Answer: The length is 16 meters and the width is 3 meters.
Step-by-step explanation:
Since we know the length and w, we will represent the length by l and the width by w.
We know the length is 13 more than the width so we will represent it by the equation l = w + 13 .
The width will be represented by w.
We know the area of a rectangle is the length being multiplied by the width.
Since we know the area, multiply the length by the width and set it equal the area and solve for w.
w(w+ 13) = 48 Multiply on the left side
w^2 + 13w = 48 subtract 48 from both sides
-48 -48
w^2 + 13w - 48 = 0 Now find two numbers that their product is -48 and their sum 13.
The numbers 16 and -3 works, because 16* -3 = -48 and 16 + (-3) = 13.
Rewrite the whole equation in this form.
w^2 + 16w -3w - 48 = 0 Now factor on the left side.
w(w + 16) -3(w+16) = 0 Factor out w+16
(w+16)( w-3) = 0 Now set each of the expressions to equal to 0 and solve for w.
w+ 16 = 0 or w-3 = 0
-16 -16 +3 +3
w = -16 or w = 3
-16 can't be use to represent distance so w has to equal 3 and this means the width is 3.
The length is 13 meters more than the width so 3 + 13 will be the width.
l = 3 + 13
l = 16
-1/3u-4=1/4u-1/4
Solve and check
9514 1404 393
Answer:
u = -45/7 = -6 3/7
Step-by-step explanation:
It can work well to eliminate fractions first. Here, we can do that by multiplying by the product of their denominators: 12.
-4u -48 = 3u -3
-45 = 7u . . . . . . . . add 3+4u
-45/7 = u . . . . . . divide by the coefficient of u
__
Check
(-1/3)(-45/7) -4 = (1/4)(-45/7) -1/4
15/7 -4 = -45/28 -7/28
-13/7 = -52/28 . . . true
Which expression would be easier to simplify if you used the commutative property to change the order of the numbers? A. 30+(-12)+70 B. -10 +(-20) + 1/2 C. 60+40+(-25)
Answer: A
Step-by-step explanation:
Ok, some that we always try to do in math is to look for "nice" numbers.
The nice numbers are numbers that are easy to work with.
Examples of these are numbers like 10, 100, etc.
suppose the next example:
9 + 3 + 1 + 7
That may seem a long addition, but we can rearange the numbers in such a way to get:
(9 + 1) + ( 3 + 7) = 10 + 10 = 20
This is specially useful when doing mental calculus.
In the given options, we have:
A) 30 + (-12) + 70
Doing it straightforward, we must:
Subtract 12 from 30, which will give us a not nice number.
30 - 12 = 18
And now add 70 to that:
18 + 70 = 88.
Now, we could use the commutative properety and get:
30 + (-12) + 70 = 30 + 70 + (-12)
in this way, in the first addition we get to 100, and then we subtract 12 units.
(30 + 70) + (-12) = 100 - 12 = 88.
Then the correct option is A.
help and explain!!!
Answer:
the difference is 60 because 55 - 60 = -5
Step-by-step explanation:
what is equivalent to X3. X3.X2
Answer:
X6. X2
Step-by-step explanation:
FedEx charges $8 for the first pound and $0.25 for each additional pound Amazon Prime charges $6 for the first pound and $0.30 for each additional pound which equation determine how many pounds it will take for FedEx and Amazon Prime to cost the same
Answer:
0.20p + 8 = 0.30p + 6
Step-by-step explanation:
Given:
1st case
Fixed charge = $8
Additional charge = $0.25 pound Amazon Prime charges
2nd case
Fixed charge = $6
Additional charge = $0.30 pound Amazon Prime charges
Find:
Equation
Computation:
1st case = 0.20p + 8
2nd case = 0.30p + 6
So,
0.20p + 8 = 0.30p + 6
Find the zero of the function f(x)=4x^2-12x+9
Answer:
x = [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Given
f(x) = 4x² - 12x + 9
To obtain the zero let f(x) = 0 , that is
4x² - 12x + 9 = 0 ← in standard form
(2x - 3)² = 0 ← in factored form , then
2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]
The zero of the function f (x) = 4x² - 12x + 9 will be 3/2.
What is Quadratic polynomial?
A polynomial which has highest power 2 is called a quadratic polynomial.
Given that;
The function is;
f (x) = 4x² - 12x + 9
Now, To find zero of the function we equate the function to zero.
We get;
f (x) = 4x² - 12x + 9
4x² - 12x + 9 = 0
Solve the function by quadratic formula we get;
x = - (-12) ± √12² - 4 × 4 × 9 / 2 × 4
x = 12 ± √144 - 144 / 8
x = 12 ± 0 / 8
x = 12/8
x = 3/2
Thus, The zero of the function f (x) = 4x² - 12x + 9 will be 3/2.
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How many terms are in
3k + m
A hotel has 30 floors with 40 rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to select 120 rooms and survey the registered guest in each of the selected rooms about his or her overall satisfaction with the property. The manager gets an SRS of rooms on the first floor with a water view and another SRS of rooms on the 30th floor with a golf course view. What type of sample was obtained
Answer: Stratified Random Sample
Step-by-step explanation: The type of sampling exemplified by the manager's selection is Stratified Random Sampling whereby the entire population (guests in the hotel) are divided into subpopulation(independent subgroups) called strata; those with rooms facing the golf course and those facing the water view. The sample this have two strata based on the view in which the rooms are facing. Taking a simple random samples from each sub group of the entire population may lead to less bias since the customers may experience different level of satisfaction based on this condition.
The type of sample was obtained when manager gets an SRS of rooms on the first floor with a water view and another SRS of rooms on the 30th floor with a golf course view is Cluster sampling.
What is sampling?
Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population.
Now here, the manager wants to select 120 rooms and survey the registered guest in each of the selected rooms about his or her overall satisfaction with the property.
So, here cluster sampling would be preferred because there are 30 floors and they can be classified as clusters and surveyed per floor.
Thus, the type of sample was obtained when manager gets an SRS of rooms on the first floor with a water view and another SRS of rooms on the 30th floor with a golf course view is Cluster sampling.
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Select all the expressions that are equivalent to (–60) ÷ 5.
(60)÷(−5)
(−60)÷(−5)
(−60)×15
(60)×(−15)
(−60)÷(−15)
help me please !!!!!!
Answer:
yes the answer is C ! none of the other answers are logical
The half-life of cesium-137 is 30 years. Suppose we have a 170-mg sample. What is the rate of decay after 150 years? (Round your answer to three decimal places.)
Answer:
5.313mg
Step-by-step explanation:
The half-life of cesium-137 is 30 years. Suppose we have a 170-mg sample. What is the rate of decay after 150 years? (Round your answer to three decimal places.)
Half life formula
= N(t) = No(1/2)^t/t½
N(t) = Amount after t years
No = Initial amount
t = time
t½ = half life
N(t) = 170 (1/2) ^150/30
N(t) = 170 × (1/2)^5
N(t) = 5.3125mg
Approximately the quantity left after t years = 5.313mg
9 more than 2 multiplied by z
Answer:
9+ 2z
Step-by-step explanation:
What is another word for initial value?
Answer:
Synonyms for initial. basic. introductory. original. antecedent. commencing. first. fundamental. germinal.
Step-by-step explanation:
In ΔUVW, \overline{UW} UW is extended through point W to point X, \text{m}\angle UVW = (3x+4)^{\circ}m∠UVW=(3x+4) ∘ , \text{m}\angle VWX = (8x-12)^{\circ}m∠VWX=(8x−12) ∘ , and \text{m}\angle WUV = (x+20)^{\circ}m∠WUV=(x+20) ∘ . What is the value of x?X?
Answer:
The value of x is 9°
Step-by-step explanation:
The given parameters are;
ΔUVW with side UW extended to X
m∠UVW = (3x + 4)°
m∠VWX = (8x -12)°
m∠WUV = (x + 20)°
We have that m∠UVW + m∠WUV + m∠VWU = 180° (Sum of the interior angles of a triangle theorem)
∴ m∠VWU = 180° - (m∠UVW + m∠WUV)
Also we have that m∠VWX and m∠VWU are supplementary angles, (The sum of angles on a straight line)
∴ m∠VWX + m∠VWU = 180° (Definition of supplementary angles)
m∠VWU = 180° - m∠VWX
∴ m∠VWX = (m∠UVW + m∠WUV)
Substituting the values, gives;
(8x -12)° = (3x + 4)° + (x + 20)°
8x - 3x - x = 4 + 20 + 12
4x = 36
x = 36/4 = 9
x = 9°.
group pf 8 students was asked How many hours of television did you watch last week ? here are their responses ( 11, 19, 18, 17, 5, 19, 16, 19) Find the mean and median number of hours for these student, If necessary round to the nearest tenth
Answer:
Median is 17.5. Mean is 15.5
Step-by-step explanation:
Median is the middle number when ordered from smallest to largest. In this case 17 and 18 are the middle numbers so you split them. Median is the same as the average. Add all the numbers up ( They add to 124) and divide by the total number of responses (8 responses)
Find the standard deviation, , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n503; p0.7
Answer: 10.28
Step-by-step explanation:
For the binomial distribution ,
standard deviation : [tex]\sigma=\sqrt{p(1-p)n}[/tex], where p = population proportion, n = sample size.
Given: n= 503 and p=0.7
Then, [tex]\sigma=\sqrt{503\times0.7(1-0.7)}=\sqrt{105.63}\approx10.28[/tex]
Hence, the standard deviation = 10.28
If the income tax rate is 4%, determine the amount of income tax paid on
an income of $40,000. *
Faith practices the piano 1785 minutes in 5 weeks. At what rate did she practice, in minutes per day?
Answer:
51 minutes of piano practice a day for 5 weeks
Step-by-step explanation:
Is this parallel perpendicular or neither please help
Answer:
Parallel
Step-by-step explanation:
Answer:
pretty sure they're parallel, sorry if I'm incorrect ^^''
3 (j - 1) + 8 < 2
Please solve this do not know the answer I need answer before 9:00
Answer:
j < -1
Step-by-step explanation:
3 (j - 1) + 8 < 2
Distribute
3j -3 +8 < 2
Combine like terms
3j +5 < 2
Subtract 5 from each side
3j+5-5 < 2-5
3j < -3
Divide each side by 3
3j/3 < -3/3
j < -1
Answer:
I < -6 1/3
Step-by-step explanation:
2 divide 3
Subtract 8
Add 1
A restaurant built a ramp to make their facility more accessible to people in wheelchairs. They covered the entire surface of the ramp with metal to make it more durable. How much metal did they use to cover the ramp, including the bottom? Give an exact answer (do not round).
Answer:
3.41 m² of metal would be needed to cover the ramp
Step-by-step explanation:
The ramp has the shape of a triangular prism.
A triangular prism is a prism that has two equal triangles as base connected by three lateral faces.
The surface area of a triangular prism is the sum of the area of its base and lateral faces.
The surface area = 2B + PH
Where B is the area of the base , H is the height of the prism and P is the perimeter of the triangular base
Hence:
B = 0.5 * 1 m * 0.8 m = 0.4 m²
h = 1 m
P = 1 m + 0.8 m + 0.81 m = 2.61 m
Surface area = 2 * 0.4 m² + 2.61 m × 1 m = 3.41 m²
3.41 m² of metal would be needed to cover the ramp
Answer:
1.79
Step-by-step explanation:
1. An industrial machine is able to make 30 pens in 5 seconds. What is the rate made per second?
2. A fair owner made 8 dollars when a group of 2 people entered, which is a rate of ___ dollar per person.
3. A bouquet had 6 flowers and sold for $30, which is a rate of $___ per flower
4. It took a pet store 7 weeks to sell 56 cats. What is the rate sold per week?
5. During the lunch rush a fast food joint sold 10 sodas and earned $50, which is a rate of ___ dollars per soda.
6.Cody earned $50 for mowing 5 lawns. What is the rate earned per lawn mowed?
7. A jogger travelled 14 kilometers in 2 days. What is the rate he travelled per day?
8. A toy company used 8 pints of plastic to make 4 action figures, which is a rate of ___ pints per figure.
9. A scientist used 6 gallons of liquid for every 8 hours he works. He uses ____ of a gallon each hour he works.
NEED ALL ASAP PLZ
Compare using >, =, or < 3 -3
Answer:
3>-3
Step-by-step explanation:
3 is larger than -3
write the linear equation is standard form
slope is 4/7, and (1, 3) is on the line.
Answer:
4/7x - y = -17/7
Step-by-step explanation:
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
Step 1: Define
m = 4/7
Random point (1, 3)
Step 2: Find slope-intercept form
y = 4/7x + b
3 = 4/7(1) + b
3 = 4/7 + b
b = 17/7
y = 4/7x + 17/7
Step 3: Find Standard Form
-4/7x + y = 17/7
-(4/7x - y) = 17/7
4/7x - y = -17/7
Find the distance between -433 and 237 on the number line.
Answer:
670
Step-by-step explanation:
433+237=670
because to find it you are supposed to subtract like this
x-y
but for this equation, it will look like this
237-(-433) (Negative times negative is always positive)
which is 433+237 which is 670
Hope this helps!
-3x-y=-24
convert to slope intercept form
Answer:
y = - 3x + 24
Step-by-step explanation:
Step 1:
y = mx + b Slope Intercept Form
Step 2:
- 3x - y = - 24 Equation
Step 3:
- 3x = y - 24 Add y on both sides
Step 4:
- 3x + 24 = y Add 24 on both sides
Answer:
y = - 3x + 24
Hope This Helps :)
At age 23, someone sets up an IRA (individual retirement account) with an APR of 8%. At the end of each month he deposits $35 in the account. How much will the IRA contain when he retires at age 65? Compare that amount to the total deposits made over the time period
Answer:
FV= $146,002.59
Step-by-step explanation:
Giving the following information:
Monthly deposit= $35
Number of periods= (65 - 23)*12= 504 months
Interest rate= 0.08/12= 0.0067
To calculate the future value, we need to use the following formula:
FV= {A*[(1+i)^n-1]}/i
A= monthly deposit
FV= {35*[(1.0067^504) - 1]} / 0.0067
FV= $146,002.59
Susan has a collection of 50 nickels and dimes. If the number of nickels is four times the number of dimes, how many nickels and how many dimes does she have?
Answer:
Susan has:
40 nickels & 10 dimes
Step-by-step explanation:
Since she has a total of 50 nickles and dimes I knew that it could be separated into 5 sets of 10. Knowing that 4(10) is equal to 40+10 is equal to 50, I used the 10 for the amount of dimes and used 40 for the amount of nickles. So the nickles (40) are 4 times the dimes (10). We can prove this by multiplying the dimes by 4 (4(10)) and you get 40 and add on the 10 you get the total amount of 50.
I hope this helps:)
There are 40 nickels and 10 Dimes.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let N be the number of nickels
Let D be the number of dimes
Susan has a collection of 50 nickels and dimes.
N + D =50...(1)
Number of nickels is four times the number of dimes
N = 4D
Substitute N in equation 1
4D+D=50
5D=50
Divide both sides by 5
D=10
Now put D value in equation 1
N+10=50
Subtract 10 from both sides
N=40
Hence, there are 40 nickels and 10 Dimes.
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Dave and Steve are 700 meters apart from each other on a straight path. Both start walking toward each other and meet each other after 7 minutes. Dave covers a distance of x meters in one minute, which is 20 meters less than the distance Steve covers in a minute. Which of these equations can be used to find the rate at which Steve and Dave walk?
Options :
A. 7x -(7x+20)=700
B.7x + 7(x+20) =700
C. 7x + (7x-20)=700
D.7x - 7(x-20) =700
Answer:
B.) 7x + 7(x+20) =700
Step-by-step explanation:
Given that :
Dave and Steven are 700m apart
They start walking towards each other and meet after 7 minutes
Distance covered by Dave per minute = x
Distance covered by Steven per minute = x + 20
rate = distance per minute
Dave's rate = x / minute
Steven's rate = (x + 20) / minute
Distance = rate * time
Distance covered by DAVE :
X /min * 7 = 7x
Distance covered by STEVEN :
(x + 20) * 7
= 7(x + 20)
Hence, the sum of distances covered by both Dave and Steven should add up to the total distance :
7x + 7(x + 20) = 700
The rate of change for a vertical line is zero.
Answer:
Not a question, and also incorrect (sorry)
Step-by-step explanation:
The rate of change for a vertical line is undefined.
The rate of change for a HORIZONTAL line is 0
Theoretically, the rate of change for a vertical line is not zero it is undefined.
What is the average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Zero rates of change refer to a quantity that does not fluctuate over time.
But bear in mind these two separate circumstances: Horizontal lines have a slope of 0 since the vertical change is 0.
As 0 cannot be split into any integer, there is no slope for vertical lines since there is no horizontal change.
Because of this, the rate of change for a vertical line is not zero but rather is unknown.
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