Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE = 11x -3 and CE = 12 - 4x. find x.
Answers
Please check it.
Answer: The value of x = 1
Step-by-step explanation:
Given : Parallelogram ABCD, diagonals AC and BD intersect at point E.
such that
[tex]AE = 11x -3 \text{ and} CE = 12- 4x.[/tex]
We know that the diagonal of a parallelogram bisects each other.
Therefore , we have the following equation :-
[tex]11x -3= 12- 4x\\\\\Righatrrow11x+4x=12+3\\\\\rightarrow\ 15x=15\\\\\Rightarrow\x=\dfrac{15}{15}=1[/tex]
Hence, the value of x = 1
Related Questions
If f(x) = 2x2 + 2 and g(x) = x2 - 1, find (f - g)(x).
Answers
Answer:
x^2 +3
Step-by-step explanation:
f(x) = 2x^2 + 2
g(x) = x^2 - 1
(f - g)(x) = 2x^2 + 2 -( x^2 - 1)
Distribute the minus sign
2x^2 +2 -x^2 +1
x^2 +3
[tex](f-g)(x)=2x^2+2-(x^2-1)=2x^2+2-x^2+1=x^2+3[/tex]
Calculate (Round two decimal places for final answer) 15L is approximately ___gal.
Answers
For this case we must make a conversion. We have that by definition 1 liter equals 0.264172 gallons.
So, making a rule of three we have to:
1L ----------------> 0.264172 gallons
15L --------------> x
Where:
x: Represents gallons equivalent to 15 liters.
[tex]x = \frac {15 * 0.264172} {1}\\x = 3.96258[/tex]
Rounding out we have that 15 liters equals 3.96 gallons.
Answer:
3.96 gallons
15 liters is approximately 3.96 gallons.
Given that we need to calculate 15L is approximately how many gallons rounded two decimal places for final answer.
To convert liters (L) to gallons (gal), you need to know the conversion factor between the two units.
The conversion factor between liters and gallons is 1 L = 0.264172 gal.
Now, let's calculate how many gallons are approximately equal to 15 liters:
15 L x 0.264172 gal/L = 3.96258 gal
Rounding to two decimal places, the approximate value is 3.96 gallons.
Therefore, 15 liters is approximately 3.96 gallons.
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Complete the proportion you can use to convert 110 inches to centimeters. Enter your answer with one decimal place. 1 inch = 2.54 centimeters
Answers
Answer: 279.4 centimeters hope this helped
Step-by-step explanation: 110 x 2.54 = 279.4
How many solutions does this linear system have y= 1/2x+4
x+2y=-8
Answers
Answer:
one
Step-by-step explanation:
y = 1/2x + 4
x + 2y = -8
x + 2(1/2 x + 4) = -8
x + x + 8 = -8
2x = -16
x = -8
y = 1/2 (-8) + 4
y = 0
solution: (-8, 0)
Answer: one
The given linear system has a single solution at the point (-8, 0) after solving the equations by substitution.
To determine how many solutions the given linear system has, we can substitute y from the first equation into the second equation:
y = rac{1}{2}x + 4
x + 2(rac{1}{2}x + 4) = -8
x + x + 8 = -8
2x = -16
x = -8
Then, substituting x into the first equation:
y = rac{1}{2}(-8) + 4
y = -4 + 4
y = 0
The linear system has a single solution, which is (x, y) = (-8, 0).
15 points
7. You did not get enough sleep on Tuesday night.Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the following true statements.
If you have an income, then you must pay taxes.
If you have a job, then you have an income.
You work as a cashier in a convenience store.
You work as a cashier.
You have a job.
You must pay taxes.
You have an income.
Answers
Since you work as a cashier you must have a source of income, so you must pay taxes, because when you have an income you MUST pay taxes
Answer:
1)
Law of Detachment
If you have an income, then you must pay taxes.
You have an income.
You must pay taxes.
Law of Syllogism
If you have an income, then you must pay taxes.
If you must pay taxes, then you have a job.
If you have an income, then you have a job
2)
Law of Detachment
If you work as a cashier in a convenience store then you have a job.
You work as a cashier in a convenience store.
You have a job.
Law of Syllogism
If you work as as a cashier in a convenience store then you have a job
If you have a job then you must pay taxes
If you work as as a cashier in a convenience store then you must pay taxes
Step-by-step explanation:
To answer it properly we need to remind those Laws in Mathematical Logic.
The Law of Detachment says that if a Logical Implication and the second Statement is true, we can derive a true conclusion
1. If p→q (True)
2) p (True)
3) q (True)
On the other hand, The Law of Syllogism says:
1) If p→q (True)
2) If q→r (True)
Subsequently, we can conclude by derivation as true this Logical Implication:
3) If p→r (True)
-----
If you have an income, then you must pay taxes.
If you have a job, then you have an income.
Law of Detachment
If you have an income (p), then you must pay taxes. (q)
If you have a job(r), then you have an income.
1)If you have an income, then you must pay taxes. (T) If p→q (True)
2)You have an income (T) p (True)
3) You must pay taxes q (True)
Law of Syllogism
If you have an income (p), then you must pay taxes. (q) If p→q (True)
If you must pay taxes (q), then you have a job. (r) If q→r (True)
If you have an income (p), then you have a job (r) If p→r (True)
--
If you work as a cashier in a convenience store (p) then you have a job (q)
If you must pay taxes (r) then you have an income
Law of Detachment
If you work as a cashier in a convenience store (p) then you have a job (q) If p→q (True)
You work as a cashier in a convenience store (p) p (True)
You have a job (q) q (True)
Law of Syllogism
*If you work as as a cashier in a convenience store(p) then you have a job (q) If p→q (True)
*If you have a job (q) then you must pay taxes (r) If q→r (True)
If you work as as a cashier in a convenience store (p) then you must pay taxes (r) If p→r
The total cost to rent a row $18 times the number of hours the boat is used . Write an equation to model this situation if c = total cost and h = number of hours
Answers
Hope this helps!
Answer:
c=1`8h
Step-by-step explanation:
Change each dimension on the store toy box to feet 36”__ feet 18”=__feet
Answers
Answer: 36" = 3 feet
18" = 1.5 feet
Explanation: 1 foot = 12 inches
Complete the table of values from left to right for the quadratic function
y = -x + X-3.
x. -5 -3 1 -1 2
y.
OA) 17,3, -3, 3
OB) 17,3, -5, -5
OC) -33, -15, -5, -5
OD) -33, -15, -5, 3
Answers
Answer:
The values of y are -33 , -15 , -5 , -5 ⇒ answer C
Step-by-step explanation:
* We will use the substitution method to solve the problem
- The quadratic equation is y = -x² + x - 3
- The values of x are -5 , -3 , -1 , 2
- We will substitute the values of x in the equation to find the
values of y
# At x = -5
∵ y = -x² + x - 3
∵ x = -5
∴ y = -(-5)² + (-5) - 3 = - 25 - 5 - 3 = -33
∴ y = -33
# At x = -3
∵ y = -x² + x - 3
∵ x = -3
∴ y = -(-3)² + (-3) - 3 = - 9 - 3 - 3 = -15
∴ y = -15
# At x = -1
∵ y = -x² + x - 3
∵ x = -1
∴ y = -(-1)² + (-1) - 3 = - 1 - 1 - 3 = -5
∴ y = -5
# At x = 2
∵ y = -x² + x - 3
∵ x = 2
∴ y = -(2)² + (2) - 3 = - 4 + 2 - 3 = -5
∴ y = -5
* The values of y are -33 , -15 , -5 , -5 ⇒ from left to right
The first few steps in deriving the quadratic formula are shown.
Which best explains why b2/4a2 is not added to the left side of the equation in the last step shown in the table?
• The term b2/4a2 is added to the right side of the equation, so it needs to be subtracted from the left side of the equation to balance the sides of the equation.
• The distributive property needs to be applied to determine the value add to the left side of the equation to balance the sides of the equation.
• The term b2/4a2 needs to be converted so it has a common denominator before adding it to the left side of the equation to balance the equation.
• The square root of the term needs to be found before adding the term to the left side of the equation to balance the sides of the equation.
Answers
Answer:
• The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation.
Step-by-step explanation:
We have to multiply the term b2/4a2 by a in order to determine the value to add to the left side of the equation so as to balance both sides of the equation.
If we multiply the terms, we get;
[tex]\frac{b^{2} }{4a^{2} }*a=\frac{b^{2} }{4a}[/tex]
Therefore, we shall be adding the term [tex]\frac{b^{2} }{4a}[/tex] to the left side of the equation.
Answer: The answer is choice B.
Step-by-step explanation:
A salesperson has January sales of $20,000(1,$20,000) and April sales of $80,000 (4,$80,000). What is the rate of change?
Answers
Answer:
60000/4 pr 15000
Step-by-step explanation:
Rate of change = change in population / change in time
80000 - 20000 = 60000
January to April is 4 months
so the rate of change will be 60000/4 or 15000
Use the properties of exponents to rewrite the expression
(-4qr)(-4qr)(-4qr)(-4qr)
Answers
[tex](-4qr)(-4qr)(-4qr)(-4qr)=(-4qr)^4=256q^4r^4[/tex]
To rewrite the expression (-4qr)(-4qr)(-4qr)(-4qr) using the properties of exponents, we can rewrite it as (-4qr)^4 = 256q^4r^4.
Explanation:To rewrite the given expression (-4qr)(-4qr)(-4qr)(-4qr) using the properties of exponents, we need to understand that multiplying the same base with different exponents is equivalent to adding the exponents. In this case, the base is (-4qr) and the exponents are 1 for each occurrence. So, we can rewrite the expression as:
(-4qr)4 = -44q4r4 = 256q4r4
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HELP PLS GIVING BRAINLIEST
Answers
For this case we have by definition, that the equation of a line in the slope-intersection form is given by:
[tex]y = mx+b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We need two points through which the line passes to find the slope:
[tex](0,1)\\(1, -2)[/tex]
We found the slope:
[tex]m = \frac {y2-y1} {x2-x1}\\m = \frac {-2-1} {1-0} = \frac {-3} {1} = - 3[/tex]
So, the equation is of the form:
[tex]y = -3x + b[/tex]
We substitute a point to find "b":
[tex]1 = -3 (0) + b\\1 = b[/tex]
Finally, the equation is:
[tex]y = -3x+1[/tex]
Answer:
Option C
The following function describes the number of employees working at a company, in thousands, where t represents the number of years since the company revised the benefits package. f(t)=1.5(.90)^t Select the correct statement.
A. The number of employees is increasing by 50% every year.
B. The number of employees is decreasing by 10% every year.
C. The number of employees is decreasing by 90% every year.
D. The number of employees is increasing by 90% every year.
Answers
Answer:
The answer is (B)
Step-by-step explanation:
Try out each of the situations. It can't be A, since the 0.9 is less than 1, so it has to be decreasing. This leaves only B and C. Since decreasing by 90 percent is the same as multiplying by 10 percent, the only possible answer left is B.
Hope this helps!
Answer:
the number of employees is decreasing by 10% every year
Step-by-step explanation:
[tex]f(t)=1.5(.90)^t[/tex]
In the given function 1.5 represents the initial number of employees
Exponential function in the form of [tex]f(x) = a(b)^x[/tex]
When the value of b is less than 1 then it is exponential decay
When the value of b is greater than 1 then it is exponential growth
Exponential decay factor is 0.90
[tex]1-0.90= 0.10[/tex]
0.10 times 100 = 10%
So the number of employees is decreasing by 10% every year
Question 13 (1 point)
Jerome is starting a new job. His contract states he will earn $42,000 the first year, and will
get a 4% raise per year. Which function S(x) represents Jerome's salary after a certain number
of years, x?
Answers
Answer:
S(x)=42000 * 1.04^x
Step-by-step explanation:
now = 42000
in 1 year = 42000 *1,04, because 4% increase is to multiply 1,04
in 2 years = 42000 *1,04*1.04 = 42000*1.04^2
in x years = 42000 * 1.04^x
Answer:
[tex]S(x)=42,000*(1.04)^{x}[/tex]
Step-by-step explanation:
We have as data
a = $42,000 (salary during the first year)
x = number of years
i = 4% = 0.04 (annual increase interest)
S(x) = Salary based on the years elapsed
"a" and "i" are constant for each year, while "x" increases one each year.
The function S(x) can be calculated like this:
[tex]S(x)=a*(1+i)^{x}[/tex]
Substituting constant values, we have
[tex]S(x)=42,000*(1+0.04)^{x}[/tex]
Simplifying, we have
[tex]S(x)=42,000*(1.04)^{x}[/tex]
Hope this helps!
What is the product?
Answers
Answer:
2) -81t² +16
Step-by-step explanation:
(9t -4)(-9t -4) = (9t x -9t) + (9t x -4) + (-4 x -9t) + (-4 x -4)
= -81t² - 36t + 36t + 16
= -81t² + 16
Answer:
- 81t² + 16
Step-by-step explanation:
Simply expand the equation by factoring
(9t-4)(-9t-4) factor out negative sign
= -(9t - 4) (9t +4)
= -(9t + 4) (9t - 4) recall a² - b² = (a+b) (a-b)
= - [ (9t)² - 4²]
= - ( 81t² - 16)
= - 81t² + 16
HELP in the image above please!
Answers
Answer:
D
Step-by-step explanation:
Using the section formula
x = [tex]\frac{5(-8)+8(7)}{5+8}[/tex] = [tex]\frac{-40+56}{13}[/tex] = [tex]\frac{16}{13}[/tex] ≈ 1.2
y = [tex]\frac{5(-9)+8(-2)}{5+8}[/tex] = [tex]\frac{-45-16}{13}[/tex] = [tex]\frac{-61}{13}[/tex] ≈ - 4.7
Coordinates are (1.2, - 4.7 ) → D
(4-2i).(6-3i) / (1-i).(1+i)
Answers
Answer:
2i + 6
Step-by-step explanation:
4-2 = 2
6-3 = 3
2 * 3 = 6
2i
Answer:
9 - 12i
Step-by-step explanation:
Noting that i² = - 1
Expand the factors on the numerator and denominator
(4 - 2i)(6 - 3i) = 24 - 12i - 12i + 6i² = 24 - 24i - 6 = 18 - 24i
(1 - i)(1 + i) = 1 + i - i - i² = 1 + 1 = 2
The division reduces to
[tex]\frac{18-24i}{2}[/tex]
= [tex]\frac{18}{2}[/tex] - [tex]\frac{24}{2}[/tex] i
= 9 - 121i
Larissa is considering two summer jobs. A job at the mall pays $400 per week plus $15 for every hour of overtime. A job at the movie theater pays $360 per week plus $20 for every hour of overtime. How many hours of overtime would Larissa have to work in order for the job at the movie theater to pay a higher salary than the job at the mall?
Answers
Let y=total amount of money and x=hours of overtime.
mall: y=400+15x
movies: y=360+20x
Solve! Set the equations equal to each other to find x.
400+15x=360+20x
40=5x
x=8
After 8 hours of overtime the movies would pay her more.
Ignore my writing
Solve the inequality
Answers
Answer:
x=1
Step-by-step explanation:
-5 - (15x-1) = 2(7x-16) -x
Distribute the negative sign
-5-15x+1 = 2(7x-16)-x
Distribute the 2
-5-15x+1 = 14x -32-x
Combine like terms
-4-15x = 13x-32
Add 15x to each side
-4-15x+15x = 13x+15x-32
-4 = 28x-32
Add 32 to each side
-4+32 = 28x-32+32
28 = 28x
Divide each side by 28
28/28 = 28x/28
1 =x
Look at the sample below 2x-8=12
Answers
Answer:
x = 10
Step-by-step explanation:
Make x the subject
2x - 8 = 12
2x = 12 + 8
2x = 20
x = 20/2
x = 10
!!
Based on the graph, which inequality is correct for a number that is to the right of -3?
A number line is shown from negative 8 to 8 at increments of 1. A circle is shown at negative 3. The entire portion of the number line to the right of negative 3 is shaded.
A 4 > −3
B −3 > 4
C −2 < −3
D−3 < −6
Answers
Two spray paint machines are used to paint different portions of a large wall. The first machine (nicknamed "Paint Pro") is used for two hours. The second machine (nicknamed "Goldilocks") is used for an hour and a half. When they are working at the same time, they can paint 55 square feet per minute. Together they painted 5850 square feet of wall. How many square feet of wall per minute can each machine paint?e used to paint different portions of a large wall. The first machine (nicknamed "Paint Pro") is used for two hours. The second machine (nicknamed "Goldilocks") is used for an hour and a half. When they are working at the same time, they can paint 55 square feet per minute. Together they painted 5850 square feet of wall. How many square feet of wall per minute can each machine paint?
Answers
Answer:
Step-by-step explanation:
To solve this problem we need to solve a system of equations. We have two machines:
The machine "Paint Pro" is used for two hours.
The machine "Goldilocks" is used for an hour and a half.
When they are working at the same time, they can paint 55 square feet per minute. Together they painted 5850 square feet of wall.
Therefore, we have the following system of equations:
P + G = 55 ft^2/m
120P + 90G = 5850 ft^2 → 4P + 3G = 195
Solving the system of equations we have that:
P = 25
G = 30
Therefore, the paint pro paints 30sqft per minute and Goldilocks paints 25 sqft per minute.
What is the approximate value of a local maximum for the polynomial?
Answers
Answer:
2.4
Step-by-step explanation:
for the edge question the answer is actually 0.5
If there are 6 cats 5 run away 10 came how many cats are there.
Answers
Originally there are 6 cats
5 run away so take 5 away from 6:
6 - 5 = 1
This means there is only one cat left, but now 10 more cats came:
1 + 10 = 11
There are 11 cats
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
11.
Step-by-step explanation:
6 - 5 + 10
= 11.
Which is true regarding the system of equations?
x-4y=1
5x-20y=4
The system results in a false statement.
The system results in an intersection at one point.
The system results in many solutions because they are the same line.
The system results in a true statement.
Answers
Answer:
NO SOLUTION
Step-by-step explanation:
Let's actually solve the system
x-4y=1
5x-20y=4
Let's eliminate y. To do this, multiply the first equation by -5, obtaining
-5x + 20y = -5
Now add this result to the second equation:
-5x + 20y = -5
5x - 20y = 4
--------------------
0 = -1
This result is never true. Thus, this system of linear equations has NO SOLUTION.
The system of equations results in a false statement.
How to estimate the value of the system of equations?Let's solve the system of equation
x - 4y = 1 ......(1)
5x - 20y = 4 ........(2)
By using the elimination method
Eliminate y by multiplying (1) by -5
We have,
-5x + 20y = -5 ...........(3)
Adding (3) and (2), then we get
(x - 4y = 1) + (-5x + 20y = -5)
-5x + 20y = -5
5x - 20y = 4
---------------------
0 = -1
Therefore, the correct answer is option (a). The system results in a false statement.
To learn more about algebraic equations
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A restaurant owner needs to order at least 176 filet mignon steaks to be stocked for a busy Friday night. He only has
room to store 321 steaks in his refrigerator. Model the number of steaks the restaurant owner can order, using a
compound inequality.
Answers
Answer:
[tex]176 \leq x \leq 321[/tex]
Step-by-step explanation:
Let
x -----> the number of steaks the restaurant owner can order
we know that
[tex]x\geq 176[/tex] ----> inequality A
[tex]x\leq 321[/tex] ----> inequality B
so
the compounded inequality is equal to
[tex]176 \leq x \leq 321[/tex]
Answer:
FLVS
a
Step-by-step explanation:
x ≥ 176 and x ≤ 321
Which statement about a system of linear equations is incorrect?
A) A system can be solved by using the graphical method.
B) A system always has a unique solution.
C) The elimination method can be used to find the solution to a system.
D) Some systems of linear equations have no solution at all.
Answers
Answer:
B
Step-by-step explanation:
B is incorrect. Some systems have infinitely many solutions.
What is the solution to log_48x=3
Answers
Answer:
x=110592
Step-by-step explanation:
[tex]log_{48}x=3 \text{ means } 48^3=x\\\\[/tex]
So x=110592
For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.
Answers
Answer:
The the vertex is: (2, 4)
Domain: all real numbers
Range: [tex][4 \infty)[/tex]
Step-by-step explanation:
Quadratic functions can be written vertically as follows
[tex]f(x) = a(x-h)^2 +k[/tex]
Quadratic functions can be written vertically as follows
Where the point (h, k) represents the vertex of the quadratic function.
For this type of functions the domain is always all real numbers and the range is [tex][k, \infty)[/tex] or if [tex]a <0[/tex] then the range is [tex](-\infty, k][/tex]
In this case the function is:
[tex]f(x) = (x - 2)^2 + 4[/tex]
So
[tex]h = 2\\k=4[/tex]
The the vertex is: (2, 4)
Domain: all real numbers
Range: [tex][4, \infty)[/tex]
y varies directly as x. y =90 when x=6. find y when x=13
Answers
Answer:
195
Step-by-step explanation:
y varies directly with x means y=kx
k is a constant of proportionality (meaning no matter what the variable pair (x,y) is k will forever remain the same value)
we have while x=6, y=90
so plug in 90=k(6)
Solve for k: k=90/6=30/2=15
So no matter (x,y) you have the equation y=15x for this problem
Now what is y when x=13
plug in and find out
y=15(13)
y= 45+150= 195