SOLUTION
The polynomials expression given are
[tex]\mleft(3a^2+5a-2\mright)\mleft(5a^2-3a+4\mright)[/tex]Expand the expression by distributing the parentheses
[tex]3a^2\cdot\: 5a^2+3a^2\mleft(-3a\mright)+3a^2\cdot\: 4+5a\cdot\: 5a^2+5a\mleft(-3a\mright)+5a\cdot\: 4-2\cdot\: 5a^2-2\mleft(-3a\mright)-2\cdot\: 4[/tex]Simplify
[tex]\begin{gathered} 15a^4-9a^3+12a^2+25a^3-15a^2+20a-10a^2+6a-8 \\ \text{Rearranging and simplify} \\ 15a^4-9a^3+25a^3+12a^2-15a^2-10a^2+20a+6a-8 \\ 15a^4+16a^3-13a^2+26a-8 \end{gathered}[/tex]Hence, the answer is
[tex]15a^4+16a^3-13a^2+26a-8[/tex]Marcus can choose between a monthly salary of $1,500 plus 5.5% of sales or $2,600 plus 2% of sales. He expects sales between $5,000 and $10,000 a month. Complete the explanation to show which salary option he should choose based on how much he could make.
Marcus should choose $2400 plus 3% of sales.
His salary is composed of a fixed salary and a variable salary.
Fixed Salary + Variable Salary = Monthly Salary
2400 150 (3% of 5k) = 2350 - minimum salary he'll receive
2400 300 (3% of 10k) = 2700 - maximum salary he'll receive
VS
Fixed Salary + Variable Salary = Monthly Salary
1500 275 (5.5% of 5k) = 1775 - minimum salary he'll receive
1500 550 (5.5% of 10k) = 2,050 - maximum salary he'll receive
As you can see, despite the high percentage of sales offered, it is not a good option because the fixed salary is low as compared to the other option. Even the maximum salary he'll receive under the option of $1500 is way lower than the minimum salary he'll receive under the option of $2400.
Fixed salary means that each employee receives exactly the same pay and fairness as any other employee in the same pay grade. The level is determined by years of experience and position. For example, all analysts are paid exactly the same all directors are paid the same and all executives are paid the same.
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find the area of this parallelogram in unit9yd13 yd10 yd
Given: A parallelogram with the dimension below
[tex]\begin{gathered} b=\text{base}=13yd \\ h=\text{height}=9yd \\ a=\text{slant side=10yd} \end{gathered}[/tex]To Determine: The area of the given parallelogram
The area of a paralleogram is given by the formula
[tex]A_{\text{PARALLELOGRAM}}=\text{base}\times height[/tex]Substitute the base and the height into the formula
[tex]\begin{gathered} A_{\text{PARALLELOGRAM}}=13yd\times9yd \\ A_{\text{PARALLELOGRAM}}=117yd^2 \end{gathered}[/tex]Hence, the area of the given parallelogram is 117yd²
1 print is equal to 2 cups or 16 fulid ounces how many fulid onces are in 4 prints 3 cups
Answer:
There would be 88 fluid ounces in 4 prints and 3 cups.
Step-by-step explanation:
So, if 1 print is equal to two cups, and we have 4 prints, that would mean we can multiply 4 x 2, which equals 8 cups. Now that the prints are out of the way, we add the 3 cups still remaining, to get 11 cups. Now, it wants us to find the fluid ounces, which 16 fluid ounces are in 2 cups, so, 11 divided by 2 = 5.5. So, 5.5 x 16 = 88 fluid ounces.
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Answer:
88
Step-by-step explanation:
16x4=64
8x3=24
64+24=88
Consider the equation, x2 3x + 4, where x represents a real number.a. Are the expressions x2 and 3x + 4 algebraically equivalent?b. The following table shows how we might "sift” through various values to assign to the variable symbol x in the hunt for values that would make the equation true.
(a)
The expression are equivalent to each ohter if both expressions give same value for all assign values of x. From the table it can be observed that both expression do not give same value for all values of x. Thus expression
[tex]x^2[/tex]and 3x + 4 are not eqivalent to each other.
(b)
From the table, it can be observed that values of the expression are equal for x = 4. So equation
[tex]x^2=3x+4[/tex]holds true for x = 4.
For f(x)=2^x, find for for f(5) and f (-6)
It order to find f(5) and f ( -6 ) we just replace x on the equation with
x = 5 and x = -6
In the first case, x = 5
[tex]\begin{gathered} f(x)=2^x \\ f(5)=2^5 \\ =2\cdot2\cdot2\cdot2\cdot2 \\ =32 \end{gathered}[/tex]In the second case, x = -6
[tex]\begin{gathered} f(x)=2^x \\ f(-6)=2^{-6} \\ =\frac{1}{2^6} \\ =\frac{1}{2\cdot2\cdot2\cdot2\cdot2\cdot2} \\ =\frac{1}{64} \end{gathered}[/tex]Answer: f(5) = 32 and f(-6) = 1/649 more than the quotient of a number and 6 is 3
The expression "a number" can be represented with any letter. Use, for instance, the letter n.
Then, the expression "The quotient of a number and 6" can be represented as:
[tex]\frac{n}{6}[/tex]9 more than the quotient of a number and 6 can be expressed as:
[tex]9+\frac{n}{6}[/tex]If that expression is equal to 3, then:
[tex]9+\frac{n}{6}=3[/tex]Which is an algebraic expression for "9 more than the quotient of a number and 6 is 3".
How much interest will Harley earn in 3 years if she deposits $1,200 into a savings account that pays 6% simple interest?
14 08.08LCChoose the brand of chips with the lowest price per ounce.Brand A 20 ounces for $2.50Brand 6 32 ounces for $3.25 (1 point)O Brand ABrandBoth brands have the same price per ounce.Not enough information is given
Brand 6
1) In this problem, we need to find the unit rate. So let's do it and then compare for both brands
2) Brand A
[tex]\begin{gathered} 20oz----2.5 \\ 1oz-----x \\ 20x=2.5 \\ \frac{20x}{20}=\frac{2.5}{20} \\ x=\$0.125 \end{gathered}[/tex]So for Brand A, 1 oz is approximately 13 cents ( rounding up to the nearest hundredth)
3) Brand 6
We can write out another proportion:
[tex]\begin{gathered} 32oz----3.25 \\ 1oz----y \\ 32y=3.25 \\ \frac{32y}{32}=\frac{3.25}{32} \\ y=\$0.101 \end{gathered}[/tex]So brand 6, 1 oz is approximately 10 cents.
Combined gas law
Please reply with the steps, I'm confused
Answer:
V₂ = 1.0 L
Step-by-step explanation:
Combined Gas Law
[tex]\sf \dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}[/tex]
where:
P₁ is the initial pressure.V₁ is the initial volume.T₁ is the initial temperature.P₂ is the final pressure.V₂ is the final volume.T₂ is the final temperature.Temperature must be in kelvins (K).
To convert Celsius to kelvins, add 273.15.
Volume can be in any unit.
Given values:
P₁ = 5 atmV₁ = 1 LT₁ = 300 KP₂ = 10 atmT₂ = 600 KRearrange the equation to isolate V₂:
[tex]\implies \sf V_2=\dfrac{P_1V_1T_2}{P_2T_1}[/tex]
Substitute the given values into the equation:
[tex]\sf \implies V_2=\dfrac{5 \cdot 1 \cdot 600}{10 \cdot 300}[/tex]
[tex]\sf \implies V_2=\dfrac{3000}{3000}[/tex]
[tex]\sf \implies V_2=1.0\;L[/tex]
Therefore, the volume of V₂ is 1.0 L.
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What is the difference between, obtuse, right, and scalene angles?
Answer:
Obtuse angles are angles with a measure over 90 degrees.
Right angles are angles with a measure of exactly 90 degrees.
A scalene triangle can be defined as a triangle whose all three sides have different lengths, and all three angles are of different measures. The angles of a scalene triangle follow the angle sum property and always add up to 180.
Step-by-step explanation:
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A number n plus 4.1 is less than or equal to 7 . Write this word sentence as an inequality.
Answer:
The word sentence you are looking for is:
n + 4.1 ≤ 7
Step-by-step explanation:
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In the word BALLOONS, the ratio of vowels to all letters is
3/5
5:3
8/5
3 to 8
Pls show me step by step
The ratio of vowels to all letters in the word is 3 to 8
Given,
The word BALLOONS
We have to find the ratio of vowels to all letters in this word.
Ratio;
Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.
So,
The number of letters in BALLOONS = 8
The number of vowels = 3
The ratio of vowels to all letters in the word = 3 to 8
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Rey wrapped 6 presents every 10 hours. At that rate, how long, in hours, will it take to wrap 18 presents? label optional
Data
Rey wrapped 6 presents every 10 hours.
will it take to wrap 18 presents?
Procedure
[tex]18\text{ presents }\cdot\frac{10\text{ hours}}{6\text{ presents}}=30\text{ hours}[/tex]
It will take 30 hours
Answer: it will take 30 hours to wrap 18 gifts
Step-by-step explanation:
I cant really explain it so i will show you.
() = h (hours)
| = g (gifts)
( | | | | | | ) }-6
( | | | | | | ) }-6
( | | | | | | ) }-6
10h + 10h + 10h = 30h
6g + 6g + 6g = 18g
I hope this helped
Suppose both factors are multiples of 10 . Explain why the number of zeros may be different in factor than product
By using the concept of factors and multiples, it can be inferred that
Product of a and b i.e. ab has atleast (m + n) trailing zeroes which is greater than both m and n
What are factors and multiples?
Suppose the number is k. Factors of k are those numbers that divide k.
For example: Factors of 6 are 1, 2, 3 and 6
Multiples of k are those numbers which are divided by k.
For example Multiples of 6 are 6, 12, 18, ....
Since the factors are of multiple of 10, then the factors will have atleast one trailing zero. Let the factors be a and b
Suppose a has m trailing zeroes and b has n trailing zeroes.
Product of a and b i.e. ab has (m + n) atleast trailing zeroes which is greater than both m and n
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When we apply the concept of factors and multiples, we concluded that the product of a and b i.e. ab has at least (m + n) trailing zeroes that are greater than both m and n.
What are factors and multiples?
A multiple is a number that, up to a given number of times, can be divided by another number without leaving a leftover.
A factor is a pair of integers or more that divide a given number by itself without leaving a residue.
Here,
the factors are of multiple of 10, then the factors will have at least one trailing zero.
We let the factors be a and b
Suppose a has m trailing zeroes and b has n trailing zeroes then, the Product of a and b i.e. ab has (m + n) at least trailing zeroes which are greater than both m and n.
Hence, we concluded that the product of a and b i.e. ab has at least (m + n) trailing zeroes that are greater than both m and n.
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Consider the line 8x-2y=-5.
Find the equation of the line that is parallel to this line and passes through the point (-4, 3).
Find the equation of the line that is perpendicular to this line and passes through the point (-4, 3).
Answer:
4x - y = - 19 and x + 4y = 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
8x - 2y = - 5 ( subtract 8 from both sides )
- 2y = - 8x - 5 ( divide through by - 2 )
y = 4x + [tex]\frac{5}{2}[/tex] ← in slope- intercept form
with slope m = 4
• Parallel lines have equal slopes , then
y = 4x + c ← is the partial equation
to find c substitute (- 4, 3 ) into the partial equation
3 = - 16 + c ⇒ c = 3 + 16 = 19
y = 4x + 19 ← equation of parallel line in slope- intercept form
subtract y from both sides
0 = 4x - y + 19 ( subtract 19 from both sides )
- 19 = 4x - y , that is
4x - y = - 19 ← equation in standard form
----------------------------------------------------------------------
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute (- 4, 3 ) into the partial equation
3 = 1 + c ⇒ c = 3 - 1 = 2
y = - [tex]\frac{1}{4}[/tex] x + 2 ← equation of perpendicular line in slope- intercept form
multiply through by 4 to clear the fraction
4y = - x + 8 ( add x to both sides )
x + 4y = 8 ← equation in standard form
soving equations variable on both sides 3x=2x+50
Answer:
x = 50
Step-by-step explanation:
Solve the equation:3x = 2x + 50
Subtract 2x from both sides,
3x - 2x = 2x -2x + 50
x = 50
Can anyone do this equation of a straight line problem?
The required equation for line M will be 4x+72=y as in the form of y=ax+b because line L is perpendicular to line M.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign. A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Here,
If x-intercept=B and y-intercept=E
Point B=(16,0)
Point E=(0,4)
point A=(-16,4+4)
=(-16,8)
line M is perpendicular to line L,
slope of L=-4/16
=-1/4
slope of M=-1/-1/4=4
The equation of line M will be,
point=(-16,8)
slope=4
y-8=4(x+16)
y-8=4x+64
4x-y+72=0
Line L is perpendicular to line M, so the required equation for line M will be 4x+72=y in the form of y=ax+b.
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Decimals into frictions -13.25=
Answer:-53/4
Step-by-step explanation:
Answer: -53/4
Step-by-step explanation:
[tex]\displaystyle\\-13.25=\\\\-13\frac{25}{100}=\\\\-13\frac{25(1)}{25(4)}=\\\\-13\frac{1}{4} =\\\\-\frac{13(4)+1}{4} =\\\\-\frac{52+1}{4}=\\\\-\frac{53}{4}[/tex]
A coordinate plane with a graphed system of inequalities. The x- and y-axes both scale by one. There is a dashed line representing an inequality that goes through the plotted points (0,5) and (3,1). The shaded region for the inequality is below the line. Find the inequality represented by the graph.
The linear inequality that represented by the graph is given as follows:
y < -4x/3 + 5.
How to obtain the inequality?The inequality is represented by a line, which has the following format:
y = mx + b.
In which the coefficients of the equation of the line are listed as follows:
m is the slope, representing the rate of change, that is, by how much y changes when x increases by one.b is the y-intercept, representing the value of y when x = 0.The two points of the line are given as follows:
(0,5) and (3,1).
Hence the intercept is:
b = 5.
The slope is given by the change in y divided by the change in x, hence it is of:
m = (1 - 5)/(3 - 0) = -4/3.
Hence the line is:
y = -4x/3 + 5.
The inequality is below the shaded line, hence it is:
y < -4x/3 + 5.
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Answer:
y < -4/3x + 5.
Step-by-step explanation:
Line f passes through 4, 0) and is parallel to a line that passes through (7, -3) and (-10. -2)
A straight line can be written in the form of a two variable linear equation.
The equation of line passing through point (4,0) is y = -1 / 17 x + 4.
How to represent a straight line on a graph?To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.
Given that,
The line is passing through the point (4,0).
It is parallel to the line passing through (7, -3) and (-10. -2).
The slope of the line passing through (7, -3) and (-10. -2) is
m₁ = (-2-(-3)) / (-10 - 7)
m₁ = - 1 / 17
Since the slope of two lines parallel to each other is equal, the slope of the line passing through point (4,0) is - 1 / 17.
Thus, the equation of line passing through point (4,0) can be written as,
(y - 4) / (x - 0) = - 1 / 17
=> y = -1 / 17 x + 4
Hence, the equation of the given line is y = -1 / 17 x + 4.
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Use the partial quotients strategy to solve the following equations. Show your work. 1. 70.4 ÷ 11 = 2. 43.2 ÷ 16 =
Answer:
70.4/11 = 6.4
Step-by-step explanation:
A dance studio charges an application fee and a monthly rate for dance classes. This is represented by the equation, C=50x+75. In this function, x represents the
Responses
number of dance classes taken each month
cost per dance class
application fee
total cost of dance classes each month
In linear equation, 50x is the total cost of dance classes each month.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).C = 50x + 75, where 75 is the application fee. When they take out the application fee, it will become:
C = 50x +75 (-75)
C = 50x
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At a real estate agency, an agent sold a house for $344,000. The commission rate is 4.5% for the real estate agency and the commission rate for the agent is 25% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
Answer:
Commission - $15,480 | Money the agency made - $86,000
Step-by-step explanation:
4.5% of $344,000 is $15,480
25% of $344,000 is $86,000
can you plsss help me due now
Answer:
D
Step-by-step explanation:
I'll try to be brief
Let's plug in our 'y' variable (2x)
2x + (2x) = 20
4x = 20
x = 5
Now, plug in our 'x' variable to get our 'y' variable:
y = 2(5)
y = 10
So, our answer in (5, 10)
Or, D
Given a line segment that contains the points A,B, & C in order, and given that B is the midpoint of AC, if AB = 3x + 6, and BC = X + 14,find x.
Since B is the midpoint of AC.
AB = BC
3x + 6 = x + 14
Solve for x :
3x - x = 14 - 6
2x = 8
x= 8/2
x= 4
what does this equal
-5/6+(-5/6)=
Answer:
-5/3
Step-by-step explanation:
guys can u help me with this question, please
The cross marked at the points (-2.5 , -5) and (0 , -1.5) is shown below .
The x and y coordinate helps in identifying a point in the coordinate axis and it is written as a ordered pair (x,y) .
where x represents the position of point with reference to the x-axis
and y represents the position of point with reference to the y axis .
In the question ,
points are given , we have to plot them and mark a cross .
Part(a)
point is (-2.5 , -5)
So , the x coordinate is -2.5
means the point is 2.5 units left from the origin ,
and y coordinate is -5 .
means the point is 2.5 units down from the origin .
the cross mark on the point is shown below .
Part(b)
point is (0 , -1.5)
So , the x coordinate is -2.5
means the point is 0 units units from the origin ,
and y coordinate is -1.5 ,
means the point is 1.5 units down from the origin .
the cross mark on the point is shown below .
Therefore , The cross marked at the points (-2.5 , -5) and (0 , -1.5) is shown below .
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1/3b+11/18 when b=1/6
To answer this question, we have that the expression is:
[tex]\frac{1}{3}b+\frac{1}{18}[/tex]Answer:
Solve for b by simplifying both sides of the equation, then isolating the variable. Exact Form:
b = 3/17 Decimal Form: b=0.17647058
Step-by-step explanation:
х1451°Find the value of x. Round to the nearest tenth.x=
To solve this question, we employ the sine relation;
[tex]\begin{gathered} \frac{14}{x}=\sin 51 \\ \end{gathered}[/tex]Rearranging the equation, we obtain ;
[tex]x=\frac{14}{\sin 51}=20.88\approx20.9[/tex]Therefore, x = 20.9
Please Help!
Solve the inequality for y. y+15 less than 14Simplify your answer as much as possible.
im in accelerated algebra
Answer:
y < - 1
Step-by-step explanation:
y + 15 < 14 ( isolate y by subtracting 15 from both sides )
y < - 1
Answer: y < - 1
Step-by-step explanation:
y + 15 < 14 (isolate y by subtracting 15 from both sides)
y < - 1