What is the length of a side of an equilateral triangle whose altitude is 5?
Answers
To make things easier to understand, let's see this figure, which represents the given situation:
According to this diagram, to find x, which is the length of the side of the triangle, we can use pythagorean theorem, this way:
[tex]\begin{gathered} x^2=(\frac{x}{2})^2+5^2 \\ x^2=\frac{x^2}{4}+25 \\ x^2-\frac{x^2}{4}=25 \\ \frac{3}{4}x^2=25 \\ x^2=\frac{25}{3}\cdot4^{} \\ x=\sqrt[]{33.3333} \\ x=5.77 \end{gathered}[/tex]
Related Questions
Which of the following is an example of the associative property of multiplication?7 . (3 . 5) = (7 . 3) . 507. (3+5) = 21 + 357.(3.5) = 7 . (5. 3)0.1=1
Answers
The associative property of multiplication states that you can choose any pair of numbers to multiply first when there are more than two numbers being multiplied. This doesn't change the final result:
a . b . c = (a . b) . c = a . (b . c)
So, we see an example of such property in the first option:
7 . (3 . 5) = (7 . 3) . 5
Let's check this is indeed true:
7 . (3 . 5) = 7 . 15 = 105
(7 . 3) . 5 = 21 * 5 = 105
Therefore, the first option is correct.
Notice that the second option uses the distributive property of multiplication over addition:
a . (b + c) = a . b + a . c
The third uses the commutative property of multiplication:
a . b = b . a
The fourth is wrong since zero multiplied by any number is zero, not one:
0 . a = 0, for all values of a.
Each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. How could one express the number of ways those textbooks could be distributed among the students?
Answers
The way that expresses the number of ways those textbooks could be distributed among the students is ⁵C₂.
What is combination?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr
Combination formula will be:
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
In this case, each of 5 students wishes to buy a particular textbook, but only 2 textbooks are available. This will be illustrated as ⁵C₂.
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There are ten ways (which are ⁵C₂ = 10) to distribute those textbooks could be among the students in this situation.
What is the Combination?Combinations indicate the choosing of items from a predetermined list of items.
The combination is given by the relation, ⁿCₓ = n!/{x!(n-x)!}
The quantity is given by n. and x is equal to how many objects are taken at once.
Each of the five students in this situation wants to purchase a specific textbook, but there are only 2 books available.
The expression for the number of possible distributions of such textbooks among the students is
⇒ ⁵C₂
⇒ 10
Hence, there are ten ways to distribute those textbooks could be among the students.
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Multiply and combine like terms to degerming the product of these polynomials.
(2 n-3)(5 n+6)
Enter your results in the response box.
Answers
Answer:
7n-18
Step-by-step explanation:
The working out is attached. Hope it helps!
What what solid is generated when the semi circle is rotated about the line
Answers
Sphere solid is generated when the semicircle is rotated about the line.
Given,
The semi circle is rotated about the line.
To find the what solid is generated?
Now, According to the question:
We know that when a semicircle is rotated about any line then the three dimensional figure or a solid that is formed on this rotation transformation is Sphere.
Hence, Sphere solid is generated when the semicircle is rotated about the line.
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The graph depicts the growth in costs using a line segment. Use the midpoint formula to approximate the cost during the year 1987.The approximate cost during the year 1987 was $ ____.
Answers
Answer:
The approximate cost during the years 1987 was $7527
Explanation:
The midpoint formula is:
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]For two given points.
In this case, we can see in the graph the points (1983, 5021) and (1991, 10033)
Then, using the midpoint formula:
[tex]M(\frac{1983+1991}{2},\frac{5021+10033}{2})=M(1987,7527)[/tex]Thus, the approximation for the year 1987 is $7527
A line intersects the points
(-2, 9) and (3, -11).
m = -4
Write an equation in point-slope form
using the point (-2, 9).
y - [?] =(x-)
Answers
Answer: (3,11)
Step-by-step explanation:
What is the degree of the second term in this polynomial
Answers
The degree of the second term in the polynomial;
[tex]5x^{27}+5x^{19}+9x^9[/tex]is 19
I need help with this practice problem The subject is trigonometry It asks to graph the function If you can ❗️ use Desmos to graph
Answers
We will have the following:
Need help answering the following polynomial
Answers
The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
The given expression is [tex]-x^{2}-\frac{1}{6}[/tex].
We have to complete the given sentence;
The expression represents a ........... polynomial with ........terms. The constant term is .........., the leading term is..........., and the leading coefficient is .................... .
we first complete the given sentence then we explain the sentence.
The expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
Firstly about Quadratic Polynomial
When the highest degree term in a second-degree polynomial equals to 2, the polynomial is said to be quadratic.
Now about Constant Term
A number that is constant and does not have any variables in an algebraic expression is a constant term.
Now about Leading Coefficient
The numbers placed in front of the variable with the biggest exponent are known as leading coefficients.
Hence, the expression represents a quadratic polynomial with two terms. The constant term is [tex]-\frac{1}{6}[/tex], the leading term is [tex]x^{2}[/tex], and the leading coefficient is [tex]-1[/tex].
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−2 4/5×(−3 1/2)
I really need help.
Answers
Explanation: First make the mixed numbers improper fractions.
-2 4/5 would be -14/7 because -2 x 5 + (-4) is -14. -3 1/2 is -7/2 because -3 x 2 + (-1).
Now times both the denominators and numerators. -14 x -7 is 98 and 5 x 2 is 10. The improper fraction is 98/10
Now make the improper fraction a mixed number which would be 9 4/5. 10 goes into 98 9 times and there is 8 left, keep the denominator 10.
8/10 isn’t simplified as you divide both by 2 which is 4/5
Don’t forget your mixed number and the answer is 9 4/5
There are two numbers whose sum is 50. Three times the first is 5 more than twice the second. What are the numbers?
Answers
The two numbers whose sum is 50 and three times the first is 5 more than twice the second are 21 and 29.
What do you mean by sum?
A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms.
Let the two numbers be X and Y.
There are two condition given in the question through which we can form a system of equation containing two equations.
First condition: The sum of the numbers is 50.
Therefore,
X + Y = 50
Second Condition: Three times the first is 5 more than twice the second
Therefore,
3X = 2Y + 5
We get the system of equation:
X + Y = 50
3X = 2Y + 5
Solving this system of equation
3X - 5 = 2(50 - X)
3X - 5 = 100 - 2X
X = 105/5
X = 21
Putting the value of X in one of the equation:
Y = 50 - X
Y = 50 - 21
Y = 29
Therefore, two numbers are 21 and 29
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Part 3: Solve a real-world problem using a cube root function.
Once Isabel rented the warehouse space, she decided to post ads on several social media sites to advertise her online bookstore. Let x represent the number of months the ads have been posted. Isabel finds that the function below describes the number of books sold as a function of the number of months her ads have been posted.
f(x) = 1000 + 1000
⦁ How many books were sold after 8 months? (3 points)
⦁ Graph the function. (10 points)
Answers
Considering the given function, it is found that 3000 books were sold after eight months.
FunctionThe function in this problem is defined as follows:
f(x) = 1000(∛x) + 1000
In which f(x) represents the number of books sold after x months.
After eight months, we have that x = 8, hence the number of books is calculated as follows:
f(8) = 1000(∛8) + 1000
The lone instance of x in the function was replaced by eight to find the numeric value.
The cube root of eight is calculated as follows:
8 = 2 x 2 x 2 = 2³
Hence:
∛8 = 2
Thus the numeric value of the expression is:
f(8) = 1000(∛8) + 1000 = 1000 x 2 + 1000 = 2000 + 1000 = 3000 books.
The graph of the situation is given by the image at the end of the answer, at a domain of x >= 0, as the number of months cannot assume negative values.
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this is the last one i need help with. please & thank you asap
Answers
Answer:
slope = 3/7
Step-by-step explanation:
Locations of points: (-4 , 1) and (3 , 4)
slope = rise / run
between two plotted points this means that:
slope = change in y / change in x
slope = (4 - 1) / (3 - (-4))
slope = (4 - 1) / (3 + 4)
slope = 3/7
Write the number positioned at point D.
Answers
(The intervals are in 0.25)
)) Sonoma bikes 5 miles to Paige's house. On a map, 5 they measure that distance as 7 cm. The same map shows that the mall is 3 cm from Paige's house. What is the actual distance between Paige's house and the mall?
Answers
Find the scale factor by dividing the real length by the map length. Since Sonoma's house is 5 miles away from Paige's house but they appear 7cm appart in the map, then the scale factor is:
[tex]undefined[/tex]Sue traveled 96 miles in 12 hours. A unit rate to describe Sue's travel is 8 miles per hour. What is another unit rate in this situation?
Answers
Answer:
Sue travels 8 miles per hour.
Step-by-step explanation:
3² +4² + 12² is equal to n² for some positive number n . Find n.
Answers
Answer:
n = 13
Step-by-step explanation:
For this, you need to square all of the numbers and then add them together. Most of the time, you can put them into a calculator but I will work it out below.
Squaring means multiplying a number by itself, so we get:
3² + 4² +12² =n²
Turns into:
(3*3) + (4*4) +(12*12) = n²
Then work out the multiplication:
9 + 16 + 144 = n²
Add everything together
169 = n²
Now take the square root of each side:
[tex]\sqrt{169} =\sqrt{n^{2}}[/tex]
This comes out to be:
± 13 = n
The question asks for the positive number, so you answer is:
n = 13
Find three number in arithmetic progression whose sun is 21 and product is 315
Answers
Answer:
Step-by-step explanation:
It should be option D
Reason
The correct answer to the 3 numbers with a sum of 21 is 6,7,8 but those 3 numbers don’t make a product of 315
8,9,10 sum is 27 product is 720
2,3,4 sum is 9 product is 24
11,12,13 sum is 36 product is 1716
5,6,7 sum is 18 product is 210
So none of these will fit that criteria
You can find the sum of 3 numbers with equation
x+ x+1 + x+2 = 21
3x + 3 = 21
3x = 18
x = 6
x +1 = 7
x + 2 = 8
Write the correct inequality for the following statement and then solve for the given number of
yards.
You have found a used car and your parents have agreed to pay the first
$750 for you. You have a summer job mowing yards for $25 per yard.
Write and inequality that will calculate the number of yards (y) you will
have to mow to get to at least the cost (C) of the car.
If the car cost a total of $4500 how many yards will you have to mow?
Answers
The inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car is 25y + 750 ≥ C.
If the car costs a total of $4500 number of yards you will have to mow is 150 yards at least.
What is inequality in math?In mathematics, a statement of an order relationship between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to) is called an Inequality.
Given:
Price of the car paid by your parents = $750
You have a summer job mowing yards for $25 per yard.
We have to determine an inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car.
So, the required inequality is
25y + 750 ≥ C
Now, the Cost of the car given is $4500.
Substituting this in the inequality to find the number of yards,
25y + 750 ≥ 4500
Subtracting 750 from both sides
25y ≥ 3750
Dividing both sides by 25,
y ≥ 150
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Find the slope of the line passing through the pair of points or state that the slope is
undefined. Then indicate whether the line through the points rises, falls, is horizontal, or
is vertical.
(3,-5) and (-7,-5)
...
Select the correct choice below and, if necessary, fill in the answer box within your
choice.
Answers
Answer:
The slope is o. The line will be vertical and the equation of the line is y = -5
Step-by-step explanation:
Triangle XWY is transformed to produce triangle URL. Select all the transformations that would guarantee triangles XWY and URL are congruent.
O reflection, then a translation
O dilation, then a reflection a
O rotation, then a dilation a
O translation, then a rotation.
O rotation, then a reflection
Answers
The correct transformations are;
1. Reflection, then a translation
2. Rotation, then a reflection
3. Translation, then a rotation.
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
Triangle XWY is transformed to produce triangle URL.
Now,
The images arise from transformation should remain the same with respect to the size or shape.
So, we get;
The correct transformations are;
1. Reflection, then a translation
2. Rotation, then a reflection
3. Translation, then a rotation.
Thus, The correct transformations are;
1. Reflection, then a translation
2. Rotation, then a reflection
3. Translation, then a rotation.
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Hi, can you help me with this Exercise , please!
Answers
The weekly cost C of producing x units in a manufacturing process is given by
[tex]C(x)=60x+750[/tex]The number of units x produced in t hours is given by
[tex]x(t)=50t[/tex](a) The composite function C(x(t)) is given by
[tex]\begin{gathered} C(x)=60x+750 \\ C(x(t))=60(50t)+750 \\ C(x(t))=3000t+750 \end{gathered}[/tex]The function C(x(t)) gives us the cost of production for t hours.
(b) The number of units produced in 4 hours is given by
[tex]\begin{gathered} x(t)=50t \\ x(t)=50(4) \\ x(t)=200 \end{gathered}[/tex]200 units will be produced in 4 hours.
(c) Let us graph the function C(x(t)) = 3000t + 750 to find the value of t for which the cost increases to $15,000
As you can see, the value of t is 4.75 hours when the cost is $15,000.
Therefore, 4.75 hours must elapse until the cost increases to $15,000.
15) What is the range of the following set of points: {(3, 4), (7,-2), (11, -8)}? Al{-8, -2,3,7,11} B {3,7, 11} C{-8, -2,4} D{-19, -9,1}
Answers
The range is the set of y-values of the points given.
The points given are:
{(3, 4), (7,-2), (11, -8)}
The range would be:
4, -2, and -8
Range = {4,-2,-8}
Option C
A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of 10 corn plants. He labels the 100 plants 00–99. Refer to the given line from a random number table. Which numbers represent the sample of 10 corn plants?
58160 09695 38399 40400 32662 46254
58, 16, 00, 96, 95, 38, 39, 94, 04, 00
58, 16, 00, 96, 95, 38, 39, 94, 04, 32
58, 16, 96, 95, 38, 39, 94, 04, 32, 66
58, 16, 09, 69, 38, 39, 40, 32, 66, 46
Answers
Answer: Here the correct option is 2) 58, 16, 00, 96, 95, 38, 39, 94, 04, 32
Step-by-step explanation:
f(2x)
13
-5
2
-3
What is x?
Answers
The solution for the given equivalent equation f(2x) is 10.
What is equation?
In mathematics, the term equation can be defined as the two algebraic expression which are equal to each other. This method is used to calculate the values of the parameters in the problems.
According to the question, the given equivalent equation is as follows:
Equivalent equation: f(2x) = 3x + 3 = x + 13
By using the addition-subtraction property, to generate the equivalent equations.
3x + 3 = x + 13, 3x = x + 10, 2x = 10, and x = 5
Now, f(2x) = 2x = 10
Hence, the solution for the given equivalent equation is 10.
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The correct equation is: f(2x) = 3x + 3 = x + 13
Determine the solutions of the equation [x - 30 = 11. 1. Rewrite for two solutions: (x – 3) = 11, -(x - 3) = 11 Solve for x in each equation. What are the solutions to the equation? O x= -14, -8 O x= -14,8 O X=-8, 14 O x= 8,14
Answers
First solution
(x-3)=11
x=11+3
x=14Second solution
-(x-3)-11
multiply by -1 both sides
x-3=-11
x=-11+3
x=-8therefore
answer is
-8,14
For the following, find f(2.1) and f(4).
Answers
Answer:
option A
Step-by-step explanation:
put x= 4 in condition 4<=x<8
as it satisfied condition
and put x= 2.1 in condition 2<x<4
A bag with 10 marbles has 3 yellow marbles, 2 blue marbles, and 5 red marbles. A marble is chosen from the bag at random. What is the probability that it is yellow or blue? Write your answer as a fraction in simplest form.
Answers
what is ST? I've included a photo of the problem
Answers
Answer
ST = 14
According to the diagram
UV = VW
ST = UT
UT = VT - UV
UV = 14 and VT = 29
UT = 29 - 14
UT = 15
SInce UT = ST, Therefore, ST = 14
The total bill for dinner was $43.75 (including tax and a tip). paid a 22.9% tip, what was his bill before adding the tip?
Answers
Answer:
$33.75
Step-by-step explanation:
22.9% of $43.75 = $10.0
43.75 - 10.0 = $33.75
Hope that helps
Answer:
$35.60
Step-by-step explanation:
I cross multiplied related numbers:
[tex]\frac{43.75}{x}[/tex]=[tex]\frac{122.9}{100}[/tex] cross multiply
4375=122.9x, divide both sides by 122.9
35.598=x round to hundredths
35.60