Answer:
[tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex]
Step-by-step explanation:
Hello!
We can solve the quadratic by using the Quadratic Formula.
Standard form of a Quadratic: [tex]ax^2 + bx +c = 0[/tex]
Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Given our equation: [tex]2x^2 + x - 4 = 0[/tex]
a = 2b = 1c = -4Plug in the values into the quadratic formula to solve.
Solve the quadratic[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-1 \pm \sqrt{1^2 - 4(2)(-4)}}{2(2)}[/tex][tex]x = \frac{-1 \pm \sqrt{1 + 32}}{4}[/tex][tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex]The solution to the quadratic is [tex]x = \frac{-1 \pm \sqrt{33}}{4}[/tex].
Solve the following using distributive property:
9(x+3)=4x-3
Answer:
x = -6
Explanation:
⇒ 9(x + 3) = 4x - 3
apply distributive method: a(b + c) = ab + ac
⇒ 9(x) + 9(3) = 4x - 3
multiply variables
⇒ 9x + 27 = 4x - 3
collect like terms
⇒ 9x - 4x = -3 - 27
subtract like terms
⇒ 5x = -30
divide both sides by 5
⇒ x = -6
Answer:
x = -6
Step-by-step explanation:
distribute 9(x+3) = 9x+27
9x+27 = 4x-3 subtract -27 and -4x on each side
9x-4x = -3-27 combine like terms
5x = -30 divide by 5
x = -6
1) a jewelry store sells gold and platinum
rings. each ring is available in ten styles
and is fitted with one of nine gemstones.
a) 187 b) 265
c) 180
d) 195
find the number of possible outcomes
un wd
The number of possible outcomes are 180.
How do you find the number of possible outcomes?To find the total number of possible outcomes for two or more events, multiply the number of outcomes for each event together.
Given that,
We have two types of rings Gold and platinum
For this event (material) we have 2 outcomes.
Each ring is available in 10 style
For this event (style) we have 10 outcomes.
Each ring is fitted with 9 gemstones
For this event (gem) we have 9 outcomes.
Total number of possible outcomes = 2×10×9
= 180
Hence, The number of possible outcomes are 180.
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Solve the inequality c−32≥0 and write the solution in interval notation.
Answer:
[32, ∞]
Step-by-step explanation:
c - 32 ≥ 0 can be rewritten as c ≥ 32 (adding 32 on both sides)
So for any value of between 32 and infinity both inclusive is a solution
A bag contains 2 gold marbles, 9 silver marbles, and 24 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game
The expected value on playing this game is -5/36.
Given: 2 gold marbles, 9 silver marbles, and 24 black marbles.If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
To find: Expected value on playing the game
Chance of occurrence of gold = 1/36
Chance of occurrence of silver = 9/36
Chance of occurrence of black = 26/36
On multiplying the given probability of occurence with the amount you would lose or win
we get,
1/36 * 3 + 9/36 * 2 - 26/36 * 1
3/36 + 18/36 - 26/36
=$ -5/36
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What is the decimal expansion of the following fraction? 1/10
Answer:
0.1
Step-by-step explanation:
break 1 into 10 parts, and take one part: hence 0.1
Answer:
0.1
Step-by-step explanation:
? Question
Each set of ordered pairs represents two points on a line. Match each set of ordered pairs with the description of the line
they are on.
Tiles
(-5,-3) and (-5,3) (-7,-1) and (-1,-7)
(-6,-2) and (6,-2)
The correct matching of the ordered pairs and the line they are on are:
(-5,-3) and (-5,3) - No slope. (-7,-1) and (-1,-7) - Slope = -1(-6,-2) and (6,-2) - No slope What lines do the ordered pairs belong to?The slope of the first pair is:
= (3 - (-3)) / (-5 - (-5))
= No slope as slope is 0
The slope of the second pair is:
= (-7 - (-1)) / (-1 - (-7))
= -1
The slope for the third pair is:
= (-2 - (-2)) / (6 - (-6))
= 0 or No slope
Rest of the question is:
slope = -1
No slope
No slope
slope = 2
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Answer: vertical line- (-5,-3) and (-5,3)
neither- (-7,1) and (-1,-7)
horizontal line- (-6,-2) and (6,-2)
hopefully this helps
Step-by-step explanation:
Joe
,
sarah
and
katie
share a sum of money in the ratio
5
:
8
:
4
. If
sarah
receives $
32
more than
katie
, find the amount of money that is being shared.
Answer:
muji chus mero lado madeaghw you mother machinery
Answer:
After finding all the amount add them and your amount shared will be dollar 136
Does the parabola open up or down?
What would the sign of the second differences be?
What are the coordinates of the vertex?
What is the equation of the axis of symmetry?
What is the optimal value?
Is the optimal value considered a max or min?
What are the x-intercepts?
What is the y-intercept?
The parabola opens down, the sign of the second difference is positive and the equation of the axis of symmetry is x = 1
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have given a graph of a parabola.
From the graph:
The parabola opens down.
The sign of the second difference is positive.
The coordinates of the vertex is at (1, 3)
The equation of the axis of symmetry is x = 1
The optimal value of the parabola is at y = 3
The optimal value is considered a max value.
The x-intercepts is at (-1, 0) and (3, 0)
The y-intercept is at (0, 5/2)
Thus, the parabola opens down, the sign of the second difference is positive and the equation of the axis of symmetry is x = 1
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In spherical geometry, lines are called
OA. line segments
OB. radii
O c. diameters
O D. great circles
Answer:
Diameters
Step-by-step explanation:
In spherical geometry, lines are called diameters.
Answer:
Diameter
Step-by-step explanation:
In spherical geometry, lines are called diameter .
Also this makes sense the most .
Consider the polynomial function h(x)= -7x^6+3x^4-5x^2
The end behavior of the function is [tex]\mathrm{as}\:x\to \:+\infty \:,\:h\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:h\left(x\right)\to \:-\infty \:[/tex]
How to determine the end behavior?The function is given as:
[tex]h(x)= -7x^6+3x^4-5x^2[/tex]
Next, we plot the graph of the function (see attachment)
From the attached graph, we can see that:
The function approaches negative infinity, irrespective of the direction of the x value
Hence, the end behavior of the function is [tex]\mathrm{as}\:x\to \:+\infty \:,\:h\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:h\left(x\right)\to \:-\infty \:[/tex]
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Volume=
Help me please, thanks
Answer: [tex]144\pi[/tex]
Step-by-step explanation:
The area of the base is [tex]36\pi[/tex].
If we consider the right triangle, by the Pythagorean theorem, the unknown leg, which has a length of 4, is the height.
So, the volume is [tex]144\pi[/tex].
An open-top rectangular box with square base is to be made from 100 square feet of material, as shown.
What is the largest possible volume of the box?
The largest possible volume of the given box is; 96.28 ft³
How to maximize volume of a box?Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is;
S = b² + 4bh
We are given S = 100 ft². Thus;
b² + 4bh = 100
h = (100 - b²)/4b
Volume of the box in terms of b will be;
V(b) = b²h = b² * (100 - b²)/4b
V(b) = 25b - b³/4
The volume is maximum when dV/db = 0. Thus;
dV/db = 25 - 3b²/4
25 - 3b²/4 = 0
√(100/3) = b
b = 5.77 ft
Thus;
h = (100 - (√(100/3)²)/4(5.77)
h = 2.8885 ft
Thus;
Largest volume = [√(100/3)]² * 2.8885
Largest Volume = 96.28 ft³
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Find x.
02
3√2
04√3
02√3
Answer:
x
Step-by-step explanation:
2^3
Which of the following is equivalent to (8 – 5) ÷ 23 ?
A 3/8
B 19/8
C 27/8
D 1/125
Answer:
none
Step-by-step explanation:
(8-5)=3
8-5÷23
=179/23
Which phrases describe the graph of f(x)=|x|? Check all that apply
Take a look at the graph of [tex]f(x)=|x|[/tex], also known as the absolute value of [tex]x[/tex].
As shown by the graph attached, it is V-shaped, opens up, and is symmetric with respect to the vertical/y-axis.
Lizette wanted to see if it would be possible to use a little less materials in a tea infuser but still not be required to be at full capacity. Her rectangular pyramidal tea infuser would be 7 cm high, 3 cm long and 1.5 cm wide. The tea infuser from the example, was the same except 7.9 cm high and was filled to 80% capacity.
Would these dimensions work, if so to what percent would Lizette's infusers have to be filled to use the same amount of tea?
The percentage that the infuser will have to be filled to use the same amount of tea will be 90.23%.
How to calculate the percentage?The infuser for Lizeete is 7 cm high, 3 cm long and 1.5 cm wide. The volume will be:
= 7 × 3 × 1.5
= 31.5cm³
The tea infuser from the example, was the same except 7.9 cm high. Therefore, the volume will be:
= 7.9 × 3 × 1.5
= 35.5
Since it was filed to 80%, this will be:
= 80% × 35.5
= 31.5cm³
Therefore, the dimensions will work and the percentage to use the same amount of tea will be:
= 28.44/31.5 × 100
= 90.23%
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The length of a rectangle is a centimeters, and the width of this rectangle is b centimeters. Write an expression for the area of the rectangle. "a" and "b" are variables.
Answer:
Area = ab
Step-by-step explanation:
Area is length × width, so fill in a for the length and b for the width. Multiply a and b together.
A = a×b
A = ab
Plot all ordered pairs for the values in the domain D: (-8, -4, 0, 2, 6)
All ordered pairs for the values in the domain will be (-8, -3), (-4, -1), (0, 1), (2, 2), and (6, 4).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space.
The function is given below.
y = (1/2) x + 1
Then the domain is D: (-8, -4, 0, 2, 6)
Then the ordered pair will be
For x = -8
y = (1/2)(-8) + 1
y = -3
For x = -4
y = (1/2)(-4) + 1
y = -1
For x = 0
y = (1/2)(0) + 1
y = 1
For x = 2
y = (1/2)(2) + 1
y = 2
For x = 6
y = (1/2)(6) + 1
y = 4
All ordered pairs for the values in the domain will be (-8, -3), (-4, -1), (0, 1), (2, 2), and (6, 4).
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Scientist released 8 rabbits into a new habitat in a year 0.each year, there were twice as many rabbits as the year before.
The question is incomplete. Below you will find the missing part of the question.
How many rabbits were there after x years? Write a function to represent this scenario.
[tex]8(2)^{x}[/tex] rabbits were there after x years.
The function form is [tex]f(x)=8(2)^{x}[/tex]
The number of rabbits released each year is 8.
During 0 year, there will be 8 rabbits;
During year 1, the number of rabbits will be 8+8 = 16, i.e. 8×2¹ = 16
Similarly, during the year 2, the number of rabbits will be 16+16 i.e. 8×2² = 32
So, according to the pattern we can say that the function would be
[tex]f(x)=8(2)^{x}[/tex]
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What is the probability that a simple random sample of 45 unemployed individuals will provide a sample mean within 1 week of the population mean
The probability that a simple random sample of 45 unemployed individuals will provide is 0.7372
Here, μ = 17.5, σ = 0.8944, x1 = 16.5 and x2 = 18.5.
We need to compute P(16.5<= X <= 18.5).
The corresponding z-value is calculated using Central Limit Theorem.
z = (x - μ)/σ
z1 ⇒ (16.5 - 17.5)/0.8944 = -1.12
z2 ⇒ (18.5 - 17.5)/0.8944 = 1.12
Therefore, we get
P(16.5 <= X <= 18.5) = P((18.5 - 17.5)/0.8944) <= z <= (18.5 - 17.5)/0.8944)
⇒ P(-1.12 <= z <= 1.12) = P(z <= 1.12) - P(z <= -1.12)
⇒ 0.8686 - 0.1314 = 0.7372
The principal limit theorem states that if you have a population with imply μ and trendy deviation σ and take sufficiently huge random samples from the populace with alternative, then the distribution of the pattern method may be about usually distributed.
The relevant limit theorem (CLT) states that the distribution of pattern manner approximates a normal distribution as the pattern size gets larger, regardless of the population's distribution. sample sizes identical to or extra than 30 are often considered enough for the CLT to preserve.
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f CA = 8, what is C'A'?
10 units
12 units
16 units
20 units
Segment AC was dilated by a scale factor of 2 to form A'C' measuring 16 units
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
Let us assume that segment AC was dilated by a scale factor of 2 to form C'A', hence:
A'C' = 2 * AC = 2 * 8 = 16 units
Segment AC was dilated by a scale factor of 2 to form A'C' measuring 16 units
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if Ben has 10.4L of deride and Madison has 940 cal of diesel how much does the pair have altogether
Based on the calculations, the total volume which the pair have altogether is equal to 19.8 Liters.
How to calculate the total volume?In Science, volume is a unit of measurement which indicates the capacity of a container and it has the following units:
Liters (L)Centiliter (cL)Cubic meter (m³)Next, we would convert the volume of Madison's diesel in centiliter to liter as follows:
1 centiliter = 0.01 liter
940 centiliter = X liter
Cross-multiplying, we have:
X = 940 × 0.01
X = 9.4 L.
Total volume = 9.4 + 10.4
Total volume = 19.8 Liters.
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Question 1 of 10
Which number sentence below matches this word problem?
Jen and Marcus got 15 miles up river before they ran out of gas. They floated
9 miles back down river before they reached the shore. How far did they get?
A. 135÷9 = 15
B. 15-9=6
C. 15-6=9
D. 9+15=24
Answer:
They get 15×9=135
135÷15=9 is your answer
What is the first quartile of the data set: 11, 24, 13, 18, 16, 21, 23, and 29?
Answer: 15, 15, 16, 21, 23, 29
Step-by-step explanation:
Please Help Me Asap I Need Units Too
Hello and Good Morning/Afternoon
Let's take this problem step by step:
To find the rate of change is essentially like finding a line's slope:
⇒ the x-values are the number of sodas
⇒ the y-values are the total costs
⇒ choose two sets of coordinates and find the slope
Let's put that into action
Choose any two points⇒ (24, 18)
⇒ (28, 21)
Calculate Slope[tex]Rate_.of_.change = \frac{21-18}{28-24} =\frac{3}{4}[/tex]
Since the rate of change is total cost over number of sodas
⇒ unit is 'total cost/number of sodas'
Answer: 3/4 total cost/number of sodas
Hope that helps!
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Use the given graph to determine the limit, if it exists. (4 points)
A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3.
Find limit as x approaches three from the right of f of x.
The limit as x approaches three from the right of f(x) is 3
What is the Limit of a function ?The value a function approaches when the variable approaches its limit.
A graph is given which shows a piece wise function ,
As when the limit approaches from the right the function can be seen approaching 3 , it is not 3 at 3 but approaching to 3
The right hand lim x--> 3 f(x) approaches 3 .
Therefore , limit as x approaches three from the right of f(x) is 3
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Let's say you rolled a dice twice, and you got at least a 6. What is the probability that the sum of both rolls is at least 9
The probability that the sum of both rolls is at least 9 is 2/36.
Probability is the chance that a given event will occur. the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
Given:
Total sample spaces: 36.
Number on one dice: 6
For sum of both rolls to be 9 , the only possible way is (6,3)(3,6)
Using probability formula,
Thus The probability that the sum of both rolls is at least 9 is 2/36.
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HELP PLEASE
factor completely.
25d^8−80d^4+64=
Answer:
(5d⁴ − 8)²
Step-by-step explanation:
I hope this is helpful!
A girl ran from her home to a store at the rate of 6 mph, and she walked back home at the rate of 4 mph. if it took 15 minutes for the round trip, how far away is the home from the store?
Home is 0.6 miles away from the store
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Given:-
Total time taken by girl to complete the trip = 15 minutes = [tex]\frac{1}{4}[/tex] hours
Speed while riding going = 6 miles per hour
Speed while coming back = 4 miles per hour
Total time taken by girl =
Time taken while going + Time taken while coming back - (1)
Let x be distance from home to store
[tex]\frac{x}{6}[/tex] = Time taken while going
[tex]\frac{x}{4}[/tex] = Time taken while coming back
Substituting in (1) we get
[tex]\frac{1}{4} = \frac{x}{6} + \frac{x}{4}[/tex]
[tex]\frac{1}{4} = \frac{2x + 3x}{12}[/tex]
[tex]\frac{1}{4} = \frac{5x}{12}[/tex]
[tex]x= \frac{12}{20}[/tex]
x = 0.6 miles
Thus home is 0.6 miles away from the store
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Which steps would be used to solve the equation? Check all that apply. 2 and two-thirds + r = 8
The correct steps are given below:-
a) Subtract 2 and two-thirds from both sides of the equation
b) 8 minus 2 and two-thirds = 5 and one-third
c) Substitute the value for r to check the solution.
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.
The given expression will be solved by using the following steps:-
[tex]2 \dfrac{2}{3}[/tex] + r = 8
Subtract [tex]2 \dfrac{2}{3}[/tex] from each side
[tex]2 \dfrac{2}{3}[/tex] + r - [tex]2 \dfrac{2}{3}[/tex] = 8 - [tex]2 \dfrac{2}{3}[/tex]
r = 5 1/3
Check the solution,
[tex]2 \dfrac{2}{3}[/tex] + [tex]5 \dfrac{1}{3}[/tex] =8
8 = 8
The complete question is given below:-
Which steps would be used to solve the equation? Check all that apply. 2 and two-thirds + r = 8 Subtract 2 and two-thirds from both sides of the equation. Add 2 and two-thirds to both sides of the equation. 8 minus 2 and two-thirds = 5 and one-third 8 + 2 and two-thirds = 10 and two-thirds Substitute the value for r to check the solution.
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Answer:
A,C,E >:3.
your welcome!