How do i do this problem x-2y=1,for y?
A rectangle's width is 6 feet less than its length. If the area of the rectangle is 247 square feet, what is its length, in feet?
Answer:
Length is 19 feet.
Width is 13 feet.
Step-by-step explanation:
Let the length of the rectangle be = L feet
The width is 6 feet less than its length, so width is = L-6 feet
The area of the rectangle is 247 square feet, means length x width = 247
[tex]L(L-6)=247[/tex]
[tex]L^{2} -6L=247[/tex]
[tex]L^{2} -6L-247=0[/tex]
Now here a = 1, b = -6 and c = -247
So, putting these in quadratic equation formula, we get
[tex]L=\frac{-(-6)+\sqrt{(-6)^{2}-(4)*(1)*(-247) } }{2*1}[/tex]
This gives L=19 or -13
As it is a dimension, so we will neglect the negative value.
Hence, L = 19 feet
Width = [tex]19-6[/tex] = 13 feet
If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction.
Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"? (Hint: cross products)
Answer: 4n + 12 = 3d
Step-by-step explanation:
The equation representing "If the numerator of a fraction is increased by 3, the fraction becomes 3/4" is 4(x + 3) = 3y. This, alongside the second condition of the denominator decreased by 7 leading to the fraction becoming 1, provides two equations that can be solved for the original fraction.
Explanation:To represent the situation "If the numerator of a fraction is increased by 3, the fraction becomes 3/4," we can use the variable x for the numerator and y for the denominator of the original fraction. Therefore, the equation would be (x + 3)/y = 3/4. Applying the cross-product rule, we multiply each side of the fraction by the denominator on the other side, leading to 4(x + 3) = 3y. Simplified, this equation is 4x + 12 = 3y, which helps us solve for the original fraction along with the other given condition that reducing the denominator by 7 makes the fraction equal to 1. So, the second condition can be written as x/(y - 7) = 1. These two equations together can be solved simultaneously to find the values of x and y.
The lengths of plate glass parts are measured to the nearest 1/10 mm. The lengths are discretely and uniformly distributed with values at every 1/10th mm, starting at 590.0 thru 590.9 mm. Determine the mean & variance of lengths.
PLEEEEEEEEASE HELP! How the heck do i figure this out!!!?
Find m
Solve the exponential equation
9^2x = 27
Answer:
The value of x is, [tex]\frac{3}{4}[/tex]
Explanation:
Given:
The exponential equation [tex]9^{2x} =27[/tex] ....[1]
Exponential Identities:
[tex](x^a) =x^{ab}[/tex]
we can write equation [1] as;
[tex](3^2)^{2x} = 3^3[/tex] [ [tex]3 \times 3= 9 , 3 \times 3 \times 3 = 27 [/tex] we can rewrite as [tex]3^2 =9 , 3^3 =27[/tex]]
by using above identities, we have
[tex](3)^{4x} = 3^3[/tex] then,
[tex]4x =3[/tex] [ if [tex]x^a =x^b[/tex] then a =b]
Simplify:
[tex]x = \frac{3}{4}[/tex]
Xavier watched 3/5 of a movie. The entire length of the movie is 2 1/2 hours long. How much of the movie did he watch?
A:1 1/4 hours
B:1 1/2 hours
C:2 1/3 hours
When solving negative one over eight (x + 35) = −7, what is the correct sequence of operations?
Multiply each side by negative one over eight , add 35 to each side
Multiply each side by negative one over eight , subtract 35 from each side
Multiply each side by −8, subtract 35 from each side
Multiply each side by −8, add 35 to each side
"An air traffic controller observes two airplanes approaching the airport. The displacement from the control tower to plane 1 is given by the vector A⃗ , which has a magnitude of 220 km and points in a direction 32 ∘ north of west. The displacement from the control tower to plane 2 is given by the vector B⃗ , which has a magnitude of 140 km and points 65 ∘ east of north.
Sketch the vectors A⃗ , B⃗ , and D⃗ =A⃗ −B⃗ . Notice that D⃗ is the displacement from plane 2 to plane 1. Draw the vectors with their tails at the dot. The orientation of your vectors will be graded. The exact length of you"
Sketch vectors A and B based on their descriptions. To find D = A - B, make B go in the opposite direction (namely, -B), put it tip to tail with A, and then vector D is from tail of A to tip of -B.
Explanation:To answer this, we need to sketch the two vectors - vector A which represents the displacement of plane 1 from the control tower, and vector B which represents the displacement of plane 2 from the control tower. Vector A has a magnitude of 220 km and points 32 degrees north of west. This can be sketched as a line of certain length angling upwards from directly west. Vector B is 140 km in magnitude and angles 65 degrees east of north, thus it can be drawn shorter than Vector A and leaning more towards east from north.
Vector D = A - B is the displacement from plane 2 to plane 1. It represents the direction you would need to go if you were at plane 2 and wanted to get directly to plane 1. To find D, rearrange the equation to D = A + (-B). -B is just the B vector in the opposite direction. After making the B vector go in the opposite direction, place it tip to tail with A and the result from tail of A to tip of -B is vector D. Hence, the vectors would be sketched with their tails at the same point and their heads indicating the direction they point towards.
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In this triangle, the product of sin B and tan C is _____ , and the product of sin C and tan B is _______.
Answer
part 1 = c/a
part 2 = b/a
Sine is the ratio of opposite to hypotenuse respect to as a given angle while tangent is the ratio of opposite to adjacent lengths of a given angle.
Part 1
Sine = opposite/hypotenuse
SinB = b/a
Tangent = opposite/adjacent
TanC = c/b
SinB × TanC = b/a×c/b
= c/a
Part 2
SinC = c/a
TanB = b/c
SinC×TanB= c/a×b/c
= b/a
Please answer !!!the system of equations graphed below has how many solutions ?
A. infinitely many
B. 1
C. 0
D.2
convert the fractions to decimals.
3/20
7/50
9/25
4/15
1/9
9/40
5/16
7/9
13/20
37/50
11/30
19/40
A secretary at the police department makes $8 less per hour than the dispatcher. The combined hourly wage of the secretary and the dispatcher is $40. Which equation could be used to find the hourly wage of the dispatcher?
Is the ordered pair a solution to the system of linear equations?
Select Yes or No.
Yes No
Ordered pair: (−2,2)(−2,2)
System of equations:
−7x+2y=0
6x+6y=0
Sam is five years old his older brother tom is three times as old is sam when salmon is 20 how old will tom be
if 5a = 20b, then b/a=
A. 4
B. 1/4
C. 4/1
D. 10
The ratio b/a is found by dividing both sides of the equation 5a = 20b by 5a, resulting in b/a being B) 1/4.
The question asks us to solve for the ratio b/a given the equation 5a = 20b. To find b/a, we can divide both sides of the equation by 5a:
5a = 20bFrom this, we can see that b/a must be 1/4, since 4 multiplied by 1/4 equals 1. Therefore, the correct answer is B. 1/4.
Doomtown is 300 miles due west of Sagebrush and Joshua is due west of Doomtown. At 9 a.m. Mr. Archer leaves Sagebrush for Joshua. At 1 p.m. Mr. Sassoon leaves Doomtown for Joshua. If Mr. Archer travels at an average speed 20 mph faster than Mr. Sassoon and they each reach Joshua at 4 p.m., how fast is each traveling?
Mr. Archer was going at a speed of approximately 67 mph and Mr. Sassoon was going at a speed of 47 mph (rounded to the nearest whole number).
Explanation:This problem is a typical distance-rate-time problem. Firstly, we can infer based on the travel times for Mr. Archer and Mr. Sassoon that Mr. Archer traveled for 7 hours (from 9 am to 4 pm) and Mr. Sassoon traveled for 3 hours (from 1 pm to 4 pm) to reach Joshua.
Equalizing the distance travelled by both individuals, we have: its clear that 20 mph * 7 hours = Mr. Sassoon's speed * 3 hours. From this, we can easily infer that Mr. Sassoon's speed is [tex]20*7/3 = 46.67[/tex] mph
Since Mr. Archer travelled 20 mph faster than Mr.Sassoon, Mr.Archer's speed was [tex]46.67 + 20 = 66.67[/tex] mph. Therefore, Mr. Archer was going at a speed of approximately 67 mph and Mr. Sassoon was going at a speed of 47 mph (rounded to the nearest whole number).
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Does the equation y = (0.9)x represents exponential growth or decay?Answer
Exponential Growth
Exponential Decay
Exponential decay is demonstrated in the equation y = (0.9)x, showcasing a decrease as x increases.
Exponential decay occurs when the base of the exponential function is between 0 and 1, causing the function to decrease as x increases.
For example, if x = 1, y = 0.9; if x = 2, y = 0.81; and so on.
During a football game, a team lost 9 yards on the first play, then gained 3 yards on each of the next 3 plays. Which integer represents the total number of yards at the end of the first four plays? –3 0 9 18
Answer:
0
Step-by-step explanation:
Translate this sentence into an equation.
The product of Matt's score and
6
is
96
.
Use the variable
m
to represent Matt's score.
Final answer:
The sentence 'The product of Matt's score and 6 is 96' translates to the equation m × 6 = 96. By dividing both sides by 6, the value of Matt's score, denoted as m, is found to be 16.
Explanation:
To translate the given sentence into an equation, you start by identifying the mathematical operation described. The sentence states 'The product of Matt's score and 6 is 96'. The word 'product' indicates multiplication. Next, you use the variable m to represent Matt's score.
The equation that represents this situation is:
m × 6 = 96
To solve for m, you divide both sides of the equation by 6:
m = 96 ÷ 6
m = 16
Therefore, Matt's score is 16.
Is the term (x + 2) a factor of the polynomial shown below?
ƒ(x)=x^4+5x^3+10x^2+20x+24
A. Yes, the remainder is 48.
B. Yes, the remainder is 0. ...?
A certain forest covers an area of 5000km^2 . Suppose that each year this area decreases by 5.75% . What will the area be after 14 years?
...?
The forest with an area of 5000 km² decreases by 5.75% annually. After 14 years, the forest area will be approximately 2,182 km².
The interest that is computed using both the principal and the interest that has accrued during the previous period is called compound interest.
The compound interest formula is:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where,
A is compounded amount
P is principal amoutn
r is the rate of interest
n is the number of times it is compounded
Given that,
Initial forest area (P): 5000 km²
Rate of decrease per year: 5.75% or 0.0575
Number of years (n): 14
Since the area is decreasing,
Therefore r = -0.0575
Plugging in the values in the compound interest formula,
[tex]A = 5000 \times (1 - 0.0575)^{14} \\\\\approx 2,182 \text{ square km}[/tex]
Hence,
After 14 years, the forest area would be approximately 2,182 km².
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What is .66667 as fraction
The decimal .66667 is approximately equivalent to the fraction 2/3. It is understood by recognizing that fractions are essentially divisions, and .66667 is the result of 2 divided by 3.
Explanation:The decimal value of .66667 can be expressed as a fraction. In this case, .66667 is approximately equal to 2/3. To derive this, understand that fractions are a division operation. The decimal .66667 is a result of division where the numerator is smaller than the denominator, which is a characteristic of fractions between 0 and 1. So, if you divide 2 by 3, you will get 0.66667 proving that .66667 is a representation of the fraction 2/3.
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Solve for x.
25/60 = 30/x
25
36
50
72
Answer:
d
Step-by-step explanation:
Which is the correct description of the transformation of figure QRST to figure QꞌRꞌSꞌTꞌ?
A. a 90° counterclockwise rotation around point R of pre-image QRST
B. a 180° clockwise rotation around point R of pre-image QRST
C. a 90° clockwise rotation around point R of pre-image QRST
D. a reflection across point R of pre-image
Answer:
D. a reflection across point R of pre-image
Step-by-step explanation:
Considering this question is over 4 years old I highly doubt you're going to see this question, or maybe you're not even in school anymore. Even after all that being said, I'm still going to ask this:
May I have brainliest please? :)
What is equivalent to 4/16 as a whole number?
2/5, 9/10, 7/5, 19/10, 12/5
Find the common difference between the terms of the following arithmetic sequence. ...?
at a particular college 2/5 of the students take a math class. Of these students 1/4 take basic algebra. WHat fraction of the students take basic algebra. Please show your steps.
A bank account has a beginning balance of $560.00. After 6 months, the balance in the account has increased to $572.60. What interest rate is being earned annually on this account?
15 POINTS. What is the area of the circle segment/shaded area? Picture included please help. Please answer in a way that will fill in the blanks, explanation preferred.
To find the area of a circle segment, you need to know the radius and central angle of the segment. Use the formula Area of Circle Segment = ((central angle/360) x πr²) - 0.5r²sin(central angle) to calculate the area.
Explanation:To calculate the area of the segment or shaded area of a circle, you must first need to know the radius of the circle and the central angle of the segment, as these will be necessary for the calculation. The formula for calculating the area of a segment in a circle is Area of Circle Segment = ((central angle/360) x πr²) - 0.5r²sin(central angle).
For instance, if the circle has a radius of 5 cm and the central angle of the segment is 60 degrees, the area is ((60/360) x π5²) - 0.5 x 5²sin(60), which will give the result when evaluated.
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