Answer:
αλ and βλ
Step-by-step explanation:
if alpha beta are the roots of ax² + bx + c = 0, then:
Sum of roots = α + β = -coefficient of x / coefficient of x² = -b/a
product of roots = αβ = Constant / coefficient of x² = c/a
Let x and y be the roots of ax² + bλx + cλ² = 0
Sum of roots = x + y = -coefficient of x / coefficient of x² = -bλ/a
product of roots = xy = Constant / coefficient of x² = cλ²/a
x + y = -bλ/a = λ(α + β) = αλ + βλ
Comparing terms gives:
x = αλ and y= βλ
Therefore the roots of ax² + bλx + cλ² = 0 are αλ and βλ
The HCP prescribes methotrexate 7.5 mg PO weekly, in 3 divides doses for a child with rheumatoid arthritis whose body surface area (BSA) is 0.6 m2. The therapeutic dosage of methotrexate PO is 5 to 15 mg/m2/week. How many mg should the nurse administer in each of the three doses given weekly? (Enter the numeric value only. If round is required, round to the nearest tenth.)
Answer:
1.5mg
Step-by-step explanation:
From the question, we are told that the HCP prescribed 7.5 mg of PO weekly
The therapeutic dosage is given in the question as 5 - 15 mg/m² weekly.
The child's body surface area is given = 0.6m²
The mg of PO that the nurse should administer in each of the three doses given weekly is calculated as
7.5mg/ 5mg/m²
= 1.5 mg of PO
5 meters.
The rectangle below has an area of x2 – 112 + 30 square meters and a length of x
What expression represents the width of the rectangle?
2 - 5
Width
22 – 110 + 30
Width
meters
Answer: The width is x-6
Step-by-step explanation:
To find the with factor out the area x^2 - 11x + 30
[tex]x^{2}[/tex] - 11x +30 to factor it find two numbers that multiply to get 30 and add up to get -11 . And that two numbers are -6 and -5 .
[tex]x^{2}[/tex] - 5x - 6x + 30 now group them
([tex]x^{2}[/tex] - 5x) (-6x+ 30) factor them out.
x(x - 5) - 6(x -5) Factor x-5 out
(x-5)(x-6) since the length is x-5 then the width is x-6.
two angles of a triangle measure 41 degrees and 44 degrees what is the measure of the third angle? A) 75 degrees B) 85 degrees C) 95 degrees D) 105 degrees
Answer:
95 degrees
Step-by-step explanation:
All triangles have an interior measure of 180 degrees
180-41-44=95
Answer:
95 degrees
Step-by-step explanation:
Hi please help meeee
An experiment consists of tossing 3 coins at the same time.
1. Identify the sample space.
2. What is the probability of tossing 2 tails and 1 head?
3. Which is more likely to occur: tossing exactly 1 tail or tossing at least 2 heads? Explain.
Answer:
Step-by-step explanation:
The attachment will help you with your question:
Give the function f(x)= 0.5lx - 4| -3, for what values of x is f(x) = 7
I hope this helps you
find 1st, 2nd, 3rd, 4th and 10th nTh term. rule is 3n+4
Answer:
When n is 1
3n+4
=3*1+4
=3+4
=7
When n is 2
3n+4
=3*2+4
=6+4
=10
When n is 3
3n+4
=3*3+4
=9+4
=13
When n is 4
3n +4
=3*4+4
=12+4
=16
When n is 10
3n+4
=3*10+4
=30+4
34
solve 7+x÷3=2x-5 pls help me with this
Answer:
4.4
Step-by-step explanation:
Write the question out as an equation:
7+x/3 = 2x - 5
Rearrange , simplify and solve:
7+x = 3(2x-5) = 6x - 15
7+x = 6x-15
6x - 15 = 7+x
6x = 7+x+15 = 22+x
6x = 22+x
6x-x = 22
5x = 22
x = 4.4
hope this helps.
Good Luck.
Please Mark Brainiest
Answer:
Step-by-step explanation:
7+x/3=2x-5
taking 3 on the RHS
7+x=6x-15
22=5x
x=22/5
=4.4
solve for x 42=7(x+5)
Answer:
42=7(x+5)
42=7x+35
42-35=7x
7=7x
X=7/7=1
Simplify.
Rewrite the expression in the form b^n
(b^3)^2
Step-by-step explanation:
[tex]a^n={\underbrace{a\cdot a\cdot a\cdot...\cdot a}_{n}[/tex]
METHOD 1.[tex]\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_{2}=\underbrace{b\cdot b\cdot b}_{3}\cdot\underbrace{b\cdot b\cdot b}_{3}=\underbrace{b\cdot b\cdot b\cdot b\cdot b\cdot b}_{6}=b^6[/tex]
METHOD 2.[tex]\left(b^3\right)^2=\underbrace{b^3\cdot b^3}_{2}=b^{3+3}=b^6\qquad\text{used}\ a^n\cdot a^m=a^{n+m}[/tex]
METHOD 3.[tex]\left(b^3\right)^2=\left(\underbrace{b\cdot b\cdot b}_{3}\right)^2=b^2\cdot b^2\cdot b^2=b^{2+2+2}=b^6\\\text{used}\ (ab)^n=a^nb^n,\ a^n\cdot a^m=a^{n+m}[/tex]
METHOD 4.[tex]\left(b^3\right)^2=b^{3\cdot2}=b^6\qquad\text{used}\ \left(a^n\right)^m=a^{nm}[/tex]
Please Answer Now Identify the function’s vertical asymptotes. h(x)=x-4/x^2-4 x = 2 x = 4 x = -2, x = 2 x = -4, x = 4
Answer:
x = 2 and x = +2
Step-by-step explanation:
It's essential that you use parentheses to clarify what's happening here:
h(x)=x-4/x^2-4 => h(x)=(x-4) / (x^2-4)
We have vertical asymptotes at x values at which the denominator (x^2 - 4) is zero. That would be x = 2 and x = +2.
make x subject of m =n + x/p
Answer:
[tex]x = p(m-n)[/tex]
Step-by-step explanation:
m = n + [tex]\frac{x}{p}[/tex]
Subtracting n to both sides
=> m-n = [tex]\frac{x}{p}[/tex]
Multiplying p to both sides
=> [tex]x = p(m-n)[/tex]
Answer:
x=p(m-n)
Step-by-step explanation:
m =n + x/p
x/p=m-n
x=p(m-n)
What are the values of the variables in the triangle below? If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.
Answer:
x = 12y = 4√3Step-by-step explanation:
To find x we use cosine
cos∅ = adjacent / hypotenuse
x is the adjacent
8√3 is the hypotenuse
cos 30 = x / 8√3
x = 8√3 cos 30
x = 12To find y we use sine
sin∅ = opposite / hypotenuse
y is the opposite
8√3 is the hypotenuse
sin 30 = y / 8√3
y = 8√3 sin 30
y = 4√3Hope this helps you
Here is a circle, centre O, and the tangent to the circle at the
point (8, 15) on the circle.
x
P (8, 15)
-17
O
17
Find an equation of the tangent at the point P.
Give your answer in the form y = ax + b where a and b are both
fractions with denominator 15.
Answer:
The equation of the tangent is [tex]y=-\frac{8}{15}x+\frac{289}{15}[/tex].
Step-by-step explanation:
Center = (0, 0). Point on the circle = (8, 15).
OP is a radius. The slope of the radius = [tex]\frac{15-0}{8-0}=\frac{15}{8}[/tex].
The tangent is perpendicular to the radius.
So, its slope is = [tex]-\frac{8}{15}[/tex].
The tangent passes through (8, 15).
So, the equation is:
[tex]y-15=-\frac{8}{15}\left(x-8\right)\\y-15=-\frac{8}{15}x+\frac{64}{15}\\y=-\frac{8}{15}x+\frac{289}{15}[/tex]
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Find the probability of rolling a sum of 10 or a sum that is an odd number when two number cubes are rolled.
Answer:
7/12 chance
Step-by-step explanation:
(1 2 3 4 5 6)
(1 2 3 4 5 6)
All the possibilities:
(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)
(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)
(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)
(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)
(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)
(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)
There are 18 odd sums.
(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)
(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)
(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)
(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)
(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)
(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)
There are 3 possibilities whose sums add up to 10.
Since there are 36 total possibilities and 21 numbers that fit the rule of having an odd sum or a sum of 10. There is a 21/36 chance or simplified, 7/12 chance.
If the sin 60° is 3/2
then the cos___=___
Answer:
30, root 3 over 2 or the third option
I did it on my quiz :)
But basically it is 30, root 3 over 2 because sin and cos are complements to one another.
Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C; 30°, (√3)/2.
What are Trigonometric Identities?Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.
Given that sin(60°) is (√3)/2. Therefore, the value of cos can be written as,
sin(60°) = (√3)/2
cos(90° - 60°) = (√3)/2 {Cos(90° - x) = Sin(x)}
cos 30° = (√3)/2
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What is the range of the function y= 3 startroot x+8 endroot?
Answer:
First Option
Step-by-step explanation:
When we graph the expression, we should see that an infinite amount of y-values work. Since the domain comprises of all working x-values, we have (negative infinity, positive infinity) or all real numbers as our range, since we have an infinite amount of y-value outputs.
Brian is solving the equation x squared minus three-fourths x = 5. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?
Answer:
Term to add is (3/8)^2 = 9/64
Step-by-step explanation:
Here, we want to know the value that must be added to make the equation a perfect square.
x^2 - 3/4x = 5
x^2 -3/4x -(3/8)^2+ (3/8)^2 = 5
x^2 -3/4x + (3/8)^2 = 5 + (3/8)^2
= (x-3/8)^2 = 5 + (3/8)^2
So the term to add is (3/8)^2 = 9/64
Answer:
[tex]\dfrac{9}{64}[/tex]
Step-by-step explanation:
Given the equation: [tex]x^2-\frac{3}{4}x=5[/tex]
To make the left hand side of the equation a perfect trinomial, we follow these steps.
Step 1: Divide the coefficient of x by 2.
Coefficient of x [tex]=-\frac{3}{4}[/tex]
[tex]-\frac{3}{4} \div 2 =-\frac{3}{8}[/tex]
Step 2: Square your result from step 1
[tex]\implies (-\frac{3}{8})^2 \\=\dfrac{9}{64}[/tex]
Therefore, to make the Left-Hand side a perfect-square trinomial, we add 9/64.
Pleas answer it in two minutes
Answer:
b=69 degrees
Step-by-step explanation
Use the remote interior angle theorem which states that the sum of the two remote interior angles is equal to the exterior angle. Basically, b=(b-36)+(b-33). That will give you b=2b-69. Then b=69. There's ur answer.
How many sides does a regular polygon have if the measure of each exterior angle is 24°?
Answer: 15 sides
Step-by-step explanation: Because the sum of the outer angles is always 360 degrees, if you divide 360 degrees by 24 degrees you get 15 which is the number of equivalent outer angles and therefore 15 vertices and sides to the polygon
Answer: angle is 24 degrees meaning that a regular polygon has more than 6 sides hope this is helpful
Step-by-step explanation:
This table values that represent a quadratic function.
Answer:
A
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 3, 5 ] , thus
f(b) = f(5) = - 26 ← value of y for x = 5 from table
f(a) = f(3) = - 10 ← value of y for x = 3 from table
average rate of change = [tex]\frac{-26-(-10)}{5-3}[/tex] = [tex]\frac{-16}{2}[/tex] = - 8 → A
A box had twice as many grapes as a basket. Once 2 kg of grapes were added to the basket, it contained 0.5 kg more than the box. How many kilograms of grapes are in the basket now?
Answer:
there are now 3.5 kilograms of grapes in the basket (the mystery number is 1.5)
Let us suppose that the number of grapes in the box is x and the number of grapes in the basket is y.
It means that the weight of the grapes in the box is x kg and that of basket is y kg.
It has been given that the box had twice as many grapes as a basket. Therefore, we have
Now when we add 2 kg to the basket then the weight of the basket is y+2 and the weight of box will remain same.
Now, we have been given that after 2 kilograms were added to the basket it contained 0.5 kilograms more than the box. Hence, we have
Substituting the value x=2y in the equation, we get
Therefore, the basket contains 1.5 kilograms of grapes.
A True/False quiz has three questions. When guessing, the probability of getting a question correct is the same as the probability of getting a question wrong. What is the probability that a student that guesses gets at least 2 questions correct
Answer:
1/4 or 25% chance
Step-by-step explanation:
the probability of getting each question right is 1/2, so for getting 2 questions right its 1/2 × 1/2, which is 1/4
The probability that a student that guesses gets at least 2 questions correct is 1/4.
GivenThe probability of getting a question correct is the same as the probability of getting a question wrong.
The probability of getting the question is correct is;
[tex]= \dfrac{1}{2}[/tex]
The probability of getting the question is wrong is;
[tex]= \dfrac{1}{2}[/tex]
Therefore,
The probability that a student that guesses gets at least 2 questions correct is;
[tex]= \dfrac{1}{2} \times \dfrac{1}{2}\\\\= \dfrac{1}{4}[/tex]
Hence, the probability that a student that guesses gets at least 2 questions correct is 1/4.
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what is the simplified value of 1/3 divied by 2/3
Answer:
1/2 or 0.5
Step-by-step explanation:
1/3 divided by 2/3
1/3 times 3/2
3/6
1/2, or 0.5
Answer:
1/2
Step-by-step explanation:
1/3 ÷2/3= 1/3×3/2( this is because fractions cannot be divided and the reciprocal of the fraction by which 1/3 had to be divided has to be taken which makes 2/3 as 3/2 and division as multiplication)
so, 1/3×3/2 gives 3/6, when simplified, gives 1/2.
When a certain number is subtracted from 10 and the result is multiplied by 2, the final result is 4. Find the number.
Answer:
8
Step-by-step explanation:
10-8 x 2 = 4
2 x 2 = 4
4 = 4
The number is 8, which is when subtracted from 10 and the result is multiplied by 2, then the result is 4.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
Let the required number is x.
According to given condition,
When x is subtracted from 10 and the result is multiplied by 2, final result comes as 4.
Implies that,
2 (10 - x) = 4
10 - x = 2
x = 10 - 2
x = 8
The required number is 8.
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prove the following identity: sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x please provide a proof in some shape form or fashion :/
Answer:
Step-by-step explanation:
Hello,
Is this equality true ?
sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x
1. let 's estimate the left part of the equation
[tex]sec(x)csc(x)(tan(x) + cot(x)) =\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin(x)}{cos(x)}+\dfrac{cos(x)}{sin(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin^2(x)+cos^2(x)}{sin(x)cos(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{1}{sin(x)cos(x)})\\\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]
1. let 's estimate the right part of the equation
[tex]2+tan^2(x) + cot^2(x)=2+\dfrac{sin^2(x)}{cos^2(x)}+\dfrac{cos^2(x)}{sin^2(x)}\\\\=\dfrac{2cos^2(x)sin^2(x)+cos^4(x)+sin^4(x)}{cos^2(x)sin^2(x)}\\\\=\dfrac{(cos^2(x)+sin^2(x))^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]
This is the same expression
So
sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x
hope this helps
Solve (x+3)^2=8 using the quadratic formula.
Answer:
Step-by-step explanation:
= x^2+6x+9-8=0
=x^2+6x+1=0
D=b^2-4ac
D= 36-4
D=32
x=-b±root D/2a
x=-6+4root2/2 , x = -6-4root2/2
simplify you get the least form...
hope it helps
The graph of the function f(x)=-(x+3)(x-1) is shown below. What is true about the domain and range of the function?
Answer:
The 3rd one is correct.
Step-by-step explanation:
What is the range of the linear parent function?
O A. All real numbers
B. Negative real numbers (y< 0)
C. Nonnegative real numbers (y=0)
D. Positive real numbers (y> 0)
Answer:
A. All real numbers
Step-by-step explanation:
We assume that the "linear parent function" is ...
y = x.
Its range is "all real numbers."
Answer:
all real numbers
Step-by-step explanation:
AP-EX
Tanya wants to order 50 pizzas for a party. However, the pizza supplier can deliver only 45 pizzas on the given date. How will you describe the relationship between demand and supply of pizzas? A. Demand is equal to supply. B. Demand is greater than supply. C. Demand is less than supply.
Answer:
B
Step-by-step explanation:
The demand is 50 and the supply is 45. Since 50 > 45 the answer is that the demand is greater than the supply.
Answer:
b
Step-by-step explanation:
PLVHGCHVBJGUYFTDCGVHJGYUJH
Answer:
The correct option is (B).
Step-by-step explanation:
The conditional probability of an event, say A is the probability of that events (A) when it is known that another event, say X has already occurred.
For example, consider the experiment of drawing two marbles from jar consisting of 8 white and 2 red, without replacement. The probability of selecting a red marble after a white marble is known as conditional probability.
In this case it is provided that:
40% of the students are licensed drivers55% students are female.The statement:
"the probability that a student who is a licensed driver is a male"
Is a statement of conditional probability.
This is because it is known from previous information that the student is a licensed driver and we need to determine the probability of this student being a male.
Thus, the correct option is (B).