Answer:
[tex]x=-2, x=\frac{4}{3}, x = 3[/tex]
Step-by-step explanation:
First, factor it.
[tex](x+2)(3x-4)(x-3)=0[/tex]
Use the Zero Factor Principle and equate them each to 0.
[tex]x+2=0\\x=-2\\\\3x-4=0\\x=\frac{4}{3}\\\\x-3=0\\x=3[/tex]
This is how you find the roots of [tex]3x^3-7x^2-14x+24[/tex].
Calculate the force created from an object with a mass of 1250 grams and an acceleration of 3 m/s^2
Please help!! I will mark as brainliest
The force created by the object is 3.75 Newton.
Given
Mass of the object (m) = 1250 grams
Convert 1250 grams to kilograms by dividing it by 1000.
Mass (m) = 1.25 kg
Acceleration of the body (a) = 3 [tex]m/s^{2}[/tex]
From Newton's second law we know [tex]F= m *a[/tex]
By Substituting in the above equation we get
Force = 1.25 x 3
Force = 3.75 [tex]kg/m /s^{2}[/tex]
It can also be written as force = 3.75 N
Hence Force created by the body is 3.75 Newton.
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What is the product of 1.0 times 10^2 and 1.8 times 10^3 expressed in scientific notation?
PLSS HELPPPPPP
The product of 1.0×[tex]10^{2}[/tex] and 1.8×[tex]10^{3}[/tex] expressed in scientific notation is 1.8×[tex]10^{5}[/tex]
Scientific notation is the notation that used to express a very large number or very smaller number is the simplest form. In scientific notation there will be number between 1 to 10 times multiplied by the power of 10.
The first number = 1.0×[tex]10^{2}[/tex]
The second number = 1.8×[tex]10^{3}[/tex]
Multiply the first number by second number, then the result will be
( 1.0×[tex]10^{2}[/tex] )×(1.8×[tex]10^{3}[/tex] )= 100×1800
= 180000
Convert the result to the scientific notation
180000 = 1.8×[tex]10^{5}[/tex]
Hence, the product of 1.0×[tex]10^{2}[/tex] and 1.8×[tex]10^{3}[/tex] expressed in scientific notation is 1.8×[tex]10^{5}[/tex]
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Kai received a $40 Amazon gift card that she wanted to use to rent movies. After she rented 5 movies at $x each, she had $25 left. What was the cost x of each movie Kai rented?
Answer: x=3
Step-by-step explanation:
40-25=15
15 divided by the 5 movies is 3
so $3 per movie
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Find the surface area of the
&
rectangular prism.
2 cm
6 cm
3 cm
[? ] sq cm
Answer: 36
Step-by-step explanation:
The answer is 36 because if you multiply:
6 * 2 = 12
12 * 3 = 36
And so that equals 36 sq cm
OR:
6 * 2 * 3 = 36 sq cm
I hope this helped!
The slope of the line that passes through the point (2, 4) and (3, 8) is
[tex]m=\frac{y_{2-y_{1} } }{x_{2} -x_{1} } \\m=\frac{8-4}{3-2} \\m=\frac{4}{1} \\m=4[/tex]
I also provided the formula on how to calculate the slope between the points
Need help on probability. Please explain how you did it so I can know how to do it.
Answer:
I believe it should be 5/6
Step-by-step explanation:
Here's why, the probability of getting a B, or an even number is 3/6 since there are 3 even numbers on a dice. The probability of getting a multiple of 3 is 2/6 since the only multiples of 3 are 1 and 3. Add the 2 together to get 5/6. Hope this helps.
Answer:
[tex]\text{P}(B \text{ or }C)=\dfrac{5}{6}[/tex]
Step-by-step explanation:
Mutually Exclusive Events
For two events, A and B, where A and B are mutually exclusive:
[tex]\boxed{\text{P}(A \text{ or }B)=\text{P}(A)+\text{P}(B)}[/tex]
Probability distribution table:
[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6 \\\cline{1-7} \text{P}(X=x)\phantom{\dfrac11}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}\\\cline{1-7}\end{array}[/tex]
where X is the score on a fair, six-sided dice.
P(B or C) means "the probability of rolling an even number or a multiple of 3".
As an even number of a fair, six-sided dice can never be a multiple of 3, the two events B and C are mutually exclusive.
Calculate the probabilities for events B and C.
Event B
Rolling an even number.
[tex]\begin{aligned}\implies \text{P}(X \text{ is even})&=\text{P}(2 \text{ or }4\text{ or }6)\\\\&=\text{P}(X=2)+\text{P}(X=4)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{3}{6}\end{aligned}[/tex]
Event C
Rolling a multiple of 3.
[tex]\begin{aligned}\implies \text{P}(X \text{ is multiple of 3})&=\text{P}(3 \text{ or }6)\\\\&=\text{P}(X=3)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{2}{6}\end{aligned}[/tex]
Solution
[tex]\begin{aligned}\implies \text{P}(B \text{ or }C)&=\text{P}(B)+\text{P}(C)\\\\& = \dfrac{3}{6}+\dfrac{2}{6}\\\\& = \dfrac{5}{6}\end{aligned}[/tex]
A car uses 3 1/8 gallons of gasoline per hour when driving on the highway, how many gallons will it use after three hours?
Answer:
The car will use 9 3/8 or 9.375(simple form) gallons of gasoline on the highway
Step-by-step explanation:
if a car uses 3 1/8 gollon per one hour
Multiply the gallon usage of the car by the hours the car will travel on the road
3 1/8(gallons) x 3(hours on the road)
9 3/8 or if you change it to simple form it will be equal to 9.375
How to make x the subject if m=n+x/p
Variable x as the subject of the equation given is expressed as: x = p(m - n).
How to Make a Variable the Subject of the Formula?To make a variable the subject of a formula implies that we express the equation in terms of the variable. Thus, to make a variable the subject of the formula, we have to make the variable stand alone on one side of the equation.
Given the equation, m = n + x/p, make x the subject as explained below:
m = n + x/p [given]
Subtract n from both sides
m - n= n + x/p - n (subtraction property of equality)
m - n = x/p
Multiply both sides by p
p(m - n) = x/p(p) (multiplication property)
p(m - n) = x
x = p(m - n)
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Find the approximate side length of a square game board with an area of 160
in2.
The approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.
As given in the question,
Area of the square game board is equal to 160in².
Let 'x' inches be the side length of the square game board.
Area of the square game board = (side length)²
⇒ 160 = ( x )²
Take square root both the sides we get,
x = √160
⇒ x = 12.649 inches
⇒ x = 12.6 inches( approximately)
Therefore, the approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.
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Which of the following is an equation of a line that passes through the point
(
−
10
,
2
)
and is perpendicular to the line
4
x
+
5
y
=
15
?
The equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.
What is the equation of a perpendicular line?If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation is given below.
4x + 5y = 15
5y = −4x + 15
y = −(4/5)x + 3
The slope of the equation is −4/5. Then the slope of the perpendicular line will be 5/4. Then the equation is given as,
y = (5/4)x + c
The equation that passes through (−10, 2) will be
2 = (5/4)(−10) + c
2 = −12.5 + c
c = 14.5
Then the equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.
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if you right the number from 1 to 100 how many times would you repeat 3
The number 3 will come 20 times in 1 to 100 .
In mathematics, a number serves as both a unit of measurement and a label.
The first examples are the natural numbers 1, 2, 3, 4, and so forth. Language can express numbers through the use of number terms. Numerals are symbols that are more frequently used to symbolize specific numbers; for example, the number "5" stands in for the number five. Because just a few symbols can be learnt, basic numerals are usually organized into numeral systems, which provide an ordered way to represent any number. The Hindu-Arabic number system, which enables the representation of any number using a combination of 10 fundamental numerical symbols, or "digits," is the most extensively used number system.We know that the number 3 will come up in 3 ,13 ,23,30 , 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93.
Therefore the number 3 will come up 20 times.
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Ann bowled 115,121,125,118 and 122 in five games. What must Ann bowl in the sixth game so that she will have an average score of 120 for the six games?
Ann must bowl 119 in the sixth game to have an average score of 120.
What is average?
Average is defined as the mean value that is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
According to question,
155+121+125+118+112+x= 6(120)
601+x=720
x= 720-601
x= 119
Hence, she must bowl 119 in the sixth game.
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Katie has 5 1/3 of potting soil to use in her flowerpots. It takes 1/4 pound of soil to fill one flowerpot. If Katie's flowerpots all hold the same amount of soil, how many flowerpot can she fill?
If Katie has [tex]5\frac{1}{3}[/tex] pounds of plotting soil to use in her flowerpots and it takes 1/4 pounds of soil to fill one flowerpot, then the number of flowerpot that she can fill is 21 pots
The total quantity of potting soil that she has = [tex]5\frac{1}{3}[/tex] pounds
Convert the mixed fraction to the simple fraction
[tex]5\frac{1}{3}[/tex] pounds = 16/3 pounds
The quantity of potting soil that required to fill one flowerpot = 1/4 pounds
Number of flowerpot that she can fill = The total quantity of potting soil that she has / The quantity of potting soil that required to fill one flowerpot
= 16/3 ÷ 1/4
= 16/3 × 4
= 64/3
= 21.33
≈ 21 flowerpot
Hence, if Katie has [tex]5\frac{1}{3}[/tex] pounds of plotting soil to use in her flowerpots and it takes 1/4 pounds of soil to fill one flowerpot, then the number of flowerpot that she can fill is 21 pots
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10. The sales tax rate in a certain state
Find the total price paid for a pair of shoes
that cost $35.
the total price paid for a pair of shoes after tax is included is $37.1.
A sales tax is a tax paid to the government for sales of certain types of goods and services.
According to the question,
Cost of the shoes = $35. (given)
Total amount/price paid = cost + tax
As the tax percentage is not given in the question, we will assume it to be 6% for example. Then,
Tax amount = 6% of $35
= 6/100*35
= $2.1
Now, total price = cost + tax
= $35+$2.1
= $37.1
Therefore, we conclude that the total price paid for a pair of shoes after tax is included is $37.1.
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What would 6 + -4 3/4 + -2 1/8 be?
Answer: -0.875
Step-by-step explanation:
Answer: -1 1/8
Step-by-step explanation:
6 - 4 3/4 = 1 1/4
1 1/4 - 2 1/8 = -1 1/8
The number of bald eagles in the state in the winter of 2000 is
(Round to the nearest whole number.)
Save
The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function
f(x) = -3.334x4 +35.607x3-97.645x² +41.268x + 177.537
where x is the number of years since 1996. Find the number of bald eagles in the state in the winter of 2000.
Answer:
206
Step-by-step explanation:
Let x=4.
[tex]f(4)=-3.334(4)^4+35.607(3)^3-97.645(4)^2+41.268(4)+177.537 \approx 206[/tex]
Damien played golf on each of the four days of his vacation. His scores on the first three days were 93, 92, and 89, and his average for the four days was 90. What was his score on the fourth day?.
Damien score on the fourth day is 86.
Damien played golf on each of the four days of his vacation and the average for the four days of was 90.
so, his score on the fourth day.
so firstly let, X, be his score on the fourth day. then, the other four day's score is already given so, by using the formula for average.
the average for four numbers is given by, the sum of all numbers divided by the total numbers. so, by using this formula we have
=>(93+92+89+X)/4=90.and ,
on solving this we got,
X=86.
that is our answer.
so, His score on the fourth day is 86
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Type of Probability
Based on prior experience, a teacher estimated that 95% of the
Senior class would attend the prom. Which of the following is the
type of probability is the teacher is using?
Select one:
O Experimental Probability
O Theoretical Probability
O Subjective Probability
The correct option c: Subjective Probability, defined by teacher estimated that 95% of the Senior class would attend the prom.
What is termed as the Subjective Probability?The probability of a situation expresses the possibility or chance that the event will occur as a number ranging from zero to one (or 0% and 100%), with zero indicating an impossible outcome and 1 representing a certain outcome. The calculated value of the probability could be calculated in a variety of ways.The subjective probability meaning is establishing the likelihood of a situation based solely on one's own opinion or belief, rather than on any observational data or calculations. Although this opinion may be informed by prior experience or specific observations, subjective probability is eventually just a personal preference. As a result, it is also referred to as personal probability.For the given question,
As the probability estimated by the teacher that 95% of the Senior class would attend the prom, is the personal opinion.
Thus, the given case is of Subjective Probability.
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find a polynomial that when added to 5x^2-3x-9 that has the following sum of 0
Answer:
[tex]-5x^2 + 3x+9[/tex]
Step-by-step explanation:
Let the polynomial be p(x).
[tex]p(x)+(5x^2 -3x-9)=0 \\ \\ p(x)=-(5x^2 -3x-9) \\ \\ =-5x^2 + 3x+9[/tex]
Suppose 84% of students chose to study German their sophomore year, and that meant that there were 525 such students. How many students chose not to take German their sophomore year?
Answer: 100
Step-by-step explanation:
525/84 x 100= 625 total students
625 - 525 = 100
Each handmade pin needs inch 1/4 of wood. How much wood would you need to make 120 pins?
We can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.
What do we mean by mathematical operations?A mathematical "operation" is the process of calculating a value using operands and a math operator.There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.The arithmetic operators perform the operations of addition, subtraction, multiplication, division, exponentiation, and modulus.So, the wood we need to make 120 pins:
The wood used to make 1 pin is ¼.Then, 120 pins:120 × ¼ = 30Therefore, we can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.
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A car dealership wants to try out a new leasing arrangment, which will allow a buyer to trade a car back to the dealership for a certain amount of credit at any time throughout the first three years of ownership. For a car in good condition, the arrangement will value the car at 1/3 the original price at the end of three years, and will depreciate the value of the car linearly over the course of the three years. What is the value of a car with initial purchase price P at the end of the second year? Write your answer as an expression in terms of P. Write the exact answer. Do not round.
The expression in term numerator and denomerator of P the write answer would be
25.
Sol-
we have a deal an arrangement where, at the end of 5 years, the value of the car is going to be a fifth, the original price. So that's what i have written here after 5 years, the value of the car will be the price, the original price divided by 5 point. What we also know is that at 0 years, our initial value, the output here- should be the price of the car. So what we're going to do is when we use these 2 values to find the slope of this line, so we're going to do y 2, minus 1 y 1 over x, 2 minus x 1. It doesn't matter which 1 is y 2 and which 1 is y 1 as long as you're consistent here, i'm going to do p minus p over 5, and since i started here in the numerator, i need to start there in the denominator.
So we know here that x equals 4 we're doing that in the problem. So i'm goin t go ahead and replace this right here. We'Re gonna have y equals 16 p over negative 25 plus p, and if we get a common denominator here to add this, we have y equals 16 p plus 25 over 25. With this p right here, because it's gonna be 25 p over 25 here and then i recognize that are y value here, that was that was v or value here. All right and, let's see 25 p minus 16 p is going to give us 9 p. All right, so 9 p over 25 is going to be the value of the car, giving the original price p after 4 years.
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A cylindrical drum is 20m tall and has the inner diameter of 30m. How many liters of water can be stored in it ?
Answer:
14137167 liters approximately
Step-by-step explanation:
Total Volume of a cylinder
V = π R² H
where R - base radius
H = height
Given diameter of base = 30m, base radius R = 30/2 = 15
H = 20m
Volume = π x 15² x 20 = 4500π m³ = 14,137.16694 m³
Since 1 m³ = 1000 liters
this works out to 14137.16694 x 1000 ≈ 14137167 liters
Write the quadratic equation whose roots are -3 and -1, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
The quadratic equation will be; 3x² + 6x + 9
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given that roots are x = -3 and x = - 1, and whose leading coefficient is 3.
The factors are; (x + 3) and (x + 1)
f(x) = a(x + 3)(x + 1)
As, a = 3.
Then we get;
f(x) = 3(x + 3)(x + 1)
= 3(x² + 2x + 3)
= 3x² + 6x + 9
The quadratic equation will be; 3x² + 6x + 9
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A printer prints 75 pages in 5 minutes.
At the same rate, how many pages does the printer print in 7 minutes?\
Answer:
105
Step-by-step explanation:
5 minutes=75 pages
1 minute=15 pages
7 minutes=15*7
7 minutes=105pages
Answer: 105
Step-by-step explanation:
75pg —-> 5mins
X ——> 7 mins
•
•
x= (75 x 7)/5 = 105pages
2x³-3x²-kx-17 divided by x-3 has a reminder of -2
find the value of k
Answer:
k = 4
Step-by-step explanation:
Polynomials:
p(x) = 2x³ - 3x² - kx - 17
x - 3 = 0
x = 3
It is given that when p(x) is divided by (x - 3), it leaves the remainder -2
⇒ p(3) = -2
2(3)³ - 3(3)² - k *3 - 17 = -2
2*27 -3*9 - 3k -17 = -2
54 - 27 - 3k -17 = -2
-3k + 10 = -2
-3k = -2 - 10
-3k = -12
k = (-12) ÷ (-3)
[tex]\sf \boxed{k = 4}[/tex]
Find the nth term of this quadratic sequence
-1, 2, 7, 14, 23, . . .
Answer:
The pattern the sequence follows is a perfect square, minus 2
Step-by-step explanation:
esentially use ( n^2 - 2 ) to find the nth number in the sequence.
the 5th number ( n = 5 ), would look like ( 5^2 - 2 ), simplfiying to ( 25 - 2 ), then being 23.
The same applies to all numbers listed in the sequence.
Chrystal helps her grandmother plant seeds in the garden.they plant squash, corn, sunflower, and tomatoe seeds. they plant 6 rows of each type of seed and they plant 20 seeds in each row. how many seeds do they plant?
They plant a total number of 480 seeds.
In the given question, Chrystal and her grandmother plant seeds in the garden. They plant a total of 4 types of seeds: Squash, Corn, Sunflower, and Tomato. They plant 6 rows of each type of seed. Also, each row has 20 seeds. We have to calculate the total number of seeds that they plant.
Given that,
=> Total number of types of seeds, T = 4
=> Number of rows, R = 6
=> Number of seeds in each row, S = 20
To calculate the Total Number of seeds planted we use the formula:
=> Total = T * R * S, Putting values we get:
=> Total = 4 * 6 * 20
=> Total = 480
Hence, the Total number of seeds planted is 480.
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Ang has x dollars in his savings account, and Julia has y dollars in her savings account. Ang gives Julia 1/3 of the money in his savings account, which Julia deposits into her savings account. Julia then spends 1/4 of the total in her savings account. Express the amount of money Julia spent non terms of x and y.
Answer choices
1. y/4 + x/12
2. y/4 + x/3
3. y/4 + x/7
4. 3y/4 + x/4
In terms of x and y, Julia's withdrawal from her savings account was equal to y/4 + x/12.
What does algebraic expression mean?An expression obtained by performing a finite number of algebraic fundamental operations on symbols representing numbers.
What is an illustration of an algebraic expression?Algebraic expressions have at least one variable and one operation (addition, subtraction, multiplication, division). 2(x + 8y) is an example of an algebraic expression.Both Ang and Julia have savings balances of x and y dollars, respectively.
Ang = x dollars
Julia = y dollars
Ang offers Julia a third of his savings, which she then transfers to her own savings account.
Amount in Julia's account = (1/3)x + y
Julia then spends a quarter of the total into her savings account.
Amount of money Julia spent = 1/4 × [(1/3)x + y]
= (1/12)x + (1/4)y
= y/4 + x/12
Therefore, in terms of x and y, the amount Julia spent from her savings account is y/4 + x/12.
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Jordan needs to order some new supplies for the restaurant where he works. The restaurant needs at least 730 knives. There are currently 204 knives. If each set on sale contains 10 knives, write and solve an inequality which can be used to determine xx, the number of sets of knives Jordan could buy for the restaurant to have enough knives
Answer:
53 sets
Step-by-step explanation:
730 - 204 = 526
526 / 10 = 52 r 6
therefore he'd have to buy 53 sets to have enough knives.
There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The restaurant needs at least 730 knives.
There are currently 204 knives.
And, each set on sale contains 10 knives.
Now,
By the given condition, we formulate;
⇒ 730 ≤ 204 + 10x
Solve for x as;
⇒ 730 ≤ 204 + 10x
⇒ 730 - 204 ≤ 204 + 10x - 204
⇒ 529 ≤ 10x
Divide by 10 as;
⇒ 52.9 ≤ x
After rounding, we get;
⇒ 53 ≤ x
Thus, There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.
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