Answer:
[tex]\displaystyle p > \frac{1}{4}[/tex].
Step-by-step explanation:
Expand the left-hand side of this equation:
[tex]p\, (x + 1)\, (x - 3) = p\, \left(x^2 - 2\, x - 3\right) = p\, x^2 - 2\, p\, x - 3\, p[/tex].
Collect the terms, so that this quadratic equation is in the form [tex]a\, x^2 + b\, x+ c = 0[/tex]:
[tex]p\, x^2 - 2\, p\, x - 3\, p = x - 4\, p - 2[/tex].
[tex]p\, x^2 - (2\, p + 1)\, x + (p + 2) = 0[/tex].
In this equation:
[tex]a = p[/tex].[tex]b = -(2\, p + 1)[/tex].[tex]c = p + 2[/tex].Calculate the quadratic discriminant of this quadratic equation:
[tex]\begin{aligned}b^2 - 4\, a\, c &= (-(2\, p + 1))^2 - 4\, p\, (p + 2) \\ &= 4\, p^2 + 4\, p + 1 - 4\, p^2- 8\, p = -4\, p + 1\end{aligned}[/tex].
A quadratic equation has no real root if its quadratic discriminant is less then zero. As a result, this quadratic equation will have no real root when [tex]-4\, p + 1 < 0[/tex]. Solve for the range of [tex]p[/tex]:
[tex]\displaystyle p > \frac{1}{4}[/tex].
Please help very easy.
Write an equation for "there are 20 more chickens than rabbits and together there are 256"
Answer:
20+r +r = 256
Step-by-step explanation:
Let r = rabbits
c = chickens
c = 20 +r since there are 20 more chickens than rabbits
Together there are 256
c+r = 256
Replacing c with 20+r
20+r +r = 256
Please help I don’t understand this
Answer: 25 hours
Step-by-step explanation:
Let r = rate, t = time
From 1st sentence,
5r x 12 = 3
60r = 3
r = 3/60 = 1/20
From the next,
4r x t = 5
4 x 1/20 x t = 5
4/20t = 5 = 25
people. Houses Hours
5. 3 12
4. 5. ?
Cross multiply and get the reciprocal
4*3/5*5/12
12/25 *1/12
= 25
a salesperson earns a commission based on the number and type of vechile sold.A person selling 6 cars and 3 trucks earns $4,800.A person selling 8 cars and 1 truck earns $4,600.How much does a salesperson earn for selling 2 cars and 3 trucks?
Answer:
$2800
Step-by-step explanation:
First divide $4800 by 3 which will give you $1600 which is the price for 2 cars and 1 truck.
= [tex]\frac{4800}{3} = $1600[/tex]
Next, subtract the $1600, which is the price of 2 cars and 1 truck from $4600, which is the price of 8 cars and 1 truck giving you the price of 6 cars.
$4600 - $1600 = $3000
Now divide the $3000, the price of six cars, by three to get the price of 2 cars.
[tex]\frac{3000}{3} = $1000[/tex]
Lastly, multiply the $1000 by 2 to get the price of 4 cars. Then subtract this $2000, the price of 4 cars from the $4800, the price of 6 cars and three trucks to give you the price of 2 cars and 3 trucks.
$4800 - $1000 = $2800
To make 100g of jam you need 41g of strawberries, 29g of blackberries and the rest should be sugar. What is the ratio of blackberries to sugar? Give your answer in its simplest form.
Answer:
The ratio is 29:30
Step-by-step explanation:
First, we need to calculate the mass of sugar in the mix
That would be 100-41-29 = 100-70 = 30g
So the ratio of blackberry to sugar would be mass of the blackberry : mass of sugar
From the question, mass of blackberry = 29g while the mass of sugar = 30g
Mass of blackberry to mass of sugar = 29:30
4 cows and 12 horses on the farm there are 6 cows in the other farm how many horses are on the other farm
Answer:
One solution was found :
x = 18
mark me as brainliest
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
4/12-(6/x)=0
Step by step solution :
Step 1 :
6
Simplify —
x
Equation at the end of step 1 :
4 6
—— - — = 0
12 x
Step 2 :
1
Simplify —
3
Equation at the end of step 2 :
1 6
— - — = 0
3 x
If you bike 8 miles south and then 6 miles east, what is the distance you are from your starting point? 10 miles 100 miles 14 miles
Answer:
10 miles
Step-by-step explanation:
Given: Bike goes 8 miles south and then 6 miles east
To find: distance between the final point and the starting point
Solution:
Pythagoras Theorem
In a right angled triangle, square of hypotenuse is equal to the sum of squares of the two sides.
In ΔOAB,
[tex]OB^2=OA^2+AB^2[/tex]
Put [tex]OA=8\,,\,AB=6[/tex]
[tex]OB^2=8^2+6^2=64+36=100[/tex]
Take square root on both sides.
[tex]OB=\sqrt{100}=10\,\,miles[/tex]
So, distance between the final point and the starting point is 10 miles
Answer:
10 miles
Step-by-step explanation:
What is the length of jk
10.) A study recorded the reactions of 186 polar
bears as they were approached by a tundra
buggy. Some bears did not appear to respond,
while others responded by sitting, standing,
walking away, or running away. There were 94
more bears that did not respond than did
respond. How many bears responded and how
many bears did not respond?
the answer is 94 bears reponded and 92 did not II thnk
Please please please help me!
Answer: 37.68 feet.
Step-by-step explanation:
To find the diameter of a circle, use the equation:
C = 2 * pi * r, where r is the radius of the circle.
The diameter is 12 feet, and the radius is 6 feet.
C = 12 * pi
C = 37.68 feet.
Simplify
3m + 2n - (m + n)
Answer:
2m +n
Step-by-step explanation:
3m + 2n - (m + n)
Distribute the minus sign
3m + 2n - m - n
Combine like terms
3m -m +2n -n
2m +n
In a local city, the temperature at noon is Negative 3 degrees Celsius. The temperature is expected to decrease by 2.5 degrees Celsius each hour until the temperature reaches Negative 18 degrees Celsius. How many hours will it take for the temperature to reach Negative 18 degrees Celsius? 6 hours 7 hours 7.2 hours 8.4 hours
Answer:
6
Step-by-step explanation:
It takes 6 hours to reach -18°C. Therefore, option A is the correct answer.
Given that, the temperature at noon=-3°C, every hour temperature decreased by -2.5°C.
How do multiply whole numbers and decimals?Multiplying Decimals has the same procedure as that of multiplication of the whole numbers, except for the placement of the decimal point in the product.
Now, every hour temperature decreases by -2.5°C, we need to find how many hours it takes to -18°C.
So, -2.5×6=-15°C
Then, final temperature=initial temperature+increased temperature.
=-3°C+(-15°C)=-18°C
Therefore, option A is the correct answer.
To learn more about the integers visit:
https://brainly.com/question/15276410.
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Caily bought 5.2 pounds of grapes for $7.75. Using the unit rate, how much would 3 pounds of grapes cost? *
What instruments are used in the song airplanes by B.o.B?
Answer:
Piano, guitars, drum set, and voices
Step-by-step explanation:
Solve the following equation 7a-9=12
7a-9=12
Add 9 to both sides:
7a= 21
Divide both sides by7
A= 3
Answer:
The value of a is 3.
Step-by-step explanation:
First, you have to add 9 to both sides to eliminate -9 on the left side :
[tex]7a - 9 = 12[/tex]
[tex]7a - 9 + 9 = 12 + 9[/tex]
[tex]7a = 21[/tex]
In order, to find a, you have to divide it by 7 :
[tex]a = 21 \div 7[/tex]
[tex]a = 3[/tex]
The bowl of a circular birdbath has an inside diameter of 18 inches, as shown in the drawing below.
When the bowl of the birdbath is full, which of the following is the closest to the area of the top surface of the water? Use 3.14 for π.
1017 square inches
254 square inches
113 square inches
57 square inches
please someone answer.
Answer:
The area of the surface of the water is approximately 254 square inches.
Step-by-step explanation:
When the bowl of the birdbath is full, the top surface area of the water is equal to the area of the circumference that contours the bowl, therefore in order to calculate its area we need to apply the following formula:
[tex]area = \pi*r^2\\r = \frac{d}{2} = \frac{18}{2} = 9 \text{ in}\\area = 3.14159*(9)^2 = 254.46879 \text{ in}^2[/tex]
The area of the surface of the water is approximately 254 square inches.
GIVE BRAINLIEST :) Morgan can paint a room in 10 hours, while Sophia can paint it in 4 hours. If Morgan paints for x hours and Sophia paints for y hours, they will finish half of the painting, while if Morgan paints for y hours and Sophia paints for x hours they will paint the whole room. Find the ordered pair (x,y), expressing both x and y as simplified fractions.
Answer:
x,y = ( 3 17/21 , 10/21)
Step-by-step explanation:
Painting the room = 1 whole job
Morgan rate = 1/10
Sophia rate = 1/4
Rate x time = 1 job
1/10 x + 1/4 y = 1/2 and
1/10 y + 1/4 x = 1 solve for x,y
Multiply the top equation by - 2.5
(-2.5)/10 x - (2.5/4) y = -1.25
-1/4 x - 5/8 y = -1 .25
and add to the second equation to get
1/10 y - 5/8 y = -.25 solve for y
4/40 y - 25/40 y = -.25
-21/40 y = - .25
y = 10/21 hr Substitute this into one of the original equations to find 'x'
1/10 (10/21) + 1/4 x = 1
1/21 + 1/4 x = 1
1/4 x = 20/21
x = 80/21 x,y = ( 3 17/21 , 10/21)
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A manufacturer designs a circular ornament with lines of glitter as shown. Identify m∠PSR.
m=60
m=30
m=90
m=120
Answer:
120
Step-by-step explanation:
The measure of the arc QR⏜ intercepted by the inscribed ∠QPR is given.
According to the Inscribed Angle Theorem, the measure of the inscribed angle is equal to one-half the measure of the arc.
m∠QPR=12mQR⏜
Substitute 60° for mQR⏜.
m∠QPR=12(60°)
Simplify.
m∠QPR=30°
The figure shows the same circle as in the beginning of the task. Triangle P R S is highlighted in red. Angle S P R measures 30 degrees.
It is given that m∠SRP=30°. Use the Triangle Sum Theorem to find the measure of the unknown ∠PSR.
m∠SRP+m∠SPR+m∠PSR=180°
Substitute the known values.
30°+30°+m∠PSR=180°
Simplify.
60°+m∠PSR=180°
Subtract 60° from both sides.
m∠PSR=120°
Therefore, m∠PSR=120°.
what expression is equal to (3d^4)^2
Answer:
Simplify the expression using the rules of exponents.
9d^8
Step-by-step explanation:
answer is 9d^8
Write this equation in slope-intercept form. y - 3 = 5(x +
3)
Answer:
y = 5x+18
Step-by-step explanation:
y - 3 = 5(x + 3)
Distribute
y -3 = 5x+15
Add 3 to each side
y - 3+3 = 5x + 15 +3
y = 5x+18
This is slope intercept form (y = mx+b) where m is the slope and b is the y intercept
Can i Get help please ASAP I will Give Brainliest
Answer:
MN is not congruent to QR
Step-by-step explanation:
If you look at the way the triangles are written, you have, MNO, and PQR. These should be written in the same order if they are congruent. Therefore, MN corresponds to PQ as they are both the first two, and likewise, QR corresponds with NO
Ms. Alvarez wants to determine the seventh graders’ preferences for the location of the end-of-year field trip. Which of the samples is representative of the population?
Using sampling concepts, the representative sample is given as follows:
D. Every fifth student from an alphabetical list of all seventh graders in the school.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, the population is all seventh graders, hence the sample has to be representative of all seventh graders. Thus the correct option is:
D. Every fifth student from an alphabetical list of all seventh graders in the school.
More can be learned about sampling concepts at https://brainly.com/question/25122507
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Sean is playing a board game. To win he needs to roll a sum of 10 or more with a pair of dice on his next turn. There are 11 possible sums when you roll 2 dice and 3 of these outcomes will result in him winning this game. Sean therefore says that the probability that he will win the game is 3/11. Explain the mistake in Sean's thinking.
Answer: 1/6
Step-by-step explanation:
Two fair dice is rolled once,
To win sum of the two dice should equal 10 or more
To get a sum equal 10 or more,
The total possible outcome when two dice is rolled once = 6^2 = 36
Sample space is attached below
Total required outcome to win (probability of having a sum of 10 or more)
n(sum of 10 or more) = 6
Therefore, probability of winning equals :
P(winning) = (Total required outcome / Total possible outcomes)
P(winning) = n(sum of 10 or more) / total possible outcomes
P(winning) = 6/36 = 1/6
In a class of 101010, there are 222 students who forgot their lunch. If the teacher chooses 222 students, what is the probability that both of them forgot their lunch?
Answer:
1/455
Step-by-step explanation:
place 222 over 101010 and divide
Answer:
1/45
Step-by-step explanation:
Step-by-step explanation
Explain how to model the problem with algebra tiles and
then write an algebraic expression that represents the
situation.
Adrian lost one of his hats.
Answer:
The variable, the number of golf balls, is modeled by an orange x tile.
Finding 8 more golf balls is modeled by 8 orange + tiles.
The expression that represents the situation is x + 8.
Answer:
x-1 tile
Step-by-step explanation: trust me
Here is some information about a play starts at 7:30pm first act last 46 minutes interval lasts 20 minutes second act last 53 minutes at what time does the second act end
Answer:
9:29 PM
Step-by-step explanation:
Let us add the number of minutes the first act, interval and second act lasted:
46 + 20 + 53 = 119 minutes
Converting this to hours and minutes:
60 minutes = 1 hour
119 minutes = 1 hour 59 minutes
Therefore, the time that the second act ends is:
H M
7 : 30 PM
+ 1 : 59
9 : 29
The second act will end by 9:29 PM
1. If (1, -2) is a solution of a linear equation 2x – y = p, then find the value of p.
Answer:
Just put the values of x and y
x = 1
y = -2
2x – y = p
2(1) - (- 2) = p
p = 4
Answer:
The value of p is 4.
Step-by-step explanation:
In order to find p, you have to substitute the value of x and y into the linear equation :
[tex]2x - y = p[/tex]
[tex]let \: x = 1 \\ let \: y = - 2[/tex]
[tex]2(1) - ( - 2) = p[/tex]
[tex]2 + 2 = p[/tex]
[tex]p = 4[/tex]
1/3(2x-8)=4 algebraic properties
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
[tex]1/3(2x-8)=4[/tex]
[tex]2/3x-8/3=4[/tex]
[tex]2/3x=4+8/3[/tex]
[tex]2/3x=20/3[/tex]
[tex]x=20/3 \times3/2[/tex]
[tex]x=60/6[/tex]
[tex]x=10[/tex]
Answer:
10
please see the attached picture for full solution
hope it helps
Good luck on your assignment
please help will mark brainliest
Answer:
17 cm²
Step-by-step explanation:
First I cut this figure into 2 rectangles. One big and small one. (the big one is on top of the small rectangle).
For the big rectangle, I multiplied its length by its width.
The area of the big rectangle: 3cm * 5cm = 15cm²
For the smaller rectangle, I also multiplied its length and width.
The area of the small rectangle: 1cm * 2 cm = 2cm²
Add up its areas: 15+2
To get 17cm² as your final answer
Solve the literal equation -cy + 8 = 4d – 3y for y.
Answer:
y=(4d-8)/(3-c)
Step-by-step explanation:
-cy + 8 = 4d – 3y3y-cy=4d-8y(3-c)=4d-8y=(4d-8)/(3-c)HELP PLEASE ASAP!!!!
Adult Golden Retrievers have a mean weight of 64 pounds with a standard deviation of 8 pounds. If you take a random sample of 35 gold retrievers, what is the probability the sample mean will be less than 65.5 pounds?
0.8643
0.1357
0.8665
0.1335
Answer:
Step-by-step explanation:
Let x be the random variable representing the mean weight of Adult Golden Retrievers. Assuming the weights are normally distributed(number of samples is greater than 30), we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
n = number of samples
From the information given,
µ = 64
σ = 8
n = 35
the probability that the sample mean will be less than 65.5 pounds is expressed as
P(x < 65.5)
For x = 65.5,
z = (65.5 - 64)/(8/√35) = 1.11
Looking at the normal distribution table, the probability corresponding to the z score is 0.8665
Therefore, the probability that the sample mean will be less than 65.5 pounds is 0.8665