The distance between base of tree and swing set is 24 feet.
We are given the angle of depression and the vertical height. Joining the three points, which are top and base of tree and swing set forms a right angled triangle. The height of tree will be perpendicular of triangle and base will be the distance between base of tree and swing set.
The angle at the swing set will be equal to 30.26°, as alternate angles are equal.
So, the angle formed can be related with perpendicular and base by -
tan theta = perpendicular ÷ base
Keep the values in formula to find the value of base
Base = perpendicular ÷ tan theta
Base = 14 ÷ tan 30.26°
Base = 14 ÷ 0.5834
Performing division
Base = 24
Hence, the distance between base of tree and swing set is 24 feet.
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A high school decided to spend $ 750 on student academic achievement awards. At least 5 awards will be given, they should be equal in value, and each award should not be less than $ 50 . Write and sketch a function that models the relationship between the number a of awards and the cost c of each award. What are the domain and range of the function?
b. What information can you use to determine the domain and range?
Following is domain and range for given function -
A)The function's range is -5≤ a≤50.
The function's range is -50≤c≤150.
B) The information we got from equation of the function is used to determine domain and range.
Given,
The whole amount spent is $750.
As a result, our equation is
ca = 750
calculating c,
c = 750 / a
The function's domain and range are:
a ≤ 5
Each prize now needs to be under 50.
= 50 ≤ c
Using the formula, ac = 750
A's maximum value is 75.
we can say that domain is
5 ≤ a ≤ 50
Finally, by substituting a = 5 we can see that the maximum for c is 150.
This gives range for c as -
50 ≤ c ≤ 150
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Etsuko practices origami. The square papers she used have a side length of either 7.5 cm or 25.4 cm. Etsuko says the length of the larger paper is 32.9 cm greater than the length of the smaller paper
To find how many centimeters greater the length of the larger paper is than the length of the smaller paper, the lesser number of centimeters needs to be subtracted from the greater number of centimeters which gives the result that is 17.9cm. Etsuko is incorrect because 25.4 is greater than 7.5cm.
How much greater is the side length of the paper?The mathematical operation that would be used to determine how much greater the larger paper is compared to the smaller paper is subtraction. Subtraction is the process used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.
To subtract the numbers, the length of the longer paper would be subtracted from the shorter paper.
Difference in the length of the papers = 25.4 - 7.5 = 17.9cm
Etsuko is wrong because instead of subtracting the lengths, she added the lengths. Addition is used to determine the sum of two or more numbers.
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Answer:
It's easy,
To find how many centimeters greater the length of the larger paper is than the length of the smaller paper, the lesser number of centimeters needs to be subtracted from the greater number of centimeters, which gives a result that is between 7.5 and 25.4. Etsuko is not correct because 25.4 cm is 17.9 cm more than 7.5 cm.
Step-by-step explanation:
*Wish you luck on the test*
Question attached below.
Using linear functions, we have that:
a) The rate of change for Job A is of $14, while the rate of change for Job B is of $17, and these are the hourly pay for each job.
b) The slope represent the hourly pay for each job.
c) The intercepts represent the fixed salary for each job.
d) The pay will be the same on both jobs after 25 hours, of $425, as given by the intersection point on the graph.
e) For 40 hours, the payment on Job A is of $635 and on Job B of $680, hence, due to the higher payment, Tommy should accept Job B.
What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For this problem, the two functions are given as follows:
A(h) = 75 + 14h. (slope of 14 as when x changes by 2 y changes by 28).B(h) = 17h. (slope of 17 as when x changes by 2 y changes by 34).The functions are graphed at the end of the answer.
Hence:
a) The rate of change for Job A is of $14, while the rate of change for Job B is of $17, and these are the hourly pay for each job.
b) The slope represent the hourly pay for each job.
c) The intercepts represent the fixed salary for each job.
The pay will be equal when:
A(h) = B(h)
Hence:
75 + 14h = 17h
3h = 75
h = 25.
d) The pay will be the same on both jobs after 25 hours, of $425, as given by the intersection point on the graph.
For 40 hours, the payments are given as follows:
A(40) = 75 + 14 x 40 = $635.B(40) = 17 x 40 = $680.Hence:
e) For 40 hours, the payment on Job A is of $635 and on Job B of $680, hence, due to the higher payment, Tommy should accept Job B.
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Classify each number as rational or irrational:
Help asap
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\textsf{\textbf{Rational} and \textbf{Irrational} numbers}[/tex]
[tex].\qquad\bullet\textsf{\textbf{Rational} numbers can be written in fraction form, p/q.}\\.\qquad\bullet\textsf{\textbf{Rationals} can be \textbf{terminating} fractions.}[/tex]
[tex]\therefore[/tex]
[tex].\qquad\bullet\textsf{\textbf{Irrational} numbers \textbf{cannot} be written \textbf{as fractions.}}[/tex]
[tex]\textsf{These are the \textbf{rationals:}}[/tex]
[tex]\boldsymbol{\dfrac{11}{3}}[/tex]
[tex]\boldsymbol{0.01045}[/tex]
[tex]\boldsymbol{\sqrt{\dfrac{16}{81}} }[/tex]
[tex]\boldsymbol{6.25}[/tex]
[tex]\boldsymbol{0.\overline{42}\Leftarrow it's\:a\:terminating\:fraction}[/tex]
[tex]\textsf{These are the \textbf{irrationals:}}[/tex]
[tex]\boldsymbol{\sqrt{48}}[/tex]
[tex]\boldsymbol{16\pi}[/tex]
[tex]\boldsymbol{\sqrt{\dfrac{3}{16}} }[/tex]
[tex]\textsf{We come to the conclusion that there are more rationals than irrationals. \ddot\smile}[/tex] [tex]\ddot\smile[/tex]
[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection\:-RoSe}}}}^\star_\star[/tex]
What is the slope of the line through (-1,8)(−1,8)left parenthesis, minus, 1, comma, 8, right parenthesis and (3,-4)(3,−4)left parenthesis, 3, comma, minus, 4, right parenthesis?
Choose 1 answer:
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-1)}}} \implies \cfrac{-12}{3 +1}\implies \cfrac{-12}{4}\implies -3[/tex]
At the gym, Hillary swims every 5 days and runs every 7 days. If she did both activities today, in how many days will she do both activities again on the same day?
Answer:
She will actually do it on the 35th day of gym
DF
bisects LEDG. Find the value of x. The diagram is not to scale.
Answer:
x = 6
Step-by-step explanation:
Since ray DF bisects angle EDG, angles EDF and GDF are congruent. By reflexive property of congruence, ray DF is congruent to ray DF. Since all right angles are congruent, angles FED and FGD are congruent. By AAS, triangles FED and FGD are congruent. Since corresponding parts of congruent triangles are congruent, segments EF and GF are congruent, so 8x + 42 = 15x
7x = 42
x = 6
What is the solution of the equation x²-24 x+144=0 ?
The solution of the equation x² - 24 x + 144 = 0 is x = 12 .
It is a quadratic equation , it will have 2 roots .
Using factorisation ,
x²-24 x+144=0
( [tex]x^{2}[/tex] - 12 x - 12 x + 144 ) = 0
x ( x - 12 ) - 12 ( x - 12 ) = 0
( x - 12 ) * ( x - 12 ) = 0
x = 12
Both roots are same and are equal to 12 .
Hence , the solution of the equation x² - 24 x + 144 = 0 is 12 .
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Molly is making a punch for the school picnic. The recipe calls for 3/4 quart of lemonade, 3 cups of cranberry juice, 4 cans of orange juice concentrate, and 5 cups of water. If Molly uses 1(2/5) quarts of lemonade, how many cups of cranberry juice will she need?
She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
To make the recipe,
3/4 quart of lemonade and 3 cups of cranberry juice
The ratio of cranberry juice to a quart of lemonade
⇒ 3/(3/4) = 4
To make the same recipe with 1(2/5) quarts of lemonade the ratio of cranberry juice to a quart of lemonade must be maintained.
So,
4 = cranberry juice / 1(2/5)
(5/7) × cranberry juice = 4
Cranberry juice = 28/5 ⇒ 5 (3/5).
Hence "She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade".
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HELP................................
Answer: Letter C
Step-by-step explanation:
just look at the problem a little closely
I NEEDDDD HELPPPP ASAPPPP
Answer:
24
Step-by-step explanation:
the angle should be the same on the other side so wouldn't it be 120 divided by 5 which is 24. I could def be wrong tho sorry hun
All of the students at Mountain Ridge Middle School take a foreign language. of the students take Spanish. of the students take French. The remaining students take Chinese. What fraction of the students take Chinese?
Based on the fraction of students who take Spanish, and French and Mountain Ridge Middle School, the fraction of students who take Chinese are 3/40
How to find out the fraction?To find the fraction of students who take Chinese, subtract the fraction of students who take Spanish and French from 1.
The number of students who take Chinese is therefore:
= 1 - 5/8 - 3/10
= 1 - 25/40 - 12 /40
= 3/40
The full question is:
All of the students at Mountain Ridge Middle School take a foreign language. 5/8 of the students take Spanish. 3/10 of the students take French. The remaining students take Chinese. What fraction of the students take Chinese?
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1. I look like this _ _ _ _ . _
2. all of my digits are odd.
3. my thousands digit is equal to the sum of my tens, ones, and tenths digit.
4. my tenths and ones digits are equal
5. the product of my tenths and ones is more than my tens digit
6. my hundreds digit is larger than my thousands digit
Answer:
I think the answer could be 7913.3
Step-by-step explanation:
Using clue number 2 we know that all the numbers in this are odd so that mean the only numbers that can be there are 1,3,5,7 and 9 Using clues 3 and 4 there are a few combinations some of which can be 1 + 1 + 3 = 5 , 1 + 1 + 7 = 9, 1 + 1 + 5 = 7, and 3 + 3 + 1 = 7 With clue 5 in being mentioned the dights in the ones place can't be 1 and 1 because it would equal one and any other dight besides it would be greater then that so I went with 3 and 3 as the tenths and ones dights since 3 × 3 = 9 and 1 being in the tenths place is less then 1The only other clue is clue 6 which means that the hundreds dights has to be a odd number greater than 7 and 9 is the only option that's greater than 7. The number is 7,913.3the characteristics and properties of a linear equation
The graph of a linear function is a straight line. One independent variable and one dependent variable make up a linear function.
What are the characteristics of a linear function?
The graph of a linear function is a straight line. One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.What are the properties of equation?
The properties of the relationship of equality, reflexivity, symmetry, transitivity, and the properties of operations are employed to solve an equation.A mathematical relationship (function) that can be graphically represented as a straight line is said to be linear.Learn more about linear function
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Solve each equation. log₇(2 x-3)²=2
The solution of the given logarithmic equation is 16.189.
What are the various properties of the logarithm?
Out of several properties of logarithms, some of the main properties are given below:
Product Rule
log (ab) = log a + log b
Change of base
log ₇ x = log x / log 7
Power Rule
log a² = 2 log a
Quotient Rule
log (a / b) = log a - log b
Solving the given equation log₇(2x - 3)² = 2
We are given a logarithmic expression: log₇(2x - 3)² = 2
Using properties of the logarithm, we have
log (2x - 3)² / log 7 = 2
log (2x - 3)² = 2 × log 7
2 log (2x - 3) = 1.6901
log (2x - 3) = 3.3802
Using exponential on both sides,
e^[log (2x - 3)] = e^(3.3802)
2x - 3 = 29.3766
2x = 32.3766
x = 16.189
Hence, the solution of the given equation is 16.189.
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What is the product of -15 and -3
Answer:
45
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Guide to follow:}[/tex]
[tex]\large\text{The word \boxed{\rm{difference}} means subtraction/subtract.}[/tex]
[tex]\large\text{The word \boxed{\rm{product}} means addition/add.}[/tex]
[tex]\large\text{The word \boxed{\rm{quotient}} means division/divide.}[/tex]
[tex]\large\text{The word \boxed{\rm{product}} means multiplication/multiply.}[/tex]
[tex]\large\text{Also guide to follow:}[/tex]
[tex]\large\text{2 negatives gives you a positive}[/tex]
[tex]\large\text{2 positives gives you a positive as well}[/tex]
[tex]\large\text{1 negative \& 1 positive gives you a negative}[/tex]
[tex]\large\text{1 positive \& 1 negative gives you a negative as well}[/tex]
[tex]\large\textsf{So, in this particular question we're doing multiplication because the}\\\large\textsf{key term in the word phrase is \boxed{\textsf{product}}. }[/tex]
[tex]\large\text{Now, that we have that information out of the way we can answer}\\\large\text{your given question.}[/tex]
[tex]\large\text{The product of }\large\text{-15 and -3 is translated to \boxed{\rm{-}\large\text{15 }\times\ -\large\text{3}}}[/tex]
[tex]\large\text{Equation: }\rm{-15\times-3}[/tex]
[tex]\large\text{Simplify the equation we have gathered above and you should have}\\\large\text{pverall answer.}[/tex]
[tex]\large\text{We have received was 45}[/tex]
[tex]\huge\text{Therefore, your answer should be \boxed{\mathsf{45}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]is the expression (17)/(2)g-(9)/(2)h the same as (9)/(2)h-(17)/(2)g ? Explain.
The fraction expression (17)/(2)g - (9)/(2)h is not the same as (9)/(2)h-(17)/(2)g.
How to subtract fractions?
We are given the fraction expression;
(17/2)g - (9/2)h
Now, the fraction (17/2) is greater than (9/2) and as such the result of the subtraction of the fractions will be positive.
Now, if we change the order of the subtraction to be;
(9/2)h - (17/2)g
This means that the result will now be negative since (9/2) is less than (17/2).
Thus, we can conclude that the expression (17)/(2)g - (9)/(2)h is not the same as (9)/(2)h-(17)/(2)g.
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Can u help me figure this out
Step-by-step explanation:
what is it you need help in?
Suppose there are 6 pennies on a meter stick so that the mean position is the 50
centimeter mark and the mad is 10 centimeters.
1. find possible locations for the 6 pennies.
2. find a different set of possible locations for the 6 pennies.
Using the mean absolute deviation concept, it is found that:
1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).
2. Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.Hence, for a mean of 50 and a mean absolute deviation of 10, with 6 pennies, we want data-sets with these following characteristics:
Sum of 50 x 6 = 300.Sum of the differences of the observations and 50 of 6 x 10 = 60.Hence:
1. One set of possible locations is given as follows: (40, 40, 40, 60, 60, 60).
2. Another set of possible locations is given as follows: (39, 40, 41, 59, 60, 61).
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Germaine is saving money to buy a $367 mountain bike. He plans to save $45 every week from his paycheck until he has enough money. So far, he has saved $62. How many weeks will it take Germaine to get the mountain bike?
It will take Germaine to get the mountain bike 6.77 weeks (approximately)
let X represent the number of weeks it will take to save enough money
Money to buy a mountain bike = $367
He planned to save money every week from his paycheck = $45
So far, He had saved money already to buy bike = $62
now the required amount to buy a mountain bike is
$367-$62 = $305
Number of weeks Germaine will take to get the mountain bike is
X = 305/45
X = 6.77 weeks (approx)
It will take Germaine to get the mountain bike 6.77 weeks (approximately).
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!!! HELP QUICKLY PLEASE !!! 40 POINTS!
Find the correct standard form for the expanded forms listed.
A. 500 + 20 + 5 + 0.3 + 0.04
B. 10 + 2 + 0.8 + 0.006
C. 7 + 0.2 + 0.09 + 0.004
D. 30 + 1 + 0.5 + 0.02
All you need to do is answer the questions you don't have to explain the answers, answer all of the questions for brainiest, full star, and of course a thanks!!!
A. 525.34
B. 12.086
C. 7.294
D. 31.52
Hope it helps ^^
Simplify each expression.
ln e⁴/8
We will get Ine⁴/8 after simplifying the given expression ln · e⁴/8.
What exactly is an expression?An expression in mathematics is a sentence that contains at least two numbers or variables and at least one mathematical operation.Math operations include addition, subtraction, multiplication, and division.The structure of an expression is as follows: An expression is (Number/variable, Math Operator, Number/variable).So,
Given: ln · e⁴/8
Then,
ln · e⁴/8Ine⁴/8Therefore, we will get Ine⁴/8 after simplifying the given expression ln · e⁴/8.
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A line with slope 12 passes through the point (-6,14)
Answer:
y = 12x + 86
Step-by-step explanation:
y = mx + b
slope is 12 so m = 12
Using (-6,14) then
14 = 12(-6) + b
14 = -72 + b
b = 72 + 14 = 86
What is the volume of the cuboid in cm3 ?
What is the volume of the cuboid in mm3
Answer:
3150mm
Step-by-step explanation:
1cm is 10mm you convert it then times it together l x b x h will equal 3150
Stefan and Kendrick both walk to work each day. It takes them the same amount of time, even though Stefan lives farther away. One morning, they decide to meet at a coffee shop. The coffee shop is the same distance from each of their apartments. Who will likely get to the coffee shop in less time?
Answer:
Stefan
Step-by-step explanation:
Stefan
x+y+z=−42x+3y−2z=10−x+2y−3z=−12
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
Answer:
x = 13
Step-by-step explanation:
i need help
simplify: 4^8/4^-4
Answer:
[tex]4^{12}[/tex]
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{4^{8} }{4^{-4} }[/tex] = [tex]4^{(8-(-4))}[/tex] = [tex]4^{(8+4)}[/tex] = [tex]4^{12}[/tex]
Find the result graphically. Click and drag the arrows to represent each term. Type in the result.
3+(-10)
The arrow is in -7 on the number line since 3 + (-10) = -7.
What is a number line?A number line is a pictorial representation of numbers on a straight line.
It is a horizontal line that has equally spread number increments.
We have,
3 + (-10)
This can be written as:
= 3 - 10
= -7
We can draw a number line to represent graphically:
<↓-------(subtracting 10)-------------->
< ---------(-9)-(-8)-(-7)-(-6)-(-5)-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4-5-6-7-8------------->
Thus the equation can be represented graphically with an arrow in -7 on the number line since 3 + (-10) = -7.
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A football team has P points.
P= 3W + D
Wis the number of wins.
D is the number of draws.
a) A team has 5 wins and 3 draws.
How many points does the team have?
b) After 35 games a different team has 50 points.
14 games were draws.
How many games has this team lost?
Answer:
a)18 points
Step-by-step explanation:
a)
[tex]p = 3(w) + d[/tex]
therefore
[tex]p = 3(5 \: wins ) + 3 \: draws [/tex]
find the product of 5 and 3
[tex]p = 15 + 3[/tex]
[tex]p = 18[/tex]
B) how many games lost
[tex]3x + 14 = 50[/tex]
[tex]3x + 14 - 14 = 50 - 14[/tex]
[tex]3x = 36[/tex]
[tex] \frac{3x}{3} = \frac{36}{3} [/tex]
[tex]x = 12 \: games \: won| [/tex]total Games= Games won + games drawn + games lost
[tex]35 = 12 + 14 + x[/tex]
[tex]35 - 26 = 26 - 26 + x[/tex]
[tex] \times = 18 \: games \: lost[/tex]
Solve each equation. Check your answers.
1.1+ln x²=6
After solving the equation 1.1+ln x²=6, the value of x is equal to [tex]\sqrt{e^{4.9}}[/tex]
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
We have been asked to find x in 1.1+ln x²=6
⇒ 1.1+ln x²=6
⇒ ln x² = 6 - 1.1
⇒ ln x² = 4.9
⇒ x² = [tex]e^{4.9}[/tex]
⇒ x = [tex]\sqrt{e^{4.9}}[/tex]
Thus, x = [tex]\sqrt{e^{4.9}}[/tex] in 1.1+ln x²=6
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