Answer:
$640
Step-by-step explanation:
3 checks at $120 each = 3 x 120 = $360
This will reduce the balance so we should treat it as -360
2 paychecks at 240 = 2 x 240 = $480
This will increse the balance so we should treat it as +480
Net balance = 520 - 360+480=640
Balance = $640
(Equivalent Algebraic Expressions LC)
Simplify this please!!!
Answer: X^3 / Y^5
The first answer choice
Step-by-step explanation:
Make a table of values for the following equation. Then graph the equation.
y = |x| + 2
Complete the table of values below. (Simplify your answers.)
x | y
-3 | []
-1 | []
0 | []
1 | []
3 | []
The complete table of values of the absolute value equation is
x | y
-3 | [5]
-1 | [3]
0 | [2]
1 | [3]
3 | [5]
How to make a table of values for the following equation. Then graph the equation?The absolute value equation of the function is given as
y = |x| + 2
On the incomplete table of values, we have the following x values
x = -3, -1, 0, 1 and 3
Next, we substitute x = -3, -1, 0, 1 and 3 in the equation y = |x| + 2
So, we have:
y = |-3| + 2 = 5
y = |-1| + 2 = 3
y = |0| + 2 = 2
y = |1| + 2 = 3
y = |3| + 2 = 5
So, the complete table of values of the absolute value equation is
x | y
-3 | [5]
-1 | [3]
0 | [2]
1 | [3]
3 | [5]
See attachment for the graph of the absolute value equation
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Pls help
On the photo
Answer:Sect A
1)X1=-3,X2=-2
2)X1=-3/4,X2=3
3)X1=-2/3,X2=5/2
4)X1=-2,X2=4
5)X1=1/2,X2=3
6)X1=-4,X2=4/3
Answer: Sect B
1)X1=-5,X2=-3
2)X1=3,X2=4
3)X1=-5,X2=3
4)X1=4,X2=7
5)X1=-5,X2=6
6)X1=-13,X2=2
7)X1=-3,X2=8
8)X1=-7,X2=-2
9)X1=2,X2=16
10)X1=8,X2=9
section a:
1. x = -2, -3
2. x = 3, [tex]-\frac{3}{4}[/tex]
3. x = [tex]\frac{5}{2},-\frac{2}{3}[/tex]
4. x = -2,4
5. x=3, 1/2
6. 4/3, -4
section b
1.x=-3,-5
2. x= 4,3
3. x = 5
4. x =-4,-7
5. x=6,-5
6. x=2,-13
7. x=8,-3
8. x= -2, -7
9. x= 16, 2
10. x= 9,8
Step-by-step explanation:section a:
1.
(x + 2)(x + 3)= 0
x + 2 = 0 x + 3 = 0
x + 2 - 2 = 0 - 2 x + 3 - 3 = 0 - 3
x = -2 x = -3
2.
(4x + 3)(x - 3)=0
4x + 3 = 0 x - 3 = 0
4x + 3 - 3 = 0 - 3 x - 3 + 3 = 0 + 3
4x = -3 x = 3
4x = - 3 / 4
x = [tex]-\frac{3}{4}[/tex] x = 3
3.
(2x-5)(3x+2)=0
2x-5=0 3x+2=0
2x-5+5=0+5 3x+2-2=0-2
2x= 5 3x=-2
2x=5/2 3x=-2/3
x= 5/2 x= [tex]-\frac{2}{3}[/tex]
4.
(4x+8)(2x-8)=0
4x + 8 = 0 2x - 8= 0
4x = -8 2x = 8
4x = -8/ 4 2x=8/2
x=-2 x=4
5.
(5x-15)(4x-2)=0
5x-15=0 4x-2=0
5x = 15 4x=2
5x = 15 /5 4x=2/4
x=3, 1/2
6.
(9x-12)(5x+20)=0
9x -12=0 5x+20=0
9x=12 5x=-20
9x = 12/ 9 5x= -20/5
x= 4/3 x = -4
make a conjecture about the relationship between two intersecting lines that form four congruent angles
Answer:
u need to put a picture of the lines so we know what ur talking about
Which graph of ordered pairs shows a proportional relationship?
On a coordinate plane, points (negative 1, 2) and (2, negative 1) are plotted.
On a coordinate plane, points (negative 2, negative 3) and (2, 3) are plotted.
On a coordinate plane, points (negative 2, negative 1) and (2, 3) are plotted.
On a coordinate plane, points (negative 1, 3) and (1, 1) are plotted.
Mark this and return
The graph of ordered pairs that shows a proportional relationship is; B: On a coordinate plane, points (negative 2, negative 3) and (2, 3) are plotted.
What is the proportional Relationship?We are given different ordered pairs as seen in the given options to find the one that represents a proportional relationship.
Now, the option that will have the ratio of its' y-coordinates as (y2/y1) = 1 would be the one that shows a proportional relationship.
Looking at the options, the only option that meets the criteria of (y2/y1) = 1 is option B.
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9.) Given:
m
Prove: m
We’re writing this in the form of a two column proof, please help.
The point where two lines meet is known as an angle.
What are some applications of two column proofs?
A two-column proof moves a reader from premise to conclusion by using a table to give a logical argument and assigning each column to carry out a specific task.
Given the following angles from the diagram
m < 2 = m < 4
m < 2 = 100°
Prove that m<3 = 70⁰
m<2 = m<4 (vertically opposite angles)
m<3 and m<4 are supplementary, hence
m < 3 + m < 4 = 180° ( linear pair )
Substitute m<4 = 110⁰ into the expression
m < 3 + 110 = 180
m < 3 = 180 - 110
m < 3 = 70
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The complete question is -
Complete the two column proof. given 2=4 m<2=110 prove m<3=70
Pls help me. Questions are attached!!!
The hatched percentage is the 50% of the total area of the rectangle, the correct option is a.
What percentage of the area is hatched?Let's define the height of the rectangle as H and the length as L, then the area of the rectangle is:
L*H
Now we can see that the hatched area is defined by two right triangles, both of height H and of bases b₁ and b₂, such that:
b₁ + b₂ = L
Then the area of these triangles is:
[tex]A = b_1*H/2 + b_2*H/2 = (b_1 + b_2)*H/2 = L*H/2[/tex]
This is half the area of the rectangle, so the hatched percentage is the 50%.
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Rewrite in simplest rational exponent form
Show each step of your process.
The simplest rational exponent form is [tex]x^\frac{3}{4}[/tex] .
A rational exponent is defined as an exponent that can be expressed as p/q. where q ≠ 0. The common notation for rational exponents is x^m/n. where x is the base (a positive number) and m/n is a rational number.An exponential expression of the form am has a rational exponent if m is a rational number. Powers and roots of numbers are represented together in rational exponents.We have given a rational exponent [tex]\sqrt{x} .\sqrt[4]{x}[/tex] . ...(1)
By formula [tex]\sqrt[4]{x}[/tex] can be written as [tex]x^\frac{1}{4}[/tex] and [tex]\sqrt{x}[/tex] can be written as [tex]x^\frac{1}{2}[/tex] .
Put in equation (1) , we get
[tex]\sqrt{x} .\sqrt[4]{x}=x^\frac{1}{2} .x^\frac{1}{4} \\[/tex] ...(2)
Using formula [tex]a^\frac{m}{n} \times a^\frac{p}{q} = a^{\frac{m}{n} +\frac{p}{q} }[/tex]
Equation (2) can be written as
[tex]\sqrt{x} .\sqrt[4]{x}=x^{\frac{1}{2} +\frac{1}{4}}\\\\\sqrt{x} .\sqrt[4]{x}=x^{\frac{2+1}{4} }\\\\\sqrt{x} .\sqrt[4]{x}=x^{\frac{3}{4} }[/tex]
Hence , on simplification , we get [tex]x^\frac{3}{4}[/tex] .
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x^2 + 9x + 14 = ( x+_)(x+_)
quickly!!!
Answer:
[tex](x+7)(x+2)[/tex]
Step-by-step explanation:
We have the equation:
[tex]x^{2} +9x+14[/tex].
The factors of 14 are 1, 2, 7 and 14.
Now, all we have to do is find two numbers that add up to 9.
We see that 2 and 7 add up to 9.
Therefore,
[tex]x^2+9x+14=(x+7)(x+2)[/tex]
Hope this helped! Have a great day!
Answer:
(x+7)(x+2)
Step-by-step explanation:
x^2+2x+7x+14 (Because 7 and 2 add to give 9 and multiply to give 14)
x(x+2) +7(x+2) (Take out common factors, factorising)
(x+2)(x+7) (Put the things common in a bracket together and the bits that are outside in another bracket)
How do you write this in slope intercept form
11. Passes through x-intercept at -1 and (5, 6)
Answer:
y = x + 1
Step-by-step explanation:
An x-intercept of 1 would have the coordinates (-1, 0)
Slope can be found with rise / run. In this case, rise (the number of units going up) would be 6, because 6 - 0 = 6. The run would also be 6 because 5 - (-1) = 6. Following the formula, the rise divided by the run, 6 / 6 = 1, so the slope is 1.
We also have to consider the y-intercept, hence the intercept in the name Slope Intercept Form ( y = mx + b). You can find this by substituting coordinates for y and x, using the slope, and solving for b.
Either (-1, 0) or (5, 6) can be used.
6 = 5(1) + b
6 = 5 + b
b = 1, because 5 + 1 = 6
Need help ASAP! (algebra 2)
•Write a system of equations that can model the situation: A moving company charges a flat rate of $150, and an additional $5 for each box. If a taxi service would charge $20 for each box, how many boxes would you need for it to be cheaper to use the moving company, and what would be the total cost?
•Create another example of a real life situation that would use systems of equations and write the system.
The equation that can model the situation will be 150 + 5n and 20n
How to illustrate the information?Moving Company = 150 + 5n
(n = the number of boxes)
Taxi = 20n
The break-even point is when these are the same.
150 + 5n = 20n
150 = 15n
n = 150/15 = 10
So with 10 boxes, it costs the same ($200) either way.
With 11 boxes, the Moving Company costs $205
With 11 boxes, the Taxi would cost $220.
It is cheaper to use the moving company with 11 or more boxes.
Another example of a real life situation that would use systems of equations and write the system is that Company A charges a flat rate of $150, and an additional $5 for each box asn there is another taxi service that would charge $20 for each box.
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During surgery a patient was given medication administered by an iv. for the first 150 minutes the medication was flowing at a rate of 14 ml/h and for the next 4 hours the rate was set at 30 ml/h. what is the average flow rate of the medication administered to the patient in millilitres per hour. round to the nearest whole number. input the unit symbol.
During surgery, the average flow rate of the medications administered to the patient is 23 milliliters per hour.
Flow rate, denoted by Q, is defined as the amount of volume V flowing after time t. The formula for flow rate is given by:
Q = V/t
where V is volume and t is time.
For the two medication administered, given the flow rate and time, solve for the volume of each, and its total volume.
V = Q/t
1 : V1 = Q1t1 = (14ml/h)(150 minutes)(1hour/60 minutes)
V1 = 35 ml
2 : V2 = Q2t2 = (30 ml/h)(4hrs)
V2 = 120 ml
Solving for the average flow rate by dividing the sum of the volume to the sum of the time.
Qave = (V1 + V2)/(t1 + t2)
Qave = (35 + 120)ml/(2.5 + 4)hrs
Qave = 23.84615385 ml/h
Rounding off to the nearest whole number.
Qave = 23 ml/h
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Which of the following is equivalent to a real number?
A. (-324)¹4
B. (-6745)¹
C. (-2346)
D. (-874)¹2
The correct option is C. (-2346) is the real number.
What is referred as the real numbers?A real number is any number which can be discovered in the real world.
Natural numbers are used to count objects, rational numbers for fraction representation, irrational numbers for determining the square root of the a number, integers for temperature measurement, and so on. These various types of numbers combine to form a gathering of real numbers. The union of a set of rational numbers (Q) as well as the set of irrational numbers ( Q¬ ) yields the set of real numbers, denoted by R. As a result, we can consider writing the set of real numbers as R = Q ∪ Q¬. This means that natural numbers, whole numbers, integers, rational numbers, as well as irrational numbers are all real numbers. Real numbers include 3, 10, 1.0, 3/2, 5, and so on.For the given options in the question;
Any negative number raised to any root and fractional power given a imaginary number which is a part of complex number.
Thus, only option C which have (-2346) is the real number more specifically negative integer.
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The correct question is-
Which of the following is equivalent to a real number?
A. (-324)¹/₄
B. (-6745)¹/³
C. (-2346)
D. (-874)¹/₂
Jin earned $79.60 at his job when he worked for 4 hours. How much money did he
earn each hour?
A:B = 6:7 and A=30. Find B.
Please help me out with this, i dont know how to work it out, thank you.
Step-by-step explanation:
it is a ratio, and as such it is simply a fraction.
we can also write it
A/B = 6/7
and it gives us the same information.
and so,
30/B = 6/7
30 = 6B/7
210 = 6B
B = 210/6 = 35
Brandon has 23 3/5 yards of upholstery fabric and 18 1/2 yards of drapery fabric into 2 5/6 yard pieces. How many more drapery pieces than upholstery pieces does Brandon have?
The number of more drapery pieces than upholstery pieces does Brandon have is 2.03 pieces
FractionUpholstery fabric = 23 3/5 yardsDrapery fabric = 18 1/2 yardEach fabric piece = 2 5/6 yardsNumber of pieces of upholstery fabric = 23 3/5 ÷ 2 5/6
= 118/5 ÷ 17/6
= 118/5 × 6/17
= 708 / 85
= 8 28/85
Number of pieces of drapery fabric = 18 1/2 ÷ 2 5/6
= 37/2 ÷ 17/6
= 37/2 × 6/17
= 222/34
= 6 18/34
= 6 9/17
How many more drapery pieces than upholstery pieces does Brandon have = 708 / 85 - 222/34
= (24072-18204) / 2890
= 5,868 / 2890
= 2.03 pieces
Therefore, the number of more drapery pieces than upholstery pieces does Brandon have is 2.03 pieces
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An employee earns $15 an hour for the first 20 hours worked during the week. The employee earns an extra $5 per hour for every additional hour over 20 hours worke per week. The scenario is represented by the function f(x). How much does the employee earn by working 25 hours in one week?
The money that the employee earn by working 25 hours in one week is $400.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let f(x) represent the amount of money that the employee earn by working x hours. If the employee work more than 20 hours, then:
f(x) = 15x + 5(x - 20)
For 25 hours:
f(25) = 15(25) + 5(25 - 20) = 400
The money that the employee earn by working 25 hours in one week is $400.
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If ∠A = 5x – 6 and ∠C = 3x + 14, what is the measure of ∠A?
Lifesaver:
∠A = ∠C
⇒ AB = BC (Equal angles have equal sides opposite to them)
⇒ 5x+6 = 3x+14
⇒ 5x-3x = 14-6
⇒ 2x = 8
⇒ x= 4
Let f(x)=7 x+5 and g(x)=x². Perform each function operation and then find the domain of the result.
f/g(x)
The domain of the result f/g(x) is (7 /x ) + (5/x^2).
The two functions are:
f(x) = 7x + 5
and
g(x) = x^2
For calculating f/g(x)
f/g(x) is equivalent to f(x) / g(x)
Hence (f / g)(x) = f(x) / g(x)
= 7x + 5 / x^2
= (7 /x ) + (5/x^2)
the domain of the result f/g(x) is (7 /x ) + (5/x^2).
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4. Use the equations below to find the indicated values.
a. f(x) = 6x +5
i) f(2)=
b. g(x) = 3x
i) g(4) =
ii) f(-2) =
ii) g(0) =
iii) f(1/2) =
iii) g(-4)=
Answer:
f(2) = 17g(4) = 12f(-2) = -7g(0) = 0f(1/2) = 8g(-4) = -12Step-by-step explanation:
We have
[tex]f(x) = 6x + 5[/tex]
[tex]g(x) = 3x[/tex]
To find the value of either of these functions for a specific value of x, simply substitute that value into the corresponding function equation.
[tex]\bold{f(2)}[/tex]
Substitute x with 2 in 6x + 5
==> [tex]6\cdot \:2+5=17[/tex] (Answer)
[tex]\bold{g(4)}[/tex]
Substitute x with 4 in g(x) = 3x
==> [tex]3 \cdot4=12[/tex] (Answer)
[tex]\bold{f(-2)}[/tex]
Substitute x with -2 in 6x + 5
[tex]6\left(-2\right)+5=-7[/tex] (Answer)
[tex]\bold{g(0)}[/tex]
Substitute x with 0 in g(x) = 3x
==> [tex]3\cdot0=0[/tex] (Answer)
[tex]\bold{f(\frac{1}{2})}[/tex]
Substitute x with [tex]\frac{1}{2}[/tex] in 6x + 5
==> [tex]6\cdot \frac{1}{2}+5 = 3 + 5 = 8[/tex] (Answer)
[tex]\bold{g(-4)}[/tex]
Substitute x with -4 in g(x) = 3x
==> [tex]3\left(-4\right) = -12[/tex] (Answer)
(the cube root of 125 − 14 ÷ 2)(3 − 5)2 step by step
Answer:
18
Step-by-step explanation:
[tex] \sf( \frac{ ∛125 \: - \: 14 }{2})(3 - 5)2[/tex]
Apply rule: ([tex] a[/tex]) = [tex] a[/tex]
[tex] \sf( \frac{ ∛125 \: - \: 14 }{2}) = \: \sf\frac{ ∛125 \: - \: 14 }{2}[/tex]
[tex] = \sf \frac{∛125 \: - \: 14 }{2}(3 - 5)2[/tex]
Substract the numbers (3-5) = (-2)
[tex] = \sf \frac{∛125 \: - \: 14 }{2}( - 2)2[/tex]
Change 2 to fraction: [tex] \sf \frac{2}{1} [/tex]
[tex] = \sf \frac{∛125 \: - \: 14 }{2} \times \frac{2}{1} ( - 2)[/tex]
Cross- cancel common factor 2
[tex] = \sf \frac{∛125 \: - \: 14 }{1} ( - 2)[/tex]
Let's calculate [tex] \sf \frac{∛125 \: - \: 14 }{1} [/tex]
[tex] = \sf \frac{∛125 \: - \: 14 }{1} [/tex]
Apply a fraction rule = a/1 = a
[tex] = \sf ∛125 \: - \: 14 [/tex]
[tex] \sf = - 9[/tex]
[tex] \sf \: = - 9( - 2)[/tex]
[tex] \sf \: = 18[/tex]
Find the domain, points of discontinuity, and x - and y - intercepts of each rational function. Determine whether the discontinuities are removable or non-removable. y=2x²+5 / x²-2 x
The domain of given points are :
IR x ≠ ± √2
Points of discontinuity - x = ± √2 ( non removable / asymptote )
x - intercept =± √-5/2 , y - intercept = 5/2
What is rational functions ?Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).
CALCULATIONy=2x²+5 / x²-2 x
= 2[tex]x^{2}[/tex]+5/(x-√2)(x+√2)
The domain of given points are :
IR x ≠ ± √2
Points of discontinuity - x = ± √2 ( non removable / asymptote)
x-intercept :
2√10x=2[tex]x^{2}[/tex]+5+2√10x
2[tex]x^{2}[/tex] = -5
[tex]x^{2}[/tex]=-5/2
x = ±√-5/2
y - intercept :
2 * [tex]0^{2}[/tex] + 5 / ( 0-√2)(0+√2)
= 5/2
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The 4th term of an A.P. is 27. and the sum of the 1st and the fourth term is 42. Find the common difference
Answer:
d = 4
Step-by-step explanation:
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₄ = 27 , then
a₁ + 3d = 27 → (1)
Also
a₁ + a₄ = 42 ← substitute a₄ = 27
a₁ + 27 = 42 ( subtract 27 from both sides )
a₁ = 15
substitute a₁ = 15 into (1)
15 + 3d = 27 ( subtract 15 from both sides )
3d = 12 ( divide both sides by 3 )
d = 4
For each pair of functions, find f(g(x)) and g(f(x)) .
f(x)=x+5/2, g(x)=x²,
The value for f(g(x)) =[tex](\frac{x^{2} +5}{2} )[/tex]
g(f(x)) =[tex](\frac{x+5}{2} )^2[/tex]
What are the domain of the function f(g(x)) and g(f(x))?Given:
f(x)=x+5/2 and g(x)=x²
Take, g(x) = x²
substitute x = f(x) into the function g(x). Then:
g(f)x)) =[tex](\frac{x+5}{2} )^2[/tex]
Now, the next step is to substitute g(x) into the function f(x)
f(x) = x+5/2
f(g(x)) =[tex](\frac{x^{2} +5}{2} )[/tex]
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Please show how u got the answer (due: at 11:59)
Answer: 5. 420, 6. 450, 7. 750, 8. 756
Step-by-step explanation:
If the median of a data set is 760, the third quartile is 950, and the first quartile is 650, what is the interquartile range?
The required interquartile range of the data set along the median is 300.
The question has given, the median of a data set is 760, the third quartile is 950, and the first quartile is 650,
To determine the interquartile range.
Statistics is the study of mathematics that deals with relations between comprehensive data.
Here,
The first quartile is 650,
The third quartile is 950,
Since, the interquartile range is given as,
IQR = third quartile - first Quartile
IQR = 950 - 650
IOR = 300
Thus, the required interquartile range of the data set along the median is 300.
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What values of x and y satisfy the system of equations 10x=5y−8 15x=−5y−2?
[tex]\begin{array}{llll} 10x=5y-8\\\\ 15x=-5y-2\\\\ \end{array}\implies \stackrel{\textit{using elimination}}{\begin{array}{llll} 10x-5y=-8\\\\ 15x+5y=-2\\\cline{1-1} 25x+0=-10 \end{array}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]25x=-10\implies x=\cfrac{-10}{25}\implies x=-\cfrac{2}{5} \\\\\\ \stackrel{\textit{substituting "x" in the 1st equation}}{10\left(-\frac{2}{5} \right)=5y-8\implies }-4=5y-8\implies 4=5y\implies \cfrac{4}{5}=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} \left( -\frac{2}{5}~~,~~\frac{4}{5} \right) \end{array}}~\hfill[/tex]
Jacqui is making a stained glass piece. She cuts the top and bottom pieces at a 30° angle. If the corners are right angles, explain how Jacqui knows that each pair of opposite sides are parallel.
A right angle is an angle of 90 degrees. A right angle is formed when two lines that are perpendicular to each other intersect. A right angle assumes the shape L.
Parallel lines are lines that do not meet or intersect at any point no matter how long they are extended. The sided of most quadrilaterals are parallel to each other and intersect at right angles. For example: squares and rectangles.
In our question, Jacqui will know that each pair of opposite sides are parallel since the corners are right angles, each pair of opposite sides will be perpendicular to the same line. As a result, each pair of opposite sides will be parallel.
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Nick has $50 to spend during fall break. he decides to spend $10 each day. which equation represents the amount of money nick has left, y, and the number of days x?
Answer:
$50 = 5 days
$40 = 4 days
$30 = 3 days
$20 = 2 days
$10 = 1 day
Step-by-step explanation:
hope this helps = )
Find the area of a rectangle with a base of 2 and a height of 6.
Step-by-step explanation:
the area of a rectangle is
length × width
or
base × height
it all depends on how you make the 2 dimensions.
anyway, the area is in our case
2×6 = 12 square units