Answer:
The area of the square is 324 square inches.
Step-by-step explanation:
The apothem of the square is 9 inches.
The side of the square is twice the length of the apothem.
Hence, the side of the square is given by
[tex]a=2\times 9=18\text{ in}[/tex]
The area of a square is the given by
[tex]A=a^2\\A=18^2\\A=324\text{ in}^2[/tex]
Therefore, the area of the square is 324 square inches.
ten less than twice a number is the same as 7 times the number. find the number
Evaluate the determinant for the following matrix: [1 4 4 5 2 2 1 5 5]
(This is a 3x3 matrix)
Final answer:
The determinant of the given 3x3 matrix [1 4 4 5 2 2 1 5 5] is calculated by expanding across the first row and is found to be -60.
Explanation:
To evaluate the determinant of a 3x3 matrix, you can use the method of expansion across any row or any column. Given the matrix [1 4 4 5 2 2 1 5 5], let's expand across the first row:
The determinant of the matrix is the sum of the products of each element in the chosen row or column and the determinant of the 2x2 matrix that remains after removing the row and column of that element.
Multiply the first element of the first row by the determinant of the remaining 2x2 matrix, then subtract the product of the second element and its associated 2x2 matrix, and add the product of the third element and its 2x2 matrix.
Calculating the values, we get: 1*(2*5 - 2*5) - 4*(5*5 - 2*1) + 4*(5*2 - 2*1) = 1*0 - 4*23 + 4*8 = 0 - 92 + 32.
Therefore, the determinant of the given matrix is -60.
What is the end point and mid point
Answer:
end point is (-5/3 , 3)
mid-point: (5/6, 3/2)
Step-by-step explanation:
F leonard bought 2 packs of batteries for x amount of dollars, how many packs of batteries could he purchase for $5.00 at the same rate
A line contains points (−2,−2) and (1,4). Find the distance between the line and the point (6,−1).
The table below represents the distance of a car from its destination as a function of time: Time (hours) x Distance (miles) y 0 900 1 850 2 800 3 750 Part A: What is the y-intercept of the function, and what does this tell you about the car? (4 points) Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3, and tell what the average rate represents. (4 points) Part C: What would be the domain of this function if the car traveled the same rate until it reached its destination? (2 points)
The y-interception is y=900 or(0,900) which means that a car must travel 900 miles for the final destination. And every hour driven is 50 miles.
The average rate of change isIt represents how many miles per one hour changes the distance from a destination.
Domain of this function if the car traveled the same rate until it reached its destination:
0=-50x+900
50x=900
x=900/50=18
Domain: x∈ [0, 18].
Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2). Find the coordinates of the center of the circle.
What is the formula for finding the area of a regular polygon with perimeter P and apothem length a?
Answer:
[tex]A=\frac{1}{2}Pa[/tex]
Step-by-step explanation:
Let
P------> the perimeter of a regular polygon
a-----> the apothen
A-----> the area of a regular polygon
we know that
The formula to calculate the area of a regular polygon is equal to
[tex]A=\frac{1}{2}Pa[/tex]
The formula for finding the area of a regular polygon with
perimeter P and apothem length a is 1/2Pa.
What is a Polygon?This is referred to as a plane figure which has a finite number of
straight line segments connected to form a closed polygonal
chain.
The formula for calculating the area of a regular polygon is
1/2Pa where P is the perimeter of a regular polygon and a is the
apothem.
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Four is no less than the quotient of a number x and 2.1
The slopes of perpendicular line segments are 1/2 and d/3 What is the value of d?
d=-6
d=-3/2
d=3/4
d=6
Write the product cos(2x)sin(5x) as a sum
Answer:
[tex]\cos(2x)\sin(5x)=\dfrac{\sin (7x)+\sin (3x)}{2}[/tex]
Step-by-step explanation:
Given: [tex]\cos(2x)\sin(5x)[/tex]
Formula:
[tex]\sin A+\sin B=2\sin(\dfrac{A+B}{2})\cos(\dfrac{A-B}{2})[/tex]
[tex]\sin(\dfrac{A+B}{2})\cos(\dfrac{A-B}{2})=\dfrac{\sin A+\sin B}{2}[/tex]
Compare the given expression with formula
[tex]\cos(2x)\sin(5x)=\sin(\dfrac{A+B}{2})\cos(\dfrac{A-B}{2})=\dfrac{\sin A+\sin B}{2}[/tex]
Therefore,
[tex]\dfrac{A+B}{2}=5x\Rightarrow A+B=10x[/tex]
[tex]\dfrac{A-B}{2}=2x\Rightarrow A-B=4x[/tex]
Using two system of equation of A and B to solve for A and B
Add both equation to eliminate B
[tex]2A=14x[/tex]
[tex]A=7x[/tex]
Substitute A into A+B=10x
[tex]7x+B=10x[/tex]
[tex]B=3x[/tex]
Substitute A and B into formula
[tex]\cos(2x)\sin(5x)=\sin(\dfrac{7x+3x}{2})\cos(\dfrac{7x-3x}{2})=\dfrac{\sin (7x)+\sin (3x)}{2}[/tex]
Hence, Product as sum form [tex]\cos(2x)\sin(5x)=\dfrac{\sin (7x)+\sin (3x)}{2}[/tex]
We use ________ to determine the actual rate of change over intervals.
the dependent variable
the independent variable
absolute value
none of the above
On a rotating turntable, how do tangential speed and rotational speed vary with distance from the center?
HELP PLEASE!!!!
The amount of people in the city of Blonton is increasing due to children being born and because people are moving to the area.
~The population is increasing due to births by 13% each year and about 2300 people move to the area in any given year.
~The increase due to people moving to the area is represented by the function M(t) = 2300t.
~The population at any time when taking into account new births is found by P(t) = 375,000(1.013)t where 375000 was the initial population and t stands for the number of years after 1990.
If we added these functions together, what would the sum represent?
i need help with this question
Find the distance between each pair of points
Find the length of the hypotenuse of a right triangle whose legs measure 6 and 5
The length of the hypotenuse is: [tex]\[ c = \sqrt{61} \][/tex]
To find the length of the hypotenuse of a right triangle with legs measuring 6 and 5, we use the Pythagorean theorem, which states:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Given:
a = 6
b = 5
We need to find c . Plugging the values into the Pythagorean theorem, we get:
[tex]\[ 6^2 + 5^2 = c^2 \][/tex]
Calculating the squares:
[tex]\[ 36 + 25 = c^2 \][/tex]
Adding the numbers:
[tex]\[ 61 = c^2 \][/tex]
To find c , we take the square root of both sides:
[tex]\[ c = \sqrt{61} \][/tex]
Therefore, the length of the hypotenuse is:
[tex]\[ c = \sqrt{61} \][/tex]
Watermelon cost $0.39 per pound. Joesphs watermelon costs between $4.00 and $5.00. Which compound inequality correctly represents the possible weights of this watermelon? Round to the nearest tenth.
Answer:
10.26<w<12.82 represents the weight of the watermelon.
Step-by-step explanation:
Watermelon cost $0.39 per pound. Let the weight of Joseph's water melon be w pounds.
Joesph watermelon costs between $4.00 and $5.00.
[tex]\frac{4}{0.39}= 10.26[/tex]
[tex]\frac{5}{0.39}= 12.82[/tex]
Means the melons are between 10.26 and 12.82 pounds.
Hence, the compound inequality is 10.26<w<12.82 which represents the weight of watermelon.
Find the degree of the monomial. 6y2w8
Can square root of 27 be simplified
what is the maximum value of the function y = −3x2 − 15x + 9?
Assume that a researcher randomly selects 14 newborn babies and counts the number of girlsâ selected, x. the probabilities corresponding to the 14 possible values of x are summarized in the given table. find the probability of selecting 9 or more girls.
To find the probability of selecting 9 or more girls out of 14 newborn babies, sum the probabilities for selecting 9 to 14 girls from the given table.
Explanation:To find the probability of selecting 9 or more girls out of 14 babies, we need to calculate the sum of the probabilities of selecting 9, 10, 11, 12, 13, and 14 girls. Refer to the given table that summarizes the probabilities for each value of x. Add the probabilities for these values to get the probability of selecting 9 or more girls.
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Labor rate = $7.50 per hour Labor time = 6.5 hours Retail price of parts = $0 Total job cost = $82.00 Overhead rate?
If the price of an item is $34 and the sales tax on it is $1.36, what is the sales-tax rate?
1.36/34 = 0.04
0.04 = 4%
In a fast-food restaurant, the ratio of people eating hamburgers to people eating chicken is 4 : 3. There are 84 people in the restaurant. How many people are eating hamburgers and how many are eating chicken? A. 36 people are eating hamburgers; 48 people are eating chicken. B. 12 people are eating hamburgers; 72 people are eating chicken. C. 48 people are eating hamburgers; 36 people are eating chicken. D. 21 people are eating hamburgers; 63 people are eating chicken.
Final answer:
By using the ratio 4:3 and the total number of people (84), we calculate that each part of the ratio represents 12 people. Multiplying 4 parts by 12 gives us 48 people eating hamburgers, and multiplying 3 parts by 12 gives us 36 people eating chicken, making option C correct.
Explanation:
To solve the problem of determining how many people are eating hamburgers and how many are eating chicken given the ratio and the total number of people, we need to divide the total number of people by the sum of the parts of the ratio to find out the value of each part. The ratio given is 4:3, which means for every 4 people eating hamburgers, there are 3 people eating chicken. To find the value of each part of the ratio, we add the parts of the ratio (4 + 3 = 7) and divide the total number of people in the restaurant (84) by this sum.
84 ÷ 7 = 12. This means that each part of the ratio is equivalent to 12 people. Now, we need to multiply the number of each part by the number of people that each part represents. For hamburgers, it's 4 parts, so 4 × 12 = 48 people. For chicken, it's 3 parts, so 3 × 12 = 36 people.
Therefore, the correct answer is C: 48 people are eating hamburgers and 36 people are eating chicken.
An activity book has 21 pages of crossword puzzles, 18 pages of cryptograms, and 12 pages of mazes. bianca randomly selects a page, completes the activity, and then randomly selects another page to complete. what is the probability that bianca first completes a maze and then completes a crossword puzzle?
Final answer:
The probability that Bianca first completes a maze and then completes a crossword puzzle is approximately 9.8%.
Explanation:
To find the probability that Bianca first completes a maze and then completes a crossword puzzle, we need to calculate the probability of each event occurring and then multiply them together.
The total number of pages in the activity book is 21 + 18 + 12 = 51 pages.
The probability of selecting a maze page first is 12/51, and after completing the maze page, there are now 50 pages remaining in the book, 21 of which are crossword puzzles.
So, the probability of selecting a crossword puzzle page after completing a maze page is 21/50.
To find the probability of both events happening, we multiply the probabilities: (12/51) * (21/50) = 0.098 or 9.8%.
Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)
The equation of a hyperbola is:
(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1
So what we have to do is to look for the values of the variables:
For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9
c = 7 (distance from center to vertices; given from the foci)
c^2 = 49
By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2
b^2 = 49 – 9
b^2 = 40
Therefore the equation of the hyperbola is:
(x^2 / 9) – (y^2 / 40) = 1
Answer:
Hope this helps :)
Step-by-step explanation:
A triangle has an area of 180 cm2 and the base that is 20 cm long. what is the height of the triangle answers
Choose the best definition for the following term:substitution
I Need Help ASAP! This is Due in 30 Minutes!
I don't Understand it at all and I need Help
Create a factorable polynomial with a GCF of 7. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.