or that n must be a divisor of 180. The only positive integers that divide 180 are 1, 2, 3, 4, 5, 6, 9, 10, 15, 18, 30, and 180.

So the only values of n for which an n-sided regular polygon has interior angles with integral measures are 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, and 20.

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Answer:   -36

Step-by-step explanation:

so when a variable and a number are together you multiply, 8 times c, c is found equal to -6, so 8 x -6 would be -48 so then its -48 minus d d is found equal to -12 so -48 minus -12 would equal -36               hope this helped ^^

The medication would you choose to take will be mean value of relieving headaches of 65% and the standard error of the mean was 2%.

The huge standard error of the mean means that A will undoubtedly be much riskier. A could very likely relieve your headache, but it could also very unlike to do so because of this large standard error of the mean. Therefore, in an extremely urgent situation, option B would likely be the safer choice because you're more likely to be very close to that 65 percent rate, which is fairly reliable.

There are various mean types in mathematics, particularly in statistics. Each mean helps to summarize a certain set of data, frequently to help determine the overall significance of a specific data set.

The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error. It reveals how much the sample mean would change if a study were to be repeated with fresh samples drawn from a single population.

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Option C) For the given input the value of f(3) for the function is 25.

Each element of X receives precisely one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

The whole range of independent variable values is the domain of a function. This concept may 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.

A function's range can be used to describe one of two related ideas: The function's codomain a representation of the action A binary relation f between two sets X and Y is a function if there is precisely one y in Y such that f connects x to y for every x in X.

The function is

f(x) = (x +2)²

so f(3) = (3 + 2)² = 5² = 25

for x = 6

f(x) = f(6) = (6+ 2)² = 8² = 64

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Function f is represented by f(x)=5(x+11), the value of x such that fix)-90 is true; x = -29.

The function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the another variable).

A function is described as a relationship between a group of inputs and one output each. A function is, to put it simply, a connection between inputs in which each input is connected to exactly one output.

f(x) = 5(x + 11)

or, f(x) = 5x + 55

now, putting the value of f(x) = -90

-90 = 5x + 55

or, 5x = - 145

or, x = - 29

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A) Evaluate f(0)

f(0) = 3*0 - 6 = 0 - 6 = -6

What does a math function mean?

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

B) Evaluate f(2)

f(2) = 3*2 - 6 = 6 - 6 = 0

C) Evaluate f(-2)

f(-2) = 3*(-2) - 6 = -6 - 6 = -12

D) Evaluate f(1)

f(1) = 3*1 - 6 = 3 - 6 = -3

E) Evaluate f(-4)

f(-4) = 3*(-4) - 6 = -12 - 6 = -18

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There is only one equilateral triangle possible for the given side length.

What is equilateral triangles?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

Given: The side length of triangle = 7 centimeters.

We know that a equilateral triangle is a triangle in which all three sides and internal angles are equal.  

So if it is given that the side length of triangle is 7 cm, then side-lengths of all the side of the triangle will be 7 cm.

Suppose there is another equilateral triangle having same side lengths, then that triangle will be congruent to the given triangle by SSS congruency criteria.

Hence, there is only one equilateral triangle possible for the given side length.

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