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]
Labor rate = $7.50 per hour Labor time = 6.5 hours Retail price of parts = $0 Total job cost = $82.00 Overhead rate?
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
On a rotating turntable, how do tangential speed and rotational speed vary with distance from the center?
what is the maximum value of the function y = −3x2 − 15x + 9?
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].
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.
On Saturday Mike ran 5.5 kilometers swam 300M and invite 23 hectometers how many kilometers did he travel in total
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
i need help with this question
Pretty sure this is super easy I'm just an idiot pls help!
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.
Read more about Polygon here https://brainly.com/question/1592456
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.
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]
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.
Suppose three out of every five people said they would prefer a television over a computer. If we surveyed 5,000 people, how many would prefer a television? A. 1,875 B. 5,000 C. 3,125 D. 3,000
We use ________ to determine the actual rate of change over intervals.
the dependent variable
the independent variable
absolute value
none of the above
If x and y are not both equal to zero 1/x+y = 1/x + 1/y
Look at the picture provided below
|
V
Answer:
True
Step-by-step explanation:
All work is shown and pictured
Solve 3x2 + 13x = 10
a. x = two over three and x = −5
b. x = 3 and x = −3
c. x = −2 and x = five over three
d. x = −7 and x = 13
Answer:
A. x = two over three and x = -5
The equation 3x^2 + 13x = 10 can be solved using the quadratic formula. The solutions are given by:
[tex]$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]
Substituting the values from the equation (where a = 3, b = 13, and c = -10), we get:
[tex]$$x = \frac{-13 \pm \sqrt{13^2 - 4*3*(-10)}}{2*3}$$[/tex]
This simplifies to:
[tex]$$x = \frac{-13 \pm \sqrt{289}}{6}$$[/tex]
So, the solutions are:
[tex]$$x = \frac{-13 + \sqrt{289}}{6} = \frac{2}{3}$$[/tex]
and
[tex]$$x = \frac{-13 - \sqrt{289}}{6} = -5$$[/tex]
So, the correct answer is A. x = two over three and x = −5.
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:
Scientists are studying the temperature on a distant planet. Let y represent the temperature (in degrees Celsius).
Let x represent the height above the surface (in kilometers). Suppose that x and y are related by the equation =y−235x .
Answer the questions below. Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the temperature change for each kilometer we go up from the surface?
Final answer:
For each kilometer increase in altitude, the temperature on the distant planet decreases by 235 degrees Celsius, according to the given equation y = -235x.
Explanation:
The question pertains to the relationship between altitude and temperature on a distant planet. Given the equation y = -235x, where y represents the temperature in degrees Celsius and x represents the height above the surface in kilometers, we are asked to determine the temperature change for each kilometer as we increase elevation from the surface.
To find the temperature change per kilometer, we examine the coefficient of x in the equation. Since the coefficient is -235, it signifies that for every kilometer increase in altitude, the temperature on this planet decreases by 235 degrees Celsius.
If there are x teams in a sports league, and all the teams play each other twice, a total of n(x) games are played, where n(x)equals
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%
Four is no less than the quotient of a number x and 2.1
A triangle has an area of 180 cm2 and the base that is 20 cm long. what is the height of the triangle answers
Find the distance between each pair of points
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.
Some facts about powers of ten are shown.
Use what you know about powers of ten to enter numbers that make the equation true
Enter numbers to write 256,000 in scientific notation.
The number 256,000 can be written as 2.56 x [tex]10^5[/tex] in scientific notation
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex]
The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).
Scientific notations value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
To write 256,000 in scientific notation.
[tex]10^5[/tex] is followed by 5 zeros, so, it is 100,000.
Now Multiply 2.56 and 100,000 we get
2.56 x 100,000 = 256,000.
Therefore, First box is 100,000 and the second box is 5
Learn more about scientific notation here:
https://brainly.com/question/3112062
#SPJ2
Can square root of 27 be simplified
Assume that y varies inversely with x. If y=6.4when x=4.4, find y when x=3.2
the answer is 8.8
that is the answer