the congruent sides of an isosceles triangle are each $5$ cm long, and the perimeter is $17$ cm. in centimeters, what is the length of the base?

Answer:

f(y - 3) = y - 2

Step-by-step explanation:

to find f(y - 3) , substitute x = y - 3 into f(x) , that is

f(y - 3) = y - 3 + 1 = y - 2

By using trigonometric relations, we can see that the angle x on the right triangle is:

x = 62.96°

On the image, we can see a right triangle, and we want to find the value of x, which is the measure of an angle on the right triangle.

On the given triangle we can see that the hypotenuse measures 77 units, and the adjacent cathetus to the angle has a measure of 35.

Then we can use the trigonometric relation:

cos(x) = (adjacent cathetus)/(hypotenuse)

Replacing the values that we know:

cos(x) = 35/77

Now we can apply the inverse cosine function in both sides:

Acos(cos(x)) = Acos(35/77)

x = Acos(35/77) = 62.96°

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Note that after the expression 2x³-5x²-19x+42, has been factorized, we have (x−2)(x+3)(2x−7).

Factorization or factoring in mathematics is the process of expressing a number or any mathematical object as a product of numerous factors, generally smaller or simpler objects of the same sort.

The polynomial 2x³-5x²-19x+42 can be factorized by using the rational root test. To apply this test first we need to find at least one rational zero.

In this case one rational zero is x=2.

This means that we can divide polynomial 2x³-5x²-19x+42 by x−2 (the factor theorem)

That is:

2x³-5x²-19x+42/ x-2

= 2x² - x - 21, this means that

2x³-5x²-19x+42 =  (2x² - x - 21) * (x-2)

From the above, our constants are given as:

a = 2, b = -1 and c = 21

Multiply the constant terms by the leading coefficient.

a *x = -42

Find out two number that multiply to a*c = -42 and add b = -1

Next we identify all pairs of numbers with a product of -42. They are:

Next we find all factor pair that sum up to b = -1. It is given as 6 +-7 which is identical to item 8 above.

Next, replace the middle term -1x with 6x-7x to get:

(2x²  −x−21) * (x-2) =(2x²  +6x−7x−21) * (x-2)

If we thus apply factoring by grouping, and factor 2x out of the first group and -7 out of the second group, we have: (2x-7) (x+3) (x-2).

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Full Question:

Factorise 2x³-5x²-19x+42

Answer: We can find the inequalities. One inequality has a line with y-intercept 2 and slope -1. The inequality is y >= -x + 2.

Step-by-step explanation:

The definition of sequence is an ordered list of objects.

The term ordered list is known as the way to uses numbers or some sort of notation that indicates a series of items.

in math the term sequence is defined as an arrangement of numbers in a particular order.

Where as which is also known as a series is defined as the sum of the elements of a sequence.

in the sequence the listed of objects are an arrangement of two or more things in a successive order and the successive order of two or more things which means that they are in chronological sequence.

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The probability that the student really knew the correct answer is 0.9375, or 93.75%.

(i) If the probability that the student knows the answer to the question is 0.75 and the probability that the student guesses is 0.25, the probability that the question is answered correctly is:

P(correct) = P(knowing the answer) * P(guessing correctly given knowing the answer) + P(guessing) * P(guessing correctly given guessing)

In this case, the probability of guessing correctly given knowing the answer is 1, since the student knows the correct answer. And the probability of guessing correctly given guessing is 0.25.

Therefore, P(correct) = 0.75 * 1 + 0.25 * 0.25 = 0.75 + 0.0625 = 0.8125

(ii) If it is answered correctly, what is the probability that the student really knew the correct answer?

This is called conditional probability and is represented as P(knowing the answer | correct). To calculate it we use Bayes' theorem,

P(knowing the answer | correct) = P(correct | knowing the answer) * P(knowing the answer) / P(correct)

In this case, P(correct | knowing the answer) = 1, P(knowing the answer) = 0.75 and P(correct) = 0.8125

Therefore, P(knowing the answer | correct) = 1 * 0.75 / 0.8125 = 0.9375

So the probability that the student really knew the correct answer is 0.9375, or 93.75%.

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Answer:

Here are the answers in fraction form.

[tex]x > \frac{1.7}{0.7}[/tex]

[tex]x < - \frac{11.7}{0.7}[/tex]

Here are the answers in decimal form.

[tex]x > 2.43[/tex]

[tex]x < -16.71[/tex]

Step-by-step explanation:

We will have 2 answers.

Answer 1

[tex]0.7x+5 > 6.7[/tex]

Move all terms not containing [tex]x[/tex] to the right side of the inequality.

[tex]0.7x > 6.7-5\\0.7x > 1.7[/tex]

Divide both sides by [tex]0.7[/tex].

[tex]\frac{0.7x}{0.7} > \frac{1.7}{0.7}\\[/tex]

[tex]x > \frac{1.7}{0.7}[/tex]

[tex]x > 2.43[/tex]

Answer 2

[tex]-0.7x-5 > 6.7[/tex]

Move all terms not containing [tex]x[/tex] to the right side of the inequality.

[tex]-0.7x > 6.7+5\\-0.7x > 11.7[/tex]

Divide both sides by [tex]-0.7[/tex].

When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

[tex]\frac{-0.7x}{-0.7} < \frac{11.7}{-0.7}[/tex]

[tex]x < \frac{11.7}{-0.7}[/tex]

[tex]x < -16.71[/tex]

Simplest radical form means the radical form of a number or algebraic expression in simplest terms.

The simplest radical form of the square root of 16 is √16. Generally, the radical form of the square root of a number can be written, if we know the prime factorization of a number. Thus, the prime factorization of 16 is 2×2×2×2.

Square root of 16 is +4 or -4. Since -4 is not a natural number, the square root can be described as an integer.

16 (sixteen) is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4.

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A quadratic equation has two roots.

A function can have two roots. A root of a function is a point at which the function's value is equal to zero. This means that the function crosses the x-axis, and two roots means that it crosses the x-axis twice. Depending on the type of function, these two points can be either real or complex numbers. For example, the quadratic equation x2-3x+2 has two real roots, namely x = 1 and x = 2.A quadratic polynomial may have one, two, or zero roots. Quadratic polynomials have a degree of two.

Let's consider a quadratic polynomial

[tex]ax^2+bx+c=0[/tex]

where [tex]a\neq 0[/tex]

The quadratic polynomial is of degree two. Therefore, a quadratic equation has no more than two roots.

There is a formula to find the roots of quadratic polynomials, which is called the quadratic formula.

[tex]x=\frac{-b\frac{+}{-}\sqrt{b^2-4ac} }{2a}[/tex]

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The best units for Kiley to report her findings are millimeters or centimeters.

Kiley is conducting an experiment to measure the change in length of a blade of grass over time. To accurately record her findings, she must choose the right units of measurement.

The best units for Kiley to use in her experiment would be millimeters or centimeters, as they provide a precise measurement of the length of the blade.

Using these units, Kiley can accurately measure and report any changes in the length of the blade of grass from day to day.

By keeping a consistent unit of measurement, she'll be able to accurately track the changes in the blade of grass' length over time.

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Answer:

tenth

Step-by-step explanation:

b. Total Sample = 300 college students

The question is asking how many people were in the sample of 300 college students that were asked if they were interested in playing video games. The answer is option B: 300.

To answer this question, we must first understand the context of the question. It is asking about the number of English-speaking people on the planet who want to play a new kind of online video game. To answer this, 300 college students were asked if they were interested in playing video games. Of those 300 students, 100 said yes, and 20 of those students preferred this new game to an existing game that is widely used. Therefore, the sample size was 300.

The sample size is 300 college students. From the 300 college students, 100 said yes to playing video games. Of these 100, 20 preferred the new game to an existing game. Therefore, the sample size is 300 college students.

Total Sample = 300

No. of Yes = 100

No. of Prefers new game = 20

So, Total Sample = 300 college students

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Answer:

$445.20

Step-by-step explanation:

Discounted price:

$530 × (100% - 40%) = $318

Markup:

$318 × (100% + 40%) = $445.20

So, the price of the tablet computer after the markup is $445.20

The age of my sister and her three children in 4 years will be 70 years

The age is added in 6 years to get 90 years> the addition is done as follows

Sister + 6 + Child1 + 6 + Child2 + 6 + Child3 + 6 + Child4 + 6 = 90 years

Sister + Child1 + Child2 + Child3 + Child4 + 6 + 6 + 6 + 6 + 6 = 90

Sister + Child1 + Child2 + Child3 + Child4 + 6 * 5 = 90

Sister + Child1 + Child2 + Child3 + Child4 = 90 - 30

Sister + Child1 + Child2 + Child3 + Child4 = 60

In 4 years the age will be

Sister + Child1 + Child2 + Child3 + Child4 + 4 * 5 = 90

Sister + Child1 + Child2 + Child3 + Child4 = 90 - 20

Sister + Child1 + Child2 + Child3 + Child4 = 70

in 4 years the ages will be 70 years

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Answer:

b. |−37| + |−28|

Step-by-step explanation:

The absolute value of a number is its distance from 0 on the number line. Since the divers are below sea level, both 37 and 28 will be negative numbers.

To find the distance between the two divers, we need to add the absolute values of their depths.

The first diver is at -37 ft and the second diver is at -28 ft, so we can calculate the distance between them as |-37| + |-28| = 37 + 28 = 65 ft

Answer:

Step-by-step explanation:

x=#of minutes

y= cost

Laceys equation: y=3x+398

Sebastions equation: y=x+466              

intersection (34, 500)

itll take 34 minutes and cost $500

The exponential function y = 0.5(34)t has the form y = a*b^t, where a is the initial amount and b is the rate of decay. In this case, a = 0.5 and b = 34.

To find the rate of decay as a percent, we need to find the decimal form of b and then convert it to a percent. To find the decimal form, we need to take the square root of b = 34.

√34 = 5.83

To convert this decimal to a percent, we need to multiply it by 100.

5.83 * 100 = 583%

Therefore, the rate of decay is 583%.

Now we can use these values to evaluate the function when t = 3.

y = 0.5(34)^3

y = 0.5(363)

y = 181.5

So when t = 3, the value of y is 181.5, rounded to the nearest tenth.

Note that the initial amount a = 0.5, the rate of decay r = 583% and the function at t = 3 is 181.5.

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Answer:

Step-by-step explanation:

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the polynomial is 4w - 1. The highest power of the variable w is 1, so the degree of the polynomial is 1.Therefore, the correct answer is A) 1

The weighted average of the numbers −1 and 1 is 0.3. Hence option A is the correct option.

What is the weighted average?

A weighted mean is similar to an average. Rather than contributing equally to the final mean, some data points contribute more "weight" than others. If all of the weights are equal, the weighted mean equals the arithmetic mean (the familiar "average").

Given numbers are  -1 and 1.

The first number is -1 and the second number is 1.

Two third of the first number is

= -1 × (2/3)

= -2/3

The one third of second number is

= 1 × (1/3)

= 1/3

The average weight is the sum of two third of the first number and one-third of the second number is -2/3 + 1/3 = -1/3 = -0.33.

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Answer:

y = -[tex]\frac{9}{7}[/tex] + [tex]\frac{8}{7}[/tex]

Step-by-step explanation:

Answer:

y = [tex]-\frac{9}{7} x +\frac{8}{7}[/tex]

Step-by-step explanation:

To turn the coordinates into y=mx+b, you first need the slope, m.

To find that you would use [tex]m = \frac{y2 - y1}{x2 - x1}[/tex],

Let (-3, 5) = (x2, y2)

and (4, -4) = (x1, y1)

[tex]m = \frac{5 - (-4)}{-3 -4}[/tex]

or, [tex]m = -\frac{9}{7}[/tex].

Now you have the slope, you will need the y-intercept, b, which you will need to use the point-slope formula (y - y2) = m(x - x2) and plug one of the points and slope into the equation (It does not matter which point you use).

So, (y - 5) = [tex]-\frac{9}{7}[/tex](x - (-3) or (y - 5) = [tex]-\frac{9}{7}[/tex](x + 3)

Then you would distribute the -9/7 to the (x + 3),

which turns into

(y - 5) = [tex]-\frac{9}{7}x[/tex] + ([tex]-\frac{9}{7}[/tex])3

y - 5 = [tex]-\frac{9}{7} x -\frac{27}{7}[/tex]

After that , add 5 from both sides,

y - 5 = [tex]-\frac{9}{7} x -\frac{27}{7}[/tex]

 + 5               +5

--------------------------------

y = [tex]-\frac{9}{7} x +\frac{8}{7}[/tex]

And that should be in y=mx+b form!

Hope it helps!

The surface area of the hemispherical vessel is 715.92 square centimeter and the cost to paint is Rs. 3579.62.

An object's surface area is the total area that all of its surfaces occupy. Different 3D shapes in geometry have various surface areas. There are two groups for the surface area:

Surface area of the lateral Surface that is curved Surface area overall.

Given that the external diameter of the hemispherical vessel is 16cm, hence the radius is 8cm.

The internal diameter of the hemispherical vessel is 12cm, hence the radius is 6cm.

The total surface area of the vessel is given by the following formula:

[tex]SA= 2\pi R^2 + 2\pi r^2 + \pi (R^2 - r^2)\\\\SA= 2(3.14)(8)^2 + 2(3.14)(6)^2 + (3.14)(8^2 - 6^2)\\\\SA= 401.92 + 226.08 + 87.92\\\\SA= 715.92[/tex]

The total surface area of the vessel is 715.92 square centimeters.

The cost to paint 1 square centimeter is Rs. 5, hence the cost to paint 715.92 square centimeters is:

C = (715.92)(5)

C = 3579.6

Hence, the cost to paint 715.92 square centimeters is Rs. 3579.62.

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To use substitution to determine which value of x makes the inequality true, we need to have an inequality with x as one of the variables. Without more information on the inequality, it is not possible to determine which value of x makes the inequality true. The set {10, 18, 21} does not contain any variable x.

The quadratic equation written in the vertex form is:

y = 2*(x - 3)^2 - 1

We know that for a leading coefficient a, and a vertex (h, k), we can write the quadratic equation as:

f(x) = a*(x - h)^2 + k

Here we know that the leading coefficient is 2, and the vertex of our quadratic equation is (3, -1)

Then the values that we have are:

a = 2

h = 3

k = -1

Then we can write the quadratic equation in the vertex form as:

y = 2*(x - 3)^2 - 1

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Points P and Q are 3/8 unit away from 0, and because absolute values cannot be zero, the absolute values are the same. Tim is the correct one here, and the correct argument is the second answer option.

Absolute values are numbers that are either zero or positive. They can never be negative, since it is the very definition of absolute values. If a given number is negative, then you only need to change the sign to positive so that you get the absolute value of the number. For example, the absolute value of - 0.001 is 0.001.

Points P and Q are equally 3/8 unit away from 0, but P is negative and Q is positive. The distance of both are not 3/8 unit but twice as that. Even though - 3/8 and 3/8 are not the same because of the different signs, they have the same absolute value, which is 3/8. Therefore, Tim is the correct one.

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The remaining area of the square is 16(4 - π) square inches.

To find the remaining area of the square after four circles are removed from it, we first need to find the area of the square and then subtract the combined area of the four circles.

The area of a square can be found by multiplying the length of one side by itself. If the circles have a radius of 2 inches, the side length of the square would be 2 inches + 2 inches + 2 inches + 2 inches = 8 inches. Therefore, the area of the square is 8 inches * 8 inches

= 64 square inches.

The area of a circle can be found by using the formula:

A = πr^2,

where A is the area, π is a constant (approximately 3.14) and r is the radius of the circle.

So the area of each circles is

A = πr^2

= π*2^2

= 4π square inches

The combined area of the four circles is 4*4π = 16π square inches.

So the remaining area of the square would be 64 square inches - 4*4π square inches

= 64 square inches - 16π square inches

= 16(4 - π) square inches

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Answer:(64-16pi)in.^2

Step-by-step explanation:

I got it right on e2020

annual salary of the 6 employees of a toy company is given below:

Correct option is: Statements (1) and (2) TOGETHER are not sufficient.

The average, sometimes referred to as the arithmetic mean, is calculated by dividing the total number of variables by their sum. Mean, however, represents the data's average. The mean is the sum of the data divided by the total of observations in statistics.

If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.

x, x + 6300, x + (2 × 6300), x + (3 ×6300), x + (4 × 6300), x + (5 × 6300)

Avg = ( x + ( x + 5 × 6300 )) / 2

Avg = ( 2x + 5 × 6300 ) / 2

The range of the 6 annual salaries is $31,500

Thus, no new information, Statement 2) can be derived from Statement 1) itself.

So, Statements (1) and (2) TOGETHER are not sufficient, this is correct option.

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The complete question is as follows:

What is the average (arithmetic mean) annual salary of the 6 employees of a toy company?

(1) If the 6 annual salaries were ordered from least to greatest, each annual salary would be $6,300 greater than the preceding annual salary.

(2) The range of the 6 annual salaries is $31,500.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are not sufficient.

The lowest temperature recorded in International Falls is - 40°.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

Given, The lowest temperature in Fraser, Colorado is - 54°, and the difference between the lowest temperature in Fraser, Colorado, and the lowest temperature in International Falls, Minnesota is 14°.

There the lowest temperature recorded in International Falls is,

- 54° + 14°.  (as stated warmer we put a positive sign)

= - 40°.

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Calculate the length of the longest side of the triangle use following methods :

Pythagoras theorem : (hypotenuse)² = (Base)² + (altitude)²

Sine rule : AB/sin C = AC / sin B = BC / sin A.

As given in the question,

To find the length of the longest side of a triangle use following methods:

a. Triangle is right angle triangle.

In the right angle triangle ,

Hypotenuse is the longest side.

To find the length of the hypotenuse use Pythagoras theorem:

(Hypotenuse)² = (Base)² + (Altitude)²

b. Triangle is not right angle triangle.

Use sine rule:

AB be the longest side in triangle ABC.

Side opposite to ∠A , ∠B , ∠C in ΔABC are BC, AC,AB respectively.

If measure of angles and other sides are given apply sine rule:

 AB/sin C = AC / sin B = BC / sin A.

Therefore, the measure of the longest side of the triangle is calculated by :

Pythagoras theorem : (hypotenuse)² = (Base)² + (altitude)²

Sine rule : AB/sin C = AC / sin B = BC / sin A.

The above question is incomplete , the complete question is :

How do you find the long side of the triangle?

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Answer: 32/9, or 3 5/9

Step-by-step explanation:

1. convert the mixed number to an improper fraction. It would turn into 16/9 x 2

2. Calculate the product : 32/9

3. Use division to get a mixed number: 3 5/9.