Answer:
Length =12
Width= 10
Step-by-step explanation:
The difference between two consecutive integers is 2.
Thus the difference between the length and the width of the rectangle also differ by 2.
width- x
length- x+2
AREA=L×W
120=x(x+2)
x²+2x-120=0
Factorizing:
x² - 10x + 12x - 120=0
x(x-10) + 12( x-10)=0
(x-10)(x+12)=0
either x-10=0 or x+12=0
x=10 0r -12
We consider positive roots only. thus x=10
width = 10
length = 10+2 =12
Simplify:
2[3 - 5(2+1)2 + 5]
Hello! My name is Zalgo and I am here to help you out today. The answer is -44. The real way to solve it is like this --> "2(3-5(2+1)2+5)".
I hope that this helps! :D
"Stay Brainly and stay proud!" - Zalgo
(By the way, can you mark me as Brainliest? I'd greatly appreciate it! Thank you! XP)
A building is in the shape of a square pyramid each side of the base is 54 M long and the height is 260 M what is the volume of the building
Answer:
V≈2.53×105^5
Step-by-step explanation:
Base edge: 54
Height: 260
Formula to find volume is: V=a^2h /3
Hope this helps!
For this case we have that by definition, the volume of a square base pyramid is given by:
[tex]V = \frac {1} {3} * L ^ 2 * h[/tex]
Where:
L: It's the side of the square base
h: It's the height of the pyramid
According to the data we have:
[tex]L = 54\m\\h = 260\m[/tex]
Substituting in the formula:
[tex]V = \frac {1} {3} * (54) ^ 2 * 260\\V = \frac {1} {3} * 2916 * 260\\V = \frac {1} {3} * (758160)\\V = 252,720 \ m ^ 3[/tex]
Thus, the volume of the building is [tex]252,720 \ m ^ 3[/tex]
Answer:
[tex]252,720 \ m ^ 3[/tex]
The sum of two numbers is 20, and the difference is 40
[tex]x+y=20\\\underline{x-y=40}\\2x=60\\x=30\\\\30+y=20\\y=-10[/tex]
-10 and 30
Answer:
The numbers are 30 and -10.
Step-by-step explanation:
The sum of two numbers is 20 (addition)
x + y = 20
The difference is 40 (subtraction)
x - y = 40
To solve an equation, you can only have one variable. Solve one of these for a variable (it doesn't matter which one).
x - y = 40 Add y to both sides
x = 40 + y
Now you have a new value for x (40 + y), so you can plug it into your other equation.
x + y = 20 Plug in (40 + y) for x
40 + y + y = 20 Combine like terms (y + y)
40 + 2y = 20 Subtract 40 from both sides
2y = -20 Divide both sides by 2
y = -10
Now, plug your y into either equation.
x + y = 20 Plug in -10 for y
x + (-10) = 20 Simplify
x - 10 = 20 Add 10 to both sides
x = 30
Check your work by plugging these numbers into both equations.
x + y = 20 Plug in
30 + (-10) = 20 Simplify
30 - 10 = 20 Simplify
20 = 20
and
x - y = 40 Plug in
30 - (-10) = 40 Simplify
30 + 10 = 40
40 = 40
The measure of angle theta is 3 pi over 2. The measure of its reference angle is pi /
Answer:
[tex]\frac{\pi }{2}[/tex]
Step-by-step explanation:
In order to find the reference angle of a given angle, we have to determine its quadrant.
Since the angle given is:
[tex]\frac{3\pi }{2}[/tex]
The angle lies in third quadrant.
If the angle lies in the third quadrant, [tex]\pi[/tex] is subtracted from the given angle:
So,
[tex]Reference\ Agnle= \frac{3\pi }{2}-\pi\\= \frac{3\pi -2\pi }{2}\\=\frac{\pi }{2}[/tex]
So the reference angle for [tex]\frac{3\pi }{2}[/tex] is [tex]\frac{\pi }{2}[/tex] ..
Find the value of k such that the quadratic polynomials x2-(k+6)x+2(2k+1) as sum of the zeroes as the half of their product
Answer:
k = 5
Step-by-step explanation:
The sum of the zeros is the opposite of the coefficient of x, so is (k+6).
The product of zeros is the constant term, 2(2k+1), so half their product is (2k+1).
The problem statement asks us to find k so that these values are the same:
k +6 = 2k +1
5 = k . . . . . . . . subtract k+1
The value of k is 5.
_____
The zeros are 5.5±√8.25. Their sum is 11; their product is 22.
Writing about Translating Phras
Explain how to translate the phrase into an algebra
expression
a number squared decreased by ten
Answer:
Step-by-step explanation:
This can only be written one way.
Let the number = x
x^2 - 10
is how the statement translates.
x^2 = x*x
the 2 means that you need two xs.
The ^ means that you multiply the two xs.
Answer:
Hey there.. I will be more than happy to help you today.. :)
A Number squared decreased by ten
We will do this with steps:-
Step 1 - "A number ". So, Let's say any number be x
Step 2 - "A number squared". Our number x is squared i.e. x²
Step 3 - "A number squared" ( i.e. x² ) is decreased by ten
x² - 10
This is your answer.
Hope this helps you :)
Step-by-step explanation:
Hope you got helped
Please help me I AM STUCK, and please explain how you get the answer.
Answer:
C) 5
Step-by-step explanation:
[tex]\frac{6x²+19x+10}{2x+5}[/tex]
= [tex]\frac{3x(2x+5)+2(2x+5)}{2x+5}[/tex]
= [tex]\frac{(2x+5)(3x+2)}{2x+5}[/tex]
= 3x+2
which means that if they want us to find what ax+b is, you can figure out that ax+b is similar to 3x+2 and plug in what they want us to solve for, a+b.
ax+b=3x+2 (hence 3=a and 2=b)
wants: a+b
answer: 3+2= 5
hope this helps! :)
Can someone please help me
Answer:
36
Step-by-step explanation:
Note that the missing side is X
30/20 = X/24
30/20(24) = X
36 = X
Which expression are equivalent?
Answer:
B and F
Step-by-step explanation:
the are equivalent but the are just is different orders
Answer:
8d + 1/3 + 5/7
1/3 + 5/7 + 8d
Step-by-step explanation:
The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a
tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds,
how far is the ball off the ground?
30 meters
40 meters
50 meters
60 meters
Answer: 50 meters
Step-by-step explanation: I just finished the pretest
Answer: The ball is 50 m off the ground after 2 seconds
Step-by-step explanation:
Given the function relating the height of an object off the ground to the time spent falling is a quadratic relationship.
Therefore if h=height and t=time then
[tex]h=a+bt+ct^{2}[/tex] ----------(A)
where a,b and c are constants
Apply given conditions
At t=0s h=90 m
=> 90 m = a+0+0
=>a=90 m
Also the ball has been just dropped at t=0 s
=>[tex]\frac{\partial h}{\partial t}=0=>\frac{\partial (a+bt+ct^{2})}{\partial t}=0[/tex]
=>[tex]b+2ct=0[/tex]
For t=0s b = 0
Thus equation (A) is reduced to [tex]h=90+ct^{2}[/tex]
At t= 3 s , h=0 m
[tex]\therefore 0= 90 +9c=>c=-10 \frac{m}{s^{2}}[/tex]
Finally we get [tex]h=90-10t^{2}[/tex]
Therefore at t= 2.0 s , [tex]h=(90-10\times 2^{2})m=50 m[/tex]
Thus the ball is 50 m off the ground after 2 seconds
Solve for x: 4 over x equals 5 over 10
Answer:
x = 8,
Step-by-step explanation:
[tex]\displaystyle \frac{4}{x} = \frac{5}{10}[/tex].
[tex]x \ne 0[/tex] for it is a denominator. Multiply both sides with the product of the two denominators: [tex]10\;x[/tex]:
[tex]\displaystyle \frac{4}{x}\cdot (10\; x) = \frac{5}{10}\cdot (10\;x)[/tex].
[tex]40 = 5\; x[/tex].
Multiply both sides by one over the coefficient of x:
[tex]\displaystyle \frac{1}{5} \times 40 = \frac{1}{5}\times 5\; x[/tex].
[tex]x = 8[/tex].
Answer : Answer is 8
Step-by-step explanation:
Took the test
PLEASE HELP!
What is the y-intercept of the line shown?
Answer:
the answer is y=-1
Answer: -1
Step-by-step explanation: The horizontal line represents the x axis and the verticle line represents the y axis. The line comes into contact with the verticle line at -1, making it your point of interception.
Use ADEF to complete the statements.
Angle E is the included angle between sides
The included angle between sides FE and DF is angle
Answer:
Angle E is the included angle between the sides FE and DE
The included angle between sides FE and DF is the angle F
Step-by-step explanation:
we know that
An included angle is the angle between two sides of a triangle
In the triangle DEF
we have
The included angle F is the angle between the sides FE and FD
The included angle E is the angle between the sides FE and DE
The included angle D is the angle between the sides DF and DE
therefore
In this problem
Angle E is the included angle between the sides FE and DE
The included angle between sides FE and DF is the angle F
Slope = 5, passing through (4,3)
y - y1 = m(x - x1) is the general point slope form
y - 3 = 5(x - 4) plug in the given values
y - 3 = 5x - 20
y = 5x - 20 + 3
y = 5x - 17
The answer in slope intercept form is y = 5x-17
If you want to convert to standard form, then
y = 5x - 17
y+17 = 5x
17 = 5x - y
5x - y = 17 which is the answer in standard form (Ax + By = C)
Solve for x.
c-1/x+d=cd
A)1/d
B)d
C)c/d
Answer: OPTION A.
Step-by-step explanation:
Given the equation [tex]\frac{c-1}{x}+d=cd[/tex], you need to solve for the variable "x":
Subtract "d" from both sides of the equation:
[tex]\frac{c-1}{x}+d-d=cd-d\\\\\frac{c-1}{x}=cd-d[/tex]
Multiply both sides of the equation by "x":
[tex](\frac{c-1}{x})x=x(cd-d)\\\\c-1=x(cd-d)[/tex]
Divide both sides of the equation by [tex](cd-d)[/tex]:
[tex]\frac{c-1}{cd-d}=\frac{x(cd-d)}{cd-d}\\\\\frac{c-1}{cd-d}=x[/tex]
Factor out "d" in the denominator and simplify. Therefore:
[tex]\frac{(c-1)}{d(c-1)}=x\\\\x=\frac{1}{d}[/tex]
The correct solution for the equation c-1/x+d=cd is x = -1/(cd - c - d). Unfortunately, none of the provided options, 1/d, d, or c/d match this solution.
Explanation:To solve the equation c-1/x+d=cd, we first move the terms involving x to one side and the constant to the other side. So the equation becomes:
-1/x = cd - c - d.
We then take reciprocals on both sides (since we do not want x in the denominator) to get:
x = -1/ (cd - c - d). Thus, the solution of the given equation is x = -1/(cd - c - d).
Unfortunately, none of the options A) 1/d, B) d, or C) c/d match the obtained solution.
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What are the foci of the graph y2 – 25x2 = 25?
Answer: [tex]\bold{(0,-\sqrt{26})\quad \&\quad (0,\sqrt{26})}[/tex]
Step-by-step explanation:
[tex].\qquad y^2-25x^2=25\\\\\implies \dfrac{y^2}{25}-\dfrac{25x^2}{25}=\dfrac{25}{25}\\\\\\\implies \dfrac{y^2}{25}-\dfrac{x^2}{1}=1\\\\\\Center: (0, 0)\\Length\ of\ foci:25+1=c^2\implies \sqrt{26}=c\\Foci: (0,0\pm \sqrt{26})[/tex]
Point P partitions the directed segment from A to B into a 1:3 ratio. Q partitions the directed segment from B to A into a 1:3 ratio. Are P and Q the same point? Why or why not?
Yes, they both partition the segment into a 1:3 ratio.
Yes, they are both the distance from one endpoint to the other.
No, P is the distance from A to B, and Q is the distance from B to A.
No, Q is closer to A and P is closer to B.
Points P and Q are not the same due to their different positions in the division of the directed segment. Point P is closer to A while Point Q is closer to B.
Explanation:Point P and Q are not the same point. In the directed segment from A to B, Point P divides the segment in a way that the ratio of AP to PB is 1:3, meaning Point P is closer to A. On the contrary, Point Q divides the segment from B to A in a way that the ratio of QB to QA is 1:3, implying that Point Q is closer to B. Therefore, P and Q have different positions on the segment.
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No, Point P and Q are not the same. P is closer to A because it partitions the directed segment from A to B, whereas Q is closer to B as it partitions the segment from B to A, taking into account the directionality of the segments.
Explanation:In mathematics, partitioning points on a directed segment refers to dividing the segment into distinct parts according to a given ratio. Point P partitions the directed segment from A to B into a 1:3 ratio, which means P is one part from A and three parts from B. On the other hand, Point Q partitions the directed segment from B to A into a 1:3 ratio, indicating that Q is one part from B and three parts from A.
Given this, P and Q are not the same point. P is closer to point A and Q is closer to point B since the directionality of the segment is taken into account. The direction from A to B is not the same as the direction from B to A, so the points P and Q that partition these segments in a 1:3 ratio will end up at different locations.
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question attached below
Answer:
B . [tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]
Step-by-step explanation:
Given function is:
[tex]f(x)=\frac{x}{1+x}[/tex]
Sall h is used to denote minor change in function. The value of the new function f(x+h) will be calculated by putting x+h in place of x in the function.
So putting x+h in place of x
[tex]f(x+h)= \frac{x+h}{1+(x+h)}\\=\frac{x+h}{1+x+h}[/tex]
So, option B is the correct answer ..
8a4b+1/125ab4
Factorise it
Answer:
Step-by-step explanation:
First pull out the common factor of ab
ab(8a^3 + (1/125)b^3)
This is basically the sum of cubes. The linear factor is
(2a + 1/5 b)
The other factor is these two factors squared and their multiplicand subtracted.
(2a^2 - 2/5 ab + 1/25b^2)
Now put all this together and you get
ab(2a + 1/5 b)((2a^2 - 2/5 ab + 1/25b^2)
Help please!........
Answer:
circumference is 21.99 and area is 47 and 2/35 unit squared sorry if its a little late
Does anyone know the answer to this question?
Answer:
Option C is correct.
Step-by-step explanation:
We need to solve the equation:
tan 45° - 10 cos 60°
Finding value of tan 45° and cos 60° and solving:
tan 45° = 1 and
cos 60° = 0.5
= 1 - 10(0.5)
= 1- 5
= -4
So, Option C is correct.
evaluate the expression 91/31
3
6
60,480
362,874
Answer:
The best possible answer is 3.
[tex]91 \div 31[/tex]
is the equivalent to 91/31. When divided, the answer comes out to 2.935483871 which, when rounded up, is 3.
The value of the given expression 91/31 will be; 3. The correct option is A.
What is an expression?Expression in maths can be defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The given expression will be calculated by;
= 91 / 31
= 2.93
≅ 3
Therefore the value of the given expression is 3. The correct option is A.
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The oil company removed 5421 liters of gas from a tank that contained 5855 liters
Answer:
The tank now has 434 liters
Step-by-step explanation:
5855-5421=434
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer
000
DONE
000
Answer:
[tex]\large\boxed{y=\dfrac{1}{4}x+3}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
From the graph we have the points (4, 4) and (0, 3) → b = 3.
We have the equation:
[tex]y=mx+3[/tex]
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Put the coordinates of the points:
[tex]m=\dfrac{3-4}{0-4}=\dfrac{-1}{-4}=\dfrac{1}{4}[/tex]
Finally we have:
[tex]y=\dfrac{1}{4}x+3[/tex]
elapsed time five in the afternoon to 1 minute after midnight
Answer:
The elapsed time is 7hrs and 1 minute.
The elapsed time from 5 in the afternoon to 1 minute after midnight is 7 hours and 1 minute, taking into consideration the division of a day into a.m. and p.m.
Explanation:The key to solving this question is first understanding how we measure time in day and night, which are demarcated by a.m. and p.m.. Each cycle of 24 hours is divided into two parts: 12 hours from midnight to noon (a.m.) and another 12 hours from noon to midnight (p.m.).
Let's calculate the elapsed time from 5 in the afternoon to 1 minute past midnight. From 5 p.m to midnight, there are 7 hours. Adding the 1 minute past midnight, the total elapsed time is 7 hours and 1 minute.
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Help me out please with this question
Answer:
100 + 40 + 40 + 40 + 40
Step-by-step explanation:
area of base = 10 x 10 = 100 square units
area of each triangular side = 0.5 x 10 x 8 = 40 square units.
Total area = 1 base + 4 sides
= 100 + 40 + 40 + 40 + 40
help me with this pleaae
Answer:
(D) 30pi inches
Step-by-step explanation:
First, we use the given volume, the given height, and the formula of the volume of a cylinder to find the radius of the base. Then we use the radius of the base to find the circumference of the base.
[tex] volume = \pi r^2 h [/tex]
[tex] volume = 6750 \pi~in.^3 [/tex]
We set the formula equal to the volume and replace h with 30 in.
[tex] \pi r^2 h = 6750 \pi~in.^3 [/tex]
[tex] \pi r^2 \times 30 ~in. = 6750 \pi~in.^3 [/tex]
Divide both sides by 30pi in.
[tex] r^2 = 225 ~in.^2 [/tex]
Take the square root of each side.
[tex] \sqrt{r^2} = \sqrt{225 ~in.^2} [/tex]
[tex] r = 15~in. [/tex]
The radius of the base is 15 in.
Now we use the radius of the base and the formula of the circumference of a circle to find the answer.
[tex] circumference = 2 \pi r [/tex]
[tex] circumference = 2 \pi \times 15~in. [/tex]
[tex] circumference = 30 \pi ~in. [/tex]
Which system of equations is represented by the graph?
A) y= x2 − 6x − 7
x − y = 1
B) y = x2 − 6x + 7
x + y = −1
C) y = x2 + 6x − 7
x − y = 1
D) y = x2 + 6x + 7
x + y = 1
Answer:
D) y = x² + 6x + 7
x + y = 1
Step-by-step explanation:
Just simply substitute the solution into the equations to confirm their authenticities.
I am glad to help.
Answer:
The answer is D. y = x2 + 6x + 7
x + y = 1
Step-by-step explanation:
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function? The domain is all real numbers. The range is {y|y < 16}. The domain is all real numbers. The range is {y|y ≤ 16}. The domain is {x|–5 < x < 3}. The range is {y|y < 16}. The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}.
Answer:
The domain is all real numbers. The range is {y|y ≤ 16}
Step-by-step explanation:
we have
[tex]f(x)=-x^{2}-2x+15[/tex]
This is a the equation of a vertical parabola open downward
The vertex is a maximum
The vertex is the point (-1,16)
see the attached figure
therefore
The domain of the function is all real numbers ----> interval (-∞,∞)
Te range of the function is
[tex]y\leq 16[/tex]
All real numbers less than or equal to 16 ----> interval (-∞,16]
Answer:
The domain is all real numbers. The range is {y|y ≤ 16}.
Step-by-step explanation:
B on edg
Which is the first step in simplifying the expression 2(7 + 3) + 5?
Answer: The first choice
Step-by-step explanation: You alsways distribute inside the paranethesis, so 2(x+3)+5 > 2x+ (2*3)+5