The solution for the inequality | x | + 9 ≤ 7 is (option d) x ≤ -2 and x > -16
You can solve an inequality by: adding the same amount to each side; taking the same amount away from each side; multiplying or dividing each side by the same positive amount. The inequality symbol needs to be turned around if either side is multiplied or divided by a negative number. Therefore, the answer is x > 1.
Given,
The expression: | x | + 9 ≤ 7
If | x | ≤ a ⇒ -a ≤ x ≤ a
Then,
-7 ≤ | x | + 9 ≤ 7
⇒ -7 - 9 ≤ x ≤ 7 - 9
⇒ -16 ≤ x ≤ -2
That is x ≤ -2 and x > -16.
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What quartic polynomial equation has roots 2-3 i, 8,2 ?
The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96
Given,
Zeros are: x = 2, x = -3, x = 8, and x = 2
That is: x + 2 = 0, x - 3 = 0, x + 8 = 0, and x + 2 = 0
So the factors are: (x + 2) (x - 3) (x + 8) (x + 2) = 0
Multiply two at a time:
(x + 2)(x - 3) = x² - x - 6
(x + 8)(x + 2) = x² + 10x + 16
Now multiply those polynomials together using distributive method:
x² (x² + 10x + 16) - x(x² + 10x + 16) - 6(x² + 10x + 16)
= x⁴ + 10x³ + 16x² + x³ + 10x² + 16x - 6x² - 60x - 96
= x⁴ + 11x³ + 20x² - 44x - 96
The Quatric polynomial is x⁴ + 11x³ + 20x² - 44x - 96
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pls help i don't understand
Find the AREA (base x height), in square microns, of a rectangular object with a width of 6,000 microns and a length of 2,000,000 microns.
Show your work and write your final answer in scientific notation.
The area of this rectangular object is equal to 12 × 10⁹ square microns.
Given the following data:
Length of rectangle, L = 2,000,000 microns.Width of rectangle, W = 6,000 microns.How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Substituting the given parameters into the formula, we have;
Area of a rectangle = 6,000 microns × 2,000,000 microns
Area of a rectangle = 12 × 10⁹ square microns.
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34. Samir can rent a moving truck
from Company A for $135 plus
$0.50 per mile or from Company B
for $125 plus $0.70 per mile. Which
statement is true?
® Renting from Company A will
always be cheaper.
® Renting from Company B will
always be cheaper.
Renting from both companies
will cost the same if Samir drives
the truck 50 miles.
Renting from Company B will be
cheaper if Samir drives the truck
100 miles.
According to linear equation, Renting from Company A will always be cheaper. Thus option A is correct option.
According to the statement
We have to find that the correct statement.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
Samir can rent a moving truck from Company A for $135 plus $0.50 per mile or from Company B for $125 plus $0.70 per mile.
Then
The equation is given as,
y = mx + c
Where m is that the slope of the road and c is that the y-intercept of the line.
Let y be the whole amount and x be the amount of miles.
Samir can rent a moving truck from Company A for $135 plus $0.50 per mile. Then the equation are going to be
y = 0.5x + 135 ....1
Company B for $125 plus $0.70 per mile. then the equation are going to be
y = 0.7x + 125 ....2
For the identical rent, the amount of miles are going to be
0.7x + 125 = 0.5x + 135
0.2x = 100
x = 500 miles
Renting from Company A are going to be cheaper if Samir drives the truck 500 miles. Then the right option is A .
So, According to linear equation, Renting from Company A will always be cheaper. Thus option A is correct option.
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The circle represents a pizza.
Using only four straight slices
(straight lines) see if you can
make a pizza with 10 pieces
(pieces don't have to be the
same size or shape):
Answer:
Cross two lines then put one line above the point of intersection and below the point of intersection. straightforward though
Identify if slope is negative or positive (please)
The slopes are:
the top graphs, we have (from left to right): Negative, positive, positive, positive.Now the bottom ones: Negative, positive, negative, positive.How to identify if the slope is positive or negative?A general linear equation in the slope-intercept form is written as:
y = m*x + k
Where m is the slope and k is the y-intercept.
Particularly, if the slope is positive, we will see that the line goes upwards when read from left to right, while if it is negative, it goes downwards.
First the top graphs, we have (from left to right)
Negative, positive, positive, positive.
Now the bottom ones:
Negative, positive, negative, positive.
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can someone help me really quick
Answer:
2.5£ =25tacos
1£ =?
=1*25/2.5
=10 tacos:
A farmer, Sarah, has 54 hectares of hay to harvest. She hires a harvester
at £1200 a day. If Sarah can harvest 12 ha per day, what will it cost her to
harvest this hay?
round the square root of 62 to 1 dp
Answer:
7.9
Step-by-step explanation:
yep
Is it possible for a number to be both a whole number and an integer why and why not
A number system is defined as the representation of numbers by using digits or other symbols. It is possible for a number to be both a whole number and an integer.
What is a Number system?A number system is defined as the representation of numbers by using digits or other symbols in a consistent manner.
The given question is Is it possible for a number to be both a whole number and an integer why and why not.
The answer is yes because every whole number is an integer but not every integer to be a whole number.
For example 5 is both a whole number and integer but -5 is a integer but ot a whole number because in whole numbers we do not have negative numbers.
Therefore it is possible for a number to be both whole number and integer.
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14. The nth term of a quadratic sequence is n²+ 3n-2
(a) Find the fourth term of this sequence.
Here are the first five terms of a different quadratic sequence.
1, 7, 17, 31, 49
(b) Find, in terms of n, an expression for the nth term of this sequence.
Step-by-step explanation:
14a)
the 4th term = 4² + 3×4 - 2 = 16 + 12 - 2 = 26
b)
1, 7, 17, 31, 49
s1 = 1
s2 = s1 + 6
s3 = s2 + 10
s4 = s3 + 14
s5 = s4 + 18
the added term d grows with every step by 4. starting with a constant "+ 2" on top of -1 to create s1.
d1 = 2
d2 = d1 + 4
d3 = d2 + 4
dn = dn-1 + 4 = d1 + 4(n-1)
s1 = -1 + d1
s2 = s1 + d2 = -1 + d1 + d1 + 4
s3 = s2 + d3 = -1 + d1 + d1 + 4 + d1 + 4 + 4
s4 = s3 + d4 = -1 + d1 + d1 + 4 + d1 + 4 + 4 + d1 + 4 + 4 + 4
sn = -1 + n×d1 + sum(4(n - 1)) = -1 + 2n + 4n(n - 1)/2 =
= -1 + 2n + 2n(n - 1) = -1 + 2n(1 + n - 1) = -1 + 2n² =
= 2n² - 1
simplify the following expression. 7^5/6 x 7^7/6
A. 1/14
B. 14
C. 1/49
D. 49
The simplified form of the given expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is option d 49.
Given,
The expression = [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]
We can simplify this expression by using Laws of Indices;
The first rule: [tex]a^{n}[/tex] × [tex]a^{m}[/tex] = [tex]a^{m+n}[/tex]
The second rule: [tex](a^{n}) ^{m}[/tex] = [tex]a^{mn}[/tex]
The third rule: [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]
The fourth rule: [tex]a^{0}[/tex] = 1
The fifth rule: [tex]a^{-1}[/tex] = [tex]\frac{1}{a}[/tex] ; [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
The sixth rule: [tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex] ; [tex]a^{\frac{1}{m} }[/tex] = [tex]\sqrt[m]{a}[/tex] ; [tex]a^{\frac{n}{m} }[/tex] = [tex](a^{\frac{1}{m} } )^{n}[/tex] = [tex](\sqrt[m]{a} )^{n}[/tex]
Here we can use First, Second, Fifth and Sixth rule:
[tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex]
= [tex](7^{5} )^{\frac{1}{6} }[/tex] ×[tex](7^{7} )^{\frac{1}{6} }[/tex]
= [tex]16807^{\frac{1}{6} }[/tex] × [tex]823543^{\frac{1}{6} }[/tex]
= 5.061140185 × 9.68161288
= 49
That is, the simplified form of the expression [tex]7^{\frac{5}{6} }[/tex] × [tex]7^{\frac{7}{6} }[/tex] is 49.
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if a bag contains 10 red 6 yellow 24 blue and 8 white balloons what si the part to whole ratio of blue balloons to all baloons
Answer: Part to whole is 1:2
Unit 2A sample work the distributive property
PLEASE HELP
Answer: 1b. 5x - 30, 1c. -8x - 32, -8x + 12, 1e. -6x + 21, 1f. 3( 3x - 9)
Step-by-step explanation:
You multiply the number outside of the parentheses by the numbers inside, if it's just an "x", you assume there's a 1 beside it, ex: 8(x + 2)... 8 multiplied by x will give you 8x, 8 multiplied by 2 will give you 16.
if the numbers are both negative when you multiply them it becomes a positive, ex: -8(x - 2)... -8 multiplied by x will be -8, and -8 multiplied by -2 will become positive 16.
But if one number is negative and the other is positive then the answer will be negative.
at a clothing store a pair of jeans costs 50$. Using a coupon, shanice can pay 20$ less than the original price. Determine the percentage off the original price the coupon represents. Show your work in the space provided. The coupon gives shanice _____% off the original price. HELP HELP
The coupon gives Shanice 40% off the original price, based on the coupon of $20 on an original price of $50
What is the price after having considered the coupon?
The price of the pair of jeans after having considered the coupon is the original price of $50 minus the $20 coupon
price after the coupon=$50-$20
price after the coupon=$30
However, the task at hand is to determine the coupon as a percentage of the original price
coupon as % of original price=$20/$50
coupon as % of original price=40.00%
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solve: 1/2 x 3.4/4. Why is this your answer? How do you know this is correct?
Answer: 3.4/8 or 0.425
Step-by-step explanation:
Use this Rule: a/b * c/d = ac/bd
Simplify numerator (top): 1 * 3.4 = 3.4
Than Simplify denominator (bottom): 2 * 4 = 8
Finally: 3.4/8 or 0.425 (decimal)
This is my answer and I know this is correct because of using the Rule which demostrates that you should multiply top and bottom
PLEASE HURRY THIS WAS DUE A HOUR AGO
What is the sum
-8 + 6 =
Answer:
-2
Step-by-step explanation:
Integer math!
Cody decreased the speed of his car by 3.5 miles per second over the period of 60 seconds. find the average change in speed each second
The average change in speed each second is 0.0583 miles per squared second
How to find the average change in speed each second?The given parameters are:
Speed = 3.5 miles per second
Time = 60 seconds
The average change in speed each second is calculated as
Average change = Speed/Time
This gives
Average change = (3.5 miles per second)/60 seconds
Evaluate the quotient
Average change = 0.0583 miles per squared second
Hence, the average change in speed each second is 0.0583 miles per squared second
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You jog at a rate of 6 miles per hour. Your friend is 55 feet ahead of you and jogs at a rate of 6.6 feet per second. Write and solve an inequality that represents the amounts of time, t , that your friend is ahead of you.
The inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to write and solve an inequality that represents the amounts of time your friend is ahead of you?The given parameters are
Your rate, r1 = 6 miles per hour
Your friend's rate, r2 = 6.6 feet per second
Distance apart = 55 feet
Convert your rate to feet per second, we have
Your rate, r1 = 6 * 1.47 feet per second
Evaluate
Your rate, r1 = 8.8 feet per second
To calculate the time that your friend is ahead of you, we use the following expression
r1 * t < distance apart + r2 * t
So, we have
8.8t < 55 + 6.6t
Collect the like terms
So, we have
8.8t - 6.6t < 55
Evaluate the like terms
So, we have
2.2t < 55
Divide both sides by 2.2
So, we have
t < 25
Hence, the inequality expression is 8.8t < 55 + 6.6t and your friend will be ahead for at most 25 seconds
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The methods used to analyze data produced by scientific studies are called:_____.
a. experiments.
b. correlations.
c. statistics.
d. replications.
The methods used to analyze data produced by scientific studies are called statistics. Option (c) is correct.
What are experiments and how do we analyze them using statistics?
Experiments are procedures or methods carried out under controlled conditions to discover a new fact or to test or establish a hypothesis that already exists.
From experiments we generate certain scientific data but to analyze data we need statistics.
Statistics is a process of collecting and analyzing and interpreting data.
Therefore the methods used to analyze data produced by scientific studies will be done by statistics.
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Answer:
Step-by-step explanation: Hello,
the answer
Which number is closest to 161 ?
positive square roots
in decimal form
The number that is closest to the square root of 161 is 13.
How to calculate the square root?In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer.
A number y such that y² = x, or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, -4 and 4 are the square roots of 16.
It should be noted that the square root of 161 is 12.689. Therefore, the number that is closest to the square root of 161 is 13.
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Which number is closest to the square root of 161 ?
2x - 6y = 6
6x- 4y = 2
Answer:
3/7y= -8/7
Step-by-step explanation:
reduce the greatest common factor on both sides of th equation
find the circumference and the area of a circle with diameter 8 cm.
Answer:
Step-by-step explanation:
If the diameter is 8 cm, and the formula is A=pie*radius^2, the radius is 4.
The area would be 16*pie
The formula for finding the circumference 2*pie*radius, so the circumference is 8*pie.
An online music store is having a promotion. Customers receive a $ 5 rebate if they buy any regular priced CD at $ 13 each. They can also recelve 15% off if they register as a store member.
c. Use your answer from part (b) to determine the amount a customer will save if she buys 5 CDs.
The amount a customer will save if she buys 5 CDs will be equal to $ 30.25
We are given that:
Rebate a customer receives if he buys a regular priced CD at $ 13 each = $ 5.
If a customer registers for the store member, he get a discount = 15 %.
Now, let the regular priced CD purchased be x and the application for store member be y.
So, the functions will become:
For rebate:
R (x) = 5 x
For discount:
M (y) = 15 % of x
M (y) = 0.15 x
Now, the amount a customer has to pay if she takes the membership and then takes the rebate =(1 − 0.15) (13 x) − 5 x = 6.05 x
If x = 5 ( number of CD)
= 6.05 ( 5)
= $ 30.25
Therefore, we get that, the amount a customer will save if she buys 5 CDs will be equal to $ 30.25
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Using the graph below which of the following is a gas
A: NaCI
B: KCI
C: NaNO3
D: Ce2(SO4)3
Using the graph of solubility, D. Ce₂(SO₄)₃ is a gas
What is a gas?A gas is a state of matter with no fixed shape or volume.
What is solubility?Solubility of a substance is the amount of solute that can dissolve in unit volume of solvent at a given temperature.
Which of the following compounds is a gas?Note that the solubility of a substance depends on the temperature
For gases, the solubility decreses with incresing temperatureFor liquids, temperature has no effect on solubility and For solids, the solubility increases with temperature if the reaction is endothermixc and dedreases with temperature if the reaction is exothermic.From the graph above, we see that the compound with the least solubility is Ce₂(SO₄)₃. Since the solubility of gases derease with increasing temperature, thus Ce₂(SO₄)₃ is a gas
So, using the graph of solubility, D. Ce₂(SO₄)₃ is a gas
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what is the equation 2(h+3.5)=-11
Answer:
h = -9
Step-by-step explanation:
Open the parentheses:
2(h+3.5) = -11
2h+7 = -11
Subtract 7 both sides
2h = -11 - 7
2h = -18
h = -9
Simplify each number. 125 . 125¹/₃
[tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.
Prime factorization is the process of breaking down a number into its prime factors. Multiplying these prime numbers gives back the original number.
Prime factorization of 125 = 5 x 5 x 5 = [tex]5^{3}[/tex]
According to the law of indices, if a term with a power is raised to a power, then the powers are multiplied together.
i.e., [tex](x^{m})^{n} = x^{mn}[/tex]
Another law of indices says that if two terms having same base are multiplied together, then their indices are added.
i.e., [tex]a^{m} X a^{n} = a^{m+n}[/tex]
According to the given condition,
[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3} )^{\frac{1}{3} }[/tex]
Applying the laws of indices mentioned above,
[tex]125. 125^{\frac{1}{3} }[/tex] = [tex]5^{3} .( 5^{3 X} ^{\frac{1}{3} })[/tex]
= [tex]5^{3} .( 5 )[/tex] = [tex]5^{3 + 1}[/tex]
= [tex]5^{4} = 625.[/tex]
Thus, [tex]125. 125^{\frac{1}{3} }[/tex] can be simplified into 625.
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Find the measure of
Answer:
12
Step-by-step explanation:
See attachment for step-by-step instructions
Evaluate the expression. 1 4 + 1 2 ÷ 2 3 ÷ 3 5 Write your answer as a fraction or as a whole or mixed number.
The solution of the expression 1/4 + 1/2 ÷ 2/3 ÷ 3/5 is 1 1/2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution of the expression?The expression is given as
1/4 + 1/2 ÷ 2/3 ÷ 3/5
Express the quotient as a product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 1/2 x 3/2 ÷ 3/5
Evaluate the product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 3/4 ÷ 3/5
Express the quotient as a product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 3/4 x 5/3
Evaluate the product
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1/4 + 5/4
Evaluate the sum
So, we have
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 6/4
Simplify
1/4 + 1/2 ÷ 2/3 ÷ 3/5 = 1 1/2
Hence, the solution of the expression 1/4 + 1/2 ÷ 2/3 ÷ 3/5 is 1 1/2
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Use synthetic division to determine whether each binomial is a factor of 3x³+10 x²-x-12 x+3.
What is the
equation of the line through (-2, 5) and (0, 3)?
Answer:
y=-x+3
Step-by-step explanation:
the gradient of the equation is -1
and the y intercept is 3