Answers
Answer:
1. LI=18
2. x=10
3. Yes (Y)
4. Yes (Y)
5. x=15
6. x=18
7. x=8
8. x=6
y=6.5
Step-by-step explanation:
1. LI/JL=KH/JK
Replacing the given values:
LI/6=21/7
Dividing on the right side of the equation:
LI/6=3
Solving for LI: Multiplying both sides of the equation by 6:
6(LI/6)=6(3)
LI=18
2.TV/VS=RU/US
Replacing the given values:
x/17.5=8/14
Simplifying the fraction on the right side of the equation: Dividing numerator and denominator by 2:
x/17.5=(8/2) / (14/2)
x/17.5=4/7
Solving for x: Multiplying both sides of the equation by 17.5:
17.5(x/17.5)=17.5(4/7)=(17.5/1)(4/7)
Multiplying:
x=(17.5 x 4) / (1 x 7)
x=70/7
Dividing:
x=10
3. BC is parallel to DE if AD/DB is equal to AE/EC:
AD/DB=15/12=(15/3) / (12/3)→AD/DB=5/4
AE/EC=10/8=(10/2) / (8/2)→AE/EC=5/4
Like AD/DB=5/4=AE/EC → BC is parallel to DE
4. BC is parallel to DE if AD/DB is equal to AE/EC:
AD/DB= 2DB / DB→AD/DB=2
AE/EC=30 / (AC-AE)=30 / (45-30)=30/15→AE/EC=2
Like AD/DB=2=AE/EC → BC is parallel to DE
5. If JH is a midsegment of triangle KLM:
x=(1/2)(30)
x=15
6. If JH is a midsegment of triangle KLM:
x=2(9)
x=18
7. If JH is a midsegment of triangle KLM: x=8
8. 2x+1=x+7
Solving for x. Grouping the x's on the left side of the equation: Subtracting x both sides of the equation:
2x+1-x=x+7-x
Subtracting:
x+1=7
Subtracting 1 both sides of the equation:
x+1-1=7-1
Subtracting:
x=6
2x+1=2(6)+1=12+1→2x+1=13
x+7=6+7→x+7=13
(3y-8)/(y+5)=(2x+1)/(x+7)
(3y-8)/(y+5)=13/13
(3y-8)/(y+5)=1
3y-8=y+5
Solving for y. Grouping the y's on the left side of the equation: Subtracting y both sides of the equation:
3y-8-y=y+5-y
Subtracting:
2y-8=5
Adding 8 both sides of the equation:
2y-8+8=5+8
Subtracting:
2y=13
Dividing both sides of the equation by 2:
2y/2=13/2
Dividing:
y=6.5
Related Questions
In combining like terms, what do these equations equal?
1: 5+6(2x+3)-2x
2: 3(4x+8) + 3(2x-6)
3: (32-8x)
____
4
4: 24x+18
____
6
If you can, please explain it! Thanks!
Answers
Answer:
Look below. The answers are bolded!
Step-by-step explanation:
1. 10x + 23
5+6(2x+3)-2x
Distribute first!
5 + 12x + 18 -2x.
Now you can combine like terms.
23 + 10x
2. 18x + 6
3(4x+8) + 3(2x-6)
Distribute first!
12x + 24 + 6x - 18
Now you can combine like terms.
18x + 6
3. -2x + 8
(32-8x)
____ ___
4
Divide 32 and -8x by 4.
32/4 = 8
-8x/4 = -2x
-2x + 8
4. 4x + 3
24x+18
______
6
Divide 24x and 18 by 6
24x/6 = 4x
18/6 = 3
4x + 3
An equation that expresses a mathematical rule or relationship is a ___.
proportion
conversion factor
formula
ratio
Answers
Answer:
formula
Step-by-step explanation:
3rd option is correct which is formula.
What is a formula ?
A mathematical relationship or rule which expressed only in symbols and which is the connection between two or more variable.
What is the correct option ?An equation that expresses a mathematical rule or relationship is a formula.
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Use the substitution method to solve the system of equation.choose the correct ordered pair.
2y+4x=18
2y-3x=4
Answers
[tex]\left\{\begin{array}{ccc}2y+4x=18\\2y-3x=4&\text{add 3x to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}2y+4x=18&(**)\\2y=3x+4&(*)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\3x+4+4x=18\qquad\text{subtract 4 from both sides}\\7x=14\qquad\text{divide both sides by 7}\\\boxed{x=2}\\\\\text{Put the value of x to the first equation:}\\\\2y+4(2)=18\\2y+8=18\qquad\text{subtract 8 from both sides}\\2y=10\qquad\text{divide both sides by 2}\\\boxed{y=5}\\\\Answer:\ \boxed{x=2\ and\ y=5}[/tex]
rounding decimals 4.3
Answers
Answer:
Step-by-step explanation:
If you round 4.3 to the nearest whole number, you will get 4.The reason is because a number less than 5 is closer to 4 but a number greater than five or is five will be rounded to five.
Please mark brainliest!!!!!!!
How do I do this please dumb this down
Answers
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept fprm is
y = mx + b ( m is the slope and b the y-intercept )
y = [tex]\frac{5}{4}[/tex] x - 4 is in this form
with m = [tex]\frac{5}{4}[/tex] and b = - 4
Plot the point (0, - 4)
using the slope add 5 to the y-coordinate and 4 to the x-coordinate
(0, - 4 ) → (0 + 4, - 4 + 5) → (4, 1) ← point on the line
Plot the points (0, - 4) and (4, 1) and draw a straight line through them to obtain a sketch of the graph
Identify the slope of the line shown in the graph below: slope = -1
Slope = 0
Slope = undefined
Slope = 1
Answers
It's a vertical line. The slope of vertical line is undefined.
The equation of a vertical line is x = a (a - any real number).
Answer: Slope = undefinedEquation of line: x = -1Answer:
Slope = undefined
Step-by-step explanation:
A vertical STRAIGHT line that represents a slope is undefined.
Please explain your answer.
Answers
Answer:
x=4.4
Step-by-step explanation:
To get from A to B, the scale factor is 2.5, since 4*2.5 = 10
So, to get from B to A, you divide by 2.5.
11/2.5 = 4.4
11/2.5=4.4
The answer is x=4.4
What is the geometric mean of 5 and 4
Answers
Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
Geometric mean of two numbers of the square root of their product:
[tex]\sqrt{20}=\sqrt{4\cdot5}=2\sqrt{5}[/tex]
The geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
What is the geometric mean of two numbers?The Geometric mean of the two numbers formula is defined as the square root of the product of 2 numbers.
The following formula is used to calculate the geometric mean;
[tex]\rm Geometric \ mean = \sqrt{a \times b}[/tex]
Where a is the first term and b is the second term.
Therefore,
The geometric mean of 5 and 4 is;
[tex]\rm Geometric \ mean = \sqrt{a \times b}\\\\a=5 \ and \ b=4\\\\\rm Geometric \ mean = \sqrt{5 \times 4}\\\\\rm Geometric \ mean = \sqrt{20}\\\\\rm Geometric \ mean = 2\sqrt{5}[/tex]
Hence, the geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
To know more about the Geometric mean click the link given below.
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On a car trip Sam drove m miles Kara drove twice as many miles as Sam and Darin drove 20 fewer miles than Kara in terms of m many miles did Darin drive
Answers
Answer:
Darin drove '2m - 20' miles.
Step-by-step explanation:
We are given that Sam drove 'm' no. of miles.
As, it is also given that Kara drove twice as many miles as Sam. Therefore we get that Kara drove '2m' no. of miles.
Now, it is given that Darin drove 20 miles fewer than Kara .i.e. Darin drove '2m - 20' no. of miles.
Hence, in terms of m, Darin drove '2m - 20' miles.
use the diagram to answer the questions
1. which ray is a bisector of ABC
A. BC
B. BD
C. BA
D. BF
2. what is GH
A. 5
B. 10
C. 15
D. 25
3. what is the value of y
A. 2
B. 4
C. 16
D. 20
Answers
Answer:
1. B. BD
2. C. 15
3. A. 2
Step-by-step explanation:
1. From the figure,
∠DAB = ∠DAC
Therefore, BD is the bisector of ∠ABC.
2. From the figure, IG = GH
3x = 5x - 10
10 = 5x - 3x
2x = 10
x = 5
So, GH = 5x - 10
= 5(5) - 10
= 25 - 10
= 15
Therefore, GH = 15.
3. From the figure,
∠DAB = ∠DAC
10y = 8y + 4
10y - 8y = 4
2y = 4
y = 2
the sum of two numbers is 76. The difference is 24. Find the two numbers doing the elimination method
Answers
Answer:
50 and 26
Step-by-step explanation:
Make an equation! That makes it much simpler and has helped me a lot.
x+x-24=76
Combine like terms
2x+24=76
Add 24 on both sides
2x=52
Divide both sides by 2
x=26
72-26=50
To check that their difference is correct, subtract 26 from 50
50-26=24
Hope this helps!
you are a plumber installing a pipe the ratio of the outside diameter to the inside diameter is 1.5 to 1. you use a pipe with a 0.5 inch inside diameter what is the smallest diameter that you will need to drill to allow the pipes to pass through the wall
Answers
So the smallest diameter possible would be 0.75 inches.
The smallest diameter needed to drill through the wall is 0.75 inches, which is calculated by multiplying the inside diameter of the pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). Always measure and plan ahead to avoid mistakes.
Explanation:The subject matter of this question is mathematics, specifically ratios. To find the smallest diameter you would need to drill into the wall, you would need to multiply the inside diameter of your pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). So, 0.5 inches * 1.5 = 0.75 inches.
This means, to allow the pipes to pass through the wall, you will need to drill a hole at least 0.75 inches in diameter. This is assuming the wall is thin enough that the entire length of the pipe that needs to pass through the wall is less than the thickness of the wall.
Remember, it's always better to pre-measure and plan ahead to avoid unnecessary work and potentially costly mistakes.
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Huma, Hubna and Seema received a total of ₨2,016 as monthly allowance from their mother such that Seema gets 12 of what Huma gets and Hubna gets 123 times Seema’s share. How much money do the three sisters get individually?
i need correct answer no signs used
Answers
Answer:
Huma's share =Rs x = Rs. 1.35392881
Seema's share =Rs. 12x = Rs (12 * 1.35392881) = Rs. 16.2471457
Hubna's share =Rs. 123*12x = Rs. (123*16.2471457) = Rs. 1998.39892
Step-by-step explanation:
Given :
Huma , Hubna and Seema received a total of ₨2,016 as monthly allowance from their mother.
Seema gets 12 of what Huma gets
Hubna gets 123 times Seema’s share
To find : How much money do the three sisters get individually?
Solution :
Let Huma's share be Rs. x.
Since we are given that Seema gets 12 of Huma's share
⇒ Seema's share = Rs 12x.
Since we are given that Hubna gets 123 times Seema’s share
⇒Hubna's share = Rs. (123 * 12x) = Rs. 1476x.
We are given that they received together Rs. 2016 in total .
⇒[tex]x+12x+1476x= 2016[/tex]
⇒[tex]1489x= 2016[/tex]
⇒[tex]x = \frac{2016}{1489}[/tex]
⇒[tex]x = 1.35392881[/tex]
Thus Huma's share =Rs x = Rs. 1.35392881
Thus Seema's share =Rs. 12x = Rs (12 * 1.35392881) = Rs. 16.2471457
Thus Hubna's share =Rs. 123*12x = Rs. (123*16.2471457) = Rs. 1998.39892
Each year, the number of students taught by Mr. Wright increases by 2. The first year, he taught 18 students. The total number of students taught after 25 years can be represented using the expression . How many students has Mr. Wright taught in 25 years?
450
500
1,050
2,100
Answers
1st yr = 18 students
25 yrs = x
Cross multiply
x = 18 × 25
x = 450
Answer:
Mr. Wright taught 1,050 students in 25 years.
Step-by-step explanation:
Given,
The number of students Mr. Wright taught = 18,
Also, every year the number of student is increased by 2,
So, in second year, the number of students = 18 + 2 = 20,
In third year = 20 + 2 = 22,
In fourth year = 22 + 2 = 24,
.............., so on,
Hence, we get an A.P. that shows the given situation,
18, 20, 22, 24, ............. till 25 years.....
First term, a = 18,
Common difference, d = 2,
And, number of terms, n = 25,
Hence, the total number of students that have been taught by him are,
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_{25}=\frac{25}{2}[36+(25-1)2][/tex]
[tex]=\frac{25}{2}[36+24\times 2][/tex]
[tex]=\frac{25}{2}[36+48][/tex]
[tex]=\frac{25}{2}(84)[/tex]
[tex]=\frac{2100}{2}[/tex]
[tex]=1050[/tex]
Third option is correct.
Find the value of the permutation.
8P1 ?
Answers
____
(n-r)!
= 8!
____
(8-1)!
= 8
Answer:
8P1 = 8
Step-by-step explanation:
Permutation
The number of elements can be selected from a set of elements.
Let r be the number of elements want to select and n be the set of elements.
It can be written as nPr
nPr = n!/(n - r)!
To find 8P1
n= 8 and r = 1
8P1 = 8!/(8-1)! = 8!/7! = (8 x 7!)/7! = 8
Therefore 8P1 = 8
Need help with Mathematics. I can't copy and paste so I screenshot it
Answers
Answer: 1.44
Step-by-step explanation:
1.2×1.2
1.2
1.2
__
24
120
__
144
Add two decimal places: 1.44
Answer:
1.44
Step-by-step explanation:
1.2^2 = 1.2 * 1.2
1.2 * 1.2 = 1.44
Your just finding the squad route of it. It can also be done the same way when your ^3 or even ^4 since its all timing the same number. Hope this helps out!
Find the value of
[tex] {x}^{i} [/tex]
for all x belongs to Real Numbers and i = √(-1).
Answers
Answer: cis (ln x) ; x > 0
Step-by-step explanation:
[tex]x^i[/tex]
[tex]= e^{ln(x^i)}[/tex]
[tex]=e^{i \ln(x)}[/tex]
= cos (ln x) + i sin (ln x)
AKA: cis (ln x)
NOTE: I found this following formula which you may find useful:
[tex]A^i = x + iy[/tex]
Write the equation in slope intercept form: Passes through = (2,3) (0,9)
Answers
Answer:
Y=-3x+9
Step-by-step explanation:
Slope is found using
9-3 over 0-2
This gets 6/-2
This gets -3
-3 is the slope
9 is the y-intercept
Name the angle in 2 different ways and name the 2 rays from the diagram below please show work
Answers
Answer:
3) TB and NT
4) ∠KLM and ∠MLK
Step-by-step explanation:
3) those two rays intersect to form the angle shown in the diagram
4) an angle can always be named from left to right or right to left as long as the middle letter is always the vertex of the angle
for number 3 remember the definition of a ray which is a point that has a line sticking out of it that doesn't end and doesn't cause the line to follow the definition of a line segment. BT and BN follow this definition .
for number 4 remember that naming angles is pretty much consistent as left to right and right to left. but either way the same letter should be in the center and the same three letters should be involved. so u get KLM and MLK
Which expression will give the new price of a $15 item marked up by 28%
A. 28+0.15 X 28
B. 28-0.15 X 28
C. 15+0.28 X 15
D. 15-0.28 X 15
Answers
Answer:
the answer is
C
if i am wrong let me know
Step-by-step explanation:
These triangles are similar. find Y and X
Answers
It these triangles are similar, then the sides of the triangles are in proportion:
[tex]\dfrac{y}{10}=\dfrac{y+4}{15}[/tex] cross multiply
[tex]15y=10(y+4)[/tex] use distributive property
[tex]15y=10y+40[/tex] subtract 10y from both sides
[tex]5y=40[/tex] divide both sides by 5
[tex]\boxed{y=8}[/tex]
[tex]\dfrac{x}{4}=\dfrac{6}{8}[/tex] cross multiply
[tex]8x=(4)(6)[/tex]
[tex]8x=24[/tex] divide both sides by 8
[tex]\boxed{x=3}[/tex]
Find the value of x such that PQ = QRwhere P, Q and Rare the pints (2, 5), (x, -3) and (7, 9) respectively.
Answers
Answer: x = 12.5
Step-by-step explanation:
P = (2, 5)
Q = (x, -3)
R = (7, 9)
[tex]d_{PQ}=d_{QR}[/tex]
[tex]d_{PQ}=\sqrt{(2-x)^2+(5+3)^2}, \quad d_{QR} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex]\sqrt{(2-x)^2+(5+3)^2} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex](2-x)^2+(5+3)^2 = (x-7)^2+(-3-9)^2[/tex]
[tex]4-4x+x^2+64 = x^2-14x+49+144[/tex]
[tex]4x+68 = -14x+193[/tex]
[tex]10x+68 = 193[/tex]
[tex]10x= 125[/tex]
x = 12.5
PLEASE HELP ME !! Carter has 3 statues of various sizes in his garden. Statue A is one foot taller than statue B. Statue is one-half of a foot taller than statue B. A) write an algebraic expression for the total combined height of statue A and c. (equations for statues A and C) B) If the total combined height of the 3 statues is 10 feet, find the height of statue B in inches.
Answers
Answer:
Step-by-step explanation:
helpppppppppppppppppppppppppppppppppppppp
Answers
Answer:
For every 15 students scoring in the 60's there were 9 students scoring in the 70's.
Step-by-step explanation:
Your first step would be to rewrite the numbers into an easier to understand form like fractions, 45/3 and 27/3. Then you divide both numbers by 3, so you get comparable numbers. 45/3= 15, 27/3=9.
Gabe Amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. He currently has a 50% solution and a 70% solution. How many liters of each does he need to make the needed 60 liters of 60% acid solution? Gabe needs 30 liters for a 50% solution .
He also needs a ___ for a 70% solution . whats __?
Answers
Answer:
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
Step-by-step explanation:
Equation:
acid + acid = acid
0.40x + 0.70(60-x) = 0.60*60
40x + 70*60 - 70x = 60*60
-30x = -10*60
x = 20 liters
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
At the popular restaurant Fire Wok,
55% of guests order the signature dish.
What fraction of guests order the signature dish?
Answers
Answer:
11/20
Step-by-step explanation:
Answer: [tex]\dfrac{11}{20}[/tex] represents the fraction of guests order the signature dish.
Step-by-step explanation:
Since we have given that
Percentage of guest who order the signature dish = 55%
Total percentage = 100
We need to find the fraction of guests order the signature dish.
So, Fraction of guests order the signature dish is given by
[tex]\dfrac{\text{Percentage of guest order the signature dish}}{\text{Total percentage}}\\\\=\dfrac{55}{100}\\\\=\dfrac{11}{20}[/tex]
Hence, [tex]\dfrac{11}{20}[/tex] represents the fraction of guests order the signature dish.
Jian’s family sells honey from beehives. They collected 3,311 ounces of honey from the beehives this season. They will use the honey to completely fill 4-ounce jars or 6-ounce jars. Jian’s family will sell 4-ounce jars for $5 each or 6-ounce jars for $8 each. Jian says if they use only 4-ounce jars, they could make $4,140 because 3,311 / 4 =827 R3. That rounds up to 828, and 828 multiplied by $5 is $4,140. Part A-Explain the error that Jian made when finding the amount of money his family could make if they use only 4-ounce jars. Enter your explanation in the space provided. Part B- Explain how to determine the money Jian’s family could make if they use only 6-ounce jars. Include the total amount of money and the total number of 6-ounce jars in your explanation. Enter your answers and your explanation in the space provided.
Answers
Answer:
A. Jian rounded the number of 4-ounce jars to 828 which is wrong. There are only 827 jars that can be completely filled.
B. Total number of 6-ounce jars = 551
Total money earned from 6-ounce jars = $4408
Step-by-step explanation:
A. Jian's family's collection = 3311 ounces
Number of 4-ounce jars = [tex]\frac{3311}{4}[/tex]
= 827.75
Jian rounded it to 828 which is wrong. There are 827 jars that can be completely filled.
Cost per 4-ounce jar = $5.
Total cost = 827 × 5 = 4135
B. Now, number of 6-ounce jars = [tex]\frac{3311}{6}[/tex]
= 551.83
≅ 551 jars
Cost per 6-ounce jar = $8
Total cost = 551 × 8 = 4408
Dianna earns $8.50 an hour working as a lifeguard write an equation to find Dianna’s money earned?
Answers
h is for number of hours, can be changed to different letter if preferred
What is the LCD of 4/7 and 1/2 ? get this right you will be marked brainlest dont put random anwsers!
Answers
Answer:
14
Step-by-step explanation:
The LCD is the LCM of the denominators, 7 and 2. Since these numbers have no common factors, their LCM is simply their product:
... 7·2 = 14
HELP FAST 100 POINTS: The manager of a basketball arena randomly selected 150 fans and asked if they were pleased with the new selection of food offered in the arena. In this sample, 120 fans said that they were pleased.
How many of the 8000 fans at the game could be expected to be pleased?
7880
6400
7970
7850
Answers
Answer:
6400 fans will be pleased.
Step-by-step explanation:
Out of 150 fans, 120 were pleased. Assuming the same ratio, out of 8000 fans, 8000x120/150 = 6400 will be pleased.
Answer:
6400
Step-by-step explanation:
We need to find the fraction of fans that are pleased
120 out of 150 are please
120/150 = 12/15 =4/5
We multiply this fraction by the fans at the game
4/5 * 8000 = 6400
6400 fans should be pleased