A rectangle has an area of 50 square
centimeters. The width is 5 more than 1 times
the length. Find the length and width, in
centimeters, of the rectangle.
Show your work here
The measurements of the rectangle are 10 cm and 5cm.
What is rectangle?
A rectangle could be a quadrilateral with four right angles in geometer geometry. It may be outlined as an angulate quadrilateral as a result of all of its angles square measure equal; or a quadrangle with a right angle.
Main Body:
Let the width be x.
According to question :
width is 5 more than 1 times the length(l), so
length (l) = width -5
Area if rectangle = 50 cm²
Formula for area of rectangle = length * width
⇒50 = x*(x-5)
⇒50 = x² - 5x
⇒x² - 5x - 50 =0
splitting the middle term
⇒x²- 10x +5x -50 = 0
⇒x(x-10) +5(x-10)
⇒(x-10)(x+5)
Hence the value for x = 10 or -5 .
but length can never be -ve so x= 10.
Width = 10 cm
length = width -5
length = 10 -5
l = 5cm
Hence Measurements of rectangle are 10cm and 5cm.
To know more about rectangle clicK on the link below
https://brainly.com/question/25292087
#SPJ1
the sum of two nonzero real numbers is 44 times their product. what is the sum of the reciprocals of the two numbers?
The sum of the reciprocal of the two numbers is 44.
Let a and b be the two number
It is given that the sum of the number is equal to 44 times their product.
So from this, we get an equation:
a + b = 44 ab -------(1)
Now we have to find the sum of the reciprocal of the two numbers.
1/a + 1/b = b + a/ ab
= a + b / ab -------(2)
As from equation (1) we have
a + b/ ab = 44
Now put this value in equation (2) we get
1/a + 1/ b = 44
Therefore the sum of the reciprocal of the two numbers is 44.
To know more about the reciprocal refer to the link given below:
https://brainly.com/question/27590585
#SPJ4
A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.
Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.
Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.
a. The ramp dimensions of 15 feet away and 3 feet above do not meet the ADA guidelines.
b. A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.
How to verify if the ramp meets the guideline?The verification if the ramp meets the guidelines is made with the slope of the ramp, which is the ratio of the vertical distance of the ramp by the horizontal distance of the ramp, obtained dividing these two measures.
The measures are given as follows:
Vertical distance: The rise of 3 feet.Horizontal distance: 15 feet.Hence the ratio is given as follows:
3/15 = 1/5.
The ratio is greater than the threshold of 1/12, hence the ramp does not meet the guideline.
Keeping the vertical distance, the adequate horizontal distance is obtained multiplying the vertical distance by 13, as the ratio would be of 1/13, hence:
13 x 3 = 39 feet.
More can be learned about the slope concept at brainly.com/question/18090623
#SPJ1
Toby submitted the following work when asked to convert 12 2/3 to an improper fraction
Answer:
a) He didn't add 2.
b) 38/3
plss need help with this
Answer:
The solution is (-2, 4).
Which of the following rational functions is graphed below?
Answer:
C
Step-by-step explanation:
In the graph, you can see an asymptote is happening for x=-5, so look for an equation that divides by 0 for x=-5. That is clearly C, for x=-5 the denominator is 0.
SOS PLEASE HELP QUICKLY WILL MARK BRAINLYIST 15 POINTS
The equations of two parallel lines are given below. Write an equation that gives the relationship between h and k.
Y=3/Kx + 14
y = H/2x + 3
Answer:
See below
Step-by-step explanation:
The equations are in form y = mx + b where m = slope
if the lines are parallel then the slopes are equal :
3/K = H/2 Done.
A line has a slope of -2/3 and passes through the point (-3,8). What is the equation of the line?
A. y = -2/3 x + 6
B. y = -2/3 x + 8
C. y = 6x - 2/3
D. y = 8x - 2/3
Answer:
A
Step-by-step explanation:
a hospital director is told that 54% of the treated patients are insured. the director wants to test the claim that the percentage of insured patients is below the expected percentage. a sample of 200 patients found that 100 were insured. find the value of the test statistic. round your answer to two decimal places.
The value of test statistic is -1.14
Define Standard error.
The standard error (SE)of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM).
Null Hypothesis
P = 0.54
Alternate Hypothesis
P < 0.54
For 0.05 level , the value of Z = 1.645
Decision rule ,
reject null Hypothesis if test statistic Z < -1.645
sample size (n) = 200
sample success (x) = 100
Standard error SE = √(p * (1 - p) / n
= √0.54 * (1 - 0.54) / 200
Standard error SE= 0.0352
Sample proportion (р) = x/n
= 100 / 200 ⇒ 0.5
test statistic Z = (р - P) / SE
= (0.5 - 0.54) / 0.0352
test statistic Z = -1.136 or -1.14
Therefore, the value of test statistic is -1.14
To read more about Standard error.
https://brainly.com/question/1191244
#SPJ4
write and equation for a line that's parallel to y=2x-3 that passes through (-1,6)
Answer:
y=2x+8
Step-by-step explanation:
The slope must be the same so the equation so far is y=2x+b
To find b, you have to multiply the given x value (-1 is the given x value) and then see how much you have to add to reach the given y value (aka 6)
-1*2=-2
6--2=8
b=8
That means that the equation is y=2x+8
What is the area of a triangle if the vertices are at
A(-11, 4)
B(-7, 8)
C(-4, 4)
Answer:
14 square units
Step-by-step explanation:
You want the area of the triangle whose vertices are the points A(-11, 4), B(-7, 8), C(-4, 4).
Area formulaThe area of a triangle is given by the formula ...
A = 1/2bh
where b is the base of the triangle, and h is the height, the1 perpendicular distance to the opposite vertex.
DimensionsThe diagram shows one side is the horizontal line AC. The length of that is the difference of the x-coordinates of the end points:
b = -4 -(-11) = 7
The opposite vertex, B, has a y-coordinate of 8, so the height of the triangle is ...
h = 8 -4 = 4
ApplicationWe now have the information we need to use the area formula:
A = 1/2(7)(4) = 14 . . . . square units
The area of ∆ABC is 14 square units.
__
Additional comment
You can use the diagram and count grid squares to find the dimensions of the triangle.
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.
How do you find the maximum and minimum value of the function?
Calculus can be used to find the critical point, or the x-value of the vertex, by taking the derivative of the function, or f'(x). To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f"(x). The second derivative will have a minimal value if it is positive. The second derivative will be the highest value if it is negative.
Given function:
[tex]-3x^2+18x+3[/tex]
To find the maximum and minimum value of the function use second derivative test.
On differentiating the above function we get,
-6x + 18
Now, find critical point
-6x + 18 = 0
-6x = - 18
x = - 18/-6 = 3
x = 3
Here, x = 3 is the critical point. Now again differentiate the above function we get,
-6
As , [tex]f^{''}(x)[/tex] < 0 , therefore x = 3 will given a maximum value of function and maximum value is
f(3) = [tex]-3(3)^2+18x+3 = -3(9) + 18(3) + 3 = -27 + 54 + 3 = 27 + 3 = 30[/tex]
Hence , function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.
To learn more about the maximum and minimum value of the function from the given link.
https://brainly.com/question/82347
#SPJ1
I need help like asap !!!
only numbers and decimal points
Answer:
a = 4.52 km
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (7.2)² = a² + (5.6)²
→ 51.84 = a² + 31.36
→ a² = 51.84 - 31.36
→ a = √20.48
→ [ a = 4.52 km ]
Hence, value of a is 4.52 km.
Please help!! Im so confused on this and need help badly
Answer: 11 months
Step-by-step explanation:
You do this by 73 times 11 equals 803
Then 49 times 11 equals 539 then add on the registration fee and it equals to 779 which is less than 803
Question For Middle School........
[tex]1.what \: is \: the \: value \: of \: pie \: (\pi)[/tex]
Find the missing base.
Write your answer as a whole number.
2=100
The missing base for the expression x² = 100 is given by:
± x = 10.
How to find the missing base?The expression in this problem is given as follows:
x² = 100.
The missing base is represented by the variable x, hence we have to solve the above expression x² = 100 for the variable x.
To solve for x, we need to isolate the variable x, applying the inverse operation to the second power, which is the square root, hence the variable x is isolated as follows:
x = plus/minus square root of 100.
The plus/minus sign is necessary because the x-squared function is even, then the missing base is obtained as follows:
x = ± 10.
Plus/minus 10 because both of these statements are true:
10² = 100.(-10)² = 100.More can be learned about the square root of an amount at https://brainly.com/question/428672
#SPJ1
Write the fraction or mixed number as a percent . 6/25
Answer:
24%
Step-by-step explanation:
6/25 is also the same as 24/100 because
(6/25)*(4/4)=24/100
Since the denominator is 100, the numerator is the percentage.
6/25=24%
Answer:
24%
Step-by-step explanation:
One way to figure this out is to multiply the denominator by 4 so that it becomes 100. This makes it easy to see what the percentage will be.
6/25 x 4/4 = 24/100
6/25 = 24%
A salesman earns 9% commissions on all the merchandise that he sells.last month he sold $3000 worth of merchandise.how much commissions in dollars did he earn last month
The commission earned by selling the merchandise worth $3000 is $270
The percentage of the commission earned by the salesman is 9%
The worth of the merchandise is $3000
A sales commission is typically an amount paid to an employee upon completion of a task for the sale of a specified quantity of goods or services.
Therefore, the commission earned can be found using the formula,
Commission = SP x CP
where SP is the selling price and
CP is the commission percentage.
Let us substitute the known values in the above equation, we get
Commission = 3000 x 9%
= 3000 x 9/100
= 30 x 9
= $270
Therefore, the commission earned is $270
Learn more about the commission in
https://brainly.com/question/20987196
#SPJ4
Make d the subject of the formula h=d/3+2
Answer:
d = 3h - 6
Step-by-step explanation:
h = [tex]\frac{d}{3}[/tex] + 2 ( multiply through by 3 to clear the fraction )
3h = d + 6 ( subtract 6 from both sides )
3h - 6 = d
mr. bray prepares a list of 434343 us presidents, 888 of whom died in office. then 181818 of his students each select a president at random (there can be repeats) for their creative writing assignments. what is the probability that at least one of the students select a president who died in office? round your answer to the nearest hundredth.
There is a 0.97541 or 97.541% probability that at least one student will choose a president who passed away in office.
Take into account the details offered.
43 US presidents are listed by Mr. Bray, 8 of them passed away while in office.
Consequently, p= 8/43.
If 8 of the 43 presidents died while in office, then 43-8=35 presidents survived.
q= 35/43
Let X represent how many presidents have passed away while in office.
The probaility that at least one student will choose a president who passed away in office is:
P(X[tex]\geq[/tex]1 ) = 1 -P(X=0)
P(X[tex]\geq[/tex]1 ) = 1 -¹⁸c₀(8/43)⁰(35/43)¹⁸
By using Combinations Formula,
By solving we get,
P(X[tex]\geq[/tex]1 ) = 0.97541
As a result, there is a 0.97541 or 97.541% chance that at least one student will choose a president who passed away in office.
Learn more about probability :
brainly.com/question/14210034
#SPJ4
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!
Answer:
The rocket reaches its maximum height at 2.25 seconds.
It’s maximum height is 88 feet.
This can be found by finding the derivative of the function and setting it to zero.
-16x² +72x + 7
Taking first derivative and setting to zero:
-32x + 72 = 0
x = -72/-32=2.25
Find the height when x is 2 seconds by substituting this value into the original function:
-16 * (2.25)² + 72 * 2.25 + 7 = 88
Therefore the maximum turning point of the parabola will be (2.25, 88)
A collector of rare books has a first-edition book worth $262, which he anticipates will grow in
value at a rate of 15% per year. How much will this book be worth 10 years from now?
If necessary, round your answer to the nearest cent.
Que
ans
2
The worth of the book after 10 years is $1061.1
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First edition book worth = $262
Rate of increase per year = 15%
The worth of the book after t years can be given by the expression.
= 262 x [tex]1.15^{t}[/tex]
Now,
The worth of the book when t = 10.
= 262 x [tex]1.15^{10}[/tex]
= 262 x 4.05
= $1061.1
Thus,
The book is worth $1061.1 after 10 years.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
two cars start moving from the same point. one travels south at 60 mi/h and the other travels west at 25 mi/h. at what rate is the distance between the cars increasing three hours later? 3 hours
The distance between the two cars varies at a speed of 65 m/h after two hours.
Let y represent the car's southward travel distance.
Let x be the distance traveled by the westbound automobile.
Allow a to be the distance between the two vehicles.
A right-angled triangle can be used to symbolize these three distances. So, we can state:
a^2 = x^2 + y ^2
Given that the distances vary with respect to time, let's make a distinction.:__________(1)
2a da/dt = 2x dx/dt +2y dy/dt
Rate of distance change between two cars, da/dt
The car is traveling west (dx/dt) at 25 m/h, while the car traveling south (dy/dt) is traveling at 60 m/h.
Therefore:
dy/dt = 60 m/h and dx/dt = 25 m/h
The separation between the two cars will be after two hours:
y = 3* 60 = 180 miles
x = 3 * 25 = 75 miles
Therefore:
a^2 = x^2 + y ^2
a^2 = 75 ^2+ 180 ^2
a= [tex]\sqrt{5625 + 32400}[/tex]
a= 195
From (1):
195(da/dt) = 75(25) + 180(60)
195(da/dt) = 1875 + 10800 = 12675
da/dt = 12675 / 195 = 65 m/h
As a result, after two hours, the two automobiles' separation is varying at a speed of 65 m/h.
Learn more about distance :
brainly.com/question/15172156
#SPJ4
How do you write 5 11/16 and 7 24/25 as a decimal?
Answer:
5 11/16 as a decimal = 5.6875
7 24/25 as a decimal is 7.96
Step-by-step explanation:
Answer:
5 11/16 = 5.6875
7 24/25 = 7.97
Step-by-step explanation:
you keep the whole numbers then you turn the fractions into decimals so to do that you divide 100 by the denominator and whatever the answer is you multiply it by the numerator to get your answer, 100 divided by 16 is 6.25 and 6.25 multiplied by 11 is 68.75 but since the 5 is already the whole number you basically just forget the decimal in 68.75 ( I hope that makes sense)
And for 7 24/25 you do 100 divided by 25 and that’s 4 so now you multiply 24 by 4 and that’s 96 so that goes after the decimal so it’s 7.96 (I hope that helped and all made sense.)
Need help
Solve 4(x-5) = 18
Answer:
x = 19/2 or 9.5
Step-by-step explanation:
a) Distribute.
(4)(x) + (4)(−5) = 18
4x + −20 = 18
4x − 20 = 18
b) Add 20 to both sides.
4x − 20 + 20 = 18 + 20
4x = 38
c) Divide both sides by 4.
4x/4 = 38/4
x = 19/2 or 9.5
Answer:
9.5 or 19/2
Step-by-step explanation:
4 ( x - 5 ) = 18
Step 1 : Divide 4 on both sides.
x - 5 = 18/4
x - 5 = 4.5
Step 2 : Add 5 on both sides.
x = 4.5 + 5
x = 9.5
Value of x in fraction = 95/10 = 19/2
Value of x in decimal = 9.5
What’s the answer plss
Answer:
<ABD = 67.17
Step-by-step explanation:
Comment
This requires 2 steps.
Find <AFind <ABDFinding <A
<A is found by taking the inverse tangent of the ratio 8/19.
<A = tan-1*(8/19)
<A = 22.83 degrees. We'll round it later.
Finding <ABD
You have to use 2 facts here.
All triangle angles add up to 180 degrees.
You find the third angle by subtracting the other 2.
<A = 22.83 Found above
<ADB = 90 degrees Given
<ABD = ?
Equation
< A + <ADB + <ABD = 180
Solution
22,83 + 90 + <ABD = 180 Combine the left
112.83 + <ABD = 180 Subtract 112.83 from both sides.
112.83-112.83 +<ABD = 180 - 112.83 Combine
<ABD = 67.17
The answer to the nearest degree is 67.
How will you solve problems involving equations of circles and coordinates?
NEED ASAP
An equation is a mathematical statement showing the equality of two
opposite variables
How to determine the equation of the circle using coordinates?
The equation of a circle is determined by the function r²=(x-x1)² +(y-y1)²
where :
(x1,y1,) marks the centre of the circlex,y marks the points on the circumference of the circumference of the circler marks the radius of the circlethen, the last thing is to write the equation of the circle and input the values of the coordinates to arrive at your answer,
learn more about the equation of the circle and coordinates on
brainly.com/question/23799314
#SPJ1
what is the probability that a positive integer not exceeding 100 selected at random is divisible by 5 or 7
Answer:
So, the probability of selecting a number from 1 to 100 that is divisible by 5 or 7 is 0.32.
Hope this helped!
30°
(5y-8)°
(6x-2)°
(11x-9)
72⁰
Answer:
x = 7°y = 18°Step-by-step explanation:
Find x:-
[tex]\sf 11x-9+72+6x-2=180[/tex]
[tex]\sf 17x+61=180[/tex]
[tex]\sf 17x=119[/tex]
[tex]\sf x=7[/tex]
Find y:-
[tex]\sf 30+11(7)-9+5y-8=180[/tex]
[tex]\sf 5y+90=180[/tex]
[tex]\sf 5y=90[/tex]
[tex]\sf y=18[/tex]
So, therefore, x = 7° & y = 18°!!
____________________
Hope this helps!
Have a great day! :)
Simplify by expressing fractional exponents instead of radicals 8 sqrd x^2 y^4
After the use of fractional exponents give us the value 8√(x²y⁴) is 2³(x²y⁴)¹/₂.
Exponent:
Exponent is refers the way of writing the words, "raised to the power". And it is used to show that a number has been raised to a certain power.
Given,
Here we have the expression 8√(x²y⁴).
Now, we need to simplify the fractional exponents.
When we rewritten the expression like the following,
=> 8√(x²y⁴)
While we looking at these expression we know that, the number 8 can be written as the multiple of 2,
So, it can be written as,
=> 8√(x²y⁴) = 2³√(x²y⁴).
So, in the simplified form it can be written as,
=>8√(x²y⁴) = 2³(x²y⁴)¹/₂.
Therefore, the simplified form is 2³(x²y⁴)¹/₂.
To know more about Exponent here.
https://brainly.com/question/15993626
#SPJ1