Answer:
D.)
Step-by-step explanation:
A 19-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piecefind the lengths of the pieces. 3 + 5x
Using algebraic expressions and equations to solve this problem, a 19- inch piece of steel is cut into three pieces measuring 2 inches, 4 inches, and 13 inches.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
If the second piece is twice as long as the first piece, we can write this as an algebraic expression "2x" where x is the length of the first piece.
If the third piece is three inches more than five times the length of the first piece, we can write this as an algebraic expression "3 + 5x" where x is the length of the first piece.
If the three pieces were cut from a single piece of steel 19-inches long, we can write the equation for the sum using the algebraic expressions.
let x = length of first piece
2x = length of second piece
3 + 5x = length of third piece
x + 2x + 3 + 5x = 19 inches
Solving for x,
8x = 19 -3
8x = 16
x = 2 inches
length of first piece = 2 inches
Substitute the value of x in the expressions for the second and third piece.
length of second piece = 2x
length of second piece = 2(2)
length of second piece = 4 inches
length of third piece = 3 + 5x
length of third piece = 3 + 5(2)
length of third piece = 3 + 10
length of third piece = 13 inches
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Solve the quadratic equation by completing the square.
x²+18x+79=0
Step-by-step explanation:
completing the square means finding an expression
(x + a)² = b²
or
(x - a)² = b²
(x + a)² = x² + 2ax + a²
(x - a)² = x² - 2ax + a²
because of the "+ 18x" in the original equation we know that we are looking for (x + a)².
now, let's compare the different terms :
x² = x²
18x = 2ax
18 = 2a
a = 9
so, the complete square would look like
(x + 9)² = x² + 18x + 81
but we have only "+ 79" in the original equation.
so, we add the missing 2 (to both sides to keep the equation true)
x² + 18x + 79 + 2 = 0 + 2
x² + 18x + 81 = 2
(x + 9)² = 2
x + 9 = ±sqrt(2)
x1 = sqrt(2) - 9
x2 = -sqrt(2) - 9
x = sqrt(2) - 9, -sqrt(2) - 9
yes, every quadratic equation has 2 solutions.
as every cubic equation has 3 solutions.
and so on.
PLEASE ANSWER THIS I NEED IT URGENTLY WILL GIVE BRAINIEST 3 TIMES OR MORE AND 100 POINTS AND MORE!!
Answer:
What is the question so I can answer
A water well drilling rig has dug to a height of -30 feet after one full day (24 hours),of continuous use. assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours (5/8 days)?
The Height of the drill after 15 hours was 18.75 feet deep or (-18.75) feet.
Given that in 24 hours
the water well drilling rig dig -30 feet .
we know that ,
24 hours = 1 day
So,
1 hour =1/24 day
15 hours = [tex]\frac{15}{24} =\frac{5}{8} day[/tex]
Now according to the question ,
in 1 day the drilling rig dug -30 feet
So in [tex]\frac{5}{8} day[/tex] the drilling rig will dig =[tex]\frac{5}{8} *(-30)=-18.75feet[/tex]
in 15 hours (5/8 days ) drilling rig dig -18.75 feet.
Therefore , The Height of the drill after 15 hours (5/8 days) was 18.75 feet deep or (-18.75) feet.
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(a) What was the maximum height the rocket reached?
After how many seconds?
Answer:
Can you provide more info? Like is there a graph that comes along with this question?
Step-by-step explanation:
I do not understand UPSE what am I so sapouse to do and how?
First of all let me tell you UPSC is the body which conducts the civil services examination in our country. To prepare for the civil services you must know it is the highest offered post by the government to an citizen of India.
You have many subjects in order to complete the syllabus of civil services.
The examination takes place in two parts. In the first part there are multiple choice questions and in the second part there are subjective questions which must be answered in a descriptive format.
The candidate also has to face interview after clearing both the examinations.
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Simplify by combining like terms. Write the answer with the variables in alphabetical order and any constant term last.
a+ ab^3 + ab^3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. a+ ab^3 + ab^3 simplifies to [ ]
O B. The expression cannot be simplified.
a+ ab³ + ab³ simplifies to 2ab³+a.
For simplifying the terms first we have to add Like Terms.
Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)). When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and adding or subtracting the numerical coefficients.
In Algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.
So hence we will add ab³ + ab³= 2ab³
For any given term, we almost always list the variables in alphabetical order and any constant terms last — this is helpful in identifying common terms, a topic discussed in the next section. So, for example, it is simply not cool to write 15yx, 15 y x , we want to stay alphabetical and write 15xy. Exponents play no role in this decision.
Therefore a+ ab³ + ab³ simplifies to 2ab³+a.
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If they gave you $440 in quarters. how many coins would you receive?
Answer:
$110
Step-by-step explanation:
quarter is 1/4 of a thing
so $440 ÷ 4 = 110
hence we can conclude that if you get $440 in quarters you will get $110 each time
Hope it helps!!!
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An epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, P, who contracted the flu t days after it broke out is given by the model P = -2²+ 17t + 180, where 1 st≤ 6. Find the day that 210 students had the flu. Recall that the restriction on this at most 6.
Submit Answer
Answer:
At the 3rd day 160 students caught flu.
Step-by-step explanation:
Consider the provided model P = − t ² + 13t + 130 where 1 ≤ t ≤ 6
The total number of students is represents by P.
We need to find the day that 160 students had the flu.
Substitute the value of P=160 in above formula.
Hence the value of t=10 or t=3
But it is given that 1 ≤ t ≤ 6, Therefore select t=3
Hence, at the 3rd day 160 students caught flu.
Janet rents a car while spending her vacation traveling in Argentina. When she returns the car, she has driven 1400 miles and used about 56 gallons of gas. If gas costs an average of $4.099 per gallon, estimate how much she spent on fuel.
Janet spent $230 on fuel
How to calculate the amount of money spent on fuel ?Janet rented a car to travel to Argentina
After the journey, she discovered that she had driven 1400 miles and used 56 gallons of gas
The gas costs $4.099 per gallon
Therefore the amount Janet spent thought out the journey for fuel can be calculated as follows
= 4.099 × 56
= 229.5
= 230
Hence when estimated, Janet spent $230 on fuel
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factorise completely m^2n-mn^2
Answer: nm(m-n)
Step-by-step explanation:
m^2n-mn^2=
n*m(m)-m*n(n)=
n*m(m-n)=nm(m-n)
solve by completing the square
2x^2-12x-20=0
The square of the equation 2[tex]x^{2}[/tex] – 12x – 20=0 is
What is a quadratic equation?
A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0.
a[tex]x^{2}[/tex]+bx+c , a, b, c are integers .
formula: −b±√b2−4ac/2a
Given equation ,
2[tex]x^{2}[/tex] -12x-20=0
By comparing with the quadratic equation
Here, a=2, b= -12, c= -20.
X=−b±[tex]\sqrt{b^2-4ac}[/tex]/2a
X= -(-12) + [tex]\sqrt{(-12)2-4(2)(20)}[/tex] /2(2)
X=12+- [tex]\sqrt{144-160}[/tex]/4
X=12+- [tex]\sqrt{-16}[/tex]/4,
X=12+- (-4)/4
X=12+(-4)/4 and x=12-(-4)/4
X= 12-4/4 and x=12+4/4
X=8/4 and x= 16/4
X=2 and x= 4
Therefore, the square of the equation 2x2-12x-20=0 is x= 2 and x=4.
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answer plsss rn !!!
an equation will not pass through the origin if:
Answer:An equation will not pass through the origin if the points are 0,0.
Need help badly, I also need to know how you got the answer.
Answer:
-1/5
y=-1/5 x-8
-1/5 is the slope
Step-by-step explanation:
-1/5
Formula- y=mx+b
The slope-intercept form is
y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Rewrite in slope-intercept form.
Simplify the left side
Simplify each term.
Combine 1/8 and x.
x/9+5y/8=-5
Subtract x/8 from both sides of the equation.
5y/8=-5-x/8
Multiply both sides of the equation by8/5.
8/5.5y/8=8/5(-5-x/8)
Simplify both sides of the equation.
Simplify the left side.
Simplify 8/5.5y/8
y=-x/5-8
y=-1/5 x-8
Step-by-step explanation:
Given equation:
1/8x + 5/8y =-5
Now write it in standard form like ax+by+c=0
1/8x + 5/8y + 5= 0
Now,slope of line (m) = -a/b
here value of a is 1/8 and value of b is 5/8
now by formula..
-(1/8)÷(5/8) = m(slope)
-1/8 × 8/5 = m
-1/5 = m
here ia your answer
Which list shows the numbers in order from least to greatest?
A)−3π,−9.4,−283,−95−−√
B)−95−−√,−3π,−9.4,−283,
C)−95−−√,−283,−9.4,−3π
D)−283,−9.4,−3π,−95−−√
Answer:
judging from the list of numbers i would pick a
Jack takes 10 minutes to ride his stakeboard down the hill to his friend's house and 20 minutes to ride up the hill from his friend's house. he goes to his friend's house monday through friday. how many minutes does he spend riding his stakeboard to and from his friend's house in two weeks? write an equation to model your work.
Jack spends 300 minutes in two weeks riding his skateboard to and from his friend's house Monday through Friday.
Time taken by Jack to ride his skateboard down the hill to his friend's house = 10 minutes
Time taken by Jack to ride his skateboard up the hill to his friend's house = 20 minutes
Total time combined = 30 minutes
Total days in a week Monday through Friday= 5 days
Total days in 2 weeks = 10 days
Therefore, time spent by jack riding his skateboard up and down the hill to his friend's house in two weeks Monday through Friday = 10*30 = 300 minutes
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Evaluate
4(x+3)(x+1)
(x+5)(x-5)
for x = 3.
Answer: -1536
Step-by-step explanation:
1: 4(3+3) (3+1) (3+5) (3-5)
2: 4(6) (4) (8) (-2)
3: 24 (4) (8) (-2)
4: 96 (8) (-2)
5: 768 (-2)
= -1536
Solve the simultaneous equation
-4x+3y=1
6x-y=2
Let's change the equation,
→ 6x - y = 2
→ y = 6x - 2
Then the value of x will be,
→ -4x + 3y = 1
→ -4x + 3(6x - 2) = 1
→ -4x + 18x - 6 = 1
→ 14x = 1 + 6
→ x = 7/14
→ [ x = 1/2 ]
Hence, the value of x is 1/2 (or) 0.5.
Now the value of y will be,
→ y = 6x - 2
→ y = 6(1/2) - 2
→ y = 3 - 2
→ [ y = 1 ]
Hence, the value of y is 1.
If the polynomial function f(x)=(x+1)(x+3)9x-4) is rewritten in standard form, the degree would be ______ and the constant term would be _______.
.
If the polynomial function f(x)=(x+1)(x+3)9x-4) is rewritten in standard form, the degree would be 3 and the constant term would be 12 .
What is polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.A quadratic, cubic, quartic, and other functions involving only non-negative integer powers of x are examples of polynomial functions. We can define a polynomial's degree and provide a generic definition for it.f(x)=(x+1)(x+3)9x-4)
f(x ) = 3x³ + 36x² + 27x - 4x² - 16x - 12
f(x) = 3x³ + 32 x² + 11x - 12
in above function highest degree would be 3 and constant -12 .
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.
Can you help me with this please?
The solution associated with rational numbers is descriptively illustrated below with a detailed explanation.
What is a rational number?
An irrational number can sometimes be stated using fractions, but a rational number may be expressed even as a ratio of two integers with the denominator not equal to zero. Irrational numbers were non-terminating and non-recurring, whereas rational numbers have terminating decimals.Problems with the division of Rational Numbers:
(a) [tex]\frac{5}{7}[/tex] ÷ [tex]\frac{-11}{5} = \frac{5}{7} * \frac{5}{11} = \frac{25}{77}[/tex]
(b) [tex]\frac{\frac{-4}{5} }{\frac{3}{10} }[/tex]
[tex]\frac{-4}{5}[/tex]÷[tex]\frac{3}{10}[/tex]
[tex]\frac{-4}{5} *\frac{10}{3} \\=\frac{-8}{3}[/tex]
(c) [tex]\frac{-7}{17}[/tex]÷[tex]\frac{13}{34}[/tex]
[tex]\frac{-7}{17} X\frac{34}{13}[/tex]
(d) [tex]\frac{-2}{7}[/tex]÷[tex](\frac{-2}{21}[/tex] ÷ [tex]\frac{1}{7} )[/tex]
[tex]\frac{-2}{7}[/tex] ÷[tex](\frac{-2}{21} X\frac{7}{1} )[/tex]
[tex]= \frac{-2}{7} X \frac{-3}{2}[/tex]
[tex]=\frac{3}{7}[/tex]
He multiplied the denominator and numerator.
(e)
[tex]\frac{-1 \frac{1}{2} }{1\frac{2}{3} } \\\\=\frac{\frac{3}{2} }{\frac{5}{3} } \\\\=\frac{3}{2} X \frac{3}{5} \\\\=\frac{9}{10}[/tex]
(f) [tex]\frac{-3}{4}[/tex] ÷ [tex]\frac{2}{5} = \frac{-3}{4} X \frac{5}{2} =\frac{-15}{8}[/tex]
0.75÷0.4 = 1.875
[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{2}{5} = \frac{3}{4} X \frac{-5}{2} =\frac{-15}{8}[/tex]
(g)
Reciprocal of [tex]-1\frac{1}{17} = \frac{-17}{18}[/tex]
Reciprocal of [tex]\frac{-17}{18} = \frac{-18}{17}[/tex]
The above expressions are multiplicative inverse as [tex]\frac{-17}{18} X \frac{-18}{17} =1[/tex]
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below is a list of volume of lava rates from four volcanoes. Which of the following is true of the rates at which lava flows? Choose all that apply.
HELP!!!! WILL MARK BRAINLIEST!!!!
18x+3=21
Solve for x.
Answer:
x=1
Step-by-step explanation:
18x+3=21
-3 = -3
18x= 18
18x/18 = 18/18
x= 1
Answer:
x = 1
Step-by-step explanation:
[tex]18x + 3 = 21\\18x = 21 - 3\\18x = 18\\18x/18 = 18/18\\x= 1[/tex]
I need help please!!
Answer:
9.6*10^-12
Step-by-step explanation:
To calculate this, you will do the mass of 2 times 10^(-12) gram. So, 2*(10)^-12. Then we know 30 hours = 480,000,000 bacteria.
So now now you calculate the mass, 480,000,000 * 2(10)^-12 which gives you 9.6*10^-4.
Sorry if it sounds confusing! I hope this helps, have a good day! :D
robert spends 30.45$, before tax, at the store.
The cost of Robert purchase of books after the paid tax is $32.66.
What is defined as the percentage increase?The percentage increase would be the difference between both the final and initial values expressed as a percentage. For other sayings, it is the difference here between final and initial values divided by the original value and multiplied by 100.For the given question;
The original cost of the book purchased by the Robet = $30.45.
The tax of 7.25% is applied on the original cost of the book.
7.25% of $30.45 = (7.25×30.45)/100
7.25% of $30.45 = $2.21
The final cost of the book = original cost + tax
The final cost of the book = $30.45 + %2.21
The final cost of the book = 32.66
Therefore, the total price paid by the Robert for the book after 7.5% of the tax is applied is $36.66.
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The complete question is-
Robert spends $30.45 before tax at the bookstore. If the sales tax rate in his city is 7.25%, what is the total cost of his purchase?
I neeeddd the answer
Answer: 80 degrees because a line is 180°.
So if you subtract
180 - 100 = 80°
Answer:
x=80°
Step-by-step explanation:
The measures of angle x and the 100° angle form a straight angle.
This straight angle is 180°.
You can subtract the measure of one angle from the whole to find the measure of the other angle.
180°-100°=80°
This means angle x is 80°.
What is 8 and 3/4 into inproper fraction
Answer:
35/4
Step-by-step explanation:
8*4=32
32+3
=35
35/4
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 1000 lb. How many boxes of books can the delivery person bring up at one time?
If a delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 1000 lb. The number of boxes of books that the delivery person can bring up at one time is: 16.8 boxes.
Number of boxes of booksGiven:
Weight of the delivery person=160 lb
Weight of box of book=50 lb
Maximum capacity=1,000lb
Let b represent the number of boxes of books
Hence,
160+50b=1,000
Collect like terms
50b=1000-160
50b=840
Divide both side by
b=840/50
b=16.8 boxes of books
Therefore the maximum capacity of the elevator is 1000 lb. The number of boxes of books that the delivery person can bring up at one time is: 16.8 boxes.
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When you divide an even number by an even number, is the result always an even number
Answer: No, for example, 50/2=25, 25 isn't even
Step-by-step explanation:
Answer:
No, it's not
Step-by-step explanation:
when u divide an even number with even number,the ans maybe appear in even as well as odd number also
For e.g:
1. 36/12=3
2. 12/6=2
3. 30/6=5
4. 60/10=6
d= √(7₂ (x2 − ₁)² + (Y2 − ₁)² Evaluate d if (x1, y₁) = (-3, 4) and (x2, Y2) = (−2, 4).
Solve for X
[tex]\log _ { 3 } x = 9 \log _ { x } 3[/tex]
pls gv step by step explaination
Answer:
[tex]x=27, \quad x= \dfrac{1}{27}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{3.7 cm}\underline{Logs Laws}\\\\$\log_ba=\dfrac{\log_ca}{\log_cb}$\\\\\\$\log_ab=c \iff a^c=b$\\\end{minipage}}[/tex]
Given equation:
[tex]\log_3x=9\log_x3[/tex]
Change the base of 9logₓ3 to base 3:
[tex]\begin{aligned}\implies \log_3x & =9\log_x3\\\\& =\dfrac{9\log_33}{\log_3x}\\\\&=\dfrac{9(1)}{\log_3x}\\\\&=\dfrac{9}{\log_3x}\end{aligned}[/tex]
Therefore:
[tex]\implies \log_3x=\dfrac{9}{\log_3x}[/tex]
[tex]\textsf{Let }\log_3x=u:[/tex]
[tex]\implies u=\dfrac{9}{u}[/tex]
[tex]\implies u^2=9[/tex]
[tex]\implies u=\pm3[/tex]
[tex]\textsf{Substitute back in }u=\log_3x:[/tex]
[tex]\implies \log_3x=\pm3[/tex]
Case 1
[tex]\implies \log_3x=3[/tex]
[tex]\implies 3^3=x[/tex]
[tex]\implies x=27[/tex]
Case 2
[tex]\implies \log_3x=-3[/tex]
[tex]\implies 3^{-3}=x[/tex]
[tex]\implies \dfrac{1}{3^3}=x[/tex]
[tex]\implies x=\dfrac{1}{27}[/tex]
Answer: x=3 x=1/27
Step-by-step explanation:
[tex]log_3x=9log_x3\\[/tex]
The area of acceptable values:
[tex]x > 0\ \ \ \ x\neq 1\\Hence,\\x\in(0,1)U(1,+\infty)[/tex]
Solution:
[tex]\displaystyle\\log_3x=\frac{9}{log_3x} \ \ \ \ \ \boxed{ log_ab=\frac{1}{log_ba} }\\\\Multiply\ both\ parts\ of\ the\ equation\ by\ log_3x :\\\\log^2_3x=9\\log^2_3x=3^2\\ log_3x=б3\\\\log_3x=3\\\\x=3^3\\x=3*3*3\\x=27\\\\\\log_3x=-3\\x=3^{-3}\\\displaystyle\\x=(\frac{1}{3})^3\\ x=\frac{1}{3}*\frac{1}{3}*\frac{1}{3} \\ x=\frac{1}{27}[/tex]
