How do you find the legs of a 45-45-90 triangle if you know the length of the hypotenuse?

Answer:

A

Step-by-step explanation:

[tex]\frac{9x+7}{2}[/tex] - [ x - [ [tex]\frac{-2}{7}[/tex] ]] = 36← distribute bracket by - 1

[tex]\frac{9x+7}{2}[/tex] - x +[tex]\frac{x-2}{7}[/tex] = 36

multiply through by 14 ( the LCM of 2 and 7 ) to clear the fractions

7(9x + 7) - 14x + 2(x - 2) = 504 ← distribute parenthesis on left side

63x + 49 - 14x +2x - 4 = 504 ← simplify left side

51x + 45 = 504 ( subtract 45 from both sides )

51x = 459 ( divide both sides by 51 )

x = 9

The measure of angle FCD is 130 degrees.

What is an angle?

In planar geometry, an angle is a shape made up of two rays or lines that share an endpoint. The Latin word "angulus" (which means "corner") is where the word "angle" first arose.

The pair of alternative internal angles that are congruent must first be found. The angles formed on the opposing sides of the transversal EF are known as alternate internal angles since AB and CD are parallel lines. We possess

Angle AGE and angle FCD are alternate interior angles.

Angle AGE measures 130 degrees.

Therefore, we can conclude that angle FCD also measures 130 degrees. So, the measure of angle FCD is 130 degrees.

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Identify the predictor and response variables, then create a scatterplot in Minitab. Characterize the association between the variables as linear or nonlinear and negative, none, or positive.

In exploratory data analysis, the first step is to identify the research question and the two variables of interest. The predictor variable (also known as the explanatory variable or independent variable) is the one that is used to explain or predict the outcome of the response variable (also known as the dependent variable).

After identifying the two variables, one can use software such as Minitab to create a scatterplot of the data. The scatterplot helps to visualize the relationship between the two variables.

To characterize the association between the two variables, we would first determine if the relationship appears to be linear or nonlinear. If the relationship is roughly linear, we would then determine if it is negative (meaning that as one variable increases, the other tends to decrease), positive (meaning that as one variable increases, the other tends to increase), or none (meaning that there is no clear trend).

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The axis of symmetry for y = (x - 1)² - 4 is x = 1.

Given the equation in the question;

y = (x - 1)² - 4

The axis of symmetry for a parabola in standard form is expressed as:

y = a(x - h)² + k is the vertical line passing through the vertex (h, k).

Comparing y = (x - 1)² - 4 to the standard form

We can see that h = 1 and k = -4.

Therefore, the vertex is (1, -4).

Since the axis of symmetry is the vertical line passing through the vertex, the equation of the axis of symmetry is

x = 1.

Therefore, the axis of symmetry is x = 1.

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Answer: Look below:

Step-by-step explanation:

when n = 1:

a1 = 4 x 3^(1-1) = 4 x 3^0 = 4 x 1 = 4

so a1 = 4

similarly working:

a2 = 4 x 3^1 = 12

a3 = 36

a4 = 108

a5 = 324
a6 = 972

Answer:

$51,500 in her savings account.

Step-by-step explanation:

If Pamela has $50,000 in a savings account with an interest rate of 3% per year and the interest is not compounded, then in 1 year she will earn an interest of $50,000 * 0.03 = $1,500.

So, after 1 year, Pamela will have a total of $50,000 + $1,500 = $51,500 in her savings account.

Answer:

the answer is 2) m11 p18.

Step-by-step explanation:

m5 p8 m6 p10 = (m5 m6) (p8 p10) = m11 p80

Therefore, the answer is 2) m11 p18.

Alex will pay 13.8 for her lunch after adding a 15% tip.

We will calculate the amount she paid for her lunch by calculating the tip she paid and adding it to the original price of the lunch(i.e. 12).

[tex]\implies{\sf{15 \% \ of \ 12 \ = \ 12 \times \dfrac{\cancel{15}}{\cancel{100}} }}[/tex]

[tex]\implies{\sf{Tip = \cancel{12} \times \dfrac{3}{\cancel{20}}}}[/tex]

[tex]\implies{\sf{Tip = 3 \times \dfrac{3}{5}}}[/tex]

[tex]\implies{\sf{Tip = \dfrac{9}{5}}}[/tex]

[tex]\implies{\sf{ Tip = 1.8}}[/tex]

Now, add the amount of lunch and tip

[tex]\implies{\bf{ Total \ amount = 12 + 1.8}} \\ \implies{\bf{Total \ amount = 13.8}[/tex]

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Answer:

12

Step-by-step explanation:

to divide by a fraction use the acronym K.C.F or keep change flip to re-arrange the problem.

[tex]\frac{3}{\frac{1}{4} }[/tex] can be re-written as

[tex]\frac{3}{1} *\frac{4}{1}[/tex]

or 3*4 which equals 12

If the cabinets are 34 inches tall, 24 inches deep, and 16 inches wide, the volume of the kitchen cabinets is 16,384 cubic inches.

To find the volume of the rectangular prisms-shaped kitchen cabinets, we need to multiply the three dimensions: height, depth, and width. We are given the following measurements:

Height = 34 inches

Depth = 24 inches

Width = 16 inches

So the formula for the volume is:

Volume = Height x Depth x Width

Substituting the given values, we get:

Volume = 34 x 24 x 16

Volume = 16,384 cubic inches

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Enhance your academic performance by formulating specific, attainable objectives.

This includes identifying a mark for every course, simplifying complex projects into feasible assignments, and devising a timetable that incorporates allocated intervals for homework, test review, and preparation.

Furthermore, seeking assistance from educators or tutors, remaining organized, and practicing sound time management techniques can all augment one's grades.

It must be emphasized, however, that measurable progress is the result of patience and diligence, but with unwavering dedication, anyone can surmount their scholastic aspirations.

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y=-3x + 10 is neither of these.

y − 5 = − 1/3(x + 2) is  perpendicular to p

y = 1/3x is neither of these.

-3x + y = 1 is parallel to p

What are parallel lines?

Parallel lines are coplanar infinite straight lines in geometry that never intersect. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a fixed minimum distance between them and no contact or intersection are said to be parallel.

The line p passes through the points (2,2) and (-1,1).

The slope of the line is m = (-1-2) /(1-2)= 3.

Now compare the y=-3x + 10 with y = mx +c:

m₁ = -3, c=10

The slope of the line y=-3x + 10 is -3.

The product m and m₁ is  3 ×(-3) = -9

y=-3x + 10 is neither of these.

Rewrite the equation y − 5 = − 1/3(x + 2)

y = (− 1/3)x - (2/3) + 5

Now compare they = (− 1/3)x - (2/3) + 5 with y = mx +c:

m₂ = − 1/3, c=10

The product m and m₂ is  3 ×( − 1/3) = -1

Thus y − 5 = − 1/3(x + 2) is perpendicular to p.

Now compare the y=1/3x  with y = mx +c:

m₃ = 1/3, c=0

The slope of the line  y=1/3x + 10 is 1/3.

m₃≠m and mm₃ ≠ -1 , thus  y=1/3x is neither of these.

Rewrite the equation -3x + y = 1

y= 3x +1

Now compare the y= 3x +1 with y = mx +c:

m₄ =3, c=1

Since m₄ = m. thus -3x + y = 1 is parallel to p.

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The order of the given fractions after arranging from least to greatest is 1/5, 2/5, 4/5.

To put the fractions 1/5, 2/5, and 4/5 in order from least to greatest, we can either convert them to decimals or find a common denominator and compare the numerators. Here, we will use the latter method.

First, we need to find a common denominator. The smallest denominator that all three fractions share is 5. So, we can rewrite the fractions as follows:

1/5 = 1/5

2/5 = 2/5

4/5 = 4/5

Now, we can compare the numerators since the denominators are the same. Clearly, 1/5 is the smallest, followed by 2/5, and then 4/5 is the largest.

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The Earth is estimated to be around 4.54 billion years old, while the oldest known rocks found on Earth date back to about 4 billion years ago.

Determining the age of the Earth is a complex process that involves a variety of scientific disciplines. Geologists and other scientists have used a variety of methods to estimate the age of the planet, including radiometric dating, which involves measuring the decay of radioactive isotopes in rocks and other materials.

The age of the oldest known rocks found on Earth has also been determined using radiometric dating techniques. These rocks, which are primarily found in Western Greenland, have been dated to around 3.8 to 4.0 billion years old. The rocks are believed to have formed during the Hadean Eon, a period of Earth's history when the planet was still in its early stages of formation and was subject to intense meteorite bombardment.

It's important to note that the age of the Earth and the age of the oldest known rocks found on its surface are not precise measurements.

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The required domain of the given function f(x) = √x+4 is (D) {x|x ≥ -4} respectively.

The domain of a function is the set of values that we are allowed to enter into our function.

This collection includes the x values for functions like f(x).

The set of values that a function can accept as input is known as its range.

The function outputs this list of values once we enter an x value.

Think about the equation y = f(x), where x and y are the independent and dependent variables.

If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

Considering the function's expression:

f(x) = √x+4

We are aware that the set of input values for which the function is real and defined constitutes the function's domain.

We are aware that for the function to continue to be defined, the value included within the radical expression must be larger than or equal to 0.

x+4 ≥ 0

Take 4 off of both sides.

x+4-4 ≥ 0-4

x ≥ 4

Then, the domain is:
{x|x ≥ -4}

Therefore, the required domain of the given function f(x) = √x+4 is (D) {x|x ≥ -4} respectively.

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Correct question:

The graph of the function f(x)=V x+4 is shown below. The domain of the function?

Rodger's weekly unemployment amount will be $ 705.0225

Given that the total of the quarterly wages of two consecutive quarters and divided by 26.

The weekly unemployment is 65% of that amount.

Rodger made a total of $13,950.80.

Then he made a total of $14,250.10

Step 1:  the total of the quarterly wages of two consecutive quarters.

= $ 13,950.80 + $ 14,250.10

= $28,200.90

Now Divide the total  by 26

 = $28,200.90 / 26

 =  1,084.65

Then,  =   1,084.65 x 65%

 =  1,084.65 x 65/100

=   705.0225

Hence, Rodger's weekly unemployment amount is; $ 705.0225

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Answer:

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To expand and simplify 5(x + 4) 3(x + 2), we can use the distributive property of multiplication over addition which states that a(b + c) = ab + ac.

So, we have:

5(x + 4) 3(x + 2) = (5x + 20)(3x + 6)

Now, we can use the distributive property again to expand this expression:

(5x + 20)(3x + 6) = 5x * 3x + 5x * 6 + 20 * 3x + 20 * 6

= 15x^2 + 90x + 60

Therefore, the answer is 15x^2 + 90x + 60.

I hope this helps!

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Answer:

15

Step-by-step explanation:

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In linear equation, The required days for which Bryan's workout would be the same in either pool is 2 days.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

Here.

Let the number of days of B'ryan workout be x, the total yard he swims be y,

According to the question,

he swims at the rec center pool, will complete a 100-yard warm-up, and then swim laps in a lane that is 39 yards long.

y = 100 + 39x

Jason swims at the indoor pool at his gym, he will complete a 104-yard warmup, plus the main set that consists of 37 yards per lap.

y = 104 + 37x

Equating both the equation,

100 + 39x =  104 + 37x

39x - 37x =  104 - 100

2x = 4

x = 2  days

Thus, the requried days for which Bryan's workout would be the same in either pool is 2 days.

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Answer:

hence the value of w is 12

Step-by-step explanation:

[tex]area = 2 {w}^{2} - 16w \\ by \: the \: question \: if \: area \: is \: equal \: to \: 8w \\ 8w = 2w {}^{2} - 16w \\ 8w + 16w = 2 {w}^{2} \\ 24w = 2 w {}^{2} \\ w = 12[/tex]

The factored form of the trinomial x² - 7x + 12 is (x - 3)(x - 4).The involved trinomial is x² - 7x + 12.

Here is a detailed explanation:

a = 1 (coefficient of x²),

b = -7 (co - efficient of x), and

c = 12 are the trinomial's coefficients and constant (constant term).

Step 2: Find two numbers that multiply to a*c (1*12) and add up to b (-7).

The two numbers are -3 and -4.

Step 3: Modify the middle word as x²- 3x - 4x + 12 using the two integers

Step 4: Factor by grouping. Group the first two terms and the last two terms separately: (x² - 3x) + (-4x + 12).

Step 5: Factor out the greatest common factor (GCF) from each group: x(x - 3) - 4(x - 3).

Step 6: Factor out the common binomial (x - 3) from both terms: (x - 3)(x - 4).

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Answer:

y = (-5/9)x + 30/9

Step-by-step explanation:

To rewrite the equation 5x + 9y = 30 in slope-intercept form, we need to isolate y on one side of the equation.

5x + 9y = 30

Subtract 5x from both sides of the equation to isolate 9y:

5x - 5x + 9y = -5x + 30

9y = -5x + 30

Divide both sides of the equation by 9 to solve for y:

9y/9 = (-5x + 30)/9

y = (-5/9)x + 30/9

The standard error measures the variability of the sample mean from the true population mean. It represents the standard deviation of the sampling distribution of the mean and gives an estimate of how much the sample means will vary from one sample to another.

b. When calculating the standard error of the mean, we assume that the sample was randomly selected from the population, and that the sample size is large enough (usually, n > 30) for the central limit theorem to apply.

c. To reduce the standard error of their estimate of the mean home range size, researchers could increase the sample size, which will decrease the standard error by reducing the variability of the sampling distribution of the mean.

Alternatively, they could improve the precision of their measurements or reduce measurement errors to decrease the standard deviation of the sample, which will also decrease the standard error.

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The value of  51. 2 divided by 6. 4 using long division is 8.0

To find the value of 512 divided by 64, we can use long division. We start by dividing 5 (the first digit of 512) by 6 (the first digit of 64). Since 5 is less than 6, we bring down the next digit (1) to form the new dividend, 51. We then add a decimal point to the quotient and bring down the next digit (2) to form 512.

We repeat the process of dividing 51 by 6, which gives us 8 with a remainder of 3. We write the quotient (8) above the next digit of the dividend (2) and bring down the next digit (0) to form the new dividend, 30. We continue this process until we have brought down all the digits of the dividend.

At the end of the process, we get a quotient of 8.0, which is the value of our original expression, 51.2 divided by 6.4.

Therefore, 512 divided by 64 is equal to 8.0.

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The line(s) or plane(s) that contain point N and appear to fit the description are as follows;

Line perpendicular to QR is NR.

Line parallel to QR is PN.

Line(s) skew to JN.

Plane parallel to plane LMQ is JNP.

All the pairs of angles have been identified below.

The values of x and y are shown below.

In this exercise, all of the various pairs of angles should be identified as follows;

Consecutive interior = ∠3 and ∠5.

Consecutive interior = ∠4 and ∠6.

Alternate interior = ∠3 and ∠6.

Alternate interior = ∠4 and ∠5.

Alternate exterior = ∠1 and ∠8.

Alternate exterior = ∠2 and ∠7.

Corresponding = ∠1 and ∠5.

Corresponding = ∠2 and ∠6.

Corresponding = ∠3 and ∠7.

Corresponding = ∠4 and ∠8.

Next, we would determine the values of x and y as follows;

x + 35 = 180 (sum of angles on a line)

x = 180 - 35

x = 145°

y = 35 (corresponding angles theorem).

y + 48 = 180

y = 180 - 48

y = 132°

5x - 17 = 48 (vertical angles theorem).

5x = 65

x = 13°.

2x + 58 = 180 (sum of angles on a line)

2x = 238

x = 119°.

2y = 58 (corresponding angles theorem).

y = 29°.

5y - 21 = (180 - 116)

5y = 21 + 64

y = 85/5

y = 17

6x + 32 = 116

6x = 116 - 32

x = 84/6

x = 14

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A good prediction for the number of times a 5 will be rolled out of 50 rolls of a 6-sided number cube is 8 times.

Assuming the number cube is fair and each outcome has an equal probability of occurring, we can use the concept of probability to make a prediction for the number of times a 5 will be rolled.

Since there are six possible outcomes, each with a probability of 1/6, the expected frequency of rolling a 5 in one roll is:

1/6 x 50 = 8.33

This means that if the number cube is rolled 50 times, we would expect to see a 5 appear approximately 8.33 times. However, since we cannot roll a fraction of a time, we need to round this number to the nearest whole number.

Rounding 8.33 to the nearest whole number, we get:

8

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Complete question is:

A 6-sided number cube with sides labeled 1,2,3,4,5, and 6 is rolled 50 times. What is a good prediction for the number of times a 5 will be rolled?

Answer:22x121=2662

Step-by-step explanation:

The multiplicand is 22, the multiplier is 121 and the product is 2662.

The equation represents a linear function.

What is quadratic equation?

A quadratic equation is a polynomial equation of degree two which can be written in the form: ax² + bx + c = 0, where x is the variable and a, b, and c are constants with 'a' not equal to 0. The term 'quadratic' comes from the Latin word 'quadratus', which means 'square'.

The equation given in the image is a quadratic equation in standard form, which means it is written in the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

To determine which statement is true about this equation, we need to analyze its discriminant, which is given by the expression b^2 - 4ac. The discriminant tells us about the nature of the solutions of the quadratic equation.

If the discriminant is positive, then the equation has two distinct real roots.

If the discriminant is zero, then the equation has one real root (also known as a double root).

If the discriminant is negative, then the equation has two complex roots (conjugate pairs).

In the given equation, a = 3, b = -4, and c = 1. Substituting these values into the discriminant formula, we get:

b^2 - 4ac = (-4)^2 - 4(3)(1) = 16 - 12 = 4

Since the discriminant is positive, we know that the quadratic equation has two distinct real roots. Therefore, statement (A) is true.

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