Answer:
[tex]\large\boxed{LCM(x^2-2x-15,\ x^2+2x-3)=(x+3)(x-5)(x-1)}\\\boxed{=x^3-3x^2-13x+15}[/tex]
Step-by-step explanation:
[tex]x^2-2x-15=x^2+3x-5x-15=x(x+3)-5(x+3)=(x+3)(x-5)\\\\\\x^2+2x-3=x^2+3x-1x-3=x(x+3)-1(x+3)=(x+3)(x-1)\\\\LCM(x^2-2x-15,\ x^2+2x-3)=(x+3)(x-5)(x-1)\\\\=(x^2-2x-15)(x-1)\qquad\text{use FOIL}\\\\=(x^2)(x)+(x^2)(-1)+(-2x)(x)+(-2x)(-1)+(-15)(x)+(-15)(-1)\\\\=x^3-x^2-2x^2+2x-15x+15\qquad\text{combine like terms}\\\\=x^3+(-x^2-2x^2)+(2x-15x)+15\\\\=x^3-3x^2-13x+15[/tex]
I really need help on this question
Answer:
31
Step-by-step explanation:
CPCTC and Parallel concurrency theorem
At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels at the zoos.
How many baby camels are at the zoo?
Find the common ratio, by adding the adults and babies together: 6+5 = 11
Divide the total by that:
44/11 = 4
the common ratio is 4.
Now multiply the given ratios by the common ratio:
Adults = 6 x 4 = 24
Babies = 5 x 4 = 20
There are 20 babies.
Graph the function f(x)=x3-5x2+6
x 1 2 3 4 5
y 6 0 -4 0 18
Which equation does the graph represent?
Answer:
B.
Step-by-step explanation:
I plugged it into a graphing calculator which got me this.
What are the roots of the function f(x)=x^2+x-6
A. X=3 and x= -2
B. X= -3 and x= -6
C. X=1 and x=-6
Answer:
None of the above
Step-by-step explanation:
A is the closest but it should be 2 and -3
For this case we have the following quadratic function:
[tex]f (x) = x ^ 2 + x-6[/tex]
We must find its roots. We can factor, looking for two numbers that when added to +1 and multiplied by -6. These are:
+3 and -2
[tex]+ 3-2 = 1\\(+3) * (- 2) = - 6[/tex]
Then, the factored form is:
[tex](x + 3) (x-2) = 0[/tex]
So, the roots are:
[tex]x_ {1} = - 3\\x_ {2} = 2[/tex]
Answer:
[tex]x_ {1} = - 3\\x_ {2} = 2[/tex]
How can u study for a test?
When I study o usually get a bad grade!! Please help
Answer:
stay focused on a single topic until u understand that topic well .. use sticky notes to make short notes and clue to make it easier .. when u have test u can use the sticky notes to make ur own answer .. instead of writing the same words in test use ur pwn wordsband create a short one. make a timetable for each subject everyday at least 1 - 2 hrs ..
PLEASE ANSWER RIGHT AWAY!!!
Answer:
$5
Step-by-step explanation:
Given in the question a graph,
We have clearly see that graph can be divided into 3 parts.
Part 1
we can see that $5 will be charged for the package which weight is 3 Ibs or less than 3 Ibs.
Part 2
we can see that $10 will be charged for the package which weight 6 Ibs or than less 6 but greater than 3 Ibs
Part 3
We can see that after 6kg the cost is linear to the weight of the package.
Ampicillin 250 mg IM every 12 hours is ordered. After reconstitution, there's 125 mg/mL. How many mL would you give?
A. 20 mL
B. 10 mL
C. 2 mL
D. 125 mL
Answer:
Correct choice is C. 2 mL.
Step-by-step explanation:
Given that Ampicillin 250 mg IM every 12 hours is ordered. After reconstitution, there's 125 mg/mL. Now we need to find about how many mL would you give.
Let number of ml needed = x.
Since ratio of mg per mL will be fixed so we get equation:
[tex]\frac{mL}{mg}=\frac{x}{250}=\frac{1}{125}[/tex]
[tex]\frac{x}{250}=\frac{1}{125}[/tex]
[tex]x=\frac{1}{125} \times 250[/tex]
[tex]x=\frac{250}{125}[/tex]
[tex]x=2[/tex]
Hence correct choice is C. 2 mL.
Final answer:
To calculate the volume of ampicillin to be given, divide the ordered dose by the concentration of the solution. For a dose of 250 mg and a concentration of 125 mg/mL, the volume to administer is 2 mL. The correct option is: 2ml.
Explanation:
The question is asking us to calculate the volume of ampicillin required for one dose when it has been reconstituted to a concentration of 125 mg/mL, and the ordered dose is 250 mg given intramuscularly (IM) every 12 hours. To find out how many mL of the ampicillin solution should be administered in one dose, we use the formula:
Dose ordered / Concentration of solution = Volume to administer
In this case:
250 mg (Dose ordered) / 125 mg/mL (Concentration) = 2 mL
Therefore, you would administer 2 mL of the reconstituted ampicillin solution.
According to the stem and leaf plot above how many students scored grade of 70 or above. CANT GET IT WRONG!
You read a steam and leaf plot in this way: the first column is the first digit of the score, and we're grouping scores by their first digits.
So, for example, if we read the row starting with 5, we deduce that there have been three scores in the 50's, namely two 57 and one 58.
To answer the question, we have to count how many occurrences we have in the row of the 70's and higher.
We have 4 scores in the 70's: 70, 70, 71, 78
We have 4 scores in the 80's: 82, 84, 87, 88
We have 3 scores in the 90's: 91, 93, 97
We have 2 perfect scores of 100.
These are all the scores of 70 or above.
Cramer's rule:
What is [Ax] in the system below?
Answer:
Ax = [tex]\left[\begin{array}{cc}-3&-1\\5&1\end{array}\right][/tex] ⇒ 3rd answer
Step-by-step explanation:
Lets revise the Cramer's rule
- If the system of equation is ax + by = c and dx + ey = f
- A is the matrix represent this system of equation
- The first column has the coefficients of x, and
the second column has the coefficients of y
∴ A = [tex]\left[\begin{array}{cc}a&b\\d&e\end{array}\right][/tex]
- Ax means replace the column of x by the answers of the equation
∴ Ax = [tex]\left[\begin{array}{cc}c&b\\f&e\end{array}\right][/tex]
- Ay means replace the column of y by the answers of the equation
∴ Ay = [tex]\left[\begin{array}{cc}a&c\\d&f\end{array}\right][/tex]
* Now lets solve the problem
∵ 4x - y = -3 and -2x + y = 5
∴ A = [tex]\left[\begin{array}{cc}4&-1\\-2&1\end{array}\right][/tex]
- Replace the column of x by the answer to get Ax
∴ Ax = [tex]\left[\begin{array}{cc}-3&-1\\5&1\end{array}\right][/tex]
* Ax in the system of equation is [tex]\left[\begin{array}{cc}-3&-1\\5&1\end{array}\right][/tex]
Answer:
C
Step-by-step explanation:
Edge2021
Which of the following represents the factored form of f(x) = x3 − 64x?
Answer:
x(x + 8)(x - 8)
Step-by-step explanation:
Given
x³ - 64x ← factor out x from each term
= x(x² - 64) ← x² - 64 is a difference of squares
= x(x + 8)(x - 8) ← in factored form
Which complex number has a distance of the root of 17 from the origin on the complex plane?
2 + 15i
17 + i
20 – 3i
4 – i
Answer:
4 -i
Step-by-step explanation:
For your condition to be met, neither the real part nor the imaginary part can exceed √17 in magnitude. That excludes the first three answer choices.
The magnitude of 4-i is ...
√(4^2 +(-1)^2) = √17.
Answer:
4 – iStep-by-step explanation:
First, we need to know that a complex number, which has a real part and an imaginary part, it's like a vector, where the horizontal coordinate is the real part, and the vertical coordinate is the imaginary part.
So, to find the distances we applied the conventional definition:
[tex]d=\sqrt{r^{2}+i^{2} }[/tex]
Where [tex]r[/tex] refers to the real part and [tex]i[/tex] refers to the imaginary part.
So, we test each answer and see which one gives us the root of 17.
Option 1.[tex]d=\sqrt{2^{2}+15^{2} }=\sqrt{4+225}=\sqrt{229}[/tex]
Option 2.[tex]d=\sqrt{17^{2}+1^{2} }=\sqrt{290}[/tex]
Option 3.[tex]d=\sqrt{20^{2}+(-3)^{2} }=\sqrt{409}[/tex]
Option 4.[tex]d=\sqrt{4^{2}+(-1)^{2} }=\sqrt{17}[/tex]
Therefore, the right answer is the last one, because the distance is the squared root of 17.
What's the total value of 40 quarters, 30 dimes, 20 nickels, and 10 pennies?
Answer:
14.10
Step-by-step explanation:
Quarters are worth .25 of a dollar
40 *.25 = 10
Dimes are worth .10 of a dollar
30 *.10 = 3
Nickels are worth .05 of a dollar
20 *.05 = 1
Pennies are worth .01 of a dollar
10 *.01 = .1
Add this together
10+3+1+.1
14.10
A and b have opposite directions, and they both have a magnitude of 7 what must be true about a and b
Answer:
D) They are opposite and parallel.
Step-by-step explanation:
Given:
There are two vectors "a" and "b" have opposite directions having the same magnitude of 7.
If the two vectors "a" and "b" have opposite directions mean one moves right and other moves left.
Which means they are opposite.
Here they have a same magnitude of 7. So they are parallel.
Therefore, the answer is D) They are opposite and parallel.
What is the value of the arithmetic series below?
Answer:
- 494
Step-by-step explanation:
Breaking down the summation into it;s component parts
= 4k - [tex]\frac{3}{2}[/tex] k(k + 1) ← substitute k = 19
= (4 × 19 ) - 1.5 × (19 × 20)
= 76 - (1.5 × 380)
= 76 - 570
= 494
The value of the arithmetic series below is - 494
We have
To break down the summation into its component parts
What is the formula of the kth sum?
[tex]S_{19}= 4k - \frac{3}{2} k(k + 1)[/tex]
[tex]= 4k - \frac{3}{2} k(k + 1) .... substitute\ k = 19[/tex]
[tex]= (4 \times 19 ) - 1.5 \times (19 \times 20)[/tex]
[tex]= 76 - (1.5 \times 380)[/tex]
[tex]=76-570[/tex]
= -494
The value of the arithmetic series below is 494.
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Mr. Thompson cut
the grass on the
golf course in 1683
minutes. How many
hours did it take
to cut the grass?
Write the answer
as a mixed number
To convert to hours, we should do 1683/60 because one hour is 60 minutes
1683/60=28 3/60
28 3/60= 28 1/20
Answer: 28 1/20
The number of hours that it takes to cut the grass will be 28 ¹/₂₀ hours.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Mr. Thompson cut the grass on the golf course in 1683 minutes.
We know that in one hour, there are 60 minutes. Then the number of hours that it takes to cut the grass will be given as,
⇒ 1683 / 60
⇒ 28 + 1/20
⇒ 28 ¹/₂₀ hours
The number of hours that it takes to cut the grass will be 28 ¹/₂₀ hours.
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A bicycle depreciates at a rate of 15% therese bought a bicycle for $250. How much should it be worth 6 years later ?
Answer:
[tex]\$94.29[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]V=P(1-r)^{x}[/tex]
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
[tex]P=\$250\\r=15\%=0.15\\x=6\ years[/tex]
[tex]V=\$250(1-0.15)^{6}[/tex]
[tex]V=\$250(0.85)^{6}=\$94.29[/tex]
Answer:
94.29
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
where
V is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is Number of Time Periods
in this problem we have
Jake studied x hours for a big test. Julie studied twice as long.
Write an algebraic expression for long Julie studied.
The algebraic expression that expresses how long Julie studied is: 2x.
What is an Algebraic Expression?Algebraic expression can be described as a mathematical statement that uses variables and digits, as well as operation signs.
Number of hours Jake studied = x
Julie studied twice as long as x
Thus, algebraic expression for how long Julie studied would be: 2x.
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If Jake's study time can be represented as 'x', then, given that Julie studied twice as long as Jake, her study time can be represented as '2x'. This is because she studied twice the amount of time that Jake did.
Explanation:The question describes a relationship between the amount of time Jake studied and the amount of time Julie studied. We know from the question that Julie studied twice as long as Jake did. In mathematical terms, we would represent Jake's studying time as x hours, since we don't have a specified amount. Therefore, because Julie studied twice as long as Jake did, we can represent Julie's studying time as 2x.
Hence, "the algebraic expression for the number of hours that Julie studied is 2x".
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When triangle ABC is rotated about side AB, what figure is formed?
cylinder
prism
pyramid
cone
I think it’s a pyramid
What’s is 13.75 of 2/5
Answer:
5.5
Step-by-step explanation:
Of means multiply
13.75 * 2/5
27.5/5
5.5
[tex]\text{Hey there!}[/tex]
[tex]\text{When you come across the word of in mathematics (high learning math at that)}[/tex][tex]\text{, it means to multiply.}[/tex]
[tex]\text{So, your new equation becomes: 13.75}\times\frac{2}{5}\text{multiply those two}[/tex] [tex]\text{numbers.}[/tex]
[tex]\text{The formula to solving for these times of equation is:\ }\frac{b\times c}{d}[/tex]
[tex]\text{So,}\frac{2 \times13.5}{5}[/tex]
[tex]2\times 13.75=27.5[/tex]
[tex]\frac{27.5}{5}=27.5\div5=5.5[/tex]
[tex]\boxed{\boxed{\text{Answer: 5.5}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
What’s exponential growth
Hello There!
Definition Is In Image Attached
Answer:
ex·po·nen·tial growth
noun
growth whose rate becomes ever more rapid in proportion to the growing total number or size.
"the exponential growth of the world's population"
Step-by-step explanation:
Question 2 of 25
2 Points
For which values of x will the rational expression below be undefined? Check
all that apply.
(x-1)(x + 1)
x+2
If the denominator is 0, and the numerator ≠ 0, your answer will undefined.
If the numerator is 0, and the denominator is a number, it will always = 0.
So you can set the denominator equal to 0
x + 2 = 0 Find x, so subtract 2 on both sides
x = -2
Ten random members at a gym were asked how many servings of fruits and vegetables they had yesterday. The results are shown in the table. Use the point tool to create a scatter plot that represents the data shown in the table.
Answer: so the red dots are incorrect
the green ones are correct
the yellow ones are also correct (that i missed)
Step-by-step explanation:
A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. The scatter plot of the given data can be made as shown below.
What is a scatter plot?A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.
Let the x-axis represent the number of fruit servings, while the y-axis represents the number of vegetable servings. Therefore, The scatter plot of the given data can be made as shown below.
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Please help!!!!!!!!!!
The cost of 1 pound of cashew nuts would be 4 dollars.
You divide 32 by 8
Multiply the following complex numbers: (8-3i)(6+5i)
The a answer is 8-13i
For one; Your answer doesn't help those who are on apex. Also doesn't appear to be any of the answer choices,
The answer I got from apex, is;
63+22i.
Hope this helps :)
What is 346.49 rounded to the nearest square inch
Answer:
346 square inches
Step-by-step explanation:
Let's say you have a piece of paper that measures 2.3 inches by 2 inches.the area is 4.6 square inches. The closest whole number is 5, so rounded to the nearest square inch is 5 square inches. Fractions equal to half or greater get rounded up to the next whole number. Fractions less than half get rounded down. SO that means that 346.49 should be rounded down to just 346 although it may be almost 50.
What is the common ratio between successive terms in the sequence?
2, –4, 8, –16, 32, –64, ...
Answer:
-2
Step-by-step explanation:
A common ratio can be found by dividing any term by the one before it in the sequence:
-4/2 = 8/-4 = -16/8 = 32/-16 = -64/32 = -2
The common ratio is -2.
Answer:
-2
Step-by-step explanation:
the perimeter of a rectangular table is 132 inches the length of the table is 1 3/4 times its width what is the area of the table
Answer:
The area of the table is [tex]1,008\ in^{2}[/tex]
Step-by-step explanation:
Let
x----> the length of the rectangular table
y---> the width of the rectangular table
we know that
The perimeter is equal to
[tex]P=2(x+y)[/tex]
[tex]P=132\ in[/tex]
so
[tex]132=2(x+y)[/tex]
[tex]66=x+y[/tex] ------> equation A
[tex]x=1\frac{3}{4}y[/tex]
[tex]x=\frac{1*4+3}{4}y[/tex]
[tex]x=\frac{7}{4}y[/tex] ---> equation B
substitute equation B in equation A and solve for y
[tex]66=\frac{7}{4}y+y[/tex]
[tex]66=\frac{11}{4}y[/tex]
[tex]y=66*4/11=24\ in[/tex]
Find the value of x
[tex]x=\frac{7}{4}(24)=42\ in[/tex]
Find the area of the table
The area is equal to
[tex]A=xy=(42)(24)=1,008\ in^{2}[/tex]
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
A and C
Step-by-step explanation:
Vertical angles are angles formed by 2 lines. Those angles are right across from each other.
Answer:
a and c
Step-by-step explanation:
Vertical angles are angles formed by 2 lines. Those angles are right across from each other.
Sixty-five percent of what number is 32.5?
21.125
140
30
50
Final answer:
To find 65% of a number, use the equation 0.65x = 32.5 and solve for x by dividing both sides by 0.65 to get x = 50.
Explanation:
Sixty-five percent of what number is 32.5?
Let's denote the unknown number as x.
Translate the given information into an equation: 0.65x = 32.5
To solve for x, divide both sides by 0.65 giving x = 32.5 / 0.65 = 50.