Answer:
20 ft.
Step-by-step explanation:
There are two different (yet similar) ways to solve this problem:
a. Pythagorean theorem
b. Pythagorean triplet recognition
With option "a", you set it up:
12² + 16² = x²
144 + 256 = x²
400 = x²
x = 20
But, the arguably "easier" way to find out the distance is to use the Pythagorean's triplet recognition.
We know that the most common right triangle is the 3-4-5 right triangle.
If you take the three side lengths, and multiple them by the same thing, those are the sides to another right triangle.
ex. 3-4-5 * 5
15-20-25 are the sides of another right triangle!
This also means that if you have a triangle that has the sides 15, 20, and 25, you immediately know it's a right triangle.
When we look at 12 and 16, we know they are the legs of the triangle.
We also know that if we multiply 4 times 3 and 4, it will equal 12 and 16.
So what's 5 times 4? 20!
Final answer:
To find how far the bird will fly to the top of the tree, we use the Pythagorean Theorem. By squaring the height of the tree and the distance from the bird to the tree, we find that the hypotenuse, or the distance the bird will fly, is 20 feet.
Explanation:
The question asks about the distance a bird will fly from the ground to the top of a tree, which involves the application of the Pythagorean Theorem to solve for the hypotenuse of a right triangle. The tree's height (12 feet) represents one leg of the right triangle, and the distance from the bird to the tree (16 feet) represents the other leg. To find the distance the bird flies (the hypotenuse), we use the equation:
a² + b² = c²
Where ‘a’ and ‘b’ are the lengths of the legs, and ‘c’ is the length of the hypotenuse. Now we can calculate it:
12² + 16² = c²
144 + 256 = c²
400 = c²
[tex]\sqrt{400}[/tex] = c
20 feet = c
Therefore, the bird will fly 20 feet to reach the top of the oak tree.
What is the equation of the line that passes through the point (-4, 4) and has a
slope of -3
Answer:
[tex]y=-3x+4[/tex]
Two triangles have a scale factor of 5:7, If the area of the smaller triangle is 225cm squared what is the area of the larger triangle
Answer:
441
Step-by-step explanation:
The ratio of sidelengths squares is the ratio of the areas, so the ratio of the area of the smaller triangle's area to the larger triangle's is 25:49.
Using ratios, you figure out that the area of the larger triangle must be 225/25 *49, which is equal to 9*49 = 441
Final answer:
The area of the larger triangle, given a scale factor of 5:7 and the smaller triangle's area of 225cm squared, is 441cm squared. The areas scale as the square of the scale factor, in this case, 25:49.
Explanation:
The question involves working with the scaling of the area of a triangle when given a scale factor between two similar triangles. Since the scale factor of the linear dimensions between the two triangles is 5:7, the ratio of the areas is the square of the scale factor, which is (5:7)2 or 25:49.
If the area of the smaller triangle is 225 cm², to find the area of the larger triangle, we need to use the area ratio. Given that 25 parts correspond to 225 cm²in the smaller triangle, we can calculate the value of 1 part as 225 cm² / 25 = 9 cm2. Hence, the area of the larger triangle corresponds to 49 parts, which gives us 49 * 9 cm² = 441 cm².
Andre says that 10x + 11 and 5x + 11 are equivalent because they both equal 16 when x is 1. do you agree with Andre?
Answer: No
Step-by-step explanation:
10x + 11 when x= 1 is equal to 21
While 5x + 11, when x=1 is equal to 16
what are the measures of center
Answer: mean, median, mode and range
Step-by-step explanation:
The measures of centre are referred to as mean, median, mode and range.
Mean also referred to as average, it is the sum of values in a data set divided by the number of values in the given data set.
Median is the middle point number in a given data set. Median of an even data set is the average of two values in the middle of the data set.
Mode is the most occurring number in the given data set. It is the number with the highest frequency in the set.
Range is the difference between the highest number and the lowest number in a given data set.
I hope this answers your question.
The measures of center in a dataset are statistical values that represent the central point of the data. These include the mean (arithmetic average), median (middle value), and mode (most frequent value). Another common measure of center is the weighted mean, which is used when some data points carry more significance than others.
Explanation:Measures of the center are statistical measures that provide information about the central point of a dataset. The main measures include the mean, median, and mode.
The mean is the arithmetic average of the data set. This is usually the sum of all data points divided by the number of data points.
The median is the middle value of the data set when it is ordered from smallest to largest. If there is an even number of data points, the median would be the average of the two middle numbers.
The mode is the data point that occurs most frequently in the data set. A data set may have one mode, more than one mode, or no mode at all.
Another common measure of center is the weighted mean, which is useful when some data points carry more significance than others. For example, you might want to calculate the average grade in a class where some assignments are worth more than others.
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what is the positive solution to the equation 4x^2 + 12x = 135
The positive solution to the equation 4x^2 + 12x = 135 is; x = 9/2
By quadratic formula;
x = {-b ±√(b² - 4ac)}/2awhere, a = 4, b = 12 and c = -135.
By solving the equation quadratically;
The solutions are;
x = 9/2. OR. x = -15/2In essence, the positive solution of the equation is; x = 9/2
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The positive solution to the equation 4x^2 + 12x = 135 is found using the quadratic formula, resulting in a positive root of approximately x ≈ 3.375.
Explanation:The positive solution to the equation 4x^2 + 12x = 135 can be found by first rearranging the equation into the standard quadratic form of ax^2 + bx + c = 0. Bringing all terms to one side gives us 4x^2 + 12x - 135 = 0. This equation can be solved by either factoring, completing the square or using the quadratic formula. Since the original equation does not easily factor into a product of binomials, and the instructions indicate a preference for recognizing a perfect square when possible, we should attempt to complete the square or use the quadratic formula.
To complete the square, we would add (b/2a)^2 to both sides of the equation after dividing the linear coefficient by 2 and squaring the result. However, in this case, it's more straightforward to employ the quadratic formula, which is x = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values from our equation gives two roots, but since we are only interested in the positive root, we take the solution where the square root term is added to the negative b value.
After calculating, we find that the positive root is x ≈ 3.375, which is the solution to the equation in question.
The measure of an angle is 63.7°. What is the measure of its supplementary angle?
Answer:
116.3
Step-by-step explanation:
Supplementary angles add to 180
One angle is 63.7, the other is x
63.7+x = 180
Subtract 63.7 from each side
63.7-63.7+x = 180-63.7
x = 116.3
it costs $6 for a dozen donuts how much does 1 donut cost
Answer:
.50 for one donut
Step-by-step explanation:
do a ratio 6$ for 12 donuts
so for $ for 1 donut
reduce the first equation for a ration of $1 per two donuts
so it be 50 cents
$6. $0.50
____ = ______
12 donuts. 1 donut
The boat is going 10 miles per hour in still water it takes 2 hours to go downstream and 3 hours to go upstream. What’s the speed of the current and distance of the trip?
Answer:
2 mph24 miles one-way; 48 miles round tripStep-by-step explanation:
Let c represent the speed of the current. The travel time is inversely proportional to the travel speed. In one direction the current speed is added to the boat speed; in the other direction, it is subtracted. You can write the relation ...
(10 +c)/(10 -c) = 3/2
2(10 +c) = 3(10 -c) . . . . . . "cross multiply"
20 +2c = 30 -3c . . . . . . . eliminate parentheses
5c = 10 . . . . . . . . . . . . . . . add 3c -20
c = 2 . . . . . . . . . . . . . . . . . divide by 5
The speed of the current is 2 miles per hour.
__
The speed downstream is then (10 +2) = 12 miles per hour. The travel time in that direction is 2 hours, so the distance covered is ...
(12 mi/h)(2 h) = 24 mi
The one-way distance of the trip is 24 miles.
78/17 round to the nearest 10
Answer:
0
Step-by-step explanation:
78/17 gives 4.588
In rounding up numbers, 1 to 4 is rounded up to zero, while numbers 5 to 9 will be rounded up to 1.
In the question above, we are asked to round up to the nearest 10. And then 78/17 gives 4.588
This number is between 0 and 10.
The whole number there is 4. Therefore, 4 will be rounded up to Zero.
If the question and us to round up to the nearest whole number, as we have 4.588
The number before the whole number 4 is 5 (the tenth digit), and then 5 will be rounded up to 1. That 1 will hence be added to 4.
4+1= 5. To nearest whole number, it is 5 but to nearest ten, it is 0
can someone answer 8-11 please
Answer:
7.9
4.2
9.3
17.8
Step-by-step explanation:
8. √63
the square of 8 is 64 √63 is close to 64 so we can say it's 7.9 approximately
9. √18
the square of 4 is 16, √18 is greater than 16 so we can say it's 4.2 approximately
10. √87
the square of 9 is 81, √87 is greater than 81 so we can say the value of it is approximately 9.3
11. √319
the square of 18 is 324, √319 is smaller than 324 so we can say it's 17.8
How many cubic meters of material are there in a conical pile of dirt that has radius 11 meters and height 6 meters? Use 3.14 for pi.
The volume of a conical pile of dirt with an 11-meter radius and a 6-meter height is approximately 754.24 cubic meters.
The question is asking for help in calculating the volume of a conical pile of dirt.
The formula for finding the volume of a cone is [tex]V = (1/3) \pi r^2h[/tex], where V is the volume, r is the radius, and h is the height of the cone.
Substituting the given values, the radius r is 11 meters, the height h is 6 meters, and using 3.14 for
π, the calculation would be -
V = (1/3) * 3.14 * 112 * 6.
To find the volume: V = (1/3) * 3.14 * 121 * 6
= 3.14 * 40.333333 * 6
= 754.24 cubic meters.
So, there are approximately 754.24 cubic meters of material in the conical pile of dirt.
Write a sequence that has two geometric means between -6 and 2/9
A farm is 350 acres .72% of the farm is suitable for farming. How many acres can be used to farm?
Answer:
252
Step-by-step explanation:
Multiply 350 by the decimal form of 72%. To find the decimal form of 72%, divide 72 by 100 or move every number two places to the right:
72/100 = 0.72
Then multiply 350 by 0.72:
350 x 0.72 = 252
I hope this helps!
How many five-digit numbers are there for which each digit is either equal to both adjacent ones, or differs from its neighbors exactly by 1 (from one smaller by 1, and from the other larger by 1) and which contain the digit 5?
The question is about finding the total count of possible 5-digit numbers that either has identical adjacent digits or differ from its neighbor digits by exactly 1 and containing at least one 5. Providing an exact solution without knowing students' pre-existing knowledge on the subject can be difficult. This kind of problem typically involves methodologies like recursive relationships.
Explanation:This question pertains to combinatorics, a topic in mathematics that deals with countable structures. Specifically, the question is asking how many five-digit numbers are there that follows the conditions given in the question.
The condition that the number contains the digit 5 is applicable for both the cases where the digit is the same as or differs by 1 from its neighbors. This is because 5 is a middle digit from 0 to 9, and it can satisfy both conditions.
The problem can be approached by finding the total count of five digit numbers that satisfy just the adjacent difference conditions, and then subtracting the count of such numbers that do not contain the digit 5.
However, providing a step-by-step solution to this problem would be complex and lengthy, especially without the proper context of the student's pre-existing knowledge. The method to solve it would involve recursive relationships and possibly programming or usage of a suitable mathematical software.
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Which of the following numbers could be added to 3/14 to make a sum greater than 1/2
Answer:
x > 2/7
Step-by-step explanation:
Step 1: Make an inequality
3/14 + x > 1/2
Step 2: Solve for x
3/14 + x - 3/14 > 1/2 - 3/14
x > 2/7
Answer: x > 2/7
mel paid for three-fourths of the cost of a cake and Gretchen paid the rest. If Mel paid $21, how much did Gretchen pay
Multipli the numbers
$7.00
21/3=7, and 21 is 3/4 of 7*4
Tammy is going for a walk she walks at a speed of 3 miles per hour for 7.5 miles. For how many hours does she walk.
Tammy does walk a time of 3.75 hours
Explanation:
Given-
Speed, (which can be represented as s) = 2 miles/hour
Distance, (which can be represented as d) = 7.5 miles of distance .
Time, t = ?
We know,
d = s t
7.5 miles of distance = 2 miles/hour × t
3.75 hour of time = t
Therefore, Tammy does walk a time of 3.75 hours
Combine like terms to simplify the expression: 9 + 3b − 1 + 7b − 2 = ______ 9 − 10b 6 + 10b 8 + 10b 16b 9 + 10b
Answer:6 +10b
Step-by-step explanation:
Like terms 9-1-2 =6 and 3b + 7b = 10b
For what integer value of x is 4x – 2 >17 and 3x +5<24 ?
Help me please !!
Answer:
The integer values of x are 5 and 6
Step-by-step explanation:
we have
Inequality A
[tex]4x-2>17[/tex]
solve for x
adds 2 both sides
[tex]4x>19[/tex]
divide by 4 both sides
[tex]x> 4.75[/tex]
solution A is the interval (4.75,∞)
Inequality B
[tex]3x+5<24[/tex]
solve for x
subtract 5 both sides
[tex]3x<19[/tex]
divide by 3 both sides
[tex]x<6.33[/tex]
solution B is the interval (-∞,6.33)
The solution of the inequality A and the inequality B is
(4.75,∞) ∩ (-∞,6.33)=(4.75,6.33)
The integer values of x are 5 and 6
Final answer:
The integer value of x for which both inequalities 4x - 2 > 17 and 3x + 5 < 24 are true is x = 5.
Explanation:
To find the integer value of x for which the inequalities 4x – 2 > 17 and 3x + 5 < 24 are both true, we solve each inequality step by step.
For the first inequality, 4x – 2 > 17, add 2 to both sides to get 4x > 19. Then divide by 4 to isolate x, yielding x > 4.75.For the second inequality, 3x + 5 < 24, subtract 5 from both sides to get 3x < 19. Then divide by 3 to isolate x, resulting in x < 6.3333.Both inequalities must be true, so we need to find the interval where x > 4.75 and x < 6.3333. Since x must be an integer, the only integer within this range is x = 5.
please help me i need help
Step-by-step explanation:
(a)
[tex] In\: \triangle ABC \& \triangle DEF \\\\
\frac {AB} {DE} = \frac {40} {48} = \frac {5} {6}...(1)\\\\
\angle ABC \cong \angle DEF... (each\: 90°)...(2)\\\\
\frac {BC} {EF} = \frac {30} {36} = \frac {5} {6}...(3)\\\\[/tex]
From equations (1), (2) & (3)
[tex] \triangle ABC \sim \triangle DEF[/tex]
(By SAS Postulate)
Hence both of the triangles are similar.
(b)
Prism DEF will have greater volume, because length of its sides are larger than that of prism ABC.
6/5 = 1.2 times greater.
what is the expression in simplified form (-9√2)(4√6)
A. -5√8
B. -72√3
C. -36√8
D. -72√2
Answer: -72√3
Step-by-step explanation:
(-9√2)(4√6)
−9√2*4√6
-9*4√2*6
-9*4√12
-9*4*2√3
-72√3
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)
- Cutiepatutie ☺❀❤
Final answer:
To simplify (-9√2)(4√6), we multiply numerical coefficients (-9) and (4), and the square roots √2 and √6, simplifying to get -72√3 which is option B.
Explanation:
To simplify the expression (-9√2)(4√6), we need to follow the rules of algebraic multiplication for square roots. Here are the steps to simplify the expression:
Multiply the numerical coefficients together: (-9) × (4) = -36.Multiply the square roots together: √2 × √6 = √(2×6) = √12.Now, we simplify √12 by breaking it down into its prime factors: √(4×3) = √4 × √3 = 2√3.Combine the results: -36 × 2√3 = -72√3 which is our final simplified form.The correct option from the given choices is thus B. -72√3.
write an equation that is parallel to 3x-2y=14 and passes through point (-6,-11)
y = ([tex]\frac{3}{2}[/tex])x -2 is the equation of the required line
Step-by-step explanation:
Step 1 :
Equation of the given line is 3x-2y=14
Re writing this in the form y = mx + c , we have
-2y = -3x +14
y = ([tex]\frac{3}{2}[/tex])x - 7
The co efficient of x , m is the slope of the line. So for the given line the slope is [tex]\frac{3}{2}[/tex]
Step 2 :
We have to find equation of a line which is parallel to this line. All parallel lines will have the same slope. Hence the required line has a slope of [tex]\frac{3}{2}[/tex].
Step 3 :
Equation of line with slope m and passing through a point ([tex]x_{1} ,y_{1}[/tex]) is
(y-[tex]y_{1}[/tex]) = m((x-[tex]x_{1}[/tex])
So equation of line passing through (-6,-11) and with a slope of [tex]\frac{3}{2}[/tex] is
(y-(-11)) = [tex]\frac{3}{2}[/tex] ( x - (-6))
y + 11 = [tex]\frac{3}{2}[/tex] ( x + 6)
y = ([tex]\frac{3}{2}[/tex])x + 9 - 11
y = ([tex]\frac{3}{2}[/tex])x -2
Step 4 :
Answer :
y = ([tex]\frac{3}{2}[/tex])x -2 is the required equation
The given equation has the slope 3/2 after converting to the slope-intercept form. Because parallel lines share the same slope, the equation for the line parallel to the given line, passing through the point (-6,-11), is found to be y = (3/2)x - 9 using the point-slope form.
Explanation:To find an equation that is parallel to a given equation, we must first find the slope of the given line. The equation provided is in the form Ax + By = C. To convert this into slope-intercept form (y = mx + b), where m is the slope, we rearrange the equation to get y = (3/2)x - 7. Therefore, the slope of the given line is 3/2.
Parallel lines share the same slope, the equation of the line parallel to the given one that passes through point (-6,-11) will also have the slope 3/2. We stick this and our point into the point-slope form of a line (y - y1 = m(x - x1)) to get: y + 11 = 3/2(x + 6). Simplifying, we get y = (3/2)x - 9 which is the equation of the line parallel to the given equation that passes through the point (-6,-11).
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What missing number would complete the factorization?
k2 + 5k + 6 = (k + 2)(k + ?)
A. 3
B. 6
C. 12
D. 4
Answer:
A. 3Step-by-step explanation:
[tex]k^2+5k+6=k^2+2k+3k+6=k(k+2)+3(k+2)\\\\=(k+2)(k+3)[/tex]
Other method:
[tex]k^2+5k+6=(k+2)(k+x)\qquad\text{use}\ FOIL\\\\k^2+5k+6=(k)(k)+(k)(x)+(2)(k)+(2)(x)\\\\k^2+5k+6=k^2+kx+2k+2x\\\\k^2+5k+6=k^2+(x+2)k+2x\Rightarrow x+2=5\ \wedge\ 2x=6\\\\x+2=5\qquad\text{subtract 2 from both sides}\\x=3\\\\2x=6\qquad\text{divide both sides by 2}\\x=3[/tex]
What was the population density per square meter ?
Answer:
The population density in people per square meter is 0.005377 people per square meter.
Answer: [tex]0.005377\frac{people}{m^{2}}[/tex]
Step-by-step explanation:
You want to convert [tex]\frac{people}{km^{2} }[/tex] to [tex]\frac{people}{m^{2}}[/tex]
To do this, multiply [tex]\frac{people}{km^{2} }[/tex] * [tex]\frac{1 km}{1000 m}[/tex] * [tex]\frac{1 km}{1000 m}[/tex]=[tex]\frac{people}{1000 * 1000 m^{2}}[/tex]
sub in 5377 for people to get
[tex]\frac{5377people}{1000 * 1000 m^{2}}=0.005377\frac{people}{m^{2}}[/tex]
Simplify this algebraic expression completely 9x-6(x+4)
Answer:
3x - 24
Step-by-step explanation:
9x - 6x - 24
3x - 24
terry sees this offer : reburfished phone 35% off now only £78 , how much was the phone before the discount
Translate this sentence into an equation. 48 is the product of Greg’s score and 3. Use the variable g to represent Greg’s score
Answer:
G x 3 = 48
Step-by-step explanation:
let G be Greg's score
And product means multiplication.
so G x 3 = 48.
finding Greg's score means 3g = 48.
g = 48/3
g = 16.
sam has a collection of 76 marbles. In the collection, 25% of the marbles are red and the rest are blue. Which statement accurately describes Samuel's marble collection? 19 marbles are red and 57 marbles are blue. 57 marbles are red and 19 marbles are blue. 16 marbles are red and 60 marbles are blue.
Answer:
Red is 19
Blue is 57
Step-by-step explanation:
According to the question,it says Sam has 25% red marble out of the 76.
It means 25/100×76
It gives 19
To get the value for blue
Blue + red=76
Red is 19
Blue + 19=76
Blue=76-19
Blue=57
Therefore,red is 19 and blue is 57
nononononononononono
Answer:
yesyesyesyes
Step-by-step explanation:
yesyesyesyesyes
Answer:
yesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyes
Mary and her friends set out to sea on their annual fishing trip. Their distance from the shore in miles, y, increases by 3 miles each hour, x. write an equation to model this relationship.
y=3x
y=3/2x
y=x+3
y=2x
y=x-4
y=x+5
Answer:
y=3x
Step-by-step explanation:
If y is the total distance from the shore and it increases by 3 miles every hour, then by plugging in the amount of hours that have passed into x we will find the distance they have traveled. For example, if they have been out for 5 hours then you would do y=3(5) which would be 15 miles from the shore.
The correct equation to represent the relationship between Mary's distance from shore and time is y=3x. This is a linear equation, with 3 representing the rate of increase in distance for each time unit (each hour).
Explanation:In this case, Mary is moving at a constant rate, which means we are dealing with a linear relationship. The problem states that her distance from shore, y, increases by 3 miles for each hour, x. Therefore, the correct equation to model this scenario would be y=3x.
This is an equation of a line where 3 is the slope, signifying the change in distance for each time unit (in this case, an hour), and x is the time in hours. So, as time increases, the distance from the shore also increases at a rate of 3 miles per hour.
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