two triangles.are.similar, solve for x if au=20x +108, ub=273, bc= 703, uv=444, AV = 372 and AC=589
If two triangles are similar then the corresponding sides are in proportion. Thus,
AB / AU = BC / UV = AC / AV
AB / (20x+108) = 703 / 444
Where AB is equivalent to:
AB = AU + UB
AB = 20x + 108 + 273
AB = 20x + 381
Therefore going back to the first equation:
(20x + 381) / (20x + 108) = 703/444
444 (20x + 381) = 703 (20x + 108)
8880x + 169164 = 14060x + 75924
14060x - 8880x = 169164 – 75924
5180 x = 93240
x = 93240 / 5180
x = 18 (ANSWER)
The correct value of x is [tex]\(\frac{1}{20}\)[/tex].
To solve for x, we need to use the properties of similar triangles. The sides of similar triangles are proportional. Given that triangles AU V and ABC are similar, we can set up the following proportion:
[tex]\[\frac{AU}{AB} = \frac{UV}{BC} = \frac{AV}{AC}\][/tex]
We are given the lengths of the sides as follows:
- (AU = 20x + 108)
- (UB = 273) (which is part of AB, since (AB = AU + UB)
- (BC = 703)
- (UV = 444)
- (AV = 372)
- (AC = 589)
Using the proportion involving the sides AU, UB, UV, and BC, we have:
[tex]\[\frac{AU}{UB} = \frac{UV}{BC}\][/tex]
Substituting the given values, we get:
[tex]\[\frac{20x + 108}{273} = \frac{444}{703}\][/tex]
Cross-multiplying to solve for x, we have:
[tex]\[(20x + 108) \cdot 703 = 444 \cdot 273\][/tex]
Expanding both sides gives us:
[tex]\[14060x + 76184 = 121172\][/tex]
Subtract (76184) from both sides to isolate the term with x:
[tex]\[14060x = 121172 - 76184\] \[14060x = 49888\][/tex]
[tex]\[x = \frac{49888}{14060}\][/tex]
Simplifying the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20, we get:
[tex]\[x = \frac{2494.4}{703}\][/tex]
Since (2494.4) is very close to (2496), and \(2496\) divided by (703) is (3.55), which is (20) times (0.1775), we can see that:
[tex]\[x = \frac{1}{20}\][/tex]
Therefore, the value of x is [tex]\(\frac{1}{20}\)[/tex].
given A = {a, e, i, o, u} and B = {a, l, g, e, b, r}, find A ∪ B.
{}
{a,e}
{a, b, e, g, i, l, o, r, u}
Solve for x. Rs/x =1/4 A. X=rs/4 B. X=4/rs C. X=1/4rs D. X=4rs
Answer:
The correct option is D.
Step-by-step explanation:
The given equation is
[tex]\frac{Rs}{x}=\frac{1}{4}[/tex]
We need to solve the given equation for x.
On cross multiplication we get
[tex]Rs\times 4=1\times x[/tex]
On further simplification we get
[tex]4Rs=x[/tex]
The value of x is 4 times of Rs. Only option D represents this situation.
Therefore, the correct option is D.
Which of the following points is a solution to the system of linear inequalities
Which of the following points is a solution to the system of linear inequalities?
{2x+y<-5
{-x+y>0
A.
(4, 1)
B.
(–4, –1)
C.
(–8, –21)
D.
(8, 11)
Answer:
(-4,-1) satisfies the given system of inequalities
Step-by-step explanation:
[tex]2x+y<-5[/tex]
[tex]-x+y>0[/tex]
To find out the solution we check with each option
(4,1) , x=4 and y=1 (Plug in x and y values in the given inequalities)
[tex]2(4)+1<-5[/tex]
[tex]9<-5[/tex] False
(-4,-1) , x=-4 and y=-1 (Plug in x and y values in the given inequalities)
[tex]2(-4)-1<-5[/tex]
[tex]-9<-5[/tex] True
Now plug it in second inequality
[tex]-(-4)-1>0[/tex]
[tex]3>0[/tex] True
(-8,-21) , x=-8 and y=-21 (Plug in x and y values in the given inequalities)
[tex]2(-8)-21<-5[/tex]
[tex]-37<-5[/tex] True
Now plug it in second inequality
[tex]-(-8)-21>0[/tex]
[tex]-13>0[/tex] False
(8,11) , x=8 and y=-11(Plug in x and y values in the given inequalities)
[tex]2(8)+11<-5[/tex]
[tex]-9<-5[/tex] false
A professor teaches a small lecture class with 25 students. For a certain class, 22 students attend the lecture. What is the experimental probability that a student is absent?
I NEED HELP ASAP!!!!!!
4 +12 = 16 crates
16 x 32 = 512 juice boxes
so both A & C are correct
Tess and Dan have $24.00 each to spend at a book fair, where all students receive a 15% discount. They both want to purchase a copy of the same book, which normally sells for $24.50 plus 10% sales tax. To check if she has enough to purchase the book, Tess takes 15% of $24.50 and subtracts that amount from the normal price. She takes 10% of the discounted selling price and adds it back to find the purchase amount. Dan takes 85% of the normal purchase price and then computes 110% of the reduced price. Is Tess correct? Is Dan correct? Do they have enough money to purchase the book? Explain your answer using complete sentences, and show your work.
Answer:
Tess is wrong and Dan is correct because the tax is calculated after discount.
Step-by-step explanation:
Write the linear inequality shown in the graph. The gray area represents the shaded region
The inequality from the given graph is y≤-3x+5.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
From the graph, the coordinate points are (2, -1) and (1, 2).
Here, slope (m)=(2+1)/(1-2)
m=-3
Substitute m=-3 and (x, y)=(2, -1) in y=mx+c, we get
-1=-3(2)+c
-1=-6+c
c=5
Substitute m=-3 and c=5 in y=mx+c, we get
y=-3x+5
So, the inequality is y≤-3x+5
Therefore, the inequality is y≤-3x+5.
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What's the answer to this!! The highest point on the state of Louisiana is driskall mountain. It rises 535 feet above sea level. Write the elevation of driskall mountain as an integer
During an 8 hour car ride to Georgia, my dog Pepper whined for 1/3 of the ride. How many hours did she whine
multiply 8 by 1/3
8* 1/3 = 8/3 =2 2/3 hours
Pittsburgh international airport had approximately 714,587 passengers in august 2009. Write a number that is greater than 714,587.
Which statement best explains the value of 18 − (−5)?
The additive inverse of −5 is +5, so 18 − (−5) = 23.
The additive inverse of −5 is −5, so 18 − (−5) = 23.
The additive inverse of −5 is −5, so 18 − (−5) = 13.
The additive inverse of −5 is +5, so 18 − (−5) = 13.
A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6t, where t represents time in minutes and p represents how far the paint is spreading.
The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.
Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)
Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate π in this problem. (4 points)
Answer:
r(t) = 3t ; where t represents the time in minutes and r represents how far the paint is spreading.
A(r) = πr²
Part A:
A[r(t)] = π (3t)² = 3.14 * 9t² = 28.26t²
Part B:
r(10) = 3(10) = 30
A(r) = 3.14 * 30² = 3.14 * 900 = 2,826 square unit
Step-by-step explanation:
The shaded area of the following shape can be found by subtracting the area of the circle from the area of the triangle. True False
3000000000 times 9000000000
Create a factorable polynomial with a GCF of 5z. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
The original factorable polynomial 15z^2 + 10z can be rewritten in two different equivalent forms by factoring out the GCF to get 5z(3z + 2) and by applying the Zero Product Property to find its roots z = 0, -2/3.
Explanation:To begin, we will create a factorable polynomial with a Greatest Common Factor (GCF) of 5z. An example might be: 15z^2 + 10z. This polynomial has two terms, and each term includes the GCF of 5z in its make up.
Now, let's rewrite this polynomial in two other equivalent forms using different methods of factorization and simplification.
Form 1: Factor by GCF
In this form, we factor out the GCF from the original polynomial. For our provided example, the GCF is 5z, so we get: 5z(3z + 2).
Form 2: Use the Zero Property
We can also rewrite this polynomial using the Zero Product Property. This naturally complements factoring because it allows us to set the factors equal to zero and solve for z. In this case, this provides the roots of the polynomial but not in factor form: z = 0, -2/3.
Therefore, the original polynomial and the different equivalent forms all represent the same relationship, just expressed in different manners.
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To create a factorable polynomial with a GCF of 5z, multiply it with another term like (4z+2). The resulting polynomial is 20z² + 10z. You can rewrite it in another equivalent form by factoring out the common term from each term, resulting in 2z(8z + 2) = 16z² + 4z.
Explanation:To create a factorable polynomial with a GCF of 5z, we can start by multiplying 5z with another term. Let's say we multiply it with (4z+2). The polynomial becomes 5z(4z+2), which can be expanded to 20z² + 10z. This is one form of the polynomial.
To rewrite the polynomial in another equivalent form, we can factor out the common term from each term of the polynomial. Doing so, we get 5z(4z+2) = 5z * 4z + 5z * 2 = 20z² + 10z. Thus, the second equivalent form is 20z² + 10z.
The third equivalent form can be obtained by factoring out a common term, 2z, from each term: 5z(4z+2) = 2z * (2 * 4z + 2) = 2z(8z + 2) = 16z² + 4z.
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Which of the following numbers has a value that is between 10% and 1/9? (a) 0.151 (b) 0.112 (c) 0.108 (d) 0.019
Among the given options, (c) 0.108 is the only number that lies between 0.10 (which is the decimal equivalent of 10%) and 0.111 (which is approximate decimal equivalent of 1/9).
Explanation:To answer the question "Which of the following numbers has a value that is between 10% and 1/9?", we first need to convert 10% and 1/9 into decimal form. 10% is equivalent to 0.10, and 1/9 is approximately 0.111. We are therefore looking for a number between 0.10 and 0.111.
Reviewing the options, (a) 0.151, (b) 0.112, (c) 0.108, and (d) 0.019, we see that only (c) 0.108 fits because it falls between 0.10 and 0.111.
Therefore, the correct answer is (c) 0.108.
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A monkey is happy if it eats 3 types of fruit. There are 20 pears, 30 bananas, 40 peaches and 50 oranges. How do you distribute the fruit to make the most number of monkeys happy? What is this number?
To make the most monkeys happy we need 20 number of pair of pears, peaches, and oranges. and 20 number of pair of peaches bananas and oranges.
What is sampling distribution?In statistics, sampling distribution refers to the study of multiple random samples drawn from a particular population depending on a specified property. The acquired data paint a clear picture of the changes in the likelihood of the outcomes determined. As a consequence, the analysts are aware of the outcomes ahead of time, allowing them to plan their actions accordingly.
Given, A monkey is happy if it eats 3 types of fruit. There are 20 pears, 30 bananas, 40 peaches, and 50 oranges. to formulate the equation we need to divide them by 10 and make the pair of three.
Hence,
2pears + 3 bananas + 4 peaches + 5 oranges
2(pears + oranges + peaches) + 2(banana + peach + oranges) + peach +1 orange.
Therefore to make the most monkey happy. we need to make 20 pairs of pears, oranges, and peaches and 20 pairs of banana peaches and oranges.
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is 3 sin(alpha)+4 cos(beta)=8 possible
Answer:
No, it's not possible
Step-by-step explanation:
We know that for various values of x , [tex]-1\leq \sin x\leq 1[/tex]
and [tex]-1\leq \cos x \leq 1[/tex]
For values of [tex]\alpha[/tex], [tex]-1\leq \sin \alpha\leq 1[/tex]
On multiplying all sides by 3, we get
[tex]-3\leq 3\sin \alpha\leq 3[/tex]
For values of [tex]\beta[/tex], [tex]-1\leq\cos \beta\leq 1[/tex]
On multiplying all sides by 4, we get
[tex]-4\leq 4\cos \beta\leq 4[/tex]
On adding all sides of [tex]-3\leq 3\sin \alpha\leq 3\,\,,\,\,-4\leq 4\cos \beta\leq 4[/tex] , we get
[tex]-3-4\leq 3\sin \alpha+ 4\cos \beta\leq 3+4\\-7\leq 3\sin \alpha+ 4\cos \beta\leq 7[/tex]
Therefore, maximum value of [tex]3\sin \alpha+ 4\cos \beta[/tex] is 7.
So, it's not possible that [tex]3\sin \alpha+ 4\cos \beta=8[/tex]
Emily made 75% of the baskets that she attempted if she may nine baskets how many attempts did you make?
There are two 6th grade classes one with 29 students and the other with 31 students. There are 26 male students between the two classes. What is the ratio of female students to total students?
Given the following functions f(x) and g(x), solve for (f ⋅ g)(2) and select the correct answer below:
f(x) = 3x2 + 2
g(x) = x − 8 (1 point)
Answer:
Given the functions:
[tex]f(x) = 3x^2+2[/tex]
[tex]g(x) = x-8[/tex]
we have to find [tex](f \cdot g)(2)[/tex]
[tex](f \cdot g)(2) = f(2) \cdot g(2)[/tex] ....[1]
Substitute the value of x = 2 in f(x) and g(x) we have;
[tex]f(2) = 3(2)^2+2 =12+2 = 14[/tex] and
[tex]g(2) = 2-8 = -6[/tex]
Substitute these in [1] we have;
[tex](f \cdot g)(2) = 14 \cdot -6 = -84[/tex]
Therefore, the value of [tex](f \cdot g)(2)[/tex] is, -84
a number divided by 7 is 9
What is the average speed (miles/hour) for an object going 1500 feet in 1 minute. Round answer to two decimal places.
there are 3600 seconds per hour
5280 feet per mile
1 foot per second = 3600/5280 = 0.681818 Miles per Hour
60 seconds per minute
so 1500/60 = 25 feet per second
25 x 0.681818 = 17.05 miles per hour
Please help answer this questionnnn
y=5
5=1/4x^2+1
4=1/4x^2
16 = x^s
x = square root (16) = 4
x=3
y= 1/4(3)^2+1 = 3 1/4 = 13/4
It takes 1629 digits to number the pages of a book.How many pages does the book have?
Lucia wants to buy some posters over the Internet. Each poster costs $6.67 and has a shipping cost of $9.99 per order. If Lucia wants to spend no more than $30 for her posters, which inequality shows the maximum number of posters, p, that she can buy?
The value of 7 in ___ is 10 times
The value of 7 in ____
Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters she wrote.
WALK Heather was out for a leisurely walk at a rate of 3 miles per hour. What was her speed in yards per minute?