Given:
Triangle ABC is similar to triangle XYZ.
In triangle ABC AB=2, BC=4, CA=3.
In triangle XYZ, XY=7, YZ=14, ZX=N.
To find:
The length of ZX.
Solution:
If two triangles are similar, then their corresponding sides are proportional.
Since [tex]\Delta ABC\sim \Delta XYZ[/tex], therefore
[tex]\dfrac{AB}{XY}=\dfrac{BC}{YZ}=\dfrac{CA}{ZX}[/tex]
[tex]\dfrac{2}{7}=\dfrac{4}{14}=\dfrac{3}{N}[/tex]
[tex]\dfrac{2}{7}=\dfrac{2}{7}=\dfrac{3}{N}[/tex]
[tex]\dfrac{2}{7}=\dfrac{3}{N}[/tex]
On cross multiplication, we get
[tex]2\times N=3\times 7[/tex]
[tex]2N=21[/tex]
Divide both sides by 2.
[tex]N=\dfrac{21}{2}[/tex]
[tex]N=10.5[/tex]
Therefore, the length of side ZX is 10.5 units.
Jaycee has a VIP membership to a movie theater, so she pays $27.09 a year and $6 fir each movie she sees. Claire doesn’t have a membership, so she pays $8.25 each movie she sees. How many movies would they have to see in a year in order to pay the same amount that year?
Answer:
12 movies
Step-by-step explanation:
About 12 movies in a year in order to pay the same amount that year
How many addition signs should be put between digits of the number 987654321 and where should we put them to get a total of 99?
Answer:
6 +s
Step-by-step explanation:
9+8+7+6+5+43+21 = 99
whats 2×1..... ............. . .......
Answer:
2
Step-by-step explanation:
Answer:
2x1 is 2
Step-by-step explanation:
For each function, what is the output of the given input? For f ( x ) = 4 x + 7 , find f ( 4 ) . 1
Answer:
let's see what to do buddy...
Step-by-step explanation:
To find the output of a number in a function, we must put it in the equation of the function instead of the x .
So to find output of ( x = 4 ) , we must put 4 instead of x in the equation .
Let's do it :
[tex]f(4) = 4 \times (4) + 7 \\ \\ f(4) = 16 + 7 = 23 \\ [/tex]
So the output number of ( x = 4 ) is 23 .
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
The manager of a local fast-food restaurant is interested in improving the service provided to customers who use the restaurant's drive-up window. As a first step in this process, the manager asks an assistant to record the time (in seconds) it takes to serve a large number of customers at the final window in the facility's drive-up system. The file P08 07 xlsx contains a random sample of 200 service times during the busiest hour of the day
a. Identify the relevant population.
b. Calculate and interpret a 95% confidence interval for the mean service time of all customers arriving during the busiest hour of the day at this fast-food operation.
c. If the manager wants to improve service, at least during the busiest time of day, does this contidence interval provide useful inlormation? What useful information does it not provide?
Answer and explanation:
Find answer and explanation attached
A person standing on moving walkway travels 90 feet in 30 seconds . What equation represents this relationship? How many feet will the person travel in 10 seconds?
y=kx
Answer: y=3x;30 feet
Step-by-step explanation:
Every day a zookeeper feeds 4 adult elephants a total of 320lb of food. At this rate, how many pounds of food would the zookeeper need every day to feed 6 adult elephants?
Answer:
34343
Step-by-step explanation:
Be it the right thing for a reason
Answer:
480lb
Step-by-step explanation:
320/4 = 80/1
80 x 6 = 480lb of food to feed 6 adult elephants
your welcome!!
If the number has 6 hundreds. The tens digit has a value of 50. The ones digit is the difference between the digits in the hundreds place and tens place. What is the number?
Answer:
90
Step-by-step explanation:
because it is between the hundred and tens place
The graphs below show some data from a coffee shop menu. One of the graphs shows cost (in dollar) vs. drink volume (in ounces), and one of the graphs shows calories vs. drink volume (in ounces.)
a. Which graph is which? Given them the correct titles.
Graph A: _______vs volume......... Graph B:_______vs volume
b. Which quantities appear to be in a proportional relationship?
1. cost vs volume or
2. calories vs volume
For the proportional relationship, find the constant of proportionality.
a. 0.21 per ounce,
b. 12 calories per ounce,
c. 0.38$ per ounce, or
d. 15 calories per ounce
Answer:
a. Graph A: Cost vs Volume
Graph B: Calories vs Volume
b. Graph B (Calories vs Volume)
c. k = 15
Step-by-step explanation:
a. It is not possible for a volume of 10 oz of drink to be sold for $150. It doesn't make common sense. Also, calorie level of 150 in 10 oz of drink seem plausible.
It makes more sense if 10 oz of the drink cost $3.75. Therefore, the graphs should be titled as follows:
Graph A: Cost vs Volume
Graph B: Calories vs Volume
b. The quantities in Graph B (Calories vs Volume) appear to be in a proportional relationship. We know this because if we try drawing a line to connect the points on the graph, it will give us a straight line. A straight line connotes proportionality.
Also the ratio of the quantities of the two known points given are the same. I.e. [tex] \frac{150}{10} = \frac{360}{24} = 15 [/tex]
Therefore the quantities compared in Graph B shows a proportional relationship.
c. Constant of proportionality = [tex] \frac{150}{10} = \frac{360}{24} = 15 [/tex]
If a biking tour group traveled at a constant rate of 34 miles per day for 5 days, how many miles did they cycle?
HURRY! WILL GIVE BRAINLY!!
Answer:170
Step-by-step explanation:
34 miles times 5 days is 170 miles
Answer:
170 miles
Step-by-step explanation:
They are traveling 34 miles per day, and if they travel for 5 days, just multiply the miles per day, or 34, by the number of days, or 5.
34*5=170
ABCD~LMNO Find the value of MN if AB=12cm, BC=9.6cm and LM= 16cm
A) 13cm
B) 7.2cm
C) 12.8cm
D) 13.6cm
As the music plays,the volume changes In the beginning of the piece can be modeled by the equation s=10Ix-4I+50 where s represents the sound level in decibels and x represents the number of measures of music played. explain in words each step to find the following equation at what number(s) measures played would the sound level be at 80
Answer:
-127
Step-by-step explanation:
s = 101x-41+50
80 = 101x - 4+ 50
-101x
-181 = x - 4 +50
-181 = x -54
+ 54
-127 = x
I hope this helps
Assessment
Direction. Write the letter of the correct answer on a separate answer sheet.
1. The following are notations for composite functions EXCEPT,
a. hip(x))
b. f(x) g(x)
C. (
sot) (x)
d. f(g(x))
Find h(3) + d(2) if h(x) = x - 1 and d(x) = 7x + 3
b.5
c. 14
d. 19
3. t(x) = -x2 + 7x + 1 and r(x) = 5x2 - 2 x + 8, find (t - r)(2).
6.-18
2.
C. -13
d. 13
4. f(x) = 4x + 2 and g(x) = 3x - 1, find (f - )(4).
c. 7
5. If g(x) = x - 4 and f(x) = x + 5 Find f(x) = g(x)
a. x2 + x + 20
C.X2 - X - 20
b. x2-x+20
d. x² + x - 20
26
>
Answer:
Step-by-step explanation:
1) Composite functions are function of two or more functions to serve as one function. For example, given d(x) and g(x), we can write both as composite function as d(g(x)). We can call it function of a function. Hence, from the following function, the following options except option B are composite.
d(x)g(x) is the product of the two functions not a composite.
Option B is correct.
b) Given h(x) = x-1 and d(x) = 7x+3
H(3) = 3-1
H(3) = 2
d(2) = 7(2)+3
d(2) = 14+3
d(2) = 17
h(3)+d(2) = 2+17
h(3)+d(2) = 19 (option D)
c) Given t(x) = -x² + 7x + 1 and r(x) = 5x² - 2x + 8, we are to first find the function
t(x)-r(x)
t(x)-r(x) = -x²+7x+1-5x²+2x-8
t(x)-r(x) = -x²-5x²+7x+2x+1-8
t(x)-r(x) = -6x²+9x-7
Substitute x as 2
(t-r)(2) = -6(2)²+9(2)-7
t-r (2) = -6(4)+18-7
(t-r)(2) = -24+11
(t-r)(2) = -13 (option C)
d) If h(x) = 4x + 2 and g(x) = 3x - 1,
h-g = 4x+2-(3x-1)
h-g = 4x+2-3x+1
h-g = 4x-3x+2+1
h-g = x+3
h-g(4) = 4+3
(h-g)(4) = 7
e) If g(x) = x - 4 and h(x) = x + 5, we are to find f(x)h(x)
h(x)g(x) = (x-4)(x+5)
h(x)g(x) = x(x)+5x-4x-20
h(x)g(x) = x²+x-20
Hence the product of h(x) and g(x) is x²+x-20. Option D is correct
Find the sum for each expression ?
A.-66+ 42
B.-57 + 57
C. 29 +(-28)
Answer:
A is -24
B is 0
C is 1
Step-by-step explanation:
Hope this helps and please give me brainlest
Trisha ran 10 km in 2.5h. Jason ran 7.5 km in 2h. Olga ran 9.5 km in 2.25h. Who had the fastest average speed.
Answer:
Olga
Step-by-step explanation:
Question 1 Triangle ABC is a right triangle. The lengths of the legs are 60 centimeters and 80 centimeters. What is the length, in centimeters of the hypotenuse?
HELP HURRY!!
List the numbers from greatest to least.
7/9, 51%, 0.65, 41
My list : 41, 7/9, 0.65, 51%
Tell me if im correct or not <33
Answer:
pretty sure you're right :)
F is between EG. If EF = 2x-12, FG = 3X-15 and EG = 23. find the values of x, EF, and FG.
Answer:
The answer is A
Step-by-step explanation:
The first thing to do is see which two lengths of EF and FG equals EG which is 23. If you add together B's options you get -12 and if you add C's options, you get 77. So that leaves us with the options of A and D. From there, just plug in each value of x and see which one gets you the right values. Hope this helps
Write an augmented matrix for the system. Then state the dimensions. x+8y−7z=12 5x+9y+5z=15 6z−3y−8x=1
Answer: Write an augmented matrix for the system. Then state the dimensions. x+8y−7z=12 5x+9y+5z=15 6z−3y−8x=1
Step-by-step explanation: x+8y-7z=12 5x+9y+5z=15 6z-3y-8x=1. - 18028782.
There are 15 students in my first period class. If 6 of the students in the class are boys, what percent of the students are boys?
A. 60%
B. 25%
C. 40%
D. 30%
Answer:
C
Step-by-step explanation:
If you were to multiply 15 by 40% it would equal 6.
No. of students in 1st class= 15
No. of boys = 6
Percentage of boys = 6/15 ×100
= 2/3×100
= 40%
If this answer helps you plz mark as brainlist..TQ..A cake needs 1/4 cup of oil i need 5 cakes how many cups of oil do i need
Answer:
Oil needed for 1 cake = 1/4
So, for 5 cakes = 1/4 * 5
=> 5/4
Therefore you will require 5/4 cups of oil.
If my answer helped, kindly mark me as the brainliest!!
Thank You!!
A conical tank has height 3 m and radius 2 m at the base. Water flows in at a rate of 2 mº/min.
3
2
How fast is the water level rising when the level is 1 m and when the level is 1.6 m?
(Use decimal notation. Give your answers to four decimal places.)
dh
dt
=
m
dh
dt
=
=1.6
4.5ml=.........L
help meeeeee
0.0045 L
1000 ml in a L
So divide 4.5 by 1000
You get 0.0045
3a) (4 NF B.4.b. 4.NBTA1, 4.0AA.1) 28 is 7 times what number? Write your answer as a number. If a fraction is necessary, use the "/" key as the fraction symbol. Your
Answer:
4
Step-by-step explanation:
28/7=4
If you multiply a number by four and then subtract negative ten, the difference is negative twenty-two. What is the number?
Answer:
n=-3
Step-by-step explanation:
To solve start with the 4n-10=-22
+10 to both sides and you get 4n=-12
Divide each side by 4 and you get n=-3
To check plug -3 in for n and you'll get the -2 once you solve it.
Find x. Give reasons to justify your solution.
b
Lines
AB
and
CD
are straight lines.
Answer:
x = 28
Step-by-step explanation:
If AB and CD are the straight lines, sum all the angles formed at a point lying on this line will be 180°.
m∠COE + m∠EOF + m∠FOB + m∠BOD = 180° [Angles at a point O on line AB]
3x + x + (x + 12) + m∠BOD = 180°
m∠BOD = 180° - (5x + 12)
Similarly, m∠AOD + m∠AOC = 180°
152° + m∠AOC = 180°
m∠AOC = 28°
Since, ∠AOC and ∠BOD are the vertical angles,
m∠AOC = m∠BOD
180° - (5x + 12)° = 28°
5x + 12 = 180 - 28
5x = 140
x = 28
solve each problem. a. what is -4.3-(-6.8)? b. what is 1 3/5+(-2 7/10)?
Answer:
4
Step-by-step explanation:
using the fact that the black triangle represents the mean and/or the understanding of what a deviation is, explain why this balancing beam would stay balanced went to Blue circles are removed. Be thorough with your explanation and use Multiple sources of evidence
Answer: the left side is balanced with the right side
Step-by-step explanation:
Left side:
1 barrel (located at 2) is 1 unit from the fulcrum (triangle) → 1(1) = 1
2 barrels (located at 1) are 2 units from the fulcrum (triangle) → 2(2) = 4
1 barrel (located at 0) is 3 units from the fulcrum (triangle) → 1(3) = 3
Total = 8
Right side:
1 barrel (located at 6) is 3 units from the fulcrum (triangle) → 1(3) = 3
1 barrel (located at 8) is 5 units from the fulcrum (triangle) → 1(5) = 5
Total = 8
The distribution of the weight on the left side equals the distribution of weight on the right side so the beam is balanced.
A line has a slope of - 1/4 and passes through point(-5/4,1)
What is the equation of the line?
Answer:
y= -1/4x - 1/4
Step-by-step explanation:
y - y1 = m(x - x1)
y - 1 = -1/4 (x -(-5/4))
y - 1 = -1/4x - 5/4
y = -1/4x - 1/4
A farm covers an area of 13square mile. The farm is divided into 4 equal sections, as shown in this diagram.
Answer: xd O.o rawr lmasos
Step-by-step explanation:
T^T