The solution to the inequality is x > 0
What is Inequality?Inequality in mathematics differentiate two values, if one is less than, greater than, or not equal to another value
Evaluate the equation by letting the unknow to be on one side
−1 − 10x < −1
-10x < -1+1
Add +1 to both sides
= -1-10x+1 < -1+1
= -10x < 0
Divide both sides by -10 same factor and flip the relation because of negative factor
= -10x /-10 > 0/-10
= x > 0
Therefore the solution to the inequality is x>0
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PLS HELP ME ANSWER THIS QUESTIONNAIRE
The correct value of the simplified expressions found using the laws of indices gives;
d. [tex]\sqrt[4]{4}[/tex]a. [tex]\sqrt{\frac{5}{6} }[/tex]d. 3a. [tex]x\cdot \sqrt{y}[/tex]b. x²·yb. 1a. 1/315·x²·y⁴e. 6·x³·y⁵c. [tex]\frac{5}{9}[/tex]What are the laws of indices?The laws of indices state rules that enable the simplification of the combination of expressions of numbers and variables that are given in index form or involve powers of other numbers or variables
1. [tex]3^{\frac{1}{4} } = \sqrt[4]{4}[/tex]
The radical sign is used for expressing fractional indices.
The correct option is d. [tex]\sqrt[4]{4}[/tex]
2. The radical is in its simplest form when it cannot be further simplified, which gives the radical in its simplest form as option a. [tex]\sqrt{\dfrac{5}{6} }[/tex]
3. The index of a number is the number to which the variable or number is raised
The index of x³ in [tex]\sqrt{x^3}[/tex] is d. 3
4. The given expression has y raised to the power of [tex]\frac{1}{2}[/tex], which gives;
[tex]x\cdot y^\frac{1}{2} = x\cdot \sqrt{y}[/tex]
The correct option is a. [tex]x\cdot \sqrt{y}[/tex]
5. The common index of the expression within the parenthesis is [tex]\frac{1}{2}[/tex], which gives;
[tex](x^4\cdot y^2)^\frac{1}{2} = (x^{4\times \frac{1}{2} }\cdot y^{2 \times \frac{1}{2} })=x^2\cdot y[/tex]
The correct option is b. x²·y
6. The value of all numbers raised the power of zero is 1, therefore;
[tex](2^{1/3}\cdot 3^{1/4})^0\cdot (2^{1/5}\cdot 3)^0 = 1 \times 1=1[/tex]
The correct option is b. 1
7. The given expression can be simplified as follows;
[tex]\sqrt[5]{\dfrac{1}{243} } = \sqrt[5]{\dfrac{1}{3^5} } = \sqrt[5]{\left(\dfrac{1}{3} \right)^5} = \dfrac{1}{3}[/tex]
The correct option is therefore; a. 1/3
8. The given expression [tex]\sqrt{225\cdot x^4\cdot y^8} = \sqrt{15^2\cdot x^4\cdot y^8} = 15\cdot x^2\cdot y^4[/tex]
The correct option is [tex]15\cdot x^2\cdot y^4[/tex]
9. The given expression is [tex]\sqrt[3]{216\cdot x^9\cdot y^{15}}[/tex]
[tex]\sqrt[3]{216\cdot x^9\cdot y^{15}} = \sqrt[3]{6^3\cdot x^9\cdot y^{15}} = 6\cdot x^3\cdot y^5[/tex]
The correct option is e. [tex]6\cdot x^3\cdot y^5[/tex]
10. [tex]\sqrt{\dfrac{50}{162} } = \sqrt{\dfrac{25\times 2}{81\times 2} } = \sqrt{\dfrac{25}{81} } = \dfrac{5}{9}[/tex]
The correct option is c. [tex]\frac{5}{9}[/tex]
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how do you simplify the distributive property ?
Answer:
for example 2(3+1)
to solve with the distributive property you multiply the number outside the parentheses(2) with each inside number(3 and 1) individually.
2(3)+2(1)
now solve
6+2=8
now to check it by solving the regular way
2(3+1), 3+1=4 so
2(4)
8
we can see that the answers are the same.
to use the distributive property with x in it
for example, -3(x-6)
multiply the outside number(-3) with each inside number(x and -6)
-3(x)+(-3)(-6)
simplify
-3x-(-18)
-3x+18
hope this helps!
f(-3) evaluate the function of the graph
The composition f(-3) has a value of 1
How to evaluate the function on the graph?The definition of the function is represented by the graph
So, we call the graph function f(x)
To find the function f(-3), we set the value of x in the function of the graph f(x) to -3
This is represented by
Calculate f(x), when x = -3
So, we look for the corresponsing points on the graph where x = -3
In this case;
The value of the function is 1 when the value of x is -3
This means that
f(-3) = 1
Hence, the value of the function is 1
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The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number? Justify your reasoning
.
Answer:
40
Step-by-step explanation:
Looking at the other examples, its shows the the second number is always 4 times bigger/ahead then/of the first number.
write ax +by =c in terms of a? solve for a
Answer:
a = (c - by) / x
Step-by-step explanation:
ax + by = c
ax = c - by
a = (c - by) / x
How do you find if the vertical or horizontal asymptote is going to be approaching negative infinity or positive infinity. Provide examples.
Answer:
to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.
Step-by-step explanation:
PLEASE HELP ME!!!!!!!!!!!!
1. Simplify the expression: 13 [6²÷(52-42) +9]
ERROR ANALYSIS Describe and correct the error. QRS=VWX by the ASA Congruence Theorem
Answer:
The error made is that the ASA theorem cannot be used here because the congruent side is not directly in between the two congruent angles in either triangle. Really, the information we are given is Angle-Side-Side, not Angle-Side-Angle, and this is not a congruence theorem unless the triangles given are right triangles.
Find the value of x. Then find the measure of each labeled angle
(3x+6)
(4x-12)
answer:
x = 18, 60.
step-by-step explanation:
evaulating (3x+6) = (4x-12) and solving for x gives us x = 18. you didn't include the angle, so i can't give you that. but
(3x+6) = 60
(4x-12) = 60
if those were your angles, you would have an equilalateral triangle (all sides/angles even) and your missing angle would also be 60.
The temperature drooped 2F every hour for 6 hours. What was the total number of degrees the temperature changed in the 6 hours?
please help me I’m really stuck on this
Answer:
x < 1 and x > -4 (more down below)
Step-by-step explanation:
First we have to solve the algebra
|-2x - 3| + 2 < 7
|-2x - 3| < 5
1. -2x - 3 < -5 2. -2x -3 < 5
-2x < -2 -2x < 8
x < 1 x > -4 (switch the expression)
Now... The two answers are x < 1 and x > -4
The interval notation is a number line with circles on the two points (answers)
Sorry I can't exactly explain what that is you might have to search it up, but you need a number line like this, and you need to draw another line above the -5 and 1 with an open circle on -5 and 1
O-----------------------O
<---5, -4, -3, -2, -1, 0, 1, 2-->
For graphing, make a graph with 5 points on each side with 4 quadrants or whatever reasonable size, and draw a vertical line that extends all the way above and below your graph above 1 on line x and a vertical line all the way above and below your graph above above -5 on x, then shade everything in between those two lines.
This helps you to know what value you plug in for X makes the inequality true (shaded region)
Determine whether the relation is a function.
(0, 1) (5, 6) (7, 9) (8, 9)
A. Not a function, there is not a unique y-value for each x-value
B. Not a function, there is not a unique x-value for each y-value
C. Function, there is a unique x-value for each y-value
D. Function, there is a unique y-value for each x-value
Answer:
C. Function, there is a unique x-value for each y-value
Simplify the expression:
(–5.5 + 2p)(–2) =
The expression, (–5.5 + 2p)(–2), after simplification is 11-4p.
According to the question,
We have the following expression:
(–5.5 + 2p)(–2)
Now, in order to simplify this expression, we will multiply -2 into the bracket:
(Note that when a number or a variable is multiplied into the bracket then it is multiplied into every number or term within the bracket.)
-5.5*-2+2p*(-2)
We know that when two negative integers are multiplied then the result is positive and when one negative and one positive integer is multiplied then the result is negative.
11-4p
Hence, the expression, (–5.5 + 2p)(–2), after simplification is 11-4p.
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Solve for y.
4y + 5/3=y-10/2
Answer:
y= -20/9
Step-by-step explanation:
4y+5/3=y-5
3y= -(5+5/3)
3y= -20/3
y= -20/9
Answer:
Collect like terms
4y-y=-10/2-5/3
3y=-5-5/3
5-5/3
LCM=3
3/1=3×5=15
3/3=1×5=5
15-5÷3
10/3
3y=10/3÷3
3y=30/3
y=10
1. [-/1 Points]
DETAILS
Find the x- and y-intercepts.
7x - 6y = 1
x-intercept (x, y) = (
y-intercept (x, y) = (
(x, y) = (
multiply x times y divide by 6 on both sides and you got your answer
Find the distance from the point 4(2-1) to the liney=-x+4. Round your answer to the nearest fenth.
Answer:
2.12
Step-by-step explanation:
Discussion
The answer is given in the graph I've made for you. The distance you want is a contained in a line that is perpendicular to the given line and goes through (2,-1). If I have not interpreted this correctly please leave a comment under the question and I will edit it. I have ignored the 4.
The steps needed are
Find the slope of the line perpendicular to y = - x + 4Find the intersection point on y = - x + 4 and the new line.Use the distance formula to find the distance from (2,-1) to the intersection point found in the second stepGivens
line y = -x + 4
point (2,-1)
Solution
The slope of the second line is
m1 * m2 = - 1
m1= -1 From the given equation
m2 = ?
-1 * m2 = - 1
m2 = 1
Find the equation of the new line
x = 2
y = - 1 from the given point
-1 = 2 + b Subtract 2 from both sides
-1 - 2 = 2-2 + b Combine
-3 = b
Equation of the new line
y = x - 3
Intersection point of the two lines
y = -x + 4
y = x - 3 Add The xs cancel
2y = 1 Divide by 2
y = 1/2
1/2 = -x + 4 Subtract 4 from both sides
1/2 - 4 = -x + 4 -4 Combine
-3 1/2 = -x Multiply both sides by - 1
3 1/2 = x
So the intersection point is (3.5, 0.5)
Find the distance between (2,-1) and (3.5,0.5)
d = sqrt( (2 - 3.5)^2 + (-1 - 0.5)^2 )
d = sqrt( (-1.5)^2 + (-1.5)^2 )
d = ( 1..5 * sqrt(2) )
d = 2.12
the line passes through (6,6) and (-2,2)
Answer:
Step-by-step explanation:
slope=change in y over change in x
6-2=4
6--2=6+2=8
-4/-8=1/2
1. If f(2)= -5, what does 2 represent?
2. If f(2)=-5, what does -5 represent?
3. What does f(2)= -5 mean?
In the function f(2)= -5, 2 is the preimage of the function and 5 is an image of the function.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
Suppose that f(a) = b
In that case, element "b" is the image of element "under the function," while element "a" is the preimage of element "under the function."
In the given function f(2)= -5
2 is the preimage of the function and 5 is an image of the function.
Hence, the 2 is the preimage of the function and 5 is an image of the function.
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(a) Annie and Dermot share $600 in the ratio 11:9.
(i) Show that Annie receives $330.
Ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount received by Annie is $330 and Dermot is $270.
As given in the question,
Total amount share by Annie and Dermot is $600.
Ratio of amount share by Annie and Dermot is 11 : 9
Let x be the amount of money.
11x + 9x = $600
⇒ 20x = $600
⇒20x/20 = $600/20
⇒x= $30
Amount received by Annie is equal to
= 11 × 30
= $330
Amount received by Dermot is equal to
= 9 × 30
= $270
Therefore, ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount received by Annie is $330 and Dermot is $270.
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19. Spotify revealed that about 47% of its users are aged 13-24, 25% are aged 25-34, and 28%
are 35 or older. Suppose that for the 13- to 24-year-olds, 85% identified pop as their favorite
music genre, 59% of the 25- to 34-year-olds identified pop as their favorite music genre, and
23% of the users 35 or older identified pop as their favorite music genre. Suppose we select
one Spotify user at random and record his or her age and whether his or her favorite music
genre is pop.
The probability is 0.061 to record his or her age for her favorite music genre is pop.
What is meant by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur. An event's probability is a number between 0 and 1, where 0 indicates impossibility and 1 represents certainty. The more likely an occurrence is, the more likely it will occur. A simple example is tossing a fair (unbiased) coin. Because the coin is fair, all outcomes are equally likely; the probability of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of "heads" or "tails" is 1/2.
Given,
Age Users Pop-music
13-24 47% 85%
25-34 25% 59%
35-more 28% 23%
Let the total population be 100 then
Age Users Pop-music
13-24 47% 85% of 47=39.95
25-34 25% 59% of 25=14.75
35-more 28% 23% of 28=6.44
Persons having favorite music game as pop=34.95+14.75+6.44
=61.14
Probability=61.14/100c₁
=0.061
Therefore, the probability is 0.061.
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Which function represents the i shown in the graph below
A. G(x)=-x+2
B. G(x)=2^x-1
C. G(x)=(x+2)^2
D. -2x
Which of the
following best describes the
slope of the line below?
• A. Positive
• B. Negative
• C. Zero
• D. Undefined
Answer:
negative
Step-by-step explanation:
Please help me I need this I'm behind
Answer:
25.5 feet because of some
Step-by-step explanation:
.,........
Answer:
Step-by-step explanation:
divide 14 7/8 by 6 because you want to find out how much 6 inches is their in 14 7/8 because that the giving inchwhen you do 6 ÷ 14 7/8 you get 2.47916666667now you multiply by 3 1/2 with is the same as 3.5 and you get 8.67708333333 and that rounds to 8.68.Answer: 8.68 feetAnthony's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=57+7.4x, where y represents the expected quiz score and x represents hours spent on homework that week. What is the meaning of the x-value when y=90
The meaning of the x-value when y=90 means that Anthony will use 3.1 hours.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The relationship that can be represented by the equation y=57+7.4x,
where
y represents the expected quiz score
x represents hours spent on homework that week.
When y = 90, the value of x will be:
y=57+7.4x
57 + 7.4x = 90
Collect like terms
7.4x = 90 - 57
7.4x = 23
Divide
x = 23/7.4
x = 3.1
He'll use 3.1 hours.
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What is the solution of the inequality -8(x + 7.5) ≤ 10?
Step-by-step explanation:
-8(x + 7.5) ≤ 10?
expand left side:
-8x - 60 ≤ 10
subtract 60 to both sides:
-8x - 60 + 60 ≤ 10 + 60
-8x ≤ 70
dive both sides by -8: (Remember when dividing by a negative number, you flip the direction of the inequality sign)
-8x/-8 ≥ 70/-8
x ≥ -35/4
reduce right side:
x ≥ -35/4 or x ≥ -8.75 [depends on if you need fractional or decimal format]
so in set builder format: [-35/4 , ∞) or [-8.75 , ∞) [depends on if you need fractional or decimal format]
how many three-digit positive integers leave a remainder of 2 when divided by 5 and a remainder of 6 when divided by 7?
There are 180 three-digit numbers that leave a remainder of 2 when divided by 5 and 128 three-digit numbers that leave a remainder of 6 when divided by 7.
The smallest 3-digit number to leave a remainder of 2 when divided by 5 is 102.
The next number will be 107, and then 112,
The last 3 digit number to leave a remainder 2 when divided by 5 is 997
Therefore here we get an Arithmetic Progression
102, 107, 112, ..., 997
We know that for any term of an A.P
aₙ = a + (n - 1)d
where,
a = first term
n = the order number of that particular value
d = common difference
Here,
a = 102
d = 107 - 102
= 5
The number of 3 digit number for the above problem will be the value of n for 997
Hence we get
997 = 102 + (n - 1)5
or, 102 + 5n - 5 = 997
or, 5n + 97 = 997
or, 5n = 997 - 97
or, 5n = 900
or, n = 900/5
or, n = 180
Next, we need to find the no. of three-digit numbers that leave the remainder of 6 when divided by 7
The smallest 3-digit number to leave the remainder of 6 when divided by 7 is 104
The largest is 993
Therefore, just like before, we get the A.P
104, 111, 118, ..., 993
here,
a = 104
d = 7
aₙ = 993
Hence we get,
993 = 104 + (n - 1)7
or, 104 + 7n - 7 = 993
or, 97 + 7n = 993
or, 7n = 993 - 97
or, 7n = 896
or, n = 128
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Help asap please and I will give brainliest!
Anson estimated he would need 17 hours to complete is science project. He actually needed 19 1/2 hours. What was his percent error?
Answer: 14.7%
Step-by-step explanation:
% error = (estimated - actual) / (actual) x 100
% error = (17 - 19.5) / 17 x 100 = - 14.7%
The negative sign means that he underestimated the time needed
a person's blood glucose level and diabetes are closely related, let x be a measurement in milligrams of glucose per deciliter of blood, after 12-hour fast, the variable x will have a Distribution that is approximately normal with a mean of 85 and standard deviation of 25. this is only true for adults under 50. Use this information to answer the question that follow:
what percentage of people have a blood glucose level between 100 and 125?
The percentage of people that have a blood glucose level between 100 and 125 is 21.945%
How to determine the percentage between 100 and 125?From the question, the given parameters about the distribution are
Mean value of the set of data = 85
Standard deviation value of the set of data = 25
The actual data values = 100 and 125
The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
For x = 100, we have:
Substitute the given parameters in the above equation
z = (100 - 85)/25 = 0.6
For x = 125, we have:
Substitute the given parameters in the above equation
z = (125 - 85)/25 = 1.6
The percentage between 100 and 125 is then calculated as:
P(100 < x < 125) = P(z < 1.6) - P(z < 0.6)
From the z table of probabilities, we have;
P(100 < x < 125) = 0.9452 - 0.72575
This gives
P(100 < x < 125) = 0.21945
Express as percentage
P(100 < x < 125) = 21.945%
Hence, the percentage is 21.945%
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