In each of the equations or inequalities below, find all the integer values of x that make the equation or the pair of inequalities true. Explain reasoning for each part.
Part A: |x|=17
Value Of X:
Part B: |x+9|=15
Value Of X:
Part C: |x-10| ≤ 13 and |x-10| ≥ 9
(Find the values of x that make both inequalities true)
Values of X:
Help me with 1-6 please
Find the side and measure B
When angle opposite to the unknown sides and other two sides are given then we use law of cosines
Law of cosine
[tex] c^2 = a^2 + b^2 - 2ab cos(c) [/tex]
From the given diagram
[tex] AB^2 = CB^2 + AC^2 - 2(CB)(AC) cos( c) [/tex]
CB = 108
AC= 55
Angle c= 59
[tex] AB^2 = 108^2 + 55^2 - 2(108)(55) cos( 59 ) [/tex]
[tex] AB^2 = 8570.34767 [/tex]
Take square root on both sides
AB = 92.6 m
To find out angle B we use sine law
[tex] \frac{sin(a)}{a} = \frac{sin b}{b} = \frac{sin c}{c} [/tex]
[tex] \frac{sin b}{b} = \frac{sin c}{c} [/tex]
From the figure
[tex] \frac{sin B}{AC} = \frac{sin C}{AB} [/tex]
[tex] \frac{sin B}{55} = \frac{sin 59}{92.6} [/tex]
sin(B) = 0.50916647
B = [tex] sin^{-1} [/tex](0.50916647)
Angle B= 30.61 degrees
x^2-40x Complete the square for the expression. Then factor the trinamial.
in an ordered pair,the x-coordinate represents the number of hexagons and the y-coordinate represents the total number of sides.If the x-coordinate is 7, what is the y coordinate
A figure is made up of 5 identical squares, the area of the figure is 405 squares inches, what is the perimeter
To find the perimeter of a figure made up of 5 identical squares with a total area of 405 square inches, you would calculate the side length of one square as 9 inches and then consider the shared sides. The perimeter would be 180 inches.
The question describes a figure made up of 5 identical squares with a total area of 405 square inches. To find the area of one square, we divide the total area by the number of squares, resulting in 405 ÷ 5 = 81 square inches per square. Knowing that the area of a square is given by the formula A = side length × side length (or A = a²), we can determine that each side of the square is
The square root of 81, which is 9 inches. Since there are 5 squares, the figure will have overlapping sides when the squares are combined. To calculate the perimeter, we need to consider that each square shares a side with another, except for the starting and ending squares in the arrangement. Therefore, the perimeter of the entire figure will be 9 inches times 4 for the first or outer square, plus 9 inches times 3 for each of the remaining squares (as one side is shared). This gives us a total perimeter of 4 × 9 + (4 × 9 × (5-1)) inches.
When calculating the perimeter of the entire figure, the formula for the perimeter is P = 4×side + 4×(number of squares - 1) × side, resulting in a final computation of P = 4×9 + 4×4 × 9, which equals 180 inches.
A scale drawing of a house addition shows a scale factor of 1 in. = 3.3 ft. Josh decides to make the house addition smaller, and he changes the scale of the drawing to 1 in. = 1.1 ft. What is the change in the scale factor from the old scale to the new scale? Help Please!!
The change in the scale factor from the old scale to the new scale is option A; 3 to 1.
What is Scale?The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.
Given, A scale drawing of a house addition shows a scale factor of 1 in. = 3.3 ft.
Since Josh decides to make the house addition smaller,
he changes the scale of the drawing to 1 in. = 1.1 ft.
Old: 1 inch = 3.3 feet.
New: 1 inch = 1.1 feet.
Old; 3.3 / 1.1 = 3.
New; 1.1 / 1.1 = 1
The change in the scale factor from the old scale to the new scale is option A; 3 to 1.
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Write the following equation in standard form: x^5+2x^3+6x+1/5
Answer:
[tex]x^5+2x^3+6x+\frac{1}{5}[/tex]
Step-by-step explanation:
We have been given an equation [tex]x^5+2x^3+6x+\frac{1}{5}[/tex]. We are asked to write our given equation in standard form.
We know that to write an equation in standard form, we need to write the degree terms in descending order.
Upon looking at our given equation, we can see that all terms are in descending order of degree, therefore, our given equation is already writen in standard form.
The exchange rate at the post office is £1 = €1.17 how many euros will you get for £280
To calculate the number of euros you will get for £280, divide £280 by £1 and then multiply by €1.17. You will get approximately €327.60.
Explanation:To calculate the number of euros you will get for £280, we can use the given exchange rate of £1 = €1.17.
First, we need to find the value of 1 pound in euros by dividing £280 by £1.
This gives us 280.
Then, we can multiply 280 by €1.17 to get the number of euros you will get.
Therefore, you will get approximately €327.60 for £280.
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Combine any like terms in the expression. If there are no like terms, rewrite the expression.
7w3+8t2u2–2t2u2–4t2u2
A property sells for $620,000 two years after it was purchased. If the annual appreciation rate was 4%, how much did the original buyer pay for the property (round to the nearest $1,000)?
The original purchase price of the property, after accounting for 4% annual appreciation over two years with a final selling price of $620,000, is approximately $573,000 when rounded to the nearest $1,000.
Explanation:The question involves finding the original price of a property given its final selling price after a period of annual appreciation. To calculate the original purchase price, we need to use the formula for compound appreciation in reverse, known as discounting. Since the appreciation is 4% per year for two years and the final selling price is $620,000, the original purchase price (P) can be found using the formula:
P = Final Price / (1 + rate of appreciation)^number of years
So, substituting the given values, we get:
P = $620,000 / (1 + 0.04)^2
Now, calculate the denominator:
(1 + 0.04)^2 = 1.0816
And then divide by the final price:
P = $620,000 / 1.0816
P = $573,029.94
When rounded to the nearest $1,000, the original purchase price is approximately $573,000.
the volume of the sphere is 500/3 pie cubic units . what is the value of X?
How do you do this problem? It isn't C is all I know.
The length of an equilateral triangle is increased by 7 inches, so the perimeter is now 36 inches. Find the original length of each side of the equilateral triangle.
Which ordered pair could represent the coordinates of point k
how do you get the percent of 20% off 7.12
Please help with 17 part b
What is the answer please
Which statement is NOT true?
F. A set of ordered pairs describes a function if each x-value is paired with only one y-value.
G. A table of values describes a function if each x-value appears in the table only once.
H. A mapping is a function if each x-value is mapped to only one y-value.
J. Any graph that is a line represents a function.
A function assigns the value of each element of one set to the other specific element of another set. The statement that is not true about the function is option G.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A function from a set X to a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
The given following statements are about functions. Of the given four statements the one that is not correct is G. This is because if the x-value appears just for one time in a table does not mean it can not have multiple outputs.
Hence, the statement that is not true about the function is option G.
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3/7x + 4 = -1/2
explain pls
To solve the equation 3x−2=4x−1 3 x − 2 = 4 x − 1 , Veronica graphs the functions f(x)=3x−2 f ( x ) = 3 x − 2 and g(x)=4x−1 g ( x ) = 4 x − 1 on the same set of coordinate axes.
Which statement describes the solution of the equation 3x−2=4x−1
The solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect.
The solution of the equation is the y-intercept of the linear equations.
The solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect.
The solution of the equation cannot be found graphically. Veronica should solve the equation algebraically.
What is 50% of 80?
part ? 50
—— = ——- ] percent
whole. 80. 100
what is the part since we don’t know what “what” is.
50% is the percent
and 80 is the whole
50% of 80 is the number 40.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We have to find the number of 50% of 80
Convert the percentage to deicmal number.
To do this we have to divide percentage by 100.
50/100=0.5
Now multiply 0.5 with 80
0.5×80
Which we get is 40
Hence, 50% of 80 is the number 40.
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Use completing the square to solve for x in the equation (x-12)(x+4)=9.
a. x = –1 or 15
b. x = 1 or 7
c. x=4+√41
d. x=4+√73
Answer:
The correct answer is
D
End time 10:30 elapsed time 3/4 of an hr what is starting time
How does tripling the circumference of the circle affect the diameter of the circle?
ana tiene 5000000 en una cuenta bancaria. le dan un interes de 3.2%, ¿cuanto dinero trndra dentro de 2 meses y 10 dias ( todos los meses tienes 30 dias)
In a six-sided dice game, a prize is won if the arithmetic mean of number rolled is 3.25-3.75. In a second game, a prize is won if the arithmetic mean is more than 4.5. In which game would you rather roll the dice 20 times or 200 times
For rolling the dice 200 times, the same logic applies. Regardless of the number of rolls, the game with the higher probability of winning, which is the second game, is preferred.
To determine which game is more favorable for rolling the dice, we need to calculate the expected value for each game. The expected value represents the average outcome of rolling the dice.
For the first game, the possible outcomes are integers between 1 and 6. The arithmetic mean should be between 3.25 and 3.75 to win a prize. So, we need to find the probability of rolling numbers that satisfy this condition.
Let's denote [tex]\( p_1 \)[/tex] as the probability of winning the first game. To find [tex]\( p_1 \)[/tex], we calculate the probability of rolling numbers between 13 and 18 (inclusive) since the sum of these numbers falls within the range of 3.25 to 3.75.
[tex]\[ p_1 = \frac{6}{6^2} = \frac{1}{6} \][/tex]
For the second game, we need the arithmetic mean to be more than 4.5. This means the sum of the numbers should be more than [tex]\( 4.5 \times 6 = 27 \)[/tex]. Since the maximum sum of rolling six dice is 36, all outcomes satisfy this condition.
Let's denote [tex]\( p_2 \)[/tex] as the probability of winning the second game. Since all outcomes are favorable, [tex]\( p_2 = 1 \)[/tex].
Now, we calculate the expected values for each game:
[tex]\[ E_1 = p_1 \times \text{Prize amount for game 1} \][/tex]
[tex]\[ E_2 = p_2 \times \text{Prize amount for game 2} \][/tex]
Given that the prize amount is the same for both games, we can compare the expected values directly.
For rolling the dice 20 times:
[tex]\[ E_1 = \frac{1}{6} \times \text{Prize amount} \][/tex]
[tex]\[ E_2 = 1 \times \text{Prize amount} \][/tex]
Since [tex]\( \frac{1}{6} \)[/tex] is less than 1, it's better to choose the game with the higher probability, which is the second game.
For rolling the dice 200 times, the same logic applies. Regardless of the number of rolls, the game with the higher probability of winning, which is the second game, is preferred.
The complete question is:
In a six-sided dice game, a prize is won if the arithmetic mean of number rolled is 3.25-3.75. In a second game, a prize is won if the arithmetic mean is more than 4.5. In which game would you rather roll the dice 20 times or 200 times
Find the outlier of the set of data: 80, 71, 75, 69, 74, 17, 82 A. 82 B. 81 C. 74 D. 17
Answer:
Use the drop-down menus to identify the key values of the box plot.
The median is
✔ C
.
The minimum is
✔ A
.
The maximum is
✔ E
.
The lower quartile (Q1) is
✔ B
.
The upper quartile (Q3) is
✔ D
.
Step-by-step explanation:
i took the test
Write an expression based on the given description.
In Spencer’s garden, the number of rose bushes is 7 less than 1.5 times the number of carnation bushes. If the number of carnation bushes is c, then the expression representing the number of rose bushes is 7c – 1.5 1.5c – 7 7(c – 1.5) 1.5(c – 7) .
Answer:
7c -1.5
Step-by-step explanation:
Answer:
7c -1.5
I hope this helps
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