Considering the sum of the internal angles of a triangle, it is found that the correct student is Paige.
What is the sum of the internal angles of a triangle?The sum of the three internal angles of a triangle is of 180º, and none of the angles can be zero.
Hence, a triangle can have at most one right angle(angle of 90º), and researching the question on the internet, the student who states this is Paige.
More can be learned about the sum of the internal angles of a triangle at https://brainly.com/question/25215131
Solve the equation by using the quadratic formula.
3x² - 1 = 7x
Answer:
Solutions: [tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex] , [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex]Step-by-step explanation:
We are given the following quadratic equation, 3x² - 1 = 7x, which requires us to find its possible solutions using the quadratic formula.
Definitions:In a quadratic equation, the leading term has a second-degree (or squared) variable. The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are real numbers, and that a ≠ 0. Quadratic Formula:The quadratic formula is given by:
[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
We will use this formula to solve for the roots or the solution of the given quadratic equation.
Solution:Step 1: transform the given equaton into standard form.
First, we must subtract "7x" from both sides of the equation:
3x² - 7x - 1 = 7x - 7x
3x² - 7x - 1 = 0 ⇒ This is the standard form of the given quadratic equation where a = 3, b = -7, and c = - 1.
Step 2: Plug in the values for a, b, & c into the quadratic formula.
The derived values for a, b, & c from the previous step are: a = 3, b = -7, and c = - 1. Substitute these values into the following quadratic formula:
[tex]\displaystyle\mathsf{x\:=\:\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{(-7)^2-4(3)(-1)}}{2(3)}}[/tex]
Step 3: Following the PEMDAS Order of Operations, start by applying the Power rule of Exponents [tex]\displaystyle\mathsf{(a^m)^n = (a^{m*n})}[/tex] (under the radical) :
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{49-4(3)(-1)}}{2(3)}}[/tex]
Step 4: Next, multiply the integers under the radical, PEMDAS Order of Operations.
[tex]\displaystyle\mathsf{x\:=\:\frac{-(-7)\pm\sqrt{61}}{2(3)}}[/tex]
Step 5: Multiply the integers in the denominator, and apply the multiplication integer rule, -(-a) = a.
[tex]\displaystyle\mathsf{x\:=\:\frac{7\pm\sqrt{61}}{6}}[/tex]
Since [tex]\displaystyle\mathsf{\sqrt{61}}[/tex] is not a perfect square, it can remain the same.Step 6: Separate the solutions.
[tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex] , and [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex]
Final Answer:Therefore, the solution to 3x² - 1 = 7x are: [tex]\displaystyle\mathsf{x\:=\:\frac{7+ \sqrt{61}}{6}}[/tex], [tex]\displaystyle\mathsf{x\:=\:\frac{7 - \sqrt{61}}{6}}[/tex].
_____________________Keywords:Quadratic equation
Quadratic function
Standard form
Parabola
______________________Learn more about quadratic equations here:
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Find the range, median, upper extreme, lower extreme, and interquartile range of the following data: 85, 85, 2, 1, 204, 123, 24, 139, 20
what is the solution for 11 = y-6
Answer:
y = 17
Step-by-step explanation:
11 = y - 6
11 + 6 = y17 = yprove that the value of y is 17
11 = y - 6
11 = 17 - 611 = 11proven
Hello.
Let's solve this equation for y.
First, subtract 11 from both sides:
[tex]\mathrm{11-11=y-6-11}[/tex]
[tex]\mathrm{0=y-6-11}[/tex]
[tex]\mathrm{0=y-17}[/tex]
Subtract y from both sides:
[tex]\mathrm{-y=-17}[/tex]
[tex]\Large\boxed{\sf{y=17}}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
An engineer wants to test the complex and dangerous process of filling and emptying a tank of liquid hydrogen. The tank has a volume of 400 cm3. The tank can be filled 50 cm3 per hour faster than it can be emptied.
Part A. Write an expression for the number of hours it takes to fill this tank, in terms of r
Part B. Wrote an expression for the number of hours it takes to empty this tank, in terms of r:
Part C. Wrote an equation for the total time in hours it takes to fill and empty this tank in terms of r. Simplify.
Part D. Find the rate that would allow you to fill and empty the tank in 100 hours. Check for extraneous solutions, and show your work. Round to the nearest tenth.
Answer:
the answer is 45%.
Step-by-step explanation:
if you add 5% divided by 3 = 15%.
So if you add all of those plus the 30% you will be getting 45%.
Which graph correctly represents the quadratic equation?
D (last slide) is the graph to the given equation.
As the equation is positive, the line of the graph will give smile shape.
Graph plotted below:
Solve the inequality.
21 < 2x + 3
Answer:
x>9 I included a picture of the number line as well
Answer:
The answer is 9 > x
Step-by-step explanation:
Hope that helps!
First, create 3 equations of the form ax+by+cz=d , where a, b, c, and d are constants (integers between – 5 and 5). For example, x+2y-z=-1 . Perform row operations on your system to obtain a row-echelon form and the solution.
Go to the 3D calculator website GeoGebra: www.geogebra.org/3d?lang=pt and enter each of the equations.
After you have completed this first task, choose one of the following to complete your discussion post.
1. Reflect on what the graphs are suggesting for one equation, two equations, and three equations, and describe your observations. Think about the equation as a function f of x and y, for example, x+2y+1=z in the example above. Geogebra automatically interprets this way, that is, like z=f(x, y)=x+2y+1 , it isolates z in the equation.
Answer:
The solution is x=0, y=0, z=1
Step-by-step explanation:
Step1: -row2 + row1; -row2 + row3
x + 2y - z = -1
x + y + z = 1
x - y - z = -1
1 2 -1 -1
1 1 1 1
1 -1 -1 -1
0 1 -2 -2
1 1 1 1
0 -2 -2 -2
Step 2: row3/-2
0 1 -2 -2
1 1 1 1
0 1 1 1
step 3: -row3 + row1
0 0 -3 -3
1 1 1 1
0 1 1 1
step 4: row1/-3
0 0 1 1
1 1 1 1
0 1 1 1
step 4: -row1 + row3; -row1 + row2
0 0 1 1
1 1 0 0
0 1 0 0
step 5: -row3 + row2
0 0 1 1
1 0 0 0
0 1 0 0
The reduced row echelon form is:
1 0 0 0
0 1 0 0
0 0 1 1
in how many ways can 8 people line up for movie tickets
Answer:
40320 way
Step-by-step explanation:
Given:
In how many ways can 8 people line up for movie tickets?
You can do the following:
⇒ Tree diagram
⇒ List
⇒ Table
⇒ Multiply
Solve:
For me, I like to use Multiply for this question.
1 ×2×3×4×5×6×7×8
2 ×3×4×5×6×7×8
6×4×5×6×7×8
24×5×6×7×8
120 ×6×7×8
720×7×8
5040×8
40320
Hence, in 40320 ways can 8 people line up for movie tickets.
~Learn with Lenvy~
How do you write 48,600,000 in scientific notation?
Answer:4.8^10 power of 7
Step-by-step explanation:
How many triangles can we make with two 7-centimeter sides. Explain why
Answer:
infinite number
Step-by-step explanation:
We can make infinite number of triangles with two 7-centimeter sides as long as the third side is less than 7 + 7 = 14 cm
Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 10 m, the new total area of the garden will be 169 m2. Find the length of each side of the original garden
Answer:
6m
Step-by-step explanation:
To find the original length you must take away the add-ons. To do so we know that they added 7 and A= l*l (or l squared). They added the 7 to the length so multiply 7*7 (49) subtract your answer from 169 (120) and that's your new area. To find the original length divide by 4 (I believe) and get 30m2
Suppose a car is initially worth $20,000, and suppose that after one year, the car is now worth $18,673. Write an exponential function that models this scenario, and then estimate the value of the car after five years
Aiko works in the fish department of a pet store. She is asked to drain, clean, and refill two reef tanks.
The first tank holds 175 gallons of water and the second tank holds 200 gallons of water. The hoses that
she uses drain the tanks at a rate of 25 gallons of water per hour.
1. write an equation for each tank that represents the total amount of water in the gallons in the tank in terms of the number of hours that the tanks are draining
tank one equation ________
tank two equation ________
2. how much water is in each tank after 3 hours?
tank one ___
tank two___
The equation for the first tank will be 175 - 25h and the equation for the second tank is 200 - 25h.
How to solve the equation?From the information given, the first tank holds 175 gallons of water and the second tank holds 200 gallons of water while the hoses that she uses drain the tanks at a rate of 25 gallons of water per hour.
Therefore, the equation for the first tank will be:
= 175 - (25 × h)
= 175 - 25h
The equation for the second tank will be:
= 200 - (25 × h)
= 200 - 25h
The quantity in the first tank after three hours will be:
= 175 - 25h
= 175 - (25 × 3)
= 175 - 75
= 100 gallons.
The quantity in the second tank after three hours will be:
= 200 - 25h
= 200 - (25 × 3)
= 200 - 75
= 125 gallons.
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The colony of bacteria grows according to the law of inhibited growth of a function N(t)=100e^0.045t where N is measured in grams and t is measured in days. Determine the initial amount of bacteria.
can u answer with steps?
If the ratio a: b = 2 : 3, and b : c = 3 : 4. Find the ration a : c
ASAP
Answer:
if a:c=2:3 andb:c=3:4therefore a:c=2:4
X3-Y3=28, X-Y=2, X2+XY+Y2=
it is = 14 but how?
Step-by-step explanation:
x³ - y³ = (x - y)³ + 3x²y - 3xy²
28 = (2)³ + 3xy(x - y)
28 = 8 + 3xy(2)
28 - 8 = 6xy
20 = 6xy → xy = 20/6 = 10/3
(x - y)² = 2²
x² - 2xy + y² = 4
x² - 2(10/3) + y² = 4
x² + y² = 4 + 20/3 = 32/3
x² + xy + y² = 32/3 + 10/3 = 42/3 = 14
select all the expressions that are equivalent to 4 x 4 x 4 x 4 x 4
a. 4
b.5⁴
c.4² x 4³
d. 5² x 4(5)
e. 4¹ x 4(5)
Answer:
c
Step-by-step explanation:
4 x 4 x 4 x 4 x 4 = 1,024
-----
a. 4
b. 625
c. 1,024
d. 500
e. 80
Hey there!
4 × 4 × 4 × 4 × 4
= 16 × 16 × 4
= 256 × 4
= 256 + 256 + 256 + 256
= 512 + 512
= 1,024
Looking for something that’s equivalent to: 1,024
Option A. is INCORRECT because it is too small.
Option B. 5^4
5^4
= 5 × 5 × 5 × 5
= 25 × 25
= 625
Option B. is also INCORRECT because it is also too small.
Option C. 4^2 × 4^3
4^2 × 4^3
= 4^5
= 4 × 4 × 4 × 4 × 4
= 16 × 16 × 4
= 256 × 4
= 1,024
Option C. could possibly be one of the answers
Option D. 5^2 × 4(5)
5^2 × 4(5)
= 5 × 5 × 20
= 25 × 20
= 500
Option D. is also INCORRECT because it’s too small.
Option E. 4^1 × 4(5)
4^1 × 4(5)
= 4 × 4(5)
= 4 × 20
= 20 + 20 + 20 + 20
= 40 + 40
= 80
Option E. is last to be INCORRECT because it is also too small
MET the ANSWER:
Therefore, your answer is: Option C.
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Tammy runs 8 miles in 45 minutes. How many minutes does she take per mile? If necessary, round your answer to the nearest hundredth.
Answer:
5.63
Step-by-step explanation:
what is the equation for Penny had some money. After she pays $5 for her new kitten, she will have $27. How much money did she start with? you will get 20 points
Answer:
X + 5 = 27 or 27 - 5 = X
the answer is $22
Step-by-step explanation:
Answer:
x-5=27 or 27=x-5 or x=27+5
Step-by-step explanation:
let x be the total amount of money Penny has.
after she deducts 5 dollars to pay for her bunny she is left with 27
therefore
x-5=27 (which is the same as representing it in any other way shown above)
if they ask for X, then solve your equation
x=27+5
x=$32
Could I get some help? QUESTION: This table shows the profit for a company (in millions of dollars) in different years.
The quadratic regression equation that models these data is y=-0.34x^2+4.43x+3.46. Using the quadratic regression equation, what was the predicted profit in year 8?
A. $17.14 million
B. $16.8 million
C. $17 million
D. $16 million
Answer:
17 million
Step-by-step explanation:
-0.34([tex]8^{2}[/tex]) + 4.43(8) + 3.46
-21.76 + 35.44 + 3.46
13.68 + 3.46
17.14
Answer: C 17 million
Have an amazing day!
PLEASE RATE!
PLEASE HELP!!
WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!
Graph the line with slope 1/3 passing through the point (-4,-5).
Answer:
graphing done below.
Step-by-step explanation:
using the formula: y - y₁ = m(x - x₁)
equation:
[tex]\sf y - -5 = \frac{1}{3} (x - - 5)[/tex]
[tex]\sf y +5 = \frac{1}{3} x + \frac{5}{3}[/tex]
[tex]\sf y = \frac{1}{3} x + \frac{5}{3}-5[/tex]
[tex]\sf y = \frac{1}{3} x - \frac{10}{3}[/tex]
find the slope of the line through the given points (-6,17),(-6,13)
Answer:
As Per Provided Information
Given points are (-6,17) & (-6,13).
here
x₁ = -6
x₂ = -6
y₁ = 17
y₂ = 13
We have been asked to find the slope of the line.
Using Formula
[tex] \bf \: m \: = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex]
m is the slope of line
Put the given value we get
[tex] \qquad \sf \longrightarrow \: m = \ \dfrac{ - 6 - ( - 6)}{13 - 17} \\ \\ \\ \qquad \sf \longrightarrow \: m = \ \dfrac{ - 6 + 6}{13 - 17} \\ \\ \\ \qquad \sf \longrightarrow \: m = \dfrac{0}{ - 4} \\ \\ \\ \qquad \sf \longrightarrow \: m = 0[/tex]
Therefore,
Slope of the line is 0 .Write expression 4+ k as a verbal statement
Answer:
Four plus a number= a number
Step-by-step explanation:
I got this from my teacher
Bethany bought 42 liters of water for the running team. There are 16 members on the team. If each member gets an equal amount of water, how many liters does each memberget?
pls help with this math homework.
Answer:
the first answer is 2/6 and 4/6 both (pick)
Step-by-step explanation:
second is 8/12
third is 9/15
fourth is 16/72
fifth is 2/5,
sixth is 4/10
seventh is 8/18
last one is 2/8
What is the current temperature in Fahrenheit on the thermometer below?
A.
B.
C.
D.
Answer:
the answer is D just did the quiz hope this helps!!!!!
Step-by-step explanation:
The Box is being packed without gaps or overlaps with unit cubes
The volume of a box is the product of its dimensions
The volume of the box is 11 unit cube
How to determine the volumeFrom the question, we have the following highlights
The cubes are unit cubesThe boxes are packed without gapsThe volume of a unit cube is:
Volume = 1 unit cube
There are 11 cubes in the box. So, the volume of the box is:
Volume = 11 *1 unit cube
Volume = 11 unit cube
Hence, the volume of the box is 11 unit cube
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4,000 i savings at end of 3 years earn 960 in simple interest how much in account
Answer:
She would have had $120 more should the rate were 1% greater.
Step-by-step explanation:
At the end of 3 years the amount in the account = Principal + Interest
Amount = 4000 + 960 = 4960
Amount at the end of 3 years = $4960
b) Formula for Rate , R = 100I/(PT)
Where I = Interest = 960, P = Principal = 4000, T= Time = 3 years
R = (100 × 960) / ( 4000 × 3)
R = 8
Rate, R = 8% per annum.
c) If the rate was 1% more, R = 8 + 1 = 9% per annum
Interest, I = PRT/100
Interest, I = 4000 × 9 × 3 /100 = 1080
Amount in her account would have been = $4000 + $1080 = $5080
Amount more = $5080 - $4960 = $120
100 POINTS!
Victoria will borrow $8,711 at 14.5% APR. She will pay it back over 5 years. What will her monthly payments be? (Use the table)
Show work for 100 POINTS!
Answer:
$204.95
Step-by-step explanation:
[tex]\mathsf{monthly \ payment=\dfrac{\frac{r}{12}\times P}{(1-(1+\frac{r}{12})^{-n}}}[/tex]
where:
P = total amount borrowedr = APR in decimal formn = total number of months of term of loanGiven:
P = 8711r = 14.5% = 0.145n = 5 × 12 = 60 monthsSubstituting given values into formula:
[tex]\implies \mathsf{monthly \ payment=\dfrac{\frac{0.145}{12}\times 8711}{(1-(1+\frac{0.145}{12})^{-60}}}[/tex]
[tex]\implies \mathsf{monthly \ payment=\$204.95}[/tex]
Roger can type 1530 words in 1/2 hour. How many words can he type per
minute?
PLS HELP ME
Answer:
25.5
Step-by-step explanation:
1530 divided by 60 is 25.5 and 25.5 multiplied by 60 is 1530.