Solve the following inequality. Write the solution set using interval notation.23 + 8x ≥2x-7
Answers
Given the inequality below
\(23+8x\ge2x-7\)To find the solution set of the inequality above, there would be need to sovle for x and interprete the resulting inequality.
Firstly, collect like terms
\(8x-2x\ge-7-23\)Evaluate the equation above
\(6x\ge-30\)Divide both sides by the coefficient of x, which is 6
\(\frac{6x}{6}\ge\frac{-30}{6}\)\(x\ge-5\)In interval notation, the solution set is wriiten as
\(\lbrack-5,\infty)\)Hence, the solution set of the inequality 23 + 8x ≥ 2x - 7 is
[ -5, ∞)
Related Questions
PLEASE HELP AS SOON AS POSSIBLE
Answers
Answer:
B
Step-by-step explanation:
Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.
Cat este 5 la puterea 24
Answers
Answer:
5.9604645e+16
Step-by-step explanation:
Iată ce a apărut într-un calculator
What is the diameter of a circle with a circumference of 29.4ft?
Answers
Answer:
9.358
9.36 (rounded to the nearest hundredths)
9.4 (rounded to the nearest tenth)
Step-by-step explanation:
d = C/π = 29.4/π ≈ 9.358
Match each equation to its solution.
A. 7 + x^2 = 16. 1. x = 4
B. 5- x^2 = 1 2. x = 1
C. 2 x 2^3 = 2^x 3. x = 2
D 3^4 / 3^x = 27. 4. x = 3
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B is x=2
C is x=4
D is x = 1
plz answer my question
Answers
When you diffuse (multiply) the 4 to the rest of the number r become 4r and 3 becomes 12 giving you the equivalent of 4r+12
What are the centimeters to the nearest tenth of the hypotenuse and leg?
Answers
Answer:
Hypotenuse = 10.4cm
Leg = 6.7cm
Explanation:
Let x represent the unknown leg of the triangle.
To be able to find x, we have to take the tangent of angle 40 degrees as shown below;
\(\begin{gathered} \tan 40=\frac{x}{8} \\ 8\tan 40=x \\ x=6.7\operatorname{cm} \end{gathered}\)Let y represent the length of the hypotenuse.
To find y, we have to take the cosine of angle 40 degrees;
\(\begin{gathered} \cos 40=\frac{8}{y} \\ y\cos 40=8 \\ y=\frac{8}{\cos 40} \\ y=10.4\operatorname{cm} \end{gathered}\)A gas can hold 10 L of gas how many cans could we filled filled with 7 L of
Answers
Answer:
2 cans
Step-by-step explanation:
How many miles will light travel in one day if the speed of light is 300,000,000 meters per second.
(1.62 km = 1 mi)
Answers
Answer:
\(d=1.61\times 10^{10}\ miles\)
Step-by-step explanation:
Given that,
The speed of light, v = 300,000,000
eWe need to find the distance light travel in 1 day. We know that,
1 day = 86400 seconds
Distance = speed × time
So,
\(d=3\times 10^8\times 86400\)
\(d=2.592\times 10^{13}\ m\)
or
\(d=0.001610\times 10^{13}\\\\d=1.61\times 10^{-3}\times 10^{13}\\\\d=1.61\times 10^{10}\ miles\)
So, the required distance is equal to \(1.61\times 10^{10}\ miles\).
If $5.00 were invested at 3% interest 600 years ago, how much would that investment be worth today?
Answers
A = P * (1 + r/n)^(n*t)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $5.00, the annual interest rate (r) is 3% (or 0.03 as a decimal), the investment has been held for 600 years (t), and the interest is compounded annually (n = 1).
Plugging these values into the formula, we get:
A = 5 * (1 + 0.03/1)^(1*600)
Calculating this expression:
A = 5 * (1.03)^600
A ≈ 5 * 37.282
A ≈ 186.41
Therefore, the $5.00 investment would be worth approximately $186.41 today after 600 years at a 3% interest rate.
What is 5 1/2 is its simple form?
Answers
Aaron rolls a die 40 times. On 25 of those rolls, he has a 3. Michelle rolls a die 80 times. On 40 of those rolls, she has a 6. Which
statement is TRUE about the experimental and theoretical probabilities?
A)The theoretical probability for rolling a 3 is the same as for rolling a 6.
B)The theoretical probability for rolling a 3 is greater than for rolling a 6.
C)The experimental probability for Aaron's tries is the same as Michelle's
tries.
D)The experimental probability for Aaron's tries is less than the experimental
probability for Michelle's tries.
Answers
Answer:
Pretty sure its D lemme know if I'm right
Question 6 of 10
What is the solution to the system of equations graphed below?
y = -2x + 4
y=x-5
Answers
Answer:
the solution to the system of equations is (x, y) = (3, -2).
Step-by-step explanation:
y = -2x + 4 (Equation 1)
y = x - 5 (Equation 2)
To solve for x, we can equate the right sides of the equations:
-2x + 4 = x - 5
Now, we can solve for x:
-2x - x = -5 - 4
-3x = -9
x = (-9) / (-3)
x = 3
Substituting the value of x back into Equation 2, we can solve for y:
y = 3 - 5
y = -2
find the slope and y-intercept.
Answers
The slope and the y-intercept of the line y = 4x + 5 are given as follows:
Slope of 4.y-intercept of 4.How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.The function for this problem is given as follows:
y = 4x + 5.
Hence the slope and the intercept are given as follows:
m = 4.b = 5.Missing InformationThe problem asks for the slope and the intercept of y = 4x + 5.
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the length of two sides of a triangle are 5.3 and 0.4. find the length of the third side if it is an integer.
Answers
Answer: It is not possible for the length of the third side of a triangle to be an integer when the lengths of the other two sides are not integer.
Step-by-step explanation:
When the other two sides of a triangle are 5.3 and 0.4 in length, the third side cannot possibly have an integer length. This is so because any two sides of a triangle must have lengths that are greater than the length of the third side. In this instance, 5.3 + 0.4 = 5.7, which still falls short of any integer number for the third side's length.
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Answer: 5
Step-by-step explanation:
5.3+0.4=5.7
5.3-0.4=4.9
4.9<x<5.7
The only possible integer between these two numbers is 5, so the correct answer is 5.
13 A young girl standing on a cliff is throwing stones up into the air so that they land in the ocean below. The height h, in meters, of each stone above the ocean is related to the
time 1, in seconds, after it has been thrown by the function
h = -21? + 21 + 40. What is the maximum height reached by
each stone?
Answers
The maximum height reached by each stone is 40.5 meters.
The height of each stone above the ocean is given by the function:
h = -2t² + 2t + 40
This is a quadratic function in standard form, with a = -2, b = 2, and c = 40.
The maximum height reached by the stone occurs at the vertex of the parabolic curve described by this function.
The t-coordinate of the vertex is given as:
t = -b / 2a
Substitute the values of a and b,
t = -2 / (2×(-2)) = 0.5
So the maximum height is reached 0.5 seconds after the stone is thrown.
To find the maximum height, substitute the value of t into the function:
h = -2(0.5)² + 2(0.5) + 40 = 40.5 meters
Therefore, the maximum height reached by each stone is 40.5 meters.
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3. What is generation of a computer
Answers
Charlie the trainer has two solo workout plans that he offers his clients: Plan A and plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did plan A and 6 who did plan B. On Thursday there were 3 clients who did plan A and 2 who did plan B. Charlie trained his Wednesday clients for a total of 7 hours and his Thursday clients for a total of 3 hours. How long does each of the workout plans last?
Answers
Plan A lasts for 0.5 hours, and Plan B lasts for 0.75 hours based on the given information and the solution to the System of equations.
To determine the duration of each workout plan, let's assume that both Plan A and Plan B have a fixed duration. Let's denote the duration of Plan A as "x" hours and the duration of Plan B as "y" hours.
From the given information, we can form the following equations:
On Wednesday:
5 clients did Plan A, so the total duration for Plan A is 5x hours.
6 clients did Plan B, so the total duration for Plan B is 6y hours.
The total training duration on Wednesday is 7 hours, so we have the equation: 5x + 6y = 7 ... Equation (1)
On Thursday:
3 clients did Plan A, so the total duration for Plan A is 3x hours.
2 clients did Plan B, so the total duration for Plan B is 2y hours.
The total training duration on Thursday is 3 hours, so we have the equation: 3x + 2y = 3 ... Equation (2)
We now have a system of equations (Equation 1 and Equation 2) that we can solve to find the values of x and y.
Multiplying Equation (1) by 2 and Equation (2) by 5 to eliminate the y variable, we get:
10x + 12y = 14 ... Equation (3)
15x + 10y = 15 ... Equation (4)
Multiplying Equation (3) by 3 and Equation (4) by 2 to create a new system of equations:
30x + 36y = 42 ... Equation (5)
30x + 20y = 30 ... Equation (6)
Subtracting Equation (6) from Equation (5), we can eliminate the x variable:
(30x + 36y) - (30x + 20y) = 42 - 30
16y = 12
y = 12/16
y = 0.75
Substituting the value of y into Equation (2), we can solve for x:
3x + 2(0.75) = 3
3x + 1.5 = 3
3x = 3 - 1.5
3x = 1.5
x = 1.5/3
x = 0.5
Therefore, the duration of Plan A is 0.5 hours, and the duration of Plan B is 0.75 hours.
Plan A lasts for 0.5 hours, and Plan B lasts for 0.75 hours based on the given information and the solution to the system of equations.
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Find the least number which when divided by 12, 18 and 20 leaves no reminder.
Answers
Answer:
180
Step-by-step explanation:
Find the LCM of 12, 18, and 20
\(12 = 2 \times 2 \times 3\)
\(18 = 2 \times 3 \times 3\)
\(20 = 2 \times 2 \times 5\)
LCM = 2 × 2 × 3 × 3 × 5 = 180
NO LINKS!! Use the diagram to name each of the following pairs of angles. If the name doesn't exist say "none" Part 1
a. <10 and < 15
b. <2 and <5
c. <1 and <12
d. <4 and 13
e. <9 and <11
Answers
Answer:
a) Alternate interior angles
b) Same-side interior angles
c) Alternate exterior angles
d) None
e) Supplementary
Step-by-step explanation:
Part a∠10 and ∠15 are alternate interior angles.Alternate interior angles
When two lines are intersected by a transversal, the angles that are interior to the two lines and are on opposite sides of the transversal line are called "alternate interior angles".
Part b∠2 and ∠5 are same-side interior angles.Same-side interior angles
When two lines are intersected by a transversal, the angles that are interior to the two lines and on the same side of the transversal line are called "same-side interior angles".
Part c∠1 and ∠12 and alternate exterior angles.Alternate exterior angles
When two lines are intersected by a transversal, the angles that are exterior to the two lines and are on opposite sides of the transversal line are called "alternate exterior angles".
Part d∠4 and ∠13 - NonePart e∠9 and ∠11 are supplementary angles.Supplementary angles are two angles whose measures sum to 180°.
They do not need to be adjacent to be supplementary.
As ∠9 and ∠11 form a linear pair, they are supplementary angles.
Tyler wrote the function f(x)=25x–15 to find the amount of money he would make after washing x cars. Select all of the values below that are in the domain of Tyler's function.
A) 2
B. 2.3
D. 7.1
E.) 10
Answers
what is the input set of a function called
Answers
Answer:
A function is a mathematical device that converts one value to another in a known way. ... The set of allowable inputs to a given function is called the domain of the function. The set of possible outputs is called the range of the function.
Step-by-step explanation:
Hopefully this was mindfull
The input set of a function is called the "Domain" of the function.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
For any function, the values which we are putting form a set of intervals called domain.
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.
Hence "The input set of a function is called the "Domain" of the function".
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Consider the probability statements regarding events A and
B below.
P(A or B) = 0.3
P(A and B) = 0.2
P(AB) =0.8
What is P(B)?
A) 0.1
B) 0.375
C) 0.25
D) 0.667
Answers
The calculated value of the probability of B is (c) 0.25
How to calculate the probability of BFrom the question, we have the following parameters that can be used in our computation:
P(A or B) = 0.3
P(A and B) = 0.2
P(A/B) =0.8
First, we have
P(A/B) = P(A and B)/P(B)
Substitute the known values in the above equation, so, we have the following representation
0.2/P(B) = 0.8
So, we have
P(B) = 0.2/0.8
Evaluate
P(B) = 0.25
Hence, the probability of B is 0.25
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Which triangle is a reflection of the green triangle
Answers
Tthe triangle that is a reflection of the green triangle is figure 1
Which triangle is a reflection of the green triangleFrom the question, we have the following parameters that can be used in our computation:
The figures
Where, we have:
Figure 1 and the green figure have the opposite orientationFigure 1 and the green figure have the same sizeThis means that the triangle that is a reflection of the green triangle is figure 1
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a) Use the triangle below to answer questions a) and b). B 10 cm A 14 cm Determine which interior angle of the triangle is the largest,
Answers
The largest interior angle of the triangle is the angle A
Determining the largest interior angle of the triangleThe side lengths of the triangles are given as
b = 10 cm
a = 14 cm
The other side length is not given
So, we solve the question using the two side lengths
Having said that:
The general rule is that; the higher the side length, the larger the angle
14 cm is greater than 10 cm
This means that the angle A is greater than the angle B
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Pls pls pls pls pls pls pls pls pls helppp meee i will give BRAINLIEST!!!!!!
Answers
Answer:
D. x = 22.5
Step-by-step explanation:
A company is interested in testing sample sets of 20 Widgets to see how they withstand a heat test. Widgets fail the heat test when they develop cracks in their top paint coating. Suppose historically that 10% of the Widgets develop paint cracks. a. Does this problem represent the application of a Continuous or Discrete Distribution
Answers
Answer:
Discrete Distribution.
Step-by-step explanation:
For each widget, there are only two possible outcomes. Either they develop paint cracks, or they do not. The probability of a widget developing paint cracks is independent of any other widgets, which means that the binomial probability distribution, which is a discrete distribution, is used to solve this question. Thus the answer is a Discrete Distribution.
What are the coordinates of point A(-22, 1) after it is reflected across the x-axis?
O A) (22,1)
O B) (1.-22)
oc) (23,-1)
OD) (-2,-1)
Answers
The required correct answer is (D) (-22, -1).
What is reflected across the x-axis?By graphing y=-f(x), we can reflect the graph of any function f about the x-axis, and by plotting y=f, we can reflect the graph about the y-axis.(-x). By graphing y=-f, we can even mirror it about both axes.(-x).
According got question:When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same.
Therefore, to find the coordinates of point A after it is reflected across the x-axis, we change the sign of the y-coordinate of A.
So, if the original coordinates of point A are (-22, 1), the coordinates of A after it is reflected across the x-axis are (-22, -1).
Therefore, the correct answer is (D) (-22, -1).
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Find the value of the length x rounded to 1 decimal place.
The diagram is not drawn accurately.
Answers
Answer:
Here
Step-by-step explanation:
What is the value of x?
Answers
ans is 21
Step-by-step explanation:
you see the right angle plus 15 degree angle equal to the 5x angle
so the quation is
90+15=5x
105=5x
21=x
A line passes through the points (4,17) and (7,20). Write a linear function rule in terms of x and y
for this line.
The linear function rule is y=?
Answers
Answer:
The linear function rule is \(\mathbf{y=x+13}\)
Step-by-step explanation:
A line passes through the points (4,17) and (7,20). Write a linear function rule in terms of x and y
for this line.
The function rule is of form: y=mx+b
Where m is slope and b is y-intercept
Finding slope using formula: \(Slope=\frac{y_2-y_1}{x_2-x_1}\)
We have \(x_1=4, y_1=17, x_2=7, y_2=20\)
Putting values and finding slope
\(Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{20-17}{7-4}\\Slope=\frac{3}{3}\\Slope=1\)
Finding y-intercept b
Using the point (4,17) to find y-intercept b
\(y=mx+b\\17=1(4)+b\\17=4+b\\b=17-4\\b=13\)
So, the linear function rule is:
\(y=mx+b\\y=1x+13\\\mathbf{y=x+13}\)
The linear function rule is \(\mathbf{y=x+13}\)
A line passes through the points (4,17) and (7,20).
The linear function rule is y= 1x+13
Given :
A line passes through the points (4,17) and (7,20).
The linear function is y=mx+b where m is the slope
lets find out slope using formula
\(m=\frac{y_2-y_1}{x_2-x_1} \\(4,17) and (7,20)\\m=\frac{20-17}{7-4}=1 \\\)
Slope of the line using the given points is 1
Lets pick any one point (4,17) and use slope to find function rule y
y=mx+b
x is 4 and y is 17 and m=1
\(17=1(4)+b\\17=4+b\\17-4=b\\13=b\)
Replace the value of 'b' and write the equation
\(y=mx+b\\y=1x+13\)
The linear function rule is y= 1x+13
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