For this case we have that by definition, the discriminant of a quadratic equation [tex]ax ^ 2 + bx + c = 0[/tex], is given by:
[tex]d = b ^ 2-4 (a) (c)[/tex]
[tex]d> 0[/tex]: Two different real roots
[tex]d = 0[/tex]: Two equal real roots
[tex]d <0[/tex]: Two different complex roots
If we have [tex]9x ^ 2 + 12x + 4 = 0[/tex], then:
[tex]a = 9\\b = 12\\c = 4[/tex]
Substituting the values:
[tex]d = 12 ^ 2-4 (9) (4)\\d = 144-144\\d = 0[/tex]
Thus, we have two equal real roots.
ANswer:
We have two equal real roots.
5x - 1= 3х + 9
Find x
Answer:
X=5
Step-by-step explanation:
[tex]5x - 1 = 3x + 9 \\ 5x - 3x = 9 + 1 \\ 2x = 10 \\ x = 5[/tex]
5x-1=3x+9
collect like terms
5x-3x=9+1
2x=10
divide both sides by 2
x=5
What is square root of 42 to the nearest tenth
Answer: 6.48 or 6.5 rounded up!
Step-by-step explanation: hope i can help please give brainliest!
just try my answer its
6.48 or 6.5 rounded up!
What is the slope of the line that passes through the points (4, -2) and (24, -17)?
Write your answer in simplest form.
Order the numbers from least to greatest 3\7,0.44,42%
Answer:
42%, 3/7, .44
Step-by-step explanation:
what i would do is turn them all into decimals
3/7 is .4285
.44 is already a decimal
42% is .42
In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. Circle D is shown. Points A, B, and C are on the circle. Point C is on the opposite side of points A and C. LInes are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. Angle A D C measures (7 x + 2) degrees. Arc A C measures (8 x minus 8) degrees. What is the measure of Angle A B C ? 36° 43° 72° 144°
Answer:
In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°.
Circle D is shown. Points A, B, and C are on the circle. Point C is on the opposite side of points A and C. LInes are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. Angle A D C measures (7 x + 2) degrees. Arc A C measures (8 x minus 8) degrees.
What is the measure of Angle A B C ?
36° *****
43°
72°
144°
Step-by-step explanation:
its 36°
Applying the central angle theorem, the measure of angle ABC is: a. 36°
What is the Central Angle Theorem?The central angle theorem states that the angle measure of a central angle equals the measure of the intercepted arc.Inscribed angle = half the intercepted arc.Given:
m∠ADC = (7x + 2)° (central angle)
measure of intercepted arc AC = (8x - 8)°
Therefore:
(7x + 2)° = (8x - 8)°
Solve for x7x + 2 = 8x - 8
8 + 2 = 8x - 7x
10 = x
x = 10
Thus:
m∠ABC is an inscribed angle = half of measure of intercepted arc AC
Therefore:m∠ABC = 1/2(8x - 8)°
Plug in the value of xm∠ABC = 1/2[8(10) - 8]
m∠ABC = 36°
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The manufacturer of cell phones spends $320 to make each cell phone and sells them for 440 . The manufacturer also has fixed costs each month of $11400 .
Answer:
x=95
Step-by-step explanation:
320x+11400=440x
320*95+11400=440*95
30,400+11,400=41,800
41,800=41,800
The manufacturer needs to sell approximately 95 cell phones to cover its fixed costs of $11,400 per month. The profit per month depends on the number of units sold, with a contribution margin of $120 per unit after covering variable costs.
To analyze the manufacturer's costs and profitability, we can break down the information provided:Cost to Make Each Cell Phone: $320 per unitSelling Price of Each Cell Phone: $440 per unitFixed Costs: $11,400 per monthFirst, let's calculate the variable cost per unit, which is the cost to make each cell phone:Variable Cost per Unit = Cost to Make Each Cell Phone = $320Now, we can calculate the contribution margin per unit, which is the amount each phone contributes to covering fixed costs and generating profit:Contribution Margin per Unit = Selling Price - Variable Cost per UnitContribution Margin per Unit = $440 - $320 = $120Next, calculate the break-even point in units, which is the number of units the manufacturer needs to sell to cover its fixed costs:Break-Even Point (in units) = Fixed Costs / Contribution Margin per UnitBreak-Even Point (in units) = $11,400 / $120 ≈ 95 unitsSo, the manufacturer needs to sell approximately 95 cell phones to cover its fixed costs.To determine the profit, we can calculate the profit per month after covering fixed costs:Profit per Month = (Selling Price - Variable Cost per Unit) * Number of Units Sold - Fixed CostsSuppose the manufacturer sells "X" cell phones per month. Then:Profit per Month = ($440 - $320) * X - $11,400Now, you can calculate the profit for any given number of cell phones sold.For more questions on profit -
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Serenity Spa charges $59 for a one hour massage. They charge $0.95 per minute for each additional minute over an hour. If
x represents the number of minutes over one hour, which of the following functions represents the cost of a massage?
Answer:
D. y = 0.8x + 79
Choices:
A.
y = 79x + 0.8
B.
y = -0.8x + 79
C.
y = 79.8x
D.
y = 0.8x + 79
The following functions represent the cost of a massage as: Cost = 59 + 0.95x
What is the Linear function?A linear function is defined as an equation in which the highest exponent of the variable is always one.
A one-hour massage at Serenity Spa costs $59 USD. They charge $0.95 per minute for every minute over an hour.
The cost of a massage can be represented by the function:
Cost = 59 + 0.95x
This function states that the cost of the massage is equal to the base cost of $59 plus an additional charge of $0.95 for each minute over an hour (represented by the variable x).
For example, if the massage lasts for 70 minutes (10 minutes over an hour), the cost would be calculated as:
Cost = 59 + 0.95(10) = 59 + 9.5 = $68.50
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I need help with this question
The answers are 15 guests, 7 tables, 24 guests, and 10 tables respectively.
Step-by-step explanation:
Step 1: Find relation between the number of tables and guests. Given that for every 6 guests, Maya uses 2 tables.2 tables ⇒ 6 guests
1 table ⇒ 6/2 = 3 guests
Step 2: Find number of guests for 5 tables.5 tables = 5 × 3 = 15 guests
Step 3: Find number of tables for 21 guests.Number of tables = 21/3 = 7 tables
Step 4: Find number of guests for 8 tables.Number of guests = 8 × 3 = 24 guests
Step 5: Find number of tables for 30 guests.Number of tables = 30/3 = 10 tables
What is the justification for step 1 in the solution process?
8x + 15 = 11x + 2
Step 1: 8x = 11x − 13
A.
the division property of equality
B.
the addition property of equality
C.
the subtraction property of equality
D.
the multiplication property of equality
Answer:
C.
the subtraction property of equality
Step-by-step explanation:
Given
8x + 15 = 11x + 2
Subtract 15 from both sides of the equation
8x + 15 - 15 = 11x + 2 - 15
8x = 11x - 13
Answer:
the addition property of equality
Step-by-step explanation:
Compare step 1 with step 2 in the solution process:
step 1: -5x = -4x - 15
step 2: -x = -15
The variable was isolated on the left side of the equation by adding 4x to both sides. This is justified by the addition property of equality.
i was watching mineHUB in lesson and the Bluetooth was not on and everyone heard what should i do i have been sent out of class
Answer:
act like you dont care next time keep the volume down
Step-by-step explanation:
a store had three baskets with an equal number of flower bouquets in each. customers purchased 8 bouquets from each basket, and there are now a total of 18 bouquets left. Write and solve an equation to find how many bouquets of flowers were initially in each basket.
Answer:
8
Step-by-step explanation:
18+8=26
26 / 3 = 8
8
hope this helped!
~ angilina
PLS HELP
What is the volume of the right rectangular prism shown?
A. 8 un3
B. 20 un3
C. 24 un3
D. 12 un3
Answer:
12 UN 3
Step-by-step explanation:
ok i hope this is right answer
there i s 15 boys and 13 girls what is the probability that she will pick a boy
Answer:
54% or 15/28
Step-by-step explanation:
You find the sum of 15 and 13 to get 28. 15/28 = 53.5 If you round you get 54%.
Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value
of the function.
fx) = x2 - 6x + 5
Answer:
(3,-4)
Step-by-step explanation:
minimum is shown if you were to graph it,
i dont really know how else to explain it, its sorta self explanatory.. :)
Answer:
Since the leading coefficient of x^2 is positive. Therefore, it is a minimum.
The value of the minimum is: (3, -4)
Identify the vertex of each graph. Tell whether it is a minimum or a maximum.
Answer: Minimum
Step-by-step explanation:
Answer:1,-6 minimum
Step-by-step explanation:Minimum vertex will look like a smiley face and a maximum will look somewhat like a frown. As for the vertex just follow the lines the x and y are on.
y = x -5x + 1 y= 3x - 2
is ( 3 , 8 ) a solution of the system ?
Find the surface area of a rectangular prism with base 4 m by 5 m and height 8 m.
Answer:
Step-by-step explanation:
surface area=area of sides +area of top and bottom
=2(4+5)×8+2×(4×5)
=2[(9×8)+20]
=2[72+20]
=2×92
=184 m²
The total surface area of the given rectangular prism is square meters.
How to calculate the surface area of a rectangular prism?The surface area of a rectangular prism can be calculated by adding the areas of all its faces.
Given that a rectangular prism with a base 4 m by 5 m and a height 8 m,
The surface area can be calculated as follows:
The surface area = area of sides + area of top and bottom
The surface area = 2(4+5)×8+2×(4×5)
The surface area = 2[(9×8)+20]
The surface area = 2[72+20]
The surface area = 2 × 92
The surface area = 184 m²
Therefore, the total surface area of the rectangular prism is 184 square meters.
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Original Price: $125
Discount: ?
Sale Price: $81.25
Answer:
The discount is 43.75 dollars.
Step-by-step explanation:
125 - 81.25 = 43.75
Final answer:
The discount percentage applied to reduce the original price of $125 to the sale price of $81.25 is 35%.
Explanation:
A student is trying to find out the discount percentage that was applied to an item originally priced at $125 to have a final sale price of $81.25. To calculate the discount, one can use the formula: Discount percentage = ((Original Price - Sale Price) / Original Price) imes 100%. Applying this to the given values: ($125 - $81.25) / $125 imes 100% = $43.75 / $125 imes 100% = 35%. Thus, the discount percentage applied is 35%.
Jake swims a distance from one end of a 50 meter pool to the other end in 25 seconds. What is his average speed?
Answer:
2 meters/ second
Step-by-step explanation:
Speed is equal to distance divided by time
Speed = 50 meters / 25 seconds
= 2 meters/ second
need help with 3x48 and 48x3
Answer:
144
Step-by-step explanation:
48×3= 144
48×3=144
to make it easier just add the number being multiplied the amount of times its being multiplied.
48+48+48=144
Both 3x48 and 48x3 yield the same result, which is 144, because multiplication is commutative.
Both expressions involve multiplying the numbers 3 and 48.
In the first expression, 3x48 means you're multiplying 3 by 48. This gives you 144, because 3 times 48 equals 144.
In the second expression, 48x3 means you're multiplying 48 by 3. This also gives you 144, because multiplication is commutative, which means the order of the numbers doesn't change the result. So, whether you multiply 3 by 48 or 48 by 3, you'll always get the same answer, which is 144.
So, to summarize:
3x48 = 144
48x3 = 144
Both expressions result in the same value of 144.
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5. A standard-size volleyball court has an
area of 1,800 square feet. The length of the
court is 60 feet. What is the width of the
court?
Answer: The width of the court is 30 feet.
Step-by-step explanation:
We know that the area of a rectangle is given by :-
Area = length x width (1)
Given : A standard-size volleyball court has an area of 1,800 square feet.
The length of the court is 60 feet.
To find : The width of the court.
According to (1) , we have
[tex]1800 = 60\times \text{width}[/tex]
Then,
[tex]\text{Width}=\dfrac{1800}{60}=30[/tex]
Hence, the width of the court is 30 feet.
Final answer:
The width of a standard-size volleyball court, with an area of 1,800 square feet and a length of 60 feet, is calculated to be 30 feet using the formula for the area of a rectangle.
Explanation:
To find the width of a standard-size volleyball court with an area of 1,800 square feet and a length of 60 feet, we need to use the formula for the area of a rectangle, which is Area = length × width. Since we know the area and the length, we can solve for the width.
Let the width be w feet.
Then, 1,800 sq ft = 60 ft × w ft,
So, w = 1,800 sq ft / 60 ft,
Therefore, w = 30 feet.
The width of the volleyball court is 30 feet.
Three persons EB and C work together on a job and finish it finish it in 18 days if E and be working together can finish the job in 45 days find how long C working alone would take to complete it
Answer: 30 days
Step-by-step explanation:
Working together, E & B get 1/45 of the job done per day
Working alone, C gets 1/x of the job done per day
Working together, E, B, & C get 1/18 of the job done per day.
[tex]EB:\dfrac{1}{45}\qquad C: \dfrac{1}{x}\qquad EBC:\dfrac{1}{18}\\\\\\\\EB+C=EBC\\\\ \dfrac{1}{45}\ +\dfrac{1}{x}=\dfrac{1}{18}\\\\\\(45\cdot 18\cdot x)\bigg(\dfrac{1}{45}+\dfrac{1}{x}=\dfrac{1}{18}\bigg)\\\\\\.\qquad \qquad 18x+810=45x\\\\.\qquad \qquad \qquad 810=27x\\\\.\qquad\qquad \qquad \large\boxed{30=x}[/tex]
a line goes through the points. (3,-5) and (5,-1)
Answer:
9+10 equals 21
Step-by-step explanation:
Just bc im big brain
how to write 137% as a fraction and decimal
Answer: 1.37 and 137/100
Step-by-step explanation:
hope this help make me brainliest plest thanks
Final answer:
137% can be written as the fraction 137/100, which is already simplified. To convert 137% to a decimal, divide 137 by 100 to get the decimal 1.37.
Explanation:
To write 137% as a fraction, you should consider that percent means 'per hundred.' Therefore, 137% can be written as a fraction with a denominator of 100: 137/100, which is already in its simplest form.
To express 137% as a decimal, you divide the numerator by the denominator. In this case, you would divide 137 by 100. This gives you the decimal 1.37, which is the decimal equivalent of 137%.
Understanding these conversions is crucial when working with percentages, and they can often simplify calculations in various mathematical problems.
If gasoline costs $47.86 for 12.5 gallons of gasoline, how much does it cost for 8 gallons?
Round your answer to the nearest cent.
Answer:
8 gallons of gasoline costs $30.63.
Step-by-step explanation:
Set up a proportion to solve for x, or the cost of 8 gallons of gasoline. The $47.86 goes on top of the first ratio, and 12.5 goes on top of the second. This is because the $47.86 is the cost of the 12.5 gallons of gasoline. Next, put x on the bottom of the first ratio and 8 on the bottom of the second ratio. This is because the amount of money you are trying to find, x, is the cost of the 8 gallons of gasoline. The proportion should look like this: [tex]\frac{47.86}{x} = \frac{12.5}{8}[/tex]
To solve the proportion, use cross multiplication. To do that, multiply 8 by 47.86 to get 382.88. Then, divide 382.88 by 12.5. The answer is 30.6304, so round to the nearest cent to get a total of $30.63.
I hope this helps! ☺
Kiran and 3 of his friends are going to split the lunch bill of $24.48 how much will each person pay
To split a $24.48 lunch bill between Kiran and 3 friends ,,divide the total by 4, resulting in each person paying $6.12.
Kiran and 3 of his friends want to split the lunch bill of $24.48 evenly. Since there are 4 people in total, we simply divide the total bill by 4 to find out how much each person will pay. Here's the step-by-step calculation:
Find the total number of people: 1 (Kiran) + 3 friends = 4 people.Divide the total bill by the number of people: $24.48 ÷ 4.Perform the division to find the amount per person: $24.48 ÷ 4 = $6.12.Therefore, each person will pay $6.12 to split the lunch bill of $24.48 equally.
1 3/4+z= 2 2/3
Wat is z
Answer:
11/12 is Z
Step-by-step explanation:
Do you need the explanation?
The required value of z is 11/12 in the given equation.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The equation is given in the question as:
1 3/4 + z = 2 2/3
We have to determine the value of z in the given equation,
As per the question, we have
⇒ 1 3/4 + z = 2 2/3
Convert the mixed numbers into fractions,
⇒ 7/4 + z = 8/3
Rearrange the terms in the above equation,
⇒ z = 8/3 - 7/4
Take LCM in the term of fractions,
⇒ z = (32 - 21)/12
⇒ z = 11/12
Therefore, the required value of z is 11/12 in the given equation.
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Solve the equation log (x + 20) = 3
Answer:
Step-by-step explanation:
[tex](x+20)=3\\ -20 -20\\x=-17[/tex]
Hope this helps please give brainliest!
**A rock dropped from a 100 foot tower.
The height of the rock as a function of time
can be modeled by the equation: h(t) =
- 16t2 + 10t + 100. How long does it take
for the rock to reach the ground?
Final answer:
The rock takes approximately 2.032 seconds to reach the ground.
Explanation:
The height of the rock can be modeled by the equation h(t) = -16t² + 10t + 100, where h(t) is the height of the rock and t is the time in seconds. To find the time it takes for the rock to reach the ground, we need to solve the equation when h(t) is equal to zero. We can do this by setting the equation equal to zero and using the quadratic formula.
Using the quadratic formula, we get: [tex]t = (-b \± \sqrt(b^2 - 4ac))/(2a)[/tex]
Plugging in the values of a, b, and c from the equation, we get: [tex]t = (-10 \± \sqrt{10^2 - 4(-16)(100)/2(-16)[/tex]
Simplifying, we get: [tex]t = (-10 \± \sqrt{100 + 6400/(-32)[/tex]
Continuing to simplify, we get: [tex]t = (-10 \± \sqrt{6500/(-32)}[/tex]
So, it takes approximately 2.032 seconds for the rock to reach the ground.
Please answer ASAP! Due today, thank you in advance and remember to wash your hands with antibacterial soap for 1 minute.
Answer:
1/2x15(30+40)
Step-by-step explanation:
Just put this in your calculator