Solve by graphing. x2 + 2x – 3 = 0
Answers
By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.
To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.
First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.
We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.
1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:
0 = x^2 + 2x - 3.
This quadratic equation can be factored as (x + 3)(x - 1) = 0.
Therefore, x = -3 or x = 1.
2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.
3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).
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Related Questions
which grows at the fastest rate for increasing values of x
\(f(x)=4*2^x\\h(x)=9x^2+25\\\\g(x)=15x+6\)
Answers
The function that grows at the fastest rate for increasing values of x is f(x) = 4×2ˣ.
We can see this by comparing the growth rates of the three functions for larger and larger values of x.
As x gets larger, the exponential function f(x) grows much faster than the other two functions, which are both polynomial functions.
if we plug in x = 10, we get:
f(10) = 4×2¹⁰ = 4×1024 = 4096
h(10) = 9×10² + 25 = 925
g(10) = 15×10 + 6 = 156
As we can see, f(10) is much larger than h(10) and g(10), indicating that f(x) grows at a much faster rate than the other two functions.
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What slope pass through (2,1)(-3,-2)
Answers
what you mean but heres the points on the map u were talking about
Answer: The slope m = 3/5
Step-by-step explanation:
The slope can be found by using the formula: m = y2 - y1 / x2-x1
Where m is the slope and (x1, y1) and (x2, y2) are the two points on the line.
x1 = 2 , y1 = 1
x2 = -3 , y2 = -2
Substituting the values from the points in the problem gives :
m = -2-1 / -3-2
m = 3/5
Hence, the slope that passes through (2, 1) and (-3, -2) is 3/5.
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In a trapezoid with bases of lengths a and b, a line parallel to the bases is drawn through the intersection point of the diagonals. Find the length of the segment that is cut from that line by the legs of the trapezoid. Plz explain thx
Answers
Answer:
Consider the trapezoid ABCD. In this trapezoid BC=a and AD=b.
Since triangles BOC and AOD are somilar, then
\( \dfrac{AO}{OC}=\dfrac{DO}{OB}=\dfrac{AD}{BC}=\dfrac{b}{a}. [\tex]
OC/AO = OB/DO = BC/AD=/ba
Triangles OAE and CAB are similar
EO/BC=b/(a+b)
EO=ab/(a+b)
again
OF=ba/(b+a)
and.
EF=2a/(a+b) is arequired length.
Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 30 passengers.
• (a) Explain why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds.
• (b) Find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds. Show your work. (Hint: To apply the central limit theorem, restate the problem in terms of the mean weight.)
Answers
The probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.
What is the Central Limit Theorem?
The Central Limit Theorem states that the sum of a large number of independent and identically distributed random variables is approximately Normally distributed.
(a) The reason why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds is that the weight of passengers is not Normally distributed.
The Normal distribution is a symmetric bell-shaped distribution that is defined by its mean and standard deviation.
The weight of passengers is not symmetric and it may not follow a bell shape.
Therefore, we cannot use the Normal distribution to calculate the probability of a weight greater than 200 pounds.
(b) To calculate the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the Central Limit Theorem.
Since we don't know the exact distribution of the weight of the passengers, we can use the Central Limit Theorem to approximate the total weight of the passengers on a full flight.
The mean weight of a passenger is 190 pounds, and the standard deviation is 35 pounds. Since a full flight carries 30 passengers, the mean weight of the passengers on a full flight is 19030 = 5700 pounds and the standard deviation is 35sqrt(30) = 175 pounds.
To find the probability that the total weight of the passengers on a full flight exceeds 6000 pounds, we can use the standard normal distribution table.
z = (6000 - 5700) / 175 = 2.2857
Probability P(X > 6000) = P(Z > 2.2857) = 1 - P(Z < 2.2857) = 1 - 0.9853 = 0.0147
Hence, the probability that the total weight of the passengers on a full flight exceeds 6000 pounds is about 0.0147 or 1.47%.
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Simplify 4(3v + 2)
12v + 8
12v + 2
7v - 2
5v
Answers
Explanation: you would need to distribute (multiply) whatever is in the parentheses
A cake recipe calls for the following dry ingredients: 3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa. To the nearest cup, how much dry ingredients will be used?
Answers
The amount of dry ingredients used in the cake recipe is approximately 7 cups.
To find the total amount of dry ingredients used in the cake recipe, we need to add up the amounts of flour, sugar, and cocoa.
3 ½ cups of flour is equal to 3 cups plus 0.5 cups, or 3 cups and 8 ounces.
2 ⅔ cups of sugar is equal to 2 cups plus 0.67 cups, or 2 cups and 10.72 ounces.
1 ¾ cups of cocoa is equal to 1 cup plus 0.75 cups, or 1 cup and 12 ounces.
Adding these amounts together, we get:
3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces
To the nearest cup, this is equal to 7 cups.
Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.
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How many real solutions does the system have ? y = - 3x - 1; y = x ^ 2 - 3x + 4
Answers
The only solution the system of the equation has is x = -1/3.
The number of solutions is one.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
The system of equations:
y = -3x - 1
y = x² - 3x + 4
The solutions of the equation.
y = 0
So,
-3x - 1 = 0
-3x = 1
x = -1/3
x² - 3x + 4 = 0
It is in the form of ax² + bx + c = 0
a = 1, b = -3, and c = 4
Now,
x = -b ± √(b² - 4ac) / 4a
x = 3 ± √(9 - 16) / 4
x = 3 ±√-7 / 4
x = 3 ±i√7 / 4
This is a complex root.
So,
These are not real solutions.
Thus,
The only solution the system of the equation has is x = -1/3.
The number of solutions is one.
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Solve f(x) = 0 for x.
f(x) = 3x - 5
Answers
Answer:
-5
Step-by-step explanation:
well you could just impute the 0 for x
f(0)= 3(0)-5
multiply 3 and 0 to get 0
0-5
subtract 5 from 0 to get = -5
Answer: 5/3
Step-by-step explanation:
f(x) has to be 0
Therefore 3x-5 = 0
3x=5
3x/3 = 5/3
x = 5/3
Find the value of m.
C
1190
mº
A
B
A 61
B 30°
C 45
D 41°
Answers
Answer:
b
Step-by-step explanation:
ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯
R
T
? Round to the nearest hundredth. Enter your answer in the box.
Answers
\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22\)
Find the difference between the actual quotient and the estimated quotient of 54,114÷29 . (Dividend is rounded off to nearest thousand and divisor to nearest ten)
Answers
The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.
To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.
Actual quotient:
Dividing 54,114 by 29, we get:
54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)
Estimated quotient:
Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:
54,000 ÷ 30 = 1,800
Difference between actual and estimated quotient:
Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379
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Lisa is a single taxpayer whose total income before deductions are $57,392. She was able to reduce her total income by $9,347 by filing Schedule A. Use the tax rate schedule below. How much did she save using Schedule A?
Answers
Answer:
$5554.91
Step-by-step explanation:
The cost of a yoga class is $15 per session. In addition,
a mat fee of $2 is charged per session. Which of the
following represents the total cost in dollars, of the
class and mat for y sessions?
Answers
You're charged $15 + $2 or $17 per session
If y = # of sessions,
$17y represents the total amount of dollars charged for y sessions
The total cost in dollars, of the class and mat for y sessions will be 17y. Then the correct option is C.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The cost of a yoga class is $15 per session.
In addition, a mat fee of $2 is charged per session.
Then the total cost in dollars, of the class and mat for y sessions will be
C = 15y + 2y
C = 17y
Then the total cost in dollars, of the class and mat for y sessions will be 17y.
Then the correct option is C.
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Does anyone know what the table is? I need help
Answers
Answer:
yea its the thing you eat your food on at breakfast lunch dinner etc.
Step-by-step explanation:
6. The sum of three numbers A, B, and C, is $840. A is 2 times of B and C is half of B. Find the values of each number.
Answers
What is the area W. Please help geometry
Answers
Answer:
C. 9π
Step-by-step explanation:
r=x-1
A=πr^2
--------
(x-1)^2+(2x-4)^2= (x-1+2)^2x^2-2x+1+4x^2- 16x+16= x^2+2x+14x^2 -20x +16=0x^2-5x+4=0(x-1)(x-4)=0x=1 - not possible as radius can't be zerox=4 is the solution--------
A= πr^2= π*(4-1)^2= 9π, option C.
If x = 3i, y = 2i, and z = m + i, the expression xyz equals
1.) -12-12mi
2.)-6-6mi
3.)12-12mi
4.)6-6mi
Answers
Answer:
Step-by-step explanation:
I am assuming that i = √(-1)
3i*2i*(m + i)
= 6i^2(m + i)
= -6(m+ i)
= -6m - 6i.
Find the value of each variable.
Answers
Answer:
Step-by-step explanation:
The sum of exterior angles in a quadrilateral is always 360 degrees.
So, 2x+x+4x+3x=10x=360
Soling for x, we get x=36 degrees.
-12h+24 = 6-10h what is h
Answers
Answer:
h=9
Step-by-step explanation:
-12h+10h=6-24
-2h=-18
-2h/-2h= -18/-2
h= -9
I hope this helps! :) If it does could you please mark be brainliest?
Answer:
h = 9
Step-by-step explanation:
Given equation,
→ -12h + 24 = 6 - 10h
Now the value of h will be,
→ -12h + 24 = 6 - 10h
→ -12h + 10h = 6 - 24
→ -2h = -18
→ h = (-18)/(-2)
→ h = 18/2
→ [ h = 9 ]
Hence, the value of h is 9.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer:
C
Step-by-step explanation:
cot²θ = 1/tan²θ
plug this in to get
1/(1/tan²θ + 1)
1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ
we then have
1/((1+tan²θ)/tan²θ)
1/(x/y) = y/x, so this is equal to
tan²θ/(1+tan²θ)
tan²θ = sin²θ/cos²θ, so plug this in to get
(sin²θ/cos²θ)/(1+sin²θ/cos²θ)
1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ
sin²θ + cos²θ = 1, so we have
(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get
(sin²θ/cos²θ)/(1/cos²θ)
(a/b)/(c/d) = (d/c) * (a/b), so we have
(sin²θ/cos²θ)/(1/cos²θ) = cos²θ/1 * sin²θ/cos²θ = sin²θ
What is the percent of 1 - 3√(5/35) ?
Answers
Answer:
1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755
0.0755 * 100 = 7.55%
Step-by-step explanation:
To find the percentage of 1 - 3√(5/35), we need to first evaluate the expression.
1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755
To convert this decimal to a percentage, we simply multiply by 100:
0.0755 * 100 = 7.55%
6 points Emily’s family needs to rent a moving truck to move their belongings to a different house. The rental cost for Trucks-A-Lot is $42 per day plus $0.72 per mile. The rental cost for Move-It-Truckers is $70 per day plus $0.12 per mile. Let m represent Emily’s mileage. Write an equation to represent the cost of renting each truck, and determine what will be the number if miles for which the truck cost the same amount.
Answers
Truck A: 42d+0.72m
We also know that Truck Company B charges $70 per day and an additional $0.12 a mile. Again, we can use d for the number of days and m for the number of miles:
Truck B: 70d+0.12m
Now if we start plugging in values, we will find when they cost the same. The rest is in the picture. Your answer is m≈47
Review the federal income tax table.
Single
If Taxable Income Is between: Then the Tax Due Is:
$0 – $9700 10% of taxable income
$9701 – $39,475 $970+12% of the amount over $9700
$39,476 – $84,200 $4543+22% of the amount over $39,475
$84,201 – $160,725 $14,382.50+24% of the amount over $84,200
$160,726 – $204,100 $32,748.50+32% of the amount over $160,725
$204,101 – $510,300 $46,628.50+35% of the amount over $204,100
$510,301+ $153,798.50+37% of the amount over $510,300
Mustafa earned $95,000 in taxable income in a year from his job as a software developer. How much federal income tax does he owe? Enter your answer as a number rounded to the nearest cent, such as: $42,536.47.
Answers
9514 1404 393
Answer:
$16,974.50
Step-by-step explanation:
$14,382.50+24% of the amount over $84,200 is ...
$14,382.50 +0.24×(95,000 -84,200) = $14,382.50 +2592.00 = $16,974.50
Mustafa owes $16974.50 in federal income tax.
_____
Additional comment
Each row of the tax table can be simplified by multiplying out the expression it describes. For the row applicable to this problem, that becomes ...
14382.50 +0.24(amount -84200) = 14382.50 +0.24×amount -20208
= 024×amount -5825.50
1/4x-2=-6+5/12x solve the equation for the variable
Answers
Answer:
\(\huge\boxed{x=24}\)
Step-by-step explanation:
\(\dfrac{1}{4}x-2=-6+\dfrac{5}{12}x\qquad|\text{add 2 to both sides}\\\\\dfrac{1}{4}x-2+2=-6+2+\dfrac{5}{12}x\\\\\dfrac{1}{4}x=-4+\dfrac{5}{12}x\qquad|\text{subtract}\ \dfrac{5}{12}x\ \text{from both sides}\\\\\dfrac{1}{4}x-\dfrac{5}{12}x=-4+\dfrac{5}{12}x-\dfrac{5}{12}x\\\\\dfrac{1\cdot3}{4\cdot3}x-\dfrac{5}{12}x=-4\\\\\dfrac{3}{12}x-\dfrac{5}{12}x=-4\\\\\dfrac{3-5}{12}x=-4\\\\\dfrac{-2}{12}x=-4\\\\\dfrac{-2:2}{12:2}x=-4\)
\(-\dfrac{1}{6}x=-4\qquad|\text{multiply both sides by (-6)}\\\\\left(-6\!\!\!\!\diagup\right)\cdot\left(-\dfrac{1}{6\!\!\!\!\diagup}\right)x=(-4)(-6)\\\\x=24\)
Keenan is throwing an Independence Day party he wants to buy sparklers each pack of 12 smugglers cost $3.99 kina needs 120 sparklers that each gas can have two how much will Keenan spend on sparklers?
Answers
Answer:
$478.8
Step-by-step explanation:
1 sparkler costs= $3.99
120 sparklers cost= $3.99 x 120 = $478.8
which is the best estimate of 2/5 + 1/7?
Answers
Answer:
2 / 35
Step-by-step explanation:
evaluate f ( - 5 ) =
Answers
Answer: −5
Step-by-step explanation:
simplify: (−5)
Re-order terms so constants are on the left:
(−5)f(−5)−5
Please answer this correctly without making mistakes
Answers
Answer:
1 pound 3.4 ounces
Step-by-step explanation:
In AJKL, the measure of L=90°, the measure of K=35°, and KL = 48 feet. Find the
length of JK to the nearest tenth of a foot.
Answers
Answer:58.6 trust me
Step-by-step explanation:
I need a help with this hw
Answers
The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5 d ) -25/12
What is trigonometric ratio?
Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent. Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse
the give parameters are:
tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2
a) sin(α+β)
Using the trig ratios tan = opp/adj
but from pyth. rule, 4² + 3² = h²
16+9 = h²
h = √25 = 5
Now from trig Sin(α+β)
4/5 + 3/5
=- 7/5
b) cos(α+β)
cos = ad/hypo
4/5 + 3/5
= -7/5
c) Sin(α-β)
4/5 - 3/5
-1/5
d) tan(α-β)
= -4/3 - 3/4
= (-16 - 9)/ 12
-25/12
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