Final answer:
a. The equation for the line in point-slope form is y + 9 = 4(x - 9), with a slope of 4.
b. The equation can be rewritten in standard form as 4x - y = 45.
Explanation:
a. To write the equation for the line in point-slope form, we need to determine the slope (m) and one point on the line (x1, y1).
The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1).
Taking the points (9, -9) and (10, -5), we can substitute the values into the formula to get m = (-5 - (-9)) / (10 - 9) = 4 / 1 = 4.
Now we can use the formula y - y1 = m(x - x1) with the point (9, -9) to get y - (-9) = 4(x - 9). Simplifying, we have y + 9 = 4x - 36.
b. To rewrite the equation in standard form, we need to bring the equation to the form Ax + By = C, where A, B, and C are integers.
Starting from the point-slope form, we can expand and simplify the equation to get y + 9 = 4x - 36 becomes y = 4x - 45.
To make all the coefficients integers, we can multiply the equation by 5 to get 5y = 20x - 225, rearrange the terms as -20x + 5y = -225, and divide every term by -5 to get the standard form 4x - y = 45.
A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building.
In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot
The height of the building from the top of the ladder is 12.6 ft
The situation forms a right angle triangle.
Right angle triangle:A right angle triangle is a triangle that has one of its sides as 90 degrees.
Therefore,
The length of the ladder is the hypotenuse side.
The bottom of the ladder distance from the base of the building is the adjacent side of the triangle. Therefore,
The height of the building from the top of the ladder is the opposite sides. Therefore, using Pythagoras theorem.
c² = a² + b²
14² - 6² = b²
b² = 196 - 36
b² = 160
b = √160
b = 12.6491106407
b = 12.6 ft
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The highest score that is a record for a particular video game is 19,749 points. The lowest score on record for the same video game is 176 points. Which of the following inequalities best shows the range of scores recorded on the game?
The area of a triangle is 6.75m2. If the base of the triangle is 3 m, what is the height of the triangle?
A moving company charges $0.60 per pound for a move from New York to Florida. A family estimates that their belongings weigh about 4 tons. About how much would it cost the family to move from New York to Florida?
1 ton = 2000 pounds
4* 2000 = 8000 pounds total
8000 * 0.60 = $4,800.00
it will cost $4,800 to move
Answer:
Step-by-step explanation:
1 ton = 2000 pounds
4* 2000 = 8000 pounds total
8000 * 0.60 = $4,800.00
it will cost $4,800 to move
First right answer gets brain
How to solve: (looking for b)
y =mx+b
The area of a triangle is 6 square feet. The base is 3 times its height. What is the base of the triangle?
Area=1/2 bh
6=1/2bh
12=bh
height is x, base 3x
12=3x^2
x^2=4
x=2
height = 2 feet
base = 3*2 = 6 feet
You are watching your favorite soccer player on TV. Statistics show that he has a 37% chance of scoring a goal each time he shoots. He shoots twice. What is the probability that he scores a goal both times?
what is 18 divided by negative 3
What is the equation of the line that is parallel to y = -2x + 4 and goes through the point (1,7)
math question down below
An arrow is shot upward with a velocity of 64 feet per second. Using the formula h(t)=64t-16t^2, how long after the arrow is released does it hit the ground?
Answer:
After the 4 second arrow is released, it will hit the ground.
Step-by-step explanation:
Consider the provided formula.
[tex]h(t)=64t-16t^2[/tex]
We need to find how long after the arrow is released does it hit the ground.
If the arrow hit the ground that means the value of h(t)=0.
Substitute the value of h(t)=0 and solve the equation as shown.
[tex]64t-16t^2=0[/tex]
[tex]16t(4-t)=0[/tex]
Now use zero product rule: If ab=0 then either a=0 or b=0
[tex]16t=0\ or\ 4-t=0[/tex]
[tex]t=0\ or\ -t=-4[/tex]
[tex]t=0\ or\ t=4[/tex]
Hence, after the 4 second arrow is released, it will hit the ground.
Simplify (9.5)(−2)(−5).
Which of the sets of ordered pairs represents a function?
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
Which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?
Answer:
Which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?
A
A quarterback completes 65% of his passes. Out of his next 40 passes, how many can you expect to be completed.
Which is colder 0°F or 6°F
From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?
To find the height of the mat off the ground, we can use trigonometry.
Explanation:To find the height of the mat off the ground, we can use trigonometry. Since the angles of the right triangle formed by the mat are 60° and 30°, we can determine the height using the sine function. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the side opposite the 30° angle is the height of the mat, and the hypotenuse is the length of the mat, which is 5 feet. So, we have sin(30°) = height/5. Solving for the height, we get height = 5 * sin(30°) = 5 * 0.5 = 2.5 feet.
Therefore, the mat is 2.5 feet off the ground.
The correct answer is option B. The height of the gymnastics mat off the ground is [tex]\frac{5\sqrt{3}}{3}}[/tex] feet.
Given that the gymnastics mat extends 5 feet across the floor, this length corresponds to the side opposite the 60° angle in the right triangle.
Let's denote the length of the side opposite the 30° angle as [tex]$x$[/tex].
According to the properties of a 30-60-90 triangle, the side opposite the 60° angle is [tex]\sqrt{3}[/tex] times the side opposite the 30° angle, so we have:
[tex]\[ 5 = x\sqrt{3} \][/tex]
To find [tex]$x$[/tex], we divide both sides of the equation by [tex]$\sqrt{3}$[/tex]:
[tex]\[ x = \frac{5}{\sqrt{3}} \][/tex]
To rationalize the denominator, we multiply the numerator and the denominator by [tex]$\sqrt{3}$[/tex]:
[tex]\[ x = \frac{5\sqrt{3}}{3} \][/tex]
The complete question is:
From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?
A. [tex]\frac{5}{2}[/tex] ft.
B. [tex]\frac{5\sqrt{3}}{3}[/tex] ft.
C. [tex]5\sqrt{3}}[/tex] ft.
D. 10 ft.
plz help you have to turn your phone to the side
7.06) If the greatest value the variable m can be is less than 9, which of the following inequalities best shows all the possible values of m? m < 9 m > 9 m ≤ 9 m ≥ 9
Hello,
The correct answer is A) m < 9
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Jaidee made her trip to the train station and back. The trip there took two hours and the trip back took five hours. She averaged 30 mph faster on the trip there than on the return trip. What was Jaidee's average speed on the outbound trip?
Rick and Ben had the same amount of money. Ben spent $138. In the end,Rick had 4 times as much as Ben.How much did Rick have?
"Exponents and Multiplication- Simplify. Your answer should only contain positive exponents." Please help quickly !!
Can some one please help me ?
110% =1.10
multiply the old price by that
2.85 *1.10 = 3.135
round to 3.14
new price is $3.14
Carmen buys 153 shares of Cawh Consolidated Banks, each of which pays a constant yearly dividend of $7.14. After six years, how much has Carmen received in dividends?
Answer: $6554.52
Step-by-step explanation:
Total number of shares bought by Carmen =153
A constant yearly dividend paid by each share=$7.14
Thus, 153 shares pays yearly dividend =[tex]153\times7.14=\$1092.42[/tex]
After 6 years, total dividend received by Carmen=[tex]6\times1092.42=\$6,554.52[/tex]
Hence, The total dividend received by Carmen in 6 years = $6554.52
the selling price of a house dropped from 250,000 to 210,000 over a period of five years. By what percentage didnthe sellling price decrease?
The selling price of the house decreased by 16%.
Explanation:To find the percentage decrease in the selling price of the house, we need to calculate the difference between the initial selling price and the final selling price, and then divide that by the initial selling price. Finally, we multiply the result by 100 to get the percentage decrease.
Difference = Initial Selling Price - Final Selling Price = $250,000 - $210,000 = $40,000Percentage decrease = (Difference / Initial Selling Price) x 100 = ($40,000 / $250,000) x 100 = 16%Therefore, the selling price of the house decreased by 16%.
The selling price of the house decreased by 16%.
Explanation:To find the percentage decrease in the selling price of the house, we can use the following formula:
Percentage decrease = ((Initial price - Final price) / Initial price) x 100
In this case, the initial price is $250,000 and the final price is $210,000. Plugging these values into the formula, we get:
((250,000 - 210,000) / 250,000) x 100 = (40,000 / 250,000) x 100 = 0.16 x 100 = 16%
Therefore, the selling price of the house decreased by 16%.
A factory employs 3 full-time workers and 6 part-time workers; the amount earned by each is: $36,000 for the production supervisor; $27,000 for the machine operator; $21,000 for the general assistant; a total of $50,000 for part-time staff. How much was the wage bill for the 3 full-time staff?
The total wage for full-time workers is 84000$.
What is simplification?Simplifying a value simply means finding it in its most basic form. To simplify the problem, we use a number of approaches, including PEMDAS and BODMAS. Aside from the value, the variables must also be made simpler.
Given, A factory employs 3 full-time workers and 6 part-time workers; the amount earned by each is $36,000 for the production supervisor; $27,000 for the machine operator; $21,000 for the general assistant; a total of $50,000 for part-time staff.
The Total wage for the full-time staff = 36000 + 27000 + 21000
The total wage for the full-time staff = 84000
Therefore 84000$ was the wage bill for the 3 full-time staff.
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Rewrite the set M by listing its elements. Make sure to use the appropriate set notation
M= {x | x is an integer and -2 < x < 1}
Model the function rule y = -2x - 3 with a table of values. Show your work.
A water tower is used to store fire fighting water at an industrial plant. The tank on top of the tower is in the shape of a cylinder with a height of 15 feet and a diameter of 7 feet. One cubic foot is approximately 7.5 gallons. how many gallons are in the tank if its 55% full?