The factors of the quadratic expression 2n^2 - 5n - 42 are found by looking for two numbers that multiply to -84n^2 and add up to -5n. The correct pair is 7n and -12n, leading to the factors (2n + 7) and (n - 6).
Explanation:The factors of 2n^2 - 5n - 42 need to be determined by finding two numbers that multiply to 2n^2 times -42 (which is -84n^2) and add up to -5n. To factor this quadratic expression, we should look for a pair of numbers that meet these criteria.
Upon inspecting possible pairs, we find that 7n and -12n are the numbers that work since (7n) * (-12n) = -84n^2 and 7n + (-12n) = -5n. The quadratic trinomial can be expressed as:
2n^2 - 5n - 42 = (2n + 7)(n - 6)
By factoring this way, we have broken down the expression into its factors, which are (2n + 7) and (n - 6).
The factors of the quadratic expression [tex]\(2n^2 - 5n - 42\)[/tex] are [tex]\(2n + 7\)[/tex] and [tex]\(n - 6\)[/tex].
To find the factors of the quadratic expression \(2n^2 - 5n - 42\), we can use the factoring method. This involves finding two numbers that multiply to give the product of the coefficient of \(n^2\) (which is 2) and the constant term (which is -42), and also add up to the coefficient of \(n\) (which is -5).
The product of the coefficient of [tex]\(n^2\)[/tex] and the constant term is:
[tex]\(2 \times -42 = -84\)[/tex]
Now we need two numbers that multiply to -84 and add up to -5. These numbers are -12 and 7 because:
[tex]\(-12 \times 7 = -84\)[/tex]
[tex]\(-12 + 7 = -5\)[/tex]
Now we can rewrite the middle term of the quadratic expression using -12 and 7:
[tex]\(2n^2 - 12n + 7n - 42\)[/tex]
Next, we can factor by grouping. Group the first two terms and the last two terms:
[tex]\(2n(n - 6) + 7(n - 6)\)[/tex]
Notice that [tex]\(n - 6\)[/tex] is a common factor. We can factor this out:
[tex]\((2n + 7)(n - 6)\)[/tex].
A lab technician worked 48 3/4 hours over a six day period. If she worked the same number of hours each day, how many hours did she work each day?
A bag holds 500 grams of sand. About how many grains of sand are in the bag? There are about 1,000 grains of sand in 1 gram.
Find the value of x.
Answer: The required value of x is 64.
Step-by-step explanation: We are given to find the value of x from the figure.
From the figure, we see a right-angled triangle in which an acute angle has measurement x°.
And, for the angle with measurement x°, the base has a length of 3.0 units and hypotenuse has a length of 6.8 units.
Therefore, the cosine of that angle will be
[tex]\cos x^\circ=\dfrac{base}{hypotenuse}\\\\\\\Rightarrow \cos x^\circ=\dfrac{3.0}{6.8}\\\\\\\Rightarrow \cos x^\circ=0.4411\\\\\Rightarrow x^\circ=\cos^{-1}(0.4411)\\\\\Rightarrow x^\circ=63.83^\circ\\\\\Rightarrow x=63.83.[/tex]
So, to the nearest whole number, we get
x = 64.
Thus, the required value of x is 64.
Help please I need to get this right
Answer:
[tex] a_{n} = - 5 {( - 2)}^{n - 1} [/tex]
[tex]b = - 5[/tex]
[tex]c = - 2[/tex]
the following data are the numbers of customers at a coffee shop over a 10 day period 135,124,140,122,409,132,119,128,136,125 which measure of center best represents the daily average of customers at the coffee shop?
The measure of center that best represents the daily average of customers at the coffee shop is the mean, which is calculated by summing up all the numbers and dividing by the total count.
Explanation:To find the measure of center that best represents the daily average of customers at the coffee shop, we can calculate the mean, median, and mode of the given data set. The mean is the sum of all the numbers divided by the total count, the median is the middle value when the numbers are arranged in increasing order, and the mode is the number that appears most frequently.
Mean: Add up all the numbers and divide by the total count: (135+124+140+122+409+132+119+128+136+125)/10 = 157.
Median: Arrange the numbers in increasing order: 119, 122, 124, 125, 128, 132, 135, 136, 140, 409. The middle value is the median, which is 132.Mode: The number 122 appears twice, which is more frequent than any other number. Therefore, the mode is 122.Based on these calculations, we can conclude that the measure of center that best represents the daily average of customers at the coffee shop is the mean since it takes into account all the values in the data set.
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A forrest ranger wants to determine the radius of the trunk of a tree. She measures the circumference to be 8.6 feet. What is the trunk's radius to the nearest tenth foot?
Answer:
As per the given statement: A forest ranger wants to determine the radius of the trunk of a tree. She measures the circumference to be 8.6 feet.
Shape of the trunk of a tree is circle.
Use the circumference formula:
[tex]C = 2\pi r[/tex]
where C is the circumference of a circle and r is the radius of a circle.
Solve for r;
Given: C = 8.6 feet and use [tex]\pi = 3.14[/tex]
Substitute the given value we get;
[tex]8.6 = 2 \times 3.14 \times r[/tex]
Simplify:
[tex]8.6 = 6.28r[/tex]
Divide both sides by 6.28 we get;
r = 1.6942675 feet
Therefore, the trunk's radius to the nearest tenth foot is, 1.4 ft
Answer:1.4
Step-by-step explanation:
that is it its not that hard
The graph shows the number of public service announcements that a radio station played throughout the day. Public Service Announcements (PSAs) Aired. Which equation can be used to represent the number of public service announcements, y, in x hours?
it would be C. Y=4X
A satellite is to be put into an elliptical orbit around a moon. A vertical ellipse is shown surrounding a spherical object labeled moon The moon is a sphere with radius of 959 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 357 km to 710 km.
Answer:
The equation of the ellipse is :
[tex]\frac{x^2}{1316^2}+\frac{y^2}{1669^2}=1[/tex]
Step-by-step explanation:
Formula for the equation of an ellipse is given by :
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
where a and b are the horizontal and vertical intercepts of the ellipse on the coordinate axis.
Here, a = 959 + 357
= 1316
And, b = 959 + 710
= 1669
So, the equation of the ellipse is :
[tex]\frac{x^2}{1316^2}+\frac{y^2}{1669^2}=1[/tex]
Which two lakes are they?
NEED HELP ASAP
Read the complete problem before answering. Josh worked 2 1/2 hours of overtime on the weekend. He makes $20.50 an hour for overtime. How much did Josh make in overtime on the weekend? A student solved the problem this way: Let n represent the amount of money Josh earned working overtime. 2 1/2 hours = 2.5 hours n = 2.5 × $20.50 n = $51.25 Josh made $51.25 in overtime on the weekend. Use a similar strategy to solve this problem. Maria needed 3 1/10 cups of white flour and 4 1/2 cups of whole wheat flour for her cookie recipe. Flour cost $0.50 a cup. How much will Maria spend on flour to make her cookies? A. $1.55 B. $2.25 C. $3.80 D. $5.35
By converting mixed numbers to decimals and multiplying the total number of cups of flour by the cost per cup, we find out Maria will spend $3.80 on flour, which is option C.
To find out how much Maria will spend on flour to make her cookies, we need to calculate the total cost of white and whole wheat flour. Maria needs 3 1/10 cups of white flour and 4 1/2 cups of whole wheat flour. First, we convert the mixed numbers to decimal form: 3 1/10 cups is 3.1 cups, and 4 1/2 cups is 4.5 cups. Then we add them together to find the total number of cups Maria will use:
3.1 cups + 4.5 cups = 7.6 cups
Next, since flour costs $0.50 per cup, we multiply the total number of cups by the cost per cup:
7.6 cups × $0.50 per cup = $3.80
Therefore, Maria will spend a total of $3.80 on flour for her cookie recipe, making the correct answer C. $3.80.
Luna ray has 5 orange picks and no green picks you add some green picks so 1 in every 3 picks is orange how many picks are there now
each side of rectangular polygon is 2.5cm in length .the perimeter of the polygon is 12.5cm.how many sides does the polygon have
There are 5 sides (a pentagon). The perimeter is the length of one side times the number of sides.
Regular polygon has same length for all sides.The polygon has 5 sides. The specific type of polygon with 5 sides is called a pentagon.
The perimeter of a polygon is the total length of all its sides. In a regular polygon, all sides are equal in length. So, if each side of the polygon is 2.5 cm and the perimeter is 12.5 cm, we can find the number of sides by dividing the perimeter by the side length:
Number of sides = Perimeter / Side length
Number of sides = 12.5 cm / 2.5 cm
Number of sides = 5
Delilah does 184184184 jumping jacks in 444 minutes. She does her jumping jacks at a constant rate. How many jumping jacks can Delilah do per minute?
Answer:
46 jumps per minute.
Step-by-step explanation:
We have been given that Delilah does 184 jumping jacks in 4 minutes.
Since Delilah is jumping jacks at a constant rate, so the number of jumps per minute would be 184 divided by 4.
[tex]\text{Number of jumps per minute}=\frac{\text{184 jumps}}{\text{4 minutes}}[/tex]
[tex]\text{Number of jumps per minute}=\frac{\text{46 jumps}}{\text{minute}}[/tex]
Therefore, Delilah is jumping at a rate of 46 jumps per minute.
The Perimeter of a triangle is 50 cm. One side is 7cm longer than the another side and 5 cm shorter than the third side. Find all the sides of the triangle.
Suppose a triangle has sides 3, 4, and 5. Which of the following must be true? A. The triangle in question is a right triangle. B. The triangle in question is not a right triangle. C. The triangle in question may or may not be a right triangle.
Melissa and Joey enjoyed dinner at a restaurant. They paid the waiter $100.50 plus a 20% tip. How much did each person pay if they split the total bill in half?
The formula for the area of a trapezoid is A = h(b1 + b2), where A = area, h = height, b1 = base 1, and b2 = base 2. For a trapezoid with a height of 7 centimeters and base lengths of 6 centimeters and 10 centimeters, the area is square centimeters
Find the next two numbers in the pattern
12500, -2500, 500, -100,...
You paint a border around the top of the walls in your room. What angle does x need to be to repeat the pattern?
To repeat the pattern, the angle of x needs to be 360 degrees divided by the number of times the pattern is repeated.
Explanation:To repeat the pattern of the border around the top of the walls in your room, the angle of x needs to be 360 degrees divided by the number of times the pattern is repeated. For example, if the pattern is repeated 4 times around the room, the angle x would be 360 degrees divided by 4, which is 90 degrees.
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Georgie needs to paint the wall with a fixing mixture.
She mixes glue and water in the ratio 3:1 to make the mixture.
Georgie needs 5 litres of the mixture.
She has 3.5 litres of glue. Does Georgie have enough glue to make 5 litres of the mixture?
Answer:
You will need approximately 1.17 L of water with 3.5 L of glue. This is a total of 4.67 L, which is NOT enough.
Step-by-step explanation:
Georgie has 3.75 litres of glue which is enough to make 5 litres of the mixture.
What is the ratio?A ratio indicates how many times one number contains another. If a and b are to objects then ratio of a to the b is given as a : b.
Now it is given that,
Ratio of glue and water = 3 : 1
Amount of mixture = 5 litres
Georgie has glue = 3.5 litres
Now let x be the number,
So, Amount of glue in the mixture = 3x
and, amount of water in the mixture = x
⇒ Amount of mixture = 3x + x
⇒ 3x + x = 5
⇒ 4x = 5
⇒ x = 5/4
⇒ x = 1.25
Thus, Amount of glue in the mixture = 3*1.25 litres
⇒ Amount of glue in the mixture = 3.75 litres
So, Amount of glue in the mixture is greater than amount of glue Georgie has.
Thus, Georgie has 3.75 litres of glue which is enough to make 5 litres of the mixture.
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what is 39.6 times 5.20
if you had a rectangular sheet cake do you need to cut into 15 pieces how many pieces would have to be on each side to achieve that many servings out of the whole cake
A 12-sided number cube with the numbers 1 through 12 is rolled.
Select from the drop-down menu to correctly complete the statement.
Rounded to the nearest hundredth, the probability that the number cube lands on a number greater than 10 is .
0.17
0.25
0.75
0.83
Margie has a $50 budget to purchase a $45 pair of boots. If there is an 8% sales tax rate, then how much under budget will Margie be.
How do you find a missing height in a triangle?
what is the height of a building in meters if it takes a rock 3.8 seconds to drop from its roof
Final answer:
Using the formula for the distance fallen under gravity, the height of the building is found to be approximately 70.856 meters, given a drop time of 3.8 seconds.
Explanation:
The question asks, "What is the height of a building in meters if it takes a rock 3.8 seconds to drop from its roof?" To solve this, we'll use the physics formula for the distance (height) fallen by an object under gravity, which is given by d = ½ gt², where d is the distance in meters, g is the acceleration due to gravity (approximately 9.8 m/s²), and t is the time in seconds.
Substituting the given values into the equation, we have:
d = ½ × 9.8 m/s² × (3.8 s)²
= ½ × 9.8 × 14.44
= 70.856 meters
Therefore, the height of the building is approximately 70.856 meters.
what is the area of a circle with a circumference of 12pi?
The area of the circle for the given circumference is 36π square units.
What is a circle?Every point in the plane of a circle, which is a closed, two-dimensional object, is evenly separated from the center. All lines that cross the circle join together to produce the line of reflection symmetry. Every angle also possesses rotational symmetry about the center.
Given circumference of circle = 12π
the circumference is given by 2πr
where r is the radius,
2πr = 12π
2r = 12
r = 6 units
and the area of a circle is πr²
A = πr² = π(6²)
A = 36π square units
Hence the area of circle is 36π square units.
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The area of the circle with circumference [tex]\( 12\pi \)[/tex] is [tex]\( \boxed{36\pi} \)[/tex] square units.
To find the area of a circle when given its circumference, we start by using the formula relating circumference ([tex]\( C \)[/tex]) and radius ([tex]\( r \)[/tex]):
[tex]\[ C = 2\pi r \][/tex]
Given that the circumference [tex]\( C \)[/tex] is [tex]\( 12\pi \)[/tex], we set up the equation:
[tex]\[ 12\pi = 2\pi r \][/tex]
Next, solve for [tex]\( r \)[/tex] by dividing both sides by [tex]\( 2\pi \)[/tex]:
[tex]\[ r = \frac{12\pi}{2\pi} \][/tex]
[tex]\[ r = 6 \][/tex]
Now that we have found the radius [tex]\( r = 6 \)[/tex], we can find the area ([tex]\( A \)[/tex]) of the circle using the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
Substitute [tex]\( r = 6 \)[/tex]:
[tex]\[ A = \pi \cdot (6)^2 \][/tex]
[tex]\[ A = \pi \cdot 36 \][/tex]
[tex]\[ A = 36\pi \][/tex]
Therefore, the area of the circle with a circumference of [tex]\( 12\pi \)[/tex] is [tex]\( \boxed{36\pi} \)[/tex].
Simplify:(picture)
and can you please show your work so that i can understand how to do it myself? Thank you
(Photo) Please help mee
The two solids below are similar, and the ratio between the lengths of their edges is 3:5. What is the ratio of their surface areas?
Answer:
Step-by-step explanation:
Alright, lets get started.
The surface area of green solid is :
[tex]2 (3*3 + 3*3 + 3*3) = 2*27=54[/tex]
The surface area of orange solid is :
[tex]2(5*5 + 5*5 + 5*5) =2*75= 150[/tex]
So the ratios of their surface area will be :
[tex]\frac{54}{150}[/tex]
[tex]\frac{18}{50}[/tex]
[tex]\frac{9}{25}[/tex]
Hence the answer is 9:25 : Answer Hope it will help :)
The expression 5(3 + 7) is a
sum.
product.
difference.