Answer:
120 pounds
Step-by-step explanation:
We can use systems of equations to solve this problem. Assuming j is Jim's weight and b is Bob's weight, the equations are:
j + b = 180
b - j = 1/2b
Let's get b - j = 1/2b into standard form (b, then j, then the equal sign, then the constant.)
[tex]b - j = \frac{b}{2}\\\frac{b}{2} - j = 0[/tex]
Now we can solve using the process of elimination.
[tex]b + j = 180\\\\\frac{b}{2} - j = 0\\\\b + \frac{b}{2} = 180\\\\b + b \cdot 2 = 180\cdot 2\\3b = 360\\b = 120[/tex]
Now we know how much Bob weighs, for fun, let's find Jim's weight by substituting into the equation.
[tex]120 + j = 180\\j = 180-120\\j = 60[/tex]
So Bob weighs 120 pounds and Jim weight 60 pounds.
Hope this helped!
Answer:
Bob weighs 120 pounds
Step-by-step explanation:
Our first equation will be J(Jim) + B(Bob) = 180 pounds. Our second equation will be 2J = B because it says " if you subtract Jim's weight from Bob's weight, you get half of Bob's weight." This is basically saying that Jim is half of Bob's weight. So that's why our second equation is 2J=B. In our first equation, J+b=180, if we substitute b for 2J, our second equation, then we get the equation 3J = 180. After dividing 3 from both sides, we get j=60. Since Bob weighs twice as much as Jim, his weight will be 120. Now if we want to double-check, we can substitute Jim and Bob's weight for all of the equations.
1) 60 + 120 = 180 This equation is correct
2) 2(60) = 120 This is correct because 2 times 60 equals to 120
3) 3(60) = 180 This is correct because 60 times 3 equals to 180
Plzz solve this for me... The Question is to simplify this.
Answer:
[tex] \boxed{ \frac{ \sqrt{3} }{2} }[/tex]Step-by-step explanation:
[tex] \frac{2 \sqrt{3} }{3} - \frac{ \sqrt{3} }{6} [/tex]
Expand the fraction to get the Least common denominator
[tex] \mathsf{ = \frac{2 \times 2 \sqrt{3} }{2 \times 3} - \frac{ \sqrt{3} }{6} }[/tex]
Multiply the numbers
[tex] \mathsf{ = \frac{4 \sqrt{3} }{6} - \frac{ \sqrt{3} }{6} }[/tex]
Write all numerators above the common denominator
[tex] \mathsf{ = \frac{4 \sqrt{3} - \sqrt{3} }{6} }[/tex]
Collect like terms
[tex] \mathsf{ = \frac{3 \sqrt{3} }{6} }[/tex]
Reduce the fractions with 3
[tex] \mathsf{ = \frac{ \sqrt{3} }{2} }[/tex]
Hope I helped!
Best regards!
A video rental company offers a plan that includes a membership fee of $7 and charges $1 for every DVD borrowed. They also offer a second plan, that costs $29 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan? If a customer rents ___ DVDs, each option costs $___.
If a customer rents 22 DVDs, each option costs $29
This only applies to one month.
=================================================
Work Shown:
x = number of DVDs borrowed
y = total cost
Plan A has a cost of x+7 dollars since x represents the cost of renting the x DVDs plus the membership fee of $7. We can say y = x+7.
Plan B has a fixed cost of $29 per month, so y = 29. There is no x here to worry about as the cost is the same no matter how many DVDs you rent.
y = x+7 and y = 29 are dealing with the same y value. We can use substitution to solve for x
----------------
y = 29 ... start with second equation
x+7 = 29 .... replace y with x+7 (valid because y = x+7)
x+7-7 = 29-7 ... subtract 7 from both sides
x = 22
If the customer rents 22 DVDs, then plan A will charge y = x+7 = 22+7 = 29 dollars, which is the same as the flat rate cost plan B charges.
If the customer rents more than 22 DVDs per month, then its smarter to go with plan B (since plan A's cost will be larger). Otherwise, go for plan A.
----------------
In terms of a graph, you can graph both y = x+7 and y = 29 together on the same xy axis. The line y = x+7 goes through (0,7) and (1,8). The line y = 29 goes through (0,29) and (1,29). Both lines intersect at (22,29) to indicate that x = 22 and y = 29 pair up together.
If sine theta equals one over three, what are the values of cos θ and tan θ?
Answer:
cos theta = √8/3
tan theta = √8/8
Step-by-step explanation:
sin theta = 1/3
1² + x² = 3²
x = √8
cos theta = √8/3
tan theta = 1/√8 = √8/8
Please answer this question now
Answer:
94 degrees
Step-by-step explanation:
Measure of arc BCD = 53+135 = 188 degrees.
Measure of angle A = 188/2 = 94 degrees
Answer:
50
Step-by-step explanation:
If a person invests $120 at 8% annual interest, find the approximate value of the investment at the end of 5 years. A. $164 B. $180 C. $401 D. $176
Answer:
[tex]\large \boxed{\sf \bf \ \ \ D. \ \$ 176 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
After 5 years, we will get
[tex]120*(1+8\%)*(1+8\%)*(1+8\%)*(1+8\%)*(1+8\%)\\\\=120*(1+8\%)^5\\\\=120\cdot 1.08^5\\\\= 176.3193...[/tex]
Thank you
How would I simplify 14.8+6.25+0.97
Answer:
22.02
Step-by-step explanation:
14.8+6.25+0.97 is 22.02
don't know what you mean by simplify
A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance. (4 marks)
It is impossible to measure the length of a particular swamp directly. Kendra put a stake in the ground and measured from the stake to opposite ends of the swamp, the results being 410 m and 805 m. She measured the angle between the distances to be 57°. What is the length of the swamp? (4 marks)
Answer:
1) The ship is closer
2) 675.73 m
Step-by-step explanation:
1) The given parameters are;
The initial angle between the ship's course and the lighthouse = 32°
The final angle between the ship's course and the lighthouse = 72°
The distance traveled by the sip between he two positions = 1500 m
Therefore we have a triangle formed between the distance covered by the ship and the two distances of the ship from the lighthouse, a and b
Where;
a = The initial distance fro the lighthouse
b = The final distance fro the lighthouse
The angles of the triangle are
32°, (180 - 72) = 108° and 180 - 32 - 108 = 40°
By sine rule we have;
1500/(sin(40)) = a/(sin(108)) = b/(sin(32)) =
Therefore, a = sin(108°) × 1500/(sin(40°)) = 2219.37 m
b = (sin(32°)) × 1500/(sin(40°)) = 1236.61 m
Therefore, a > b
The initial distance fro the lighthouse > The final distance fro the lighthouse, which shows that the ship is closer
2) By cosine rule we have
a² = b² + c² - 2× b×c×cos(A)
Where the given measurements by Kendra are;
410 m and 805 m with an included (in between) angle of 57°, we have;
Let b = 410 m, c = 805 m, and A = 57°, we have;
a² = 410^2 + 805^2 - 2× 410×805×cos(57 degrees) = 456608.77 m²
a = The length of the stream = 675.73 m.
Find x
A. 4√6
B. 4√6/3
C. 16√6/3
D. 32√3/3
Answer:
C
Step-by-step explanation:
let hypotenuse of triangle with 60°=y
[tex]\frac{8\sqrt{2}}{y} =sin ~60\\8 \sqrt{2}=y \times \frac{\sqrt{3}}{2} \\y=\frac{16 \sqrt{2}}{\sqrt{3}} =\frac{16 \sqrt{6}}{3}[/tex]
Find the 2nd term in the sequence. Will give Brainliest.
Answer:
17
Step-by-step explanation:
b(1) = 16
b(2) = b(2-1) +1
= b(1) +1
= 16+1
= 17
can some1 help me out with this problem
Answer:
see explanation
Step-by-step explanation:
Compare the coordinates of corresponding vertices.
C(7, - 2 ) → C'(- 3, 7 )
x- direction 7 → - 3 , that is - 10 of a shift
y- direction - 2 → 7, that is + 9 of a shift
Thus the translation rule is
(x, y ) → (x - 10, y + 9 )
Maria is buying new carpet for her bedroom .Her bedroom is in the shape of a square and the length of each side is 12 feet write and simplify an exponential express to find how much carpet she needs.
Answer:
well just do area, and since it's the same in each side 12×4= 144
If I get 20 pound a day how much do i make in a month
Answer:
£600
Step-by-step explanation:
1 months= 30 days
here,
money made in 1 day= £20
now,
money made in 30 days= 20×30
= 600
[:• In one month you earn £600]
Answer:560 pounds
Step-by-step explanation:
If 1 day is equal to 20 pounds, to find how much pounds will you have a month, first check how many days are there in a month. Then multiply the number of days in a month to the given pound in one day.
So =1 month = 28 days
=1 day = 20 pounds
So= 20 pounds × 28 = 560 pounds
Please answer question now
Answer:
MN = 3
Step-by-step explanation:
The following are congruent to each other as each pair are tangents of a circle drawn from the same external point:
PQ = QJ = 1
JK = KL = 4 - 1 = 3
MN = ML
Thus, ML = KM - KL
ML = 6 - 3 = 3
Therefore, MN = ML = 3 (both are tangents drawn from the same external point, M.
a) Simplify the expression and explain each step. (2 points)
4(3x+2) -2
= ?
Answer:
6 (2 x + 1)
Step-by-step explanation:
Simplify the following:
4 (3 x + 2) - 2
Hint: | Distribute 4 over 3 x + 2.
4 (3 x + 2) = 12 x + 8:
12 x + 8 - 2
Hint: | Group like terms in 8 + 12 x - 2.
Grouping like terms, 8 + 12 x - 2 = 12 x + (8 - 2):
12 x + (8 - 2)
Hint: | Subtract 2 from 8.
8 - 2 = 6:
12 x + 6
Hint: | Factor out the greatest common divisor of the coefficients of 12 x + 6.
Factor 6 out of 12 x + 6:
Answer: 6 (2 x + 1)
The volume of a sphere whose diameter is 18 centimeters is π cubic centimeters. If its diameter were reduced by half, its volume would be of its original volume.
Answer:
3053.5517 cm^3 ; 1/8
Step-by-step explanation:
Given the following :
Volume (V) of sphere = (4/3)πr^3 where r = radius
Diameter of sphere = 18 ; radius(r) = diameter / 2 = 18/2 = 9cm
V = (4/3) × π × 9^3
V = 1.3333 × π × 729
V = 3053.5517 cm^3
When diameter(d) is reduced to half
d = d/2
Volume (V1) of sphere with diameter 'd' =
V1 = (4/3)π(d/2)^3
Volume (V2) of sphere with diameter 'd' reduced to half, d = d/2, d/2 * 1/2 = d/4
V2 = (4/3)π(d/4)^3
V1 / V2 = [(4/3)π(d/2)^3] / [(4/3)π(d/4)^3]
V1 / V2 = (d/2)^3 / (d/4)^3
V1 / V2 = [d^3 / 2^3] / [d^3 / 4^3]
V1 / V2 = 8 / 64
V1 / V2 = 1 / 8
Answer:
first blank is 972
second blank is 1/8
yup
Step-by-step explanation:
The Muller family are on holiday in New Zealand. a. They change some euros (€) and receive $1962 (New Zealand dollars). The exchange rate is €1 = $1.635. Calculate the number of euros they change. [3] b. The family spend 15% of their New Zealand dollars on a tour. Calculate the number of dollars they have left. [4]
Answer:
a. €1200;$1667.70
Step-by-step explanation:
a. Number of euros
[tex]\text{euros} = \$1962 \times \dfrac{\text{1 euro}}{\text{\$1.635}} = \textbf{1200 euros}[/tex]
b. Dollars remaining
Dollars on hand = $1962.00
Less 15 % spent = 0.15 × 1962 = -294.30
Balance remaining = $1667.70
A cook uses fifteen 2litter bottles of cooking oil in a week. If he decides to buy 5 litter tins of cooking oil instead how many tins of cooking oil will he use over a 10 week period if the rate at which he uses it remains unchanged.
Answer:
300 liters
Step-by-step explanation:
If he uses 15, 2 liter bottles in a week,
then 15 * 2 = 30 liters in a week.
If he uses the same rate in 10 weeks then,
10 * 30 = 300 liters
Jeania's parents have given her a interest-free loan of $100 to buy a new pair of running shoes She has to
pay back the loan with monthly payments of $20 each.
Write a function rule for the balance of the function (p), where p represents the number of
payments Jeania has made.
Answer:
The balance on the loan f(p) = $100 - $20 × p
Step-by-step explanation:
The parameters of the question are;
The loan amount = $100
The amount of monthly payment for the loan = $20
The function rule for the balance of the function f(p) where p is the number of payments is given as follows;
The balance on the loan, f(p) = The loan amount less the total amount paid
The total amount payment Jeania has made = Amount of monthly payment × Number of months paid, p
The total amount payment Jeania has made = $20 × p
∴ The balance on the loan, f(p) = $100 - $20 × p
Which gives;
f(p) = $100 - $20 × p.
Select the correct answer. This set of ordered pairs defines a function. {(-49,7), (-56,8), (-63,9), (-70,10)} Which table represents the inverse of the function defined by the ordered pairs? A.
In the future, you should post all possible answer choices to have a complete post. However, there's enough information to get the answer.
The original set has points in the form (x,y)
The first point is (x,y) = (-49,7) making x = -49 and y = 7. When we find the inverse, we simply swap the x and y values. The inverse undoes the original function and vice versa. So if (-49, 7) is in the original function, then (7, -49) is in the inverse. The rest of the points follow the same pattern.
We end up with this answer
{ (7, -49), (8, -56), (9, -63), (10, -70) }
help me plz plz....
Answer:
4775.9 [tex]cm^3[/tex]
Step-by-step explanation:
To find the volume of a cone use the expression [tex]\pi r^2\frac{h}{3}[/tex]
r = radius
h = height
Now substitute h for 27 and r for 13, [tex]\pi 13^2\frac{27}{3}[/tex]
First do 13 x 13 (because of the exponent), then divide 27 and 3, which is 9
169 x 9 = 1521
Lastly multiply by pi or use 3.14
1521 x 3.14 = 4775.94
Since it asks to round to the tenth it is just 4775.9
Answer:
4778.4 cm^3
Step-by-step explanation:
The formula for the volume of a cone is [tex]V=\pi r^2\frac{h}{3} \\[/tex].
In this case, the height is 27 and the radius is 13, so we plug in the values and get [tex]V = \pi (13)^2 \frac{27}{3}\\[/tex].
We solve and get the volume of the cone as [tex]1521\pi[/tex] or 4778.4 cm^3.
* Graph these numbers on a number line.
-5,3, -2,1
-5
-5,3,-2,1 on a number line
<-|----|----|----|----|----|----|----|----|->
-5 -2 0 1 3
This is a very hard math question. Whoever answers correctly will get a brainlist too! Find the value of b. Then find the angle measures of the pentagon.
Answer:
Below
Step-by-step explanation:
The sum of the 5 angles is 540°
● b+(b+45)+90+(2b-90)+(3/2)b = 540
3/2 is 1.5
● b+b+45+90+2b-90+1.5b = 540
● 2b +45+2b+1.5b = 540
● 5.5 b +45 = 540
● 5.5b = 495
● b = 495/5.5
● b = 90°
Answer:
b = 90
Step-by-step explanation:
b + (b + 45) + 90 + (2b - 90) + (3/2)b = 540
b + b + 45 + 90 + 2b - 90 + (3/2)b - 90 = 540 - 90
b + b + 45 + 2b - 90 + (3/2)b = 450
2b + 2b + (45 * 2) + (2 *2b) - (90 * 2) + (2 * (3/2)b) = 450 * 2
2b + 2b + 90 + 4b - 180 + 3b = 900
11b - 90 = 900
11b - 90 + 90 = 900 + 90
11b = 990
b = 990 / 11
b = 90
check:
b + (b + 45) + 90 + (2b - 90) + (3/2)b = 540
90 + (90 + 45) + 90 + (2*90 - 90) + (3/2)*90 = 540
90 + 135 + 90 + 90 + 135 = 540
540 = 540 --- OK
pls help. A granola mix sells for $8.99 a pound. Tung wants to buy a bag of granola mix that weighs 7.8 pounds. The bag of granola mix will cost about $16. $17. $63. $72.
Answer:
about 72 dollars
Step-by-step explanation
"about" tells us to round our numbers. Therefore, 7.8 becomes 8. As each pound is $8.99, we multiply the two and get 71.92, which is "about" 72.
Answer:
$72
Step-by-step explanation:
To find the cost, multiply the price per pound by the number of pounds.
8.99(7.8)
= 70.12
This is closest to $72
round 12.1975 to the nearest thousandth.
Answer:
12.198
Step-by-step explanation:
the thousandth is the third digit after the decimal point, so you round the next number after it, which is 5. so you round it up, ends with 12.198
We get 12.198 after rounding it to the nearest thousandth.
How to round off decimal places?The rounding off decimal places is similar to the basic round-off. We check the previous number. If it is greater than or equal to 5, we increase the value up to which we are rounding by 1, or else keep it the same when the previous digit is less than 5.
The order of digits for decimal places is opposite to the normal number system.
In the number system we have units place, then tens place, then hundreds place, then thousands place, and like that.
In the decimal number system, we start from the highest and go on decreasing.
The first decimal place is the tenth place.
The second decimal place is the hundredth place.
The third decimal place is the thousandth place.
And so on.
How to solve the question?In the question, we are asked to round 12.1975 to the nearest thousandth.
As discussed above, the nearest thousandth means rounding off up to the third decimal place.
So we round off 12.1975 up to the third decimal place, that is, we round off up to 7.
The next digit is 5, so we increase 7 by 1 to 8.
Thus, we get 12.198 after rounding it to the nearest thousandth.
Learn more about rounding off decimal places at
https://brainly.com/question/21583892
#SPJ2
A soma de dois números consecutivos é 11, qual expressão algébrica representa este contexto? * 1 ponto a) X + X + 1 = 11 b) X + X = 11 c) X + X – 1 = 11 d) X + 1 = 11
Answer:
a) X + X + 1 = 11
Step-by-step explanation:
Em matemática, a soma de consecutivos é expressa matematicamente como:
X + (X + 1) + (X + 2) + (X + 3) .............
Na pergunta acima, somos solicitados a encontrar a expressão algébrica que indica que a soma de DOIS inteiros consecutivos é igual a 11
Portanto, esta expressão algébrica é dada como:
X + (X + 1) = 11
X + X + 1 = 11
Portanto, a opção a) X + X + 1 = 11 é a opção correta
What is the y−intercept of the line that passes through the point (4,9)and is parallel to the line y=12x+2?
Answer:
y- intercept = - 39
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 12x + 2 ← is in slope- intercept form
with slope m = 12
Parallel lines have equal slopes, thus
y = mx + c ← is the partial equation
To find c substitute (4, 9) into the partial equation
9 = 48 + c ⇒ c = 9 - 48 = - 39 ← y- intercept
Answer:
y-intercept = -39
Step-by-step explanation:
if two lines are parallel it means they have the same gradient so we compare the equation given to the default equation of a line
y=mx+c
y=12x+2
comparing we have the gradient m=12 now finding the equation of the line parallel to the given line we use
y-y1=m(x-x1)
y1=9 and x1=4
y-9=12(x-4)
y-9=12x-48
y=2x-48+9
y=2x-39
comparing to the default equation of a line y=mx+c where c is the y-intercept
therefore the y-intercept is -39
If a person invests $250 at 9% annual interest, find the approximate value of the investment at the end of 15 years
Answer:
The end balance is $910.62 and the total interest $660.62. (That is without tax or inflation rate) I hope this helps.
Step-by-step explanation:
Answer:
without tax: interest total=$660.62
Step-by-step explanation:
I multiplied...
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
Answer:
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Step-by-step explanation:
what is the perimeter of rhombus ABCD ?
Answer:
20
Step-by-step explanation:
Since you can use the Pythagorean theorem to calculate the length of the hypotenuse, each side can be found to be 5. There are four equal sides, so it is 20.
9/2 divided by 1/4= ? in simplest form
Answer: 18
Do Keep Change Flip (KCF)
Keep: 9/2
Change: ÷ into ×
Flip: 1/4 into 4/1
Your new problem should be 9/2×4/1
Multiply
9/2×4/1=36/2
36/2=18
Final Answer: 18
