There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.
[1] using the quadratic formula
When the equation is in the form of ax² + bx + c = 0.
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
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[2] factoring
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[3] completing the square
To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c
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A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101.
Find the substance's half-life, in days. Round your answer to the nearest tenth.
A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101. The half-life is 2.98 days.
What is the formula for half-life?Exponential decay obeys the equation
[tex]m(t) = m_0 e^{-kt}[/tex]
where t = time, days
Given:
Initial mass, m₀ = 8 g
Decay constant, k = 0.101
For half-life, the mass is m = m₀/2.
Therefore,
[tex]m(t) = m_0 e^{-kt}[/tex]
e^{-0.101t} = 1/2
-0.101t = ln 0.5
t = ln 0.5/-0.101
t = 2.98
Therefore, The half-life is 2.98 days.
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What are the zeros of the quadratic function f(x)=8^2-16-15
Answer:
C)
Step-by-step explanation:
f(x)=[tex]8x^{2} -16x-15[/tex]
[tex]8x^{2} -16x-15=0[/tex]
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex] , a=8, b= - 16, c= - 15
[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4*8*(-15)} }{2*8} = \frac{16+-\sqrt{736} }{16} =\frac{16+-4\sqrt{46} }{16} = 1 +- \frac{\sqrt{46} }{4} = 1+- \frac{\sqrt{23} \sqrt{2}}{2\sqrt{2} \sqrt{2} } =1+-\frac{\sqrt{23} }{2\sqrt{2} } = 1+-\frac{\sqrt{23} }{\sqrt{8} }[/tex]
EASY POINTS LM is the midsegment of & ABC. If IM is 8 centimeters long, how long is AC
I think it's 12 because here it comes out
Bulls can develop respiratory issues as they get older. This may compromise their ability to breath properly which affects their energy level and overall health. A researcher wishes to conduct a study to find which of two injection therapies, Therapy A or Therapy B, is more effective in improving respiratory health. A total of 180 bulls that are at least 12 years old will be randomly selected from ranches in the state of Texas. The researcher will get consent from all owners, treat the bulls for eight months and evaluate changes in respiratory health.
Part A: How would the study benefit from adding a control group? (2 points)
Part B: What is the best way to randomly place the bulls into the Therapy A, Therapy B, and control groups? (4 points)
Part C: The researcher wants to use a blocking variable to place the bulls into groups instead of doing it randomly. He decides to block either by breed or ranch. Explain which would be the best blocking method. (4 points)
The study benefit from adding a control group as it would help in the correlation
What is a control group?A control group is s used to establish a cause-and-effect relationship by isolating the effect of an independent variable.
The best way to randomly place the bulls into the Therapy A, Therapy B, and control groups is random testing. The best blocking method will be breeding.
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Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $110 per hour. The mechanics worked for a combined total of 35 hours, and together they charged a total of $3550. How long did each mechanic work?
Firstmechanic:hours
Secondmechanic:hours
Answer:
1st mechanic:20hours
2ndmechanic:15hours
Step-by-step explanation:
1stmechanic:20hours=20x95
=$1900
2nd mechanic:15hours=15x110
=$1650
total=$1900+$1650
=$3550
Solve for x
(2^2/x) (2^4/x) = 2^12
[tex] \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \:(2 {}^{ \frac{2}{x} } ) \sdot(2 {}^{ \frac{4}{x} } ) = 2 {}^{12} [/tex]
[tex]\qquad \sf \dashrightarrow \:(2 {}^{ \frac{2}{x} + \frac{4}{x} } ) = 2 {}^{12} [/tex]
[tex]\qquad \sf \dashrightarrow \:(2 {}^{ \frac{6}{x} } ) = 2 {}^{12} [/tex]
Now, since the base on both sides are equal, therefore their exponents are equal as well ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{6}{x} = 12[/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{6}{12} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{1}{2} [/tex]
or
[tex]\qquad \sf \dashrightarrow \:x = 0.5[/tex]
Hope you got the required Answer ~
Worth 30 points! Select the correct answer.
What is the value of x in the triangle? (file is attached below)
Answer:
A
Step-by-step explanation:
tan60=opp/adj
tan60=15/x
15tan60=x
25.98=x (when you calculate 15 root 3 it is the same number)
Hi there !
What is a Pythagoras theorem ?
Nonsense = Reported
Thank you
Answer:
Hi! I think you are referring to the Pythagorean Theorem.
Essentially, given a right triangle, the sum of the squares of the shorter sides equals the square of the longer (slant) side or hypotenuse.
The formula is a squared + b squared = c squared
If the triangle has side lengths 3 and 4 (for the shorter sides), the longer side can be solved like this:
3 squared + 4 squared = x squared
(Let x = the longer side)
3 squared = 9
4 squared = 16
9+16 = x squared
25 = x squared
x = 5
So there you go, that's the Pythagorean theorem.
Let me know if this helped!
Answer:
a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Step-by-step explanation:
Which statement best describes Inflation?
О А. Inflation decreases the amount of goods and services that can be purchased with a dollar.
Inflation Increases the amount of goods and services that can be purchased with a dollar.
Inflation increases the purchasing power of a dollar.
O C.
OD.
Inflation decreases the prices of goods and services.
O E. Inflation doesn't affect the prices of goods and services but increases wages.
Answer:
A
Step-by-step explanation:
Inflation decreases the amount of goods and services that can be purchased with a dollar.
A recipe calls for (1 3/8) cups of sugar to make 2 dozens cupcakes. How much sugar is needed to make 60 cupcakes?
Answer:
55/16 cups or 3.4375 cups
Step-by-step explanation:
there are 5 dozens (12) in 60, so there are 2.5 2 dozens in 60, so you would multiply 1 3/8 by 2.5 to find how many cups are needed in 60 cupcakes because 1 3/8 cups is for 2 dozen cupcakes
SHOW ALL WORK PLEASE!!!!!!!
The rat population in a major metropolitan city is given by the formula n(t)=89e^0.02t where t is measured in years since 1992 and n(t) is measured in millions
What was the rat population in 1992?
What does the model predict the rat population was in the year 2003?
Answer:
See below ~
Step-by-step explanation:
What was the rat population in 1992?⇒ t represents the years after 1992
⇒ So, in 1992, t = 0
⇒ Apply in the formula
⇒ n(0) = 89e^(0.02 × 0)
⇒ n(0) = 89e⁰
⇒ n(0) = 89,000,000
The rat population in 1992 was 89,000,000.
===========================================================
What does the model predict the rat population was in the year 2003?⇒ Number of years after 1992 : 2003 - 1992 = 11
⇒ Substitute for t in the formula
⇒ n(11) = 89e^(0.02 × 11)
⇒ n(11) = 89e^(0.22)
⇒ n(11) = 89 × 1.24607673
⇒ n(11) = 110,900,829 rats
The model predicts that in the year 2003 there will be a rat population of 110,900,829 rats.
Answer:
(a) 89,000,000 rats
(b) 110,900,829 rats
Explanation:
Given equation:
n(t)=89e^0.02tTo find the initial population (1992):
insert t = 0
n(0) = 89e^0.02(0) = 89 million ≈ 89,000,000To find the rat population in 2003 (after 11 years):
insert t = 11
n(11) = 89e^0.02(11) = 89e^0.22 ≈ 110,900,829simplify (4x^3)^2 (3x^5)
Answer:
16x^6(3x^5)
48x^11
What additional piece of information would prove △LMK≅△NMK by Side Angle Side?
Answer:
angle M
Step-by-step explanation:
if you are using side angle side the two sides may be
line LK and NK
and angle M
what is the volume of the solid
Answer:
A.264
Step-by-step explanation:
((Area Of triangle*height)=Volume
Area of triangle is the base of the triangle multiplied by height of triangle divided by 2
((8*6)/2)*11=264
HELP!!!!!! 100 POINTS!!!!!!
Kyle and Lauren teach swimming lessons during the summer. Kyle has 8 classes with g students in each class and 6 classes with h students in each class. Lauren has 5 classes with g students in each class and 10 classes with h students in each class.
If Kyle has a total of 62 students and Lauren has a total of 70 students, which equation shows the solution to the system of equations that represents this situation?
The equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.
What is an expression?
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Kyle and Lauren teach swimming lessons during the summer. Kyle has 8 classes with g students in each class and 6 classes with h students in each class. Lauren has 5 classes with g students in each class and 10 classes with h students in each class.If Kyle has a total of 62 students and Lauren has a total of 70 students,The equation made by the given situation is:-
For kyle, there are g students attending 8 classes sp total number of students will be 8g similarly for h students there are 6 classes so the total number of h students will be 6h. The total number of students for both g and h students attending kyle's class is 62. So the equation will be given as:-
8g + 6h = 62
Now for Lauren, there are g students attending 5 classes so the total number of students will be 5g similarly for h students there are 10 classes so the total number of h students will be 10h. The total number of students for both g and h students attending Lauren's class is 70. So the equation will be given as:-
5g + 10h = 70
Therefore the equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.
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Given: ABCD is a parallelogram.
Prove: ∠A ≅ ∠C and ∠B ≅ ∠D
Parallelogram A B C D is shown.
By the definition of a ▱, AD∥BC and AB∥DC.
Using, AD as a transversal, ∠A and ∠
are same-side interior angles, so they are
. Using side
as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary.
Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠
.
A parallelogram is a quadrilateral with four sides and the opposite sides of the parallelogram are equal and parallel.
How to show the proof?In the given figure, AB||DC. AD is the transversal, such that:
∠A + ∠D = 180-degrees.
The parallelogram is a quadrilateral with equal such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees.
From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.
From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.
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I need help I don’t understand please help
can you please help me? 2.1.3
[tex]~~~~~~2I_2 - A\\\\\\=2\begin{bmatrix}1&0\\0&1 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2&0\\0&2 \end{bmatrix}-\begin{bmatrix}4&2\\3&-3 \end{bmatrix}\\\\\\=\begin{bmatrix}2-4&0-2\\0-3&2+3 \end{bmatrix}\\\\\\=\begin{bmatrix}-2&-2\\-3&5 \end{bmatrix}[/tex]
What is the solution to this equation? (1/27)2-x =9^3x
Answer:
x = -2
Step-by-step explanation:
Prime factorize, 27 and 9
27 = 3 *3 * 3 = 3³
9 = 3*3 = 3²
[tex]\sf \left(\dfrac{1}{27}\right)^{2-x}=9^{3x}\\\\[/tex]
[tex]\left(\dfrac{1}{3^3}\right)^{2-x}=9^{3x}\\\\(3^{-3})^{2-x}=(3^2)^{3x}\\\\3^{(-3)*(2-x)}=3^{2*3x}\\\\3^{-6+3x} = 3^{6x}[/tex]
Bases are same, so now compare the exponents
-6 + 3x = 6x
3x = 6x + 6
3x - 6x = 6
-3x = 6
x = 6/(-3)
[tex]\sf \boxed{\bf x = -2}[/tex]
Exponent law:[tex](x^m)^n=x^{m*n}\\\\\left(\dfrac{1}{a^{m}}\right)=a^{-m}\\[/tex]
the perimeter of a rectangular field is 302 yards. if the length of the field is 92 yards what is its width
Answer:
the width is 59
Step-by-step explanation:
302/2-92=59
Sophia determined that the expression Negative (4 x minus 5) + 2 (x minus 3) is equivalent to –2x – 5 by using the steps below.
Expression: Negative (4 x minus 5) + 2 (x minus 3)
Expression: –2x – 5
Step 1:
Choose a value of x
Choose x = 1.
Choose x = negative 1.
Step 2: Substitute
Negative (4 (1) minus 5) + 2 (1 minus 3)
Negative 2 (negative 1) minus 5
Step 3: Evaluate
Negative (4 (1) minus 5) + 2 (1 minus 3) = negative (negative 1) + 2 (negative 2) = negative 3
Negative 2 (negative 1) minus 5 = 2 minus 5 = negative 3
Step 4:
Compare
Since –3 = –3, the two expressions are equivalent.
Which explains whether Sophia is correct?
She is correct because the value of the two expressions are the same in Step 3.
She is correct because she substituted opposite values in Step 1.
She is not correct because she did not substitute the same number in both expressions in Step 1.
She is not correct because she did not perform the correct order of operations in Step 3.
The correct statement is:
"She is not correct because she did not substitute the same number in both expressions in Step 1."
Is Sophia correct?First, let's see if Sophia is correct.
She starts with the expression:
-(4x - 5) + 2*(x - 3) = -2x - 5
Expanding the left side:
-4x + 5 + 2x - 6 = -2x - 5
-2x -1 = -2x - 5
So the constant term is different.
Now, what Sophia does is evaluating in x = 1 and x = -1. You can't do that when finding equivalent expressions. (never evaluate in different numbers).
"She is not correct because she did not substitute the same number in both expressions in Step 1."
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add 6370 square to 6370 square
PLEASE HELP!!!!!!!!!!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!!!!!!!!!!!!A moving-van rental company uses the polynomial 110 + 0.65(m – 200) to calculate the rental charges if a customer drives a van more than 200 miles in one day. In the polynomial, m is the total number of miles that the customer drove the van during the day. Use the Distributive Property to write an equivalent expression for the total cost of renting the van and driving it more than 200 miles in one day.
Answer:I think it would be 84 + 0.45m + 108.
Which simplified could be 0.45m + 192.
hope this helps!
Step-by-step explanation:
The y-intercept is the place where a line crosses the y-axis. hat is true about the y-intercept?
A. It always has an x coordinate of 0.
B. It always has any coordinate of 0
C. Both x and y coordinates are 0.
Answer:
It always has an x coord of 0
The first step that we must take before attempting to solve a problem is to understand what it is asking for and what is given to us to help solve the problem. Looking at the problem statement, we can see that they are asking what is true about the y-intercept. We are given the information that the y-intercept is the place where a line crosses the y-axis.
Now that we have collected all that information, let us move onto understanding and solving the problem. So first of all, using the information that was given to us, we know that the y-intercept is the place where a line crosses the y-axis. The y-axis occurs where the x-coordinate is 0 and the x-axis occurs where the y-coordinate is 0. Therefore, the option that would best fit the description that we have would be option A, it always has an x coordinate of 0.
HELP PLS! A kiddie pool is 9 feet long and 6 feet wide. Surrounding wach side of the kiddie pool is a cement walkway of uniform width. The combined area of the pool and walk way is 108 ft^2. Find the width of the walkway
Answer:
wait I will edit and answer it in a few minutes
7,000 dollars is placed in a savings account with an annual interest rate of 3%. If no money is added or removed from the account, which equation represents how much will be in the account after 7 years?
Answer:
See below
Step-by-step explanation:
Interest 3% in decimal form is .03
interest in ONE year 7000 * .03
interest in SEVEN years 7000 * .07 * 7
this is added to the original deposit of 7000
to become 7000 + 7000 * .03 * 7
or 7000 ( 1 + .03*7 )
or 7000 ( 1.21 ) = $ 8470
IF the interest is compounded
the money in the account will be 7000 ( 1+.03)^7
Work out the length of
x.
Give your answer rounded to 3 significant figures.
The triangle is an isosceles right triangle. Then the value of x will be 1.27 cm.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The right-angle triangle is given below.
The given triangle is an isosceles right triangle.
P = B = x
Then we have
1.8² = x² + x²
2x² = 3.24
x² = 1.62
x = 1.27 cm
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what is the answer ???
Answer: Heyaa!~
- Write 63 as the product of prime factors -
Since, the prime factors of 63 are 3, 7. Therefore, the product of prime factors = 3 × 7 = 21.- Write the prime factors in ascending order -
I think it would be 3/7- what's the highest common factor of 63 and 105 -
21, divides both 63 and 105, i.e., 21.Hopefully this helps you! ^^^
A company orders 24 boxed lunches from a deli for $177.60. If each boxed lunch
costs the same amount, what is the unit cost of each boxed lunch?
Answer: $7.40
Step-by-step explanation:
You can use $177.60 divide by 24 boxed lunches equals $7.40
Since you have to distribute 177.60 in 24 boxes.
Match each graph with the function it represents.
A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The graph of the function f(x) and g(x) can be plotted as shown in the below image.
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