Answer:
The equation which is equivalent to [tex]t^2-8t+15=0[/tex] is
[tex](t-3)(t-5)=0[/tex]
Step-by-step explanation:
Given that the time a projectile spends in the air can be modeled by the equation [tex]t^2-8t+15=0[/tex], where t represents the amount of time traveled in seconds.
To find the equation is equivalent to [tex]t^2-8t+15=0[/tex] :
[tex]t^2-8t+15=0[/tex]
[tex]t^2-3t-5t+15=0[/tex]
[tex]t(t-3)-5(t-3)=0[/tex]
[tex](t-3)(t-5)=0[/tex]
Therefore the equation which is equivalent to [tex]t^2-8t+15=0[/tex] is
[tex](t-3)(t-5)=0[/tex]
Final answer:
The equivalent equation to the quadratic equation representing the time a projectile spends in the air, t² -8t + 15 = 0, is (t - 3)(t - 5) = 0, which results from correctly factoring the original equation.
Explanation:
The time a projectile spends in the air is represented by the quadratic equation t² -8t + 15 = 0. To find an equivalent equation, we must factor the quadratic equation correctly. The correct factored form that corresponds to the original equation is (t - 3)(t - 5) = 0, based on the rules of factoring quadratics and finding roots that sum up to -8 (the coefficient of t) and multiply to 15 (the constant term).
The process of factoring involves finding two numbers that add up to the coefficient of the linear term (-8 in this case) and multiply to the constant term (15 here). The numbers -3 and -5 satisfy both these conditions as (-3) + (-5) = -8 and (-3) × (-5) = 15. Therefore, the equivalent equation is (t - 3)(t - 5) = 0.
Will make brainliest if answered right
Answer:
d 10x=-3
Step-by-step explanation:
a science test is worth 100 points and has 25 questions. There are multiple-choice questions worth three points each and short essay questions worth 8 points each. How many short essay questions are on the test?
There are 5 short essay questions on test
Solution:
Let "a" be the number of multiple choice questions
Let "b" be the number of short essay questions
Worth of each multiple choice questions = 3 points
Worth of each short essay questions = 8 points
There are 25 questions in total
number of multiple choice questions + number of short essay questions = 25
a + b = 25
a = 25 - b --------- eqn 1
The test is worth 100 points. Theerefore, we frame a equation as:
number of multiple choice questions x Worth of each multiple choice questions + number of short essay questions x Worth of each short essay questions = 100
[tex]a \times 3 + b \times 8=100[/tex]
3a + 8b = 100 --------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
3(25 - b) + 8b = 100
75 - 3b + 8b = 100
5b = 100 - 75
5b = 25
b = 5
Thus there are 5 short essay questions on test
The number of short essay questions on the test is 5.
Explanation:The science test is worth 100 points and has 25 questions. Let's represent the number of multiple-choice questions as 'x' and the number of short essay questions as 'y'. Each multiple-choice question is worth three points, so the total number of points for the multiple-choice questions is 3x. Each short essay question is worth eight points, so the total number of points for the short essay questions is 8y. We can write two equations to represent the given information:
x + y = 25 (since there are 25 questions in total)
3x + 8y = 100 (since the total points for the test is 100)
To find the number of short essay questions on the test, we need to solve these two equations. By substituting x = 25 - y into the second equation, we can solve for y.
3(25 - y) + 8y = 100
75 - 3y + 8y = 100
5y = 25
y = 5
Therefore, there are 5 short essay questions on the test.
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An online store is offering 15% off all items in your order. Before the discount is applied, the items in your cart are: shampoo for $6.35, conditioner for $6.35, granola bars for $12.50, dish soap for $13.40, and toothpaste for $2.50. What is the discounted total price for all the items, assuming no sales tax is added? Report your answer to two decimal places. Do not include the dollar sign, $, in the answer box below.
Answer:
The total discounted price is 34.93
Step-by-step explanation:
The items in the cart are:
Shampoo for $6.35Conditioner for $6.35Granola bars for $12.50Dish soap for $13.40 Toothpaste for $2.50Total cart = $ 41.10
Discount = 41.10 * 0.15 = $ 6.17
Discounted total price = 41.10 - 6.17
Discounted total price = 34.93
Answer:
34.94.
Step-by-step explanation:
First we must find the total price of all the items: =$6.35+$6.35+$12.50+$13.40+$2.50=$41.10.
Next, we can calculate the discount: =(15/100)×$41.10=$6.165.
Therefore, our discounted price is $41.10−$6.165=$34.935≈$34.94.
fractions greater than 1
Answer:
Anything with a numerator (top) greater then the denominater (bottom) here are some examples:
[tex] \frac{11}{2} [/tex]
[tex] \tfrac{8}{5} [/tex]
[tex] \frac{399}{7} [/tex]
[tex] \frac{6}{2} [/tex]
Hope this information helps my friend!
How to you use a unit rate to solve a rate problem for any number of units?
Answer:
Here, we have used the unit rate i.e. speed of 30 mph to get the distance traveled in 5 number of units i.e. 5 hours.
Step-by-step explanation:
We are asked the way to use a unit rate to solve a rate problem for any number of units.
Let, us assume that a car is moving at a unit rate of 30 miles per hour. And we have to calculate the distance it travels in 5 units of time i.e. 5 hours.
Now, the distance traveled in 5 hours will be given by 30 × 5 = 150 miles.
Since [tex]\textrm {Speed} = \frac{\textrm {Distance}}{\textrm {Time}}[/tex] and here, speed is 30 miles per hour and the time is 5 hours. (Answer)
Multiply the polynomials.
* (x + 4)(x2 - 5x + 3)
O
O
O
A. x2 - 5x2 - 17x+ 12
B. x3 – x2 + 3x + 12
c. x2 - 5x2 + 3x + 12
2 2 17 10
Answer:
x^3-x^2-17x+12
Step-by-step explanation:
(x+4)(x^2-5x+3)
x^3-5x^2+3x+4x^2-20x+12
x^3-5x^2+4x^2+3x-20x+12
x^3-x^2-17x+12
Explain the Pythagorean Theorem
Answer:
Pythagorean theorem theorem that states that the sum of the squares of the two legs is equal to the square of the hypotenuse in a right triangle
The price of milk has been increasing over the last month. Audrey believes there is a positive correlation between the number of predicted storms and the price of milk.
Number of Storms Predicted Milk Price
1 $2.70
3 $2.89
4 $3.50
6 $3.88
7 $3.91
Use the table to determine the average rate of change from 3 to 6 storms.
3
0.98
1.21
0.33
Answer:
0.33
Step-by-step explanation:
Aight so all we do is use the formula, as shown here:
[tex]\frac{\Delta x}{\Delta y}[/tex]
[tex]x[/tex] is this amount it changed, which is 0.99. So we plug that for [tex]\Delta x[/tex]:
[tex]\frac{0.99}{\Delta y}[/tex]
Then, we find the amount of times the storm changed, and we plug that for [tex]\Delta y[/tex]:
[tex]\frac{0.99}{3}[/tex]
So, now that we have utilized the formula, we can now solve!
[tex]\frac{0.99}{3} = 0.33[/tex]
Good luck!
Answer:
0.33
Step-by-step explanation:
What are the opposites of 6, −3.4, 2.25, and 8 1/ 5 ? Enter the answers in respective order, each separated by comma.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
6= -6, -3.4=3.4, 2.25=-2.25, 8 1/5=-81/5
Use the grouping method to factor the polynomial below completely.
3x3 + 9x2 + 5x + 15
O A. (3x2 + 3)(x+5)
O B. (3x2 + 5)(x + 5)
O C. (3x2 + 3)(x+3)
O D. (3x2 + 5)(x + 3)
The correct answer is D. (3x2 + 5)(x + 3). Here’s how you can use the grouping method to factor the polynomial completely:
Group the first two terms and the last two terms: (3x3 + 9x2) + (5x + 15)
Factor out the greatest common factor from each group: 3x2(x + 3) + 5(x + 3)
Factor out the common binomial factor: (3x2 + 5)(x + 3)
So, the polynomial 3x3 + 9x2 + 5x + 15 can be factored completely as (3x2 + 5)(x + 3).
Hope it helps.
Show step by step for equation -8/3x + 4(x + 9/4) = -2/3(x + 12/8) + 3
Answer:
see attached picture please
How would I solve (6r +3)2 and show my work?
Answer:
12r+6
Step-by-step explanation:
2(6r+3)
2(6r)+2(3)
12r+6
Find the Lowest Common Multiple of 108 and 120
Answer:
Step-by-step explanation:
108 = 2*2*3*3*3=2² * 3³
120 = 2*2*2*3*5=2³*3*5
LCM = 2³*3³*5 = 8*27*5= 1080
To find the LCM of 108 and 120, first find their prime factorizations and then multiply the highest power of each prime factor.
Explanation:To find the Lowest Common Multiple (LCM) of 108 and 120, we can first find their prime factorizations. The prime factorization of 108 is 2 × 2 × 3 × 3 × 3, while the prime factorization of 120 is 2 × 2 × 2 × 3 × 5. We can then find the LCM by taking the highest power of each prime factor from both numbers. So, the LCM of 108 and 120 is 2 × 2 × 2 × 3 × 3 × 3 × 5 = 2,160.
The Lowest Common Multiple (LCM) of 108 and 120 is 1080. This is found by finding the prime factors of each number, and then multiplying together the highest power of each factor.
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If an employee earns $20.00 per hour plus $1.50 per hour for vacation and you pay $2.00 per hour in tax and $9.00 for every $100.00 in payroll for workers compensation what is the total hourly wage for the employee ?
A rectangle park measures 300 ft by 400 ft. A sidewalk runs diagonally from one comer to the opposite corner. Find the length o
the sidewalk
a 400 ft
c 250 ft
b. 500 ft
d. 650 ft
The length of side walk is 500 feet
Solution:
Given that, A rectangle park measures 300 ft by 400 ft
Length = 300 feet
Width = 400 feet
A sidewalk runs diagonally from one comer to the opposite corner
We have to find the length of side walk
Which means, we have to find the length of diagonal of rectangle
The diagonal of rectangle is given by formula:
[tex]d = \sqrt{w^2+l^2}[/tex]
Where,
d is the length of diagonal
w is the width and l is the length of rectangle
Substituting the values in formula, we get
[tex]d = \sqrt{400^2+300^2}\\\\d = \sqrt{160000+90000}\\\\d = \sqrt{250000}\\\\d = 500[/tex]
Thus length of side walk is 500 feet
What is the algebraic expression for the following word phrase: the quotient of 6 and z?
A. 6+z
B. 6z
C. 6-z
D. 6/z
Answer:
Step-by-step explanation:
the quotient is the result of division
the quotient of 6 and z...
6/z <===
** pay attention to the wording...because if it would have said : the quotient of z and 6, it would have been z/6
Please help ASAP!!!!
The simplified answer is [tex]5\frac{2}{9}[/tex].
Option: C.
Step-by-step explanation:
To simply [tex]-3\frac{1}{9} - (-8\frac{1}{3} )[/tex]:
First convert this improper fraction into normal fraction.
[tex]-3\frac{1}{9}[/tex] = [tex]\frac{-28}{9}[/tex].
[tex]-8\frac{1}{3}[/tex] = [tex]\frac{-25}{3}[/tex].
Now we have to simplify [tex]-\frac{28}{9} - (-\frac{25}{3} )[/tex].
= [tex]-\frac{28}{9} + \frac{25}{3}[/tex].
After applying LCM to the denominators, Multiply the second term with 3 in both numerator and denominator.
= [tex]-\frac{28}{9} + \frac{75}{9}[/tex].
=[tex]\frac{-28+75}{9}[/tex].
=[tex]\frac{47}{9}[/tex].
Convert the answer in improper fraction form.
[tex]\frac{47}{9}[/tex] = [tex]5\frac{2}{9}[/tex].
Thus the simplified answer is [tex]5\frac{2}{9}[/tex].
A baby goes to sleep at 8 p.m., wakes up after two hours, stays awake for 15 minutes, and then goes back to sleep. If the baby repeats this sleep pattern until she is awakened at 6 a.m., what percent of the time from 8 p.m. to 6 a.m. was the baby asleep?
Answer:
Step-by-step explanation:
If the baby repeats this sleep pattern until she is awakened at 6 a.m., what ... We have 10 hours between 8PM and 6AM = 10 * 60 = 600 minutes ... Awake 12:15 - 12:30 ... There are 4 periods of 2 hour sleep and 1 period of 1 hour sleep = 4*2(60) + 1(60) ... So 540/600 = 54/60 = 9/10 = 90% of the time asleep.
Answer:
87.5%
Step-by-step explanation:
I am not sure how to set this up....so I am just gonna try to figure this a different way....without any formula
8 p.m - 10 pm.......awake for 15 minutes
10 pm - 12 am......awake 15 minutes
12 am - 2 am.......awake 15 minutes
2 am to 4 am.....awake 15 minutes
4 am to 6 am....awake 15 minutes
so from 8 pm to 6 am....that is a total of 10 hrs.....and in those 10 hrs, the baby was awake 5(15) = 75 minutes.....change 10 hrs to minutes.....1 hr = 60 min...so 10 hrs = (10 * 60) = 600 minutes
so in 600 minutes, the baby was awake 75 minutes.....that means the baby was asleep (600 - 75) = 525 minutes
525/600 = 0.875 = 87.5% <=== baby was asleep
or maybe this way....for every 2 hrs, the baby was awake 15 minutes....means the baby was asleep (120 - 15) = 105 minutes.
2 / 105 = 10 / x
2x = 1050
x = 1050/2
x = 525 minutes.....so the baby was asleep 525 minutes out of 600 minutes.
525/600 = 0.875 = 87.5%
I am getting the same answer either way
What is 3x + 4 = x + 8
Answer:
x is equal to 2
Step-by-step explanation:
2x+4=8
2x=4
x=2
Answer:
x = 2
Step-by-step explanation:
First you must subtract x to both sides leaving you with 2x + 4=8 and you subtract 4 to both sides giving you 2x=4 and lastly to get the x by itself you divide both sides by 2 leaving you with x=2
30 points
Which expression is equivalent to | a | ≤ 4 ?
1. a ≥ –4 and a ≤ 4
2. a ≤ –4 or a ≥ 4
3. a ≤ –4 and a ≥ 4
4. a ≥ –4 or a ≤ 4
Answer:
1. a ≥ –4 and a ≤ 4
Step-by-step explanation:
Rule : | a | ≤ 4 ⇔ -4 ≤ a ≤ 4
:)
Find the quotient. 22x2y2 ÷ 11x2y2
Quotient = 2
Solution:
Given expression is [tex]22x^2y^2\div11x^2y^2[/tex].
To find the quotient.
[tex]22x^2y^2\div11x^2y^2=\frac{22x^2y^2}{11x^2y^2}[/tex]
In numerator 22 can be written as 2 × 11.
[tex]\frac{22x^2y^2}{11x^2y^2}=\frac{2\times11x^2y^2}{11x^2y^2}[/tex]
Take common term out in the numerator and denominator.
[tex]\frac{22x^2y^2}{11x^2y^2}=\frac{(11x^2y^2)(2)}{11x^2y^2}[/tex]
Common terms in the numerator and denominator will be cancelled.
[tex]\frac{22x^2y^2}{11x^2y^2}=2[/tex]
Hence the quotient is 2.
Answer:
The guy up top is right its 2 with no mistake.
Step-by-step explanation:
If 5 is an element in the domain of f(x)= 8x-21/5, what is the corresponding element in the range?
The corresponding element in the range when 7 is an element in the domain is f(5)=179/5
Step-by-step explanation:
Given that the 5 is an element in the domain of f(x)
The function f is defined by f(x)=8x-21/5
To find the corresponding element in the range:
That is put x=5 in the given function f(x)
Therefore f(x) becomes
f(5) = 8(5)-21/5
=40-21/5
=179/5
Therefore corresponding element in the range when 5 is an element in the domain is f(5)=179/5
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Is 15/18 an equivalent ratio
Answer:
no
Step-by-step explanation:
bc
15/18 cant be simplified no matter what
Answer:
No
Step-by-step explanation:
15/18 can not be simplified
which expression is equivalent to 8/9 divided by 3/4
The expression is equivalent to 8/9 divided by 3/4 is 32/27.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is put at the upper half of the fraction above the fractional bar.We have to divide the fraction 8/9 by 3/4.
As, the fraction does not allow division then we will perform the multiplication.
So, 8/9 x 4/3
= 32 / 27
Thus, the required fraction is 32/27.
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How many liters of water must be added to 15 liters of 40 % sugar syrup to obtain 30 % sugar syrup?
Answer:
5 liters of water.
Step-by-step explanation:
Let [tex]y[/tex] be the liters of water that must be added to 15 liters of 40% sugar syrup.
Initially, we have [tex]0.4(15)=6[/tex] liters of sugar syrup, and since adding water does not add any new syrup, the amount of sugar syrup must be the same after the water has been added. After the water has been added, 30% of the solution is sugar syrup, or
[tex]Sugar\:syrup =0.3(15+y)[/tex]
And since this must equal the amount of syrup we had before:
[tex]0.3(15+y)=0.4(15)[/tex]
[tex]4.5+0.3y=6[/tex]
[tex]0.3y=1.5[/tex]
[tex]\boxed{y=5}[/tex]
Thus, 5 liters of water must be added to obtain 30% sugar syrup.
Answer:
5 liters of water
Can you help me on a math problem?
Answer: -3 and +3
Step-by-step explanation:
The cost of 5 squash and 2 zucchini is $1.32. 3 squash and 1 zucchini cost $0.75. Find the cost of each vegetable
Identify a decimal number between 0.25 and 0.125
Answer: 0.126?
Step-by-step explanation:
A decimal number between 0.25 and 0.125 could be 0.2 or 0.15. These numbers sit within the specified range and comply with the principles of decimal number placement.
Explanation:The task here is to identify a decimal number that lies between 0.25 and 0.125. To achieve this, we can carefully select a decimal value that stands in the middle of these two numbers. An example of a suitable decimal would be 0.2, as it comfortably sits within this specified range. Another example could be 0.15. These are both valid decimal numbers that reside between 0.25 and 0.125, and their selection adheres to the principles of decimal number placement on a number line.
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Rewrite the following expression using the distributive property and the GCF: 36+48
Answer:
12(3+4)
Step-by-step explanation:
Answer:
Etc: 12 34
Step-by-step explanation:
Roger served 5/8 pound of crackers, which was 2/3 of entire box. What was the weight of crackers originally in box?
Answer:
original weight of the box = 15 / 16 pounds
Step-by-step explanation: