Answer:
The dimensions of rectangle are 11 feet and 7 feet.Step-by-step explanation:
Given, The length of a rectangle is 10 ft less than three times the width, and the area of the rectangle is 77 ft²
Let's assume width of rectangle be x feet and Length of rectangle be 3x - 10. Using the formula of area of the rectangle we'll find the dimensions of the Rectangle.
[tex] \\ \dashrightarrow{ \red{\underline{\underline{\sf{Area (rectangle) = Length \times width }}}}} \\ \\ [/tex]
Substituting the required values:
[tex]\dashrightarrow \: \: (3x-10)(x) = 77 \\ [/tex]
[tex]\dashrightarrow \: \: 3x^2 - 10x = 77 \\ [/tex]
[tex]\dashrightarrow \: \: 3x^2 -10x -77 = 0 \\ [/tex]
[tex]\dashrightarrow \: \:3x^2 + 11x -21x -77 = 0 \\ [/tex]
[tex]\dashrightarrow \: \: x(3x+11)-7(3x+11) = 0 \\ [/tex]
[tex]\dashrightarrow \: \: (x-7)(3x+11) = 0 \\ [/tex]
[tex]\dashrightarrow \: \: { \red{\underline{\underline { x = 7 \: or \: \dfrac{-11}{3}}}} } \\ \\ [/tex]
Hence,
Width of rectangle = x = 7 feetLength of rectangle = 3x -10 = 3(7) - 10 = 11 feet[tex] \therefore[/tex] The required dimensions of rectangle are 11 feet and 7 feet.
The dimensions of the given rectangle with an area of 77 ft^2 and given dimensions are; Length = 11 ft and Width = 7 ft
How to find the Area of a rectangle?
Formula for area of a rectangle is;
A = Length * Width
We are given;
Length; L = 3W - 10
Thus;
Area; A = W(3W - 10)
Thus;
W(3W - 10) = 77
3W² - 10W - 77 = 0
Using online quadratic equation calculator, we have;
W = 7
Thus;
L = (3*7) - 10
L = 11 ft
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A culture started with 6000 becteria. after 3 hours it grew to 7200 becteria. Predict how many bacteria will be present after 19 hours. Round your answer to the nearest whole number. p=ae^kt
Answer: 13,600.
Step-by-step explanation: every hour is 400 bacteria produced. 400x19= 7600. 7600+6000=13600
help me help me help me
Answer:
For the third one,
3, 8, 15, 24, 35, 48, 63
For the fourth one,
4, 6, 10, 18, 30, 46, 66
Step-by-step explanation:
A babysitter charges a rate of $15 per hour. how long was the babysitter there if she makes $5
Answer:
20 mins.
Step-by-step explanation:
A babysitter charges a rate of $15 per hour. How long was the babysitter there if she makes $5?
x = hours she babysat
Equation:
15x = 5
Divide to isolate x:
15x = 5
/15 /15
x = 1/3 hrs.
Now, we convert into minutes, since she didn't work for a whole hour, to earn the $15
We know that there are 60 mins. in an hour
60 * 1/3
60/3
20 mins.
Therefore, the babysitter was there for 20 mins.
Hope this helps!
Dan made $5000 in taxable income last year.
Suppose the income tax rate is 10% for the first $7500 plus 15% for the amount over $7500
How much must Dan pay in income tax for last year?
well, we know is 10% for the first 7500, but Dan only made 5000 of taxable income, so he's in that range of 0 - 7500, so he only gets to pay 10% of 5000.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 5000}}{\left( \cfrac{10}{100} \right)5000}\implies 500[/tex]
Simplify the expression. (–8.6)0
A)–1
B)–8.6
C)1
D)0
Answer: D
Explanation: Anything times 0 is 0.
A club elects a president, vice president and secretary treasurer. How many sets of officers are possible if there are 8 members and any member can be elected to each position? No person can hold more than one office.
Ahhh yes, the time-honored permutations.
The permutation format, to start with, is P(n, r).
The formula is:
[tex]\frac{n!}{(n-r)!}[/tex]In this instance, we have P(8, 3).
8 will go in for n and 3 for r. So now let's solve.
[tex]\frac{8!}{(8 - 3)!}[/tex] → [tex]\frac{8!}{5!}[/tex] → [tex]\frac{8*7*6*5*4*3*2*1}{5*4*3*2*1}[/tex] → [tex]8*7*6[/tex] → [tex]336[/tex]
Therefore 336 is our answer. I hope this answers your question.
-Toremi
Rodney says that he can draw two rectangles that have the same areas but different perimeters.
Which of the following pairs of rectangles could Rodney draw?
Select all that apply.
LIVE
A rectangle with side lengths 4 cm and 6 cm and a rectangle with side lengths 2 cm and 12 cm
LIVE
A rectangle with side lengths 4 cm and 6 cm and a rectangle with side lengths 2 cm and 8 cm
LIVE
A rectangle with side lengths 3 cm and 6 cm and a rectangle with side lengths 2 cm and 9 cm
LIVE
A rectangle with side lengths 5 cm and 6 cm and a rectangle with side lengths 2 cm and 9 cm
LIVE
A rectangle with side lengths 5 cm and 4 cm and a rectangle with side lengths 2 cm and 7 cm
Answer:
A rectangle with sides lengths 4cm and 6cm and a rectangle with side lengths 2cm and 12 cm...
QUESTION 3 I [12] A student must answer a multiple-choice question with five possible answers. He knows the correct answer with probability 0.55. If he does not know the correct answer, he randomly guesses one of the possible answers. a) Draw a tree diagram and clearly define all relevant events.
The probability that the student does not know the answer but he randomly guesses it is 0.146025
How to solve for the probability of having a correct guessThe question has only one right answer out of 5 choices.
Probability he answers incorrectly:
1 - 0.55 * 4/5
= 0.45 * 0.8
= 0.36
Probability he does not know answer but answers the question correctly
[tex]\frac{(1-0.55)\frac{1}{5} }{0.55+(1-0.55)\frac{1}{5} }[/tex]
= 0.09/0.55+0.09
= 0.140625
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The points (4,7) and (r. – 5) lie on a line with slope – 3. Find the missing coordinate r
Answer:
[tex]r=\frac{14}{3}[/tex]
Step-by-step explanation:
Set up an equation and solve for r using the formula for slope:
[tex]\frac{5-7}{r-4}=-3\\ \\-2=-3(r-4)\\\\-2=-3r+12\\\\-14=-3r\\\\\frac{14}{3}=r[/tex]
Find 12 1/2% of #400.00
find 12 1/2 percentage of 400 naira
Answer:
I think its 50 if this is correct can u mark me brainliest?
What is entrepreneurial finance?
Answer:
The process of making financial decisions for new ventures (i.e. startups). New ventures are inherently different from established ventures, as are entrepreneurs inherently different from conventional business managers.
The recursive formula for an arithmetic sequence is:
{a1 = -6
{an-an-1+2
What is the 3rd term in the sequence?
A. - 2
B. -4
C. -10
D. -18
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.3 inches, and standard deviation of 1 inches. What is the probability that the height of a randomly chosen child is between 53.3 and 55.3 inches
Answer:
a) We need to find p(x<68.15)
Standardize x to z, we have, z = (68.15-μ)/σ
=(68.15-57)/8.1
=1.38
Reading from standard normal tables,
p(z<1.38) =0.9162.
b) We need to find p(x>54.4)
Standardize x to z, we have, z = (54.4-μ)/σ
=(54.4-57)/8.1
=-0.32
Reading from standard normal tables,
p(z>-0.32) = 0.6255
Solve for x in the equation x2-12x+36 = 90
X
=
O X=6+3/10
O x=6+217
X
X= 12+3^22
X= 12+3/10
Answer:
Step-by-step explanation:
hello : (x-6)² = 90 .....continu
Mr.Smith has p pounds of cookie dough. He is going to split it equally among his three children. Each child will get 0.42 pounds of cookie dough. Write and solve an equation that can be used to determine the weight of the cookie dough Mr. Smith has.
Answer:
p = 1.26
Step-by-step explanation:
We know that the total weight (p) is going to be split equally (divided) by 3.
We also know that divided weight will be equal to 0.42 pounds.
p / 3 = 0.42
To solve:
multiply both sides by 3 to cancel the division by 3
p = 1.26
To test this you could divide 1.26 by 3 again to get 0.42
15 There are 30 students in a class. 1 5 like football. How many students do not like football?
Which point is located at (-1, 1 1/4)
A
B
C
D
Answer: Point A.
Step-by-step explanation: To find the location of points such as (-1, 1 1/4), you need to know what part of the point is the x-axis and the y-axis. The first part of the point is the x-axis, which is the horizontal line that goes left to right on the coordinate graph. The first part of the point (-1, 1 1/4), is -1. The second part of the point is the y-axis, which is the vertical line that goes up and down on the coordinate graph. The second part of the point (-1, 1 1/4), is 1 1/4. Therefore, we first find the x-axis to the point (-1, 1 1/4), which is -1, and so far, point A is the only option that matches. However, we need to make sure that the point (-1, 1 1/4)'s y-axis matches to point A as well. The y-axis to the point (-1, 1 1/4) is 1 1/4 so we need to go up 1 1/4 times, and the point that matches these actions is point A. Therefore, that's your answer.
Let me know if this is right! :)
The transformation of triangle ABC is an example of what?
Answer:
The relation between preimage and image
Step-by-step explanation:
Find the measure picture below
By the vertical angle theorem, angle K is equal to the angle of measure 28 degrees.
--> so k is 28 degrees
Def. of vertical angle theorem: states that the opposite (vertical) angles of two intersecting lines are congruent
Hope that helps!
Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many
number solutions does the equation have?
real
Discriminant = b2-4ac
O 0
O 1
O 2
O 12
Number of solution for the given quadratic equation as Discriminant=0 is equals to 1.
What is quadratic equation?" Quadratic equation is defined as the polynomial containing variables with highest exponent equals to 2."
Formula used
For quadratic equation
[tex]ax^{2} +bx+c=0[/tex]
Discriminant = b²-4ac
According to the question,
Given quadratic equation
[tex]-3 = x^{2} +4x+1[/tex]
⇒[tex]x^{2} +4x+1 +3 =0[/tex]
⇒[tex]x^{2} +4x+4 =0[/tex]
Here, a=1 , b= 4 , c =4
Substitute the value in the formula we get,
Discriminant = [tex]4^{2} - 4(1)(4)[/tex]
= [tex]16 -16[/tex]
= 0
Number of solution discriminant =0 is 1.
[tex]x^{2} +4x+4 =0[/tex]
⇒[tex](x+2)^{2} =0[/tex]
⇒[tex]x= -2[/tex] has unique solution.
Hence, number of solution for the given quadratic equation as Discriminant=0 is equals to 1.
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On Friday, Hayley has purchased more flour and eggs, but only has 22 cups of sugar and 4 sticks of butter. Which combination of loaves of zucchini bread and banana bread can Hayley make?
Answer:
It is C
Step-by-step explanation:
Mae has 36 orange slices. She will fill each of
7 bags with the same number of orange slices.
How many slices will be in each bag? How many
slices will be left over?
Answer:
5 orange slices will be in each bag with 1 left over
Step-by-step explanation:
36 ÷ 7 = 5 with a remainder of 1
. Mai skated miles, and Clare skated farther than that. Write an equation to Accelerated 6 Unit 6 Lesson 1 represent the relationship between the distance Mai skated ( ) and the distance Clare skated ( ).
Answer:
X over y or x/y since y is claire and she skated more
Step-by-step explanation:
since y is claire and she skated more
Y=Clarie skated
X= Mai skated
joshua drinks 8 cups of water a day. The recommended daily amout is given in fluid ounces.How many fluid ounces of water does he drink each day?
Question:
Joshua drinks 8 cups of water a day. The recommended daily amout is given in fluid ounces. How many fluid ounces of water does he drink each day?
What were being asked:
How many fluid ounces of water does he drink each day?
Answer:
The answer is
→ 64 fluid ounces
Step-by-step explanation:
1 cup of water = 8 fluids.
8 cups of water x 8 fluids = 64 ounces
Therefore, your answer is 64 fluid ounces.
Hope this helped! :^)
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Submitted on 4/18/2022 at 4:08 PM
(To avoid plagarism, by users whom decide to copy.)
According to an article, 75% of high school seniors have a driver's license. Suppose we take a random sample of 300 high school seniors and find the proportion who have a driver's license. Find the probability that more than 77% of the sample have a driver's license. Begin by verifying that the conditions for the Central Limit Theorem for Sample Proportions have been met.
Answer:
33%
Step-by-step explanation:
77 + 233= 300 so 33% don't have a license
The doubling time of a population of flies is 8 hours. By what factor does the population increase in 34 hours? By what factor does the population increase in 1 week ?
Answer:
19.017 in 34 hours2,097,152 in 1 weekStep-by-step explanation:
An exponent is used to signify repeated multiplication. When the population doubles, it is multiplied by 2. The number of times the population has doubled will be an exponent of 2.
a)In 34 hours, the population will have doubled 34/8 = 4.25 times. The multiplier is 2 with an exponent of 4.25:
factor = 2^4.25 ≈ 19.027
__
b)The population will double 24/8 = 3 times each day. After 7 days, the population will have doubled 7×3 = 21 times. The multiplication factor is ...
factor = 2^21 = 2,097,152
Justify the first step that David took in verifying that x = 5 is a solution for the equation
8x – 13 = 2x + 17.
8x – 13 = 2x + 17
8(5) – 13 = 2(5) + 17
A.
David multiplied 8 by 5.
B.
David subtracted 13 from both sides.
C.
David replaced x with 5.
D.
David added 17 to both sides.
Answer:
Step by step I don't see the correct first step.
Step-by-step explanation:
Solve for x:
8 x - 13 = 2 x + 17
Hint: | Move terms with x to the left hand side.
Subtract 2 x from both sides:
(8 x - 2 x) - 13 = (2 x - 2 x) + 17
Hint: | Combine like terms in 8 x - 2 x.
8 x - 2 x = 6 x:
6 x - 13 = (2 x - 2 x) + 17
Hint: | Look for the difference of two identical terms.
2 x - 2 x = 0:
6 x - 13 = 17
Hint: | Isolate terms with x to the left hand side.
Add 13 to both sides:
6 x + (13 - 13) = 13 + 17
Hint: | Look for the difference of two identical terms.
13 - 13 = 0:
6 x = 17 + 13
Hint: | Evaluate 17 + 13.
17 + 13 = 30:
6 x = 30
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 6 x = 30 by 6:
(6 x)/6 = 30/6
Hint: | Any nonzero number divided by itself is one.
6/6 = 1:
x = 30/6
Hint: | Reduce 30/6 to lowest terms. Start by finding the GCD of 30 and 6.
The gcd of 30 and 6 is 6, so 30/6 = (6×5)/(6×1) = 6/6×5 = 5:
Answer: x = 5
Find the area
Please!
(Give explanation)
Answer:
58.8 ft^2
Step-by-step explanation:
The formula for the area of a parallelogram is simply base times height.
the base is 9.8, and the height is 6.
9.8 * 6 = 58.8.
If you found this helpful, I would appreciate if you gave me brainliest :D
Tracy has 40 feet of material to make the perimeter of a rectangular sandbox for her little brother.
What rectangle with whole-number side lengths would give the sandbox with the greatest area?
Answer:
11 and 9
Step-by-step explanation:
With a width of 11 and a length of 9 the area of the rectangle would be
11 * 9 = 99
By adding 11 and 9, then mulitplying it by 2 we get the perimeter
11 + 9 = 20
20 * 2 = 40
Find the area
A. 300 units
B. 520
C. 500 units
Answer:
b.520 units
Step-by-step explanation:
find the area of the bigger triangle the base is 20 which is 10×2 while the height is 28. 1/2×20×28=280units find the area of the smaller triangle. the base is also 20 while the height is 24. 1/2×20×24=240. sum the areas of the two triangles. 280+240=520units
