Answers
[tex]\bold{\huge{\underline{ Solution \:1}}}[/tex]
Yes, ΔEDF and ΔBCA are similarIf we look at the both the triangles then the
[tex]\sf{ {\angle} E = {\angle}B }[/tex][tex]\sf{ {\angle} F = {\angle}A }[/tex]From above, we can conclude that :-
Both the triangles are similar by AA Similarity
Hence, Option A is correct.
[tex]\bold{\huge{\underline{ Solution \:2}}}[/tex]
Let consider the given triangle be ABC and the line that divides the triangle consider it as DE
Here, DE || BCSo,
[tex]\sf{\dfrac{ AD }{ AB }}{\sf{ = }}{\sf{\dfrac{AE}{AC}}}{\sf{=}}{\sf{\dfrac{DE}{BC}}}[/tex]Therefore, ΔABC similar to ΔADE by SSS congruence similarity criterion. Now,We have to find the value of x
In ΔABC, By using BPT theorem
If the line is drawn parallel to one side of the triangle which intersect the other two sides at specific points then the other two sides are in proportion .That is,
[tex]\sf{\dfrac{ AD }{ AB }}{\sf{ = }}{\sf{\dfrac{DE}{BC}}}[/tex]
Subsitute the required values,
[tex]\sf{\dfrac{ 6 }{ 6 + 4 }}{\sf{ = }}{\sf{\dfrac{8}{x}}}[/tex]
[tex]\sf{\dfrac{ 6 }{ 10 }}{\sf{ = }}{\sf{\dfrac{8}{x}}}[/tex]
[tex]\sf{\dfrac{ 3 }{ 5 }}{\sf{ = }}{\sf{\dfrac{8}{x}}}[/tex]
[tex]{\sf{ x = 8{\times} }}{\sf{\dfrac{5}{3}}}[/tex]
[tex]{\sf{ x = }}{\sf{\dfrac{40}{3}}}[/tex]
[tex]{\sf{ x = 13}}{\sf{\dfrac{1}{3}}}[/tex]
Hence, Option C is correct
[tex]\bold{\huge{\underline{ Solution \:3}}}[/tex]
Here,
SRT similar to BACFor x,
By using BPT theorem,
[tex]\sf{\dfrac{ AB }{ RS }}{\sf{ = }}{\sf{\dfrac{BC}{ST}}}[/tex]
Subsitute the required values,
[tex]\sf{\dfrac{ 2 }{ 4 }}{\sf{ = }}{\sf{\dfrac{x}{6}}}[/tex]
[tex]\sf{\dfrac{ 1 }{ 2 }}{\sf{ = }}{\sf{\dfrac{x}{6}}}[/tex]
[tex]\sf{ x = }{\sf{\dfrac{6}{2}}}[/tex]
[tex]\sf{ x = 3 }[/tex]
Thus, The value of x is 3
For y
Again by using BPT theorem,
[tex]\sf{\dfrac{ AB }{ RS }}{\sf{ = }}{\sf{\dfrac{AC}{RT}}}[/tex]
Subsitute the required values,
[tex]\sf{\dfrac{ 2 }{ 4 }}{\sf{ = }}{\sf{\dfrac{5}{y}}}[/tex]
[tex]\sf{\dfrac{ 1 }{ 2 }}{\sf{ = }}{\sf{\dfrac{5}{y}}}[/tex]
[tex]\sf{ y = 5{\times}2 }[/tex]
[tex]\sf{ y = 10 }[/tex]
Thus, The value of y is 10
Hence, Option A is correct.
Related Questions
please help me asap
Answers
Answer: D. The moon is located perpendicular to Earth and the sun.
Step-by-step explanation: I studied astronomy. :)
What is the value of 3n at n = 11
Answers
Answer:
33
Step-by-step explanation:
replace n with 11 and multiply 3x11
Solve the formula V = 1/3b^2 h for b.
Answers
Answer:
[tex]b=\sqrt{\frac{3V}{h}}[/tex]
Step-by-step explanation:
To solve a formula for one of its variables do that
Underline the variableSeparate it on one side and the other terms on the other sideMake its coefficient equals 1Let us use these steps to solve our question
∵ V = [tex]\frac{1}{3}[/tex] b²h
→ Underline b
∴ V = [tex]\frac{1}{3}[/tex] b²h
→ Multiply both sides by 3 to cancel the denominator on the right side
∴ 3V = b²h
→ Divide both sides by h to move it to the other side
∴ [tex]\frac{3V}{h}=b^{2}[/tex]
→ To find b take √ for both sides
∴ [tex]\sqrt{\frac{3V}{h}}=\sqrt{b^{2} }[/tex]
→ The square root will cancel the power 2 of b
∴ [tex]\sqrt{\frac{3V}{h}}=b[/tex]
→ Switch the two sides
∴ [tex]b=\sqrt{\frac{3V}{h}}[/tex]
Write an equation describing the relationship of the given variables.
y varies directly as the fourth power of x and when x=3, y=162.
y =
Answers
Answer:
[tex]y = 2x^4[/tex]
Step-by-step explanation:
The given statement can be represented as:
[tex]y\ \alpha\ x^4[/tex]
[tex]x =3; y = 162[/tex]
Given
Represent this as an equation
[tex]y\ \alpha\ x^4[/tex]
Convert variation to equation
[tex]y = kx^4[/tex]
Where k is a constant of variation.
Substitute [tex]x =3; y = 162[/tex]
[tex]162 = k * 3^4[/tex]
[tex]162 = k * 81[/tex]
Solve for k
[tex]k = 162/81[/tex]
[tex]k =2[/tex]
To get the equation, we have:
[tex]y = kx^4[/tex]
Substitute 2 for k
[tex]y = 2x^4[/tex]
The equation describing the relationship of the given variables is [tex]y=\frac{81}{162}x^4[/tex]
If y varies directly to the fourth power of x, this can be expressed as:
[tex]y \alpha x^4\\y=kx^4\\[/tex]
Given that x = 3 and y = 162, the equation becomes;
[tex]162 = k(3^4)\\162 = 81k\\k=\frac{81}{162}[/tex]
Substitute the value of k into the expression above to have:
[tex]y=kx^4\\y=\frac{81}{162}x^4[/tex]
Hence the equation describing the relationship of the given variables is [tex]y=\frac{81}{162}x^4[/tex]
Learn more on direct variation here: https://brainly.com/question/6499629
scott wants to rent a boat and spend at most $79. The boat costs 8 per hour, and Scott has a discount coupon for $9 off. What are the possible numbers of hours Scott could rent the boat?
Answers
Answer:
11 hours
Step-by-step explanation:
Using the $79 dollars, Scott can get up to 9 hours with the boat. Scott will be left with $7, adding the $7 to the $9 coupon, Scott will then have $16 which can give Scott an additional 2 hours summing the total hours up to 11 hours Scott can rent the boat for.
What formula to use for determining the probability that the mean stress level for a sample of 70 employees will fall above 52? (mean =50; STD 10)
Answers
Answer:
0.4207
Step-by-step explanation:
Determine z-score
[tex]z=\frac{\bar{x}-\mu}{\sigma/\sqrt{n}}\\ \\z=\frac{52-50}{10/\sqrt{70}}\\ \\z\approx1.6733[/tex]
Find P(Z>1.6733)
[tex]P(Z > 1.6733)=normalcdf(1.6733,\infty)\approx0.4207[/tex]
Therefore, the probability that the mean stress level for a sample of 70 employees will fall above 52 is 0.4207
find gradient for
xe^y + y e^x = 2e at (1,1)
Answers
Answer:
Step-by-step explanation:
Y
=
−
[
e
+
1
]
x
+
1
Simplify 6 - 23 + (-9 + 5) · 2.
Answers
6 - 23 + (-9+5) * 2
-17 + (-4)*2
-17 + (-8)
-17 - 8
-25
Answer:
-25
Step-by-step explanation:
follow the order for pemdas which is (parenthesis,exponent,multiplication/division, and then addition/subtraction)
Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X?
45°
60°
120°
135°
Answers
[tex]x + y = 90[/tex]
[tex]x = 3y[/tex]
[tex]3y + y = 90[/tex]
[tex]4y = 90[/tex]
[tex]y = 15[/tex]
[tex]x = 3(15) = 45[/tex]
Answer:
45 °
Step-by-step explanation:
Knowing that:
Supplementary Angle = 180 °
Angle x is 3 time the measure of angle y.
Solve:
Equation below:
x + y = 180
x = 3y
Substitute
3y + y =180
4y = 180
Divide both sides by 4
4y/4 = 180/4
y = 45
Value of x:
x = 3 × 45
x = 135
Therefore the measure of angle x is 135.
x = 45
y = 135
~Lenvy~
Use a table of trigonometric values to find the angle θ in the right triangle in the following problem. Round to the nearest degree, if necessary.
sin θ = ? O = 8 H = 16
Answers
The value of θ in the given triangle is equal to 30 degrees.
Data;
opposite = 8hypothenuse = 16sin θ = ?Trigonometric RatiosTo solve this problem, we have to use trigonometric ratios on this which is SOHCAHTOA.
since sin θ is the ratio between the opposite side to the hypothenuse,
[tex]sin\theta = \frac{opposite}{hypothenuse}[/tex]
Let's substitute the values into the function and solve.
[tex]sin\theta = \frac{8}{16} \\\theta = sin^-^1 (0.5)\\\theta = 30^0[/tex]
The value of θ is equal to 30 degrees.
Learn more on trigonometric ratios here;
https://brainly.com/question/24349828
Assume
that you are good and beverage Director of a large
hotel
You are planning
For your New Year's Eve gala, and require a large
amount of wine and champagne. you conduct a competitive
bidding. Process with the pur veyors in you area, and, based
upan quality and price, you
place a very large order (in excess of $20,000) with a
single purve you one week later o you recieve a case
OF very expensive champagne delivered to you
home with side a nice note from the purveyor's
representative stating how much they appreciated the
order and that they are really looking forward to
doing business with you in the years ahead. What
do you do with the champagne?
Answers
Step-by-step explanation:
Assume that you are the Food and Beverage Director of a large hotel. You are planning for your New Year’s Eve gala, and require a large amount of wine and champagne. You conduct a competitive bidding process with the purveyors in your area, and, based upon quality and price, you place a very large order (in excess of $20,000) with a single purveyor. One week later, you receive a case of very expensive champagne, delivered to your home with a nice note from the purveyor’s representative stating how much they appreciated the order and that they are really looking forward to doing business with you in the years ahead. What do you do with the champagne?
Expert Answer
ANSWER From your perspective, it might not be illegal for you to accept a case of champagne. However, there could be liquor laws in your state that prohi…View the full answer
When drawing a card, find the probability of drawing a spade or selecting a number less
than five.
Answers
Answer:
Therefore, there 16 chances of getting a spade OR a five.
Step-by-step explanation:
40% of 40
Percentage of whole numbers (10-100)
Answers
Hello
40% de 40
(40*40)/100 =>16
Can anyone help me on this question?
Answers
Answer:
B
Step-by-step explanation:
The definition of an inverse is a reflection over y=x.
21. Find 50% of 1500 km.
Answers
Answer: 750km
Step-by-step explanation:
50% x 1500 or 1500 divided by 2
exercise 15 b i will mark u as brainlist
Answers
15b
10 balls...........200
15 balls.......... = 15x200 : 10 = 300
Rs 300 for 15 balls
8
9
10
TIME REMAINING
14:56
SERE
The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this
information at certain times during a given day. The following temperatures were recorded on a January day in New York
City.
Time of Day
10 AM 12 Noon 2 PM 4 PM 16 PM
SPM 10 PM
Temperature (°F) 30 35 36 36 34 30 28
a.
What is the average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM?
Interpret this value in a complete sentence.
6°F degrees per hour; The temperature drops at an average rate of 6 degrees per hour from 6
PM to 10 PM
b. -6°F degrees per hour: The temperature drops at an average rate of 6 degrees per hour from 6
PM to 10 PM
C.
-1.5°F degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour
from 6 PM to 10 PM.
d. 1.5°F degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from
6 PM to 10 PM
Mark this and return
Save and Exit
Nex
Submit
cript:void(0)
Answers
Answer:
D. 0.019 years of age per year
Step-by-step explanation:
for the function f(x)=1/2(x-3)2 +6, what is the value of f(2)
so basically solve f(2)=1/2(x-3)2 +6
the third two is a small two btw next to x-3
Answers
1/2 times 2 = 1, 1/2 times 3= 1.5
(1-1.5)2+6
(-0.5) 2 + 6
1+6=7
lewis can run a 40-yard dash in 4.8 seconds. On average, how many feet does he run per second?
Answers
over 5 seconds, a guy that runs a 4.4 runs about 5 extra yards further than a guy running a 4.9
Coach Harns wanted to buy new basketballs. He has a $200 budget to purchase
basketballs. He found 40 basketballs for $300. Coach Cary gave him a coupon
for 45% off. What is his new price and can he purchase the 40 basketballs?
Original:
Discount:
New price:
Helppp me.
Answers
discount- $135
new price- $165
The new price for 40 basketballs is $165, coach Harns can buy these balls because they fit into his budget.
Hope this helps:)
A man won a lotto jackpot and he spent 2/5 of the money on luxury cars and 1/4 on buying a house. What fraction of his lotto earnings is remaining
Answers
spent : 2/5 + 1/4 = 8/20 + 5/20 = 13/20
remains = 7/20
The 7/20th fraction of his lotto earnings is remaining.
Let us say the man has $100
Money spent on luxury cars = 2/5 of the money
Money spent on luxury cars = 2/5 * 100 = $40
Money spent on buying a house = 1/4 of the money
Money spent on buying a house = 1/4 * 100 =$25
Money left with the man = 100-40-25 = $35
$35 is what fraction of $100?$35 is 35/100 fraction of $100.
35/100 = 7/20
So, the 7/20th fraction of his lotto earnings is remaining.
Hence, the 7/20th fraction of his lotto earnings is remaining.
To get more about fractions visit:
https://brainly.com/question/78672
Iman had twice as much money as Daphne at first. After Iman had spent $128 of her money on a bag and Daphne had spent $40 of her money on a dress, they had an equal amount of money left. How much money did each of them have left? pls help me.
Answers
Step-by-step explanation:
x = Iman's money
y = Daphne's money
x = 2y
x - 128 = y - 40
now we use the first equation as identity in the second equation and get
2y - 128 = y - 40
y - 128 = -40
y = $88
x = 2y = $176
these were the starting values.
now, after spending, they have both left
176 - 128 = 88 - 40 = $48
Pls help I’ll give brainlisest it’s 7th grade math
Answers
Answer:
-2.3 to 2.9
Step-by-step explanation:
The range is kinda self explanatory, range is the space between the lowest value and the greatest value. You can solve it by subtracting 2.9 - (-2.3)
Hope that helps and have a great day!
lines M and N are parallel which angle has a measure of 110
a.1
b.2
c.3
d.4
Answers
Answer:
B. angle 2
Step-by-step explanation:
Angle 2 is opposite to the 110 degrees, and opposite angles are congruent
Hope this helps :)
Help please!!! Algebra 3, Find Tan 0
Answers
Answer:
Step-by-step explanation:
Carlos is using a number line to add another integer to –4. He begins by showing –4 on the number line, as shown below. Carlos adds the other integer on the number line and says that the sum is negative.
A number line going from negative 5 to positive 5. The area between negative 4 to 0 is highlighted.
Which is true of the number Carlos added to –4?
The number must be a negative integer.
The number must be a positive integer.
The number could be 3 or any integer less than 3.
The number could be 4 or any integer greater than 4.
Answers
Answer:
The number must be a negative integer because -4+ any negative is a negative
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
sale price: $66.30 percent of discount: 65%
find the regular price
Answers
Answer:
$189.43
Step-by-step explanation:
P = regular price
65% as a decimal = [tex]\frac{65}{100}[/tex] = .65
Discount = .65
To get the amount of the discount we would multiply P * .65
To find the sale price we subtract the discount from the original price.
Now we write our equation:
P - P(.65) = $66.30
Solve for P
P - P(.65) = $66.30
1P - P(.65) = $66.30
1P - .65P = $66.30
.35P = 66.30 Divide each side by .35
.35P.35 = 66.30/.35
P = 66.30/.35
P ≈ $189.43
match the google drive applications to its best use.
Answers
Answer:i need brainy answered sorry
Step-by-step explanation:sorry
Answer:
first google docs second google sheets
Step-by-step explanation:
first google docs second google sheets third google forms forth google drawing 5th google maps 6th google slides
Express as a sum
a-5
(please give explanation too)
Answers
The sum is a+1*(-5) since you have a multiplication with different signs (+ -).
Multiplication Sign RulesThe rules to multiplication of numbers are:
+ + or - -The result presents a positive sign (+) because the signs are same.
+ - or - +The result presents a negative sign (-) because the signs are different.
The given function is a linear equation with one variable (a). You can rewrite the expression a-5 as a sum. See below.
a+ 1*(-5) =a-5 since when you have a multiplication with different signs (+ -).
Read more about rules for multiplication here:
https://brainly.com/question/16119150
Find 3 equivalent fractions to this number. 16/40
Answers
Answer:
[tex]\frac{8}{20}[/tex] , [tex]\frac{4}{10}[/tex] , [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
to find equivalent fractions multiply or divide the numerator and denominator by the same value.
[tex]\frac{16}{40}[/tex] ( divide numerator/ denominator by 2 )
= [tex]\frac{8}{20}[/tex] ( divide numerator/ denominator by 2 )
= [tex]\frac{4}{10}[/tex] ( divide numerator/ denominator by 2 )
= [tex]\frac{2}{5}[/tex] ← in simplest form