The solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)
Simultaneous linear and quadratic equationsFrom the question, we are to determine the solutions to the given system of equations
The given system of equations are
x + y = 3 ----------- (1)
y = x² - 9 ----------- (2)
From equation (1)
x + y = 3
We can write that
y = 3 - x -------- (3)
Substitute this into equation (2)
y = x² - 9
3 - x = x² - 9
x² +x -3 - 9 = 0
x² +x -12 = 0
Solve quadratically
x² +x -12 = 0
x² +4x -3x -12 = 0
x(x +4) -3(x +4) = 0
(x -3)(x +4) = 0
∴ x -3 = 0 OR x +4 = 0
x = 3 OR x = -4
Now, using equation (3)
When x = 3
y = 3 - x
y = 3 - 3
y = 0
When x = -4
y = 3 - -4
y = 3+4
y = 7
∴ When x = 3, y = 0; and when x = -4, y = 7
Hence, the solutions to the given system of equations is (3, 0) and (-4, 7). The correct option is the third option (3, 0) and (−4, 7)
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can someone do this for me please?! Just the answer pls
1. Both triangles are congruent by: a. angle-angle-side congruence theorem.
Using the trigonometric ratios, we have:
2. C. 9
3. C. 4√3
4. B. sin C
What is the Angle-angle-side Congruence Theorem?The angle-angle-side congruence theorem states that two triangles are congruent to each other if they both have two pairs of corresponding congruent angles and a pair of non-included congruent side.
What is the Trigonometric Ratio?To solve any right triangle, the following Trigonometric ratios can be employed:
sin ∅ = opp/hyp
cos ∅ = adj/hyp
tan ∅ = opp/adj.
1. Both triangles can be proven to be congruent based on: a. angle-angle-side congruence theorem.
2. Given the points, A(-2, 6) and B(-2, -3), the distance between both points is:
AB = |6 - (-3)| = 9 units
The answer is: C. 9
3. Apply the sine ratio:
sin 60 = opp/hyp = m/8
m = (sin 60)(8)
m = (√3/2)(8) [sin 60 = √3/2]
m = 4√3
The answer is: C. 4√3
4. Using the sine ratio:
sin C = opp/hyp = 8/17
The answer is: B. sin C
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if a= 2x - 3 and b= 2x+5
find the value of a+b
help pleaseeee i would really appreciate
Answer:
4x+2
Step-by-step explanation:
a= 2x - 3 and b= 2x+5
a+b = 2x-3 + 2x+5
Combine like terms
a+b = 4x+2
Answer:
a + b = 4x + 2
Step-by-step explanation:
a = 2x - 3
b = 2x + 5
a + b = (2x-3) + (2x+5)
a + b = 2x + 2x - 3 + 5
a + v = 4x + 2
SIMPLIFY HELP !!!!!!
Simplify (-2)² + 15 ÷ 3
Answer: 9
Hope this helps :))
P.s. Can you mark me as the brainliest? <3
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 18 times t squared plus 54 times t end quantity over the quantity t squared plus 7 times t plus 10 end quantity comma where the time, t is hours after injection.
Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points)
Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
The domain of the function is 0 ≤ t ≤ 3 and the greatest concentration of the medication is 2mg/L
The domain of the functionThe equation of the function is given as:
[tex]C(t) = \frac{-18t^2 + 54t}{t^2 + 7t + 10}[/tex]
Time can be 0 or greater but cannot be negative.
So, the domain of the function includes t ≥ 0
Set the function to 0 to determine the maximum value of t.
[tex]\frac{-18t^2 + 54t}{t^2 + 7t + 10} = 0[/tex]
Cross multiply
[tex]-18t^2 + 54t = 0[/tex]
Factor out -18t
-18t(t - 3) = 0
Divide both sides by -18t
t - 3 = 0
Add 3 to both sides
t = 3
This means that the maximum value of t is 3
Hence, the domain of the function is 0 ≤ t ≤ 3
The greatest concentration of the medicationFrom the graph of the function (see attachment), we have the maximum value to be;
C(t) = 2
Hence, the greatest concentration of the medication is 2mg/L
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WILL GIVE BRAINLIST
Tamara found that as she increased the amount of chlorine in her pool, the amount of mold in the pool decreased. What is the correlation?
Answer:
Step-by-step explanation:
Find out the how much chlorine is in the pool .
To prove
As given
The amount of chlorine in a swimming pool varies directly with the volume of water.
The pool has 2.5 milligrams of chlorine per liter of water.
i.e
2.5 milligrams of chorine = 1 litre of water
There are 8000 gallons of water in the swimming pool.
As 1 gallons = 3.78541 litre (Approx)
Now convert 8000 gallons of water in litres.
8000 gallons = 8000 × 3.78541 litre
= 30283.28 litres
Now calculate chlorine in the pool for 30283.28 litres of waters.
As
2.5 milligrams of chlorine = 1 litre of water
2.5 × 30283.28 milligrams of chlorine = 30283.28 litre of water
75708.2 milligrams of chlorine for 30283.28 litre of water .
Answer:
Negative correlation
Step-by-step explanation:
As one value increases when the other one decreases, we can say the correlation is a negative correlation.
Which function has the greatest x-intercept?
Of(x) = 3x -9
Og(x)= x + 31
h(x) = 2* - 16
Oj(x) = -5(x - 2)²
Answer:
I think the greatest x- intercept is f(x)=3x-9
20 points!!! Which of the following functions represent the graph of? Question and answers linked below, thank you!
Answer:
the second picture shown
Step-by-step explanation:
it’s has on the x axis (-3,0) and on y axis (0,-2.26)
Leticia simplified an expression. Her work is shown below.
4.5 divided by one-fourth + 2 and one-half minus 0.75 times 8
Step 1 18 + 2 and one-half minus 0.75 times 8
Step 2 18 + 1.75 times 8
Step 3 18 + 14
Step 4 32
Where did Leticia make her first mistake?
step 1
step 2
step 3
step 4
Leticia made a mistake in her step 2. She did subtraction before multiplication.
How to simplify an expression?The expression can be simplified as follows;
4.5 ÷ 0.25 + 2.5 - 0.75 × 8
Hence, using Pemdas rule,
4.5 ÷ 0.25 + 2.5 - 0.75 × 8
18 + 2.5 - 0.75 × 8
18 + 2.5 - 6 = 14.5
Therefore, she made mistake in her step 2 because she was suppose to solve the multiplication before subtraction.
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*URGENT 20 POINTS*
If the area of a regular 12-gon is 2,004 meters^2, what is the length of one of the sides? Please show how you figured this out as well.
Answer:
13.3787 m
Step-by-step explanation:
A = 3 × ( 2 + √3 ) × s2
If a is 2004 just do the reverse order and u get the answer
1. Kimi Skuban deposits $2,000 at the beginning of each year into an Individual Retirement Account at
Boise Bank. The account pays 7% compounded annually. How much will be in the account in 25 years?
Answer:
53500
Step-by-step explanation:
if we take 2,000 and multiply it by 0.07 the resulting percentage equates to 140, or $140, add 140 to 2,000 and multiply by 25 will yield 53500
This table represents a proportional relationship between x and y.
X
2.5
3.25
2.7
3.51
2.9
3.77
3.1
4.03
What is the constant of proportionality?
Enter your answer as a decimal in the box.
The constant of proportionality of the proportional relationship between x and y is: 1.3.
How to Find the Constant of Proportionality?The constant of proportionality, k = y/x, of a proportional relationship.
To find the constant of proportionality of the relationship between x and y, select any given pair from the table, say, (2.5, 3.25).
Constant of proportionality (k) = 3.25/2.5
Constant of proportionality (k) = 1.3
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The tables show linear functions representing the estimated time it takes for the math and language arts portions of standardized tests with different numbers of questions. Which function has the greater slope and what does it indicate? The math function has the greater slope, which shows that the estimated time per question for math is less than the estimated time per question for language arts. The math function has the greater slope, which shows that the estimated time per question for math is greater than the estimated time per question for language arts. The language arts function has the greater slope, which shows that the estimated time per question for language arts is less than the estimated time per question for math. The language arts function has the greater slope, which shows that the estimated time per question for language arts is greater than the estimated time per question for math.
The language arts function has the greater slope. Then the correct option is C.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The tables show linear functions representing the estimated time it takes for the math and language arts portions of standardized tests with different numbers of questions.
The table is shown below.
The slope of math will be
Slope of math = (207 - 87)/ (65 - 25)
Slope of math = 120/40
Slope of math = 3
The slope of language arts will be
Slope of language arts = (248 - 88)/(60 - 20)
Slope of language arts = 160/40
Slope of language arts = 4
The language arts function has the greater slope, which shows that the estimated time per question for language arts is less than the estimated time per question for math.
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Answer:D-The language arts function has the greater slope, which shows that the estimated time per question for language arts is greater than the estimated time per question for math.
Step-by-step explanation:
If Sammy starts drinking his tea at 11:25 P.M. and he finishes it at 12:20 A.M., how long does it take him to drink his tea?
Answer:
55 minutes
Step-by-step explanation:
add 35 to 11:25 should equal to 12AM then add 20 to it should give you the answer of 12:20AM combining the 35 and 20 should give you 55
Answer:
55 Minutes
Step-by-step explanation:
Assuming the start time is on the previous day, the time between 11:25:00 PM and 12:20:00 AM is:
0 hour, 55 minutes, and 0 second
0.917 hour
55 minutes
3,300 seconds
Hope this helps!
20 cm
15 cm 8 cm
20 cm
8 cm
15 cm
Find the area of the arrow above.
[?] square centimeters
The area of the arrow given in the figure is 610 square cm
Area of composite figureThe given figure is made up of rectangle and triangle. The area is expressed as:
Area = Area of rectangle + area of triangle
Substitute the given parameters
Area of the arrow = (15*20) + 0.5(31 * 20)
Area of the arrow = 300 + 310
Area of the arrow = 610 square cm
Hence the area of the arrow given in the figure is 610 square cm
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If you roll a dice four times, what is the chance that you roll two 3s?
Answer:
11.57%
Step-by-step explanation:
The probability of rolling two 3s is the product of the probability of rolling two 3s and two not-3s, and the number of ways that combination of rolls can appear.
__
combinations of rollsOf the four die rolls, we want two of them to be 3s. The 3s can appear anywhere in the sequence. For example, we could have 33xx, or xx33, or any of a number of other combinations (where x is a "not 3"). The total number of ways two 3s can appear an a sequence of 4 rolls is ...
C(4, 2) = 4!/(2!(4 -2)!) = 4·3/(2·1) = 6
__
probability of two 3s and two not-3sThe probability of rolling a 3 on a fair 6-sided die with one face labeled 3 is presumed to be 1/6. Then the probability of rolling something else is ...
1 -1/6 = 5/6
So, two 3s and two not-3s in a given sequence have a probability of ...
(1/6)(1/6)(5/6)(5/6) = 25/1296
__
two 3s in 4 rollsThe probability that four rolls of the die will show exactly two 3s is the product of the probability it can happen and the number of ways it can happen:
(25/1296) × 6 = 25/216 ≈ 11.57%
_____
The attachment shows the probability function of a calculator gives the same result.
e^(3x)+e^x-6=0
stuck on step u = e^x, u^3 + u - 6 = 0
The Solution to the given equation is gotten as; x = 0.4913
How to solve differential equations?We are given the equation;
e³ˣ + eˣ - 6 = 0
Let u = eˣ. Thus, our equation is now;
u³ + u - 6 = 0
Factorizing this to find the roots gives us;
u = 1.6344
Thus;
eˣ = 1.6344
x = In 1.6344
x = 0.4913
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A larger error variance makes it difficult to estimate the partial effect of any of the independent variables on the dependent variable. a. True b. False
A larger error variance making it difficult to estimate the partial effect of any of the independent variables on the dependent variable is True.
What is Variance?This is used to measure how far a data is spread out and the effect independent variables has on the dependent ones.
When there is an error in the variance, the effect calculated is inaccurate which brings about difficulty in ascertaining it.
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Find the difference or type
"impossible"
Answer:
hope you can understand
How do you feel about the plant
The sum of 3 numbers is 33. The second number is 2 more than the first number. The third number is 2 more than the second number. What is the smallest number?
Answer:
9
Step-by-step explanation:
The information given can be written as:
x + y + z = 33y = x + 2z = y + 2 = (x + 2) + 2 = x + 4So, x + x + 2 + x + 4 = 33. This simplified is 3x + 6 = 33
Subtract 6 from both sides: 3x = 27
Divide both sides by 3: x = 9
This means that the numbers are 9, 11, and 13, so 9 is the smallest number.
To check, we can add together 9, 11 and 13, which is 33.
Hope this helps!
Find the mean and median of the data. 31, 14, 18, 26, 17, 32
Answer:
The mean is 23
The median is 22
Step-by-step explanation:
To find the mean you have to do 2 steps:
Step 1: Add up all your numbers:
31 + 14 + 26 + 17 + 32 + 18
= 138
Step 2: Divide you answer by how many numbers there are(6):
138 ÷ 6
= 23
Now to find you median
First put the numbers in order:
14, 17, 18, 26, 31, 32
Now grab the middle number and since there are an even amount of numbers grab the 2 middle numbers:
14, 17, 18, 26, 31, 32
Now add the 2 numbers:
18 + 26
= 44
The last step is to divide your answer by 2:
44 ÷ 2
= 22
4x what = 364
please put the calculation
Answer:
91
Step-by-step explanation:
4 x 91 = 364
To work this out, we must do the inverse operation. The inverse (opposite) of x (times or multiply) is ÷ (divide).
So, we do 364 ÷ 4 = 91
Hope this helps!
- profparis
Condense the expression to the logarithm of a single quantity.
I'm going to be so thankful if anyone could solve this for me please... because I can't understand any of it right now.
[tex]\dfrac 12 \log_3 x - 2\log_3 (y +8)\\ \\=\log_3 x^{\tfrac 12}- \log_3(y+8)^2~~~~~~~~~~~~~~~~~~;[\log_b m^n = n \log_b m]\\\\=\log_3 \left( \dfrac {x^{\tfrac 12}}{y+8)^2} \right)~~~~~~~~~~~~~~~~~~~~~~~~;\left[\log_b \left( \dfrac mn \right) = \log_b m - \log_b n \right][/tex]
Jill jogs 3/4 of a mile in 1/10 of an hour at this rate how fast does she run one mile.
10 minutes
6 minutes
8 minutes
Answer:
8 minutes
Step-by-step explanation:
Jill jogs 3/4 of a mile in 1/10 hour.
⇒ 3/4 of a mile takes 6 minutes
For one mile :
3/4 mile x 4/3 : 6 x 4/3 minutes1 mile : 2 x 4 minutes1 mile takes 8 minutes1 mile she can run
1/10÷3/44/3(1/10)4/302/15hour8/60hour8 mins
Which statement is true?
A Two points can be noncollinear.
B Any two points can be noncoplanar.
C Any two points are sufficient to determine a line.
D Two points are sufficient to determine a plane.
Answer:
C is true as 2 pionts = a line
Step-by-step explanation:
I'm smartest in my class
Find f(2) if f(x)= (x +1)^2
Answer:
9
Step-by-step explanation:
substitute the x which is x= 2, so
f(2)= (2+1)^2
=(3)^2
=9
Answer:
9
Step-by-step explanation:
a swimming pool is 10 feet and 14 feet long. A
concrete border was poured that was 3 feet wide
around the pool. Find the perimeter of the
concrete walk.
Answer:
72 ft
Step-by-step explanation:
The perimeter of the concrete walk is the sum of the lengths of its outside edges. Each of those is two border-widths longer than the parallel pool dimension.
__
The border width is ...
(10 ft) + 2(3 ft) = 16 ft
The border length is ...
(14 ft) + 2(3 ft) = 20 ft
The perimeter is the sum of the lengths of the four sides. It can be found using the formula ...
P = 2(L +W)
P = 2(20 ft + 16 ft) = 2(36 ft) = 72 ft
The perimeter of the concrete walk is 72 feet.
_____
Additional comment
The term "perimeter of the concrete walk" is actually somewhat ambiguous. It could refer to the total length of all of the edges of the concrete walk. If that is the case, then the 48 foot length of the inside edge must be added to the length of the outside edge for a total of 120 feet. That is, if one were to mark the edges of the walk with tape, for example, 120 feet of tape would be needed.
Karen needs to make a total of 60 deliveries this week. So far she has completed 33 of them What percentage of her total deliveries has Karen completed?
Answer:
55%
Step-by-step explanation:
(33/60) * 100
leave a comment if u need further explanation
If f(x)=3x+5/x, what is f(a + 2)?
a. 3a + 5/a + 2
b. 3(f(a)) + 5/f(a)+2
c. 3(a+2) + 5/a+2
Answer:
Answer C is correct
Step-by-step explanation:
1. We replace x as (a + 2)
2. Then we just rewrite this function with the new value
3. Result: 3(a+2) + 5/(a+2)
3. How many solutions does the equation have?
−8x+6+20x = 2/3(18x + 9)
O No Solutions
○ Two Solutions
O One Solution
An infinite number of solutions