After factorization, the factors are (x - 22) (x + 10).
What is factorization?In mathematics, factorization is the process of dividing a large number into smaller numbers that, when multiplied together, yield the original number. Factorization occurs when you divide a number into its factors or divisors. For example, the factorization of the number 12 could be 3 times 4. The Greatest common factor (GCF), the Grouping method, the difference in two squares, and the sum or difference in cubes are the four main types of factoring.So, x² - 12x - 220:
x² - 12x - 220x² - x( 22 - 10 ) - 220x² - 22x + 10x - 220x(x - 22) + 10(x - 22)Factors: (x - 22) (x + 10)Therefore, the factors are (x - 22) (x + 10).
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What is the solution to the equation StartFraction m Over m + 4 EndFraction + StartFraction 4 Over 4 minus m EndFraction = StartFraction m squared Over m squared minus 16 EndFraction? m = –4 m = –2 m = 2 m = 4
The solution to the equation is mathematically given as
m=-2
This is further explained below.
What is the solution to the equation?Generally, the equation is mathematically given as
[tex]\frac{m}{m+4}+\frac{1}{4-m}=\frac{m^2}{m^2-16}[/tex]
Where
The LCM of the denominators are
m^2-16=(m+4)(m-4)
Hence
[tex](m+4)(m-4)\left(\frac{m}{m+4}+\frac{4}{4-m}\right)=(m+4)(m-4) \cdot \frac{m^2}{m^2-16} \\[/tex]
m(m-4)-4(m+4)=m^2
m^2-4 m-4 m-16=m^2
8 m=-16
m=-2
In conclusion, the solution to the equation is
m=-2
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Answer:m=-2
Step-by-step explanation:
just answered
Given 7(x, y) = (x + 5, y + 4) and the point P (2, 3), what is 7(P)? please show work so sorry
Answer:
(7, 7)
Step-by-step explanation:
We are given the formula 7(x, y) = (x+5, y+4) for a pair of coordinates (x,y).
P is given as the coordinates: (2, 3), therefore if we substitute P into the equation, we can replace x and y in the given equation for the coordinates of P (2,3).
P is given as (2,3), so 7(P) = 7(2,3).
Using the given formula:
7(2,3) = (2+5, 3+4)
2+5 = 7, 3+4 = 7
Therefore 7(P) = (7, 7)
Hope this helped!
The nearest star to us, Alpha Centauri, is 4.3 light years away. A light year is 5, 865,696,000,000 miles. How far away is Alpha Centauri in miles? Express your a swer in scientific notation?
Answer:
2.52224885 x [tex]10^{13}[/tex]
Step-by-step explanation:
4.3 x 5.865695 x [tex]10^{12}[/tex]
25.2224885 x [tex]10^{12}[/tex]
2.52224885 x [tex]10^{13}[/tex]
A company prices its tank-style water heaters at $1,505 per unit and its tankless water heaters at $2,990 per unit. Last week, the company sold 152 tank-style water heaters and 46 tankless water heaters. What is the closest estimate of the total sales revenue the company generated by selling both types of water heaters last week?
A.
$250,000
B.
$375,000
C.
$525,000
D.
$675,000
Answer:
B. $375,000 but I could be wrong
Step-by-step explanation:
We do:
1,505(152) = 228,760 (we are multiplying)
2,990 (46) = 137,540
We multiply 1,505 by 152 because 1,505 is the per tank-style water heater unit and we sold 152 of them.
We multiply 2,990 by 46 because 2,990 is the per tankless water heater unit and we sold 46 of them.
Now that we multiply, we add 228,760 and 137,540 together and get a total of $366,300
Since the question is asking for the closest estimate $366,300 is best option to option (B)
A nut store normally sells cashews for $4.00 per pound and peanuts for $1.50 per poundBut at the end of the month the peanuts had not sold well, so, in order to sell 60 pounds of peanuts, the manager decided to mix the 60 pounds of peanuts with some cashews and sell the mixture for $2.50 per poundHow many pounds of cashews should be mixed with the peanuts to ensure no change in the revenue? The manager should mix pounds of cashews with the peanuts
In a nut store the required quantity of the cashews in the mix = x / 4 = 3 / 4 pound.
Here,
Cost of 1 pound of cashew = $4.00
Cost of 1 pound of peanut = $1.50
Total cost = 5.50
The average cost of per pound = 5.50 / 2 = 2.75
Now, peanut and cashews mixes,
quantity of the cashews in the mix = x / 4.00
quantity of the peanuts in the mix = x / 1.50
x/4.00 + x/1.50 = 2.75
x = 3
Now,
The required quantity of the cashews in the mix = x / 4 = 3 / 4 pound
and the mix of the peanut in the mix x / 1.50 = 3 / 1.50 = 2 pounds
Thus, The required quantity of the cashews in the mix = x / 4 = 3 / 4 pound
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Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint 1: (−5,2) Midpoint: (2,−5) Endpoint 2=
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -5}{2}~~~ ,~~~ \cfrac{ y +2}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(2~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -5}{2}=2\implies x-5=4\implies \boxed{x=9} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +2}{2}=-5\implies y+2=-10\implies \boxed{y=-12}[/tex]
go step by step to reduce the radical 80
The radical of 80 can be reduced to 4√5
How to reduce radical expression?A radical is a symbol that represents a particular root of a number.
A radical expression is defined as any expression containing a radical (√) symbol.
Radical expression can be reduced.
We are asked to reduce the radical of 80.
Hence,
√80 = √16 × 5
where
√16 = 4
Therefore,
√80 = √16 × 5 = 4√5
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Find the domain of the following function and show your work
The domain of the given function [tex]f(x)=\frac{\sqrt[3]{1+2 x}}{2+\sqrt[13]{2 x}}[/tex] is x < -4096 or x > - 4096.
What do we mean by domain?The set of possible inputs into a function, or the set of input values for which the function is defined, is known as the domain of the function. The set of objects that the machine will accept as inputs are known as the domain in the function machine metaphor. Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.So, [tex]f(x)=\frac{\sqrt[3]{1+2 x}}{2+\sqrt[13]{2 x}}[/tex]:
[tex]f(x)=\frac{\sqrt[3]{1+2 x}}{2+\sqrt[13]{2 x}}[/tex][tex]\left[\begin{array}{cc}\text { Solution: } & x < -4096 \text { or } \quad x > -4096 \\\text { Interval Notation: } & (-\infty,-4096) \cup(-4096, \infty)\end{array}\right][/tex]Therefore, the domain of the given function is x < -4096 or x > - 4096.
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1. Give an example of a radical inequality that would not need restrictions. Explain your reasoning.
Step-by-step explanation:
a restricting is only necessary, if we need to limit the x values or the y values for various reasons.
the limit for the x values are to eliminate any values that would create an invalid or otherwise undefined result.
otherwise the inequality itself establishes a restriction already.
e.g. sqrt(x) + 3 >= 1 would need an additional restriction
x >= 0 to know we can't even try small negative x to find out verify the solution.
something like
sqrt(x² + 3) >= 1 does not need any further restrictions, because we can use any value for x, from - infinity to +infinity. and the inequality will always be valid.
also consider, that the left side can never get smaller than sqrt(3) which is larger than 1. so, really everything goes.
we could say something like
sqrt(x² + 16) >= 5
we still don't need to give any additional restrictions, but the inequality itself rules out all x that are
-3 < x < 3.
Unit Test
Unit Test Active
11
12 13
14 15
125
16
Two parallel lines are crossed by a transversal.
d
17
18
What is the value of d?
Od=55
Od=75
Od=125
Od = 155
TIME REMAINING
01:27:10
Answer:
d=125
Step-by-step explanation:
since its a vertical angles and vertical angles are congruent (the same)
The value of d would be,
⇒ d = 125 degree
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
Two parallel lines are crossed by a transversal.
Now, We have;
Angle d and 125° are vertically opposite angles.
Hence, Both are equal.
Thus, We get;
⇒ d = 125°
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Select an equivalent form of this equation:
X/12-7= X/4
A. X-84 = 3X
B. X-74= 12X
C. X-7=3X
Pls Help
Find the Least Common Denominator of 5/6 and 3/8, show all of your work:
Answer:
24
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line y=-1/4 x-1
Answer:
The slope would be 4.
Step-by-step explanation:
To find a slope of a line perpendicular to another line, you would find the inverse (+/-) and reciprocal (a & 1/a). So -1/4 is the slope of this line, its inverse is 1/4, and the reciprocal is 4.
Hope this helps! :)
2(
5
1
m−
5
2
)+
5
3 =
Answer:
102m-51
Step-by-step explanation:
2(51m-52)+53
= 102m - 104+53
102m-51
Factorize the expression:
[tex]2(51m-52)+53[/tex]
[tex]102m-104 +53[/tex]
[tex]102m-51[/tex]
[tex]51(2m-51)[/tex]
⬆️
Simplify the expression:
[tex]2(51m-52)+53[/tex]
[tex]2*51m-2*52+53[/tex]
[tex]102m-2*52+53[/tex]
[tex]102m-104+53[/tex]
[tex]102m(-104+53)[/tex]
[tex]102m-51[/tex]
⬆️
Write inequalities to represent the situations below.
To qualify for the championship, a runner must complete the race in no more than 55 minutes.
Use t to represent the time (in minutes) of a runner who qualifies for the championship.
To be eligible for financial aid, a student must earn less than $20,000 per year.
Use s to represent the yearly earnings (in dollars) of a student eligible for financial aid.
The inequalities which represent the situations as described in the task content are as follows;
t <= 55 minutes.s < $20,000 per year.What inequalities correctly represents the given situations as in the task content?It follows from the task content that the inequalities which correctly represents the situations as described in the task content be determined.
On this note, since the time, t in minutes of a runner who qualifies for the championship must be no more than 55 minutes, it follows that t can be less or at most, equal to 55.
t <= 55.Also, since the yearly earnings of a student must be less than $20,000 per year, it follows that the inequality which represents the situation is;
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can someone do this pls i need it right now plsssss
Considering the given frequency table, the estimate of the mean height is of 7.5 units.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
Given a frequency table, for each interval, we consider each observation the halfway point of the interval, hence:
On the first interval, we consider each of the 21 observations as 2.5.On the second interval, we consider each of the 5 observations as 7.5....Until the last interval, in which we consider each of the 2 observations as 22.5.Hence the mean is given by:
M = (21 x 2.5 + 5 x 7.5 + 9 x 12.5 + 3 x 17.5 + 2 x 22.5)/(21 + 5 + 9 + 3 + 2) = 7.5.
Hence the estimate of the mean height is of 7.5 units.
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Answer for this problem please
Answer:
f(2) = -9, and f(-2) = 19
Step-by-step explanation:
Just plug it in.
If [tex]f(x) =2x^{2} -3x+5[/tex], and you have f(2), and f(- 2), you can do, [tex]f(2) = -2(2^{2} )-3(2)+5[/tex], and [tex]f(-2)=-2(-2^{2} )-3(-2)+5[/tex].
Once you do all the math, you get f(2) = -9, and f(-2) = 19.
Find the value of x.
m∠2 = 6x + 12
. State the property used to rewrite the following
expressions.
a. ( 8 + 4 ) + 12 = ( 4 + 8 ) + 12
b. ( 8 + 4 ) + 12 = 8 + ( 4 + 12 )
The properties used to rewrite the expressions are
(8 + 4) + 12 = (4 + 8) + 12 ⇒ Associative property(8 + 4) + 12 = 8 + (4 + 12)⇒ Associative propertyHow to determine the properties?The expressions are given as
(8 + 4) + 12 = (4 + 8) + 12
(8 + 4) + 12 = 8 + (4 + 12)
The associative property of expression states that
(x + y) + z = x + (y + z)
This means that the properties used to rewrite the expressions are associative property
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$21,023 is invested, part at 13% and the rest at 11%. If the interest earned from the amount invested at 13% exceeds the interest earned from the amount invested at 11% by $1045.31, how much is invested at each rate?
The amount invested at 11% by $1045.31 and investment rate is -
amount invested at 13%. is $13991
amount invested at 11%. is $7032
Let x represent the amount invested at 13%.
Let y represent the amount invested at 11%.
$21,023 is invested, part at 13 % and the rest at 11%. This means that
x + y = 21023
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the amount invested at 13%,
P = x
R = 13%
T =1 year
I = (x × 13 × 1)/100 = 0.13x
Considering the amount invested at 11%,
P = y
R =11%
T = 1 year
I = (x × 11 × 1)/100 = 0.11y
If the interest earned from the amount invested at
13% exceeds the interest earned from the amount invested at
5% by $1045.31, it means that
0.13x - 0.11y = 1045.31 - - -- - - - - -1
Substituting x = 21023 - y into equation 1, it becomes
0.13(121023 - y) - 0.11y = 1045.31
y = 7032
x = 21023 - y = 21023-7032
x = 13991
amount invested at 13%. is $13991
amount invested at 11%. is $7032
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The table below shows the amounts of cooked rice that can be made using different amounts of dry rice. Based on the information in the table, how many cups of cooked rice can be made from 1 cup of dry rice?
Answer:
1 cup dry rice makes 4 cups of cooked rice.
Step-by-step explanation:
Comment
Assuming this is a linear relationship, the equation is
cooked rice = k * dry rice
cooked rice = k
dry rice = x
Now all you need do is find k to get the answer.
Givens
x value = 2/3 of a cup.
y value = 2 2/3 cups
k = ?
Solution
y = k*x
2 2/3 = k * 2/3 Change to an improper fraction
8 / 3 = k * 2/3 Multiply both sides by 3
8 = 2k Divide both sides by 2
8/2 = 2k/2
k = 4
Now for one cup of dry rice, we have
y = ?
k = 4
x = 1
y = k*x
y = 4*1
y = 4 cups
The answer should be that the relationship is linear, because it lies between 3 cups (when 3/4 cup of dry rice is used and over 5 cups when 1 abd 1/3 cuprs of dry rice are used,)
-2 3/4 divided by 1/2
Answer:
-11/2
Step-by-step explanation:
Directions: Write the following algebraic expressions and equations as verbal expressions and sentences. 9 - 6x
Verbal expression or sentence of algebraic expression of 9 - 6x are Six times x is substracted from nine and Nine is substracting six times x.
It is given that algebraic expressions = 9 - 6x
There are many ways to write 9 - 6x as verbal expression, but today we will learn to the given algebraic expression in two ways.
First way :
Here we can see that 6 is multiplied by x, so
we can specify 9 - 6x as
Six times x is substracted from nine.
Second way :
Nine is substracting six times x.
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Alejandro is taking a multiple choice test with a total of 80 points available. Each question is worth exactly 5 points. What would be Alejandro's test score (out of 80) if he got 7 questions wrong? What would be his score if he got x questions wrong?
Answer:
The answer is 45points
100-5x
Step-by-step explanation:
80/5=16questions
16-7=9questions
9x5=45points
Answers and Explanation:
- Total of 80 point available.
- Each question is worth 5 points.
If he gets 7 questions wrong --> he loses 7 x 5 points = 35 points.
100 - 35 = 65 --> So, his score would be 65.
If he got x questions wrong --> he would lose 5x points.
So, his score would be 100 - 5x.
--
Have a nice day!
-1 1/2 - (+3 1/2) - (-5/8)
Answer:
−3.375
Step-by-step explanation:
Hope this helps :)
Answer:
[tex]\boldsymbol{-\dfrac{35}{8}}[/tex]
or, in decimal
-4.375
Step-by-step explanation:
[tex]\textrm{The expression is }\rm -1\frac{1}{2}-\left(+3\frac{1}{2}\right)-\left(-5/8\right)[/tex]
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\\-1\dfrac{1}{2} = -\dfrac{1\cdot 2+1}{2} = -\dfrac{3}{2}\\\\\\+3\dfrac{1}{2} = +\dfrac{3\cdot 2+1}{2} = +\dfrac{7}{2} = \dfrac{7}{2}[/tex]
[tex]\textrm{The expression is }\rm -1\frac{1}{2}-\left(+3\frac{1}{2}\right)-\left(-5/8\right)\\= -\dfrac{3}{2}-\left(\dfrac{7}{2}\right)-\dfrac{-5}{8}\\\\\\= -\dfrac{3}{2}-\dfrac{7}{2}\right)+\dfrac{5}{8}\\\\\\[/tex]
The LCM of 2 and 8 is 8
Multiply each term by 8 and divide the result by 8
We get for numerator:
[tex]8\cdot\dfrac{-3}{2} - 8\cdot \dfrac{7}{2} + 8\cdot \dfrac{5}{8}\\\\= -12 - 28 + 5 = -35\\[/tex]
Denominator is 8
So answer is
[tex]\boldsymbol{-\dfrac{35}{8}}[/tex]
In decimal that would be -4.375
Choose whichever form you like
-2x - 8y = 14, 2x + 8y = - 14
Investing for college, Jake originally put $5000 into a savings account that paid 3.5%. There is now $6400 in the account. How long did Jake have the money in the savings account?
Jake put the money in the savings account for about 17.5 years.
Simply explained, a savings account is a place where you can deposit funds and earn interest.
Most people won't pay any tax on their savings interest because it is paid tax-free. Only people with extremely big sums of savings would need to be concerned about this, which is less than 5% of us as basic-rate taxpayers can earn £1,000/year tax-free and higher-rate taxpayers £500.
The interest calculated in a savings account is compound interest:
So let us now calculate the savings rate of interest at 3.5% for the whole time
We know that
[tex]A=P(1+r)^n[/tex]
Where A is the amount , P is the principal , r is the rate and n is the time.
Substituting the values we calculate the value of x.
6400 = 3500 ( 1+0.035 )ⁿ
or, n = 17.54..
So the time required will be about 17.5 years in the savings account.
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Part 1: Identify each pair of angles adjacent vertical complementary supplementary and/or a linear pair
Part 2: use the figure at the right to answer each question
Answer:
1. adjacent
2. vertical
3. adjacent
Step-by-step explanation:
adjacent angles: angles next to each other with one common side
vertical angles: 2 non-adjacent angles formed by the intersection of 2 lines
complementary angles: two angles whose measures add to 90 deg
supplementary angles: two angles whose measures add to 180 deg
linear pair: 2 adjacent angles whose non-common side lie on a single line
Part 1
1 Adjacent
2. Vertical
3. Adjacent
4. Linear pair
5. Adjacent
6. Linear pair
7. Vertical
8. Complementary angles
9.Supplementary angles
Part 2
10. <BGC and <CGD
11. <AGD and <CGF
12. <BGC and <CGD
13. <AGF and <AGD
14. <AGB and <BGC
15. <FGC
What are Adjacent angles?This term refers to angles sitting side by side, like next to each other.
What are Vertical Opposite angles?This term refers to angles sitting in the face of the each other or opposite to each other.
What are Complementary angles?This term refers to angles that sum up to 90 degrees.
What are Supplementary angles?This term refers to angles that sum up to 180 degrees. When the angles are formed by a single point of intersection in a straight line it is called Linear pair.
What are Linear pair angles?This term refers to a form of supplementary angles where the angles are formed from a single point of intersection. The angles formed in linear pair are adjacent to each other
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Wendi got 15 out of 20 questions correct on her English quiz and 9 out of 10 question correct on her math quiz which quiz did she do better on
Answer:
she did better on her math quiz
Step-by-step explanation:
15/20<9/10
15/20<18/20
Simple but effective
Let me know if this helps
Algebra 1 honors (9th grade) I NEED HELP ASAP I BEG YOU
Answer:
3.5
Step-by-step explanation:
cross multiply
5/0.50 35/x
35 times 0.50 = 17.5
17.5/5 = 3.5