Answer:
x=3.5
Step-by-step explanation:
x × 2 = 7
÷2 ÷2
x=3.5
Which expression is equivalent to |8|+|-7|
Answer:
8 + 7.
Step-by-step explanation: It is absolute value.
In an instant lottery, your chances of winning are 0.1. if you play the lottery five times and outcomes are independent, the probability that you lose all five times is
The probability that you lose all five times will be 0.59.
How to calculate the probability?From the information given, the chances of winning are 0.1. Therefore, the chance of losing will be:
= 1 - 0.1 = 0.9
Therefore, the probability that you lose all five times will be:
= 0.9 × 0.9 × 0.9 × 0.9 × 0.9
= 0.59
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!!HELP PLS!! a triangle has side lengths measuring 3x cm 6xcm and h cm which expression describes the possible values of h in cm? 4x < h < 10x, 10x < h < 4x, h=4x, h=10x
Based on the triangle inequality theorem, the possible values of h in cm is: A. 4x < h < 10x
What is the Triangle Inequality Theorem?Based on the triangle inequality theorem, two sides of a triangle must be equal or more than the third sides.
Given a values of the side lengths of a triangle as, 3x, 6x, and h cm, the possible values would be determined as shown below:
h < 3x + 7x or 7x - 3x < h
h < 10x or 4x < h
The possible values of h would be: 4x < h < 10x.
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Find an explicit formula for the arithmetic sequence -11, -3, 5, 13, ....
Note: the first term should be b(1).
b(n) =
Answer:
b(n) = -11 + (n-1)*8
Step-by-step explanation:
Let n be the sequence number, with n=1 the first number b(1) -11
The sequence changes by +8 each step.
b(1) -11 + 8 = -3
b(2) -3 + 8 = 5
b(3) 5 + 8 = 13
b(4) 13
b(1) = -11
b(2) = -3. or b(1) + 1*8
b(3) = 5, or b(1) + 2*8
b(4) = 13, or b(1) + 3*8
We note that each step adds a multiple of 8 to the initial value of -11. This can be stated as (n-1)*8
The formula for this sequence would be b(n) = b(1) + (n-1)*8
b(n) = -11 + (n-1)*8
Check: Does n=3 return the value of 5?
b(n) = -11 + (n-1)*8
b(3) = -11 + ((3)-1)*8
b(3) = -11 + (2)*8
b(3) = -11 + 16
b(3) = 5 YES
logarithmic differentiation for
[tex]y = x {}^{2} [/tex]
someone help me
Answer:
[tex]\boxed {\frac{dy}{dx}= 2x}[/tex]
Step-by-step explanation:
Solving :
⇒ log y = log (x²)
⇒ log y = 2 log x
⇒ [tex]\mathsf {\frac{1}{y} \frac{dy}{dx} = \frac{1}{x} \times 2}[/tex]
⇒ [tex]\mathsf {\frac{dy}{dx}= 2x}[/tex]
Answer:
y’ = 2x
Step-by-step explanation:
Let y = f (x), take the natural logarithm of both sides ln (y) = ln (f (x))
ln (y) = ln (x²)
Differentiate the expression using the chain rule, keeping in mind that y is a function of x.
Differentiate the left hand side ln (y) using the chain rule.
y’/y = 2 In (x)
Differentiate the right hand side.
Differentiate 2 ln (x)
y’/y = d/dx = [ 2 In (x) ]
Since 2 is constant with respect to xx, the derivative of 2 ln (x) with respect to x is 2 d/dx [ln (x)]
y’/y = 2 d/dx [In (x)]
The derivative of ln (x) with respect to x is 1/x.
y’/y = 2 1/x
Combine 2 and 1/x
y’/y = 2/x
Isolate y' and substitute the original function for y in the right hand side.
y’ = [tex]\frac{2}{x}[/tex] x²
Factor x out of x².
y’ = [tex]\frac{2}{x}[/tex] (x * x)
Cancel the common factor.
y’ = [tex]\frac{2}{x}[/tex] (x * x) (The x that is under 2 and the other x that I have underlined are the ones that cancel out)
Rewrite the expression.
y’ = 2x
So therefore, the answer would be 2x.
*HELP**NEEDS IT RIGHT NOW*
Without using a calculator, match each expression to the correct point.
Answer:
a=-2π
b=-17/3
c=-sqrt18
Step-by-step explanation:
eyeball it.
-2π≈-6.28
-17/3 is less than -5 but more than -6, so it's between those 2
-sqrt 18 is between -sqrt 16 and -sqrt 25, so it's a little less than -4
The French club is sponsoring a bake sale to raise at least $305. How many pastries must they sell at $2.05 each in order to reach their goal?
Answer:
148.7804878
Step-by-step explanation:
All you have to do is divide!
can someone please help meee
Answer:
the y intercept is (0,2)
slope = -4
Step-by-step explanation:
from the graph the y intercept is (0,2) and we can consider it as p1
p2 (2,-6)
slope = y2-y1 / x2-x1
= -6 - 2/ 2 -0 = -8/2 = -4
There are some counters in a bag.
the counters are blue or green or red or yellow.
the table shows the probabilities that a counter taken at random from the bag
will be blue or will be green.
red
yellow
colour
blue
green
probability
0.32
0.20
the probability that a counter taken at random from the bag will be red is five times the
probability that the counter will be yellow.
there are 300 counters in the bag.
work out the number of yellow counters in the bag.
Answer:
187
Step-by-step explanation:
Consider the quadratic function y = 1/5 (x – 2)2 + 5.
Which statements are true about the function and its graph? Select TWO options.
A) The vertex of the function is (–2, 5).
B) There are no real roots for the function.
C) The graph of the function opens down.
D) The graph contains the point (2, 5).
E) The graph intersects the x-axis at one unique point.
Answer:
B and D
Step-by-step explanation:
vertex(2,5) so D is correct
there are no real roots for the function B is correct
prove that Cos4x=8Cosx -8Cosx
what is equivalent to 7/5y
Answer:
1.4y
Step-by-step explanation:
A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of `pi`.)
The volume of the air space surrounding the cone inside the cylinder is 1055.04 cm³
How to find volume?The volume of the air space surrounding the cone inside the cylinder is as follows:
volume of the air space = volume of cylinder - volume of a cone
volume of cylinder = πr²h
volume of cylinder = π16 × 5²
volume of cylinder = 400π
volume of the cone = 1 / 3 πr²h
volume of the cone = 1 / 3 × π × 12 × 4²
volume of the cone = 64π
Therefore,
volume of the air space = 400π - 64π
volume of the air space = 336π
volume of the air space = 1055.04 cm³
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1. Find the range for the given domain: {-2, -1, and 0} and the function is y = 3x^2
2. Find the range of the given function y = 8x + 1, where x > 2
3. Find the range of the given function y = 5x + 2, where x > -2
can someone explain how to do these?
1. The range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.
2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).
3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).
We know that the range of a function is the entire set of all possible values for the dependent variable (typically y), after substituting the domain.
1. For the function y = 3x²,
Here the domain is {- 2, - 1, and 0}. So, we have to find the y values for the x values - 2, - 1, and 0 to find the range of the function.
Now, at x = - 2,
y = 3(- 2)² = 3 × 4 = 12
At x = - 1,
y = 3(- 1)² = 3 × 1 = 3
At x = 0,
y = 3(0)² = 3 × 0 = 0
So, the range of this function is {12, 3, 0}.
2. Now, for the function y = 8x + 1,
At x = 2,
y = 8 × 2 + 1 = 16 + 1 = 17
Since the domain is x > 2, we can say that the range set will contain values greater than 17.
So, the range of this function is (17, ∞).
3. For the function y = 5x + 2,
Now, at x = - 2,
y = 5 × (- 2) + 2 = - 10 + 2 = - 8
Since the domain is x > - 2, we can say that the range set will contain values greater than - 8.
So, the range of this function is (-8, ∞).
1. Therefore, the range of the given function y = 3x² for the given domain: {- 2, - 1, and 0} is {12, 3, 0}.
2. The range of the given function y = 8x + 1, where x > 2 is (17, ∞).
3. The range of the given function y = 5x + 2, where x > -2 is (- 8, ∞).
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Part A: Is there any correlation between the number of hours spent practicing and the score in the game? Justify your answer. (4 points) Part B: Write a function that best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate? (3 points)
All the parts are answered , y = 6x + 5 represents the scatter data points given.
The complete question is
A coach is assessing the correlation between the number of hours spent practising and the average number of points scored in a game. The table shows the data:
Number of hours spent practising
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4
Score in the game
(y) 5 8 11 14 17 20 23 26 29
Part A: Is there any correlation between the number of hours spent practising and the score in the game? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate? (3 points)
What is a Function ?A function is a law that connects the y and x variable , i.e. the dependent and independent variable.
Part (A)
There is a positive correlation between the number of hours spent practising and the score in the game , as the time is increasing the scores is also seen to be increasing.
Part (B)
From the online scatter point equation calculator or by using three points which best fits the linear regression the equation can be determined
y = 6x + 5
x represents the timeline spent in practising
Part C:
slope = 6
When the time spent practising increases by 1 hour, the average scores increases by 1 hour, the score in a game is predicted to increase by an average of 6 and
as intercept = 5
When no time is spent on the practice the score obtained is 5.
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What is the distance between the points (4, 5) and (10, 13) on a coordinate
plane?
Answer:
10
Step-by-step explanation:
square root of 6^2 + 8^2
55. The Cone Problem Begin with a circular piece of paper with
4-in. radius as shown in (a). Cut out a sector with an arc length o
x. Join the two edges of the remaining portion to form a cone
with radius r and height h, as shown in (b).
4 in.
4 in.
(a)
(b)
(a) Explain why the circumference of the base of the cone is
8T X
(b) Express the radius r as a function of x.
(c) Express the height has a function of x.
(d) Express the volume V of the cone as a function of x.
pls helpppp
The circumference of the base of the cone is 8π - x since the base is equal to go the arc length of the remainder of the circle.
How to calculate the values?The radius r as a function of x will be:
8π - x = 2πr
r = (8π - x)/2π
r = 4 - x/2π
The height has a function of x will be:
r² + h² = 16
h² = 16 - r²
where r = 4 - x/2π
h = √16 - ✓(4 - x/2π)²
h = 4✓(4 - x/2π)²
The volume V of the cone as a function of x will be:
= 1/3 πr²h
= π/3(4 - x/2π)² 4✓(4 - x/2π)²
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(a+b)^2=10
and ab=1
then find a^2+b^2
[tex] \underline{\large \bf{Required \: Answer}} : - [/tex]
[tex] \dashrightarrow \: \red{\large8}[/tex]
[tex] \sf[/tex]
[tex] \underline{ \large{ \rm \pink{SolutioN}}} \: -[/tex]
[tex] \quad \qquad\sf \: {(a + b)}^{2} = 10[/tex]
[tex] \qquad \: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2ab = 10[/tex]
[tex] \qquad\: \: \to\: \: \sf{a}^{2} + {b}^{2} + 2(1) = 10[/tex]
[tex] \qquad\: \: \to\: \: \sf \: {a}^{2} + {b}^{2} = 10 - 2[/tex]
[tex] \qquad\: \:\bf \to\: \: \: {a}^{2} + {b}^{2} = 8[/tex]
[tex] \sf[/tex]
[tex] \sf \therefore \: 8 \: \: is \: \: the \: \: required \: \: answer[/tex]
[tex] \rule{200pt}{2pt}[/tex]
How many solutions are there for the system of equations of shown on the graph?
O No solution
O One solution
O Two solutions
O Infinitely many solutions
Answer:
1
Step-by-step explanation:
the number of solutions corelatea with number of cross-points in the graphs, in our exame, 1 point, hence 1 solution
NEED HELP TODAY PLEASE solve 4(2/5x+7)=−8−4/5x show your work
Answer:
x = -15
Step-by-step explanation:
what are the roots of the polynomial below. x^3-3x^2+2
Polynomial is an expression that consists of indeterminates(variable) and coefficients. The roots of the polynomial are 1, 2.7321, and -0.7321.
What are polynomials?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The roots of the polynomial are:
x³ - 3x² + 2
If we divide the polynomial by (x-1), then
(x³ - 3x² + 2)/(x-1) = x² - 2x - 2
now, factorize the given polynomial,
x² - 2x - 2
x = 1 ± √3
x = 1, 2.7321, -0.7321
Hence, the roots of the polynomial are 1, 2.7321, and -0.7321.
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Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
The answer would be D 7mn+3m/2+5n/4
Step-by-step explanation:
A polynomial is a combination of terms separated by +
or − signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms.
3. Angle r* = 2wº. What is the measure of angle rº1 Show your work. 125⁰ Thangle A wo Wo Triangle B 125⁰ 3. Angle r * = 2wº . What is the measure of angle rº1 Show your work . 125⁰ Thangle A wo Wo Triangle B 125⁰
Answer:
r = 290°
Step-by-step explanation:
Exterior angle property:In a triangle, exterior angles equals the sum of interior opposite angle.
In triangle A,
x + 90 = 125 {Exterior angle property}
x = 125 - 90
x = 35°
In triangle B,
y + 90 = 125
y = 125 - 90
y = 35°
x + y + r = 360 {Complete angle}
35 + 35 + r = 360
70 +r = 360
r = 360 - 70
r = 290°
(75 POINTS PLEASE RESPOND ASAP)
Explain how to solve 4x + ^3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
Answer:
1.596
Step-by-step explanation:
So you can rewrite log as: [tex]log_{b}a=x = > b^x=a[/tex] So in this case it's already in exponential form which we'll use to rewrite into logarithm form.
[tex]4^{x+3} = 7\\log_47=x+3\\\\\frac{log7}{log4}=x+3\\1.404\approx x+3\\x\approx1.596[/tex]
Answer:
x = -1.596
Explanation:
[tex]\rightarrow \sf 4^{x + 3} = 7[/tex]
take log on both sides
[tex]\rightarrow \sf log(4^{x + 3}) = log(7)[/tex]
[tex]\rightarrow \sf (x + 3)log(4) = log(7)[/tex]
[tex]\rightarrow \sf x + 3= \dfrac{log(7)}{log(4)}[/tex]
[tex]\rightarrow \sf x= \dfrac{log(7)}{log(4)} -3[/tex]
calculate
[tex]\rightarrow \sf x= -1.596322539[/tex]
[tex]\rightarrow \sf x= -1.596 \quad (rounded \ to \ nearest \ thousand)[/tex]
A passenger jet plane cruises at 550 knots. It enters a jet stream with
a tailwind speed of 120 knots. If the speed of sound is 661 knots,
will the jet travel faster or slower than sound during its journey?
Considering the direction of the wind, it is found that the jet travels faster than the sound during it's journey.
What is the ground speed?The jet's speed, considering that there is a tailwind, is given by:
J = Plane speed + Wind speed.
In this problem, we have that the speeds are given as follows:
Plane: 550 knots.Wind: 120 knots.Hence the jet's speed is given by:
J = 550 + 120 = 670 knots.
670 knots > 661 knots, hence the jet travels faster than the sound during it's journey.
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Please help! What is 4 yards 2 feet 7 inches + 2 yards 1 foot 6 inches?
Answer:
7 yds 1 ft 1 inch
Step-by-step explanation:
Quick Solve!
Side #1:
1 yard = 36 inches4 * 36 = 144 inches1 foot = 12 inches2 * 12 = 24 inches144 inches + 24 inches + 7 inches = 175 inches
Side #2:
2 yards = 2 * 36 = 72 inches1 foot = 12 inches + the 6 inches = 18 inches72 inches + 18 inches = 90 inches72 inches + 18 inches = 90 inches + 6 inches = 96 inches
Conclusion:
175 inches + 96 inches = 271 inches
Answer:
⇒ 7 yds 1 ft 1 inch
Answer:
7 yards 1 foot 1 inch
Step-by-step explanation:
Adding both of them together, you get:
6 yards 3 feet 13 inches
Since 1 foot = 12 inches, and 13 inches exceeds that, add a foot to the previous 3 feet and subtract 12 from the 13 inches
Therefore: 6 yards 4 feet 1 inch
Since 1 yard = 3 feet, and 4 feet exceeds that, add a yard to the previous 6 yards and subtract 3 feet from the remaining 4 feet
Hence:
7 yards 1 foot 1 inch
I need the answer to
y = -x - 3
y=-x-5
Answer:
if you're supposed to be solving for x then the top one is x=-y+3 and the bottom is x=-y+5
Please help! Consider the following subset of the real number line. How can this set be expressed using inequalities?
Inequalities help us to compare two unequal expressions. The correct option is A.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The set of numbers that the number line represents is -1, -2,-3, and -4. Thus, The inequalities that can express the given set are -4≤x≤-1.
Hence, the correct option is A.
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Find the number of turns or bumps in the graph of the function f(x) = x² - 25
Answer:
1 turn
Step-by-step explanation:
this is what the graph would look like:
The total pages a person reads in x days, if the person reads 6 pages a day
the cost of x boxes of mangoes, if 1 box costs $6 and the shipping charge is $6 per order (for any number of boxes)
the total cost of x notebooks, if one notebook costs $6 and students receive a discount of $1 off their total bill
the total cost of x novels and a pocket dictionary if you buy x novels each at $6 and get a pocket dictionary at $1
what are the corresponding functions for each situation?
The given expression will be written as follows:-
y = 6x
y = 6x + 6
y = 6x - 1
y = 6x +1
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.
A) The total pages a person reads in x days, if the person reads 6 pages a day
y = 6x
B) The cost of x boxes of mangoes, if 1 box costs $6 and the shipping charge is $6 per order (for any number of boxes)
y = 6x + 6
C) The total cost of x notebooks if one notebook costs $6 and students receive a discount of $1 off their total bill
y = 6x - 1
D) The total cost of x novels and a pocket dictionary if you buy x novels each at $6 and get a pocket dictionary at $1
y = 6x + 1
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