Answers
The value of x in the figure given is E. √70.
The answer is E. √70.
The two triangles are similar by the AAA Similarity Theorem, since they have two pairs of congruent angles, namely ∠ABD and ∠CAD, and ∠BAD and ∠CDA.
Since the triangles are similar, the ratio of corresponding sides is constant. In particular, the ratio of AD to CD is the same as the ratio of BD to AD.
We are given that AD = 14 and CD = 20, so the ratio of AD to CD is 14/20. We are also given that BD = x, so the ratio of BD to AD is x/14.
Setting these two ratios equal to each other, we get x/14 = 14/20, which simplifies to x = √70.
Here is a proof that shows why the two triangles are similar:
AAA Similarity: Triangles ABD and CAD have two pairs of congruent angles, namely <ADB> and <CAD>, because they are both right angles.
SSS Similarity: Triangles ABD and CAD have three pairs of corresponding sides that are proportional, namely AD/CD = 14/20, BD/AD = x/14, and AB/CD = √70/20. Therefore, the two triangles are similar by the SSS Similarity Theorem.
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Related Questions
A zebra ran at a speed of 20 feet per second. Which operation should you use to find the distance the zebra ran in 10 seconds?
Answers
you would multiply speed by time
20 feet per second times 10 seconds = 200 feet total
Giving you 200ft/10s.
Your answer would be, 200ft.
I hope this helps!
what is 10.85 divided by blank equals 1.55. what is the missing number
Answers
10.85 / 7 = 1.55
The missing number is 7.
Hope this helps!
10.85/1.55 = x
x = 7
Answer: 7 is your missing number because 10.85/7 = 1.55 is true.
Add.
Joe practiced his trumpet 3/4 hour on Monday and 7/12 hour on Tuesday. How long did he practice altogether?
a. 2 hours
b. 1 1/3 hours
c. 2 2/3 hours
d. 5 1/3 hours
Answers
Joe practiced his trumpet 3/4 of an hour on Monday and 7/12 of an hour on Tuesday. How long did he practice altogether?
Result
b. 1 1/3 hours.
Solution
We need to turn the fractions into time first. This is done with division, multiplication, and addition.
Let's divide and multiply
3/4 · 60 = 45
7/12 ·60 = 35
Let's add
45 + 35 = 80
From here, 80 is 60 + 20 minutes, or 1 and 1/3
Hope this helped!
The sum of two consecutive integers is 131. What are the integers?
Answers
x+x+1=131
2x+1=131
2x=131-1=130
x=130÷2 = 65
the integers are 65 and 66
Answer:
The Integers are 65&66
Step-by-step explanation:
Because I got correct with these awnsers
Which point is on the graph of a direct variation equation in which k = 1.8? A. (4, 0.45) B. (7.2, 4) C. (4, 7.2) D. (0.45, 4)
Answers
Answer: C
(4, 7.2)
Step-by-step explanation: Just took this test
Jon has two trees in his yard. one is 20 feet taller than the other. if we let h h be the height of the shorter tree, write an algebraic expression for the sum of the two trees' heights. be sure to simplify your expression.
Answers
Answer:
[tex]2h+20[/tex]
Step-by-step explanation:
It is given that there are two trees in Jon yard, where one tree is 20 feet taller than the other.
We need to find the algebraic expression for the sum of the two trees' heights.
So, in order to solve that we first need to find the height of individual trees then we have to add.
Also, It is given that the height of the smaller tree is h.
So, height of the larger tree is [tex]h+20[/tex]
Now, the total height of both the trees [tex]=h+h+20[/tex]
[tex]=2h+20[/tex]
Hence, the total height of both the trees is [tex]2h+20[/tex].
A car repair shop shop charged 80$ per hour for labor and210 for car parts it it all cost 490 how many hours did it take
Answers
$80x + 210 = 490
80x= 490-210
80x = 280
x = 280/80
x= 3.5 hours
Hope I helped :)
A person can burn about 9 calories per minute bicycling. Let x represent the number of minutes bicycled, and let y represent the number of calories burned. Create a mapping diagram to show the number of calories burned by bicycling for 50, 100, 150, or 200 minutes. Determine the domain and range of the relation in context and explain whether or not this represents a function.
Answers
Final answer:
A mapping diagram to show the number of calories burned by bicycling for different durations has been created. The domain is {50, 100, 150, 200} minutes, and the range is {450, 900, 1350, 1800} calories. This represents a function because each time duration maps to exactly one calorie value.
Explanation:
To create a mapping diagram that represents the number of calories burned by bicycling for 50, 100, 150, or 200 minutes, we consider that a person burns about 9 calories per minute. Let x represent the number of minutes bicycled, and let y represent the number of calories burned. The mapping diagram looks like this:
50 minutes → 50 × 9 = 450 calories
100 minutes → 100 × 9 = 900 calories
150 minutes → 150 × 9 = 1350 calories
200 minutes → 200 × 9 = 1800 calories
The domain of this relation is the set of minutes bicycled, which is {50, 100, 150, 200}, and the range is the set of calories burned, which is {450, 900, 1350, 1800}. This does represent a function because for each value in the domain, there is exactly one corresponding value in the range.
LaTonya works two part-time jobs while attending college. She works 12 hours per week as a work-study student at the college and is paid once a month. After taxes, her net pay is $289. On her second job, LaTonya works 16 hours each week and is paid $7.25 per hour. Deductions from her weekly paycheck total $22.10. LaTonya's husband works full-time and is paid every two weeks. His take home pay after taxes is $1,108.
What is the total household income they should use in creating a budget for the next six months?
Answers
Answer:
Your answer should be $18,579.40
Step-by-step explanation:
Which of the following points is a solution of the inequality y > -2x + 5?
(1 ,4)
(0 ,5)
(-2, 8)
(1, -2)
Answers
After testing each given point by substituting them into the inequality y > -2x + 5, only the point (1, 4) satisfies the condition, making it the correct answer.
The question is asking to find which point among the options given satisfies the inequality y > -2x + 5. To solve this, we will substitute the x and y values from each option into the inequality and check whether the inequality holds.
For (1, 4), if we substitute x = 1 and y = 4 we get 4 > -2(1) + 5, which simplifies to 4 > 3. Since this is true, this point is a solution.
For (0, 5), if we substitute x = 0 and y = 5 we get 5 > -2(0) + 5, which simplifies to 5 > 5. Since this is not true (it should be strictly greater), this point is not a solution.
For (-2, 8), if we substitute x = -2 and y = 8 we get 8 > -2(-2) + 5, which simplifies to 8 > 9. Since this is not true, this point is not a solution.
For (1, -2), if we substitute x = 1 and y = -2 we get -2 > -2(1) + 5, which simplifies to -2 > 3. Since this is not true, this point is not a solution.
Therefore, the correct answer is the point (1, 4) as it is the only one that satisfies the given inequality.
A salesman makes both a base salary and also a commission, which is a percentage of what he sells. Each month, if his sales total s dollars, he makes a total of 2000 + 0.1s dollars. What does 2000 represent?
Answers
Pleasssss answer me
Elena plans to ride her bicycle 5 miles to a park and then ride several times around a loop in the park that is 3 miles long. Then she’ll ride the same way home. She wants to ride a total of at least 22 miles. The inequality 3t + 10 ≥ 22 models this situation, where t is the number of times Elena rides around the loop.
Solve the inequality. How many times does Elena need to ride around the loop?
A. 5 or more times
B. At most 4 times
C. At most 5 times
D. 4 or more times
Answers
Answer:
Option D. 4 or more times
Step-by-step explanation:
we have
[tex]3t+10\geq 22[/tex]
Solve for t
Subtract 10 both sides
[tex]3t+10-10\geq 22-10[/tex]
[tex]3t\geq 12[/tex]
Divide by 3 both sides
[tex]t\geq 4\ times[/tex]
The solution is all real numbers greater than or equal to 4
therefore
4 or more times
Answer:
Option D is the correct answer.
Step-by-step explanation:
The inequality is given by 3t + 10 ≥ 22, where t is the number of loops Elena rides in the park.
Solving we will get
3t + 10 ≥ 22
3t ≥ 22 - 10
3t ≥ 12
t ≥ 4
That is t is 4 or more times,
Number of times Elena need to ride around the loop is 4 or more times.
Option D is the correct answer.
145% of what number is 870
Answers
Answer=600
Answer:
600
Step-by-step explanation:
145% can be written as 145/100.
"of" is another word for multiplication in math
"x" will be the variable for the number
The equation:
145/100x=870
Here, we simplify the equation:
Step 1 (write the equation): 145/100x=870
Step 2 (multiply both sides by 100): 145x = 87000
Step 3 (divide both sides by 145): x=600
:)
Kevin has $4.85 in nickels and dimes. If he has 34 fewer dimes than nickels, how many coins (nickels and dimes) does he have altogether?
A.) 74 coins
B.) 75 coins
C.) 76 coins
D.) 77 coins
Answers
Answer:the awnser is c 76
Step-by-step explanation:
A factor for (f/g, i, n) could be obtained by multiplying the (p/g, i, n) factor by the _______________ factor.
Answers
Answer:
hm
Step-by-step explanation:
good question
The factor that needs to be multiplied by the (p/g, i, n) factor to obtain the (f/g, i, n) factor is the conversion factor between the two units of measurement being used for the factor.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
In this case, the units of measurement for both factors are not specified, so it's not possible to determine the specific conversion factor needed. However, in general, if the two factors are expressing the same quantity but in different units (for example, feet and meters), then the conversion factor between those two units would be used to convert the (p/g, i, n) factor to the appropriate units before multiplying it by the (f/g, i, n) factor.
Thus,
The factor that needs to be multiplied by the (p/g, i, n) factor to obtain the (f/g, i, n) factor is the conversion factor between the two units of measurement being used for the factor.
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which of the following equations describe the graph shown below?
Answers
Hope this helps!
eight out of ten dentists prefer crest toothpaste.what is the ratio of dentist who do not prefer crest to those who do.
Answers
8 do, 2 don't
so the ratio would be 2:8 which can reduce to 1:4
Find the value of the following expression [(17-9)×(3×2)]÷2
Answers
3*2=6
Then Multiply the parentheses.
6*8=48
48/2=24
24
P
E
M
D
A
S
You could get you answer so here's a picture to show you how I did it
What is the probability of flipping heads with a biased coin?
Answers
What is the justification for each step in the solution of the equation?
−2(x−1)+12=4x−6−2(x−1)+12=4x−6
Select from the drop-down menus to correctly justify each step.
−2(x−1)+12=4x−6−2(x−1)+12=4x−6 Given
−2x+2+12=4x−6−2x+2+12=4x−6
−2x+14=4x−6−2x+14=4x−6 Combine like terms.
−2x=4x−20−2x=4x−20
−6x=−20−6x=−20 Addition or Subtraction Property of Equality
x=206x=206
x=103x=103 Simplify.
Answers
Here are the following justifications:
Given: -2 (x-1) +12=4x-6
Distribute property = -2x+2+12=4x-6
Combine like terms= -2x+14=4x-6
Transpose = -2x = 4x – 20
Addition or Subtraction Property of Equality = -6x = -20
Division property of equality = x = 20/6
Simplify = x = 10/3
Answer:
Step-by-step explanation:
Find the equation of the line passing through (4,3) and parallel to the line whose equation is y=2x-6
Answers
(X, Y)
3=2(4)+b
3=8+b
-5=b
Y=2x-5
Which of the following is true for the relation f(x) = 2x2 + 1?
Only the equation is a function.
Neither the equation nor its inverse is a function.
Both the equation and its inverse are functions.
Only the inverse is a function.
Answers
Answer:
Both the equation and its inverse are functions.
Step-by-step explanation:
Since, a relation is called a function when an input value of the relation has only one output value,
Here, the given relation,
[tex]f(x) = 2x^2 + 1[/tex]
When we plot the graph of this function,
We observed that all vertical line intersects the graph exactly once, except
, x = 0,
Thus, by vertical line test,
In the given equation every x has only one output value,
⇒ f(x) is a function,
Now, the inverse of a function is also a function,
⇒ [tex]f^{-1}(x)[/tex] is also a function,
Hence, Both the equation and its inverse are functions.
Cyndi bought an extra large pizza, cut into 12 pieces, for today's meeting of the mystery club. She ate 1/6 of the pizza yesterday afternoon. Her brother ate 1/5 of what was left last night. Cyndi knows that she needs 8 pieces of pizza for the club meeting. Help Cyndi figure out if she has ebough pizza left for the meeting.
Answers
She ate 1/6 of the pizza which left her with 10 slices left (she ate two slices of the 12).
Then her brother ate 1/5 of the pizza which means that he also ate two slices (because 1/5 of 10 is 2).
That means she has 8 slices left: enough for her meeting.
Answer:
Thus, she has enough pizza left for the meeting.
Step-by-step explanation:
It is given that, Cyndi cut pizza in 12 pieces.
Also, She ate 1/6 of pizza yesterday afternoon.
⇒ She ate = [tex]12\times\frac{1}{6} = 2\ \text{pieces}[/tex]
Her Brother ate 1/5 of left pizza
⇒ Her Brother ate = [tex]10\times\frac{1}{5} = 2\ \text{pieces}[/tex]
Then she has left pieces of pizza = 12 - (2 + 2) = 8 pieces
And also that much pieces she wants for the club meeting.
Thus, she has enough pizza left for the meeting.
Evaluate this piecewise function at x=-4 and x=4.
(Can someone show me how to solve this because i don't know what to do to solve this)
Answers
f(x) = x², x≤ -4
= x³, -4 < x ≤ 1
= √x, x > 1
To find f(-4), we note that f(x) = x², x ≤ 4, so we should use this part of the function.
f(-4) = (-4)² = 16
To find f(4), we note that f(x) = √x, x > 1, so we should use this part of the function.
f(4) = √4 = +2 or -2.
A graph of the function is shown below. It indicates that f(4) = +2 for continuity.
Answer:
f(-4) = 16
f(4) = 2.
find the derivative of the given function at the indicated point f(x)=1/x a=2
Answers
Final answer:
The derivative of the function f(x) = 1/x at x = 2 is -1/4, found using the power rule of differentiation.
Explanation:
To find the derivative of the function f(x) = 1/x at the point where a = 2, we employ the power rule of differentiation. The function can be rewritten as f(x) = x-1. Applying the power rule (f'(x) = n*xn-1) to this function, the derivative is f'(x) = -1*x-2 or f'(x) = -1/x2. To find the derivative at x = 2, we simply substitute x with 2, giving us f'(2) = -1/22 = -1/4.
A sample in which every member of the sampling frame has an equal chance of being selected.
Answers
The function f(x) is graphed on the coordinate plane.
What is f(−1) ?
Answers
Answer:
3
Step-by-step explanation:
Similar problem to a previous one that I solved
How to simplify equations with fractional exponents?
Answers
[tex]a^{ \frac{m}{n} }[/tex] which can be rewritten as [tex] (\sqrt[n]{a} )^m[/tex]
for example: [tex](x + 3)^ \frac{2}{3} =( \sqrt[3]{x+3})^2 [/tex]
Final answer:
To simplify equations with fractional exponents, divide the digit term of the numerator by the digit term of the denominator and subtract the exponents of the exponential terms. Then multiply the numerators and denominators together and simplify by common factors if needed.
Explanation:
When simplifying equations with fractional exponents, we can follow these steps:
Divide the digit term of the numerator by the digit term of the denominator.Subtract the exponents of the exponential terms.Multiply the numerators and denominators together and simplify by common factors if needed.For example, let's simplify the equation √(x³ / y²). We divide x³ by y², which gives us x/y. Then we subtract the exponents, resulting in √(x/y). Finally, we can simplify the fractional exponent by taking the square root of x/y, which gives us √(x/y).
How many minutes will it take to drive 82 miles with the speed of 65 miles per hou?
Answers
time|hr = 82/65 hour
but 60minutes = 1hour. so
82/65 hr = 82/65×60 minutes = 75.7 minutes
What conversion factor would you use to convert cubic decimeters to milliliters?