Answer:
[tex]x = 24[/tex] ---- Hao Sheng
[tex]y =51[/tex] --- His father
[tex]z = 84[/tex] ---- His grandfather
Step-by-step explanation:
Given
[tex]x \to Hao\ Sheng[/tex]
[tex]y \to his\ father[/tex]
[tex]z \to his\ grandfather[/tex]
From the question, we have:
[tex]\frac{x + y + z}{3} = 53[/tex] --- The average of their age
[tex]\frac{z}{2} + \frac{y}{3} +\frac{x}{4}= 65[/tex]
[tex]z - 4 = 4(x - 4)[/tex] --- 4 years ago
Required
Their current age
[tex]z - 4 = 4(x - 4)[/tex]
Open bracket
[tex]z -4 = 4x-16[/tex]
Make z the subject
[tex]z = 4x-16+4[/tex]
[tex]z = 4x-12[/tex]
Multiply [tex]\frac{z}{2} + \frac{y}{3} +\frac{x}{4}= 65[/tex] by 12
[tex]6z + 4y + 3x = 780[/tex]
Substitute [tex]z = 4x-12[/tex] in [tex]6z + 4y + 3x = 780[/tex]
[tex]6(4x - 12) + 4y + 3x = 780[/tex]
[tex]24x - 72 + 4y + 3x = 780[/tex]
Collect like terms
[tex]24x + 3x + 4y = 780+ 72[/tex]
[tex]27x + 4y = 852[/tex]
Substitute [tex]z = 4x-12[/tex] in [tex]\frac{x + y + z}{3} = 53[/tex]
[tex]\frac{x + y + 4x - 12}{3} = 53\\[/tex]
Multiply through by 3
[tex]x + y + 4x - 12 = 159[/tex]
Collect like terms
[tex]x + 4x + y = 159+12[/tex]
[tex]5x + y = 171[/tex]
Make y the subject
[tex]y = 171 - 5x[/tex]
Substitute [tex]y = 171 - 5x[/tex] in [tex]27x + 4y = 852[/tex]
[tex]27x + 4(171 - 5x) = 852[/tex]
[tex]27x + 684 - 20x = 852[/tex]
Collect like terms
[tex]27x - 20x = 852-684[/tex]
[tex]7x = 168[/tex]
Divide by 7
[tex]x = 24[/tex]
Solve for y in [tex]y = 171 - 5x[/tex]
[tex]y =171 -5*24[/tex]
[tex]y =171 -120[/tex]
[tex]y =51[/tex]
Solve for z in [tex]z = 4x-12[/tex]
[tex]z = 4 * 24- 12[/tex]
[tex]z = 96- 12[/tex]
[tex]z = 84[/tex]
What would this shape be folded?
It would be a rectangular prism
Study the given data set. {77,4,62,10,45,9,38,80,2}. What is the standard deviation of the data?
Answer:
29.7 is the standard deviation :)
Which of the following is a sinusoid? A. y = cos(x) - 2 B. x^2 + y^2 = 1 C. y = 3sqrtx D. x^2/3+y^2/6=1
Answer:
A. y = cos(x) - 2
Step-by-step explanation:
The word "sinusoid" means the graph has a shape of the sine function that smoothly goes up and down.
However, the cosine function also has the same shape but the only thing is that it is horizontally translated. Thus, the cosine function is the sinusoid.
Using the image find the slope of the lineReduce all fractions and enter using a forward slash (i.e. "/). If the slope is undefined, enter "undefined."
Answer:
2
Step-by-step explanation:
find the slope of a line from a graph following those steps
-pick any two points on the graph that belong to the line,
for example (1,1) and (2,3)
-find out how did you get from one point to the other
to get from (1,1) to (2,3) I went 2 up (rise) and 1 to the right (run)
slope= rise /run = 2/1 =2
Few things to keep in mind:
-To find the slope, always move vertical first (y-axis) and than horizontal( x-axis) , because m=change in y/change in x
-For vertical movement, moving up is positive , moving down is negative
For horizontal movement, moving right is positive , moving left is negative
giving brainly to who ever was right
Answer:
it has two factors and one term
Step-by-step explanation:
7 and 9 are numbers whose values are given to us, making them factors, and y is a term representing an answer that is unknown
Answer:
I.d.k if I am right, but here's my answer
It has two factors and the factor (7 + y) has two terms.
Step-by-step explanation:
Notice that the there is an addition of two terms (y and9 ) inside the parentheses.
Outside the parentheses you can notice that the number is 7 multiplying the sum of the terms mentioned before.
Therefore, you can conclude that the best description for this expression is:
It has two factors and the factor (7 + y) has two terms.
What is the length of the line segment?
Answer:
SQRT(8-1)^2+(3-7)^2
sqrt49+16= sqrt65
Step-by-step explanation:
The girls in Lana’s troop set a goal to sell 1,000 boxes of cookies this year. There are 13 girls in the troop. At least how many boxes of cookies should each girl sell to reach their goal?
Answer:
77
Step-by-step explanation:
Each girl would have to sell at least 77 boxes of cookies to get over 1,000.
1000 boxes divided by 13 girls is 76.9230... but round up to 77.
Check answer by multiplying 13 by 77 and you get 1,001.
:) ur welcome
Answer:
77 boxesStep-by-step explanation:
Let each cell x boxes, then the sum is:
13x ≥ 1000x ≥ 1000/13x ≥ 76.9 ≈ 77A system of linear equations is graphed. Which ordered pair is the best estimate for the solution to the system? (0, −2) (−412, 212) (−4, 212) (0, 7)
Answer:
(0,-2)
Step-by-step explanation:
It would be (0,-2) because that is the only one in the solution range,. Solution range is everything above the intersection that is not outside line.
The solution of graphed equations is (-4, 2 1/2).
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
From the graph, we have the following highlights.
The x-coordinate of the point of intersection is close to 4
The y-coordinate of the point of intersection is close to 2 1/2.
So, the coordinates can be estimated to be -4 and 2 1/2
Learn more about system of equations here:
brainly.com/question/14677018
#SPJ5
The diameter of our solar system (depending on how you define “solar system”) is about 8,980,000,000,000 kilometers. The distance from our solar system to the nearest star, Proxima Centauri, is about 39,900,000,000,000,000 kilometers. A light-year is the distance light travels in one year, and it is equal to about 9,460,000,000,000 kilometers. a) Write each of these numbers in scientific notation. Explain how you got your answers, and explain why you know that your method works. b) You’d like to both know the end-to-end distance within the solar system and the distance to Proxima Centauri in light-years. Using your scientific notation numbers, convert these distances. What is the ratio of the solar system’s length to the Proxima Centauri distance? c) Light travels at 300,000 kilometers per second. Write this rate in scientific notation. When Proxima Centauri sends out light at that speed, how long does it take to reach our solar system? Can you convert to minutes, hours, days, or years? Does your answer in years correspond to the distance in light-years from our solar system to Proxima Centauri? Why or why not?
Answer:
Step-by-step explanation:
Place a decimal point to the right of the first real number. write the real number with decimal point
Then count the number of places after the decimal point and this with the power of ten. For example, in diameter of solar system, after keeping decimal after 8, there are 12 places. so power of 10 is 12
a) 8,980,000,000,000 kilo meters. = 8.98 * 10¹² km
39,900,000,000,000,000 kilo meters = 3.99* 10¹⁶ km
9,460,000,000,000 kilo meters = 9.46 * 10¹² km
b)the distance to Proxima Centauri in light-years = 3.99* 10¹⁶ 9.46 * 10¹²
= 0.4218 * 10⁽¹⁶⁻¹²) = 0.4218 * 10⁴
= 4.218 * 10³ light year
c) Speed of light= 3 * 10⁵ km per second
200 reduced by twice my age is 20 years of age
Answer:
90 years
Step-by-step explanation:
Equation =
200 - 2x = 20
2x = 200 - 20
2x = 180
x = 180 / 2
x = 90
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
plz help me plz plz plz plz plz
Step-by-step explanation:
456 x 3 = 1368 (goes to the left)
72 x 36 = 2592 (goes to the right)
594 x 4 = 2376 (goes to the right)
180 x 19 = 3420 ( goes to the right)
139 x 13 = 1807 (goes to the left)
Together, teammates Pedro and Ricky got 2681 base hits last season. Pedro had 275 more hits than Ricky. How many hits did each player have?
Answer:
R= 1203 P= 1478
Step-by-step explanation:
2681- 275= 2406/2 = 1203+ 275= 1478
Find (9.3 × 106) + (1.8 × 104). Express your answer in scientific notation.
1.674 × 1011
9.318 × 106
1.11 × 104
7.5 × 102
IF YOU GET THIS RIGHT I WILL GIVE YOU A BRAINIST!
Help! Possess I will give brainiest!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
Since both fractions have a different denominator, we need to look for a common denominator.
[tex]\frac{1}{3}=\frac{3}{9}[/tex] Multiply 3 in both numerator and denominator
[tex]\frac{5}{9} -\frac{3}{9} =\frac{2}{9}[/tex]
Hence, 2/9 is the answer
i need help identifying solutions
Answer:
3,1 I'm pretty sure lol....
Which of the following points would be a solution to the system of inequalities shown below
y>2x+1
y<-3/4x-2
A. (0,1)
B. (-5, -3)
C. (5,-3
Answer:
the answer would be C
Step-by-step explanation:
if you replace y with 5 and x with -3 they should make the equations "solvable"
- Susan drives north on the 405 Freeway at 50
miles per hour. Two hours after Susan
passes under Westminster Blvd, Maria
enters the 405 Freeway at Westminster Blvd
and heads north at 60 miles per hour. If both
cars maintain their average speeds, how long
will it take Mary to catch up with Susan?
Answer:
If both cars maintain their average speeds, it will take 12 hours for Mary to catch up with Susan.
Step-by-step explanation:
Since Susan drives north on the 405 Freeway at 50 miles per hour, and two hours after Susan passes under Westminster Blvd, Maria enters the 405 Freeway at Westminster Blvd and heads north at 60 miles per hour, if both cars maintain their average speeds, to determine how long will it take Mary to catch up with Susan the following calculation must be performed:
Hour 1 = 50
Hour 2 = 100
Hour 3 = 150 - 60
Hour 4 = 200 - 120
Hour 5 = 250 - 180
Hour 6 = 300 - 240
Hour 7 = 350 - 300
Hour 8 = 400 - 360
Hour 9 = 450 - 420
Hour 10 = 500 - 480
Hour 11 = 550 - 540
Hour 12 = 600 - 600
Therefore, if both cars maintain their average speeds, it will take 12 hours for Mary to catch up with Susan.
Solve x+1>3. Graph the solution.
Answer:
x>2
Step-by-step explanation:
x+1>3.
Subtract 1 from each side
x+1-1 > 3-1
x>2
There is an open circle at 2 and the lines goes to the right
Find the value Z a/2 needed to construct a confident
interval with the given level of 99.7%
Answer:
The critical value is [tex]Z_{\frac{\alpha}{2}} = 2.96[/tex]
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.997}{2} = 0.0015[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.0015 = 0.9985[/tex], so Z = 2.96.
The critical value is [tex]Z_{\frac{\alpha}{2}} = 2.96[/tex]
king monatla surprised his wife on birthday by buying her 55 inch television set.the repayment period is 36 months and the monthly installment is R570,00
write down the item number of the television
Answer:
The final price of the television set is $ 20,520.
Step-by-step explanation:
Given that King Monatla surprised his wife on birthday by buying her a 55 inch television set, and the repayment period is 36 months and the monthly installment is $ 570.00, to determine the final price of the television set the following calculation must be performed:
570 x 36 = X
20.520 = X
Therefore, the final price of the television set is $ 20,520.
A car is 180 inches long.A truck is 75% longer than the car
How long is the truck?
(easy math question please help) find the value of x question #8
Answer:
X = 2
Step-by-step explanation:
44 + 104 + (18+7x) = 180
Simplify
The measures of the angles in triangle UVW are shown in the diagram below.
Answer:
(B) 39°
Step-by-step explanation:
30° + 24° + (3x -9°) = 180°
3x = 180° - 30° - 24° + 9°
3x = 117°|:3
x = 39°
The difference between two positive numbers is 18.
Answer:
9+9=18
Step-by-step explanation:
as they are positive numbers so by adding it we get 18
A girl work a works a basic week of 40 hours,and her basic rate is 6.25per hour .calculate her basic wage for that week
Answer:
250
Step-by-step explanation:
Basic wage is 40 * 6.25
Answer:
40x6.25=250
Step-by-step explanation:
She makes 6.25 per hour
she works 40 hours
Multiply the two to find how much she made in a week, not a day
someone knows thiss?
Function A and Function B are linear functions. Function A Function B v = 1x - 2 X -7. -19 2 Which statement is true? The slope of Function A is greater than the slope of Function B. The slope of Function A is less than the slope of Function B.
Answer:
Slope of function A is less than slope of function B
Step-by-step explanation:
Given :
Function A:
1/2x - 2
Function B:
Fitting the data using technology, the linear model obtained is :
1.424x - 7.373
The general form of a linear model is :
y = bx + c
Where, b = slope
The slope of each function is :
Function A ; slope = 1/2 = 0.5
Function B ; 1.4
Slope A < Slope B
Please I need help with this
Answer:
Third quartile
Step-by-step explanation:
I hope this helps!
If two pencils cost $1.50 how many pencils can you buy with $9.00?
Answer:
12 PENCILS
Step-by-step explanation:
1.50 / 2 = .75
9.00/0.75 = 12
Determine the slope of a line that is perpendicular to the line 2y = 3x – 6.
Answer:
perpindicular slope = -2/3
Step-by-step explanation:
