Answer:
They are equivalent
Step-by-step explanation:
x/4 multiplied by y/y equals to xy/4y. Therefore, they are equivalent
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?
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.
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.
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
Show all work to multiply (3+√-16)(6√-64)
Answer:
[tex]\large\boxed{(3+\sqrt{-16})(6\sqrt{-64})=-192+144i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-1}=i\to i^2=-1\\\\(3+\sqrt{-16})(6\sqrt{-64})=(3+\sqrt{(16)(-1)})(6\sqrt{(64)(-1)})\\\\=(3+\sqrt{16}\cdot\sqrt{-1})(6\cdot\sqrt{64}\cdot\sqrt{-1})=(3+4i)\bigg((6)(8i)\bigg)\\\\=(3+4i)(48i)\qquad\text{use the distributive property}\ (b+c)a=ba+ca\\\\=(3)(48i)+(4i)(48i)=144+192i^2\\\\=144i+192(-1)=-192+144i[/tex]
The value of the given expression (3+√-16)(6√-64) is (-192+144i).
What is the product of (3+√-16)(6√-64)?As the given two factors are complex numbers, therefore, we must know about the value of i
i = √(-1)
i² = (-1)
The solution of the product,
[tex](3+\sqrt{-16})(6\sqrt{-64})\\\\ = (3\times 6\sqrt{-64}) + (\sqrt{-16}\times 6\sqrt{-64})\\\\= (3+4i)(6\cdot 8i)\\\\= (3+4i)(48i)\\\\= 144i + 192(i)^2\\\\= 144i + 192(\sqrt{-1})^2\\\\= 144i + 192(-1)\\\\= -192+144i[/tex]
Hence, the value of the given expression (3+√-16)(6√-64) is (-192+144i).
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For a given input value b, the function g outputs a value a to satisfy the following equation.
a-7=3(b+2)
Write a formula for g(b) in terms of b.
g(b)=
[tex]g(b)=3b+13[/tex]
Hope this helps.
r3t40
To find the formula for g(b), isolate the variable a in the given equation by solving step by step. The formula for g(b) is g(b) = 3b + 13.
Explanation:To write a formula for g(b) in terms of b, we need to isolate the variable a in the equation given. Let's simplify the given equation step by step:
Add 7 to both sides of the equation to isolate a: a - 7 + 7 = 3(b + 2) + 7Therefore, the formula for g(b) is g(b) = 3b + 13
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Graph the solution of this inequality:
9 (35x - 14) < 24 + 3
(4-2i).(6-3i) / (1-i).(1+i)
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
Calculate (Round two decimal places for final answer) 15L is approximately ___gal.
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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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.
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:
Julius went on a volunteer trip to Central
America and took medical supplies with him.
He packed a bag with 50 pounds of supplies.
He brought pieces of equipment that weighed
10 pounds each and bottles of medicine that
weighed pound each prepresents the
number of pieces of equipment he brought
and b represents the number of bottles of
medicine he brought then the total weight can
be represented by the equation 10p+b 50.
the brought 3 pieces of equipment, how many
bottles of medicine did he bring?
Answer:
20 bottles
Step-by-step explanation:
10*3+b=50
30+b=50
-30 -30
b=20
Help
On a map, 1 in. represents 50 mi. Two cities are 6 1/2 in apart on the map.
How far apart are the actual cities?
325 mi
300 1/2
300
56 1/2
Answer:
325 mi
Step-by-step explanation:
We can write a proportion to solve, putting distance over inches
50 miles x miles
------------- = -------------
1 inch 6.5 inches
Using cross products
50 * 6.5 = 1*x
325 = x
The distance is 325 miles
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.
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
What is the product?
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
Which of the following is the graph of the quadratic function y - x? +10x+16 ?
A. Graph C
B. Graph B
C. Graph A
D. Graph D
Find the vertex:
[tex]\textrm{Use the formula } \frac{-b}{2a} \textrm{ to find the vertex}\\ \\ \frac{-10}{2} = -5\\ \\ \textrm{In order to find the y value plug in -5 back into the function}\\ \\ y=(-5)^2+10(-5)+16\\ y=-9\\\\ \textrm{The vertex of the function is} (-5,-9)[/tex]
Determine if the parabola will open up or down:
[tex]a > 0 \\ \\ 1>0[/tex]
Since the value of a is positive, the parabola will open upwards
Find the x and y intercepts:
Factor [tex]y = x^2+10x + 16[/tex] to find the x intercepts
(x+8)(x+2)
x + 8 = 0
x = -8
x + 2 = 0
x = -2
x intercepts:
x = -2
x = -8
Find the y intercept
[tex]y = 0^2+10(0) + 16\\\\ y=16[/tex]
Hence, C. Graph A best represents the quadratic function [tex]y = x^2+10x + 16[/tex]
For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range.
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]
Find the equation of the line perpendicular to y= -2x+1 that also intersects the point (8, 2)
Help me!!!
The slope of the perpendicular is the negative reciprocal of the original line, so m = -1/(-2) = 1/2.
The general line of slope m through (a,b) is
[tex]y - b = m(x-a)[/tex]
So the line we seek is
[tex] y - 2 = \frac 1 2 ( x - 8)[/tex]
[tex] y = \frac 1 2 x - 2[/tex]
Answer: y = 1/2 x + -2
What is the solution to log_48x=3
Answer:
x=110592
Step-by-step explanation:
[tex]log_{48}x=3 \text{ means } 48^3=x\\\\[/tex]
So x=110592
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.
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.
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HELP PLS GIVING BRAINLIEST
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
For two functions, a(x) and b(x), a statement is made that a(x) = b(x) at x = 2. What is definitely true about x = 2?
Both a(x) and (x) have a maximum or minimum value at x = 2.
Both a(x) and b(x) have the same output value at x = 2.
Both a(x) and b(x) cross the x-axis at 2.
Both a(x) and (x) cross the y-axis at 2.
Answer:
The answer is Both a(x) and b(x) have the same output value at x = 2.
Step-by-step explanation:
The answer is Both a(x) and b(x) have the same output value at x = 2. Because when a(x)=b(x) the lines intersect at that point lines intersect they have a point in common. Also, a(x)=b(x) means that the outcomes are the same
The statement that is true about a(x) = b(x) at x = 2 is
Both a(x) and b(x) have the same output value at x = 2.
Option B is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
a(x) and b(x)
At x = 2,
a(x) is equal to b(x)
a(x) = b(x)
This means that,
a(x) and b(x) have the same output value at x = 2.
Both a(x) and (x) have a maximum or minimum value at x = 2.
This is not true because we have to differentiate the function and put it as zero to get the maximum and minimum value at x=2.
Both a(x) and b(x) crosses the x-axis at 2.
This is not true because the function on the graph is at a point of intersection between x = 2 and the y value.
Both a(x) and (x) crosses the y-axis at 2.
This is not true because the function on the graph is at a point of intersection between x = 2 and the y value.
Thus,
The statement that is true about a(x) = b(x) at x = 2 is
Both a(x) and b(x) have the same output value at x = 2.
Option B is the correct answer.
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How many solutions does this linear system have y= 1/2x+4
x+2y=-8
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).
y varies directly as x. y =90 when x=6. find y when x=13
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
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
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
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?
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
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.
Answer:
B
Step-by-step explanation:
B is incorrect. Some systems have infinitely many solutions.
What is the approximate value of a local maximum for the polynomial?
Answer:
2.4
Step-by-step explanation:
for the edge question the answer is actually 0.5
Change each dimension on the store toy box to feet 36”__ feet 18”=__feet
Answer: 36" = 3 feet
18" = 1.5 feet
Explanation: 1 foot = 12 inches
What is the slope intercept equation of the line below?
Answer:
D
Step-by-step explanation:
I graphed each equation on a piece of paper and on desmos.com
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?
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!
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.
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