Given:
[tex]h:k=2:5,x:y=3:4,2h+x:k+2y=1:2[/tex]
To find:
[tex]h-x:k-y[/tex]
Solution:
We have, [tex]h:k=2:5[/tex] and [tex]x:y=3:4[/tex].
Let the values of h and k are 2a and 5a respectively.
Let the values of x and y are 3b and 4b respectively.
We have,
[tex]2h+x:k+2y=1:2[/tex]
It can be written as
[tex]\dfrac{2h+x}{k+2y}=\dfrac{1}{2}[/tex]
[tex]\dfrac{2(2a)+(3b)}{5a+2(4b)}=\dfrac{1}{2}[/tex]
[tex]\dfrac{4a+3b}{5a+8b}=\dfrac{1}{2}[/tex]
[tex]2(4a+3b)=1(5a+8b)[/tex]
On further simplification, we get
[tex]8a+6b=5a+8b[/tex]
[tex]8a-5a=8b-6b[/tex]
[tex]3a=2b[/tex]
[tex]a=\dfrac{2b}{3}[/tex]
Now,
[tex]h-x:k-y=\dfrac{h-x}{k-y}[/tex]
[tex]h-x:k-y=\dfrac{2-3b}{5a-4b}[/tex]
[tex]h-x:k-y=\dfrac{2\times \dfrac{2b}{3}-3b}{5\times \dfrac{2b}{3}-4b}[/tex]
[tex]h-x:k-y=\dfrac{\dfrac{4b}{3}-3b}{\dfrac{10b}{3}-4b}[/tex]
On further simplification, we get
[tex]h-x:k-y=\dfrac{\dfrac{4b-9b}{3}}{\dfrac{10b-12b}{3}}[/tex]
[tex]h-x:k-y=\dfrac{-5b}{-2b}[/tex]
[tex]h-x:k-y=\dfrac{5}{2}[/tex]
[tex]h-x:k-y=5:2[/tex]
Therefore, the ratio [tex]h-x:k-y[/tex] is [tex]5:2[/tex].
1. "-4 less than a number is 17."
Answer:
yes
Step-by-step explanation:
Allen wants to have a mean of 90 on his math quizzes. So far, he has scored 86, 94, 88, 95, and 89. What is the least score that Allen needs on his next quiz to have a mean of 90?
Answer:
88
Step-by-step explanation:
[tex] \frac{86 + 94 + 88 + 95 + 89 + x}{6} = 90[/tex]
The mean would be the sum of all the math quiz grades divided by the number of quizzes taken.
Solve for x:
[tex]86 + 94 + 88 + 95 + 89 + x = 540[/tex]
[tex]452 + x = 540[/tex]
[tex]x = 88[/tex]
Thus, Allen needs at least an 88 to obtain a mean of at least 90.
Need help asap Please. Thank you
Answer:
B. 477°, -243°Step-by-step explanation:
Coterminal angles with 117° are:
117° + 360°x, where x is an integerWhen x = 1 and -1 we get:
117° + 360° = 477° and 117° - 360° = -243°It can be easily verified that all the other pairs are incorrect
Correct one is B
Data that's displayed randomly on a scatter plot graph illustrates (please help asap!)
positive correlation.
negative correlation.
none of these.
no correlation.
Cole wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor is 4 5 6 ft by 2 1 3 ft. Find the area the carpet needs to cover. Solve on paper. Then check your work on Zearn. 711 1 3 tiled floor The carpet needs to cover ft2.
Answer:
[tex]Area = 49\frac{25}{36}[/tex]
Step-by-step explanation:
Given
Tile
[tex]Length = 4\frac{5}{6}[/tex]
[tex]Width = 2\frac{1}{3}[/tex]
See attachment for dimension of the floor
Required
Determine the area covered by the carpet
From the attachment, the dimension of the floor is:
[tex]Length = 12\frac{1}{4}[/tex]
[tex]Width = 5[/tex]
Calculate Area
[tex]Area = Length * Width[/tex]
[tex]Area = 12\frac{1}{4} * 5[/tex]
[tex]Area = 61\frac{1}{4}[/tex]
The area of the tiles is:
[tex]Area = 4\frac{5}{6} * 2\frac{1}{3}[/tex]
[tex]Area = \frac{29}{6} * \frac{7}{3}[/tex]
[tex]Area = \frac{203}{18}[/tex]
[tex]Area = 11\frac{5}{18}[/tex]
So, the carpet area is:
[tex]Area = Floor\ Area - Tile\ Area[/tex]
[tex]Area = 61\frac{1}{4} - 11\frac{5}{18}[/tex]
To improper number
[tex]Area = \frac{245}{4} - \frac{208}{18}[/tex]
Take LCM
[tex]Area = \frac{2205 - 416}{36}[/tex]
[tex]Area = \frac{1789}{36}[/tex]
[tex]Area = 49\frac{25}{36}[/tex]
PLSS HELP ME ASAP I WILL EVEN GIVE U BRAINLYEST BUT PLAA HELP ME!!
Is the probability of red a simple event, complement of a
simple event, or neither?
A. complement of a simple event
B. nelther
C. simple event
Answer:
Complement of an Event: All outcomes that are NOT the event. So the Complement of an event is all the other outcomes (not the ones we want). And together the Event and its Complement make all possible outcomes.
Help help help help help help
Answer:
volume = 160 cm³
Step-by-step explanation:
volume = 4 x 4 x 10 = 160 cm³
CAN SOME0NE PLEASE HELP MEEE ASAP!!
Answer:
[tex]x = 35.6[/tex]
Step-by-step explanation:
It is given that figure (HGFE) and figure (LKJI) are similar. Meaning that one must multiply a side of the figure (HGFE) by a number to get the corresponding side length from the figure (LKJI). To find this number, one must divide two corresponding sides.
[tex]\frac{KL}{FE}[/tex]
[tex]=\frac{55}{17}[/tex]
Now to find a missing side in figure (LKJI) one must multiply its corresponding side by ([tex]\frac{55}{17}[/tex]) in figure (HGFE) to find the length of the missing side.
[tex]EF * \frac{55}{17} = JI\\\\11 * \frac{55}{17} = JI\\\\\frac{605}{17} = JI[/tex]
[tex]x = \frac{605}{17}\\\\x=35.6[/tex]
Answer:
IJ ≈ 35.6
Step-by-step explanation:
Since the quadrilaterals are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{IJ}{EF}[/tex] = [tex]\frac{KL}{GH}[/tex] , substitute values
[tex]\frac{IJ}{11}[/tex] = [tex]\frac{55}{17}[/tex] ( cross- multiply )
17 IJ = 605 ( divide both sides by 17 )
IJ ≈ 35.6 ( to the nearest tenth )
5. find M<C congruent triangles
Answer:
x = 18 / M<C = 114
Step-by-step explanation:
9x - 24 = (2x - 12) + (4x + 42)
9x - 24 = 6x + 30
+24 +24
9x = 6x + 54
-6x -6x
3x = 54
/3 /3
x = 18
C = (4x + 42) = 4(18) + 42 = 72 + 42 = 114
plsss help i’ll give brainliest if you give a correct answer
Answer:
(-2) and 3
Step-by-step explanation:
Answer:
f=-2, f=3, f=-4, they are all smaller than 4!!!
Plz show work if ya can so I can understand this thanks
Answer:
area = 57√3 cm²
Step-by-step explanation:
lower polygon:
14-8 = 6, 6/2 = 3
3 is the base of the lower left triangle
cos 60° = 3/hypotenuse
hypotenuse = 6
height of triangle² = 6² - 3² = 45
height of triangle² = 36 - 9 = 27
height of triangle = √27 = √(9 x 3) = 3√3
area of lower polygon = 1/2(8+14)(3√3) = 33√3 cm²
upper parallelogram:
area = 8(3√3) = 24√3 cm²
total area = 24√3 + 33√3 = 57√3 cm²
8% of the High School students have their license. If there are 1000 high school students in your neighborhood, how many have their license internet Enter your answer in the sface below. ??? teachers
Answer:
80.
............................
A giraffe is 5 meters 20 centimeters tall. An elephant is 1 meter 77 centimeters shorter than the giraffe. A rhinoceros is 1 meter 58 centimeters shorter than the elephant. How tall is the rhinoceros?
Answer:1 meter and 58 centimeters
) Hiroki's goal is to collect $40 for a school fundraiser. He has already collected $26.50. Hiroki wants
to know how much more money he needs to collect.
that use the word correctly
ices, press the "Check Me" butto
6 POTE
.) Let m be the amount of money Hiroki still needs to collect.
Describe the situation with an equation.
this town made the first eleva
er and wrote a note on it
vater from the sink is leaking
color of copper coins
m
26.50
40
corper pipes for this project
De
Answer:
$13.50
Step-by-step explanation:
Subtract 40 from 26.50 to get the answer
Can someone tell me how to do this? This is so confusing to me.
Answer:
A. Rate of Change: 25/1
B. Initial Value: 100
C. Y=25x+100
D. After 6 months the cost is 250$
E. 475=25x+100
475=25x+100
375=25x
x=15
So E. is 15 months
Step-by-step explanation:
Which expression is equivalent to 3x+2
Answer:
(3 x X) + 2
Can be a possible way if you factor it out I think.
Dax is buying hot chocolate for 5 people in his office (including himself). He pays for the 5 drinks and leaves a $2.00 tip.
If the total, with tip, is $18.25, how much is each cup of hot chocolate?
Enter your answer as a decimal, like this: 42.53
Answer: Each cup of hot chocolate is $3.25
Step-by-step explanation:
Please help me simplify this expression!!
Answer:
[tex]w^{14}[/tex]
Step-by-step explanation:
[tex]\frac{1}{w^{11} } *w^{25}\\\\\\\frac{w^{25}}{w^{11}} \\\\w^{14}[/tex]
A gardener is planting two types of trees: Type A is 4 feet tall and grows at a rate of 24 inches per year. Type B is 5 feet tall and grows at a rate of 21 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
If you were to roll a standard six sided die, what is the probability of rolling a number less than what three other people rolled?
find the product of (5x+4)(5x-4)
Answer:
25x² - 16
Step-by-step explanation:
Given
(5x + 4)(5x - 4)
Each term in the second factor is multiplied by each term in the first factor, that is
5x(5x - 4) + 4(5x - 4) ← distribute parenthesis
= 25x² - 20x + 20x - 16 ← collect like terms
= 25x² - 16
Consider the function represented by the graph. What is the domain of this function?
A. {x|x=>0}
B. {x|x<=8}
C. {x|0<=x<=8}
D. {x|x<=0x=>8}
Answer:
I think it is B but i'm not 100% sure.
Step-by-step explanation:
ANDWER CHOICES:
14cm
20cm
8cm
6cm
I NED HELP ASAP!!!!
A pendulum's first swing has an arc of 36 inches. As the pendulum swings back and forth, the arc length for each successive swing is 95% of the previous swing. If this pattern continues, at which swing of the pendulum will the length of the arc be less than 27 inches? A. 5th B. 6th C. 7th D. 9th
Answer:
7th
Step-by-step explanation:
Given :
Arc length on first swing = 36 inches
After successive swing, arc length decreases by 95%
Length on 2nd swing = 0.95 * 36 = 34.2
Length on 3rd swing = 0.95 * 34.2 = 32. 49
Length on 4th swing = 0.95 * 32.49 = 30.8085
Length on 5th swing = 0.95 * 30.8085 = 29.268075
Length on 6th swing = 0.95 * 29.268075 = 27.80467125
Length on 7th swing = 0.95 * 27.80467125 = 26.4144376875
26.4144376875 < 27
Hence, length falls below 27 on 7th swing
Can yu guys help me out
Answer:
they are already answered
Step-by-step explanation:
Right?
Find the midpoint between A (8, 2) and B (10, 4)
Answer:
(9,3)
Step-by-step explanation:
m={(x1+x2)/2,(y1+y2)/2}
m={(8+10)/2,(2+4)/2}
m={9,3}
Hope that helps :)
HELPPP PLEASEE!!!DONT ANSWER IF YOU DONT KNOW!!
Answer:
-4
Step-by-step explanation:
If Triangle ABC~ triangle DEC, find the value of x and the scale factor from DEC to ABC
Answer:
see explanation
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original, that is
scale factor = [tex]\frac{AC}{DC}[/tex] = [tex]\frac{25}{20}[/tex] = [tex]\frac{5}{4}[/tex]
Then
[tex]\frac{AB}{DE}[/tex] = [tex]\frac{3x-2}{2x}[/tex] = [tex]\frac{5}{4}[/tex] ( cross- multiply )
4(3x - 2) = 10x
12x - 8 = 10x ( subtract 10x from both sides )
2x - 8 = 0 ( add 8 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
john has 19 cookies aailyah has 89 cooking how many do they both have
Answer:
108 cookies total
Step-by-step explanation:
19+89=108
Answer:
108
Step-by-step explanation:
Good Luck!
If 54% of all people between the ages of 35 and 50 ride a bike, find the probability for a sample of 30 people in that age group exactly 15 ride a bike
Answer:
The probability is 0.1312
Step-by-step explanation:
Here, let us set up a binomial system
From the question, 54% ride a bike
Let p = people that rides a bike
54% = 54/100 = 0.54
p = 0.54
q = 1 - p = 1 -0.54 = 0.46 ( 46% do not ride bikes)
Now, for the binomial system, we have
P(X = 15) = 30 C 15 • p^15•q^15
We have;
30 C 15 * 0.54^15 * 0.46^15
= 0.131200268998
The probability is 0.1312