The solution to the equations are:
9x² - 36x + 36 = 0 has two equal real solutionsx² - x + 4 = 0 has no real solutionsThe factored expression of 4x² + 23 – 35 is 4(x² -3)Part A: Describe the solutionThe equation is given as:
9x² - 36x + 36 = 0
The above equation is a quadratic equation which can be represented as:
ax² + bx + c = 0
The discriminant (d) is calculated as:
d = b² - 4ac
So, we have:
d = (-36)² - 4 * 9 * 36
d = 0
A discriminant of 0 means that the equation has two equal real solutions
Hence, 9x² - 36x + 36 = 0 has two equal real solutions
Part B: Describe the solution
The equation is given as:
x² - x + 4 = 0
The above equation can be represented as:
ax² + bx + c = 0
The discriminant (d) is calculated as:
d = b² - 4ac
So, we have:
d = (-1)² - 4 * 1 * 4
d = -15
A discriminant of -15 means that the equation has no real solutions
Hence, x² - x + 4 = 0 has no real solutions
Part C: The solution to the expression
We have:
4x² + 23 – 35
Evaluate the difference
4x² -12
Factor out 4
4(x² -3)
Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)
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Need help with my question
Answer:
See below ~
Step-by-step explanation:
What is the rat population in 1993?⇒ Number of years since = 0 ⇒ t = 0
⇒ Apply in the formula
⇒ n(0) = 73e^(0.02 × 0)
⇒ n(0) = 73e⁰
⇒ n(0) = 73,000,000 rats
=============================================================
What does the model predict the rat population was in the year 2009?⇒ Number of years since 1993 : 2009 - 1993 = 16 ⇒ t = 16
⇒ Applying in the formula
⇒ n(16) = 73e^(0.02 × 16)
⇒ n(16) = 73e^(0.32)
⇒ n(16) = 73 × 1.37712776 × 10⁶
⇒ n(16) = 100.530326 x 10⁶
⇒ n(16) = 100,530,326 rats
Answer:
Given function:
[tex]\large \text{$ n(t)=73e^{0.02t} $}[/tex]
where:
t is the number of years since 1993n(t) is the rat population measured in millionsTo calculate the rat population in 1993, substitute [tex]t = 0[/tex] into the function:
[tex]\large \begin{aligned}\implies n(0) & =73e^{0.02(0)}\\& = 73 \cdot 1\\& = 73 \sf \: million\end{aligned}[/tex]
To calculate a prediction of the rat population in 2009, first determine the value of t by subtracting the initial year of 1993 from the given year of 2009:
[tex]\large \text{$ \implies t=2009-1993=16 $}[/tex]
Substituting the found value of t into the function to find the predicted number of rats in 2009:
[tex]\large \begin{aligned}\implies n(16) & =73e^{0.02(16)}\\& = 73e^{0.32}\\& = 100.5303268...\\ & = 100.5 \sf \: million\:(1\:dp)\end{aligned}[/tex]
100 points and i will mark brainiest.
What is 131072 divided by 2 to the power of 4
Answer:
1942
Step-by-step explanation:
31072 / (2^4) = 31072
Hope This Helped
Question
What is 131072 divided by 2 to the power of 4?
Solution in steps:
131072 / 2⁴ Find 2 to the power of 4131072 / 16 Divide 131072 by the value found at previous step8192 Calculated quotientAnswer:
8192
For her phone service, Charmaine pays a monthly fee of $15, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is
$66.90.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Step-by-step explanation:
after subtracting the monthly fee (which she has to pay, even if she does not make a single call) we have
66.9 - 15 = $51.90
for actual phone call minutes.
1 minute is $0.05
so, in the month with the lowest charge she had used
51.9 / 0.05 = 1038 minutes for calls.
since this was the minimum, for all the numbers of minutes m she used in a month we have
m >= 1038 minutes
Which item is the U.S. Treasury most known for issuing?
-CDs
-savings notes
-bonds
-investment notes
Answer:
Bonds
Step-by-step explanation:
A bond is a fixed-income instrument that represents a loan made by an investor to a borrower (typically corporate or governmental).
which of the sequences is an arithmetic sequence A. -20,-27,-34,-41,-48, ... B. 1,5,10,15,20, ... C.154,71,8,5,2, ... D. 12,-24,36,-48.60, ...
Answer:
A and B are arithmetic sequences. they have a set and consistent increase/decrease in each term.
Step-by-step explanation:
HELPP PLEASE!!!
Harry is 5 years older than his sister, and the product of their
ages is 84.
Let h represent Harry's age, then h- 5 represents his
sister's age, and h (h-5) = 84 models the situation.
The equation can also be written as h² - 5h = 84.
Rewrite the equation so that it is in the form polynomial = 0.
Enter the polynomial, in standard form, in the box.
= 0
Answer:
See below
Step-by-step explanation:
h^2 - 5h = 84
h^2 - 5h - 84 = 0
correlation and regression analysis
A water barrel has a total volume of 1.25 cubic meters (m3). Use the fact that 1 foot is approximately equal to 0.3048 m to convert this volume to cubic feet (ft3). Round your answer to the nearest tenth. Do not type the units in the space below.
Answer:
see the attachment photo!
To calculate the density of an object,you wpuld?
Find the area of the following parallelgram
Answer:
6 cm²
Step-by-step explanation:
The formula to find the area of the parallelogram is :
Area = Base × Height
Given that,
Base ⇒ 3cm
Height ⇒ 2 cm
Let us find now.
Area = Base × Height
Area = 3cm × 2cm
Area = 6 cm²
for 12 days, Keisha keeps track of how much water she drinks per day. her results are shown below
1 1/2quarts 2 1/4quarts 2quarts 1 1/2quarts 1 3/4 quarts 1 1/2 quarts
1 1/4quarts 2quarts 2 1/4quarts 1 1/2quarts 2 quarts 1 /2quarts
what is the amount of water that Keisha drinks during 12 days ?
what is the average amount of water that Keisha drinks per day ?
at how many days did Keshia drink at least the average amount of water?
STRETCH YOUR THINKING on day 13 Keisha drinks 1 quart of water how does that affect the average amount of water she drinks ? EXPLAIN
The total amount of water that Kiesha drinks in 12 days is 20 quarts
The average amount of water she drinks per day is 1 2/3 quarts
The number of days that Keshia drinks at least the average amount of water is 6 days
If she drinks 1 quart of day 13, the average reduces.
What is the average ?The total amount of water drank in the 12 days can be determined by adding the quarts for each day together. When they are added together, the number is 20 quarts.
Average = total amount drank / number of days 1 2/3 quarts
New average = 20 + 1 / 13 = 21 / 13 = 1 7/13 quarts
The average reduces because the quart drank on the 13th day is less than the amount of water drank on the other days.
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Paula and Pedro were selling water bottles to raise money for their school. The ratio of water bottles Paula sold to water bottles Pedro sold is 3:5. If together Paula & Pedro sold a total of 72 water bottles, how many did each sell?
Step-by-step explanation:
x = number of bottles Paula sold
y = number of bottles Pedro sold
x + y = 72
x = 72 - y
x/y = 3/5
(72 - y)/y = 3/5
5(72 - y) = 3y
360 - 5y = 3y
360 = 8y
y = 45
x + y = 72
x + 45 = 72
x = 27
so,
Paula sold 27 water bottles, and Pedro sold 45.
8 marks] In how many ways can the letters of the word "UNDERDOG" be arranged such that the first and last letters are same and no two vowels are together?
The letters of the word "UNDERDOG" can be arranged in 144 ways.
Number of ways "UNDERDOG" can be arrangedThere are only two letters that are the same which are D, then the remaining letters are 6 letters.
V, E, O are vowels
N R G
The vowels are not joined together
For N, R, G A³3
There are 4 openings A³4
Hence:
A³4· A³3=4×3×2×3×2×1
A³4· A³3=144
Therefore the letters of the word "UNDERDOG" can be arranged in 144 ways.
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Please help, having trouble. Show all work if you can :) Photo is attached.
Answer:
hope it helpssssssss youj
Lashonda rolled a number cube 500 times and got the following results.
Outcome Rolled
1
2
3
4
5
6
Number of Rolls
77
89
73
69
110
82
Answer the following. Round your answers to the nearest thousandths.
(a) From Lashonda's results, compute the experimental probability of rolling an odd number.
0
(b) Assuming that the cube is fair, compute the theoretical probability of rolling an odd number.
0
(c) Assuming that the cube is fair, choose the statement below that is true.
O The larger the number of rolls, the greater the likelihood that the experimental probability
will be close to the theoretical probability.
O The smaller the number of rolls, the greater the likelihood that the experimental
probability
will be close to the theoretical probability.
The experimental probability will never be very close to the theoretical probability, no
X
Step-by-step explanation:
if I understand this correctly, then
1 was rolled 77 times
2 89 times
3 73 times
4 69 times
5 110 times
6 82 times
remember, a probability is always desired cases over total possible cases.
a)
the experimental probability to roll an odd number (1, 3, 5) is the number of desired cases (77 + 73 + 110) over the total cases (500).
260 / 500 = 26/50 = 13/25 = 0.52
b)
if the cube would be totally equal, so that every side has truly the same probability to appear we would have for every roll 6 total possible outcomes (1 .. 6), and 3 desired outcomes (1, 3, 5).
so the theoretical probability is
3/6 = 1/2 = 0.5
c)
if the cube is truly "fair" (all sides really have the same probability to show), then the first answer is true.
the more rolls of the die, the greater the likelihood that both probabilities will get closer and closer.
that is actually a main point of probabilities : to find the most likely behavior or structure of a large number of items or objects out of the structure or behavior of a smaller sample. or out of theoretical considerations that can be tested with smaller samples.
PLEASE HELP ASAP!!
The table of values represents the function g(x) and the graph shows the function f(x). Which statement about the functions is true?
-all of the x-intercepts of f(x) are common to those of g(x)
-f(x) and g(x) intersect at exactly two points
-the minimum value of f(x) is less than the minimum value of g(x)
-f(x) and g(x) have the same y-intercept
Using function concepts, it is found that the correct statement is given by:
all of the x-intercepts of f(x) are common to those of g(x).
What are the x-intercepts of the functions?They are the values of x when x = 0, hence:
For g(x), it is of x = -1 and x = 1.For f(x), it is of x = -1.Hence, the first statement is correct, and the x-intercept x = -1 of f(x) is common to the x-intercept x = -1 of g(x).
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please help question attached below!
Answer:
4.97
Step-by-step explanation:
h(x) = -3x² + 5
h(0.1)
x = 0.1
h(0.1) = -3(0.1)² + 5
0.1² = 0.01
-3(0.01) + 5
-3(0.01) = -0.03
-0.03 + 5 = 4.97
please please help. i need to submit this in 15 minutes!!!
∆ADB is ~ ∆BEC because <D and <E are right angles which are equal to 90°.
What is a right angle?A right angle is defined as an angle that is formed when two straight line are perpendicular at an intersection creating a 90° angle when measured.
From the diagram, ∆ADB is ~ ∆BEC because <D and <E are right angles which are equal to 90°.
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The diagram shows a right angled triangle. 11cm 8cm and x degrees. Find the size of angle x. Give your answer correct to 1 decimal place.
The size of the unknown angle "x"
Solution:We'll have to check which one is appropriate from SOHCAHTOA.
In this question hypotenuse and adjacent is given so, we'll have to use cos.
[tex]\large\boxed{Formula: cos \: (A)= \frac{adj}{hyp}}[/tex]
Let's solve!
Let's substitute the values according to the formula.
[tex]cos \: x= \frac{8}{11}[/tex]
We'll have to use cos inverse.
[tex]x= {cos}^{-1}( \frac{8}{11} )[/tex]
[tex]x= 43.34175823[/tex]
Now we'll have to round off to 1 decimal place.
The value in hundredths place is less than 5 so we won't have to round up.
So, the final answer is:
[tex]\large\boxed{x= 43.3°}[/tex]
Therefore, the size of the unknown angle "x" is 43.3°
Jax drew an angle that turns through
80 one-degree angles. Which is the
measure of the angle Jax drew?
When Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.
How to depict the angle?It should be noted that when an angle turns through a particular degree, it'll be said to have an identical degree.
In this case, when Jax drew an angle that turns through 80 one-degree angles, the measure of the angle will be 80°.
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Charles has eight different winter scarves, and he wears three at a time. How many different ways can Charles wear three scarves? 6,720 56 112 336
Answer:
Ans= 6720 ways
Step-by-step explanation:
From Combination rule from Permutation and Combination, nCr
We use 8^C3 or 8C3,
8x7x6x5x4x3x2x1
-------------------------- =6,720
3x2x1
or
8x7x6x5x4x3! /3!, here the 3! cancels each other out, and we're left with 8x7x6x5x4, which equals 6720.
in euclidean geometry any three points not on the same line can lie on how many planes?
Answer:
1 plane
Step-by-step explanation:
In Euclidean geometry, three non-collinear points will define exactly one plane.
__
Two points will define a line. That line can exist in an infinity of different planes.
A third point not on the line can only lie in exactly one plane with that line.
Three non-collinear points in Euclidean geometry can lie on one unique plane.
In Euclidean geometry, any three non-collinear points (points not lying on the same line) uniquely determine a plane.
This means that there is only one plane that contains all three of those points.
So, given three non-collinear points, you can find exactly one plane that passes through all of them.
Hence, if the three points not on the same line can lie on one plane.
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50 pts!!! Please answer without links!
The value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
From the graph:
P(X ≤ 1) = 0.05
P(X ≤ 2) = 0.1
P(X ≤ 3) = 0.15
P(X ≤ 4) = 0.2
P(X ≤ 5)= 0.2
Add all the probability:
P = 0.05+0.1+0.15+0.2+0.2 = 0.7
P(X≤a)=0.6 (that means the value of the area under the curve 'a' is 0.6)
So the value of a should be 5
Thus, the value of 'a' in the P(X≤a)=0.6 is 5 because at X =5 we get a probability of 0.7. a = 5 is the answer.
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Answer:
Put 5 in the input
In how many ways can 7 persons be arranged in a line such that (a) two particular persons are never together.
Answer:
3600 ways
Step-by-step explanation:
person A has 7 places to choose from :
→ He has 2 places ,one to the extreme left of the line ,the other to the extreme right of the line
If he chose one of those two ,person B will have 5 choices and the other 5 persons will have 5! Choices.
⇒ number of arrangements = 2×5×5! = 1 200
→ But Person A also , can choose one of the 5 places in between the two extremes .
If he chose one of those 5 ,person B will have 4 choices and the other 5 persons wil have 5! Choices.
⇒ number of arrangements = 5×4×5! = 2 400
In Total they can be arranged in :
1200 + 2400 = 3600 ways
Which expression represents “2 times the difference of x and 5”?
Answer:
2(x-5)
Step-by-step explanation:
Hope this helps
Answer:
2 · (x - 5)
Step-by-step explanation:
2 · (x - 5)
2 ·
"2 times"
when multiplication- or "times" is said, it can be shown in multiple ways. Multiplication can be shown as a×b , a·b , (a)(b)
(x - 5)
"difference of x and 5"
when difference is noted, the first number listed is the one written first. The difference between 2 and x is ( 2 - x ); the difference between x and 2 is ( x - 2).
Convert the degree measure to radian measure. Round to three decimal places.
75°
radians
The conversion from degree to radian will be 180° = π radian. Then the measure of angle 75° is 1.31 radians.
What is conversion?Conversion means to convert the same thing into different units.
Convert the degree measure to the radian measure.
⇒ 75°
We know the conversion is given as
180° = π radian
1° = π/180°
Then we have
75° = 75° x π/180° radian
75° = 1.30899 radian
75° ≅ 1.31 radian
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A leak in a pool causes the height of the water to decrease by 0.25 foot over 2 hours. After the leak is fixed, the height of the water is 4.75 feet. The equation 4.75 = x + (negative 0.25) can be used to find x, the original height of the water in a pool.
What was the original height of the water in the pool in feet?
4.5
5.0
6.5
7.0
An equation is formed of two equal expressions. The original height of the water in the pool in feet is 5.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the equation, 4.75 = x + (-0.25) can be used to find x, the original height of the water in a pool. Therefore, the height of the fool in the beginning is,
4.75 = x + (-0.25)
4.75 + 0.25 = x
x = 5
Hence, the original height of the water in the pool in feet is 5.
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Will give 50 points for the answer to this
Answer:
( 3, -2 )
Step-by-step explanation:
3, -2 is on the line so it is a solution
the rest of the points aren't in the shaded area or on the line therefore they are not a solution
Have a great day! :)
Hi I’m really confused and it’s a new topic
[tex]\large\boxed{Formula:\frac{sum \: of \: interior \: angles}{n}}[/tex]
n means the number of sides.
Sum of interior angles of a dodecagon is 1800°
Let's substitute the values according to the formula.
[tex]\frac{1800}{12}[/tex]
[tex]\large\boxed{ = 150°}[/tex]
Now, we can find the size of one exterior angle.
[tex]\large\boxed{Formula:\frac{360}{n}}[/tex]
n means the number of sides.
A dodecagon has 12 sides.
Let's substitute the values according to the formula.
[tex]\frac{360}{12}[/tex]
[tex]\large\boxed{ = 30°}[/tex]
Hence, the size of 1 interior angle of a dodecagon is 150° and 1 exterior angle is 30°
Here are two fractions.
7/6
6/7
Work out which of the fractions is closer to 1
You must show your working.
Here are two fractions.
The correct answer is 6 / 7 as it is closer to 1.
What is a fraction?The fraction is defined as the division of the whole part into an equal number of parts.
The number near 1 will be calculated as:-
7/ 6 = 1.1666
6 / 7 = 0.8571
Difference of the first ratio from one.
1.1666 - 1 = 0.1666
Difference of the second ratio:-
1 - 0.8571 = 0.1429
So the difference of 6 / 7 is lower than the difference of the fraction 7 / 6 from one.
Therefore the correct answer is 6 / 7 as it is closer to 1.
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