Answer:
[tex]\bold{x_1=\dfrac{7+\sqrt{29}}2\ ,\qquad x_2=\dfrac{7-\sqrt{29}}2}[/tex]Step-by-step explanation:
[tex]x^2 - 7x+9 = 4\\\\\underline{x^2 - 2\cdot x\cdot\frac72+\big(\frac72\big)^2}-\big(\frac72\big)^2+9 = 4\\\\\big(x-\frac72\big)^2-\frac{49}4+9 = 4\\\\ \big(x-\frac72\big)^2=\frac{49}4-\frac{36}4+\frac{16} 4\\\\ \big(x-\frac72\big)^2=\frac{29}4\\\\ x-\frac72=\pm\sqrt{\frac{29}4}\\\\ x=\frac72\pm\frac{\sqrt{29}}2[/tex]
Which triangle makes this statement true?
Answer:
A.
Step-by-step explanation:
i pretty sure
Type the missing number that makes these fractions equal: 4/?=8/14
Answer:
4/7 = 8/14
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
[tex]\frac{4}{x} =\frac{8}{14} \\[/tex]
cross multiply
8x = 14 x 4
8x = 56
x = 7
Jamal's friends toss 12 balls to him at the same time. Three balls are red, 3 are green, 3 are blue, and 3 are white. Jamal manages to catch 5 of the balls.
What is the probability that he catches 2 red balls and 1 ball of each of the other colors?
Answer:
81/792 or 9/88 or 10.2%
Step-by-step explanation:
Possibility: nCr(12,5) = 792
Red: nCr(3,2) = 3
Blue, Green, White: nCr(3,1) = 3
3 * 3 * 3 * 3 = 81
81/792 simplified is 9/88 percentage is 10.22%
The probability that Jamal will catch 2 red balls and 1 ball of each of the other colors is 0.1025.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
The total numbers of balls are 12.
Each color has 3 balls.
If total 12 balls are tossed, the number of ways of catching 5 of them is,
¹²C₅ = 792
The number of ways of catching 2 red balls out of 3 is ³C₂ = 3
The number of ways of catching 1 green ball out of 3 is ³C₁ = 3
The number of ways of catching 1 blue ball out of 3 is ³C₁ = 3
The number of ways of catching 1 white ball out of 3 is ³C₁ = 3
Thus, the probability as per the question is given as follows,
(3 × 3 × 3 × 3)/792
= 81/792
= 0.1025
Hence, the probability of catching 2 red balls and 1 ball of each of the other colors is 0.1025.
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The curve
[tex]y = \sqrt{x - 3} [/tex]
has a tangent with gradient
[tex] \frac{1}{2} [/tex]
at point N.
Find the coordinates of N.
Answer:
Point N(4, 1)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)FunctionsFunction NotationTerms/CoefficientsAnything to the 0th power is 1Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \sqrt{x - 3}[/tex]
[tex]\displaystyle y' = \frac{1}{2}[/tex]
Step 2: Differentiate
[Function] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y = (x - 3)^{\frac{1}{2}}[/tex]Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)[/tex]Simplify: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1[/tex]Multiply: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}[/tex][Derivative] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{1}{2\sqrt{x - 3}}[/tex]Step 3: Solve
Find coordinates
x-coordinate
Substitute in y' [Derivative]: [tex]\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply 2 on both sides: [tex]\displaystyle 1 = \frac{1}{\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply √(x - 3) on both sides: [tex]\displaystyle \sqrt{x - 3} = 1[/tex][Equality Property] Square both sides: [tex]\displaystyle x - 3 = 1[/tex][Addition Property of Equality] Add 3 on both sides: [tex]\displaystyle x = 4[/tex]y-coordinate
Substitute in x [Function]: [tex]\displaystyle y = \sqrt{4 - 3}[/tex][√Radical] Subtract: [tex]\displaystyle y = \sqrt{1}[/tex][√Radical] Evaluate: [tex]\displaystyle y = 1[/tex]∴ Coordinates of Point N is (4, 1).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Plz help I will give BRAINLY
Answer:
I believe it is C
Step-by-step explanation:
Sorry if I got it wrong but hopefully you got it right
No one wants to help me ! :(((( need help on algebra: modeling dot plots Box plots and histograms.!
600 raffle tickets were sold for $5 each. There is one $500 first prize and three $200 second prizes. The remainder of the tickets do not win anything. What is the expected value of this raffle?
Answer:
its -$3.17
Step-by-step explanation:
500-5=495
200-5=195
the remainder of the tickets is -$5
the expected value is $495 x 1/600 + $ 19583/600 + (-$5) 596/600= -$3.17
PLEASE HELP ME URGENT what is the correct answer to my question.
I'm fully sure but maybe you add 12+40
Is knowing the coordinates of the vertex of a parabola enough to determine the domain and range? a. No: we would have no information about the domain. c. Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≤ n. b. No: we would need to know if the vertex is a minimum or a maximum. d. Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≥ n.
Answer:
The answer would have to be B
Step-by-step explanation:
explains itself
Answer:it’s B
Step-by-step explanation:
Find the value of -8 - 12 - (-20).
24
-40
16
0
Answer:
it's = 0
you have to use the steps of maths
Mike has 2 bank accounts. In his checking he has $136.89 and in his savings account he has $653.23.
Answer:
Whats the question and if its adding the answer is 790.12
Step-by-step explanation:
Also, if you could answer my question that'dd be great!
PLEASE HURRY! i’ll give brainliest
Answer:
1
Step-by-step explanation:
What is the value of 1,608 divided by 10 cubed
Answer:
16 2/25
Step-by-step explanation:
1608 / 10^2
1608/100
16 8/100
16 4/50
16 2/25
Answer:
1.608
Step-by-step explanation:
1608 ÷ 1000 = 1.608
A hiking trail is 2 3/5 miles long. Lucy walks 1/2 of the trail before stopping for a water break. How many miles does Lucy walk before stopping?
Answer:
look at the picture I have sent
Answer:
1.3
Step-by-step explanation:
First you simplify 2 3/5, which can be 2.6. You will find half of it so 2.6 divided by 2 equals 1.3. She traveled 1.3 miles or 1 3/10 miles before she stopped.
Write the equation of this line from the table provided.
SOMEONE PLEASE HELP ASAP I WILL GIVE YOU BRAINLIEST!!!
Answer:
y=2x-1
Step-by-step explanation:
If you are supposed to write the equation in slope-intercept format, (y=mx+b), then y=2x-1 would be the answer. 2 is the slope(m), and -1 is the y-intercept(b). I hope thus helped :).
PLEASE HELP WILL AWARD BRAINLIEST:)
Answer:
x = 4 units
Step-by-step explanation:
By geometric mean theorem:
Length of perpendicular
[tex] =\sqrt{2\times 6}[/tex]
[tex] =\sqrt{12}[/tex]
Next, by Pythagoras theorem:
[tex] x^2 = 2^2 + (\sqrt {12})^2 [/tex]
[tex] \therefore x^2 = 4 + 12 [/tex]
[tex] \therefore x^2 = 16 [/tex]
[tex] \therefore x =\sqrt{ 16 }[/tex]
[tex] \therefore x =4\: units[/tex]
Write the recursive formula for the sequence
37, 67, 97, 127, 157
Answer:
The recursive formula for this arithmetic sequence would be [tex]a_{1} = 37[/tex], [tex]a_{i} = a_{i-1} + 30[/tex].
Step-by-step explanation:
A recursive formula is a formula that defines each term of a sequence using the preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence, as well as an equation defining [tex]a_{i}[/tex] in terms of preceding terms. Since the first term of this sequence is 37, that means [tex]a_{1} = 37[/tex]. The pattern in this arithmetic sequence between each term in ascending order would be 30 more than the previous term, so you can create the function [tex]a_{i} = a_{i-1} + 30[/tex]. So the recursive formula for this arithmetic sequence would be [tex]a_{1} = 37[/tex] and [tex]a_{i} = a_{i-1} + 30[/tex].
it takes luis 4.5 minutes to read 3 pages. how long will it take him to read 32 pages?
Answer:
48 minutes
Step-by-step explanation:
4.5/3 = 1.5
1.5 x 32 = 48
the difference between two numbers is 14. if 1/3 of the larger number is subtracted from the smaller number ,the result equals 1/10 of their sum. find both numbers
Step by step please
Answer:
Step-by-step explanation:
x-y=14
x-1/3y=1/10
-y=14-x
y=-14+x
take out the factors
x-10/30y=3/30
30x-10y=3
substitute
30x-10(-14+x)=3
30x+140-10x=3-140
20x/20=-137/20
x=-6.85
y=-14+(-6.85)
y=-20.85
The two numbers are 143/20 and 423/20.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Given that, the difference between two numbers is 14.
Let the smaller number be x and the larger number be y.
Here, y-x=14 ------------(i)
If 1/3 of the larger number is subtracted from the smaller number ,the result equals 1/10.
1/3 of larger number is 1/3 y
x-y/3 =1/10 ------------(ii)
From equation (i), substitute y=14+x in equation (ii), we get
x-(14+x)/3 =1/10
10(3x-14-x)=3
30x-140-10=3
20x-140=3
20x=143
x=143/20
Substitute x=143/20 in equation (i), we get
y-143/20=14
y=14+143/20
y=(280+143)/20
y=423/20
Therefore, the two numbers are 143/20 and 423/20.
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Find the measure of angle 1
HELP
Answer:
75°
Step-by-step explanation:
The chord- chord angle is half the sum of of the arcs intercepted by the angle and its vertical angle, then
∠ 1 = [tex]\frac{1}{2}[/tex] (110 + 40)° = 0.5 × 150° = 75°
The square root 24 is between which two numbers on the number line
A)
1 and 2
B)
2 and 3
C)
3 and 4
D)
4 and 5
Answer:
Step-by-step explanation:
4²=16
5²=25
so √24 is between 4 and 5.
4/5 divided by 3/4
I need help please!! :)
Answer:
1 1/5 in fraction form :))
write the equation of the circle in standard form: Center (7,0) R=1
Answer:
[tex](x-7)^2+y^2=1[/tex]
Step-by-step explanation:
Hi there!
Equation of a circle: [tex](x-h)^2+(y-k)^2=r^2[/tex] where the circle is centered at (h,k) and the radius is r
1) Plug in the given center (7,0)
[tex](x-7)^2+(y-0)^2=r^2\\(x-7)^2+y^2=r^2[/tex]
2) Plug in the radius (1)
[tex](x-7)^2+y^2=1^2\\(x-7)^2+y^2=1[/tex]
I hope this helps!
Joseph runs 2 miles on Monday. Each day after that, he runs the same 1 1/3 mile route every
morning. His goal is to run at least 6 miles by the end of the week.
Which inequality represents the least number of days after Monday that Joseph needs to run
to reach his goal? *
Answer:
2 + 1 1/3x ≥ 6
x ≥ 3 days
Step-by-step explanation:
Monday = 2 miles
Other days = 1 1/3 miles
x = least number of days after Monday that Joseph needs to run
to reach his goal
Total miles = 6 miles
The inequality is
2 + 1 1/3x ≥ 6
1 1/3x ≥ 6 - 2
1 1/3x ≥ 4
4/3x ≥ 4
Divide both sides by 4/3
4/3x ÷ 4/3 ≥ 4 ÷ 4/3
x ≥ 4 × 3/4
x ≥ 3 days
Triangle PQR is similar to triangle DEF as shown.*
A.
B.
D.
C.
HELP ME IM STUCK PLEASE QUICK
Answer:
C) 24>x
Step-by-step explanation:
The inequality is just turned around. 24>x is thw same thing as x<24.
Hope this helped :)
Answer:
D
Step-by-step explanation:
x+3≥12
<=> x≥8
so 8 is less than x
x is less than 24 means 24>8 but in this case we must follow a model so x is less than 24 can be write 24≥x (read x is less than 24 or is equal to 24)
Which would it be please?Help if you can.
Answer:
B
Step-by-step explanation:
Area = length times width, in this case, both length and width is x.
While 5 and 2 are the lengths and widths for the unshaded part.
x^2 = whole square
x^2 - (5)(2) = area of shaded region
Someone help me please with this ? Like right now please
Answer: 6472
Step-by-step explanation:
You have to multiply and add
Samantha has chocolate bars and lollipops in the the ratio 4:5. If she has 12 chocolate bars,how many lollipops does she have?
Ms. Benton drew a right angle and split it into 2 angles. one of the labels inside was labeled 5x and the other angle was labeled 4x. what does x equal?
Answer choices:
5°
10°
15°
20°
please help
Answer:
B-10⁰
Step-by-step explanation:
5 x 10 is 50, 4 x 10 is 40, add those and you get 90⁰