Which theorem or postulate justifies that angle HEF~angle HGE ?
A. AA similarity postulate
B. SAS similarity theorem
C. SSS similarity theorem
D. SSA similarity theorem
Answers
Answer:
Option A is correct.
AA similarity postulate justifies that [tex]\triangle HEF \sim \triangle HGE[/tex]
Step-by-step explanation:
The sum of the measures of a angles in a triangle add up to 180 degree.
In the triangle HGE:
[tex]\angle EHG+\angle EGH+\angle GEH = 180^{\circ}[/tex]
Substitute the given values;
[tex]90^{\circ}+37^{\circ}+\angle GEH = 180^{\circ}[/tex]
[tex]127^{\circ}+\angle GEH = 180^{\circ}[/tex]
Simplify:
[tex]\angle GEH = 180 -127 = 53^{\circ}[/tex]
In triangle HEF and triangle HGE
[tex]\angle FHE = \angle GHE = 90^{\circ}[/tex] [Angle]
[tex]\angle EFH = \angle GEH = 53^{\circ}[/tex] [Angle]
AA (Angle-Angle) similarity postulates states that two triangle are similar if they have two corresponding angles that are congruent or equal.
by AA similarity postulates;
[tex]\triangle HEF \sim \triangle HGE[/tex]
Related Questions
What is v in this formula v=3u 5t if u=5.1 and t=27.3 v?
Answers
v=3×5,1+5×27,3
v=15,3+136,5
v=151,8
v=15,3-136,5
v= -121,2
All real numbers n that are less than -3
Answers
(-∞,-3)
or
n∠-3
The set of all real numbers n that are less than -3 can be represented as: [tex]\[ \{ n \mid n < -3 \} \][/tex]
The set of real numbers less than -3 encompasses an infinite range of values extending to the left of -3 on the number line. These numbers are characterized by being smaller than -3, denoted as ( n < -3 ). In interval notation, this set is represented as (-∞, -3), indicating that it includes all real numbers from negative infinity up to, but not including, -3.
This set is unbounded, as there is no limit to how far left the numbers extend, encompassing an infinite continuum of values that are progressively smaller than -3.
The inverse of the function f(x) = 1/2x + 10 is shown.
h(x) = 2x – ?
What is the missing value?
Answers
Answer:
d. 20
Step-by-step explanation:
Replace the x and y values in the equation
(y = 0.5x + 10) to (x = 0.5y + 10)
Now, solve for the y value in the new equation. You'll get y = 2x + 20.
So, the intercept of the inverse function is 20.
If two pounds of meat will serve 5 people, how many pounds will be needed to serve 13 people?
Answers
If 2 pounds of meat serves 5 that means that 2/5 of a pound serves 1 person.
In ratio form-
1:2/5
The problem is asking how many pounds are needed to serve 13 people, so if you set up a proportion using ratios it would look like this-
1:2/5
13:x
"x" represents the unknown amount of pounds
1 times 13 gets you to 13, so multiply 2/5 by 13 as well.
You should get 5(And)1/5 pounds of meat!
To convert from pounds to ounces, multiply the number of pounds by the unit equivalence of 1 pound = 16 ounces.
Conversion from pounds to ounces:
First, find the unit equivalence: 1 pound = 16 ounces.
Next, multiply the number of pounds by the unit equivalence. Thus, 5 pounds x 16 equals 80 ounces.
-x^2=23 in standard form
Answers
-x^2 = 23
-x^2+x^2 = 23+x^2
0x^2 = x^2 + 23
0 = x^2 + 23
x^2 + 23 = 0
You want to deposit $12,000 in a bank at an interest rate of 8 percent per year. What is the future value of this money after five years?
Answers
Answer: For Plato users the answer is
B . $ 17,631.94
Step-by-step explanation:
ricardo has a bag of mixed fruit snacks. in the bag, there are 8 cherry fruit snacks and 12 strawberry fruit snacks. what is the ratio of strawberry to cherry?
Answers
but this can be simplified to 3:2
hope this helps you
The sum of two numbers is 48. If one third of one number is 5 greater than one sixth of another number, which of the following is the smaller number?
6
22
26
42
please just tell me the answer.
Answers
The sum of two numbers is 48:
x + y = 48 ⇒ x = 48 - y
One third of one number is 5 greater than one sixth of another number:
1/3x =5 + 1/6 y
1/3(48 - y) = 5 + 1/6y
1/3 * 48 - 1/3 * y = 5 + 1/6 y
16 - 1/3y = 5 + 1/6y
16 - 5 = 1/6y + 1/3y
11 = 1/6y + 2/6y
11 = 3/6y
y = 11 * 6 / 3
y = 22
x = 48 - y
x = 48 - 22
x = 26
The smallest number is 22.
Answer:
b: 22
Step-by-step explanation:
if 5^-x=3 what does 5^3x equal?
Answers
Plug in -.68260619 for x: 5 raised to 3x = .03703703
If that's how you intended to solve it then that's the correct answer.
[tex]5^{-x} = 3 \\ \\ \frac{1}{ 5^{x} } =3 \\ \\ 1 = 3* 5^{x} \\ \\ 5^{x} = \frac{1}{3} \\ \\ (5^{x})^{3} = (\frac{1}{3})^{3} \\ \\ 5^{x*3}= \frac{1^{3}}{3^{3}} \\ \\ 5^{3x}= \frac{1}{27} [/tex]
Which expression represents, six times a number plus 8 times a number?
6a + 8
6 + 8 + a + b
48(ab)
6a + 8b
Answers
The answer is 6a+8b, so *D*, hope it helps!
Convert the function into intercept form. Show your work. y=-x^2+5x+36
Answers
~ please mark my answer as brainliest if it helped you :) ~
= - ( x² - 5 x - 36 ) =
= - ( x² - 9 x + 4 x - 36 ) =
= - ( x ( x - 9 ) + 4 ( x - 9 ) ) =
= - ( x - 9 ) ( x + 4 )
Optimization. A rectangle is to have an area of 32 square cms. Find its dimensions so that
the distance from one corner to the mid point of a non-adjacent edge is a
minimum ...?
Answers
xy = 32 makes y = 32/x z² = (32/x)² + (x/2)²
Isolate z
z = 32/x + x/2
Find dz/dx
fr(z) = (x² - 64)/ (2x²)
Set z' = 0, algebraically solving for x having
x +- 18
Since you cannot have a dimension of -8, the only answer for x is 8.
Go back to the original area equation; 32 = xy and plug in x making
32 = 8y
y = 4
To optimize the dimensions of a rectangle with an area of 32 square cm such that the distance from one corner to the midpoint of a non-adjacent edge is minimized, one must use the Pythagorean theorem and calculus. The minimum distance occurs when the rectangle is a square with sides measuring 4√2 cm.
Assume the rectangle's dimensions are length L and width W, with the given area 32 cm2 such that LW = 32. To minimize the distance (D) from one corner to the midpoint of the non-adjacent edge, we can use the Pythagorean theorem, given by D = √(L2 + (W/2)²).
Since the area is fixed, W can be expressed as 32/L, and we can write D as a function of L. After substituting 32/L for W and differentiating with respect to L, we can find the minimum by setting the derivative equal to zero and solving for L.
The minimum distance is achieved when the rectangle is a square, with length and width both equal to √32, which simplifies to 4√2 cm, which is approximately 5.66 cm for both dimensions.
PLEASE HELP!! the measures of two complementary angles are in the ratio 2:3. What is the measure of the smaller angle?
Answers
Complementary angles are those angles whose sum is 90°.
Let angles be x and y.
x + y = 90°
x : y = 2 : 3
_____
3 * x = 2 * y
3x = 2y
x + y = 90°
_____
x = 2/3*y
x + y = 90°
2/3y + y = 90°
2/3y + 3/3y = 90°
5/3y = 90°
5y = 90° * 3
5y = 270°
y = 54°
x + 54° = 90°
x = 90° - 54°
x = 36°
The smaller angle is 36°
Kim, Laura and Molly share £385
The ratio of the amount of money Kim gets to the amount of money Mollley gets is 2:5
Kim gets £105 less than Molly gets
What percentage of the £385 does Laura get ?
With working out
Answers
To find out what percentage of the £385 Laura gets, we need to determine the amounts that Kim and Molly get. By solving equations and subtracting their amounts from the total, we find that Laura gets approximately 45.45% of the £385.
Explanation:To find out what percentage of the £385 Laura gets, we need to first find out the amounts that Kim and Molly get. Let's assume that Kim gets x amount. According to the ratio, Molly gets 5x amount. From the information given, we know that Kim gets £105 less than Molly, so we can write the equation: 5x - x = £105. Solving this equation, we get x = £35. Therefore, Kim gets £35 and Molly gets 5x £35 = £175. Now, to find out the amount Laura gets, we subtract the amounts of Kim and Molly from the total amount: £385 - £35 - £175 = £175. So Laura gets £175. To find out the percentage, we divide the amount Laura gets by the total amount (£385) and multiply by 100: (175 / 385) * 100 = 45.45%. Therefore, Laura gets approximately 45.45% of the £385.
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give me an example of a unit rate used in a real world sutuation
Answers
Examples of that:
[tex] 300\frac{l}{ s } [/tex]
This is rate of fluid flow of some pump for example. It pumps 300 liters every second.
Other example:
[tex]50 \frac{km}{h} [/tex]
This is example for speed. Somebody is moving at 50 kilometers per hour (every hour he travels 50 kilometers)
a dragon traveled at a rate of 35 miles per hour for 2.5 hours .what distance did the dragonfly travel?
Answers
Here, Speed = 35 mi/hr
Time = 2.5 hr
Substitute their values into the expression,
Distance = 35 * 2.5 = 87.5
So, your final answer is 87.5 miles
Hope this helps!
A point is moving along the graph of a given function such that dx/dt is 2 centimeters per second. Find dy/dt for the given values of x.
y = 9x2 + 5
(a) x = -1
dy/dt =____ cm/sec
(b) x = 0
dy/dt =____cm/sec
(c) x = 3
dy/dt =_____ cm/sec
...?
Answers
Use the change rule:
dy / dt = [dy / dx] * [dx / dt]
dy / dx = 18x
and dx / dt = constant = 2 cm / s
Then dy / dt = [18 x] * 2 = 2*18x = 36x
(a) x = -1
dy/dt = 36(-1) = - 36 cm/sec
(b) x = 0
dy/dt = 36(0) = 0 cm/sec
(c) x = 3
dy/dt =36(3) = 108 cm/sec
The rates of change in y for the given values of x are -36 cm/sec, 0 cm/sec, and 108 cm/sec respectively by using the derivative dy/dt = 18*x*dx/dt.
Explanation:This problem is a case of related rates in calculus. Given that dx/dt is constant at 2 cm/sec and the function y = 9x2 + 5, we need to differentiate the function with respect to t to find dy/dt. Solving for dy/dt, you get dy/dt = 18x * dx/dt.
When x = -1, dy/dt = 18*-1*2 cm/sec = -36 cm/sec.When x = 0, dy/dt = 18*0*2 cm/sec = 0 cm/secWhen x = 3, dy/dt = 18*3*2 cm/sec = 108 cm/secSo, the rates of change in y with respect to time for the given values of x are -36 cm/sec, 0 cm/sec, and 108 cm/sec respectively.
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What is the sum of the first five terms of a geometric series with a1 = 20 and r = 1/4?
Answers
Answer: The required sum of first terms of the series is [tex]\dfrac{1705}{64}.[/tex]
Step-by-step explanation: We are given to find the sum of the first five terms of a geometric series with first term and common ratio as follows :
[tex]a_1=20~~~~~\textup{and}~~~~~r=\dfrac{1}{4}.[/tex]
We know that
the sum of first n terms of a geometric series with first term [tex]a_1[/tex] and common ratio r is given by
[tex]S_n=\dfrac{a(1-r^n)}{1-r}.[/tex]
Therefore, the sum of first 5 terms of the given geometric series is given by
[tex]S_5\\\\\\=\dfrac{a(1-r^5)}{1-r}\\\\\\=\dfrac{20(1-(\frac{1}{4})^5)}{1-\frac{1}{4}}\\\\\\=\dfrac{20\left(1-\frac{1}{1024}\right)}{\frac{3}{4}}\\\\\\=20\times\dfrac{4}{3}\times\dfrac{1023}{1024}\\\\\\=20\times\dfrac{341}{256}\\\\\\=\dfrac{5\times 341}{64}\\\\\\=\dfrac{1705}{64}.[/tex]
Thus, the required sum of first terms of the given geometric series is [tex]\dfrac{1705}{64}.[/tex]
How many kg in 1 gram?
Answers
1 kg = 1000 g
Elena has 32 hair ties. Melanie has 8 hair ties the ratio of elena's hair ties to Melanie's hair ties is
Answers
The new ratio of Elena’s hair ties to Melanie’s hair ties is 8 : 3.
Given that Elena has 32 hair ties and Melanie has 8 hair ties, let’s analyze the situation:
Initial Ratio:
The ratio of Elena’s hair ties to Melanie’s hair ties is: [ \text{Elena : Melanie} = 32 : 8 = 4 : 1 ]
Melanie Gets 4 More Hair Ties:
After Melanie receives 4 additional hair ties, her total becomes: [ \text{Melanie’s new total} = 8 + 4 = 12 ]
New Ratio:
Now, let’s find the new ratio of Elena’s hair ties to Melanie’s hair ties: [ \text{Elena : Melanie} = 32 : 12 = 8 : 3 ]
Therefore, the new ratio of Elena’s hair ties to Melanie’s hair ties is 8 : 3.
Complete question:
Elena has 32 hair ties. Melanie has 8 hair ties. The ratio of Elena’s hair ties to Melanie’s hair ties is : 1. If, Melanie gets 4 more hair ties, the new ratio of Elena’s hair ties to Melanie’s hair ties is 8 :
The equation y=1.2x+8.9 is a linear model for data comparing the ages of babies between 1 and 11 months old (x) and their average weights in pounds (y). About how much weight does a baby gain per month?
Answers
For all the people that actually have this question:
For babies between 1 and 11 months old, the equation y = 1.2x + 8.9 models the baby's weight when the baby is x months old. A baby in that age range weighs 17.5 lbs. What is the best estimate for the age of the baby?
Answer:
7 months
Step-by-step explanation:
1.2 * 7 + 8.9 = 17.3 & 17.3 is close to 17.5
I just took the test!
The weight that a baby gain per month is 1.2.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given is a linear equation,
y = 1.2x + 8.9
This equation compares the ages of babies between 1 and 11 months old (x) and their average weights in pounds (y).
This equation is in the slope intercept form, where 1.2 is the slope and 8.9 is the y intercept.
Slope is the change in y coordinates by change in x coordinates.
So, weight baby gain per month is 1.2.
Hence 1.2 is the weight that the baby gain per month.
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Ciara solved the exponential equation 3x+1 = 15 and her work is shown below. What is the first step she did incorrectly?
Step 1: log 3x+1 = log15
Step 2: (x + 1)log 3 = log15
Step 3: log3 = log 15 over x plus 1
Step 4: 0.477121 = 1.176091 over x plus 1
Step 5: 0.477121(x + 1) = 1.176091
Step 6: x + 1 = 1.176091 over 0.477121
Step 7: x + 1 = 2.464975
Step 8: x = 1.464975
(I think it is Step 3)
Answers
❀Good luck❀
What is the slope of the line joining (5, 9) and (−2, 9)?
A. -7/4
B.-4/7
C.0
D.No slope
Answers
Hope this helps.
answer is C.0
......................
If line segment AB = 12 feet, what is the length of line segment AC?
Select one of the options below as your answer:
A.
6 feet
B.
10 feet
C.
12 feet
D.
24 feet
Answers
A children's book has dimensions 20 cm by 24 cm.
What scale factor should be used to make an enlarged version that has dimensions 25 cm by 30 cm?
A. 5
B. 1.5
C. 1.25
D. 0.8
Answers
25/20 = 1.25
30/24 = 1.25
Thus, it is a scale of 1.25
Answer:
We should use C. 1.25
Step-by-step explanation:
We know that the children's book dimensions are 20 cm x 24 cm
We need to find a scale factor (which is a number) that will turn the dimensions 20 cm x 24 cm ⇒ 25 cm x 30 cm
We can write :
(20 cm) . a = 25 cm
Where ''a'' is the scale factor.
Solving for a :
[tex](20cm).a=25cm\\a=\frac{25cm}{20cm}=1.25 \\a=1.25[/tex]
This result is reasonable because the scale factor won't have units
A scale factor of 1.25 turns 20 cm ⇒ 25 cm
We can use the another dimension to verify :
(24 cm) . a = 30 cm
(24 cm) . (1.25) = 30 cm
30 cm = 30 cm
The scale factor is option C. 1.25
what are three equivalent fractions for 80/100 ...?
Answers
Since the fraction given above which is 80/100 is not in its simple form, there are equivalent fractions for this. And these are the following.
We can have 40/50, 8/10 and 4/5. We can also have 16/20. Hope this answer helps.
Three equivalent fractions for [tex]\( \frac{80}{100} \) are \( \frac{4}{5} \), \( \frac{160}{200} \), and \( \frac{400}{500} \)[/tex].
To find three equivalent fractions for [tex]\( \frac{80}{100} \)[/tex], we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 20 in this case.
1. Divide both the numerator and denominator by 20:
[tex]\[ \frac{80 \div 20}{100 \div 20} = \frac{4}{5} \][/tex]
So, [tex]\( \frac{80}{100} \)[/tex] is equivalent to [tex]\( \frac{4}{5} \)[/tex].
2. Multiply both the numerator and denominator by the same non-zero integer:
[tex]\[ \frac{80 \times 2}{100 \times 2} = \frac{160}{200} \][/tex]
So, [tex]\( \frac{80}{100} \) is also equivalent to \( \frac{160}{200} \)[/tex].
3. Similarly, we can multiply both the numerator and denominator by another non-zero integer:
[tex]\[ \frac{80 \times 5}{100 \times 5} = \frac{400}{500} \][/tex]
So, [tex]\( \frac{80}{100} \) is also equivalent to \( \frac{400}{500} \)[/tex].
Consider the sequence 2, 5, 10, 17, ...
What is the value of a4?
2
5
10
17
Answers
so it is 17
Answer:
The answer is [tex]a4=17[/tex]
Step-by-step explanation:
we have the sequence
[tex]2,5,10,17,...[/tex]
Let
a1-----> the first term
a2----> the second term
a3----> the third term
a4----> The fourth term
In this problem we have
[tex]a1=2[/tex]
[tex]a2=5[/tex]
[tex]a3=10[/tex]
[tex]a4=17[/tex]
therefore
the answer is
[tex]a4=17[/tex]
Which expressions simplify to a rational answer?
A. √11 ⋅ √5
B. √9 ⋅ √16
C. 5√2 ⋅ √2
D. √3 ⋅ √2
Answers
Answer:
if your a k12 kid this is old and was once not a multip choice question but the answer is b
Step-by-step explanation:
-Former k12 kid
Water flowing from a faucet can fill 1/4 of a tank in 3 minutes. How long does it take to fill the tank completely with water?
Answers
. Zalia meets her friend at the science museum to see a special exhibition. The admission to the museum is $12.50 plus tax. Zalia pays for herself and her friend. They have lunch at the museum’s cafe. Zalia has a sandwich for $5.95, an apple for $1.25 and a drink for $1.69. She is charged tax and also tips her server 15%. If tax is 7.25%, how much did Zalia pay all total for her day at the science museum?
a.
$41.43
b.
$37.68
c.
$36.35
d.
$24.27
Answers
The total comes to $37.67, so the closest answer is (b) $37.68.
We will calculate how much Zalia paid for her day at the science museum including admission fees, lunch, and the tax and tip for both of these.
Firstly, let's calculate the total cost of admission for Zalia and her friend:
Admission for one person: $12.50
Admission for two people: $12.50 x 2 = $25.00
Now, let's find the total cost of Zalia's lunch:
Sandwich cost: $5.95
Apple cost: $1.25
Drink cost: $1.69
Total lunch cost before tax and tip: $5.95 + $1.25 + $1.69 = $8.89
Next, we add the tax:
Tax for admission: $25.00 x 7.25% = $1.81
Tax for lunch: $8.89 x 7.25% = $0.64
Total tax: $1.81 + $0.64 = $2.45
Now, we calculate the tip for the lunch:
Tip: $8.89 x 15% = $1.33
Finally, add everything up to get the total amount Zalia paid:
Total cost without tax and tip: $25.00 + $8.89 = $33.89
Total tax and tip: $2.45 + $1.33 = $3.78
Grand total: $33.89 + $3.78 = $37.67
Examining the provided options, we can see that the closest amount to our calculation is $37.68, considering the possibility of a rounding difference in the final tax and tip calculations. Thus, the correct answer is (b) $37.68.