Solve each equation. Factor and use the zero product property to solve. Show all work algebraically.
Answers
5n^2 = 4n^2 - 4n
n^2 + 4n = 0
n(n + 4) = 0
n = 0 or n + 4 = 0
n = 0 or n = -4
24.
d^2 - 4d = 3d
d^2 - 7d = 0
d(d - 7) = 0
d = 0 or d - 7 = 0
d = 0 or d = 7
25.
3 - 13h = 3 - 8h + h^2
Subtract 3 from both sides.
-13h = -8h + h^2
Add 13h to both sides.
0 = 5h + h^2
0 = h(5 + h)
h = 0 or 5 + h = 0
h = 0 or h = -5
Related Questions
how do you solve this
Answers
a rectangular field has sides with the length of 120 yards in 62 yards to the nearest tenth of a yard find the length of the diagonal of the field
Answers
.. diagonal = √(120² +62²) = √18244 ≈ 135.1 . . . . yards
If BC -16 and BD-9 then find the length of BA. Show the work you use to find your answer. Draw the two similar triangles separately to help set up the proportion.
Answers
In right triangle the leg is geometrical mean of its projection on the hypotenuse and the hypotenuse. Thus,
[tex] AB^2=BD\cdot BC [/tex].
Substitude BC=16, BD=9, then
[tex] AB^2=9\cdot 16,\\ AB^2=144,\\ AB=12 [/tex].
Answer: AB=12
What do you call a person who makes faces all day long
Answers
A person who makes faces all day is often described as expressive or animated, and may be humorously termed a 'mugger' or 'face-puller'. Facial expressions are crucial for conveying emotion in human interaction and can be particularly striking in literature and dramatic performances.
The question 'What do you call a person who makes faces all day long?' is asking about a term or description for someone who frequently changes their facial expressions. While there is no specific term that describes this behavior in a clinical or professional sense, in a colloquial context, you might call such a person expressive, animated, or if the expressions are humorous or exaggerated, a 'mugger' or 'face-puller'. In literature and drama, characters known for their expressive faces can bring a story to life or provide comic relief.
Facial expressions are an integral part of human communication. They can underscore the emotional state of a person, such as the sense of pride on the face of a monomaniacal king, the devotion seen in a religious fanatic, or the terror described in the imagery of wallpaper patterns appearing to have expressive eyes. Whether in social interactions, literature, or public speaking, the alignment of facial expressions with spoken words is important for conveying meaning and emotion.
When a=-9, and b=-6, which expression has a value of -3?
A. a+b
B. a-b
C. |a+b|
D. |a-b|
Answers
Hope this helps
How do you factor 4x^2+20x-3xy-15y?
Answers
Rational and Irrational Numbers what is it explain
Answers
what does it mean to "square a circle"?
Answers
Final answer:
In mathematics, 'squaring the circle' means to create a square with the same area as a given circle, though it is impossible to achieve precisely due to the nature of π. When fitting a circle in a square, the side of the square is twice the radius of the circle, and the circle's area is approximately three-quarters that of the square.
Explanation:
To "square a circle" in mathematical terms traditionally means to create a square with the same area as a given circle, using only a finite number of steps with compass and straightedge. This problem is known to be impossible to solve exactly due to the transcendental nature of π (pi). However, when we discuss fitting a circle within a square, we often refer to having the diameter of the circle, which is twice the radius (2r), fit exactly across the side length of the square (a).
The area of the circle is πr², and when the circle fits within a square the area of the square is a². Since a = 2r, the area of the square can be expressed as 4r². From this, we can approximate that a circle's area would be less than the area of the square but more than half, possibly around three-quarters, thus approximately 3r².
Perimeter-wise, a circle within a square would have a circumference less than the perimeter of the square but significantly longer than a straight line passing through the center of the square. This understanding allows for practical estimations without requiring exact precision, which can be particularly useful in everyday contexts where an approximation suffices.
what are the mean median mode and range of the data set given the altitude of lakes in feet -9, -36, -23, -8, -17, -52, -27, and -36 A. mean=-25; median=-26; mode=-44; range=36 B. mean=-25; median=-36; mode=-36; range=44 C. mean=-26; median=-25; mode=-36; range=44 D. mean=-26; median=-44; mode=-25; range=36
Answers
The first step in solving this should be to determine what mean, median, mode and range are and how to find them.
The "mean" is essentially just the average of a set of numbers, and it's found by finding the sum of the numbers then dividing by the number of add-ins.
The "median" is the middle number in a set. This is found by arranging the numbers from smallest to largest and finding the center number. Sometimes, if there is an even number of items in a set, you'll have to find the median by taking the mean of the two middle number. (For example, if your set is 1, 2, 3, 4 you would find the median by looking or the middle number(s) which in this case would be 2 and 3. To find the median, you'd take 2+3 which equal 5 and divide that by the number of items- 2 which gives you 2.5).
The "mode" is the is simply whichever number occurs the most in a set.
The "range" is the difference between the largest and smallest numbers in a set; in other words, you take the largest number in the set and subtract the smallest number in the set from it (i.e if the largest number is 5 and the smallest number is 3, you'd take 5-3 which gives you the range of 2).
Now the, on to solving your problem!
The set you were given consists of the numbers -9, -36, -23, -8, -17, -52, -27, and -36.
To find the mean, we would take all of the numbers and add them up:
-9+(-36)+(-23)+(-8)+(-17)+(-52)+(-27)+(-36) = 208
Then, you divide the sum by the number of add-ins, in this case, 8 (since there are 8 numbers in the set).
-208/8 = -26.
So the mean = -26.
The median can be found next, by arranging the numbers from smallest to largest:
-52, -36, -36, -27, -23, -17, -9, -8
As we can see, the middle-most numbers are -27 and -23, so what we have to do is add the number which gives us -50 and divide by 2 which gives us the answer of -25.
So the median is -25.
Next is the mode, which can be found by seeing which number occurs the most. As we can see by looking at the set, -36 is the only number that occurs more than once (occurring twice).
Since it occurs the most, the mode is -36.
Finally, we need to find the range. In order to do this, we take the highest number (-8) and subtract the lowest number (-52).
-8-(-52)= 44
Keep in mind that when you're subtracting a negative, it becomes addition.
And there we go, the range is 44.
So now we just have to look at your choices, and you can see that option C matches the answers, since the mean= -26, the median= -25, the mode= -36, and the range = 44.
Truly hope this helps!
Answer:
C
Step-by-step explanation:
deena has a set of 4 coasters on her coffee table, and each coaster is shaped like a cylinder with a height of 0.5 inches and a radius of 2.5 inches. which is the total surface area of the 4 coasters?
Answers
Final answer:
The total surface area for the 4 cylindrical coasters, each with a height of 0.5 inches and a radius of 2.5 inches, is approximately 188.4956 square inches.
Explanation:
Deena has a set of 4 coasters, each shaped like a cylinder.
To calculate the surface area of one coaster, we need to find the area of the two circular bases and the area of the side that wraps around the cylinder (the lateral surface area).
The formula for the surface area of a cylinder is SA = 2πr(h+R), where r is the radius, h is the height, and R is the radius of the bases.
Given a height of 0.5 inches and a radius of 2.5 inches:
SA = 2π(2.5)(0.5+2.5)
SA = 2π(2.5)(3)
SA = 2π(7.5)
SA = 15π
The result is the surface area for one coaster. As we have 4 coasters, we multiply this result by 4:
Total surface area for 4 coasters = 4 × 15π ≈ 4 × 47.1239 ≈ 188.4956 square inches.
Which measure is equivalent to 48 quarts? 1 cup = 8 fluid ounces 1 quart = 4 cups
Answers
A balloon that is tied to a stake in the ground is being blown sideways by the wind. The length of the string from the stake to the balloon is 26 feet, and the distance from the stake to a point directly under the balloon is 24 feet.
Answers
The volume of a cube is 1,953.125 centimeters cubed. Find the length of the sides.
Answers
Part 2!
I REALLY, REALLY NEED HELP ON THIS QUESTION!!!!!!!! 50 POINTS!!!!!!!!! WILL GIVE THE BRAINLIEST TO CORRECT ANSWER!!!!!!!!!!!!! nth term
__________________________________________________________________________________________
Look at the picture!
*******If you don't answer with correct answers or give something absurd or don't give enough details, your answer WILL BE REPORTED AND DELETED AND YOU WILL LOSE THE POINTS FOR THIS QUESTION!!!!!
Answers
The picture below is pretty much all you need to know to answer these questions. It is a short course on arithmetic and geometric sequences. (We have left out some simplifications that can be made to the formulas for Nth term, and we have not shown formulas for the sum of a sequence.)
1. Geometric sequence with first term 5, common ratio 2. It will have the formula
.. f(n) = 5*2^(n-1) . . . . . . I can't read your picture to tell whether that is B or D
2. Arithmetic sequence with first term 1 and common difference 3. It will have the formula
.. f(n) = 1 +3(n -1) . . . . . . matches A
3. Geometric sequence with first term 2 and common ratio 3/2 = 1.5. It will have the formula
.. f(n) = 2*1.5^(n -1) . . . . . matches C
4. Geometric sequence with first term 600 and common ratio 60/600 = 0.1. It will have the formula
.. f(n) = 600*0.1^(n-1)
This can be simplified using the rules of exponents to
.. f(n) = 600*(0.1^-1)*(0.1^n)
.. f(n) = 6000*0.1^n . . . . . . matches A
5. The sequence is 12, 11, 10, 9, .... It is an arithmetic sequence with first term 12 and common difference -1. It will have the formula
.. f(n) = 12 +(-1)*(n -1)
.. f(n) = 12 -(n -1) . . . . . . matches B
6. This is an arithmetic sequence with first term 8 and common difference -0.5. It will have the formula
.. f(n) = 8 -0.5(n -1)
.. f(n) = 8.5 -0.5n . . . . . . matches C
At a ski resort there are three different chair lifts that will take you to the top of the mountain. There are six ski trails to the bottom of the mountain. How many different paths are there to go up and down the mountain?
Answers
A student is selling baked goods in the halls before school as a fundraiser. She sells cinnamon rolls, donuts, and croissants. Students purchase the goods according to the probability distribution:
X(Product): cinnamon roll, donut, croissant
P(x): 0.20, 0.55, 0.25
A): If a cinnamon roll yields $0.25 profit, a donut yields $0.20 profit, and a croissant yields a $0.30 profit, how much profit will be made on each customer?
B):If there are 50 customers, how much can you expect her to make?
Answers
b). Money made if there are 50 customers: $0.235 * 50 = $11.75
Iris had $900. She spend 22% of this amount on a mobile phone. How much did she pay for the mobile phone
Answers
Answer:
198
Step-by-step explanation:
Of means multiply and 22% as a decimal is 0.22, so multiply 0.22 by 900.
900*0.22=198
Ratio of dogs to cats is 9:4. If there are 54 dogs, how many cats?
Answers
What is 1 1/2 subtracted from the sum of 4 2/3 and 5 2/5
Answers
First, we need to add 4 2/3 and 5 2/5.
We should begin with converting the fractions into improper fractions.
4 2/3 + 5 2/5
= 14/3 + 27/5
Now, we find the common denominator.
= 70/15 + 71/15
We can add:
= 141/15
And simplify.
= 9 2/5
Finally, we subtract 1 1/2 from 9 2/5.
9 2/5 - 1 1/2
= 47/5 - 3/2
= 94/10 - 15/10
= 79/10
= 7 9/10
Your answer is 7 9/10.
Hope this helps!
7 9/10 is the correct answer. I use the wonderful world of google to help me with questions like that one
What components are important in a linear function?
Answers
The slope tells us how the line changes as it goes along, and the y-intercept tells where it begins on the positive x-axis.
Each small cube is 1 cm3. The length of the large cube is 12 cm. What is the volume of the large cube? A. 24 cm3 B. 144 cm3 C. 864 cm3 D. 1,728 cm3
Answers
Answer:
d
Step-by-step explanation:
How do I find the slope of the line through (–9, –10) and (–2, –5)?
Answers
Steps:
Identify two points on the line
Select one to be (x 1, y 1) and the other to be (x 2, y 2)
Use the slope the slope equation to calculate slope.
Thank you
slope of line is 5/7
Explanation:
The slope of the line can be calculated using the following rule:
slope = [tex] \frac{y2-y1}{x2-x1} [/tex]
The given points are:
(-9,-10) which represent (x1,y1)
(-2,-5) which represent (x2,y2)
Substitute with the points in the above equation to get the slope as follows:
slope = [tex] \frac{-5-(-10)}{-2-(-9)} [/tex] = 5/7
Hope this helps :)
Christopher just found beautiful yarn for 20% off at his favorite yarn store. He can make one scarf from 2/3 of a ball of yarn. If Christopher buys 12 balls of yarn, how many scarves can he make?
Answers
Answer:
16
Step-by-step explanation:
if 2/3 is used by one scarf, then we can divide 2/3 into 12
12/1 × 2/3
12/1 ×3/2= 36/2
36/2= 16
Christopher can create a total of 12 scarves with the 12 balls of yarn he buys, based on the ratio of 2/3 of a ball needed for one scarf.
Christopher can make scarves from yarn, where it takes 2/3 of a ball of yarn to make one scarf. If he buys 12 balls of yarn, we need to calculate the total number of scarves he can make.
Let's find out how many scarves he can create with 12 balls:
Firstly, determine how many scarf units are in one ball of yarn. Since it takes 2/3 of a ball to make a scarf, 1 ball equals 1.5 scarf units (since 1 / (2/3) = 1.5).Next, multiply the number of scarf units in one ball by the total number of balls. 1.5 scarf units per ball \\times 12 balls = 18 scarf units.Finally, since each scarf uses 2/3 of a ball, we divide the total number of scarf units by 1.5 to get the number of scarves. 18 scarf units / 1.5 = 12 scarves.Therefore, Christopher can make 12 scarves with 12 balls of yarn.
Carlos is 63 inches tall. What is his height in feet?
Answers
find the length of the base indicated for each trapezoid
Answers
To find the base of a trapezoid, you can view the trapezoid as two right triangles joined together. The base of the trapezoid is the sum of the bases of these triangles. Depending on the orientations of the sides of the trapezoid and the height, you might need to use the Pythagorean theorem.
Explanation:The question asks to find the length of the base for a given trapezoid. In order to do this, we can use concepts from geometry and trigonometry. Consider the trapezoid as two right triangles back to back. The base of the trapezoid is the sum of the bases of the two right triangles.
For example, if you have a trapezoid with sides A and B, and the height is H, you can use these sides and the trigonometric principles to calculate the lengths of the bases. If side A or B is not perpendicular to the base, you would need to use the Pythagorean theorem. That formula is A^2+B^2=C^2, where C is the hypotenuse of the right triangle formed.
In case, the sides A and B are perpendicular to the base, the lengths of the bases would simply be side A + side B. This would give you the total length of the base of the trapezoid.
Learn more about Trapezoid Base Length here:https://brainly.com/question/31380175
#SPJ12
How could you calculate each product? Describe the strategy you would use. Then calculate.
a) 9 x 5
b) 5 x 8
Answers
1. To solve 9 x 5 , I could add the number 9 five times . . .
9 + 9 + 9 + 9 + 9 = 45
9 x 5 = 45 <----
2. I would use the same strategy as the first one, except add the number 8 five times . . .
8 + 8 + 8 + 8 + 8 = 40
8 x 5 = 40 <----
Hope this helps you.
Have a great day!
The radius of a circular hat is 3.7 inches. Find the circumference. Use 3.14 for π. (1 point)
1.85 in.
11.618 in.
23.236 in.
22.2 in.
Answers
the equation for circumference is C=2(pie)r
So you take 2x3.14 which equals 6.28.
Then you multiply 6.28 by 3.7 to get your answer.
Answer:
The circumference is [tex]23.236\ in[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=3.7\ in[/tex]
substitute
[tex]C=2(3.14)(3.7)=23.236\ in[/tex]
HELP ME @LOULI pleaseeeeeeeee
Answers
am i right?
y = x - 700
Explanation:
The equation of the line in slope-intercept form has the following formula:
y = mx + c
where:
m is the slope
c is the y-intercept
1- getting the slope:
To get the slope, we will need two points from the graph. I will choose (700,0) and (0,-700)
slope = (y2-y1) / (x2-x1) = (-700-0) / (0-700) = 1
The equation now is:
y = 1x + c
y = x + c
2- getting the y-intercept:
The y-intercept means the value of the y at x = 0. We can get this directly from the graph.
From the graph, we can find that:
at x = 0, y = -700
Therefore:
c = -700
Based on the above, the equation of the line is:
y = x - 700
Hope this helps :)
A field is shaped like the figure shown. What is the area of the field? Use 3.14 for pi
Answers
Answer:
area of field = 146.24 m²
Explanation:
Noticing the figure, we can see that it is composed of three regular shapes:
1- a square
2- a triangle
3- quarter of a circle
We will get the area of each shape separately and then add them to get the total area of the field.
1- getting the area of the square:
area of the square = (side)²
we have the side = 8 m
Therefore:
area of square = (8)² = 64 m² ...............> I
2- getting the area of the triangle:
area of triangle = [tex] \frac{1}{2} [/tex] * base * height
We have the base = 8 m and the height = 8 m
Therefore:
area of triangle = [tex] \frac{1}{2} [/tex] * 8 * 8 = 32 m² ..........> II
3- getting the area of the quarter circle:
area of circle = πr²
area of quarter circle = [tex] \frac{1}{4} [/tex] * πr²
We have π = 3.14 and r = 8 m
Therefore:
area of quarter circle = [tex] \frac{1}{4} [/tex] * 3.14 * (8)² = 50.24 m² .....> III
4- getting the total area of field:
Total area of field = I + II + III
Total area of field = 64 + 32 + 50.24
Total area of field = 146.24 m²
Hope this helps :)
Answer:
Please Vote 1 Star
Step-by-step explanation:
And Don't Click "Thanks"
In a layout of Mark’s backyard, the ratio is 1 centimeter = 10 meters. The length of the deck on the layout is 4 cm and the width is 4 cm. What is the perimeter of Mark’s deck?
Answers
The perimeter of Mark's deck in real life is calculated by converting the layout measurements to actual measurements using the scale factor and then applying the perimeter formula. The perimeter is found to be 160 meters.
To calculate the perimeter of Mark's deck, which is represented on a layout where the scale is 1 centimeter = 10 meters, we use the perimeter formula for a rectangle: Perimeter (P) = 2 * (length + width). Since both the length and width of Mark's deck are provided as 4 centimeters each, and each centimeter corresponds to 10 meters in reality, we first convert the measurements from centimeters to meters by multiplying them by the scale factor.
Length in meters = 4 cm * 10 meters/cm = 40 meters
Width in meters = 4 cm * 10 meters/cm = 40 meters
Now, calculate the perimeter:
P = 2 * (40 meters + 40 meters)
P = 2 * 80 meters
P = 160 meters
The real-life perimeter of Mark's deck is 160 meters.