Answers
The approximate height of the tree is given as follows:
45.6 ft.
What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The altitude segment for this problem is given as follows:
14.5 ft.
The bases are given as follows:
5.2 ft and x ft.
Hence the value of x is given as follows:
5.2x = 14.5²
x = 14.5²/5.2
x = 40.4 ft.
Hence the height of the three is given as follows:
5.2 + 40.4 = 45.6 ft.
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Related Questions
2x² - 4y for x = -4 and y = 6.
Answers
Answer:
8
Step-by-step explanation:
2x² - 4y ( substitute x = - 4 and y = 6 into the expression )
= 2(- 4)² - 4(6)
= 2(16) - 24
= 32 - 24
= 8
2 questions.
Find the lenght and width
Find the admission price for an adult ticket and student ticket.
Answers
1) The length of the rectangle is 15 feet and its width is 9 feet.
2) The admission price for an adult ticket is $10 and a student ticket is $6.
How to solve the problems?1) We shall use the formula for the area of a rectangle to find the length and the width:
A = l * w
where:
A = Area.
l = length
w = width.
Given:
l = 6 feet more than the width.
A = 135 feet square meter
First, we write an equation for the area like this:
(w + 6) * w = 135
Expanding the equation:
w² + 6w - 135 = 0
Next, solve the quadratic equation by factoring:
(w - 9)(w + 15) = 0
So either w - 9 = 0 or w + 15 = 0. This means that either w = 9 or w = -15. Since the width cannot be negative, we have w = 9.
Finally, we shall find the length since we know the width. This can be done by using the fact that it is 6 feet more than the width:
l = w + 6 = 9 + 6 = 15
So, the length is 15 feet and the width is 9 feet.
2) We can find the admission price for an adult ticket and a student ticket by using Mathematical operators:
Let,
a = an adult ticket price
s = a student ticket price
From the given information, we get these equations:
5a + 11s = 116
3a + 4s = 54
Next, solve by substitution.
Solving for 'a' in the second equation:
a = (54 - 4s) / 3
Then, substitute the second expression for 'a' into the first equation:
5((54 - 4s) / 3) + 11s = 116
Multiply both sides by 3:
5(54 - 4s) + 33s = 348
Finally, expand and simplify:
270 - 20s + 33s = 348
13s = 78
s = 6
So, a student ticket costs $6.
Plug this value into either equation to get the adult ticket price:
3a + (4 * 6) = 54
3a + 24 = 54
3a = 30
a = 10
So, an adult ticket costs $10.
Therefore,
1) The length of a rectangle is 15 feet and the width is 9 feet
2) The admission price for an adult ticket is $10 and that of a student is $6
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Please gimme the variables to define the sytem and 2 system of equations
Answers
Answer:
[tex]8.5x+4y=99.5,\ x+y=17[/tex]
Step-by-step explanation:
[tex]\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}[/tex]
p^q is logically equivalent to
Answers
The logically equivalent statement to p → q is:
~q → ~p
How to find the logically equivalent statement?The conditional statement:
p → q
Assuming p and q are propositions, the conditional statement may be expressed as:
"If p holds true, then q follows suit. "
'
Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.
We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.
~p and ~q
These mean:
Not p and Not q respectively.
Then the statement:
"If q is not true, then p is not true"
Is written as:
~q → ~p
So this is the logically equivalent statement.
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The Complete Question
Given a conditional statement p → q, which statement is logically equivalent?
~p → ~q
~q → ~p
q → p
p → ~q
PROPIEDADES DE LOS LOGARITMOS
3log(x+2)+4log(x-4)- 2log(x+5)-3log(x-9)
Answers
The original expression simplifies to log((x+2)^3 * (x-4)^4) + log((x+5)^-2 / (x-9)^3) This represents a sum of Logarithms with different bases and arguments.
The given expression is 3log(x+2) + 4log(x-4) - 2log(x+5) - 3log(x-9). Let's simplify this expression using the properties of logarithms:
1. Product Rule: log(a) + log(b) = log(ab)
We can apply this rule to the first two terms:
3log(x+2) + 4log(x-4) = log((x+2)^3) + log((x-4)^4)
= log((x+2)^3 * (x-4)^4)
2. Quotient Rule: log(a) - log(b) = log(a/b)
We can apply this rule to the third and fourth terms:
-2log(x+5) - 3log(x-9) = log((x+5)^-2) + log((x-9)^-3)
= log((x+5)^-2 / (x-9)^3)
Therefore, the original expression simplifies to:
log((x+2)^3 * (x-4)^4) + log((x+5)^-2 / (x-9)^3)
This represents a sum of logarithms with different bases and arguments.
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Find all solutions of each equation on the interval 0≤ x <2pie
tan² x sec² x +2 sec²x - tan²x =2
Answers
The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.
How to solve a trigonometric equation
In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:
tan² x · sec² x + 2 · sec² x - tan² x = 2
Second, use trigonometric formulas to reduce the number of trigonometric functions:
tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2
Third, expand the equation:
tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2
tan⁴ x + 2 · tan² x = 0
Fourth, factor the expression:
tan² x · (tan² x - 2) = 0
tan² x = 0 or tan² x = 2
tan x = 0 or tan x = ± √2
Fifth, determine the solutions to trigonometric equation:
x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.
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If you have Muro 128 5% solution. How many mL will give you 0.1 g of sodium chloride?
Answers
You would need 2 mL of Muro 128 5% solution to obtain 0.1 g of sodium chloride.
To determine the volume of Muro 128 5% solution needed to obtain 0.1 g of sodium chloride, we need to consider the concentration of sodium chloride in the solution and perform some calculations.
Muro 128 5% solution refers to a solution containing 5 grams of sodium chloride per 100 mL of solution. This means that in 1 mL of the solution, there is 0.05 grams of sodium chloride (5 grams divided by 100 mL).
To find the volume of the solution needed to obtain 0.1 g of sodium chloride, we can use the following equation:
Volume (mL) = (Mass of sodium chloride (g)) / (Concentration of sodium chloride (g/mL))
In this case, the mass of sodium chloride is 0.1 g, and the concentration of sodium chloride is 0.05 g/mL.
Volume (mL) = 0.1 g / 0.05 g/mL = 2 mL
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What is the future value of $500 invested at 8 percent for five years under semi-annual compounding conditions?
Note: provide answer in full dollars/cents form, e.g., $123.45
Answers
To calculate the future value (FV) of an investment, we can use the formula:
FV = P(1 + r/n)^(nt)
Where:
FV = Future Value
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
In this case, the principal amount is $500, the annual interest rate is 8% (or 0.08 as a decimal), and the compounding is done semi-annually (n = 2). The investment is held for 5 years (t = 5).
Using the formula, we can calculate the future value:
FV = $500 * (1 + 0.08/2)^(2*5)
FV = $500 * (1.04)^(10)
FV ≈ $734.66
Therefore, the future value of $500 invested at 8% for five years under semi-annual compounding conditions is approximately $734.66.
Kindly Heart and 5 Star this answer and especially don't forgot to BRAINLIEST, thanks!a question was asked by a teacher to a student. She gave the student a jumbled word and told him to make words out of it. The jumbled word is gzeysktqix. Now you know what to do. see ya!
Answers
The teacher's question, the student can provide a List of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
Let unscramble the jumbled word "gzeysktqix" and find the possible words that can be formed.
Upon unscrambling, we can find several possible words:
1. Sixty
2. Zesty
3. Skit
4. Site
5. Size
6. Exit
7. Yeti
8. Kits
9. Kite
10. Ties
These are some of the words that can be formed from the jumbled letters "gzeysktqix." There may be additional words that can be created, depending on the specific rules or restrictions given by the teacher.
Unscrambling words can be a fun and challenging exercise that helps improve vocabulary, word recognition, and problem-solving skills. It allows students to enhance their language abilities and discover new words they might not have known before.
Remember, the key is to rearrange the given letters systematically and try different combinations until meaningful words are formed.
So, in response to the teacher's question, the student can provide a list of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
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Write 8 x 105 in standard notation.
Answers
Hello!
8 x 10⁵
= 8 x 100000
= 800000
A gardener has 800 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.
garden bordered by a river
What dimensions would guarantee that the garden has the greatest possible area?
shorter side:
ft (feet)
longer side:
ft (feet)
greatest possible area:
ft2 (square-feet)
Answers
Step-by-step explanation:
I'm assuming the sides can only be integers.
The most optimal area would be a square. We need to distribute 800 to 3 sides, which of course is not possible with integers. We will have to distribute the 800 as evenly as possible.
800/3 = 266.666666667.
We can let 2 sides be 267 and 1 side be 266. This will distribute it evenly. However, notices that the river side can be any length. Meaning that we can make one side be 268 and the other 2 sides be 266. This still satisfies our 800 feet of fencing, while being larger than 267 * 266.
Shorter side: 266 ft
Longer side: 268 ft
Greatest Possible Area: 71288
Caitlin has 9 3/8 feet of red yarn and
5 5/8 feet of purple yarn. How much more
red yarn does Caitlin have than purple
yarn?
Answers
Caitlin has 3 3/4 feet more of red yarn than purple yarn.
To find out how much more red yarn Caitlin has compared to purple yarn, we need to subtract the length of the purple yarn from the length of the red yarn.
Given:
Red yarn: 9 3/8 feet
Purple yarn: 5 5/8 feet
To subtract mixed numbers, we need to convert them to improper fractions.
9 3/8 = (8 * 9 + 3)/8 = 75/8
5 5/8 = (8 * 5 + 5)/8 = 45/8
Now, we can subtract the fractions:
75/8 - 45/8 = (75 - 45)/8 = 30/8
Simplifying the fraction, we get:
30/8 = 15/4 = 3 3/4
Therefore, Caitlin has 3 3/4 feet more of red yarn than purple yarn.
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help help help help help help help please
Answers
2.) x=5.5
3.)x=52
4.)it’s cut off so i can’t see the full question
5.)measure A is 35, x=30
After graduating from college, Trevor gets a job at a software company with a starting salary of 50,000 dollars and is given a 10% raise every year. After 10 years, what will his total earnings have been at the company? (Round to the nearest dollar)
Answers
Answer:
796871
Step-by-step explanation:
Based on the given conditions, formulate:
5000 x (1 - (1 + 10%) 10)
-------------------------------
1 - (1 + 10%)
Evaluate the equation/expression:
796871.23005
Find the closest integer to
798871.23005
= 796871
A paper bag contains 7 chillies, 9 beetroot and 11 carrots. Find P(not a carrot) (Express your answer as a fraction)
Answers
Work Shown:
A = 7 chilies + 9 beetroots = 16 items that aren't a carrot
B = 7 chilies + 9 beetroots + 11 carrots = 27 items total
P(not a carrot) = A/B = 16/27
11. Which number does NOT round to 4.61?
a) 4.61372
c) 4.60728
b) 4.61478
d) 4.60182
Answers
Answer: D
D would round to 4.6, as the third significant figure is 0, we round down, not up unlike the rest of the options.
for the function , continuity
Answers
Answer: Choice C
Condition 1 fails. [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x})[/tex] does not exist
====================================
Explanation:
Use a table or a graph to determine that [tex]\ln(\text{x}^2)[/tex] approaches negative infinity as x gets closer to 0.
Symbolically [tex]\displaystyle \lim_{\text{x} \to 0}\ln(\text{x}^2) = -\infty[/tex]. Since this result is not a finite number, we consider the limit to not exist. Write "DNE" as shorthand for "does not exist".
Therefore, [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x}) = -\infty[/tex] making [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x})[/tex] not exist as well.
Can someone help me please. I have to find the mean, medium and the mode for each data. Thank you this is due tomorrow.
Answers
5) The measures of central tendency for the monthly rainfall (in inches) are as follows:
Mean = 1 inch
Median = 0.5 inches
Modes = 0.25 inches.
6) The measures of central tendency for the July 4th Temperatures (°F) are as follows:
Mean = 94.75°F
Median = 95.5°F
Modes = 96°F
7) The measures of central tendency for the Baby Sleep Log (in hours) are as follows:
Mean = 8.7 hours
Median = 8.5 hours
Modes = 8 hours
8) The measures of central tendency for the Daily running log (in kilometers) are as follows:
Mean = 3 km
Median = 3 km
Modes = 2.5 km
9) The measures of central tendency for the Reading log (in pages) are as follows:
Mean = 33.4 pages
Median = 34 pages
Modes = None
10) The measures of central tendency for the Monthly snowfall (in inches) are as follows:
Mean = 1.75 inches
Median = 1
Modes = None
What are the measures of central tendency?The measures of central tendency are summary statistics of a data set which present the typical values about the data set.
Generally, the measures of central tendency are as follows:
The mean (which is the average value computed as the quotient of the total values by the number of data items).The median (the middle value arranged in ascending or descending order).The mode (the most occurring values).5) Monthly Rainfall (in inches):1, 0, 2, 0.5, 0.25, 3, 0.25
Arranged data: 0, 0.25, 0.25, 0.5, 1, 2, 3
Total value = 7 (0 + 0.25 + 0.25 + 0.5 + 1 + 2 + 3)
Number of items = 7
Mean = 1 inch (7 ÷ 7)
Median = 0.5 inches
Modes = 0.25 inches
6) July 4th Temperatures (°F):89, 94, 96, 99, 96, 97, 95, 92
Arranged data: 89, 92, 94, 95, 96, 96, 97, 99
Total value = 758°F (89 + 92 + 94 + 95 + 96 + 96 + 97 + 99)
Number of items = 8
Mean = 94.75°F (758 ÷ 8)
Median = 95.5°F (95 + 96)
Modes = 96°F
7) Baby Sleep Log (in hours):10, 8, 9, 8, 8.25, 9.25, 8.5
Arranged data: 8, 8, 8.25, 8.5, 9, 9.25, 10
Total value = 61 (8 + 8 + 8.25 + 8.5 + 9 + 9.25 + 10)
Number of items = 7
Mean = 8.7 hours (61 ÷ 7)
Median = 8.5 hours
Modes = 8 hours
8) Daily running log (in kilometers):3.5, 0, 2.5, 5, 2.5, 3, 4.5
Arranged data: 0, 2.5, 2.5, 3, 3.5, 4.5, 5
Total value = 21 (0 + 2.5 + 2.5 + 3 + 3.5 + 4.5 + 5)
Number of items = 7
Mean = 3 km (21 ÷ 7)
Median = 3 km
Modes = 2.5 km
9) Reading log (in pages):21, 42, 25, 45, 37, 34, 30
Arranged data: 21, 25, 30, 34, 37, 42, 45
Total value = 234 (21 + 25 + 30 + 34 + 37 + 42 + 45)
Number of items = 7
Mean = 33.4 pages (234 ÷ 7)
Median = 34 pages
Modes = None
10) Monthly snowfall (in inches):0.5, 2, 5, 0.25, 1
Arranged data: 0.25, 0.5, 1, 2, 5
Total values = 8.75 inches(0.25 + 0.5 + 1 + 2 + 5)
Number of items = 5
Mean = 1.75 inches (8.75÷ 5)
Median = 1
Modes = None
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Five times a number is divided by $7$ more than that number. If the result is $8,$ then what was the original number?
Answers
The original number is -56/3. Let's assume the original number is represented by the variable "x."
According to the given information, "Five times a number is divided by $7$ more than that number," we can express this mathematically as:
5x / (x + 7) = 8
To find the original number, we need to solve this equation for x.
Cross-multiplying the equation gives us:
5x = 8(x + 7)
Expanding the equation:
5x = 8x + 56
Subtracting 8x from both sides:
-3x = 56
Dividing both sides by -3:
x = -56 / 3.
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Both sets of values have an average of 13. Is Set A's standard deviation smaller, larger, or about the same as Set B's?
(Note: This question can be answered by knowing the concept of standard deviation, without actually computing the standard
deviation).
Set A: 1 2 3 23 24 25
Set B: 9 10 11 14 16 18
A Larger
B) About the same
Not enough information provided to tell
D) Smaller
Answers
The answer is D) Smaller Set B's standard deviation is expected to be smaller than Set A's due to its tighter range.
To determine whether Set A's standard deviation is smaller, larger, or about the same as Set B's, we can analyze the spread of the values in each set. The standard deviation measures the dispersion or variability of a data set.
Looking at Set A, we can see that the values range from 1 to 25, with a progression that is relatively spread out. On the other hand, Set B has values ranging from 9 to 18, with a more limited range.
Based on this observation, we can infer that Set B's values are more tightly grouped together compared to Set A. Consequently, Set B is expected to have a smaller standard deviation since the values are less dispersed around the mean.
Therefore, the answer is D) Smaller. Set B's standard deviation is likely to be smaller than Set A's. However, to precisely determine the standard deviations and compare them, it would be necessary to calculate the actual values using the formulas for standard deviation or use statistical software.
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Which equation represents a line that has a slope of -1/2 and goes through the point (8, 1)
Answers
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given slope m = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (8, 1 ) into the partial equation
1 = - [tex]\frac{1}{2}[/tex] (8) + c = - 4 + c ( add 4 to both sides )
5 = c
y = - [tex]\frac{1}{2}[/tex] x + 5 ← equation of line
The equation is :
↬ y = -1/2x + 5Solution:
Let's write the equation in point slope first.
Point slopeThe formula is [tex]\bf{y-y_1=m(x-x_1)}[/tex].
Wherem = slope(x₁, y₁) is a point on the lineSubstitute all the data:
[tex]\begin{gathered}\bf{y-1=-\frac{1}{2}(x-8)}\\\bf{y-1=-\frac{1}{2} x+4}\\\bf{y=-\frac{1}{2}x+5}\end{gathered}[/tex]
Hence, the answer is y = -1/2x + 51. Buying on time is called _____ Buying.
2. The ____ number is used to identify checks on a deposit slip
3. A ____ is a plan used to spend money on wisely.
Answers
Describe the volatility of chloride across period 3
experimentos aleatorios con orden y repeticion
Answers
A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.
How to explain the information.For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.
The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.
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Victoria is paid a salary of $550 a week at her job. She worked 5 hr of overtime during the holidays, and her weekly paycheck came to $690. What is her overtime pay per hour?
Answers
Answer:
$28 per hour
Step-by-step explanation:
Let's first find out how much extra Victoria was paid during the week she worked overtime.
Without overtime, Victoria's weekly paycheck would be $550. However, she received $690 that week. The difference between the two amounts is the extra pay for overtime:
Extra pay = Total pay - Regular pay = $690 - $550 = $140
Now, we know that Victoria worked 5 hours of overtime. To find her overtime pay per hour, we can divide the total overtime pay by the number of overtime hours:
Overtime pay per hour = Total overtime pay / Overtime hours = $140 / 5 = $28
Victoria's overtime pay is $28 per hour.
Hope this helps!
Answer:
Victoria is paid $28 per hour of overtime.
Step-by-step explanation:
Get the difference of Victoria's paycheck with and without overtime.
Difference = $690 - $550
Difference = $140
The difference is the amount that she was paid for the overtime.
Since she worked for 5 hours then we can just divide the amount over the time.
Rate = $140/5hours
Rate = $28/hr
25) Find the measure of the side MN.
A) 17.1
B) 18.1
C) 19.1
Answers
The measure of the side MN is 19.1.
What are trigonometric functions?In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
The different trigonometric identities are expressed as:
cosine, tangent, cotangent, cosecant, secant, and sineFrom the information given, we have that:
The opposite side of the triangle is MNThe adjacent side is 11ftUsing the tangent identity:
[tex]\text{tan} \ \theta = \dfrac{\text{opposite}}{\text{adjacent}}[/tex]
Substitute the values
[tex]\text{tan}(60) =\dfrac{\text{MN}}{11}[/tex]
Cross multiply the values, we have:
[tex]\text{MN} = \sf 1.73(11)[/tex]
[tex]\text{MN} = 19. 05 \thickapprox\bold{\underline{19.1 \ ft}}[/tex]
Hence, the measure of the side MN is 19.1.
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what are the elements found in both a narrative and a story
Answers
The theme is the underlying message, lesson, or central idea conveyed by the narrative or story.
Both a narrative and a story share several common elements that contribute to their structure and presentation. These elements include characters, setting, plot, conflict, and theme.
Characters are essential components of both narratives and stories. They are the individuals or entities that drive the events and experiences within the narrative or story. The setting is the time and place in which the events occur and provide the context for the story.
The plot refers to the sequence of events that unfold and create a structure for the narrative or story. Conflict represents the central problem or challenge faced by the characters and is often a driving force behind the plot's progression.
These shared elements create a framework for both narratives and stories, enabling the development and communication of experiences, ideas, and emotions to the audience. They contribute to the engagement, coherence, and impact of the narrative or story, regardless of the medium or genre in which they are presented.
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When x > 0 and y > 0, what expression is equivalent to √180x^9y^16 in simplest form?
Answers
Answer:
[tex]6x^4y^8\sqrt{5x}[/tex]
Step-by-step explanation:
[tex]\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}[/tex] [tex]\sqrt{180x^9y^{16}}.[/tex]
[tex]\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
[tex]\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}[/tex]
[tex]\textsf{Rewrite $x^9$ as $x^{8+1}$:}[/tex]
[tex]\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c[/tex]
[tex]\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}[/tex]
[tex]\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}[/tex]
[tex]\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0[/tex]
[tex]\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}[/tex]
[tex]\sqrt{180}\;x^4\sqrt{x}\;y^8[/tex]
[tex]\sqrt{180}\sqrt{x}\;x^4\;y^8[/tex]
[tex]\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}[/tex]
[tex]\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]
[tex]\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]6 \sqrt{5}\sqrt{x}\;x^4\;y^8[/tex]
[tex]\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}[/tex]
[tex]6 \sqrt{5x}\;x^4\;y^8[/tex]
[tex]\textsf{Rearrange:}[/tex]
[tex]6x^4y^8\sqrt{5x}[/tex]
[tex]\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}[/tex]
[tex]\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.[/tex]
Please help me with this I need it quickly
Answers
Answer:
Step-by-step explanation:
-3/3m is the answer
[tex]\frac{13}{3m}[/tex]
This is the same thing as subtracting two fractions.
First find the lowest common denominator.
You can multiply the first denominator by 3 to make it
[tex]\frac{24}{3m}[/tex] - [tex]\frac{11}{3m}[/tex]
Now subtract the fractions
21 - 11 = 13
Our answer = [tex]\frac{13}{3m}[/tex]
Una pastelería es famosa por dos de sus especialidades de pasteles: el Especial y el Supremo. El Especial requiere para su elaboración medio kilo de azúcar y 8 huevos, teniendo un precio de venta de $200. El Supremo necesita un kilo de azúcar y 8 huevos, teniendo un precio de venta de $270. En el almacén les quedaban 10 kilos de azúcar y 120 huevos.
Answers
Given statement solution is :-The ingredients available in the warehouse, a maximum of 15 "Special" cakes and 10 "Supreme" cakes can be made.
To determine how many cakes they can make of each specialty, we need to review the amount of ingredients available in the warehouse and then calculate how many cakes can be made with that amount.
Amount of ingredients in the warehouse:
Sugar: 10 kilos
Eggs: 120
For the "Special" cake:
It requires half a kilo of sugar per cake.
It requires 8 eggs per cake.
Sale price: $200 per cake.
To calculate how many "Special" cakes can be made, we divide the amount of sugar and eggs available in the store by the ingredients required per cake:
"Special" cakes that can be made:
Available sugar / Sugar required per cake = 10 kilos / 0.5 kilos = 20 cakes
Eggs Available / Eggs Required per Cake = 120 Eggs / 8 Eggs = 15 Cakes
Therefore, with the ingredients available in the store, a maximum of 15 "Special" cakes can be made.
For the "Supreme" cake:
It requires a kilo of sugar per cake.
It requires 8 eggs per cake.
Sale price: $270 per cake.
To calculate how many "Supreme" cakes can be made, we again divide the amount of sugar and eggs available in the store by the ingredients required per cake:
"Supreme" cakes that can be made:
Available sugar / Sugar required per cake = 10 kilos / 1 kilo = 10 cakes
Eggs Available / Eggs Required per Cake = 120 Eggs / 8 Eggs = 15 Cakes
Thus, with the ingredients available in the warehouse, a maximum of 10 "Supreme" cakes can be made.
In short, with the ingredients available in the warehouse, a maximum of 15 "Special" cakes and 10 "Supreme" cakes can be made.
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Create similar right triangles by changing the scale factor of the right triangle.
When the scale factor is 1, what is the ratio of the side length of the side opposite ∠A and the length of the hypotenuse?
Change the scale factor to 3. What is the ratio of the side length of the side opposite ∠A to the length of the hypotenuse?
What is the ratio of the side length of the side opposite any 30° angle and the length of the
hypotenuse?
Answers
When the scale factor is 1, the triangle is a 30-60-90 triangle. The ratio of the side length of the side opposite ∠A and the length of the hypotenuse is 1:√3.
When the scale factor is 3, the triangle is still a 30-60-90 triangle. The ratio of the side length of the side opposite ∠A and the length of the hypotenuse is 3:√3.
The ratio of the side length of the side opposite any 30° angle and the length of the hypotenuse is always 1:√3. This is because the side opposite the 30° angle is always the shorter leg of the triangle, and the hypotenuse is always twice the length of the shorter leg.
30-60-90 triangle with a scale factor of 3
The side opposite ∠A is 3 units long, and the hypotenuse is √3 units long. The ratio of the side length of the side opposite ∠A and the length of the hypotenuse is 3:√3.
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