in quadrilateral $abcd$, sides $\overline{ab}$ and $\overline{bc}$ both have length 10, sides $\overline{cd}$ and $\overline{da}$ both have length 17, and the measure of angle $adc$ is $60^\circ$. what is the length of diagonal $\overline{ac}$?

The point (-5,6), which is (0,0), is √61 units away from the origin.

A pair of numbers called coordinates are used to locate a point or a shape in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane. The term "ordinate" refers to a point's separation from the x-axis when scaled with the y-axis. Coords are the collective noun for the abscissa and ordinate. The study of algebraic equations on graphs is known as coordinate geometry. The plotting of points, lines, and curves on an x and y axis is an illustration of coordinate geometry.

Here,

distance=√(y2²-y1²)+(x2²-x1²)

=√(6²-0²)+((-5)²-0²)

=√6²+-5²

=√36+25

=√61

The distance of the point (-5,6) from the origin that is (0,0) is √61 units.

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Answer: The equator is an imaginary line that circles the Earth, dividing it into the Northern Hemisphere and the Southern Hemisphere. It is located at 0 degrees latitude.

If Kyle uses the number 400 to represent a location 400 miles north of the equator, and uses the number -2,000 miles to the south equator. The location of the equator would be represented by the number 0.

Step-by-step explanation:

Yes, the height of the tree is a function of the number of months and it is a linear function x = 5 + n.

In Mathematics, a linear function is described as a function that has either one or two variables without exponents. It is a function that has a graph in a straight line. In case, if the function includes more variables, then the variables should be constant, or it might be the known variables for the function to remain in the same linear function condition.

Height of tree = 5 ft

Grow per month = 1 ft

Assume;

The new height of the tree = x

Number of months = n

x = 5 + 1(n)

x = 5 + n

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Therefore , the solution of the given problem of equation comes out to be x=8 for the given equation.

A mathematical formula between the two statements is employed to denote equality when the equivalent letter (=) is utilized. The equivalence of numerous mathematical variables is demonstrated using algebraic equations, which are statements of fact. For instance, the expression data d + 6 = 12 separates the values document d + 6 or 12 with an equal sign. One can quantify the number of syllables that each sides of each symbol corresponds to. A symbol's meaning usually runs counter to itself.

Here,

Given:

=> 5x/3x =  x+12 /12

=> 5/3 = x/12 + 1

=> 5/3 -1 = x/12

=> 2/3 = x/12

=>2/3*12 = x

=> 24/3 =x

=>8=x

Therefore , the solution of the given problem of equation comes out to be x=8 for the given equation.

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The solution that represents the given equality is x<= 20

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

The inequality that represents the word sentence is:

x/4 <= 5

The solution is x<=20

The quotient is the division of the first number by the second, thus the quotient of x and 4 is given by:

x/4

At most 5 means that the result is of 5 or less, thus, the inequality is:

x/4<=5

Solving it, similarly to an equation:

x <= 4*5

x <= 20

The solution is x<= 20 .

Hence, The solution that represents the given equality is x<= 20

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The expression to represent the total cost of joining the gym using m as a variable is 100 + 30m.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Local gym:

one time fee = $100

Monthly fee = $30

The total cost for m months.

= 100 + 30m

Thus,

The total cost for m months is 100 + 30m.

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The only solution to an equation 2x² + 8x = x² - 16 is z = -4

Consider given equation.

2x² + 8x = x² - 16

Subtract x² from each side of equation.

2x² + 8x - x² = x² - 16 - x²

x² + 8x = -16

Add 16 to each side of equation.

x² + 8x + 16 = -16 + 16

x² + 8x + 16 = 0

We factorize above quadratic equation.

x² + 4x + 4x + 16 = 0

x(x + 4) + 4(x + 4) = 0

(x + 4) (x + 4) = 0

(x + 4)² = 0

x + 4 = 0

x = -4

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The complete question is:

What is the only solution of 2x^2 + 8x = x^2 - 16?

A function is a set of ordered pairs in which for each x value, there is only one y value. A parent function is the simplest form of a function, with the basic form of the equation.

A parent function with an inverse that is also a function must have an equation that is invertible. In other words, the equation must be able to be rearranged so that the y variable is on one side and the x variable is on the other.

For example, let's look at the parent function f(x) = x^2. To find its inverse, we can rearrange the equation to make y the subject: y = x^2. Then, we can take the square root of both sides, giving us x = sqrt(y). This is the equation of the inverse of the parent function, which is also a function. Similarly, the parent function f(x) = ln(x) has an inverse of f-1(x) = e^x. This is also a function, as each x value has only one y value.

Therefore, for a parent function to have an inverse that is a function, the equation must be invertible. This means that the equation must be rearrangeable so that the y variable is on one side and the x variable is on the other.

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Answer:

3

Step-by-step explanation:

y=7x

x+y=24

x+7x=24

8x=24

x=3

mark brainliest

Answer:

X is an element of real numbers

Answer: The range of a function f(x) is the domain of the inverse function f−1(x). The domain of f(x) is the range of f−1(x)

Step-by-step explanation:

The standard deviation of D= M - T is the measure of the spread of the distribution of D. It is calculated by subtracting the mean of D (uD = 8.6) from each observed value of D and then squaring the result.

The variance is then calculated by summing up all of these squared deviations and dividing by the number of observations. The standard deviation is simply the square root of the variance. In this case, the standard deviation of D is 9.5.

This means that the spread of the values of D is 9.5, which means that Morgan and Tim’s scores are spread out over a range of 19 points. This implies that when Morgan and Tim play Hoop Fever, the difference between their scores is usually around 8.6 points, but on occasion can be much higher or lower.

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Quantitative variables offer measurable numerical values that can be added to or subtracted from to produce accurate results. Quantitative discrete variables have a finite or countable number of positive values.

Continuous variables are quantitative and have an endless range of uncountable possible values. Discrete and continuous data are both types of quantitative or numerical information. Measurements are often continuous, while counts are typically discrete. Discrete data are counts that can never be more precisely calculated. Usually, this entails integers.

A family's number of children would serve as an illustration. Individuals are complete, indivisible entities, hence this data is discrete. A family does not contain 1.7 or 2.3 children.

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A triangle with one right angle and two acute angles is called a right-angled triangle.

A right angle is one that is 90 degrees in length. It is the most frequently encountered angle in our daily lives. It can be noticed in room corners, box edges, mobile phone screens, and so on.

A square's and a rectangle's sides always make a right angle with each other. It is represented in radians as /2.

The angle formed by two lines that are perpendicular to each other is called a right angle. A right angle is equal to 90° and is in the shape of the letter "L". In the following figure, ray AB and BC form a right angle ABC.

Thus, a triangle with one right angle and two acute angles is called a right-angled triangle.

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The result of the numeric expression is given as follows:

110.

The arithmetic expression for this problem is defined as follows:

-7+[-5+2 × (3-8×5)] - (-3) (-1) + 9

Outside the brackets, the multiplication takes precedence, hence:

Hence the expression can be simplified as follows:

-1 + [-5+2 × (3-8×5)]

Outside the parenthesis, we have that:

-5 + 2 = -3.

Inside the parenthesis, the multiplication takes precedence, hence:

3 - 8 x 5 = 3 - 40 = -37.

Hence:

-1 + [-5+2 × (3-8×5)] = -1 + [-3 x (-37)]

Applying the multiplication and the addition, the result of the expression is given as follows:

-1 + [-3 x (-37)] = -1 + 111 = 110.

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The percentage of the data that is less than 76.4 will be 50% if scores of an exam follow an approximately bell-shaped distribution with a mean of 76.4 and a standard deviation of 6.1.

To determine by how many standard deviations the raw score is above or below the mean z score used.

z = (x - μ)/σ

x: raw score, σ: standard deviation, μ: mean

For x = 76.4 points:

z = (76.4 - 76.4)/6.1 = 0

Now, the percentage of data is less than 76.4:

P(x < 76.4) = P(z < 0)

We know that the area is equally distributed around the y-axis.

So, P(z<0) = 50 %

Therefore, the percentage of the data is less than 76.4 will be 50%.

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The result will be A'B' ║ C'D' and A'D' ║ B'C'

A rotation is a type of transformation which is a turn. A figure can be turned clockwise or counterclockwise on the coordinate plane. In both transformations, the size and shape of the figure stays exactly the same. A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.

Given that parallelogram ABCD is being rotated by 180°

Since, we know that, rotating a figure gives the figures which is congruent to the original.

Therefore, the results will be,

A'B' ║ C'D'

A'D' ║ B'C'

Also,

AB = A'B'

CD = C'D'

AD = A'D'

BC = B'C'

And,

Corresponding angles are also equal,

Hence, ABCD ≅ A'B'C'D'

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(f+g)(x)=4x2+94x−7Explanation:(f+g)(x)=f(x)+g(x)Substitute f(x)=x4−3:(f+g)(x)=x4−3+g(x)Substutitute g(x)=4x2+2x−4:(f+g)(x)=x4−3+4x2+2x−4Combine like terms:(f+g)(x)=4x2+94x−7

200 decreased by 30% is 140 for the given question.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent sign, "%". For example, 45% can be written as 0.45 or 45/100. Percentage is used to express how large or small one quantity is relative to another quantity. For example, if a student scores 45 out of 50 on a test, the student's score can be expressed as a percentage by dividing 45 by 50 and then multiplying by 100, which equals 90%.

Given data,

200

It decreased the price the price by 30%.

=30/100*200

=0.3*200

=60

= 200-60

=140.

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The stock market crash of 1929 was caused by a combination of factors, including overvaluation of stocks and economic policies that favored the wealthy.

The effects of the crash were widespread and long-lasting, leading to the Great Depression and causing significant economic and social upheaval.

One of the causes of the stock market crash of 1929 was the overvaluation of stocks, where prices were much higher than the underlying value of the companies. Many investors were buying stocks on margin, which means they were borrowing money to buy stocks, this lead to the overvaluation of stocks. Another cause was the economic policies that favored the wealthy, such as the high tariffs on imported goods and the lack of regulations on the stock market, which allowed for speculation and manipulation.

The effects of the stock market crash of 1929 were far-reaching and long-lasting. One of the most significant effects was the Great Depression, which led to high unemployment, widespread poverty, and significant declines in industrial production and economic activity. The crash also led to a decline in consumer confidence, which further slowed economic growth and led to a decline in consumer spending. The crash also led to a decline in the standard of living for many Americans and the loss of savings for many investors.

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Answer:8*11=80

8*10+1*10=90

Step-by-step explanation:

The Ying-yang symbol has rotational symmetry, the flag has radial symmetry, and the three-leg figure has radial symmetry.

The word symmetry refers to the characteristic of figures being the same in terms of proportion and shape.

Bilateral symmetry: This means the two sides of a shape are the same.

Radial symmetry:  This implies that there are symmetric sections if lines are drawn from the radius or center.

Rotational symmetry: This implies two sides are the same but they are rotated.

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The value of n from 8/11(n - 10) = 64 is 98.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

8/11(n - 10) = 64.

Now, to find n first multiply both side by 11/8

8/11 (n- 10) x 11/8 = 64 x 11/8

n- 10 = 88

Now, add 10 both side

n - 10 + 10 = 88 + 10

n = 98

Hence, the value of n is 98.

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The solutions to both simultaneous equations are;

1) x = -2 and y = -13

2) x = -1 and y = -6

Simultaneous equations are defined as two or more algebraic equations that share variables e.g. x and y

1) The simultaneous equations we have are;

7x - y = -1

-7x + 3y = -25

Using elimination method, add both equations to get;

2y = -26

divide both sides by 2 to get;

y = -13

7x - (-13) = -1

7x + 13 = -1

7x = -14

x = -2

2) The simultaneous equations we have are;

7x - y = -1

7x + 3y = -25

Using elimination method, subtract eq 1 from eq 2 to get;

4y = -24

divide both sides by 4 to get;

y = -6

7x - (-6) = -1

7x + 6 = -1

7x = -7

x = -1

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Answer:

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

m = y2 - y1/x2 - x1

m = (-2 - 6)/(8 - 6)

m = -8/2

m = -4

The equation of line with slope 3 and y-intercept 6 is y = 3x + 6.

In the given question, we have to find the equation of the line with slope 3 and y-intercept 6.

The slope-intercept version of the line's equation is what we need. In other words, we want y=mx+b in the form of ax+by=c. M is the slope and b is the y-intercept in the slope-intercept form.

From the given question, m = 3 and c = 6.

Now putting the value in the equation y = mx +c

y = 3x + 6

Hence, the equation of the line with slope 3 and y-intercept 6 is y = 3x + 6.

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Answer: 13 2/9 or 13.23

Step-by-step explanation:

5 2/3 + 7 5/9 = 119/9= 13 2/9

Therefore , the solution of the given problem of percentage comes out to be she spend $39 on the sandals.

A number or figure that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the "%" symbol used to represent it is often employed. No dimensions exist; the % amount is flat. Percentages are essentially fractions because their numerator is 100. A percent symbol (%) should be placed in front of a number to indicate that it is a percentage. For instance, if you answered correctly 75 out of questions in total on a test, you'd get a 75%.

Here,

Given :

Money = $80

Spent 25% on pair of shorts

=> 25/100 * 80 = 20

and

left money = 80 -20 =60

After that she spend 65% on sandals:

=> 65/100 * 60

=> 39

Thus , She spend $39 on the sandals.

Therefore , the solution of the given problem of percentage comes out to be she spend $39 on the sandals.

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Answer: the plant has grown 8x inches

Step-by-step explanation:

The plant has grown 8 times more than it's height last week so,

8 x [tex]x[/tex] = 8x

Answer:

8x

Step-by-step explanation:

Plant inches: x

Amount it has grown: 8 times x (original height)

8 times x

simplify as

8x