The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
x² + 14x − 24 = 4x
Simplify the equation, then we have
x² + 14x − 24 = 4x
x² + 10x − 24 = 0
Factorize the equation, then we have
x² + 10x − 24 = 0
x² + 12x − 2x − 24 = 0
x(x − 12) − 2(x − 12) = 0
(x − 2)(x − 12) = 0
x = 2, 12
The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.
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Casho has a points card for a movie theater. She receives 55 rewards points just for signing up. She earns 2.5 points for each visit to the movie theater. She needs at least 90 points for a free movie ticket. Use the drop-down menu below to write an inequality representing v, the number of visits she needs to make in order to get a free movie ticket.
Answer: She need 14 visits to reach 90 points
Step-by-step explanation:
Let y be the number of points and v be the number of visits
We will have an equation
y= 2.5v + 55
Now we want to find the number of visits she needs to reach 90 points; we put 90 in the y.
90 = 2.5v +55
Subtracted 55 from both sides
35 = 2.5v
Divided both sides by 2.5
v= 14 visits
So she need 14 visits to reach 90 points
what is the probability that the number of systems sold is within 1 standard deviation of its mean value?
The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.
Explain the term Discrete Variable?The term "discrete variable" refers to a variable that has a finite range of possible values. such as using only integer numbers. For instance, the total number of students in a class, the quantity of faulty goods in a batch, etc.The given data is
x 1 2 3 4 5 6 7 8
p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01
(a) calculate mean value of x:
μ = E(x)
= ∑(xi.P(xi))
= 4.13
(b) calculate variance of x:
σ² = ∑(xi - E(x))².P(xi)
= 1.81331
(c) calculate standard deviation of x:
σ = √σ²
σ = √1.831
σ = 1.3539
The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:
P(μ - σ < x < μ + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)
= P(2.7761 < x < 5.4839)
= P(x = 3) + P(x = 4) + P(x = 5)
= 0.13 + 0.30 + 0.31
= 0.74
Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.
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The complete question is-
Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.
x 1 2 3 4 5 6 7 8
p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01
What is the probability that the number of systems sold is within 1 standard deviation of its mean value?
g. 390, 702 and 468 lcm of the following
Answer:
7020
Step-by-step explanation:
2÷390,702,468
2÷195,351,234
3÷
4. Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest
compounded daily. What is the annual percentage yield?
The annual percentage yield is 4.835%. Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest compounded daily.
Define annual percentage.An annual percentage rate, or APR, is a figure that expresses the entire cost of borrowing money as a proportion of the loan's principle. An accurate picture of how much it costs to borrow money is intended to be provided by the APR on a loan or credit card.
Given
Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest
compounded daily.
1.048353
The table on page A14 shows the cost per $1.00 (over the course of a year).
$35,000×1.048353=$36,692.36
The sum of the initial principle and the amount per $1.00 is the amount (for a year).
$36,692.36−$35,000=$1,692.36
The difference between the amount (for one year) and the initial principal is the interest (for one year).
$1,692.36÷$35,000
=0.04835
=4.835%
The interest (for a year) divided by the initial principle results in the annual percentage yield.
4.835%
The annual percentage yield is 4.835%. Mabel Causino has $35,000 to invest in a certificate of deposit for 4 years. The CD earns 4.75% interest compounded daily.
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Rewrite -cot^2x/ 1+ cscx so its not in fraction form.
Rewriting the given trigonometric form using trigonometric identities by eliminating fraction form gives [tex]-cotx.cosx.(sinx+1)[/tex]
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.
The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.
Calculation:We know that,
[tex]cot^{2} x = \frac{cos^{2}x }{sin^{2}x }[/tex]
[tex]1+cscx = (1+\frac{1}{sinx} ) = \frac{sinx+1}{sinx}[/tex]
Rewriting the given trigonometric form using trigonometric identities by eliminating the fraction form gives[tex]-cotx.cosx.(sinx+1)[/tex]
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-2x² + 41=0
Solve quadratic formula
Answer:
Step-by-step explanation:
A landscaper has 6 pounds of seed available. He uses of a pound of grass seed for each acre he plants. Determine how many whole acres can be planted with the available seed.
Answer: Only 1 pound.
Step-by-step explanation: It saying it Infront of ya as it said "1 pound fills each acre each".
A manufacturing company produces 380 units per day currently. The company's goal is to increase the number of units manufactured per day by 30 each year. If the company meets its goal, how many units will it be producing per day 4 years from now?
Answer:
500
Step-by-step explanation:
You want to know the rate in 4 years if it is 380 units per day, and increasing by 30 units per day per year.
RateThe rate in 4 years will be the sum of the current rate and the amount of increase. The amount of increase is the rate of increase, multiplied by time:
amount of increase = (30 units/day)/year × (4 years) = 120 units/day
Then the rate in 4 years will be ...
new rate = current rate + increase
new rate = 380 units/day + 120 units/day = 500 units/day
The company will be producing 500 units per day in 4 years.
For the function defined by f (x) = startfraction 12 over x squared endfraction, what is the constant of proportionality? a. 120 c. 12 b. Undefined d. 1200.
The correct option c. 12, is the constant of proportionality.
Define the term constant of proportionality?The ratio between two quantities that are directly proportional is the constant of proportionality.
When two quantities grow and shrink at the same rate, they are directly proportional. When y and x are two values that really are directly proportional to one another, the proportionality constant k is defined as k=y/x.For the stated question-
f (x) = startfraction 12 over x squared endfraction
Rewrite the function as;
f(x)=12/x^2,
Constant of proportionality = 12 (only fixed term in the function)
Thus, the constant of proportionality for the function f(x)=12/x^2, is found as 12.
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Mia' plant grow at an average rate of 5cm each month. When he bought it, it wa 18 cm tall. Select the function that model the relationhip between y, the height of the plant in cm, and x, the time in month that it grow. A. Y = 18x 5
B. Y = 18 5x
C. Y = x 18
D. Y = 23x
The function that models the relationship between plant height (y) and growth time (x) is y = 18 + 5x
The linear equation of two variables
The two-variable linear equation is a solving system for a mathematical problem in which there are two case variables.
In the problem, we get the info that the plant's initial height is 18 cm, meaning this value will not change.
We also get information that the height of the plants increases by 5 cm every month, meaning this value will change over time. If x is the growth time (in months), then the increase in height over time can be written mathematically as 5x.
Based on the two statements above, if y is the plant height (in cm) after x months, then mathematically it can be written as:
y = 18 + 5x
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The point F( – 4, – 1) i rotated 270° counterclockwie around the origin. What are the coordinate of the reulting point, F'?
The point F( – 4, – 1) i rotated 270° counterclockwie around the origin. then The coordinates of the point F' is (-1 ,4 )
Given that the point J(-2,1) is rotated about 270° about the origin.
Coordinates of the resulting point F':
Since, we know that, when rotating a point 270° counterclockwise about the origin, the point (x,y) becomes (y,-x) which means we switch the places of x and y coordinates and make x as negative.
Therefore, the transformation is given by
(x ,y) -> ( y , -x)
Using the above transformation, we have,
(-4 ,-1) ⇒ ( -1 , -(-4)) ⇒ (-1 , 4)
Therefore, the resulting point of the coordinates of the point F' is (-1 ,4)
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Why is it even? There is 3 arrays in total.
Answer: welp what is inside of the arrays
Step-by-step explanation:
7. 20,000 pounds equals how many us tons? a. 2,000 tons b. 10 tons c. 10,000 tons d. 1 ton
20,000 pounds equals to 10 US ton.
Pound is the name of a type of currency. It was used in many different countries both in the past and at the present time. The Latin expression libra pond, in which pond is an adverb meaning "by weight" and libra is a noun meaning "pound," is where the English term "pound" comes from. US Mass is measured in tons, which is one ton. In the United States, where it is frequently used, it is referred to as a common ton.Value conversion from Pound to US Ton
Add the value and the conversion ratio together.
1 pound = 0.0005 US ton
20,000 pounds worth
20,000 pounds × value of one US ton
20,000 × 0.0005
10 tons
Therefore, 20,000 pounds equals to 10 US ton.
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is 65% grater or less than 3/ 5
Answer:
Greater than
Step-by-step explanation:
65% =65/100=6.5/10=3.25/5
Answer 1+13-b
I just built diff
A family member has two and one fifth yds of ribbon, and you add two thirds yds to it. How much ribbon would you each get if you split the total amount in half?
forty three over fifteen
thirty four over fifteen
forty three over thirty
twenty two over thirty
Answer:
C) forty three over thirty----------------------------------------------------
Add up the two numbers:
two and one fifth + two thirds = 2 1/5 + 2/3 = 11/5 + 2/3 = Covert mixed number to fraction3*11/(3*5) + 5*2/(5*3) = Common denominator is 3*5 = 1533/15 + 10/15 = Add up fractions43/15 SumSplit this in half:
43/15 : 2 = 43/30This is matching the third option.
Can someone please help me with this problem?
Answer: 18/9 if not it's something along that-
Step-by-step explanation:
7^2 = 49 so like 49-31 equals 18 and the denominator 3^2 = 9 , so if it's not 18/9 then it's like 1/2 or something bc 9 + 9 is 18 yk-
Please I need help, please answer the question in the image, please and thank you.
The rate of change of the given data between 3 and 7 hours is; 19 miles per hour
How to calculate the rate of change?We are told that rate of change is the difference between what the value of the data began at versus the value the data ended at.
Now, the formula for the rate of change between two coordinates (x₁, y₁) and (x₂, y₂) is;
Rate of change = (y₂ - y₁)/(x₂ - x₁)
Now, we are told that we should find the rate of change from 3 to 7 hours and so we first write the coordinates;
(3, 209) and (7, 285)
Thus;
Rate of change = (285 - 209)/(7 - 3)
Rate of change = 76/4
Rate of change = 19 miles per hour
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The ratio of red marble to blue marble in a bag i 3:4. If there are 42 marble in the bag how many of the marble are red
The ratio of red marble to blue marble in a bag is 3:4. If there are 42 marble in the bag,There would be 30 red marbles in the bag.
Red and blue marbles are distributed in a 3:4 ratio.This means that for every 4 blue marbles, there are 3 red marbles.
If we divide 42 (the total number of marbles in the bag) by 4, we get 10.5. This tells us that if there are 4 blue marbles, there are 10.5 red marbles. We can't have a fraction of a marble, so we round down to 10.
Since for every 4 blue marbles there are 3 red marbles, if there are 10 blue marbles, there must be 10 x 3 = 30 red marbles.
Therefore, there are 30 red marbles in the bag.
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Please quick I’ll give brainliest
one segment measures 161 cm. Calculate its multiple according to the number 3 and its submultiple according to the number 7
Multiple according to the number 3 is 162 and its submultiple according to the number 7 is 7.
What is called multiplication?
Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes.
Given that :
One segment measures 161 cm
To find the multiple according to the number 3, divide 161 by 3.
161 ÷ 3 = 53.67
Nearest integer of 53.67 is 54
The multiple according to the number 3 = 54 × 3
= 162
To find the submultiple according to the number 7, divide 161 by 7.
161 ÷7 = 23
Nearest integer of 23 is 23
The submultiple according to the number 7 = 161 ÷ 23
= 7
Multiple according to the number 3 is 162 and its submultiple according to the number 7 is 7.
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Find the 5 times the difference of 22 and 16 added to 5 multiplied by the sum of 10 and 8.
Answer:
120
Step-by-step explanation:
5(22-16) + 5(10+8)
5(6) + 5(18)
30 + 90
120
A model rocket is launched with an initial upward velocity of 35 m/s. The rocket's height h (in meters) after t seconds is given by the followi
h=35t-5t
Find all values of 1 for which the rocket's height is 12 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
h
-ground
t= seconds
Dor
X
S
Answer:
The possible values of t for which the rocket's height is 12 meters are approximately 1.1 or -1.1.
Step-by-step explanation:
The height of the rocket after t seconds is given by the equation12 = 35t - 5t^2
t = (-b ± √(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. In this case, a = -5, b = 35, and c = -12.Plugging these values into the quadratic formula, we gett = (35 ± √(35^2 - 4(-5)(-12))) / 2(-5)
t = (35 ± √(35^2 + 240)) / -10
t = (35 ± √575) / -10
This gives us two possible values fort = (35 + √575) / -10 = (35 + 24) / -10 = 11/10 = 1.1
t = (35 - √575) / -10 = (35 - 24) / -10 = -11/10 = -1.1
Therefore, the rocket's height is 12 meters when t is approximately 1.1 or -1.1.The rocket's height is 12 meters at time t = 0.4 seconds.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
A model rocket is launched with an initial upward velocity of 35 m/s.
The rocket's height h (in meters) after t seconds is h=35t-5t
We have to find the time(s) when the rocket's height is 12 meters, we need to solve the equation:
h = 35t - 5t = 30t
We want to find all values of t that make h = 12. So we set h = 12 and solve for t:
12 = 30t
Divide both sides by 30
t = 12/30
t = 0.4
Therefore, the rocket's height is 12 meters at time t = 0.4 seconds.
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Samuel and Joyce both bought CDs. Samuel bought 3x CDs and Joyce bought 2x-1 CDs.
¿Drive
mS
amS
Part A: If each CD had a regular price of $18 and a discount of $2, then which expression would show the amount of discount for all of their CDs?
Part B: What is the expression for the COST of their CDs, combined (ignore tax)?
Step-by-step explanation:
Part A: 3(-2) + 2(-2)
Part B: [3(8) + 2(18) - 1] - [3 + 2(-2)]
Price Discount
ANSWER ASAP
L=M-N solve for N
1. N=M - L
2. N= LM
3. N= M + L
4. N= L - M
Answer:
1) N = M - L
Step-by-step explanation:
Given equation,
→ L = M - N
Now the value of N will be,
→ L = M - N
→ M - N = L
→ -N = L - M
→ N = -L + M
→ [ N = M - L ]
Hence, value of N is M - L.
Write an equation of the line that passes through (-2, 4) and is perpendicular to y = -2x + 4
Answer:
y=-2x
Step-by-step explanation:
Julia decided to pend 5 1/4 hour exerciing over the weekend. She pent 3 1/3 hour exerciing on Saturday. How much longer doe he need to pend exerciing on Sunday in order to reach her goal?
Julia needs to spend 1.92 hours exercising on Sunday in order to reach her goal.
The number of hours Julia needs to spend exercising on Sunday can be calculated as follows;
Total number of hours to spend exercising = 5 1/4 = 21/4 = 5.25 hours
Total number of hours spent exercising on Saturday = 3 1/3 = 10/3 = 3.33 hours
Now the number of hours she needs to spend exercising on Sunday can be determined by subtraction as follows;
Hours on Sunday = Total hours - Hours on Saturday
Hours on Sunday = 5.25 hours - 3.33 hours
Hours on Sunday = 1.92 Hours
Thus the number of hours she needs to spend exercising on Sunday is calculated to be 1.92 hours.
Although a part of your question is incorrect, you might be referring to this question:
Julia decided to spend 5 1/4 hours exercising over the weekend. She spent 3 1/3 hours exercising on Saturday. How much longer doe he need to spend exercising on Sunday in order to reach her goal?
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sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.
Answer:
Step-by-step explanation:Sketch the curve with equation x^(2/3) + y^(2/3) = 1 and usesymmetry to find its length.
Latanya needs to order some new supplies for the restaurant where she works. The restaurant needs at least 739 glasses. There are currently 390 glasses. If each set on sale contains 6 glasses, which inequality can be used to determine xx, the minimum number of sets of glasses Latanya should buy?
The solution to this inequality is x >= 58. This means that Latanya should buy at least 58 sets of glasses in order to have at least 739 glasses.
What is the inequality equation?
Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤, or ≥.
To determine the minimum number of sets of glasses that Latanya should buy, we can set up the following inequality:
x * 6 + 390 >= 739
This inequality states that the number of glasses Latanya has after buying x sets of glasses should be greater than or equal to the minimum number of glasses the restaurant needs.
To solve for x, we can subtract 390 from both sides of the inequality to get:
x * 6 >= 739 - 390
x * 6 >= 349
x >= 349/6
x >= 58.16
x >= 58
Hence, The solution to this inequality is x >= 58. This means that Latanya should buy at least 58 sets of glasses in order to have at least 739 glasses.
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What is the equation of the line that passes through the point (8, 6) and has a slope
of o?
Answer:
y=6
Step-by-step explanation:
The equation of a line in slope-intercept form is given by:
y = mx + b
where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis. In this case, we are given that the line passes through the point (8, 6) and has a slope of 0, so we can plug these values into the equation to find the equation of the line.
Since the slope of the line is 0, the equation of the line becomes:
y = 0x + b
To find the value of b, we need to plug in the coordinates of the point (8, 6) into the equation and solve for b. This gives us:
6 = 0 * 8 + b
b = 6
Therefore, the equation of the line is given by:
y = 0x + 6
This equation tells us that the y-coordinate of any point on the line is always 6, regardless of the x-coordinate of the point. This means that the line is horizontal and passes through the point (8, 6).
A student takes an exam. The ratio of her right answers to her wrong answers is 11 to 3. Which of the following could describe this situation?
Answer:
She answered 9 wrong and 33 right.
Step-by-step explanation:
Choices:
She answered 9 wrong and 33 right.
She answered 33 wrong and 9 right.
She answers 14 wrong and 22 right.
She answered 22 wrong and 14 right.
11:3 = 22:6 = 33:9 = 44:12 = 55:15 = 66:18 = 77:21 = 88:24 = ...
33 right 9 wrong works.
Answer: She answered 9 wrong and 33 right.
There are 10 finalists in a figure skating competition. How many ways can gold, silver, and bronze medals be awarded?
Answer:
720
Step-by-step explanation:
[tex]\frac{n!}{(n-r)!}[/tex]
[tex]\frac{10!}{(10-3)!}[/tex]
[tex]\frac{10!}{7!}[/tex]
720