Answer:
The system has infinite solutions
Is a consistent dependent system
Step-by-step explanation:
we have
First equation
[tex]\frac{1}{2}x-\frac{1}{3}y=5[/tex]
Isolate the variable y
[tex]\frac{1}{3}y=\frac{1}{2}x-5[/tex]
Multiply by 3 both sides
[tex]y=\frac{3}{2}x-15[/tex] ----> equation A
Second equation
[tex]x=\frac{2}{3}y+10[/tex] -
Isolate the variable y
[tex]\frac{2}{3}y=x-10[/tex]
Multiply by 3/2 both sides
[tex]y=\frac{3}{2}x-15[/tex] ---> equation B
Compare equation A and equation B
The equations are identical
therefore
The system has infinite solutions
Is a consistent dependent system
If 2d÷4=5, does 2d÷4+6=5+4
Answer:
3/2d
Step-by-step explanation:
ad 5 and 4 then subtracts 6 from both sides then divide 2 from 3 and get 3/2
Solve the equation.
9 + n/5 = 19
A 50
B 140
C 104
D 86
Answer:
50
Step-by-step explanation:
If a(x)=2x-4 and b(x) =x+2, which of the following expressions produces a quadratic function?
Answer:
[tex](ab)(x)[/tex]
Step-by-step explanation:
The complete question in the attached figure
we have
[tex]a(x)=2x-4\\b(x)=x+2[/tex]
we know that
(ab)(x) is equal to the product of a(x) and b(x)
so
[tex](ab)(x)=(2x-4)(x+2)[/tex]
Applying distributive property
[tex](ab)(x)=2x(x)+2x(2)-4(x)-4(2)[/tex]
[tex](ab)(x)=2x^2+4x-4x-8[/tex]
[tex](ab)(x)=2x^2-8[/tex]
This is a quadratic equation
The other expressions not produce a quadratic equation
will the account balance be aller 17 years!
3) Ashley invests $4,650 in a savings
account with a fixed annual interest rate of
9% compounded 12 times per year. What
will the account balance be after 12 years?
Answer:
Account balance after 17 years: $21,352.27
Step-by-step explanation:
Use the formula for amount after compound interest.
A = P(1+i)ⁿ
What the variables mean:
"A" is for amount after the time period.
"P" is principal, meaning starting money.
"i" is the interest per compounding period.
"n" is the total number of compounding periods.
"c" is the compounding periods each year. (annual = 1; monthly = 12, etc)
To calculate "i":
i = r/c
"r" is the annual interest rate in decimal form.
To calculate "n":
n = t*c
"t" is the time, usually the number of years.
Now can combine these formulas:
[tex]A = P(1+\frac{r}{c})^{t*c}[/tex]
What do we know from the problem?
t = 17 years
P = 4650
r = 9% = 0.09
c = 12
Substitute them into the formula.
[tex]A = P(1+\frac{r}{c})^{t*c}[/tex]
[tex]A = 4650(1+\frac{0.09}{12})^{17*12}[/tex] Simplify
[tex]A = 4650(1.0075)^{204}[/tex] Do the exponent with a calculator
[tex]A = 4650(4.59188689)[/tex] Multiply
[tex]A = 21352.274[/tex] Unrounded answer
A ≈ 21352.27 Round down because "4" is less than 5.
Therefore Ashley's account balance after 17 years will be $21,352.27.
Consider the line segment shown on the coordinate plane. What are the coordinates of midpoint AB?
A- (-1, 1/2)
B- (1, 1/2)
C - (1, -1)
D-(1,2)
91.8% of 648 toy robots on an assembly line will be approved by the quality control inspector. Write and
solve a proportion to find how many robots will be approved.
Answer:
595 will be approved.
Step-by-step explanation:
Multiply 648 by 0.918: the result is 594.9, which should be rounded up to 595.
An item is regularly placed at $87. Laura bought it on sale for 55% off the regular price. How much did Laura pay?
Answer:
$39.15
Step-by-step explanation:
87 x .55 = 47.85
87-47.85= 39.15
Answer:
$39.15
Step-by-step explanation:
87 x 55%
87 x 0.55 = 47.85
87 - 47.85 = 39.15
ILL MARK YOU BRAINLIEST IF YOU ANSWER CORRECTLY
Write in scientific notation: 0.0042
A) 42 x 10^-2
B) 4.2 x 10^-4
C)4.2 x 10^-3
D).42 x 10^-4
---------------------------------------------------
write in standard notation:6.12 x 10^3
A)6120
B)612
C) 61,200
D)61.2
Answer:
Scientific Notation:
4.2 × 10^-3
E-Notation:
4.2e-3
Engineering Notation:
4.2 × 10^-3
Real Number:
0.0042
Step-by-step explanation:
What is the area of the figure?
Answer:
you have to multiply to get the answer because it's an area not premiter. premiter you at all at once
Answer:
Total area= [tex]28 +25.12= 53.12[/tex] square feet
Step-by-step explanation:
The total area of the 2-D figure= Area of triangle in the fig. + Area of the semicircle in it.
Area of the triangle in the figure [tex]=\frac{1}{2}*Base*Altitude \\\\=\frac{1}{2}*8*7\\\\ =\frac{56}{2} \\\\=28[/tex] square feet
Area of the semicircle=
[tex]\frac{\pi r^2}{2} \\\\\frac{3.14*4*4}{2}\\\\ 3.14*8\\\\25.12square feet[/tex]
Total area= [tex]28 +25.12= 53.12[/tex] square feet
There are 5 pennies for every 6 quarters in Ahmed's pocket. Could Ahmed have a total of 30 coins in his pocket? Explain
Ahmed cannot have total of 30 coins in his pocket
Solution:
Given that,
There are 5 pennies for every 6 quarters in Ahmed's pocket
We are asked if Ahmed can have a total of 30 coins in his pocket
From given,
5 pennies for every 6 quarters
Therefore, ratio is:
penny : quarter = 5 : 6
Total = 5 + 6 = 11
Then the total number of coins must be multiple of 11
But 30 is not a multiple of 11
Therefore, Ahmed cannot have total of 30 coins in his pocket
No, Ahmed cannot have a total of 30 coins in his pocket.
Explanation:Yes, Ahmed could have a total of 30 coins in his pocket.
To determine how many quarters and pennies Ahmed could have, we can set up a ratio.
The ratio of pennies to quarters is 5:6.
Let the number of quarters be represented by 6x, where x is a positive integer. Then, the number of pennies would be 5x.
To find out if Ahmed could have a total of 30 coins, we need to solve the equation 6x + 5x = 30.
Combining like terms, we obtain 11x = 30. By dividing both sides of the equation by 11, we find that x = 2.7272 (repeating).
Since x must be a positive integer, we can conclude that Ahmed cannot have a total of 30 coins in his pocket.
Learn more about Coins here:https://brainly.com/question/29869268
#SPJ3
one fifth ÷ 4 = ⬜
Luis said the solution is 20.
Matt said the solution is .1/20
Who is correct? Explain your reasoning.
Matt said the solution 1/20 is the correct answer.
Step-by-step explanation:
step 1 :
one fifth ÷ 4 = one part in five equal parts / 4
= (1/5) / 4
The expression can be written as (1/5) / (4/1)
step 2 :
To solve the division of fractions, take reciprocal of the denominator and do multiplication.
The reciprocal of denominator (4/1) is 1/4.
step 3 :
(1/5) / (4/1) = (1/5) [tex]\times[/tex] (1/4)
= 1/20
∴ Matt said the solution is 1/20 is correct.
You have two fair, six-sides dice. However, the dice have been modified so that instead or 1,2,3,4,5,6 the sides are numbered 1,2,2,2,3,4.
What is the probability the total of the two dice is an even number?
Answer:
.
Step-by-step explanation:
Answer:
5/9.
Step-by-step explanation:
Prob ( first dice = 2 and second = 2) = 1/2 * 1/2 = 1/4
Prob ( first = 2 , second = 4) = 1/2 * 1/6 = 1/12
Prob ( first = 4 and second = 2) = 1/12.
Prob ( first = 3 and second = 1 ) = 1/36
Prob ( first = 1 and second = 3) = 1/36.
Prob ( first = 3 and second = 3) = 1/6 *1/6 = 1/36.
Prob (first = 1 and second = 1 = 1/36.
Prob (first = 4 and second = 4 = 1/36.
Required probability is the sum of these which is:
5/9.
I hope I've thought of all the possible outcomes.
What is the quotient of the following division problem?
x + 1 StartLongDivisionSymbol x squared + 3 x + 2 EndLongDivisionSymbol. minus x squared + x to get a remainder of 0 ) 2 x + 2. minus 2 x + 2 to get a remainder of 0 and a quotient of x + 2.
The quotient of x + 1 StartLongDivisionSymbol x squared + 3 x + 2 EndLongDivisionSymbol is x+2
Step-by-step explanation:
We need to find quotient of x^2+3x+2 divided by x+1
The division is shown in figure attached.
Quotient: x+2
Remainder: 0
The quotient of x + 1 StartLongDivisionSymbol x squared + 3 x + 2 EndLongDivisionSymbol is x+2
Answer:
x+2
Step-by-step explanation:
15 inches increased by 20%
Answer:
18
Step-by-step explanation:
15 + Percentage increase =
15 + (20% × 15) =
15 + 20% × 15 =
(1 + 20%) × 15 =
(100% + 20%) × 15 =
120% × 15 =
120 ÷ 100 × 15 =
120 × 15 ÷ 100 =
1,800 ÷ 100 =
18
16^(3-3r)=256 can someone please help me solve this!! Thanks!!
Answer:
The value of r is 1/3
Step-by-step explanation:
Let's solve for r in the equation:
16 ^(3-3r) = 256
16 ^(3-3r) = 16²
3 - 3r = 2
-3r = 2 - 3
-3r = -1
r = -1/-3
r = 1/3
Let's prove r = 1/3 is correct:
16 ^(3-3r) = 256
16 ^ (3 - (3 * 1/3)) = 256
16 ^ (3 - 1) = 256
16 ² = 256
16 * 16 = 356
We proved that r = 1/3 is correct
Write an equation for h.
Answer:
h = 96/8
Step-by-step explanation:
In this image, we're being shown a rectangle. To solve for a rectangle, you use:
Area = base x height
We know the base and area already, so we can plug those values in. It will then look like this:
96 ft = 8ft x height
In order to make it into "h = _____" we need to isolate the height. We can use inverse operation for that. We can divide 8 on both sides. This will then give us the equation:
h = 96/8
Hence, the answer to this is "h = 96/8". If you have any further concerns or questions, feel free to leave a comment below! Have a great day!!! :)
Amy has a collection of marbles in three sizes, small, medium, and large. She has five times as many small marbles as medium marbles. The number of large marbles is two more than three times the number of medium marbles.
Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
Write an algebraic expression to represent the number of large marbles she has.
If Amy has a total of 560 marbles, how many of each size does she have? Show your work.
Answer:
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
i) Let the number of small marbles be x
ii) let the number of medium marbles be y
iii) let the number of large marbles be z
iv) Amy has 5 times as many small marbles as medium marbles therefore we can write 5y = x
v) the number of large marbles is two more than than three times the number of medium marbles therefore we can write
z = 3y + 2
vi) Amy has a total of 560 marbles therefore we can write x + y + z = 560
vii) Therefore from i) we can write x = 5y
viii) using vii) and v) in vi) we can write
x + y + z = 5y + y + 3y + 2 = 560
ix) Therefore 9y = 558 .... therefore y = [tex]\frac{558}{9}[/tex] = 62
x) Therefore from i) we get x = y [tex]\times[/tex] 5 = 62 [tex]\times[/tex] 5 = 310
xi) Therefore z = (3 [tex]\times[/tex] 62) + 2 = 188
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Given tan A =7/24, find the sin B and tan b. A. 7/25 B. 24/7 C. 24/25 D. 7/24
Question:
Given tan B =7/24, find the sin B
Answer:
Option A
[tex]sin\ B = \frac{7}{25}[/tex]
Solution:
Given that,
[tex]tan\ B = \frac{7}{24}[/tex]
We have to find sin B
We know that by trignometric ratios,
[tex]tan = \frac{opposite}{adjacent}[/tex]
From given,
[tex]tan\ B = \frac{7}{24}[/tex]
On comparing we get,
Opposite = 7
Adjacent = 24
We can find the hypotenuse
[tex]hypotenuse^2 = opposite^2 + adjacent^2\\\\hypotenuse^2 = 7^2 + 24^2\\\\hypotenuse^2 = 49 + 576\\\\hypotenuse^2 = 625\\\\Take\ square\ root\ on\ both\ sides\\\\hypotenuse = 25[/tex]
Thus Sin B is given as:
[tex]sin\ B = \frac{opposite}{hypotenuse}\\\\sin\ B = \frac{7}{25}[/tex]
Thus, sin B is [tex]\frac{7}{25}[/tex]
The equation of a straight line is y+10=5x
Answer:
y=5x-10
Step-by-step explanation:
y+10=5x
y=5x-10
At how many points does the graph of the function below intersect the x-
axis?
y= 16x2 - 8x+1
Apex
Answer:
1
Step-by-step explanation:
Which function is not linear?
tof
Select one:
O a. f(x)=5/x
O b. f(x)=3x4
O c. f(x)=-7x
O d. f(x)=5
Answer:
f(x)=-7x is the only one linear
Step-by-step explanation:
I'm wondering if this is mistake or not with your question, but if you graph each function, all but one graph is linear.
Amy drove to her mothers house, which is 204 miles away. If it took her 3 hours, what was her average speed?
68 m/s was her average speed
Amy's average speed was 68 mph (miles per hour)
Calculating average speedFrom the question, we are to determine what Amy's average speed was
Average speed can be calculated by using the formula,
[tex]Average\ speed =\frac{Distance}{Time}[/tex]
From the given information,
Distance covered = 204 miles
Time = 3 hours
Then
Average speed = [tex]\frac{204}{3}[/tex]
Average speed = 68 mph (miles per hour)
Hence, Amy's average speed was 68 mph (miles per hour)
Learn more on Calculating average speed here: https://brainly.com/question/6504879
(15x+29)=(26x-4) whats value of x
Summer exercises for 0.5 hour on Monday Wednesday and Friday each week. How many hours will she exercise in four weeks
Answer:
She will exercise for 6 hours in four weeks.
Step-by-step explanation:
Summer exercises for 0.5 hour on Monday, 0.5 hour on Wednesday, and 0.5 hour on Friday. There are 3 days where she exercises for 0.5 hour.
3 days X 0.5h = 1.5h each week
For four weeks, multiply the hours each week by 4.
1.5h X 4 weeks = 6h
Therefore Summer will exercise for 6 hours over the course of 4 weeks.
Answer:
6 hours
Step-by-step explanation:
We know that Summer exercises for 0.5 (Or a half) hour every day, three days a week (Monday, Wednesday, Friday). We need to found out how many hours she exercises in 4 weeks.
To solve this we first find out how many hours she exercises in one week. To do so, we set up an equation like this:
(Time exercising) x (# of days exercising) = (Hours spent exercising in one week)
Plug in the given numbers:
0.5 x 3 = 1.5 hours
If we know she exercises 1.5 (Or one and a half) hours in 1 week, we multiply this number by 4 to find out how many hours she exercises in 4 weeks. This can be shown in an equation like this:
1.5 x 4 = 6
So Summer will exercise for 6 hours in 4 weeks.
A metal worker makes a box from a 15inch by 20inch piece of tin by cutting a square with a side length x out of each corner and folding up the sides
a) write expressions for length width and height of the box
b) write a polynomial for the volume of the box
Answer:
a) Length = (20 - 2x) inches
Width = (15 - 2x) inches
b) Volume = (20 - 2x)(15 - 2x)x cubic inches.
Step-by-step explanation:
A metalworker makes a box from 15 inches by 20 inches piece of tin by cutting a square with a side length x out of each corner and folding up the sides.
a) So, the length of the box will become (20 - 2x) inches.
And, the width of the box will become (15 - 2x) inches.
b) The volume of the box will be = (Length × Width × Height)
= (20 - 2x)(15 - 2x)x cubic inches. (Answer)
(b) John begins his jogging workout by running faster and faster for about a minute. Once he hits a comfortable pace, he
runs at that pace for several minutes. Then he gradually slows down to a stop over the next few minutes.
Speed
Speed
Speed
Speed
Time
Time
Time
Time
Answer:
What am i supposed to answer?
A post it note has an area of A square inches. The width of the post it note is 4 inches.which equation represents X the length of the post it note in inches A X=4/A. B. X=A+2(4) C. X=A/4. D. X=A-2(4)
Answer:
Option C. X=A/4
Step-by-step explanation:
we know that
The area of the rectangular post it note is equal to
[tex]A=LW[/tex]
where
L is the length
W is the width
In this problem we have
[tex]W=4\ in\\L=X\ in[/tex]
substitute
[tex]A=4X[/tex]
solve for x
That means ----> isolate the variable x
Divide by 4 both sides
[tex]X=\frac{A}{4}[/tex]
1/2 + 1/3 (6/7 + 15/28)
452 multiplied by 36
Answer:
16272
Step-by-step explanation:
Answer:
16272
Step-by-step explanation:
the answer would be 16272.
and if u need help with anything else you can easily use me :) jkjk use a calculator
James is considering buying a home priced at $104,000. If the current market
is a buyer's market, which of the following is most likely not the price James
will end up paying for the house?
A. $100,000
B. $106,000
C. $102,000
D. $103,000
Answer:
B. $106,000
Step-by-step explanation: