Width of the rectangle is 4 units
Step-by-step explanation:
Step 1: Let the width of the rectangle be x. Then the length = x + 1. Find dimensions if area = 20 sq. unitsArea of the rectangle = length × width
⇒ 20 = x (x + 1)
⇒ 20 = x² + x
⇒ x² + x - 20 = 0
⇒ x² + 5x - 4x - 20 = 0 (Using Product Sum rule to factorize)
⇒ x(x + 5) - 4(x + 5) = 0
⇒ (x + 5)(x - 4) = 0
⇒ x = -5, 4 (negative value is neglected)
x = 4
Final answer:
The solution reveals that the width of the rectangle is 4 units.
Explanation:
The student is asking to find the width of the rectangle when the length is given as the sum of the width and 1 unit, and the area of the rectangle is 20 square units.
To solve this, we can set up an equation using the area formula for a rectangle, A = length * width, where the area (A) is 20 square units.
Let's denote the width as w units.
Then the length can be expressed as w + 1 units. Substituting these expressions into the area formula gives us:
20 = w * (w + 1)
Expanding the right side, we get:
20 = w² + w
This is a quadratic equation, which we can solve by setting it equal to zero:
w² + w - 20 = 0
Factoring the quadratic equation, we find:
(w + 5)(w - 4) = 0
Therefore, w could be -5 or +4. Since a width cannot be negative, the only reasonable solution is w = 4 units.
Thus, the width of the rectangle is 4 units.
what is 1735/1000 written as a decimal?
Answer:
[tex]\frac{1735}{1000}[/tex] as a decimal is 1.735.
Step-by-step explanation:
To convert a fraction into a decimal, you first have to put the fraction into simplest form.
1. Simplest form
[tex]\frac{1735}{1000} = \frac{347}{200}\\\[/tex]
To do this you must find a number you can equally divide both numbers by.
That number in this situation, 5.
[tex]1000/5= 200\\1735/5= 347\\1735:1000 = 347:200\\\frac{1735}{1000} =\frac{347}{200}[/tex]
Now you must make this simplest formed fraction into a mixed number.
2. Simplest form into Mixed number
[tex]\frac{347}{200}= 1\frac{147}{200}[/tex]
To do this you see how many times the denominator, the bottom number of the fraction, goes into the numerator, the upper part of the fraction.
Since 200 x 2 = 400 and since 400 > 347 this means...
200 goes into 347, once.
Finally, subtract and divide.
Remember put the whole number in front of the mixed number, before the decimal
3. Subtract, divide, decimalize
[tex]147/200= 0.735\\\\1\frac{147}{200}= 1.735[/tex]
Hopes this helps you!
Have a good afternoon!
After one hour, the hare had finished 2/3 of a 100-yard race. In that same time, the tortoise had finished 42 3/4 yards. How much farther had the hare run than the tortoise?
Answer:
23 11/12 yards or 23.9166 yards
Step-by-step explanation:
2/3 of 100 yard race is equivalent to 66 2/3 yards. Tge difference between the above and 42 3/4 yards covered by tortoise will be
66 2/3- 42 3/4= 23 11/12 yards or 23.91666 yards
Question 3 (Multiple Choice Worth 1 points)
(02.05 MC)
Write the equation of a function whose parent function, f(x) = x + 8, is shifted 2 units to the right.
Og(x) = x - 6
O g(x) = x -
11111
x
0
|
+ III
x
M
|
x
M
O g(x) = x + 2
|
O g(x) = x + 6
Answer:
[tex]g(x) = x + 6[/tex]
Step-by-step explanation:
The parent function is given as:
[tex]f(x) = x + 8[/tex]
We want to find a new function that results after shifting f(x), 2 units to the right.
Let that function be g(x), then
[tex]g(x) = f(x - 2)[/tex]
We replace x by x-2 in f(x) to get:
[tex]g(x) = x - 2 + 8[/tex]
When we simplify, we obtain:
[tex]g(x) = x + 6[/tex]
What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 39
Step-by-step explanation:
The sum of all three angles of a triangle will ALWAYS be 180 degrees.
So, simply subtract 39 and 103 from 180 and you will find your answer.
180 - 39 - 102 = 39
Answer:
39
Step-by-step explanation:
There are 180degrees in a triangle. So 102+39=141than we have to do 180-141 to get out answer of 39
To ride your favorite roller coaster, you must be at least five feet tall but
less than seven feet tall. Let h represent any height that can ride the roller
coaster.
Answer:
5 ≤ h<7
Step-by-step explanation:
the rider has to be more than at least 5 feet tall, so h is greater than or equal to 5 (5 ≤ h), but they have to be less than 7 feet tall (h<7) so, therefore, we get 5 ≤ h<7
Eric can wrap 50 gift boxes in one hour. On this basis, Samantha computed the number of gifts he can wrap in 0.05 hour. How many significant digits are there in Samantha’s result?
A) 1
B) 2
C) 3
D) 4
Answer:
The answer is B).2
Step-by-step explanation:
any 0 after the decimal is significant. .05 should be the answer.
Answer:
It is not 2 i got it wrong
Step-by-step explanation:
i think it is one
Please help! Question is attached to the image :)
The volume of the smaller room is B. 768 cubic feet.
Step-by-step explanation:
Step 1:
The entire length for both rooms is 20 feet. As the large room has a length of 12 feet, the length of the smaller room is [tex]20-12=[/tex] 18 feet long.
The width of the prism is 12 feet and a height of 8 feet.
The volume of a rectangular prism is determined by multiplying its length, its width, and its height.
The small room's length = 8 feet,
The small room's width = 12 feet, and
The small room's height = 8 feet.
Step 2:
The volume of a rectangular prism [tex]= (l)(w)(h).[/tex]
The volume of the smaller room [tex]= (8)(12)(8)= 768.[/tex]
So the volume of the smaller room is 768 cubic feet which is option B.
3 Maddie's little brother spilled ketchup on one of her homework problems.
Assuming that the number under the spill is greater than zero, fill in the bubble
to show what Maddie should be able to tell for sure about the answer, even
though she can't see the other number.
O The answer will be less than 3.
O The answer will be less than the ketchup-covered number.
O The answer will be a fraction.
O The answer will be greater than the ketchup-covered number.
b.Explain your answer. How do you know the statement you chose is true?
Final answer:
Maddie should be able to tell for sure that the answer will be greater than the ketchup-covered number.
Explanation:
Based on the information provided, Maddie should be able to tell for sure that the answer will be greater than the ketchup-covered number. We can make this determination by comparing the known quantity, which is '3', with the fact that the obscured number is greater than zero. As long as the missing number is positive, any amount added to '3' would result in a sum that is larger than '3'.
If the hidden number is greater than zero and we add it to '3', the result must logically be greater than '3'. This concept is grounded in the basic principles of arithmetic, where adding a positive number to another number increases the total. Therefore, regardless of what the ketchup-covered number is, provided it is more than zero, the sum will indeed be larger than the visible number '3'.
The graph of which function has an axis of symmetry at x = 3?
The graph of y = 2(x - 3)² + 2 has an axis of symmetry at x = 3
The graph of which function has an axis of symmetry at x = 3?
From the question, we have the following parameters that can be used in our computation:
The quadratic functions
A quadratic function is represented as
y = a(x - h)² + k
Where,
The axis of symmetry is at x = h
Using the above as a guide, we have the following:
The graph of y = 2(x - 3)² + 2 has an axis of symmetry at x = 3
Question
The graph of which function has an axis of symmetry at x = 3?
y = 4(x + 3)²
y = 2(x - 3)² + 2
y = x² + 2
y = 2(x + 5)² + 2
A square calendar has sides that are 20 Inches long. What is the calendar's perimeter?
inches
Answer:
80 in.
Step-by-step explanation:
to find the perimeter of a shape you add all of the side lengths together
20+20+20+20
Rewrite the equation below so that it does not have fractions four -4/9 times equals two over three do not use decimals in your answer please help me I’ll give you 10 points
The equation is 36 - 4x = 6.
Solution:
To write the equation without fraction.
[tex]$4-\frac{4}{9} x=\frac{2}{3}[/tex]
[tex]$\frac{4}{1} -\frac{4}{9} x=\frac{2}{3}[/tex]
The denominators must be same to add/subtract the fractions.
LCM of 1, 9 and 3 = 9.
Multiply first term by [tex]\frac{9}{9}[/tex] and [tex]\frac{2}{3}[/tex] by [tex]\frac{3}{3}[/tex] to make the denominator same.
[tex]$\frac{4\times9}{1\times9} -\frac{4}{9} x=\frac{2\times3}{3\times3}[/tex]
[tex]$\frac{36}{9} -\frac{4}{9} x=\frac{6}{9}[/tex]
[tex]$\frac{36-4x}{9} =\frac{6}{9}[/tex]
Multiply by 9 on both sides.
[tex]$\frac{36-4x}{9}\times9 =\frac{6}{9}\times9[/tex]
Both 9 in the numerator and denominator get canceled.
36 - 4x = 6
This term does not have fraction.
Hence the equation is 36 - 4x = 6.
Consider m= y2-y1 x2 - x1 which x1 and x2-values would determine that he line is vertical? Justify your answer
Answer:
Step-by-step explanation:
hello :
m= (y2-y1)/( x2 - x1) is the slope
this line is verticalwhen : x2 = x1
Using digits 0-9 at most one time,fill in the boxes o make the sum of the interior angles of a triangle .
Step-by-step explanation:
The interior angles of a triangle add up to 180.
There are many possible answers. One example is 90 + 12 + 78.
Suppose you invest 1500$ in an account payin 4.75% Annual interest. Find the account balance after 5 years
Answer:4850.51
Step-by-step explanation:
Factor out the greatest common monomial factor from the polynomial. (If the polynomial has no common monomial factor, enter NCF.)
8x + 8
Answer:
Step-by-step explanation:
8x = 8 * x
8 = 8 * 1
Greatest common factor = 8
8x + 8 = 8(x+ 1)
A system of equations is shown.
x + y = 7
2x – y = – 1
What is the solution to the system of equations?
Final answer:
To solve the system of equations (x + y = 7 and 2x - y = -1), use the addition method to find that the solution is x = 2 and y = 5.
Explanation:
The question asks for the solution to the following system of equations:
x + y = 7
2x – y = – 1
To solve this system, we can use the method of addition (also known as elimination) to eliminate one of the variables. Here's how:
Add the two equations directly to eliminate variable y:
(x + y) + (2x - y) = 7 – 1
3x = 6
Therefore, x = 2.
Substitute the value of x into one of the original equations to find y:
2 + y = 7
Therefore, y = 5.
So, the solution to the system of equations is x = 2 and y = 5.
The solution to the system of equations is [tex]x = 2[/tex] and [tex]y = 5[/tex].
To solve the system of equations [tex]x + y = 7[/tex] and [tex]2x - y = -1[/tex], we can use a method called substitution or elimination. Let's use substitution for this case.
Start with the first equation:
[tex]x + y = 7[/tex]
Solve this equation for one of the variables, say [tex]y[/tex]:
[tex]y = 7 - x[/tex]
Substitute [tex]y = 7 - x[/tex] into the second equation:
[tex]2x - (7 - x) = -1[/tex]
Simplify and solve for [tex]x[/tex]:
[tex]2x - 7 + x = -1[/tex]
[tex]3x - 7 = -1[/tex]
[tex]3x = 6[/tex]
[tex]x = 2[/tex]
Substitute [tex]x = 2[/tex] back into the expression for [tex]y[/tex]:
[tex]y = 7 - 2[/tex]
[tex]y = 5[/tex]
This means that the point [tex](2, 5)[/tex] is where the two lines represented by these equations intersect. Therefore, the solution is [tex](2, 5)[/tex].
jeds market has a total of 26 employees. Each full time employee makes $275/ week, and each part-time employee makes $140/ week. Jed pays a total of $5935 in wages each How many full-time and part-time employees does he have? Let f= number of fulltime employees, and p= number of part-time employees.
Answer:
[tex]f=17\\p=9\\[/tex]
Step-by-step explanation:
Let
[tex]f= Full-time\\p=Part-time[/tex]
Full time rates-$275, Part-time rates-$140
The problem can be expressed as:
[tex]f+p=26...eqtn1\\275f+140p=5935....eqtn2\\[/tex]
Express eqtn1 in terms of f,[tex]f=26-p[/tex]
Substitute f value in eqtn 2.
[tex]=>275(26-p)+140p=5935\\7150-275p+140p=5935\\1215=135p\\p=9\\f=26-9=17\\[/tex]
Therefore, jeds has 17 fulltime and 9 parttime employees.
PLEASE HELP ME!!! 5 POINTS
What does Florida's state constitution include in its first article?
A. Declaration of rights
B. Description of the state flower
C.Image of the state flag
D. Plans for the Capitol building
Hello.
The answer is A. The Declaration of Rights.
Answer:
c. image of the state flag
Which figure has only one line of symmetry? A. rhombus B. square C. circle D. isosceles triangle
Answer:
D. isosceles triangle
Step-by-step explanation:
Answer:
D. Isosceles Triangle
Step-by-step explanation:
An Isoceles triangle can only be folded once, it has one line of symetry. A square has 4, a circle has infinete and a rhombus has 2 so it has to be an isoceles triangle.
x∙5∙25∙4÷5, if x=813
Final answer:
When x equals 813, the algebraic expression x⋅5⋅25⋅4÷5 simplifies to 81300 by substituting x with 813 and following the order of operations through multiplication and division.
Explanation:
The question asks for the calculation of an algebraic expression with the substitution of x=813. The expression is x⋅5⋅25⋅4÷5. To solve this, we first substitute x with 813, and then we follow the order of operations.
Substitute x with 813: 813⋅5⋅25⋅4÷5.Multiply the numbers together: 813⋅5 equals 4065, 4065⋅25 equals 101625, and 101625⋅4 equals 406500.Finally, divide by 5: 406500÷5 equals 81300.Therefore, when x=813, the solution to the expression is 81300.
identify the numerical coefficient of the term 5xy
Stop 1: first, let's pay the bills.
1) Henna's cell phone company has a basic monthly plan of $60 plus $0.12
per minute. At the end of the month she was charged with a total of
$123.00. How many minutes has she used this month?
Answer:
525 Minutes
Step-by-step explanation:
The equation would be...
$60 + $0.12m = $123
Now we can simplify
($60 - $60) + $0.12m = ($123 - $60)
$0.12m = $63
($0.12m/$0.12) = ($63/$0.12)
M = 525
Jason went to the post office and bought both 41-cent stamps and 26-cent postcards and spent $10.28. The number of stamps was 4 more than twice the number of postcards. How many of each did he buy?
Solution:
Let stamps be s and postcards be p
Given that,
The number of stamps was 4 more than twice the number of postcards
s = 4 + 2p -------- eqn 1
Jason bought both 41-cent stamps and 26-cent postcards and spent $10.28
41 cent = $ 0.41
26 cent = $ 0.26
Therefore,
[tex]s \times 0.41 + p \times 0.26 = 10.28[/tex]
0.41s + 0.26p = 10.28 --------- eqn 2
Substitute eqn 1 in eqn 2
0.41(4 + 2p) + 0.26p = 10.28
1.64 + 0.82p + 0.26p = 10.28
1.08p = 10.28 - 1.64
1.08p = 8.64
Divide both sides by 1.08
p = 8
Substitute p = 8 in eqn 1
s = 4 + 2(8)
s = 4 + 16
s = 20
Thus Jason bought 20 stamps and 8 post cards
What is the answer 4x+10=-26
Answer: x = -9
Step-by-step explanation:
Subtract 10 from both sides:
4x + 10 - 10 = -26 - 10
Simplify:
4x = -36
Divide both sides by 4:
4x/4 = -36/4
simplify:
-36/4 = -9
Answer: x = -9
Answer:
x = -9
Step-by-step explanation:
4x+10 = -26
-10 -10
[tex]\frac{4x=-30}{4}[/tex]
x = -9
The phone company charges a 1.5% service fee on all long distance calls. If a long distance call bill is $32, how much is the service fee?
Answer:
$0.48
Step-by-step explanation:
Step 1: Make an equation to help show the relation ship
The phone company charges a 1.5% service fee on all long distance calls.
%1.5x
0.015x
Step 2: Plug in and then multiply
0.015x
0.015(32)
$0.48
Answer: $0.48
22/25, end fraction of a number is what percentage of that number
Answer:
88%
Step-by-step explanation:
To get the percentage of 22/25. All that is needed to do is to multiply it with 100. Because A percentage is 100.
Thus: 22/25 gives 0.88 as a decimal, multiplied by the percentage figure 100
0.88 times 100 will give 88%.
Which means 22 is 88% of 25.
In other words to turn a fraction or decimal to a percentage, all that is needed to do of just to multiply that fraction or decimal by 100, and then it will give the percentage.
Find the next 3 terms in each sequence
1). 8, 24, 72, 216.... ____, ______, _____,
Answer: 648, 1,944, and 5,832.
Step-by-step explanation: Begin by studying the pattern.
Here, notice that 8 × 3 is equal to 24.
24 × 3 is equa to 72.
72 × 3 is equal to 216.
Continuing the same pattern, 216 × 3 is equal to 648.
648 × 3 is equal to 1,944.
1,944 × 3 is equal to 5,832.
I have also attached in image below showing my work.
So the three missing terms in the pattern are 648, 1,944, and 5,832.
What is the length of D.
8ft
Answer:
96 inches
Step-by-step explanation:
8 ft is 8(12) inches, which is 96 inches
There are 12 animals in a farm.
Some are cows
The rest are chickens
There are 28 animal legs in all.
How many cows are there?
How many chickens are there?
Answer:
2 cows 10 chickens
Step-by-step explanation:
2 X 10 = 20
4 X 2 = 8
20 + 8 = 28
3 (x+2) = 18
Can you please use the distributive property thx?
Answer:4
Step-by-step explanation:3x+6=18 minus 6 on both sides and divide by 3