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]
find the value of x (URGENT/GIVING BRAINLIEST)
Answer:
B)10
Step-by-step explanation:
Because this is a right angle(indicated by the red box) the total measure should be 90°.
And based on that we say 5X +40=90
Subtract 40 from both sides to get 5x=50
And then divide both sides by 5 to get x=10
Answer:
x = 10°
Step-by-step explanation:
5x° + 40° = 90°
5x° = 90°-40°
5x°=50°
x°= 50°/5
x = 10°
The answer I put is wrong. SO don't put that as a answer. NEED TO EXPLAIN VERY IMPORTANT
Brainleist
Answer:
Solution given:
Annie needs 250 lb of cement to fix the outer step.
Each bag hold 40 lb of cement.
Now
40 lb =1bag
we need
250lb= ? bag.
we have
no of bag =needed lb/1 bag's lb=250/40=250/40=6.25
we do not need more than 7 bags
Annie needs 7 bags.
So
The required inequality is:
b≥7.
A soft drink company bottles and sells lemon iced tea. They mix 15 gallons of lemonade with 8 gallons of tea and then pour the mixture into pint sized bottles. How many pint sized bottles will this mixture produce?
Answer:
Thus this mixture contains 184 pints of Zesty lemon tea.
graph the number that represents the situation on a number line. please help with this question i will mark you brainliest!
Answer:
OMGGGG OMGGG I NEEDTHIS QUESTION TOOOOOO
Help!!! what is the pattern and what is the next number 3,-9,27,-81,?
Answer:
243.
Step-by-step explanation:
they are multiplying by -3.
3x(-3)= -9
-9x(-3)= 27
27x(-3)= -81
so you would do -81x(-3) which equals 243.
PLS HELP ASAP !!!!!!!!!!!!
Answer:
D-780 squared inches
Step-by-step explanation:
you multiply 2(l)(w)+2(l)(h)+2(w)(h)
Answer:
Last option 780.
Step-by-step explanation:
To get the surface area for this you will need to get the area of each square that you see is in the net version. Once you do that you add them all together. Here is the math. . .
(4*25)+(4*10)+(4*25)+(10*25)+(10*25)+(4*10) = 780 total surface area.
If this looks confusing just look at the net version of the rectangular prism and you can see there is a duplicate of the different dimension triangles. These areas would be (4*25), (4*10), (10*25). There are a total of 3 different size triangles and all of them have duplicates. So we just multiply everything by 2
(4*25)+ (4*10)+(10*25) = 390 now multiply that by 2 and you get 780 again.
Hope the explanation helps :)
PLEASE HELP!!! So the answer I got was 19.14 however that is not the correct answer. How do I solve this problem. Not sure what else to do.
Check the picture below.
so we know the radius of the semicircle is 2 and the rectangle below it is really a 4x4 square, so let's just get their separate areas and add them up.
[tex]\stackrel{\textit{area of the semicircle}}{\cfrac{1}{2}\pi r^2}\implies \cfrac{1}{2}(\stackrel{\pi }{3.14})(2)^2\implies 3.14\cdot 2\implies 6.28 \\\\\\ \stackrel{\textit{area of the square}}{(4)(4)}\implies 16 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{sum of both areas}}{16+6.28=22.28}~\hfill[/tex]
Solve for x if ab ≠ 2c
[tex]x = \frac{ac + b}{2c - ab} [/tex]
Refer to the attachment for step by step explaination.
Answer:
[tex]x=\frac{b+ax}{2c-ba}[/tex]
Step-by-step explanation:
When given the following expression, one is asked to solve for (x):
[tex]\frac{2x-a}{b}=\frac{ax+1}{c}[/tex]
Use cross products to rid the variable in the denominator,
[tex]c(2x-a)=b(ax+1)[/tex]
Simplify, distribute, multiply every term in the parenthesis by the term outside of it,
[tex]2xc-ac=bax+b[/tex]
Inverse operations, collect all terms with variable (x) on one side of the equation:
[tex]2xc-ac = bax + b\\\\2xc - bax = b + ac[/tex]
Factor, remove a like term that exists in both of these expressions,
[tex]x(2c-ba)=b+ax[/tex]
Inverse operations,
[tex]x=\frac{b+ax}{2c-ba}[/tex]
Question 5 of 10
What is the slope of the line x = 3?
Answer here
Answer:
Undefined
Step-by-step explanation:
This equation is just a vertical line, so the slope is undefined.
An infinite sheet of charge, oriented perpendicular to the x-axis, passes through x = 0. It has a surface charge density ?1 = -4.6 ?C/m2. A thick, infinite conducting slab, also oriented perpendicular to the x-axis occupiees the region between a = 2.8 cm and b = 4.5 cm. The conducting slab has a net charge per unit area of ?2 = 60 ?C/m2.
1) What is Ex(P), the value of the x-component of the electric field at point P, located a distance 6.3 cm from the infinite sheet of charge?N/C 2)
2) What is Ey(P), the value of the y-component of the electric field at point P, located a distance 6.3 cm from the infinite sheet of charge?N/C 3)
3) What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.4 cm from the infinite sheet of charge?N/C 4)
4) What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1.4 cm from the infinite sheet of charge?N/C 5)
5) What is b, the charge per unit area on thesurface of the slab located at x = 4.9 cm??C/m2 6)
6) What is Ex, the value of the x-component of the electric field at a point on the x-axis located at x = 3.64 cm ?N/C 7)
7) What is ?a, the charge per unit area on the surface of the slab located at x = 2.8 cm??C/m2 8)
Element X is a radioactive isotope such that every 25 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 910 grams, how long
would it be until the mass of the sample reached 400 grams, to the nearest tenth of a
year?
Answer:
It will take 25.6 years for the mass of the sample to reach 400 grams.
Step-by-step explanation:
Element X is a radioactive isotope such that every 25 years, its mass decreases by half.
This means that the amount of the substance after t years can be modeled by a function in the following format:
[tex]A(t) = A(0)(0.5)^{\frac{t}{25}}[/tex]
In which A(0) is the initial amount.
Initial mass of a sample of Element X is 910 grams.
This means that [tex]A(0) = 910[/tex]
So
[tex]A(t) = A(0)(0.5)^{\frac{t}{25}}[/tex]
[tex]A(t) = 910(0.5)^{\frac{t}{25}}[/tex]
How long would it be until the mass of the sample reached 400 grams?
This is t for which [tex]A(t) = 400[/tex]
So
[tex]A(t) = 910(0.5)^{\frac{t}{25}}[/tex]
[tex]400 = 910(0.5)^{\frac{t}{25}}[/tex]
[tex](0.5)^{\frac{t}{25}} = \frac{400}{910}[/tex]
[tex](0.5)^{\frac{t}{25}} = 0.43956[/tex]
[tex]\log{(0.5)^{\frac{t}{25}}} = \log{0.43956}[/tex]
[tex]\frac{t}{25}\log{0.5} = \log{0.43956}[/tex]
[tex]t = \frac{25\log{0.43956}}{\log{0.5}}[/tex]
[tex]t = 25.6[/tex]
It will take 25.6 years for the mass of the sample to reach 400 grams.
Answer:
29.6
Step-by-step explanation:
$450 at 1.4%
for 3 years
Answer:
$639
Step-by-step explanation:
$450 * .14 = 63
63 * 3 = 189
450 + 189 = 639
PLEASE HELP I WILL GIVE BRAINLIEST AND 50 POINTS!!!
Reese has a greenhouse and is growing daisies. The table shows the average number of sunflowers that bloomed over four months:
Month 1 2 3 4
Daisies 10 13.1 16.2 19.3
Did the number of daisies increase linearly or exponentially?
Linearly, because the table shows a constant percentage increase in daisies each month
Exponentially, because the table shows that the daisies increased by the same amount each month
Linearly, because the table shows that the daisies increased by the same amount each month
Exponentially, because the table shows a constant percentage increase in daisies each month
Answer:
linearly because the table shows that the daisies increased by the same amount each month
Step-by-step explanation:
Answer:
Linearly, because the table shows that the daisies increased by the same amount each month
Step-by-step explanation:
Take the second term and subtract the first term for the output
13.1 -10 = 3.1
Do the same for the third and the second
16.2 -13.1 = 3.1
And the fourth and third
193. -16.2 = 3.1
This is a linear increase since we add the same amount each time
Which graph represents the given inequality? y > 4x + 2
Two classmates have decided to read all the volumes in a popular series of books. Carly has
already read 10 volumes and will continue to read new ones at a rate of 2 volumes per week.
Lisa, who hasn't started reading the series yet, will read 4 volumes per week. At some point,
Lisa will catch up with Carly and they will be reading the same book. How many volumes will
each girl have read by then? How long will that take?
Answer:
the volumes they would have read is 20
so it will take them 5 weeks
Step-by-step explanation:
C ( started with 10) < 12<14<16<18<20 =5 weeks
L (started with 0) <4 <8<12<16<20 = 5 weeks
for them to read the same book will take them 5 weeks and each of them would have read 20 volumes by then
A survey asked buyers whether color, size, or brand influence their choice of cell phone. The results are below. How many people were influenced by brand
Answer:
wheres the photo
Step-by-step explanation:
what is the answer for "?" please.
Answer:
24 inches
Step-by-step explanation:
Answer:
7.5 or 7 1/2
Step-by-step explanation:
since in the original you divide by 4 and multiply by 5,
the same rule applies for the second.
6/4=1.5x5=7.5
What is the net price if a purchase would have come to $1,500 at the regular price, but a 3% discount applies to this purchase.
Step-by-step explanation:
100%-3%=97%
$1500*97%=$1455
Please help will mark BRAINLIEST!
=====================================================
Explanation:
We have n = 5 sides. This means the interior angles sum up to...
S = 180(n-2)
S = 180(5-2)
S = 180(3)
S = 540
All five interior angles of this pentagon add up to 540 degrees.
what is the length of x of the side of the triangle below?
Answer:
9.1
Step-by-step explanation:
what is the length of x of the side of the triangle below?
PLS HELP
What is the value of (3-5) *(2) - 16+ 2?
040
0-16
O 24
O 56
Pls help quickly
A rectangle is placed around a semi-circle. The width of the rectangle is 5cm. Find the area of the shaded region. use the value of 3.14 for pi
Answer:
i don't now to arrange thats
Draw the image of under the dilation with scale factor 5/3 and center of dilation(2,-2) . Label the image .
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The center of dilation is point S, so S' is at the same location. The other points move to 5/3 of their distance from S.
Simplify the expression by distributing. 4(w+8)
a)4w + 8
b)12w
с)4w + 32
d)4(8 + W)
Answer:
Option C
4w + 4(8)
=4w + 32.
To solve this problem I multiplied $9.50 x 168 to figure out how much it would cost to feed the lambs. Unfortunately my answer, $1596, was incorrect. How would I solve this type of problem?
===========================================================
Explanation:
That calculation you wrote out would only apply if each lamb ate 1 full bale of alfalfa.
Instead, each lamb eats 1/8 of a bale. So you'll divide the 1596 value by 8 to get 1596/8 = 199.50
This is the same as saying (1/8)*1596 = 0.125*1596 = 199.50
---------------------
Or we can think of it like this
1 day = 1/8 bale of alfalfa
168*(1 day) = 168*(1/8 bale of alfalfa)
168 days = 21 bales of alfalfa
This says that one lamb will eat 21 bales of alfalfa over the course of 168 days
At $9.50 per bale, the total cost for one lamb is 9.50*21 = 199.50 dollars
This cost applies to one lamb only. So if you had say 3 lambs overall, then you'd multiply that by 3.
Travis has hired Charlie and Dora to plant flowers . Dora can plant 150 flowers in the same time it takes Charlie to plant 120 flowers , which can be shown using the following relationship where d and c are the respective rates at which Dora and Charlie can plant flowers :
150 =120
——. ——
d. c
Also , Dora can plant 18 flowers more per day than Charlie
How many flowers can Charlie plant per day ?
Answer:
21 flowers
Step-by-step explanation:
because if dora can plant 18 plants then Charlie can plant 21 flowers
Write an expression showing the quotient of J and 3
Answer:
j/3
Step-by-step explanation:
quotient is division
j/3
can someone help me really please
Answer:
26
Step-by-step explanation:
Let x represent the missing number
[tex] 8\frac{11}{15} = 7\frac{x}{15} [/tex]
Convert both fractions to improper fractions
[tex] \frac{131}{15} = \frac{105 + x}{15} [/tex]
Cross multiply
[tex] 15(105 + x) = 15(131) [/tex]
[tex] 1,575 + 15x = 1,965 [/tex]
Subtract both sides by 1,575
[tex] 15x = 1,965 - 1,575 [/tex]
[tex] 15x = 390 [/tex]
Divide both sides by 15
[tex] x = \frac{390}{15} [/tex]
x = 26
Find M < A the diagram is not to scale
Answer:
107 i think
Step-by-step explanation:
last question of the unit test
Answer:
Step-by-step explanation:
Take angle A as reference angle
using sin rule
sin A=opposite/hypotenuse
sin A=10/13
sin A=0.76
[tex]sin^{-1}[/tex] 0.76=49.46 degree
A=49.5 degree