Final answer:
The original expression 2x² - 50 is equivalent to option a) 2(x-5)(x+5) and option c) -2(5-x)(x+5), but not to option b) -2(x+5)(x+5).
Explanation:
The student has asked whether each given expression is equivalent to 2x² - 50.
a) 2(x-5)(x+5): Yes, this is equivalent to 2x² - 50 because when you apply the difference of squares formula, you get 2(x² - 25), which simplifies to 2x² - 50.
b) -2(x+5)(x+5): No, this results in -2(x² + 10x + 25), which simplifies to -2x² - 20x - 50, and is not equivalent to 2x² - 50.
c) -2(5-x)(x+5): No, this expression simplifies to -2(-x² - 5x + 5x + 25) or 2x² - 50, which is actually equivalent to the original expression. The negative sign inside the parentheses changes the sign of x when multiplied by the outside negative factor, leading to a positive result for the x² term.
a women has a ladder that is 13 ft long. if she sets the base of the ladder on level ground 5ft from the side of a house, how many feet above the ground will the top of the ladder be when it rests against the houlad
Final answer:
Using the Pythagorean theorem, it is determined that the ladder reaches 12 feet up the side of the house when the base is placed 5 feet away.
Explanation:
To solve for the height at which the ladder reaches the house, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.
In this scenario, the ladder represents the hypotenuse (c), the distance from the base of the ladder to the house gives one leg of the triangle (a), and the height the ladder reaches up the side of the house is the other leg (b).
Let a = 5 ft (distance from the ladder's base to the house).Let c = 13 ft (length of the ladder).We need to find b (the height the ladder reaches the house).According to the Pythagorean theorem, a² + b² = c². Plugging in our known values allows us to solve for b²:
a² = 5² = 25.c² = 13² = 169.Subtract a² from c² to get b²: 169 - 25 = 144.Take the square root of b² to find b: √144 = 12.Therefore, the top of the ladder will be 12 feet above the ground.
triangle XYZ has vertices X(6,-2.3), Y(7.5,5), and Z(8,4). when translated X' has coordinates (2.8,-1.3). Write a rule to describe this transformation. Then find the coordinates of Y' and Z'.
Final answer:
The transformation is a translation where you subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate. Using this rule, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).
Explanation:
The student is asking about a translation transformation in a coordinate plane. Given the original and translated coordinates for point X, we can determine the translation rule by calculating the differences between the coordinates.
The x-coordinate has changed from 6 to 2.8, a decrease of 3.2, and the y-coordinate has changed from -2 to -1.3, an increase of 0.7. Thus, the translation rule is to subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate.
To find the translated coordinates for points Y and Z, we apply the same rule:
Y'(Y after translation) will have coordinates (7.5 - 3.2, 5 + 0.7) which simplifies to (4.3, 5.7).Z'(Z after translation) will have coordinates (8 - 3.2, 4 + 0.7) which simplifies to (4.8, 4.7).In summary, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).
To find the translation rule, we used the given coordinates of X and X' to determine a translation vector of (-3.2, 1). Using this rule, the coordinates of Y' are (4.3, 6) and Z' are (4.8, 5).
Given the vertices of triangle XYZ: X(6, -2.3), Y(7.5, 5), and Z(8, 4), and knowing that vertex X when translated has coordinates X'(2.8, -1.3), we need to determine the translation rule.
First, find the translation vector by comparing the coordinates of X and X'.The translation from X to X' is (2.8 - 6, -1.3 + 2.3) which equals (-3.2, 1).Therefore, the translation rule is: (x, y) → (x - 3.2, y + 1).Apply this rule to the coordinates of Y and Z to find Y' and Z'.For point Y(7.5, 5):Hence, the coordinates of the translated points are Y'(4.3, 6) and Z'(4.8, 5).
here is the complete question-Triangle XYZ has vertices X(6, -2.3), Y(7.5, 5), and Z(8, 4). When translated, X` has coordinates (2.8, -1.3). Write a rule to describe this transformation. Then find the coordinates of Y' and Z'.
find the area of a triangle with sides a=5 b=8 c=11
Joe walked 4/9 of a mile in 4/5 of an hour. What is his unit rate in miles per hour? 4/9 over 4/5 = 5/9 mile per hour 4/5 over 4/9 = 1 and 4/5 miles per hour 4/9 over 4/5 = 1 and 4/5 miles per hour 4/5 over 4/9 = 5/9 mile per hour
If Joe walked 4/9 of a mile in 4/5 of an hour then the unit rate is 5/9 miles/hour.
What is Division?A division is a process of splitting a specific amount into equal parts.
The distance walked by Joe is 4/9 of a mile.
The time taken by Joe to walk 4/9 of a mile is 4/5 of an hour.
We need to find the unit rate in miles per hour.
To find this we just need to divide 4/9 by 4/5.
Rate = Distance/Time
Distance = 4/9 miles
Time = 4/5 hour
Rate = 4/9 ÷ 4/5
Rate = 4/9 × 5/4
Rate = 5/9 miles/hour.
Hence, if Joe walked 4/9 of a mile in 4/5 of an hour then the unit rate is 5/9 miles/hour.
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9x+10y=29
10x+9y=28
Solve by elimination
By what percent will a fraction increase if its numerator is increased by 60% and its denominator is decreased by 20%?
Mr. Saba owns two food trucks. He rents two spots at the state fair. This table shows the number of tacos the two food trucks sold each day for 10 days.
Food Truck 1 721 658 437 527 601 468 425 431 508 515
Food Truck 2 462 471 426 654 647 732 701 684 632 698
Which conclusion can be drawn from the data?
The medians for the two taco trucks are the same
.
The two food trucks sold the most tacos on Day 3.
The range between the maximum and minimum values for taco truck 2 is greater than the range between the maximum and minimum values for taco truck 1.
On average, food truck 1 sold more tacos over the 10 days than food truck 2.
Answer: C) The range between the maximum and minimum values for taco truck 2 is greater than the range between the maximum and minimum values for taco truck 1.
please help and explain how u got your answer :)
Write a problem that uses a fraction greater than 1
7.2 + ( -5.55) = -5.5 + 7.2 identify what property is shown
What is the value of the following function when x = 0?
Answer:
It’s y=-2 on edge
YOU WILL GET 50 POINTS IF YOU EXPLAIN HOW YOU GOT THE ANSWER TO THIS PROBLEM. I WILL MARK YOU AS BRAINLIEST TOO. THANK YOU :)
Phil used 3 gallons of paint to cover 1,125 square feet of a wall. at this same rate, what is the total area of the wall, in square feet, that Phil will cover using 5 gallons of paint ?
A) 675 square feet
B) 1,575 square feet
C) 1,800 square feet
D) 1,875 square feet
Thank you :)
The area of a trapezoid is 18sq. ft and the sum of its bases is 6 ft. Find the area of a square whose side is equal to the height of the trapezoid.
Area = (L1 + L2)*h/2
Area = 18
L1 + L1 = 6
h = ???
18 = (L1 + L2)*h/2
18 = (6) * h/2 Multiply both sides by 2
36 = 6h Divide by 6
36/6 = h
h = 6
So the square is 6 by 6
Area square = s^2 where s is the side of the square.
Area = 6^2 = 36
so your answer will be 6^2 = 36
Angles ABC is dilated using scale factor of 2. what happens to its angle measures?
a picture of a school mascot is 18 in. Wide and 24 in. Long. It is enlarged proportionally to banner size. If the width is enlarged to 63 in., what is the length of the banner?
help me please!!!!!!
pls help and show some steps
What is the answer to problem 13
Chantelle is going on an 8 day hike of 82.5 miles. she plans to hike 8.25 hours everyday for each of those 8 days. how many miles will she covet each hour of her trip?
Final answer:
Chantelle will cover 1.25 miles each hour of her hike.
Explanation:
To find out how many miles Chantelle will cover each hour of her trip, we need to divide the total distance of 82.5 miles by the total time of 8.25 hours per day for 8 days.
First, we calculate the total time of the trip by multiplying the hours per day (8.25) by the number of days (8): 8.25 hours/day x 8 days = 66 hours.
Next, we divide the total distance by the total time: 82.5 miles / 66 hours = 1.25 miles/hour.
Therefore, Chantelle will cover 1.25 miles each hour of her hike.
Given: ΔABC; a= 10; b = 4, and c = 11. Find the measurement of ∠B to the nearest tenth of a degree. A) 21.3° B) 24.7° C) 25.1° D) 31.4°
If 2(x + 3) = x + 10, then x equals what
To solve the equation, we first distribute the 2 on the left, then collect like terms and finally isolate x. The solution to the equation 2(x + 3) = x + 10 is x = 4.
Explanation:Solution for the EquationTo solve the equation 2(x + 3) = x + 10, we will first distribute the 2 on the left-hand side of the equation to get 2x + 6. Therefore, the equation becomes: 2x + 6 = x + 10.
The next step is to collect like terms. To do this, we subtract x from both sides, which gives us: x + 6 = 10.
Finally, to solve for x, we subtract 6 from both sides of the equation: x = 4. Hence, the solution to the equation 2(x + 3) = x + 10 is x = 4.
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Final answer:
x = 4
Explanation:
To solve the equation 2(x + 3) = x + 10, we first expand the left side of the equation:
2 × x + 2 × 3 = x + 10
2x + 6 = x + 10
Now subtract x from both sides to move all x terms to one side:
2x - x + 6 = 10
1x + 6 = 10
Subtract 6 from both sides to solve for x:
x = 10 - 6
x = 4
Thus, the solution to the equation is x = 4. Checking the solution, we substitute x back into the original equation:
2(4 + 3) = 4 + 10
2(7) = 14
14 = 14
find the value of this pronumeral
Help I don’t understand
HELP ME PLZ
Using V = lwh , find an expression in factored form for the volume of this prism. Explain the general steps you used to arrive at this answer.
The volume of the prism with the given dimensions is;
V = 12x³ - 30x²
We are given that the formula for the volume of a cube is;
V = Lwh
where;
L is length
w is width
h is height
We are given;
L = (24x² + 6x)/(x -1)
w = 2x - 5
h = (x² - x)/(4x + 1)
This means that;
V = [(24x² + 6x)/(x - 1)] × (2x - 5) × [(x² - x)/(4x + 1)]
Now, let us factorize the terms that can be factorized;
(24x² + 6x)/(x - 1) can be factorized into; [6x(4x + 1)/(x - 1)]
Similarly;[(x² - x)/(4x + 1)] can be factorized into [x(x - 1)/(4x - 1)]
Using the factorized terms to get the volume now;
V = [tex]\frac{6x(4x + 1)}{x -1} * (2x - 5) * \frac{x(x - 1)}{4x + 1}[/tex]
(x - 1) will cancel out and also 4x + 1 will cancel out to give;
V = 6x * x * (2x - 5)
V = 6x²(2x - 5)
V = 12x³ - 30x²
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I really need the answer I’ve been stuck on this all day
Which measurement is the closest approximation of the rectangle’s area? A. 15 m² B. 30 m² C. 40 m² D. 50 m²
Can the sides of a triangle have lengths 7.2, 13.3, and 19.3?
yes or no
The period T of a pendulum in seconds depends on its length L in feet, and is given by the formula T=
a desert has both fruit and yogurt inside altogether the mass of the desert is 185g the ratio of the mass to fruit to the mass of yoghurt is 2:3 what is the mass of yoghurt?
The mass of the fruit is 74 grams and the mass of the yoghurt is 111 grams.
Given :
Total mass of the desert is 185 g.The ratio of the mass to fruit to the mass of yoghurt is 2:3.Solution :
This question is solved by making a linear equation in one variable. Linear equations are nothing but yet another subset of "equations". Any linear calculations requiring more than one variable can be done with the help of linear equations. The standard form of a linear equation in one variable is of the form ax + b = 0. Here, x is a variable, and a and b are constants.Now to form a linear equation first let x be the mass in gram. Than total mass of the desert is given by:
[tex]3x+2x=185[/tex]
[tex]5x = 185[/tex]
[tex]x = \dfrac{185}{5}[/tex]
x = 37 grams
Therefore the mass of the fruit = [tex]2 \times 37[/tex] = 74 grams and the mass of the yoghurt = [tex]3\times 37[/tex] = 111 grams.
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Find the area of the triangle or quadrilateral.