Answer:
Step-by-step explanation:
John's age = w
His brother's age = 2*w = 2w
His sister's age = 16 years
Total age of all siblings = 31
w + 16 + 2w = 31
w + 2w + 16 = 31
Combine like terms
3w + 16 = 31
Subtract 16 from both sides
3w = 31 - 16
3w = 15
w = 15/3
w = 5
[tex]\boxed{\text{John's age = 5 years }}[/tex]
His brother's age = 2w
= 2*5
= 10
[tex]\boxed{\text{John's brother's age = 10 years}}[/tex]
a paper has an area of 84 square inches.what is the paper’s area in square centimeters?
Answer:
541.9344 square centimeters
Step-by-step explanation:
one square inch is 6.4516 square centimeters
that means that you can multiple 84 by the above number
that gives you
541.9344
Consider the line - 3x +9y = 5.
Find the equation of the line that is perpendicular to this line and passes through the point (5, -1).
Find the equation of the line that is parallel to this line and passes through the point (5, -1).
Answer:
[tex]\textsf{Perpendicular to given line}:y=-3x+14[/tex]
[tex]\textsf{Parallel to given line}: y=\dfrac13x-\dfrac83[/tex]
Step-by-step explanation:
Rewrite the given equation to make y the subject:
[tex]\begin{aligned}-3x+9y &=5 \\ \implies 9y &=3x+5 \\ \implies y &=\dfrac13x+\dfrac59\end{aligned}[/tex]
Therefore, the slope of the given equation is [tex]\frac13[/tex].
If two lines are perpendicular to each other, the product of their slopes will be -1. Therefore, the slope (m) of the line that is perpendicular to the given line is:
[tex]\begin{aligned}m \times \dfrac13 & =-1\\ \implies m & =-3\end{aligned}[/tex]
To find the equation of the line, substitute the found slope (-3) and the point (5, -1) into the point-slope form of a linear equation:
[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\ \implies y-(-1) &=-3(x-5) \\ y+1 & =-3x+15 \\ y &=-3x+14\end{aligned}[/tex]
If two lines are parallel to each other, their slopes will be the same. Therefore, the slope (m) of the line that is parallel to the given line is [tex]\frac13[/tex]
To find the equation of the line, substitute the slope ([tex]\frac13[/tex]) and the point (5, -1) into the point-slope form of a linear equation:
[tex]\begin{aligned}y-y_1 & =m(x-x_1)\\\\ \implies y-(-1) &=\dfrac13(x-5) \\\\ y+1 & =\dfrac13x-\dfrac53 \\\\ y &=\dfrac13x-\dfrac83\end{aligned}[/tex]
Slope =m=1/3
Note that perpendicular lines have slopes negative reciprocal to each other .
Slope of the perpendicular line=-3Equation in point slope form
y+1=-3(x-5)y+1=-3x+15y=-3x+14And
parallel lines have equal slope
Equation of parallel line
y+1=1/3(x-5)3y+3=x-53y=x-8y=x/3-8/3How many times greater Is 8.4 x 10^9 than 1.5 x 10^2?
A. 5.6 x 10^6
B. 5.6 x 10^7
C. 5.6 x 10^8
D. 5.6 x 10^9
I will give Brainliest!!!!!!!
Reason:
There are 6 angles shown. If they are all the same measure, then they must be 360/6 = 60 degrees each. This is because the angles all glue together to form a full 360 degree rotation. There are no gaps or overlaps.
A certain ore contains 21 percent gold. How much ore (in tons) is needed to obtain 882 tons of gold?
Answer:
it would be 4200 ore
Step-by-step explanation:
because 882/.21
The cube has a volume of 340 cubic inches. Approximate the length d of the diagonal to the nearest whole number.
Considering the volume of the cube, it is found that it has a diagonal with a length of 12 inches.
What is the volume of a cube?The volume of a cube of side length a is given by:
V = a³.
The diagonal is given by:
[tex]D = \sqrt{3}a[/tex]
In this problem, the volume is of 340 in³, hence:
[tex]a³ = 340 \rightarrow a = \sqrt[3]{340} \rightarrow a = 6.98[/tex]
Hence, the diagonal is given by:
[tex]D = \sqrt{3} \times 6.98 = 12[/tex]
The cube has a diagonal with a length of 12 inches.
More can be learned about the volume of a cube at https://brainly.com/question/13030328
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Benson has a bankruptcy on his credit report, so he pays higher interest rates on his current loans. he calculates that the extra money he pays in additional interest each year, if invested at the rate of 2% for one year, could earn him simple interest totaling $180. how much does benson pay in additional interest each month? a. $360 b. $750 c. $900 d. $1,000 please select the best answer from the choices provided. a b c d
The additional interest Benson pay each month is $750 if he invested at the rate of 2% for one year, option (b) is correct.
What is simple interest?It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.
We know the formula for the simple interest is given by:
I = PRT
Where I is the simple interest.
P is the principal amount
R is the rate of interest
We have in the question:
I = $180
R = 2% = 0.02
T = 1 year
Put the above values in the formula, we get:
180 = P(0.02)(1)
P = $9000
The additional interest Benson pay each month is:
= 9000/12
= $750
Thus, the additional interest Benson pay each month is $750 if he invested at the rate of 2% for one year option (b) is correct.
Learn more about the simple interest here:
https://brainly.com/question/22621039
2k=18
Find the value of k that makes the equation true.
Group of answer choices
k=10
k=9
k=7
k=6
Answer:
k=9
Step-by-step explanation:
K=9, because if you plug in 9 as k(2(9)=18)the equation is true.
Answer:
k=9
Step-by-step explanation:
2 × 9 = 18 which is the same as 9 + 9=18
luka tried to define a rotation about point c
Answer:
C
Step-by-step explanation:
As properties are preserved
Determine the value of each variable.
Answer:
a=9, b=45, c=31.5, d=18, f=27
Step-by-step explanation:
To find the value of a, you can take 72-54=18 and do 18/2=9
a=9
To find the value of b, you can multiply the three a's. 27 is the product of the 3 a's. Next, you will do 72-27 to find the value of b
b=45
To find the value of c, you can take 9 and subtract it from 72, or in other words: 72-9=63. You will then divide 63/2 to find the value of c
c=31.5
To find the value of d, you can multiply (9*4)=36. You can then take 72-36 and get 36. To find the value of d, you will then divide 36/2.
d=18
To find F, you are given a clue that 1 a and 1 d together=f.
9+18=f
f=27
Answer:
a=9
b=36
c=45
d=31.5
f=40.5
Step-by-step explanation:
Phew! that was pretty tough. But I solved it! Your welcome! :)
Suppose a jar contains 14 red marbles and 31 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red. Answer should be in fractional form.
Answer:
P = 91/990
Step-by-step explanation:
first red marble: [tex]\frac{14}{45}[/tex]
second red marble: [tex]\frac{13}{44}[/tex]
The probability
[tex]P=(\frac{14}{45})(\frac{13}{44} )=\frac{(14)(13)}{(45)(44)} =\frac{182}{1980} =\frac{91}{990}[/tex]
Hope this helps
What is the slope below?
A bag of marbles contains: 50 green, 12 blue, 2 yèllow, 10 purple and 10 red. Write
each answer as a DECIMAL.
23. P (blue) =
24. P(not red)
25. P(green) =
Answer:
p(blue)=0.14
p(not red)=0.9
p(green)=0.6
Step-by-step explanation:
p(blue)=12/84=0.14
p(not red)=74/84=0.9
p(green)=50/84=0.6
Hope it helps
Answer:
See below ~
Step-by-step explanation:
Q23)
P (blue) = No. of blue marbles / Total marblesP (blue) = 12/(50 + 12 + 2 + 10 + 10)P (blue) = 12/84P (blue) = 1/7P (blue) = 0.14Q24)
P (not red) = No. of marbles that are not red / Total marblesP (not red) = 74/84P (not red) = 37/42P (not red) = 0.88Q25)
P (green) = No. of green marbles / Total marblesP (green) = 50/84P (green) = 25/42P (green) = 0.59
-725628 - 178042
Show how you worked it out
Answer:
-903,670
Step-by-step explanation:
-725628
- 178042
—-------------
_903,670
There were 30 cookies in a basket. Haley ate 10% of the cookies. Erin ate 1 6 of the cookies. Hannah ate 1 5 of the cookies. Madison ate 30% of the cookies. How many cookies are left in the basket?
The number of cookies left in the basket after everyone has eaten out of the cookies is 7.
How many cookies are left?The first step is to convert the fractions to percentages.
1/6 x 1000 = 16.67%
1/5 x 100 = 20%
Now determine the sum of the percentages of the cookies eaten : 10% + 30% + 16.67 + 20% = 76.67%
Determine the percentage of cookies left = 100 - 76.67 = 23.33%
Number of cookies left = (23.33 / 100) x 30 = 7
To learn more about percentages, please check: https://brainly.com/question/25764815
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What is the area of the parallelogram?
Which statement is true of a rectangle that has an area of 4x2 39x – 10 square units and a width of (x 10) units? the rectangle is a square. the rectangle has a length of (2x – 5) units. the perimeter of the rectangle is (10x 18) units. the area of the rectangle can be represented by (4x2 20x – 2x – 10) square units.
The length and width of the rectangle are (4x - 1) and (x + 10) then the perimeter of the rectangle is 10x + 18. Then the correct option is C.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The polynomial of the rectangle will be given below.
4x² + 39x – 10
The factor of the polynomial will be
(4x - 1)(x + 10)
Then the perimeter of the rectangle will be
Perimeter = 4x - 1 + 4x - 1 + x + 10 + x + 10
Perimeter = 10x + 18
More about the factorization link is given below.
https://brainly.com/question/6810544
Plllsss solve dis three questions pls simplify it I’ll mark da critical answer as brainlist
Answer:
use a calculator and you can find:
3. 3.9342208 x 10^(-6)
4. 162/3125
5. 1/60
Answer:
Step-by-step explanation:
Exponent Law:
[tex]\sf \left(\dfrac{a}{b} \right)^{m}=\dfrac{a^{m}}{b^n}\\\\a^m *a^n =a^{m+n}\\\\\dfrac{a^{m}}{a^n}=a^{m-n}[/tex]
In exponent law, in multiplication, if bases are same add the powers and in division, if the bases are same, subtract the powers.
3)
[tex]\sf \left(\dfrac{7}{3} \right)^{-2}*\left(\dfrac{1}{7}\right)^{5}*\left(\dfrac{3}{5} \right)^{2}=\dfrac{7^{-2}}{3^{-2}}*\dfrac{1}{7^5}*\dfrac{3^2}{5^{2}}[/tex]
[tex]= \dfrac{7^{-2-5}*3^{2-[-2]}}{5^2}\\\\= \dfrac{7^{-7}*3^{2+2}}{5^{2}}\\\\=\dfrac{3^{4}}{7^7*5^{2}}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~```
4)
[tex]\sf \left(\dfrac{2}{5}\right)^3*\left(\dfrac{2}{3}\right)^{-2}*\left(\dfrac{3}{5}\right)^2=\dfrac{2^3}{5^3}*\dfrac{2^{-2}}{3^{-2}}*\dfrac{3^2}{5^2}[/tex]
[tex]= \dfrac{2^{3-2}*3^{2-[-2]}}{5^{3+2}}\\\\=\dfrac{2*3^{2+2}}{5^{5}}\\\\=\dfrac{2*3^4}{5^5}[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`````
5)
[tex]\sf \left(\dfrac{3}{10}\right)^4*\left(\dfrac{10}{15}\right)^{2}*\left(\dfrac{5}{3}\right)^{3}=\left(\dfrac{3}{2*5}\right)^4*\left(\dfrac{2*5}{3*5}\right)^{2}*\left(\dfrac{5}{3}\right)^{3}[/tex]
[tex]=\left(\dfrac{3}{2*5}\right)^4*\left(\dfrac{2}{3}\right)^{2}*\left(\dfrac{5}{3}\right)^{3}\\\\=\dfrac{3^4}{2^4*5^4}*\dfrac{2^2}{3^2}*\dfrac{5^3}{3^3}\\\\=3^{4-2-3}*2^{2-4}*5^{3-4}\\\\=3^{-1}*2^{-2}*5^{-1}\\\\=\dfrac{1}{3*2^{2}*5}\\\\=\dfrac{1}{3*4*5}\\\\=\dfrac{1}{60}[/tex]
Could use some help! :(
Step-by-step explanation:
14(3.8) ×3 + 2(1/2)×3×4
= 159.6 + 12
= 171. 6
Find the surface area of each prism 2cm
8cm
8cm
Answer:
128 square cm
Step-by-step explanation:
2 x 8 x 8 x = 128 cm
Hope this Helps
5. How long is the diagona of a 12 ft-by-16 ft rectangular garden?
A. 6 ft
B. 14 ft
C. 18 ft
D. 20 ft
Answer:
The correct answer is option D, 20ft
Step-by-step explanation:
After drawing the picture below, you can just use pythagorean theorem to solve for the diagonal, or the hypotenuse in this case;
(Length)² + (Width)² = (Diagonal)²
(16)² + (12)² = (Diagonal)²
256 + 144 = (Diagonal)²
400 = (Diagonal)²
[tex]\sqrt{400}[/tex] = [tex]\sqrt{Diagonal^{2} }[/tex]
20 = Diagonal
Hope this helps!
Answer:
D. 20 ft
Step-by-step explanation:
Use pythagorus! We can imagine the rectangle is split into 2 equal triangles, one side of the triangle being 12, and the width being 16.
Pythagorus theorum is used to calculate the hypotenuse (long side) of a right-angled triangle. This is the formula:
[tex]\sf{a^{2}+b^{2} = c^{2} }[/tex]
So, we do 12^2 (squared) + 16^2 =
144 + 256 = 400
Now, we have to find the square root of 400, which is equal to
20
So our answer is 20ft
Hope this makes sense! If you need further explanation, do let me know...
- profparis
what is the cube root of 27/64?
Answer:
⅜
Step-by-step explanation:
We want to find the cube root of 27/64.
∛(27/64)
We know that;
3³ = 27 and 8³ = 64
Thus;
∛(27/64) = ⅜
Dan weighs 205 pounds but is only 5 feet 8 inches tall. Evan is 6 feet tall. How much would you expect Evan to weigh if they have the same height/weight ratio?
Answer:
217.1 lbs
Step-by-step explanation:
I did set up cross multiplication using the height/weight ratio.
68/205 and 72/?.
72*205=14760
14760/68=217.05
Then I rounded to get 217.1 lbs
A kangaroo chases a rabbit that starts 150 feet ahead of the kangaroo. For every 12-foot leap of
the kangaroo, the rabbit makes a 7-foot leap. How many leaps will the kangaroo have to make to
catch up to the rabbit if the two animals always leap at the same time?
Answer:
30 leaps
Step-by-step explanation:
Equation of rabbit:
y=7x+150
Equation of kangaroo:
y=12x
To solve the system of equations, use substitution
12x=7x+150
5x=150
x=30
please mark brainliest!
consider the table below that represents the function.
Answer:
-8
Step-by-step explanation:
with the way the table is it makes sense
I am really bad at percentages, please help me. Thank you so much!!
what percentage did Mr. Tanaka use of the stock in the recipe.
Answer:
80%
Step-by-step explanation:
We can find this by dividing 4 by 5 to get 0.8. Then we can convert this to a percent.
help please i will give u brainlest
Answer:
For the first question, your answer would be 65 degrees. The reason for this is that complementary angles add up to 90 degrees. So, 90-25= 65 degrees.
Step-by-step explanation:
For supplementary angles- 180-the angle given= ?
Please help me with this one!
Answer:
how do u do that....I have never did this before
the shape of this graph is best described as 2012 housing prices
Answer:
tell the full question
Step-by-step explanation:
bro
What is the graph of each function? 4. y = -x² - 6x - 11
Answer: The graph will appear as a parabola opening downwards with a maximum point. It will cut the y-axis at -11.
Step-by-step explanation:
The coefficient of x^2 is negative, thus the graph will look "sad" ie. max a maximum point and open downwards. And bc it's x^2, it's a parabola.
Sub. x=0 and you'll get -11. Or just inspect and get the ans from the eqn.
to get the roots. ( x-intercepts). Just sub y=0 and solve.